%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV892-1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 10:59:39 AM UTC 2026
% Result : Unsatisfiable 243.85s 40.94s
% Output : CNFRefutation 243.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 705
% Syntax : Number of formulae : 6884 (4262 unt; 0 typ; 0 def)
% Number of atoms : 35452 (13461 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 117109 (7781 ~;9904 |; 0 &;99424 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 97 ( 94 usr; 13 con; 0-9 aty)
% Number of variables : 29076 ( 0 ^;29076 !; 0 ?;29076 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1,type,
c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3,type,
c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3,type,
c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3: $i > $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Set__XballE__1__1,type,
c_ATP__Linkup_Osko__Set__XballE__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Set__XbexCI__1__1,type,
c_ATP__Linkup_Osko__Set__XbexCI__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Set__XbexE__1__1,type,
c_ATP__Linkup_Osko__Set__XbexE__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Set__XbexI__1__1,type,
c_ATP__Linkup_Osko__Set__XbexI__1__1: $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Set__Xbex__Un__1__3,type,
c_ATP__Linkup_Osko__Set__Xbex__Un__1__3: $i > $i > $i > $i > $i ).
thf(tp_c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1,type,
c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1: $i > $i > $i > $i ).
thf(tp_c_COMBB,type,
c_COMBB: $i > $i > $i > $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_Com_OWT,type,
c_Com_OWT: $i > $o ).
thf(tp_c_Com_OWT__bodies,type,
c_Com_OWT__bodies: $o ).
thf(tp_c_Com_Obody,type,
c_Com_Obody: $i ).
thf(tp_c_Com_Ocom_OAss,type,
c_Com_Ocom_OAss: $i > $i > $i ).
thf(tp_c_Com_Ocom_OBODY,type,
c_Com_Ocom_OBODY: $i > $i ).
thf(tp_c_Com_Ocom_OCond,type,
c_Com_Ocom_OCond: $i > $i > $i > $i ).
thf(tp_c_Com_Ocom_OLocal,type,
c_Com_Ocom_OLocal: $i > $i > $i > $i ).
thf(tp_c_Com_Ocom_OSKIP,type,
c_Com_Ocom_OSKIP: $i ).
thf(tp_c_Com_Ocom_OSemi,type,
c_Com_Ocom_OSemi: $i > $i > $i ).
thf(tp_c_Com_Ocom_OWhile,type,
c_Com_Ocom_OWhile: $i > $i > $i ).
thf(tp_c_Com_Osko__Com__XWTs__elim__cases__7__1,type,
c_Com_Osko__Com__XWTs__elim__cases__7__1: $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_Ocard,type,
c_Finite__Set_Ocard: $i > $i > $i ).
thf(tp_c_Finite__Set_Ofinite,type,
c_Finite__Set_Ofinite: $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_Osetsum,type,
c_Finite__Set_Osetsum: $i > $i > $i > $i > $i ).
thf(tp_c_Fun_Ofun__upd,type,
c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Fun_Oinj__on,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
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_OMGT,type,
c_Hoare__Mirabelle_OMGT: $i > $i ).
thf(tp_c_Hoare__Mirabelle_Ohoare__derivs,type,
c_Hoare__Mirabelle_Ohoare__derivs: $i > $i > $i > $o ).
thf(tp_c_Hoare__Mirabelle_Ostate__not__singleton,type,
c_Hoare__Mirabelle_Ostate__not__singleton: $o ).
thf(tp_c_Hoare__Mirabelle_Otriple_Otriple,type,
c_Hoare__Mirabelle_Otriple_Otriple: $i > $i > $i > $i > $i ).
thf(tp_c_Lattices_Olower__semilattice__class_Oinf,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i > $i > $i ).
thf(tp_c_Lattices_Oupper__semilattice__class_Osup,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i > $i ).
thf(tp_c_Map_Odom,type,
c_Map_Odom: $i > $i > $i > $i ).
thf(tp_c_Map_Omap__add,type,
c_Map_Omap__add: $i > $i > $i > $i > $i ).
thf(tp_c_Map_Omap__le,type,
c_Map_Omap__le: $i > $i > $i > $i > $o ).
thf(tp_c_Map_Osko__Map__XdomD__1__1,type,
c_Map_Osko__Map__XdomD__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_Map_Osko__Map__Xmap__le__def__1__1,type,
c_Map_Osko__Map__Xmap__le__def__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_Natural_Oevalc,type,
c_Natural_Oevalc: $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_Option_Ooption_OSome,type,
c_Option_Ooption_OSome: $i > $i > $i ).
thf(tp_c_Option_Othe,type,
c_Option_Othe: $i > $i > $i ).
thf(tp_c_Orderings_Obot__class_Obot,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(tp_c_SetInterval_Oord_OatLeastAtMost,type,
c_SetInterval_Oord_OatLeastAtMost: $i > $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OatLeastLessThan,type,
c_SetInterval_Oord_OatLeastLessThan: $i > $i > $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OatMost,type,
c_SetInterval_Oord_OatMost: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OgreaterThan,type,
c_SetInterval_Oord_OgreaterThan: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OgreaterThanAtMost,type,
c_SetInterval_Oord_OgreaterThanAtMost: $i > $i > $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OgreaterThanLessThan,type,
c_SetInterval_Oord_OgreaterThanLessThan: $i > $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord_OlessThan,type,
c_SetInterval_Oord_OlessThan: $i > $i > $i > $i ).
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_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_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_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(tp_class_Ring__and__Field_Oring,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(tp_hAPP,type,
hAPP: $i > $i > $i ).
thf(tp_hBOOL,type,
hBOOL: $i > $o ).
thf(tp_tc_Com_Ocom,type,
tc_Com_Ocom: $i ).
thf(tp_tc_Com_Opname,type,
tc_Com_Opname: $i ).
thf(tp_tc_Com_Ostate,type,
tc_Com_Ostate: $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_c,type,
v_c: $i ).
thf(tp_v_pn,type,
v_pn: $i ).
thf(tp_v_sko__Hoare__Mirabelle__XMGF__lemma1__1,type,
v_sko__Hoare__Mirabelle__XMGF__lemma1__1: $i > $i ).
thf(tp_v_sko__Hoare__Mirabelle__Xsingle__stateE__1,type,
v_sko__Hoare__Mirabelle__Xsingle__stateE__1: $i > $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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',clsarity_Option__Ooption__Finite__Set_Ofinite_Ofinite) ).
thf(4,axiom,
class_HOL_Oord @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(5,axiom,
class_Orderings_Obot @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(6,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(7,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(8,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(9,axiom,
class_Finite__Set_Ofinite_Ofinite @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
thf(10,axiom,
class_Lattices_Obounded__lattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(11,axiom,
class_Lattices_Odistrib__lattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
thf(12,axiom,
class_Lattices_Olower__semilattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(13,axiom,
class_Lattices_Oupper__semilattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(14,axiom,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
thf(15,axiom,
class_HOL_Oord @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(16,axiom,
class_Orderings_Obot @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(17,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(18,axiom,
class_Lattices_Olattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(19,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(20,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(21,axiom,
class_Lattices_Odistrib__lattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
thf(22,axiom,
class_Lattices_Olower__semilattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
thf(23,axiom,
class_Lattices_Oupper__semilattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
thf(24,axiom,
! [T_2: $i,T_1: $i] :
( ( class_HOL_Oord @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_HOL_Oord @ T_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(25,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Obot @ T_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(26,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(27,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(28,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(29,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/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
thf(30,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/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(31,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/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
thf(32,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/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(33,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/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(34,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/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(35,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/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(36,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/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(37,axiom,
! [V_x: $i,V_xa: $i] :
( c_Hoare__Mirabelle_Ostate__not__singleton
| ( V_x = V_xa ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_state__not__singleton__def_1) ).
thf(38,axiom,
! [V_pn: $i,V_b: $i] :
( ( ( hAPP @ c_Com_Obody @ V_pn )
!= ( c_Option_Ooption_OSome @ V_b @ tc_Com_Ocom ) )
| ~ c_Com_OWT__bodies
| ( c_Com_OWT @ V_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT__bodiesD_0) ).
thf(39,axiom,
c_Finite__Set_Ofinite @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) @ tc_Com_Opname,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__dom__body_0) ).
thf(40,axiom,
! [V_l1: $i,V_l2: $i,T_a: $i,T_b: $i,V_m: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_l1 @ V_l2 @ T_a @ T_b ) @ V_m )
= ( hAPP @ V_l2 @ V_m ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_m ) @ ( c_Map_Odom @ V_l2 @ T_a @ T_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I1_J_0) ).
thf(41,axiom,
! [V_m_092_060_094isub_0621: $i,V_x: $i,V_m_092_060_094isub_0622: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_m_092_060_094isub_0621 @ V_x )
= ( hAPP @ V_m_092_060_094isub_0622 @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Map_Odom @ V_m_092_060_094isub_0621 @ T_a @ T_b ) ) )
| ~ ( c_Map_Omap__le @ V_m_092_060_094isub_0621 @ V_m_092_060_094isub_0622 @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__def_0) ).
thf(42,axiom,
! [V_m: $i,V_a: $i,V_b: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_m @ V_a )
!= ( c_Option_Ooption_OSome @ V_b @ T_a ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_a ) @ ( c_Map_Odom @ V_m @ T_b @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_domI_0) ).
thf(43,axiom,
! [V_m: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ V_m @ V_a )
!= ( c_Option_Ooption_ONone @ T_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Map_Odom @ V_m @ T_a @ T_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_domIff_0) ).
thf(44,axiom,
! [T_a: $i,V_a: $i,V_m: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Map_Odom @ V_m @ T_a @ T_b ) ) )
| ( ( hAPP @ V_m @ V_a )
= ( c_Option_Ooption_ONone @ T_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_domIff_1) ).
thf(45,axiom,
! [V_l1: $i,V_l2: $i,T_a: $i,T_b: $i,V_m: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_l1 @ V_l2 @ T_a @ T_b ) @ V_m )
= ( hAPP @ V_l2 @ V_m ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_m ) @ ( c_Map_Odom @ V_l1 @ T_a @ T_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I2_J_0) ).
thf(46,axiom,
! [V_l1: $i,V_l2: $i,T_a: $i,T_b: $i,V_m: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_l1 @ V_l2 @ T_a @ T_b ) @ V_m )
= ( hAPP @ V_l1 @ V_m ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_m ) @ ( c_Map_Odom @ V_l2 @ T_a @ T_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__dom__app__simps_I3_J_0) ).
thf(47,axiom,
! [V_t: $i] :
( ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ V_t )
!= V_t )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__stateE_0) ).
thf(48,axiom,
! [V_G: $i,V_c: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ V_c ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Com_OWT @ V_c )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ tc_Com_Opname ) @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ V_G ) ) @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) ) )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MGF__lemma1_0) ).
thf(49,axiom,
! [V_c: $i,V_Y: $i,V_a: $i] :
( ( c_Com_OWT @ V_c )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ V_Y @ V_a @ V_c ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I3_J_0) ).
thf(50,axiom,
! [V_Y: $i,V_a: $i,V_c: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ V_Y @ V_a @ V_c ) )
| ~ ( c_Com_OWT @ V_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OLocal_0) ).
thf(51,axiom,
! [V_c: $i,V_b: $i] :
( ( c_Com_OWT @ V_c )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I6_J_0) ).
thf(52,axiom,
! [V_b: $i,V_c: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) )
| ~ ( c_Com_OWT @ V_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_While_0) ).
thf(53,axiom,
! [V_X: $i,V_a: $i] : ( c_Com_OWT @ ( c_Com_Ocom_OAss @ V_X @ V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OAssign_0) ).
thf(54,axiom,
c_Com_OWT @ c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OSkip_0) ).
thf(55,axiom,
! [V_b: $i,V_c0: $i,V_c1: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ V_b @ V_c0 @ V_c1 ) )
| ~ ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ V_c0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OIf_0) ).
thf(56,axiom,
! [V_c2: $i,V_c1: $i] :
( ( c_Com_OWT @ V_c2 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_1) ).
thf(57,axiom,
! [V_c1: $i,V_c2: $i] :
( ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_0) ).
thf(58,axiom,
! [V_c0: $i,V_c1: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) )
| ~ ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ V_c0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OSemi_0) ).
thf(59,axiom,
! [V_c2: $i,V_b: $i,V_c1: $i] :
( ( c_Com_OWT @ V_c2 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I5_J_1) ).
thf(60,axiom,
! [V_c1: $i,V_b: $i,V_c2: $i] :
( ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I5_J_0) ).
thf(61,axiom,
! [V_x: $i,T_a: $i] :
( ( c_Option_Othe @ ( c_Option_Ooption_OSome @ V_x @ T_a ) @ T_a )
= V_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the_Osimps_0) ).
thf(62,axiom,
! [V_P: $i,V_s: $i,V_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ V_P ) @ tc_Com_Ocom ) ) @ V_s ) @ V_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ V_P ) ) @ V_s ) @ V_s1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I6_J_0) ).
thf(63,axiom,
! [V_pn: $i,V_s0: $i,V_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ V_pn ) ) @ V_s0 ) @ V_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ V_pn ) @ tc_Com_Ocom ) ) @ V_s0 ) @ V_s1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OBody_0) ).
thf(64,axiom,
! [V_pn: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ V_pn ) )
| ( ( hAPP @ c_Com_Obody @ V_pn )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WT_OBody_0) ).
thf(65,axiom,
! [V_m_092_060_094isub_0621: $i,V_m_092_060_094isub_0622: $i,T_a: $i,T_b: $i] :
( ( c_Map_Omap__le @ V_m_092_060_094isub_0621 @ V_m_092_060_094isub_0622 @ T_a @ T_b )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ V_m_092_060_094isub_0621 @ V_m_092_060_094isub_0622 @ T_a @ T_b ) ) @ ( c_Map_Odom @ V_m_092_060_094isub_0621 @ T_a @ T_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__def_1) ).
thf(66,axiom,
! [V_m: $i,V_a: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_m @ V_a )
= ( c_Option_Ooption_OSome @ ( c_Map_Osko__Map__XdomD__1__1 @ V_a @ V_m @ T_a @ T_b ) @ T_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Map_Odom @ V_m @ T_a @ T_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_domD_0) ).
thf(67,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/sandbox2/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(68,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/sandbox2/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(69,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/sandbox2/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(70,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/sandbox2/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(71,axiom,
! [V_P: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ V_A @ V_P @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__bexI_1) ).
thf(72,axiom,
! [T_a: $i,V_A: $i,V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ V_A @ V_P @ T_a ) ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__bexI_0) ).
thf(73,axiom,
! [V_less__eq: $i,V_l: $i,V_i: $i,T_a: $i,V_less: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_l ) @ V_i ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatLeastLessThan @ V_less__eq @ V_less @ V_l @ V_u @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatLeastLessThan__iff_0) ).
thf(74,axiom,
! [V_less: $i,V_i: $i,V_u: $i,T_a: $i,V_less__eq: $i,V_l: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_i ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatLeastLessThan @ V_less__eq @ V_less @ V_l @ V_u @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatLeastLessThan__iff_1) ).
thf(75,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/sandbox2/benchmark/theBenchmark.p',cls_SUP1__I_0) ).
thf(76,axiom,
! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,T_c: $i,V_b: $i,V_c: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_bool ) ) ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ V_B @ V_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP2__I_0) ).
thf(77,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/sandbox2/benchmark/theBenchmark.p',cls_SUP1__iff_2) ).
thf(78,axiom,
! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,T_c: $i,V_b: $i,V_c: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_bool ) ) ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP2__iff_2) ).
thf(79,axiom,
! [V_less: $i,V_i: $i,V_k: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_i ) @ V_k ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OlessThan @ V_less @ V_k @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OlessThan__iff_0) ).
thf(80,axiom,
! [T_a: $i,V_i: $i,V_less: $i,V_k: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OlessThan @ V_less @ V_k @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_i ) @ V_k ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OlessThan__iff_1) ).
thf(81,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/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(82,axiom,
! [T_a: $i,V_A: $i,V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ V_A @ V_P @ T_a ) ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexE_0) ).
thf(83,axiom,
! [V_P: $i,V_A: $i,V_B: $i,T_a: $i,V_xa: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ V_A @ V_B @ V_P @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__Un_5) ).
thf(84,axiom,
! [V_P: $i,V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ V_A @ V_B @ V_P @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__Un_7) ).
thf(85,axiom,
! [V_less__eq: $i,V_l: $i,V_i: $i,T_a: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_l ) @ V_i ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatLeastAtMost @ V_less__eq @ V_l @ V_u @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_0) ).
thf(86,axiom,
! [V_less__eq: $i,V_i: $i,V_u: $i,T_a: $i,V_l: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_i ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatLeastAtMost @ V_less__eq @ V_l @ V_u @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_1) ).
thf(87,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/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).
thf(88,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/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__lower_0) ).
thf(89,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/sandbox2/benchmark/theBenchmark.p',cls_vimageD_0) ).
thf(90,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/sandbox2/benchmark/theBenchmark.p',cls_vimageE_0) ).
thf(91,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/sandbox2/benchmark/theBenchmark.p',cls_vimageI_0) ).
thf(92,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/sandbox2/benchmark/theBenchmark.p',cls_vimageI2_0) ).
thf(93,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/sandbox2/benchmark/theBenchmark.p',cls_vimage__eq_1) ).
thf(94,axiom,
! [V_P: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i,V_xa: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ V_A @ V_B @ V_P @ T_b @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ ( hAPP @ V_B @ V_x ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__UN_4) ).
thf(95,axiom,
! [V_less: $i,V_k: $i,V_i: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_k ) @ V_i ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThan @ V_less @ V_k @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OgreaterThan__iff_0) ).
thf(96,axiom,
! [T_a: $i,V_i: $i,V_less: $i,V_k: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThan @ V_less @ V_k @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_k ) @ V_i ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OgreaterThan__iff_1) ).
thf(97,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/sandbox2/benchmark/theBenchmark.p',cls_UN__I_0) ).
thf(98,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/sandbox2/benchmark/theBenchmark.p',cls_UN__iff_2) ).
thf(99,axiom,
! [T_a: $i,V_A: $i,V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ V_A @ V_P @ T_a ) ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexI_0) ).
thf(100,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/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(101,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 @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ V_A @ V_P @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ballE_1) ).
thf(102,axiom,
! [V_P: $i,V_xe: $i,T_a: $i,V_A: $i,V_Q: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xe ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xe ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ V_A @ V_P @ V_Q @ T_a ) ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_0) ).
thf(103,axiom,
! [V_Q: $i,V_xd: $i,T_a: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_xd ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xd ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ V_A @ V_P @ V_Q @ T_a ) ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_1) ).
thf(104,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/sandbox2/benchmark/theBenchmark.p',cls_DiffI_0) ).
thf(105,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/sandbox2/benchmark/theBenchmark.p',cls_Diff__iff_2) ).
thf(106,axiom,
! [V_less__eq: $i,V_i: $i,V_k: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_i ) @ V_k ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatMost @ V_less__eq @ V_k @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatMost__iff_0) ).
thf(107,axiom,
! [T_a: $i,V_i: $i,V_less__eq: $i,V_k: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatMost @ V_less__eq @ V_k @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_i ) @ V_k ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatMost__iff_1) ).
thf(108,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/sandbox2/benchmark/theBenchmark.p',cls_CollectD_0) ).
thf(109,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/sandbox2/benchmark/theBenchmark.p',cls_CollectI_0) ).
thf(110,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/sandbox2/benchmark/theBenchmark.p',cls_pred__equals__eq_0) ).
thf(111,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/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(112,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/sandbox2/benchmark/theBenchmark.p',cls_inj__onD_0) ).
thf(113,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__def_0) ).
thf(114,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).
thf(115,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).
thf(116,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_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_0) ).
thf(117,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_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_1) ).
thf(118,axiom,
! [V_less: $i,V_i: $i,V_u: $i,T_a: $i,V_l: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_i ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ V_less @ V_l @ V_u @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OgreaterThanLessThan__iff_1) ).
thf(119,axiom,
! [V_less: $i,V_l: $i,V_i: $i,T_a: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_l ) @ V_i ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ V_less @ V_l @ V_u @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OgreaterThanLessThan__iff_0) ).
thf(120,axiom,
! [V_P: $i,V_A: $i,T_a: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ V_A @ V_P @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexCI_3) ).
thf(121,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 @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ V_A @ V_P @ T_a ) ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ballE_0) ).
thf(122,axiom,
! [V_P: $i,V_xg: $i,T_a: $i,V_A: $i,V_Q: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xg ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xg ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ V_A @ V_P @ V_Q @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ V_A @ V_P @ V_Q @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_2) ).
thf(123,axiom,
! [V_Q: $i,V_xf: $i,T_a: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_xf ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xf ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ V_A @ V_P @ V_Q @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ V_A @ V_P @ V_Q @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_3) ).
thf(124,axiom,
! [V_P: $i,V_x: $i,T_a: $i,V_A: $i,V_Q: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_4) ).
thf(125,axiom,
! [V_Q: $i,V_x: $i,T_a: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_5) ).
thf(126,axiom,
! [V_P: $i,V_xc: $i,T_a: $i,V_A: $i,V_Q: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xc ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xc ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_10) ).
thf(127,axiom,
! [V_Q: $i,V_xc: $i,T_a: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_xc ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xc ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_11) ).
thf(128,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/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(129,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/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(130,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/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(131,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/sandbox2/benchmark/theBenchmark.p',cls_psubsetD_0) ).
thf(132,axiom,
! [V_less__eq: $i,V_i: $i,V_u: $i,T_a: $i,V_less: $i,V_l: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_i ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ V_less__eq @ V_less @ V_l @ V_u @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OgreaterThanAtMost__iff_1) ).
thf(133,axiom,
! [V_less: $i,V_l: $i,V_i: $i,T_a: $i,V_less__eq: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_l ) @ V_i ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ V_less__eq @ V_less @ V_l @ V_u @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OgreaterThanAtMost__iff_0) ).
thf(134,axiom,
! [V_P: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ V_A @ V_P @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexE_1) ).
thf(135,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/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(136,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/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(137,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/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(138,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(139,axiom,
! [V_com1_H: $i,V_com2_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).
thf(140,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/sandbox2/benchmark/theBenchmark.p',cls_Collect__mem__eq_0) ).
thf(141,axiom,
! [V_c2: $i,V_s: $i,V_t: $i,V_c1: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c2 ) @ V_s ) @ V_t ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s ) @ V_t ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_2) ).
thf(142,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/sandbox2/benchmark/theBenchmark.p',cls_vimage__empty_0) ).
thf(143,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/sandbox2/benchmark/theBenchmark.p',cls_finite__imageD_0) ).
thf(144,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/sandbox2/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
thf(145,axiom,
! [V_vname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname_H @ V_fun_H )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I9_J_0) ).
thf(146,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/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(147,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/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(148,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(149,axiom,
! [V_G: $i,V_t: $i,V_ts: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ V_t @ V_ts @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ V_t @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).
thf(150,axiom,
! [V_G: $i,V_ts: $i,T_a: $i,V_t: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ V_t @ V_ts @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_derivs__insertD_1) ).
thf(151,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/sandbox2/benchmark/theBenchmark.p',cls_vimage__code_1) ).
thf(152,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/sandbox2/benchmark/theBenchmark.p',cls_vimage__code_0) ).
thf(153,axiom,
! [V_pname_H: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I19_J_0) ).
thf(154,axiom,
! [T_a: $i,V_x: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Collect @ V_P @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Collect_2) ).
thf(155,axiom,
! [V_fun: $i,V_com: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I58_J_0) ).
thf(156,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/sandbox2/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(157,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/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).
thf(158,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/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__singleton_0) ).
thf(159,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
thf(160,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/sandbox2/benchmark/theBenchmark.p',cls_singleton__conv_0) ).
thf(161,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/sandbox2/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
thf(162,axiom,
! [V_A: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(163,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_x @ T_a )
= V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(164,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/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
thf(165,axiom,
! [V_b: $i,V_s: $i,V_t: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ( V_t = V_s )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__WHILE__case_0) ).
thf(166,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/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__empty_0) ).
thf(167,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/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).
thf(168,axiom,
! [V_fun_H: $i,V_com_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I47_J_0) ).
thf(169,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/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).
thf(170,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/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).
thf(171,axiom,
! [V_loc: $i,V_fun: $i,V_com: $i,V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) )
| ( V_loc = V_loc_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_0) ).
thf(172,axiom,
! [V_loc: $i,V_fun: $i,V_com: $i,V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) )
| ( V_fun = V_fun_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_1) ).
thf(173,axiom,
! [V_loc: $i,V_fun: $i,V_com: $i,V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) )
| ( V_com = V_com_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_2) ).
thf(174,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(175,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(176,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(177,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/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(178,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/sandbox2/benchmark/theBenchmark.p',cls_empty__Collect__eq_0) ).
thf(179,axiom,
! [V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).
thf(180,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/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).
thf(181,axiom,
! [V_vname: $i,V_fun: $i,V_vname_H: $i,V_fun_H: $i] :
( ( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OAss @ V_vname_H @ V_fun_H ) )
| ( V_vname = V_vname_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I1_J_0) ).
thf(182,axiom,
! [V_vname: $i,V_fun: $i,V_vname_H: $i,V_fun_H: $i] :
( ( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OAss @ V_vname_H @ V_fun_H ) )
| ( V_fun = V_fun_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I1_J_1) ).
thf(183,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/sandbox2/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).
thf(184,axiom,
! [V_m: $i,V_n: $i,T_b: $i,T_a: $i,V_k: $i,V_x: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
!= ( c_Option_Ooption_OSome @ V_x @ T_a ) )
| ( ( hAPP @ V_n @ V_k )
= ( c_Option_Ooption_ONone @ T_a ) )
| ( ( hAPP @ V_n @ V_k )
= ( c_Option_Ooption_OSome @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__SomeD_0) ).
thf(185,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/sandbox2/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(186,axiom,
! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
thf(187,axiom,
! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
thf(188,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/sandbox2/benchmark/theBenchmark.p',cls_cut_0) ).
thf(189,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/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(190,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_P: $i,T_b: $i,V_xa: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ V_A @ V_B @ V_P @ T_b @ T_a ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ ( hAPP @ V_B @ V_x ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__UN_3) ).
thf(191,axiom,
! [V_fun_H: $i,V_com_H: $i,V_vname: $i,V_fun: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OAss @ V_vname @ V_fun ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I29_J_0) ).
thf(192,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/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).
thf(193,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/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__insert_0) ).
thf(194,axiom,
! [V_vname_H: $i,V_fun_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OAss @ V_vname_H @ V_fun_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I8_J_0) ).
thf(195,axiom,
! [V_b: $i,V_c0: $i,V_c1: $i,V_s: $i,V_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c0 @ V_c1 ) ) @ V_s ) @ V_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s ) @ V_s1 ) )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OIfFalse_0) ).
thf(196,axiom,
! [V_c2: $i,V_s: $i,V_t: $i,V_b: $i,V_c1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c2 ) @ V_s ) @ V_t ) )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_0) ).
thf(197,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/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(198,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/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(199,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/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(200,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/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(201,axiom,
! [V_m_092_060_094isub_0621: $i,V_m_092_060_094isub_0622: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_m_092_060_094isub_0621 @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ V_m_092_060_094isub_0621 @ V_m_092_060_094isub_0622 @ T_a @ T_b ) )
!= ( hAPP @ V_m_092_060_094isub_0622 @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ V_m_092_060_094isub_0621 @ V_m_092_060_094isub_0622 @ T_a @ T_b ) ) )
| ( c_Map_Omap__le @ V_m_092_060_094isub_0621 @ V_m_092_060_094isub_0622 @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__def_2) ).
thf(202,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/sandbox2/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
thf(203,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__infI1_0) ).
thf(204,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__infI2_0) ).
thf(205,axiom,
! [V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I11_J_0) ).
thf(206,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(207,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(208,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(209,axiom,
! [V_f: $i,V_g: $i,T_a: $i,T_b: $i] :
( ( V_f = V_g )
| ~ ( c_Map_Omap__le @ V_g @ V_f @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_f @ V_g @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__antisym_0) ).
thf(210,axiom,
! [V_u: $i,V_t: $i,V_c: $i,V_s: $i] :
( ( V_u = V_t )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com__det_0) ).
thf(211,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/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(212,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(213,axiom,
! [V_com1_H: $i,V_com2_H: $i,V_vname: $i,V_fun: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OAss @ V_vname @ V_fun ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I25_J_0) ).
thf(214,axiom,
! [V_s: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ V_s ) @ V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OSkip_0) ).
thf(215,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/sandbox2/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).
thf(216,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/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(217,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(218,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/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(219,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/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_1) ).
thf(220,axiom,
! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
thf(221,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_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
thf(222,axiom,
! [V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I10_J_0) ).
thf(223,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/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_6) ).
thf(224,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/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).
thf(225,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).
thf(226,axiom,
! [V_C: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
thf(227,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/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(228,axiom,
! [V_f: $i,V_g: $i,T_a: $i,T_b: $i] :
( ( ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b )
!= ( c_Map_Omap__add @ V_g @ V_f @ T_a @ T_b ) )
| ( c_Map_Omap__le @ V_f @ ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__iff__map__add__commute_1) ).
thf(229,axiom,
! [V_f: $i,V_g: $i,T_a: $i,T_b: $i] :
( ( ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b )
= ( c_Map_Omap__add @ V_g @ V_f @ T_a @ T_b ) )
| ~ ( c_Map_Omap__le @ V_f @ ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__iff__map__add__commute_0) ).
thf(230,axiom,
! [V_fun_H: $i,V_com_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I16_J_0) ).
thf(231,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/sandbox2/benchmark/theBenchmark.p',cls_empty_0) ).
thf(232,axiom,
! [V_vname: $i,V_fun: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I26_J_0) ).
thf(233,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/sandbox2/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
thf(234,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/sandbox2/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_0) ).
thf(235,axiom,
! [V_P: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ V_A @ V_P @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexI_1) ).
thf(236,axiom,
! [T_a: $i,V_A: $i,V_P: $i,V_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ V_A @ V_P @ T_a ) ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexCI_0) ).
thf(237,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/sandbox2/benchmark/theBenchmark.p',cls_DiffE_0) ).
thf(238,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/sandbox2/benchmark/theBenchmark.p',cls_DiffE_1) ).
thf(239,axiom,
! [T_a: $i,V_i: $i,V_less__eq: $i,V_less: $i,V_l: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ V_less__eq @ V_less @ V_l @ V_u @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_i ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_l ) @ V_i ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OgreaterThanAtMost__iff_2) ).
thf(240,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/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(241,axiom,
! [T_a: $i,V_i: $i,V_less: $i,V_l: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ V_less @ V_l @ V_u @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_i ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_l ) @ V_i ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OgreaterThanLessThan__iff_2) ).
thf(242,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/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(243,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/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(244,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/sandbox2/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(245,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/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(246,axiom,
! [T_a: $i,V_A: $i,V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ V_A @ V_P @ T_a ) ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexCI_2) ).
thf(247,axiom,
! [T_a: $i,V_i: $i,V_less__eq: $i,V_l: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatLeastAtMost @ V_less__eq @ V_l @ V_u @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_i ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_l ) @ V_i ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_2) ).
thf(248,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/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(249,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/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(250,axiom,
! [T_a: $i,V_i: $i,V_less__eq: $i,V_less: $i,V_l: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatLeastLessThan @ V_less__eq @ V_less @ V_l @ V_u @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_i ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_l ) @ V_i ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatLeastLessThan__iff_2) ).
thf(251,axiom,
! [V_P: $i,V_xa: $i,T_a: $i,V_A: $i,V_Q: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_6) ).
thf(252,axiom,
! [V_Q: $i,V_xa: $i,T_a: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_xa ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_7) ).
thf(253,axiom,
! [V_P: $i,V_xb: $i,T_a: $i,V_A: $i,V_Q: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xb ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xb ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_8) ).
thf(254,axiom,
! [V_Q: $i,V_xb: $i,T_a: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_xb ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xb ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_9) ).
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_Lattices_Olower__semilattice__class_Oinf @ 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/sandbox2/benchmark/theBenchmark.p',cls_IntI_0) ).
thf(256,axiom,
! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ 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/sandbox2/benchmark/theBenchmark.p',cls_Int__iff_2) ).
thf(257,axiom,
! [V_P: $i,V_A: $i,T_a: $i,V_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ V_A @ V_P @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexCI_1) ).
thf(258,axiom,
! [V_f: $i,V_g: $i,T_a: $i,T_b: $i,V_h: $i] :
( ( c_Map_Omap__le @ ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b ) @ V_h @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_f @ ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b ) @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_g @ V_h @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_f @ V_h @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__le__mapI_0) ).
thf(259,axiom,
! [V_F: $i,V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_0) ).
thf(260,axiom,
! [V_F: $i,V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_1) ).
thf(261,axiom,
! [V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I1_J_0) ).
thf(262,axiom,
! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Ovimage @ V_f @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_a @ T_b )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_vimage__Int_0) ).
thf(263,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/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
thf(264,axiom,
! [V_f: $i,V_g: $i,T_a: $i,T_b: $i] : ( c_Map_Omap__le @ V_f @ ( c_Map_Omap__add @ V_g @ V_f @ T_a @ T_b ) @ T_a @ T_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__map__add_0) ).
thf(265,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(266,axiom,
! [V_B: $i,V_x: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(267,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/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
thf(268,axiom,
! [V_pname_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I18_J_0) ).
thf(269,axiom,
! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i,V_vname: $i,V_fun: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OAss @ V_vname @ V_fun ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I27_J_0) ).
thf(270,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).
thf(271,axiom,
! [V_n: $i,V_k: $i,V_x: $i,T_a: $i,V_m: $i,T_b: $i] :
( ( ( hAPP @ V_n @ V_k )
!= ( c_Option_Ooption_OSome @ V_x @ T_a ) )
| ( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
= ( c_Option_Ooption_OSome @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__Some__iff_2) ).
thf(272,axiom,
! [V_n: $i,V_k: $i,V_xx: $i,T_a: $i,V_m: $i,T_b: $i] :
( ( ( hAPP @ V_n @ V_k )
!= ( c_Option_Ooption_OSome @ V_xx @ T_a ) )
| ( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
= ( c_Option_Ooption_OSome @ V_xx @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__find__right_0) ).
thf(273,axiom,
! [V_m: $i,V_k: $i,T_a: $i,V_n: $i,T_b: $i] :
( ( ( hAPP @ V_m @ V_k )
!= ( c_Option_Ooption_ONone @ T_a ) )
| ( ( hAPP @ V_n @ V_k )
!= ( c_Option_Ooption_ONone @ T_a ) )
| ( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
= ( c_Option_Ooption_ONone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__None_2) ).
thf(274,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 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Collect @ V_P @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Collect_0) ).
thf(275,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/sandbox2/benchmark/theBenchmark.p',cls_finite_0) ).
thf(276,axiom,
! [V_fun_H: $i,V_com_H: $i,V_fun: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I53_J_0) ).
thf(277,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
thf(278,axiom,
! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I15_J_0) ).
thf(279,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/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
thf(280,axiom,
! [V_fun: $i,V_com: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) )
| ( V_com = V_com_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_1) ).
thf(281,axiom,
! [V_fun: $i,V_com: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) )
| ( V_fun = V_fun_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_0) ).
thf(282,axiom,
! [V_pname: $i,V_pname_H: $i] :
( ( ( c_Com_Ocom_OBODY @ V_pname )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) )
| ( V_pname = V_pname_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).
thf(283,axiom,
! [V_loc: $i,V_fun: $i,V_com: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I34_J_0) ).
thf(284,axiom,
! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
thf(285,axiom,
! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
thf(286,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/sandbox2/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(287,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/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(288,axiom,
! [V_loc: $i,V_fun: $i,V_com: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I40_J_0) ).
thf(289,axiom,
! [V_G: $i,V_t: $i,T_a: $i,V_ts: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ V_t @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ V_t @ V_ts @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_derivs__insertD_0) ).
thf(290,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/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(291,axiom,
! [V_m: $i,V_n: $i,T_b: $i,T_a: $i,V_k: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
!= ( c_Option_Ooption_ONone @ T_a ) )
| ( ( hAPP @ V_n @ V_k )
= ( c_Option_Ooption_ONone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__None_0) ).
thf(292,axiom,
! [V_m: $i,V_n: $i,T_b: $i,T_a: $i,V_k: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
!= ( c_Option_Ooption_ONone @ T_a ) )
| ( ( hAPP @ V_m @ V_k )
= ( c_Option_Ooption_ONone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__None_1) ).
thf(293,axiom,
! [V_m: $i,V_k: $i,V_x: $i,T_a: $i,V_n: $i,T_b: $i] :
( ( ( hAPP @ V_m @ V_k )
!= ( c_Option_Ooption_OSome @ V_x @ T_a ) )
| ( ( hAPP @ V_n @ V_k )
!= ( c_Option_Ooption_ONone @ T_a ) )
| ( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
= ( c_Option_Ooption_OSome @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__Some__iff_3) ).
thf(294,axiom,
! [V_m: $i,V_n: $i,T_b: $i,T_a: $i,V_k: $i,V_x: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
!= ( c_Option_Ooption_OSome @ V_x @ T_a ) )
| ( ( hAPP @ V_m @ V_k )
= ( c_Option_Ooption_OSome @ V_x @ T_a ) )
| ( ( hAPP @ V_n @ V_k )
= ( c_Option_Ooption_OSome @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__SomeD_1) ).
thf(295,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/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(296,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/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
thf(297,axiom,
! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I14_J_0) ).
thf(298,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/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_Odual__complete__lattice_0) ).
thf(299,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(300,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(301,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(302,axiom,
! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) )
| ( ( c_Set_Oinsert @ V_x @ ( c_Map_Odom @ V_f @ T_b @ T_a ) @ T_b )
= ( c_Map_Odom @ V_f @ T_b @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__dom_0) ).
thf(303,axiom,
! [V_m1: $i,T_a: $i,T_b: $i,V_m2: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Map_Odom @ V_m1 @ T_a @ T_b ) @ ( c_Map_Odom @ V_m2 @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( c_Map_Omap__add @ V_m1 @ V_m2 @ T_a @ T_b )
= ( c_Map_Omap__add @ V_m2 @ V_m1 @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__comm_0) ).
thf(304,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
thf(305,axiom,
! [V_c0: $i,V_c1: $i,V_s0: $i,V_s2: $i,V_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) ) @ V_s0 ) @ V_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s1 ) @ V_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c0 ) @ V_s0 ) @ V_s1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OSemi_0) ).
thf(306,axiom,
! [V_b: $i,V_s: $i,V_c1: $i,V_t: $i,V_c2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s ) @ V_t ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_1) ).
thf(307,axiom,
! [V_b: $i,V_c0: $i,V_c1: $i,V_s: $i,V_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c0 @ V_c1 ) ) @ V_s ) @ V_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c0 ) @ V_s ) @ V_s1 ) )
| ~ ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OIfTrue_0) ).
thf(308,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/sandbox2/benchmark/theBenchmark.p',cls_image__empty_0) ).
thf(309,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/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(310,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/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(311,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/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(312,axiom,
! [V_b: $i,V_c: $i,V_s0: $i,V_s2: $i,V_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) @ V_s0 ) @ V_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) @ V_s1 ) @ V_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s0 ) @ V_s1 ) )
| ~ ( hBOOL @ ( hAPP @ V_b @ V_s0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OWhileTrue_0) ).
thf(313,axiom,
! [T_a: $i,V_a_H: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I2_J_0) ).
thf(314,axiom,
! [T_a: $i,V_y: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Some__eq_1) ).
thf(315,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/sandbox2/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
thf(316,axiom,
! [V_com1: $i,V_com2: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I48_J_0) ).
thf(317,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/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(318,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/sandbox2/benchmark/theBenchmark.p',cls_INT__extend__simps_I4_J_0) ).
thf(319,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/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(320,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).
thf(321,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(322,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/sandbox2/benchmark/theBenchmark.p',cls_psubset__trans_0) ).
thf(323,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/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(324,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 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Collect @ V_P @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Collect_1) ).
thf(325,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( 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/sandbox2/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
thf(326,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/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(327,axiom,
! [V_pname_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I49_J_0) ).
thf(328,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
thf(329,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/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
thf(330,axiom,
! [V_loc: $i,V_fun: $i,V_com: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I36_J_0) ).
thf(331,axiom,
! [V_G: $i,V_pn: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ V_pn ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ V_pn ) ) @ V_G @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ V_pn ) @ tc_Com_Ocom ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MGT__BodyN_0) ).
thf(332,axiom,
! [V_vname: $i,V_fun: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I24_J_0) ).
thf(333,axiom,
! [V_f: $i,V_x: $i,T_a: $i,T_b: $i,V_A: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( c_Option_Ooption_ONone @ T_a ) )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ V_f @ T_b @ T_a ) @ ( c_Set_Oinsert @ V_x @ V_A @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ V_f @ T_b @ T_a ) @ V_A @ ( tc_fun @ T_b @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__minus_0) ).
thf(334,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/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_1) ).
thf(335,axiom,
( ( c_Hoare__Mirabelle_OMGT @ v_c )
= ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_fequal @ tc_Com_Ostate ) @ v_c @ ( c_Natural_Oevalc @ v_c ) @ tc_Com_Ostate ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MGT__def__raw_0) ).
thf(336,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/sandbox2/benchmark/theBenchmark.p',cls_image__constant_0) ).
thf(337,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/sandbox2/benchmark/theBenchmark.p',cls_Diff1__fold__graph_0) ).
thf(338,axiom,
! [V_f: $i,V_A: $i,V_a: $i,T_a: $i] :
( ( ( c_Finite__Set_Osetsum @ 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 @ tc_nat )
= ( c_Finite__Set_Osetsum @ V_f @ V_A @ T_a @ tc_nat ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff1__nat_1) ).
thf(339,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/sandbox2/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).
thf(340,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).
thf(341,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).
thf(342,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/sandbox2/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I2_J_0) ).
thf(343,axiom,
! [V_f: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b )
= ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_in @ T_b ) @ V_f @ T_b @ ( tc_fun @ ( tc_fun @ T_b @ tc_bool ) @ tc_bool ) @ T_a ) @ T_a @ ( tc_fun @ T_b @ tc_bool ) @ tc_bool ) @ V_B ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__def_0) ).
thf(344,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/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_9) ).
thf(345,axiom,
! [V_e1: $i,V_m: $i,V_u1: $i,T_b: $i,T_a: $i,V_e2: $i] :
( ( ( c_Map_Omap__add @ ( c_Fun_Ofun__upd @ V_e1 @ V_m @ ( c_Option_Ooption_OSome @ V_u1 @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ V_e2 @ T_a @ T_b )
= ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ V_e1 @ V_e2 @ T_a @ T_b ) @ V_m @ ( c_Option_Ooption_OSome @ V_u1 @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_m ) @ ( c_Map_Odom @ V_e2 @ T_a @ T_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__upd__left_0) ).
thf(346,axiom,
! [V_G: $i,V_P: $i,T_a: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ c_Com_Ocom_OSKIP @ V_P @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_OSkip_0) ).
thf(347,axiom,
! [V_G: $i,V_P: $i,V_c: $i,V_d: $i,V_R: $i,T_a: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ ( c_Com_Ocom_OSemi @ V_c @ V_d ) @ V_R @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_Q @ V_d @ V_R @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ V_c @ V_Q @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comp_0) ).
thf(348,axiom,
! [V_A: $i,V_x: $i,T_a: $i] :
( ( ( c_Finite__Set_Ocard @ ( 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 ) ) @ T_a )
= ( c_Finite__Set_Ocard @ V_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/sandbox2/benchmark/theBenchmark.p',cls_card__Diff__singleton__if_1) ).
thf(349,axiom,
! [T_b: $i,V_f: $i,V_A: $i,V_a: $i,T_a: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_b )
| ( ( c_Finite__Set_Osetsum @ 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_Finite__Set_Osetsum @ V_f @ V_A @ T_a @ T_b ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff1_1) ).
thf(350,axiom,
! [V_f: $i,V_x: $i,V_y: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_b @ T_a ) @ V_A @ T_b @ T_a )
= ( c_Set_Oinsert @ V_y @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__image_0) ).
thf(351,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/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_5) ).
thf(352,axiom,
! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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 ) @ ( tc_fun @ T_b @ tc_bool ) )
!= ( 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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_3) ).
thf(353,axiom,
! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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 ) @ ( tc_fun @ T_b @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_2) ).
thf(354,axiom,
! [V_f: $i,V_x: $i,T_b: $i,T_a: $i] :
( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ V_f @ V_x @ ( c_Option_Ooption_ONone @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ T_a @ T_b )
= ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ V_f @ T_a @ T_b ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_dom__fun__upd_0) ).
thf(355,axiom,
! [V_P: $i] :
( ( ( hAPP @ c_Com_Obody @ V_P )
= ( c_Option_Ooption_OSome @ ( c_Com_Osko__Com__XWTs__elim__cases__7__1 @ V_P ) @ tc_Com_Ocom ) )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ V_P ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WTs__elim__cases_I7_J_0) ).
thf(356,axiom,
! [T_b: $i,V_f: $i,V_A: $i,V_a: $i,T_a: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_b )
| ( ( c_Finite__Set_Osetsum @ 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_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ V_f @ V_A @ T_a @ T_b ) @ ( hAPP @ V_f @ V_a ) @ T_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff1__ring_0) ).
thf(357,axiom,
! [T_b: $i,V_f: $i,V_A: $i,V_a: $i,T_a: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_b )
| ( ( c_Finite__Set_Osetsum @ 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_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ V_f @ V_A @ T_a @ T_b ) @ ( hAPP @ V_f @ V_a ) @ T_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff1_0) ).
thf(358,axiom,
! [V_G: $i,V_P: $i,V_pn: $i,V_Q: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ ( c_Com_Ocom_OBODY @ V_pn ) @ V_Q @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ ( c_Com_Ocom_OBODY @ V_pn ) @ V_Q @ T_a ) @ V_G @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ V_pn ) @ tc_Com_Ocom ) @ V_Q @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_BodyN_0) ).
thf(359,axiom,
! [V_G: $i,V_P: $i,V_pn: $i,V_Q: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ ( c_Com_Ocom_OBODY @ V_pn ) @ V_Q @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ V_pn ) @ tc_Com_Ocom ) @ V_Q @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_weak__Body_0) ).
thf(360,axiom,
! [V_loc: $i,V_fun: $i,V_com: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I38_J_0) ).
thf(361,axiom,
! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(362,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(363,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(364,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(365,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(366,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(367,axiom,
! [V_pname_H: $i,V_fun: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I55_J_0) ).
thf(368,axiom,
! [V_fun: $i,V_com1: $i,V_com2: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I54_J_0) ).
thf(369,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/sandbox2/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).
thf(370,axiom,
! [V_vname: $i,V_fun: $i,V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I22_J_0) ).
thf(371,axiom,
! [V_m1: $i,V_m2: $i,V_m3: $i,T_a: $i,T_b: $i] :
( ( c_Map_Omap__add @ V_m1 @ ( c_Map_Omap__add @ V_m2 @ V_m3 @ T_a @ T_b ) @ T_a @ T_b )
= ( c_Map_Omap__add @ ( c_Map_Omap__add @ V_m1 @ V_m2 @ T_a @ T_b ) @ V_m3 @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__assoc_0) ).
thf(372,axiom,
! [V_vname: $i,V_fun: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I28_J_0) ).
thf(373,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/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
thf(374,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/sandbox2/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
thf(375,axiom,
! [V_a: $i,T_a: $i,V_a_H: $i] :
( ( ( c_Option_Ooption_OSome @ V_a @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) )
| ( V_a = V_a_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Oinject_0) ).
thf(376,axiom,
! [V_xa: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_xa @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__None__eq_1) ).
thf(377,axiom,
! [V_a_H: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_a_H @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_option_Osimps_I3_J_0) ).
thf(378,axiom,
! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) )
| ( V_fun = V_fun_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_0) ).
thf(379,axiom,
! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) )
| ( V_com1 = V_com1_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_1) ).
thf(380,axiom,
! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) )
| ( V_com2 = V_com2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_2) ).
thf(381,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/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).
thf(382,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/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).
thf(383,axiom,
! [V_G: $i,V_c: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ V_c ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Com_OWT @ V_c )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ V_G ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MGF__lemma1_1) ).
thf(384,axiom,
! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I45_J_0) ).
thf(385,axiom,
! [T_a: $i] : ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
thf(386,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/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_1) ).
thf(387,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/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_0) ).
thf(388,axiom,
! [V_A: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Orderings_Obot__class_Obot @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
thf(389,axiom,
! [T_a: $i,V_B: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
thf(390,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
thf(391,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
thf(392,axiom,
! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I37_J_0) ).
thf(393,axiom,
! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I52_J_0) ).
thf(394,axiom,
! [V_pname_H: $i,V_vname: $i,V_fun: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OAss @ V_vname @ V_fun ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I31_J_0) ).
thf(395,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/sandbox2/benchmark/theBenchmark.p',cls_UNION__empty__conv_I2_J_0) ).
thf(396,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/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(397,axiom,
! [V_loc_H: $i,V_fun_H: $i,V_com_H: $i,V_vname: $i,V_fun: $i] :
( ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OAss @ V_vname @ V_fun ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I23_J_0) ).
thf(398,axiom,
! [V_m1: $i,V_m3: $i,T_a: $i,T_b: $i,V_m2: $i] :
( ( c_Map_Omap__le @ V_m1 @ V_m3 @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_m2 @ V_m3 @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_m1 @ V_m2 @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__trans_0) ).
thf(399,axiom,
! [V_f: $i,T_a: $i,T_b: $i] : ( c_Map_Omap__le @ V_f @ V_f @ T_a @ T_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__refl_0) ).
thf(400,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/sandbox2/benchmark/theBenchmark.p',cls_finite__UN_0) ).
thf(401,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/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(402,axiom,
! [V_g: $i,V_h: $i,T_a: $i,T_b: $i,V_f: $i] :
( ( c_Map_Omap__le @ V_g @ V_h @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b ) @ V_h @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__le__mapE_0) ).
thf(403,axiom,
! [V_a: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
thf(404,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/sandbox2/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).
thf(405,axiom,
! [V_com1_H: $i,V_com2_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I35_J_0) ).
thf(406,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/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(407,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/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff2_1) ).
thf(408,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/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).
thf(409,axiom,
! [V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I44_J_0) ).
thf(410,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/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
thf(411,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/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
thf(412,axiom,
! [V_com1: $i,V_com2: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I46_J_0) ).
thf(413,axiom,
! [V_com1: $i,V_com2: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com1 = V_com1_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).
thf(414,axiom,
! [V_com1: $i,V_com2: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com2 = V_com2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).
thf(415,axiom,
! [V_vname: $i,V_fun: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I30_J_0) ).
thf(416,axiom,
! [V_P: $i,T_a: $i] :
( ( c_Collect @ V_P @ T_a )
= V_P ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__def_0) ).
thf(417,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/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_8) ).
thf(418,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/sandbox2/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).
thf(419,axiom,
! [V_b: $i,V_c: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) @ V_s ) @ V_s ) )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_evalc_OWhileFalse_0) ).
thf(420,axiom,
! [V_fun_H: $i,V_com_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I39_J_0) ).
thf(421,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/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
thf(422,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).
thf(423,axiom,
! [V_pname_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I41_J_0) ).
thf(424,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/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff_0) ).
thf(425,axiom,
! [V_pname_H: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OWhile @ V_fun @ V_com ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I59_J_0) ).
thf(426,axiom,
! [V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I17_J_0) ).
thf(427,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/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_4) ).
thf(428,axiom,
! [V_m1: $i,V_x: $i,T_b: $i,T_a: $i,V_m2: $i,V_y: $i] :
( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ V_m1 @ V_x @ ( c_Option_Ooption_ONone @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ ( c_Fun_Ofun__upd @ V_m2 @ V_x @ ( c_Option_Ooption_OSome @ V_y @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_m1 @ V_m2 @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__imp__upd__le_0) ).
thf(429,axiom,
! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i] :
( ( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ T_a @ T_b )
= ( c_Set_Oinsert @ V_x @ ( c_Map_Odom @ V_f @ T_a @ T_b ) @ T_a ) )
| ( V_y
= ( c_Option_Ooption_ONone @ T_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__fun__upd_1) ).
thf(430,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).
thf(431,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 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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 ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__insert_0) ).
thf(432,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_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).
thf(433,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/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).
thf(434,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/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).
thf(435,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/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_7) ).
thf(436,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/sandbox2/benchmark/theBenchmark.p',cls_vimage__const_1) ).
thf(437,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/sandbox2/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).
thf(438,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/sandbox2/benchmark/theBenchmark.p',cls_endo__inj__surj_0) ).
thf(439,axiom,
! [V_f: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
!= ( c_Finite__Set_Ocard @ V_A @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__card__imp__inj__on_0) ).
thf(440,axiom,
! [V_f: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
= ( c_Finite__Set_Ocard @ V_A @ T_a ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__iff__eq__card_0) ).
thf(441,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).
thf(442,axiom,
! [V_a: $i,V_B: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_B @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ T_a ) @ T_a @ T_a @ tc_bool ) @ V_a ) @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__def_0) ).
thf(443,axiom,
! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i,V_A: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_a @ T_b ) @ V_A @ T_a @ T_b )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_y ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__fun__updI_0) ).
thf(444,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/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
thf(445,axiom,
! [V_x: $i,V_A: $i,T_a: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a )
= ( c_Finite__Set_Ocard @ V_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/sandbox2/benchmark/theBenchmark.p',cls_card__insert__if_0) ).
thf(446,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_P: $i,V_xa: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ V_A @ V_B @ V_P @ T_a ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__Un_4) ).
thf(447,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ V_A @ V_B @ V_P @ T_a ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__Un_6) ).
thf(448,axiom,
! [V_c: $i] :
( ( c_Hoare__Mirabelle_OMGT @ V_c )
= ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_fequal @ tc_Com_Ostate ) @ V_c @ ( c_Natural_Oevalc @ V_c ) @ tc_Com_Ostate ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_MGT__def_0) ).
thf(449,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 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(450,axiom,
! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(451,axiom,
! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(452,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/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(453,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/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(454,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/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(455,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/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(456,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/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(457,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__supI2_0) ).
thf(458,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__supI1_0) ).
thf(459,axiom,
! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
thf(460,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
thf(461,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).
thf(462,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).
thf(463,axiom,
! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i] :
( ( ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_a @ T_b )
!= V_f )
| ( ( hAPP @ V_f @ V_x )
= V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).
thf(464,axiom,
! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Ovimage @ V_f @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_a @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_vimage__Un_0) ).
thf(465,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(466,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(467,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(468,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(469,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(470,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(471,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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 ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
thf(472,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 @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
thf(473,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 @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
thf(474,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI2_0) ).
thf(475,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI1_0) ).
thf(476,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 @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_1) ).
thf(477,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 @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_0) ).
thf(478,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 @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
thf(479,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 @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
thf(480,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
thf(481,axiom,
! [V_B: $i,V_A: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
thf(482,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(483,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(484,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( 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/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(485,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(486,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/sandbox2/benchmark/theBenchmark.p',cls_vimage__mono_0) ).
thf(487,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/sandbox2/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I1_J_0) ).
thf(488,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/sandbox2/benchmark/theBenchmark.p',cls_fold__graph_OemptyI_0) ).
thf(489,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
thf(490,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/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
thf(491,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
thf(492,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__partition_0) ).
thf(493,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(494,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(495,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(496,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(497,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(498,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(499,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(500,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(501,axiom,
! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(502,axiom,
! [V_B: $i,V_A: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(503,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ 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/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(504,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
thf(505,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
!= V_x )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
thf(506,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
thf(507,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
thf(508,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
thf(509,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(510,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(511,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(512,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(513,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(514,axiom,
! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(515,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/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(516,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/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_1) ).
thf(517,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(518,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(519,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(520,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(521,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(522,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(523,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/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(524,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/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(525,axiom,
! [V_P: $i,V_Q: $i,T_b: $i,T_a: $i,T_c: $i,V_R: $i] :
( ( hAPP @ ( c_COMBB @ V_P @ V_Q @ T_b @ T_a @ T_c ) @ V_R )
= ( hAPP @ V_P @ ( hAPP @ V_Q @ V_R ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
thf(526,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_x @ T_a )
= V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(527,axiom,
! [V_A: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(528,axiom,
! [V_f: $i,T_a: $i,T_b: $i,V_g: $i] :
( ( c_lessequals @ ( c_Map_Odom @ V_f @ T_a @ T_b ) @ ( c_Map_Odom @ V_g @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Map_Omap__le @ V_f @ V_g @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__implies__dom__le_0) ).
thf(529,axiom,
! [V_f: $i,V_x: $i,T_b: $i,T_a: $i] : ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ V_f @ V_x @ ( c_Option_Ooption_ONone @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ V_f @ T_a @ T_b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_upd__None__map__le_0) ).
thf(530,axiom,
! [V_m: $i,V_n: $i,T_a: $i,T_b: $i] :
( ( c_Map_Odom @ ( c_Map_Omap__add @ V_m @ V_n @ T_a @ T_b ) @ T_a @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Map_Odom @ V_n @ T_a @ T_b ) @ ( c_Map_Odom @ V_m @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dom__map__add_0) ).
thf(531,axiom,
! [V_f: $i,V_g: $i,V_x: $i,V_y: $i,T_b: $i,T_a: $i] :
( ( c_Map_Omap__add @ V_f @ ( c_Fun_Ofun__upd @ V_g @ V_x @ ( c_Option_Ooption_OSome @ V_y @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ T_a @ T_b )
= ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b ) @ V_x @ ( c_Option_Ooption_OSome @ V_y @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__add__upd_0) ).
thf(532,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/sandbox2/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).
thf(533,axiom,
! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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 ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int_0) ).
thf(534,axiom,
! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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 ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Un_0) ).
thf(535,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).
thf(536,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/sandbox2/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
thf(537,axiom,
! [V_f: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
= ( c_Finite__Set_Ocard @ V_A @ T_a ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__image_0) ).
thf(538,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_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
| ( V_A = V_B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).
thf(539,axiom,
! [V_f: $i,V_A: $i,T_c: $i,T_b: $i,V_B: $i,T_a: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oimage @ V_f @ V_A @ T_c @ T_b ) @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ ( c_COMBB @ V_B @ V_f @ T_b @ ( tc_fun @ T_a @ tc_bool ) @ T_c ) @ T_c @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__simps_I10_J_0) ).
thf(540,axiom,
! [V_A: $i,V_B: $i,V_f: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ ( c_COMBB @ V_B @ V_f @ T_c @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_c ) @ V_B @ T_c @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I10_J_0) ).
thf(541,axiom,
! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] : ( c_lessequals @ ( c_Set_Oimage @ V_f @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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 ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
thf(542,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 ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ V_B @ V_a ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__insert_0) ).
thf(543,axiom,
! [V_A: $i,T_b: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ 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/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).
thf(544,axiom,
! [T_b: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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 @ ( tc_fun @ T_a @ tc_bool ) )
= V_B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).
thf(545,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/sandbox2/benchmark/theBenchmark.p',cls_SUP__const_0) ).
thf(546,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/sandbox2/benchmark/theBenchmark.p',cls_pred__subset__eq_1) ).
thf(547,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/sandbox2/benchmark/theBenchmark.p',cls_pred__subset__eq_0) ).
thf(548,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/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).
thf(549,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/sandbox2/benchmark/theBenchmark.p',cls_finite__surj_0) ).
thf(550,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/sandbox2/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(551,axiom,
! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(552,axiom,
! [V_A: $i,V_k: $i,V_I: $i,T_a: $i,T_b: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ V_A @ V_k ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_I @ V_A @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_UN__absorb_0) ).
thf(553,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/sandbox2/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).
thf(554,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/sandbox2/benchmark/theBenchmark.p',cls_UN__upper_0) ).
thf(555,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/sandbox2/benchmark/theBenchmark.p',cls_le__SUPI_0) ).
thf(556,axiom,
! [V_f: $i,V_x: $i,V_y: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_b @ T_a ) @ V_A @ T_b @ T_a )
= ( 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/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__image_1) ).
thf(557,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/sandbox2/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
thf(558,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/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(559,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/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(560,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(561,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(562,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(563,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(564,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/sandbox2/benchmark/theBenchmark.p',cls_fold__graph_OinsertI_0) ).
thf(565,axiom,
! [V_A: $i,T_a: $i,V_B: $i,T_b: $i,V_g: $i,V_f: $i] :
( ( ( c_Finite__Set_Ocard @ V_A @ T_a )
= ( c_Finite__Set_Ocard @ V_B @ T_b ) )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_b )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_lessequals @ ( c_Set_Oimage @ V_g @ V_B @ T_b @ T_a ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_g @ V_B @ T_b @ T_a )
| ~ ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__bij__eq_0) ).
thf(566,axiom,
! [T_b: $i,V_f: $i,V_A: $i,V_B: $i,T_a: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_b )
| ( ( c_Finite__Set_Osetsum @ 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_Finite__Set_Osetsum @ V_f @ V_A @ T_a @ T_b ) @ ( c_Finite__Set_Osetsum @ V_f @ V_B @ T_a @ T_b ) @ T_b ) )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff_0) ).
thf(567,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(568,axiom,
! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(569,axiom,
! [V_m: $i,V_a: $i,V_x: $i,T_b: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_Fun_Ofun__upd @ V_m @ V_a @ ( c_Option_Ooption_OSome @ V_x @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) )
!= ( c_Fun_Ofun__upd @ V_n @ V_a @ ( c_Option_Ooption_OSome @ V_y @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__eqD1_0) ).
thf(570,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(571,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(572,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/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(573,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/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(574,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/sandbox2/benchmark/theBenchmark.p',cls_subset__iff__psubset__eq_0) ).
thf(575,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/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(576,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/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(577,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/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_2) ).
thf(578,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(579,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(580,axiom,
! [T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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 ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(581,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/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(582,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/sandbox2/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
thf(583,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/sandbox2/benchmark/theBenchmark.p',cls_image__mono_0) ).
thf(584,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/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(585,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/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(586,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/sandbox2/benchmark/theBenchmark.p',cls_double__diff_0) ).
thf(587,axiom,
! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i,V_z: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_a @ T_b ) @ V_z )
= ( hAPP @ V_f @ V_z ) )
| ( V_z = V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).
thf(588,axiom,
! [V_f: $i,V_x: $i,V_y: $i,T_b: $i,T_a: $i,V_z: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_b @ T_a ) @ V_z )
= ( hAPP @ V_f @ V_z ) )
| ( V_z = V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_1) ).
thf(589,axiom,
! [V_A: $i,V_B: $i,T_b: $i,V_M: $i,T_a: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ V_M @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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 ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__Un_0) ).
thf(590,axiom,
! [V_t: $i,V_k: $i,V_x: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_t @ V_k )
!= ( c_Option_Ooption_OSome @ V_x @ T_a ) )
| ( ( c_Fun_Ofun__upd @ V_t @ V_k @ ( c_Option_Ooption_OSome @ V_x @ T_a ) @ T_b @ ( tc_Option_Ooption @ T_a ) )
= V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__triv_0) ).
thf(591,axiom,
! [V_m: $i,V_xa: $i,V_x: $i,T_a: $i,T_aa: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ V_m @ V_xa @ ( c_Option_Ooption_OSome @ V_x @ T_a ) @ T_aa @ ( tc_Option_Ooption @ T_a ) ) @ V_xa )
= ( c_Option_Ooption_OSome @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_3) ).
thf(592,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_Int__mono_0) ).
thf(593,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/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(594,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/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(595,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/sandbox2/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
thf(596,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/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(597,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/sandbox2/benchmark/theBenchmark.p',cls_subset__psubset__trans_0) ).
thf(598,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/sandbox2/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).
thf(599,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/sandbox2/benchmark/theBenchmark.p',cls_finite__subset_0) ).
thf(600,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(601,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(602,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/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(603,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/sandbox2/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).
thf(604,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/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(605,axiom,
! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(606,axiom,
! [V_x: $i,T_a: $i] : ( c_lessequals @ V_x @ V_x @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(607,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/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(608,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(609,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(610,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(611,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(612,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(613,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(614,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(615,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(616,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(617,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(618,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(619,axiom,
! [V_f: $i,V_g: $i,V_A: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Set_Oimage @ V_g @ V_A @ T_c @ T_b ) @ T_b @ T_a )
= ( c_Set_Oimage @ ( c_COMBB @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_A @ T_c @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__image_0) ).
thf(620,axiom,
! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
thf(621,axiom,
! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
thf(622,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
thf(623,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_z @ V_x @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
thf(624,axiom,
! [V_C: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
thf(625,axiom,
! [V_C: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
thf(626,axiom,
! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
thf(627,axiom,
! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
thf(628,axiom,
! [V_b: $i,V_y: $i,V_m: $i,V_x: $i,T_aa: $i,T_a: $i] :
( ( V_b = V_y )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ V_m @ V_x @ ( c_Option_Ooption_OSome @ V_b @ T_aa ) @ T_a @ ( tc_Option_Ooption @ T_aa ) ) @ V_x )
!= ( c_Option_Ooption_OSome @ V_y @ T_aa ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_1) ).
thf(629,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_z @ V_x @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
thf(630,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
thf(631,axiom,
! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
thf(632,axiom,
! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
thf(633,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/sandbox2/benchmark/theBenchmark.p',cls_fold__graph__imp__finite_0) ).
thf(634,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/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(635,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(636,axiom,
! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(637,axiom,
! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(638,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/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(639,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/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(640,axiom,
! [V_m: $i,V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_x: $i,V_y: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ V_m @ V_a @ ( c_Option_Ooption_OSome @ V_b @ T_a ) @ T_b @ ( tc_Option_Ooption @ T_a ) ) @ V_x )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) )
| ( ( hAPP @ V_m @ V_x )
= ( c_Option_Ooption_OSome @ V_y @ T_a ) )
| ( V_x = V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_0) ).
thf(641,axiom,
! [V_m: $i,V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_x: $i,V_y: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ V_m @ V_a @ ( c_Option_Ooption_OSome @ V_b @ T_a ) @ T_b @ ( tc_Option_Ooption @ T_a ) ) @ V_x )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) )
| ( ( hAPP @ V_m @ V_x )
= ( c_Option_Ooption_OSome @ V_y @ T_a ) )
| ( V_b = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_2) ).
thf(642,axiom,
! [V_m: $i,V_x: $i,V_y: $i,T_a: $i,V_a: $i,V_b: $i,T_b: $i] :
( ( ( hAPP @ V_m @ V_x )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) )
| ( V_x = V_a )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ V_m @ V_a @ ( c_Option_Ooption_OSome @ V_b @ T_a ) @ T_b @ ( tc_Option_Ooption @ T_a ) ) @ V_x )
= ( c_Option_Ooption_OSome @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__upd__Some__unfold_4) ).
thf(643,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(644,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/sandbox2/benchmark/theBenchmark.p',cls_empty__fold__graphE_0) ).
thf(645,axiom,
! [V_F: $i,V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_2) ).
thf(646,axiom,
! [V_F: $i,V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__UnI_0) ).
thf(647,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
thf(648,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
thf(649,axiom,
! [V_f: $i,V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_g: $i] :
( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ V_f @ V_a @ V_b @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ ( c_Fun_Ofun__upd @ V_g @ V_a @ V_b @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_f @ V_g @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__le__upd_0) ).
thf(650,axiom,
! [V_m: $i,V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_c: $i,V_d: $i] :
( ( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ V_m @ V_a @ V_b @ T_a @ T_b ) @ V_c @ V_d @ T_a @ T_b )
= ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ V_m @ V_c @ V_d @ T_a @ T_b ) @ V_a @ V_b @ T_a @ T_b ) )
| ( V_a = V_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).
thf(651,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(652,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(653,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(654,axiom,
! [V_F: $i,T_a: $i,V_G: $i] :
( ( c_Finite__Set_Ofinite @ V_F @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_0) ).
thf(655,axiom,
! [V_G: $i,T_a: $i,V_F: $i] :
( ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_1) ).
thf(656,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(657,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(658,axiom,
! [T_a: $i,V_B: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(659,axiom,
! [V_A: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(660,axiom,
! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i,V_z: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_a @ T_b ) @ V_x @ V_z @ T_a @ T_b )
= ( c_Fun_Ofun__upd @ V_f @ V_x @ V_z @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).
thf(661,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/sandbox2/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
thf(662,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
thf(663,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/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(664,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/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_2) ).
thf(665,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
thf(666,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/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(667,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/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(668,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/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(669,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/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(670,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/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(671,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
thf(672,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/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_0) ).
thf(673,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/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_0) ).
thf(674,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/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(675,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/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(676,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(677,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(678,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(679,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(680,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(681,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= V_B )
| ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(682,axiom,
! [V_f: $i,V_x: $i,T_b: $i,T_a: $i] :
( ( c_Fun_Ofun__upd @ V_f @ V_x @ ( hAPP @ V_f @ V_x ) @ T_b @ T_a )
= V_f ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).
thf(683,axiom,
! [V_f: $i,V_x: $i,V_y: $i,T_b: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_b @ T_a ) @ V_x )
= V_y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).
thf(684,axiom,
! [V_f: $i,V_x: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Ofun__upd @ V_f @ V_x @ ( hAPP @ V_f @ V_x ) @ T_a @ T_b )
= V_f ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).
thf(685,axiom,
! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,T_aa: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_a @ T_aa ) @ V_x )
= V_y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).
thf(686,axiom,
! [V_f: $i,V_x: $i,T_aa: $i,T_a: $i] :
( ( c_Fun_Ofun__upd @ V_f @ V_x @ ( hAPP @ V_f @ V_x ) @ T_aa @ T_a )
= V_f ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).
thf(687,axiom,
! [V_fun1: $i,V_com: $i,V_fun2: $i,T_a: $i,V_fun1_H: $i,V_com_H: $i,V_fun2_H: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ V_fun1 @ V_com @ V_fun2 @ T_a )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ V_fun1_H @ V_com_H @ V_fun2_H @ T_a ) )
| ( V_fun1 = V_fun1_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_0) ).
thf(688,axiom,
! [V_fun1: $i,V_com: $i,V_fun2: $i,T_a: $i,V_fun1_H: $i,V_com_H: $i,V_fun2_H: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ V_fun1 @ V_com @ V_fun2 @ T_a )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ V_fun1_H @ V_com_H @ V_fun2_H @ T_a ) )
| ( V_com = V_com_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_1) ).
thf(689,axiom,
! [V_fun1: $i,V_com: $i,V_fun2: $i,T_a: $i,V_fun1_H: $i,V_com_H: $i,V_fun2_H: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ V_fun1 @ V_com @ V_fun2 @ T_a )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ V_fun1_H @ V_com_H @ V_fun2_H @ T_a ) )
| ( V_fun2 = V_fun2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_2) ).
thf(690,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/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(691,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/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(692,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(693,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
thf(694,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
thf(695,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
thf(696,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
thf(697,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI_0) ).
thf(698,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le2_0) ).
thf(699,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le1_0) ).
thf(700,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(701,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[700]) ).
thf(702,negated_conjecture,
~ ( c_Com_OWT @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ v_pn ) @ tc_Com_Ocom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(703,negated_conjecture,
hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ tc_Com_Opname ) @ v_pn ) @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(704,negated_conjecture,
c_Com_OWT @ v_c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(705,negated_conjecture,
c_Com_OWT__bodies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(706,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(707,plain,
$false = $false,
inference(unfold_def,[status(thm)],[701]) ).
thf(708,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(709,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(710,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(711,plain,
( ( class_HOL_Oord @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(712,plain,
( ( class_Orderings_Obot @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(713,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(714,plain,
( ( class_Lattices_Olattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(715,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(716,plain,
( ( class_Finite__Set_Ofinite_Ofinite @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(717,plain,
( ( class_Lattices_Obounded__lattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(718,plain,
( ( class_Lattices_Odistrib__lattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(719,plain,
( ( class_Lattices_Olower__semilattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(720,plain,
( ( class_Lattices_Oupper__semilattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(721,plain,
( ( class_Complete__Lattice_Ocomplete__lattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(722,plain,
( ( class_HOL_Oord @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(723,plain,
( ( class_Orderings_Obot @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(724,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(725,plain,
( ( class_Lattices_Olattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(726,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(727,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(728,plain,
( ( class_Lattices_Odistrib__lattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(729,plain,
( ( class_Lattices_Olower__semilattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(730,plain,
( ( class_Lattices_Oupper__semilattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(731,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)],[24]) ).
thf(732,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)],[25]) ).
thf(733,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)],[26]) ).
thf(734,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)],[27]) ).
thf(735,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)],[28]) ).
thf(736,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)],[29]) ).
thf(737,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)],[30]) ).
thf(738,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)],[31]) ).
thf(739,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)],[32]) ).
thf(740,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)],[33]) ).
thf(741,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)],[34]) ).
thf(742,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)],[35]) ).
thf(743,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)],[36]) ).
thf(744,plain,
( ( ! [V_x: $i,V_xa: $i] :
( c_Hoare__Mirabelle_Ostate__not__singleton
| ( V_x = V_xa ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(745,plain,
( ( ! [V_pn: $i,V_b: $i] :
( ( ( hAPP @ c_Com_Obody @ V_pn )
!= ( c_Option_Ooption_OSome @ V_b @ tc_Com_Ocom ) )
| ~ c_Com_OWT__bodies
| ( c_Com_OWT @ V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(746,plain,
( ( c_Finite__Set_Ofinite @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) @ tc_Com_Opname )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(747,plain,
( ( ! [V_l1: $i,V_l2: $i,T_a: $i,T_b: $i,V_m: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_l1 @ V_l2 @ T_a @ T_b ) @ V_m )
= ( hAPP @ V_l2 @ V_m ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_m ) @ ( c_Map_Odom @ V_l2 @ T_a @ T_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(748,plain,
( ( ! [V_m_092_060_094isub_0621: $i,V_x: $i,V_m_092_060_094isub_0622: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_m_092_060_094isub_0621 @ V_x )
= ( hAPP @ V_m_092_060_094isub_0622 @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Map_Odom @ V_m_092_060_094isub_0621 @ T_a @ T_b ) ) )
| ~ ( c_Map_Omap__le @ V_m_092_060_094isub_0621 @ V_m_092_060_094isub_0622 @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(749,plain,
( ( ! [V_m: $i,V_a: $i,V_b: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_m @ V_a )
!= ( c_Option_Ooption_OSome @ V_b @ T_a ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_a ) @ ( c_Map_Odom @ V_m @ T_b @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(750,plain,
( ( ! [V_m: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( ( hAPP @ V_m @ V_a )
!= ( c_Option_Ooption_ONone @ T_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Map_Odom @ V_m @ T_a @ T_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(751,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Map_Odom @ V_m @ T_a @ T_b ) ) )
| ( ( hAPP @ V_m @ V_a )
= ( c_Option_Ooption_ONone @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(752,plain,
( ( ! [V_l1: $i,V_l2: $i,T_a: $i,T_b: $i,V_m: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_l1 @ V_l2 @ T_a @ T_b ) @ V_m )
= ( hAPP @ V_l2 @ V_m ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_m ) @ ( c_Map_Odom @ V_l1 @ T_a @ T_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(753,plain,
( ( ! [V_l1: $i,V_l2: $i,T_a: $i,T_b: $i,V_m: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_l1 @ V_l2 @ T_a @ T_b ) @ V_m )
= ( hAPP @ V_l1 @ V_m ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_m ) @ ( c_Map_Odom @ V_l2 @ T_a @ T_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(754,plain,
( ( ! [V_t: $i] :
( ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ V_t )
!= V_t )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(755,plain,
( ( ! [V_G: $i,V_c: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ V_c ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Com_OWT @ V_c )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ tc_Com_Opname ) @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ V_G ) ) @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) ) )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(756,plain,
( ( ! [V_c: $i,V_Y: $i,V_a: $i] :
( ( c_Com_OWT @ V_c )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ V_Y @ V_a @ V_c ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(757,plain,
( ( ! [V_Y: $i,V_a: $i,V_c: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ V_Y @ V_a @ V_c ) )
| ~ ( c_Com_OWT @ V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(758,plain,
( ( ! [V_c: $i,V_b: $i] :
( ( c_Com_OWT @ V_c )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(759,plain,
( ( ! [V_b: $i,V_c: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) )
| ~ ( c_Com_OWT @ V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(760,plain,
( ( ! [V_X: $i,V_a: $i] : ( c_Com_OWT @ ( c_Com_Ocom_OAss @ V_X @ V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(761,plain,
( ( c_Com_OWT @ c_Com_Ocom_OSKIP )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(762,plain,
( ( ! [V_b: $i,V_c0: $i,V_c1: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ V_b @ V_c0 @ V_c1 ) )
| ~ ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ V_c0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(763,plain,
( ( ! [V_c2: $i,V_c1: $i] :
( ( c_Com_OWT @ V_c2 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(764,plain,
( ( ! [V_c1: $i,V_c2: $i] :
( ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(765,plain,
( ( ! [V_c0: $i,V_c1: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) )
| ~ ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ V_c0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(766,plain,
( ( ! [V_c2: $i,V_b: $i,V_c1: $i] :
( ( c_Com_OWT @ V_c2 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(767,plain,
( ( ! [V_c1: $i,V_b: $i,V_c2: $i] :
( ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(768,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_Option_Othe @ ( c_Option_Ooption_OSome @ V_x @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(769,plain,
( ( ! [V_P: $i,V_s: $i,V_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ V_P ) @ tc_Com_Ocom ) ) @ V_s ) @ V_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ V_P ) ) @ V_s ) @ V_s1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(770,plain,
( ( ! [V_pn: $i,V_s0: $i,V_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ V_pn ) ) @ V_s0 ) @ V_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ V_pn ) @ tc_Com_Ocom ) ) @ V_s0 ) @ V_s1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(771,plain,
( ( ! [V_pn: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ V_pn ) )
| ( ( hAPP @ c_Com_Obody @ V_pn )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(772,plain,
( ( ! [V_m_092_060_094isub_0621: $i,V_m_092_060_094isub_0622: $i,T_a: $i,T_b: $i] :
( ( c_Map_Omap__le @ V_m_092_060_094isub_0621 @ V_m_092_060_094isub_0622 @ T_a @ T_b )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ V_m_092_060_094isub_0621 @ V_m_092_060_094isub_0622 @ T_a @ T_b ) ) @ ( c_Map_Odom @ V_m_092_060_094isub_0621 @ T_a @ T_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(773,plain,
( ( ! [V_m: $i,V_a: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_m @ V_a )
= ( c_Option_Ooption_OSome @ ( c_Map_Osko__Map__XdomD__1__1 @ V_a @ V_m @ T_a @ T_b ) @ T_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Map_Odom @ V_m @ T_a @ T_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(774,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)],[67]) ).
thf(775,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)],[68]) ).
thf(776,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)],[69]) ).
thf(777,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)],[70]) ).
thf(778,plain,
( ( ! [V_P: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ V_A @ 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)],[71]) ).
thf(779,plain,
( ( ! [T_a: $i,V_A: $i,V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ V_A @ V_P @ T_a ) ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(780,plain,
( ( ! [V_less__eq: $i,V_l: $i,V_i: $i,T_a: $i,V_less: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_l ) @ V_i ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatLeastLessThan @ V_less__eq @ V_less @ V_l @ V_u @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(781,plain,
( ( ! [V_less: $i,V_i: $i,V_u: $i,T_a: $i,V_less__eq: $i,V_l: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_i ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatLeastLessThan @ V_less__eq @ V_less @ V_l @ V_u @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(782,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)],[75]) ).
thf(783,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,T_c: $i,V_b: $i,V_c: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_bool ) ) ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ V_B @ V_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(784,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)],[77]) ).
thf(785,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,T_c: $i,V_b: $i,V_c: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_bool ) ) ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(786,plain,
( ( ! [V_less: $i,V_i: $i,V_k: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_i ) @ V_k ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OlessThan @ V_less @ V_k @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(787,plain,
( ( ! [T_a: $i,V_i: $i,V_less: $i,V_k: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OlessThan @ V_less @ V_k @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_i ) @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(788,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)],[81]) ).
thf(789,plain,
( ( ! [T_a: $i,V_A: $i,V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ V_A @ V_P @ T_a ) ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(790,plain,
( ( ! [V_P: $i,V_A: $i,V_B: $i,T_a: $i,V_xa: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ V_A @ V_B @ V_P @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(791,plain,
( ( ! [V_P: $i,V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ V_A @ V_B @ V_P @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(792,plain,
( ( ! [V_less__eq: $i,V_l: $i,V_i: $i,T_a: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_l ) @ V_i ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatLeastAtMost @ V_less__eq @ V_l @ V_u @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(793,plain,
( ( ! [V_less__eq: $i,V_i: $i,V_u: $i,T_a: $i,V_l: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_i ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatLeastAtMost @ V_less__eq @ V_l @ V_u @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(794,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)],[87]) ).
thf(795,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)],[88]) ).
thf(796,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)],[89]) ).
thf(797,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)],[90]) ).
thf(798,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)],[91]) ).
thf(799,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)],[92]) ).
thf(800,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)],[93]) ).
thf(801,plain,
( ( ! [V_P: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i,V_xa: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ V_A @ V_B @ V_P @ T_b @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ ( hAPP @ V_B @ V_x ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(802,plain,
( ( ! [V_less: $i,V_k: $i,V_i: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_k ) @ V_i ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThan @ V_less @ V_k @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(803,plain,
( ( ! [T_a: $i,V_i: $i,V_less: $i,V_k: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThan @ V_less @ V_k @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_k ) @ V_i ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(804,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)],[97]) ).
thf(805,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)],[98]) ).
thf(806,plain,
( ( ! [T_a: $i,V_A: $i,V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ V_A @ V_P @ T_a ) ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(807,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)],[100]) ).
thf(808,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 @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ V_A @ V_P @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(809,plain,
( ( ! [V_P: $i,V_xe: $i,T_a: $i,V_A: $i,V_Q: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xe ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xe ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ V_A @ V_P @ V_Q @ T_a ) ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(810,plain,
( ( ! [V_Q: $i,V_xd: $i,T_a: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_xd ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xd ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ V_A @ V_P @ V_Q @ T_a ) ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(811,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)],[104]) ).
thf(812,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)],[105]) ).
thf(813,plain,
( ( ! [V_less__eq: $i,V_i: $i,V_k: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_i ) @ V_k ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatMost @ V_less__eq @ V_k @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(814,plain,
( ( ! [T_a: $i,V_i: $i,V_less__eq: $i,V_k: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatMost @ V_less__eq @ V_k @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_i ) @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(815,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)],[108]) ).
thf(816,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)],[109]) ).
thf(817,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)],[110]) ).
thf(818,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)],[111]) ).
thf(819,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)],[112]) ).
thf(820,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)],[113]) ).
thf(821,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)],[114]) ).
thf(822,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)],[115]) ).
thf(823,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_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(824,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_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(825,plain,
( ( ! [V_less: $i,V_i: $i,V_u: $i,T_a: $i,V_l: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_i ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ V_less @ V_l @ V_u @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(826,plain,
( ( ! [V_less: $i,V_l: $i,V_i: $i,T_a: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_l ) @ V_i ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ V_less @ V_l @ V_u @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(827,plain,
( ( ! [V_P: $i,V_A: $i,T_a: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ V_A @ V_P @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(828,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 @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ V_A @ V_P @ T_a ) ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(829,plain,
( ( ! [V_P: $i,V_xg: $i,T_a: $i,V_A: $i,V_Q: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xg ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xg ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ V_A @ V_P @ V_Q @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ V_A @ V_P @ V_Q @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(830,plain,
( ( ! [V_Q: $i,V_xf: $i,T_a: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_xf ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xf ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ V_A @ V_P @ V_Q @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ V_A @ V_P @ V_Q @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(831,plain,
( ( ! [V_P: $i,V_x: $i,T_a: $i,V_A: $i,V_Q: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(832,plain,
( ( ! [V_Q: $i,V_x: $i,T_a: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(833,plain,
( ( ! [V_P: $i,V_xc: $i,T_a: $i,V_A: $i,V_Q: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xc ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xc ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(834,plain,
( ( ! [V_Q: $i,V_xc: $i,T_a: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_xc ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xc ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(835,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)],[128]) ).
thf(836,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)],[129]) ).
thf(837,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)],[130]) ).
thf(838,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)],[131]) ).
thf(839,plain,
( ( ! [V_less__eq: $i,V_i: $i,V_u: $i,T_a: $i,V_less: $i,V_l: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_i ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ V_less__eq @ V_less @ V_l @ V_u @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(840,plain,
( ( ! [V_less: $i,V_l: $i,V_i: $i,T_a: $i,V_less__eq: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_l ) @ V_i ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ V_less__eq @ V_less @ V_l @ V_u @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(841,plain,
( ( ! [V_P: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ V_A @ 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)],[134]) ).
thf(842,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)],[135]) ).
thf(843,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)],[136]) ).
thf(844,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)],[137]) ).
thf(845,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)],[138]) ).
thf(846,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(847,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)],[140]) ).
thf(848,plain,
( ( ! [V_c2: $i,V_s: $i,V_t: $i,V_c1: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c2 ) @ V_s ) @ V_t ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s ) @ V_t ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) @ V_s ) @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(849,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)],[142]) ).
thf(850,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)],[143]) ).
thf(851,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)],[144]) ).
thf(852,plain,
( ( ! [V_vname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname_H @ V_fun_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(853,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)],[146]) ).
thf(854,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)],[147]) ).
thf(855,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(856,plain,
( ( ! [V_G: $i,V_t: $i,V_ts: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ V_t @ V_ts @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ V_t @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(857,plain,
( ( ! [V_G: $i,V_ts: $i,T_a: $i,V_t: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ V_t @ V_ts @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(858,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)],[151]) ).
thf(859,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)],[152]) ).
thf(860,plain,
( ( ! [V_pname_H: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(861,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Collect @ V_P @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(862,plain,
( ( ! [V_fun: $i,V_com: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(863,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)],[156]) ).
thf(864,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)],[157]) ).
thf(865,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)],[158]) ).
thf(866,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(867,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)],[160]) ).
thf(868,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)],[161]) ).
thf(869,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(870,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(871,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)],[164]) ).
thf(872,plain,
( ( ! [V_b: $i,V_s: $i,V_t: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ( V_t = V_s )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) @ V_s ) @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(873,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)],[166]) ).
thf(874,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)],[167]) ).
thf(875,plain,
( ( ! [V_fun_H: $i,V_com_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(876,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)],[169]) ).
thf(877,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)],[170]) ).
thf(878,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) )
| ( V_loc = V_loc_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(879,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) )
| ( V_fun = V_fun_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(880,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) )
| ( V_com = V_com_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(881,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(882,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(883,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(884,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)],[177]) ).
thf(885,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)],[178]) ).
thf(886,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(887,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)],[180]) ).
thf(888,plain,
( ( ! [V_vname: $i,V_fun: $i,V_vname_H: $i,V_fun_H: $i] :
( ( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OAss @ V_vname_H @ V_fun_H ) )
| ( V_vname = V_vname_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(889,plain,
( ( ! [V_vname: $i,V_fun: $i,V_vname_H: $i,V_fun_H: $i] :
( ( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OAss @ V_vname_H @ V_fun_H ) )
| ( V_fun = V_fun_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(890,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)],[183]) ).
thf(891,plain,
( ( ! [V_m: $i,V_n: $i,T_b: $i,T_a: $i,V_k: $i,V_x: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
!= ( c_Option_Ooption_OSome @ V_x @ T_a ) )
| ( ( hAPP @ V_n @ V_k )
= ( c_Option_Ooption_ONone @ T_a ) )
| ( ( hAPP @ V_n @ V_k )
= ( c_Option_Ooption_OSome @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(892,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)],[185]) ).
thf(893,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(894,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(895,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)],[188]) ).
thf(896,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)],[189]) ).
thf(897,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_P: $i,T_b: $i,V_xa: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ V_A @ V_B @ V_P @ T_b @ T_a ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ ( hAPP @ V_B @ V_x ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(898,plain,
( ( ! [V_fun_H: $i,V_com_H: $i,V_vname: $i,V_fun: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OAss @ V_vname @ V_fun ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(899,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)],[192]) ).
thf(900,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)],[193]) ).
thf(901,plain,
( ( ! [V_vname_H: $i,V_fun_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OAss @ V_vname_H @ V_fun_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(902,plain,
( ( ! [V_b: $i,V_c0: $i,V_c1: $i,V_s: $i,V_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c0 @ V_c1 ) ) @ V_s ) @ V_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s ) @ V_s1 ) )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(903,plain,
( ( ! [V_c2: $i,V_s: $i,V_t: $i,V_b: $i,V_c1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c2 ) @ V_s ) @ V_t ) )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) @ V_s ) @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(904,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)],[197]) ).
thf(905,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)],[198]) ).
thf(906,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)],[199]) ).
thf(907,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)],[200]) ).
thf(908,plain,
( ( ! [V_m_092_060_094isub_0621: $i,V_m_092_060_094isub_0622: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_m_092_060_094isub_0621 @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ V_m_092_060_094isub_0621 @ V_m_092_060_094isub_0622 @ T_a @ T_b ) )
!= ( hAPP @ V_m_092_060_094isub_0622 @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ V_m_092_060_094isub_0621 @ V_m_092_060_094isub_0622 @ T_a @ T_b ) ) )
| ( c_Map_Omap__le @ V_m_092_060_094isub_0621 @ V_m_092_060_094isub_0622 @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(909,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)],[202]) ).
thf(910,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(911,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(912,plain,
( ( ! [V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(913,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)],[206]) ).
thf(914,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)],[207]) ).
thf(915,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)],[208]) ).
thf(916,plain,
( ( ! [V_f: $i,V_g: $i,T_a: $i,T_b: $i] :
( ( V_f = V_g )
| ~ ( c_Map_Omap__le @ V_g @ V_f @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_f @ V_g @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(917,plain,
( ( ! [V_u: $i,V_t: $i,V_c: $i,V_s: $i] :
( ( V_u = V_t )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(918,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)],[211]) ).
thf(919,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)],[212]) ).
thf(920,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i,V_vname: $i,V_fun: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OAss @ V_vname @ V_fun ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(921,plain,
( ( ! [V_s: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ V_s ) @ V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(922,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)],[215]) ).
thf(923,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)],[216]) ).
thf(924,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)],[217]) ).
thf(925,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)],[218]) ).
thf(926,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)],[219]) ).
thf(927,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(928,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_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(929,plain,
( ( ! [V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(930,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)],[223]) ).
thf(931,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)],[224]) ).
thf(932,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(933,plain,
( ( ! [V_C: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(934,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)],[227]) ).
thf(935,plain,
( ( ! [V_f: $i,V_g: $i,T_a: $i,T_b: $i] :
( ( ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b )
!= ( c_Map_Omap__add @ V_g @ V_f @ T_a @ T_b ) )
| ( c_Map_Omap__le @ V_f @ ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(936,plain,
( ( ! [V_f: $i,V_g: $i,T_a: $i,T_b: $i] :
( ( ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b )
= ( c_Map_Omap__add @ V_g @ V_f @ T_a @ T_b ) )
| ~ ( c_Map_Omap__le @ V_f @ ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(937,plain,
( ( ! [V_fun_H: $i,V_com_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(938,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)],[231]) ).
thf(939,plain,
( ( ! [V_vname: $i,V_fun: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(940,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)],[233]) ).
thf(941,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)],[234]) ).
thf(942,plain,
( ( ! [V_P: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ V_A @ V_P @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(943,plain,
( ( ! [T_a: $i,V_A: $i,V_P: $i,V_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ V_A @ V_P @ T_a ) ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(944,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)],[237]) ).
thf(945,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)],[238]) ).
thf(946,plain,
( ( ! [T_a: $i,V_i: $i,V_less__eq: $i,V_less: $i,V_l: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ V_less__eq @ V_less @ V_l @ V_u @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_i ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_l ) @ V_i ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(947,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)],[240]) ).
thf(948,plain,
( ( ! [T_a: $i,V_i: $i,V_less: $i,V_l: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ V_less @ V_l @ V_u @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_i ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_l ) @ V_i ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(949,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)],[242]) ).
thf(950,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)],[243]) ).
thf(951,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)],[244]) ).
thf(952,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)],[245]) ).
thf(953,plain,
( ( ! [T_a: $i,V_A: $i,V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ V_A @ V_P @ T_a ) ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(954,plain,
( ( ! [T_a: $i,V_i: $i,V_less__eq: $i,V_l: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatLeastAtMost @ V_less__eq @ V_l @ V_u @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_i ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_l ) @ V_i ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(955,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)],[248]) ).
thf(956,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)],[249]) ).
thf(957,plain,
( ( ! [T_a: $i,V_i: $i,V_less__eq: $i,V_less: $i,V_l: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatLeastLessThan @ V_less__eq @ V_less @ V_l @ V_u @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_i ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_l ) @ V_i ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(958,plain,
( ( ! [V_P: $i,V_xa: $i,T_a: $i,V_A: $i,V_Q: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(959,plain,
( ( ! [V_Q: $i,V_xa: $i,T_a: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_xa ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(960,plain,
( ( ! [V_P: $i,V_xb: $i,T_a: $i,V_A: $i,V_Q: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xb ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xb ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(961,plain,
( ( ! [V_Q: $i,V_xb: $i,T_a: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_xb ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xb ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(962,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ 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(963,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ 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)],[256]) ).
thf(964,plain,
( ( ! [V_P: $i,V_A: $i,T_a: $i,V_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ V_A @ V_P @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(965,plain,
( ( ! [V_f: $i,V_g: $i,T_a: $i,T_b: $i,V_h: $i] :
( ( c_Map_Omap__le @ ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b ) @ V_h @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_f @ ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b ) @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_g @ V_h @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_f @ V_h @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(966,plain,
( ( ! [V_F: $i,V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(967,plain,
( ( ! [V_F: $i,V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(968,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ V_s ) @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(969,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Ovimage @ V_f @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_a @ T_b )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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)],[262]) ).
thf(970,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)],[263]) ).
thf(971,plain,
( ( ! [V_f: $i,V_g: $i,T_a: $i,T_b: $i] : ( c_Map_Omap__le @ V_f @ ( c_Map_Omap__add @ V_g @ V_f @ T_a @ T_b ) @ T_a @ T_b ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(972,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(973,plain,
( ( ! [V_B: $i,V_x: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(974,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)],[267]) ).
thf(975,plain,
( ( ! [V_pname_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(976,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i,V_vname: $i,V_fun: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OAss @ V_vname @ V_fun ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(977,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)],[270]) ).
thf(978,plain,
( ( ! [V_n: $i,V_k: $i,V_x: $i,T_a: $i,V_m: $i,T_b: $i] :
( ( ( hAPP @ V_n @ V_k )
!= ( c_Option_Ooption_OSome @ V_x @ T_a ) )
| ( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
= ( c_Option_Ooption_OSome @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(979,plain,
( ( ! [V_n: $i,V_k: $i,V_xx: $i,T_a: $i,V_m: $i,T_b: $i] :
( ( ( hAPP @ V_n @ V_k )
!= ( c_Option_Ooption_OSome @ V_xx @ T_a ) )
| ( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
= ( c_Option_Ooption_OSome @ V_xx @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(980,plain,
( ( ! [V_m: $i,V_k: $i,T_a: $i,V_n: $i,T_b: $i] :
( ( ( hAPP @ V_m @ V_k )
!= ( c_Option_Ooption_ONone @ T_a ) )
| ( ( hAPP @ V_n @ V_k )
!= ( c_Option_Ooption_ONone @ T_a ) )
| ( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
= ( c_Option_Ooption_ONone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(981,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 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Collect @ V_P @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(982,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)],[275]) ).
thf(983,plain,
( ( ! [V_fun_H: $i,V_com_H: $i,V_fun: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(984,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( 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)],[277]) ).
thf(985,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(986,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)],[279]) ).
thf(987,plain,
( ( ! [V_fun: $i,V_com: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) )
| ( V_com = V_com_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(988,plain,
( ( ! [V_fun: $i,V_com: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) )
| ( V_fun = V_fun_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(989,plain,
( ( ! [V_pname: $i,V_pname_H: $i] :
( ( ( c_Com_Ocom_OBODY @ V_pname )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) )
| ( V_pname = V_pname_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(990,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(991,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(992,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(993,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)],[286]) ).
thf(994,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)],[287]) ).
thf(995,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(996,plain,
( ( ! [V_G: $i,V_t: $i,T_a: $i,V_ts: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ V_t @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ V_t @ V_ts @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(997,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)],[290]) ).
thf(998,plain,
( ( ! [V_m: $i,V_n: $i,T_b: $i,T_a: $i,V_k: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
!= ( c_Option_Ooption_ONone @ T_a ) )
| ( ( hAPP @ V_n @ V_k )
= ( c_Option_Ooption_ONone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(999,plain,
( ( ! [V_m: $i,V_n: $i,T_b: $i,T_a: $i,V_k: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
!= ( c_Option_Ooption_ONone @ T_a ) )
| ( ( hAPP @ V_m @ V_k )
= ( c_Option_Ooption_ONone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(1000,plain,
( ( ! [V_m: $i,V_k: $i,V_x: $i,T_a: $i,V_n: $i,T_b: $i] :
( ( ( hAPP @ V_m @ V_k )
!= ( c_Option_Ooption_OSome @ V_x @ T_a ) )
| ( ( hAPP @ V_n @ V_k )
!= ( c_Option_Ooption_ONone @ T_a ) )
| ( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
= ( c_Option_Ooption_OSome @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(1001,plain,
( ( ! [V_m: $i,V_n: $i,T_b: $i,T_a: $i,V_k: $i,V_x: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
!= ( c_Option_Ooption_OSome @ V_x @ T_a ) )
| ( ( hAPP @ V_m @ V_k )
= ( c_Option_Ooption_OSome @ V_x @ T_a ) )
| ( ( hAPP @ V_n @ V_k )
= ( c_Option_Ooption_OSome @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(1002,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)],[295]) ).
thf(1003,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)],[296]) ).
thf(1004,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(1005,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)],[298]) ).
thf(1006,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(1007,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(1008,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(1009,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) )
| ( ( c_Set_Oinsert @ V_x @ ( c_Map_Odom @ V_f @ T_b @ T_a ) @ T_b )
= ( c_Map_Odom @ V_f @ T_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(1010,plain,
( ( ! [V_m1: $i,T_a: $i,T_b: $i,V_m2: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Map_Odom @ V_m1 @ T_a @ T_b ) @ ( c_Map_Odom @ V_m2 @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( c_Map_Omap__add @ V_m1 @ V_m2 @ T_a @ T_b )
= ( c_Map_Omap__add @ V_m2 @ V_m1 @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(1011,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)],[304]) ).
thf(1012,plain,
( ( ! [V_c0: $i,V_c1: $i,V_s0: $i,V_s2: $i,V_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) ) @ V_s0 ) @ V_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s1 ) @ V_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c0 ) @ V_s0 ) @ V_s1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(1013,plain,
( ( ! [V_b: $i,V_s: $i,V_c1: $i,V_t: $i,V_c2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s ) @ V_t ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) @ V_s ) @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(1014,plain,
( ( ! [V_b: $i,V_c0: $i,V_c1: $i,V_s: $i,V_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c0 @ V_c1 ) ) @ V_s ) @ V_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c0 ) @ V_s ) @ V_s1 ) )
| ~ ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(1015,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)],[308]) ).
thf(1016,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)],[309]) ).
thf(1017,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)],[310]) ).
thf(1018,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)],[311]) ).
thf(1019,plain,
( ( ! [V_b: $i,V_c: $i,V_s0: $i,V_s2: $i,V_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) @ V_s0 ) @ V_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) @ V_s1 ) @ V_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s0 ) @ V_s1 ) )
| ~ ( hBOOL @ ( hAPP @ V_b @ V_s0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(1020,plain,
( ( ! [T_a: $i,V_a_H: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(1021,plain,
( ( ! [T_a: $i,V_y: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(1022,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)],[315]) ).
thf(1023,plain,
( ( ! [V_com1: $i,V_com2: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(1024,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)],[317]) ).
thf(1025,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)],[318]) ).
thf(1026,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)],[319]) ).
thf(1027,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)],[320]) ).
thf(1028,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)],[321]) ).
thf(1029,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)],[322]) ).
thf(1030,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)],[323]) ).
thf(1031,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 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Collect @ V_P @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(1032,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( 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)],[325]) ).
thf(1033,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)],[326]) ).
thf(1034,plain,
( ( ! [V_pname_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(1035,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)],[328]) ).
thf(1036,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)],[329]) ).
thf(1037,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(1038,plain,
( ( ! [V_G: $i,V_pn: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ V_pn ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ V_pn ) ) @ V_G @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ V_pn ) @ tc_Com_Ocom ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(1039,plain,
( ( ! [V_vname: $i,V_fun: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(1040,plain,
( ( ! [V_f: $i,V_x: $i,T_a: $i,T_b: $i,V_A: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( c_Option_Ooption_ONone @ T_a ) )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ V_f @ T_b @ T_a ) @ ( c_Set_Oinsert @ V_x @ V_A @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ V_f @ T_b @ T_a ) @ V_A @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(1041,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)],[334]) ).
thf(1042,plain,
( ( ( c_Hoare__Mirabelle_OMGT @ v_c )
= ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_fequal @ tc_Com_Ostate ) @ v_c @ ( c_Natural_Oevalc @ v_c ) @ tc_Com_Ostate ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(1043,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)],[336]) ).
thf(1044,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)],[337]) ).
thf(1045,plain,
( ( ! [V_f: $i,V_A: $i,V_a: $i,T_a: $i] :
( ( ( c_Finite__Set_Osetsum @ 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 @ tc_nat )
= ( c_Finite__Set_Osetsum @ V_f @ V_A @ T_a @ tc_nat ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(1046,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)],[339]) ).
thf(1047,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)],[340]) ).
thf(1048,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)],[341]) ).
thf(1049,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)],[342]) ).
thf(1050,plain,
( ( ! [V_f: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b )
= ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_in @ T_b ) @ V_f @ T_b @ ( tc_fun @ ( tc_fun @ T_b @ tc_bool ) @ tc_bool ) @ T_a ) @ T_a @ ( tc_fun @ T_b @ tc_bool ) @ tc_bool ) @ V_B ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(1051,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)],[344]) ).
thf(1052,plain,
( ( ! [V_e1: $i,V_m: $i,V_u1: $i,T_b: $i,T_a: $i,V_e2: $i] :
( ( ( c_Map_Omap__add @ ( c_Fun_Ofun__upd @ V_e1 @ V_m @ ( c_Option_Ooption_OSome @ V_u1 @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ V_e2 @ T_a @ T_b )
= ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ V_e1 @ V_e2 @ T_a @ T_b ) @ V_m @ ( c_Option_Ooption_OSome @ V_u1 @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_m ) @ ( c_Map_Odom @ V_e2 @ T_a @ T_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(1053,plain,
( ( ! [V_G: $i,V_P: $i,T_a: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ c_Com_Ocom_OSKIP @ V_P @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(1054,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_d: $i,V_R: $i,T_a: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ ( c_Com_Ocom_OSemi @ V_c @ V_d ) @ V_R @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_Q @ V_d @ V_R @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ V_c @ V_Q @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(1055,plain,
( ( ! [V_A: $i,V_x: $i,T_a: $i] :
( ( ( c_Finite__Set_Ocard @ ( 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 ) ) @ T_a )
= ( c_Finite__Set_Ocard @ V_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)],[348]) ).
thf(1056,plain,
( ( ! [T_b: $i,V_f: $i,V_A: $i,V_a: $i,T_a: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_b )
| ( ( c_Finite__Set_Osetsum @ 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_Finite__Set_Osetsum @ V_f @ V_A @ T_a @ T_b ) )
| ( 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)],[349]) ).
thf(1057,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_b @ T_a ) @ V_A @ T_b @ T_a )
= ( c_Set_Oinsert @ V_y @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(1058,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)],[351]) ).
thf(1059,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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 ) @ ( tc_fun @ T_b @ tc_bool ) )
!= ( 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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(1060,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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 ) @ ( tc_fun @ T_b @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(1061,plain,
( ( ! [V_f: $i,V_x: $i,T_b: $i,T_a: $i] :
( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ V_f @ V_x @ ( c_Option_Ooption_ONone @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ T_a @ T_b )
= ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ V_f @ T_a @ T_b ) @ ( 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)],[354]) ).
thf(1062,plain,
( ( ! [V_P: $i] :
( ( ( hAPP @ c_Com_Obody @ V_P )
= ( c_Option_Ooption_OSome @ ( c_Com_Osko__Com__XWTs__elim__cases__7__1 @ V_P ) @ tc_Com_Ocom ) )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ V_P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(1063,plain,
( ( ! [T_b: $i,V_f: $i,V_A: $i,V_a: $i,T_a: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_b )
| ( ( c_Finite__Set_Osetsum @ 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_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ V_f @ V_A @ T_a @ T_b ) @ ( hAPP @ V_f @ V_a ) @ T_b ) )
| ~ ( 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)],[356]) ).
thf(1064,plain,
( ( ! [T_b: $i,V_f: $i,V_A: $i,V_a: $i,T_a: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_b )
| ( ( c_Finite__Set_Osetsum @ 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_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ V_f @ V_A @ T_a @ T_b ) @ ( hAPP @ V_f @ V_a ) @ T_b ) )
| ~ ( 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)],[357]) ).
thf(1065,plain,
( ( ! [V_G: $i,V_P: $i,V_pn: $i,V_Q: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ ( c_Com_Ocom_OBODY @ V_pn ) @ V_Q @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ ( c_Com_Ocom_OBODY @ V_pn ) @ V_Q @ T_a ) @ V_G @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ V_pn ) @ tc_Com_Ocom ) @ V_Q @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(1066,plain,
( ( ! [V_G: $i,V_P: $i,V_pn: $i,V_Q: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ ( c_Com_Ocom_OBODY @ V_pn ) @ V_Q @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ V_pn ) @ tc_Com_Ocom ) @ V_Q @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(1067,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(1068,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(1069,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362]) ).
thf(1070,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(1071,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(1072,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365]) ).
thf(1073,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(1074,plain,
( ( ! [V_pname_H: $i,V_fun: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(1075,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(1076,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)],[369]) ).
thf(1077,plain,
( ( ! [V_vname: $i,V_fun: $i,V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(1078,plain,
( ( ! [V_m1: $i,V_m2: $i,V_m3: $i,T_a: $i,T_b: $i] :
( ( c_Map_Omap__add @ V_m1 @ ( c_Map_Omap__add @ V_m2 @ V_m3 @ T_a @ T_b ) @ T_a @ T_b )
= ( c_Map_Omap__add @ ( c_Map_Omap__add @ V_m1 @ V_m2 @ T_a @ T_b ) @ V_m3 @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(1079,plain,
( ( ! [V_vname: $i,V_fun: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(1080,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)],[373]) ).
thf(1081,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)],[374]) ).
thf(1082,plain,
( ( ! [V_a: $i,T_a: $i,V_a_H: $i] :
( ( ( c_Option_Ooption_OSome @ V_a @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375]) ).
thf(1083,plain,
( ( ! [V_xa: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_xa @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(1084,plain,
( ( ! [V_a_H: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_a_H @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(1085,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) )
| ( V_fun = V_fun_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(1086,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) )
| ( V_com1 = V_com1_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(1087,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) )
| ( V_com2 = V_com2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(1088,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)],[381]) ).
thf(1089,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)],[382]) ).
thf(1090,plain,
( ( ! [V_G: $i,V_c: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ V_c ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Com_OWT @ V_c )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ V_G ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(1091,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(1092,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)],[385]) ).
thf(1093,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)],[386]) ).
thf(1094,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)],[387]) ).
thf(1095,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Orderings_Obot__class_Obot @ ( 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)],[388]) ).
thf(1096,plain,
( ( ! [T_a: $i,V_B: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(1097,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(1098,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(1099,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392]) ).
thf(1100,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393]) ).
thf(1101,plain,
( ( ! [V_pname_H: $i,V_vname: $i,V_fun: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OAss @ V_vname @ V_fun ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(1102,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)],[395]) ).
thf(1103,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)],[396]) ).
thf(1104,plain,
( ( ! [V_loc_H: $i,V_fun_H: $i,V_com_H: $i,V_vname: $i,V_fun: $i] :
( ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OAss @ V_vname @ V_fun ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(1105,plain,
( ( ! [V_m1: $i,V_m3: $i,T_a: $i,T_b: $i,V_m2: $i] :
( ( c_Map_Omap__le @ V_m1 @ V_m3 @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_m2 @ V_m3 @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_m1 @ V_m2 @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(1106,plain,
( ( ! [V_f: $i,T_a: $i,T_b: $i] : ( c_Map_Omap__le @ V_f @ V_f @ T_a @ T_b ) )
= $true ),
inference(unfold_def,[status(thm)],[399]) ).
thf(1107,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)],[400]) ).
thf(1108,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)],[401]) ).
thf(1109,plain,
( ( ! [V_g: $i,V_h: $i,T_a: $i,T_b: $i,V_f: $i] :
( ( c_Map_Omap__le @ V_g @ V_h @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b ) @ V_h @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(1110,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(1111,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)],[404]) ).
thf(1112,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405]) ).
thf(1113,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)],[406]) ).
thf(1114,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)],[407]) ).
thf(1115,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)],[408]) ).
thf(1116,plain,
( ( ! [V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(1117,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)],[410]) ).
thf(1118,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)],[411]) ).
thf(1119,plain,
( ( ! [V_com1: $i,V_com2: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412]) ).
thf(1120,plain,
( ( ! [V_com1: $i,V_com2: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com1 = V_com1_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(1121,plain,
( ( ! [V_com1: $i,V_com2: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com2 = V_com2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414]) ).
thf(1122,plain,
( ( ! [V_vname: $i,V_fun: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[415]) ).
thf(1123,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( c_Collect @ V_P @ T_a )
= V_P ) )
= $true ),
inference(unfold_def,[status(thm)],[416]) ).
thf(1124,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)],[417]) ).
thf(1125,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)],[418]) ).
thf(1126,plain,
( ( ! [V_b: $i,V_c: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) @ V_s ) @ V_s ) )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[419]) ).
thf(1127,plain,
( ( ! [V_fun_H: $i,V_com_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(1128,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)],[421]) ).
thf(1129,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)],[422]) ).
thf(1130,plain,
( ( ! [V_pname_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423]) ).
thf(1131,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)],[424]) ).
thf(1132,plain,
( ( ! [V_pname_H: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OWhile @ V_fun @ V_com ) ) )
= $true ),
inference(unfold_def,[status(thm)],[425]) ).
thf(1133,plain,
( ( ! [V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(unfold_def,[status(thm)],[426]) ).
thf(1134,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)],[427]) ).
thf(1135,plain,
( ( ! [V_m1: $i,V_x: $i,T_b: $i,T_a: $i,V_m2: $i,V_y: $i] :
( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ V_m1 @ V_x @ ( c_Option_Ooption_ONone @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ ( c_Fun_Ofun__upd @ V_m2 @ V_x @ ( c_Option_Ooption_OSome @ V_y @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_m1 @ V_m2 @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[428]) ).
thf(1136,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i] :
( ( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ T_a @ T_b )
= ( c_Set_Oinsert @ V_x @ ( c_Map_Odom @ V_f @ T_a @ T_b ) @ T_a ) )
| ( V_y
= ( c_Option_Ooption_ONone @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[429]) ).
thf(1137,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)],[430]) ).
thf(1138,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 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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 ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(1139,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_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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)],[432]) ).
thf(1140,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)],[433]) ).
thf(1141,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)],[434]) ).
thf(1142,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)],[435]) ).
thf(1143,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)],[436]) ).
thf(1144,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)],[437]) ).
thf(1145,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)],[438]) ).
thf(1146,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
!= ( c_Finite__Set_Ocard @ V_A @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(1147,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
= ( c_Finite__Set_Ocard @ V_A @ T_a ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(1148,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)],[441]) ).
thf(1149,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_B @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ T_a ) @ T_a @ T_a @ tc_bool ) @ V_a ) @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[442]) ).
thf(1150,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i,V_A: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_a @ T_b ) @ V_A @ T_a @ T_b )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_y ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(1151,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)],[444]) ).
thf(1152,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a )
= ( c_Finite__Set_Ocard @ V_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)],[445]) ).
thf(1153,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_P: $i,V_xa: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ V_A @ V_B @ V_P @ T_a ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(1154,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ V_A @ V_B @ V_P @ T_a ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(1155,plain,
( ( ! [V_c: $i] :
( ( c_Hoare__Mirabelle_OMGT @ V_c )
= ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_fequal @ tc_Com_Ostate ) @ V_c @ ( c_Natural_Oevalc @ V_c ) @ tc_Com_Ostate ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(1156,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 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(1157,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(1158,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(1159,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)],[452]) ).
thf(1160,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)],[453]) ).
thf(1161,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)],[454]) ).
thf(1162,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)],[455]) ).
thf(1163,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)],[456]) ).
thf(1164,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(1165,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(1166,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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)],[459]) ).
thf(1167,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(1168,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461]) ).
thf(1169,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[462]) ).
thf(1170,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i] :
( ( ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_a @ T_b )
!= V_f )
| ( ( hAPP @ V_f @ V_x )
= V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(1171,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Ovimage @ V_f @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_a @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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)],[464]) ).
thf(1172,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(1173,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[466]) ).
thf(1174,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467]) ).
thf(1175,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(1176,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(1177,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(1178,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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 ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(1179,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 @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(1180,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 @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(1181,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474]) ).
thf(1182,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(1183,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 @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[476]) ).
thf(1184,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 @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[477]) ).
thf(1185,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 @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[478]) ).
thf(1186,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 @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[479]) ).
thf(1187,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[480]) ).
thf(1188,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[481]) ).
thf(1189,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[482]) ).
thf(1190,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[483]) ).
thf(1191,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( 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)],[484]) ).
thf(1192,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( 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)],[485]) ).
thf(1193,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)],[486]) ).
thf(1194,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)],[487]) ).
thf(1195,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)],[488]) ).
thf(1196,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[489]) ).
thf(1197,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)],[490]) ).
thf(1198,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(1199,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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)],[492]) ).
thf(1200,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(1201,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(1202,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ 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)],[495]) ).
thf(1203,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ 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)],[496]) ).
thf(1204,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[497]) ).
thf(1205,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498]) ).
thf(1206,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ 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)],[499]) ).
thf(1207,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ 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)],[500]) ).
thf(1208,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[501]) ).
thf(1209,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[502]) ).
thf(1210,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ 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)],[503]) ).
thf(1211,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[504]) ).
thf(1212,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
!= V_x )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[505]) ).
thf(1213,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[506]) ).
thf(1214,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[507]) ).
thf(1215,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[508]) ).
thf(1216,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[509]) ).
thf(1217,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[510]) ).
thf(1218,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[511]) ).
thf(1219,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512]) ).
thf(1220,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[513]) ).
thf(1221,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(1222,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)],[515]) ).
thf(1223,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)],[516]) ).
thf(1224,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)],[517]) ).
thf(1225,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)],[518]) ).
thf(1226,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)],[519]) ).
thf(1227,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)],[520]) ).
thf(1228,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)],[521]) ).
thf(1229,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)],[522]) ).
thf(1230,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)],[523]) ).
thf(1231,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)],[524]) ).
thf(1232,plain,
( ( ! [V_P: $i,V_Q: $i,T_b: $i,T_a: $i,T_c: $i,V_R: $i] :
( ( hAPP @ ( c_COMBB @ V_P @ V_Q @ T_b @ T_a @ T_c ) @ V_R )
= ( hAPP @ V_P @ ( hAPP @ V_Q @ V_R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[525]) ).
thf(1233,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526]) ).
thf(1234,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[527]) ).
thf(1235,plain,
( ( ! [V_f: $i,T_a: $i,T_b: $i,V_g: $i] :
( ( c_lessequals @ ( c_Map_Odom @ V_f @ T_a @ T_b ) @ ( c_Map_Odom @ V_g @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Map_Omap__le @ V_f @ V_g @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[528]) ).
thf(1236,plain,
( ( ! [V_f: $i,V_x: $i,T_b: $i,T_a: $i] : ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ V_f @ V_x @ ( c_Option_Ooption_ONone @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ V_f @ T_a @ T_b ) )
= $true ),
inference(unfold_def,[status(thm)],[529]) ).
thf(1237,plain,
( ( ! [V_m: $i,V_n: $i,T_a: $i,T_b: $i] :
( ( c_Map_Odom @ ( c_Map_Omap__add @ V_m @ V_n @ T_a @ T_b ) @ T_a @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Map_Odom @ V_n @ T_a @ T_b ) @ ( c_Map_Odom @ V_m @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530]) ).
thf(1238,plain,
( ( ! [V_f: $i,V_g: $i,V_x: $i,V_y: $i,T_b: $i,T_a: $i] :
( ( c_Map_Omap__add @ V_f @ ( c_Fun_Ofun__upd @ V_g @ V_x @ ( c_Option_Ooption_OSome @ V_y @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ T_a @ T_b )
= ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b ) @ V_x @ ( c_Option_Ooption_OSome @ V_y @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[531]) ).
thf(1239,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)],[532]) ).
thf(1240,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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 ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[533]) ).
thf(1241,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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 ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[534]) ).
thf(1242,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[535]) ).
thf(1243,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)],[536]) ).
thf(1244,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
= ( c_Finite__Set_Ocard @ V_A @ T_a ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[537]) ).
thf(1245,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_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
| ( V_A = V_B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(1246,plain,
( ( ! [V_f: $i,V_A: $i,T_c: $i,T_b: $i,V_B: $i,T_a: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oimage @ V_f @ V_A @ T_c @ T_b ) @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ ( c_COMBB @ V_B @ V_f @ T_b @ ( tc_fun @ T_a @ tc_bool ) @ T_c ) @ T_c @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(1247,plain,
( ( ! [V_A: $i,V_B: $i,V_f: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ ( c_COMBB @ V_B @ V_f @ T_c @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_c ) @ V_B @ T_c @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(1248,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] : ( c_lessequals @ ( c_Set_Oimage @ V_f @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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 ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[541]) ).
thf(1249,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 ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ V_B @ V_a ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542]) ).
thf(1250,plain,
( ( ! [V_A: $i,T_b: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ 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)],[543]) ).
thf(1251,plain,
( ( ! [T_b: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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 @ ( tc_fun @ T_a @ tc_bool ) )
= V_B ) )
= $true ),
inference(unfold_def,[status(thm)],[544]) ).
thf(1252,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)],[545]) ).
thf(1253,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)],[546]) ).
thf(1254,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)],[547]) ).
thf(1255,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)],[548]) ).
thf(1256,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)],[549]) ).
thf(1257,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)],[550]) ).
thf(1258,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[551]) ).
thf(1259,plain,
( ( ! [V_A: $i,V_k: $i,V_I: $i,T_a: $i,T_b: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ V_A @ V_k ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_I @ V_A @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ ( 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)],[552]) ).
thf(1260,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)],[553]) ).
thf(1261,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)],[554]) ).
thf(1262,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)],[555]) ).
thf(1263,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_b @ T_a ) @ V_A @ T_b @ T_a )
= ( 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)],[556]) ).
thf(1264,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)],[557]) ).
thf(1265,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)],[558]) ).
thf(1266,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)],[559]) ).
thf(1267,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)],[560]) ).
thf(1268,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)],[561]) ).
thf(1269,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)],[562]) ).
thf(1270,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)],[563]) ).
thf(1271,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)],[564]) ).
thf(1272,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i,T_b: $i,V_g: $i,V_f: $i] :
( ( ( c_Finite__Set_Ocard @ V_A @ T_a )
= ( c_Finite__Set_Ocard @ V_B @ T_b ) )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_b )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_lessequals @ ( c_Set_Oimage @ V_g @ V_B @ T_b @ T_a ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_g @ V_B @ T_b @ T_a )
| ~ ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[565]) ).
thf(1273,plain,
( ( ! [T_b: $i,V_f: $i,V_A: $i,V_B: $i,T_a: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_b )
| ( ( c_Finite__Set_Osetsum @ 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_Finite__Set_Osetsum @ V_f @ V_A @ T_a @ T_b ) @ ( c_Finite__Set_Osetsum @ V_f @ V_B @ T_a @ T_b ) @ T_b ) )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[566]) ).
thf(1274,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)],[567]) ).
thf(1275,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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)],[568]) ).
thf(1276,plain,
( ( ! [V_m: $i,V_a: $i,V_x: $i,T_b: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_Fun_Ofun__upd @ V_m @ V_a @ ( c_Option_Ooption_OSome @ V_x @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) )
!= ( c_Fun_Ofun__upd @ V_n @ V_a @ ( c_Option_Ooption_OSome @ V_y @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[569]) ).
thf(1277,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)],[570]) ).
thf(1278,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)],[571]) ).
thf(1279,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)],[572]) ).
thf(1280,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)],[573]) ).
thf(1281,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)],[574]) ).
thf(1282,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)],[575]) ).
thf(1283,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)],[576]) ).
thf(1284,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)],[577]) ).
thf(1285,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)],[578]) ).
thf(1286,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)],[579]) ).
thf(1287,plain,
( ( ! [T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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 ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[580]) ).
thf(1288,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)],[581]) ).
thf(1289,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)],[582]) ).
thf(1290,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)],[583]) ).
thf(1291,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)],[584]) ).
thf(1292,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)],[585]) ).
thf(1293,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)],[586]) ).
thf(1294,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i,V_z: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_a @ T_b ) @ V_z )
= ( hAPP @ V_f @ V_z ) )
| ( V_z = V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[587]) ).
thf(1295,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_b: $i,T_a: $i,V_z: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_b @ T_a ) @ V_z )
= ( hAPP @ V_f @ V_z ) )
| ( V_z = V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[588]) ).
thf(1296,plain,
( ( ! [V_A: $i,V_B: $i,T_b: $i,V_M: $i,T_a: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ V_M @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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 ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[589]) ).
thf(1297,plain,
( ( ! [V_t: $i,V_k: $i,V_x: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_t @ V_k )
!= ( c_Option_Ooption_OSome @ V_x @ T_a ) )
| ( ( c_Fun_Ofun__upd @ V_t @ V_k @ ( c_Option_Ooption_OSome @ V_x @ T_a ) @ T_b @ ( tc_Option_Ooption @ T_a ) )
= V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[590]) ).
thf(1298,plain,
( ( ! [V_m: $i,V_xa: $i,V_x: $i,T_a: $i,T_aa: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ V_m @ V_xa @ ( c_Option_Ooption_OSome @ V_x @ T_a ) @ T_aa @ ( tc_Option_Ooption @ T_a ) ) @ V_xa )
= ( c_Option_Ooption_OSome @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[591]) ).
thf(1299,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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)],[592]) ).
thf(1300,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)],[593]) ).
thf(1301,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)],[594]) ).
thf(1302,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)],[595]) ).
thf(1303,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)],[596]) ).
thf(1304,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)],[597]) ).
thf(1305,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)],[598]) ).
thf(1306,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)],[599]) ).
thf(1307,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)],[600]) ).
thf(1308,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)],[601]) ).
thf(1309,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)],[602]) ).
thf(1310,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)],[603]) ).
thf(1311,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)],[604]) ).
thf(1312,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)],[605]) ).
thf(1313,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)],[606]) ).
thf(1314,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)],[607]) ).
thf(1315,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)],[608]) ).
thf(1316,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)],[609]) ).
thf(1317,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)],[610]) ).
thf(1318,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[611]) ).
thf(1319,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[612]) ).
thf(1320,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[613]) ).
thf(1321,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[614]) ).
thf(1322,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[615]) ).
thf(1323,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[616]) ).
thf(1324,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[617]) ).
thf(1325,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[618]) ).
thf(1326,plain,
( ( ! [V_f: $i,V_g: $i,V_A: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Set_Oimage @ V_g @ V_A @ T_c @ T_b ) @ T_b @ T_a )
= ( c_Set_Oimage @ ( c_COMBB @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_A @ T_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[619]) ).
thf(1327,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[620]) ).
thf(1328,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[621]) ).
thf(1329,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[622]) ).
thf(1330,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_z @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[623]) ).
thf(1331,plain,
( ( ! [V_C: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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)],[624]) ).
thf(1332,plain,
( ( ! [V_C: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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)],[625]) ).
thf(1333,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[626]) ).
thf(1334,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[627]) ).
thf(1335,plain,
( ( ! [V_b: $i,V_y: $i,V_m: $i,V_x: $i,T_aa: $i,T_a: $i] :
( ( V_b = V_y )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ V_m @ V_x @ ( c_Option_Ooption_OSome @ V_b @ T_aa ) @ T_a @ ( tc_Option_Ooption @ T_aa ) ) @ V_x )
!= ( c_Option_Ooption_OSome @ V_y @ T_aa ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[628]) ).
thf(1336,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_z @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[629]) ).
thf(1337,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[630]) ).
thf(1338,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[631]) ).
thf(1339,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[632]) ).
thf(1340,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)],[633]) ).
thf(1341,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)],[634]) ).
thf(1342,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)],[635]) ).
thf(1343,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[636]) ).
thf(1344,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[637]) ).
thf(1345,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)],[638]) ).
thf(1346,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)],[639]) ).
thf(1347,plain,
( ( ! [V_m: $i,V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_x: $i,V_y: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ V_m @ V_a @ ( c_Option_Ooption_OSome @ V_b @ T_a ) @ T_b @ ( tc_Option_Ooption @ T_a ) ) @ V_x )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) )
| ( ( hAPP @ V_m @ V_x )
= ( c_Option_Ooption_OSome @ V_y @ T_a ) )
| ( V_x = V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[640]) ).
thf(1348,plain,
( ( ! [V_m: $i,V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_x: $i,V_y: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ V_m @ V_a @ ( c_Option_Ooption_OSome @ V_b @ T_a ) @ T_b @ ( tc_Option_Ooption @ T_a ) ) @ V_x )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) )
| ( ( hAPP @ V_m @ V_x )
= ( c_Option_Ooption_OSome @ V_y @ T_a ) )
| ( V_b = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[641]) ).
thf(1349,plain,
( ( ! [V_m: $i,V_x: $i,V_y: $i,T_a: $i,V_a: $i,V_b: $i,T_b: $i] :
( ( ( hAPP @ V_m @ V_x )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) )
| ( V_x = V_a )
| ( ( hAPP @ ( c_Fun_Ofun__upd @ V_m @ V_a @ ( c_Option_Ooption_OSome @ V_b @ T_a ) @ T_b @ ( tc_Option_Ooption @ T_a ) ) @ V_x )
= ( c_Option_Ooption_OSome @ V_y @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[642]) ).
thf(1350,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)],[643]) ).
thf(1351,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)],[644]) ).
thf(1352,plain,
( ( ! [V_F: $i,V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[645]) ).
thf(1353,plain,
( ( ! [V_F: $i,V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[646]) ).
thf(1354,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[647]) ).
thf(1355,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[648]) ).
thf(1356,plain,
( ( ! [V_f: $i,V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_g: $i] :
( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ V_f @ V_a @ V_b @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ ( c_Fun_Ofun__upd @ V_g @ V_a @ V_b @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_f @ V_g @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[649]) ).
thf(1357,plain,
( ( ! [V_m: $i,V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_c: $i,V_d: $i] :
( ( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ V_m @ V_a @ V_b @ T_a @ T_b ) @ V_c @ V_d @ T_a @ T_b )
= ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ V_m @ V_c @ V_d @ T_a @ T_b ) @ V_a @ V_b @ T_a @ T_b ) )
| ( V_a = V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[650]) ).
thf(1358,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[651]) ).
thf(1359,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[652]) ).
thf(1360,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[653]) ).
thf(1361,plain,
( ( ! [V_F: $i,T_a: $i,V_G: $i] :
( ( c_Finite__Set_Ofinite @ V_F @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[654]) ).
thf(1362,plain,
( ( ! [V_G: $i,T_a: $i,V_F: $i] :
( ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[655]) ).
thf(1363,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[656]) ).
thf(1364,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[657]) ).
thf(1365,plain,
( ( ! [T_a: $i,V_B: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B ) )
= $true ),
inference(unfold_def,[status(thm)],[658]) ).
thf(1366,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ 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)],[659]) ).
thf(1367,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i,V_z: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_a @ T_b ) @ V_x @ V_z @ T_a @ T_b )
= ( c_Fun_Ofun__upd @ V_f @ V_x @ V_z @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[660]) ).
thf(1368,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)],[661]) ).
thf(1369,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[662]) ).
thf(1370,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)],[663]) ).
thf(1371,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)],[664]) ).
thf(1372,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[665]) ).
thf(1373,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)],[666]) ).
thf(1374,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)],[667]) ).
thf(1375,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)],[668]) ).
thf(1376,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)],[669]) ).
thf(1377,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)],[670]) ).
thf(1378,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[671]) ).
thf(1379,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)],[672]) ).
thf(1380,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)],[673]) ).
thf(1381,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)],[674]) ).
thf(1382,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)],[675]) ).
thf(1383,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[676]) ).
thf(1384,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[677]) ).
thf(1385,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[678]) ).
thf(1386,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( 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)],[679]) ).
thf(1387,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[680]) ).
thf(1388,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( 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)],[681]) ).
thf(1389,plain,
( ( ! [V_f: $i,V_x: $i,T_b: $i,T_a: $i] :
( ( c_Fun_Ofun__upd @ V_f @ V_x @ ( hAPP @ V_f @ V_x ) @ T_b @ T_a )
= V_f ) )
= $true ),
inference(unfold_def,[status(thm)],[682]) ).
thf(1390,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_b: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_b @ T_a ) @ V_x )
= V_y ) )
= $true ),
inference(unfold_def,[status(thm)],[683]) ).
thf(1391,plain,
( ( ! [V_f: $i,V_x: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Ofun__upd @ V_f @ V_x @ ( hAPP @ V_f @ V_x ) @ T_a @ T_b )
= V_f ) )
= $true ),
inference(unfold_def,[status(thm)],[684]) ).
thf(1392,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,T_aa: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_a @ T_aa ) @ V_x )
= V_y ) )
= $true ),
inference(unfold_def,[status(thm)],[685]) ).
thf(1393,plain,
( ( ! [V_f: $i,V_x: $i,T_aa: $i,T_a: $i] :
( ( c_Fun_Ofun__upd @ V_f @ V_x @ ( hAPP @ V_f @ V_x ) @ T_aa @ T_a )
= V_f ) )
= $true ),
inference(unfold_def,[status(thm)],[686]) ).
thf(1394,plain,
( ( ! [V_fun1: $i,V_com: $i,V_fun2: $i,T_a: $i,V_fun1_H: $i,V_com_H: $i,V_fun2_H: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ V_fun1 @ V_com @ V_fun2 @ T_a )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ V_fun1_H @ V_com_H @ V_fun2_H @ T_a ) )
| ( V_fun1 = V_fun1_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[687]) ).
thf(1395,plain,
( ( ! [V_fun1: $i,V_com: $i,V_fun2: $i,T_a: $i,V_fun1_H: $i,V_com_H: $i,V_fun2_H: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ V_fun1 @ V_com @ V_fun2 @ T_a )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ V_fun1_H @ V_com_H @ V_fun2_H @ T_a ) )
| ( V_com = V_com_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[688]) ).
thf(1396,plain,
( ( ! [V_fun1: $i,V_com: $i,V_fun2: $i,T_a: $i,V_fun1_H: $i,V_com_H: $i,V_fun2_H: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ V_fun1 @ V_com @ V_fun2 @ T_a )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ V_fun1_H @ V_com_H @ V_fun2_H @ T_a ) )
| ( V_fun2 = V_fun2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[689]) ).
thf(1397,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)],[690]) ).
thf(1398,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)],[691]) ).
thf(1399,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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)],[692]) ).
thf(1400,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[693]) ).
thf(1401,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[694]) ).
thf(1402,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[695]) ).
thf(1403,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[696]) ).
thf(1404,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[697]) ).
thf(1405,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[698]) ).
thf(1406,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[699]) ).
thf(1407,plain,
( ( ~ ( c_Com_OWT @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ v_pn ) @ tc_Com_Ocom ) ) )
= $true ),
inference(unfold_def,[status(thm)],[702]) ).
thf(1408,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ tc_Com_Opname ) @ v_pn ) @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) ) )
= $true ),
inference(unfold_def,[status(thm)],[703]) ).
thf(1409,plain,
( ( c_Com_OWT @ v_c )
= $true ),
inference(unfold_def,[status(thm)],[704]) ).
thf(1410,plain,
c_Com_OWT__bodies = $true,
inference(unfold_def,[status(thm)],[705]) ).
thf(1411,plain,
c_Hoare__Mirabelle_Ostate__not__singleton = $true,
inference(unfold_def,[status(thm)],[706]) ).
thf(1412,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[707]) ).
thf(1413,plain,
( ( ! [V_X: $i,V_Y: $i] :
( ( V_X = V_Y )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[708]) ).
thf(1414,plain,
( ( ! [V_S: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_S @ V_x ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_S ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[742]) ).
thf(1415,plain,
( ( ! [V_x: $i,V_xa: $i] : ( V_x = V_xa )
| c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ),
inference(extcnf_combined,[status(esa)],[744]) ).
thf(1416,plain,
( ( ! [V_pn: $i,V_b: $i] :
( ( ( hAPP @ c_Com_Obody @ V_pn )
!= ( c_Option_Ooption_OSome @ V_b @ tc_Com_Ocom ) )
| ~ c_Com_OWT__bodies
| ( c_Com_OWT @ V_b ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[745]) ).
thf(1417,plain,
( ( ! [V_m_092_060_094isub_0621: $i,V_x: $i,V_m_092_060_094isub_0622: $i] :
( ( ( hAPP @ V_m_092_060_094isub_0621 @ V_x )
= ( hAPP @ V_m_092_060_094isub_0622 @ V_x ) )
| ! [T_a: $i,T_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Map_Odom @ V_m_092_060_094isub_0621 @ T_a @ T_b ) ) )
| ~ ( c_Map_Omap__le @ V_m_092_060_094isub_0621 @ V_m_092_060_094isub_0622 @ T_a @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[748]) ).
thf(1418,plain,
( ( ! [V_m: $i,V_a: $i,V_b: $i,T_a: $i] :
( ( ( hAPP @ V_m @ V_a )
!= ( c_Option_Ooption_OSome @ V_b @ T_a ) )
| ! [T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_a ) @ ( c_Map_Odom @ V_m @ T_b @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[749]) ).
thf(1419,plain,
( ( ! [V_m: $i,V_a: $i,T_b: $i] :
( ( ( hAPP @ V_m @ V_a )
!= ( c_Option_Ooption_ONone @ T_b ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Map_Odom @ V_m @ T_a @ T_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[750]) ).
thf(1420,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,T_b: $i] :
( ( ( hAPP @ V_m @ V_a )
= ( c_Option_Ooption_ONone @ T_b ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Map_Odom @ V_m @ T_a @ T_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[751]) ).
thf(1421,plain,
( ( ! [V_t: $i] :
( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ V_t )
!= V_t )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ),
inference(extcnf_combined,[status(esa)],[754]) ).
thf(1422,plain,
( ( ! [V_c: $i] :
( ( c_Com_OWT @ V_c )
| ! [V_Y: $i,V_a: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ V_Y @ V_a @ V_c ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[756]) ).
thf(1423,plain,
( ( ! [V_c: $i] :
( ( c_Com_OWT @ V_c )
| ! [V_b: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[758]) ).
thf(1424,plain,
( ( ! [V_c2: $i] :
( ( c_Com_OWT @ V_c2 )
| ! [V_c1: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[763]) ).
thf(1425,plain,
( ( ! [V_c1: $i] :
( ( c_Com_OWT @ V_c1 )
| ! [V_c2: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[764]) ).
thf(1426,plain,
( ( ! [V_c2: $i] :
( ( c_Com_OWT @ V_c2 )
| ! [V_b: $i,V_c1: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[766]) ).
thf(1427,plain,
( ( ! [V_c1: $i] :
( ( c_Com_OWT @ V_c1 )
| ! [V_b: $i,V_c2: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[767]) ).
thf(1428,plain,
( ( ! [V_pn: $i] :
( ( ( hAPP @ c_Com_Obody @ V_pn )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) )
| ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ V_pn ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[771]) ).
thf(1429,plain,
( ( ! [T_b: $i,V_x: $i,V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) )
| ! [T_a: $i,V_f: $i] : ( 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(extcnf_combined,[status(esa)],[776]) ).
thf(1430,plain,
( ( ! [T_aa: $i,V_x: $i,V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_aa ) @ V_x ) @ V_A ) )
| ! [T_a: $i,V_f: $i] : ( 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(extcnf_combined,[status(esa)],[777]) ).
thf(1431,plain,
( ( ! [V_P: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ V_A @ V_P @ T_a ) ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[778]) ).
thf(1432,plain,
( ( ! [T_a: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ V_A @ V_P @ T_a ) ) @ V_A ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[779]) ).
thf(1433,plain,
( ( ! [V_less__eq: $i,V_l: $i,V_i: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_l ) @ V_i ) )
| ! [V_less: $i,V_u: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatLeastLessThan @ V_less__eq @ V_less @ V_l @ V_u @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[780]) ).
thf(1434,plain,
( ( ! [V_less: $i,V_i: $i,V_u: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_i ) @ V_u ) )
| ! [V_less__eq: $i,V_l: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatLeastLessThan @ V_less__eq @ V_less @ V_l @ V_u @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[781]) ).
thf(1435,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ V_b ) )
| ! [V_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[782]) ).
thf(1436,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,T_c: $i,V_b: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_bool ) ) ) @ V_b ) @ V_c ) )
| ! [V_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ V_B @ V_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[783]) ).
thf(1437,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ V_b ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[784]) ).
thf(1438,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,T_c: $i,V_b: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_bool ) ) ) @ V_b ) @ V_c ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[785]) ).
thf(1439,plain,
( ( ! [V_less: $i,V_i: $i,V_k: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_i ) @ V_k ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OlessThan @ V_less @ V_k @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[786]) ).
thf(1440,plain,
( ( ! [T_a: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ V_A @ V_P @ T_a ) ) @ V_A ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[789]) ).
thf(1441,plain,
( ( ! [V_P: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ V_A @ V_B @ V_P @ T_a ) ) )
| ! [V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ V_A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[790]) ).
thf(1442,plain,
( ( ! [V_P: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ V_A @ V_B @ V_P @ T_a ) ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[791]) ).
thf(1443,plain,
( ( ! [V_less__eq: $i,V_l: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_l ) @ V_i ) )
| ! [T_a: $i,V_u: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatLeastAtMost @ V_less__eq @ V_l @ V_u @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[792]) ).
thf(1444,plain,
( ( ! [V_less__eq: $i,V_i: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_i ) @ V_u ) )
| ! [T_a: $i,V_l: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatLeastAtMost @ V_less__eq @ V_l @ V_u @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[793]) ).
thf(1445,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] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_x ) @ ( hAPP @ V_Sup @ V_A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ! [V_bot: $i,V_top: $i] :
~ ( 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(extcnf_combined,[status(esa)],[794]) ).
thf(1446,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] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ ( hAPP @ V_Inf @ V_A ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ! [V_bot: $i,V_top: $i] :
~ ( 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(extcnf_combined,[status(esa)],[795]) ).
thf(1447,plain,
( ( ! [T_b: $i,V_f: $i,V_a: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ V_A ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Ovimage @ V_f @ V_A @ T_a @ T_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[796]) ).
thf(1448,plain,
( ( ! [T_b: $i,V_f: $i,V_a: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ V_B ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[797]) ).
thf(1449,plain,
( ( ! [V_P: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ V_A @ V_B @ V_P @ T_b @ T_a ) ) )
| ! [V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ ( hAPP @ V_B @ V_x ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[801]) ).
thf(1450,plain,
( ( ! [V_less: $i,V_k: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_k ) @ V_i ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThan @ V_less @ V_k @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[802]) ).
thf(1451,plain,
( ( ! [T_b: $i,V_b: $i,V_A: $i,V_B: $i,T_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 ) ) ) )
| ! [V_a: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[804]) ).
thf(1452,plain,
( ( ! [T_a: $i,V_b: $i,V_A: $i,V_B: $i,T_b: $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 ) ) ) )
| ! [V_x: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[805]) ).
thf(1453,plain,
( ( ! [T_a: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ V_A @ V_P @ T_a ) ) @ V_A ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[806]) ).
thf(1454,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 ) )
| ( V_A = V_B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[807]) ).
thf(1455,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ! [V_P: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ V_A @ V_P @ T_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[808]) ).
thf(1456,plain,
( ( ! [V_P: $i,V_xe: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xe ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xe ) @ V_A ) )
| ! [V_Q: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ V_A @ V_P @ V_Q @ T_a ) ) @ V_A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[809]) ).
thf(1457,plain,
( ( ! [V_Q: $i,V_xd: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_xd ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xd ) @ V_A ) )
| ! [V_P: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ V_A @ V_P @ V_Q @ T_a ) ) @ V_A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[810]) ).
thf(1458,plain,
( ( ! [V_less__eq: $i,V_i: $i,V_k: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_i ) @ V_k ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatMost @ V_less__eq @ V_k @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[813]) ).
thf(1459,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Collect @ V_P @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[815]) ).
thf(1460,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(extcnf_combined,[status(esa)],[817]) ).
thf(1461,plain,
( ( ! [V_P: $i,V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[818]) ).
thf(1462,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,V_A: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( hAPP @ V_f @ V_y ) )
| ! [T_a: $i] :
( ! [T_b: $i] :
~ ( 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(extcnf_combined,[status(esa)],[819]) ).
thf(1463,plain,
( ( ! [V_f: $i,V_x: $i,V_xa: $i,T_a: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( hAPP @ V_f @ V_xa ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ! [T_b: $i] :
~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ( V_x = V_xa ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[820]) ).
thf(1464,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( hAPP @ V_f @ V_y ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_y ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ! [T_b: $i] :
~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ( V_x = V_y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[821]) ).
thf(1465,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( hAPP @ V_f @ V_y ) )
| ! [V_A: $i] :
( ~ ( 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 )
| ! [T_b: $i] :
~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[822]) ).
thf(1466,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) )
| ! [V_B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[823]) ).
thf(1467,plain,
( ( ! [T_a: $i,V_c: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ! [V_A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[824]) ).
thf(1468,plain,
( ( ! [V_less: $i,V_i: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_i ) @ V_u ) )
| ! [T_a: $i,V_l: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ V_less @ V_l @ V_u @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[825]) ).
thf(1469,plain,
( ( ! [V_less: $i,V_l: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_l ) @ V_i ) )
| ! [T_a: $i,V_u: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ V_less @ V_l @ V_u @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[826]) ).
thf(1470,plain,
( ( ! [V_P: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ V_A @ V_P @ T_a ) ) )
| ! [V_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[827]) ).
thf(1471,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ! [V_P: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ V_A @ V_P @ T_a ) ) @ V_A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[828]) ).
thf(1472,plain,
( ( ! [V_P: $i,V_xg: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xg ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xg ) @ V_A ) )
| ! [V_Q: $i] :
( ~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ V_A @ V_P @ V_Q @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ V_A @ V_P @ V_Q @ T_a ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[829]) ).
thf(1473,plain,
( ( ! [V_Q: $i,V_xf: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_xf ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xf ) @ V_A ) )
| ! [V_P: $i] :
( ~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ V_A @ V_P @ V_Q @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ V_A @ V_P @ V_Q @ T_a ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[830]) ).
thf(1474,plain,
( ( ! [V_P: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ! [V_Q: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) @ V_A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[831]) ).
thf(1475,plain,
( ( ! [V_Q: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) @ V_A ) )
| ! [V_P: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) @ V_A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[832]) ).
thf(1476,plain,
( ( ! [V_P: $i,V_xc: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xc ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xc ) @ V_A ) )
| ! [V_Q: $i] :
~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[833]) ).
thf(1477,plain,
( ( ! [V_Q: $i,V_xc: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_xc ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xc ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) )
| ! [V_P: $i] :
~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[834]) ).
thf(1478,plain,
( ( ! [T_a: $i,V_c: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ! [V_A: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[838]) ).
thf(1479,plain,
( ( ! [V_less__eq: $i,V_i: $i,V_u: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_i ) @ V_u ) )
| ! [V_less: $i,V_l: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ V_less__eq @ V_less @ V_l @ V_u @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[839]) ).
thf(1480,plain,
( ( ! [V_less: $i,V_l: $i,V_i: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_l ) @ V_i ) )
| ! [V_less__eq: $i,V_u: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ V_less__eq @ V_less @ V_l @ V_u @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[840]) ).
thf(1481,plain,
( ( ! [V_P: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ V_A @ V_P @ T_a ) ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[841]) ).
thf(1482,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_b: $i,V_a: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[842]) ).
thf(1483,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[843]) ).
thf(1484,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[844]) ).
thf(1485,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_a: $i,V_b: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[845]) ).
thf(1486,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[846]) ).
thf(1487,plain,
( ( ! [V_c2: $i,V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c2 ) @ V_s ) @ V_t ) )
| ! [V_c1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s ) @ V_t ) )
| ! [V_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) @ V_s ) @ V_t ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[848]) ).
thf(1488,plain,
( ( ! [V_A: $i,T_b: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_b )
| ! [V_f: $i,T_a: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[850]) ).
thf(1489,plain,
( ( ! [V_vname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname_H @ V_fun_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_combined,[status(esa)],[852]) ).
thf(1490,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ! [V_x_H: $i,V_y_H: $i] :
( ( ( 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(extcnf_combined,[status(esa)],[853]) ).
thf(1491,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ! [V_x_H: $i,V_y_H: $i] :
( ( ( 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(extcnf_combined,[status(esa)],[854]) ).
thf(1492,plain,
( ( ! [V_G: $i,V_ts: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ! [V_t: $i] :
~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ V_t @ V_ts @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[857]) ).
thf(1493,plain,
( ( ! [V_A: $i,V_f: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_A @ ( hAPP @ V_f @ V_x ) ) )
| ! [T_a: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ V_f @ V_A @ T_a @ T_b ) @ V_x ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[859]) ).
thf(1494,plain,
( ( ! [V_pname_H: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_combined,[status(esa)],[860]) ).
thf(1495,plain,
( ( ! [V_fun: $i,V_com: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[862]) ).
thf(1496,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] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= V_a )
| ! [V_bot: $i,V_top: $i] :
~ ( 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(extcnf_combined,[status(esa)],[864]) ).
thf(1497,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] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= V_a )
| ! [V_bot: $i,V_top: $i] :
~ ( 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(extcnf_combined,[status(esa)],[865]) ).
thf(1498,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(extcnf_combined,[status(esa)],[868]) ).
thf(1499,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[870]) ).
thf(1500,plain,
( ( ! [V_b: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ! [V_t: $i] :
( ( V_t = V_s )
| ! [V_c: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) @ V_s ) @ V_t ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[872]) ).
thf(1501,plain,
( ( ! [V_Inf: $i,T_a: $i,V_top: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_inf: $i] :
( ( ( hAPP @ V_Inf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_top )
| ! [V_sup: $i,V_bot: $i] :
~ ( 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(extcnf_combined,[status(esa)],[873]) ).
thf(1502,plain,
( ( ! [V_Sup: $i,T_a: $i,V_bot: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i] :
( ( ( hAPP @ V_Sup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_bot )
| ! [V_sup: $i,V_top: $i] :
~ ( 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(extcnf_combined,[status(esa)],[874]) ).
thf(1503,plain,
( ( ! [V_fun_H: $i,V_com_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[875]) ).
thf(1504,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 )
| ! [V_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 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[877]) ).
thf(1505,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_loc_H: $i] :
( ! [V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) )
| ( V_loc = V_loc_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[878]) ).
thf(1506,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_loc_H: $i,V_fun_H: $i] :
( ! [V_com_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) )
| ( V_fun = V_fun_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[879]) ).
thf(1507,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) )
| ( V_com = V_com_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[880]) ).
thf(1508,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[882]) ).
thf(1509,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[883]) ).
thf(1510,plain,
( ( ! [T_a: $i,V_P: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Collect @ V_P @ T_a ) )
| ! [V_x: $i] :
~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[885]) ).
thf(1511,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_combined,[status(esa)],[886]) ).
thf(1512,plain,
( ( ! [V_vname: $i,V_fun: $i,V_vname_H: $i] :
( ! [V_fun_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OAss @ V_vname_H @ V_fun_H ) )
| ( V_vname = V_vname_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[888]) ).
thf(1513,plain,
( ( ! [V_vname: $i,V_fun: $i,V_vname_H: $i,V_fun_H: $i] :
( ( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OAss @ V_vname_H @ V_fun_H ) )
| ( V_fun = V_fun_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[889]) ).
thf(1514,plain,
( ( ! [V_f: $i,V_a: $i,V_b: $i] :
( ( ( hAPP @ V_f @ V_a )
= V_b )
| ! [T_a: $i,T_b: $i] :
~ ( 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(extcnf_combined,[status(esa)],[890]) ).
thf(1515,plain,
( ( ! [V_m: $i,V_n: $i,T_b: $i,T_a: $i,V_k: $i,V_x: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
!= ( c_Option_Ooption_OSome @ V_x @ T_a ) )
| ( ( hAPP @ V_n @ V_k )
= ( c_Option_Ooption_ONone @ T_a ) )
| ( ( hAPP @ V_n @ V_k )
= ( c_Option_Ooption_OSome @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[891]) ).
thf(1516,plain,
( ( ! [V_G: $i,V_ts: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ! [V_G_H: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[895]) ).
thf(1517,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(extcnf_combined,[status(esa)],[896]) ).
thf(1518,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_P: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ V_A @ V_B @ V_P @ T_b @ T_a ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ! [V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ ( hAPP @ V_B @ V_x ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[897]) ).
thf(1519,plain,
( ( ! [V_fun_H: $i,V_com_H: $i,V_vname: $i,V_fun: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OAss @ V_vname @ V_fun ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[898]) ).
thf(1520,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] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) )
= ( hAPP @ ( hAPP @ V_inf @ V_a ) @ ( hAPP @ V_Inf @ V_A ) ) )
| ! [V_bot: $i,V_top: $i] :
~ ( 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(extcnf_combined,[status(esa)],[899]) ).
thf(1521,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] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) )
= ( hAPP @ ( hAPP @ V_sup @ V_a ) @ ( hAPP @ V_Sup @ V_A ) ) )
| ! [V_bot: $i,V_top: $i] :
~ ( 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(extcnf_combined,[status(esa)],[900]) ).
thf(1522,plain,
( ( ! [V_vname_H: $i,V_fun_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OAss @ V_vname_H @ V_fun_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[901]) ).
thf(1523,plain,
( ( ! [V_c2: $i,V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c2 ) @ V_s ) @ V_t ) )
| ! [V_b: $i] :
( ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ! [V_c1: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) @ V_s ) @ V_t ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[903]) ).
thf(1524,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(extcnf_combined,[status(esa)],[904]) ).
thf(1525,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(extcnf_combined,[status(esa)],[905]) ).
thf(1526,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(extcnf_combined,[status(esa)],[906]) ).
thf(1527,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(extcnf_combined,[status(esa)],[907]) ).
thf(1528,plain,
( ( ! [V_m_092_060_094isub_0621: $i,V_m_092_060_094isub_0622: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_m_092_060_094isub_0621 @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ V_m_092_060_094isub_0621 @ V_m_092_060_094isub_0622 @ T_a @ T_b ) )
!= ( hAPP @ V_m_092_060_094isub_0622 @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ V_m_092_060_094isub_0621 @ V_m_092_060_094isub_0622 @ T_a @ T_b ) ) )
| ( c_Map_Omap__le @ V_m_092_060_094isub_0621 @ V_m_092_060_094isub_0622 @ T_a @ T_b ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[908]) ).
thf(1529,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(extcnf_combined,[status(esa)],[909]) ).
thf(1530,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[910]) ).
thf(1531,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[911]) ).
thf(1532,plain,
( ( ! [V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_combined,[status(esa)],[912]) ).
thf(1533,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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(extcnf_combined,[status(esa)],[913]) ).
thf(1534,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( 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(extcnf_combined,[status(esa)],[914]) ).
thf(1535,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( 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(extcnf_combined,[status(esa)],[915]) ).
thf(1536,plain,
( ( ! [V_f: $i,V_g: $i] :
( ( V_f = V_g )
| ! [T_a: $i,T_b: $i] :
( ~ ( c_Map_Omap__le @ V_g @ V_f @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_f @ V_g @ T_a @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[916]) ).
thf(1537,plain,
( ( ! [V_u: $i,V_t: $i] :
( ( V_u = V_t )
| ! [V_c: $i,V_s: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_t ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[917]) ).
thf(1538,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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(extcnf_combined,[status(esa)],[918]) ).
thf(1539,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( 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(extcnf_combined,[status(esa)],[919]) ).
thf(1540,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i,V_vname: $i,V_fun: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OAss @ V_vname @ V_fun ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[920]) ).
thf(1541,plain,
( ( ! [V_P: $i] :
( ! [T_a: $i] :
( ( c_Collect @ V_P @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ! [V_x: $i] :
~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[922]) ).
thf(1542,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[923]) ).
thf(1543,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[924]) ).
thf(1544,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[925]) ).
thf(1545,plain,
( ( ! [T_a: $i,V_x: $i,V_B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[928]) ).
thf(1546,plain,
( ( ! [V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[929]) ).
thf(1547,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_x: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[931]) ).
thf(1548,plain,
( ( ! [V_f: $i,V_g: $i,T_a: $i,T_b: $i] :
( ( ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b )
!= ( c_Map_Omap__add @ V_g @ V_f @ T_a @ T_b ) )
| ( c_Map_Omap__le @ V_f @ ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[935]) ).
thf(1549,plain,
( ( ! [V_fun_H: $i,V_com_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[937]) ).
thf(1550,plain,
( ( ! [V_vname: $i,V_fun: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[939]) ).
thf(1551,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 ) ) )
| ! [V_x: $i] :
( ( ( 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(extcnf_combined,[status(esa)],[941]) ).
thf(1552,plain,
( ( ! [V_P: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ V_A @ V_P @ T_a ) ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[942]) ).
thf(1553,plain,
( ( ! [T_a: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ V_A @ V_P @ T_a ) ) @ V_A ) )
| ! [V_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[943]) ).
thf(1554,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) )
| ! [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 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[944]) ).
thf(1555,plain,
( ( ! [T_a: $i,V_c: $i,V_B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ! [V_A: $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 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[945]) ).
thf(1556,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ! [V_b: $i] :
( ( V_a = V_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[947]) ).
thf(1557,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[951]) ).
thf(1558,plain,
( ( ! [T_a: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ V_A @ V_P @ T_a ) ) @ V_A ) )
| ! [V_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[953]) ).
thf(1559,plain,
( ( ! [V_P: $i,V_xa: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ V_A ) )
| ! [V_Q: $i] :
~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) @ V_A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[958]) ).
thf(1560,plain,
( ( ! [V_Q: $i,V_xa: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_xa ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) )
| ! [V_P: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) @ V_A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[959]) ).
thf(1561,plain,
( ( ! [V_P: $i,V_xb: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xb ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xb ) @ V_A ) )
| ! [V_Q: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[960]) ).
thf(1562,plain,
( ( ! [V_Q: $i,V_xb: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_xb ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xb ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) @ V_A ) )
| ! [V_P: $i] :
~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[961]) ).
thf(1563,plain,
( ( ! [V_P: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ V_A @ V_P @ T_a ) ) )
| ! [V_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[964]) ).
thf(1564,plain,
( ( ! [V_A: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ! [V_B: $i,T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[972]) ).
thf(1565,plain,
( ( ! [V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ! [V_A: $i,T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[973]) ).
thf(1566,plain,
( ( ! [V_pname_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[975]) ).
thf(1567,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i,V_vname: $i,V_fun: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OAss @ V_vname @ V_fun ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[976]) ).
thf(1568,plain,
( ( ! [V_n: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( ( hAPP @ V_n @ V_k )
!= ( c_Option_Ooption_OSome @ V_x @ T_a ) )
| ! [V_m: $i,T_b: $i] :
( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
= ( c_Option_Ooption_OSome @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[978]) ).
thf(1569,plain,
( ( ! [V_n: $i,V_k: $i,V_xx: $i,T_a: $i] :
( ( ( hAPP @ V_n @ V_k )
!= ( c_Option_Ooption_OSome @ V_xx @ T_a ) )
| ! [V_m: $i,T_b: $i] :
( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
= ( c_Option_Ooption_OSome @ V_xx @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[979]) ).
thf(1570,plain,
( ( ! [V_m: $i,V_k: $i,T_a: $i] :
( ( ( hAPP @ V_m @ V_k )
!= ( c_Option_Ooption_ONone @ T_a ) )
| ! [V_n: $i] :
( ( ( hAPP @ V_n @ V_k )
!= ( c_Option_Ooption_ONone @ T_a ) )
| ! [T_b: $i] :
( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
= ( c_Option_Ooption_ONone @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[980]) ).
thf(1571,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ! [V_P: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Collect @ V_P @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[981]) ).
thf(1572,plain,
( ( ! [T_a: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ T_a )
| ! [V_A: $i] : ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[982]) ).
thf(1573,plain,
( ( ! [V_fun_H: $i,V_com_H: $i,V_fun: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[983]) ).
thf(1574,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_combined,[status(esa)],[985]) ).
thf(1575,plain,
( ( ! [V_fun: $i,V_com: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) )
| ( V_com = V_com_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[987]) ).
thf(1576,plain,
( ( ! [V_fun: $i,V_com: $i,V_fun_H: $i] :
( ! [V_com_H: $i] :
( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) )
| ( V_fun = V_fun_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[988]) ).
thf(1577,plain,
( ( ! [V_pname: $i,V_pname_H: $i] :
( ( ( c_Com_Ocom_OBODY @ V_pname )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) )
| ( V_pname = V_pname_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[989]) ).
thf(1578,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[990]) ).
thf(1579,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(extcnf_combined,[status(esa)],[993]) ).
thf(1580,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[995]) ).
thf(1581,plain,
( ( ! [V_G: $i,V_t: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ V_t @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ! [V_ts: $i] :
~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ V_t @ V_ts @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[996]) ).
thf(1582,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(extcnf_combined,[status(esa)],[997]) ).
thf(1583,plain,
( ( ! [V_m: $i,V_n: $i,T_b: $i,T_a: $i,V_k: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
!= ( c_Option_Ooption_ONone @ T_a ) )
| ( ( hAPP @ V_n @ V_k )
= ( c_Option_Ooption_ONone @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[998]) ).
thf(1584,plain,
( ( ! [V_m: $i,V_n: $i,T_b: $i,T_a: $i,V_k: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
!= ( c_Option_Ooption_ONone @ T_a ) )
| ( ( hAPP @ V_m @ V_k )
= ( c_Option_Ooption_ONone @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[999]) ).
thf(1585,plain,
( ( ! [V_m: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( ( hAPP @ V_m @ V_k )
!= ( c_Option_Ooption_OSome @ V_x @ T_a ) )
| ! [V_n: $i] :
( ( ( hAPP @ V_n @ V_k )
!= ( c_Option_Ooption_ONone @ T_a ) )
| ! [T_b: $i] :
( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
= ( c_Option_Ooption_OSome @ V_x @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1000]) ).
thf(1586,plain,
( ( ! [V_m: $i,V_n: $i,T_b: $i,T_a: $i,V_k: $i,V_x: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
!= ( c_Option_Ooption_OSome @ V_x @ T_a ) )
| ( ( hAPP @ V_m @ V_k )
= ( c_Option_Ooption_OSome @ V_x @ T_a ) )
| ( ( hAPP @ V_n @ V_k )
= ( c_Option_Ooption_OSome @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1001]) ).
thf(1587,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(extcnf_combined,[status(esa)],[1002]) ).
thf(1588,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1004]) ).
thf(1589,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1006]) ).
thf(1590,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1007]) ).
thf(1591,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) )
| ! [T_b: $i] :
( ( c_Set_Oinsert @ V_x @ ( c_Map_Odom @ V_f @ T_b @ T_a ) @ T_b )
= ( c_Map_Odom @ V_f @ T_b @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1009]) ).
thf(1592,plain,
( ( ! [V_m1: $i,T_a: $i,T_b: $i,V_m2: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Map_Odom @ V_m1 @ T_a @ T_b ) @ ( c_Map_Odom @ V_m2 @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( c_Map_Omap__add @ V_m1 @ V_m2 @ T_a @ T_b )
= ( c_Map_Omap__add @ V_m2 @ V_m1 @ T_a @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1010]) ).
thf(1593,plain,
( ( ! [V_c0: $i,V_c1: $i,V_s0: $i,V_s2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) ) @ V_s0 ) @ V_s2 ) )
| ! [V_s1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s1 ) @ V_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c0 ) @ V_s0 ) @ V_s1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1012]) ).
thf(1594,plain,
( ( ! [V_b: $i,V_s: $i,V_c1: $i] :
( ~ ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ! [V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s ) @ V_t ) )
| ! [V_c2: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) @ V_s ) @ V_t ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1013]) ).
thf(1595,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ! [V_x_H: $i,V_y_H: $i] :
( ( ( 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(extcnf_combined,[status(esa)],[1016]) ).
thf(1596,plain,
( ( ! [T_a: $i,V_xa: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ! [V_y: $i] :
( ! [V_x: $i] :
( ( 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(extcnf_combined,[status(esa)],[1017]) ).
thf(1597,plain,
( ( ! [V_b: $i,V_c: $i,V_s0: $i,V_s2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) @ V_s0 ) @ V_s2 ) )
| ! [V_s1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) @ V_s1 ) @ V_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s0 ) @ V_s1 ) )
| ~ ( hBOOL @ ( hAPP @ V_b @ V_s0 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1019]) ).
thf(1598,plain,
( ( ! [T_a: $i,V_a_H: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1020]) ).
thf(1599,plain,
( ( ! [T_a: $i,V_y: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1021]) ).
thf(1600,plain,
( ( ! [V_com1: $i,V_com2: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1023]) ).
thf(1601,plain,
( ( ! [T_a: $i,V_z: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ! [V_y: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1028]) ).
thf(1602,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[1029]) ).
thf(1603,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1030]) ).
thf(1604,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i,V_A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Collect @ V_P @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1031]) ).
thf(1605,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( 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(extcnf_combined,[status(esa)],[1032]) ).
thf(1606,plain,
( ( ! [V_b: $i,V_a: $i] :
( ( V_b = V_a )
| ! [T_a: $i] :
~ ( 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(extcnf_combined,[status(esa)],[1033]) ).
thf(1607,plain,
( ( ! [V_pname_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1034]) ).
thf(1608,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ! [V_a: $i] :
~ ( c_Fun_Oinj__on @ V_f @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a @ T_b ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1035]) ).
thf(1609,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1037]) ).
thf(1610,plain,
( ( ! [V_vname: $i,V_fun: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1039]) ).
thf(1611,plain,
( ( ! [V_f: $i,V_x: $i,T_a: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( c_Option_Ooption_ONone @ T_a ) )
| ! [T_b: $i,V_A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ V_f @ T_b @ T_a ) @ ( c_Set_Oinsert @ V_x @ V_A @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ V_f @ T_b @ T_a ) @ V_A @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1040]) ).
thf(1612,plain,
( ( ! [V_c: $i,T_b: $i,T_a: $i,V_A: $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 ) )
| ! [V_x: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1043]) ).
thf(1613,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_d: $i,V_R: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ ( c_Com_Ocom_OSemi @ V_c @ V_d ) @ V_R @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ! [V_Q: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_Q @ V_d @ V_R @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ V_c @ V_Q @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1054]) ).
thf(1614,plain,
( ( ! [T_b: $i,V_f: $i,V_A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_b )
| ! [V_a: $i,T_a: $i] :
( ( ( c_Finite__Set_Osetsum @ 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_Finite__Set_Osetsum @ V_f @ V_A @ T_a @ T_b ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1056]) ).
thf(1615,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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 ) @ ( tc_fun @ T_b @ tc_bool ) )
!= ( 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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1059]) ).
thf(1616,plain,
( ( ! [T_b: $i,V_f: $i,V_A: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_b )
| ! [V_a: $i,T_a: $i] :
( ( ( c_Finite__Set_Osetsum @ 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_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ V_f @ V_A @ T_a @ T_b ) @ ( hAPP @ V_f @ V_a ) @ T_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1063]) ).
thf(1617,plain,
( ( ! [T_b: $i,V_f: $i,V_A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_b )
| ! [V_a: $i,T_a: $i] :
( ( ( c_Finite__Set_Osetsum @ 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_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ V_f @ V_A @ T_a @ T_b ) @ ( hAPP @ V_f @ V_a ) @ T_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1064]) ).
thf(1618,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1067]) ).
thf(1619,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1070]) ).
thf(1620,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1071]) ).
thf(1621,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1072]) ).
thf(1622,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1073]) ).
thf(1623,plain,
( ( ! [V_pname_H: $i,V_fun: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1074]) ).
thf(1624,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1075]) ).
thf(1625,plain,
( ( ! [V_vname: $i,V_fun: $i,V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1077]) ).
thf(1626,plain,
( ( ! [V_vname: $i,V_fun: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1079]) ).
thf(1627,plain,
( ( ! [V_a: $i,T_a: $i,V_a_H: $i] :
( ( ( c_Option_Ooption_OSome @ V_a @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1082]) ).
thf(1628,plain,
( ( ! [V_xa: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_xa @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1083]) ).
thf(1629,plain,
( ( ! [V_a_H: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_a_H @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1084]) ).
thf(1630,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i] :
( ! [V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) )
| ( V_fun = V_fun_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1085]) ).
thf(1631,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i] :
( ! [V_com2_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) )
| ( V_com1 = V_com1_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1086]) ).
thf(1632,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) )
| ( V_com2 = V_com2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1087]) ).
thf(1633,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] :
( ( ( 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 ) )
| ! [V_bot: $i,V_top: $i] :
~ ( 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(extcnf_combined,[status(esa)],[1088]) ).
thf(1634,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] :
( ( ( 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 ) )
| ! [V_bot: $i,V_top: $i] :
~ ( 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(extcnf_combined,[status(esa)],[1089]) ).
thf(1635,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1091]) ).
thf(1636,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ! [V_a: $i] :
~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1094]) ).
thf(1637,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1097]) ).
thf(1638,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1098]) ).
thf(1639,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1099]) ).
thf(1640,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1100]) ).
thf(1641,plain,
( ( ! [V_pname_H: $i,V_vname: $i,V_fun: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OAss @ V_vname @ V_fun ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1101]) ).
thf(1642,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 ) ) )
| ! [V_x: $i] :
( ( ( 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(extcnf_combined,[status(esa)],[1102]) ).
thf(1643,plain,
( ( ! [V_A: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ! [V_y: $i] :
( ( V_y = V_x )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1103]) ).
thf(1644,plain,
( ( ! [V_loc_H: $i,V_fun_H: $i,V_com_H: $i,V_vname: $i,V_fun: $i] :
( ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OAss @ V_vname @ V_fun ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1104]) ).
thf(1645,plain,
( ( ! [V_m1: $i,V_m3: $i,T_a: $i,T_b: $i] :
( ( c_Map_Omap__le @ V_m1 @ V_m3 @ T_a @ T_b )
| ! [V_m2: $i] :
( ~ ( c_Map_Omap__le @ V_m2 @ V_m3 @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_m1 @ V_m2 @ T_a @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1105]) ).
thf(1646,plain,
( ( ! [V_B: $i,V_x: $i,T_b: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ V_B @ V_x ) @ T_b )
| ! [T_a: $i,V_A: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[1107]) ).
thf(1647,plain,
( ( ! [V_g: $i,V_h: $i,T_a: $i,T_b: $i] :
( ( c_Map_Omap__le @ V_g @ V_h @ T_a @ T_b )
| ! [V_f: $i] :
~ ( c_Map_Omap__le @ ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b ) @ V_h @ T_a @ T_b ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1109]) ).
thf(1648,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1112]) ).
thf(1649,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(extcnf_combined,[status(esa)],[1113]) ).
thf(1650,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ! [V_B: $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_B @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1115]) ).
thf(1651,plain,
( ( ! [V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1116]) ).
thf(1652,plain,
( ( ! [V_com1: $i,V_com2: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1119]) ).
thf(1653,plain,
( ( ! [V_com1: $i,V_com2: $i,V_com1_H: $i] :
( ! [V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com1 = V_com1_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1120]) ).
thf(1654,plain,
( ( ! [V_com1: $i,V_com2: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com2 = V_com2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1121]) ).
thf(1655,plain,
( ( ! [V_vname: $i,V_fun: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1122]) ).
thf(1656,plain,
( ( ! [V_fun_H: $i,V_com_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1127]) ).
thf(1657,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(extcnf_combined,[status(esa)],[1128]) ).
thf(1658,plain,
( ( ! [V_pname_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1130]) ).
thf(1659,plain,
( ( ! [V_pname_H: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OWhile @ V_fun @ V_com ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1132]) ).
thf(1660,plain,
( ( ! [V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1133]) ).
thf(1661,plain,
( ( ! [V_m1: $i,V_x: $i,T_b: $i,T_a: $i,V_m2: $i] :
( ! [V_y: $i] : ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ V_m1 @ V_x @ ( c_Option_Ooption_ONone @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ ( c_Fun_Ofun__upd @ V_m2 @ V_x @ ( c_Option_Ooption_OSome @ V_y @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_m1 @ V_m2 @ T_a @ T_b ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1135]) ).
thf(1662,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 ) ) )
| ! [V_C: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[1137]) ).
thf(1663,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( ( c_Set_Oimage @ V_f @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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 ) ) )
| ! [V_C: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[1139]) ).
thf(1664,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $i] :
( ( 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(extcnf_combined,[status(esa)],[1140]) ).
thf(1665,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
!= ( c_Finite__Set_Ocard @ V_A @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1146]) ).
thf(1666,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ V_A @ V_B @ V_P @ T_a ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ! [V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ V_A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1153]) ).
thf(1667,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ V_A @ V_B @ V_P @ T_a ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1154]) ).
thf(1668,plain,
( ( ! [T_a: $i,V_c: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ! [V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1156]) ).
thf(1669,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i] :
( ! [V_B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1158]) ).
thf(1670,plain,
( ( ! [T_a: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ! [V_A: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[1159]) ).
thf(1671,plain,
( ( ! [T_a: $i,V_c: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ! [V_A: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[1160]) ).
thf(1672,plain,
( ( ! [T_a: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ! [V_A: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[1161]) ).
thf(1673,plain,
( ( ! [T_a: $i,V_t: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_t ) @ V_B ) )
| ! [V_A: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[1162]) ).
thf(1674,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ! [V_g: $i] :
( ( c_lessequals @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_g @ V_x ) @ T_b )
| ! [T_a: $i] :
~ ( c_lessequals @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1163]) ).
thf(1675,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_b @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1164]) ).
thf(1676,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_a: $i] :
( ! [V_b: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1165]) ).
thf(1677,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ! [V_B: $i] :
~ ( c_Fun_Oinj__on @ V_f @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1168]) ).
thf(1678,plain,
( ( ! [V_f: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ V_f @ V_B @ T_a @ T_b )
| ! [V_A: $i] :
~ ( c_Fun_Oinj__on @ V_f @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1169]) ).
thf(1679,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i] :
( ! [T_a: $i,T_b: $i] :
( ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_a @ T_b )
!= V_f )
| ( ( hAPP @ V_f @ V_x )
= V_y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1170]) ).
thf(1680,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1172]) ).
thf(1681,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1173]) ).
thf(1682,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1175]) ).
thf(1683,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1176]) ).
thf(1684,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1179]) ).
thf(1685,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i] :
( ( c_lessequals @ V_x @ V_y @ T_a )
| ! [V_z: $i] :
~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1180]) ).
thf(1686,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1181]) ).
thf(1687,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1182]) ).
thf(1688,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i] :
( ( c_lessequals @ V_x @ V_b @ T_a )
| ! [V_a: $i] :
~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1183]) ).
thf(1689,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_a: $i] :
( ( c_lessequals @ V_x @ V_a @ T_a )
| ! [V_b: $i] :
~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1184]) ).
thf(1690,plain,
( ( ! [V_C: $i,V_A: $i,T_a: $i] :
( ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
~ ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1185]) ).
thf(1691,plain,
( ( ! [V_C: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_A: $i] :
~ ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1186]) ).
thf(1692,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_A: $i,V_B: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1189]) ).
thf(1693,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_A: $i] :
( ! [V_B: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1190]) ).
thf(1694,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( 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(extcnf_combined,[status(esa)],[1191]) ).
thf(1695,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( 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(extcnf_combined,[status(esa)],[1192]) ).
thf(1696,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1198]) ).
thf(1697,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1200]) ).
thf(1698,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_x: $i] : ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1201]) ).
thf(1699,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1202]) ).
thf(1700,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_z: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1203]) ).
thf(1701,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_x: $i] : ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1204]) ).
thf(1702,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1205]) ).
thf(1703,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1206]) ).
thf(1704,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1211]) ).
thf(1705,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
!= V_x )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1212]) ).
thf(1706,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1213]) ).
thf(1707,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1216]) ).
thf(1708,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1217]) ).
thf(1709,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1218]) ).
thf(1710,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1219]) ).
thf(1711,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1222]) ).
thf(1712,plain,
( ( ! [T_b: $i,V_g: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ! [V_f: $i,T_a: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[1223]) ).
thf(1713,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1224]) ).
thf(1714,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1225]) ).
thf(1715,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1226]) ).
thf(1716,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1227]) ).
thf(1717,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1228]) ).
thf(1718,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i] :
( ~ ( c_lessequals @ V_x @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1229]) ).
thf(1719,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1230]) ).
thf(1720,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1233]) ).
thf(1721,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_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
| ( V_A = V_B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1245]) ).
thf(1722,plain,
( ( ! [T_b: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_b )
| ! [V_M: $i,T_a: $i] :
( ( ( 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(extcnf_combined,[status(esa)],[1252]) ).
thf(1723,plain,
( ( ! [V_B: $i,T_b: $i,V_f: $i] :
( ( c_Finite__Set_Ofinite @ V_B @ T_b )
| ! [V_A: $i,T_a: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[1256]) ).
thf(1724,plain,
( ( ! [V_A: $i,V_k: $i,V_I: $i,T_a: $i] :
( ! [T_b: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ V_A @ V_k ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_I @ V_A @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ ( 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(extcnf_combined,[status(esa)],[1259]) ).
thf(1725,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ ( hAPP @ V_A @ V_x ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [T_b: $i,V_I: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[1260]) ).
thf(1726,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(extcnf_combined,[status(esa)],[1261]) ).
thf(1727,plain,
( ( ! [T_b: $i,V_M: $i,V_i: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_b )
| ! [V_A: $i,T_a: $i] :
( ( 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(extcnf_combined,[status(esa)],[1262]) ).
thf(1728,plain,
( ( ! [T_a: $i,V_f: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( hAPP @ V_f @ V_x ) ) @ V_B ) )
| ! [T_b: $i,V_A: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[1264]) ).
thf(1729,plain,
( ( ! [T_a: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ! [V_A: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1266]) ).
thf(1730,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $i] :
( ( 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(extcnf_combined,[status(esa)],[1268]) ).
thf(1731,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $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 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1270]) ).
thf(1732,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i,T_b: $i] :
( ( ( c_Finite__Set_Ocard @ V_A @ T_a )
= ( c_Finite__Set_Ocard @ V_B @ T_b ) )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_b )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ! [V_g: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ V_g @ V_B @ T_b @ T_a ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_g @ V_B @ T_b @ T_a )
| ! [V_f: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1272]) ).
thf(1733,plain,
( ( ! [T_b: $i,V_f: $i,V_A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_b )
| ! [V_B: $i,T_a: $i] :
( ( ( c_Finite__Set_Osetsum @ 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_Finite__Set_Osetsum @ V_f @ V_A @ T_a @ T_b ) @ ( c_Finite__Set_Osetsum @ V_f @ V_B @ T_a @ T_b ) @ T_b ) )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1273]) ).
thf(1734,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1274]) ).
thf(1735,plain,
( ( ! [V_m: $i,V_a: $i,V_x: $i,T_b: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_Fun_Ofun__upd @ V_m @ V_a @ ( c_Option_Ooption_OSome @ V_x @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) )
!= ( c_Fun_Ofun__upd @ V_n @ V_a @ ( c_Option_Ooption_OSome @ V_y @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) )
| ( V_x = V_y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1276]) ).
thf(1736,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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(extcnf_combined,[status(esa)],[1277]) ).
thf(1737,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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(extcnf_combined,[status(esa)],[1278]) ).
thf(1738,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( 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(extcnf_combined,[status(esa)],[1279]) ).
thf(1739,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( 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(extcnf_combined,[status(esa)],[1280]) ).
thf(1740,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( V_A = V_B )
| ! [T_a: $i] :
( ( 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(extcnf_combined,[status(esa)],[1281]) ).
thf(1741,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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(extcnf_combined,[status(esa)],[1282]) ).
thf(1742,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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(extcnf_combined,[status(esa)],[1283]) ).
thf(1743,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_b: $i,V_a: $i] :
( ( 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(extcnf_combined,[status(esa)],[1285]) ).
thf(1744,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_b: $i,V_a: $i] :
( ( 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(extcnf_combined,[status(esa)],[1286]) ).
thf(1745,plain,
( ( ! [V_x: $i,V_A: $i,T_b: $i] :
( ~ ( c_lessequals @ V_x @ V_A @ ( tc_fun @ T_b @ tc_bool ) )
| ! [V_f: $i,T_a: $i] : ( 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(extcnf_combined,[status(esa)],[1289]) ).
thf(1746,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ! [V_x_H: $i,V_y_H: $i] :
( ( ( 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(extcnf_combined,[status(esa)],[1291]) ).
thf(1747,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ! [V_x_H: $i,V_y_H: $i] :
( ( ( 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(extcnf_combined,[status(esa)],[1292]) ).
thf(1748,plain,
( ( ! [V_t: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( ( hAPP @ V_t @ V_k )
!= ( c_Option_Ooption_OSome @ V_x @ T_a ) )
| ! [T_b: $i] :
( ( c_Fun_Ofun__upd @ V_t @ V_k @ ( c_Option_Ooption_OSome @ V_x @ T_a ) @ T_b @ ( tc_Option_Ooption @ T_a ) )
= V_t ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1297]) ).
thf(1749,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
( ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1300]) ).
thf(1750,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1301]) ).
thf(1751,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ! [V_B: $i] :
( ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1302]) ).
thf(1752,plain,
( ( ! [V_Q: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ! [V_P: $i] :
( ! [T_a: $i] :
~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1303]) ).
thf(1753,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[1304]) ).
thf(1754,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[1305]) ).
thf(1755,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ! [V_B: $i] :
( ~ ( c_Finite__Set_Ofinite @ V_B @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1306]) ).
thf(1756,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1307]) ).
thf(1757,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1308]) ).
thf(1758,plain,
( ( ! [V_Q: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ! [V_P: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i] :
~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1309]) ).
thf(1759,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ! [V_B: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[1310]) ).
thf(1760,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[1311]) ).
thf(1761,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
( ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1314]) ).
thf(1762,plain,
( ( ! [T_a: $i,V_z: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ! [V_y: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1315]) ).
thf(1763,plain,
( ( ! [T_a: $i,V_z: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ! [V_y: $i] :
( ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1316]) ).
thf(1764,plain,
( ( ! [T_a: $i,V_z: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
( ( c_lessequals @ V_z @ V_x @ T_a )
| ! [V_y: $i] :
( ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1317]) ).
thf(1765,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_A: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1318]) ).
thf(1766,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1319]) ).
thf(1767,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_lessequals @ V_a @ V_x @ T_a )
| ! [V_b: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1320]) ).
thf(1768,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_lessequals @ V_b @ V_x @ T_a )
| ! [V_a: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1321]) ).
thf(1769,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_a: $i] :
( ! [V_b: $i] : ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1322]) ).
thf(1770,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1323]) ).
thf(1771,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1324]) ).
thf(1772,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_y @ V_z @ T_a )
| ! [V_x: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1325]) ).
thf(1773,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1329]) ).
thf(1774,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ! [V_z: $i,V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_z @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1330]) ).
thf(1775,plain,
( ( ! [V_b: $i,V_y: $i,V_m: $i,V_x: $i] :
( ! [T_aa: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ V_m @ V_x @ ( c_Option_Ooption_OSome @ V_b @ T_aa ) @ T_a @ ( tc_Option_Ooption @ T_aa ) ) @ V_x )
!= ( c_Option_Ooption_OSome @ V_y @ T_aa ) )
| ( V_b = V_y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1335]) ).
thf(1776,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ! [V_z: $i,V_x: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_z @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1336]) ).
thf(1777,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1337]) ).
thf(1778,plain,
( ( ! [V_A: $i,T_a: $i,V_f: $i,V_z: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ! [V_x: $i,T_b: $i] :
~ ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ V_A @ V_x @ T_a @ T_b ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1340]) ).
thf(1779,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1341]) ).
thf(1780,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Obot @ T_a )
| ! [V_x: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1346]) ).
thf(1781,plain,
( ( ! [V_m: $i,V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_x: $i,V_y: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ V_m @ V_a @ ( c_Option_Ooption_OSome @ V_b @ T_a ) @ T_b @ ( tc_Option_Ooption @ T_a ) ) @ V_x )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) )
| ( ( hAPP @ V_m @ V_x )
= ( c_Option_Ooption_OSome @ V_y @ T_a ) )
| ( V_x = V_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1347]) ).
thf(1782,plain,
( ( ! [V_m: $i,V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_x: $i,V_y: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ V_m @ V_a @ ( c_Option_Ooption_OSome @ V_b @ T_a ) @ T_b @ ( tc_Option_Ooption @ T_a ) ) @ V_x )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) )
| ( ( hAPP @ V_m @ V_x )
= ( c_Option_Ooption_OSome @ V_y @ T_a ) )
| ( V_b = V_y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1348]) ).
thf(1783,plain,
( ( ! [V_m: $i,V_x: $i,V_y: $i,T_a: $i,V_a: $i] :
( ( ( hAPP @ V_m @ V_x )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) )
| ( V_x = V_a )
| ! [V_b: $i,T_b: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ V_m @ V_a @ ( c_Option_Ooption_OSome @ V_b @ T_a ) @ T_b @ ( tc_Option_Ooption @ T_a ) ) @ V_x )
= ( c_Option_Ooption_OSome @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1349]) ).
thf(1784,plain,
( ( ! [V_x: $i,V_z: $i,V_f: $i] :
( ( V_x = V_z )
| ! [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_x @ T_a @ T_b ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1351]) ).
thf(1785,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1354]) ).
thf(1786,plain,
( ( ! [V_m: $i,V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_c: $i] :
( ! [V_d: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ V_m @ V_a @ V_b @ T_a @ T_b ) @ V_c @ V_d @ T_a @ T_b )
= ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ V_m @ V_c @ V_d @ T_a @ T_b ) @ V_a @ V_b @ T_a @ T_b ) )
| ( V_a = V_c ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1357]) ).
thf(1787,plain,
( ( ! [V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ! [V_A: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1358]) ).
thf(1788,plain,
( ( ! [V_F: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ V_F @ T_a )
| ! [V_G: $i] :
~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1361]) ).
thf(1789,plain,
( ( ! [V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ! [V_F: $i] :
~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1362]) ).
thf(1790,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1363]) ).
thf(1791,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1364]) ).
thf(1792,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1369]) ).
thf(1793,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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(extcnf_combined,[status(esa)],[1370]) ).
thf(1794,plain,
( ( ! [T_b: $i,V_f: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ! [V_g: $i,T_a: $i] :
( ( 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(extcnf_combined,[status(esa)],[1371]) ).
thf(1795,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1372]) ).
thf(1796,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( V_A = V_B )
| ! [T_a: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[1373]) ).
thf(1797,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( V_A = V_B )
| ! [T_a: $i] :
( ~ ( 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(extcnf_combined,[status(esa)],[1374]) ).
thf(1798,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1375]) ).
thf(1799,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1376]) ).
thf(1800,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1377]) ).
thf(1801,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1378]) ).
thf(1802,plain,
( ( ! [T_b: $i,V_f: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ! [V_g: $i,T_a: $i] :
( ( 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(extcnf_combined,[status(esa)],[1380]) ).
thf(1803,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1381]) ).
thf(1804,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1382]) ).
thf(1805,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1383]) ).
thf(1806,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1384]) ).
thf(1807,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1385]) ).
thf(1808,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= V_B )
| ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1388]) ).
thf(1809,plain,
( ( ! [V_fun1: $i,V_com: $i,V_fun2: $i,T_a: $i,V_fun1_H: $i] :
( ! [V_com_H: $i,V_fun2_H: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple @ V_fun1 @ V_com @ V_fun2 @ T_a )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ V_fun1_H @ V_com_H @ V_fun2_H @ T_a ) )
| ( V_fun1 = V_fun1_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1394]) ).
thf(1810,plain,
( ( ! [V_fun1: $i,V_com: $i,V_fun2: $i,T_a: $i,V_fun1_H: $i,V_com_H: $i] :
( ! [V_fun2_H: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple @ V_fun1 @ V_com @ V_fun2 @ T_a )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ V_fun1_H @ V_com_H @ V_fun2_H @ T_a ) )
| ( V_com = V_com_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1395]) ).
thf(1811,plain,
( ( ! [V_fun1: $i,V_com: $i,V_fun2: $i,T_a: $i,V_fun1_H: $i,V_com_H: $i,V_fun2_H: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ V_fun1 @ V_com @ V_fun2 @ T_a )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ V_fun1_H @ V_com_H @ V_fun2_H @ T_a ) )
| ( V_fun2 = V_fun2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1396]) ).
thf(1812,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1400]) ).
thf(1813,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1401]) ).
thf(1814,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1402]) ).
thf(1815,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1403]) ).
thf(1816,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1404]) ).
thf(1817,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1405]) ).
thf(1818,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[1406]) ).
thf(1819,plain,
c_Hoare__Mirabelle_Ostate__not__singleton = $true,
inference(copy,[status(thm)],[1411]) ).
thf(1820,plain,
c_Com_OWT__bodies = $true,
inference(copy,[status(thm)],[1410]) ).
thf(1821,plain,
( ( c_Com_OWT @ v_c )
= $true ),
inference(copy,[status(thm)],[1409]) ).
thf(1822,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ tc_Com_Opname ) @ v_pn ) @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) ) )
= $true ),
inference(copy,[status(thm)],[1408]) ).
thf(1823,plain,
( ( ~ ( c_Com_OWT @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ v_pn ) @ tc_Com_Ocom ) ) )
= $true ),
inference(copy,[status(thm)],[1407]) ).
thf(1824,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1818]) ).
thf(1825,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1817]) ).
thf(1826,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1816]) ).
thf(1827,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1815]) ).
thf(1828,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1814]) ).
thf(1829,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1813]) ).
thf(1830,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1812]) ).
thf(1831,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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)],[1399]) ).
thf(1832,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)],[1398]) ).
thf(1833,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)],[1397]) ).
thf(1834,plain,
( ( ! [V_fun1: $i,V_com: $i,V_fun2: $i,T_a: $i,V_fun1_H: $i,V_com_H: $i,V_fun2_H: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ V_fun1 @ V_com @ V_fun2 @ T_a )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ V_fun1_H @ V_com_H @ V_fun2_H @ T_a ) )
| ( V_fun2 = V_fun2_H ) ) )
= $true ),
inference(copy,[status(thm)],[1811]) ).
thf(1835,plain,
( ( ! [V_fun1: $i,V_com: $i,V_fun2: $i,T_a: $i,V_fun1_H: $i,V_com_H: $i] :
( ! [V_fun2_H: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple @ V_fun1 @ V_com @ V_fun2 @ T_a )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ V_fun1_H @ V_com_H @ V_fun2_H @ T_a ) )
| ( V_com = V_com_H ) ) )
= $true ),
inference(copy,[status(thm)],[1810]) ).
thf(1836,plain,
( ( ! [V_fun1: $i,V_com: $i,V_fun2: $i,T_a: $i,V_fun1_H: $i] :
( ! [V_com_H: $i,V_fun2_H: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple @ V_fun1 @ V_com @ V_fun2 @ T_a )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ V_fun1_H @ V_com_H @ V_fun2_H @ T_a ) )
| ( V_fun1 = V_fun1_H ) ) )
= $true ),
inference(copy,[status(thm)],[1809]) ).
thf(1837,plain,
( ( ! [V_f: $i,V_x: $i,T_aa: $i,T_a: $i] :
( ( c_Fun_Ofun__upd @ V_f @ V_x @ ( hAPP @ V_f @ V_x ) @ T_aa @ T_a )
= V_f ) )
= $true ),
inference(copy,[status(thm)],[1393]) ).
thf(1838,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,T_aa: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_a @ T_aa ) @ V_x )
= V_y ) )
= $true ),
inference(copy,[status(thm)],[1392]) ).
thf(1839,plain,
( ( ! [V_f: $i,V_x: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Ofun__upd @ V_f @ V_x @ ( hAPP @ V_f @ V_x ) @ T_a @ T_b )
= V_f ) )
= $true ),
inference(copy,[status(thm)],[1391]) ).
thf(1840,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_b: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_b @ T_a ) @ V_x )
= V_y ) )
= $true ),
inference(copy,[status(thm)],[1390]) ).
thf(1841,plain,
( ( ! [V_f: $i,V_x: $i,T_b: $i,T_a: $i] :
( ( c_Fun_Ofun__upd @ V_f @ V_x @ ( hAPP @ V_f @ V_x ) @ T_b @ T_a )
= V_f ) )
= $true ),
inference(copy,[status(thm)],[1389]) ).
thf(1842,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( 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)],[1808]) ).
thf(1843,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1387]) ).
thf(1844,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( 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)],[1386]) ).
thf(1845,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1807]) ).
thf(1846,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1806]) ).
thf(1847,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1805]) ).
thf(1848,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1804]) ).
thf(1849,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1803]) ).
thf(1850,plain,
( ( ! [T_b: $i,V_f: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ! [V_g: $i,T_a: $i] :
( ( 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)],[1802]) ).
thf(1851,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)],[1379]) ).
thf(1852,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1801]) ).
thf(1853,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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)],[1800]) ).
thf(1854,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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)],[1799]) ).
thf(1855,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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)],[1798]) ).
thf(1856,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( V_A = V_B )
| ! [T_a: $i] :
( ~ ( 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)],[1797]) ).
thf(1857,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( V_A = V_B )
| ! [T_a: $i] :
( ~ ( 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)],[1796]) ).
thf(1858,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1795]) ).
thf(1859,plain,
( ( ! [T_b: $i,V_f: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ! [V_g: $i,T_a: $i] :
( ( 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)],[1794]) ).
thf(1860,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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)],[1793]) ).
thf(1861,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1792]) ).
thf(1862,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)],[1368]) ).
thf(1863,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i,V_z: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_a @ T_b ) @ V_x @ V_z @ T_a @ T_b )
= ( c_Fun_Ofun__upd @ V_f @ V_x @ V_z @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1367]) ).
thf(1864,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ 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)],[1366]) ).
thf(1865,plain,
( ( ! [T_a: $i,V_B: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B ) )
= $true ),
inference(copy,[status(thm)],[1365]) ).
thf(1866,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1791]) ).
thf(1867,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1790]) ).
thf(1868,plain,
( ( ! [V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ! [V_F: $i] :
~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1789]) ).
thf(1869,plain,
( ( ! [V_F: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ V_F @ T_a )
| ! [V_G: $i] :
~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1788]) ).
thf(1870,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1360]) ).
thf(1871,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1359]) ).
thf(1872,plain,
( ( ! [V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ! [V_A: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1787]) ).
thf(1873,plain,
( ( ! [V_m: $i,V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_c: $i] :
( ! [V_d: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ V_m @ V_a @ V_b @ T_a @ T_b ) @ V_c @ V_d @ T_a @ T_b )
= ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ V_m @ V_c @ V_d @ T_a @ T_b ) @ V_a @ V_b @ T_a @ T_b ) )
| ( V_a = V_c ) ) )
= $true ),
inference(copy,[status(thm)],[1786]) ).
thf(1874,plain,
( ( ! [V_f: $i,V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_g: $i] :
( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ V_f @ V_a @ V_b @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ ( c_Fun_Ofun__upd @ V_g @ V_a @ V_b @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_f @ V_g @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1356]) ).
thf(1875,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1355]) ).
thf(1876,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1785]) ).
thf(1877,plain,
( ( ! [V_F: $i,V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1353]) ).
thf(1878,plain,
( ( ! [V_F: $i,V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1352]) ).
thf(1879,plain,
( ( ! [V_x: $i,V_z: $i,V_f: $i] :
( ( V_x = V_z )
| ! [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_x @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1784]) ).
thf(1880,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)],[1350]) ).
thf(1881,plain,
( ( ! [V_m: $i,V_x: $i,V_y: $i,T_a: $i,V_a: $i] :
( ( ( hAPP @ V_m @ V_x )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) )
| ( V_x = V_a )
| ! [V_b: $i,T_b: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ V_m @ V_a @ ( c_Option_Ooption_OSome @ V_b @ T_a ) @ T_b @ ( tc_Option_Ooption @ T_a ) ) @ V_x )
= ( c_Option_Ooption_OSome @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1783]) ).
thf(1882,plain,
( ( ! [V_m: $i,V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_x: $i,V_y: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ V_m @ V_a @ ( c_Option_Ooption_OSome @ V_b @ T_a ) @ T_b @ ( tc_Option_Ooption @ T_a ) ) @ V_x )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) )
| ( ( hAPP @ V_m @ V_x )
= ( c_Option_Ooption_OSome @ V_y @ T_a ) )
| ( V_b = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[1782]) ).
thf(1883,plain,
( ( ! [V_m: $i,V_a: $i,V_b: $i,T_a: $i,T_b: $i,V_x: $i,V_y: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ V_m @ V_a @ ( c_Option_Ooption_OSome @ V_b @ T_a ) @ T_b @ ( tc_Option_Ooption @ T_a ) ) @ V_x )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) )
| ( ( hAPP @ V_m @ V_x )
= ( c_Option_Ooption_OSome @ V_y @ T_a ) )
| ( V_x = V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1781]) ).
thf(1884,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Obot @ T_a )
| ! [V_x: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1780]) ).
thf(1885,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)],[1345]) ).
thf(1886,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1344]) ).
thf(1887,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1343]) ).
thf(1888,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)],[1342]) ).
thf(1889,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1779]) ).
thf(1890,plain,
( ( ! [V_A: $i,T_a: $i,V_f: $i,V_z: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ! [V_x: $i,T_b: $i] :
~ ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ V_A @ V_x @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1778]) ).
thf(1891,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1339]) ).
thf(1892,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1338]) ).
thf(1893,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1777]) ).
thf(1894,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ! [V_z: $i,V_x: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_z @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1776]) ).
thf(1895,plain,
( ( ! [V_b: $i,V_y: $i,V_m: $i,V_x: $i] :
( ! [T_aa: $i,T_a: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ V_m @ V_x @ ( c_Option_Ooption_OSome @ V_b @ T_aa ) @ T_a @ ( tc_Option_Ooption @ T_aa ) ) @ V_x )
!= ( c_Option_Ooption_OSome @ V_y @ T_aa ) )
| ( V_b = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[1775]) ).
thf(1896,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1334]) ).
thf(1897,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1333]) ).
thf(1898,plain,
( ( ! [V_C: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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)],[1332]) ).
thf(1899,plain,
( ( ! [V_C: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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)],[1331]) ).
thf(1900,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ! [V_z: $i,V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ V_x @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_z @ V_x @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1774]) ).
thf(1901,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1773]) ).
thf(1902,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1328]) ).
thf(1903,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1327]) ).
thf(1904,plain,
( ( ! [V_f: $i,V_g: $i,V_A: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Set_Oimage @ V_g @ V_A @ T_c @ T_b ) @ T_b @ T_a )
= ( c_Set_Oimage @ ( c_COMBB @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_A @ T_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1326]) ).
thf(1905,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_y @ V_z @ T_a )
| ! [V_x: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1772]) ).
thf(1906,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1771]) ).
thf(1907,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1770]) ).
thf(1908,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_a: $i] :
( ! [V_b: $i] : ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1769]) ).
thf(1909,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_lessequals @ V_b @ V_x @ T_a )
| ! [V_a: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1768]) ).
thf(1910,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_lessequals @ V_a @ V_x @ T_a )
| ! [V_b: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1767]) ).
thf(1911,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1766]) ).
thf(1912,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_A: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1765]) ).
thf(1913,plain,
( ( ! [T_a: $i,V_z: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
( ( c_lessequals @ V_z @ V_x @ T_a )
| ! [V_y: $i] :
( ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1764]) ).
thf(1914,plain,
( ( ! [T_a: $i,V_z: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ! [V_y: $i] :
( ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1763]) ).
thf(1915,plain,
( ( ! [T_a: $i,V_z: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ! [V_y: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1762]) ).
thf(1916,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
( ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1761]) ).
thf(1917,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_lessequals @ V_x @ V_x @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1313]) ).
thf(1918,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1312]) ).
thf(1919,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
( ~ ( 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)],[1760]) ).
thf(1920,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ! [V_B: $i] :
( ~ ( 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)],[1759]) ).
thf(1921,plain,
( ( ! [V_Q: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ! [V_P: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i] :
~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1758]) ).
thf(1922,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1757]) ).
thf(1923,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1756]) ).
thf(1924,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ! [V_B: $i] :
( ~ ( 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)],[1755]) ).
thf(1925,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
( ~ ( 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)],[1754]) ).
thf(1926,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
( ~ ( 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)],[1753]) ).
thf(1927,plain,
( ( ! [V_Q: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ! [V_P: $i] :
( ! [T_a: $i] :
~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1752]) ).
thf(1928,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ! [V_B: $i] :
( ~ ( 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)],[1751]) ).
thf(1929,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1750]) ).
thf(1930,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
( ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1749]) ).
thf(1931,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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)],[1299]) ).
thf(1932,plain,
( ( ! [V_m: $i,V_xa: $i,V_x: $i,T_a: $i,T_aa: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ V_m @ V_xa @ ( c_Option_Ooption_OSome @ V_x @ T_a ) @ T_aa @ ( tc_Option_Ooption @ T_a ) ) @ V_xa )
= ( c_Option_Ooption_OSome @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1298]) ).
thf(1933,plain,
( ( ! [V_t: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( ( hAPP @ V_t @ V_k )
!= ( c_Option_Ooption_OSome @ V_x @ T_a ) )
| ! [T_b: $i] :
( ( c_Fun_Ofun__upd @ V_t @ V_k @ ( c_Option_Ooption_OSome @ V_x @ T_a ) @ T_b @ ( tc_Option_Ooption @ T_a ) )
= V_t ) ) )
= $true ),
inference(copy,[status(thm)],[1748]) ).
thf(1934,plain,
( ( ! [V_A: $i,V_B: $i,T_b: $i,V_M: $i,T_a: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ V_M @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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 ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1296]) ).
thf(1935,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_b: $i,T_a: $i,V_z: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_b @ T_a ) @ V_z )
= ( hAPP @ V_f @ V_z ) )
| ( V_z = V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1295]) ).
thf(1936,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i,V_z: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_a @ T_b ) @ V_z )
= ( hAPP @ V_f @ V_z ) )
| ( V_z = V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1294]) ).
thf(1937,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)],[1293]) ).
thf(1938,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ! [V_x_H: $i,V_y_H: $i] :
( ( ( 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)],[1747]) ).
thf(1939,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ! [V_x_H: $i,V_y_H: $i] :
( ( ( 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)],[1746]) ).
thf(1940,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)],[1290]) ).
thf(1941,plain,
( ( ! [V_x: $i,V_A: $i,T_b: $i] :
( ~ ( c_lessequals @ V_x @ V_A @ ( tc_fun @ T_b @ tc_bool ) )
| ! [V_f: $i,T_a: $i] : ( 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)],[1745]) ).
thf(1942,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)],[1288]) ).
thf(1943,plain,
( ( ! [T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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 ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1287]) ).
thf(1944,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_b: $i,V_a: $i] :
( ( 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)],[1744]) ).
thf(1945,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_b: $i,V_a: $i] :
( ( 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)],[1743]) ).
thf(1946,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)],[1284]) ).
thf(1947,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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)],[1742]) ).
thf(1948,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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)],[1741]) ).
thf(1949,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( V_A = V_B )
| ! [T_a: $i] :
( ( 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)],[1740]) ).
thf(1950,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( 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)],[1739]) ).
thf(1951,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( 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)],[1738]) ).
thf(1952,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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)],[1737]) ).
thf(1953,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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)],[1736]) ).
thf(1954,plain,
( ( ! [V_m: $i,V_a: $i,V_x: $i,T_b: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_Fun_Ofun__upd @ V_m @ V_a @ ( c_Option_Ooption_OSome @ V_x @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) )
!= ( c_Fun_Ofun__upd @ V_n @ V_a @ ( c_Option_Ooption_OSome @ V_y @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[1735]) ).
thf(1955,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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)],[1275]) ).
thf(1956,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1734]) ).
thf(1957,plain,
( ( ! [T_b: $i,V_f: $i,V_A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_b )
| ! [V_B: $i,T_a: $i] :
( ( ( c_Finite__Set_Osetsum @ 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_Finite__Set_Osetsum @ V_f @ V_A @ T_a @ T_b ) @ ( c_Finite__Set_Osetsum @ V_f @ V_B @ T_a @ T_b ) @ T_b ) )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1733]) ).
thf(1958,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i,T_b: $i] :
( ( ( c_Finite__Set_Ocard @ V_A @ T_a )
= ( c_Finite__Set_Ocard @ V_B @ T_b ) )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_b )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ! [V_g: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ V_g @ V_B @ T_b @ T_a ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_g @ V_B @ T_b @ T_a )
| ! [V_f: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ V_B @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1732]) ).
thf(1959,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)],[1271]) ).
thf(1960,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $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 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1731]) ).
thf(1961,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)],[1269]) ).
thf(1962,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $i] :
( ( 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)],[1730]) ).
thf(1963,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)],[1267]) ).
thf(1964,plain,
( ( ! [T_a: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ! [V_A: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1729]) ).
thf(1965,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)],[1265]) ).
thf(1966,plain,
( ( ! [T_a: $i,V_f: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( hAPP @ V_f @ V_x ) ) @ V_B ) )
| ! [T_b: $i,V_A: $i] :
( ~ ( 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)],[1728]) ).
thf(1967,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_b @ T_a ) @ V_A @ T_b @ T_a )
= ( 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)],[1263]) ).
thf(1968,plain,
( ( ! [T_b: $i,V_M: $i,V_i: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_b )
| ! [V_A: $i,T_a: $i] :
( ( 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)],[1727]) ).
thf(1969,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)],[1726]) ).
thf(1970,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ ( hAPP @ V_A @ V_x ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [T_b: $i,V_I: $i] :
( ~ ( 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)],[1725]) ).
thf(1971,plain,
( ( ! [V_A: $i,V_k: $i,V_I: $i,T_a: $i] :
( ! [T_b: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ V_A @ V_k ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_I @ V_A @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ ( 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)],[1724]) ).
thf(1972,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1258]) ).
thf(1973,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)],[1257]) ).
thf(1974,plain,
( ( ! [V_B: $i,T_b: $i,V_f: $i] :
( ( c_Finite__Set_Ofinite @ V_B @ T_b )
| ! [V_A: $i,T_a: $i] :
( ~ ( 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)],[1723]) ).
thf(1975,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)],[1255]) ).
thf(1976,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)],[1254]) ).
thf(1977,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)],[1253]) ).
thf(1978,plain,
( ( ! [T_b: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_b )
| ! [V_M: $i,T_a: $i] :
( ( ( 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)],[1722]) ).
thf(1979,plain,
( ( ! [T_b: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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 @ ( tc_fun @ T_a @ tc_bool ) )
= V_B ) )
= $true ),
inference(copy,[status(thm)],[1251]) ).
thf(1980,plain,
( ( ! [V_A: $i,T_b: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ 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)],[1250]) ).
thf(1981,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 ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ V_B @ V_a ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1249]) ).
thf(1982,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] : ( c_lessequals @ ( c_Set_Oimage @ V_f @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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 ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1248]) ).
thf(1983,plain,
( ( ! [V_A: $i,V_B: $i,V_f: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ ( c_COMBB @ V_B @ V_f @ T_c @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_c ) @ V_B @ T_c @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1247]) ).
thf(1984,plain,
( ( ! [V_f: $i,V_A: $i,T_c: $i,T_b: $i,V_B: $i,T_a: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oimage @ V_f @ V_A @ T_c @ T_b ) @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ ( c_COMBB @ V_B @ V_f @ T_b @ ( tc_fun @ T_a @ tc_bool ) @ T_c ) @ T_c @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1246]) ).
thf(1985,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_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
| ( V_A = V_B ) ) )
= $true ),
inference(copy,[status(thm)],[1721]) ).
thf(1986,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
= ( c_Finite__Set_Ocard @ V_A @ T_a ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1244]) ).
thf(1987,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)],[1243]) ).
thf(1988,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[1242]) ).
thf(1989,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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 ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1241]) ).
thf(1990,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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 ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1240]) ).
thf(1991,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)],[1239]) ).
thf(1992,plain,
( ( ! [V_f: $i,V_g: $i,V_x: $i,V_y: $i,T_b: $i,T_a: $i] :
( ( c_Map_Omap__add @ V_f @ ( c_Fun_Ofun__upd @ V_g @ V_x @ ( c_Option_Ooption_OSome @ V_y @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ T_a @ T_b )
= ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b ) @ V_x @ ( c_Option_Ooption_OSome @ V_y @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1238]) ).
thf(1993,plain,
( ( ! [V_m: $i,V_n: $i,T_a: $i,T_b: $i] :
( ( c_Map_Odom @ ( c_Map_Omap__add @ V_m @ V_n @ T_a @ T_b ) @ T_a @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Map_Odom @ V_n @ T_a @ T_b ) @ ( c_Map_Odom @ V_m @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1237]) ).
thf(1994,plain,
( ( ! [V_f: $i,V_x: $i,T_b: $i,T_a: $i] : ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ V_f @ V_x @ ( c_Option_Ooption_ONone @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ V_f @ T_a @ T_b ) )
= $true ),
inference(copy,[status(thm)],[1236]) ).
thf(1995,plain,
( ( ! [V_f: $i,T_a: $i,T_b: $i,V_g: $i] :
( ( c_lessequals @ ( c_Map_Odom @ V_f @ T_a @ T_b ) @ ( c_Map_Odom @ V_g @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_Map_Omap__le @ V_f @ V_g @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1235]) ).
thf(1996,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[1234]) ).
thf(1997,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1720]) ).
thf(1998,plain,
( ( ! [V_P: $i,V_Q: $i,T_b: $i,T_a: $i,T_c: $i,V_R: $i] :
( ( hAPP @ ( c_COMBB @ V_P @ V_Q @ T_b @ T_a @ T_c ) @ V_R )
= ( hAPP @ V_P @ ( hAPP @ V_Q @ V_R ) ) ) )
= $true ),
inference(copy,[status(thm)],[1232]) ).
thf(1999,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)],[1231]) ).
thf(2000,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1719]) ).
thf(2001,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i] :
( ~ ( c_lessequals @ V_x @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1718]) ).
thf(2002,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1717]) ).
thf(2003,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1716]) ).
thf(2004,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1715]) ).
thf(2005,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1714]) ).
thf(2006,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1713]) ).
thf(2007,plain,
( ( ! [T_b: $i,V_g: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ! [V_f: $i,T_a: $i] :
( ~ ( 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)],[1712]) ).
thf(2008,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1711]) ).
thf(2009,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1221]) ).
thf(2010,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1220]) ).
thf(2011,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1710]) ).
thf(2012,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1709]) ).
thf(2013,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1708]) ).
thf(2014,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1707]) ).
thf(2015,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1215]) ).
thf(2016,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1214]) ).
thf(2017,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1706]) ).
thf(2018,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
!= V_x )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1705]) ).
thf(2019,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1704]) ).
thf(2020,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ 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)],[1210]) ).
thf(2021,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1209]) ).
thf(2022,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1208]) ).
thf(2023,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ 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)],[1207]) ).
thf(2024,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ 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)],[1703]) ).
thf(2025,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1702]) ).
thf(2026,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_x: $i] : ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1701]) ).
thf(2027,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_z: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ 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)],[1700]) ).
thf(2028,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ 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)],[1699]) ).
thf(2029,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_x: $i] : ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1698]) ).
thf(2030,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1697]) ).
thf(2031,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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)],[1199]) ).
thf(2032,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1696]) ).
thf(2033,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)],[1197]) ).
thf(2034,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1196]) ).
thf(2035,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)],[1195]) ).
thf(2036,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)],[1194]) ).
thf(2037,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)],[1193]) ).
thf(2038,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( 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)],[1695]) ).
thf(2039,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( 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)],[1694]) ).
thf(2040,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_A: $i] :
( ! [V_B: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1693]) ).
thf(2041,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_A: $i,V_B: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1692]) ).
thf(2042,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1188]) ).
thf(2043,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1187]) ).
thf(2044,plain,
( ( ! [V_C: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_A: $i] :
~ ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1691]) ).
thf(2045,plain,
( ( ! [V_C: $i,V_A: $i,T_a: $i] :
( ( c_lessequals @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
~ ( c_lessequals @ V_C @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1690]) ).
thf(2046,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_a: $i] :
( ( c_lessequals @ V_x @ V_a @ T_a )
| ! [V_b: $i] :
~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1689]) ).
thf(2047,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i] :
( ( c_lessequals @ V_x @ V_b @ T_a )
| ! [V_a: $i] :
~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1688]) ).
thf(2048,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1687]) ).
thf(2049,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1686]) ).
thf(2050,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i] :
( ( c_lessequals @ V_x @ V_y @ T_a )
| ! [V_z: $i] :
~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1685]) ).
thf(2051,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
~ ( c_lessequals @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1684]) ).
thf(2052,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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 ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1178]) ).
thf(2053,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1177]) ).
thf(2054,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1683]) ).
thf(2055,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1682]) ).
thf(2056,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1174]) ).
thf(2057,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1681]) ).
thf(2058,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1680]) ).
thf(2059,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Ovimage @ V_f @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_a @ T_b )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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)],[1171]) ).
thf(2060,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i] :
( ! [T_a: $i,T_b: $i] :
( ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_a @ T_b )
!= V_f )
| ( ( hAPP @ V_f @ V_x )
= V_y ) ) )
= $true ),
inference(copy,[status(thm)],[1679]) ).
thf(2061,plain,
( ( ! [V_f: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ V_f @ V_B @ T_a @ T_b )
| ! [V_A: $i] :
~ ( c_Fun_Oinj__on @ V_f @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1678]) ).
thf(2062,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ! [V_B: $i] :
~ ( c_Fun_Oinj__on @ V_f @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1677]) ).
thf(2063,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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1167]) ).
thf(2064,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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)],[1166]) ).
thf(2065,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_a: $i] :
( ! [V_b: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1676]) ).
thf(2066,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1675]) ).
thf(2067,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ! [V_g: $i] :
( ( c_lessequals @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_g @ V_x ) @ T_b )
| ! [T_a: $i] :
~ ( c_lessequals @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1674]) ).
thf(2068,plain,
( ( ! [T_a: $i,V_t: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_t ) @ V_B ) )
| ! [V_A: $i] :
( ~ ( 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)],[1673]) ).
thf(2069,plain,
( ( ! [T_a: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ! [V_A: $i] :
( ~ ( 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)],[1672]) ).
thf(2070,plain,
( ( ! [T_a: $i,V_c: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ! [V_A: $i] :
( ~ ( 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)],[1671]) ).
thf(2071,plain,
( ( ! [T_a: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ! [V_A: $i] :
( ~ ( 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)],[1670]) ).
thf(2072,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i] :
( ! [V_B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1669]) ).
thf(2073,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[1157]) ).
thf(2074,plain,
( ( ! [T_a: $i,V_c: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ! [V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1668]) ).
thf(2075,plain,
( ( ! [V_c: $i] :
( ( c_Hoare__Mirabelle_OMGT @ V_c )
= ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_fequal @ tc_Com_Ostate ) @ V_c @ ( c_Natural_Oevalc @ V_c ) @ tc_Com_Ostate ) ) )
= $true ),
inference(copy,[status(thm)],[1155]) ).
thf(2076,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ V_A @ V_B @ V_P @ T_a ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1667]) ).
thf(2077,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ V_A @ V_B @ V_P @ T_a ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ! [V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ V_A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1666]) ).
thf(2078,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a )
= ( c_Finite__Set_Ocard @ V_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)],[1152]) ).
thf(2079,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)],[1151]) ).
thf(2080,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i,V_A: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_a @ T_b ) @ V_A @ T_a @ T_b )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_y ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1150]) ).
thf(2081,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_B @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ T_a ) @ T_a @ T_a @ tc_bool ) @ V_a ) @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1149]) ).
thf(2082,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)],[1148]) ).
thf(2083,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
= ( c_Finite__Set_Ocard @ V_A @ T_a ) )
| ~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1147]) ).
thf(2084,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
!= ( c_Finite__Set_Ocard @ V_A @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1665]) ).
thf(2085,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)],[1145]) ).
thf(2086,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)],[1144]) ).
thf(2087,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)],[1143]) ).
thf(2088,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)],[1142]) ).
thf(2089,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)],[1141]) ).
thf(2090,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $i] :
( ( 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)],[1664]) ).
thf(2091,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( ( c_Set_Oimage @ V_f @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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 ) ) )
| ! [V_C: $i] :
( ~ ( 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)],[1663]) ).
thf(2092,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 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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 ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1138]) ).
thf(2093,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 ) ) )
| ! [V_C: $i] :
( ~ ( 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)],[1662]) ).
thf(2094,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_a: $i,T_b: $i] :
( ( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ T_a @ T_b )
= ( c_Set_Oinsert @ V_x @ ( c_Map_Odom @ V_f @ T_a @ T_b ) @ T_a ) )
| ( V_y
= ( c_Option_Ooption_ONone @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1136]) ).
thf(2095,plain,
( ( ! [V_m1: $i,V_x: $i,T_b: $i,T_a: $i,V_m2: $i] :
( ! [V_y: $i] : ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ V_m1 @ V_x @ ( c_Option_Ooption_ONone @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ ( c_Fun_Ofun__upd @ V_m2 @ V_x @ ( c_Option_Ooption_OSome @ V_y @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_m1 @ V_m2 @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1661]) ).
thf(2096,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)],[1134]) ).
thf(2097,plain,
( ( ! [V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(copy,[status(thm)],[1660]) ).
thf(2098,plain,
( ( ! [V_pname_H: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OWhile @ V_fun @ V_com ) ) )
= $true ),
inference(copy,[status(thm)],[1659]) ).
thf(2099,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)],[1131]) ).
thf(2100,plain,
( ( ! [V_pname_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(copy,[status(thm)],[1658]) ).
thf(2101,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)],[1129]) ).
thf(2102,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)],[1657]) ).
thf(2103,plain,
( ( ! [V_fun_H: $i,V_com_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(copy,[status(thm)],[1656]) ).
thf(2104,plain,
( ( ! [V_b: $i,V_c: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) @ V_s ) @ V_s ) )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[1126]) ).
thf(2105,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)],[1125]) ).
thf(2106,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)],[1124]) ).
thf(2107,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( c_Collect @ V_P @ T_a )
= V_P ) )
= $true ),
inference(copy,[status(thm)],[1123]) ).
thf(2108,plain,
( ( ! [V_vname: $i,V_fun: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(copy,[status(thm)],[1655]) ).
thf(2109,plain,
( ( ! [V_com1: $i,V_com2: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com2 = V_com2_H ) ) )
= $true ),
inference(copy,[status(thm)],[1654]) ).
thf(2110,plain,
( ( ! [V_com1: $i,V_com2: $i,V_com1_H: $i] :
( ! [V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com1 = V_com1_H ) ) )
= $true ),
inference(copy,[status(thm)],[1653]) ).
thf(2111,plain,
( ( ! [V_com1: $i,V_com2: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(copy,[status(thm)],[1652]) ).
thf(2112,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)],[1118]) ).
thf(2113,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)],[1117]) ).
thf(2114,plain,
( ( ! [V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(copy,[status(thm)],[1651]) ).
thf(2115,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ! [V_B: $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_B @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1650]) ).
thf(2116,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)],[1114]) ).
thf(2117,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)],[1649]) ).
thf(2118,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(copy,[status(thm)],[1648]) ).
thf(2119,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)],[1111]) ).
thf(2120,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1110]) ).
thf(2121,plain,
( ( ! [V_g: $i,V_h: $i,T_a: $i,T_b: $i] :
( ( c_Map_Omap__le @ V_g @ V_h @ T_a @ T_b )
| ! [V_f: $i] :
~ ( c_Map_Omap__le @ ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b ) @ V_h @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1647]) ).
thf(2122,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)],[1108]) ).
thf(2123,plain,
( ( ! [V_B: $i,V_x: $i,T_b: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ V_B @ V_x ) @ T_b )
| ! [T_a: $i,V_A: $i] :
( ~ ( 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)],[1646]) ).
thf(2124,plain,
( ( ! [V_f: $i,T_a: $i,T_b: $i] : ( c_Map_Omap__le @ V_f @ V_f @ T_a @ T_b ) )
= $true ),
inference(copy,[status(thm)],[1106]) ).
thf(2125,plain,
( ( ! [V_m1: $i,V_m3: $i,T_a: $i,T_b: $i] :
( ( c_Map_Omap__le @ V_m1 @ V_m3 @ T_a @ T_b )
| ! [V_m2: $i] :
( ~ ( c_Map_Omap__le @ V_m2 @ V_m3 @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_m1 @ V_m2 @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1645]) ).
thf(2126,plain,
( ( ! [V_loc_H: $i,V_fun_H: $i,V_com_H: $i,V_vname: $i,V_fun: $i] :
( ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OAss @ V_vname @ V_fun ) ) )
= $true ),
inference(copy,[status(thm)],[1644]) ).
thf(2127,plain,
( ( ! [V_A: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ! [V_y: $i] :
( ( V_y = V_x )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1643]) ).
thf(2128,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 ) ) )
| ! [V_x: $i] :
( ( ( 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)],[1642]) ).
thf(2129,plain,
( ( ! [V_pname_H: $i,V_vname: $i,V_fun: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OAss @ V_vname @ V_fun ) ) )
= $true ),
inference(copy,[status(thm)],[1641]) ).
thf(2130,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(copy,[status(thm)],[1640]) ).
thf(2131,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(copy,[status(thm)],[1639]) ).
thf(2132,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1638]) ).
thf(2133,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1637]) ).
thf(2134,plain,
( ( ! [T_a: $i,V_B: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1096]) ).
thf(2135,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Orderings_Obot__class_Obot @ ( 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)],[1095]) ).
thf(2136,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ! [V_a: $i] :
~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1636]) ).
thf(2137,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)],[1093]) ).
thf(2138,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)],[1092]) ).
thf(2139,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(copy,[status(thm)],[1635]) ).
thf(2140,plain,
( ( ! [V_G: $i,V_c: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ V_c ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Com_OWT @ V_c )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ V_G ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ) )
= $true ),
inference(copy,[status(thm)],[1090]) ).
thf(2141,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] :
( ( ( 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 ) )
| ! [V_bot: $i,V_top: $i] :
~ ( 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)],[1634]) ).
thf(2142,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] :
( ( ( 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 ) )
| ! [V_bot: $i,V_top: $i] :
~ ( 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)],[1633]) ).
thf(2143,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) )
| ( V_com2 = V_com2_H ) ) )
= $true ),
inference(copy,[status(thm)],[1632]) ).
thf(2144,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i] :
( ! [V_com2_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) )
| ( V_com1 = V_com1_H ) ) )
= $true ),
inference(copy,[status(thm)],[1631]) ).
thf(2145,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i] :
( ! [V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) )
| ( V_fun = V_fun_H ) ) )
= $true ),
inference(copy,[status(thm)],[1630]) ).
thf(2146,plain,
( ( ! [V_a_H: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_a_H @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1629]) ).
thf(2147,plain,
( ( ! [V_xa: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_xa @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1628]) ).
thf(2148,plain,
( ( ! [V_a: $i,T_a: $i,V_a_H: $i] :
( ( ( c_Option_Ooption_OSome @ V_a @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(copy,[status(thm)],[1627]) ).
thf(2149,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)],[1081]) ).
thf(2150,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)],[1080]) ).
thf(2151,plain,
( ( ! [V_vname: $i,V_fun: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(copy,[status(thm)],[1626]) ).
thf(2152,plain,
( ( ! [V_m1: $i,V_m2: $i,V_m3: $i,T_a: $i,T_b: $i] :
( ( c_Map_Omap__add @ V_m1 @ ( c_Map_Omap__add @ V_m2 @ V_m3 @ T_a @ T_b ) @ T_a @ T_b )
= ( c_Map_Omap__add @ ( c_Map_Omap__add @ V_m1 @ V_m2 @ T_a @ T_b ) @ V_m3 @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1078]) ).
thf(2153,plain,
( ( ! [V_vname: $i,V_fun: $i,V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(copy,[status(thm)],[1625]) ).
thf(2154,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)],[1076]) ).
thf(2155,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(copy,[status(thm)],[1624]) ).
thf(2156,plain,
( ( ! [V_pname_H: $i,V_fun: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 ) ) )
= $true ),
inference(copy,[status(thm)],[1623]) ).
thf(2157,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1622]) ).
thf(2158,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1621]) ).
thf(2159,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1620]) ).
thf(2160,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1619]) ).
thf(2161,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1069]) ).
thf(2162,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1068]) ).
thf(2163,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(copy,[status(thm)],[1618]) ).
thf(2164,plain,
( ( ! [V_G: $i,V_P: $i,V_pn: $i,V_Q: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ ( c_Com_Ocom_OBODY @ V_pn ) @ V_Q @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ V_pn ) @ tc_Com_Ocom ) @ V_Q @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1066]) ).
thf(2165,plain,
( ( ! [V_G: $i,V_P: $i,V_pn: $i,V_Q: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ ( c_Com_Ocom_OBODY @ V_pn ) @ V_Q @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ ( c_Com_Ocom_OBODY @ V_pn ) @ V_Q @ T_a ) @ V_G @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ V_pn ) @ tc_Com_Ocom ) @ V_Q @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1065]) ).
thf(2166,plain,
( ( ! [T_b: $i,V_f: $i,V_A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_b )
| ! [V_a: $i,T_a: $i] :
( ( ( c_Finite__Set_Osetsum @ 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_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ V_f @ V_A @ T_a @ T_b ) @ ( hAPP @ V_f @ V_a ) @ T_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1617]) ).
thf(2167,plain,
( ( ! [T_b: $i,V_f: $i,V_A: $i] :
( ~ ( class_Ring__and__Field_Oring @ T_b )
| ! [V_a: $i,T_a: $i] :
( ( ( c_Finite__Set_Osetsum @ 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_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ V_f @ V_A @ T_a @ T_b ) @ ( hAPP @ V_f @ V_a ) @ T_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1616]) ).
thf(2168,plain,
( ( ! [V_P: $i] :
( ( ( hAPP @ c_Com_Obody @ V_P )
= ( c_Option_Ooption_OSome @ ( c_Com_Osko__Com__XWTs__elim__cases__7__1 @ V_P ) @ tc_Com_Ocom ) )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ V_P ) ) ) )
= $true ),
inference(copy,[status(thm)],[1062]) ).
thf(2169,plain,
( ( ! [V_f: $i,V_x: $i,T_b: $i,T_a: $i] :
( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ V_f @ V_x @ ( c_Option_Ooption_ONone @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ T_a @ T_b )
= ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ V_f @ T_a @ T_b ) @ ( 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)],[1061]) ).
thf(2170,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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 ) @ ( tc_fun @ T_b @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ V_f @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1060]) ).
thf(2171,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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 ) @ ( tc_fun @ T_b @ tc_bool ) )
!= ( 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 @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1615]) ).
thf(2172,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)],[1058]) ).
thf(2173,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ V_f @ V_x @ V_y @ T_b @ T_a ) @ V_A @ T_b @ T_a )
= ( c_Set_Oinsert @ V_y @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1057]) ).
thf(2174,plain,
( ( ! [T_b: $i,V_f: $i,V_A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_b )
| ! [V_a: $i,T_a: $i] :
( ( ( c_Finite__Set_Osetsum @ 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_Finite__Set_Osetsum @ V_f @ V_A @ T_a @ T_b ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1614]) ).
thf(2175,plain,
( ( ! [V_A: $i,V_x: $i,T_a: $i] :
( ( ( c_Finite__Set_Ocard @ ( 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 ) ) @ T_a )
= ( c_Finite__Set_Ocard @ V_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)],[1055]) ).
thf(2176,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_d: $i,V_R: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ ( c_Com_Ocom_OSemi @ V_c @ V_d ) @ V_R @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ! [V_Q: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_Q @ V_d @ V_R @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ V_c @ V_Q @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1613]) ).
thf(2177,plain,
( ( ! [V_G: $i,V_P: $i,T_a: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ c_Com_Ocom_OSKIP @ V_P @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1053]) ).
thf(2178,plain,
( ( ! [V_e1: $i,V_m: $i,V_u1: $i,T_b: $i,T_a: $i,V_e2: $i] :
( ( ( c_Map_Omap__add @ ( c_Fun_Ofun__upd @ V_e1 @ V_m @ ( c_Option_Ooption_OSome @ V_u1 @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) @ V_e2 @ T_a @ T_b )
= ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ V_e1 @ V_e2 @ T_a @ T_b ) @ V_m @ ( c_Option_Ooption_OSome @ V_u1 @ T_b ) @ T_a @ ( tc_Option_Ooption @ T_b ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_m ) @ ( c_Map_Odom @ V_e2 @ T_a @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1052]) ).
thf(2179,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)],[1051]) ).
thf(2180,plain,
( ( ! [V_f: $i,V_B: $i,T_a: $i,T_b: $i] :
( ( c_Set_Ovimage @ V_f @ V_B @ T_a @ T_b )
= ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_in @ T_b ) @ V_f @ T_b @ ( tc_fun @ ( tc_fun @ T_b @ tc_bool ) @ tc_bool ) @ T_a ) @ T_a @ ( tc_fun @ T_b @ tc_bool ) @ tc_bool ) @ V_B ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1050]) ).
thf(2181,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)],[1049]) ).
thf(2182,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)],[1048]) ).
thf(2183,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)],[1047]) ).
thf(2184,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)],[1046]) ).
thf(2185,plain,
( ( ! [V_f: $i,V_A: $i,V_a: $i,T_a: $i] :
( ( ( c_Finite__Set_Osetsum @ 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 @ tc_nat )
= ( c_Finite__Set_Osetsum @ V_f @ V_A @ T_a @ tc_nat ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1045]) ).
thf(2186,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)],[1044]) ).
thf(2187,plain,
( ( ! [V_c: $i,T_b: $i,T_a: $i,V_A: $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 ) )
| ! [V_x: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1612]) ).
thf(2188,plain,
( ( ( c_Hoare__Mirabelle_OMGT @ v_c )
= ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_fequal @ tc_Com_Ostate ) @ v_c @ ( c_Natural_Oevalc @ v_c ) @ tc_Com_Ostate ) )
= $true ),
inference(copy,[status(thm)],[1042]) ).
thf(2189,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)],[1041]) ).
thf(2190,plain,
( ( ! [V_f: $i,V_x: $i,T_a: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( c_Option_Ooption_ONone @ T_a ) )
| ! [T_b: $i,V_A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ V_f @ T_b @ T_a ) @ ( c_Set_Oinsert @ V_x @ V_A @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ V_f @ T_b @ T_a ) @ V_A @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1611]) ).
thf(2191,plain,
( ( ! [V_vname: $i,V_fun: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(copy,[status(thm)],[1610]) ).
thf(2192,plain,
( ( ! [V_G: $i,V_pn: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ V_pn ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ V_pn ) ) @ V_G @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ V_pn ) @ tc_Com_Ocom ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate ) ) )
= $true ),
inference(copy,[status(thm)],[1038]) ).
thf(2193,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(copy,[status(thm)],[1609]) ).
thf(2194,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)],[1036]) ).
thf(2195,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ! [V_a: $i] :
~ ( c_Fun_Oinj__on @ V_f @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1608]) ).
thf(2196,plain,
( ( ! [V_pname_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(copy,[status(thm)],[1607]) ).
thf(2197,plain,
( ( ! [V_b: $i,V_a: $i] :
( ( V_b = V_a )
| ! [T_a: $i] :
~ ( 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)],[1606]) ).
thf(2198,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( 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)],[1605]) ).
thf(2199,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i,V_A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Collect @ V_P @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1604]) ).
thf(2200,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
( ~ ( 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)],[1603]) ).
thf(2201,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
( ~ ( 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)],[1602]) ).
thf(2202,plain,
( ( ! [T_a: $i,V_z: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ! [V_y: $i] :
( ~ ( 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)],[1601]) ).
thf(2203,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)],[1027]) ).
thf(2204,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)],[1026]) ).
thf(2205,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)],[1025]) ).
thf(2206,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)],[1024]) ).
thf(2207,plain,
( ( ! [V_com1: $i,V_com2: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(copy,[status(thm)],[1600]) ).
thf(2208,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)],[1022]) ).
thf(2209,plain,
( ( ! [T_a: $i,V_y: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1599]) ).
thf(2210,plain,
( ( ! [T_a: $i,V_a_H: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1598]) ).
thf(2211,plain,
( ( ! [V_b: $i,V_c: $i,V_s0: $i,V_s2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) @ V_s0 ) @ V_s2 ) )
| ! [V_s1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) @ V_s1 ) @ V_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s0 ) @ V_s1 ) )
| ~ ( hBOOL @ ( hAPP @ V_b @ V_s0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1597]) ).
thf(2212,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)],[1018]) ).
thf(2213,plain,
( ( ! [T_a: $i,V_xa: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ! [V_y: $i] :
( ! [V_x: $i] :
( ( 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)],[1596]) ).
thf(2214,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ! [V_x_H: $i,V_y_H: $i] :
( ( ( 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)],[1595]) ).
thf(2215,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)],[1015]) ).
thf(2216,plain,
( ( ! [V_b: $i,V_c0: $i,V_c1: $i,V_s: $i,V_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c0 @ V_c1 ) ) @ V_s ) @ V_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c0 ) @ V_s ) @ V_s1 ) )
| ~ ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[1014]) ).
thf(2217,plain,
( ( ! [V_b: $i,V_s: $i,V_c1: $i] :
( ~ ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ! [V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s ) @ V_t ) )
| ! [V_c2: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) @ V_s ) @ V_t ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1594]) ).
thf(2218,plain,
( ( ! [V_c0: $i,V_c1: $i,V_s0: $i,V_s2: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) ) @ V_s0 ) @ V_s2 ) )
| ! [V_s1: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s1 ) @ V_s2 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c0 ) @ V_s0 ) @ V_s1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1593]) ).
thf(2219,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)],[1011]) ).
thf(2220,plain,
( ( ! [V_m1: $i,T_a: $i,T_b: $i,V_m2: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Map_Odom @ V_m1 @ T_a @ T_b ) @ ( c_Map_Odom @ V_m2 @ T_a @ T_b ) @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( ( c_Map_Omap__add @ V_m1 @ V_m2 @ T_a @ T_b )
= ( c_Map_Omap__add @ V_m2 @ V_m1 @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1592]) ).
thf(2221,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) )
| ! [T_b: $i] :
( ( c_Set_Oinsert @ V_x @ ( c_Map_Odom @ V_f @ T_b @ T_a ) @ T_b )
= ( c_Map_Odom @ V_f @ T_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1591]) ).
thf(2222,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1008]) ).
thf(2223,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1590]) ).
thf(2224,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1589]) ).
thf(2225,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)],[1005]) ).
thf(2226,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(copy,[status(thm)],[1588]) ).
thf(2227,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)],[1003]) ).
thf(2228,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)],[1587]) ).
thf(2229,plain,
( ( ! [V_m: $i,V_n: $i,T_b: $i,T_a: $i,V_k: $i,V_x: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
!= ( c_Option_Ooption_OSome @ V_x @ T_a ) )
| ( ( hAPP @ V_m @ V_k )
= ( c_Option_Ooption_OSome @ V_x @ T_a ) )
| ( ( hAPP @ V_n @ V_k )
= ( c_Option_Ooption_OSome @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1586]) ).
thf(2230,plain,
( ( ! [V_m: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( ( hAPP @ V_m @ V_k )
!= ( c_Option_Ooption_OSome @ V_x @ T_a ) )
| ! [V_n: $i] :
( ( ( hAPP @ V_n @ V_k )
!= ( c_Option_Ooption_ONone @ T_a ) )
| ! [T_b: $i] :
( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
= ( c_Option_Ooption_OSome @ V_x @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1585]) ).
thf(2231,plain,
( ( ! [V_m: $i,V_n: $i,T_b: $i,T_a: $i,V_k: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
!= ( c_Option_Ooption_ONone @ T_a ) )
| ( ( hAPP @ V_m @ V_k )
= ( c_Option_Ooption_ONone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1584]) ).
thf(2232,plain,
( ( ! [V_m: $i,V_n: $i,T_b: $i,T_a: $i,V_k: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
!= ( c_Option_Ooption_ONone @ T_a ) )
| ( ( hAPP @ V_n @ V_k )
= ( c_Option_Ooption_ONone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1583]) ).
thf(2233,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)],[1582]) ).
thf(2234,plain,
( ( ! [V_G: $i,V_t: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ V_t @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ! [V_ts: $i] :
~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ V_t @ V_ts @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1581]) ).
thf(2235,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(copy,[status(thm)],[1580]) ).
thf(2236,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)],[994]) ).
thf(2237,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)],[1579]) ).
thf(2238,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[992]) ).
thf(2239,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_C ) ) ) )
= $true ),
inference(copy,[status(thm)],[991]) ).
thf(2240,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(copy,[status(thm)],[1578]) ).
thf(2241,plain,
( ( ! [V_pname: $i,V_pname_H: $i] :
( ( ( c_Com_Ocom_OBODY @ V_pname )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) )
| ( V_pname = V_pname_H ) ) )
= $true ),
inference(copy,[status(thm)],[1577]) ).
thf(2242,plain,
( ( ! [V_fun: $i,V_com: $i,V_fun_H: $i] :
( ! [V_com_H: $i] :
( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) )
| ( V_fun = V_fun_H ) ) )
= $true ),
inference(copy,[status(thm)],[1576]) ).
thf(2243,plain,
( ( ! [V_fun: $i,V_com: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) )
| ( V_com = V_com_H ) ) )
= $true ),
inference(copy,[status(thm)],[1575]) ).
thf(2244,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)],[986]) ).
thf(2245,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(copy,[status(thm)],[1574]) ).
thf(2246,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( 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)],[984]) ).
thf(2247,plain,
( ( ! [V_fun_H: $i,V_com_H: $i,V_fun: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 ) ) )
= $true ),
inference(copy,[status(thm)],[1573]) ).
thf(2248,plain,
( ( ! [T_a: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ T_a )
| ! [V_A: $i] : ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1572]) ).
thf(2249,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ! [V_P: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Collect @ V_P @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1571]) ).
thf(2250,plain,
( ( ! [V_m: $i,V_k: $i,T_a: $i] :
( ( ( hAPP @ V_m @ V_k )
!= ( c_Option_Ooption_ONone @ T_a ) )
| ! [V_n: $i] :
( ( ( hAPP @ V_n @ V_k )
!= ( c_Option_Ooption_ONone @ T_a ) )
| ! [T_b: $i] :
( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
= ( c_Option_Ooption_ONone @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1570]) ).
thf(2251,plain,
( ( ! [V_n: $i,V_k: $i,V_xx: $i,T_a: $i] :
( ( ( hAPP @ V_n @ V_k )
!= ( c_Option_Ooption_OSome @ V_xx @ T_a ) )
| ! [V_m: $i,T_b: $i] :
( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
= ( c_Option_Ooption_OSome @ V_xx @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1569]) ).
thf(2252,plain,
( ( ! [V_n: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( ( hAPP @ V_n @ V_k )
!= ( c_Option_Ooption_OSome @ V_x @ T_a ) )
| ! [V_m: $i,T_b: $i] :
( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
= ( c_Option_Ooption_OSome @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1568]) ).
thf(2253,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)],[977]) ).
thf(2254,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i,V_vname: $i,V_fun: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OAss @ V_vname @ V_fun ) ) )
= $true ),
inference(copy,[status(thm)],[1567]) ).
thf(2255,plain,
( ( ! [V_pname_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(copy,[status(thm)],[1566]) ).
thf(2256,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)],[974]) ).
thf(2257,plain,
( ( ! [V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ! [V_A: $i,T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1565]) ).
thf(2258,plain,
( ( ! [V_A: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ! [V_B: $i,T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1564]) ).
thf(2259,plain,
( ( ! [V_f: $i,V_g: $i,T_a: $i,T_b: $i] : ( c_Map_Omap__le @ V_f @ ( c_Map_Omap__add @ V_g @ V_f @ T_a @ T_b ) @ T_a @ T_b ) )
= $true ),
inference(copy,[status(thm)],[971]) ).
thf(2260,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)],[970]) ).
thf(2261,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Ovimage @ V_f @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_a @ T_b )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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)],[969]) ).
thf(2262,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ V_s ) @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[968]) ).
thf(2263,plain,
( ( ! [V_F: $i,V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_G @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[967]) ).
thf(2264,plain,
( ( ! [V_F: $i,V_G: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_F @ V_G @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_F @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[966]) ).
thf(2265,plain,
( ( ! [V_f: $i,V_g: $i,T_a: $i,T_b: $i,V_h: $i] :
( ( c_Map_Omap__le @ ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b ) @ V_h @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_f @ ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b ) @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_g @ V_h @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_f @ V_h @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[965]) ).
thf(2266,plain,
( ( ! [V_P: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ V_A @ V_P @ T_a ) ) )
| ! [V_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1563]) ).
thf(2267,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ 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)],[963]) ).
thf(2268,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ 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)],[962]) ).
thf(2269,plain,
( ( ! [V_Q: $i,V_xb: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_xb ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xb ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) @ V_A ) )
| ! [V_P: $i] :
~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1562]) ).
thf(2270,plain,
( ( ! [V_P: $i,V_xb: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xb ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xb ) @ V_A ) )
| ! [V_Q: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1561]) ).
thf(2271,plain,
( ( ! [V_Q: $i,V_xa: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_xa ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) )
| ! [V_P: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) @ V_A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1560]) ).
thf(2272,plain,
( ( ! [V_P: $i,V_xa: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ V_A ) )
| ! [V_Q: $i] :
~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) @ V_A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1559]) ).
thf(2273,plain,
( ( ! [T_a: $i,V_i: $i,V_less__eq: $i,V_less: $i,V_l: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatLeastLessThan @ V_less__eq @ V_less @ V_l @ V_u @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_i ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_l ) @ V_i ) ) ) )
= $true ),
inference(copy,[status(thm)],[957]) ).
thf(2274,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)],[956]) ).
thf(2275,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)],[955]) ).
thf(2276,plain,
( ( ! [T_a: $i,V_i: $i,V_less__eq: $i,V_l: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatLeastAtMost @ V_less__eq @ V_l @ V_u @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_i ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_l ) @ V_i ) ) ) )
= $true ),
inference(copy,[status(thm)],[954]) ).
thf(2277,plain,
( ( ! [T_a: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ V_A @ V_P @ T_a ) ) @ V_A ) )
| ! [V_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1558]) ).
thf(2278,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)],[952]) ).
thf(2279,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $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)],[1557]) ).
thf(2280,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)],[950]) ).
thf(2281,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)],[949]) ).
thf(2282,plain,
( ( ! [T_a: $i,V_i: $i,V_less: $i,V_l: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ V_less @ V_l @ V_u @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_i ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_l ) @ V_i ) ) ) )
= $true ),
inference(copy,[status(thm)],[948]) ).
thf(2283,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ! [V_b: $i] :
( ( 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)],[1556]) ).
thf(2284,plain,
( ( ! [T_a: $i,V_i: $i,V_less__eq: $i,V_less: $i,V_l: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ V_less__eq @ V_less @ V_l @ V_u @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_i ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_l ) @ V_i ) ) ) )
= $true ),
inference(copy,[status(thm)],[946]) ).
thf(2285,plain,
( ( ! [T_a: $i,V_c: $i,V_B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ! [V_A: $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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1555]) ).
thf(2286,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) )
| ! [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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1554]) ).
thf(2287,plain,
( ( ! [T_a: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ V_A @ V_P @ T_a ) ) @ V_A ) )
| ! [V_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1553]) ).
thf(2288,plain,
( ( ! [V_P: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ V_A @ V_P @ T_a ) ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1552]) ).
thf(2289,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 ) ) )
| ! [V_x: $i] :
( ( ( 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)],[1551]) ).
thf(2290,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)],[940]) ).
thf(2291,plain,
( ( ! [V_vname: $i,V_fun: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(copy,[status(thm)],[1550]) ).
thf(2292,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)],[938]) ).
thf(2293,plain,
( ( ! [V_fun_H: $i,V_com_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(copy,[status(thm)],[1549]) ).
thf(2294,plain,
( ( ! [V_f: $i,V_g: $i,T_a: $i,T_b: $i] :
( ( ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b )
= ( c_Map_Omap__add @ V_g @ V_f @ T_a @ T_b ) )
| ~ ( c_Map_Omap__le @ V_f @ ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[936]) ).
thf(2295,plain,
( ( ! [V_f: $i,V_g: $i,T_a: $i,T_b: $i] :
( ( ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b )
!= ( c_Map_Omap__add @ V_g @ V_f @ T_a @ T_b ) )
| ( c_Map_Omap__le @ V_f @ ( c_Map_Omap__add @ V_f @ V_g @ T_a @ T_b ) @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1548]) ).
thf(2296,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)],[934]) ).
thf(2297,plain,
( ( ! [V_C: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_C @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[933]) ).
thf(2298,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[932]) ).
thf(2299,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_x: $i] :
( ~ ( 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)],[1547]) ).
thf(2300,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)],[930]) ).
thf(2301,plain,
( ( ! [V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(copy,[status(thm)],[1546]) ).
thf(2302,plain,
( ( ! [T_a: $i,V_x: $i,V_B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1545]) ).
thf(2303,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[927]) ).
thf(2304,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)],[926]) ).
thf(2305,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1544]) ).
thf(2306,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1543]) ).
thf(2307,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1542]) ).
thf(2308,plain,
( ( ! [V_P: $i] :
( ! [T_a: $i] :
( ( c_Collect @ V_P @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ! [V_x: $i] :
~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1541]) ).
thf(2309,plain,
( ( ! [V_s: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ V_s ) @ V_s ) ) )
= $true ),
inference(copy,[status(thm)],[921]) ).
thf(2310,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i,V_vname: $i,V_fun: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OAss @ V_vname @ V_fun ) ) )
= $true ),
inference(copy,[status(thm)],[1540]) ).
thf(2311,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( 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)],[1539]) ).
thf(2312,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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)],[1538]) ).
thf(2313,plain,
( ( ! [V_u: $i,V_t: $i] :
( ( V_u = V_t )
| ! [V_c: $i,V_s: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c ) @ V_s ) @ V_t ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1537]) ).
thf(2314,plain,
( ( ! [V_f: $i,V_g: $i] :
( ( V_f = V_g )
| ! [T_a: $i,T_b: $i] :
( ~ ( c_Map_Omap__le @ V_g @ V_f @ T_a @ T_b )
| ~ ( c_Map_Omap__le @ V_f @ V_g @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1536]) ).
thf(2315,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( 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)],[1535]) ).
thf(2316,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( 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)],[1534]) ).
thf(2317,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( 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)],[1533]) ).
thf(2318,plain,
( ( ! [V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(copy,[status(thm)],[1532]) ).
thf(2319,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1531]) ).
thf(2320,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1530]) ).
thf(2321,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)],[1529]) ).
thf(2322,plain,
( ( ! [V_m_092_060_094isub_0621: $i,V_m_092_060_094isub_0622: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_m_092_060_094isub_0621 @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ V_m_092_060_094isub_0621 @ V_m_092_060_094isub_0622 @ T_a @ T_b ) )
!= ( hAPP @ V_m_092_060_094isub_0622 @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ V_m_092_060_094isub_0621 @ V_m_092_060_094isub_0622 @ T_a @ T_b ) ) )
| ( c_Map_Omap__le @ V_m_092_060_094isub_0621 @ V_m_092_060_094isub_0622 @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1528]) ).
thf(2323,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)],[1527]) ).
thf(2324,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)],[1526]) ).
thf(2325,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)],[1525]) ).
thf(2326,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)],[1524]) ).
thf(2327,plain,
( ( ! [V_c2: $i,V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c2 ) @ V_s ) @ V_t ) )
| ! [V_b: $i] :
( ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ! [V_c1: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) @ V_s ) @ V_t ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1523]) ).
thf(2328,plain,
( ( ! [V_b: $i,V_c0: $i,V_c1: $i,V_s: $i,V_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c0 @ V_c1 ) ) @ V_s ) @ V_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s ) @ V_s1 ) )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[902]) ).
thf(2329,plain,
( ( ! [V_vname_H: $i,V_fun_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OAss @ V_vname_H @ V_fun_H ) ) )
= $true ),
inference(copy,[status(thm)],[1522]) ).
thf(2330,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] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) )
= ( hAPP @ ( hAPP @ V_sup @ V_a ) @ ( hAPP @ V_Sup @ V_A ) ) )
| ! [V_bot: $i,V_top: $i] :
~ ( 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)],[1521]) ).
thf(2331,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] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) )
= ( hAPP @ ( hAPP @ V_inf @ V_a ) @ ( hAPP @ V_Inf @ V_A ) ) )
| ! [V_bot: $i,V_top: $i] :
~ ( 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)],[1520]) ).
thf(2332,plain,
( ( ! [V_fun_H: $i,V_com_H: $i,V_vname: $i,V_fun: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OAss @ V_vname @ V_fun ) ) )
= $true ),
inference(copy,[status(thm)],[1519]) ).
thf(2333,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_P: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ V_A @ V_B @ V_P @ T_b @ T_a ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ! [V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ ( hAPP @ V_B @ V_x ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1518]) ).
thf(2334,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)],[1517]) ).
thf(2335,plain,
( ( ! [V_G: $i,V_ts: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ! [V_G_H: $i] :
( ~ ( 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)],[1516]) ).
thf(2336,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_C ) ) ) )
= $true ),
inference(copy,[status(thm)],[894]) ).
thf(2337,plain,
( ( ! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oinsert @ V_a @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[893]) ).
thf(2338,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)],[892]) ).
thf(2339,plain,
( ( ! [V_m: $i,V_n: $i,T_b: $i,T_a: $i,V_k: $i,V_x: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_m @ V_n @ T_b @ T_a ) @ V_k )
!= ( c_Option_Ooption_OSome @ V_x @ T_a ) )
| ( ( hAPP @ V_n @ V_k )
= ( c_Option_Ooption_ONone @ T_a ) )
| ( ( hAPP @ V_n @ V_k )
= ( c_Option_Ooption_OSome @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1515]) ).
thf(2340,plain,
( ( ! [V_f: $i,V_a: $i,V_b: $i] :
( ( ( hAPP @ V_f @ V_a )
= V_b )
| ! [T_a: $i,T_b: $i] :
~ ( 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)],[1514]) ).
thf(2341,plain,
( ( ! [V_vname: $i,V_fun: $i,V_vname_H: $i,V_fun_H: $i] :
( ( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OAss @ V_vname_H @ V_fun_H ) )
| ( V_fun = V_fun_H ) ) )
= $true ),
inference(copy,[status(thm)],[1513]) ).
thf(2342,plain,
( ( ! [V_vname: $i,V_fun: $i,V_vname_H: $i] :
( ! [V_fun_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname @ V_fun )
!= ( c_Com_Ocom_OAss @ V_vname_H @ V_fun_H ) )
| ( V_vname = V_vname_H ) ) )
= $true ),
inference(copy,[status(thm)],[1512]) ).
thf(2343,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)],[887]) ).
thf(2344,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(copy,[status(thm)],[1511]) ).
thf(2345,plain,
( ( ! [T_a: $i,V_P: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Collect @ V_P @ T_a ) )
| ! [V_x: $i] :
~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1510]) ).
thf(2346,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)],[884]) ).
thf(2347,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1509]) ).
thf(2348,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1508]) ).
thf(2349,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[881]) ).
thf(2350,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) )
| ( V_com = V_com_H ) ) )
= $true ),
inference(copy,[status(thm)],[1507]) ).
thf(2351,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_loc_H: $i,V_fun_H: $i] :
( ! [V_com_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) )
| ( V_fun = V_fun_H ) ) )
= $true ),
inference(copy,[status(thm)],[1506]) ).
thf(2352,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_loc_H: $i] :
( ! [V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) )
| ( V_loc = V_loc_H ) ) )
= $true ),
inference(copy,[status(thm)],[1505]) ).
thf(2353,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 )
| ! [V_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 ) ) )
= $true ),
inference(copy,[status(thm)],[1504]) ).
thf(2354,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)],[876]) ).
thf(2355,plain,
( ( ! [V_fun_H: $i,V_com_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(copy,[status(thm)],[1503]) ).
thf(2356,plain,
( ( ! [V_Sup: $i,T_a: $i,V_bot: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i] :
( ( ( hAPP @ V_Sup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_bot )
| ! [V_sup: $i,V_top: $i] :
~ ( 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)],[1502]) ).
thf(2357,plain,
( ( ! [V_Inf: $i,T_a: $i,V_top: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_inf: $i] :
( ( ( hAPP @ V_Inf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_top )
| ! [V_sup: $i,V_bot: $i] :
~ ( 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)],[1501]) ).
thf(2358,plain,
( ( ! [V_b: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ! [V_t: $i] :
( ( V_t = V_s )
| ! [V_c: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) @ V_s ) @ V_t ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1500]) ).
thf(2359,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)],[871]) ).
thf(2360,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olower__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1499]) ).
thf(2361,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[869]) ).
thf(2362,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)],[1498]) ).
thf(2363,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)],[867]) ).
thf(2364,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[866]) ).
thf(2365,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] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= V_a )
| ! [V_bot: $i,V_top: $i] :
~ ( 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)],[1497]) ).
thf(2366,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] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= V_a )
| ! [V_bot: $i,V_top: $i] :
~ ( 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)],[1496]) ).
thf(2367,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)],[863]) ).
thf(2368,plain,
( ( ! [V_fun: $i,V_com: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(copy,[status(thm)],[1495]) ).
thf(2369,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ ( c_Collect @ V_P @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[861]) ).
thf(2370,plain,
( ( ! [V_pname_H: $i] :
( ( c_Com_Ocom_OBODY @ V_pname_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(copy,[status(thm)],[1494]) ).
thf(2371,plain,
( ( ! [V_A: $i,V_f: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_A @ ( hAPP @ V_f @ V_x ) ) )
| ! [T_a: $i,T_b: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ V_f @ V_A @ T_a @ T_b ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1493]) ).
thf(2372,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)],[858]) ).
thf(2373,plain,
( ( ! [V_G: $i,V_ts: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ! [V_t: $i] :
~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ V_t @ V_ts @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1492]) ).
thf(2374,plain,
( ( ! [V_G: $i,V_t: $i,V_ts: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ V_t @ V_ts @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ V_t @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[856]) ).
thf(2375,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[855]) ).
thf(2376,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ! [V_x_H: $i,V_y_H: $i] :
( ( ( 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)],[1491]) ).
thf(2377,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ! [V_x_H: $i,V_y_H: $i] :
( ( ( 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)],[1490]) ).
thf(2378,plain,
( ( ! [V_vname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OAss @ V_vname_H @ V_fun_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(copy,[status(thm)],[1489]) ).
thf(2379,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)],[851]) ).
thf(2380,plain,
( ( ! [V_A: $i,T_b: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_b )
| ! [V_f: $i,T_a: $i] :
( ~ ( 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)],[1488]) ).
thf(2381,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)],[849]) ).
thf(2382,plain,
( ( ! [V_c2: $i,V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c2 ) @ V_s ) @ V_t ) )
| ! [V_c1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ V_c1 ) @ V_s ) @ V_t ) )
| ! [V_b: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) @ V_s ) @ V_t ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1487]) ).
thf(2383,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)],[847]) ).
thf(2384,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(copy,[status(thm)],[1486]) ).
thf(2385,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_a: $i,V_b: $i] :
( ~ ( 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)],[1485]) ).
thf(2386,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ~ ( 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)],[1484]) ).
thf(2387,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ~ ( 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)],[1483]) ).
thf(2388,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_b: $i,V_a: $i] :
( ~ ( 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)],[1482]) ).
thf(2389,plain,
( ( ! [V_P: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ V_A @ V_P @ T_a ) ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1481]) ).
thf(2390,plain,
( ( ! [V_less: $i,V_l: $i,V_i: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_l ) @ V_i ) )
| ! [V_less__eq: $i,V_u: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ V_less__eq @ V_less @ V_l @ V_u @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1480]) ).
thf(2391,plain,
( ( ! [V_less__eq: $i,V_i: $i,V_u: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_i ) @ V_u ) )
| ! [V_less: $i,V_l: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ V_less__eq @ V_less @ V_l @ V_u @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1479]) ).
thf(2392,plain,
( ( ! [T_a: $i,V_c: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ! [V_A: $i] :
( ~ ( 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)],[1478]) ).
thf(2393,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)],[837]) ).
thf(2394,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)],[836]) ).
thf(2395,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)],[835]) ).
thf(2396,plain,
( ( ! [V_Q: $i,V_xc: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_xc ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xc ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) )
| ! [V_P: $i] :
~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1477]) ).
thf(2397,plain,
( ( ! [V_P: $i,V_xc: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xc ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xc ) @ V_A ) )
| ! [V_Q: $i] :
~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1476]) ).
thf(2398,plain,
( ( ! [V_Q: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) @ V_A ) )
| ! [V_P: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) @ V_A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1475]) ).
thf(2399,plain,
( ( ! [V_P: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ! [V_Q: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_Q @ T_a ) ) @ V_A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ V_A @ V_P @ T_a ) ) @ V_A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1474]) ).
thf(2400,plain,
( ( ! [V_Q: $i,V_xf: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_xf ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xf ) @ V_A ) )
| ! [V_P: $i] :
( ~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ V_A @ V_P @ V_Q @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ V_A @ V_P @ V_Q @ T_a ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1473]) ).
thf(2401,plain,
( ( ! [V_P: $i,V_xg: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xg ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xg ) @ V_A ) )
| ! [V_Q: $i] :
( ~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ V_A @ V_P @ V_Q @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ V_A @ V_P @ V_Q @ T_a ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1472]) ).
thf(2402,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ! [V_P: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ V_A @ V_P @ T_a ) ) @ V_A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1471]) ).
thf(2403,plain,
( ( ! [V_P: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ V_A @ V_P @ T_a ) ) )
| ! [V_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1470]) ).
thf(2404,plain,
( ( ! [V_less: $i,V_l: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_l ) @ V_i ) )
| ! [T_a: $i,V_u: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ V_less @ V_l @ V_u @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1469]) ).
thf(2405,plain,
( ( ! [V_less: $i,V_i: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_i ) @ V_u ) )
| ! [T_a: $i,V_l: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ V_less @ V_l @ V_u @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1468]) ).
thf(2406,plain,
( ( ! [T_a: $i,V_c: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_B ) )
| ! [V_A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1467]) ).
thf(2407,plain,
( ( ! [T_a: $i,V_c: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ V_A ) )
| ! [V_B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_c ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1466]) ).
thf(2408,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( hAPP @ V_f @ V_y ) )
| ! [V_A: $i] :
( ~ ( 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 )
| ! [T_b: $i] :
~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1465]) ).
thf(2409,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( hAPP @ V_f @ V_y ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_y ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ! [T_b: $i] :
~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ( V_x = V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[1464]) ).
thf(2410,plain,
( ( ! [V_f: $i,V_x: $i,V_xa: $i,T_a: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( hAPP @ V_f @ V_xa ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ! [T_b: $i] :
~ ( c_Fun_Oinj__on @ V_f @ V_A @ T_a @ T_b )
| ( V_x = V_xa ) ) ) )
= $true ),
inference(copy,[status(thm)],[1463]) ).
thf(2411,plain,
( ( ! [V_f: $i,V_x: $i,V_y: $i,V_A: $i] :
( ( ( hAPP @ V_f @ V_x )
!= ( hAPP @ V_f @ V_y ) )
| ! [T_a: $i] :
( ! [T_b: $i] :
~ ( 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)],[1462]) ).
thf(2412,plain,
( ( ! [V_P: $i,V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $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)],[1461]) ).
thf(2413,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)],[1460]) ).
thf(2414,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)],[816]) ).
thf(2415,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Collect @ V_P @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1459]) ).
thf(2416,plain,
( ( ! [T_a: $i,V_i: $i,V_less__eq: $i,V_k: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatMost @ V_less__eq @ V_k @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_i ) @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[814]) ).
thf(2417,plain,
( ( ! [V_less__eq: $i,V_i: $i,V_k: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_i ) @ V_k ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatMost @ V_less__eq @ V_k @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1458]) ).
thf(2418,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)],[812]) ).
thf(2419,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)],[811]) ).
thf(2420,plain,
( ( ! [V_Q: $i,V_xd: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_xd ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xd ) @ V_A ) )
| ! [V_P: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ V_A @ V_P @ V_Q @ T_a ) ) @ V_A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1457]) ).
thf(2421,plain,
( ( ! [V_P: $i,V_xe: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_xe ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xe ) @ V_A ) )
| ! [V_Q: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ V_A @ V_P @ V_Q @ T_a ) ) @ V_A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1456]) ).
thf(2422,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ! [V_P: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ V_A @ V_P @ T_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1455]) ).
thf(2423,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 ) )
| ( V_A = V_B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1454]) ).
thf(2424,plain,
( ( ! [T_a: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ V_A @ V_P @ T_a ) ) @ V_A ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1453]) ).
thf(2425,plain,
( ( ! [T_a: $i,V_b: $i,V_A: $i,V_B: $i,T_b: $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 ) ) ) )
| ! [V_x: $i] :
( ~ ( 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)],[1452]) ).
thf(2426,plain,
( ( ! [T_b: $i,V_b: $i,V_A: $i,V_B: $i,T_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 ) ) ) )
| ! [V_a: $i] :
( ~ ( 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)],[1451]) ).
thf(2427,plain,
( ( ! [T_a: $i,V_i: $i,V_less: $i,V_k: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThan @ V_less @ V_k @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_k ) @ V_i ) ) ) )
= $true ),
inference(copy,[status(thm)],[803]) ).
thf(2428,plain,
( ( ! [V_less: $i,V_k: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_k ) @ V_i ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OgreaterThan @ V_less @ V_k @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1450]) ).
thf(2429,plain,
( ( ! [V_P: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ V_A @ V_B @ V_P @ T_b @ T_a ) ) )
| ! [V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ ( hAPP @ V_B @ V_x ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1449]) ).
thf(2430,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)],[800]) ).
thf(2431,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)],[799]) ).
thf(2432,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)],[798]) ).
thf(2433,plain,
( ( ! [T_b: $i,V_f: $i,V_a: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ V_B ) )
| ! [T_a: $i] :
~ ( 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)],[1448]) ).
thf(2434,plain,
( ( ! [T_b: $i,V_f: $i,V_a: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ ( hAPP @ V_f @ V_a ) ) @ V_A ) )
| ! [T_a: $i] :
~ ( 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)],[1447]) ).
thf(2435,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] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ ( hAPP @ V_Inf @ V_A ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ! [V_bot: $i,V_top: $i] :
~ ( 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)],[1446]) ).
thf(2436,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] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_x ) @ ( hAPP @ V_Sup @ V_A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) )
| ! [V_bot: $i,V_top: $i] :
~ ( 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)],[1445]) ).
thf(2437,plain,
( ( ! [V_less__eq: $i,V_i: $i,V_u: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_i ) @ V_u ) )
| ! [T_a: $i,V_l: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatLeastAtMost @ V_less__eq @ V_l @ V_u @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1444]) ).
thf(2438,plain,
( ( ! [V_less__eq: $i,V_l: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_l ) @ V_i ) )
| ! [T_a: $i,V_u: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatLeastAtMost @ V_less__eq @ V_l @ V_u @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1443]) ).
thf(2439,plain,
( ( ! [V_P: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ V_A @ V_B @ V_P @ T_a ) ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1442]) ).
thf(2440,plain,
( ( ! [V_P: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ V_A @ V_B @ V_P @ T_a ) ) )
| ! [V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_xa ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_xa ) @ V_A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1441]) ).
thf(2441,plain,
( ( ! [T_a: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ V_A @ V_P @ T_a ) ) @ V_A ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1440]) ).
thf(2442,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)],[788]) ).
thf(2443,plain,
( ( ! [T_a: $i,V_i: $i,V_less: $i,V_k: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OlessThan @ V_less @ V_k @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_i ) @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[787]) ).
thf(2444,plain,
( ( ! [V_less: $i,V_i: $i,V_k: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_i ) @ V_k ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OlessThan @ V_less @ V_k @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1439]) ).
thf(2445,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,T_c: $i,V_b: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_bool ) ) ) @ V_b ) @ V_c ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1438]) ).
thf(2446,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ V_b ) )
| ! [V_x: $i] :
( ~ ( 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)],[1437]) ).
thf(2447,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,T_c: $i,V_b: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ ( tc_fun @ T_c @ tc_bool ) ) ) @ V_b ) @ V_c ) )
| ! [V_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ V_B @ V_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ V_A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1436]) ).
thf(2448,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ V_b ) )
| ! [V_a: $i] :
( ~ ( 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)],[1435]) ).
thf(2449,plain,
( ( ! [V_less: $i,V_i: $i,V_u: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less @ V_i ) @ V_u ) )
| ! [V_less__eq: $i,V_l: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatLeastLessThan @ V_less__eq @ V_less @ V_l @ V_u @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1434]) ).
thf(2450,plain,
( ( ! [V_less__eq: $i,V_l: $i,V_i: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_l ) @ V_i ) )
| ! [V_less: $i,V_u: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_i ) @ ( c_SetInterval_Oord_OatLeastLessThan @ V_less__eq @ V_less @ V_l @ V_u @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1433]) ).
thf(2451,plain,
( ( ! [T_a: $i,V_A: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ V_A @ V_P @ T_a ) ) @ V_A ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1432]) ).
thf(2452,plain,
( ( ! [V_P: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ V_A @ V_P @ T_a ) ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1431]) ).
thf(2453,plain,
( ( ! [T_aa: $i,V_x: $i,V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_aa ) @ V_x ) @ V_A ) )
| ! [T_a: $i,V_f: $i] : ( 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)],[1430]) ).
thf(2454,plain,
( ( ! [T_b: $i,V_x: $i,V_A: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_x ) @ V_A ) )
| ! [T_a: $i,V_f: $i] : ( 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)],[1429]) ).
thf(2455,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)],[775]) ).
thf(2456,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)],[774]) ).
thf(2457,plain,
( ( ! [V_m: $i,V_a: $i,T_a: $i,T_b: $i] :
( ( ( hAPP @ V_m @ V_a )
= ( c_Option_Ooption_OSome @ ( c_Map_Osko__Map__XdomD__1__1 @ V_a @ V_m @ T_a @ T_b ) @ T_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Map_Odom @ V_m @ T_a @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[773]) ).
thf(2458,plain,
( ( ! [V_m_092_060_094isub_0621: $i,V_m_092_060_094isub_0622: $i,T_a: $i,T_b: $i] :
( ( c_Map_Omap__le @ V_m_092_060_094isub_0621 @ V_m_092_060_094isub_0622 @ T_a @ T_b )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ V_m_092_060_094isub_0621 @ V_m_092_060_094isub_0622 @ T_a @ T_b ) ) @ ( c_Map_Odom @ V_m_092_060_094isub_0621 @ T_a @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[772]) ).
thf(2459,plain,
( ( ! [V_pn: $i] :
( ( ( hAPP @ c_Com_Obody @ V_pn )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) )
| ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ V_pn ) ) ) )
= $true ),
inference(copy,[status(thm)],[1428]) ).
thf(2460,plain,
( ( ! [V_pn: $i,V_s0: $i,V_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ V_pn ) ) @ V_s0 ) @ V_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ V_pn ) @ tc_Com_Ocom ) ) @ V_s0 ) @ V_s1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[770]) ).
thf(2461,plain,
( ( ! [V_P: $i,V_s: $i,V_s1: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ V_P ) @ tc_Com_Ocom ) ) @ V_s ) @ V_s1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ V_P ) ) @ V_s ) @ V_s1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[769]) ).
thf(2462,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_Option_Othe @ ( c_Option_Ooption_OSome @ V_x @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[768]) ).
thf(2463,plain,
( ( ! [V_c1: $i] :
( ( c_Com_OWT @ V_c1 )
| ! [V_b: $i,V_c2: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1427]) ).
thf(2464,plain,
( ( ! [V_c2: $i] :
( ( c_Com_OWT @ V_c2 )
| ! [V_b: $i,V_c1: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1426]) ).
thf(2465,plain,
( ( ! [V_c0: $i,V_c1: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) )
| ~ ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ V_c0 ) ) )
= $true ),
inference(copy,[status(thm)],[765]) ).
thf(2466,plain,
( ( ! [V_c1: $i] :
( ( c_Com_OWT @ V_c1 )
| ! [V_c2: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1425]) ).
thf(2467,plain,
( ( ! [V_c2: $i] :
( ( c_Com_OWT @ V_c2 )
| ! [V_c1: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1424]) ).
thf(2468,plain,
( ( ! [V_b: $i,V_c0: $i,V_c1: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ V_b @ V_c0 @ V_c1 ) )
| ~ ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ V_c0 ) ) )
= $true ),
inference(copy,[status(thm)],[762]) ).
thf(2469,plain,
( ( c_Com_OWT @ c_Com_Ocom_OSKIP )
= $true ),
inference(copy,[status(thm)],[761]) ).
thf(2470,plain,
( ( ! [V_X: $i,V_a: $i] : ( c_Com_OWT @ ( c_Com_Ocom_OAss @ V_X @ V_a ) ) )
= $true ),
inference(copy,[status(thm)],[760]) ).
thf(2471,plain,
( ( ! [V_b: $i,V_c: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) )
| ~ ( c_Com_OWT @ V_c ) ) )
= $true ),
inference(copy,[status(thm)],[759]) ).
thf(2472,plain,
( ( ! [V_c: $i] :
( ( c_Com_OWT @ V_c )
| ! [V_b: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) ) )
= $true ),
inference(copy,[status(thm)],[1423]) ).
thf(2473,plain,
( ( ! [V_Y: $i,V_a: $i,V_c: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ V_Y @ V_a @ V_c ) )
| ~ ( c_Com_OWT @ V_c ) ) )
= $true ),
inference(copy,[status(thm)],[757]) ).
thf(2474,plain,
( ( ! [V_c: $i] :
( ( c_Com_OWT @ V_c )
| ! [V_Y: $i,V_a: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ V_Y @ V_a @ V_c ) ) ) )
= $true ),
inference(copy,[status(thm)],[1422]) ).
thf(2475,plain,
( ( ! [V_G: $i,V_c: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ V_c ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Com_OWT @ V_c )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ tc_Com_Opname ) @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ V_G ) ) @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) ) )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ) )
= $true ),
inference(copy,[status(thm)],[755]) ).
thf(2476,plain,
( ( ! [V_t: $i] :
( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ V_t )
!= V_t )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ),
inference(copy,[status(thm)],[1421]) ).
thf(2477,plain,
( ( ! [V_l1: $i,V_l2: $i,T_a: $i,T_b: $i,V_m: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_l1 @ V_l2 @ T_a @ T_b ) @ V_m )
= ( hAPP @ V_l1 @ V_m ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_m ) @ ( c_Map_Odom @ V_l2 @ T_a @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[753]) ).
thf(2478,plain,
( ( ! [V_l1: $i,V_l2: $i,T_a: $i,T_b: $i,V_m: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_l1 @ V_l2 @ T_a @ T_b ) @ V_m )
= ( hAPP @ V_l2 @ V_m ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_m ) @ ( c_Map_Odom @ V_l1 @ T_a @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[752]) ).
thf(2479,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,T_b: $i] :
( ( ( hAPP @ V_m @ V_a )
= ( c_Option_Ooption_ONone @ T_b ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Map_Odom @ V_m @ T_a @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1420]) ).
thf(2480,plain,
( ( ! [V_m: $i,V_a: $i,T_b: $i] :
( ( ( hAPP @ V_m @ V_a )
!= ( c_Option_Ooption_ONone @ T_b ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_a ) @ ( c_Map_Odom @ V_m @ T_a @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1419]) ).
thf(2481,plain,
( ( ! [V_m: $i,V_a: $i,V_b: $i,T_a: $i] :
( ( ( hAPP @ V_m @ V_a )
!= ( c_Option_Ooption_OSome @ V_b @ T_a ) )
| ! [T_b: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_b ) @ V_a ) @ ( c_Map_Odom @ V_m @ T_b @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1418]) ).
thf(2482,plain,
( ( ! [V_m_092_060_094isub_0621: $i,V_x: $i,V_m_092_060_094isub_0622: $i] :
( ( ( hAPP @ V_m_092_060_094isub_0621 @ V_x )
= ( hAPP @ V_m_092_060_094isub_0622 @ V_x ) )
| ! [T_a: $i,T_b: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ ( c_Map_Odom @ V_m_092_060_094isub_0621 @ T_a @ T_b ) ) )
| ~ ( c_Map_Omap__le @ V_m_092_060_094isub_0621 @ V_m_092_060_094isub_0622 @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1417]) ).
thf(2483,plain,
( ( ! [V_l1: $i,V_l2: $i,T_a: $i,T_b: $i,V_m: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ V_l1 @ V_l2 @ T_a @ T_b ) @ V_m )
= ( hAPP @ V_l2 @ V_m ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_m ) @ ( c_Map_Odom @ V_l2 @ T_a @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[747]) ).
thf(2484,plain,
( ( c_Finite__Set_Ofinite @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) @ tc_Com_Opname )
= $true ),
inference(copy,[status(thm)],[746]) ).
thf(2485,plain,
( ( ! [V_pn: $i,V_b: $i] :
( ( ( hAPP @ c_Com_Obody @ V_pn )
!= ( c_Option_Ooption_OSome @ V_b @ tc_Com_Ocom ) )
| ~ c_Com_OWT__bodies
| ( c_Com_OWT @ V_b ) ) )
= $true ),
inference(copy,[status(thm)],[1416]) ).
thf(2486,plain,
( ( ! [V_x: $i,V_xa: $i] : ( V_x = V_xa )
| c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ),
inference(copy,[status(thm)],[1415]) ).
thf(2487,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)],[743]) ).
thf(2488,plain,
( ( ! [V_S: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_S @ V_x ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ V_x ) @ V_S ) ) ) )
= $true ),
inference(copy,[status(thm)],[1414]) ).
thf(2489,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)],[741]) ).
thf(2490,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)],[740]) ).
thf(2491,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)],[739]) ).
thf(2492,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)],[738]) ).
thf(2493,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)],[737]) ).
thf(2494,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)],[736]) ).
thf(2495,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)],[735]) ).
thf(2496,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)],[734]) ).
thf(2497,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)],[733]) ).
thf(2498,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)],[732]) ).
thf(2499,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)],[731]) ).
thf(2500,plain,
( ( class_Lattices_Oupper__semilattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[730]) ).
thf(2501,plain,
( ( class_Lattices_Olower__semilattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[729]) ).
thf(2502,plain,
( ( class_Lattices_Odistrib__lattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[728]) ).
thf(2503,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[727]) ).
thf(2504,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[726]) ).
thf(2505,plain,
( ( class_Lattices_Olattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[725]) ).
thf(2506,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[724]) ).
thf(2507,plain,
( ( class_Orderings_Obot @ tc_nat )
= $true ),
inference(copy,[status(thm)],[723]) ).
thf(2508,plain,
( ( class_HOL_Oord @ tc_nat )
= $true ),
inference(copy,[status(thm)],[722]) ).
thf(2509,plain,
( ( class_Complete__Lattice_Ocomplete__lattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[721]) ).
thf(2510,plain,
( ( class_Lattices_Oupper__semilattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[720]) ).
thf(2511,plain,
( ( class_Lattices_Olower__semilattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[719]) ).
thf(2512,plain,
( ( class_Lattices_Odistrib__lattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[718]) ).
thf(2513,plain,
( ( class_Lattices_Obounded__lattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[717]) ).
thf(2514,plain,
( ( class_Finite__Set_Ofinite_Ofinite @ tc_bool )
= $true ),
inference(copy,[status(thm)],[716]) ).
thf(2515,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[715]) ).
thf(2516,plain,
( ( class_Lattices_Olattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[714]) ).
thf(2517,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[713]) ).
thf(2518,plain,
( ( class_Orderings_Obot @ tc_bool )
= $true ),
inference(copy,[status(thm)],[712]) ).
thf(2519,plain,
( ( class_HOL_Oord @ tc_bool )
= $true ),
inference(copy,[status(thm)],[711]) ).
thf(2520,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)],[710]) ).
thf(2521,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[709]) ).
thf(2522,plain,
( ( ! [V_X: $i,V_Y: $i] :
( ( V_X = V_Y )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[1413]) ).
thf(2523,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[1412]) ).
thf(2524,plain,
( ( c_Com_OWT @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ v_pn ) @ tc_Com_Ocom ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1823]) ).
thf(2525,plain,
! [SV1: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV1 )
| ! [SY2704: $i,SY2705: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2704 @ SY2705 @ SV1 ) @ SY2704 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(2526,plain,
! [SV2: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV2 )
| ! [SY2706: $i,SY2707: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2706 @ SY2707 @ SV2 ) @ SY2707 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(2527,plain,
! [SV3: $i] :
( ( ! [SY2708: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV3 )
| ! [SY2709: $i,SY2710: $i] :
( ( c_lessequals @ SY2708 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2709 @ SY2710 @ SV3 ) @ SV3 )
| ~ ( c_lessequals @ SY2708 @ SY2710 @ SV3 )
| ~ ( c_lessequals @ SY2708 @ SY2709 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2528,plain,
! [SV4: $i] :
( ( ! [SY2711: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV4 )
| ! [SY2712: $i,SY2713: $i] :
( ( c_lessequals @ SY2711 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2712 @ SY2713 @ SV4 ) @ SV4 )
| ~ ( c_lessequals @ SY2711 @ SY2713 @ SV4 )
| ~ ( c_lessequals @ SY2711 @ SY2712 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(2529,plain,
! [SV5: $i] :
( ( ! [SY2714: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV5 )
| ! [SY2715: $i,SY2716: $i] :
( ( c_lessequals @ SY2714 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2715 @ SY2716 @ SV5 ) @ SV5 )
| ~ ( c_lessequals @ SY2714 @ SY2716 @ SV5 )
| ~ ( c_lessequals @ SY2714 @ SY2715 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(2530,plain,
! [SV6: $i] :
( ( ~ ( class_Lattices_Olattice @ SV6 )
| ! [SY2717: $i,SY2718: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2717 @ SY2718 @ SV6 ) @ SY2718 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(2531,plain,
! [SV7: $i] :
( ( ~ ( class_Lattices_Olattice @ SV7 )
| ! [SY2719: $i,SY2720: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2719 @ SY2720 @ SV7 ) @ SY2719 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(2532,plain,
! [SV8: $i] :
( ( ! [SY2721: $i,SY2722: $i,SY2723: $i,SY2724: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV8 @ SY2721 @ ( tc_fun @ SY2722 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2723 @ SY2724 @ ( tc_fun @ SY2722 @ tc_bool ) ) @ ( tc_fun @ SY2722 @ tc_bool ) )
| ~ ( c_lessequals @ SY2721 @ SY2724 @ ( tc_fun @ SY2722 @ tc_bool ) )
| ~ ( c_lessequals @ SV8 @ SY2723 @ ( tc_fun @ SY2722 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(2533,plain,
! [SV9: $i] :
( ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV9 @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV9 @ tc_bool ) ) @ ( tc_fun @ SV9 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(2534,plain,
! [SV10: $i] :
( ( ! [SY2725: $i] :
( ( SV10
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2725 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV10 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2725 @ tc_bool ) ) @ ( tc_fun @ SY2725 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1833]) ).
thf(2535,plain,
! [SV11: $i] :
( ( ! [SY2726: $i,SY2727: $i,SY2728: $i,SY2729: $i,SY2730: $i,SY2731: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV11 @ SY2726 @ SY2727 @ SY2728 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2729 @ SY2730 @ SY2731 @ SY2728 ) )
| ( SY2727 = SY2731 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1834]) ).
thf(2536,plain,
! [SV12: $i] :
( ( ! [SY2732: $i,SY2733: $i,SY2734: $i,SY2735: $i,SY2736: $i] :
( ! [SY2737: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV12 @ SY2732 @ SY2733 @ SY2734 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2735 @ SY2736 @ SY2737 @ SY2734 ) )
| ( SY2732 = SY2736 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(2537,plain,
! [SV13: $i] :
( ( ! [SY2738: $i,SY2739: $i,SY2740: $i,SY2741: $i] :
( ! [SY2742: $i,SY2743: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV13 @ SY2738 @ SY2739 @ SY2740 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2741 @ SY2742 @ SY2743 @ SY2740 ) )
| ( SV13 = SY2741 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1836]) ).
thf(2538,plain,
! [SV14: $i] :
( ( ! [SY2744: $i,SY2745: $i,SY2746: $i] :
( ( c_Fun_Ofun__upd @ SV14 @ SY2744 @ ( hAPP @ SV14 @ SY2744 ) @ SY2745 @ SY2746 )
= SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(2539,plain,
! [SV15: $i] :
( ( ! [SY2747: $i,SY2748: $i,SY2749: $i,SY2750: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV15 @ SY2747 @ SY2748 @ SY2749 @ SY2750 ) @ SY2747 )
= SY2748 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(2540,plain,
! [SV16: $i] :
( ( ! [SY2751: $i,SY2752: $i,SY2753: $i] :
( ( c_Fun_Ofun__upd @ SV16 @ SY2751 @ ( hAPP @ SV16 @ SY2751 ) @ SY2752 @ SY2753 )
= SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(2541,plain,
! [SV17: $i] :
( ( ! [SY2754: $i,SY2755: $i,SY2756: $i,SY2757: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV17 @ SY2754 @ SY2755 @ SY2756 @ SY2757 ) @ SY2754 )
= SY2755 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(2542,plain,
! [SV18: $i] :
( ( ! [SY2758: $i,SY2759: $i,SY2760: $i] :
( ( c_Fun_Ofun__upd @ SV18 @ SY2758 @ ( hAPP @ SV18 @ SY2758 ) @ SY2759 @ SY2760 )
= SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(2543,plain,
! [SV19: $i] :
( ( ! [SY2761: $i,SY2762: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV19 @ SY2761 @ ( tc_fun @ SY2762 @ tc_bool ) )
!= SY2761 )
| ( c_lessequals @ SV19 @ SY2761 @ ( tc_fun @ SY2762 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(2544,plain,
! [SV20: $i] :
( ( ! [SY2763: $i,SY2764: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV20 @ SY2763 @ ( tc_fun @ SY2764 @ tc_bool ) )
= SV20 )
| ~ ( c_lessequals @ SY2763 @ SV20 @ ( tc_fun @ SY2764 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1843]) ).
thf(2545,plain,
! [SV21: $i] :
( ( ! [SY2765: $i,SY2766: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV21 @ SY2765 @ ( tc_fun @ SY2766 @ tc_bool ) )
= SY2765 )
| ~ ( c_lessequals @ SV21 @ SY2765 @ ( tc_fun @ SY2766 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(2546,plain,
! [SV22: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV22 )
| ! [SY2767: $i,SY2768: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2767 @ SY2768 @ SV22 )
= SY2768 )
| ~ ( c_lessequals @ SY2767 @ SY2768 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(2547,plain,
! [SV23: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV23 )
| ! [SY2769: $i,SY2770: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2769 @ SY2770 @ SV23 )
!= SY2770 )
| ( c_lessequals @ SY2769 @ SY2770 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(2548,plain,
! [SV24: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV24 )
| ! [SY2771: $i,SY2772: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2771 @ SY2772 @ SV24 )
= SY2771 )
| ~ ( c_lessequals @ SY2772 @ SY2771 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(2549,plain,
! [SV25: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV25 )
| ! [SY2773: $i,SY2774: $i] :
( ( c_lessequals @ SY2773 @ SY2774 @ SV25 )
| ~ ( c_HOL_Oord__class_Oless @ SY2773 @ SY2774 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(2550,plain,
! [SV26: $i] :
( ( ~ ( class_Orderings_Oorder @ SV26 )
| ! [SY2775: $i,SY2776: $i] :
( ( c_lessequals @ SY2775 @ SY2776 @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ SY2775 @ SY2776 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(2551,plain,
! [SV27: $i] :
( ( ! [SY2777: $i] :
( ~ ( class_HOL_Oord @ SV27 )
| ! [SY2778: $i,SY2779: $i] :
( ( c_lessequals @ SY2777 @ SY2778 @ ( tc_fun @ SY2779 @ SV27 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2777 @ SY2778 @ ( tc_fun @ SY2779 @ SV27 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(2552,plain,
! [SV28: $i] :
( ( ! [SY2780: $i,SY2781: $i] :
( ( c_lessequals @ SV28 @ SY2780 @ ( tc_fun @ SY2781 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV28 @ SY2780 @ ( tc_fun @ SY2781 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(2553,plain,
! [SV29: $i] :
( ( ~ ( class_Lattices_Olattice @ SV29 )
| ! [SY2782: $i,SY2783: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2782 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2782 @ SY2783 @ SV29 ) @ SV29 )
= SY2782 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(2554,plain,
! [SV30: $i] :
( ( ~ ( class_Orderings_Oorder @ SV30 )
| ! [SY2784: $i,SY2785: $i] :
( ( SY2784 = SY2785 )
| ~ ( c_lessequals @ SY2784 @ SY2785 @ SV30 )
| ~ ( c_lessequals @ SY2785 @ SY2784 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(2555,plain,
! [SV31: $i] :
( ( ~ ( class_Orderings_Oorder @ SV31 )
| ! [SY2786: $i,SY2787: $i] :
( ( SY2786 = SY2787 )
| ~ ( c_lessequals @ SY2787 @ SY2786 @ SV31 )
| ~ ( c_lessequals @ SY2786 @ SY2787 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2556,plain,
! [SV32: $i] :
( ( ~ ( class_Orderings_Oorder @ SV32 )
| ! [SY2788: $i,SY2789: $i] :
( ( SY2788 = SY2789 )
| ~ ( c_lessequals @ SY2789 @ SY2788 @ SV32 )
| ~ ( c_lessequals @ SY2788 @ SY2789 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(2557,plain,
! [SV33: $i] :
( ( ! [SY2790: $i] :
( ( SV33 = SY2790 )
| ! [SY2791: $i] :
( ~ ( c_lessequals @ SY2790 @ SV33 @ ( tc_fun @ SY2791 @ tc_bool ) )
| ~ ( c_lessequals @ SV33 @ SY2790 @ ( tc_fun @ SY2791 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2558,plain,
! [SV34: $i] :
( ( ! [SY2792: $i] :
( ( SV34 = SY2792 )
| ! [SY2793: $i] :
( ~ ( c_lessequals @ SY2792 @ SV34 @ ( tc_fun @ SY2793 @ tc_bool ) )
| ~ ( c_lessequals @ SV34 @ SY2792 @ ( tc_fun @ SY2793 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(2559,plain,
! [SV35: $i] :
( ( ~ ( class_Lattices_Olattice @ SV35 )
| ! [SY2794: $i,SY2795: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2794 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2794 @ SY2795 @ SV35 ) @ SV35 )
= SY2794 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1858]) ).
thf(2560,plain,
! [SV36: $i] :
( ( ! [SY2796: $i] :
( ~ ( class_HOL_Oord @ SV36 )
| ! [SY2797: $i,SY2798: $i] :
( ( c_HOL_Oord__class_Oless @ SY2796 @ SY2797 @ ( tc_fun @ SY2798 @ SV36 ) )
| ( c_lessequals @ SY2797 @ SY2796 @ ( tc_fun @ SY2798 @ SV36 ) )
| ~ ( c_lessequals @ SY2796 @ SY2797 @ ( tc_fun @ SY2798 @ SV36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(2561,plain,
! [SV37: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV37 )
| ! [SY2799: $i,SY2800: $i] :
( ( c_HOL_Oord__class_Oless @ SY2799 @ SY2800 @ SV37 )
| ( c_lessequals @ SY2800 @ SY2799 @ SV37 )
| ~ ( c_lessequals @ SY2799 @ SY2800 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(2562,plain,
! [SV38: $i] :
( ( ! [SY2801: $i] :
( ~ ( class_Lattices_Olattice @ SV38 )
| ! [SY2802: $i,SY2803: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2801 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2802 @ SY2803 @ SV38 ) @ SV38 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2801 @ SY2802 @ SV38 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2801 @ SY2803 @ SV38 ) @ SV38 ) @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(2563,plain,
! [SV39: $i] :
( ( ! [SY2804: $i,SY2805: $i,SY2806: $i,SY2807: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV39 @ SY2804 @ ( tc_fun @ SY2805 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY2806 @ SY2807 @ ( tc_fun @ SY2805 @ tc_bool ) ) @ ( tc_fun @ SY2805 @ tc_bool ) )
| ~ ( c_lessequals @ SY2807 @ SY2804 @ ( tc_fun @ SY2805 @ tc_bool ) )
| ~ ( c_lessequals @ SV39 @ SY2806 @ ( tc_fun @ SY2805 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(2564,plain,
! [SV40: $i] :
( ( ! [SY2808: $i,SY2809: $i,SY2810: $i,SY2811: $i,SY2812: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ SV40 @ SY2808 @ SY2809 @ SY2810 @ SY2811 ) @ SY2808 @ SY2812 @ SY2810 @ SY2811 )
= ( c_Fun_Ofun__upd @ SV40 @ SY2808 @ SY2812 @ SY2810 @ SY2811 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(2565,plain,
! [SV41: $i] :
( ( ! [SY2813: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV41 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2813 @ tc_bool ) ) @ ( tc_fun @ SY2813 @ tc_bool ) )
= SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2566,plain,
! [SV42: $i] :
( ( ! [SY2814: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV42 @ tc_bool ) ) @ SY2814 @ ( tc_fun @ SV42 @ tc_bool ) )
= SY2814 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1865]) ).
thf(2567,plain,
! [SV43: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV43 )
| ! [SY2815: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ SV43 ) @ SY2815 @ SV43 )
= SY2815 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(2568,plain,
! [SV44: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV44 )
| ! [SY2816: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2816 @ ( c_Orderings_Obot__class_Obot @ SV44 ) @ SV44 )
= SY2816 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1867]) ).
thf(2569,plain,
! [SV45: $i] :
( ( ! [SY2817: $i] :
( ( c_Finite__Set_Ofinite @ SV45 @ SY2817 )
| ! [SY2818: $i] :
~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2818 @ SV45 @ ( tc_fun @ SY2817 @ tc_bool ) ) @ SY2817 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(2570,plain,
! [SV46: $i] :
( ( ! [SY2819: $i] :
( ( c_Finite__Set_Ofinite @ SV46 @ SY2819 )
| ! [SY2820: $i] :
~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV46 @ SY2820 @ ( tc_fun @ SY2819 @ tc_bool ) ) @ SY2819 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1869]) ).
thf(2571,plain,
! [SV47: $i] :
( ( ! [SY2821: $i,SY2822: $i,SY2823: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV47 @ SY2821 @ ( tc_fun @ SY2822 @ tc_bool ) ) @ SY2823 ) )
| ~ ( hBOOL @ ( hAPP @ SV47 @ SY2823 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1870]) ).
thf(2572,plain,
! [SV48: $i] :
( ( ! [SY2824: $i,SY2825: $i,SY2826: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV48 @ SY2824 @ ( tc_fun @ SY2825 @ tc_bool ) ) @ SY2826 ) )
| ~ ( hBOOL @ ( hAPP @ SY2824 @ SY2826 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(2573,plain,
! [SV49: $i] :
( ( ! [SY2827: $i] :
( ( hBOOL @ ( hAPP @ SV49 @ SY2827 ) )
| ! [SY2828: $i] :
( ( hBOOL @ ( hAPP @ SY2828 @ SY2827 ) )
| ! [SY2829: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2828 @ SV49 @ ( tc_fun @ SY2829 @ tc_bool ) ) @ SY2827 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1872]) ).
thf(2574,plain,
! [SV50: $i] :
( ( ! [SY2830: $i,SY2831: $i,SY2832: $i,SY2833: $i,SY2834: $i] :
( ! [SY2835: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ SV50 @ SY2830 @ SY2831 @ SY2832 @ SY2833 ) @ SY2834 @ SY2835 @ SY2832 @ SY2833 )
= ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ SV50 @ SY2834 @ SY2835 @ SY2832 @ SY2833 ) @ SY2830 @ SY2831 @ SY2832 @ SY2833 ) )
| ( SY2830 = SY2834 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(2575,plain,
! [SV51: $i] :
( ( ! [SY2836: $i,SY2837: $i,SY2838: $i,SY2839: $i,SY2840: $i] :
( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ SV51 @ SY2836 @ SY2837 @ SY2838 @ ( tc_Option_Ooption @ SY2839 ) ) @ ( c_Fun_Ofun__upd @ SY2840 @ SY2836 @ SY2837 @ SY2838 @ ( tc_Option_Ooption @ SY2839 ) ) @ SY2838 @ SY2839 )
| ~ ( c_Map_Omap__le @ SV51 @ SY2840 @ SY2838 @ SY2839 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(2576,plain,
! [SV52: $i] :
( ( ! [SY2841: $i,SY2842: $i,SY2843: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV52 @ SY2841 @ ( tc_fun @ SY2842 @ tc_bool ) ) @ SY2843 @ ( tc_fun @ SY2842 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV52 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2841 @ SY2843 @ ( tc_fun @ SY2842 @ tc_bool ) ) @ ( tc_fun @ SY2842 @ tc_bool ) ) )
| ~ ( c_lessequals @ SY2843 @ SV52 @ ( tc_fun @ SY2842 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(2577,plain,
! [SV53: $i] :
( ( ! [SY2844: $i,SY2845: $i,SY2846: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV53 @ SY2844 @ ( tc_fun @ SY2845 @ tc_bool ) ) @ SY2846 @ ( tc_fun @ SY2845 @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ SV53 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2844 @ SY2846 @ ( tc_fun @ SY2845 @ tc_bool ) ) @ ( tc_fun @ SY2845 @ tc_bool ) ) )
| ( c_lessequals @ SY2846 @ SV53 @ ( tc_fun @ SY2845 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1876]) ).
thf(2578,plain,
! [SV54: $i] :
( ( ! [SY2847: $i,SY2848: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV54 @ SY2847 @ ( tc_fun @ SY2848 @ tc_bool ) ) @ SY2848 )
| ~ ( c_Finite__Set_Ofinite @ SY2847 @ SY2848 )
| ~ ( c_Finite__Set_Ofinite @ SV54 @ SY2848 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(2579,plain,
! [SV55: $i] :
( ( ! [SY2849: $i,SY2850: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV55 @ SY2849 @ ( tc_fun @ SY2850 @ tc_bool ) ) @ SY2850 )
| ~ ( c_Finite__Set_Ofinite @ SY2849 @ SY2850 )
| ~ ( c_Finite__Set_Ofinite @ SV55 @ SY2850 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(2580,plain,
! [SV56: $i] :
( ( ! [SY2851: $i,SY2852: $i] :
( ( SV56 = SY2851 )
| ! [SY2853: $i,SY2854: $i] :
~ ( c_Finite__Set_Ofold__graph @ SY2852 @ SY2851 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2853 @ tc_bool ) ) @ SV56 @ SY2853 @ SY2854 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(2581,plain,
! [SV57: $i] :
( ( ! [SY2855: $i,SY2856: $i] : ( c_lessequals @ SV57 @ ( c_Set_Oinsert @ SY2855 @ SV57 @ SY2856 ) @ ( tc_fun @ SY2856 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(2582,plain,
! [SV58: $i] :
( ( ! [SY2857: $i,SY2858: $i,SY2859: $i,SY2860: $i] :
( ( ( hAPP @ SV58 @ SY2857 )
!= ( c_Option_Ooption_OSome @ SY2858 @ SY2859 ) )
| ( SY2857 = SY2860 )
| ! [SY2861: $i,SY2862: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV58 @ SY2860 @ ( c_Option_Ooption_OSome @ SY2861 @ SY2859 ) @ SY2862 @ ( tc_Option_Ooption @ SY2859 ) ) @ SY2857 )
= ( c_Option_Ooption_OSome @ SY2858 @ SY2859 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2583,plain,
! [SV59: $i] :
( ( ! [SY2863: $i,SY2864: $i,SY2865: $i,SY2866: $i,SY2867: $i,SY2868: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV59 @ SY2863 @ ( c_Option_Ooption_OSome @ SY2864 @ SY2865 ) @ SY2866 @ ( tc_Option_Ooption @ SY2865 ) ) @ SY2867 )
!= ( c_Option_Ooption_OSome @ SY2868 @ SY2865 ) )
| ( ( hAPP @ SV59 @ SY2867 )
= ( c_Option_Ooption_OSome @ SY2868 @ SY2865 ) )
| ( SY2864 = SY2868 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2584,plain,
! [SV60: $i] :
( ( ! [SY2869: $i,SY2870: $i,SY2871: $i,SY2872: $i,SY2873: $i,SY2874: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV60 @ SY2869 @ ( c_Option_Ooption_OSome @ SY2870 @ SY2871 ) @ SY2872 @ ( tc_Option_Ooption @ SY2871 ) ) @ SY2873 )
!= ( c_Option_Ooption_OSome @ SY2874 @ SY2871 ) )
| ( ( hAPP @ SV60 @ SY2873 )
= ( c_Option_Ooption_OSome @ SY2874 @ SY2871 ) )
| ( SY2873 = SY2869 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2585,plain,
! [SV61: $i] :
( ( ~ ( class_Orderings_Obot @ SV61 )
| ! [SY2875: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV61 ) @ SY2875 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2586,plain,
! [SV62: $i] :
( ( ! [SY2876: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV62 @ tc_bool ) ) @ SY2876 @ ( tc_fun @ SV62 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2587,plain,
! [SV63: $i] :
( ( ! [SY2877: $i,SY2878: $i,SY2879: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV63 @ ( c_Set_Oinsert @ SY2877 @ SY2878 @ SY2879 ) @ ( tc_fun @ SY2879 @ tc_bool ) )
= ( c_Set_Oinsert @ SY2877 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV63 @ SY2878 @ ( tc_fun @ SY2879 @ tc_bool ) ) @ SY2879 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2588,plain,
! [SV64: $i] :
( ( ! [SY2880: $i,SY2881: $i,SY2882: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV64 @ SY2880 @ SY2881 ) @ SY2882 @ ( tc_fun @ SY2881 @ tc_bool ) )
= ( c_Set_Oinsert @ SV64 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2880 @ SY2882 @ ( tc_fun @ SY2881 @ tc_bool ) ) @ SY2881 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(2589,plain,
! [SV65: $i] :
( ( ! [SY2883: $i,SY2884: $i,SY2885: $i] :
( ( c_lessequals @ SV65 @ ( c_Set_Oinsert @ SY2883 @ SY2884 @ SY2885 ) @ ( tc_fun @ SY2885 @ tc_bool ) )
| ~ ( c_lessequals @ SV65 @ SY2884 @ ( tc_fun @ SY2885 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(2590,plain,
! [SV66: $i] :
( ( ! [SY2886: $i,SY2887: $i] :
( ( c_lessequals @ SV66 @ SY2886 @ ( tc_fun @ SY2887 @ tc_bool ) )
| ! [SY2888: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SY2888 @ SV66 @ SY2887 ) @ SY2886 @ ( tc_fun @ SY2887 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2591,plain,
! [SV67: $i] :
( ( ! [SY2889: $i,SY2890: $i,SY2891: $i] :
( ( c_Finite__Set_Ofinite @ SV67 @ SY2889 )
| ! [SY2892: $i,SY2893: $i] :
~ ( c_Finite__Set_Ofold__graph @ SY2890 @ SY2891 @ SV67 @ SY2892 @ SY2889 @ SY2893 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1890]) ).
thf(2592,plain,
! [SV68: $i] :
( ( ! [SY2894: $i,SY2895: $i,SY2896: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV68 @ SY2894 @ ( tc_fun @ SY2895 @ tc_bool ) ) @ SY2896 @ ( tc_fun @ SY2895 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV68 @ SY2896 @ ( tc_fun @ SY2895 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2894 @ SY2896 @ ( tc_fun @ SY2895 @ tc_bool ) ) @ ( tc_fun @ SY2895 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1891]) ).
thf(2593,plain,
! [SV69: $i] :
( ( ! [SY2897: $i,SY2898: $i,SY2899: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV69 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2897 @ SY2898 @ ( tc_fun @ SY2899 @ tc_bool ) ) @ ( tc_fun @ SY2899 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV69 @ SY2897 @ ( tc_fun @ SY2899 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV69 @ SY2898 @ ( tc_fun @ SY2899 @ tc_bool ) ) @ ( tc_fun @ SY2899 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(2594,plain,
! [SV70: $i] :
( ( ! [SY2900: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV70 )
| ! [SY2901: $i,SY2902: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2900 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2901 @ SY2902 @ SV70 ) @ SV70 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2900 @ SY2901 @ SV70 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2900 @ SY2902 @ SV70 ) @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2595,plain,
! [SV71: $i] :
( ( ! [SY2903: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV71 )
| ! [SY2904: $i,SY2905: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2903 @ SY2904 @ SV71 ) @ SY2905 @ SV71 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2903 @ SY2905 @ SV71 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2904 @ SY2905 @ SV71 ) @ SV71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2596,plain,
! [SV72: $i] :
( ( ! [SY2906: $i,SY2907: $i,SY2908: $i] :
( ! [SY2909: $i,SY2910: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SY2907 @ SY2908 @ ( c_Option_Ooption_OSome @ SV72 @ SY2909 ) @ SY2910 @ ( tc_Option_Ooption @ SY2909 ) ) @ SY2908 )
!= ( c_Option_Ooption_OSome @ SY2906 @ SY2909 ) )
| ( SV72 = SY2906 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2597,plain,
! [SV73: $i] :
( ( ! [SY2911: $i,SY2912: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV73 @ SY2911 @ ( tc_fun @ SY2912 @ tc_bool ) ) @ SV73 @ ( tc_fun @ SY2912 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2598,plain,
! [SV74: $i] :
( ( ! [SY2913: $i,SY2914: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV74 @ SY2913 @ ( tc_fun @ SY2914 @ tc_bool ) ) @ SY2913 @ ( tc_fun @ SY2914 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1897]) ).
thf(2599,plain,
! [SV75: $i] :
( ( ! [SY2915: $i,SY2916: $i,SY2917: $i] :
( ( c_lessequals @ SV75 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2915 @ SY2916 @ ( tc_fun @ SY2917 @ tc_bool ) ) @ ( tc_fun @ SY2917 @ tc_bool ) )
| ~ ( c_lessequals @ SV75 @ SY2916 @ ( tc_fun @ SY2917 @ tc_bool ) )
| ~ ( c_lessequals @ SV75 @ SY2915 @ ( tc_fun @ SY2917 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2600,plain,
! [SV76: $i] :
( ( ! [SY2918: $i,SY2919: $i,SY2920: $i] :
( ( c_lessequals @ SV76 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2918 @ SY2919 @ ( tc_fun @ SY2920 @ tc_bool ) ) @ ( tc_fun @ SY2920 @ tc_bool ) )
| ~ ( c_lessequals @ SV76 @ SY2919 @ ( tc_fun @ SY2920 @ tc_bool ) )
| ~ ( c_lessequals @ SV76 @ SY2918 @ ( tc_fun @ SY2920 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1899]) ).
thf(2601,plain,
! [SV77: $i] :
( ( ! [SY2921: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV77 )
| ! [SY2922: $i,SY2923: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2921 @ SY2922 @ SV77 ) @ SY2923 @ SV77 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2921 @ SY2923 @ SV77 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2922 @ SY2923 @ SV77 ) @ SV77 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(2602,plain,
! [SV78: $i] :
( ( ! [SY2924: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ SV78 )
| ! [SY2925: $i,SY2926: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2924 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2925 @ SY2926 @ SV78 ) @ SV78 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2924 @ SY2925 @ SV78 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2924 @ SY2926 @ SV78 ) @ SV78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(2603,plain,
! [SV79: $i] :
( ( ! [SY2927: $i,SY2928: $i,SY2929: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV79 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2927 @ SY2928 @ ( tc_fun @ SY2929 @ tc_bool ) ) @ ( tc_fun @ SY2929 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV79 @ SY2927 @ ( tc_fun @ SY2929 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV79 @ SY2928 @ ( tc_fun @ SY2929 @ tc_bool ) ) @ ( tc_fun @ SY2929 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2604,plain,
! [SV80: $i] :
( ( ! [SY2930: $i,SY2931: $i,SY2932: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV80 @ SY2930 @ ( tc_fun @ SY2931 @ tc_bool ) ) @ SY2932 @ ( tc_fun @ SY2931 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV80 @ SY2932 @ ( tc_fun @ SY2931 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2930 @ SY2932 @ ( tc_fun @ SY2931 @ tc_bool ) ) @ ( tc_fun @ SY2931 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(2605,plain,
! [SV81: $i] :
( ( ! [SY2933: $i,SY2934: $i,SY2935: $i,SY2936: $i,SY2937: $i] :
( ( c_Set_Oimage @ SV81 @ ( c_Set_Oimage @ SY2933 @ SY2934 @ SY2935 @ SY2936 ) @ SY2936 @ SY2937 )
= ( c_Set_Oimage @ ( c_COMBB @ SV81 @ SY2933 @ SY2936 @ SY2937 @ SY2935 ) @ SY2934 @ SY2935 @ SY2937 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(2606,plain,
! [SV82: $i] :
( ( ! [SY2938: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV82 )
| ! [SY2939: $i] :
( ( c_lessequals @ SY2938 @ SY2939 @ SV82 )
| ! [SY2940: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2940 @ SY2938 @ SV82 ) @ SY2939 @ SV82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2607,plain,
! [SV83: $i] :
( ( ! [SY2941: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV83 )
| ! [SY2942: $i] :
( ( c_lessequals @ SY2941 @ SY2942 @ SV83 )
| ! [SY2943: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2941 @ SY2943 @ SV83 ) @ SY2942 @ SV83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2608,plain,
! [SV84: $i] :
( ( ! [SY2944: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV84 )
| ! [SY2945: $i,SY2946: $i] :
( ( c_lessequals @ SY2944 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2945 @ SY2946 @ SV84 ) @ SV84 )
| ~ ( c_lessequals @ SY2944 @ SY2946 @ SV84 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(2609,plain,
! [SV85: $i] :
( ( ! [SY2947: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV85 )
| ! [SY2948: $i] :
( ! [SY2949: $i] : ( c_lessequals @ SY2947 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2948 @ SY2949 @ SV85 ) @ SV85 )
| ~ ( c_lessequals @ SY2947 @ SY2948 @ SV85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2610,plain,
! [SV86: $i] :
( ( ! [SY2950: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV86 )
| ! [SY2951: $i] :
( ( c_lessequals @ SY2950 @ SY2951 @ SV86 )
| ! [SY2952: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2952 @ SY2950 @ SV86 ) @ SY2951 @ SV86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(2611,plain,
! [SV87: $i] :
( ( ! [SY2953: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV87 )
| ! [SY2954: $i] :
( ( c_lessequals @ SY2953 @ SY2954 @ SV87 )
| ! [SY2955: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2953 @ SY2955 @ SV87 ) @ SY2954 @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(2612,plain,
! [SV88: $i] :
( ( ! [SY2956: $i,SY2957: $i] :
( ( c_lessequals @ SV88 @ SY2956 @ ( tc_fun @ SY2957 @ tc_bool ) )
| ! [SY2958: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV88 @ SY2958 @ ( tc_fun @ SY2957 @ tc_bool ) ) @ SY2956 @ ( tc_fun @ SY2957 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(2613,plain,
! [SV89: $i] :
( ( ! [SY2959: $i,SY2960: $i] :
( ( c_lessequals @ SV89 @ SY2959 @ ( tc_fun @ SY2960 @ tc_bool ) )
| ! [SY2961: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2961 @ SV89 @ ( tc_fun @ SY2960 @ tc_bool ) ) @ SY2959 @ ( tc_fun @ SY2960 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1912]) ).
thf(2614,plain,
! [SV90: $i] :
( ( ! [SY2962: $i] :
( ~ ( class_Orderings_Oorder @ SV90 )
| ! [SY2963: $i] :
( ( c_lessequals @ SY2962 @ SY2963 @ SV90 )
| ! [SY2964: $i] :
( ~ ( c_lessequals @ SY2962 @ SY2964 @ SV90 )
| ~ ( c_lessequals @ SY2964 @ SY2963 @ SV90 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2615,plain,
! [SV91: $i] :
( ( ! [SY2965: $i] :
( ~ ( class_Orderings_Oorder @ SV91 )
| ! [SY2966: $i] :
( ( c_HOL_Oord__class_Oless @ SY2965 @ SY2966 @ SV91 )
| ! [SY2967: $i] :
( ~ ( c_lessequals @ SY2965 @ SY2967 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SY2967 @ SY2966 @ SV91 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(2616,plain,
! [SV92: $i] :
( ( ! [SY2968: $i] :
( ~ ( class_Orderings_Oorder @ SV92 )
| ! [SY2969: $i] :
( ( c_HOL_Oord__class_Oless @ SY2968 @ SY2969 @ SV92 )
| ! [SY2970: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY2968 @ SY2970 @ SV92 )
| ~ ( c_lessequals @ SY2970 @ SY2969 @ SV92 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2617,plain,
! [SV93: $i] :
( ( ! [SY2971: $i] :
( ~ ( class_Orderings_Opreorder @ SV93 )
| ! [SY2972: $i] :
( ( c_lessequals @ SY2971 @ SY2972 @ SV93 )
| ! [SY2973: $i] :
( ~ ( c_lessequals @ SY2973 @ SY2972 @ SV93 )
| ~ ( c_lessequals @ SY2971 @ SY2973 @ SV93 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2618,plain,
! [SV94: $i] :
( ( ! [SY2974: $i] : ( c_lessequals @ SV94 @ SV94 @ ( tc_fun @ SY2974 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2619,plain,
! [SV95: $i] :
( ( ! [SY2975: $i] : ( c_lessequals @ SV95 @ SV95 @ ( tc_fun @ SY2975 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2620,plain,
! [SV96: $i] :
( ( ! [SY2976: $i,SY2977: $i] :
( ( c_lessequals @ SV96 @ SY2976 @ ( tc_fun @ SY2977 @ tc_bool ) )
| ! [SY2978: $i] :
( ~ ( c_lessequals @ SY2978 @ SY2976 @ ( tc_fun @ SY2977 @ tc_bool ) )
| ~ ( c_lessequals @ SV96 @ SY2978 @ ( tc_fun @ SY2977 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2621,plain,
! [SV97: $i] :
( ( ! [SY2979: $i,SY2980: $i,SY2981: $i] :
( ( c_Fun_Oinj__on @ SV97 @ SY2979 @ SY2980 @ SY2981 )
| ! [SY2982: $i] :
( ~ ( c_lessequals @ SY2979 @ SY2982 @ ( tc_fun @ SY2980 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV97 @ SY2982 @ SY2980 @ SY2981 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(2622,plain,
! [SV98: $i] :
( ( ! [SY2983: $i] :
( ( hBOOL @ ( hAPP @ SV98 @ SY2983 ) )
| ! [SY2984: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2984 @ SY2983 ) )
| ! [SY2985: $i] :
~ ( c_lessequals @ SY2984 @ SV98 @ ( tc_fun @ SY2985 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2623,plain,
! [SV99: $i] :
( ( ~ ( class_Orderings_Oorder @ SV99 )
| ! [SY2986: $i] : ( c_lessequals @ SY2986 @ SY2986 @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2624,plain,
! [SV100: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV100 )
| ! [SY2987: $i] : ( c_lessequals @ SY2987 @ SY2987 @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2625,plain,
! [SV101: $i] :
( ( ! [SY2988: $i] :
( ( c_Finite__Set_Ofinite @ SV101 @ SY2988 )
| ! [SY2989: $i] :
( ~ ( c_Finite__Set_Ofinite @ SY2989 @ SY2988 )
| ~ ( c_lessequals @ SV101 @ SY2989 @ ( tc_fun @ SY2988 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2626,plain,
! [SV102: $i] :
( ( ! [SY2990: $i,SY2991: $i] :
( ( c_HOL_Oord__class_Oless @ SV102 @ SY2990 @ ( tc_fun @ SY2991 @ tc_bool ) )
| ! [SY2992: $i] :
( ~ ( c_lessequals @ SY2992 @ SY2990 @ ( tc_fun @ SY2991 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV102 @ SY2992 @ ( tc_fun @ SY2991 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1925]) ).
thf(2627,plain,
! [SV103: $i] :
( ( ! [SY2993: $i,SY2994: $i] :
( ( c_HOL_Oord__class_Oless @ SV103 @ SY2993 @ ( tc_fun @ SY2994 @ tc_bool ) )
| ! [SY2995: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY2995 @ SY2993 @ ( tc_fun @ SY2994 @ tc_bool ) )
| ~ ( c_lessequals @ SV103 @ SY2995 @ ( tc_fun @ SY2994 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1926]) ).
thf(2628,plain,
! [SV104: $i] :
( ( ! [SY2996: $i] :
( ( hBOOL @ ( hAPP @ SV104 @ SY2996 ) )
| ! [SY2997: $i] :
( ! [SY2998: $i] :
~ ( c_lessequals @ SY2997 @ SV104 @ ( tc_fun @ SY2998 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SY2997 @ SY2996 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2629,plain,
! [SV105: $i] :
( ( ! [SY2999: $i] :
( ( c_Finite__Set_Ofinite @ SV105 @ SY2999 )
| ! [SY3000: $i] :
( ~ ( c_lessequals @ SV105 @ SY3000 @ ( tc_fun @ SY2999 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY3000 @ SY2999 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2630,plain,
! [SV106: $i] :
( ( ! [SY3001: $i] :
( ~ ( class_Orderings_Opreorder @ SV106 )
| ! [SY3002: $i] :
( ( c_HOL_Oord__class_Oless @ SY3001 @ SY3002 @ SV106 )
| ! [SY3003: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY3003 @ SY3002 @ SV106 )
| ~ ( c_lessequals @ SY3001 @ SY3003 @ SV106 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(2631,plain,
! [SV107: $i] :
( ( ! [SY3004: $i] :
( ~ ( class_Orderings_Opreorder @ SV107 )
| ! [SY3005: $i] :
( ( c_HOL_Oord__class_Oless @ SY3004 @ SY3005 @ SV107 )
| ! [SY3006: $i] :
( ~ ( c_lessequals @ SY3006 @ SY3005 @ SV107 )
| ~ ( c_HOL_Oord__class_Oless @ SY3004 @ SY3006 @ SV107 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2632,plain,
! [SV108: $i] :
( ( ! [SY3007: $i,SY3008: $i,SY3009: $i,SY3010: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV108 @ SY3007 @ ( tc_fun @ SY3008 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3009 @ SY3010 @ ( tc_fun @ SY3008 @ tc_bool ) ) @ ( tc_fun @ SY3008 @ tc_bool ) )
| ~ ( c_lessequals @ SY3007 @ SY3010 @ ( tc_fun @ SY3008 @ tc_bool ) )
| ~ ( c_lessequals @ SV108 @ SY3009 @ ( tc_fun @ SY3008 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2633,plain,
! [SV109: $i] :
( ( ! [SY3011: $i,SY3012: $i,SY3013: $i,SY3014: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV109 @ SY3011 @ ( c_Option_Ooption_OSome @ SY3012 @ SY3013 ) @ SY3014 @ ( tc_Option_Ooption @ SY3013 ) ) @ SY3011 )
= ( c_Option_Ooption_OSome @ SY3012 @ SY3013 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2634,plain,
! [SV110: $i] :
( ( ! [SY3015: $i,SY3016: $i,SY3017: $i] :
( ( ( hAPP @ SV110 @ SY3015 )
!= ( c_Option_Ooption_OSome @ SY3016 @ SY3017 ) )
| ! [SY3018: $i] :
( ( c_Fun_Ofun__upd @ SV110 @ SY3015 @ ( c_Option_Ooption_OSome @ SY3016 @ SY3017 ) @ SY3018 @ ( tc_Option_Ooption @ SY3017 ) )
= SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2635,plain,
! [SV111: $i] :
( ( ! [SY3019: $i,SY3020: $i,SY3021: $i,SY3022: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV111 @ SY3019 @ ( tc_fun @ SY3020 @ tc_bool ) ) @ SY3021 @ SY3020 @ ( tc_fun @ SY3022 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV111 @ SY3021 @ SY3020 @ ( tc_fun @ SY3022 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3019 @ SY3021 @ SY3020 @ ( tc_fun @ SY3022 @ tc_bool ) ) @ ( tc_fun @ SY3022 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2636,plain,
! [SV112: $i] :
( ( ! [SY3023: $i,SY3024: $i,SY3025: $i,SY3026: $i,SY3027: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV112 @ SY3023 @ SY3024 @ SY3025 @ SY3026 ) @ SY3027 )
= ( hAPP @ SV112 @ SY3027 ) )
| ( SY3027 = SY3023 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2637,plain,
! [SV113: $i] :
( ( ! [SY3028: $i,SY3029: $i,SY3030: $i,SY3031: $i,SY3032: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV113 @ SY3028 @ SY3029 @ SY3030 @ SY3031 ) @ SY3032 )
= ( hAPP @ SV113 @ SY3032 ) )
| ( SY3032 = SY3028 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2638,plain,
! [SV114: $i] :
( ( ! [SY3033: $i,SY3034: $i,SY3035: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV114 @ ( c_HOL_Ominus__class_Ominus @ SY3033 @ SY3034 @ ( tc_fun @ SY3035 @ tc_bool ) ) @ ( tc_fun @ SY3035 @ tc_bool ) )
= SY3034 )
| ~ ( c_lessequals @ SV114 @ SY3033 @ ( tc_fun @ SY3035 @ tc_bool ) )
| ~ ( c_lessequals @ SY3034 @ SV114 @ ( tc_fun @ SY3035 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2639,plain,
! [SV115: $i] :
( ( ! [SY3036: $i,SY3037: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV115 )
| ! [SY3038: $i,SY3039: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SY3036 @ SY3037 @ SV115 )
!= ( c_HOL_Ominus__class_Ominus @ SY3038 @ SY3039 @ SV115 ) )
| ( c_lessequals @ SY3039 @ SY3038 @ SV115 )
| ~ ( c_lessequals @ SY3037 @ SY3036 @ SV115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2640,plain,
! [SV116: $i] :
( ( ! [SY3040: $i,SY3041: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV116 )
| ! [SY3042: $i,SY3043: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SY3040 @ SY3041 @ SV116 )
!= ( c_HOL_Ominus__class_Ominus @ SY3042 @ SY3043 @ SV116 ) )
| ( c_lessequals @ SY3041 @ SY3040 @ SV116 )
| ~ ( c_lessequals @ SY3043 @ SY3042 @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2641,plain,
! [SV117: $i] :
( ( ! [SY3044: $i,SY3045: $i,SY3046: $i,SY3047: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV117 @ SY3044 @ SY3045 @ SY3046 ) @ ( c_Set_Oimage @ SV117 @ SY3047 @ SY3045 @ SY3046 ) @ ( tc_fun @ SY3046 @ tc_bool ) )
| ~ ( c_lessequals @ SY3044 @ SY3047 @ ( tc_fun @ SY3045 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2642,plain,
! [SV118: $i] :
( ( ! [SY3048: $i,SY3049: $i] :
( ~ ( c_lessequals @ SV118 @ SY3048 @ ( tc_fun @ SY3049 @ tc_bool ) )
| ! [SY3050: $i,SY3051: $i] : ( c_lessequals @ ( c_Set_Oimage @ SY3050 @ SV118 @ SY3049 @ SY3051 ) @ ( c_Set_Oimage @ SY3050 @ SY3048 @ SY3049 @ SY3051 ) @ ( tc_fun @ SY3051 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(2643,plain,
! [SV119: $i] :
( ( ! [SY3052: $i,SY3053: $i,SY3054: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV119 @ SY3052 @ SY3053 ) @ ( c_Set_Oinsert @ SV119 @ SY3054 @ SY3053 ) @ ( tc_fun @ SY3053 @ tc_bool ) )
| ~ ( c_lessequals @ SY3052 @ SY3054 @ ( tc_fun @ SY3053 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2644,plain,
! [SV120: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV120 @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV120 @ tc_bool ) ) @ ( tc_fun @ SV120 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV120 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2645,plain,
! [SV121: $i] :
( ( ~ ( class_Orderings_Oorder @ SV121 )
| ! [SY3055: $i,SY3056: $i] :
( ( c_HOL_Oord__class_Oless @ SY3055 @ SY3056 @ SV121 )
| ( SY3056 = SY3055 )
| ~ ( c_lessequals @ SY3055 @ SY3056 @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2646,plain,
! [SV122: $i] :
( ( ~ ( class_Orderings_Oorder @ SV122 )
| ! [SY3057: $i,SY3058: $i] :
( ( c_HOL_Oord__class_Oless @ SY3057 @ SY3058 @ SV122 )
| ~ ( c_lessequals @ SY3057 @ SY3058 @ SV122 )
| ( SY3058 = SY3057 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2647,plain,
! [SV123: $i] :
( ( ! [SY3059: $i,SY3060: $i] :
( ( c_HOL_Oord__class_Oless @ SV123 @ SY3059 @ ( tc_fun @ SY3060 @ tc_bool ) )
| ( SV123 = SY3059 )
| ~ ( c_lessequals @ SV123 @ SY3059 @ ( tc_fun @ SY3060 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2648,plain,
! [SV124: $i] :
( ( ~ ( class_Orderings_Oorder @ SV124 )
| ! [SY3061: $i,SY3062: $i] :
( ( SY3061 = SY3062 )
| ( c_HOL_Oord__class_Oless @ SY3061 @ SY3062 @ SV124 )
| ~ ( c_lessequals @ SY3061 @ SY3062 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2649,plain,
! [SV125: $i] :
( ( ~ ( class_Orderings_Oorder @ SV125 )
| ! [SY3063: $i,SY3064: $i] :
( ( c_HOL_Oord__class_Oless @ SY3063 @ SY3064 @ SV125 )
| ( SY3063 = SY3064 )
| ~ ( c_lessequals @ SY3063 @ SY3064 @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2650,plain,
! [SV126: $i] :
( ( ! [SY3065: $i] :
( ( SV126 = SY3065 )
| ! [SY3066: $i] :
( ( c_HOL_Oord__class_Oless @ SV126 @ SY3065 @ ( tc_fun @ SY3066 @ tc_bool ) )
| ~ ( c_lessequals @ SV126 @ SY3065 @ ( tc_fun @ SY3066 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2651,plain,
! [SV127: $i] :
( ( ~ ( class_Orderings_Oorder @ SV127 )
| ! [SY3067: $i,SY3068: $i] :
( ( c_HOL_Oord__class_Oless @ SY3067 @ SY3068 @ SV127 )
| ( SY3067 = SY3068 )
| ~ ( c_lessequals @ SY3067 @ SY3068 @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2652,plain,
! [SV128: $i] :
( ( ~ ( class_Orderings_Oorder @ SV128 )
| ! [SY3069: $i,SY3070: $i] :
( ( c_HOL_Oord__class_Oless @ SY3069 @ SY3070 @ SV128 )
| ~ ( c_lessequals @ SY3069 @ SY3070 @ SV128 )
| ( SY3069 = SY3070 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2653,plain,
! [SV129: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV129 )
| ! [SY3071: $i,SY3072: $i] :
( ( SY3071 = SY3072 )
| ~ ( c_lessequals @ SY3071 @ SY3072 @ SV129 )
| ( c_HOL_Oord__class_Oless @ SY3071 @ SY3072 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2654,plain,
! [SV130: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV130 )
| ! [SY3073: $i,SY3074: $i] :
( ( SY3073 = SY3074 )
| ( c_HOL_Oord__class_Oless @ SY3073 @ SY3074 @ SV130 )
| ~ ( c_lessequals @ SY3073 @ SY3074 @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(2655,plain,
! [SV131: $i] :
( ( ! [SY3075: $i,SY3076: $i,SY3077: $i,SY3078: $i,SY3079: $i,SY3080: $i] :
( ( ( c_Fun_Ofun__upd @ SV131 @ SY3075 @ ( c_Option_Ooption_OSome @ SY3076 @ SY3077 ) @ SY3078 @ ( tc_Option_Ooption @ SY3077 ) )
!= ( c_Fun_Ofun__upd @ SY3079 @ SY3075 @ ( c_Option_Ooption_OSome @ SY3080 @ SY3077 ) @ SY3078 @ ( tc_Option_Ooption @ SY3077 ) ) )
| ( SY3076 = SY3080 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2656,plain,
! [SV132: $i] :
( ( ! [SY3081: $i,SY3082: $i,SY3083: $i,SY3084: $i] :
( ( c_Set_Oimage @ SV132 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3081 @ SY3082 @ ( tc_fun @ SY3083 @ tc_bool ) ) @ SY3083 @ SY3084 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ SV132 @ SY3081 @ SY3083 @ SY3084 ) @ ( c_Set_Oimage @ SV132 @ SY3082 @ SY3083 @ SY3084 ) @ ( tc_fun @ SY3084 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2657,plain,
! [SV133: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV133 )
| ! [SY3085: $i,SY3086: $i] :
( ( c_lessequals @ SY3085 @ SY3086 @ SV133 )
| ( c_lessequals @ SY3086 @ SY3085 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2658,plain,
! [SV134: $i] :
( ( ! [SY3087: $i,SY3088: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV134 )
| ! [SY3089: $i,SY3090: $i] :
( ( ( c_Finite__Set_Osetsum @ SY3087 @ ( c_HOL_Ominus__class_Ominus @ SY3088 @ SY3089 @ ( tc_fun @ SY3090 @ tc_bool ) ) @ SY3090 @ SV134 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SY3087 @ SY3088 @ SY3090 @ SV134 ) @ ( c_Finite__Set_Osetsum @ SY3087 @ SY3089 @ SY3090 @ SV134 ) @ SV134 ) )
| ~ ( c_lessequals @ SY3089 @ SY3088 @ ( tc_fun @ SY3090 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY3088 @ SY3090 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2659,plain,
! [SV135: $i] :
( ( ! [SY3091: $i,SY3092: $i,SY3093: $i] :
( ( ( c_Finite__Set_Ocard @ SV135 @ SY3091 )
= ( c_Finite__Set_Ocard @ SY3092 @ SY3093 ) )
| ~ ( c_Finite__Set_Ofinite @ SY3092 @ SY3093 )
| ~ ( c_Finite__Set_Ofinite @ SV135 @ SY3091 )
| ! [SY3094: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ SY3094 @ SY3092 @ SY3093 @ SY3091 ) @ SV135 @ ( tc_fun @ SY3091 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY3094 @ SY3092 @ SY3093 @ SY3091 )
| ! [SY3095: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ SY3095 @ SV135 @ SY3091 @ SY3093 ) @ SY3092 @ ( tc_fun @ SY3093 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY3095 @ SV135 @ SY3091 @ SY3093 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2660,plain,
! [SV136: $i] :
( ( ! [SY3096: $i,SY3097: $i,SY3098: $i,SY3099: $i,SY3100: $i,SY3101: $i] :
( ( c_Finite__Set_Ofold__graph @ SV136 @ SY3096 @ ( c_Set_Oinsert @ SY3097 @ SY3098 @ SY3099 ) @ ( hAPP @ ( hAPP @ SV136 @ SY3097 ) @ SY3100 ) @ SY3099 @ SY3101 )
| ~ ( c_Finite__Set_Ofold__graph @ SV136 @ SY3096 @ SY3098 @ SY3100 @ SY3099 @ SY3101 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3099 ) @ SY3097 ) @ SY3098 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2661,plain,
! [SV137: $i] :
( ( ! [SY3102: $i,SY3103: $i] :
( ( c_lessequals @ SV137 @ SY3102 @ ( tc_fun @ SY3103 @ tc_bool ) )
| ! [SY3104: $i] :
( ~ ( c_lessequals @ SV137 @ ( c_Set_Oinsert @ SY3104 @ SY3102 @ SY3103 ) @ ( tc_fun @ SY3103 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3103 ) @ SY3104 ) @ SV137 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2662,plain,
! [SV138: $i] :
( ( ! [SY3105: $i,SY3106: $i,SY3107: $i] :
( ( c_lessequals @ SV138 @ ( c_Set_Oinsert @ SY3105 @ SY3106 @ SY3107 ) @ ( tc_fun @ SY3107 @ tc_bool ) )
| ~ ( c_lessequals @ SV138 @ SY3106 @ ( tc_fun @ SY3107 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3107 ) @ SY3105 ) @ SV138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(2663,plain,
! [SV139: $i] :
( ( ! [SY3108: $i,SY3109: $i] :
( ( c_lessequals @ SV139 @ SY3108 @ ( tc_fun @ SY3109 @ tc_bool ) )
| ! [SY3110: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3109 ) @ SY3110 ) @ SV139 ) )
| ~ ( c_lessequals @ SV139 @ ( c_Set_Oinsert @ SY3110 @ SY3108 @ SY3109 ) @ ( tc_fun @ SY3109 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2664,plain,
! [SV140: $i] :
( ( ! [SY3111: $i,SY3112: $i,SY3113: $i] :
( ( c_lessequals @ SV140 @ ( c_Set_Oinsert @ SY3111 @ SY3112 @ SY3113 ) @ ( tc_fun @ SY3113 @ tc_bool ) )
| ~ ( c_lessequals @ SV140 @ SY3112 @ ( tc_fun @ SY3113 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3113 ) @ SY3111 ) @ SV140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2665,plain,
! [SV141: $i] :
( ( ! [SY3114: $i,SY3115: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV141 ) @ SY3114 ) @ SY3115 ) )
| ! [SY3116: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SY3114 @ SY3116 @ SV141 ) @ SY3115 @ ( tc_fun @ SV141 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2666,plain,
! [SV142: $i] :
( ( ! [SY3117: $i,SY3118: $i,SY3119: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV142 @ SY3117 @ SY3118 ) @ SY3119 @ ( tc_fun @ SY3118 @ tc_bool ) )
| ~ ( c_lessequals @ SY3117 @ SY3119 @ ( tc_fun @ SY3118 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3118 ) @ SV142 ) @ SY3119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2667,plain,
! [SV143: $i] :
( ( ! [SY3120: $i,SY3121: $i,SY3122: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV143 ) @ ( hAPP @ SY3120 @ SY3121 ) ) @ SY3122 ) )
| ! [SY3123: $i,SY3124: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3123 ) @ SY3121 ) @ SY3124 ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SY3120 @ SY3124 @ SY3123 @ SV143 ) @ SY3122 @ ( tc_fun @ SV143 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(2668,plain,
! [SV144: $i] :
( ( ! [SY3125: $i,SY3126: $i,SY3127: $i,SY3128: $i,SY3129: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ SV144 @ SY3125 @ SY3126 @ SY3127 @ SY3128 ) @ SY3129 @ SY3127 @ SY3128 )
= ( c_Set_Oimage @ SV144 @ SY3129 @ SY3127 @ SY3128 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3127 ) @ SY3125 ) @ SY3129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2669,plain,
! [SV145: $i] :
( ( ! [SY3130: $i,SY3131: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV145 )
| ! [SY3132: $i,SY3133: $i] :
( ( c_lessequals @ ( hAPP @ SY3130 @ SY3131 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3132 @ SY3130 @ SY3133 @ SV145 ) @ SV145 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3133 ) @ SY3131 ) @ SY3132 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2670,plain,
! [SV146: $i] :
( ( ! [SY3134: $i,SY3135: $i,SY3136: $i] :
( ! [SY3137: $i] : ( c_lessequals @ ( hAPP @ SV146 @ SY3134 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3135 @ SV146 @ SY3136 @ ( tc_fun @ SY3137 @ tc_bool ) ) @ ( tc_fun @ SY3137 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3136 ) @ SY3134 ) @ SY3135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1969]) ).
thf(2671,plain,
! [SV147: $i] :
( ( ! [SY3138: $i,SY3139: $i,SY3140: $i] :
( ( c_lessequals @ ( hAPP @ SV147 @ SY3138 ) @ SY3139 @ ( tc_fun @ SY3140 @ tc_bool ) )
| ! [SY3141: $i,SY3142: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3141 ) @ SY3138 ) @ SY3142 ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3142 @ SV147 @ SY3141 @ ( tc_fun @ SY3140 @ tc_bool ) ) @ SY3139 @ ( tc_fun @ SY3140 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2672,plain,
! [SV148: $i] :
( ( ! [SY3143: $i,SY3144: $i,SY3145: $i] :
( ! [SY3146: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV148 @ SY3143 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3144 @ SV148 @ SY3145 @ ( tc_fun @ SY3146 @ tc_bool ) ) @ ( tc_fun @ SY3146 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3144 @ SV148 @ SY3145 @ ( tc_fun @ SY3146 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3145 ) @ SY3143 ) @ SY3144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2673,plain,
! [SV149: $i] :
( ( ! [SY3147: $i,SY3148: $i] :
( ( c_Set_Oinsert @ SV149 @ SY3147 @ SY3148 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV149 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3148 @ tc_bool ) ) @ SY3148 ) @ SY3147 @ ( tc_fun @ SY3148 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2674,plain,
! [SV150: $i] :
( ( ! [SY3149: $i,SY3150: $i] :
( ( SV150
= ( c_Set_Oinsert @ SY3149 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3150 @ tc_bool ) ) @ SY3150 ) )
| ( SV150
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3150 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV150 @ ( c_Set_Oinsert @ SY3149 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3150 @ tc_bool ) ) @ SY3150 ) @ ( tc_fun @ SY3150 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2675,plain,
! [SV151: $i] :
( ( ! [SY3151: $i,SY3152: $i] :
( ( c_Finite__Set_Ofinite @ SV151 @ SY3151 )
| ! [SY3153: $i,SY3154: $i] :
( ~ ( c_lessequals @ SV151 @ ( c_Set_Oimage @ SY3152 @ SY3153 @ SY3154 @ SY3151 ) @ ( tc_fun @ SY3151 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY3153 @ SY3154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2676,plain,
! [SV152: $i] :
( ( ! [SY3155: $i,SY3156: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ SV152 @ SY3155 @ SY3156 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3156 @ tc_bool ) ) @ SY3156 @ SY3155 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3155 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2677,plain,
! [SV153: $i] :
( ( ! [SY3157: $i,SY3158: $i] :
( ( c_lessequals @ SV153 @ SY3157 @ ( tc_fun @ SY3158 @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ SY3158 ) @ SY3158 @ ( tc_fun @ SY3158 @ tc_bool ) @ tc_bool ) @ SV153 ) @ ( hAPP @ ( c_COMBC @ ( c_in @ SY3158 ) @ SY3158 @ ( tc_fun @ SY3158 @ tc_bool ) @ tc_bool ) @ SY3157 ) @ ( tc_fun @ SY3158 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2678,plain,
! [SV154: $i] :
( ( ! [SY3159: $i,SY3160: $i] :
( ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ SV154 ) @ SV154 @ ( tc_fun @ SV154 @ tc_bool ) @ tc_bool ) @ SY3159 ) @ ( hAPP @ ( c_COMBC @ ( c_in @ SV154 ) @ SV154 @ ( tc_fun @ SV154 @ tc_bool ) @ tc_bool ) @ SY3160 ) @ ( tc_fun @ SV154 @ tc_bool ) )
| ~ ( c_lessequals @ SY3159 @ SY3160 @ ( tc_fun @ SV154 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2679,plain,
! [SV155: $i] :
( ( ! [SY3161: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV155 )
| ! [SY3162: $i,SY3163: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3161 @ ( c_COMBK @ SY3162 @ SV155 @ SY3163 ) @ SY3163 @ SV155 )
= SY3162 )
| ( SY3161
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3163 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2680,plain,
! [SV156: $i] :
( ( ! [SY3164: $i,SY3165: $i,SY3166: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV156 @ tc_bool ) ) @ SY3164 @ SV156 @ ( tc_fun @ SY3165 @ tc_bool ) ) @ SY3166 @ ( tc_fun @ SY3165 @ tc_bool ) )
= SY3166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2681,plain,
! [SV157: $i] :
( ( ! [SY3167: $i,SY3168: $i,SY3169: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV157 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3167 @ tc_bool ) ) @ SY3168 @ SY3167 @ ( tc_fun @ SY3169 @ tc_bool ) ) @ ( tc_fun @ SY3169 @ tc_bool ) )
= SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2682,plain,
! [SV158: $i] :
( ( ! [SY3170: $i,SY3171: $i,SY3172: $i,SY3173: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ SV158 @ SY3170 @ SY3171 ) @ SY3172 @ SY3171 @ ( tc_fun @ SY3173 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SY3172 @ SV158 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3170 @ SY3172 @ SY3171 @ ( tc_fun @ SY3173 @ tc_bool ) ) @ ( tc_fun @ SY3173 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2683,plain,
! [SV159: $i] :
( ( ! [SY3174: $i,SY3175: $i,SY3176: $i,SY3177: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV159 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3174 @ SY3175 @ ( tc_fun @ SY3176 @ tc_bool ) ) @ SY3176 @ SY3177 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV159 @ SY3174 @ SY3176 @ SY3177 ) @ ( c_Set_Oimage @ SV159 @ SY3175 @ SY3176 @ SY3177 ) @ ( tc_fun @ SY3177 @ tc_bool ) ) @ ( tc_fun @ SY3177 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2684,plain,
! [SV160: $i] :
( ( ! [SY3178: $i,SY3179: $i,SY3180: $i,SY3181: $i,SY3182: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV160 @ ( c_COMBB @ SY3178 @ SY3179 @ SY3180 @ ( tc_fun @ SY3181 @ tc_bool ) @ SY3182 ) @ SY3182 @ ( tc_fun @ SY3181 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oimage @ SY3179 @ SV160 @ SY3182 @ SY3180 ) @ SY3178 @ SY3180 @ ( tc_fun @ SY3181 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2685,plain,
! [SV161: $i] :
( ( ! [SY3183: $i,SY3184: $i,SY3185: $i,SY3186: $i,SY3187: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oimage @ SV161 @ SY3183 @ SY3184 @ SY3185 ) @ SY3186 @ SY3185 @ ( tc_fun @ SY3187 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3183 @ ( c_COMBB @ SY3186 @ SV161 @ SY3185 @ ( tc_fun @ SY3187 @ tc_bool ) @ SY3184 ) @ SY3184 @ ( tc_fun @ SY3187 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1984]) ).
thf(2686,plain,
! [SV162: $i] :
( ( ! [SY3188: $i,SY3189: $i,SY3190: $i,SY3191: $i] :
( ( ( c_Set_Oimage @ SV162 @ SY3188 @ SY3189 @ SY3190 )
!= ( c_Set_Oimage @ SV162 @ SY3191 @ SY3189 @ SY3190 ) )
| ~ ( c_Fun_Oinj__on @ SV162 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3188 @ SY3191 @ ( tc_fun @ SY3189 @ tc_bool ) ) @ SY3189 @ SY3190 )
| ( SY3188 = SY3191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(2687,plain,
! [SV163: $i] :
( ( ! [SY3192: $i,SY3193: $i,SY3194: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ SV163 @ SY3192 @ SY3193 @ SY3194 ) @ SY3194 )
= ( c_Finite__Set_Ocard @ SY3192 @ SY3193 ) )
| ~ ( c_Fun_Oinj__on @ SV163 @ SY3192 @ SY3193 @ SY3194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2688,plain,
! [SV164: $i] :
( ( ! [SY3195: $i,SY3196: $i,SY3197: $i,SY3198: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV164 @ SY3195 @ SY3196 @ SY3197 ) @ ( c_Set_Oimage @ SV164 @ SY3198 @ SY3196 @ SY3197 ) @ ( tc_fun @ SY3197 @ tc_bool ) ) @ ( c_Set_Oimage @ SV164 @ ( c_HOL_Ominus__class_Ominus @ SY3195 @ SY3198 @ ( tc_fun @ SY3196 @ tc_bool ) ) @ SY3196 @ SY3197 ) @ ( tc_fun @ SY3197 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2689,plain,
! [SV165: $i] :
( ( ! [SY3199: $i,SY3200: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV165 @ SY3199 @ ( tc_fun @ SY3200 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 @ SY3199 @ ( tc_fun @ SY3200 @ tc_bool ) ) @ ( tc_fun @ SY3200 @ tc_bool ) )
= SV165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1988]) ).
thf(2690,plain,
! [SV166: $i] :
( ( ! [SY3201: $i,SY3202: $i,SY3203: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV166 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3201 @ SY3202 @ ( tc_fun @ SY3203 @ tc_bool ) ) @ ( tc_fun @ SY3203 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ SV166 @ SY3201 @ ( tc_fun @ SY3203 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV166 @ SY3202 @ ( tc_fun @ SY3203 @ tc_bool ) ) @ ( tc_fun @ SY3203 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2691,plain,
! [SV167: $i] :
( ( ! [SY3204: $i,SY3205: $i,SY3206: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV167 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3204 @ SY3205 @ ( tc_fun @ SY3206 @ tc_bool ) ) @ ( tc_fun @ SY3206 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV167 @ SY3204 @ ( tc_fun @ SY3206 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV167 @ SY3205 @ ( tc_fun @ SY3206 @ tc_bool ) ) @ ( tc_fun @ SY3206 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1990]) ).
thf(2692,plain,
! [SV168: $i] :
( ( ! [SY3207: $i,SY3208: $i,SY3209: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV168 @ ( c_Set_Ovimage @ SV168 @ SY3207 @ SY3208 @ SY3209 ) @ SY3208 @ SY3209 ) @ SY3207 @ ( tc_fun @ SY3209 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2693,plain,
! [SV169: $i] :
( ( ! [SY3210: $i,SY3211: $i,SY3212: $i,SY3213: $i,SY3214: $i] :
( ( c_Map_Omap__add @ SV169 @ ( c_Fun_Ofun__upd @ SY3210 @ SY3211 @ ( c_Option_Ooption_OSome @ SY3212 @ SY3213 ) @ SY3214 @ ( tc_Option_Ooption @ SY3213 ) ) @ SY3214 @ SY3213 )
= ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ SV169 @ SY3210 @ SY3214 @ SY3213 ) @ SY3211 @ ( c_Option_Ooption_OSome @ SY3212 @ SY3213 ) @ SY3214 @ ( tc_Option_Ooption @ SY3213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2694,plain,
! [SV170: $i] :
( ( ! [SY3215: $i,SY3216: $i,SY3217: $i] :
( ( c_Map_Odom @ ( c_Map_Omap__add @ SV170 @ SY3215 @ SY3216 @ SY3217 ) @ SY3216 @ SY3217 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Map_Odom @ SY3215 @ SY3216 @ SY3217 ) @ ( c_Map_Odom @ SV170 @ SY3216 @ SY3217 ) @ ( tc_fun @ SY3216 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2695,plain,
! [SV171: $i] :
( ( ! [SY3218: $i,SY3219: $i,SY3220: $i] : ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ SV171 @ SY3218 @ ( c_Option_Ooption_ONone @ SY3219 ) @ SY3220 @ ( tc_Option_Ooption @ SY3219 ) ) @ SV171 @ SY3220 @ SY3219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1994]) ).
thf(2696,plain,
! [SV172: $i] :
( ( ! [SY3221: $i,SY3222: $i,SY3223: $i] :
( ( c_lessequals @ ( c_Map_Odom @ SV172 @ SY3221 @ SY3222 ) @ ( c_Map_Odom @ SY3223 @ SY3221 @ SY3222 ) @ ( tc_fun @ SY3221 @ tc_bool ) )
| ~ ( c_Map_Omap__le @ SV172 @ SY3223 @ SY3221 @ SY3222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2697,plain,
! [SV173: $i] :
( ( ! [SY3224: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV173 @ SV173 @ ( tc_fun @ SY3224 @ tc_bool ) )
= SV173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2698,plain,
! [SV174: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV174 )
| ! [SY3225: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3225 @ SY3225 @ SV174 )
= SY3225 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2699,plain,
! [SV175: $i] :
( ( ! [SY3226: $i,SY3227: $i,SY3228: $i,SY3229: $i,SY3230: $i] :
( ( hAPP @ ( c_COMBB @ SV175 @ SY3226 @ SY3227 @ SY3228 @ SY3229 ) @ SY3230 )
= ( hAPP @ SV175 @ ( hAPP @ SY3226 @ SY3230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2700,plain,
! [SV176: $i] :
( ( ! [SY3231: $i,SY3232: $i,SY3233: $i] :
( ( hAPP @ ( c_COMBK @ SV176 @ SY3231 @ SY3232 ) @ SY3233 )
= SV176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2701,plain,
! [SV177: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV177 )
| ! [SY3234: $i,SY3235: $i] :
( ( c_HOL_Oord__class_Oless @ SY3234 @ SY3235 @ SV177 )
| ( c_lessequals @ SY3235 @ SY3234 @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2702,plain,
! [SV178: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV178 )
| ! [SY3236: $i] :
( ~ ( c_lessequals @ SY3236 @ SY3236 @ SV178 )
| ~ ( c_HOL_Oord__class_Oless @ SY3236 @ SY3236 @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(2703,plain,
! [SV179: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV179 )
| ! [SY3237: $i] :
( ( c_HOL_Oord__class_Oless @ SY3237 @ SY3237 @ SV179 )
| ( c_lessequals @ SY3237 @ SY3237 @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2704,plain,
! [SV180: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV180 )
| ! [SY3238: $i,SY3239: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY3238 @ SY3239 @ SV180 )
| ~ ( c_lessequals @ SY3239 @ SY3238 @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2705,plain,
! [SV181: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV181 )
| ! [SY3240: $i,SY3241: $i] :
( ( c_HOL_Oord__class_Oless @ SY3241 @ SY3240 @ SV181 )
| ( c_lessequals @ SY3240 @ SY3241 @ SV181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2706,plain,
! [SV182: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV182 )
| ! [SY3242: $i,SY3243: $i] :
( ~ ( c_lessequals @ SY3242 @ SY3243 @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ SY3243 @ SY3242 @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2707,plain,
! [SV183: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV183 )
| ! [SY3244: $i,SY3245: $i] :
( ( c_HOL_Oord__class_Oless @ SY3244 @ SY3245 @ SV183 )
| ( c_lessequals @ SY3245 @ SY3244 @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2708,plain,
! [SV184: $i] :
( ( ! [SY3246: $i] :
( ~ ( class_HOL_Oord @ SV184 )
| ! [SY3247: $i,SY3248: $i] :
( ~ ( c_lessequals @ SY3246 @ SY3247 @ ( tc_fun @ SY3248 @ SV184 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3247 @ SY3246 @ ( tc_fun @ SY3248 @ SV184 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2709,plain,
! [SV185: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV185 )
| ! [SY3249: $i,SY3250: $i] :
( ~ ( c_lessequals @ SY3249 @ SY3250 @ SV185 )
| ~ ( c_HOL_Oord__class_Oless @ SY3250 @ SY3249 @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2710,plain,
! [SV186: $i] :
( ( ! [SY3251: $i,SY3252: $i,SY3253: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV186 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3251 @ SY3252 @ ( tc_fun @ SY3253 @ tc_bool ) ) @ ( tc_fun @ SY3253 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3251 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV186 @ SY3252 @ ( tc_fun @ SY3253 @ tc_bool ) ) @ ( tc_fun @ SY3253 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2009]) ).
thf(2711,plain,
! [SV187: $i] :
( ( ! [SY3254: $i,SY3255: $i,SY3256: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV187 @ SY3254 @ ( tc_fun @ SY3255 @ tc_bool ) ) @ SY3256 @ ( tc_fun @ SY3255 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV187 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3254 @ SY3256 @ ( tc_fun @ SY3255 @ tc_bool ) ) @ ( tc_fun @ SY3255 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2010]) ).
thf(2712,plain,
! [SV188: $i] :
( ( ! [SY3257: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV188 )
| ! [SY3258: $i,SY3259: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3257 @ SY3258 @ SV188 ) @ SY3259 @ SV188 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3257 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3258 @ SY3259 @ SV188 ) @ SV188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2011]) ).
thf(2713,plain,
! [SV189: $i] :
( ( ! [SY3260: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV189 )
| ! [SY3261: $i,SY3262: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3260 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3261 @ SY3262 @ SV189 ) @ SV189 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3261 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3260 @ SY3262 @ SV189 ) @ SV189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2714,plain,
! [SV190: $i] :
( ( ! [SY3263: $i] :
( ~ ( class_Lattices_Olattice @ SV190 )
| ! [SY3264: $i,SY3265: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3263 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3264 @ SY3265 @ SV190 ) @ SV190 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3264 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3263 @ SY3265 @ SV190 ) @ SV190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2715,plain,
! [SV191: $i] :
( ( ! [SY3266: $i] :
( ~ ( class_Lattices_Olattice @ SV191 )
| ! [SY3267: $i,SY3268: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3266 @ SY3267 @ SV191 ) @ SY3268 @ SV191 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3266 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3267 @ SY3268 @ SV191 ) @ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2716,plain,
! [SV192: $i] :
( ( ! [SY3269: $i,SY3270: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV192 @ SY3269 @ ( tc_fun @ SY3270 @ tc_bool ) )
= SV192 )
| ~ ( c_lessequals @ SV192 @ SY3269 @ ( tc_fun @ SY3270 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2015]) ).
thf(2717,plain,
! [SV193: $i] :
( ( ! [SY3271: $i,SY3272: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV193 @ SY3271 @ ( tc_fun @ SY3272 @ tc_bool ) )
= SY3271 )
| ~ ( c_lessequals @ SY3271 @ SV193 @ ( tc_fun @ SY3272 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(2718,plain,
! [SV194: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV194 )
| ! [SY3273: $i,SY3274: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3273 @ SY3274 @ SV194 )
= SY3273 )
| ~ ( c_lessequals @ SY3273 @ SY3274 @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2017]) ).
thf(2719,plain,
! [SV195: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV195 )
| ! [SY3275: $i,SY3276: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3275 @ SY3276 @ SV195 )
!= SY3275 )
| ( c_lessequals @ SY3275 @ SY3276 @ SV195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2018]) ).
thf(2720,plain,
! [SV196: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV196 )
| ! [SY3277: $i,SY3278: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3277 @ SY3278 @ SV196 )
= SY3278 )
| ~ ( c_lessequals @ SY3278 @ SY3277 @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2721,plain,
! [SV197: $i] :
( ( ! [SY3279: $i,SY3280: $i,SY3281: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV197 @ SY3279 @ ( tc_fun @ SY3280 @ tc_bool ) ) @ SY3281 @ ( tc_fun @ SY3280 @ tc_bool ) )
| ~ ( c_lessequals @ SY3279 @ SY3281 @ ( tc_fun @ SY3280 @ tc_bool ) )
| ~ ( c_lessequals @ SV197 @ SY3281 @ ( tc_fun @ SY3280 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2722,plain,
! [SV198: $i] :
( ( ! [SY3282: $i,SY3283: $i] : ( c_lessequals @ SV198 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3282 @ SV198 @ ( tc_fun @ SY3283 @ tc_bool ) ) @ ( tc_fun @ SY3283 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2723,plain,
! [SV199: $i] :
( ( ! [SY3284: $i,SY3285: $i] : ( c_lessequals @ SV199 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV199 @ SY3284 @ ( tc_fun @ SY3285 @ tc_bool ) ) @ ( tc_fun @ SY3285 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2724,plain,
! [SV200: $i] :
( ( ! [SY3286: $i,SY3287: $i,SY3288: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ SY3286 @ ( tc_fun @ SY3287 @ tc_bool ) ) @ SY3288 @ ( tc_fun @ SY3287 @ tc_bool ) )
| ~ ( c_lessequals @ SY3286 @ SY3288 @ ( tc_fun @ SY3287 @ tc_bool ) )
| ~ ( c_lessequals @ SV200 @ SY3288 @ ( tc_fun @ SY3287 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2725,plain,
! [SV201: $i] :
( ( ! [SY3289: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV201 )
| ! [SY3290: $i,SY3291: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3289 @ SY3290 @ SV201 ) @ SY3291 @ SV201 )
| ~ ( c_lessequals @ SY3290 @ SY3291 @ SV201 )
| ~ ( c_lessequals @ SY3289 @ SY3291 @ SV201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2726,plain,
! [SV202: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV202 )
| ! [SY3292: $i,SY3293: $i] : ( c_lessequals @ SY3292 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3292 @ SY3293 @ SV202 ) @ SV202 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2727,plain,
! [SV203: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV203 )
| ! [SY3294: $i,SY3295: $i] : ( c_lessequals @ SY3294 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3295 @ SY3294 @ SV203 ) @ SV203 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2728,plain,
! [SV204: $i] :
( ( ! [SY3296: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV204 )
| ! [SY3297: $i,SY3298: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3296 @ SY3297 @ SV204 ) @ SY3298 @ SV204 )
| ~ ( c_lessequals @ SY3297 @ SY3298 @ SV204 )
| ~ ( c_lessequals @ SY3296 @ SY3298 @ SV204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2729,plain,
! [SV205: $i] :
( ( ! [SY3299: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV205 )
| ! [SY3300: $i,SY3301: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3299 @ SY3300 @ SV205 ) @ SY3301 @ SV205 )
| ~ ( c_lessequals @ SY3300 @ SY3301 @ SV205 )
| ~ ( c_lessequals @ SY3299 @ SY3301 @ SV205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2730,plain,
! [SV206: $i] :
( ( ~ ( class_Lattices_Olattice @ SV206 )
| ! [SY3302: $i,SY3303: $i] : ( c_lessequals @ SY3302 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3303 @ SY3302 @ SV206 ) @ SV206 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2731,plain,
! [SV207: $i] :
( ( ~ ( class_Lattices_Olattice @ SV207 )
| ! [SY3304: $i,SY3305: $i] : ( c_lessequals @ SY3304 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3304 @ SY3305 @ SV207 ) @ SV207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2030]) ).
thf(2732,plain,
! [SV208: $i] :
( ( ! [SY3306: $i,SY3307: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV208 @ ( c_HOL_Ominus__class_Ominus @ SY3306 @ SV208 @ ( tc_fun @ SY3307 @ tc_bool ) ) @ ( tc_fun @ SY3307 @ tc_bool ) )
= SY3306 )
| ~ ( c_lessequals @ SV208 @ SY3306 @ ( tc_fun @ SY3307 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(2733,plain,
! [SV209: $i] :
( ( ! [SY3308: $i] :
( ~ ( class_Lattices_Olattice @ SV209 )
| ! [SY3309: $i,SY3310: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3308 @ SY3309 @ SV209 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3308 @ SY3310 @ SV209 ) @ SV209 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3308 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3309 @ SY3310 @ SV209 ) @ SV209 ) @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2734,plain,
! [SV210: $i] :
( ( ! [SY3311: $i,SY3312: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV210 @ SY3311 @ ( tc_fun @ SY3312 @ tc_bool ) ) @ SV210 @ ( tc_fun @ SY3312 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2735,plain,
! [SV211: $i] :
( ( ! [SY3313: $i,SY3314: $i,SY3315: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV211 @ SY3313 @ ( tc_fun @ SY3314 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3313 @ SY3315 @ ( tc_fun @ SY3314 @ tc_bool ) ) @ ( tc_fun @ SY3314 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3315 @ SV211 @ ( tc_fun @ SY3314 @ tc_bool ) ) @ ( tc_fun @ SY3314 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV211 @ SY3313 @ ( tc_fun @ SY3314 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3313 @ SY3315 @ ( tc_fun @ SY3314 @ tc_bool ) ) @ ( tc_fun @ SY3314 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3315 @ SV211 @ ( tc_fun @ SY3314 @ tc_bool ) ) @ ( tc_fun @ SY3314 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2034]) ).
thf(2736,plain,
! [SV212: $i] :
( ( ! [SY3316: $i,SY3317: $i,SY3318: $i] : ( c_Finite__Set_Ofold__graph @ SV212 @ SY3316 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3317 @ tc_bool ) ) @ SY3316 @ SY3317 @ SY3318 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2737,plain,
! [SV213: $i] :
( ( ! [SY3319: $i,SY3320: $i,SY3321: $i] : ( c_Nitpick_Ofold__graph_H @ SV213 @ SY3319 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3320 @ tc_bool ) ) @ SY3319 @ SY3320 @ SY3321 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(2738,plain,
! [SV214: $i] :
( ( ! [SY3322: $i,SY3323: $i,SY3324: $i,SY3325: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ SV214 @ SY3322 @ SY3323 @ SY3324 ) @ ( c_Set_Ovimage @ SV214 @ SY3325 @ SY3323 @ SY3324 ) @ ( tc_fun @ SY3323 @ tc_bool ) )
| ~ ( c_lessequals @ SY3322 @ SY3325 @ ( tc_fun @ SY3324 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2739,plain,
! [SV215: $i] :
( ( ! [SY3326: $i,SY3327: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV215 @ SY3326 @ ( tc_fun @ SY3327 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3327 @ tc_bool ) ) )
| ( SY3326
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3327 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2740,plain,
! [SV216: $i] :
( ( ! [SY3328: $i,SY3329: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV216 @ SY3328 @ ( tc_fun @ SY3329 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3329 @ tc_bool ) ) )
| ( SV216
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3329 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2741,plain,
! [SV217: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV217 )
| ! [SY3330: $i] :
( ! [SY3331: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3330 @ SY3331 @ SV217 )
!= ( c_Orderings_Obot__class_Obot @ SV217 ) )
| ( SY3330
= ( c_Orderings_Obot__class_Obot @ SV217 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2742,plain,
! [SV218: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV218 )
| ! [SY3332: $i,SY3333: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3332 @ SY3333 @ SV218 )
!= ( c_Orderings_Obot__class_Obot @ SV218 ) )
| ( SY3333
= ( c_Orderings_Obot__class_Obot @ SV218 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2743,plain,
! [SV219: $i] :
( ( ! [SY3334: $i,SY3335: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV219 @ SY3334 @ ( tc_fun @ SY3335 @ tc_bool ) ) @ SY3334 @ ( tc_fun @ SY3335 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV219 @ SY3334 @ ( tc_fun @ SY3335 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2744,plain,
! [SV220: $i] :
( ( ! [SY3336: $i,SY3337: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV220 @ ( c_HOL_Ominus__class_Ominus @ SY3336 @ SV220 @ ( tc_fun @ SY3337 @ tc_bool ) ) @ ( tc_fun @ SY3337 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV220 @ SY3336 @ ( tc_fun @ SY3337 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2745,plain,
! [SV221: $i] :
( ( ! [SY3338: $i,SY3339: $i] :
( ( c_lessequals @ SV221 @ SY3338 @ ( tc_fun @ SY3339 @ tc_bool ) )
| ! [SY3340: $i] :
~ ( c_lessequals @ SV221 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3340 @ SY3338 @ ( tc_fun @ SY3339 @ tc_bool ) ) @ ( tc_fun @ SY3339 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2746,plain,
! [SV222: $i] :
( ( ! [SY3341: $i,SY3342: $i] :
( ( c_lessequals @ SV222 @ SY3341 @ ( tc_fun @ SY3342 @ tc_bool ) )
| ! [SY3343: $i] :
~ ( c_lessequals @ SV222 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3341 @ SY3343 @ ( tc_fun @ SY3342 @ tc_bool ) ) @ ( tc_fun @ SY3342 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2747,plain,
! [SV223: $i] :
( ( ! [SY3344: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV223 )
| ! [SY3345: $i] :
( ( c_lessequals @ SY3344 @ SY3345 @ SV223 )
| ! [SY3346: $i] :
~ ( c_lessequals @ SY3344 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3345 @ SY3346 @ SV223 ) @ SV223 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2748,plain,
! [SV224: $i] :
( ( ! [SY3347: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV224 )
| ! [SY3348: $i] :
( ( c_lessequals @ SY3347 @ SY3348 @ SV224 )
| ! [SY3349: $i] :
~ ( c_lessequals @ SY3347 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3349 @ SY3348 @ SV224 ) @ SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2749,plain,
! [SV225: $i] :
( ( ! [SY3350: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV225 )
| ! [SY3351: $i,SY3352: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3350 @ SY3351 @ SV225 ) @ SY3352 @ SV225 )
| ~ ( c_lessequals @ SY3350 @ SY3352 @ SV225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2750,plain,
! [SV226: $i] :
( ( ! [SY3353: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV226 )
| ! [SY3354: $i,SY3355: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3353 @ SY3354 @ SV226 ) @ SY3355 @ SV226 )
| ~ ( c_lessequals @ SY3354 @ SY3355 @ SV226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2049]) ).
thf(2751,plain,
! [SV227: $i] :
( ( ! [SY3356: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV227 )
| ! [SY3357: $i] :
( ( c_lessequals @ SY3356 @ SY3357 @ SV227 )
| ! [SY3358: $i] :
~ ( c_lessequals @ SY3356 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3357 @ SY3358 @ SV227 ) @ SV227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2752,plain,
! [SV228: $i] :
( ( ! [SY3359: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV228 )
| ! [SY3360: $i] :
( ( c_lessequals @ SY3359 @ SY3360 @ SV228 )
| ! [SY3361: $i] :
~ ( c_lessequals @ SY3359 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3361 @ SY3360 @ SV228 ) @ SV228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2051]) ).
thf(2753,plain,
! [SV229: $i] :
( ( ! [SY3362: $i,SY3363: $i,SY3364: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV229 @ SY3362 @ ( tc_fun @ SY3363 @ tc_bool ) ) @ SY3364 @ ( tc_fun @ SY3363 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV229 @ SY3364 @ ( tc_fun @ SY3363 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY3362 @ SY3364 @ ( tc_fun @ SY3363 @ tc_bool ) ) @ ( tc_fun @ SY3363 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2754,plain,
! [SV230: $i] :
( ( ! [SY3365: $i,SY3366: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV230 @ SY3365 @ ( tc_fun @ SY3366 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3365 @ SV230 @ ( tc_fun @ SY3366 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2755,plain,
! [SV231: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV231 )
| ! [SY3367: $i,SY3368: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3367 @ SY3368 @ SV231 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3368 @ SY3367 @ SV231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(2756,plain,
! [SV232: $i] :
( ( ~ ( class_Lattices_Olattice @ SV232 )
| ! [SY3369: $i,SY3370: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3369 @ SY3370 @ SV232 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3370 @ SY3369 @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2055]) ).
thf(2757,plain,
! [SV233: $i] :
( ( ! [SY3371: $i,SY3372: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV233 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV233 @ SY3371 @ ( tc_fun @ SY3372 @ tc_bool ) ) @ ( tc_fun @ SY3372 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV233 @ SY3371 @ ( tc_fun @ SY3372 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2056]) ).
thf(2758,plain,
! [SV234: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV234 )
| ! [SY3373: $i,SY3374: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3373 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3373 @ SY3374 @ SV234 ) @ SV234 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3373 @ SY3374 @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2057]) ).
thf(2759,plain,
! [SV235: $i] :
( ( ~ ( class_Lattices_Olattice @ SV235 )
| ! [SY3375: $i,SY3376: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3375 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3375 @ SY3376 @ SV235 ) @ SV235 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3375 @ SY3376 @ SV235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2058]) ).
thf(2760,plain,
! [SV236: $i] :
( ( ! [SY3377: $i,SY3378: $i,SY3379: $i,SY3380: $i] :
( ( c_Set_Ovimage @ SV236 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3377 @ SY3378 @ ( tc_fun @ SY3379 @ tc_bool ) ) @ SY3380 @ SY3379 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ SV236 @ SY3377 @ SY3380 @ SY3379 ) @ ( c_Set_Ovimage @ SV236 @ SY3378 @ SY3380 @ SY3379 ) @ ( tc_fun @ SY3380 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2761,plain,
! [SV237: $i] :
( ( ! [SY3381: $i,SY3382: $i] :
( ! [SY3383: $i,SY3384: $i] :
( ( c_Fun_Ofun__upd @ SV237 @ SY3381 @ SY3382 @ SY3383 @ SY3384 )
!= SV237 )
| ( ( hAPP @ SV237 @ SY3381 )
= SY3382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2762,plain,
! [SV238: $i] :
( ( ! [SY3385: $i,SY3386: $i,SY3387: $i] :
( ( c_Fun_Oinj__on @ SV238 @ SY3385 @ SY3386 @ SY3387 )
| ! [SY3388: $i] :
~ ( c_Fun_Oinj__on @ SV238 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3388 @ SY3385 @ ( tc_fun @ SY3386 @ tc_bool ) ) @ SY3386 @ SY3387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2763,plain,
! [SV239: $i] :
( ( ! [SY3389: $i,SY3390: $i,SY3391: $i] :
( ( c_Fun_Oinj__on @ SV239 @ SY3389 @ SY3390 @ SY3391 )
| ! [SY3392: $i] :
~ ( c_Fun_Oinj__on @ SV239 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3389 @ SY3392 @ ( tc_fun @ SY3390 @ tc_bool ) ) @ SY3390 @ SY3391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2062]) ).
thf(2764,plain,
! [SV240: $i] :
( ( ! [SY3393: $i,SY3394: $i,SY3395: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV240 @ SY3393 @ ( tc_fun @ SY3394 @ tc_bool ) ) @ SY3395 @ ( tc_fun @ SY3394 @ tc_bool ) )
| ~ ( c_lessequals @ SV240 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3393 @ SY3395 @ ( tc_fun @ SY3394 @ tc_bool ) ) @ ( tc_fun @ SY3394 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2765,plain,
! [SV241: $i] :
( ( ! [SY3396: $i,SY3397: $i,SY3398: $i] :
( ( c_lessequals @ SV241 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3396 @ SY3397 @ ( tc_fun @ SY3398 @ tc_bool ) ) @ ( tc_fun @ SY3398 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV241 @ SY3396 @ ( tc_fun @ SY3398 @ tc_bool ) ) @ SY3397 @ ( tc_fun @ SY3398 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2064]) ).
thf(2766,plain,
! [SV242: $i] :
( ( ! [SY3399: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV242 )
| ! [SY3400: $i] :
( ! [SY3401: $i] : ( c_HOL_Oord__class_Oless @ SY3399 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3400 @ SY3401 @ SV242 ) @ SV242 )
| ~ ( c_HOL_Oord__class_Oless @ SY3399 @ SY3400 @ SV242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2767,plain,
! [SV243: $i] :
( ( ! [SY3402: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV243 )
| ! [SY3403: $i,SY3404: $i] :
( ( c_HOL_Oord__class_Oless @ SY3402 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3403 @ SY3404 @ SV243 ) @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ SY3402 @ SY3404 @ SV243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2768,plain,
! [SV244: $i] :
( ( ! [SY3405: $i,SY3406: $i] :
( ~ ( class_HOL_Oord @ SV244 )
| ! [SY3407: $i] :
( ( c_lessequals @ ( hAPP @ SY3405 @ SY3406 ) @ ( hAPP @ SY3407 @ SY3406 ) @ SV244 )
| ! [SY3408: $i] :
~ ( c_lessequals @ SY3405 @ SY3407 @ ( tc_fun @ SY3408 @ SV244 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2769,plain,
! [SV245: $i] :
( ( ! [SY3409: $i,SY3410: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV245 ) @ SY3409 ) @ SY3410 ) )
| ! [SY3411: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV245 ) @ SY3409 ) @ SY3411 ) )
| ~ ( c_lessequals @ SY3411 @ SY3410 @ ( tc_fun @ SV245 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2770,plain,
! [SV246: $i] :
( ( ! [SY3412: $i,SY3413: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV246 ) @ SY3412 ) @ SY3413 ) )
| ! [SY3414: $i] :
( ~ ( c_lessequals @ SY3414 @ SY3413 @ ( tc_fun @ SV246 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV246 ) @ SY3412 ) @ SY3414 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2771,plain,
! [SV247: $i] :
( ( ! [SY3415: $i,SY3416: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV247 ) @ SY3415 ) @ SY3416 ) )
| ! [SY3417: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV247 ) @ SY3415 ) @ SY3417 ) )
| ~ ( c_lessequals @ SY3417 @ SY3416 @ ( tc_fun @ SV247 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(2772,plain,
! [SV248: $i] :
( ( ! [SY3418: $i,SY3419: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV248 ) @ SY3418 ) @ SY3419 ) )
| ! [SY3420: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV248 ) @ SY3418 ) @ SY3420 ) )
| ~ ( c_lessequals @ SY3420 @ SY3419 @ ( tc_fun @ SV248 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2071]) ).
thf(2773,plain,
! [SV249: $i] :
( ( ! [SY3421: $i,SY3422: $i] :
( ! [SY3423: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV249 ) @ SY3421 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3422 @ SY3423 @ ( tc_fun @ SV249 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV249 ) @ SY3421 ) @ SY3422 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2774,plain,
! [SV250: $i] :
( ( ! [SY3424: $i,SY3425: $i,SY3426: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV250 ) @ SY3424 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3425 @ SY3426 @ ( tc_fun @ SV250 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV250 ) @ SY3424 ) @ SY3426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2775,plain,
! [SV251: $i] :
( ( ! [SY3427: $i,SY3428: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV251 ) @ SY3427 ) @ SY3428 ) )
| ! [SY3429: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV251 ) @ SY3427 ) @ SY3429 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV251 ) @ SY3427 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3429 @ SY3428 @ ( tc_fun @ SV251 @ tc_bool ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2776,plain,
! [SV252: $i] :
( ( ( c_Hoare__Mirabelle_OMGT @ SV252 )
= ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_fequal @ tc_Com_Ostate ) @ SV252 @ ( c_Natural_Oevalc @ SV252 ) @ tc_Com_Ostate ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2777,plain,
! [SV253: $i] :
( ( ! [SY3430: $i,SY3431: $i,SY3432: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV253 ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SY3430 @ SY3431 @ SY3432 @ SV253 ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3430 @ SY3431 @ ( tc_fun @ SV253 @ tc_bool ) ) ) )
| ! [SY3433: $i] :
( ~ ( hBOOL @ ( hAPP @ SY3432 @ SY3433 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV253 ) @ SY3433 ) @ SY3431 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2076]) ).
thf(2778,plain,
! [SV254: $i] :
( ( ! [SY3434: $i,SY3435: $i,SY3436: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV254 ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SY3434 @ SY3435 @ SY3436 @ SV254 ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3434 @ SY3435 @ ( tc_fun @ SV254 @ tc_bool ) ) ) )
| ! [SY3437: $i] :
( ~ ( hBOOL @ ( hAPP @ SY3436 @ SY3437 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV254 ) @ SY3437 ) @ SY3434 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2779,plain,
! [SV255: $i] :
( ( ! [SY3438: $i,SY3439: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ SV255 @ SY3438 @ SY3439 ) @ SY3439 )
= ( c_Finite__Set_Ocard @ SY3438 @ SY3439 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3439 ) @ SV255 ) @ SY3438 ) )
| ~ ( c_Finite__Set_Ofinite @ SY3438 @ SY3439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2780,plain,
! [SV256: $i] :
( ( ! [SY3440: $i,SY3441: $i,SY3442: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV256 @ SY3440 @ SY3441 ) @ SY3442 @ SY3441 @ SY3440 )
= ( c_Set_Oinsert @ SV256 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3440 @ tc_bool ) ) @ SY3440 ) )
| ( SY3442
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3441 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2079]) ).
thf(2781,plain,
! [SV257: $i] :
( ( ! [SY3443: $i,SY3444: $i,SY3445: $i,SY3446: $i,SY3447: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ofun__upd @ SV257 @ SY3443 @ SY3444 @ SY3445 @ SY3446 ) @ SY3447 @ SY3445 @ SY3446 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3446 ) @ SY3444 ) @ ( c_Set_Oimage @ SV257 @ SY3447 @ SY3445 @ SY3446 ) ) )
| ~ ( c_Fun_Oinj__on @ SV257 @ SY3447 @ SY3445 @ SY3446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(2782,plain,
! [SV258: $i] :
( ( ! [SY3448: $i,SY3449: $i] :
( ( c_Set_Oinsert @ SV258 @ SY3448 @ SY3449 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ SY3449 ) @ SY3449 @ SY3449 @ tc_bool ) @ SV258 ) @ SY3449 ) @ SY3448 @ ( tc_fun @ SY3449 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2783,plain,
! [SV259: $i] :
( ( ! [SY3450: $i,SY3451: $i,SY3452: $i] :
( ( c_lessequals @ SV259 @ ( c_Set_Oinsert @ SY3450 @ SY3451 @ SY3452 ) @ ( tc_fun @ SY3452 @ tc_bool ) )
| ~ ( c_lessequals @ SV259 @ SY3451 @ ( tc_fun @ SY3452 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV259 @ ( c_Set_Oinsert @ SY3450 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3452 @ tc_bool ) ) @ SY3452 ) @ ( tc_fun @ SY3452 @ tc_bool ) ) @ SY3451 @ ( tc_fun @ SY3452 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2784,plain,
! [SV260: $i] :
( ( ! [SY3453: $i,SY3454: $i,SY3455: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ SV260 @ SY3453 @ SY3454 @ SY3455 ) @ SY3455 )
= ( c_Finite__Set_Ocard @ SY3453 @ SY3454 ) )
| ~ ( c_Fun_Oinj__on @ SV260 @ SY3453 @ SY3454 @ SY3455 )
| ~ ( c_Finite__Set_Ofinite @ SY3453 @ SY3454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2785,plain,
! [SV261: $i] :
( ( ! [SY3456: $i,SY3457: $i,SY3458: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ SV261 @ SY3456 @ SY3457 @ SY3458 ) @ SY3458 )
!= ( c_Finite__Set_Ocard @ SY3456 @ SY3457 ) )
| ~ ( c_Finite__Set_Ofinite @ SY3456 @ SY3457 )
| ( c_Fun_Oinj__on @ SV261 @ SY3456 @ SY3457 @ SY3458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2786,plain,
! [SV262: $i] :
( ( ! [SY3459: $i,SY3460: $i] :
( ( ( c_Set_Oimage @ SV262 @ SY3459 @ SY3460 @ SY3460 )
= SY3459 )
| ~ ( c_Fun_Oinj__on @ SV262 @ SY3459 @ SY3460 @ SY3460 )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV262 @ SY3459 @ SY3460 @ SY3460 ) @ SY3459 @ ( tc_fun @ SY3460 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY3459 @ SY3460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(2787,plain,
! [SV263: $i] :
( ( ! [SY3461: $i,SY3462: $i] :
( ( c_Fun_Oinj__on @ SV263 @ SY3461 @ SY3462 @ SY3462 )
| ~ ( c_lessequals @ SY3461 @ ( c_Set_Oimage @ SV263 @ SY3461 @ SY3462 @ SY3462 ) @ ( tc_fun @ SY3462 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY3461 @ SY3462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2788,plain,
! [SV264: $i] :
( ( ! [SY3463: $i,SY3464: $i,SY3465: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ SV264 @ SY3463 @ SY3464 ) @ SY3465 @ SY3464 @ SY3463 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3464 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3463 ) @ SV264 ) @ SY3465 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2789,plain,
! [SV265: $i] :
( ( ! [SY3466: $i,SY3467: $i,SY3468: $i] :
( ( c_HOL_Oord__class_Oless @ SV265 @ ( c_Set_Oinsert @ SY3466 @ SY3467 @ SY3468 ) @ ( tc_fun @ SY3468 @ tc_bool ) )
| ~ ( c_lessequals @ SV265 @ SY3467 @ ( tc_fun @ SY3468 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3468 ) @ SY3466 ) @ SV265 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV265 @ SY3467 @ ( tc_fun @ SY3468 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2790,plain,
! [SV266: $i] :
( ( ! [SY3469: $i,SY3470: $i,SY3471: $i] :
( ( c_HOL_Oord__class_Oless @ SV266 @ ( c_Set_Oinsert @ SY3469 @ SY3470 @ SY3471 ) @ ( tc_fun @ SY3471 @ tc_bool ) )
| ~ ( c_lessequals @ SV266 @ SY3470 @ ( tc_fun @ SY3471 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3471 ) @ SY3469 ) @ SV266 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3471 ) @ SY3469 ) @ SY3470 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2791,plain,
! [SV267: $i] :
( ( ! [SY3472: $i,SY3473: $i] :
( ( c_lessequals @ SV267 @ SY3472 @ ( tc_fun @ SY3473 @ tc_bool ) )
| ! [SY3474: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3473 ) @ SY3474 ) @ SV267 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3473 ) @ SY3474 ) @ SY3472 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV267 @ ( c_Set_Oinsert @ SY3474 @ SY3472 @ SY3473 ) @ ( tc_fun @ SY3473 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(2792,plain,
! [SV268: $i] :
( ( ! [SY3475: $i,SY3476: $i,SY3477: $i,SY3478: $i] :
( ( ( c_Set_Oimage @ SV268 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3475 @ SY3476 @ ( tc_fun @ SY3477 @ tc_bool ) ) @ SY3477 @ SY3478 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV268 @ SY3475 @ SY3477 @ SY3478 ) @ ( c_Set_Oimage @ SV268 @ SY3476 @ SY3477 @ SY3478 ) @ ( tc_fun @ SY3478 @ tc_bool ) ) )
| ! [SY3479: $i] :
( ~ ( c_lessequals @ SY3476 @ SY3479 @ ( tc_fun @ SY3477 @ tc_bool ) )
| ~ ( c_lessequals @ SY3475 @ SY3479 @ ( tc_fun @ SY3477 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV268 @ SY3479 @ SY3477 @ SY3478 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2091]) ).
thf(2793,plain,
! [SV269: $i] :
( ( ! [SY3480: $i,SY3481: $i,SY3482: $i,SY3483: $i] :
( ( c_Set_Ovimage @ SV269 @ ( c_Set_Oinsert @ SY3480 @ SY3481 @ SY3482 ) @ SY3483 @ SY3482 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ SV269 @ ( c_Set_Oinsert @ SY3480 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3482 @ tc_bool ) ) @ SY3482 ) @ SY3483 @ SY3482 ) @ ( c_Set_Ovimage @ SV269 @ SY3481 @ SY3483 @ SY3482 ) @ ( tc_fun @ SY3483 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2092]) ).
thf(2794,plain,
! [SV270: $i] :
( ( ! [SY3484: $i,SY3485: $i,SY3486: $i,SY3487: $i] :
( ( ( c_Set_Oimage @ SV270 @ ( c_HOL_Ominus__class_Ominus @ SY3484 @ SY3485 @ ( tc_fun @ SY3486 @ tc_bool ) ) @ SY3486 @ SY3487 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV270 @ SY3484 @ SY3486 @ SY3487 ) @ ( c_Set_Oimage @ SV270 @ SY3485 @ SY3486 @ SY3487 ) @ ( tc_fun @ SY3487 @ tc_bool ) ) )
| ! [SY3488: $i] :
( ~ ( c_lessequals @ SY3485 @ SY3488 @ ( tc_fun @ SY3486 @ tc_bool ) )
| ~ ( c_lessequals @ SY3484 @ SY3488 @ ( tc_fun @ SY3486 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV270 @ SY3488 @ SY3486 @ SY3487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2093]) ).
thf(2795,plain,
! [SV271: $i] :
( ( ! [SY3489: $i,SY3490: $i,SY3491: $i,SY3492: $i] :
( ( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ SV271 @ SY3489 @ SY3490 @ SY3491 @ ( tc_Option_Ooption @ SY3492 ) ) @ SY3491 @ SY3492 )
= ( c_Set_Oinsert @ SY3489 @ ( c_Map_Odom @ SV271 @ SY3491 @ SY3492 ) @ SY3491 ) )
| ( SY3490
= ( c_Option_Ooption_ONone @ SY3492 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2094]) ).
thf(2796,plain,
! [SV272: $i] :
( ( ! [SY3493: $i,SY3494: $i,SY3495: $i,SY3496: $i] :
( ! [SY3497: $i] : ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ SV272 @ SY3493 @ ( c_Option_Ooption_ONone @ SY3494 ) @ SY3495 @ ( tc_Option_Ooption @ SY3494 ) ) @ ( c_Fun_Ofun__upd @ SY3496 @ SY3493 @ ( c_Option_Ooption_OSome @ SY3497 @ SY3494 ) @ SY3495 @ ( tc_Option_Ooption @ SY3494 ) ) @ SY3495 @ SY3494 )
| ~ ( c_Map_Omap__le @ SV272 @ SY3496 @ SY3495 @ SY3494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2095]) ).
thf(2797,plain,
! [SV273: $i] :
( ( ! [SY3498: $i,SY3499: $i,SY3500: $i] :
( ( c_HOL_Oord__class_Oless @ SV273 @ ( c_Set_Oinsert @ SY3498 @ SY3499 @ SY3500 ) @ ( tc_fun @ SY3500 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3500 ) @ SY3498 ) @ SV273 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV273 @ ( c_Set_Oinsert @ SY3498 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3500 @ tc_bool ) ) @ SY3500 ) @ ( tc_fun @ SY3500 @ tc_bool ) ) @ SY3499 @ ( tc_fun @ SY3500 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3500 ) @ SY3498 ) @ SY3499 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2798,plain,
! [SV274: $i] :
( ( ! [SY3501: $i] :
( ( c_Com_Ocom_OWhile @ SV274 @ SY3501 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2799,plain,
! [SV275: $i] :
( ( ! [SY3502: $i,SY3503: $i] :
( ( c_Com_Ocom_OBODY @ SV275 )
!= ( c_Com_Ocom_OWhile @ SY3502 @ SY3503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2800,plain,
! [SV276: $i] :
( ( ! [SY3504: $i,SY3505: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV276 @ SY3504 @ ( tc_fun @ SY3505 @ tc_bool ) ) @ SY3505 )
| ~ ( c_Finite__Set_Ofinite @ SV276 @ SY3505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2099]) ).
thf(2801,plain,
! [SV277: $i] :
( ( ! [SY3506: $i,SY3507: $i,SY3508: $i] :
( ( c_Com_Ocom_OBODY @ SV277 )
!= ( c_Com_Ocom_OLocal @ SY3506 @ SY3507 @ SY3508 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2802,plain,
! [SV278: $i] :
( ( ! [SY3509: $i,SY3510: $i,SY3511: $i,SY3512: $i] :
( ( c_Fun_Oinj__on @ SV278 @ ( c_HOL_Ominus__class_Ominus @ SY3509 @ SY3510 @ ( tc_fun @ SY3511 @ tc_bool ) ) @ SY3511 @ SY3512 )
| ~ ( c_Fun_Oinj__on @ SV278 @ SY3509 @ SY3511 @ SY3512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2803,plain,
! [SV279: $i] :
( ( ! [SY3513: $i,SY3514: $i,SY3515: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV279 @ tc_bool ) )
!= ( c_Set_Oimage @ SY3513 @ SY3514 @ SY3515 @ SV279 ) )
| ( SY3514
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3515 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2804,plain,
! [SV280: $i] :
( ( ! [SY3516: $i,SY3517: $i,SY3518: $i,SY3519: $i] :
( ( c_Com_Ocom_OWhile @ SV280 @ SY3516 )
!= ( c_Com_Ocom_OLocal @ SY3517 @ SY3518 @ SY3519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2103]) ).
thf(2805,plain,
! [SV281: $i] :
( ( ! [SY3520: $i,SY3521: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV281 @ SY3520 ) ) @ SY3521 ) @ SY3521 ) )
| ( hBOOL @ ( hAPP @ SV281 @ SY3521 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2104]) ).
thf(2806,plain,
! [SV282: $i] :
( ( ! [SY3522: $i,SY3523: $i,SY3524: $i,SY3525: $i] :
( ( c_Set_Ovimage @ SV282 @ ( c_HOL_Ominus__class_Ominus @ SY3522 @ SY3523 @ ( tc_fun @ SY3524 @ tc_bool ) ) @ SY3525 @ SY3524 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Ovimage @ SV282 @ SY3522 @ SY3525 @ SY3524 ) @ ( c_Set_Ovimage @ SV282 @ SY3523 @ SY3525 @ SY3524 ) @ ( tc_fun @ SY3525 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2105]) ).
thf(2807,plain,
! [SV283: $i] :
( ( ! [SY3526: $i,SY3527: $i,SY3528: $i] :
( ( c_HOL_Oord__class_Oless @ SV283 @ ( c_Set_Oinsert @ SY3526 @ SY3527 @ SY3528 ) @ ( tc_fun @ SY3528 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3528 ) @ SY3526 ) @ SV283 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV283 @ ( c_Set_Oinsert @ SY3526 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3528 @ tc_bool ) ) @ SY3528 ) @ ( tc_fun @ SY3528 @ tc_bool ) ) @ SY3527 @ ( tc_fun @ SY3528 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV283 @ SY3527 @ ( tc_fun @ SY3528 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(2808,plain,
! [SV284: $i] :
( ( ! [SY3529: $i] :
( ( c_Collect @ SV284 @ SY3529 )
= SV284 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2107]) ).
thf(2809,plain,
! [SV285: $i] :
( ( ! [SY3530: $i,SY3531: $i] :
( ( c_Com_Ocom_OAss @ SV285 @ SY3530 )
!= ( c_Com_Ocom_OBODY @ SY3531 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2108]) ).
thf(2810,plain,
! [SV286: $i] :
( ( ! [SY3532: $i,SY3533: $i,SY3534: $i] :
( ( ( c_Com_Ocom_OSemi @ SV286 @ SY3532 )
!= ( c_Com_Ocom_OSemi @ SY3533 @ SY3534 ) )
| ( SY3532 = SY3534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2109]) ).
thf(2811,plain,
! [SV287: $i] :
( ( ! [SY3535: $i,SY3536: $i] :
( ! [SY3537: $i] :
( ( c_Com_Ocom_OSemi @ SV287 @ SY3535 )
!= ( c_Com_Ocom_OSemi @ SY3536 @ SY3537 ) )
| ( SV287 = SY3536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2110]) ).
thf(2812,plain,
! [SV288: $i] :
( ( ! [SY3538: $i,SY3539: $i,SY3540: $i] :
( ( c_Com_Ocom_OSemi @ SV288 @ SY3538 )
!= ( c_Com_Ocom_OWhile @ SY3539 @ SY3540 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2111]) ).
thf(2813,plain,
! [SV289: $i] :
( ( ! [SY3541: $i,SY3542: $i,SY3543: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV289 @ ( c_Set_Oinsert @ SY3541 @ SY3542 @ SY3543 ) @ ( tc_fun @ SY3543 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV289 @ SY3542 @ ( tc_fun @ SY3543 @ tc_bool ) ) @ ( c_Set_Oinsert @ SY3541 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3543 @ tc_bool ) ) @ SY3543 ) @ ( tc_fun @ SY3543 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2112]) ).
thf(2814,plain,
! [SV290: $i] :
( ( ! [SY3544: $i,SY3545: $i,SY3546: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV290 @ ( c_Set_Oinsert @ SY3544 @ SY3545 @ SY3546 ) @ ( tc_fun @ SY3546 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV290 @ ( c_Set_Oinsert @ SY3544 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3546 @ tc_bool ) ) @ SY3546 ) @ ( tc_fun @ SY3546 @ tc_bool ) ) @ SY3545 @ ( tc_fun @ SY3546 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2815,plain,
! [SV291: $i] :
( ( ! [SY3547: $i,SY3548: $i,SY3549: $i,SY3550: $i] :
( ( c_Com_Ocom_OSemi @ SV291 @ SY3547 )
!= ( c_Com_Ocom_OCond @ SY3548 @ SY3549 @ SY3550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2114]) ).
thf(2816,plain,
! [SV292: $i] :
( ( ! [SY3551: $i] :
( ( c_Finite__Set_Ofinite @ SV292 @ SY3551 )
| ! [SY3552: $i] :
( ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV292 @ SY3552 @ ( tc_fun @ SY3551 @ tc_bool ) ) @ SY3551 )
| ~ ( c_Finite__Set_Ofinite @ SY3552 @ SY3551 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2115]) ).
thf(2817,plain,
! [SV293: $i] :
( ( ! [SY3553: $i,SY3554: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV293 @ SY3553 @ ( tc_fun @ SY3554 @ tc_bool ) ) @ SY3554 )
| ~ ( c_Finite__Set_Ofinite @ SV293 @ SY3554 )
| ~ ( c_Finite__Set_Ofinite @ SY3553 @ SY3554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2116]) ).
thf(2818,plain,
! [SV294: $i] :
( ( ! [SY3555: $i,SY3556: $i] :
( ( c_Set_Oinsert @ SV294 @ SY3555 @ SY3556 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3556 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2819,plain,
! [SV295: $i] :
( ( ! [SY3557: $i,SY3558: $i,SY3559: $i,SY3560: $i] :
( ( c_Com_Ocom_OSemi @ SV295 @ SY3557 )
!= ( c_Com_Ocom_OLocal @ SY3558 @ SY3559 @ SY3560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2118]) ).
thf(2820,plain,
! [SV296: $i] :
( ( ! [SY3561: $i,SY3562: $i,SY3563: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV296 ) @ SY3561 ) @ ( c_Set_Ovimage @ SY3562 @ ( c_Set_Oinsert @ ( hAPP @ SY3562 @ SY3561 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3563 @ tc_bool ) ) @ SY3563 ) @ SV296 @ SY3563 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2119]) ).
thf(2821,plain,
! [SV297: $i] :
( ( ! [SY3564: $i,SY3565: $i,SY3566: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV297 @ SY3564 @ SY3565 ) @ ( c_Set_Oinsert @ SV297 @ SY3566 @ SY3565 ) @ ( tc_fun @ SY3565 @ tc_bool ) )
= ( c_Set_Oinsert @ SV297 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3564 @ SY3566 @ ( tc_fun @ SY3565 @ tc_bool ) ) @ SY3565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2120]) ).
thf(2822,plain,
! [SV298: $i] :
( ( ! [SY3567: $i,SY3568: $i,SY3569: $i] :
( ( c_Map_Omap__le @ SV298 @ SY3567 @ SY3568 @ SY3569 )
| ! [SY3570: $i] :
~ ( c_Map_Omap__le @ ( c_Map_Omap__add @ SY3570 @ SV298 @ SY3568 @ SY3569 ) @ SY3567 @ SY3568 @ SY3569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2121]) ).
thf(2823,plain,
! [SV299: $i] :
( ( ! [SY3571: $i,SY3572: $i] :
( ( c_Set_Oinsert @ SV299 @ ( c_Set_Oinsert @ SV299 @ SY3571 @ SY3572 ) @ SY3572 )
= ( c_Set_Oinsert @ SV299 @ SY3571 @ SY3572 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2122]) ).
thf(2824,plain,
! [SV300: $i] :
( ( ! [SY3573: $i,SY3574: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ SV300 @ SY3573 ) @ SY3574 )
| ! [SY3575: $i,SY3576: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3575 ) @ SY3573 ) @ SY3576 ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3576 @ SV300 @ SY3575 @ ( tc_fun @ SY3574 @ tc_bool ) ) @ SY3574 )
| ~ ( c_Finite__Set_Ofinite @ SY3576 @ SY3575 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2123]) ).
thf(2825,plain,
! [SV301: $i] :
( ( ! [SY3577: $i,SY3578: $i] : ( c_Map_Omap__le @ SV301 @ SV301 @ SY3577 @ SY3578 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2124]) ).
thf(2826,plain,
! [SV302: $i] :
( ( ! [SY3579: $i,SY3580: $i,SY3581: $i] :
( ( c_Map_Omap__le @ SV302 @ SY3579 @ SY3580 @ SY3581 )
| ! [SY3582: $i] :
( ~ ( c_Map_Omap__le @ SY3582 @ SY3579 @ SY3580 @ SY3581 )
| ~ ( c_Map_Omap__le @ SV302 @ SY3582 @ SY3580 @ SY3581 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2125]) ).
thf(2827,plain,
! [SV303: $i] :
( ( ! [SY3583: $i,SY3584: $i,SY3585: $i,SY3586: $i] :
( ( c_Com_Ocom_OLocal @ SV303 @ SY3583 @ SY3584 )
!= ( c_Com_Ocom_OAss @ SY3585 @ SY3586 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2126]) ).
thf(2828,plain,
! [SV304: $i] :
( ( ! [SY3587: $i] :
( ( hBOOL @ ( hAPP @ SV304 @ SY3587 ) )
| ! [SY3588: $i] :
( ( SY3588 = SY3587 )
| ! [SY3589: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3588 @ SV304 @ SY3589 ) @ SY3587 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2127]) ).
thf(2829,plain,
! [SV305: $i] :
( ( ! [SY3590: $i,SY3591: $i,SY3592: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV305 @ SY3590 @ SY3591 @ ( tc_fun @ SY3592 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3592 @ tc_bool ) ) )
| ! [SY3593: $i] :
( ( ( hAPP @ SY3590 @ SY3593 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3592 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3591 ) @ SY3593 ) @ SV305 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(2830,plain,
! [SV306: $i] :
( ( ! [SY3594: $i,SY3595: $i] :
( ( c_Com_Ocom_OBODY @ SV306 )
!= ( c_Com_Ocom_OAss @ SY3594 @ SY3595 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2129]) ).
thf(2831,plain,
! [SV307: $i] :
( ( ! [SY3596: $i,SY3597: $i,SY3598: $i,SY3599: $i] :
( ( c_Com_Ocom_OCond @ SV307 @ SY3596 @ SY3597 )
!= ( c_Com_Ocom_OWhile @ SY3598 @ SY3599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2130]) ).
thf(2832,plain,
! [SV308: $i] :
( ( ! [SY3600: $i,SY3601: $i,SY3602: $i,SY3603: $i,SY3604: $i] :
( ( c_Com_Ocom_OCond @ SV308 @ SY3600 @ SY3601 )
!= ( c_Com_Ocom_OLocal @ SY3602 @ SY3603 @ SY3604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2131]) ).
thf(2833,plain,
! [SV309: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV309 )
| ! [SY3605: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3605 @ ( c_Orderings_Obot__class_Obot @ SV309 ) @ SV309 )
= ( c_Orderings_Obot__class_Obot @ SV309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2132]) ).
thf(2834,plain,
! [SV310: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV310 )
| ! [SY3606: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ SV310 ) @ SY3606 @ SV310 )
= ( c_Orderings_Obot__class_Obot @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2133]) ).
thf(2835,plain,
! [SV311: $i] :
( ( ! [SY3607: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV311 @ tc_bool ) ) @ SY3607 @ ( tc_fun @ SV311 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV311 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2134]) ).
thf(2836,plain,
! [SV312: $i] :
( ( ! [SY3608: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV312 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3608 @ tc_bool ) ) @ ( tc_fun @ SY3608 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3608 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2135]) ).
thf(2837,plain,
! [SV313: $i] :
( ( ! [SY3609: $i] :
( ( c_Finite__Set_Ofinite @ SV313 @ SY3609 )
| ! [SY3610: $i] :
~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SY3610 @ SV313 @ SY3609 ) @ SY3609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2136]) ).
thf(2838,plain,
! [SV314: $i] :
( ( ! [SY3611: $i,SY3612: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV314 @ SY3611 @ SY3612 ) @ SY3612 )
| ~ ( c_Finite__Set_Ofinite @ SY3611 @ SY3612 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2137]) ).
thf(2839,plain,
! [SV315: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV315 @ tc_bool ) ) @ SV315 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2138]) ).
thf(2840,plain,
! [SV316: $i] :
( ( ! [SY3613: $i,SY3614: $i,SY3615: $i,SY3616: $i] :
( ( c_Com_Ocom_OCond @ SV316 @ SY3613 @ SY3614 )
!= ( c_Com_Ocom_OSemi @ SY3615 @ SY3616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2139]) ).
thf(2841,plain,
! [SV317: $i] :
( ( ! [SY3617: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV317 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ SY3617 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Com_OWT @ SY3617 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV317 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ SV317 ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2140]) ).
thf(2842,plain,
! [SV318: $i] :
( ( ! [SY3618: $i,SY3619: $i,SY3620: $i,SY3621: $i,SY3622: $i,SY3623: $i,SY3624: $i,SY3625: $i] :
( ( ( hAPP @ SV318 @ ( c_Set_Oinsert @ SY3618 @ ( c_Set_Oinsert @ SY3619 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3620 @ tc_bool ) ) @ SY3620 ) @ SY3620 ) )
= ( hAPP @ ( hAPP @ SY3621 @ SY3618 ) @ SY3619 ) )
| ! [SY3626: $i,SY3627: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3622 @ SV318 @ SY3623 @ SY3624 @ SY3625 @ SY3621 @ SY3626 @ SY3627 @ SY3620 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2141]) ).
thf(2843,plain,
! [SV319: $i] :
( ( ! [SY3628: $i,SY3629: $i,SY3630: $i,SY3631: $i,SY3632: $i,SY3633: $i,SY3634: $i,SY3635: $i] :
( ( ( hAPP @ SV319 @ ( c_Set_Oinsert @ SY3628 @ ( c_Set_Oinsert @ SY3629 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3630 @ tc_bool ) ) @ SY3630 ) @ SY3630 ) )
= ( hAPP @ ( hAPP @ SY3631 @ SY3628 ) @ SY3629 ) )
| ! [SY3636: $i,SY3637: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV319 @ SY3632 @ SY3633 @ SY3634 @ SY3631 @ SY3635 @ SY3636 @ SY3637 @ SY3630 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2142]) ).
thf(2844,plain,
! [SV320: $i] :
( ( ! [SY3638: $i,SY3639: $i,SY3640: $i,SY3641: $i,SY3642: $i] :
( ( ( c_Com_Ocom_OCond @ SV320 @ SY3638 @ SY3639 )
!= ( c_Com_Ocom_OCond @ SY3640 @ SY3641 @ SY3642 ) )
| ( SY3639 = SY3642 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2143]) ).
thf(2845,plain,
! [SV321: $i] :
( ( ! [SY3643: $i,SY3644: $i,SY3645: $i,SY3646: $i] :
( ! [SY3647: $i] :
( ( c_Com_Ocom_OCond @ SV321 @ SY3643 @ SY3644 )
!= ( c_Com_Ocom_OCond @ SY3645 @ SY3646 @ SY3647 ) )
| ( SY3643 = SY3646 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2144]) ).
thf(2846,plain,
! [SV322: $i] :
( ( ! [SY3648: $i,SY3649: $i,SY3650: $i] :
( ! [SY3651: $i,SY3652: $i] :
( ( c_Com_Ocom_OCond @ SV322 @ SY3648 @ SY3649 )
!= ( c_Com_Ocom_OCond @ SY3650 @ SY3651 @ SY3652 ) )
| ( SV322 = SY3650 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2145]) ).
thf(2847,plain,
! [SV323: $i] :
( ( ! [SY3653: $i] :
( ( c_Option_Ooption_OSome @ SV323 @ SY3653 )
!= ( c_Option_Ooption_ONone @ SY3653 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2146]) ).
thf(2848,plain,
! [SV324: $i] :
( ( ! [SY3654: $i] :
( ( c_Option_Ooption_OSome @ SV324 @ SY3654 )
!= ( c_Option_Ooption_ONone @ SY3654 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2147]) ).
thf(2849,plain,
! [SV325: $i] :
( ( ! [SY3655: $i,SY3656: $i] :
( ( ( c_Option_Ooption_OSome @ SV325 @ SY3655 )
!= ( c_Option_Ooption_OSome @ SY3656 @ SY3655 ) )
| ( SV325 = SY3656 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2148]) ).
thf(2850,plain,
! [SV326: $i] :
( ( ! [SY3657: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV326 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3657 @ tc_bool ) ) @ ( tc_fun @ SY3657 @ tc_bool ) )
= SV326 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2149]) ).
thf(2851,plain,
! [SV327: $i] :
( ( ! [SY3658: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV327 @ SV327 @ ( tc_fun @ SY3658 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3658 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2150]) ).
thf(2852,plain,
! [SV328: $i] :
( ( ! [SY3659: $i,SY3660: $i,SY3661: $i] :
( ( c_Com_Ocom_OAss @ SV328 @ SY3659 )
!= ( c_Com_Ocom_OWhile @ SY3660 @ SY3661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2151]) ).
thf(2853,plain,
! [SV329: $i] :
( ( ! [SY3662: $i,SY3663: $i,SY3664: $i,SY3665: $i] :
( ( c_Map_Omap__add @ SV329 @ ( c_Map_Omap__add @ SY3662 @ SY3663 @ SY3664 @ SY3665 ) @ SY3664 @ SY3665 )
= ( c_Map_Omap__add @ ( c_Map_Omap__add @ SV329 @ SY3662 @ SY3664 @ SY3665 ) @ SY3663 @ SY3664 @ SY3665 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2152]) ).
thf(2854,plain,
! [SV330: $i] :
( ( ! [SY3666: $i,SY3667: $i,SY3668: $i,SY3669: $i] :
( ( c_Com_Ocom_OAss @ SV330 @ SY3666 )
!= ( c_Com_Ocom_OLocal @ SY3667 @ SY3668 @ SY3669 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2153]) ).
thf(2855,plain,
! [SV331: $i] :
( ( ! [SY3670: $i] :
~ ( c_HOL_Oord__class_Oless @ SV331 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3670 @ tc_bool ) ) @ ( tc_fun @ SY3670 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2154]) ).
thf(2856,plain,
! [SV332: $i] :
( ( ! [SY3671: $i,SY3672: $i,SY3673: $i] :
( ( c_Com_Ocom_OCond @ SV332 @ SY3671 @ SY3672 )
!= ( c_Com_Ocom_OBODY @ SY3673 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2155]) ).
thf(2857,plain,
! [SV333: $i] :
( ( ! [SY3674: $i,SY3675: $i,SY3676: $i] :
( ( c_Com_Ocom_OBODY @ SV333 )
!= ( c_Com_Ocom_OCond @ SY3674 @ SY3675 @ SY3676 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2156]) ).
thf(2858,plain,
! [SV334: $i] :
( ( ! [SY3677: $i] :
( ~ ( class_Lattices_Olattice @ SV334 )
| ! [SY3678: $i,SY3679: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3677 @ SY3678 @ SV334 ) @ SY3679 @ SV334 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3677 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3678 @ SY3679 @ SV334 ) @ SV334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2157]) ).
thf(2859,plain,
! [SV335: $i] :
( ( ! [SY3680: $i] :
( ~ ( class_Lattices_Olattice @ SV335 )
| ! [SY3681: $i,SY3682: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3680 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3681 @ SY3682 @ SV335 ) @ SV335 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3681 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3680 @ SY3682 @ SV335 ) @ SV335 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2158]) ).
thf(2860,plain,
! [SV336: $i] :
( ( ! [SY3683: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV336 )
| ! [SY3684: $i,SY3685: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3683 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3684 @ SY3685 @ SV336 ) @ SV336 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3684 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3683 @ SY3685 @ SV336 ) @ SV336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2159]) ).
thf(2861,plain,
! [SV337: $i] :
( ( ! [SY3686: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV337 )
| ! [SY3687: $i,SY3688: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3686 @ SY3687 @ SV337 ) @ SY3688 @ SV337 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3686 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3687 @ SY3688 @ SV337 ) @ SV337 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2160]) ).
thf(2862,plain,
! [SV338: $i] :
( ( ! [SY3689: $i,SY3690: $i,SY3691: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV338 @ SY3689 @ ( tc_fun @ SY3690 @ tc_bool ) ) @ SY3691 @ ( tc_fun @ SY3690 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV338 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3689 @ SY3691 @ ( tc_fun @ SY3690 @ tc_bool ) ) @ ( tc_fun @ SY3690 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2161]) ).
thf(2863,plain,
! [SV339: $i] :
( ( ! [SY3692: $i,SY3693: $i,SY3694: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV339 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3692 @ SY3693 @ ( tc_fun @ SY3694 @ tc_bool ) ) @ ( tc_fun @ SY3694 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3692 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV339 @ SY3693 @ ( tc_fun @ SY3694 @ tc_bool ) ) @ ( tc_fun @ SY3694 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2162]) ).
thf(2864,plain,
! [SV340: $i] :
( ( ! [SY3695: $i,SY3696: $i,SY3697: $i,SY3698: $i] :
( ( c_Com_Ocom_OLocal @ SV340 @ SY3695 @ SY3696 )
!= ( c_Com_Ocom_OWhile @ SY3697 @ SY3698 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2163]) ).
thf(2865,plain,
! [SV341: $i] :
( ( ! [SY3699: $i,SY3700: $i,SY3701: $i,SY3702: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV341 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3699 @ ( c_Com_Ocom_OBODY @ SY3700 ) @ SY3701 @ SY3702 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3702 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3702 ) ) @ SY3702 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV341 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3699 @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SY3700 ) @ tc_Com_Ocom ) @ SY3701 @ SY3702 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3702 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3702 ) ) @ SY3702 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2164]) ).
thf(2866,plain,
! [SV342: $i] :
( ( ! [SY3703: $i,SY3704: $i,SY3705: $i,SY3706: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV342 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3703 @ ( c_Com_Ocom_OBODY @ SY3704 ) @ SY3705 @ SY3706 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3706 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3706 ) ) @ SY3706 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3703 @ ( c_Com_Ocom_OBODY @ SY3704 ) @ SY3705 @ SY3706 ) @ SV342 @ ( tc_Hoare__Mirabelle_Otriple @ SY3706 ) ) @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3703 @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SY3704 ) @ tc_Com_Ocom ) @ SY3705 @ SY3706 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3706 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3706 ) ) @ SY3706 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2165]) ).
thf(2867,plain,
! [SV343: $i] :
( ( ! [SY3707: $i,SY3708: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV343 )
| ! [SY3709: $i,SY3710: $i] :
( ( ( c_Finite__Set_Osetsum @ SY3707 @ ( c_HOL_Ominus__class_Ominus @ SY3708 @ ( c_Set_Oinsert @ SY3709 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3710 @ tc_bool ) ) @ SY3710 ) @ ( tc_fun @ SY3710 @ tc_bool ) ) @ SY3710 @ SV343 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SY3707 @ SY3708 @ SY3710 @ SV343 ) @ ( hAPP @ SY3707 @ SY3709 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3710 ) @ SY3709 ) @ SY3708 ) )
| ~ ( c_Finite__Set_Ofinite @ SY3708 @ SY3710 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2166]) ).
thf(2868,plain,
! [SV344: $i] :
( ( ! [SY3711: $i,SY3712: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV344 )
| ! [SY3713: $i,SY3714: $i] :
( ( ( c_Finite__Set_Osetsum @ SY3711 @ ( c_HOL_Ominus__class_Ominus @ SY3712 @ ( c_Set_Oinsert @ SY3713 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3714 @ tc_bool ) ) @ SY3714 ) @ ( tc_fun @ SY3714 @ tc_bool ) ) @ SY3714 @ SV344 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SY3711 @ SY3712 @ SY3714 @ SV344 ) @ ( hAPP @ SY3711 @ SY3713 ) @ SV344 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3714 ) @ SY3713 ) @ SY3712 ) )
| ~ ( c_Finite__Set_Ofinite @ SY3712 @ SY3714 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2167]) ).
thf(2869,plain,
! [SV345: $i] :
( ( ( ( hAPP @ c_Com_Obody @ SV345 )
= ( c_Option_Ooption_OSome @ ( c_Com_Osko__Com__XWTs__elim__cases__7__1 @ SV345 ) @ tc_Com_Ocom ) )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ SV345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2168]) ).
thf(2870,plain,
! [SV346: $i] :
( ( ! [SY3715: $i,SY3716: $i,SY3717: $i] :
( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ SV346 @ SY3715 @ ( c_Option_Ooption_ONone @ SY3716 ) @ SY3717 @ ( tc_Option_Ooption @ SY3716 ) ) @ SY3717 @ SY3716 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ SV346 @ SY3717 @ SY3716 ) @ ( c_Set_Oinsert @ SY3715 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3717 @ tc_bool ) ) @ SY3717 ) @ ( tc_fun @ SY3717 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(2871,plain,
! [SV347: $i] :
( ( ! [SY3718: $i,SY3719: $i,SY3720: $i,SY3721: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV347 @ ( c_HOL_Ominus__class_Ominus @ SY3718 @ SY3719 @ ( tc_fun @ SY3720 @ tc_bool ) ) @ SY3720 @ SY3721 ) @ ( c_Set_Oimage @ SV347 @ ( c_HOL_Ominus__class_Ominus @ SY3719 @ SY3718 @ ( tc_fun @ SY3720 @ tc_bool ) ) @ SY3720 @ SY3721 ) @ ( tc_fun @ SY3721 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3721 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SV347 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3718 @ SY3719 @ ( tc_fun @ SY3720 @ tc_bool ) ) @ SY3720 @ SY3721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2170]) ).
thf(2872,plain,
! [SV348: $i] :
( ( ! [SY3722: $i,SY3723: $i,SY3724: $i,SY3725: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV348 @ ( c_HOL_Ominus__class_Ominus @ SY3722 @ SY3723 @ ( tc_fun @ SY3724 @ tc_bool ) ) @ SY3724 @ SY3725 ) @ ( c_Set_Oimage @ SV348 @ ( c_HOL_Ominus__class_Ominus @ SY3723 @ SY3722 @ ( tc_fun @ SY3724 @ tc_bool ) ) @ SY3724 @ SY3725 ) @ ( tc_fun @ SY3725 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3725 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SV348 @ SY3723 @ SY3724 @ SY3725 )
| ~ ( c_Fun_Oinj__on @ SV348 @ SY3722 @ SY3724 @ SY3725 )
| ( c_Fun_Oinj__on @ SV348 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3722 @ SY3723 @ ( tc_fun @ SY3724 @ tc_bool ) ) @ SY3724 @ SY3725 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2171]) ).
thf(2873,plain,
! [SV349: $i] :
( ( ! [SY3726: $i,SY3727: $i,SY3728: $i] :
( ( c_HOL_Oord__class_Oless @ SV349 @ ( c_Set_Oinsert @ SY3726 @ SY3727 @ SY3728 ) @ ( tc_fun @ SY3728 @ tc_bool ) )
| ~ ( c_lessequals @ SV349 @ SY3727 @ ( tc_fun @ SY3728 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV349 @ ( c_Set_Oinsert @ SY3726 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3728 @ tc_bool ) ) @ SY3728 ) @ ( tc_fun @ SY3728 @ tc_bool ) ) @ SY3727 @ ( tc_fun @ SY3728 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3728 ) @ SY3726 ) @ SY3727 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2172]) ).
thf(2874,plain,
! [SV350: $i] :
( ( ! [SY3729: $i,SY3730: $i,SY3731: $i,SY3732: $i,SY3733: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ SV350 @ SY3729 @ SY3730 @ SY3731 @ SY3732 ) @ SY3733 @ SY3731 @ SY3732 )
= ( c_Set_Oinsert @ SY3730 @ ( c_Set_Oimage @ SV350 @ ( c_HOL_Ominus__class_Ominus @ SY3733 @ ( c_Set_Oinsert @ SY3729 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3731 @ tc_bool ) ) @ SY3731 ) @ ( tc_fun @ SY3731 @ tc_bool ) ) @ SY3731 @ SY3732 ) @ SY3732 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3731 ) @ SY3729 ) @ SY3733 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2173]) ).
thf(2875,plain,
! [SV351: $i] :
( ( ! [SY3734: $i,SY3735: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV351 )
| ! [SY3736: $i,SY3737: $i] :
( ( ( c_Finite__Set_Osetsum @ SY3734 @ ( c_HOL_Ominus__class_Ominus @ SY3735 @ ( c_Set_Oinsert @ SY3736 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3737 @ tc_bool ) ) @ SY3737 ) @ ( tc_fun @ SY3737 @ tc_bool ) ) @ SY3737 @ SV351 )
= ( c_Finite__Set_Osetsum @ SY3734 @ SY3735 @ SY3737 @ SV351 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3737 ) @ SY3736 ) @ SY3735 ) )
| ~ ( c_Finite__Set_Ofinite @ SY3735 @ SY3737 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2174]) ).
thf(2876,plain,
! [SV352: $i] :
( ( ! [SY3738: $i,SY3739: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_HOL_Ominus__class_Ominus @ SV352 @ ( c_Set_Oinsert @ SY3738 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3739 @ tc_bool ) ) @ SY3739 ) @ ( tc_fun @ SY3739 @ tc_bool ) ) @ SY3739 )
= ( c_Finite__Set_Ocard @ SV352 @ SY3739 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3739 ) @ SY3738 ) @ SV352 ) )
| ~ ( c_Finite__Set_Ofinite @ SV352 @ SY3739 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2175]) ).
thf(2877,plain,
! [SV353: $i] :
( ( ! [SY3740: $i,SY3741: $i,SY3742: $i,SY3743: $i,SY3744: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3740 @ ( c_Com_Ocom_OSemi @ SY3741 @ SY3742 ) @ SY3743 @ SY3744 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3744 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3744 ) ) @ SY3744 )
| ! [SY3745: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3745 @ SY3742 @ SY3743 @ SY3744 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3744 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3744 ) ) @ SY3744 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3740 @ SY3741 @ SY3745 @ SY3744 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3744 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3744 ) ) @ SY3744 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2176]) ).
thf(2878,plain,
! [SV354: $i] :
( ( ! [SY3746: $i,SY3747: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ SV354 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3746 @ c_Com_Ocom_OSKIP @ SY3746 @ SY3747 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3747 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3747 ) ) @ SY3747 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2177]) ).
thf(2879,plain,
! [SV355: $i] :
( ( ! [SY3748: $i,SY3749: $i,SY3750: $i,SY3751: $i,SY3752: $i] :
( ( ( c_Map_Omap__add @ ( c_Fun_Ofun__upd @ SV355 @ SY3748 @ ( c_Option_Ooption_OSome @ SY3749 @ SY3750 ) @ SY3751 @ ( tc_Option_Ooption @ SY3750 ) ) @ SY3752 @ SY3751 @ SY3750 )
= ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ SV355 @ SY3752 @ SY3751 @ SY3750 ) @ SY3748 @ ( c_Option_Ooption_OSome @ SY3749 @ SY3750 ) @ SY3751 @ ( tc_Option_Ooption @ SY3750 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3751 ) @ SY3748 ) @ ( c_Map_Odom @ SY3752 @ SY3751 @ SY3750 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2880,plain,
! [SV356: $i] :
( ( ! [SY3753: $i,SY3754: $i,SY3755: $i] :
( ( c_HOL_Oord__class_Oless @ SV356 @ ( c_Set_Oinsert @ SY3753 @ SY3754 @ SY3755 ) @ ( tc_fun @ SY3755 @ tc_bool ) )
| ~ ( c_lessequals @ SV356 @ SY3754 @ ( tc_fun @ SY3755 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV356 @ ( c_Set_Oinsert @ SY3753 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3755 @ tc_bool ) ) @ SY3755 ) @ ( tc_fun @ SY3755 @ tc_bool ) ) @ SY3754 @ ( tc_fun @ SY3755 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV356 @ SY3754 @ ( tc_fun @ SY3755 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(2881,plain,
! [SV357: $i] :
( ( ! [SY3756: $i,SY3757: $i,SY3758: $i] :
( ( c_Set_Ovimage @ SV357 @ SY3756 @ SY3757 @ SY3758 )
= ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_in @ SY3758 ) @ SV357 @ SY3758 @ ( tc_fun @ ( tc_fun @ SY3758 @ tc_bool ) @ tc_bool ) @ SY3757 ) @ SY3757 @ ( tc_fun @ SY3758 @ tc_bool ) @ tc_bool ) @ SY3756 ) @ SY3757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2180]) ).
thf(2882,plain,
! [SV358: $i] :
( ( ! [SY3759: $i,SY3760: $i,SY3761: $i,SY3762: $i,SY3763: $i,SY3764: $i] :
( ( c_Nitpick_Ofold__graph_H @ SV358 @ SY3759 @ SY3760 @ ( hAPP @ ( hAPP @ SV358 @ SY3761 ) @ SY3762 ) @ SY3763 @ SY3764 )
| ~ ( c_Nitpick_Ofold__graph_H @ SV358 @ SY3759 @ ( c_HOL_Ominus__class_Ominus @ SY3760 @ ( c_Set_Oinsert @ SY3761 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3763 @ tc_bool ) ) @ SY3763 ) @ ( tc_fun @ SY3763 @ tc_bool ) ) @ SY3762 @ SY3763 @ SY3764 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3763 ) @ SY3761 ) @ SY3760 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2181]) ).
thf(2883,plain,
! [SV359: $i] :
( ( ! [SY3765: $i,SY3766: $i,SY3767: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV359 @ ( c_Set_Oinsert @ SY3765 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3766 @ tc_bool ) ) @ SY3766 ) @ ( tc_fun @ SY3766 @ tc_bool ) ) @ SY3767 @ ( tc_fun @ SY3766 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3766 ) @ SY3765 ) @ SV359 ) )
| ~ ( c_lessequals @ SV359 @ ( c_Set_Oinsert @ SY3765 @ SY3767 @ SY3766 ) @ ( tc_fun @ SY3766 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2182]) ).
thf(2884,plain,
! [SV360: $i] :
( ( ! [SY3768: $i,SY3769: $i,SY3770: $i] :
( ( c_lessequals @ SV360 @ ( c_Set_Oinsert @ SY3768 @ SY3769 @ SY3770 ) @ ( tc_fun @ SY3770 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3770 ) @ SY3768 ) @ SV360 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV360 @ ( c_Set_Oinsert @ SY3768 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3770 @ tc_bool ) ) @ SY3770 ) @ ( tc_fun @ SY3770 @ tc_bool ) ) @ SY3769 @ ( tc_fun @ SY3770 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2183]) ).
thf(2885,plain,
! [SV361: $i] :
( ( ! [SY3771: $i,SY3772: $i,SY3773: $i] :
( ( c_lessequals @ SV361 @ ( c_Set_Oinsert @ SY3771 @ SY3772 @ SY3773 ) @ ( tc_fun @ SY3773 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3773 ) @ SY3771 ) @ SV361 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV361 @ ( c_Set_Oinsert @ SY3771 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3773 @ tc_bool ) ) @ SY3773 ) @ ( tc_fun @ SY3773 @ tc_bool ) ) @ SY3772 @ ( tc_fun @ SY3773 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2184]) ).
thf(2886,plain,
! [SV362: $i] :
( ( ! [SY3774: $i,SY3775: $i,SY3776: $i] :
( ( ( c_Finite__Set_Osetsum @ SV362 @ ( c_HOL_Ominus__class_Ominus @ SY3774 @ ( c_Set_Oinsert @ SY3775 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3776 @ tc_bool ) ) @ SY3776 ) @ ( tc_fun @ SY3776 @ tc_bool ) ) @ SY3776 @ tc_nat )
= ( c_Finite__Set_Osetsum @ SV362 @ SY3774 @ SY3776 @ tc_nat ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3776 ) @ SY3775 ) @ SY3774 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2185]) ).
thf(2887,plain,
! [SV363: $i] :
( ( ! [SY3777: $i,SY3778: $i,SY3779: $i,SY3780: $i,SY3781: $i,SY3782: $i] :
( ( c_Finite__Set_Ofold__graph @ SV363 @ SY3777 @ SY3778 @ ( hAPP @ ( hAPP @ SV363 @ SY3779 ) @ SY3780 ) @ SY3781 @ SY3782 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3781 ) @ SY3779 ) @ SY3778 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV363 @ SY3777 @ ( c_HOL_Ominus__class_Ominus @ SY3778 @ ( c_Set_Oinsert @ SY3779 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3781 @ tc_bool ) ) @ SY3781 ) @ ( tc_fun @ SY3781 @ tc_bool ) ) @ SY3780 @ SY3781 @ SY3782 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2888,plain,
! [SV364: $i] :
( ( ! [SY3783: $i,SY3784: $i,SY3785: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV364 @ SY3783 @ SY3784 ) @ SY3785 @ SY3784 @ SY3783 )
= ( c_Set_Oinsert @ SV364 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3783 @ tc_bool ) ) @ SY3783 ) )
| ! [V_x: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3784 ) @ V_x ) @ SY3785 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2187]) ).
thf(2889,plain,
! [SV365: $i] :
( ( ! [SY3787: $i,SY3788: $i,SY3789: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV365 @ ( c_Set_Oinsert @ SY3787 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3788 @ tc_bool ) ) @ SY3788 ) @ ( tc_fun @ SY3788 @ tc_bool ) ) @ SY3789 @ ( tc_fun @ SY3788 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3788 ) @ SY3787 ) @ SV365 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3788 ) @ SY3787 ) @ SY3789 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV365 @ ( c_Set_Oinsert @ SY3787 @ SY3789 @ SY3788 ) @ ( tc_fun @ SY3788 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(2890,plain,
! [SV366: $i] :
( ( ! [SY3790: $i,SY3791: $i] :
( ( ( hAPP @ SV366 @ SY3790 )
!= ( c_Option_Ooption_ONone @ SY3791 ) )
| ! [SY3792: $i,SY3793: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ SV366 @ SY3792 @ SY3791 ) @ ( c_Set_Oinsert @ SY3790 @ SY3793 @ SY3792 ) @ ( tc_fun @ SY3792 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ SV366 @ SY3792 @ SY3791 ) @ SY3793 @ ( tc_fun @ SY3792 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2190]) ).
thf(2891,plain,
! [SV367: $i] :
( ( ! [SY3794: $i,SY3795: $i,SY3796: $i] :
( ( c_Com_Ocom_OAss @ SV367 @ SY3794 )
!= ( c_Com_Ocom_OSemi @ SY3795 @ SY3796 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(2892,plain,
! [SV368: $i] :
( ( ! [SY3797: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV368 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ SY3797 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ SY3797 ) ) @ SV368 @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SY3797 ) @ tc_Com_Ocom ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(2893,plain,
! [SV369: $i] :
( ( ! [SY3798: $i,SY3799: $i,SY3800: $i,SY3801: $i,SY3802: $i] :
( ( c_Com_Ocom_OLocal @ SV369 @ SY3798 @ SY3799 )
!= ( c_Com_Ocom_OCond @ SY3800 @ SY3801 @ SY3802 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2193]) ).
thf(2894,plain,
! [SV370: $i] :
( ( ! [SY3803: $i,SY3804: $i,SY3805: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV370 @ SY3803 @ SY3804 ) @ SY3805 @ ( tc_fun @ SY3804 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SY3803 @ SY3805 @ ( tc_fun @ SY3804 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3804 ) @ SV370 ) @ SY3805 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(2895,plain,
! [SV371: $i] :
( ( ! [SY3806: $i,SY3807: $i,SY3808: $i] :
( ( c_Fun_Oinj__on @ SV371 @ SY3806 @ SY3807 @ SY3808 )
| ! [SY3809: $i] :
~ ( c_Fun_Oinj__on @ SV371 @ ( c_Set_Oinsert @ SY3809 @ SY3806 @ SY3807 ) @ SY3807 @ SY3808 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2195]) ).
thf(2896,plain,
! [SV372: $i] :
( ( ! [SY3810: $i,SY3811: $i] :
( ( c_Com_Ocom_OBODY @ SV372 )
!= ( c_Com_Ocom_OSemi @ SY3810 @ SY3811 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2196]) ).
thf(2897,plain,
! [SV373: $i] :
( ( ! [SY3812: $i] :
( ( SV373 = SY3812 )
| ! [SY3813: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3813 ) @ SV373 ) @ ( c_Set_Oinsert @ SY3812 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3813 @ tc_bool ) ) @ SY3813 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2898,plain,
! [SV374: $i] :
( ( ! [SY3814: $i,SY3815: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV374 @ SY3814 @ ( tc_fun @ SY3815 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3815 @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ SV374 @ SY3814 @ ( tc_fun @ SY3815 @ tc_bool ) )
= SV374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2198]) ).
thf(2899,plain,
! [SV375: $i] :
( ( ! [SY3816: $i] :
( ( hBOOL @ ( hAPP @ SV375 @ SY3816 ) )
| ! [SY3817: $i,SY3818: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3817 ) @ SY3816 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3818 @ ( c_Collect @ SV375 @ SY3817 ) @ ( tc_fun @ SY3817 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2199]) ).
thf(2900,plain,
! [SV376: $i] :
( ( ! [SY3819: $i] :
( ~ ( class_Orderings_Opreorder @ SV376 )
| ! [SY3820: $i] :
( ( c_HOL_Oord__class_Oless @ SY3819 @ SY3820 @ SV376 )
| ! [SY3821: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY3821 @ SY3820 @ SV376 )
| ~ ( c_HOL_Oord__class_Oless @ SY3819 @ SY3821 @ SV376 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(2901,plain,
! [SV377: $i] :
( ( ! [SY3822: $i,SY3823: $i] :
( ( c_HOL_Oord__class_Oless @ SV377 @ SY3822 @ ( tc_fun @ SY3823 @ tc_bool ) )
| ! [SY3824: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY3824 @ SY3822 @ ( tc_fun @ SY3823 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV377 @ SY3824 @ ( tc_fun @ SY3823 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2201]) ).
thf(2902,plain,
! [SV378: $i] :
( ( ! [SY3825: $i] :
( ~ ( class_Orderings_Oorder @ SV378 )
| ! [SY3826: $i] :
( ( c_HOL_Oord__class_Oless @ SY3825 @ SY3826 @ SV378 )
| ! [SY3827: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY3825 @ SY3827 @ SV378 )
| ~ ( c_HOL_Oord__class_Oless @ SY3827 @ SY3826 @ SV378 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2202]) ).
thf(2903,plain,
! [SV379: $i] :
( ( ! [SY3828: $i,SY3829: $i,SY3830: $i,SY3831: $i] :
( ( c_Fun_Oinj__on @ SV379 @ ( c_Set_Oinsert @ SY3828 @ SY3829 @ SY3830 ) @ SY3830 @ SY3831 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3831 ) @ ( hAPP @ SV379 @ SY3828 ) ) @ ( c_Set_Oimage @ SV379 @ ( c_HOL_Ominus__class_Ominus @ SY3829 @ ( c_Set_Oinsert @ SY3828 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3830 @ tc_bool ) ) @ SY3830 ) @ ( tc_fun @ SY3830 @ tc_bool ) ) @ SY3830 @ SY3831 ) ) )
| ~ ( c_Fun_Oinj__on @ SV379 @ SY3829 @ SY3830 @ SY3831 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2203]) ).
thf(2904,plain,
! [SV380: $i] :
( ( ! [SY3832: $i,SY3833: $i,SY3834: $i] :
( ( c_Set_Oinsert @ SV380 @ ( c_Set_Oinsert @ SY3832 @ SY3833 @ SY3834 ) @ SY3834 )
= ( c_Set_Oinsert @ SY3832 @ ( c_Set_Oinsert @ SV380 @ SY3833 @ SY3834 ) @ SY3834 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2204]) ).
thf(2905,plain,
! [SV381: $i] :
( ( ! [SY3835: $i,SY3836: $i,SY3837: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV381 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3835 @ tc_bool ) ) @ SY3836 @ SY3835 @ ( tc_fun @ SY3837 @ tc_bool ) ) @ ( tc_fun @ SY3837 @ tc_bool ) )
= SV381 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2906,plain,
! [SV382: $i] :
( ( ! [SY3838: $i,SY3839: $i,SY3840: $i,SY3841: $i,SY3842: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV382 @ SY3838 @ SY3839 @ SY3840 ) @ SY3841 ) @ SY3842 )
= ( hAPP @ ( hAPP @ SV382 @ SY3842 ) @ SY3841 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2206]) ).
thf(2907,plain,
! [SV383: $i] :
( ( ! [SY3843: $i,SY3844: $i] :
( ( c_Com_Ocom_OSemi @ SV383 @ SY3843 )
!= ( c_Com_Ocom_OBODY @ SY3844 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(2908,plain,
! [SV384: $i] :
( ( ! [SY3845: $i,SY3846: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV384 @ SY3845 @ ( tc_fun @ SY3846 @ tc_bool ) ) @ SY3845 @ ( tc_fun @ SY3846 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV384 @ SY3845 @ ( tc_fun @ SY3846 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2208]) ).
thf(2909,plain,
! [SV385: $i] :
( ( ! [SY3847: $i] :
( ( c_Option_Ooption_ONone @ SV385 )
!= ( c_Option_Ooption_OSome @ SY3847 @ SV385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2209]) ).
thf(2910,plain,
! [SV386: $i] :
( ( ! [SY3848: $i] :
( ( c_Option_Ooption_ONone @ SV386 )
!= ( c_Option_Ooption_OSome @ SY3848 @ SV386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2210]) ).
thf(2911,plain,
! [SV387: $i] :
( ( ! [SY3849: $i,SY3850: $i,SY3851: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV387 @ SY3849 ) ) @ SY3850 ) @ SY3851 ) )
| ! [SY3852: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV387 @ SY3849 ) ) @ SY3852 ) @ SY3851 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY3849 ) @ SY3850 ) @ SY3852 ) )
| ~ ( hBOOL @ ( hAPP @ SV387 @ SY3850 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2211]) ).
thf(2912,plain,
! [SV388: $i] :
( ( ! [SY3853: $i,SY3854: $i] :
( ( c_Set_Oinsert @ SV388 @ ( c_Set_Oinsert @ SY3853 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3854 @ tc_bool ) ) @ SY3854 ) @ SY3854 )
= ( c_Set_Oinsert @ SY3853 @ ( c_Set_Oinsert @ SV388 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3854 @ tc_bool ) ) @ SY3854 ) @ SY3854 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2212]) ).
thf(2913,plain,
! [SV389: $i] :
( ( ! [SY3855: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV389 )
| ! [SY3856: $i] :
( ! [SY3857: $i] :
( ( c_HOL_Ominus__class_Ominus @ SY3855 @ SY3856 @ SV389 )
!= ( c_HOL_Ominus__class_Ominus @ SY3857 @ SY3857 @ SV389 ) )
| ( SY3855 = SY3856 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2213]) ).
thf(2914,plain,
! [SV390: $i] :
( ( ! [SY3858: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV390 )
| ! [SY3859: $i,SY3860: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SY3858 @ SY3858 @ SV390 )
!= ( c_HOL_Ominus__class_Ominus @ SY3859 @ SY3860 @ SV390 ) )
| ( SY3859 = SY3860 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2214]) ).
thf(2915,plain,
! [SV391: $i] :
( ( ! [SY3861: $i,SY3862: $i] :
( ( c_Set_Oimage @ SV391 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3861 @ tc_bool ) ) @ SY3861 @ SY3862 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3862 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2215]) ).
thf(2916,plain,
! [SV392: $i] :
( ( ! [SY3863: $i,SY3864: $i,SY3865: $i,SY3866: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV392 @ SY3863 @ SY3864 ) ) @ SY3865 ) @ SY3866 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY3863 ) @ SY3865 ) @ SY3866 ) )
| ~ ( hBOOL @ ( hAPP @ SV392 @ SY3865 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2216]) ).
thf(2917,plain,
! [SV393: $i] :
( ( ! [SY3867: $i,SY3868: $i] :
( ~ ( hBOOL @ ( hAPP @ SV393 @ SY3867 ) )
| ! [SY3869: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY3868 ) @ SY3867 ) @ SY3869 ) )
| ! [SY3870: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV393 @ SY3868 @ SY3870 ) ) @ SY3867 ) @ SY3869 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2217]) ).
thf(2918,plain,
! [SV394: $i] :
( ( ! [SY3871: $i,SY3872: $i,SY3873: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV394 @ SY3871 ) ) @ SY3872 ) @ SY3873 ) )
| ! [SY3874: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY3871 ) @ SY3874 ) @ SY3873 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV394 ) @ SY3872 ) @ SY3874 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(2919,plain,
! [SV395: $i] :
( ( ! [SY3875: $i,SY3876: $i] : ( c_Fun_Oinj__on @ SV395 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3875 @ tc_bool ) ) @ SY3875 @ SY3876 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2219]) ).
thf(2920,plain,
! [SV396: $i] :
( ( ! [SY3877: $i,SY3878: $i,SY3879: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Map_Odom @ SV396 @ SY3877 @ SY3878 ) @ ( c_Map_Odom @ SY3879 @ SY3877 @ SY3878 ) @ ( tc_fun @ SY3877 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3877 @ tc_bool ) ) )
| ( ( c_Map_Omap__add @ SV396 @ SY3879 @ SY3877 @ SY3878 )
= ( c_Map_Omap__add @ SY3879 @ SV396 @ SY3877 @ SY3878 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2220]) ).
thf(2921,plain,
! [SV397: $i] :
( ( ! [SY3880: $i,SY3881: $i,SY3882: $i] :
( ( ( hAPP @ SV397 @ SY3880 )
!= ( c_Option_Ooption_OSome @ SY3881 @ SY3882 ) )
| ! [SY3883: $i] :
( ( c_Set_Oinsert @ SY3880 @ ( c_Map_Odom @ SV397 @ SY3883 @ SY3882 ) @ SY3883 )
= ( c_Map_Odom @ SV397 @ SY3883 @ SY3882 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2221]) ).
thf(2922,plain,
! [SV398: $i] :
( ( ! [SY3884: $i,SY3885: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV398 @ SY3884 @ ( tc_fun @ SY3885 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3884 @ SV398 @ ( tc_fun @ SY3885 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2222]) ).
thf(2923,plain,
! [SV399: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV399 )
| ! [SY3886: $i,SY3887: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3886 @ SY3887 @ SV399 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3887 @ SY3886 @ SV399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2223]) ).
thf(2924,plain,
! [SV400: $i] :
( ( ~ ( class_Lattices_Olattice @ SV400 )
| ! [SY3888: $i,SY3889: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3888 @ SY3889 @ SV400 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3889 @ SY3888 @ SV400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2224]) ).
thf(2925,plain,
! [SV401: $i] :
( ( ! [SY3890: $i,SY3891: $i,SY3892: $i,SY3893: $i,SY3894: $i,SY3895: $i,SY3896: $i,SY3897: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV401 @ SY3890 @ ( c_COMBC @ SY3891 @ SY3892 @ SY3892 @ tc_bool ) @ ( c_COMBC @ SY3893 @ SY3892 @ SY3892 @ tc_bool ) @ SY3894 @ SY3895 @ SY3896 @ SY3897 @ SY3892 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3890 @ SV401 @ SY3891 @ SY3893 @ SY3895 @ SY3894 @ SY3897 @ SY3896 @ SY3892 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(2926,plain,
! [SV402: $i] :
( ( ! [SY3898: $i,SY3899: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCond @ SV402 @ SY3898 @ SY3899 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2226]) ).
thf(2927,plain,
! [SV403: $i] :
( ( ! [SY3900: $i,SY3901: $i] :
( ( c_Set_Oinsert @ SV403 @ ( c_HOL_Ominus__class_Ominus @ SY3900 @ ( c_Set_Oinsert @ SV403 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3901 @ tc_bool ) ) @ SY3901 ) @ ( tc_fun @ SY3901 @ tc_bool ) ) @ SY3901 )
= ( c_Set_Oinsert @ SV403 @ SY3900 @ SY3901 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(2928,plain,
! [SV404: $i] :
( ( ! [SY3902: $i,SY3903: $i] :
( ( ( c_Set_Oinsert @ SV404 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3902 @ tc_bool ) ) @ SY3902 )
!= ( c_Set_Oinsert @ SY3903 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3902 @ tc_bool ) ) @ SY3902 ) )
| ( SV404 = SY3903 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2228]) ).
thf(2929,plain,
! [SV405: $i] :
( ( ! [SY3904: $i,SY3905: $i,SY3906: $i,SY3907: $i,SY3908: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV405 @ SY3904 @ SY3905 @ SY3906 ) @ SY3907 )
!= ( c_Option_Ooption_OSome @ SY3908 @ SY3906 ) )
| ( ( hAPP @ SV405 @ SY3907 )
= ( c_Option_Ooption_OSome @ SY3908 @ SY3906 ) )
| ( ( hAPP @ SY3904 @ SY3907 )
= ( c_Option_Ooption_OSome @ SY3908 @ SY3906 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2229]) ).
thf(2930,plain,
! [SV406: $i] :
( ( ! [SY3909: $i,SY3910: $i,SY3911: $i] :
( ( ( hAPP @ SV406 @ SY3909 )
!= ( c_Option_Ooption_OSome @ SY3910 @ SY3911 ) )
| ! [SY3912: $i] :
( ( ( hAPP @ SY3912 @ SY3909 )
!= ( c_Option_Ooption_ONone @ SY3911 ) )
| ! [SY3913: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SV406 @ SY3912 @ SY3913 @ SY3911 ) @ SY3909 )
= ( c_Option_Ooption_OSome @ SY3910 @ SY3911 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2230]) ).
thf(2931,plain,
! [SV407: $i] :
( ( ! [SY3914: $i,SY3915: $i,SY3916: $i,SY3917: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV407 @ SY3914 @ SY3915 @ SY3916 ) @ SY3917 )
!= ( c_Option_Ooption_ONone @ SY3916 ) )
| ( ( hAPP @ SV407 @ SY3917 )
= ( c_Option_Ooption_ONone @ SY3916 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2231]) ).
thf(2932,plain,
! [SV408: $i] :
( ( ! [SY3918: $i,SY3919: $i,SY3920: $i,SY3921: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV408 @ SY3918 @ SY3919 @ SY3920 ) @ SY3921 )
!= ( c_Option_Ooption_ONone @ SY3920 ) )
| ( ( hAPP @ SY3918 @ SY3921 )
= ( c_Option_Ooption_ONone @ SY3920 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(2933,plain,
! [SV409: $i] :
( ( ! [SY3922: $i,SY3923: $i] :
( ( ( c_Set_Oinsert @ SV409 @ SY3922 @ SY3923 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3923 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3923 ) @ SV409 ) @ SY3922 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2233]) ).
thf(2934,plain,
! [SV410: $i] :
( ( ! [SY3924: $i,SY3925: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ SY3924 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3925 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3925 ) ) @ SY3925 )
| ! [SY3926: $i] :
~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ SY3924 @ SY3926 @ ( tc_Hoare__Mirabelle_Otriple @ SY3925 ) ) @ SY3925 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2234]) ).
thf(2935,plain,
! [SV411: $i] :
( ( ! [SY3927: $i,SY3928: $i,SY3929: $i] :
( ( c_Com_Ocom_OLocal @ SV411 @ SY3927 @ SY3928 )
!= ( c_Com_Ocom_OBODY @ SY3929 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2235]) ).
thf(2936,plain,
! [SV412: $i] :
( ( ! [SY3930: $i,SY3931: $i,SY3932: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV412 @ SY3930 @ SY3931 ) @ SY3932 ) )
| ~ ( hBOOL @ ( hAPP @ SY3930 @ SY3932 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(2937,plain,
! [SV413: $i] :
( ( ! [SY3933: $i,SY3934: $i,SY3935: $i] :
( ! [SY3936: $i] :
( ( c_Set_Oinsert @ ( hAPP @ SV413 @ SY3933 ) @ ( c_Set_Oimage @ SV413 @ SY3934 @ SY3935 @ SY3936 ) @ SY3936 )
= ( c_Set_Oimage @ SV413 @ SY3934 @ SY3935 @ SY3936 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3935 ) @ SY3933 ) @ SY3934 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2237]) ).
thf(2938,plain,
! [SV414: $i] :
( ( ! [SY3937: $i,SY3938: $i,SY3939: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV414 @ ( c_Set_Oinsert @ SY3937 @ SY3938 @ SY3939 ) @ ( tc_fun @ SY3939 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV414 @ SY3938 @ ( tc_fun @ SY3939 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3939 ) @ SY3937 ) @ SV414 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2238]) ).
thf(2939,plain,
! [SV415: $i] :
( ( ! [SY3940: $i,SY3941: $i,SY3942: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV415 @ SY3940 @ SY3941 ) @ SY3942 @ ( tc_fun @ SY3941 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3940 @ SY3942 @ ( tc_fun @ SY3941 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3941 ) @ SV415 ) @ SY3942 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2239]) ).
thf(2940,plain,
! [SV416: $i] :
( ( ! [SY3943: $i,SY3944: $i,SY3945: $i,SY3946: $i] :
( ( c_Com_Ocom_OLocal @ SV416 @ SY3943 @ SY3944 )
!= ( c_Com_Ocom_OSemi @ SY3945 @ SY3946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2240]) ).
thf(2941,plain,
! [SV417: $i] :
( ( ! [SY3947: $i] :
( ( ( c_Com_Ocom_OBODY @ SV417 )
!= ( c_Com_Ocom_OBODY @ SY3947 ) )
| ( SV417 = SY3947 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2241]) ).
thf(2942,plain,
! [SV418: $i] :
( ( ! [SY3948: $i,SY3949: $i] :
( ! [SY3950: $i] :
( ( c_Com_Ocom_OWhile @ SV418 @ SY3948 )
!= ( c_Com_Ocom_OWhile @ SY3949 @ SY3950 ) )
| ( SV418 = SY3949 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2242]) ).
thf(2943,plain,
! [SV419: $i] :
( ( ! [SY3951: $i,SY3952: $i,SY3953: $i] :
( ( ( c_Com_Ocom_OWhile @ SV419 @ SY3951 )
!= ( c_Com_Ocom_OWhile @ SY3952 @ SY3953 ) )
| ( SY3951 = SY3953 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(2944,plain,
! [SV420: $i] :
( ( ! [SY3954: $i,SY3955: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV420 @ tc_bool ) )
= ( c_Set_Oimage @ SY3954 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3955 @ tc_bool ) ) @ SY3955 @ SV420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(2945,plain,
! [SV421: $i] :
( ( ! [SY3956: $i,SY3957: $i] :
( ( c_Com_Ocom_OCond @ SV421 @ SY3956 @ SY3957 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2245]) ).
thf(2946,plain,
! [SV422: $i] :
( ( ! [SY3958: $i,SY3959: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV422 @ ( c_HOL_Ominus__class_Ominus @ SY3958 @ SV422 @ ( tc_fun @ SY3959 @ tc_bool ) ) @ ( tc_fun @ SY3959 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3959 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2246]) ).
thf(2947,plain,
! [SV423: $i] :
( ( ! [SY3960: $i,SY3961: $i,SY3962: $i,SY3963: $i] :
( ( c_Com_Ocom_OWhile @ SV423 @ SY3960 )
!= ( c_Com_Ocom_OCond @ SY3961 @ SY3962 @ SY3963 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2247]) ).
thf(2948,plain,
! [SV424: $i] :
( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV424 )
| ! [SY3964: $i] : ( c_Finite__Set_Ofinite @ SY3964 @ SV424 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2248]) ).
thf(2949,plain,
! [SV425: $i] :
( ( ! [SY3965: $i,SY3966: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV425 ) @ SY3965 ) @ SY3966 ) )
| ! [SY3967: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV425 ) @ SY3965 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3966 @ ( c_Collect @ SY3967 @ SV425 ) @ ( tc_fun @ SV425 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2249]) ).
thf(2950,plain,
! [SV426: $i] :
( ( ! [SY3968: $i,SY3969: $i] :
( ( ( hAPP @ SV426 @ SY3968 )
!= ( c_Option_Ooption_ONone @ SY3969 ) )
| ! [SY3970: $i] :
( ( ( hAPP @ SY3970 @ SY3968 )
!= ( c_Option_Ooption_ONone @ SY3969 ) )
| ! [SY3971: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SV426 @ SY3970 @ SY3971 @ SY3969 ) @ SY3968 )
= ( c_Option_Ooption_ONone @ SY3969 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2250]) ).
thf(2951,plain,
! [SV427: $i] :
( ( ! [SY3972: $i,SY3973: $i,SY3974: $i] :
( ( ( hAPP @ SV427 @ SY3972 )
!= ( c_Option_Ooption_OSome @ SY3973 @ SY3974 ) )
| ! [SY3975: $i,SY3976: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SY3975 @ SV427 @ SY3976 @ SY3974 ) @ SY3972 )
= ( c_Option_Ooption_OSome @ SY3973 @ SY3974 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(2952,plain,
! [SV428: $i] :
( ( ! [SY3977: $i,SY3978: $i,SY3979: $i] :
( ( ( hAPP @ SV428 @ SY3977 )
!= ( c_Option_Ooption_OSome @ SY3978 @ SY3979 ) )
| ! [SY3980: $i,SY3981: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SY3980 @ SV428 @ SY3981 @ SY3979 ) @ SY3977 )
= ( c_Option_Ooption_OSome @ SY3978 @ SY3979 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2252]) ).
thf(2953,plain,
! [SV429: $i] :
( ( ! [SY3982: $i,SY3983: $i,SY3984: $i,SY3985: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV429 ) @ ( hAPP @ SY3982 @ SY3983 ) ) @ ( c_Set_Oimage @ SY3982 @ ( c_HOL_Ominus__class_Ominus @ SY3984 @ ( c_Set_Oinsert @ SY3983 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3985 @ tc_bool ) ) @ SY3985 ) @ ( tc_fun @ SY3985 @ tc_bool ) ) @ SY3985 @ SV429 ) ) )
| ~ ( c_Fun_Oinj__on @ SY3982 @ ( c_Set_Oinsert @ SY3983 @ SY3984 @ SY3985 ) @ SY3985 @ SV429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2253]) ).
thf(2954,plain,
! [SV430: $i] :
( ( ! [SY3986: $i,SY3987: $i,SY3988: $i,SY3989: $i] :
( ( c_Com_Ocom_OCond @ SV430 @ SY3986 @ SY3987 )
!= ( c_Com_Ocom_OAss @ SY3988 @ SY3989 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2254]) ).
thf(2955,plain,
! [SV431: $i] :
( ( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ SV431 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2255]) ).
thf(2956,plain,
! [SV432: $i] :
( ( ! [SY3990: $i,SY3991: $i,SY3992: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV432 @ SY3990 @ SY3991 ) @ SY3992 @ ( tc_fun @ SY3991 @ tc_bool ) )
= ( c_Set_Oinsert @ SV432 @ ( c_HOL_Ominus__class_Ominus @ SY3990 @ SY3992 @ ( tc_fun @ SY3991 @ tc_bool ) ) @ SY3991 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY3991 ) @ SV432 ) @ SY3992 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2256]) ).
thf(2957,plain,
! [SV433: $i] :
( ( ! [SY3993: $i] :
( ( hBOOL @ ( hAPP @ SV433 @ SY3993 ) )
| ! [SY3994: $i,SY3995: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY3994 @ SV433 @ ( tc_fun @ SY3995 @ tc_bool ) ) @ SY3993 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2257]) ).
thf(2958,plain,
! [SV434: $i] :
( ( ! [SY3996: $i] :
( ( hBOOL @ ( hAPP @ SV434 @ SY3996 ) )
| ! [SY3997: $i,SY3998: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV434 @ SY3997 @ ( tc_fun @ SY3998 @ tc_bool ) ) @ SY3996 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(2959,plain,
! [SV435: $i] :
( ( ! [SY3999: $i,SY4000: $i,SY4001: $i] : ( c_Map_Omap__le @ SV435 @ ( c_Map_Omap__add @ SY3999 @ SV435 @ SY4000 @ SY4001 ) @ SY4000 @ SY4001 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2259]) ).
thf(2960,plain,
! [SV436: $i] :
( ( ! [SY4002: $i,SY4003: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV436 @ SY4002 @ SY4003 ) @ ( c_Set_Oinsert @ SV436 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4003 @ tc_bool ) ) @ SY4003 ) @ ( tc_fun @ SY4003 @ tc_bool ) )
= SY4002 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4003 ) @ SV436 ) @ SY4002 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2260]) ).
thf(2961,plain,
! [SV437: $i] :
( ( ! [SY4004: $i,SY4005: $i,SY4006: $i,SY4007: $i] :
( ( c_Set_Ovimage @ SV437 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4004 @ SY4005 @ ( tc_fun @ SY4006 @ tc_bool ) ) @ SY4007 @ SY4006 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Ovimage @ SV437 @ SY4004 @ SY4007 @ SY4006 ) @ ( c_Set_Ovimage @ SV437 @ SY4005 @ SY4007 @ SY4006 ) @ ( tc_fun @ SY4007 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2261]) ).
thf(2962,plain,
! [SV438: $i] :
( ( ! [SY4008: $i] :
( ( SV438 = SY4008 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ SY4008 ) @ SV438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2262]) ).
thf(2963,plain,
! [SV439: $i] :
( ( ! [SY4009: $i,SY4010: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV439 @ SY4009 @ ( tc_fun @ SY4010 @ tc_bool ) ) @ SY4010 )
| ~ ( c_Finite__Set_Ofinite @ SY4009 @ SY4010 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2263]) ).
thf(2964,plain,
! [SV440: $i] :
( ( ! [SY4011: $i,SY4012: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV440 @ SY4011 @ ( tc_fun @ SY4012 @ tc_bool ) ) @ SY4012 )
| ~ ( c_Finite__Set_Ofinite @ SV440 @ SY4012 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2264]) ).
thf(2965,plain,
! [SV441: $i] :
( ( ! [SY4013: $i,SY4014: $i,SY4015: $i,SY4016: $i] :
( ( c_Map_Omap__le @ ( c_Map_Omap__add @ SV441 @ SY4013 @ SY4014 @ SY4015 ) @ SY4016 @ SY4014 @ SY4015 )
| ~ ( c_Map_Omap__le @ SV441 @ ( c_Map_Omap__add @ SV441 @ SY4013 @ SY4014 @ SY4015 ) @ SY4014 @ SY4015 )
| ~ ( c_Map_Omap__le @ SY4013 @ SY4016 @ SY4014 @ SY4015 )
| ~ ( c_Map_Omap__le @ SV441 @ SY4016 @ SY4014 @ SY4015 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2265]) ).
thf(2966,plain,
! [SV442: $i] :
( ( ! [SY4017: $i,SY4018: $i] :
( ( hBOOL @ ( hAPP @ SV442 @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SY4017 @ SV442 @ SY4018 ) ) )
| ! [V_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4018 ) @ V_a ) @ SY4017 ) )
| ! [SY4020: $i] :
( ~ ( hBOOL @ ( hAPP @ SV442 @ SY4020 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4018 ) @ SY4020 ) @ SY4017 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2266]) ).
thf(2967,plain,
! [SV443: $i] :
( ( ! [SY4021: $i,SY4022: $i,SY4023: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ SY4021 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4022 @ SY4023 @ ( tc_fun @ SV443 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ SY4021 ) @ SY4023 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ SY4021 ) @ SY4022 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2267]) ).
thf(2968,plain,
! [SV444: $i] :
( ( ! [SY4024: $i,SY4025: $i,SY4026: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ SY4024 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4025 @ SY4026 @ ( tc_fun @ SV444 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ SY4024 ) @ SY4026 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ SY4024 ) @ SY4025 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2268]) ).
thf(2969,plain,
! [SV445: $i] :
( ( ! [SY4027: $i,SY4028: $i] :
( ( hBOOL @ ( hAPP @ SV445 @ SY4027 ) )
| ! [SY4029: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4028 ) @ SY4027 ) @ SY4029 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4028 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY4029 @ SV445 @ SY4028 ) ) @ SY4029 ) )
| ! [V_P: $i] :
~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY4029 @ V_P @ SY4028 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2269]) ).
thf(2970,plain,
! [SV446: $i] :
( ( ! [SY4031: $i,SY4032: $i] :
( ( hBOOL @ ( hAPP @ SV446 @ SY4031 ) )
| ! [SY4033: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4032 ) @ SY4031 ) @ SY4033 ) )
| ! [V_Q: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4032 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY4033 @ V_Q @ SY4032 ) ) @ SY4033 ) )
| ~ ( hBOOL @ ( hAPP @ SV446 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY4033 @ SV446 @ SY4032 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2270]) ).
thf(2971,plain,
! [SV447: $i] :
( ( ! [SY4035: $i,SY4036: $i] :
( ( hBOOL @ ( hAPP @ SV447 @ SY4035 ) )
| ! [SY4037: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4036 ) @ SY4035 ) @ SY4037 ) )
| ~ ( hBOOL @ ( hAPP @ SV447 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY4037 @ SV447 @ SY4036 ) ) )
| ! [V_P: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4036 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY4037 @ V_P @ SY4036 ) ) @ SY4037 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2271]) ).
thf(2972,plain,
! [SV448: $i] :
( ( ! [SY4039: $i,SY4040: $i] :
( ( hBOOL @ ( hAPP @ SV448 @ SY4039 ) )
| ! [SY4041: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4040 ) @ SY4039 ) @ SY4041 ) )
| ! [V_Q: $i] :
~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY4041 @ V_Q @ SY4040 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4040 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY4041 @ SV448 @ SY4040 ) ) @ SY4041 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2272]) ).
thf(2973,plain,
! [SV449: $i] :
( ( ! [SY4043: $i,SY4044: $i,SY4045: $i,SY4046: $i,SY4047: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV449 ) @ SY4043 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SY4044 @ SY4045 @ SY4046 @ SY4047 @ SV449 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4045 @ SY4043 ) @ SY4047 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4044 @ SY4046 ) @ SY4043 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2273]) ).
thf(2974,plain,
! [SV450: $i] :
( ( ! [SY4048: $i,SY4049: $i,SY4050: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV450 ) @ SY4048 ) @ ( c_Set_Oinsert @ SY4049 @ SY4050 @ SV450 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV450 ) @ SY4048 ) @ SY4050 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2274]) ).
thf(2975,plain,
! [SV451: $i] :
( ( ! [SY4051: $i,SY4052: $i,SY4053: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV451 ) @ SY4051 ) @ ( c_Set_Oinsert @ SY4052 @ SY4053 @ SV451 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV451 ) @ SY4051 ) @ SY4053 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2275]) ).
thf(2976,plain,
! [SV452: $i] :
( ( ! [SY4054: $i,SY4055: $i,SY4056: $i,SY4057: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV452 ) @ SY4054 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SY4055 @ SY4056 @ SY4057 @ SV452 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4055 @ SY4054 ) @ SY4057 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4055 @ SY4056 ) @ SY4054 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2276]) ).
thf(2977,plain,
! [SV453: $i] :
( ( ! [SY4058: $i,SY4059: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV453 ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SY4058 @ SY4059 @ SV453 ) ) @ SY4058 ) )
| ! [SY4060: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV453 ) @ SY4060 ) @ SY4058 ) )
| ~ ( hBOOL @ ( hAPP @ SY4059 @ SY4060 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2277]) ).
thf(2978,plain,
! [SV454: $i] :
( ( ! [SY4061: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV454 ) @ SY4061 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV454 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2278]) ).
thf(2979,plain,
! [SV455: $i] :
( ( ! [SY4062: $i] :
( ( hBOOL @ ( hAPP @ SV455 @ SY4062 ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ SY4062 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2279]) ).
thf(2980,plain,
! [SV456: $i] :
( ( ! [SY4064: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV456 ) @ SY4064 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV456 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2280]) ).
thf(2981,plain,
! [SV457: $i] :
( ( ! [SY4065: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV457 ) @ SY4065 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV457 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2281]) ).
thf(2982,plain,
! [SV458: $i] :
( ( ! [SY4066: $i,SY4067: $i,SY4068: $i,SY4069: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV458 ) @ SY4066 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SY4067 @ SY4068 @ SY4069 @ SV458 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4067 @ SY4066 ) @ SY4069 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4067 @ SY4068 ) @ SY4066 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2282]) ).
thf(2983,plain,
! [SV459: $i] :
( ( ! [SY4070: $i,SY4071: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV459 ) @ SY4070 ) @ SY4071 ) )
| ! [SY4072: $i] :
( ( SY4070 = SY4072 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV459 ) @ SY4070 ) @ ( c_Set_Oinsert @ SY4072 @ SY4071 @ SV459 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(2984,plain,
! [SV460: $i] :
( ( ! [SY4073: $i,SY4074: $i,SY4075: $i,SY4076: $i,SY4077: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV460 ) @ SY4073 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SY4074 @ SY4075 @ SY4076 @ SY4077 @ SV460 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4074 @ SY4073 ) @ SY4077 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4075 @ SY4076 ) @ SY4073 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(2985,plain,
! [SV461: $i] :
( ( ! [SY4078: $i,SY4079: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV461 ) @ SY4078 ) @ SY4079 ) )
| ! [SY4080: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV461 ) @ SY4078 ) @ ( c_HOL_Ominus__class_Ominus @ SY4080 @ SY4079 @ ( tc_fun @ SV461 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2285]) ).
thf(2986,plain,
! [SV462: $i] :
( ( ! [SY4081: $i,SY4082: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV462 ) @ SY4081 ) @ SY4082 ) )
| ! [SY4083: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV462 ) @ SY4081 ) @ ( c_HOL_Ominus__class_Ominus @ SY4082 @ SY4083 @ ( tc_fun @ SV462 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2286]) ).
thf(2987,plain,
! [SV463: $i] :
( ( ! [SY4084: $i,SY4085: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SY4084 @ SY4085 @ SV463 ) ) @ SY4084 ) )
| ! [SY4086: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ SY4086 ) @ SY4084 ) )
| ! [SY4087: $i] :
( ~ ( hBOOL @ ( hAPP @ SY4085 @ SY4087 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ SY4087 ) @ SY4084 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2287]) ).
thf(2988,plain,
! [SV464: $i] :
( ( ! [SY4088: $i,SY4089: $i] :
( ( hBOOL @ ( hAPP @ SV464 @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ SY4088 @ SV464 @ SY4089 ) ) )
| ! [SY4090: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4089 ) @ SY4090 ) @ SY4088 ) )
| ~ ( hBOOL @ ( hAPP @ SV464 @ SY4090 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2288]) ).
thf(2989,plain,
! [SV465: $i] :
( ( ! [SY4091: $i,SY4092: $i,SY4093: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV465 @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY4091 @ SY4092 @ SY4093 @ ( tc_fun @ SV465 @ tc_bool ) ) )
| ! [SY4094: $i] :
( ( ( hAPP @ SY4092 @ SY4094 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV465 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4093 ) @ SY4094 ) @ SY4091 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2289]) ).
thf(2990,plain,
! [SV466: $i] :
( ( ! [SY4095: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV466 @ tc_bool ) ) @ SY4095 @ ( tc_fun @ SV466 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV466 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2290]) ).
thf(2991,plain,
! [SV467: $i] :
( ( ! [SY4096: $i,SY4097: $i,SY4098: $i,SY4099: $i] :
( ( c_Com_Ocom_OAss @ SV467 @ SY4096 )
!= ( c_Com_Ocom_OCond @ SY4097 @ SY4098 @ SY4099 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2291]) ).
thf(2992,plain,
! [SV468: $i] :
( ( ! [SY4100: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ SV468 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY4100 ) @ tc_bool ) ) @ SY4100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(2993,plain,
! [SV469: $i] :
( ( ! [SY4101: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OWhile @ SV469 @ SY4101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2293]) ).
thf(2994,plain,
! [SV470: $i] :
( ( ! [SY4102: $i,SY4103: $i,SY4104: $i] :
( ( ( c_Map_Omap__add @ SV470 @ SY4102 @ SY4103 @ SY4104 )
= ( c_Map_Omap__add @ SY4102 @ SV470 @ SY4103 @ SY4104 ) )
| ~ ( c_Map_Omap__le @ SV470 @ ( c_Map_Omap__add @ SV470 @ SY4102 @ SY4103 @ SY4104 ) @ SY4103 @ SY4104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2294]) ).
thf(2995,plain,
! [SV471: $i] :
( ( ! [SY4105: $i,SY4106: $i,SY4107: $i] :
( ( ( c_Map_Omap__add @ SV471 @ SY4105 @ SY4106 @ SY4107 )
!= ( c_Map_Omap__add @ SY4105 @ SV471 @ SY4106 @ SY4107 ) )
| ( c_Map_Omap__le @ SV471 @ ( c_Map_Omap__add @ SV471 @ SY4105 @ SY4106 @ SY4107 ) @ SY4106 @ SY4107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2295]) ).
thf(2996,plain,
! [SV472: $i] :
( ( ! [SY4108: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV472 @ tc_bool ) ) @ SY4108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2296]) ).
thf(2997,plain,
! [SV473: $i] :
( ( ! [SY4109: $i,SY4110: $i,SY4111: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV473 @ ( c_HOL_Ominus__class_Ominus @ SY4109 @ SY4110 @ ( tc_fun @ SY4111 @ tc_bool ) ) @ ( tc_fun @ SY4111 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV473 @ SY4109 @ ( tc_fun @ SY4111 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV473 @ SY4110 @ ( tc_fun @ SY4111 @ tc_bool ) ) @ ( tc_fun @ SY4111 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2297]) ).
thf(2998,plain,
! [SV474: $i] :
( ( ! [SY4112: $i,SY4113: $i,SY4114: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ SV474 @ SY4112 @ ( tc_fun @ SY4113 @ tc_bool ) ) @ SY4114 @ ( tc_fun @ SY4113 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV474 @ SY4114 @ ( tc_fun @ SY4113 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4112 @ SY4114 @ ( tc_fun @ SY4113 @ tc_bool ) ) @ ( tc_fun @ SY4113 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2298]) ).
thf(2999,plain,
! [SV475: $i] :
( ( ! [SY4115: $i,SY4116: $i] :
( ( c_HOL_Oord__class_Oless @ SV475 @ SY4115 @ ( tc_fun @ SY4116 @ tc_bool ) )
| ! [SY4117: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4116 ) @ SY4117 ) @ SY4115 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV475 @ ( c_Set_Oinsert @ SY4117 @ SY4115 @ SY4116 ) @ ( tc_fun @ SY4116 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2299]) ).
thf(3000,plain,
! [SV476: $i] :
( ( ! [SY4118: $i,SY4119: $i,SY4120: $i] :
( ( c_HOL_Oord__class_Oless @ SV476 @ ( c_Set_Oinsert @ SY4118 @ SY4119 @ SY4120 ) @ ( tc_fun @ SY4120 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4120 ) @ SY4118 ) @ SY4119 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV476 @ SY4119 @ ( tc_fun @ SY4120 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2300]) ).
thf(3001,plain,
! [SV477: $i] :
( ( ! [SY4121: $i,SY4122: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OLocal @ SV477 @ SY4121 @ SY4122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2301]) ).
thf(3002,plain,
! [SV478: $i] :
( ( ! [SY4123: $i,SY4124: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV478 ) @ SY4123 ) @ SY4124 ) )
| ! [SY4125: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV478 ) @ SY4123 ) @ SY4125 ) )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY4125 @ SY4124 @ ( tc_fun @ SV478 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV478 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2302]) ).
thf(3003,plain,
! [SV479: $i] :
( ( ! [SY4126: $i,SY4127: $i,SY4128: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV479 @ SY4126 @ ( tc_fun @ SY4127 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4128 @ SY4126 @ ( tc_fun @ SY4127 @ tc_bool ) ) @ ( tc_fun @ SY4127 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV479 @ SY4126 @ ( tc_fun @ SY4127 @ tc_bool ) ) @ SY4128 @ ( tc_fun @ SY4127 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(3004,plain,
! [SV480: $i] :
( ( ! [SY4129: $i] :
~ ( c_HOL_Oord__class_Oless @ SV480 @ SV480 @ ( tc_fun @ SY4129 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2304]) ).
thf(3005,plain,
! [SV481: $i] :
( ( ~ ( class_Orderings_Oorder @ SV481 )
| ! [SY4130: $i] :
~ ( c_HOL_Oord__class_Oless @ SY4130 @ SY4130 @ SV481 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2305]) ).
thf(3006,plain,
! [SV482: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV482 )
| ! [SY4131: $i] :
~ ( c_HOL_Oord__class_Oless @ SY4131 @ SY4131 @ SV482 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2306]) ).
thf(3007,plain,
! [SV483: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV483 )
| ! [SY4132: $i] :
~ ( c_HOL_Oord__class_Oless @ SY4132 @ SY4132 @ SV483 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2307]) ).
thf(3008,plain,
! [SV484: $i] :
( ( ! [SY4133: $i] :
( ( c_Collect @ SV484 @ SY4133 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4133 @ tc_bool ) ) )
| ! [SY4134: $i] :
~ ( hBOOL @ ( hAPP @ SV484 @ SY4134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2308]) ).
thf(3009,plain,
! [SV485: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ SV485 ) @ SV485 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2309]) ).
thf(3010,plain,
! [SV486: $i] :
( ( ! [SY4135: $i,SY4136: $i,SY4137: $i] :
( ( c_Com_Ocom_OSemi @ SV486 @ SY4135 )
!= ( c_Com_Ocom_OAss @ SY4136 @ SY4137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2310]) ).
thf(3011,plain,
! [SV487: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV487 )
| ! [SY4138: $i,SY4139: $i] :
( ( c_HOL_Oord__class_Oless @ SY4138 @ SY4139 @ SV487 )
| ( SY4139 = SY4138 )
| ( c_HOL_Oord__class_Oless @ SY4139 @ SY4138 @ SV487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2311]) ).
thf(3012,plain,
! [SV488: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV488 )
| ! [SY4140: $i,SY4141: $i] :
( ( SY4140 = SY4141 )
| ( c_HOL_Oord__class_Oless @ SY4141 @ SY4140 @ SV488 )
| ( c_HOL_Oord__class_Oless @ SY4140 @ SY4141 @ SV488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2312]) ).
thf(3013,plain,
! [SV489: $i] :
( ( ! [SY4142: $i] :
( ( SV489 = SY4142 )
| ! [SY4143: $i,SY4144: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY4143 ) @ SY4144 ) @ SV489 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY4143 ) @ SY4144 ) @ SY4142 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2313]) ).
thf(3014,plain,
! [SV490: $i] :
( ( ! [SY4145: $i] :
( ( SV490 = SY4145 )
| ! [SY4146: $i,SY4147: $i] :
( ~ ( c_Map_Omap__le @ SY4145 @ SV490 @ SY4146 @ SY4147 )
| ~ ( c_Map_Omap__le @ SV490 @ SY4145 @ SY4146 @ SY4147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2314]) ).
thf(3015,plain,
! [SV491: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV491 )
| ! [SY4148: $i,SY4149: $i] :
( ( c_HOL_Oord__class_Oless @ SY4148 @ SY4149 @ SV491 )
| ( SY4149 = SY4148 )
| ( c_HOL_Oord__class_Oless @ SY4149 @ SY4148 @ SV491 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2315]) ).
thf(3016,plain,
! [SV492: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV492 )
| ! [SY4150: $i,SY4151: $i] :
( ( c_HOL_Oord__class_Oless @ SY4150 @ SY4151 @ SV492 )
| ( SY4151 = SY4150 )
| ( c_HOL_Oord__class_Oless @ SY4151 @ SY4150 @ SV492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2316]) ).
thf(3017,plain,
! [SV493: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV493 )
| ! [SY4152: $i,SY4153: $i] :
( ( SY4152 = SY4153 )
| ( c_HOL_Oord__class_Oless @ SY4152 @ SY4153 @ SV493 )
| ( c_HOL_Oord__class_Oless @ SY4153 @ SY4152 @ SV493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2317]) ).
thf(3018,plain,
! [SV494: $i] :
( ( ! [SY4154: $i,SY4155: $i] :
( ( c_Com_Ocom_OLocal @ SV494 @ SY4154 @ SY4155 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2318]) ).
thf(3019,plain,
! [SV495: $i] :
( ( ! [SY4156: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV495 )
| ! [SY4157: $i,SY4158: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4156 @ SY4157 @ SV495 ) @ SY4158 @ SV495 )
| ~ ( c_HOL_Oord__class_Oless @ SY4157 @ SY4158 @ SV495 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2319]) ).
thf(3020,plain,
! [SV496: $i] :
( ( ! [SY4159: $i] :
( ~ ( class_Lattices_Olower__semilattice @ SV496 )
| ! [SY4160: $i,SY4161: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4159 @ SY4160 @ SV496 ) @ SY4161 @ SV496 )
| ~ ( c_HOL_Oord__class_Oless @ SY4159 @ SY4161 @ SV496 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2320]) ).
thf(3021,plain,
! [SV497: $i] :
( ( ! [SY4162: $i,SY4163: $i] :
( ! [SY4164: $i] : ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV497 @ SY4162 @ SY4163 @ SY4164 ) @ SY4164 )
| ~ ( c_Finite__Set_Ofinite @ SY4162 @ SY4163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2321]) ).
thf(3022,plain,
! [SV498: $i] :
( ( ! [SY4165: $i,SY4166: $i,SY4167: $i] :
( ( ( hAPP @ SV498 @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ SV498 @ SY4165 @ SY4166 @ SY4167 ) )
!= ( hAPP @ SY4165 @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ SV498 @ SY4165 @ SY4166 @ SY4167 ) ) )
| ( c_Map_Omap__le @ SV498 @ SY4165 @ SY4166 @ SY4167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2322]) ).
thf(3023,plain,
! [SV499: $i] :
( ( ! [SY4168: $i,SY4169: $i,SY4170: $i,SY4171: $i] :
( ( ( c_Set_Oinsert @ SV499 @ ( c_Set_Oinsert @ SY4168 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4169 @ tc_bool ) ) @ SY4169 ) @ SY4169 )
!= ( c_Set_Oinsert @ SY4170 @ ( c_Set_Oinsert @ SY4171 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4169 @ tc_bool ) ) @ SY4169 ) @ SY4169 ) )
| ( SV499 = SY4171 )
| ( SV499 = SY4170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2323]) ).
thf(3024,plain,
! [SV500: $i] :
( ( ! [SY4172: $i,SY4173: $i,SY4174: $i] :
( ! [SY4175: $i] :
( ( c_Set_Oinsert @ SV500 @ ( c_Set_Oinsert @ SY4172 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4173 @ tc_bool ) ) @ SY4173 ) @ SY4173 )
!= ( c_Set_Oinsert @ SY4174 @ ( c_Set_Oinsert @ SY4175 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4173 @ tc_bool ) ) @ SY4173 ) @ SY4173 ) )
| ( SY4172 = SY4174 )
| ( SV500 = SY4174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2324]) ).
thf(3025,plain,
! [SV501: $i] :
( ( ! [SY4176: $i,SY4177: $i,SY4178: $i,SY4179: $i] :
( ( ( c_Set_Oinsert @ SV501 @ ( c_Set_Oinsert @ SY4176 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4177 @ tc_bool ) ) @ SY4177 ) @ SY4177 )
!= ( c_Set_Oinsert @ SY4178 @ ( c_Set_Oinsert @ SY4179 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4177 @ tc_bool ) ) @ SY4177 ) @ SY4177 ) )
| ( SV501 = SY4179 )
| ( SY4176 = SY4179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2325]) ).
thf(3026,plain,
! [SV502: $i] :
( ( ! [SY4180: $i,SY4181: $i,SY4182: $i,SY4183: $i] :
( ( ( c_Set_Oinsert @ SV502 @ ( c_Set_Oinsert @ SY4180 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4181 @ tc_bool ) ) @ SY4181 ) @ SY4181 )
!= ( c_Set_Oinsert @ SY4182 @ ( c_Set_Oinsert @ SY4183 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4181 @ tc_bool ) ) @ SY4181 ) @ SY4181 ) )
| ( SY4180 = SY4182 )
| ( SY4180 = SY4183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2326]) ).
thf(3027,plain,
! [SV503: $i] :
( ( ! [SY4184: $i,SY4185: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV503 ) @ SY4184 ) @ SY4185 ) )
| ! [SY4186: $i] :
( ( hBOOL @ ( hAPP @ SY4186 @ SY4184 ) )
| ! [SY4187: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY4186 @ SY4187 @ SV503 ) ) @ SY4184 ) @ SY4185 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2327]) ).
thf(3028,plain,
! [SV504: $i] :
( ( ! [SY4188: $i,SY4189: $i,SY4190: $i,SY4191: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV504 @ SY4188 @ SY4189 ) ) @ SY4190 ) @ SY4191 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY4189 ) @ SY4190 ) @ SY4191 ) )
| ( hBOOL @ ( hAPP @ SV504 @ SY4190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2328]) ).
thf(3029,plain,
! [SV505: $i] :
( ( ! [SY4192: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OAss @ SV505 @ SY4192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2329]) ).
thf(3030,plain,
! [SV506: $i] :
( ( ! [SY4193: $i,SY4194: $i,SY4195: $i,SY4196: $i,SY4197: $i,SY4198: $i,SY4199: $i,SY4200: $i] :
( ( ( hAPP @ SV506 @ ( c_Set_Oinsert @ SY4193 @ SY4194 @ SY4195 ) )
= ( hAPP @ ( hAPP @ SY4196 @ SY4193 ) @ ( hAPP @ SV506 @ SY4194 ) ) )
| ! [SY4201: $i,SY4202: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY4197 @ SV506 @ SY4198 @ SY4199 @ SY4200 @ SY4196 @ SY4201 @ SY4202 @ SY4195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2330]) ).
thf(3031,plain,
! [SV507: $i] :
( ( ! [SY4203: $i,SY4204: $i,SY4205: $i,SY4206: $i,SY4207: $i,SY4208: $i,SY4209: $i,SY4210: $i] :
( ( ( hAPP @ SV507 @ ( c_Set_Oinsert @ SY4203 @ SY4204 @ SY4205 ) )
= ( hAPP @ ( hAPP @ SY4206 @ SY4203 ) @ ( hAPP @ SV507 @ SY4204 ) ) )
| ! [SY4211: $i,SY4212: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV507 @ SY4207 @ SY4208 @ SY4209 @ SY4206 @ SY4210 @ SY4211 @ SY4212 @ SY4205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2331]) ).
thf(3032,plain,
! [SV508: $i] :
( ( ! [SY4213: $i,SY4214: $i,SY4215: $i] :
( ( c_Com_Ocom_OWhile @ SV508 @ SY4213 )
!= ( c_Com_Ocom_OAss @ SY4214 @ SY4215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2332]) ).
thf(3033,plain,
! [SV509: $i] :
( ( ! [SY4216: $i,SY4217: $i,SY4218: $i,SY4219: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SY4216 @ SY4217 @ SY4218 @ SY4219 @ SV509 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY4216 @ SY4217 @ SY4219 @ ( tc_fun @ SV509 @ tc_bool ) ) ) )
| ! [SY4220: $i] :
( ~ ( hBOOL @ ( hAPP @ SY4218 @ SY4220 ) )
| ! [SY4221: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ SY4220 ) @ ( hAPP @ SY4217 @ SY4221 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4219 ) @ SY4221 ) @ SY4216 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2333]) ).
thf(3034,plain,
! [SV510: $i] :
( ( ! [SY4222: $i,SY4223: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV510 @ tc_bool ) )
!= ( c_Set_Oinsert @ SY4222 @ SY4223 @ SV510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2334]) ).
thf(3035,plain,
! [SV511: $i] :
( ( ! [SY4224: $i,SY4225: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV511 @ SY4224 @ SY4225 )
| ! [SY4226: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV511 @ SY4226 @ SY4225 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY4226 @ SY4224 @ SY4225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2335]) ).
thf(3036,plain,
! [SV512: $i] :
( ( ! [SY4227: $i,SY4228: $i,SY4229: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV512 @ SY4227 @ SY4228 ) @ SY4229 @ ( tc_fun @ SY4228 @ tc_bool ) )
= ( c_Set_Oinsert @ SV512 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4227 @ SY4229 @ ( tc_fun @ SY4228 @ tc_bool ) ) @ SY4228 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4228 ) @ SV512 ) @ SY4229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2336]) ).
thf(3037,plain,
! [SV513: $i] :
( ( ! [SY4230: $i,SY4231: $i,SY4232: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV513 @ ( c_Set_Oinsert @ SY4230 @ SY4231 @ SY4232 ) @ ( tc_fun @ SY4232 @ tc_bool ) )
= ( c_Set_Oinsert @ SY4230 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV513 @ SY4231 @ ( tc_fun @ SY4232 @ tc_bool ) ) @ SY4232 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4232 ) @ SY4230 ) @ SV513 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2337]) ).
thf(3038,plain,
! [SV514: $i] :
( ( ! [SY4233: $i,SY4234: $i,SY4235: $i,SY4236: $i] :
( ( c_Set_Oimage @ SV514 @ ( c_Set_Oinsert @ SY4233 @ SY4234 @ SY4235 ) @ SY4235 @ SY4236 )
= ( c_Set_Oinsert @ ( hAPP @ SV514 @ SY4233 ) @ ( c_Set_Oimage @ SV514 @ SY4234 @ SY4235 @ SY4236 ) @ SY4236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2338]) ).
thf(3039,plain,
! [SV515: $i] :
( ( ! [SY4237: $i,SY4238: $i,SY4239: $i,SY4240: $i,SY4241: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV515 @ SY4237 @ SY4238 @ SY4239 ) @ SY4240 )
!= ( c_Option_Ooption_OSome @ SY4241 @ SY4239 ) )
| ( ( hAPP @ SY4237 @ SY4240 )
= ( c_Option_Ooption_ONone @ SY4239 ) )
| ( ( hAPP @ SY4237 @ SY4240 )
= ( c_Option_Ooption_OSome @ SY4241 @ SY4239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2339]) ).
thf(3040,plain,
! [SV516: $i] :
( ( ! [SY4242: $i,SY4243: $i] :
( ( ( hAPP @ SV516 @ SY4242 )
= SY4243 )
| ! [SY4244: $i,SY4245: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4244 ) @ SY4242 ) @ ( c_Set_Ovimage @ SV516 @ ( c_Set_Oinsert @ SY4243 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4245 @ tc_bool ) ) @ SY4245 ) @ SY4244 @ SY4245 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2340]) ).
thf(3041,plain,
! [SV517: $i] :
( ( ! [SY4246: $i,SY4247: $i,SY4248: $i] :
( ( ( c_Com_Ocom_OAss @ SV517 @ SY4246 )
!= ( c_Com_Ocom_OAss @ SY4247 @ SY4248 ) )
| ( SY4246 = SY4248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2341]) ).
thf(3042,plain,
! [SV518: $i] :
( ( ! [SY4249: $i,SY4250: $i] :
( ! [SY4251: $i] :
( ( c_Com_Ocom_OAss @ SV518 @ SY4249 )
!= ( c_Com_Ocom_OAss @ SY4250 @ SY4251 ) )
| ( SV518 = SY4250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2342]) ).
thf(3043,plain,
! [SV519: $i] :
( ( ! [SY4252: $i,SY4253: $i,SY4254: $i] :
( ( c_Set_Oinsert @ SV519 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4252 @ tc_bool ) ) @ SY4253 @ SY4252 @ ( tc_fun @ SY4254 @ tc_bool ) ) @ SY4254 )
= ( c_Set_Oinsert @ SV519 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4254 @ tc_bool ) ) @ SY4254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(3044,plain,
! [SV520: $i] :
( ( ! [SY4255: $i] :
( ( c_Com_Ocom_OSemi @ SV520 @ SY4255 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2344]) ).
thf(3045,plain,
! [SV521: $i] :
( ( ! [SY4256: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV521 @ tc_bool ) )
!= ( c_Collect @ SY4256 @ SV521 ) )
| ! [V_x: $i] :
~ ( hBOOL @ ( hAPP @ SY4256 @ V_x ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2345]) ).
thf(3046,plain,
! [SV522: $i] :
( ( ! [SY4258: $i,SY4259: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV522 @ SY4258 @ SY4259 ) @ SV522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2346]) ).
thf(3047,plain,
! [SV523: $i] :
( ( ~ ( class_Lattices_Olattice @ SV523 )
| ! [SY4260: $i,SY4261: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY4260 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4260 @ SY4261 @ SV523 ) @ SV523 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY4260 @ SY4261 @ SV523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2347]) ).
thf(3048,plain,
! [SV524: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV524 )
| ! [SY4262: $i,SY4263: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY4262 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4262 @ SY4263 @ SV524 ) @ SV524 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY4262 @ SY4263 @ SV524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2348]) ).
thf(3049,plain,
! [SV525: $i] :
( ( ! [SY4264: $i,SY4265: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV525 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV525 @ SY4264 @ ( tc_fun @ SY4265 @ tc_bool ) ) @ ( tc_fun @ SY4265 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV525 @ SY4264 @ ( tc_fun @ SY4265 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2349]) ).
thf(3050,plain,
! [SV526: $i] :
( ( ! [SY4266: $i,SY4267: $i,SY4268: $i,SY4269: $i,SY4270: $i] :
( ( ( c_Com_Ocom_OLocal @ SV526 @ SY4266 @ SY4267 )
!= ( c_Com_Ocom_OLocal @ SY4268 @ SY4269 @ SY4270 ) )
| ( SY4267 = SY4270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2350]) ).
thf(3051,plain,
! [SV527: $i] :
( ( ! [SY4271: $i,SY4272: $i,SY4273: $i,SY4274: $i] :
( ! [SY4275: $i] :
( ( c_Com_Ocom_OLocal @ SV527 @ SY4271 @ SY4272 )
!= ( c_Com_Ocom_OLocal @ SY4273 @ SY4274 @ SY4275 ) )
| ( SY4271 = SY4274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2351]) ).
thf(3052,plain,
! [SV528: $i] :
( ( ! [SY4276: $i,SY4277: $i,SY4278: $i] :
( ! [SY4279: $i,SY4280: $i] :
( ( c_Com_Ocom_OLocal @ SV528 @ SY4276 @ SY4277 )
!= ( c_Com_Ocom_OLocal @ SY4278 @ SY4279 @ SY4280 ) )
| ( SV528 = SY4278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2352]) ).
thf(3053,plain,
! [SV529: $i] :
( ( ! [SY4281: $i,SY4282: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV529 @ SY4281 @ ( tc_fun @ SY4282 @ tc_bool ) ) @ SY4282 )
| ! [SY4283: $i] :
~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV529 @ ( c_Set_Oinsert @ SY4283 @ SY4281 @ SY4282 ) @ ( tc_fun @ SY4282 @ tc_bool ) ) @ SY4282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2353]) ).
thf(3054,plain,
! [SV530: $i] :
( ( ! [SY4284: $i,SY4285: $i,SY4286: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV530 @ ( c_Set_Oinsert @ SY4284 @ SY4285 @ SY4286 ) @ ( tc_fun @ SY4286 @ tc_bool ) ) @ SY4286 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV530 @ SY4285 @ ( tc_fun @ SY4286 @ tc_bool ) ) @ SY4286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2354]) ).
thf(3055,plain,
! [SV531: $i] :
( ( ! [SY4287: $i,SY4288: $i,SY4289: $i] :
( ( c_Com_Ocom_OWhile @ SV531 @ SY4287 )
!= ( c_Com_Ocom_OSemi @ SY4288 @ SY4289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2355]) ).
thf(3056,plain,
! [SV532: $i] :
( ( ! [SY4290: $i,SY4291: $i,SY4292: $i,SY4293: $i,SY4294: $i,SY4295: $i] :
( ( ( hAPP @ SV532 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4290 @ tc_bool ) ) )
= SY4291 )
| ! [SY4296: $i,SY4297: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY4292 @ SV532 @ SY4293 @ SY4294 @ SY4295 @ SY4296 @ SY4291 @ SY4297 @ SY4290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2356]) ).
thf(3057,plain,
! [SV533: $i] :
( ( ! [SY4298: $i,SY4299: $i,SY4300: $i,SY4301: $i,SY4302: $i,SY4303: $i] :
( ( ( hAPP @ SV533 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4298 @ tc_bool ) ) )
= SY4299 )
| ! [SY4304: $i,SY4305: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV533 @ SY4300 @ SY4301 @ SY4302 @ SY4303 @ SY4304 @ SY4305 @ SY4299 @ SY4298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2357]) ).
thf(3058,plain,
! [SV534: $i] :
( ( ! [SY4306: $i] :
( ( hBOOL @ ( hAPP @ SV534 @ SY4306 ) )
| ! [SY4307: $i] :
( ( SY4307 = SY4306 )
| ! [SY4308: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV534 @ SY4308 ) ) @ SY4306 ) @ SY4307 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2358]) ).
thf(3059,plain,
! [SV535: $i] :
( ( ! [SY4309: $i,SY4310: $i] :
( ( ( c_Set_Oinsert @ SV535 @ ( c_HOL_Ominus__class_Ominus @ SY4309 @ ( c_Set_Oinsert @ SV535 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4310 @ tc_bool ) ) @ SY4310 ) @ ( tc_fun @ SY4310 @ tc_bool ) ) @ SY4310 )
= SY4309 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4310 ) @ SV535 ) @ SY4309 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2359]) ).
thf(3060,plain,
! [SV536: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV536 )
| ! [SY4311: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY4311 @ SY4311 @ SV536 )
= SY4311 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2360]) ).
thf(3061,plain,
! [SV537: $i] :
( ( ! [SY4312: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV537 @ SV537 @ ( tc_fun @ SY4312 @ tc_bool ) )
= SV537 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2361]) ).
thf(3062,plain,
! [SV538: $i] :
( ( ! [SY4313: $i,SY4314: $i] :
( ! [SY4315: $i] :
( ( c_Set_Oimage @ SV538 @ SY4313 @ SY4314 @ SY4315 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4315 @ tc_bool ) ) )
| ( SY4313
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4314 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2362]) ).
thf(3063,plain,
! [SV539: $i] :
( ( ! [SY4316: $i] :
( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ SV539 ) @ SV539 @ SV539 @ tc_bool ) @ SY4316 ) @ SV539 )
= ( c_Set_Oinsert @ SY4316 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV539 @ tc_bool ) ) @ SV539 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2363]) ).
thf(3064,plain,
! [SV540: $i] :
( ( ! [SY4317: $i,SY4318: $i,SY4319: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ SY4317 @ ( tc_fun @ SY4318 @ tc_bool ) ) @ SY4319 @ ( tc_fun @ SY4318 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ ( c_HOL_Ominus__class_Ominus @ SY4317 @ SY4319 @ ( tc_fun @ SY4318 @ tc_bool ) ) @ ( tc_fun @ SY4318 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2364]) ).
thf(3065,plain,
! [SV541: $i] :
( ( ! [SY4320: $i,SY4321: $i,SY4322: $i,SY4323: $i,SY4324: $i,SY4325: $i,SY4326: $i] :
( ( ( hAPP @ SV541 @ ( c_Set_Oinsert @ SY4320 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4321 @ tc_bool ) ) @ SY4321 ) )
= SY4320 )
| ! [SY4327: $i,SY4328: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY4322 @ SV541 @ SY4323 @ SY4324 @ SY4325 @ SY4326 @ SY4327 @ SY4328 @ SY4321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2365]) ).
thf(3066,plain,
! [SV542: $i] :
( ( ! [SY4329: $i,SY4330: $i,SY4331: $i,SY4332: $i,SY4333: $i,SY4334: $i,SY4335: $i] :
( ( ( hAPP @ SV542 @ ( c_Set_Oinsert @ SY4329 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4330 @ tc_bool ) ) @ SY4330 ) )
= SY4329 )
| ! [SY4336: $i,SY4337: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV542 @ SY4331 @ SY4332 @ SY4333 @ SY4334 @ SY4335 @ SY4336 @ SY4337 @ SY4330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2366]) ).
thf(3067,plain,
! [SV543: $i] :
( ( ! [SY4338: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV543 ) @ SY4338 ) @ ( c_Set_Oinsert @ SY4338 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV543 @ tc_bool ) ) @ SV543 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2367]) ).
thf(3068,plain,
! [SV544: $i] :
( ( ! [SY4339: $i,SY4340: $i] :
( ( c_Com_Ocom_OWhile @ SV544 @ SY4339 )
!= ( c_Com_Ocom_OBODY @ SY4340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2368]) ).
thf(3069,plain,
! [SV545: $i] :
( ( ! [SY4341: $i,SY4342: $i,SY4343: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SY4341 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4342 @ ( c_Collect @ SY4343 @ SV545 ) @ ( tc_fun @ SV545 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SY4343 @ SY4341 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SY4341 ) @ SY4342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2369]) ).
thf(3070,plain,
! [SV546: $i] :
( ( ( c_Com_Ocom_OBODY @ SV546 )
!= c_Com_Ocom_OSKIP )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2370]) ).
thf(3071,plain,
! [SV547: $i] :
( ( ! [SY4344: $i,SY4345: $i] :
( ( hBOOL @ ( hAPP @ SV547 @ ( hAPP @ SY4344 @ SY4345 ) ) )
| ! [SY4346: $i,SY4347: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SY4344 @ SV547 @ SY4346 @ SY4347 ) @ SY4345 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2371]) ).
thf(3072,plain,
! [SV548: $i] :
( ( ! [SY4348: $i,SY4349: $i,SY4350: $i,SY4351: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV548 @ SY4348 @ SY4349 @ SY4350 ) @ SY4351 ) )
| ~ ( hBOOL @ ( hAPP @ SY4348 @ ( hAPP @ SV548 @ SY4351 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2372]) ).
thf(3073,plain,
! [SV549: $i] :
( ( ! [SY4352: $i,SY4353: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV549 @ SY4352 @ SY4353 )
| ! [SY4354: $i] :
~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV549 @ ( c_Set_Oinsert @ SY4354 @ SY4352 @ ( tc_Hoare__Mirabelle_Otriple @ SY4353 ) ) @ SY4353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2373]) ).
thf(3074,plain,
! [SV550: $i] :
( ( ! [SY4355: $i,SY4356: $i,SY4357: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV550 @ ( c_Set_Oinsert @ SY4355 @ SY4356 @ ( tc_Hoare__Mirabelle_Otriple @ SY4357 ) ) @ SY4357 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV550 @ SY4356 @ SY4357 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV550 @ ( c_Set_Oinsert @ SY4355 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY4357 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY4357 ) ) @ SY4357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2374]) ).
thf(3075,plain,
! [SV551: $i] :
( ( ! [SY4358: $i,SY4359: $i,SY4360: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV551 @ SY4358 @ ( tc_fun @ SY4359 @ tc_bool ) ) @ SY4360 ) )
| ~ ( hBOOL @ ( hAPP @ SY4358 @ SY4360 ) )
| ~ ( hBOOL @ ( hAPP @ SV551 @ SY4360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2375]) ).
thf(3076,plain,
! [SV552: $i] :
( ( ! [SY4361: $i,SY4362: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV552 )
| ! [SY4363: $i,SY4364: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SY4361 @ SY4362 @ SV552 )
!= ( c_HOL_Ominus__class_Ominus @ SY4363 @ SY4364 @ SV552 ) )
| ( c_HOL_Oord__class_Oless @ SY4363 @ SY4364 @ SV552 )
| ~ ( c_HOL_Oord__class_Oless @ SY4361 @ SY4362 @ SV552 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2376]) ).
thf(3077,plain,
! [SV553: $i] :
( ( ! [SY4365: $i,SY4366: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV553 )
| ! [SY4367: $i,SY4368: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SY4365 @ SY4366 @ SV553 )
!= ( c_HOL_Ominus__class_Ominus @ SY4367 @ SY4368 @ SV553 ) )
| ( c_HOL_Oord__class_Oless @ SY4365 @ SY4366 @ SV553 )
| ~ ( c_HOL_Oord__class_Oless @ SY4367 @ SY4368 @ SV553 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2377]) ).
thf(3078,plain,
! [SV554: $i] :
( ( ! [SY4369: $i] :
( ( c_Com_Ocom_OAss @ SV554 @ SY4369 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2378]) ).
thf(3079,plain,
! [SV555: $i] :
( ( ! [SY4370: $i] :
( ( c_Collect @ ( hAPP @ ( c_fequal @ SV555 ) @ SY4370 ) @ SV555 )
= ( c_Set_Oinsert @ SY4370 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV555 @ tc_bool ) ) @ SV555 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2379]) ).
thf(3080,plain,
! [SV556: $i] :
( ( ! [SY4371: $i] :
( ( c_Finite__Set_Ofinite @ SV556 @ SY4371 )
| ! [SY4372: $i,SY4373: $i] :
( ~ ( c_Fun_Oinj__on @ SY4372 @ SV556 @ SY4371 @ SY4373 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SY4372 @ SV556 @ SY4371 @ SY4373 ) @ SY4373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2380]) ).
thf(3081,plain,
! [SV557: $i] :
( ( ! [SY4374: $i,SY4375: $i] :
( ( c_Set_Ovimage @ SV557 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4374 @ tc_bool ) ) @ SY4375 @ SY4374 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4375 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2381]) ).
thf(3082,plain,
! [SV558: $i] :
( ( ! [SY4376: $i,SY4377: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV558 ) @ SY4376 ) @ SY4377 ) )
| ! [SY4378: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY4378 ) @ SY4376 ) @ SY4377 ) )
| ! [SY4379: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY4379 @ SY4378 @ SV558 ) ) @ SY4376 ) @ SY4377 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2382]) ).
thf(3083,plain,
! [SV559: $i] :
( ( ! [SY4380: $i] :
( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_in @ SV559 ) @ SV559 @ ( tc_fun @ SV559 @ tc_bool ) @ tc_bool ) @ SY4380 ) @ SV559 )
= SY4380 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2383]) ).
thf(3084,plain,
! [SV560: $i] :
( ( ! [SY4381: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ SV560 @ SY4381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2384]) ).
thf(3085,plain,
! [SV561: $i] :
( ( ~ ( class_Orderings_Oorder @ SV561 )
| ! [SY4382: $i,SY4383: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY4382 @ SY4383 @ SV561 )
| ~ ( c_HOL_Oord__class_Oless @ SY4383 @ SY4382 @ SV561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2385]) ).
thf(3086,plain,
! [SV562: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV562 )
| ! [SY4384: $i,SY4385: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY4384 @ SY4385 @ SV562 )
| ~ ( c_HOL_Oord__class_Oless @ SY4385 @ SY4384 @ SV562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2386]) ).
thf(3087,plain,
! [SV563: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV563 )
| ! [SY4386: $i,SY4387: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY4386 @ SY4387 @ SV563 )
| ~ ( c_HOL_Oord__class_Oless @ SY4387 @ SY4386 @ SV563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2387]) ).
thf(3088,plain,
! [SV564: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV564 )
| ! [SY4388: $i,SY4389: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY4388 @ SY4389 @ SV564 )
| ~ ( c_HOL_Oord__class_Oless @ SY4389 @ SY4388 @ SV564 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2388]) ).
thf(3089,plain,
! [SV565: $i] :
( ( ! [SY4390: $i,SY4391: $i] :
( ( hBOOL @ ( hAPP @ SV565 @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ SY4390 @ SV565 @ SY4391 ) ) )
| ! [SY4392: $i] :
( ~ ( hBOOL @ ( hAPP @ SV565 @ SY4392 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4391 ) @ SY4392 ) @ SY4390 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2389]) ).
thf(3090,plain,
! [SV566: $i] :
( ( ! [SY4393: $i,SY4394: $i,SY4395: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV566 @ SY4393 ) @ SY4394 ) )
| ! [SY4396: $i,SY4397: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4395 ) @ SY4394 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SY4396 @ SV566 @ SY4393 @ SY4397 @ SY4395 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2390]) ).
thf(3091,plain,
! [SV567: $i] :
( ( ! [SY4398: $i,SY4399: $i,SY4400: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV567 @ SY4398 ) @ SY4399 ) )
| ! [SY4401: $i,SY4402: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4400 ) @ SY4398 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV567 @ SY4401 @ SY4402 @ SY4399 @ SY4400 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2391]) ).
thf(3092,plain,
! [SV568: $i] :
( ( ! [SY4403: $i,SY4404: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV568 ) @ SY4403 ) @ SY4404 ) )
| ! [SY4405: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV568 ) @ SY4403 ) @ SY4405 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4405 @ SY4404 @ ( tc_fun @ SV568 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2392]) ).
thf(3093,plain,
! [SV569: $i] :
( ( ! [SY4406: $i,SY4407: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV569 ) @ SY4406 ) @ ( c_Set_Oinsert @ SY4406 @ SY4407 @ SV569 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2393]) ).
thf(3094,plain,
! [SV570: $i] :
( ( ! [SY4408: $i,SY4409: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV570 ) @ SY4408 ) @ ( c_Set_Oinsert @ SY4408 @ SY4409 @ SV570 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2394]) ).
thf(3095,plain,
! [SV571: $i] :
( ( ! [SY4410: $i,SY4411: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV571 ) @ SY4410 ) @ ( c_Set_Oinsert @ SY4410 @ SY4411 @ SV571 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2395]) ).
thf(3096,plain,
! [SV572: $i] :
( ( ! [SY4412: $i,SY4413: $i] :
( ( hBOOL @ ( hAPP @ SV572 @ SY4412 ) )
| ! [SY4414: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4413 ) @ SY4412 ) @ SY4414 ) )
| ~ ( hBOOL @ ( hAPP @ SV572 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY4414 @ SV572 @ SY4413 ) ) )
| ! [V_P: $i] :
~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY4414 @ V_P @ SY4413 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2396]) ).
thf(3097,plain,
! [SV573: $i] :
( ( ! [SY4416: $i,SY4417: $i] :
( ( hBOOL @ ( hAPP @ SV573 @ SY4416 ) )
| ! [SY4418: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4417 ) @ SY4416 ) @ SY4418 ) )
| ! [V_Q: $i] :
~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY4418 @ V_Q @ SY4417 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV573 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY4418 @ SV573 @ SY4417 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2397]) ).
thf(3098,plain,
! [SV574: $i] :
( ( ! [SY4420: $i,SY4421: $i] :
( ( hBOOL @ ( hAPP @ SV574 @ SY4420 ) )
| ! [SY4422: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4421 ) @ SY4420 ) @ SY4422 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4421 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY4422 @ SV574 @ SY4421 ) ) @ SY4422 ) )
| ! [V_P: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4421 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY4422 @ V_P @ SY4421 ) ) @ SY4422 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2398]) ).
thf(3099,plain,
! [SV575: $i] :
( ( ! [SY4424: $i,SY4425: $i] :
( ( hBOOL @ ( hAPP @ SV575 @ SY4424 ) )
| ! [SY4426: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4425 ) @ SY4424 ) @ SY4426 ) )
| ! [V_Q: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4425 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY4426 @ V_Q @ SY4425 ) ) @ SY4426 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4425 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY4426 @ SV575 @ SY4425 ) ) @ SY4426 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2399]) ).
thf(3100,plain,
! [SV576: $i] :
( ( ! [SY4428: $i,SY4429: $i] :
( ( hBOOL @ ( hAPP @ SV576 @ SY4428 ) )
| ! [SY4430: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4429 ) @ SY4428 ) @ SY4430 ) )
| ! [SY4431: $i] :
( ~ ( hBOOL @ ( hAPP @ SV576 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SY4430 @ SY4431 @ SV576 @ SY4429 ) ) )
| ~ ( hBOOL @ ( hAPP @ SY4431 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SY4430 @ SY4431 @ SV576 @ SY4429 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2400]) ).
thf(3101,plain,
! [SV577: $i] :
( ( ! [SY4432: $i,SY4433: $i] :
( ( hBOOL @ ( hAPP @ SV577 @ SY4432 ) )
| ! [SY4434: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4433 ) @ SY4432 ) @ SY4434 ) )
| ! [SY4435: $i] :
( ~ ( hBOOL @ ( hAPP @ SY4435 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SY4434 @ SV577 @ SY4435 @ SY4433 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV577 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SY4434 @ SV577 @ SY4435 @ SY4433 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2401]) ).
thf(3102,plain,
! [SV578: $i] :
( ( ! [SY4436: $i,SY4437: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV578 ) @ SY4436 ) @ SY4437 ) )
| ! [SY4438: $i] :
( ( hBOOL @ ( hAPP @ SY4438 @ SY4436 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV578 ) @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ SY4437 @ SY4438 @ SV578 ) ) @ SY4437 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2402]) ).
thf(3103,plain,
! [SV579: $i] :
( ( ! [SY4439: $i,SY4440: $i] :
( ( hBOOL @ ( hAPP @ SV579 @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SY4439 @ SV579 @ SY4440 ) ) )
| ! [SY4441: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4440 ) @ SY4441 ) @ SY4439 ) )
| ~ ( hBOOL @ ( hAPP @ SV579 @ SY4441 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2403]) ).
thf(3104,plain,
! [SV580: $i] :
( ( ! [SY4442: $i,SY4443: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV580 @ SY4442 ) @ SY4443 ) )
| ! [SY4444: $i,SY4445: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4444 ) @ SY4443 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV580 @ SY4442 @ SY4445 @ SY4444 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(3105,plain,
! [SV581: $i] :
( ( ! [SY4446: $i,SY4447: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV581 @ SY4446 ) @ SY4447 ) )
| ! [SY4448: $i,SY4449: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4448 ) @ SY4446 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV581 @ SY4449 @ SY4447 @ SY4448 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2405]) ).
thf(3106,plain,
! [SV582: $i] :
( ( ! [SY4450: $i,SY4451: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV582 ) @ SY4450 ) @ SY4451 ) )
| ! [SY4452: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV582 ) @ SY4450 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4452 @ SY4451 @ ( tc_fun @ SV582 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2406]) ).
thf(3107,plain,
! [SV583: $i] :
( ( ! [SY4453: $i,SY4454: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV583 ) @ SY4453 ) @ SY4454 ) )
| ! [SY4455: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV583 ) @ SY4453 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4454 @ SY4455 @ ( tc_fun @ SV583 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2407]) ).
thf(3108,plain,
! [SV584: $i] :
( ( ! [SY4456: $i,SY4457: $i,SY4458: $i] :
( ( ( hAPP @ SV584 @ SY4456 )
!= ( hAPP @ SV584 @ SY4457 ) )
| ! [SY4459: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4458 ) @ SY4457 ) @ SY4459 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4458 ) @ SY4456 ) @ SY4459 ) )
| ( SY4456 = SY4457 )
| ! [SY4460: $i] :
~ ( c_Fun_Oinj__on @ SV584 @ SY4459 @ SY4458 @ SY4460 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2408]) ).
thf(3109,plain,
! [SV585: $i] :
( ( ! [SY4461: $i,SY4462: $i,SY4463: $i] :
( ( ( hAPP @ SV585 @ SY4461 )
!= ( hAPP @ SV585 @ SY4462 ) )
| ! [SY4464: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4463 ) @ SY4462 ) @ SY4464 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4463 ) @ SY4461 ) @ SY4464 ) )
| ! [SY4465: $i] :
~ ( c_Fun_Oinj__on @ SV585 @ SY4464 @ SY4463 @ SY4465 )
| ( SY4461 = SY4462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2409]) ).
thf(3110,plain,
! [SV586: $i] :
( ( ! [SY4466: $i,SY4467: $i,SY4468: $i] :
( ( ( hAPP @ SV586 @ SY4466 )
!= ( hAPP @ SV586 @ SY4467 ) )
| ! [SY4469: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4468 ) @ SY4467 ) @ SY4469 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4468 ) @ SY4466 ) @ SY4469 ) )
| ! [SY4470: $i] :
~ ( c_Fun_Oinj__on @ SV586 @ SY4469 @ SY4468 @ SY4470 )
| ( SY4466 = SY4467 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2410]) ).
thf(3111,plain,
! [SV587: $i] :
( ( ! [SY4471: $i,SY4472: $i,SY4473: $i] :
( ( ( hAPP @ SV587 @ SY4471 )
!= ( hAPP @ SV587 @ SY4472 ) )
| ! [SY4474: $i] :
( ! [SY4475: $i] :
~ ( c_Fun_Oinj__on @ SV587 @ SY4473 @ SY4474 @ SY4475 )
| ( SY4471 = SY4472 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4474 ) @ SY4472 ) @ SY4473 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4474 ) @ SY4471 ) @ SY4473 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2411]) ).
thf(3112,plain,
! [SV588: $i] :
( ( ! [SY4476: $i] :
( ~ ( hBOOL @ ( hAPP @ SV588 @ SY4476 ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ T_a ) @ SY4476 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2412]) ).
thf(3113,plain,
! [SV589: $i] :
( ( ! [SY4478: $i,SY4479: $i] :
( ( ( hAPP @ ( c_COMBC @ ( c_in @ SV589 ) @ SV589 @ ( tc_fun @ SV589 @ tc_bool ) @ tc_bool ) @ SY4478 )
!= ( hAPP @ ( c_COMBC @ ( c_in @ SV589 ) @ SV589 @ ( tc_fun @ SV589 @ tc_bool ) @ tc_bool ) @ SY4479 ) )
| ( SY4478 = SY4479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2413]) ).
thf(3114,plain,
! [SV590: $i] :
( ( ! [SY4480: $i,SY4481: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV590 ) @ SY4480 ) @ ( c_Collect @ SY4481 @ SV590 ) ) )
| ~ ( hBOOL @ ( hAPP @ SY4481 @ SY4480 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2414]) ).
thf(3115,plain,
! [SV591: $i] :
( ( ! [SY4482: $i] :
( ( hBOOL @ ( hAPP @ SV591 @ SY4482 ) )
| ! [SY4483: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4483 ) @ SY4482 ) @ ( c_Collect @ SV591 @ SY4483 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2415]) ).
thf(3116,plain,
! [SV592: $i] :
( ( ! [SY4484: $i,SY4485: $i,SY4486: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV592 ) @ SY4484 ) @ ( c_SetInterval_Oord_OatMost @ SY4485 @ SY4486 @ SV592 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4485 @ SY4484 ) @ SY4486 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2416]) ).
thf(3117,plain,
! [SV593: $i] :
( ( ! [SY4487: $i,SY4488: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV593 @ SY4487 ) @ SY4488 ) )
| ! [SY4489: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4489 ) @ SY4487 ) @ ( c_SetInterval_Oord_OatMost @ SV593 @ SY4488 @ SY4489 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2417]) ).
thf(3118,plain,
! [SV594: $i] :
( ( ! [SY4490: $i,SY4491: $i,SY4492: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV594 ) @ SY4490 ) @ ( c_HOL_Ominus__class_Ominus @ SY4491 @ SY4492 @ ( tc_fun @ SV594 @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV594 ) @ SY4490 ) @ SY4492 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV594 ) @ SY4490 ) @ SY4491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2418]) ).
thf(3119,plain,
! [SV595: $i] :
( ( ! [SY4493: $i,SY4494: $i,SY4495: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV595 ) @ SY4493 ) @ ( c_HOL_Ominus__class_Ominus @ SY4494 @ SY4495 @ ( tc_fun @ SV595 @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV595 ) @ SY4493 ) @ SY4495 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV595 ) @ SY4493 ) @ SY4494 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2419]) ).
thf(3120,plain,
! [SV596: $i] :
( ( ! [SY4496: $i,SY4497: $i] :
( ( hBOOL @ ( hAPP @ SV596 @ SY4496 ) )
| ! [SY4498: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4497 ) @ SY4496 ) @ SY4498 ) )
| ! [SY4499: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4497 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SY4498 @ SY4499 @ SV596 @ SY4497 ) ) @ SY4498 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2420]) ).
thf(3121,plain,
! [SV597: $i] :
( ( ! [SY4500: $i,SY4501: $i] :
( ( hBOOL @ ( hAPP @ SV597 @ SY4500 ) )
| ! [SY4502: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4501 ) @ SY4500 ) @ SY4502 ) )
| ! [SY4503: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4501 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SY4502 @ SV597 @ SY4503 @ SY4501 ) ) @ SY4502 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2421]) ).
thf(3122,plain,
! [SV598: $i] :
( ( ! [SY4504: $i,SY4505: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV598 ) @ SY4504 ) @ SY4505 ) )
| ! [SY4506: $i] :
( ( hBOOL @ ( hAPP @ SY4506 @ SY4504 ) )
| ~ ( hBOOL @ ( hAPP @ SY4506 @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ SY4505 @ SY4506 @ SV598 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2422]) ).
thf(3123,plain,
! [SV599: $i] :
( ( ! [SY4507: $i,SY4508: $i,SY4509: $i] :
( ( ( c_Set_Oinsert @ SV599 @ SY4507 @ SY4508 )
!= ( c_Set_Oinsert @ SV599 @ SY4509 @ SY4508 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4508 ) @ SV599 ) @ SY4509 ) )
| ( SY4507 = SY4509 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4508 ) @ SV599 ) @ SY4507 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2423]) ).
thf(3124,plain,
! [SV600: $i] :
( ( ! [SY4510: $i,SY4511: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV600 ) @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ SY4510 @ SY4511 @ SV600 ) ) @ SY4510 ) )
| ! [SY4512: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV600 ) @ SY4512 ) @ SY4510 ) )
| ~ ( hBOOL @ ( hAPP @ SY4511 @ SY4512 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2424]) ).
thf(3125,plain,
! [SV601: $i] :
( ( ! [SY4513: $i,SY4514: $i,SY4515: $i,SY4516: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV601 ) @ SY4513 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY4514 @ SY4515 @ SY4516 @ ( tc_fun @ SV601 @ tc_bool ) ) ) )
| ! [SY4517: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV601 ) @ SY4513 ) @ ( hAPP @ SY4515 @ SY4517 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4516 ) @ SY4517 ) @ SY4514 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2425]) ).
thf(3126,plain,
! [SV602: $i] :
( ( ! [SY4518: $i,SY4519: $i,SY4520: $i,SY4521: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV602 ) @ SY4518 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY4519 @ SY4520 @ SY4521 @ ( tc_fun @ SV602 @ tc_bool ) ) ) )
| ! [SY4522: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV602 ) @ SY4518 ) @ ( hAPP @ SY4520 @ SY4522 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4521 ) @ SY4522 ) @ SY4519 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2426]) ).
thf(3127,plain,
! [SV603: $i] :
( ( ! [SY4523: $i,SY4524: $i,SY4525: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV603 ) @ SY4523 ) @ ( c_SetInterval_Oord_OgreaterThan @ SY4524 @ SY4525 @ SV603 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4524 @ SY4525 ) @ SY4523 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2427]) ).
thf(3128,plain,
! [SV604: $i] :
( ( ! [SY4526: $i,SY4527: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV604 @ SY4526 ) @ SY4527 ) )
| ! [SY4528: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4528 ) @ SY4527 ) @ ( c_SetInterval_Oord_OgreaterThan @ SV604 @ SY4526 @ SY4528 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2428]) ).
thf(3129,plain,
! [SV605: $i] :
( ( ! [SY4529: $i,SY4530: $i,SY4531: $i,SY4532: $i] :
( ( hBOOL @ ( hAPP @ SV605 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SY4529 @ SY4530 @ SV605 @ SY4531 @ SY4532 ) ) )
| ! [SY4533: $i] :
( ~ ( hBOOL @ ( hAPP @ SV605 @ SY4533 ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4532 ) @ SY4533 ) @ ( hAPP @ SY4530 @ V_x ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4531 ) @ V_x ) @ SY4529 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2429]) ).
thf(3130,plain,
! [SV606: $i] :
( ( ! [SY4535: $i,SY4536: $i,SY4537: $i,SY4538: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV606 ) @ SY4535 ) @ ( c_Set_Ovimage @ SY4536 @ SY4537 @ SV606 @ SY4538 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4538 ) @ ( hAPP @ SY4536 @ SY4535 ) ) @ SY4537 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2430]) ).
thf(3131,plain,
! [SV607: $i] :
( ( ! [SY4539: $i,SY4540: $i,SY4541: $i,SY4542: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV607 ) @ SY4539 ) @ ( c_Set_Ovimage @ SY4540 @ SY4541 @ SV607 @ SY4542 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4542 ) @ ( hAPP @ SY4540 @ SY4539 ) ) @ SY4541 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2431]) ).
thf(3132,plain,
! [SV608: $i] :
( ( ! [SY4543: $i,SY4544: $i,SY4545: $i,SY4546: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV608 ) @ SY4543 ) @ ( c_Set_Ovimage @ SY4544 @ SY4545 @ SV608 @ SY4546 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4546 ) @ ( hAPP @ SY4544 @ SY4543 ) ) @ SY4545 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2432]) ).
thf(3133,plain,
! [SV609: $i] :
( ( ! [SY4547: $i,SY4548: $i,SY4549: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV609 ) @ ( hAPP @ SY4547 @ SY4548 ) ) @ SY4549 ) )
| ! [SY4550: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4550 ) @ SY4548 ) @ ( c_Set_Ovimage @ SY4547 @ SY4549 @ SY4550 @ SV609 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2433]) ).
thf(3134,plain,
! [SV610: $i] :
( ( ! [SY4551: $i,SY4552: $i,SY4553: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV610 ) @ ( hAPP @ SY4551 @ SY4552 ) ) @ SY4553 ) )
| ! [SY4554: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4554 ) @ SY4552 ) @ ( c_Set_Ovimage @ SY4551 @ SY4553 @ SY4554 @ SV610 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2434]) ).
thf(3135,plain,
! [SV611: $i] :
( ( ! [SY4555: $i,SY4556: $i,SY4557: $i,SY4558: $i,SY4559: $i,SY4560: $i,SY4561: $i,SY4562: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV611 @ ( hAPP @ SY4555 @ SY4556 ) ) @ SY4557 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4558 ) @ SY4557 ) @ SY4556 ) )
| ! [SY4563: $i,SY4564: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY4555 @ SY4559 @ SV611 @ SY4560 @ SY4561 @ SY4562 @ SY4563 @ SY4564 @ SY4558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2435]) ).
thf(3136,plain,
! [SV612: $i] :
( ( ! [SY4565: $i,SY4566: $i,SY4567: $i,SY4568: $i,SY4569: $i,SY4570: $i,SY4571: $i,SY4572: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV612 @ SY4565 ) @ ( hAPP @ SY4566 @ SY4567 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4568 ) @ SY4565 ) @ SY4567 ) )
| ! [SY4573: $i,SY4574: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY4569 @ SY4566 @ SV612 @ SY4570 @ SY4571 @ SY4572 @ SY4573 @ SY4574 @ SY4568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2436]) ).
thf(3137,plain,
! [SV613: $i] :
( ( ! [SY4575: $i,SY4576: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV613 @ SY4575 ) @ SY4576 ) )
| ! [SY4577: $i,SY4578: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4577 ) @ SY4575 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV613 @ SY4578 @ SY4576 @ SY4577 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2437]) ).
thf(3138,plain,
! [SV614: $i] :
( ( ! [SY4579: $i,SY4580: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV614 @ SY4579 ) @ SY4580 ) )
| ! [SY4581: $i,SY4582: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4581 ) @ SY4580 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV614 @ SY4579 @ SY4582 @ SY4581 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2438]) ).
thf(3139,plain,
! [SV615: $i] :
( ( ! [SY4583: $i,SY4584: $i,SY4585: $i] :
( ( hBOOL @ ( hAPP @ SV615 @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SY4583 @ SY4584 @ SV615 @ SY4585 ) ) )
| ! [SY4586: $i] :
( ~ ( hBOOL @ ( hAPP @ SV615 @ SY4586 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4585 ) @ SY4586 ) @ SY4584 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2439]) ).
thf(3140,plain,
! [SV616: $i] :
( ( ! [SY4587: $i,SY4588: $i,SY4589: $i] :
( ( hBOOL @ ( hAPP @ SV616 @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SY4587 @ SY4588 @ SV616 @ SY4589 ) ) )
| ! [SY4590: $i] :
( ~ ( hBOOL @ ( hAPP @ SV616 @ SY4590 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4589 ) @ SY4590 ) @ SY4587 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2440]) ).
thf(3141,plain,
! [SV617: $i] :
( ( ! [SY4591: $i,SY4592: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV617 ) @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ SY4591 @ SY4592 @ SV617 ) ) @ SY4591 ) )
| ! [SY4593: $i] :
( ~ ( hBOOL @ ( hAPP @ SY4592 @ SY4593 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV617 ) @ SY4593 ) @ SY4591 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2441]) ).
thf(3142,plain,
! [SV618: $i] :
( ( ! [SY4594: $i,SY4595: $i] :
( ( ( c_Set_Oinsert @ SV618 @ SY4594 @ SY4595 )
= SY4594 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4595 ) @ SV618 ) @ SY4594 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2442]) ).
thf(3143,plain,
! [SV619: $i] :
( ( ! [SY4596: $i,SY4597: $i,SY4598: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV619 ) @ SY4596 ) @ ( c_SetInterval_Oord_OlessThan @ SY4597 @ SY4598 @ SV619 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4597 @ SY4596 ) @ SY4598 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2443]) ).
thf(3144,plain,
! [SV620: $i] :
( ( ! [SY4599: $i,SY4600: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV620 @ SY4599 ) @ SY4600 ) )
| ! [SY4601: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4601 ) @ SY4599 ) @ ( c_SetInterval_Oord_OlessThan @ SV620 @ SY4600 @ SY4601 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2444]) ).
thf(3145,plain,
! [SV621: $i] :
( ( ! [SY4602: $i,SY4603: $i,SY4604: $i,SY4605: $i,SY4606: $i,SY4607: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV621 @ SY4602 @ SY4603 @ ( tc_fun @ SY4604 @ ( tc_fun @ SY4605 @ tc_bool ) ) ) @ SY4606 ) @ SY4607 ) )
| ! [SY4608: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SY4602 @ SY4608 ) @ SY4606 ) @ SY4607 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4603 ) @ SY4608 ) @ SV621 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2445]) ).
thf(3146,plain,
! [SV622: $i] :
( ( ! [SY4609: $i,SY4610: $i,SY4611: $i,SY4612: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV622 @ SY4609 @ SY4610 @ ( tc_fun @ SY4611 @ tc_bool ) ) @ SY4612 ) )
| ! [SY4613: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4609 @ SY4613 ) @ SY4612 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4610 ) @ SY4613 ) @ SV622 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2446]) ).
thf(3147,plain,
! [SV623: $i] :
( ( ! [SY4614: $i,SY4615: $i,SY4616: $i,SY4617: $i,SY4618: $i,SY4619: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV623 @ SY4614 @ SY4615 @ ( tc_fun @ SY4616 @ ( tc_fun @ SY4617 @ tc_bool ) ) ) @ SY4618 ) @ SY4619 ) )
| ! [SY4620: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SY4614 @ SY4620 ) @ SY4618 ) @ SY4619 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4615 ) @ SY4620 ) @ SV623 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2447]) ).
thf(3148,plain,
! [SV624: $i] :
( ( ! [SY4621: $i,SY4622: $i,SY4623: $i,SY4624: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV624 @ SY4621 @ SY4622 @ ( tc_fun @ SY4623 @ tc_bool ) ) @ SY4624 ) )
| ! [SY4625: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4621 @ SY4625 ) @ SY4624 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4622 ) @ SY4625 ) @ SV624 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2448]) ).
thf(3149,plain,
! [SV625: $i] :
( ( ! [SY4626: $i,SY4627: $i,SY4628: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SY4626 ) @ SY4627 ) )
| ! [SY4629: $i,SY4630: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4628 ) @ SY4626 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SY4629 @ SV625 @ SY4630 @ SY4627 @ SY4628 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2449]) ).
thf(3150,plain,
! [SV626: $i] :
( ( ! [SY4631: $i,SY4632: $i,SY4633: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV626 @ SY4631 ) @ SY4632 ) )
| ! [SY4634: $i,SY4635: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4633 ) @ SY4632 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV626 @ SY4634 @ SY4631 @ SY4635 @ SY4633 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2450]) ).
thf(3151,plain,
! [SV627: $i] :
( ( ! [SY4636: $i,SY4637: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV627 ) @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ SY4636 @ SY4637 @ SV627 ) ) @ SY4636 ) )
| ! [SY4638: $i] :
( ~ ( hBOOL @ ( hAPP @ SY4637 @ SY4638 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV627 ) @ SY4638 ) @ SY4636 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2451]) ).
thf(3152,plain,
! [SV628: $i] :
( ( ! [SY4639: $i,SY4640: $i] :
( ( hBOOL @ ( hAPP @ SV628 @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ SY4639 @ SV628 @ SY4640 ) ) )
| ! [SY4641: $i] :
( ~ ( hBOOL @ ( hAPP @ SV628 @ SY4641 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4640 ) @ SY4641 ) @ SY4639 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2452]) ).
thf(3153,plain,
! [SV629: $i] :
( ( ! [SY4642: $i,SY4643: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV629 ) @ SY4642 ) @ SY4643 ) )
| ! [SY4644: $i,SY4645: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4644 ) @ ( hAPP @ SY4645 @ SY4642 ) ) @ ( c_Set_Oimage @ SY4645 @ SY4643 @ SV629 @ SY4644 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2453]) ).
thf(3154,plain,
! [SV630: $i] :
( ( ! [SY4646: $i,SY4647: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV630 ) @ SY4646 ) @ SY4647 ) )
| ! [SY4648: $i,SY4649: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4648 ) @ ( hAPP @ SY4649 @ SY4646 ) ) @ ( c_Set_Oimage @ SY4649 @ SY4647 @ SV630 @ SY4648 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2454]) ).
thf(3155,plain,
! [SV631: $i] :
( ( ! [SY4650: $i,SY4651: $i,SY4652: $i,SY4653: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV631 ) @ ( hAPP @ SY4650 @ SY4651 ) ) @ ( c_Set_Oimage @ SY4650 @ SY4652 @ SY4653 @ SV631 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4653 ) @ SY4651 ) @ SY4652 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2455]) ).
thf(3156,plain,
! [SV632: $i] :
( ( ! [SY4654: $i,SY4655: $i,SY4656: $i,SY4657: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV632 ) @ ( hAPP @ SY4654 @ SY4655 ) ) @ ( c_Set_Oimage @ SY4654 @ SY4656 @ SY4657 @ SV632 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4657 ) @ SY4655 ) @ SY4656 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2456]) ).
thf(3157,plain,
! [SV633: $i] :
( ( ! [SY4658: $i,SY4659: $i,SY4660: $i] :
( ( ( hAPP @ SV633 @ SY4658 )
= ( c_Option_Ooption_OSome @ ( c_Map_Osko__Map__XdomD__1__1 @ SY4658 @ SV633 @ SY4659 @ SY4660 ) @ SY4660 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4659 ) @ SY4658 ) @ ( c_Map_Odom @ SV633 @ SY4659 @ SY4660 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2457]) ).
thf(3158,plain,
! [SV634: $i] :
( ( ! [SY4661: $i,SY4662: $i,SY4663: $i] :
( ( c_Map_Omap__le @ SV634 @ SY4661 @ SY4662 @ SY4663 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4662 ) @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ SV634 @ SY4661 @ SY4662 @ SY4663 ) ) @ ( c_Map_Odom @ SV634 @ SY4662 @ SY4663 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2458]) ).
thf(3159,plain,
! [SV635: $i] :
( ( ( ( hAPP @ c_Com_Obody @ SV635 )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) )
| ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ SV635 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2459]) ).
thf(3160,plain,
! [SV636: $i] :
( ( ! [SY4664: $i,SY4665: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV636 ) ) @ SY4664 ) @ SY4665 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SV636 ) @ tc_Com_Ocom ) ) @ SY4664 ) @ SY4665 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2460]) ).
thf(3161,plain,
! [SV637: $i] :
( ( ! [SY4666: $i,SY4667: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SV637 ) @ tc_Com_Ocom ) ) @ SY4666 ) @ SY4667 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV637 ) ) @ SY4666 ) @ SY4667 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2461]) ).
thf(3162,plain,
! [SV638: $i] :
( ( ! [SY4668: $i] :
( ( c_Option_Othe @ ( c_Option_Ooption_OSome @ SV638 @ SY4668 ) @ SY4668 )
= SV638 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2462]) ).
thf(3163,plain,
! [SV639: $i] :
( ( ( c_Com_OWT @ SV639 )
| ! [SY4669: $i,SY4670: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SY4669 @ SV639 @ SY4670 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2463]) ).
thf(3164,plain,
! [SV640: $i] :
( ( ( c_Com_OWT @ SV640 )
| ! [SY4671: $i,SY4672: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SY4671 @ SY4672 @ SV640 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2464]) ).
thf(3165,plain,
! [SV641: $i] :
( ( ! [SY4673: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV641 @ SY4673 ) )
| ~ ( c_Com_OWT @ SY4673 )
| ~ ( c_Com_OWT @ SV641 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2465]) ).
thf(3166,plain,
! [SV642: $i] :
( ( ( c_Com_OWT @ SV642 )
| ! [SY4674: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV642 @ SY4674 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2466]) ).
thf(3167,plain,
! [SV643: $i] :
( ( ( c_Com_OWT @ SV643 )
| ! [SY4675: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SY4675 @ SV643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2467]) ).
thf(3168,plain,
! [SV644: $i] :
( ( ! [SY4676: $i,SY4677: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV644 @ SY4676 @ SY4677 ) )
| ~ ( c_Com_OWT @ SY4677 )
| ~ ( c_Com_OWT @ SY4676 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2468]) ).
thf(3169,plain,
! [SV645: $i] :
( ( ! [SY4678: $i] : ( c_Com_OWT @ ( c_Com_Ocom_OAss @ SV645 @ SY4678 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2470]) ).
thf(3170,plain,
! [SV646: $i] :
( ( ! [SY4679: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ SV646 @ SY4679 ) )
| ~ ( c_Com_OWT @ SY4679 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2471]) ).
thf(3171,plain,
! [SV647: $i] :
( ( ( c_Com_OWT @ SV647 )
| ! [SY4680: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ SY4680 @ SV647 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2472]) ).
thf(3172,plain,
! [SV648: $i] :
( ( ! [SY4681: $i,SY4682: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ SV648 @ SY4681 @ SY4682 ) )
| ~ ( c_Com_OWT @ SY4682 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2473]) ).
thf(3173,plain,
! [SV649: $i] :
( ( ( c_Com_OWT @ SV649 )
| ! [SY4683: $i,SY4684: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ SY4683 @ SY4684 @ SV649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2474]) ).
thf(3174,plain,
! [SV650: $i] :
( ( ! [SY4685: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV650 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ SY4685 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Com_OWT @ SY4685 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ tc_Com_Opname ) @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ SV650 ) ) @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) ) )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2475]) ).
thf(3175,plain,
( ( ( ! [V_t: $i] :
( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ V_t )
!= V_t ) )
= $true )
| ( ( ~ c_Hoare__Mirabelle_Ostate__not__singleton ) = $true ) ),
inference(extcnf_or_pos,[status(thm)],[2476]) ).
thf(3176,plain,
! [SV651: $i] :
( ( ! [SY4686: $i,SY4687: $i,SY4688: $i,SY4689: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV651 @ SY4686 @ SY4687 @ SY4688 ) @ SY4689 )
= ( hAPP @ SV651 @ SY4689 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4687 ) @ SY4689 ) @ ( c_Map_Odom @ SY4686 @ SY4687 @ SY4688 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2477]) ).
thf(3177,plain,
! [SV652: $i] :
( ( ! [SY4690: $i,SY4691: $i,SY4692: $i,SY4693: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV652 @ SY4690 @ SY4691 @ SY4692 ) @ SY4693 )
= ( hAPP @ SY4690 @ SY4693 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4691 ) @ SY4693 ) @ ( c_Map_Odom @ SV652 @ SY4691 @ SY4692 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2478]) ).
thf(3178,plain,
! [SV653: $i] :
( ( ! [SY4694: $i,SY4695: $i,SY4696: $i] :
( ( ( hAPP @ SY4695 @ SY4694 )
= ( c_Option_Ooption_ONone @ SY4696 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV653 ) @ SY4694 ) @ ( c_Map_Odom @ SY4695 @ SV653 @ SY4696 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2479]) ).
thf(3179,plain,
! [SV654: $i] :
( ( ! [SY4697: $i,SY4698: $i] :
( ( ( hAPP @ SV654 @ SY4697 )
!= ( c_Option_Ooption_ONone @ SY4698 ) )
| ! [SY4699: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4699 ) @ SY4697 ) @ ( c_Map_Odom @ SV654 @ SY4699 @ SY4698 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2480]) ).
thf(3180,plain,
! [SV655: $i] :
( ( ! [SY4700: $i,SY4701: $i,SY4702: $i] :
( ( ( hAPP @ SV655 @ SY4700 )
!= ( c_Option_Ooption_OSome @ SY4701 @ SY4702 ) )
| ! [SY4703: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4703 ) @ SY4700 ) @ ( c_Map_Odom @ SV655 @ SY4703 @ SY4702 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2481]) ).
thf(3181,plain,
! [SV656: $i] :
( ( ! [SY4704: $i,SY4705: $i] :
( ( ( hAPP @ SV656 @ SY4704 )
= ( hAPP @ SY4705 @ SY4704 ) )
| ! [SY4706: $i,SY4707: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4706 ) @ SY4704 ) @ ( c_Map_Odom @ SV656 @ SY4706 @ SY4707 ) ) )
| ~ ( c_Map_Omap__le @ SV656 @ SY4705 @ SY4706 @ SY4707 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2482]) ).
thf(3182,plain,
! [SV657: $i] :
( ( ! [SY4708: $i,SY4709: $i,SY4710: $i,SY4711: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV657 @ SY4708 @ SY4709 @ SY4710 ) @ SY4711 )
= ( hAPP @ SY4708 @ SY4711 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4709 ) @ SY4711 ) @ ( c_Map_Odom @ SY4708 @ SY4709 @ SY4710 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2483]) ).
thf(3183,plain,
! [SV658: $i] :
( ( ! [SY4712: $i] :
( ( ( hAPP @ c_Com_Obody @ SV658 )
!= ( c_Option_Ooption_OSome @ SY4712 @ tc_Com_Ocom ) )
| ~ c_Com_OWT__bodies
| ( c_Com_OWT @ SY4712 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2485]) ).
thf(3184,plain,
( ( ( ! [V_x: $i,V_xa: $i] : ( V_x = V_xa ) )
= $true )
| ( c_Hoare__Mirabelle_Ostate__not__singleton = $true ) ),
inference(extcnf_or_pos,[status(thm)],[2486]) ).
thf(3185,plain,
! [SV659: $i] :
( ( ! [SY4713: $i,SY4714: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV659 ) @ SY4713 ) @ SY4714 ) )
| ~ ( hBOOL @ ( hAPP @ SY4714 @ SY4713 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2487]) ).
thf(3186,plain,
! [SV660: $i] :
( ( ! [SY4715: $i] :
( ( hBOOL @ ( hAPP @ SV660 @ SY4715 ) )
| ! [SY4716: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4716 ) @ SY4715 ) @ SV660 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2488]) ).
thf(3187,plain,
! [SV661: $i] :
( ( ! [SY4717: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV661 @ SY4717 ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ SY4717 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2489]) ).
thf(3188,plain,
! [SV662: $i] :
( ( ! [SY4718: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV662 @ SY4718 ) )
| ~ ( class_Lattices_Olattice @ SY4718 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2490]) ).
thf(3189,plain,
! [SV663: $i] :
( ( ! [SY4719: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV663 @ SY4719 ) )
| ~ ( class_Lattices_Olattice @ SY4719 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2491]) ).
thf(3190,plain,
! [SV664: $i] :
( ( ! [SY4720: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV664 @ SY4720 ) )
| ~ ( class_Lattices_Odistrib__lattice @ SY4720 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2492]) ).
thf(3191,plain,
! [SV665: $i] :
( ( ! [SY4721: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV665 @ SY4721 ) )
| ~ ( class_Lattices_Obounded__lattice @ SY4721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2493]) ).
thf(3192,plain,
! [SV666: $i] :
( ( ! [SY4722: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ SV666 @ SY4722 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SY4722 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SV666 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2494]) ).
thf(3193,plain,
! [SV667: $i] :
( ( ! [SY4723: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ SV667 @ SY4723 ) )
| ~ ( class_Orderings_Opreorder @ SY4723 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2495]) ).
thf(3194,plain,
! [SV668: $i] :
( ( ! [SY4724: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ SV668 @ SY4724 ) )
| ~ ( class_Lattices_Olattice @ SY4724 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2496]) ).
thf(3195,plain,
! [SV669: $i] :
( ( ! [SY4725: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ SV669 @ SY4725 ) )
| ~ ( class_Orderings_Oorder @ SY4725 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2497]) ).
thf(3196,plain,
! [SV670: $i] :
( ( ! [SY4726: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ SV670 @ SY4726 ) )
| ~ ( class_Orderings_Obot @ SY4726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2498]) ).
thf(3197,plain,
! [SV671: $i] :
( ( ! [SY4727: $i] :
( ( class_HOL_Oord @ ( tc_fun @ SV671 @ SY4727 ) )
| ~ ( class_HOL_Oord @ SY4727 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2499]) ).
thf(3198,plain,
! [SV672: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_Option_Ooption @ SV672 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SV672 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2520]) ).
thf(3199,plain,
! [SV673: $i] :
( ( ! [SY4728: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV673 ) @ SY4728 ) @ SY4728 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2521]) ).
thf(3200,plain,
! [SV674: $i] :
( ( ! [SY4729: $i] :
( ( SV674 = SY4729 )
| ! [SY4730: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY4730 ) @ SV674 ) @ SY4729 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2522]) ).
thf(3201,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[2523]) ).
thf(3202,plain,
! [SV1: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV1 ) )
= $true )
| ( ( ! [SY2704: $i,SY2705: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2704 @ SY2705 @ SV1 ) @ SY2704 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2525]) ).
thf(3203,plain,
! [SV2: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV2 ) )
= $true )
| ( ( ! [SY2706: $i,SY2707: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2706 @ SY2707 @ SV2 ) @ SY2707 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2526]) ).
thf(3204,plain,
! [SV675: $i,SV3: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV3 )
| ! [SY4731: $i,SY4732: $i] :
( ( c_lessequals @ SV675 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4731 @ SY4732 @ SV3 ) @ SV3 )
| ~ ( c_lessequals @ SV675 @ SY4732 @ SV3 )
| ~ ( c_lessequals @ SV675 @ SY4731 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2527]) ).
thf(3205,plain,
! [SV676: $i,SV4: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV4 )
| ! [SY4733: $i,SY4734: $i] :
( ( c_lessequals @ SV676 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4733 @ SY4734 @ SV4 ) @ SV4 )
| ~ ( c_lessequals @ SV676 @ SY4734 @ SV4 )
| ~ ( c_lessequals @ SV676 @ SY4733 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2528]) ).
thf(3206,plain,
! [SV677: $i,SV5: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV5 )
| ! [SY4735: $i,SY4736: $i] :
( ( c_lessequals @ SV677 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4735 @ SY4736 @ SV5 ) @ SV5 )
| ~ ( c_lessequals @ SV677 @ SY4736 @ SV5 )
| ~ ( c_lessequals @ SV677 @ SY4735 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2529]) ).
thf(3207,plain,
! [SV6: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV6 ) )
= $true )
| ( ( ! [SY2717: $i,SY2718: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2717 @ SY2718 @ SV6 ) @ SY2718 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2530]) ).
thf(3208,plain,
! [SV7: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV7 ) )
= $true )
| ( ( ! [SY2719: $i,SY2720: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2719 @ SY2720 @ SV7 ) @ SY2719 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2531]) ).
thf(3209,plain,
! [SV678: $i,SV8: $i] :
( ( ! [SY4737: $i,SY4738: $i,SY4739: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV8 @ SV678 @ ( tc_fun @ SY4737 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4738 @ SY4739 @ ( tc_fun @ SY4737 @ tc_bool ) ) @ ( tc_fun @ SY4737 @ tc_bool ) )
| ~ ( c_lessequals @ SV678 @ SY4739 @ ( tc_fun @ SY4737 @ tc_bool ) )
| ~ ( c_lessequals @ SV8 @ SY4738 @ ( tc_fun @ SY4737 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2532]) ).
thf(3210,plain,
! [SV679: $i,SV10: $i] :
( ( ( SV10
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV679 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV10 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV679 @ tc_bool ) ) @ ( tc_fun @ SV679 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2534]) ).
thf(3211,plain,
! [SV680: $i,SV11: $i] :
( ( ! [SY4740: $i,SY4741: $i,SY4742: $i,SY4743: $i,SY4744: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV11 @ SV680 @ SY4740 @ SY4741 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SY4742 @ SY4743 @ SY4744 @ SY4741 ) )
| ( SY4740 = SY4744 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2535]) ).
thf(3212,plain,
! [SV681: $i,SV12: $i] :
( ( ! [SY4745: $i,SY4746: $i,SY4747: $i,SY4748: $i] :
( ! [SY4749: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV12 @ SV681 @ SY4745 @ SY4746 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SY4747 @ SY4748 @ SY4749 @ SY4746 ) )
| ( SV681 = SY4748 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2536]) ).
thf(3213,plain,
! [SV682: $i,SV13: $i] :
( ( ! [SY4750: $i,SY4751: $i,SY4752: $i] :
( ! [SY4753: $i,SY4754: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV13 @ SV682 @ SY4750 @ SY4751 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SY4752 @ SY4753 @ SY4754 @ SY4751 ) )
| ( SV13 = SY4752 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2537]) ).
thf(3214,plain,
! [SV683: $i,SV14: $i] :
( ( ! [SY4755: $i,SY4756: $i] :
( ( c_Fun_Ofun__upd @ SV14 @ SV683 @ ( hAPP @ SV14 @ SV683 ) @ SY4755 @ SY4756 )
= SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2538]) ).
thf(3215,plain,
! [SV684: $i,SV15: $i] :
( ( ! [SY4757: $i,SY4758: $i,SY4759: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV15 @ SV684 @ SY4757 @ SY4758 @ SY4759 ) @ SV684 )
= SY4757 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2539]) ).
thf(3216,plain,
! [SV685: $i,SV16: $i] :
( ( ! [SY4760: $i,SY4761: $i] :
( ( c_Fun_Ofun__upd @ SV16 @ SV685 @ ( hAPP @ SV16 @ SV685 ) @ SY4760 @ SY4761 )
= SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2540]) ).
thf(3217,plain,
! [SV686: $i,SV17: $i] :
( ( ! [SY4762: $i,SY4763: $i,SY4764: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV17 @ SV686 @ SY4762 @ SY4763 @ SY4764 ) @ SV686 )
= SY4762 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2541]) ).
thf(3218,plain,
! [SV687: $i,SV18: $i] :
( ( ! [SY4765: $i,SY4766: $i] :
( ( c_Fun_Ofun__upd @ SV18 @ SV687 @ ( hAPP @ SV18 @ SV687 ) @ SY4765 @ SY4766 )
= SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2542]) ).
thf(3219,plain,
! [SV688: $i,SV19: $i] :
( ( ! [SY4767: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV19 @ SV688 @ ( tc_fun @ SY4767 @ tc_bool ) )
!= SV688 )
| ( c_lessequals @ SV19 @ SV688 @ ( tc_fun @ SY4767 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2543]) ).
thf(3220,plain,
! [SV689: $i,SV20: $i] :
( ( ! [SY4768: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV20 @ SV689 @ ( tc_fun @ SY4768 @ tc_bool ) )
= SV20 )
| ~ ( c_lessequals @ SV689 @ SV20 @ ( tc_fun @ SY4768 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2544]) ).
thf(3221,plain,
! [SV690: $i,SV21: $i] :
( ( ! [SY4769: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV21 @ SV690 @ ( tc_fun @ SY4769 @ tc_bool ) )
= SV690 )
| ~ ( c_lessequals @ SV21 @ SV690 @ ( tc_fun @ SY4769 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2545]) ).
thf(3222,plain,
! [SV22: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV22 ) )
= $true )
| ( ( ! [SY2767: $i,SY2768: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2767 @ SY2768 @ SV22 )
= SY2768 )
| ~ ( c_lessequals @ SY2767 @ SY2768 @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2546]) ).
thf(3223,plain,
! [SV23: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV23 ) )
= $true )
| ( ( ! [SY2769: $i,SY2770: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2769 @ SY2770 @ SV23 )
!= SY2770 )
| ( c_lessequals @ SY2769 @ SY2770 @ SV23 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2547]) ).
thf(3224,plain,
! [SV24: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV24 ) )
= $true )
| ( ( ! [SY2771: $i,SY2772: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2771 @ SY2772 @ SV24 )
= SY2771 )
| ~ ( c_lessequals @ SY2772 @ SY2771 @ SV24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2548]) ).
thf(3225,plain,
! [SV25: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV25 ) )
= $true )
| ( ( ! [SY2773: $i,SY2774: $i] :
( ( c_lessequals @ SY2773 @ SY2774 @ SV25 )
| ~ ( c_HOL_Oord__class_Oless @ SY2773 @ SY2774 @ SV25 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2549]) ).
thf(3226,plain,
! [SV26: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV26 ) )
= $true )
| ( ( ! [SY2775: $i,SY2776: $i] :
( ( c_lessequals @ SY2775 @ SY2776 @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ SY2775 @ SY2776 @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2550]) ).
thf(3227,plain,
! [SV691: $i,SV27: $i] :
( ( ~ ( class_HOL_Oord @ SV27 )
| ! [SY4770: $i,SY4771: $i] :
( ( c_lessequals @ SV691 @ SY4770 @ ( tc_fun @ SY4771 @ SV27 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV691 @ SY4770 @ ( tc_fun @ SY4771 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2551]) ).
thf(3228,plain,
! [SV692: $i,SV28: $i] :
( ( ! [SY4772: $i] :
( ( c_lessequals @ SV28 @ SV692 @ ( tc_fun @ SY4772 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV28 @ SV692 @ ( tc_fun @ SY4772 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2552]) ).
thf(3229,plain,
! [SV29: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV29 ) )
= $true )
| ( ( ! [SY2782: $i,SY2783: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2782 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2782 @ SY2783 @ SV29 ) @ SV29 )
= SY2782 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2553]) ).
thf(3230,plain,
! [SV30: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV30 ) )
= $true )
| ( ( ! [SY2784: $i,SY2785: $i] :
( ( SY2784 = SY2785 )
| ~ ( c_lessequals @ SY2784 @ SY2785 @ SV30 )
| ~ ( c_lessequals @ SY2785 @ SY2784 @ SV30 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2554]) ).
thf(3231,plain,
! [SV31: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV31 ) )
= $true )
| ( ( ! [SY2786: $i,SY2787: $i] :
( ( SY2786 = SY2787 )
| ~ ( c_lessequals @ SY2787 @ SY2786 @ SV31 )
| ~ ( c_lessequals @ SY2786 @ SY2787 @ SV31 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2555]) ).
thf(3232,plain,
! [SV32: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV32 ) )
= $true )
| ( ( ! [SY2788: $i,SY2789: $i] :
( ( SY2788 = SY2789 )
| ~ ( c_lessequals @ SY2789 @ SY2788 @ SV32 )
| ~ ( c_lessequals @ SY2788 @ SY2789 @ SV32 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2556]) ).
thf(3233,plain,
! [SV693: $i,SV33: $i] :
( ( ( SV33 = SV693 )
| ! [SY4773: $i] :
( ~ ( c_lessequals @ SV693 @ SV33 @ ( tc_fun @ SY4773 @ tc_bool ) )
| ~ ( c_lessequals @ SV33 @ SV693 @ ( tc_fun @ SY4773 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2557]) ).
thf(3234,plain,
! [SV694: $i,SV34: $i] :
( ( ( SV34 = SV694 )
| ! [SY4774: $i] :
( ~ ( c_lessequals @ SV694 @ SV34 @ ( tc_fun @ SY4774 @ tc_bool ) )
| ~ ( c_lessequals @ SV34 @ SV694 @ ( tc_fun @ SY4774 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2558]) ).
thf(3235,plain,
! [SV35: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV35 ) )
= $true )
| ( ( ! [SY2794: $i,SY2795: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2794 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2794 @ SY2795 @ SV35 ) @ SV35 )
= SY2794 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2559]) ).
thf(3236,plain,
! [SV695: $i,SV36: $i] :
( ( ~ ( class_HOL_Oord @ SV36 )
| ! [SY4775: $i,SY4776: $i] :
( ( c_HOL_Oord__class_Oless @ SV695 @ SY4775 @ ( tc_fun @ SY4776 @ SV36 ) )
| ( c_lessequals @ SY4775 @ SV695 @ ( tc_fun @ SY4776 @ SV36 ) )
| ~ ( c_lessequals @ SV695 @ SY4775 @ ( tc_fun @ SY4776 @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2560]) ).
thf(3237,plain,
! [SV37: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV37 ) )
= $true )
| ( ( ! [SY2799: $i,SY2800: $i] :
( ( c_HOL_Oord__class_Oless @ SY2799 @ SY2800 @ SV37 )
| ( c_lessequals @ SY2800 @ SY2799 @ SV37 )
| ~ ( c_lessequals @ SY2799 @ SY2800 @ SV37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2561]) ).
thf(3238,plain,
! [SV696: $i,SV38: $i] :
( ( ~ ( class_Lattices_Olattice @ SV38 )
| ! [SY4777: $i,SY4778: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV696 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4777 @ SY4778 @ SV38 ) @ SV38 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV696 @ SY4777 @ SV38 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV696 @ SY4778 @ SV38 ) @ SV38 ) @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2562]) ).
thf(3239,plain,
! [SV697: $i,SV39: $i] :
( ( ! [SY4779: $i,SY4780: $i,SY4781: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV39 @ SV697 @ ( tc_fun @ SY4779 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY4780 @ SY4781 @ ( tc_fun @ SY4779 @ tc_bool ) ) @ ( tc_fun @ SY4779 @ tc_bool ) )
| ~ ( c_lessequals @ SY4781 @ SV697 @ ( tc_fun @ SY4779 @ tc_bool ) )
| ~ ( c_lessequals @ SV39 @ SY4780 @ ( tc_fun @ SY4779 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2563]) ).
thf(3240,plain,
! [SV698: $i,SV40: $i] :
( ( ! [SY4782: $i,SY4783: $i,SY4784: $i,SY4785: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ SV40 @ SV698 @ SY4782 @ SY4783 @ SY4784 ) @ SV698 @ SY4785 @ SY4783 @ SY4784 )
= ( c_Fun_Ofun__upd @ SV40 @ SV698 @ SY4785 @ SY4783 @ SY4784 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2564]) ).
thf(3241,plain,
! [SV699: $i,SV41: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV41 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV699 @ tc_bool ) ) @ ( tc_fun @ SV699 @ tc_bool ) )
= SV41 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2565]) ).
thf(3242,plain,
! [SV700: $i,SV42: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV42 @ tc_bool ) ) @ SV700 @ ( tc_fun @ SV42 @ tc_bool ) )
= SV700 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2566]) ).
thf(3243,plain,
! [SV43: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV43 ) )
= $true )
| ( ( ! [SY2815: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ SV43 ) @ SY2815 @ SV43 )
= SY2815 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2567]) ).
thf(3244,plain,
! [SV44: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV44 ) )
= $true )
| ( ( ! [SY2816: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2816 @ ( c_Orderings_Obot__class_Obot @ SV44 ) @ SV44 )
= SY2816 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2568]) ).
thf(3245,plain,
! [SV701: $i,SV45: $i] :
( ( ( c_Finite__Set_Ofinite @ SV45 @ SV701 )
| ! [SY4786: $i] :
~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4786 @ SV45 @ ( tc_fun @ SV701 @ tc_bool ) ) @ SV701 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2569]) ).
thf(3246,plain,
! [SV702: $i,SV46: $i] :
( ( ( c_Finite__Set_Ofinite @ SV46 @ SV702 )
| ! [SY4787: $i] :
~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV46 @ SY4787 @ ( tc_fun @ SV702 @ tc_bool ) ) @ SV702 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2570]) ).
thf(3247,plain,
! [SV703: $i,SV47: $i] :
( ( ! [SY4788: $i,SY4789: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV47 @ SV703 @ ( tc_fun @ SY4788 @ tc_bool ) ) @ SY4789 ) )
| ~ ( hBOOL @ ( hAPP @ SV47 @ SY4789 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2571]) ).
thf(3248,plain,
! [SV704: $i,SV48: $i] :
( ( ! [SY4790: $i,SY4791: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV48 @ SV704 @ ( tc_fun @ SY4790 @ tc_bool ) ) @ SY4791 ) )
| ~ ( hBOOL @ ( hAPP @ SV704 @ SY4791 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2572]) ).
thf(3249,plain,
! [SV705: $i,SV49: $i] :
( ( ( hBOOL @ ( hAPP @ SV49 @ SV705 ) )
| ! [SY4792: $i] :
( ( hBOOL @ ( hAPP @ SY4792 @ SV705 ) )
| ! [SY4793: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4792 @ SV49 @ ( tc_fun @ SY4793 @ tc_bool ) ) @ SV705 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(3250,plain,
! [SV706: $i,SV50: $i] :
( ( ! [SY4794: $i,SY4795: $i,SY4796: $i,SY4797: $i] :
( ! [SY4798: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ SV50 @ SV706 @ SY4794 @ SY4795 @ SY4796 ) @ SY4797 @ SY4798 @ SY4795 @ SY4796 )
= ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ SV50 @ SY4797 @ SY4798 @ SY4795 @ SY4796 ) @ SV706 @ SY4794 @ SY4795 @ SY4796 ) )
| ( SV706 = SY4797 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2574]) ).
thf(3251,plain,
! [SV707: $i,SV51: $i] :
( ( ! [SY4799: $i,SY4800: $i,SY4801: $i,SY4802: $i] :
( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ SV51 @ SV707 @ SY4799 @ SY4800 @ ( tc_Option_Ooption @ SY4801 ) ) @ ( c_Fun_Ofun__upd @ SY4802 @ SV707 @ SY4799 @ SY4800 @ ( tc_Option_Ooption @ SY4801 ) ) @ SY4800 @ SY4801 )
| ~ ( c_Map_Omap__le @ SV51 @ SY4802 @ SY4800 @ SY4801 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2575]) ).
thf(3252,plain,
! [SV708: $i,SV52: $i] :
( ( ! [SY4803: $i,SY4804: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV52 @ SV708 @ ( tc_fun @ SY4803 @ tc_bool ) ) @ SY4804 @ ( tc_fun @ SY4803 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV52 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV708 @ SY4804 @ ( tc_fun @ SY4803 @ tc_bool ) ) @ ( tc_fun @ SY4803 @ tc_bool ) ) )
| ~ ( c_lessequals @ SY4804 @ SV52 @ ( tc_fun @ SY4803 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2576]) ).
thf(3253,plain,
! [SV709: $i,SV53: $i] :
( ( ! [SY4805: $i,SY4806: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV53 @ SV709 @ ( tc_fun @ SY4805 @ tc_bool ) ) @ SY4806 @ ( tc_fun @ SY4805 @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ SV53 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV709 @ SY4806 @ ( tc_fun @ SY4805 @ tc_bool ) ) @ ( tc_fun @ SY4805 @ tc_bool ) ) )
| ( c_lessequals @ SY4806 @ SV53 @ ( tc_fun @ SY4805 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2577]) ).
thf(3254,plain,
! [SV710: $i,SV54: $i] :
( ( ! [SY4807: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV54 @ SV710 @ ( tc_fun @ SY4807 @ tc_bool ) ) @ SY4807 )
| ~ ( c_Finite__Set_Ofinite @ SV710 @ SY4807 )
| ~ ( c_Finite__Set_Ofinite @ SV54 @ SY4807 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2578]) ).
thf(3255,plain,
! [SV711: $i,SV55: $i] :
( ( ! [SY4808: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV55 @ SV711 @ ( tc_fun @ SY4808 @ tc_bool ) ) @ SY4808 )
| ~ ( c_Finite__Set_Ofinite @ SV711 @ SY4808 )
| ~ ( c_Finite__Set_Ofinite @ SV55 @ SY4808 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2579]) ).
thf(3256,plain,
! [SV712: $i,SV56: $i] :
( ( ! [SY4809: $i] :
( ( SV56 = SV712 )
| ! [SY4810: $i,SY4811: $i] :
~ ( c_Finite__Set_Ofold__graph @ SY4809 @ SV712 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4810 @ tc_bool ) ) @ SV56 @ SY4810 @ SY4811 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2580]) ).
thf(3257,plain,
! [SV713: $i,SV57: $i] :
( ( ! [SY4812: $i] : ( c_lessequals @ SV57 @ ( c_Set_Oinsert @ SV713 @ SV57 @ SY4812 ) @ ( tc_fun @ SY4812 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2581]) ).
thf(3258,plain,
! [SV714: $i,SV58: $i] :
( ( ! [SY4813: $i,SY4814: $i,SY4815: $i] :
( ( ( hAPP @ SV58 @ SV714 )
!= ( c_Option_Ooption_OSome @ SY4813 @ SY4814 ) )
| ( SV714 = SY4815 )
| ! [SY4816: $i,SY4817: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV58 @ SY4815 @ ( c_Option_Ooption_OSome @ SY4816 @ SY4814 ) @ SY4817 @ ( tc_Option_Ooption @ SY4814 ) ) @ SV714 )
= ( c_Option_Ooption_OSome @ SY4813 @ SY4814 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2582]) ).
thf(3259,plain,
! [SV715: $i,SV59: $i] :
( ( ! [SY4818: $i,SY4819: $i,SY4820: $i,SY4821: $i,SY4822: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV59 @ SV715 @ ( c_Option_Ooption_OSome @ SY4818 @ SY4819 ) @ SY4820 @ ( tc_Option_Ooption @ SY4819 ) ) @ SY4821 )
!= ( c_Option_Ooption_OSome @ SY4822 @ SY4819 ) )
| ( ( hAPP @ SV59 @ SY4821 )
= ( c_Option_Ooption_OSome @ SY4822 @ SY4819 ) )
| ( SY4818 = SY4822 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2583]) ).
thf(3260,plain,
! [SV716: $i,SV60: $i] :
( ( ! [SY4823: $i,SY4824: $i,SY4825: $i,SY4826: $i,SY4827: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV60 @ SV716 @ ( c_Option_Ooption_OSome @ SY4823 @ SY4824 ) @ SY4825 @ ( tc_Option_Ooption @ SY4824 ) ) @ SY4826 )
!= ( c_Option_Ooption_OSome @ SY4827 @ SY4824 ) )
| ( ( hAPP @ SV60 @ SY4826 )
= ( c_Option_Ooption_OSome @ SY4827 @ SY4824 ) )
| ( SY4826 = SV716 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2584]) ).
thf(3261,plain,
! [SV61: $i] :
( ( ( ~ ( class_Orderings_Obot @ SV61 ) )
= $true )
| ( ( ! [SY2875: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV61 ) @ SY2875 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2585]) ).
thf(3262,plain,
! [SV717: $i,SV62: $i] :
( ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV62 @ tc_bool ) ) @ SV717 @ ( tc_fun @ SV62 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2586]) ).
thf(3263,plain,
! [SV718: $i,SV63: $i] :
( ( ! [SY4828: $i,SY4829: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV63 @ ( c_Set_Oinsert @ SV718 @ SY4828 @ SY4829 ) @ ( tc_fun @ SY4829 @ tc_bool ) )
= ( c_Set_Oinsert @ SV718 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV63 @ SY4828 @ ( tc_fun @ SY4829 @ tc_bool ) ) @ SY4829 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2587]) ).
thf(3264,plain,
! [SV719: $i,SV64: $i] :
( ( ! [SY4830: $i,SY4831: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV64 @ SV719 @ SY4830 ) @ SY4831 @ ( tc_fun @ SY4830 @ tc_bool ) )
= ( c_Set_Oinsert @ SV64 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV719 @ SY4831 @ ( tc_fun @ SY4830 @ tc_bool ) ) @ SY4830 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2588]) ).
thf(3265,plain,
! [SV720: $i,SV65: $i] :
( ( ! [SY4832: $i,SY4833: $i] :
( ( c_lessequals @ SV65 @ ( c_Set_Oinsert @ SV720 @ SY4832 @ SY4833 ) @ ( tc_fun @ SY4833 @ tc_bool ) )
| ~ ( c_lessequals @ SV65 @ SY4832 @ ( tc_fun @ SY4833 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2589]) ).
thf(3266,plain,
! [SV721: $i,SV66: $i] :
( ( ! [SY4834: $i] :
( ( c_lessequals @ SV66 @ SV721 @ ( tc_fun @ SY4834 @ tc_bool ) )
| ! [SY4835: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SY4835 @ SV66 @ SY4834 ) @ SV721 @ ( tc_fun @ SY4834 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2590]) ).
thf(3267,plain,
! [SV722: $i,SV67: $i] :
( ( ! [SY4836: $i,SY4837: $i] :
( ( c_Finite__Set_Ofinite @ SV67 @ SV722 )
| ! [SY4838: $i,SY4839: $i] :
~ ( c_Finite__Set_Ofold__graph @ SY4836 @ SY4837 @ SV67 @ SY4838 @ SV722 @ SY4839 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2591]) ).
thf(3268,plain,
! [SV723: $i,SV68: $i] :
( ( ! [SY4840: $i,SY4841: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV68 @ SV723 @ ( tc_fun @ SY4840 @ tc_bool ) ) @ SY4841 @ ( tc_fun @ SY4840 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV68 @ SY4841 @ ( tc_fun @ SY4840 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV723 @ SY4841 @ ( tc_fun @ SY4840 @ tc_bool ) ) @ ( tc_fun @ SY4840 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2592]) ).
thf(3269,plain,
! [SV724: $i,SV69: $i] :
( ( ! [SY4842: $i,SY4843: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV69 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV724 @ SY4842 @ ( tc_fun @ SY4843 @ tc_bool ) ) @ ( tc_fun @ SY4843 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV69 @ SV724 @ ( tc_fun @ SY4843 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV69 @ SY4842 @ ( tc_fun @ SY4843 @ tc_bool ) ) @ ( tc_fun @ SY4843 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2593]) ).
thf(3270,plain,
! [SV725: $i,SV70: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV70 )
| ! [SY4844: $i,SY4845: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV725 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4844 @ SY4845 @ SV70 ) @ SV70 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV725 @ SY4844 @ SV70 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV725 @ SY4845 @ SV70 ) @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2594]) ).
thf(3271,plain,
! [SV726: $i,SV71: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV71 )
| ! [SY4846: $i,SY4847: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV726 @ SY4846 @ SV71 ) @ SY4847 @ SV71 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV726 @ SY4847 @ SV71 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4846 @ SY4847 @ SV71 ) @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2595]) ).
thf(3272,plain,
! [SV727: $i,SV72: $i] :
( ( ! [SY4848: $i,SY4849: $i] :
( ! [SY4850: $i,SY4851: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SY4848 @ SY4849 @ ( c_Option_Ooption_OSome @ SV72 @ SY4850 ) @ SY4851 @ ( tc_Option_Ooption @ SY4850 ) ) @ SY4849 )
!= ( c_Option_Ooption_OSome @ SV727 @ SY4850 ) )
| ( SV72 = SV727 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2596]) ).
thf(3273,plain,
! [SV728: $i,SV73: $i] :
( ( ! [SY4852: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV73 @ SV728 @ ( tc_fun @ SY4852 @ tc_bool ) ) @ SV73 @ ( tc_fun @ SY4852 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2597]) ).
thf(3274,plain,
! [SV729: $i,SV74: $i] :
( ( ! [SY4853: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV74 @ SV729 @ ( tc_fun @ SY4853 @ tc_bool ) ) @ SV729 @ ( tc_fun @ SY4853 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2598]) ).
thf(3275,plain,
! [SV730: $i,SV75: $i] :
( ( ! [SY4854: $i,SY4855: $i] :
( ( c_lessequals @ SV75 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV730 @ SY4854 @ ( tc_fun @ SY4855 @ tc_bool ) ) @ ( tc_fun @ SY4855 @ tc_bool ) )
| ~ ( c_lessequals @ SV75 @ SY4854 @ ( tc_fun @ SY4855 @ tc_bool ) )
| ~ ( c_lessequals @ SV75 @ SV730 @ ( tc_fun @ SY4855 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2599]) ).
thf(3276,plain,
! [SV731: $i,SV76: $i] :
( ( ! [SY4856: $i,SY4857: $i] :
( ( c_lessequals @ SV76 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV731 @ SY4856 @ ( tc_fun @ SY4857 @ tc_bool ) ) @ ( tc_fun @ SY4857 @ tc_bool ) )
| ~ ( c_lessequals @ SV76 @ SY4856 @ ( tc_fun @ SY4857 @ tc_bool ) )
| ~ ( c_lessequals @ SV76 @ SV731 @ ( tc_fun @ SY4857 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2600]) ).
thf(3277,plain,
! [SV732: $i,SV77: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV77 )
| ! [SY4858: $i,SY4859: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV732 @ SY4858 @ SV77 ) @ SY4859 @ SV77 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV732 @ SY4859 @ SV77 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4858 @ SY4859 @ SV77 ) @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2601]) ).
thf(3278,plain,
! [SV733: $i,SV78: $i] :
( ( ~ ( class_Lattices_Odistrib__lattice @ SV78 )
| ! [SY4860: $i,SY4861: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV733 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4860 @ SY4861 @ SV78 ) @ SV78 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV733 @ SY4860 @ SV78 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV733 @ SY4861 @ SV78 ) @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2602]) ).
thf(3279,plain,
! [SV734: $i,SV79: $i] :
( ( ! [SY4862: $i,SY4863: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV79 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV734 @ SY4862 @ ( tc_fun @ SY4863 @ tc_bool ) ) @ ( tc_fun @ SY4863 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV79 @ SV734 @ ( tc_fun @ SY4863 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV79 @ SY4862 @ ( tc_fun @ SY4863 @ tc_bool ) ) @ ( tc_fun @ SY4863 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2603]) ).
thf(3280,plain,
! [SV735: $i,SV80: $i] :
( ( ! [SY4864: $i,SY4865: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV80 @ SV735 @ ( tc_fun @ SY4864 @ tc_bool ) ) @ SY4865 @ ( tc_fun @ SY4864 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV80 @ SY4865 @ ( tc_fun @ SY4864 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV735 @ SY4865 @ ( tc_fun @ SY4864 @ tc_bool ) ) @ ( tc_fun @ SY4864 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2604]) ).
thf(3281,plain,
! [SV736: $i,SV81: $i] :
( ( ! [SY4866: $i,SY4867: $i,SY4868: $i,SY4869: $i] :
( ( c_Set_Oimage @ SV81 @ ( c_Set_Oimage @ SV736 @ SY4866 @ SY4867 @ SY4868 ) @ SY4868 @ SY4869 )
= ( c_Set_Oimage @ ( c_COMBB @ SV81 @ SV736 @ SY4868 @ SY4869 @ SY4867 ) @ SY4866 @ SY4867 @ SY4869 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2605]) ).
thf(3282,plain,
! [SV737: $i,SV82: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV82 )
| ! [SY4870: $i] :
( ( c_lessequals @ SV737 @ SY4870 @ SV82 )
| ! [SY4871: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4871 @ SV737 @ SV82 ) @ SY4870 @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2606]) ).
thf(3283,plain,
! [SV738: $i,SV83: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV83 )
| ! [SY4872: $i] :
( ( c_lessequals @ SV738 @ SY4872 @ SV83 )
| ! [SY4873: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV738 @ SY4873 @ SV83 ) @ SY4872 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2607]) ).
thf(3284,plain,
! [SV739: $i,SV84: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV84 )
| ! [SY4874: $i,SY4875: $i] :
( ( c_lessequals @ SV739 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4874 @ SY4875 @ SV84 ) @ SV84 )
| ~ ( c_lessequals @ SV739 @ SY4875 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2608]) ).
thf(3285,plain,
! [SV740: $i,SV85: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV85 )
| ! [SY4876: $i] :
( ! [SY4877: $i] : ( c_lessequals @ SV740 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4876 @ SY4877 @ SV85 ) @ SV85 )
| ~ ( c_lessequals @ SV740 @ SY4876 @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2609]) ).
thf(3286,plain,
! [SV741: $i,SV86: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV86 )
| ! [SY4878: $i] :
( ( c_lessequals @ SV741 @ SY4878 @ SV86 )
| ! [SY4879: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4879 @ SV741 @ SV86 ) @ SY4878 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2610]) ).
thf(3287,plain,
! [SV742: $i,SV87: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV87 )
| ! [SY4880: $i] :
( ( c_lessequals @ SV742 @ SY4880 @ SV87 )
| ! [SY4881: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV742 @ SY4881 @ SV87 ) @ SY4880 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2611]) ).
thf(3288,plain,
! [SV743: $i,SV88: $i] :
( ( ! [SY4882: $i] :
( ( c_lessequals @ SV88 @ SV743 @ ( tc_fun @ SY4882 @ tc_bool ) )
| ! [SY4883: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV88 @ SY4883 @ ( tc_fun @ SY4882 @ tc_bool ) ) @ SV743 @ ( tc_fun @ SY4882 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2612]) ).
thf(3289,plain,
! [SV744: $i,SV89: $i] :
( ( ! [SY4884: $i] :
( ( c_lessequals @ SV89 @ SV744 @ ( tc_fun @ SY4884 @ tc_bool ) )
| ! [SY4885: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4885 @ SV89 @ ( tc_fun @ SY4884 @ tc_bool ) ) @ SV744 @ ( tc_fun @ SY4884 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2613]) ).
thf(3290,plain,
! [SV745: $i,SV90: $i] :
( ( ~ ( class_Orderings_Oorder @ SV90 )
| ! [SY4886: $i] :
( ( c_lessequals @ SV745 @ SY4886 @ SV90 )
| ! [SY4887: $i] :
( ~ ( c_lessequals @ SV745 @ SY4887 @ SV90 )
| ~ ( c_lessequals @ SY4887 @ SY4886 @ SV90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2614]) ).
thf(3291,plain,
! [SV746: $i,SV91: $i] :
( ( ~ ( class_Orderings_Oorder @ SV91 )
| ! [SY4888: $i] :
( ( c_HOL_Oord__class_Oless @ SV746 @ SY4888 @ SV91 )
| ! [SY4889: $i] :
( ~ ( c_lessequals @ SV746 @ SY4889 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SY4889 @ SY4888 @ SV91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2615]) ).
thf(3292,plain,
! [SV747: $i,SV92: $i] :
( ( ~ ( class_Orderings_Oorder @ SV92 )
| ! [SY4890: $i] :
( ( c_HOL_Oord__class_Oless @ SV747 @ SY4890 @ SV92 )
| ! [SY4891: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV747 @ SY4891 @ SV92 )
| ~ ( c_lessequals @ SY4891 @ SY4890 @ SV92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2616]) ).
thf(3293,plain,
! [SV748: $i,SV93: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV93 )
| ! [SY4892: $i] :
( ( c_lessequals @ SV748 @ SY4892 @ SV93 )
| ! [SY4893: $i] :
( ~ ( c_lessequals @ SY4893 @ SY4892 @ SV93 )
| ~ ( c_lessequals @ SV748 @ SY4893 @ SV93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2617]) ).
thf(3294,plain,
! [SV749: $i,SV94: $i] :
( ( c_lessequals @ SV94 @ SV94 @ ( tc_fun @ SV749 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2618]) ).
thf(3295,plain,
! [SV750: $i,SV95: $i] :
( ( c_lessequals @ SV95 @ SV95 @ ( tc_fun @ SV750 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(3296,plain,
! [SV751: $i,SV96: $i] :
( ( ! [SY4894: $i] :
( ( c_lessequals @ SV96 @ SV751 @ ( tc_fun @ SY4894 @ tc_bool ) )
| ! [SY4895: $i] :
( ~ ( c_lessequals @ SY4895 @ SV751 @ ( tc_fun @ SY4894 @ tc_bool ) )
| ~ ( c_lessequals @ SV96 @ SY4895 @ ( tc_fun @ SY4894 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2620]) ).
thf(3297,plain,
! [SV752: $i,SV97: $i] :
( ( ! [SY4896: $i,SY4897: $i] :
( ( c_Fun_Oinj__on @ SV97 @ SV752 @ SY4896 @ SY4897 )
| ! [SY4898: $i] :
( ~ ( c_lessequals @ SV752 @ SY4898 @ ( tc_fun @ SY4896 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV97 @ SY4898 @ SY4896 @ SY4897 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2621]) ).
thf(3298,plain,
! [SV753: $i,SV98: $i] :
( ( ( hBOOL @ ( hAPP @ SV98 @ SV753 ) )
| ! [SY4899: $i] :
( ~ ( hBOOL @ ( hAPP @ SY4899 @ SV753 ) )
| ! [SY2985: $i] :
~ ( c_lessequals @ SY4899 @ SV98 @ ( tc_fun @ SY2985 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2622]) ).
thf(3299,plain,
! [SV99: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV99 ) )
= $true )
| ( ( ! [SY2986: $i] : ( c_lessequals @ SY2986 @ SY2986 @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2623]) ).
thf(3300,plain,
! [SV100: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV100 ) )
= $true )
| ( ( ! [SY2987: $i] : ( c_lessequals @ SY2987 @ SY2987 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2624]) ).
thf(3301,plain,
! [SV754: $i,SV101: $i] :
( ( ( c_Finite__Set_Ofinite @ SV101 @ SV754 )
| ! [SY4901: $i] :
( ~ ( c_Finite__Set_Ofinite @ SY4901 @ SV754 )
| ~ ( c_lessequals @ SV101 @ SY4901 @ ( tc_fun @ SV754 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2625]) ).
thf(3302,plain,
! [SV755: $i,SV102: $i] :
( ( ! [SY4902: $i] :
( ( c_HOL_Oord__class_Oless @ SV102 @ SV755 @ ( tc_fun @ SY4902 @ tc_bool ) )
| ! [SY4903: $i] :
( ~ ( c_lessequals @ SY4903 @ SV755 @ ( tc_fun @ SY4902 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV102 @ SY4903 @ ( tc_fun @ SY4902 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2626]) ).
thf(3303,plain,
! [SV756: $i,SV103: $i] :
( ( ! [SY4904: $i] :
( ( c_HOL_Oord__class_Oless @ SV103 @ SV756 @ ( tc_fun @ SY4904 @ tc_bool ) )
| ! [SY4905: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY4905 @ SV756 @ ( tc_fun @ SY4904 @ tc_bool ) )
| ~ ( c_lessequals @ SV103 @ SY4905 @ ( tc_fun @ SY4904 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2627]) ).
thf(3304,plain,
! [SV757: $i,SV104: $i] :
( ( ( hBOOL @ ( hAPP @ SV104 @ SV757 ) )
| ! [SY4906: $i] :
( ! [SY2998: $i] :
~ ( c_lessequals @ SY4906 @ SV104 @ ( tc_fun @ SY2998 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SY4906 @ SV757 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2628]) ).
thf(3305,plain,
! [SV758: $i,SV105: $i] :
( ( ( c_Finite__Set_Ofinite @ SV105 @ SV758 )
| ! [SY4908: $i] :
( ~ ( c_lessequals @ SV105 @ SY4908 @ ( tc_fun @ SV758 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY4908 @ SV758 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2629]) ).
thf(3306,plain,
! [SV759: $i,SV106: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV106 )
| ! [SY4909: $i] :
( ( c_HOL_Oord__class_Oless @ SV759 @ SY4909 @ SV106 )
| ! [SY4910: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY4910 @ SY4909 @ SV106 )
| ~ ( c_lessequals @ SV759 @ SY4910 @ SV106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2630]) ).
thf(3307,plain,
! [SV760: $i,SV107: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV107 )
| ! [SY4911: $i] :
( ( c_HOL_Oord__class_Oless @ SV760 @ SY4911 @ SV107 )
| ! [SY4912: $i] :
( ~ ( c_lessequals @ SY4912 @ SY4911 @ SV107 )
| ~ ( c_HOL_Oord__class_Oless @ SV760 @ SY4912 @ SV107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2631]) ).
thf(3308,plain,
! [SV761: $i,SV108: $i] :
( ( ! [SY4913: $i,SY4914: $i,SY4915: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV108 @ SV761 @ ( tc_fun @ SY4913 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4914 @ SY4915 @ ( tc_fun @ SY4913 @ tc_bool ) ) @ ( tc_fun @ SY4913 @ tc_bool ) )
| ~ ( c_lessequals @ SV761 @ SY4915 @ ( tc_fun @ SY4913 @ tc_bool ) )
| ~ ( c_lessequals @ SV108 @ SY4914 @ ( tc_fun @ SY4913 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2632]) ).
thf(3309,plain,
! [SV762: $i,SV109: $i] :
( ( ! [SY4916: $i,SY4917: $i,SY4918: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV109 @ SV762 @ ( c_Option_Ooption_OSome @ SY4916 @ SY4917 ) @ SY4918 @ ( tc_Option_Ooption @ SY4917 ) ) @ SV762 )
= ( c_Option_Ooption_OSome @ SY4916 @ SY4917 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2633]) ).
thf(3310,plain,
! [SV763: $i,SV110: $i] :
( ( ! [SY4919: $i,SY4920: $i] :
( ( ( hAPP @ SV110 @ SV763 )
!= ( c_Option_Ooption_OSome @ SY4919 @ SY4920 ) )
| ! [SY4921: $i] :
( ( c_Fun_Ofun__upd @ SV110 @ SV763 @ ( c_Option_Ooption_OSome @ SY4919 @ SY4920 ) @ SY4921 @ ( tc_Option_Ooption @ SY4920 ) )
= SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2634]) ).
thf(3311,plain,
! [SV764: $i,SV111: $i] :
( ( ! [SY4922: $i,SY4923: $i,SY4924: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV111 @ SV764 @ ( tc_fun @ SY4922 @ tc_bool ) ) @ SY4923 @ SY4922 @ ( tc_fun @ SY4924 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV111 @ SY4923 @ SY4922 @ ( tc_fun @ SY4924 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV764 @ SY4923 @ SY4922 @ ( tc_fun @ SY4924 @ tc_bool ) ) @ ( tc_fun @ SY4924 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2635]) ).
thf(3312,plain,
! [SV765: $i,SV112: $i] :
( ( ! [SY4925: $i,SY4926: $i,SY4927: $i,SY4928: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV112 @ SV765 @ SY4925 @ SY4926 @ SY4927 ) @ SY4928 )
= ( hAPP @ SV112 @ SY4928 ) )
| ( SY4928 = SV765 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2636]) ).
thf(3313,plain,
! [SV766: $i,SV113: $i] :
( ( ! [SY4929: $i,SY4930: $i,SY4931: $i,SY4932: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV113 @ SV766 @ SY4929 @ SY4930 @ SY4931 ) @ SY4932 )
= ( hAPP @ SV113 @ SY4932 ) )
| ( SY4932 = SV766 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2637]) ).
thf(3314,plain,
! [SV767: $i,SV114: $i] :
( ( ! [SY4933: $i,SY4934: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV114 @ ( c_HOL_Ominus__class_Ominus @ SV767 @ SY4933 @ ( tc_fun @ SY4934 @ tc_bool ) ) @ ( tc_fun @ SY4934 @ tc_bool ) )
= SY4933 )
| ~ ( c_lessequals @ SV114 @ SV767 @ ( tc_fun @ SY4934 @ tc_bool ) )
| ~ ( c_lessequals @ SY4933 @ SV114 @ ( tc_fun @ SY4934 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2638]) ).
thf(3315,plain,
! [SV768: $i,SV115: $i] :
( ( ! [SY4935: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV115 )
| ! [SY4936: $i,SY4937: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV768 @ SY4935 @ SV115 )
!= ( c_HOL_Ominus__class_Ominus @ SY4936 @ SY4937 @ SV115 ) )
| ( c_lessequals @ SY4937 @ SY4936 @ SV115 )
| ~ ( c_lessequals @ SY4935 @ SV768 @ SV115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2639]) ).
thf(3316,plain,
! [SV769: $i,SV116: $i] :
( ( ! [SY4938: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV116 )
| ! [SY4939: $i,SY4940: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV769 @ SY4938 @ SV116 )
!= ( c_HOL_Ominus__class_Ominus @ SY4939 @ SY4940 @ SV116 ) )
| ( c_lessequals @ SY4938 @ SV769 @ SV116 )
| ~ ( c_lessequals @ SY4940 @ SY4939 @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2640]) ).
thf(3317,plain,
! [SV770: $i,SV117: $i] :
( ( ! [SY4941: $i,SY4942: $i,SY4943: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV117 @ SV770 @ SY4941 @ SY4942 ) @ ( c_Set_Oimage @ SV117 @ SY4943 @ SY4941 @ SY4942 ) @ ( tc_fun @ SY4942 @ tc_bool ) )
| ~ ( c_lessequals @ SV770 @ SY4943 @ ( tc_fun @ SY4941 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2641]) ).
thf(3318,plain,
! [SV771: $i,SV118: $i] :
( ( ! [SY4944: $i] :
( ~ ( c_lessequals @ SV118 @ SV771 @ ( tc_fun @ SY4944 @ tc_bool ) )
| ! [SY4945: $i,SY4946: $i] : ( c_lessequals @ ( c_Set_Oimage @ SY4945 @ SV118 @ SY4944 @ SY4946 ) @ ( c_Set_Oimage @ SY4945 @ SV771 @ SY4944 @ SY4946 ) @ ( tc_fun @ SY4946 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2642]) ).
thf(3319,plain,
! [SV772: $i,SV119: $i] :
( ( ! [SY4947: $i,SY4948: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV119 @ SV772 @ SY4947 ) @ ( c_Set_Oinsert @ SV119 @ SY4948 @ SY4947 ) @ ( tc_fun @ SY4947 @ tc_bool ) )
| ~ ( c_lessequals @ SV772 @ SY4948 @ ( tc_fun @ SY4947 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2643]) ).
thf(3320,plain,
! [SV121: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV121 ) )
= $true )
| ( ( ! [SY3055: $i,SY3056: $i] :
( ( c_HOL_Oord__class_Oless @ SY3055 @ SY3056 @ SV121 )
| ( SY3056 = SY3055 )
| ~ ( c_lessequals @ SY3055 @ SY3056 @ SV121 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2645]) ).
thf(3321,plain,
! [SV122: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV122 ) )
= $true )
| ( ( ! [SY3057: $i,SY3058: $i] :
( ( c_HOL_Oord__class_Oless @ SY3057 @ SY3058 @ SV122 )
| ~ ( c_lessequals @ SY3057 @ SY3058 @ SV122 )
| ( SY3058 = SY3057 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2646]) ).
thf(3322,plain,
! [SV773: $i,SV123: $i] :
( ( ! [SY4949: $i] :
( ( c_HOL_Oord__class_Oless @ SV123 @ SV773 @ ( tc_fun @ SY4949 @ tc_bool ) )
| ( SV123 = SV773 )
| ~ ( c_lessequals @ SV123 @ SV773 @ ( tc_fun @ SY4949 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2647]) ).
thf(3323,plain,
! [SV124: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV124 ) )
= $true )
| ( ( ! [SY3061: $i,SY3062: $i] :
( ( SY3061 = SY3062 )
| ( c_HOL_Oord__class_Oless @ SY3061 @ SY3062 @ SV124 )
| ~ ( c_lessequals @ SY3061 @ SY3062 @ SV124 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2648]) ).
thf(3324,plain,
! [SV125: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV125 ) )
= $true )
| ( ( ! [SY3063: $i,SY3064: $i] :
( ( c_HOL_Oord__class_Oless @ SY3063 @ SY3064 @ SV125 )
| ( SY3063 = SY3064 )
| ~ ( c_lessequals @ SY3063 @ SY3064 @ SV125 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2649]) ).
thf(3325,plain,
! [SV774: $i,SV126: $i] :
( ( ( SV126 = SV774 )
| ! [SY4950: $i] :
( ( c_HOL_Oord__class_Oless @ SV126 @ SV774 @ ( tc_fun @ SY4950 @ tc_bool ) )
| ~ ( c_lessequals @ SV126 @ SV774 @ ( tc_fun @ SY4950 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2650]) ).
thf(3326,plain,
! [SV127: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV127 ) )
= $true )
| ( ( ! [SY3067: $i,SY3068: $i] :
( ( c_HOL_Oord__class_Oless @ SY3067 @ SY3068 @ SV127 )
| ( SY3067 = SY3068 )
| ~ ( c_lessequals @ SY3067 @ SY3068 @ SV127 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2651]) ).
thf(3327,plain,
! [SV128: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV128 ) )
= $true )
| ( ( ! [SY3069: $i,SY3070: $i] :
( ( c_HOL_Oord__class_Oless @ SY3069 @ SY3070 @ SV128 )
| ~ ( c_lessequals @ SY3069 @ SY3070 @ SV128 )
| ( SY3069 = SY3070 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2652]) ).
thf(3328,plain,
! [SV129: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV129 ) )
= $true )
| ( ( ! [SY3071: $i,SY3072: $i] :
( ( SY3071 = SY3072 )
| ~ ( c_lessequals @ SY3071 @ SY3072 @ SV129 )
| ( c_HOL_Oord__class_Oless @ SY3071 @ SY3072 @ SV129 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2653]) ).
thf(3329,plain,
! [SV130: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV130 ) )
= $true )
| ( ( ! [SY3073: $i,SY3074: $i] :
( ( SY3073 = SY3074 )
| ( c_HOL_Oord__class_Oless @ SY3073 @ SY3074 @ SV130 )
| ~ ( c_lessequals @ SY3073 @ SY3074 @ SV130 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2654]) ).
thf(3330,plain,
! [SV775: $i,SV131: $i] :
( ( ! [SY4951: $i,SY4952: $i,SY4953: $i,SY4954: $i,SY4955: $i] :
( ( ( c_Fun_Ofun__upd @ SV131 @ SV775 @ ( c_Option_Ooption_OSome @ SY4951 @ SY4952 ) @ SY4953 @ ( tc_Option_Ooption @ SY4952 ) )
!= ( c_Fun_Ofun__upd @ SY4954 @ SV775 @ ( c_Option_Ooption_OSome @ SY4955 @ SY4952 ) @ SY4953 @ ( tc_Option_Ooption @ SY4952 ) ) )
| ( SY4951 = SY4955 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2655]) ).
thf(3331,plain,
! [SV776: $i,SV132: $i] :
( ( ! [SY4956: $i,SY4957: $i,SY4958: $i] :
( ( c_Set_Oimage @ SV132 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV776 @ SY4956 @ ( tc_fun @ SY4957 @ tc_bool ) ) @ SY4957 @ SY4958 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ SV132 @ SV776 @ SY4957 @ SY4958 ) @ ( c_Set_Oimage @ SV132 @ SY4956 @ SY4957 @ SY4958 ) @ ( tc_fun @ SY4958 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2656]) ).
thf(3332,plain,
! [SV133: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV133 ) )
= $true )
| ( ( ! [SY3085: $i,SY3086: $i] :
( ( c_lessequals @ SY3085 @ SY3086 @ SV133 )
| ( c_lessequals @ SY3086 @ SY3085 @ SV133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2657]) ).
thf(3333,plain,
! [SV777: $i,SV134: $i] :
( ( ! [SY4959: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV134 )
| ! [SY4960: $i,SY4961: $i] :
( ( ( c_Finite__Set_Osetsum @ SV777 @ ( c_HOL_Ominus__class_Ominus @ SY4959 @ SY4960 @ ( tc_fun @ SY4961 @ tc_bool ) ) @ SY4961 @ SV134 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV777 @ SY4959 @ SY4961 @ SV134 ) @ ( c_Finite__Set_Osetsum @ SV777 @ SY4960 @ SY4961 @ SV134 ) @ SV134 ) )
| ~ ( c_lessequals @ SY4960 @ SY4959 @ ( tc_fun @ SY4961 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY4959 @ SY4961 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2658]) ).
thf(3334,plain,
! [SV778: $i,SV135: $i] :
( ( ! [SY4962: $i,SY4963: $i] :
( ( ( c_Finite__Set_Ocard @ SV135 @ SV778 )
= ( c_Finite__Set_Ocard @ SY4962 @ SY4963 ) )
| ~ ( c_Finite__Set_Ofinite @ SY4962 @ SY4963 )
| ~ ( c_Finite__Set_Ofinite @ SV135 @ SV778 )
| ! [SY4964: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ SY4964 @ SY4962 @ SY4963 @ SV778 ) @ SV135 @ ( tc_fun @ SV778 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY4964 @ SY4962 @ SY4963 @ SV778 )
| ! [SY4965: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ SY4965 @ SV135 @ SV778 @ SY4963 ) @ SY4962 @ ( tc_fun @ SY4963 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY4965 @ SV135 @ SV778 @ SY4963 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2659]) ).
thf(3335,plain,
! [SV779: $i,SV136: $i] :
( ( ! [SY4966: $i,SY4967: $i,SY4968: $i,SY4969: $i,SY4970: $i] :
( ( c_Finite__Set_Ofold__graph @ SV136 @ SV779 @ ( c_Set_Oinsert @ SY4966 @ SY4967 @ SY4968 ) @ ( hAPP @ ( hAPP @ SV136 @ SY4966 ) @ SY4969 ) @ SY4968 @ SY4970 )
| ~ ( c_Finite__Set_Ofold__graph @ SV136 @ SV779 @ SY4967 @ SY4969 @ SY4968 @ SY4970 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4968 ) @ SY4966 ) @ SY4967 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2660]) ).
thf(3336,plain,
! [SV780: $i,SV137: $i] :
( ( ! [SY4971: $i] :
( ( c_lessequals @ SV137 @ SV780 @ ( tc_fun @ SY4971 @ tc_bool ) )
| ! [SY4972: $i] :
( ~ ( c_lessequals @ SV137 @ ( c_Set_Oinsert @ SY4972 @ SV780 @ SY4971 ) @ ( tc_fun @ SY4971 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4971 ) @ SY4972 ) @ SV137 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2661]) ).
thf(3337,plain,
! [SV781: $i,SV138: $i] :
( ( ! [SY4973: $i,SY4974: $i] :
( ( c_lessequals @ SV138 @ ( c_Set_Oinsert @ SV781 @ SY4973 @ SY4974 ) @ ( tc_fun @ SY4974 @ tc_bool ) )
| ~ ( c_lessequals @ SV138 @ SY4973 @ ( tc_fun @ SY4974 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4974 ) @ SV781 ) @ SV138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2662]) ).
thf(3338,plain,
! [SV782: $i,SV139: $i] :
( ( ! [SY4975: $i] :
( ( c_lessequals @ SV139 @ SV782 @ ( tc_fun @ SY4975 @ tc_bool ) )
| ! [SY4976: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4975 ) @ SY4976 ) @ SV139 ) )
| ~ ( c_lessequals @ SV139 @ ( c_Set_Oinsert @ SY4976 @ SV782 @ SY4975 ) @ ( tc_fun @ SY4975 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2663]) ).
thf(3339,plain,
! [SV783: $i,SV140: $i] :
( ( ! [SY4977: $i,SY4978: $i] :
( ( c_lessequals @ SV140 @ ( c_Set_Oinsert @ SV783 @ SY4977 @ SY4978 ) @ ( tc_fun @ SY4978 @ tc_bool ) )
| ~ ( c_lessequals @ SV140 @ SY4977 @ ( tc_fun @ SY4978 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4978 ) @ SV783 ) @ SV140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2664]) ).
thf(3340,plain,
! [SV784: $i,SV141: $i] :
( ( ! [SY4979: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV141 ) @ SV784 ) @ SY4979 ) )
| ! [SY4980: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SV784 @ SY4980 @ SV141 ) @ SY4979 @ ( tc_fun @ SV141 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2665]) ).
thf(3341,plain,
! [SV785: $i,SV142: $i] :
( ( ! [SY4981: $i,SY4982: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV142 @ SV785 @ SY4981 ) @ SY4982 @ ( tc_fun @ SY4981 @ tc_bool ) )
| ~ ( c_lessequals @ SV785 @ SY4982 @ ( tc_fun @ SY4981 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4981 ) @ SV142 ) @ SY4982 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2666]) ).
thf(3342,plain,
! [SV786: $i,SV143: $i] :
( ( ! [SY4983: $i,SY4984: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV143 ) @ ( hAPP @ SV786 @ SY4983 ) ) @ SY4984 ) )
| ! [SY4985: $i,SY4986: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4985 ) @ SY4983 ) @ SY4986 ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV786 @ SY4986 @ SY4985 @ SV143 ) @ SY4984 @ ( tc_fun @ SV143 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2667]) ).
thf(3343,plain,
! [SV787: $i,SV144: $i] :
( ( ! [SY4987: $i,SY4988: $i,SY4989: $i,SY4990: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ SV144 @ SV787 @ SY4987 @ SY4988 @ SY4989 ) @ SY4990 @ SY4988 @ SY4989 )
= ( c_Set_Oimage @ SV144 @ SY4990 @ SY4988 @ SY4989 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4988 ) @ SV787 ) @ SY4990 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2668]) ).
thf(3344,plain,
! [SV788: $i,SV145: $i] :
( ( ! [SY4991: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV145 )
| ! [SY4992: $i,SY4993: $i] :
( ( c_lessequals @ ( hAPP @ SV788 @ SY4991 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY4992 @ SV788 @ SY4993 @ SV145 ) @ SV145 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4993 ) @ SY4991 ) @ SY4992 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2669]) ).
thf(3345,plain,
! [SV789: $i,SV146: $i] :
( ( ! [SY4994: $i,SY4995: $i] :
( ! [SY4996: $i] : ( c_lessequals @ ( hAPP @ SV146 @ SV789 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY4994 @ SV146 @ SY4995 @ ( tc_fun @ SY4996 @ tc_bool ) ) @ ( tc_fun @ SY4996 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4995 ) @ SV789 ) @ SY4994 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2670]) ).
thf(3346,plain,
! [SV790: $i,SV147: $i] :
( ( ! [SY4997: $i,SY4998: $i] :
( ( c_lessequals @ ( hAPP @ SV147 @ SV790 ) @ SY4997 @ ( tc_fun @ SY4998 @ tc_bool ) )
| ! [SY4999: $i,SY5000: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY4999 ) @ SV790 ) @ SY5000 ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY5000 @ SV147 @ SY4999 @ ( tc_fun @ SY4998 @ tc_bool ) ) @ SY4997 @ ( tc_fun @ SY4998 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2671]) ).
thf(3347,plain,
! [SV791: $i,SV148: $i] :
( ( ! [SY5001: $i,SY5002: $i] :
( ! [SY5003: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV148 @ SV791 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY5001 @ SV148 @ SY5002 @ ( tc_fun @ SY5003 @ tc_bool ) ) @ ( tc_fun @ SY5003 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY5001 @ SV148 @ SY5002 @ ( tc_fun @ SY5003 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5002 ) @ SV791 ) @ SY5001 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2672]) ).
thf(3348,plain,
! [SV792: $i,SV149: $i] :
( ( ! [SY5004: $i] :
( ( c_Set_Oinsert @ SV149 @ SV792 @ SY5004 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV149 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5004 @ tc_bool ) ) @ SY5004 ) @ SV792 @ ( tc_fun @ SY5004 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2673]) ).
thf(3349,plain,
! [SV793: $i,SV150: $i] :
( ( ! [SY5005: $i] :
( ( SV150
= ( c_Set_Oinsert @ SV793 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5005 @ tc_bool ) ) @ SY5005 ) )
| ( SV150
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5005 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV150 @ ( c_Set_Oinsert @ SV793 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5005 @ tc_bool ) ) @ SY5005 ) @ ( tc_fun @ SY5005 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2674]) ).
thf(3350,plain,
! [SV794: $i,SV151: $i] :
( ( ! [SY5006: $i] :
( ( c_Finite__Set_Ofinite @ SV151 @ SV794 )
| ! [SY5007: $i,SY5008: $i] :
( ~ ( c_lessequals @ SV151 @ ( c_Set_Oimage @ SY5006 @ SY5007 @ SY5008 @ SV794 ) @ ( tc_fun @ SV794 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY5007 @ SY5008 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2675]) ).
thf(3351,plain,
! [SV795: $i,SV152: $i] :
( ( ! [SY5009: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ SV152 @ SV795 @ SY5009 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5009 @ tc_bool ) ) @ SY5009 @ SV795 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV795 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2676]) ).
thf(3352,plain,
! [SV796: $i,SV153: $i] :
( ( ! [SY5010: $i] :
( ( c_lessequals @ SV153 @ SV796 @ ( tc_fun @ SY5010 @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ SY5010 ) @ SY5010 @ ( tc_fun @ SY5010 @ tc_bool ) @ tc_bool ) @ SV153 ) @ ( hAPP @ ( c_COMBC @ ( c_in @ SY5010 ) @ SY5010 @ ( tc_fun @ SY5010 @ tc_bool ) @ tc_bool ) @ SV796 ) @ ( tc_fun @ SY5010 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2677]) ).
thf(3353,plain,
! [SV797: $i,SV154: $i] :
( ( ! [SY5011: $i] :
( ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ SV154 ) @ SV154 @ ( tc_fun @ SV154 @ tc_bool ) @ tc_bool ) @ SV797 ) @ ( hAPP @ ( c_COMBC @ ( c_in @ SV154 ) @ SV154 @ ( tc_fun @ SV154 @ tc_bool ) @ tc_bool ) @ SY5011 ) @ ( tc_fun @ SV154 @ tc_bool ) )
| ~ ( c_lessequals @ SV797 @ SY5011 @ ( tc_fun @ SV154 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2678]) ).
thf(3354,plain,
! [SV798: $i,SV155: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV155 )
| ! [SY5012: $i,SY5013: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV798 @ ( c_COMBK @ SY5012 @ SV155 @ SY5013 ) @ SY5013 @ SV155 )
= SY5012 )
| ( SV798
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5013 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2679]) ).
thf(3355,plain,
! [SV799: $i,SV156: $i] :
( ( ! [SY5014: $i,SY5015: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV156 @ tc_bool ) ) @ SV799 @ SV156 @ ( tc_fun @ SY5014 @ tc_bool ) ) @ SY5015 @ ( tc_fun @ SY5014 @ tc_bool ) )
= SY5015 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2680]) ).
thf(3356,plain,
! [SV800: $i,SV157: $i] :
( ( ! [SY5016: $i,SY5017: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV157 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV800 @ tc_bool ) ) @ SY5016 @ SV800 @ ( tc_fun @ SY5017 @ tc_bool ) ) @ ( tc_fun @ SY5017 @ tc_bool ) )
= SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2681]) ).
thf(3357,plain,
! [SV801: $i,SV158: $i] :
( ( ! [SY5018: $i,SY5019: $i,SY5020: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ SV158 @ SV801 @ SY5018 ) @ SY5019 @ SY5018 @ ( tc_fun @ SY5020 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SY5019 @ SV158 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV801 @ SY5019 @ SY5018 @ ( tc_fun @ SY5020 @ tc_bool ) ) @ ( tc_fun @ SY5020 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2682]) ).
thf(3358,plain,
! [SV802: $i,SV159: $i] :
( ( ! [SY5021: $i,SY5022: $i,SY5023: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV159 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV802 @ SY5021 @ ( tc_fun @ SY5022 @ tc_bool ) ) @ SY5022 @ SY5023 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV159 @ SV802 @ SY5022 @ SY5023 ) @ ( c_Set_Oimage @ SV159 @ SY5021 @ SY5022 @ SY5023 ) @ ( tc_fun @ SY5023 @ tc_bool ) ) @ ( tc_fun @ SY5023 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2683]) ).
thf(3359,plain,
! [SV803: $i,SV160: $i] :
( ( ! [SY5024: $i,SY5025: $i,SY5026: $i,SY5027: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV160 @ ( c_COMBB @ SV803 @ SY5024 @ SY5025 @ ( tc_fun @ SY5026 @ tc_bool ) @ SY5027 ) @ SY5027 @ ( tc_fun @ SY5026 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oimage @ SY5024 @ SV160 @ SY5027 @ SY5025 ) @ SV803 @ SY5025 @ ( tc_fun @ SY5026 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2684]) ).
thf(3360,plain,
! [SV804: $i,SV161: $i] :
( ( ! [SY5028: $i,SY5029: $i,SY5030: $i,SY5031: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oimage @ SV161 @ SV804 @ SY5028 @ SY5029 ) @ SY5030 @ SY5029 @ ( tc_fun @ SY5031 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV804 @ ( c_COMBB @ SY5030 @ SV161 @ SY5029 @ ( tc_fun @ SY5031 @ tc_bool ) @ SY5028 ) @ SY5028 @ ( tc_fun @ SY5031 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2685]) ).
thf(3361,plain,
! [SV805: $i,SV162: $i] :
( ( ! [SY5032: $i,SY5033: $i,SY5034: $i] :
( ( ( c_Set_Oimage @ SV162 @ SV805 @ SY5032 @ SY5033 )
!= ( c_Set_Oimage @ SV162 @ SY5034 @ SY5032 @ SY5033 ) )
| ~ ( c_Fun_Oinj__on @ SV162 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV805 @ SY5034 @ ( tc_fun @ SY5032 @ tc_bool ) ) @ SY5032 @ SY5033 )
| ( SV805 = SY5034 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2686]) ).
thf(3362,plain,
! [SV806: $i,SV163: $i] :
( ( ! [SY5035: $i,SY5036: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ SV163 @ SV806 @ SY5035 @ SY5036 ) @ SY5036 )
= ( c_Finite__Set_Ocard @ SV806 @ SY5035 ) )
| ~ ( c_Fun_Oinj__on @ SV163 @ SV806 @ SY5035 @ SY5036 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2687]) ).
thf(3363,plain,
! [SV807: $i,SV164: $i] :
( ( ! [SY5037: $i,SY5038: $i,SY5039: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV164 @ SV807 @ SY5037 @ SY5038 ) @ ( c_Set_Oimage @ SV164 @ SY5039 @ SY5037 @ SY5038 ) @ ( tc_fun @ SY5038 @ tc_bool ) ) @ ( c_Set_Oimage @ SV164 @ ( c_HOL_Ominus__class_Ominus @ SV807 @ SY5039 @ ( tc_fun @ SY5037 @ tc_bool ) ) @ SY5037 @ SY5038 ) @ ( tc_fun @ SY5038 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2688]) ).
thf(3364,plain,
! [SV808: $i,SV165: $i] :
( ( ! [SY5040: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV165 @ SV808 @ ( tc_fun @ SY5040 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 @ SV808 @ ( tc_fun @ SY5040 @ tc_bool ) ) @ ( tc_fun @ SY5040 @ tc_bool ) )
= SV165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2689]) ).
thf(3365,plain,
! [SV809: $i,SV166: $i] :
( ( ! [SY5041: $i,SY5042: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV166 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV809 @ SY5041 @ ( tc_fun @ SY5042 @ tc_bool ) ) @ ( tc_fun @ SY5042 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ SV166 @ SV809 @ ( tc_fun @ SY5042 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV166 @ SY5041 @ ( tc_fun @ SY5042 @ tc_bool ) ) @ ( tc_fun @ SY5042 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2690]) ).
thf(3366,plain,
! [SV810: $i,SV167: $i] :
( ( ! [SY5043: $i,SY5044: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV167 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV810 @ SY5043 @ ( tc_fun @ SY5044 @ tc_bool ) ) @ ( tc_fun @ SY5044 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV167 @ SV810 @ ( tc_fun @ SY5044 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV167 @ SY5043 @ ( tc_fun @ SY5044 @ tc_bool ) ) @ ( tc_fun @ SY5044 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2691]) ).
thf(3367,plain,
! [SV811: $i,SV168: $i] :
( ( ! [SY5045: $i,SY5046: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV168 @ ( c_Set_Ovimage @ SV168 @ SV811 @ SY5045 @ SY5046 ) @ SY5045 @ SY5046 ) @ SV811 @ ( tc_fun @ SY5046 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2692]) ).
thf(3368,plain,
! [SV812: $i,SV169: $i] :
( ( ! [SY5047: $i,SY5048: $i,SY5049: $i,SY5050: $i] :
( ( c_Map_Omap__add @ SV169 @ ( c_Fun_Ofun__upd @ SV812 @ SY5047 @ ( c_Option_Ooption_OSome @ SY5048 @ SY5049 ) @ SY5050 @ ( tc_Option_Ooption @ SY5049 ) ) @ SY5050 @ SY5049 )
= ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ SV169 @ SV812 @ SY5050 @ SY5049 ) @ SY5047 @ ( c_Option_Ooption_OSome @ SY5048 @ SY5049 ) @ SY5050 @ ( tc_Option_Ooption @ SY5049 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2693]) ).
thf(3369,plain,
! [SV813: $i,SV170: $i] :
( ( ! [SY5051: $i,SY5052: $i] :
( ( c_Map_Odom @ ( c_Map_Omap__add @ SV170 @ SV813 @ SY5051 @ SY5052 ) @ SY5051 @ SY5052 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Map_Odom @ SV813 @ SY5051 @ SY5052 ) @ ( c_Map_Odom @ SV170 @ SY5051 @ SY5052 ) @ ( tc_fun @ SY5051 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2694]) ).
thf(3370,plain,
! [SV814: $i,SV171: $i] :
( ( ! [SY5053: $i,SY5054: $i] : ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ SV171 @ SV814 @ ( c_Option_Ooption_ONone @ SY5053 ) @ SY5054 @ ( tc_Option_Ooption @ SY5053 ) ) @ SV171 @ SY5054 @ SY5053 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2695]) ).
thf(3371,plain,
! [SV815: $i,SV172: $i] :
( ( ! [SY5055: $i,SY5056: $i] :
( ( c_lessequals @ ( c_Map_Odom @ SV172 @ SV815 @ SY5055 ) @ ( c_Map_Odom @ SY5056 @ SV815 @ SY5055 ) @ ( tc_fun @ SV815 @ tc_bool ) )
| ~ ( c_Map_Omap__le @ SV172 @ SY5056 @ SV815 @ SY5055 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2696]) ).
thf(3372,plain,
! [SV816: $i,SV173: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV173 @ SV173 @ ( tc_fun @ SV816 @ tc_bool ) )
= SV173 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2697]) ).
thf(3373,plain,
! [SV174: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV174 ) )
= $true )
| ( ( ! [SY3225: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3225 @ SY3225 @ SV174 )
= SY3225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2698]) ).
thf(3374,plain,
! [SV817: $i,SV175: $i] :
( ( ! [SY5057: $i,SY5058: $i,SY5059: $i,SY5060: $i] :
( ( hAPP @ ( c_COMBB @ SV175 @ SV817 @ SY5057 @ SY5058 @ SY5059 ) @ SY5060 )
= ( hAPP @ SV175 @ ( hAPP @ SV817 @ SY5060 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2699]) ).
thf(3375,plain,
! [SV818: $i,SV176: $i] :
( ( ! [SY5061: $i,SY5062: $i] :
( ( hAPP @ ( c_COMBK @ SV176 @ SV818 @ SY5061 ) @ SY5062 )
= SV176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2700]) ).
thf(3376,plain,
! [SV177: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV177 ) )
= $true )
| ( ( ! [SY3234: $i,SY3235: $i] :
( ( c_HOL_Oord__class_Oless @ SY3234 @ SY3235 @ SV177 )
| ( c_lessequals @ SY3235 @ SY3234 @ SV177 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2701]) ).
thf(3377,plain,
! [SV178: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV178 ) )
= $true )
| ( ( ! [SY3236: $i] :
( ~ ( c_lessequals @ SY3236 @ SY3236 @ SV178 )
| ~ ( c_HOL_Oord__class_Oless @ SY3236 @ SY3236 @ SV178 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2702]) ).
thf(3378,plain,
! [SV179: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV179 ) )
= $true )
| ( ( ! [SY3237: $i] :
( ( c_HOL_Oord__class_Oless @ SY3237 @ SY3237 @ SV179 )
| ( c_lessequals @ SY3237 @ SY3237 @ SV179 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2703]) ).
thf(3379,plain,
! [SV180: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV180 ) )
= $true )
| ( ( ! [SY3238: $i,SY3239: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY3238 @ SY3239 @ SV180 )
| ~ ( c_lessequals @ SY3239 @ SY3238 @ SV180 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2704]) ).
thf(3380,plain,
! [SV181: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV181 ) )
= $true )
| ( ( ! [SY3240: $i,SY3241: $i] :
( ( c_HOL_Oord__class_Oless @ SY3241 @ SY3240 @ SV181 )
| ( c_lessequals @ SY3240 @ SY3241 @ SV181 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2705]) ).
thf(3381,plain,
! [SV182: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV182 ) )
= $true )
| ( ( ! [SY3242: $i,SY3243: $i] :
( ~ ( c_lessequals @ SY3242 @ SY3243 @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ SY3243 @ SY3242 @ SV182 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2706]) ).
thf(3382,plain,
! [SV183: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV183 ) )
= $true )
| ( ( ! [SY3244: $i,SY3245: $i] :
( ( c_HOL_Oord__class_Oless @ SY3244 @ SY3245 @ SV183 )
| ( c_lessequals @ SY3245 @ SY3244 @ SV183 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2707]) ).
thf(3383,plain,
! [SV819: $i,SV184: $i] :
( ( ~ ( class_HOL_Oord @ SV184 )
| ! [SY5063: $i,SY5064: $i] :
( ~ ( c_lessequals @ SV819 @ SY5063 @ ( tc_fun @ SY5064 @ SV184 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY5063 @ SV819 @ ( tc_fun @ SY5064 @ SV184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2708]) ).
thf(3384,plain,
! [SV185: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV185 ) )
= $true )
| ( ( ! [SY3249: $i,SY3250: $i] :
( ~ ( c_lessequals @ SY3249 @ SY3250 @ SV185 )
| ~ ( c_HOL_Oord__class_Oless @ SY3250 @ SY3249 @ SV185 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2709]) ).
thf(3385,plain,
! [SV820: $i,SV186: $i] :
( ( ! [SY5065: $i,SY5066: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV186 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV820 @ SY5065 @ ( tc_fun @ SY5066 @ tc_bool ) ) @ ( tc_fun @ SY5066 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV820 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV186 @ SY5065 @ ( tc_fun @ SY5066 @ tc_bool ) ) @ ( tc_fun @ SY5066 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2710]) ).
thf(3386,plain,
! [SV821: $i,SV187: $i] :
( ( ! [SY5067: $i,SY5068: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV187 @ SV821 @ ( tc_fun @ SY5067 @ tc_bool ) ) @ SY5068 @ ( tc_fun @ SY5067 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV187 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV821 @ SY5068 @ ( tc_fun @ SY5067 @ tc_bool ) ) @ ( tc_fun @ SY5067 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2711]) ).
thf(3387,plain,
! [SV822: $i,SV188: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV188 )
| ! [SY5069: $i,SY5070: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV822 @ SY5069 @ SV188 ) @ SY5070 @ SV188 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV822 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5069 @ SY5070 @ SV188 ) @ SV188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2712]) ).
thf(3388,plain,
! [SV823: $i,SV189: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV189 )
| ! [SY5071: $i,SY5072: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV823 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5071 @ SY5072 @ SV189 ) @ SV189 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY5071 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV823 @ SY5072 @ SV189 ) @ SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2713]) ).
thf(3389,plain,
! [SV824: $i,SV190: $i] :
( ( ~ ( class_Lattices_Olattice @ SV190 )
| ! [SY5073: $i,SY5074: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV824 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5073 @ SY5074 @ SV190 ) @ SV190 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY5073 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV824 @ SY5074 @ SV190 ) @ SV190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2714]) ).
thf(3390,plain,
! [SV825: $i,SV191: $i] :
( ( ~ ( class_Lattices_Olattice @ SV191 )
| ! [SY5075: $i,SY5076: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV825 @ SY5075 @ SV191 ) @ SY5076 @ SV191 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV825 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5075 @ SY5076 @ SV191 ) @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2715]) ).
thf(3391,plain,
! [SV826: $i,SV192: $i] :
( ( ! [SY5077: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV192 @ SV826 @ ( tc_fun @ SY5077 @ tc_bool ) )
= SV192 )
| ~ ( c_lessequals @ SV192 @ SV826 @ ( tc_fun @ SY5077 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2716]) ).
thf(3392,plain,
! [SV827: $i,SV193: $i] :
( ( ! [SY5078: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV193 @ SV827 @ ( tc_fun @ SY5078 @ tc_bool ) )
= SV827 )
| ~ ( c_lessequals @ SV827 @ SV193 @ ( tc_fun @ SY5078 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2717]) ).
thf(3393,plain,
! [SV194: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV194 ) )
= $true )
| ( ( ! [SY3273: $i,SY3274: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3273 @ SY3274 @ SV194 )
= SY3273 )
| ~ ( c_lessequals @ SY3273 @ SY3274 @ SV194 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2718]) ).
thf(3394,plain,
! [SV195: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV195 ) )
= $true )
| ( ( ! [SY3275: $i,SY3276: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3275 @ SY3276 @ SV195 )
!= SY3275 )
| ( c_lessequals @ SY3275 @ SY3276 @ SV195 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2719]) ).
thf(3395,plain,
! [SV196: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV196 ) )
= $true )
| ( ( ! [SY3277: $i,SY3278: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3277 @ SY3278 @ SV196 )
= SY3278 )
| ~ ( c_lessequals @ SY3278 @ SY3277 @ SV196 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2720]) ).
thf(3396,plain,
! [SV828: $i,SV197: $i] :
( ( ! [SY5079: $i,SY5080: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV197 @ SV828 @ ( tc_fun @ SY5079 @ tc_bool ) ) @ SY5080 @ ( tc_fun @ SY5079 @ tc_bool ) )
| ~ ( c_lessequals @ SV828 @ SY5080 @ ( tc_fun @ SY5079 @ tc_bool ) )
| ~ ( c_lessequals @ SV197 @ SY5080 @ ( tc_fun @ SY5079 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2721]) ).
thf(3397,plain,
! [SV829: $i,SV198: $i] :
( ( ! [SY5081: $i] : ( c_lessequals @ SV198 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV829 @ SV198 @ ( tc_fun @ SY5081 @ tc_bool ) ) @ ( tc_fun @ SY5081 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2722]) ).
thf(3398,plain,
! [SV830: $i,SV199: $i] :
( ( ! [SY5082: $i] : ( c_lessequals @ SV199 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV199 @ SV830 @ ( tc_fun @ SY5082 @ tc_bool ) ) @ ( tc_fun @ SY5082 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2723]) ).
thf(3399,plain,
! [SV831: $i,SV200: $i] :
( ( ! [SY5083: $i,SY5084: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ SV831 @ ( tc_fun @ SY5083 @ tc_bool ) ) @ SY5084 @ ( tc_fun @ SY5083 @ tc_bool ) )
| ~ ( c_lessequals @ SV831 @ SY5084 @ ( tc_fun @ SY5083 @ tc_bool ) )
| ~ ( c_lessequals @ SV200 @ SY5084 @ ( tc_fun @ SY5083 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2724]) ).
thf(3400,plain,
! [SV832: $i,SV201: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV201 )
| ! [SY5085: $i,SY5086: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV832 @ SY5085 @ SV201 ) @ SY5086 @ SV201 )
| ~ ( c_lessequals @ SY5085 @ SY5086 @ SV201 )
| ~ ( c_lessequals @ SV832 @ SY5086 @ SV201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2725]) ).
thf(3401,plain,
! [SV202: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV202 ) )
= $true )
| ( ( ! [SY3292: $i,SY3293: $i] : ( c_lessequals @ SY3292 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3292 @ SY3293 @ SV202 ) @ SV202 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2726]) ).
thf(3402,plain,
! [SV203: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV203 ) )
= $true )
| ( ( ! [SY3294: $i,SY3295: $i] : ( c_lessequals @ SY3294 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3295 @ SY3294 @ SV203 ) @ SV203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2727]) ).
thf(3403,plain,
! [SV833: $i,SV204: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV204 )
| ! [SY5087: $i,SY5088: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV833 @ SY5087 @ SV204 ) @ SY5088 @ SV204 )
| ~ ( c_lessequals @ SY5087 @ SY5088 @ SV204 )
| ~ ( c_lessequals @ SV833 @ SY5088 @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2728]) ).
thf(3404,plain,
! [SV834: $i,SV205: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV205 )
| ! [SY5089: $i,SY5090: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV834 @ SY5089 @ SV205 ) @ SY5090 @ SV205 )
| ~ ( c_lessequals @ SY5089 @ SY5090 @ SV205 )
| ~ ( c_lessequals @ SV834 @ SY5090 @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2729]) ).
thf(3405,plain,
! [SV206: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV206 ) )
= $true )
| ( ( ! [SY3302: $i,SY3303: $i] : ( c_lessequals @ SY3302 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3303 @ SY3302 @ SV206 ) @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2730]) ).
thf(3406,plain,
! [SV207: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV207 ) )
= $true )
| ( ( ! [SY3304: $i,SY3305: $i] : ( c_lessequals @ SY3304 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3304 @ SY3305 @ SV207 ) @ SV207 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2731]) ).
thf(3407,plain,
! [SV835: $i,SV208: $i] :
( ( ! [SY5091: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV208 @ ( c_HOL_Ominus__class_Ominus @ SV835 @ SV208 @ ( tc_fun @ SY5091 @ tc_bool ) ) @ ( tc_fun @ SY5091 @ tc_bool ) )
= SV835 )
| ~ ( c_lessequals @ SV208 @ SV835 @ ( tc_fun @ SY5091 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2732]) ).
thf(3408,plain,
! [SV836: $i,SV209: $i] :
( ( ~ ( class_Lattices_Olattice @ SV209 )
| ! [SY5092: $i,SY5093: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV836 @ SY5092 @ SV209 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV836 @ SY5093 @ SV209 ) @ SV209 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV836 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5092 @ SY5093 @ SV209 ) @ SV209 ) @ SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2733]) ).
thf(3409,plain,
! [SV837: $i,SV210: $i] :
( ( ! [SY5094: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV210 @ SV837 @ ( tc_fun @ SY5094 @ tc_bool ) ) @ SV210 @ ( tc_fun @ SY5094 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2734]) ).
thf(3410,plain,
! [SV838: $i,SV211: $i] :
( ( ! [SY5095: $i,SY5096: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV211 @ SV838 @ ( tc_fun @ SY5095 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV838 @ SY5096 @ ( tc_fun @ SY5095 @ tc_bool ) ) @ ( tc_fun @ SY5095 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5096 @ SV211 @ ( tc_fun @ SY5095 @ tc_bool ) ) @ ( tc_fun @ SY5095 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV211 @ SV838 @ ( tc_fun @ SY5095 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV838 @ SY5096 @ ( tc_fun @ SY5095 @ tc_bool ) ) @ ( tc_fun @ SY5095 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5096 @ SV211 @ ( tc_fun @ SY5095 @ tc_bool ) ) @ ( tc_fun @ SY5095 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2735]) ).
thf(3411,plain,
! [SV839: $i,SV212: $i] :
( ( ! [SY5097: $i,SY5098: $i] : ( c_Finite__Set_Ofold__graph @ SV212 @ SV839 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5097 @ tc_bool ) ) @ SV839 @ SY5097 @ SY5098 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2736]) ).
thf(3412,plain,
! [SV840: $i,SV213: $i] :
( ( ! [SY5099: $i,SY5100: $i] : ( c_Nitpick_Ofold__graph_H @ SV213 @ SV840 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5099 @ tc_bool ) ) @ SV840 @ SY5099 @ SY5100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2737]) ).
thf(3413,plain,
! [SV841: $i,SV214: $i] :
( ( ! [SY5101: $i,SY5102: $i,SY5103: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ SV214 @ SV841 @ SY5101 @ SY5102 ) @ ( c_Set_Ovimage @ SV214 @ SY5103 @ SY5101 @ SY5102 ) @ ( tc_fun @ SY5101 @ tc_bool ) )
| ~ ( c_lessequals @ SV841 @ SY5103 @ ( tc_fun @ SY5102 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2738]) ).
thf(3414,plain,
! [SV842: $i,SV215: $i] :
( ( ! [SY5104: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV215 @ SV842 @ ( tc_fun @ SY5104 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5104 @ tc_bool ) ) )
| ( SV842
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5104 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2739]) ).
thf(3415,plain,
! [SV843: $i,SV216: $i] :
( ( ! [SY5105: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV216 @ SV843 @ ( tc_fun @ SY5105 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5105 @ tc_bool ) ) )
| ( SV216
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5105 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2740]) ).
thf(3416,plain,
! [SV217: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV217 ) )
= $true )
| ( ( ! [SY3330: $i] :
( ! [SY3331: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3330 @ SY3331 @ SV217 )
!= ( c_Orderings_Obot__class_Obot @ SV217 ) )
| ( SY3330
= ( c_Orderings_Obot__class_Obot @ SV217 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2741]) ).
thf(3417,plain,
! [SV218: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV218 ) )
= $true )
| ( ( ! [SY3332: $i,SY3333: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3332 @ SY3333 @ SV218 )
!= ( c_Orderings_Obot__class_Obot @ SV218 ) )
| ( SY3333
= ( c_Orderings_Obot__class_Obot @ SV218 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2742]) ).
thf(3418,plain,
! [SV844: $i,SV219: $i] :
( ( ! [SY5106: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV219 @ SV844 @ ( tc_fun @ SY5106 @ tc_bool ) ) @ SV844 @ ( tc_fun @ SY5106 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV219 @ SV844 @ ( tc_fun @ SY5106 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2743]) ).
thf(3419,plain,
! [SV845: $i,SV220: $i] :
( ( ! [SY5107: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV220 @ ( c_HOL_Ominus__class_Ominus @ SV845 @ SV220 @ ( tc_fun @ SY5107 @ tc_bool ) ) @ ( tc_fun @ SY5107 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV220 @ SV845 @ ( tc_fun @ SY5107 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2744]) ).
thf(3420,plain,
! [SV846: $i,SV221: $i] :
( ( ! [SY5108: $i] :
( ( c_lessequals @ SV221 @ SV846 @ ( tc_fun @ SY5108 @ tc_bool ) )
| ! [SY5109: $i] :
~ ( c_lessequals @ SV221 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5109 @ SV846 @ ( tc_fun @ SY5108 @ tc_bool ) ) @ ( tc_fun @ SY5108 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2745]) ).
thf(3421,plain,
! [SV847: $i,SV222: $i] :
( ( ! [SY5110: $i] :
( ( c_lessequals @ SV222 @ SV847 @ ( tc_fun @ SY5110 @ tc_bool ) )
| ! [SY5111: $i] :
~ ( c_lessequals @ SV222 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV847 @ SY5111 @ ( tc_fun @ SY5110 @ tc_bool ) ) @ ( tc_fun @ SY5110 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2746]) ).
thf(3422,plain,
! [SV848: $i,SV223: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV223 )
| ! [SY5112: $i] :
( ( c_lessequals @ SV848 @ SY5112 @ SV223 )
| ! [SY5113: $i] :
~ ( c_lessequals @ SV848 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5112 @ SY5113 @ SV223 ) @ SV223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2747]) ).
thf(3423,plain,
! [SV849: $i,SV224: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV224 )
| ! [SY5114: $i] :
( ( c_lessequals @ SV849 @ SY5114 @ SV224 )
| ! [SY5115: $i] :
~ ( c_lessequals @ SV849 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5115 @ SY5114 @ SV224 ) @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2748]) ).
thf(3424,plain,
! [SV850: $i,SV225: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV225 )
| ! [SY5116: $i,SY5117: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV850 @ SY5116 @ SV225 ) @ SY5117 @ SV225 )
| ~ ( c_lessequals @ SV850 @ SY5117 @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2749]) ).
thf(3425,plain,
! [SV851: $i,SV226: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV226 )
| ! [SY5118: $i,SY5119: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV851 @ SY5118 @ SV226 ) @ SY5119 @ SV226 )
| ~ ( c_lessequals @ SY5118 @ SY5119 @ SV226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2750]) ).
thf(3426,plain,
! [SV852: $i,SV227: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV227 )
| ! [SY5120: $i] :
( ( c_lessequals @ SV852 @ SY5120 @ SV227 )
| ! [SY5121: $i] :
~ ( c_lessequals @ SV852 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5120 @ SY5121 @ SV227 ) @ SV227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2751]) ).
thf(3427,plain,
! [SV853: $i,SV228: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV228 )
| ! [SY5122: $i] :
( ( c_lessequals @ SV853 @ SY5122 @ SV228 )
| ! [SY5123: $i] :
~ ( c_lessequals @ SV853 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5123 @ SY5122 @ SV228 ) @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2752]) ).
thf(3428,plain,
! [SV854: $i,SV229: $i] :
( ( ! [SY5124: $i,SY5125: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV229 @ SV854 @ ( tc_fun @ SY5124 @ tc_bool ) ) @ SY5125 @ ( tc_fun @ SY5124 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV229 @ SY5125 @ ( tc_fun @ SY5124 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV854 @ SY5125 @ ( tc_fun @ SY5124 @ tc_bool ) ) @ ( tc_fun @ SY5124 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2753]) ).
thf(3429,plain,
! [SV855: $i,SV230: $i] :
( ( ! [SY5126: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV230 @ SV855 @ ( tc_fun @ SY5126 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV855 @ SV230 @ ( tc_fun @ SY5126 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2754]) ).
thf(3430,plain,
! [SV231: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV231 ) )
= $true )
| ( ( ! [SY3367: $i,SY3368: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3367 @ SY3368 @ SV231 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3368 @ SY3367 @ SV231 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2755]) ).
thf(3431,plain,
! [SV232: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV232 ) )
= $true )
| ( ( ! [SY3369: $i,SY3370: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3369 @ SY3370 @ SV232 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3370 @ SY3369 @ SV232 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2756]) ).
thf(3432,plain,
! [SV856: $i,SV233: $i] :
( ( ! [SY5127: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV233 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV233 @ SV856 @ ( tc_fun @ SY5127 @ tc_bool ) ) @ ( tc_fun @ SY5127 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV233 @ SV856 @ ( tc_fun @ SY5127 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2757]) ).
thf(3433,plain,
! [SV234: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV234 ) )
= $true )
| ( ( ! [SY3373: $i,SY3374: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3373 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3373 @ SY3374 @ SV234 ) @ SV234 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3373 @ SY3374 @ SV234 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2758]) ).
thf(3434,plain,
! [SV235: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV235 ) )
= $true )
| ( ( ! [SY3375: $i,SY3376: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3375 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3375 @ SY3376 @ SV235 ) @ SV235 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3375 @ SY3376 @ SV235 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2759]) ).
thf(3435,plain,
! [SV857: $i,SV236: $i] :
( ( ! [SY5128: $i,SY5129: $i,SY5130: $i] :
( ( c_Set_Ovimage @ SV236 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV857 @ SY5128 @ ( tc_fun @ SY5129 @ tc_bool ) ) @ SY5130 @ SY5129 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ SV236 @ SV857 @ SY5130 @ SY5129 ) @ ( c_Set_Ovimage @ SV236 @ SY5128 @ SY5130 @ SY5129 ) @ ( tc_fun @ SY5130 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2760]) ).
thf(3436,plain,
! [SV858: $i,SV237: $i] :
( ( ! [SY5131: $i] :
( ! [SY5132: $i,SY5133: $i] :
( ( c_Fun_Ofun__upd @ SV237 @ SV858 @ SY5131 @ SY5132 @ SY5133 )
!= SV237 )
| ( ( hAPP @ SV237 @ SV858 )
= SY5131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2761]) ).
thf(3437,plain,
! [SV859: $i,SV238: $i] :
( ( ! [SY5134: $i,SY5135: $i] :
( ( c_Fun_Oinj__on @ SV238 @ SV859 @ SY5134 @ SY5135 )
| ! [SY5136: $i] :
~ ( c_Fun_Oinj__on @ SV238 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5136 @ SV859 @ ( tc_fun @ SY5134 @ tc_bool ) ) @ SY5134 @ SY5135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2762]) ).
thf(3438,plain,
! [SV860: $i,SV239: $i] :
( ( ! [SY5137: $i,SY5138: $i] :
( ( c_Fun_Oinj__on @ SV239 @ SV860 @ SY5137 @ SY5138 )
| ! [SY5139: $i] :
~ ( c_Fun_Oinj__on @ SV239 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV860 @ SY5139 @ ( tc_fun @ SY5137 @ tc_bool ) ) @ SY5137 @ SY5138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2763]) ).
thf(3439,plain,
! [SV861: $i,SV240: $i] :
( ( ! [SY5140: $i,SY5141: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV240 @ SV861 @ ( tc_fun @ SY5140 @ tc_bool ) ) @ SY5141 @ ( tc_fun @ SY5140 @ tc_bool ) )
| ~ ( c_lessequals @ SV240 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV861 @ SY5141 @ ( tc_fun @ SY5140 @ tc_bool ) ) @ ( tc_fun @ SY5140 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2764]) ).
thf(3440,plain,
! [SV862: $i,SV241: $i] :
( ( ! [SY5142: $i,SY5143: $i] :
( ( c_lessequals @ SV241 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV862 @ SY5142 @ ( tc_fun @ SY5143 @ tc_bool ) ) @ ( tc_fun @ SY5143 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV241 @ SV862 @ ( tc_fun @ SY5143 @ tc_bool ) ) @ SY5142 @ ( tc_fun @ SY5143 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2765]) ).
thf(3441,plain,
! [SV863: $i,SV242: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV242 )
| ! [SY5144: $i] :
( ! [SY5145: $i] : ( c_HOL_Oord__class_Oless @ SV863 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5144 @ SY5145 @ SV242 ) @ SV242 )
| ~ ( c_HOL_Oord__class_Oless @ SV863 @ SY5144 @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2766]) ).
thf(3442,plain,
! [SV864: $i,SV243: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV243 )
| ! [SY5146: $i,SY5147: $i] :
( ( c_HOL_Oord__class_Oless @ SV864 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5146 @ SY5147 @ SV243 ) @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ SV864 @ SY5147 @ SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2767]) ).
thf(3443,plain,
! [SV865: $i,SV244: $i] :
( ( ! [SY5148: $i] :
( ~ ( class_HOL_Oord @ SV244 )
| ! [SY5149: $i] :
( ( c_lessequals @ ( hAPP @ SV865 @ SY5148 ) @ ( hAPP @ SY5149 @ SY5148 ) @ SV244 )
| ! [SY5150: $i] :
~ ( c_lessequals @ SV865 @ SY5149 @ ( tc_fun @ SY5150 @ SV244 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2768]) ).
thf(3444,plain,
! [SV866: $i,SV245: $i] :
( ( ! [SY5151: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV245 ) @ SV866 ) @ SY5151 ) )
| ! [SY5152: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV245 ) @ SV866 ) @ SY5152 ) )
| ~ ( c_lessequals @ SY5152 @ SY5151 @ ( tc_fun @ SV245 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2769]) ).
thf(3445,plain,
! [SV867: $i,SV246: $i] :
( ( ! [SY5153: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV246 ) @ SV867 ) @ SY5153 ) )
| ! [SY5154: $i] :
( ~ ( c_lessequals @ SY5154 @ SY5153 @ ( tc_fun @ SV246 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV246 ) @ SV867 ) @ SY5154 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2770]) ).
thf(3446,plain,
! [SV868: $i,SV247: $i] :
( ( ! [SY5155: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV247 ) @ SV868 ) @ SY5155 ) )
| ! [SY5156: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV247 ) @ SV868 ) @ SY5156 ) )
| ~ ( c_lessequals @ SY5156 @ SY5155 @ ( tc_fun @ SV247 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2771]) ).
thf(3447,plain,
! [SV869: $i,SV248: $i] :
( ( ! [SY5157: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV248 ) @ SV869 ) @ SY5157 ) )
| ! [SY5158: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV248 ) @ SV869 ) @ SY5158 ) )
| ~ ( c_lessequals @ SY5158 @ SY5157 @ ( tc_fun @ SV248 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2772]) ).
thf(3448,plain,
! [SV870: $i,SV249: $i] :
( ( ! [SY5159: $i] :
( ! [SY5160: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV249 ) @ SV870 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5159 @ SY5160 @ ( tc_fun @ SV249 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV249 ) @ SV870 ) @ SY5159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2773]) ).
thf(3449,plain,
! [SV871: $i,SV250: $i] :
( ( ! [SY5161: $i,SY5162: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV250 ) @ SV871 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5161 @ SY5162 @ ( tc_fun @ SV250 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV250 ) @ SV871 ) @ SY5162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2774]) ).
thf(3450,plain,
! [SV872: $i,SV251: $i] :
( ( ! [SY5163: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV251 ) @ SV872 ) @ SY5163 ) )
| ! [SY5164: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV251 ) @ SV872 ) @ SY5164 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV251 ) @ SV872 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5164 @ SY5163 @ ( tc_fun @ SV251 @ tc_bool ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2775]) ).
thf(3451,plain,
! [SV873: $i,SV253: $i] :
( ( ! [SY5165: $i,SY5166: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV253 ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV873 @ SY5165 @ SY5166 @ SV253 ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV873 @ SY5165 @ ( tc_fun @ SV253 @ tc_bool ) ) ) )
| ! [SY3433: $i] :
( ~ ( hBOOL @ ( hAPP @ SY5166 @ SY3433 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV253 ) @ SY3433 ) @ SY5165 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2777]) ).
thf(3452,plain,
! [SV874: $i,SV254: $i] :
( ( ! [SY5168: $i,SY5169: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV254 ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV874 @ SY5168 @ SY5169 @ SV254 ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV874 @ SY5168 @ ( tc_fun @ SV254 @ tc_bool ) ) ) )
| ! [SY5170: $i] :
( ~ ( hBOOL @ ( hAPP @ SY5169 @ SY5170 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV254 ) @ SY5170 ) @ SV874 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2778]) ).
thf(3453,plain,
! [SV875: $i,SV255: $i] :
( ( ! [SY5171: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ SV255 @ SV875 @ SY5171 ) @ SY5171 )
= ( c_Finite__Set_Ocard @ SV875 @ SY5171 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5171 ) @ SV255 ) @ SV875 ) )
| ~ ( c_Finite__Set_Ofinite @ SV875 @ SY5171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2779]) ).
thf(3454,plain,
! [SV876: $i,SV256: $i] :
( ( ! [SY5172: $i,SY5173: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV256 @ SV876 @ SY5172 ) @ SY5173 @ SY5172 @ SV876 )
= ( c_Set_Oinsert @ SV256 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV876 @ tc_bool ) ) @ SV876 ) )
| ( SY5173
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5172 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2780]) ).
thf(3455,plain,
! [SV877: $i,SV257: $i] :
( ( ! [SY5174: $i,SY5175: $i,SY5176: $i,SY5177: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ofun__upd @ SV257 @ SV877 @ SY5174 @ SY5175 @ SY5176 ) @ SY5177 @ SY5175 @ SY5176 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5176 ) @ SY5174 ) @ ( c_Set_Oimage @ SV257 @ SY5177 @ SY5175 @ SY5176 ) ) )
| ~ ( c_Fun_Oinj__on @ SV257 @ SY5177 @ SY5175 @ SY5176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2781]) ).
thf(3456,plain,
! [SV878: $i,SV258: $i] :
( ( ! [SY5178: $i] :
( ( c_Set_Oinsert @ SV258 @ SV878 @ SY5178 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ SY5178 ) @ SY5178 @ SY5178 @ tc_bool ) @ SV258 ) @ SY5178 ) @ SV878 @ ( tc_fun @ SY5178 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2782]) ).
thf(3457,plain,
! [SV879: $i,SV259: $i] :
( ( ! [SY5179: $i,SY5180: $i] :
( ( c_lessequals @ SV259 @ ( c_Set_Oinsert @ SV879 @ SY5179 @ SY5180 ) @ ( tc_fun @ SY5180 @ tc_bool ) )
| ~ ( c_lessequals @ SV259 @ SY5179 @ ( tc_fun @ SY5180 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV259 @ ( c_Set_Oinsert @ SV879 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5180 @ tc_bool ) ) @ SY5180 ) @ ( tc_fun @ SY5180 @ tc_bool ) ) @ SY5179 @ ( tc_fun @ SY5180 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2783]) ).
thf(3458,plain,
! [SV880: $i,SV260: $i] :
( ( ! [SY5181: $i,SY5182: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ SV260 @ SV880 @ SY5181 @ SY5182 ) @ SY5182 )
= ( c_Finite__Set_Ocard @ SV880 @ SY5181 ) )
| ~ ( c_Fun_Oinj__on @ SV260 @ SV880 @ SY5181 @ SY5182 )
| ~ ( c_Finite__Set_Ofinite @ SV880 @ SY5181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2784]) ).
thf(3459,plain,
! [SV881: $i,SV261: $i] :
( ( ! [SY5183: $i,SY5184: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ SV261 @ SV881 @ SY5183 @ SY5184 ) @ SY5184 )
!= ( c_Finite__Set_Ocard @ SV881 @ SY5183 ) )
| ~ ( c_Finite__Set_Ofinite @ SV881 @ SY5183 )
| ( c_Fun_Oinj__on @ SV261 @ SV881 @ SY5183 @ SY5184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2785]) ).
thf(3460,plain,
! [SV882: $i,SV262: $i] :
( ( ! [SY5185: $i] :
( ( ( c_Set_Oimage @ SV262 @ SV882 @ SY5185 @ SY5185 )
= SV882 )
| ~ ( c_Fun_Oinj__on @ SV262 @ SV882 @ SY5185 @ SY5185 )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV262 @ SV882 @ SY5185 @ SY5185 ) @ SV882 @ ( tc_fun @ SY5185 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV882 @ SY5185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2786]) ).
thf(3461,plain,
! [SV883: $i,SV263: $i] :
( ( ! [SY5186: $i] :
( ( c_Fun_Oinj__on @ SV263 @ SV883 @ SY5186 @ SY5186 )
| ~ ( c_lessequals @ SV883 @ ( c_Set_Oimage @ SV263 @ SV883 @ SY5186 @ SY5186 ) @ ( tc_fun @ SY5186 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV883 @ SY5186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2787]) ).
thf(3462,plain,
! [SV884: $i,SV264: $i] :
( ( ! [SY5187: $i,SY5188: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ SV264 @ SV884 @ SY5187 ) @ SY5188 @ SY5187 @ SV884 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5187 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV884 ) @ SV264 ) @ SY5188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2788]) ).
thf(3463,plain,
! [SV885: $i,SV265: $i] :
( ( ! [SY5189: $i,SY5190: $i] :
( ( c_HOL_Oord__class_Oless @ SV265 @ ( c_Set_Oinsert @ SV885 @ SY5189 @ SY5190 ) @ ( tc_fun @ SY5190 @ tc_bool ) )
| ~ ( c_lessequals @ SV265 @ SY5189 @ ( tc_fun @ SY5190 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5190 ) @ SV885 ) @ SV265 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV265 @ SY5189 @ ( tc_fun @ SY5190 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2789]) ).
thf(3464,plain,
! [SV886: $i,SV266: $i] :
( ( ! [SY5191: $i,SY5192: $i] :
( ( c_HOL_Oord__class_Oless @ SV266 @ ( c_Set_Oinsert @ SV886 @ SY5191 @ SY5192 ) @ ( tc_fun @ SY5192 @ tc_bool ) )
| ~ ( c_lessequals @ SV266 @ SY5191 @ ( tc_fun @ SY5192 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5192 ) @ SV886 ) @ SV266 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5192 ) @ SV886 ) @ SY5191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2790]) ).
thf(3465,plain,
! [SV887: $i,SV267: $i] :
( ( ! [SY5193: $i] :
( ( c_lessequals @ SV267 @ SV887 @ ( tc_fun @ SY5193 @ tc_bool ) )
| ! [SY5194: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5193 ) @ SY5194 ) @ SV267 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5193 ) @ SY5194 ) @ SV887 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV267 @ ( c_Set_Oinsert @ SY5194 @ SV887 @ SY5193 ) @ ( tc_fun @ SY5193 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2791]) ).
thf(3466,plain,
! [SV888: $i,SV268: $i] :
( ( ! [SY5195: $i,SY5196: $i,SY5197: $i] :
( ( ( c_Set_Oimage @ SV268 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV888 @ SY5195 @ ( tc_fun @ SY5196 @ tc_bool ) ) @ SY5196 @ SY5197 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV268 @ SV888 @ SY5196 @ SY5197 ) @ ( c_Set_Oimage @ SV268 @ SY5195 @ SY5196 @ SY5197 ) @ ( tc_fun @ SY5197 @ tc_bool ) ) )
| ! [SY5198: $i] :
( ~ ( c_lessequals @ SY5195 @ SY5198 @ ( tc_fun @ SY5196 @ tc_bool ) )
| ~ ( c_lessequals @ SV888 @ SY5198 @ ( tc_fun @ SY5196 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV268 @ SY5198 @ SY5196 @ SY5197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2792]) ).
thf(3467,plain,
! [SV889: $i,SV269: $i] :
( ( ! [SY5199: $i,SY5200: $i,SY5201: $i] :
( ( c_Set_Ovimage @ SV269 @ ( c_Set_Oinsert @ SV889 @ SY5199 @ SY5200 ) @ SY5201 @ SY5200 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ SV269 @ ( c_Set_Oinsert @ SV889 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5200 @ tc_bool ) ) @ SY5200 ) @ SY5201 @ SY5200 ) @ ( c_Set_Ovimage @ SV269 @ SY5199 @ SY5201 @ SY5200 ) @ ( tc_fun @ SY5201 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2793]) ).
thf(3468,plain,
! [SV890: $i,SV270: $i] :
( ( ! [SY5202: $i,SY5203: $i,SY5204: $i] :
( ( ( c_Set_Oimage @ SV270 @ ( c_HOL_Ominus__class_Ominus @ SV890 @ SY5202 @ ( tc_fun @ SY5203 @ tc_bool ) ) @ SY5203 @ SY5204 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV270 @ SV890 @ SY5203 @ SY5204 ) @ ( c_Set_Oimage @ SV270 @ SY5202 @ SY5203 @ SY5204 ) @ ( tc_fun @ SY5204 @ tc_bool ) ) )
| ! [SY5205: $i] :
( ~ ( c_lessequals @ SY5202 @ SY5205 @ ( tc_fun @ SY5203 @ tc_bool ) )
| ~ ( c_lessequals @ SV890 @ SY5205 @ ( tc_fun @ SY5203 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV270 @ SY5205 @ SY5203 @ SY5204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2794]) ).
thf(3469,plain,
! [SV891: $i,SV271: $i] :
( ( ! [SY5206: $i,SY5207: $i,SY5208: $i] :
( ( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ SV271 @ SV891 @ SY5206 @ SY5207 @ ( tc_Option_Ooption @ SY5208 ) ) @ SY5207 @ SY5208 )
= ( c_Set_Oinsert @ SV891 @ ( c_Map_Odom @ SV271 @ SY5207 @ SY5208 ) @ SY5207 ) )
| ( SY5206
= ( c_Option_Ooption_ONone @ SY5208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2795]) ).
thf(3470,plain,
! [SV892: $i,SV272: $i] :
( ( ! [SY5209: $i,SY5210: $i,SY5211: $i] :
( ! [SY5212: $i] : ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ SV272 @ SV892 @ ( c_Option_Ooption_ONone @ SY5209 ) @ SY5210 @ ( tc_Option_Ooption @ SY5209 ) ) @ ( c_Fun_Ofun__upd @ SY5211 @ SV892 @ ( c_Option_Ooption_OSome @ SY5212 @ SY5209 ) @ SY5210 @ ( tc_Option_Ooption @ SY5209 ) ) @ SY5210 @ SY5209 )
| ~ ( c_Map_Omap__le @ SV272 @ SY5211 @ SY5210 @ SY5209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2796]) ).
thf(3471,plain,
! [SV893: $i,SV273: $i] :
( ( ! [SY5213: $i,SY5214: $i] :
( ( c_HOL_Oord__class_Oless @ SV273 @ ( c_Set_Oinsert @ SV893 @ SY5213 @ SY5214 ) @ ( tc_fun @ SY5214 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5214 ) @ SV893 ) @ SV273 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV273 @ ( c_Set_Oinsert @ SV893 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5214 @ tc_bool ) ) @ SY5214 ) @ ( tc_fun @ SY5214 @ tc_bool ) ) @ SY5213 @ ( tc_fun @ SY5214 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5214 ) @ SV893 ) @ SY5213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2797]) ).
thf(3472,plain,
! [SV894: $i,SV274: $i] :
( ( ( c_Com_Ocom_OWhile @ SV274 @ SV894 )
!= c_Com_Ocom_OSKIP )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2798]) ).
thf(3473,plain,
! [SV895: $i,SV275: $i] :
( ( ! [SY5215: $i] :
( ( c_Com_Ocom_OBODY @ SV275 )
!= ( c_Com_Ocom_OWhile @ SV895 @ SY5215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2799]) ).
thf(3474,plain,
! [SV896: $i,SV276: $i] :
( ( ! [SY5216: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV276 @ SV896 @ ( tc_fun @ SY5216 @ tc_bool ) ) @ SY5216 )
| ~ ( c_Finite__Set_Ofinite @ SV276 @ SY5216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2800]) ).
thf(3475,plain,
! [SV897: $i,SV277: $i] :
( ( ! [SY5217: $i,SY5218: $i] :
( ( c_Com_Ocom_OBODY @ SV277 )
!= ( c_Com_Ocom_OLocal @ SV897 @ SY5217 @ SY5218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2801]) ).
thf(3476,plain,
! [SV898: $i,SV278: $i] :
( ( ! [SY5219: $i,SY5220: $i,SY5221: $i] :
( ( c_Fun_Oinj__on @ SV278 @ ( c_HOL_Ominus__class_Ominus @ SV898 @ SY5219 @ ( tc_fun @ SY5220 @ tc_bool ) ) @ SY5220 @ SY5221 )
| ~ ( c_Fun_Oinj__on @ SV278 @ SV898 @ SY5220 @ SY5221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2802]) ).
thf(3477,plain,
! [SV899: $i,SV279: $i] :
( ( ! [SY5222: $i,SY5223: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV279 @ tc_bool ) )
!= ( c_Set_Oimage @ SV899 @ SY5222 @ SY5223 @ SV279 ) )
| ( SY5222
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5223 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2803]) ).
thf(3478,plain,
! [SV900: $i,SV280: $i] :
( ( ! [SY5224: $i,SY5225: $i,SY5226: $i] :
( ( c_Com_Ocom_OWhile @ SV280 @ SV900 )
!= ( c_Com_Ocom_OLocal @ SY5224 @ SY5225 @ SY5226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2804]) ).
thf(3479,plain,
! [SV901: $i,SV281: $i] :
( ( ! [SY5227: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV281 @ SV901 ) ) @ SY5227 ) @ SY5227 ) )
| ( hBOOL @ ( hAPP @ SV281 @ SY5227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2805]) ).
thf(3480,plain,
! [SV902: $i,SV282: $i] :
( ( ! [SY5228: $i,SY5229: $i,SY5230: $i] :
( ( c_Set_Ovimage @ SV282 @ ( c_HOL_Ominus__class_Ominus @ SV902 @ SY5228 @ ( tc_fun @ SY5229 @ tc_bool ) ) @ SY5230 @ SY5229 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Ovimage @ SV282 @ SV902 @ SY5230 @ SY5229 ) @ ( c_Set_Ovimage @ SV282 @ SY5228 @ SY5230 @ SY5229 ) @ ( tc_fun @ SY5230 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2806]) ).
thf(3481,plain,
! [SV903: $i,SV283: $i] :
( ( ! [SY5231: $i,SY5232: $i] :
( ( c_HOL_Oord__class_Oless @ SV283 @ ( c_Set_Oinsert @ SV903 @ SY5231 @ SY5232 ) @ ( tc_fun @ SY5232 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5232 ) @ SV903 ) @ SV283 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV283 @ ( c_Set_Oinsert @ SV903 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5232 @ tc_bool ) ) @ SY5232 ) @ ( tc_fun @ SY5232 @ tc_bool ) ) @ SY5231 @ ( tc_fun @ SY5232 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV283 @ SY5231 @ ( tc_fun @ SY5232 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2807]) ).
thf(3482,plain,
! [SV904: $i,SV284: $i] :
( ( ( c_Collect @ SV284 @ SV904 )
= SV284 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2808]) ).
thf(3483,plain,
! [SV905: $i,SV285: $i] :
( ( ! [SY5233: $i] :
( ( c_Com_Ocom_OAss @ SV285 @ SV905 )
!= ( c_Com_Ocom_OBODY @ SY5233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2809]) ).
thf(3484,plain,
! [SV906: $i,SV286: $i] :
( ( ! [SY5234: $i,SY5235: $i] :
( ( ( c_Com_Ocom_OSemi @ SV286 @ SV906 )
!= ( c_Com_Ocom_OSemi @ SY5234 @ SY5235 ) )
| ( SV906 = SY5235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2810]) ).
thf(3485,plain,
! [SV907: $i,SV287: $i] :
( ( ! [SY5236: $i] :
( ! [SY5237: $i] :
( ( c_Com_Ocom_OSemi @ SV287 @ SV907 )
!= ( c_Com_Ocom_OSemi @ SY5236 @ SY5237 ) )
| ( SV287 = SY5236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2811]) ).
thf(3486,plain,
! [SV908: $i,SV288: $i] :
( ( ! [SY5238: $i,SY5239: $i] :
( ( c_Com_Ocom_OSemi @ SV288 @ SV908 )
!= ( c_Com_Ocom_OWhile @ SY5238 @ SY5239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2812]) ).
thf(3487,plain,
! [SV909: $i,SV289: $i] :
( ( ! [SY5240: $i,SY5241: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV289 @ ( c_Set_Oinsert @ SV909 @ SY5240 @ SY5241 ) @ ( tc_fun @ SY5241 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV289 @ SY5240 @ ( tc_fun @ SY5241 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV909 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5241 @ tc_bool ) ) @ SY5241 ) @ ( tc_fun @ SY5241 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2813]) ).
thf(3488,plain,
! [SV910: $i,SV290: $i] :
( ( ! [SY5242: $i,SY5243: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV290 @ ( c_Set_Oinsert @ SV910 @ SY5242 @ SY5243 ) @ ( tc_fun @ SY5243 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV290 @ ( c_Set_Oinsert @ SV910 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5243 @ tc_bool ) ) @ SY5243 ) @ ( tc_fun @ SY5243 @ tc_bool ) ) @ SY5242 @ ( tc_fun @ SY5243 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2814]) ).
thf(3489,plain,
! [SV911: $i,SV291: $i] :
( ( ! [SY5244: $i,SY5245: $i,SY5246: $i] :
( ( c_Com_Ocom_OSemi @ SV291 @ SV911 )
!= ( c_Com_Ocom_OCond @ SY5244 @ SY5245 @ SY5246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2815]) ).
thf(3490,plain,
! [SV912: $i,SV292: $i] :
( ( ( c_Finite__Set_Ofinite @ SV292 @ SV912 )
| ! [SY5247: $i] :
( ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV292 @ SY5247 @ ( tc_fun @ SV912 @ tc_bool ) ) @ SV912 )
| ~ ( c_Finite__Set_Ofinite @ SY5247 @ SV912 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2816]) ).
thf(3491,plain,
! [SV913: $i,SV293: $i] :
( ( ! [SY5248: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV293 @ SV913 @ ( tc_fun @ SY5248 @ tc_bool ) ) @ SY5248 )
| ~ ( c_Finite__Set_Ofinite @ SV293 @ SY5248 )
| ~ ( c_Finite__Set_Ofinite @ SV913 @ SY5248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2817]) ).
thf(3492,plain,
! [SV914: $i,SV294: $i] :
( ( ! [SY5249: $i] :
( ( c_Set_Oinsert @ SV294 @ SV914 @ SY5249 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5249 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2818]) ).
thf(3493,plain,
! [SV915: $i,SV295: $i] :
( ( ! [SY5250: $i,SY5251: $i,SY5252: $i] :
( ( c_Com_Ocom_OSemi @ SV295 @ SV915 )
!= ( c_Com_Ocom_OLocal @ SY5250 @ SY5251 @ SY5252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2819]) ).
thf(3494,plain,
! [SV916: $i,SV296: $i] :
( ( ! [SY5253: $i,SY5254: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV296 ) @ SV916 ) @ ( c_Set_Ovimage @ SY5253 @ ( c_Set_Oinsert @ ( hAPP @ SY5253 @ SV916 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5254 @ tc_bool ) ) @ SY5254 ) @ SV296 @ SY5254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2820]) ).
thf(3495,plain,
! [SV917: $i,SV297: $i] :
( ( ! [SY5255: $i,SY5256: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV297 @ SV917 @ SY5255 ) @ ( c_Set_Oinsert @ SV297 @ SY5256 @ SY5255 ) @ ( tc_fun @ SY5255 @ tc_bool ) )
= ( c_Set_Oinsert @ SV297 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV917 @ SY5256 @ ( tc_fun @ SY5255 @ tc_bool ) ) @ SY5255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2821]) ).
thf(3496,plain,
! [SV918: $i,SV298: $i] :
( ( ! [SY5257: $i,SY5258: $i] :
( ( c_Map_Omap__le @ SV298 @ SV918 @ SY5257 @ SY5258 )
| ! [SY5259: $i] :
~ ( c_Map_Omap__le @ ( c_Map_Omap__add @ SY5259 @ SV298 @ SY5257 @ SY5258 ) @ SV918 @ SY5257 @ SY5258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2822]) ).
thf(3497,plain,
! [SV919: $i,SV299: $i] :
( ( ! [SY5260: $i] :
( ( c_Set_Oinsert @ SV299 @ ( c_Set_Oinsert @ SV299 @ SV919 @ SY5260 ) @ SY5260 )
= ( c_Set_Oinsert @ SV299 @ SV919 @ SY5260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2823]) ).
thf(3498,plain,
! [SV920: $i,SV300: $i] :
( ( ! [SY5261: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ SV300 @ SV920 ) @ SY5261 )
| ! [SY5262: $i,SY5263: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5262 ) @ SV920 ) @ SY5263 ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY5263 @ SV300 @ SY5262 @ ( tc_fun @ SY5261 @ tc_bool ) ) @ SY5261 )
| ~ ( c_Finite__Set_Ofinite @ SY5263 @ SY5262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2824]) ).
thf(3499,plain,
! [SV921: $i,SV301: $i] :
( ( ! [SY5264: $i] : ( c_Map_Omap__le @ SV301 @ SV301 @ SV921 @ SY5264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2825]) ).
thf(3500,plain,
! [SV922: $i,SV302: $i] :
( ( ! [SY5265: $i,SY5266: $i] :
( ( c_Map_Omap__le @ SV302 @ SV922 @ SY5265 @ SY5266 )
| ! [SY5267: $i] :
( ~ ( c_Map_Omap__le @ SY5267 @ SV922 @ SY5265 @ SY5266 )
| ~ ( c_Map_Omap__le @ SV302 @ SY5267 @ SY5265 @ SY5266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2826]) ).
thf(3501,plain,
! [SV923: $i,SV303: $i] :
( ( ! [SY5268: $i,SY5269: $i,SY5270: $i] :
( ( c_Com_Ocom_OLocal @ SV303 @ SV923 @ SY5268 )
!= ( c_Com_Ocom_OAss @ SY5269 @ SY5270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2827]) ).
thf(3502,plain,
! [SV924: $i,SV304: $i] :
( ( ( hBOOL @ ( hAPP @ SV304 @ SV924 ) )
| ! [SY5271: $i] :
( ( SY5271 = SV924 )
| ! [SY5272: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY5271 @ SV304 @ SY5272 ) @ SV924 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2828]) ).
thf(3503,plain,
! [SV925: $i,SV305: $i] :
( ( ! [SY5273: $i,SY5274: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV305 @ SV925 @ SY5273 @ ( tc_fun @ SY5274 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5274 @ tc_bool ) ) )
| ! [SY5275: $i] :
( ( ( hAPP @ SV925 @ SY5275 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5274 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5273 ) @ SY5275 ) @ SV305 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2829]) ).
thf(3504,plain,
! [SV926: $i,SV306: $i] :
( ( ! [SY5276: $i] :
( ( c_Com_Ocom_OBODY @ SV306 )
!= ( c_Com_Ocom_OAss @ SV926 @ SY5276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2830]) ).
thf(3505,plain,
! [SV927: $i,SV307: $i] :
( ( ! [SY5277: $i,SY5278: $i,SY5279: $i] :
( ( c_Com_Ocom_OCond @ SV307 @ SV927 @ SY5277 )
!= ( c_Com_Ocom_OWhile @ SY5278 @ SY5279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2831]) ).
thf(3506,plain,
! [SV928: $i,SV308: $i] :
( ( ! [SY5280: $i,SY5281: $i,SY5282: $i,SY5283: $i] :
( ( c_Com_Ocom_OCond @ SV308 @ SV928 @ SY5280 )
!= ( c_Com_Ocom_OLocal @ SY5281 @ SY5282 @ SY5283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2832]) ).
thf(3507,plain,
! [SV309: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV309 ) )
= $true )
| ( ( ! [SY3605: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3605 @ ( c_Orderings_Obot__class_Obot @ SV309 ) @ SV309 )
= ( c_Orderings_Obot__class_Obot @ SV309 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2833]) ).
thf(3508,plain,
! [SV310: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV310 ) )
= $true )
| ( ( ! [SY3606: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ SV310 ) @ SY3606 @ SV310 )
= ( c_Orderings_Obot__class_Obot @ SV310 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2834]) ).
thf(3509,plain,
! [SV929: $i,SV311: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV311 @ tc_bool ) ) @ SV929 @ ( tc_fun @ SV311 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV311 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2835]) ).
thf(3510,plain,
! [SV930: $i,SV312: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV312 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV930 @ tc_bool ) ) @ ( tc_fun @ SV930 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV930 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2836]) ).
thf(3511,plain,
! [SV931: $i,SV313: $i] :
( ( ( c_Finite__Set_Ofinite @ SV313 @ SV931 )
| ! [SY5284: $i] :
~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SY5284 @ SV313 @ SV931 ) @ SV931 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2837]) ).
thf(3512,plain,
! [SV932: $i,SV314: $i] :
( ( ! [SY5285: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV314 @ SV932 @ SY5285 ) @ SY5285 )
| ~ ( c_Finite__Set_Ofinite @ SV932 @ SY5285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2838]) ).
thf(3513,plain,
! [SV933: $i,SV316: $i] :
( ( ! [SY5286: $i,SY5287: $i,SY5288: $i] :
( ( c_Com_Ocom_OCond @ SV316 @ SV933 @ SY5286 )
!= ( c_Com_Ocom_OSemi @ SY5287 @ SY5288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2840]) ).
thf(3514,plain,
! [SV934: $i,SV317: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV317 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ SV934 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Com_OWT @ SV934 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV317 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ SV317 ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2841]) ).
thf(3515,plain,
! [SV935: $i,SV318: $i] :
( ( ! [SY5289: $i,SY5290: $i,SY5291: $i,SY5292: $i,SY5293: $i,SY5294: $i,SY5295: $i] :
( ( ( hAPP @ SV318 @ ( c_Set_Oinsert @ SV935 @ ( c_Set_Oinsert @ SY5289 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5290 @ tc_bool ) ) @ SY5290 ) @ SY5290 ) )
= ( hAPP @ ( hAPP @ SY5291 @ SV935 ) @ SY5289 ) )
| ! [SY3626: $i,SY3627: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY5292 @ SV318 @ SY5293 @ SY5294 @ SY5295 @ SY5291 @ SY3626 @ SY3627 @ SY5290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2842]) ).
thf(3516,plain,
! [SV936: $i,SV319: $i] :
( ( ! [SY5298: $i,SY5299: $i,SY5300: $i,SY5301: $i,SY5302: $i,SY5303: $i,SY5304: $i] :
( ( ( hAPP @ SV319 @ ( c_Set_Oinsert @ SV936 @ ( c_Set_Oinsert @ SY5298 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5299 @ tc_bool ) ) @ SY5299 ) @ SY5299 ) )
= ( hAPP @ ( hAPP @ SY5300 @ SV936 ) @ SY5298 ) )
| ! [SY3636: $i,SY3637: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV319 @ SY5301 @ SY5302 @ SY5303 @ SY5300 @ SY5304 @ SY3636 @ SY3637 @ SY5299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2843]) ).
thf(3517,plain,
! [SV937: $i,SV320: $i] :
( ( ! [SY5307: $i,SY5308: $i,SY5309: $i,SY5310: $i] :
( ( ( c_Com_Ocom_OCond @ SV320 @ SV937 @ SY5307 )
!= ( c_Com_Ocom_OCond @ SY5308 @ SY5309 @ SY5310 ) )
| ( SY5307 = SY5310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2844]) ).
thf(3518,plain,
! [SV938: $i,SV321: $i] :
( ( ! [SY5311: $i,SY5312: $i,SY5313: $i] :
( ! [SY5314: $i] :
( ( c_Com_Ocom_OCond @ SV321 @ SV938 @ SY5311 )
!= ( c_Com_Ocom_OCond @ SY5312 @ SY5313 @ SY5314 ) )
| ( SV938 = SY5313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2845]) ).
thf(3519,plain,
! [SV939: $i,SV322: $i] :
( ( ! [SY5315: $i,SY5316: $i] :
( ! [SY5317: $i,SY5318: $i] :
( ( c_Com_Ocom_OCond @ SV322 @ SV939 @ SY5315 )
!= ( c_Com_Ocom_OCond @ SY5316 @ SY5317 @ SY5318 ) )
| ( SV322 = SY5316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2846]) ).
thf(3520,plain,
! [SV940: $i,SV323: $i] :
( ( ( c_Option_Ooption_OSome @ SV323 @ SV940 )
!= ( c_Option_Ooption_ONone @ SV940 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2847]) ).
thf(3521,plain,
! [SV941: $i,SV324: $i] :
( ( ( c_Option_Ooption_OSome @ SV324 @ SV941 )
!= ( c_Option_Ooption_ONone @ SV941 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2848]) ).
thf(3522,plain,
! [SV942: $i,SV325: $i] :
( ( ! [SY5319: $i] :
( ( ( c_Option_Ooption_OSome @ SV325 @ SV942 )
!= ( c_Option_Ooption_OSome @ SY5319 @ SV942 ) )
| ( SV325 = SY5319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2849]) ).
thf(3523,plain,
! [SV943: $i,SV326: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV326 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV943 @ tc_bool ) ) @ ( tc_fun @ SV943 @ tc_bool ) )
= SV326 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2850]) ).
thf(3524,plain,
! [SV944: $i,SV327: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV327 @ SV327 @ ( tc_fun @ SV944 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV944 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2851]) ).
thf(3525,plain,
! [SV945: $i,SV328: $i] :
( ( ! [SY5320: $i,SY5321: $i] :
( ( c_Com_Ocom_OAss @ SV328 @ SV945 )
!= ( c_Com_Ocom_OWhile @ SY5320 @ SY5321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2852]) ).
thf(3526,plain,
! [SV946: $i,SV329: $i] :
( ( ! [SY5322: $i,SY5323: $i,SY5324: $i] :
( ( c_Map_Omap__add @ SV329 @ ( c_Map_Omap__add @ SV946 @ SY5322 @ SY5323 @ SY5324 ) @ SY5323 @ SY5324 )
= ( c_Map_Omap__add @ ( c_Map_Omap__add @ SV329 @ SV946 @ SY5323 @ SY5324 ) @ SY5322 @ SY5323 @ SY5324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2853]) ).
thf(3527,plain,
! [SV947: $i,SV330: $i] :
( ( ! [SY5325: $i,SY5326: $i,SY5327: $i] :
( ( c_Com_Ocom_OAss @ SV330 @ SV947 )
!= ( c_Com_Ocom_OLocal @ SY5325 @ SY5326 @ SY5327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2854]) ).
thf(3528,plain,
! [SV948: $i,SV331: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV331 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV948 @ tc_bool ) ) @ ( tc_fun @ SV948 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2855]) ).
thf(3529,plain,
! [SV949: $i,SV332: $i] :
( ( ! [SY5328: $i,SY5329: $i] :
( ( c_Com_Ocom_OCond @ SV332 @ SV949 @ SY5328 )
!= ( c_Com_Ocom_OBODY @ SY5329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2856]) ).
thf(3530,plain,
! [SV950: $i,SV333: $i] :
( ( ! [SY5330: $i,SY5331: $i] :
( ( c_Com_Ocom_OBODY @ SV333 )
!= ( c_Com_Ocom_OCond @ SV950 @ SY5330 @ SY5331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2857]) ).
thf(3531,plain,
! [SV951: $i,SV334: $i] :
( ( ~ ( class_Lattices_Olattice @ SV334 )
| ! [SY5332: $i,SY5333: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV951 @ SY5332 @ SV334 ) @ SY5333 @ SV334 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV951 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5332 @ SY5333 @ SV334 ) @ SV334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2858]) ).
thf(3532,plain,
! [SV952: $i,SV335: $i] :
( ( ~ ( class_Lattices_Olattice @ SV335 )
| ! [SY5334: $i,SY5335: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV952 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5334 @ SY5335 @ SV335 ) @ SV335 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY5334 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV952 @ SY5335 @ SV335 ) @ SV335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2859]) ).
thf(3533,plain,
! [SV953: $i,SV336: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV336 )
| ! [SY5336: $i,SY5337: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV953 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5336 @ SY5337 @ SV336 ) @ SV336 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY5336 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV953 @ SY5337 @ SV336 ) @ SV336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2860]) ).
thf(3534,plain,
! [SV954: $i,SV337: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV337 )
| ! [SY5338: $i,SY5339: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV954 @ SY5338 @ SV337 ) @ SY5339 @ SV337 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV954 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5338 @ SY5339 @ SV337 ) @ SV337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2861]) ).
thf(3535,plain,
! [SV955: $i,SV338: $i] :
( ( ! [SY5340: $i,SY5341: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV338 @ SV955 @ ( tc_fun @ SY5340 @ tc_bool ) ) @ SY5341 @ ( tc_fun @ SY5340 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV338 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV955 @ SY5341 @ ( tc_fun @ SY5340 @ tc_bool ) ) @ ( tc_fun @ SY5340 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2862]) ).
thf(3536,plain,
! [SV956: $i,SV339: $i] :
( ( ! [SY5342: $i,SY5343: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV339 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV956 @ SY5342 @ ( tc_fun @ SY5343 @ tc_bool ) ) @ ( tc_fun @ SY5343 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV956 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV339 @ SY5342 @ ( tc_fun @ SY5343 @ tc_bool ) ) @ ( tc_fun @ SY5343 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2863]) ).
thf(3537,plain,
! [SV957: $i,SV340: $i] :
( ( ! [SY5344: $i,SY5345: $i,SY5346: $i] :
( ( c_Com_Ocom_OLocal @ SV340 @ SV957 @ SY5344 )
!= ( c_Com_Ocom_OWhile @ SY5345 @ SY5346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2864]) ).
thf(3538,plain,
! [SV958: $i,SV341: $i] :
( ( ! [SY5347: $i,SY5348: $i,SY5349: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV341 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV958 @ ( c_Com_Ocom_OBODY @ SY5347 ) @ SY5348 @ SY5349 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY5349 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY5349 ) ) @ SY5349 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV341 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV958 @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SY5347 ) @ tc_Com_Ocom ) @ SY5348 @ SY5349 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY5349 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY5349 ) ) @ SY5349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2865]) ).
thf(3539,plain,
! [SV959: $i,SV342: $i] :
( ( ! [SY5350: $i,SY5351: $i,SY5352: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV342 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV959 @ ( c_Com_Ocom_OBODY @ SY5350 ) @ SY5351 @ SY5352 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY5352 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY5352 ) ) @ SY5352 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV959 @ ( c_Com_Ocom_OBODY @ SY5350 ) @ SY5351 @ SY5352 ) @ SV342 @ ( tc_Hoare__Mirabelle_Otriple @ SY5352 ) ) @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV959 @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SY5350 ) @ tc_Com_Ocom ) @ SY5351 @ SY5352 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY5352 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY5352 ) ) @ SY5352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2866]) ).
thf(3540,plain,
! [SV960: $i,SV343: $i] :
( ( ! [SY5353: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV343 )
| ! [SY5354: $i,SY5355: $i] :
( ( ( c_Finite__Set_Osetsum @ SV960 @ ( c_HOL_Ominus__class_Ominus @ SY5353 @ ( c_Set_Oinsert @ SY5354 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5355 @ tc_bool ) ) @ SY5355 ) @ ( tc_fun @ SY5355 @ tc_bool ) ) @ SY5355 @ SV343 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV960 @ SY5353 @ SY5355 @ SV343 ) @ ( hAPP @ SV960 @ SY5354 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5355 ) @ SY5354 ) @ SY5353 ) )
| ~ ( c_Finite__Set_Ofinite @ SY5353 @ SY5355 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2867]) ).
thf(3541,plain,
! [SV961: $i,SV344: $i] :
( ( ! [SY5356: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV344 )
| ! [SY5357: $i,SY5358: $i] :
( ( ( c_Finite__Set_Osetsum @ SV961 @ ( c_HOL_Ominus__class_Ominus @ SY5356 @ ( c_Set_Oinsert @ SY5357 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5358 @ tc_bool ) ) @ SY5358 ) @ ( tc_fun @ SY5358 @ tc_bool ) ) @ SY5358 @ SV344 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV961 @ SY5356 @ SY5358 @ SV344 ) @ ( hAPP @ SV961 @ SY5357 ) @ SV344 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5358 ) @ SY5357 ) @ SY5356 ) )
| ~ ( c_Finite__Set_Ofinite @ SY5356 @ SY5358 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2868]) ).
thf(3542,plain,
! [SV345: $i] :
( ( ( ( hAPP @ c_Com_Obody @ SV345 )
= ( c_Option_Ooption_OSome @ ( c_Com_Osko__Com__XWTs__elim__cases__7__1 @ SV345 ) @ tc_Com_Ocom ) )
= $true )
| ( ( ~ ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ SV345 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2869]) ).
thf(3543,plain,
! [SV962: $i,SV346: $i] :
( ( ! [SY5359: $i,SY5360: $i] :
( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ SV346 @ SV962 @ ( c_Option_Ooption_ONone @ SY5359 ) @ SY5360 @ ( tc_Option_Ooption @ SY5359 ) ) @ SY5360 @ SY5359 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ SV346 @ SY5360 @ SY5359 ) @ ( c_Set_Oinsert @ SV962 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5360 @ tc_bool ) ) @ SY5360 ) @ ( tc_fun @ SY5360 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2870]) ).
thf(3544,plain,
! [SV963: $i,SV347: $i] :
( ( ! [SY5361: $i,SY5362: $i,SY5363: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV347 @ ( c_HOL_Ominus__class_Ominus @ SV963 @ SY5361 @ ( tc_fun @ SY5362 @ tc_bool ) ) @ SY5362 @ SY5363 ) @ ( c_Set_Oimage @ SV347 @ ( c_HOL_Ominus__class_Ominus @ SY5361 @ SV963 @ ( tc_fun @ SY5362 @ tc_bool ) ) @ SY5362 @ SY5363 ) @ ( tc_fun @ SY5363 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5363 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SV347 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV963 @ SY5361 @ ( tc_fun @ SY5362 @ tc_bool ) ) @ SY5362 @ SY5363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2871]) ).
thf(3545,plain,
! [SV964: $i,SV348: $i] :
( ( ! [SY5364: $i,SY5365: $i,SY5366: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV348 @ ( c_HOL_Ominus__class_Ominus @ SV964 @ SY5364 @ ( tc_fun @ SY5365 @ tc_bool ) ) @ SY5365 @ SY5366 ) @ ( c_Set_Oimage @ SV348 @ ( c_HOL_Ominus__class_Ominus @ SY5364 @ SV964 @ ( tc_fun @ SY5365 @ tc_bool ) ) @ SY5365 @ SY5366 ) @ ( tc_fun @ SY5366 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5366 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SV348 @ SY5364 @ SY5365 @ SY5366 )
| ~ ( c_Fun_Oinj__on @ SV348 @ SV964 @ SY5365 @ SY5366 )
| ( c_Fun_Oinj__on @ SV348 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV964 @ SY5364 @ ( tc_fun @ SY5365 @ tc_bool ) ) @ SY5365 @ SY5366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2872]) ).
thf(3546,plain,
! [SV965: $i,SV349: $i] :
( ( ! [SY5367: $i,SY5368: $i] :
( ( c_HOL_Oord__class_Oless @ SV349 @ ( c_Set_Oinsert @ SV965 @ SY5367 @ SY5368 ) @ ( tc_fun @ SY5368 @ tc_bool ) )
| ~ ( c_lessequals @ SV349 @ SY5367 @ ( tc_fun @ SY5368 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV349 @ ( c_Set_Oinsert @ SV965 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5368 @ tc_bool ) ) @ SY5368 ) @ ( tc_fun @ SY5368 @ tc_bool ) ) @ SY5367 @ ( tc_fun @ SY5368 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5368 ) @ SV965 ) @ SY5367 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2873]) ).
thf(3547,plain,
! [SV966: $i,SV350: $i] :
( ( ! [SY5369: $i,SY5370: $i,SY5371: $i,SY5372: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ SV350 @ SV966 @ SY5369 @ SY5370 @ SY5371 ) @ SY5372 @ SY5370 @ SY5371 )
= ( c_Set_Oinsert @ SY5369 @ ( c_Set_Oimage @ SV350 @ ( c_HOL_Ominus__class_Ominus @ SY5372 @ ( c_Set_Oinsert @ SV966 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5370 @ tc_bool ) ) @ SY5370 ) @ ( tc_fun @ SY5370 @ tc_bool ) ) @ SY5370 @ SY5371 ) @ SY5371 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5370 ) @ SV966 ) @ SY5372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2874]) ).
thf(3548,plain,
! [SV967: $i,SV351: $i] :
( ( ! [SY5373: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV351 )
| ! [SY5374: $i,SY5375: $i] :
( ( ( c_Finite__Set_Osetsum @ SV967 @ ( c_HOL_Ominus__class_Ominus @ SY5373 @ ( c_Set_Oinsert @ SY5374 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5375 @ tc_bool ) ) @ SY5375 ) @ ( tc_fun @ SY5375 @ tc_bool ) ) @ SY5375 @ SV351 )
= ( c_Finite__Set_Osetsum @ SV967 @ SY5373 @ SY5375 @ SV351 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5375 ) @ SY5374 ) @ SY5373 ) )
| ~ ( c_Finite__Set_Ofinite @ SY5373 @ SY5375 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2875]) ).
thf(3549,plain,
! [SV968: $i,SV352: $i] :
( ( ! [SY5376: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_HOL_Ominus__class_Ominus @ SV352 @ ( c_Set_Oinsert @ SV968 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5376 @ tc_bool ) ) @ SY5376 ) @ ( tc_fun @ SY5376 @ tc_bool ) ) @ SY5376 )
= ( c_Finite__Set_Ocard @ SV352 @ SY5376 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5376 ) @ SV968 ) @ SV352 ) )
| ~ ( c_Finite__Set_Ofinite @ SV352 @ SY5376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2876]) ).
thf(3550,plain,
! [SV969: $i,SV353: $i] :
( ( ! [SY5377: $i,SY5378: $i,SY5379: $i,SY5380: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV969 @ ( c_Com_Ocom_OSemi @ SY5377 @ SY5378 ) @ SY5379 @ SY5380 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY5380 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY5380 ) ) @ SY5380 )
| ! [SY5381: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY5381 @ SY5378 @ SY5379 @ SY5380 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY5380 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY5380 ) ) @ SY5380 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV969 @ SY5377 @ SY5381 @ SY5380 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY5380 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY5380 ) ) @ SY5380 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2877]) ).
thf(3551,plain,
! [SV970: $i,SV354: $i] :
( ( ! [SY5382: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ SV354 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV970 @ c_Com_Ocom_OSKIP @ SV970 @ SY5382 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY5382 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY5382 ) ) @ SY5382 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2878]) ).
thf(3552,plain,
! [SV971: $i,SV355: $i] :
( ( ! [SY5383: $i,SY5384: $i,SY5385: $i,SY5386: $i] :
( ( ( c_Map_Omap__add @ ( c_Fun_Ofun__upd @ SV355 @ SV971 @ ( c_Option_Ooption_OSome @ SY5383 @ SY5384 ) @ SY5385 @ ( tc_Option_Ooption @ SY5384 ) ) @ SY5386 @ SY5385 @ SY5384 )
= ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ SV355 @ SY5386 @ SY5385 @ SY5384 ) @ SV971 @ ( c_Option_Ooption_OSome @ SY5383 @ SY5384 ) @ SY5385 @ ( tc_Option_Ooption @ SY5384 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5385 ) @ SV971 ) @ ( c_Map_Odom @ SY5386 @ SY5385 @ SY5384 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2879]) ).
thf(3553,plain,
! [SV972: $i,SV356: $i] :
( ( ! [SY5387: $i,SY5388: $i] :
( ( c_HOL_Oord__class_Oless @ SV356 @ ( c_Set_Oinsert @ SV972 @ SY5387 @ SY5388 ) @ ( tc_fun @ SY5388 @ tc_bool ) )
| ~ ( c_lessequals @ SV356 @ SY5387 @ ( tc_fun @ SY5388 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV356 @ ( c_Set_Oinsert @ SV972 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5388 @ tc_bool ) ) @ SY5388 ) @ ( tc_fun @ SY5388 @ tc_bool ) ) @ SY5387 @ ( tc_fun @ SY5388 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV356 @ SY5387 @ ( tc_fun @ SY5388 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2880]) ).
thf(3554,plain,
! [SV973: $i,SV357: $i] :
( ( ! [SY5389: $i,SY5390: $i] :
( ( c_Set_Ovimage @ SV357 @ SV973 @ SY5389 @ SY5390 )
= ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_in @ SY5390 ) @ SV357 @ SY5390 @ ( tc_fun @ ( tc_fun @ SY5390 @ tc_bool ) @ tc_bool ) @ SY5389 ) @ SY5389 @ ( tc_fun @ SY5390 @ tc_bool ) @ tc_bool ) @ SV973 ) @ SY5389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2881]) ).
thf(3555,plain,
! [SV974: $i,SV358: $i] :
( ( ! [SY5391: $i,SY5392: $i,SY5393: $i,SY5394: $i,SY5395: $i] :
( ( c_Nitpick_Ofold__graph_H @ SV358 @ SV974 @ SY5391 @ ( hAPP @ ( hAPP @ SV358 @ SY5392 ) @ SY5393 ) @ SY5394 @ SY5395 )
| ~ ( c_Nitpick_Ofold__graph_H @ SV358 @ SV974 @ ( c_HOL_Ominus__class_Ominus @ SY5391 @ ( c_Set_Oinsert @ SY5392 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5394 @ tc_bool ) ) @ SY5394 ) @ ( tc_fun @ SY5394 @ tc_bool ) ) @ SY5393 @ SY5394 @ SY5395 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5394 ) @ SY5392 ) @ SY5391 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2882]) ).
thf(3556,plain,
! [SV975: $i,SV359: $i] :
( ( ! [SY5396: $i,SY5397: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV359 @ ( c_Set_Oinsert @ SV975 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5396 @ tc_bool ) ) @ SY5396 ) @ ( tc_fun @ SY5396 @ tc_bool ) ) @ SY5397 @ ( tc_fun @ SY5396 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5396 ) @ SV975 ) @ SV359 ) )
| ~ ( c_lessequals @ SV359 @ ( c_Set_Oinsert @ SV975 @ SY5397 @ SY5396 ) @ ( tc_fun @ SY5396 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2883]) ).
thf(3557,plain,
! [SV976: $i,SV360: $i] :
( ( ! [SY5398: $i,SY5399: $i] :
( ( c_lessequals @ SV360 @ ( c_Set_Oinsert @ SV976 @ SY5398 @ SY5399 ) @ ( tc_fun @ SY5399 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5399 ) @ SV976 ) @ SV360 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV360 @ ( c_Set_Oinsert @ SV976 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5399 @ tc_bool ) ) @ SY5399 ) @ ( tc_fun @ SY5399 @ tc_bool ) ) @ SY5398 @ ( tc_fun @ SY5399 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2884]) ).
thf(3558,plain,
! [SV977: $i,SV361: $i] :
( ( ! [SY5400: $i,SY5401: $i] :
( ( c_lessequals @ SV361 @ ( c_Set_Oinsert @ SV977 @ SY5400 @ SY5401 ) @ ( tc_fun @ SY5401 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5401 ) @ SV977 ) @ SV361 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV361 @ ( c_Set_Oinsert @ SV977 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5401 @ tc_bool ) ) @ SY5401 ) @ ( tc_fun @ SY5401 @ tc_bool ) ) @ SY5400 @ ( tc_fun @ SY5401 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2885]) ).
thf(3559,plain,
! [SV978: $i,SV362: $i] :
( ( ! [SY5402: $i,SY5403: $i] :
( ( ( c_Finite__Set_Osetsum @ SV362 @ ( c_HOL_Ominus__class_Ominus @ SV978 @ ( c_Set_Oinsert @ SY5402 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5403 @ tc_bool ) ) @ SY5403 ) @ ( tc_fun @ SY5403 @ tc_bool ) ) @ SY5403 @ tc_nat )
= ( c_Finite__Set_Osetsum @ SV362 @ SV978 @ SY5403 @ tc_nat ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5403 ) @ SY5402 ) @ SV978 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2886]) ).
thf(3560,plain,
! [SV979: $i,SV363: $i] :
( ( ! [SY5404: $i,SY5405: $i,SY5406: $i,SY5407: $i,SY5408: $i] :
( ( c_Finite__Set_Ofold__graph @ SV363 @ SV979 @ SY5404 @ ( hAPP @ ( hAPP @ SV363 @ SY5405 ) @ SY5406 ) @ SY5407 @ SY5408 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5407 ) @ SY5405 ) @ SY5404 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV363 @ SV979 @ ( c_HOL_Ominus__class_Ominus @ SY5404 @ ( c_Set_Oinsert @ SY5405 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5407 @ tc_bool ) ) @ SY5407 ) @ ( tc_fun @ SY5407 @ tc_bool ) ) @ SY5406 @ SY5407 @ SY5408 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2887]) ).
thf(3561,plain,
! [SV980: $i,SV364: $i] :
( ( ! [SY5409: $i,SY5410: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV364 @ SV980 @ SY5409 ) @ SY5410 @ SY5409 @ SV980 )
= ( c_Set_Oinsert @ SV364 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV980 @ tc_bool ) ) @ SV980 ) )
| ! [V_x: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5409 ) @ V_x ) @ SY5410 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2888]) ).
thf(3562,plain,
! [SV981: $i,SV365: $i] :
( ( ! [SY5412: $i,SY5413: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV365 @ ( c_Set_Oinsert @ SV981 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5412 @ tc_bool ) ) @ SY5412 ) @ ( tc_fun @ SY5412 @ tc_bool ) ) @ SY5413 @ ( tc_fun @ SY5412 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5412 ) @ SV981 ) @ SV365 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5412 ) @ SV981 ) @ SY5413 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV365 @ ( c_Set_Oinsert @ SV981 @ SY5413 @ SY5412 ) @ ( tc_fun @ SY5412 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2889]) ).
thf(3563,plain,
! [SV982: $i,SV366: $i] :
( ( ! [SY5414: $i] :
( ( ( hAPP @ SV366 @ SV982 )
!= ( c_Option_Ooption_ONone @ SY5414 ) )
| ! [SY5415: $i,SY5416: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ SV366 @ SY5415 @ SY5414 ) @ ( c_Set_Oinsert @ SV982 @ SY5416 @ SY5415 ) @ ( tc_fun @ SY5415 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ SV366 @ SY5415 @ SY5414 ) @ SY5416 @ ( tc_fun @ SY5415 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2890]) ).
thf(3564,plain,
! [SV983: $i,SV367: $i] :
( ( ! [SY5417: $i,SY5418: $i] :
( ( c_Com_Ocom_OAss @ SV367 @ SV983 )
!= ( c_Com_Ocom_OSemi @ SY5417 @ SY5418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2891]) ).
thf(3565,plain,
! [SV984: $i,SV368: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV368 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ SV984 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ SV984 ) ) @ SV368 @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SV984 ) @ tc_Com_Ocom ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2892]) ).
thf(3566,plain,
! [SV985: $i,SV369: $i] :
( ( ! [SY5419: $i,SY5420: $i,SY5421: $i,SY5422: $i] :
( ( c_Com_Ocom_OLocal @ SV369 @ SV985 @ SY5419 )
!= ( c_Com_Ocom_OCond @ SY5420 @ SY5421 @ SY5422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2893]) ).
thf(3567,plain,
! [SV986: $i,SV370: $i] :
( ( ! [SY5423: $i,SY5424: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV370 @ SV986 @ SY5423 ) @ SY5424 @ ( tc_fun @ SY5423 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV986 @ SY5424 @ ( tc_fun @ SY5423 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5423 ) @ SV370 ) @ SY5424 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2894]) ).
thf(3568,plain,
! [SV987: $i,SV371: $i] :
( ( ! [SY5425: $i,SY5426: $i] :
( ( c_Fun_Oinj__on @ SV371 @ SV987 @ SY5425 @ SY5426 )
| ! [SY5427: $i] :
~ ( c_Fun_Oinj__on @ SV371 @ ( c_Set_Oinsert @ SY5427 @ SV987 @ SY5425 ) @ SY5425 @ SY5426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2895]) ).
thf(3569,plain,
! [SV988: $i,SV372: $i] :
( ( ! [SY5428: $i] :
( ( c_Com_Ocom_OBODY @ SV372 )
!= ( c_Com_Ocom_OSemi @ SV988 @ SY5428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2896]) ).
thf(3570,plain,
! [SV989: $i,SV373: $i] :
( ( ( SV373 = SV989 )
| ! [SY5429: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5429 ) @ SV373 ) @ ( c_Set_Oinsert @ SV989 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5429 @ tc_bool ) ) @ SY5429 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2897]) ).
thf(3571,plain,
! [SV990: $i,SV374: $i] :
( ( ! [SY5430: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV374 @ SV990 @ ( tc_fun @ SY5430 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5430 @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ SV374 @ SV990 @ ( tc_fun @ SY5430 @ tc_bool ) )
= SV374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2898]) ).
thf(3572,plain,
! [SV991: $i,SV375: $i] :
( ( ( hBOOL @ ( hAPP @ SV375 @ SV991 ) )
| ! [SY5431: $i,SY5432: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5431 ) @ SV991 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5432 @ ( c_Collect @ SV375 @ SY5431 ) @ ( tc_fun @ SY5431 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2899]) ).
thf(3573,plain,
! [SV992: $i,SV376: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV376 )
| ! [SY5433: $i] :
( ( c_HOL_Oord__class_Oless @ SV992 @ SY5433 @ SV376 )
| ! [SY5434: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY5434 @ SY5433 @ SV376 )
| ~ ( c_HOL_Oord__class_Oless @ SV992 @ SY5434 @ SV376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2900]) ).
thf(3574,plain,
! [SV993: $i,SV377: $i] :
( ( ! [SY5435: $i] :
( ( c_HOL_Oord__class_Oless @ SV377 @ SV993 @ ( tc_fun @ SY5435 @ tc_bool ) )
| ! [SY5436: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY5436 @ SV993 @ ( tc_fun @ SY5435 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV377 @ SY5436 @ ( tc_fun @ SY5435 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2901]) ).
thf(3575,plain,
! [SV994: $i,SV378: $i] :
( ( ~ ( class_Orderings_Oorder @ SV378 )
| ! [SY5437: $i] :
( ( c_HOL_Oord__class_Oless @ SV994 @ SY5437 @ SV378 )
| ! [SY5438: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV994 @ SY5438 @ SV378 )
| ~ ( c_HOL_Oord__class_Oless @ SY5438 @ SY5437 @ SV378 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2902]) ).
thf(3576,plain,
! [SV995: $i,SV379: $i] :
( ( ! [SY5439: $i,SY5440: $i,SY5441: $i] :
( ( c_Fun_Oinj__on @ SV379 @ ( c_Set_Oinsert @ SV995 @ SY5439 @ SY5440 ) @ SY5440 @ SY5441 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5441 ) @ ( hAPP @ SV379 @ SV995 ) ) @ ( c_Set_Oimage @ SV379 @ ( c_HOL_Ominus__class_Ominus @ SY5439 @ ( c_Set_Oinsert @ SV995 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5440 @ tc_bool ) ) @ SY5440 ) @ ( tc_fun @ SY5440 @ tc_bool ) ) @ SY5440 @ SY5441 ) ) )
| ~ ( c_Fun_Oinj__on @ SV379 @ SY5439 @ SY5440 @ SY5441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2903]) ).
thf(3577,plain,
! [SV996: $i,SV380: $i] :
( ( ! [SY5442: $i,SY5443: $i] :
( ( c_Set_Oinsert @ SV380 @ ( c_Set_Oinsert @ SV996 @ SY5442 @ SY5443 ) @ SY5443 )
= ( c_Set_Oinsert @ SV996 @ ( c_Set_Oinsert @ SV380 @ SY5442 @ SY5443 ) @ SY5443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2904]) ).
thf(3578,plain,
! [SV997: $i,SV381: $i] :
( ( ! [SY5444: $i,SY5445: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV381 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV997 @ tc_bool ) ) @ SY5444 @ SV997 @ ( tc_fun @ SY5445 @ tc_bool ) ) @ ( tc_fun @ SY5445 @ tc_bool ) )
= SV381 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2905]) ).
thf(3579,plain,
! [SV998: $i,SV382: $i] :
( ( ! [SY5446: $i,SY5447: $i,SY5448: $i,SY5449: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV382 @ SV998 @ SY5446 @ SY5447 ) @ SY5448 ) @ SY5449 )
= ( hAPP @ ( hAPP @ SV382 @ SY5449 ) @ SY5448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2906]) ).
thf(3580,plain,
! [SV999: $i,SV383: $i] :
( ( ! [SY5450: $i] :
( ( c_Com_Ocom_OSemi @ SV383 @ SV999 )
!= ( c_Com_Ocom_OBODY @ SY5450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2907]) ).
thf(3581,plain,
! [SV1000: $i,SV384: $i] :
( ( ! [SY5451: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV384 @ SV1000 @ ( tc_fun @ SY5451 @ tc_bool ) ) @ SV1000 @ ( tc_fun @ SY5451 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV384 @ SV1000 @ ( tc_fun @ SY5451 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2908]) ).
thf(3582,plain,
! [SV1001: $i,SV385: $i] :
( ( ( c_Option_Ooption_ONone @ SV385 )
!= ( c_Option_Ooption_OSome @ SV1001 @ SV385 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2909]) ).
thf(3583,plain,
! [SV1002: $i,SV386: $i] :
( ( ( c_Option_Ooption_ONone @ SV386 )
!= ( c_Option_Ooption_OSome @ SV1002 @ SV386 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2910]) ).
thf(3584,plain,
! [SV1003: $i,SV387: $i] :
( ( ! [SY5452: $i,SY5453: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV387 @ SV1003 ) ) @ SY5452 ) @ SY5453 ) )
| ! [SY5454: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV387 @ SV1003 ) ) @ SY5454 ) @ SY5453 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1003 ) @ SY5452 ) @ SY5454 ) )
| ~ ( hBOOL @ ( hAPP @ SV387 @ SY5452 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2911]) ).
thf(3585,plain,
! [SV1004: $i,SV388: $i] :
( ( ! [SY5455: $i] :
( ( c_Set_Oinsert @ SV388 @ ( c_Set_Oinsert @ SV1004 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5455 @ tc_bool ) ) @ SY5455 ) @ SY5455 )
= ( c_Set_Oinsert @ SV1004 @ ( c_Set_Oinsert @ SV388 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5455 @ tc_bool ) ) @ SY5455 ) @ SY5455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2912]) ).
thf(3586,plain,
! [SV1005: $i,SV389: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV389 )
| ! [SY5456: $i] :
( ! [SY5457: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV1005 @ SY5456 @ SV389 )
!= ( c_HOL_Ominus__class_Ominus @ SY5457 @ SY5457 @ SV389 ) )
| ( SV1005 = SY5456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2913]) ).
thf(3587,plain,
! [SV1006: $i,SV390: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV390 )
| ! [SY5458: $i,SY5459: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV1006 @ SV1006 @ SV390 )
!= ( c_HOL_Ominus__class_Ominus @ SY5458 @ SY5459 @ SV390 ) )
| ( SY5458 = SY5459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2914]) ).
thf(3588,plain,
! [SV1007: $i,SV391: $i] :
( ( ! [SY5460: $i] :
( ( c_Set_Oimage @ SV391 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1007 @ tc_bool ) ) @ SV1007 @ SY5460 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5460 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2915]) ).
thf(3589,plain,
! [SV1008: $i,SV392: $i] :
( ( ! [SY5461: $i,SY5462: $i,SY5463: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV392 @ SV1008 @ SY5461 ) ) @ SY5462 ) @ SY5463 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1008 ) @ SY5462 ) @ SY5463 ) )
| ~ ( hBOOL @ ( hAPP @ SV392 @ SY5462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2916]) ).
thf(3590,plain,
! [SV1009: $i,SV393: $i] :
( ( ! [SY5464: $i] :
( ~ ( hBOOL @ ( hAPP @ SV393 @ SV1009 ) )
| ! [SY5465: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY5464 ) @ SV1009 ) @ SY5465 ) )
| ! [SY5466: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV393 @ SY5464 @ SY5466 ) ) @ SV1009 ) @ SY5465 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2917]) ).
thf(3591,plain,
! [SV1010: $i,SV394: $i] :
( ( ! [SY5467: $i,SY5468: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV394 @ SV1010 ) ) @ SY5467 ) @ SY5468 ) )
| ! [SY5469: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1010 ) @ SY5469 ) @ SY5468 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV394 ) @ SY5467 ) @ SY5469 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2918]) ).
thf(3592,plain,
! [SV1011: $i,SV395: $i] :
( ( ! [SY5470: $i] : ( c_Fun_Oinj__on @ SV395 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1011 @ tc_bool ) ) @ SV1011 @ SY5470 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2919]) ).
thf(3593,plain,
! [SV1012: $i,SV396: $i] :
( ( ! [SY5471: $i,SY5472: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Map_Odom @ SV396 @ SV1012 @ SY5471 ) @ ( c_Map_Odom @ SY5472 @ SV1012 @ SY5471 ) @ ( tc_fun @ SV1012 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1012 @ tc_bool ) ) )
| ( ( c_Map_Omap__add @ SV396 @ SY5472 @ SV1012 @ SY5471 )
= ( c_Map_Omap__add @ SY5472 @ SV396 @ SV1012 @ SY5471 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2920]) ).
thf(3594,plain,
! [SV1013: $i,SV397: $i] :
( ( ! [SY5473: $i,SY5474: $i] :
( ( ( hAPP @ SV397 @ SV1013 )
!= ( c_Option_Ooption_OSome @ SY5473 @ SY5474 ) )
| ! [SY5475: $i] :
( ( c_Set_Oinsert @ SV1013 @ ( c_Map_Odom @ SV397 @ SY5475 @ SY5474 ) @ SY5475 )
= ( c_Map_Odom @ SV397 @ SY5475 @ SY5474 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2921]) ).
thf(3595,plain,
! [SV1014: $i,SV398: $i] :
( ( ! [SY5476: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV398 @ SV1014 @ ( tc_fun @ SY5476 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1014 @ SV398 @ ( tc_fun @ SY5476 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2922]) ).
thf(3596,plain,
! [SV399: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV399 ) )
= $true )
| ( ( ! [SY3886: $i,SY3887: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3886 @ SY3887 @ SV399 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3887 @ SY3886 @ SV399 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2923]) ).
thf(3597,plain,
! [SV400: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV400 ) )
= $true )
| ( ( ! [SY3888: $i,SY3889: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3888 @ SY3889 @ SV400 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3889 @ SY3888 @ SV400 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2924]) ).
thf(3598,plain,
! [SV1015: $i,SV401: $i] :
( ( ! [SY5477: $i,SY5478: $i,SY5479: $i,SY5480: $i,SY5481: $i,SY5482: $i,SY5483: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV401 @ SV1015 @ ( c_COMBC @ SY5477 @ SY5478 @ SY5478 @ tc_bool ) @ ( c_COMBC @ SY5479 @ SY5478 @ SY5478 @ tc_bool ) @ SY5480 @ SY5481 @ SY5482 @ SY5483 @ SY5478 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1015 @ SV401 @ SY5477 @ SY5479 @ SY5481 @ SY5480 @ SY5483 @ SY5482 @ SY5478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2925]) ).
thf(3599,plain,
! [SV1016: $i,SV402: $i] :
( ( ! [SY5484: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCond @ SV402 @ SV1016 @ SY5484 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2926]) ).
thf(3600,plain,
! [SV1017: $i,SV403: $i] :
( ( ! [SY5485: $i] :
( ( c_Set_Oinsert @ SV403 @ ( c_HOL_Ominus__class_Ominus @ SV1017 @ ( c_Set_Oinsert @ SV403 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5485 @ tc_bool ) ) @ SY5485 ) @ ( tc_fun @ SY5485 @ tc_bool ) ) @ SY5485 )
= ( c_Set_Oinsert @ SV403 @ SV1017 @ SY5485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2927]) ).
thf(3601,plain,
! [SV1018: $i,SV404: $i] :
( ( ! [SY5486: $i] :
( ( ( c_Set_Oinsert @ SV404 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1018 @ tc_bool ) ) @ SV1018 )
!= ( c_Set_Oinsert @ SY5486 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1018 @ tc_bool ) ) @ SV1018 ) )
| ( SV404 = SY5486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2928]) ).
thf(3602,plain,
! [SV1019: $i,SV405: $i] :
( ( ! [SY5487: $i,SY5488: $i,SY5489: $i,SY5490: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV405 @ SV1019 @ SY5487 @ SY5488 ) @ SY5489 )
!= ( c_Option_Ooption_OSome @ SY5490 @ SY5488 ) )
| ( ( hAPP @ SV405 @ SY5489 )
= ( c_Option_Ooption_OSome @ SY5490 @ SY5488 ) )
| ( ( hAPP @ SV1019 @ SY5489 )
= ( c_Option_Ooption_OSome @ SY5490 @ SY5488 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2929]) ).
thf(3603,plain,
! [SV1020: $i,SV406: $i] :
( ( ! [SY5491: $i,SY5492: $i] :
( ( ( hAPP @ SV406 @ SV1020 )
!= ( c_Option_Ooption_OSome @ SY5491 @ SY5492 ) )
| ! [SY5493: $i] :
( ( ( hAPP @ SY5493 @ SV1020 )
!= ( c_Option_Ooption_ONone @ SY5492 ) )
| ! [SY5494: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SV406 @ SY5493 @ SY5494 @ SY5492 ) @ SV1020 )
= ( c_Option_Ooption_OSome @ SY5491 @ SY5492 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2930]) ).
thf(3604,plain,
! [SV1021: $i,SV407: $i] :
( ( ! [SY5495: $i,SY5496: $i,SY5497: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV407 @ SV1021 @ SY5495 @ SY5496 ) @ SY5497 )
!= ( c_Option_Ooption_ONone @ SY5496 ) )
| ( ( hAPP @ SV407 @ SY5497 )
= ( c_Option_Ooption_ONone @ SY5496 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2931]) ).
thf(3605,plain,
! [SV1022: $i,SV408: $i] :
( ( ! [SY5498: $i,SY5499: $i,SY5500: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV408 @ SV1022 @ SY5498 @ SY5499 ) @ SY5500 )
!= ( c_Option_Ooption_ONone @ SY5499 ) )
| ( ( hAPP @ SV1022 @ SY5500 )
= ( c_Option_Ooption_ONone @ SY5499 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2932]) ).
thf(3606,plain,
! [SV1023: $i,SV409: $i] :
( ( ! [SY5501: $i] :
( ( ( c_Set_Oinsert @ SV409 @ SV1023 @ SY5501 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5501 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5501 ) @ SV409 ) @ SV1023 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2933]) ).
thf(3607,plain,
! [SV1024: $i,SV410: $i] :
( ( ! [SY5502: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ SV1024 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY5502 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY5502 ) ) @ SY5502 )
| ! [SY5503: $i] :
~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ SV1024 @ SY5503 @ ( tc_Hoare__Mirabelle_Otriple @ SY5502 ) ) @ SY5502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2934]) ).
thf(3608,plain,
! [SV1025: $i,SV411: $i] :
( ( ! [SY5504: $i,SY5505: $i] :
( ( c_Com_Ocom_OLocal @ SV411 @ SV1025 @ SY5504 )
!= ( c_Com_Ocom_OBODY @ SY5505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2935]) ).
thf(3609,plain,
! [SV1026: $i,SV412: $i] :
( ( ! [SY5506: $i,SY5507: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV412 @ SV1026 @ SY5506 ) @ SY5507 ) )
| ~ ( hBOOL @ ( hAPP @ SV1026 @ SY5507 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2936]) ).
thf(3610,plain,
! [SV1027: $i,SV413: $i] :
( ( ! [SY5508: $i,SY5509: $i] :
( ! [SY5510: $i] :
( ( c_Set_Oinsert @ ( hAPP @ SV413 @ SV1027 ) @ ( c_Set_Oimage @ SV413 @ SY5508 @ SY5509 @ SY5510 ) @ SY5510 )
= ( c_Set_Oimage @ SV413 @ SY5508 @ SY5509 @ SY5510 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5509 ) @ SV1027 ) @ SY5508 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2937]) ).
thf(3611,plain,
! [SV1028: $i,SV414: $i] :
( ( ! [SY5511: $i,SY5512: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV414 @ ( c_Set_Oinsert @ SV1028 @ SY5511 @ SY5512 ) @ ( tc_fun @ SY5512 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV414 @ SY5511 @ ( tc_fun @ SY5512 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5512 ) @ SV1028 ) @ SV414 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2938]) ).
thf(3612,plain,
! [SV1029: $i,SV415: $i] :
( ( ! [SY5513: $i,SY5514: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV415 @ SV1029 @ SY5513 ) @ SY5514 @ ( tc_fun @ SY5513 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1029 @ SY5514 @ ( tc_fun @ SY5513 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5513 ) @ SV415 ) @ SY5514 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2939]) ).
thf(3613,plain,
! [SV1030: $i,SV416: $i] :
( ( ! [SY5515: $i,SY5516: $i,SY5517: $i] :
( ( c_Com_Ocom_OLocal @ SV416 @ SV1030 @ SY5515 )
!= ( c_Com_Ocom_OSemi @ SY5516 @ SY5517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2940]) ).
thf(3614,plain,
! [SV1031: $i,SV417: $i] :
( ( ( ( c_Com_Ocom_OBODY @ SV417 )
!= ( c_Com_Ocom_OBODY @ SV1031 ) )
| ( SV417 = SV1031 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2941]) ).
thf(3615,plain,
! [SV1032: $i,SV418: $i] :
( ( ! [SY5518: $i] :
( ! [SY5519: $i] :
( ( c_Com_Ocom_OWhile @ SV418 @ SV1032 )
!= ( c_Com_Ocom_OWhile @ SY5518 @ SY5519 ) )
| ( SV418 = SY5518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2942]) ).
thf(3616,plain,
! [SV1033: $i,SV419: $i] :
( ( ! [SY5520: $i,SY5521: $i] :
( ( ( c_Com_Ocom_OWhile @ SV419 @ SV1033 )
!= ( c_Com_Ocom_OWhile @ SY5520 @ SY5521 ) )
| ( SV1033 = SY5521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2943]) ).
thf(3617,plain,
! [SV1034: $i,SV420: $i] :
( ( ! [SY5522: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV420 @ tc_bool ) )
= ( c_Set_Oimage @ SV1034 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5522 @ tc_bool ) ) @ SY5522 @ SV420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2944]) ).
thf(3618,plain,
! [SV1035: $i,SV421: $i] :
( ( ! [SY5523: $i] :
( ( c_Com_Ocom_OCond @ SV421 @ SV1035 @ SY5523 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2945]) ).
thf(3619,plain,
! [SV1036: $i,SV422: $i] :
( ( ! [SY5524: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV422 @ ( c_HOL_Ominus__class_Ominus @ SV1036 @ SV422 @ ( tc_fun @ SY5524 @ tc_bool ) ) @ ( tc_fun @ SY5524 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5524 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2946]) ).
thf(3620,plain,
! [SV1037: $i,SV423: $i] :
( ( ! [SY5525: $i,SY5526: $i,SY5527: $i] :
( ( c_Com_Ocom_OWhile @ SV423 @ SV1037 )
!= ( c_Com_Ocom_OCond @ SY5525 @ SY5526 @ SY5527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2947]) ).
thf(3621,plain,
! [SV424: $i] :
( ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV424 ) )
= $true )
| ( ( ! [SY3964: $i] : ( c_Finite__Set_Ofinite @ SY3964 @ SV424 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2948]) ).
thf(3622,plain,
! [SV1038: $i,SV425: $i] :
( ( ! [SY5528: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV425 ) @ SV1038 ) @ SY5528 ) )
| ! [SY5529: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV425 ) @ SV1038 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5528 @ ( c_Collect @ SY5529 @ SV425 ) @ ( tc_fun @ SV425 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2949]) ).
thf(3623,plain,
! [SV1039: $i,SV426: $i] :
( ( ! [SY5530: $i] :
( ( ( hAPP @ SV426 @ SV1039 )
!= ( c_Option_Ooption_ONone @ SY5530 ) )
| ! [SY5531: $i] :
( ( ( hAPP @ SY5531 @ SV1039 )
!= ( c_Option_Ooption_ONone @ SY5530 ) )
| ! [SY5532: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SV426 @ SY5531 @ SY5532 @ SY5530 ) @ SV1039 )
= ( c_Option_Ooption_ONone @ SY5530 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2950]) ).
thf(3624,plain,
! [SV1040: $i,SV427: $i] :
( ( ! [SY5533: $i,SY5534: $i] :
( ( ( hAPP @ SV427 @ SV1040 )
!= ( c_Option_Ooption_OSome @ SY5533 @ SY5534 ) )
| ! [SY5535: $i,SY5536: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SY5535 @ SV427 @ SY5536 @ SY5534 ) @ SV1040 )
= ( c_Option_Ooption_OSome @ SY5533 @ SY5534 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2951]) ).
thf(3625,plain,
! [SV1041: $i,SV428: $i] :
( ( ! [SY5537: $i,SY5538: $i] :
( ( ( hAPP @ SV428 @ SV1041 )
!= ( c_Option_Ooption_OSome @ SY5537 @ SY5538 ) )
| ! [SY5539: $i,SY5540: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SY5539 @ SV428 @ SY5540 @ SY5538 ) @ SV1041 )
= ( c_Option_Ooption_OSome @ SY5537 @ SY5538 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2952]) ).
thf(3626,plain,
! [SV1042: $i,SV429: $i] :
( ( ! [SY5541: $i,SY5542: $i,SY5543: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV429 ) @ ( hAPP @ SV1042 @ SY5541 ) ) @ ( c_Set_Oimage @ SV1042 @ ( c_HOL_Ominus__class_Ominus @ SY5542 @ ( c_Set_Oinsert @ SY5541 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5543 @ tc_bool ) ) @ SY5543 ) @ ( tc_fun @ SY5543 @ tc_bool ) ) @ SY5543 @ SV429 ) ) )
| ~ ( c_Fun_Oinj__on @ SV1042 @ ( c_Set_Oinsert @ SY5541 @ SY5542 @ SY5543 ) @ SY5543 @ SV429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2953]) ).
thf(3627,plain,
! [SV1043: $i,SV430: $i] :
( ( ! [SY5544: $i,SY5545: $i,SY5546: $i] :
( ( c_Com_Ocom_OCond @ SV430 @ SV1043 @ SY5544 )
!= ( c_Com_Ocom_OAss @ SY5545 @ SY5546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2954]) ).
thf(3628,plain,
! [SV431: $i] :
( ( c_Com_Ocom_OSKIP
= ( c_Com_Ocom_OBODY @ SV431 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2955]) ).
thf(3629,plain,
! [SV1044: $i,SV432: $i] :
( ( ! [SY5547: $i,SY5548: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV432 @ SV1044 @ SY5547 ) @ SY5548 @ ( tc_fun @ SY5547 @ tc_bool ) )
= ( c_Set_Oinsert @ SV432 @ ( c_HOL_Ominus__class_Ominus @ SV1044 @ SY5548 @ ( tc_fun @ SY5547 @ tc_bool ) ) @ SY5547 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5547 ) @ SV432 ) @ SY5548 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2956]) ).
thf(3630,plain,
! [SV1045: $i,SV433: $i] :
( ( ( hBOOL @ ( hAPP @ SV433 @ SV1045 ) )
| ! [SY5549: $i,SY5550: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5549 @ SV433 @ ( tc_fun @ SY5550 @ tc_bool ) ) @ SV1045 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2957]) ).
thf(3631,plain,
! [SV1046: $i,SV434: $i] :
( ( ( hBOOL @ ( hAPP @ SV434 @ SV1046 ) )
| ! [SY5551: $i,SY5552: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV434 @ SY5551 @ ( tc_fun @ SY5552 @ tc_bool ) ) @ SV1046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2958]) ).
thf(3632,plain,
! [SV1047: $i,SV435: $i] :
( ( ! [SY5553: $i,SY5554: $i] : ( c_Map_Omap__le @ SV435 @ ( c_Map_Omap__add @ SV1047 @ SV435 @ SY5553 @ SY5554 ) @ SY5553 @ SY5554 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2959]) ).
thf(3633,plain,
! [SV1048: $i,SV436: $i] :
( ( ! [SY5555: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV436 @ SV1048 @ SY5555 ) @ ( c_Set_Oinsert @ SV436 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5555 @ tc_bool ) ) @ SY5555 ) @ ( tc_fun @ SY5555 @ tc_bool ) )
= SV1048 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5555 ) @ SV436 ) @ SV1048 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2960]) ).
thf(3634,plain,
! [SV1049: $i,SV437: $i] :
( ( ! [SY5556: $i,SY5557: $i,SY5558: $i] :
( ( c_Set_Ovimage @ SV437 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1049 @ SY5556 @ ( tc_fun @ SY5557 @ tc_bool ) ) @ SY5558 @ SY5557 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Ovimage @ SV437 @ SV1049 @ SY5558 @ SY5557 ) @ ( c_Set_Ovimage @ SV437 @ SY5556 @ SY5558 @ SY5557 ) @ ( tc_fun @ SY5558 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2961]) ).
thf(3635,plain,
! [SV1050: $i,SV438: $i] :
( ( ( SV438 = SV1050 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ SV1050 ) @ SV438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2962]) ).
thf(3636,plain,
! [SV1051: $i,SV439: $i] :
( ( ! [SY5559: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV439 @ SV1051 @ ( tc_fun @ SY5559 @ tc_bool ) ) @ SY5559 )
| ~ ( c_Finite__Set_Ofinite @ SV1051 @ SY5559 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2963]) ).
thf(3637,plain,
! [SV1052: $i,SV440: $i] :
( ( ! [SY5560: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV440 @ SV1052 @ ( tc_fun @ SY5560 @ tc_bool ) ) @ SY5560 )
| ~ ( c_Finite__Set_Ofinite @ SV440 @ SY5560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2964]) ).
thf(3638,plain,
! [SV1053: $i,SV441: $i] :
( ( ! [SY5561: $i,SY5562: $i,SY5563: $i] :
( ( c_Map_Omap__le @ ( c_Map_Omap__add @ SV441 @ SV1053 @ SY5561 @ SY5562 ) @ SY5563 @ SY5561 @ SY5562 )
| ~ ( c_Map_Omap__le @ SV441 @ ( c_Map_Omap__add @ SV441 @ SV1053 @ SY5561 @ SY5562 ) @ SY5561 @ SY5562 )
| ~ ( c_Map_Omap__le @ SV1053 @ SY5563 @ SY5561 @ SY5562 )
| ~ ( c_Map_Omap__le @ SV441 @ SY5563 @ SY5561 @ SY5562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2965]) ).
thf(3639,plain,
! [SV1054: $i,SV442: $i] :
( ( ! [SY5564: $i] :
( ( hBOOL @ ( hAPP @ SV442 @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1054 @ SV442 @ SY5564 ) ) )
| ! [SY5565: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5564 ) @ SY5565 ) @ SV1054 ) )
| ! [SY5566: $i] :
( ~ ( hBOOL @ ( hAPP @ SV442 @ SY5566 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5564 ) @ SY5566 ) @ SV1054 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2966]) ).
thf(3640,plain,
! [SV1055: $i,SV443: $i] :
( ( ! [SY5567: $i,SY5568: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ SV1055 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5567 @ SY5568 @ ( tc_fun @ SV443 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ SV1055 ) @ SY5568 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ SV1055 ) @ SY5567 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2967]) ).
thf(3641,plain,
! [SV1056: $i,SV444: $i] :
( ( ! [SY5569: $i,SY5570: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ SV1056 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5569 @ SY5570 @ ( tc_fun @ SV444 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ SV1056 ) @ SY5570 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ SV1056 ) @ SY5569 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2968]) ).
thf(3642,plain,
! [SV1057: $i,SV445: $i] :
( ( ! [SY5571: $i] :
( ( hBOOL @ ( hAPP @ SV445 @ SV1057 ) )
| ! [SY5572: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5571 ) @ SV1057 ) @ SY5572 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5571 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY5572 @ SV445 @ SY5571 ) ) @ SY5572 ) )
| ! [V_P: $i] :
~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY5572 @ V_P @ SY5571 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2969]) ).
thf(3643,plain,
! [SV1058: $i,SV446: $i] :
( ( ! [SY5574: $i] :
( ( hBOOL @ ( hAPP @ SV446 @ SV1058 ) )
| ! [SY5575: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5574 ) @ SV1058 ) @ SY5575 ) )
| ! [V_Q: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5574 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY5575 @ V_Q @ SY5574 ) ) @ SY5575 ) )
| ~ ( hBOOL @ ( hAPP @ SV446 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY5575 @ SV446 @ SY5574 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2970]) ).
thf(3644,plain,
! [SV1059: $i,SV447: $i] :
( ( ! [SY5577: $i] :
( ( hBOOL @ ( hAPP @ SV447 @ SV1059 ) )
| ! [SY5578: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5577 ) @ SV1059 ) @ SY5578 ) )
| ~ ( hBOOL @ ( hAPP @ SV447 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY5578 @ SV447 @ SY5577 ) ) )
| ! [V_P: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5577 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY5578 @ V_P @ SY5577 ) ) @ SY5578 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2971]) ).
thf(3645,plain,
! [SV1060: $i,SV448: $i] :
( ( ! [SY5580: $i] :
( ( hBOOL @ ( hAPP @ SV448 @ SV1060 ) )
| ! [SY5581: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5580 ) @ SV1060 ) @ SY5581 ) )
| ! [V_Q: $i] :
~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY5581 @ V_Q @ SY5580 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5580 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY5581 @ SV448 @ SY5580 ) ) @ SY5581 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2972]) ).
thf(3646,plain,
! [SV1061: $i,SV449: $i] :
( ( ! [SY5583: $i,SY5584: $i,SY5585: $i,SY5586: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV449 ) @ SV1061 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SY5583 @ SY5584 @ SY5585 @ SY5586 @ SV449 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY5584 @ SV1061 ) @ SY5586 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY5583 @ SY5585 ) @ SV1061 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2973]) ).
thf(3647,plain,
! [SV1062: $i,SV450: $i] :
( ( ! [SY5587: $i,SY5588: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV450 ) @ SV1062 ) @ ( c_Set_Oinsert @ SY5587 @ SY5588 @ SV450 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV450 ) @ SV1062 ) @ SY5588 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2974]) ).
thf(3648,plain,
! [SV1063: $i,SV451: $i] :
( ( ! [SY5589: $i,SY5590: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV451 ) @ SV1063 ) @ ( c_Set_Oinsert @ SY5589 @ SY5590 @ SV451 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV451 ) @ SV1063 ) @ SY5590 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2975]) ).
thf(3649,plain,
! [SV1064: $i,SV452: $i] :
( ( ! [SY5591: $i,SY5592: $i,SY5593: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV452 ) @ SV1064 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SY5591 @ SY5592 @ SY5593 @ SV452 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY5591 @ SV1064 ) @ SY5593 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY5591 @ SY5592 ) @ SV1064 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2976]) ).
thf(3650,plain,
! [SV1065: $i,SV453: $i] :
( ( ! [SY5594: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV453 ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1065 @ SY5594 @ SV453 ) ) @ SV1065 ) )
| ! [SY5595: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV453 ) @ SY5595 ) @ SV1065 ) )
| ~ ( hBOOL @ ( hAPP @ SY5594 @ SY5595 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2977]) ).
thf(3651,plain,
! [SV1066: $i,SV454: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV454 ) @ SV1066 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV454 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2978]) ).
thf(3652,plain,
! [SV1067: $i,SV455: $i] :
( ( ( hBOOL @ ( hAPP @ SV455 @ SV1067 ) )
| ! [SY5596: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5596 ) @ SV1067 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5596 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2979]) ).
thf(3653,plain,
! [SV1068: $i,SV456: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV456 ) @ SV1068 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV456 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2980]) ).
thf(3654,plain,
! [SV1069: $i,SV457: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV457 ) @ SV1069 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV457 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2981]) ).
thf(3655,plain,
! [SV1070: $i,SV458: $i] :
( ( ! [SY5597: $i,SY5598: $i,SY5599: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV458 ) @ SV1070 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SY5597 @ SY5598 @ SY5599 @ SV458 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY5597 @ SV1070 ) @ SY5599 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY5597 @ SY5598 ) @ SV1070 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2982]) ).
thf(3656,plain,
! [SV1071: $i,SV459: $i] :
( ( ! [SY5600: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV459 ) @ SV1071 ) @ SY5600 ) )
| ! [SY5601: $i] :
( ( SV1071 = SY5601 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV459 ) @ SV1071 ) @ ( c_Set_Oinsert @ SY5601 @ SY5600 @ SV459 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2983]) ).
thf(3657,plain,
! [SV1072: $i,SV460: $i] :
( ( ! [SY5602: $i,SY5603: $i,SY5604: $i,SY5605: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV460 ) @ SV1072 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SY5602 @ SY5603 @ SY5604 @ SY5605 @ SV460 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY5602 @ SV1072 ) @ SY5605 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY5603 @ SY5604 ) @ SV1072 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2984]) ).
thf(3658,plain,
! [SV1073: $i,SV461: $i] :
( ( ! [SY5606: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV461 ) @ SV1073 ) @ SY5606 ) )
| ! [SY5607: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV461 ) @ SV1073 ) @ ( c_HOL_Ominus__class_Ominus @ SY5607 @ SY5606 @ ( tc_fun @ SV461 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2985]) ).
thf(3659,plain,
! [SV1074: $i,SV462: $i] :
( ( ! [SY5608: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV462 ) @ SV1074 ) @ SY5608 ) )
| ! [SY5609: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV462 ) @ SV1074 ) @ ( c_HOL_Ominus__class_Ominus @ SY5608 @ SY5609 @ ( tc_fun @ SV462 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2986]) ).
thf(3660,plain,
! [SV1075: $i,SV463: $i] :
( ( ! [SY5610: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1075 @ SY5610 @ SV463 ) ) @ SV1075 ) )
| ! [SY5611: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ SY5611 ) @ SV1075 ) )
| ! [SY5612: $i] :
( ~ ( hBOOL @ ( hAPP @ SY5610 @ SY5612 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ SY5612 ) @ SV1075 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2987]) ).
thf(3661,plain,
! [SV1076: $i,SV464: $i] :
( ( ! [SY5613: $i] :
( ( hBOOL @ ( hAPP @ SV464 @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ SV1076 @ SV464 @ SY5613 ) ) )
| ! [SY5614: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5613 ) @ SY5614 ) @ SV1076 ) )
| ~ ( hBOOL @ ( hAPP @ SV464 @ SY5614 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2988]) ).
thf(3662,plain,
! [SV1077: $i,SV465: $i] :
( ( ! [SY5615: $i,SY5616: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV465 @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1077 @ SY5615 @ SY5616 @ ( tc_fun @ SV465 @ tc_bool ) ) )
| ! [SY5617: $i] :
( ( ( hAPP @ SY5615 @ SY5617 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV465 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5616 ) @ SY5617 ) @ SV1077 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2989]) ).
thf(3663,plain,
! [SV1078: $i,SV466: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV466 @ tc_bool ) ) @ SV1078 @ ( tc_fun @ SV466 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV466 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2990]) ).
thf(3664,plain,
! [SV1079: $i,SV467: $i] :
( ( ! [SY5618: $i,SY5619: $i,SY5620: $i] :
( ( c_Com_Ocom_OAss @ SV467 @ SV1079 )
!= ( c_Com_Ocom_OCond @ SY5618 @ SY5619 @ SY5620 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2991]) ).
thf(3665,plain,
! [SV1080: $i,SV468: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV468 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1080 ) @ tc_bool ) ) @ SV1080 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2992]) ).
thf(3666,plain,
! [SV1081: $i,SV469: $i] :
( ( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OWhile @ SV469 @ SV1081 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2993]) ).
thf(3667,plain,
! [SV1082: $i,SV470: $i] :
( ( ! [SY5621: $i,SY5622: $i] :
( ( ( c_Map_Omap__add @ SV470 @ SV1082 @ SY5621 @ SY5622 )
= ( c_Map_Omap__add @ SV1082 @ SV470 @ SY5621 @ SY5622 ) )
| ~ ( c_Map_Omap__le @ SV470 @ ( c_Map_Omap__add @ SV470 @ SV1082 @ SY5621 @ SY5622 ) @ SY5621 @ SY5622 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2994]) ).
thf(3668,plain,
! [SV1083: $i,SV471: $i] :
( ( ! [SY5623: $i,SY5624: $i] :
( ( ( c_Map_Omap__add @ SV471 @ SV1083 @ SY5623 @ SY5624 )
!= ( c_Map_Omap__add @ SV1083 @ SV471 @ SY5623 @ SY5624 ) )
| ( c_Map_Omap__le @ SV471 @ ( c_Map_Omap__add @ SV471 @ SV1083 @ SY5623 @ SY5624 ) @ SY5623 @ SY5624 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2995]) ).
thf(3669,plain,
! [SV1084: $i,SV472: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV472 @ tc_bool ) ) @ SV1084 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2996]) ).
thf(3670,plain,
! [SV1085: $i,SV473: $i] :
( ( ! [SY5625: $i,SY5626: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV473 @ ( c_HOL_Ominus__class_Ominus @ SV1085 @ SY5625 @ ( tc_fun @ SY5626 @ tc_bool ) ) @ ( tc_fun @ SY5626 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV473 @ SV1085 @ ( tc_fun @ SY5626 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV473 @ SY5625 @ ( tc_fun @ SY5626 @ tc_bool ) ) @ ( tc_fun @ SY5626 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2997]) ).
thf(3671,plain,
! [SV1086: $i,SV474: $i] :
( ( ! [SY5627: $i,SY5628: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ SV474 @ SV1086 @ ( tc_fun @ SY5627 @ tc_bool ) ) @ SY5628 @ ( tc_fun @ SY5627 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV474 @ SY5628 @ ( tc_fun @ SY5627 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1086 @ SY5628 @ ( tc_fun @ SY5627 @ tc_bool ) ) @ ( tc_fun @ SY5627 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2998]) ).
thf(3672,plain,
! [SV1087: $i,SV475: $i] :
( ( ! [SY5629: $i] :
( ( c_HOL_Oord__class_Oless @ SV475 @ SV1087 @ ( tc_fun @ SY5629 @ tc_bool ) )
| ! [SY5630: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5629 ) @ SY5630 ) @ SV1087 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV475 @ ( c_Set_Oinsert @ SY5630 @ SV1087 @ SY5629 ) @ ( tc_fun @ SY5629 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2999]) ).
thf(3673,plain,
! [SV1088: $i,SV476: $i] :
( ( ! [SY5631: $i,SY5632: $i] :
( ( c_HOL_Oord__class_Oless @ SV476 @ ( c_Set_Oinsert @ SV1088 @ SY5631 @ SY5632 ) @ ( tc_fun @ SY5632 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5632 ) @ SV1088 ) @ SY5631 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV476 @ SY5631 @ ( tc_fun @ SY5632 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3000]) ).
thf(3674,plain,
! [SV1089: $i,SV477: $i] :
( ( ! [SY5633: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OLocal @ SV477 @ SV1089 @ SY5633 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3001]) ).
thf(3675,plain,
! [SV1090: $i,SV478: $i] :
( ( ! [SY5634: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV478 ) @ SV1090 ) @ SY5634 ) )
| ! [SY5635: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV478 ) @ SV1090 ) @ SY5635 ) )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY5635 @ SY5634 @ ( tc_fun @ SV478 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV478 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3002]) ).
thf(3676,plain,
! [SV1091: $i,SV479: $i] :
( ( ! [SY5636: $i,SY5637: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV479 @ SV1091 @ ( tc_fun @ SY5636 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5637 @ SV1091 @ ( tc_fun @ SY5636 @ tc_bool ) ) @ ( tc_fun @ SY5636 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV479 @ SV1091 @ ( tc_fun @ SY5636 @ tc_bool ) ) @ SY5637 @ ( tc_fun @ SY5636 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3003]) ).
thf(3677,plain,
! [SV1092: $i,SV480: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV480 @ SV480 @ ( tc_fun @ SV1092 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3004]) ).
thf(3678,plain,
! [SV481: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV481 ) )
= $true )
| ( ( ! [SY4130: $i] :
~ ( c_HOL_Oord__class_Oless @ SY4130 @ SY4130 @ SV481 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3005]) ).
thf(3679,plain,
! [SV482: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV482 ) )
= $true )
| ( ( ! [SY4131: $i] :
~ ( c_HOL_Oord__class_Oless @ SY4131 @ SY4131 @ SV482 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3006]) ).
thf(3680,plain,
! [SV483: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV483 ) )
= $true )
| ( ( ! [SY4132: $i] :
~ ( c_HOL_Oord__class_Oless @ SY4132 @ SY4132 @ SV483 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3007]) ).
thf(3681,plain,
! [SV484: $i] :
( ( ( ! [SY4133: $i] :
( ( c_Collect @ SV484 @ SY4133 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4133 @ tc_bool ) ) ) )
= $true )
| ( ( ! [SY4134: $i] :
~ ( hBOOL @ ( hAPP @ SV484 @ SY4134 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3008]) ).
thf(3682,plain,
! [SV1093: $i,SV486: $i] :
( ( ! [SY5638: $i,SY5639: $i] :
( ( c_Com_Ocom_OSemi @ SV486 @ SV1093 )
!= ( c_Com_Ocom_OAss @ SY5638 @ SY5639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3010]) ).
thf(3683,plain,
! [SV487: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV487 ) )
= $true )
| ( ( ! [SY4138: $i,SY4139: $i] :
( ( c_HOL_Oord__class_Oless @ SY4138 @ SY4139 @ SV487 )
| ( SY4139 = SY4138 )
| ( c_HOL_Oord__class_Oless @ SY4139 @ SY4138 @ SV487 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3011]) ).
thf(3684,plain,
! [SV488: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV488 ) )
= $true )
| ( ( ! [SY4140: $i,SY4141: $i] :
( ( SY4140 = SY4141 )
| ( c_HOL_Oord__class_Oless @ SY4141 @ SY4140 @ SV488 )
| ( c_HOL_Oord__class_Oless @ SY4140 @ SY4141 @ SV488 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3012]) ).
thf(3685,plain,
! [SV1094: $i,SV489: $i] :
( ( ( SV489 = SV1094 )
| ! [SY5640: $i,SY5641: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY5640 ) @ SY5641 ) @ SV489 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY5640 ) @ SY5641 ) @ SV1094 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3013]) ).
thf(3686,plain,
! [SV1095: $i,SV490: $i] :
( ( ( SV490 = SV1095 )
| ! [SY5642: $i,SY5643: $i] :
( ~ ( c_Map_Omap__le @ SV1095 @ SV490 @ SY5642 @ SY5643 )
| ~ ( c_Map_Omap__le @ SV490 @ SV1095 @ SY5642 @ SY5643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3014]) ).
thf(3687,plain,
! [SV491: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV491 ) )
= $true )
| ( ( ! [SY4148: $i,SY4149: $i] :
( ( c_HOL_Oord__class_Oless @ SY4148 @ SY4149 @ SV491 )
| ( SY4149 = SY4148 )
| ( c_HOL_Oord__class_Oless @ SY4149 @ SY4148 @ SV491 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3015]) ).
thf(3688,plain,
! [SV492: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV492 ) )
= $true )
| ( ( ! [SY4150: $i,SY4151: $i] :
( ( c_HOL_Oord__class_Oless @ SY4150 @ SY4151 @ SV492 )
| ( SY4151 = SY4150 )
| ( c_HOL_Oord__class_Oless @ SY4151 @ SY4150 @ SV492 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3016]) ).
thf(3689,plain,
! [SV493: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV493 ) )
= $true )
| ( ( ! [SY4152: $i,SY4153: $i] :
( ( SY4152 = SY4153 )
| ( c_HOL_Oord__class_Oless @ SY4152 @ SY4153 @ SV493 )
| ( c_HOL_Oord__class_Oless @ SY4153 @ SY4152 @ SV493 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3017]) ).
thf(3690,plain,
! [SV1096: $i,SV494: $i] :
( ( ! [SY5644: $i] :
( ( c_Com_Ocom_OLocal @ SV494 @ SV1096 @ SY5644 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3018]) ).
thf(3691,plain,
! [SV1097: $i,SV495: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV495 )
| ! [SY5645: $i,SY5646: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1097 @ SY5645 @ SV495 ) @ SY5646 @ SV495 )
| ~ ( c_HOL_Oord__class_Oless @ SY5645 @ SY5646 @ SV495 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3019]) ).
thf(3692,plain,
! [SV1098: $i,SV496: $i] :
( ( ~ ( class_Lattices_Olower__semilattice @ SV496 )
| ! [SY5647: $i,SY5648: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1098 @ SY5647 @ SV496 ) @ SY5648 @ SV496 )
| ~ ( c_HOL_Oord__class_Oless @ SV1098 @ SY5648 @ SV496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3020]) ).
thf(3693,plain,
! [SV1099: $i,SV497: $i] :
( ( ! [SY5649: $i] :
( ! [SY5650: $i] : ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV497 @ SV1099 @ SY5649 @ SY5650 ) @ SY5650 )
| ~ ( c_Finite__Set_Ofinite @ SV1099 @ SY5649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3021]) ).
thf(3694,plain,
! [SV1100: $i,SV498: $i] :
( ( ! [SY5651: $i,SY5652: $i] :
( ( ( hAPP @ SV498 @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ SV498 @ SV1100 @ SY5651 @ SY5652 ) )
!= ( hAPP @ SV1100 @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ SV498 @ SV1100 @ SY5651 @ SY5652 ) ) )
| ( c_Map_Omap__le @ SV498 @ SV1100 @ SY5651 @ SY5652 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3022]) ).
thf(3695,plain,
! [SV1101: $i,SV499: $i] :
( ( ! [SY5653: $i,SY5654: $i,SY5655: $i] :
( ( ( c_Set_Oinsert @ SV499 @ ( c_Set_Oinsert @ SV1101 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5653 @ tc_bool ) ) @ SY5653 ) @ SY5653 )
!= ( c_Set_Oinsert @ SY5654 @ ( c_Set_Oinsert @ SY5655 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5653 @ tc_bool ) ) @ SY5653 ) @ SY5653 ) )
| ( SV499 = SY5655 )
| ( SV499 = SY5654 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3023]) ).
thf(3696,plain,
! [SV1102: $i,SV500: $i] :
( ( ! [SY5656: $i,SY5657: $i] :
( ! [SY5658: $i] :
( ( c_Set_Oinsert @ SV500 @ ( c_Set_Oinsert @ SV1102 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5656 @ tc_bool ) ) @ SY5656 ) @ SY5656 )
!= ( c_Set_Oinsert @ SY5657 @ ( c_Set_Oinsert @ SY5658 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5656 @ tc_bool ) ) @ SY5656 ) @ SY5656 ) )
| ( SV1102 = SY5657 )
| ( SV500 = SY5657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3024]) ).
thf(3697,plain,
! [SV1103: $i,SV501: $i] :
( ( ! [SY5659: $i,SY5660: $i,SY5661: $i] :
( ( ( c_Set_Oinsert @ SV501 @ ( c_Set_Oinsert @ SV1103 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5659 @ tc_bool ) ) @ SY5659 ) @ SY5659 )
!= ( c_Set_Oinsert @ SY5660 @ ( c_Set_Oinsert @ SY5661 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5659 @ tc_bool ) ) @ SY5659 ) @ SY5659 ) )
| ( SV501 = SY5661 )
| ( SV1103 = SY5661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3025]) ).
thf(3698,plain,
! [SV1104: $i,SV502: $i] :
( ( ! [SY5662: $i,SY5663: $i,SY5664: $i] :
( ( ( c_Set_Oinsert @ SV502 @ ( c_Set_Oinsert @ SV1104 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5662 @ tc_bool ) ) @ SY5662 ) @ SY5662 )
!= ( c_Set_Oinsert @ SY5663 @ ( c_Set_Oinsert @ SY5664 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5662 @ tc_bool ) ) @ SY5662 ) @ SY5662 ) )
| ( SV1104 = SY5663 )
| ( SV1104 = SY5664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3026]) ).
thf(3699,plain,
! [SV1105: $i,SV503: $i] :
( ( ! [SY5665: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV503 ) @ SV1105 ) @ SY5665 ) )
| ! [SY5666: $i] :
( ( hBOOL @ ( hAPP @ SY5666 @ SV1105 ) )
| ! [SY5667: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY5666 @ SY5667 @ SV503 ) ) @ SV1105 ) @ SY5665 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3027]) ).
thf(3700,plain,
! [SV1106: $i,SV504: $i] :
( ( ! [SY5668: $i,SY5669: $i,SY5670: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV504 @ SV1106 @ SY5668 ) ) @ SY5669 ) @ SY5670 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY5668 ) @ SY5669 ) @ SY5670 ) )
| ( hBOOL @ ( hAPP @ SV504 @ SY5669 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3028]) ).
thf(3701,plain,
! [SV1107: $i,SV505: $i] :
( ( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OAss @ SV505 @ SV1107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3029]) ).
thf(3702,plain,
! [SV1108: $i,SV506: $i] :
( ( ! [SY5671: $i,SY5672: $i,SY5673: $i,SY5674: $i,SY5675: $i,SY5676: $i,SY5677: $i] :
( ( ( hAPP @ SV506 @ ( c_Set_Oinsert @ SV1108 @ SY5671 @ SY5672 ) )
= ( hAPP @ ( hAPP @ SY5673 @ SV1108 ) @ ( hAPP @ SV506 @ SY5671 ) ) )
| ! [SY4201: $i,SY4202: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY5674 @ SV506 @ SY5675 @ SY5676 @ SY5677 @ SY5673 @ SY4201 @ SY4202 @ SY5672 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3030]) ).
thf(3703,plain,
! [SV1109: $i,SV507: $i] :
( ( ! [SY5680: $i,SY5681: $i,SY5682: $i,SY5683: $i,SY5684: $i,SY5685: $i,SY5686: $i] :
( ( ( hAPP @ SV507 @ ( c_Set_Oinsert @ SV1109 @ SY5680 @ SY5681 ) )
= ( hAPP @ ( hAPP @ SY5682 @ SV1109 ) @ ( hAPP @ SV507 @ SY5680 ) ) )
| ! [SY4211: $i,SY4212: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV507 @ SY5683 @ SY5684 @ SY5685 @ SY5682 @ SY5686 @ SY4211 @ SY4212 @ SY5681 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3031]) ).
thf(3704,plain,
! [SV1110: $i,SV508: $i] :
( ( ! [SY5689: $i,SY5690: $i] :
( ( c_Com_Ocom_OWhile @ SV508 @ SV1110 )
!= ( c_Com_Ocom_OAss @ SY5689 @ SY5690 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3032]) ).
thf(3705,plain,
! [SV1111: $i,SV509: $i] :
( ( ! [SY5691: $i,SY5692: $i,SY5693: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SV1111 @ SY5691 @ SY5692 @ SY5693 @ SV509 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1111 @ SY5691 @ SY5693 @ ( tc_fun @ SV509 @ tc_bool ) ) ) )
| ! [SY5694: $i] :
( ~ ( hBOOL @ ( hAPP @ SY5692 @ SY5694 ) )
| ! [SY5695: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ SY5694 ) @ ( hAPP @ SY5691 @ SY5695 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5693 ) @ SY5695 ) @ SV1111 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3033]) ).
thf(3706,plain,
! [SV1112: $i,SV510: $i] :
( ( ! [SY5696: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV510 @ tc_bool ) )
!= ( c_Set_Oinsert @ SV1112 @ SY5696 @ SV510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3034]) ).
thf(3707,plain,
! [SV1113: $i,SV511: $i] :
( ( ! [SY5697: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV511 @ SV1113 @ SY5697 )
| ! [SY5698: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV511 @ SY5698 @ SY5697 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY5698 @ SV1113 @ SY5697 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3035]) ).
thf(3708,plain,
! [SV1114: $i,SV512: $i] :
( ( ! [SY5699: $i,SY5700: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV512 @ SV1114 @ SY5699 ) @ SY5700 @ ( tc_fun @ SY5699 @ tc_bool ) )
= ( c_Set_Oinsert @ SV512 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1114 @ SY5700 @ ( tc_fun @ SY5699 @ tc_bool ) ) @ SY5699 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5699 ) @ SV512 ) @ SY5700 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3036]) ).
thf(3709,plain,
! [SV1115: $i,SV513: $i] :
( ( ! [SY5701: $i,SY5702: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV513 @ ( c_Set_Oinsert @ SV1115 @ SY5701 @ SY5702 ) @ ( tc_fun @ SY5702 @ tc_bool ) )
= ( c_Set_Oinsert @ SV1115 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV513 @ SY5701 @ ( tc_fun @ SY5702 @ tc_bool ) ) @ SY5702 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5702 ) @ SV1115 ) @ SV513 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3037]) ).
thf(3710,plain,
! [SV1116: $i,SV514: $i] :
( ( ! [SY5703: $i,SY5704: $i,SY5705: $i] :
( ( c_Set_Oimage @ SV514 @ ( c_Set_Oinsert @ SV1116 @ SY5703 @ SY5704 ) @ SY5704 @ SY5705 )
= ( c_Set_Oinsert @ ( hAPP @ SV514 @ SV1116 ) @ ( c_Set_Oimage @ SV514 @ SY5703 @ SY5704 @ SY5705 ) @ SY5705 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3038]) ).
thf(3711,plain,
! [SV1117: $i,SV515: $i] :
( ( ! [SY5706: $i,SY5707: $i,SY5708: $i,SY5709: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV515 @ SV1117 @ SY5706 @ SY5707 ) @ SY5708 )
!= ( c_Option_Ooption_OSome @ SY5709 @ SY5707 ) )
| ( ( hAPP @ SV1117 @ SY5708 )
= ( c_Option_Ooption_ONone @ SY5707 ) )
| ( ( hAPP @ SV1117 @ SY5708 )
= ( c_Option_Ooption_OSome @ SY5709 @ SY5707 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3039]) ).
thf(3712,plain,
! [SV1118: $i,SV516: $i] :
( ( ! [SY5710: $i] :
( ( ( hAPP @ SV516 @ SV1118 )
= SY5710 )
| ! [SY5711: $i,SY5712: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5711 ) @ SV1118 ) @ ( c_Set_Ovimage @ SV516 @ ( c_Set_Oinsert @ SY5710 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5712 @ tc_bool ) ) @ SY5712 ) @ SY5711 @ SY5712 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3040]) ).
thf(3713,plain,
! [SV1119: $i,SV517: $i] :
( ( ! [SY5713: $i,SY5714: $i] :
( ( ( c_Com_Ocom_OAss @ SV517 @ SV1119 )
!= ( c_Com_Ocom_OAss @ SY5713 @ SY5714 ) )
| ( SV1119 = SY5714 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3041]) ).
thf(3714,plain,
! [SV1120: $i,SV518: $i] :
( ( ! [SY5715: $i] :
( ! [SY5716: $i] :
( ( c_Com_Ocom_OAss @ SV518 @ SV1120 )
!= ( c_Com_Ocom_OAss @ SY5715 @ SY5716 ) )
| ( SV518 = SY5715 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3042]) ).
thf(3715,plain,
! [SV1121: $i,SV519: $i] :
( ( ! [SY5717: $i,SY5718: $i] :
( ( c_Set_Oinsert @ SV519 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1121 @ tc_bool ) ) @ SY5717 @ SV1121 @ ( tc_fun @ SY5718 @ tc_bool ) ) @ SY5718 )
= ( c_Set_Oinsert @ SV519 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5718 @ tc_bool ) ) @ SY5718 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3043]) ).
thf(3716,plain,
! [SV1122: $i,SV520: $i] :
( ( ( c_Com_Ocom_OSemi @ SV520 @ SV1122 )
!= c_Com_Ocom_OSKIP )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3044]) ).
thf(3717,plain,
! [SV1123: $i,SV521: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV521 @ tc_bool ) )
!= ( c_Collect @ SV1123 @ SV521 ) )
| ! [SY5719: $i] :
~ ( hBOOL @ ( hAPP @ SV1123 @ SY5719 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3045]) ).
thf(3718,plain,
! [SV1124: $i,SV522: $i] :
( ( ! [SY5720: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV522 @ SV1124 @ SY5720 ) @ SV522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3046]) ).
thf(3719,plain,
! [SV523: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV523 ) )
= $true )
| ( ( ! [SY4260: $i,SY4261: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY4260 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4260 @ SY4261 @ SV523 ) @ SV523 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY4260 @ SY4261 @ SV523 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3047]) ).
thf(3720,plain,
! [SV524: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV524 ) )
= $true )
| ( ( ! [SY4262: $i,SY4263: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY4262 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4262 @ SY4263 @ SV524 ) @ SV524 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY4262 @ SY4263 @ SV524 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3048]) ).
thf(3721,plain,
! [SV1125: $i,SV525: $i] :
( ( ! [SY5721: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV525 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV525 @ SV1125 @ ( tc_fun @ SY5721 @ tc_bool ) ) @ ( tc_fun @ SY5721 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV525 @ SV1125 @ ( tc_fun @ SY5721 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3049]) ).
thf(3722,plain,
! [SV1126: $i,SV526: $i] :
( ( ! [SY5722: $i,SY5723: $i,SY5724: $i,SY5725: $i] :
( ( ( c_Com_Ocom_OLocal @ SV526 @ SV1126 @ SY5722 )
!= ( c_Com_Ocom_OLocal @ SY5723 @ SY5724 @ SY5725 ) )
| ( SY5722 = SY5725 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3050]) ).
thf(3723,plain,
! [SV1127: $i,SV527: $i] :
( ( ! [SY5726: $i,SY5727: $i,SY5728: $i] :
( ! [SY5729: $i] :
( ( c_Com_Ocom_OLocal @ SV527 @ SV1127 @ SY5726 )
!= ( c_Com_Ocom_OLocal @ SY5727 @ SY5728 @ SY5729 ) )
| ( SV1127 = SY5728 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3051]) ).
thf(3724,plain,
! [SV1128: $i,SV528: $i] :
( ( ! [SY5730: $i,SY5731: $i] :
( ! [SY5732: $i,SY5733: $i] :
( ( c_Com_Ocom_OLocal @ SV528 @ SV1128 @ SY5730 )
!= ( c_Com_Ocom_OLocal @ SY5731 @ SY5732 @ SY5733 ) )
| ( SV528 = SY5731 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3052]) ).
thf(3725,plain,
! [SV1129: $i,SV529: $i] :
( ( ! [SY5734: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV529 @ SV1129 @ ( tc_fun @ SY5734 @ tc_bool ) ) @ SY5734 )
| ! [SY5735: $i] :
~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV529 @ ( c_Set_Oinsert @ SY5735 @ SV1129 @ SY5734 ) @ ( tc_fun @ SY5734 @ tc_bool ) ) @ SY5734 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3053]) ).
thf(3726,plain,
! [SV1130: $i,SV530: $i] :
( ( ! [SY5736: $i,SY5737: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV530 @ ( c_Set_Oinsert @ SV1130 @ SY5736 @ SY5737 ) @ ( tc_fun @ SY5737 @ tc_bool ) ) @ SY5737 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV530 @ SY5736 @ ( tc_fun @ SY5737 @ tc_bool ) ) @ SY5737 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3054]) ).
thf(3727,plain,
! [SV1131: $i,SV531: $i] :
( ( ! [SY5738: $i,SY5739: $i] :
( ( c_Com_Ocom_OWhile @ SV531 @ SV1131 )
!= ( c_Com_Ocom_OSemi @ SY5738 @ SY5739 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3055]) ).
thf(3728,plain,
! [SV1132: $i,SV532: $i] :
( ( ! [SY5740: $i,SY5741: $i,SY5742: $i,SY5743: $i,SY5744: $i] :
( ( ( hAPP @ SV532 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1132 @ tc_bool ) ) )
= SY5740 )
| ! [SY5745: $i,SY5746: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY5741 @ SV532 @ SY5742 @ SY5743 @ SY5744 @ SY5745 @ SY5740 @ SY5746 @ SV1132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3056]) ).
thf(3729,plain,
! [SV1133: $i,SV533: $i] :
( ( ! [SY5747: $i,SY5748: $i,SY5749: $i,SY5750: $i,SY5751: $i] :
( ( ( hAPP @ SV533 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1133 @ tc_bool ) ) )
= SY5747 )
| ! [SY5752: $i,SY5753: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV533 @ SY5748 @ SY5749 @ SY5750 @ SY5751 @ SY5752 @ SY5753 @ SY5747 @ SV1133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3057]) ).
thf(3730,plain,
! [SV1134: $i,SV534: $i] :
( ( ( hBOOL @ ( hAPP @ SV534 @ SV1134 ) )
| ! [SY5754: $i] :
( ( SY5754 = SV1134 )
| ! [SY5755: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV534 @ SY5755 ) ) @ SV1134 ) @ SY5754 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3058]) ).
thf(3731,plain,
! [SV1135: $i,SV535: $i] :
( ( ! [SY5756: $i] :
( ( ( c_Set_Oinsert @ SV535 @ ( c_HOL_Ominus__class_Ominus @ SV1135 @ ( c_Set_Oinsert @ SV535 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5756 @ tc_bool ) ) @ SY5756 ) @ ( tc_fun @ SY5756 @ tc_bool ) ) @ SY5756 )
= SV1135 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5756 ) @ SV535 ) @ SV1135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3059]) ).
thf(3732,plain,
! [SV536: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV536 ) )
= $true )
| ( ( ! [SY4311: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY4311 @ SY4311 @ SV536 )
= SY4311 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3060]) ).
thf(3733,plain,
! [SV1136: $i,SV537: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV537 @ SV537 @ ( tc_fun @ SV1136 @ tc_bool ) )
= SV537 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3061]) ).
thf(3734,plain,
! [SV1137: $i,SV538: $i] :
( ( ! [SY5757: $i] :
( ! [SY5758: $i] :
( ( c_Set_Oimage @ SV538 @ SV1137 @ SY5757 @ SY5758 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5758 @ tc_bool ) ) )
| ( SV1137
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5757 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3062]) ).
thf(3735,plain,
! [SV1138: $i,SV539: $i] :
( ( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ SV539 ) @ SV539 @ SV539 @ tc_bool ) @ SV1138 ) @ SV539 )
= ( c_Set_Oinsert @ SV1138 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV539 @ tc_bool ) ) @ SV539 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3063]) ).
thf(3736,plain,
! [SV1139: $i,SV540: $i] :
( ( ! [SY5759: $i,SY5760: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ SV1139 @ ( tc_fun @ SY5759 @ tc_bool ) ) @ SY5760 @ ( tc_fun @ SY5759 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ ( c_HOL_Ominus__class_Ominus @ SV1139 @ SY5760 @ ( tc_fun @ SY5759 @ tc_bool ) ) @ ( tc_fun @ SY5759 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3064]) ).
thf(3737,plain,
! [SV1140: $i,SV541: $i] :
( ( ! [SY5761: $i,SY5762: $i,SY5763: $i,SY5764: $i,SY5765: $i,SY5766: $i] :
( ( ( hAPP @ SV541 @ ( c_Set_Oinsert @ SV1140 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5761 @ tc_bool ) ) @ SY5761 ) )
= SV1140 )
| ! [SY4327: $i,SY4328: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY5762 @ SV541 @ SY5763 @ SY5764 @ SY5765 @ SY5766 @ SY4327 @ SY4328 @ SY5761 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3065]) ).
thf(3738,plain,
! [SV1141: $i,SV542: $i] :
( ( ! [SY5769: $i,SY5770: $i,SY5771: $i,SY5772: $i,SY5773: $i,SY5774: $i] :
( ( ( hAPP @ SV542 @ ( c_Set_Oinsert @ SV1141 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5769 @ tc_bool ) ) @ SY5769 ) )
= SV1141 )
| ! [SY4336: $i,SY4337: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV542 @ SY5770 @ SY5771 @ SY5772 @ SY5773 @ SY5774 @ SY4336 @ SY4337 @ SY5769 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3066]) ).
thf(3739,plain,
! [SV1142: $i,SV543: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV543 ) @ SV1142 ) @ ( c_Set_Oinsert @ SV1142 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV543 @ tc_bool ) ) @ SV543 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3067]) ).
thf(3740,plain,
! [SV1143: $i,SV544: $i] :
( ( ! [SY5777: $i] :
( ( c_Com_Ocom_OWhile @ SV544 @ SV1143 )
!= ( c_Com_Ocom_OBODY @ SY5777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3068]) ).
thf(3741,plain,
! [SV1144: $i,SV545: $i] :
( ( ! [SY5778: $i,SY5779: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1144 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5778 @ ( c_Collect @ SY5779 @ SV545 ) @ ( tc_fun @ SV545 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SY5779 @ SV1144 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1144 ) @ SY5778 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3069]) ).
thf(3742,plain,
! [SV546: $i] :
( ( ( c_Com_Ocom_OBODY @ SV546 )
= c_Com_Ocom_OSKIP )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3070]) ).
thf(3743,plain,
! [SV1145: $i,SV547: $i] :
( ( ! [SY5780: $i] :
( ( hBOOL @ ( hAPP @ SV547 @ ( hAPP @ SV1145 @ SY5780 ) ) )
| ! [SY5781: $i,SY5782: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV1145 @ SV547 @ SY5781 @ SY5782 ) @ SY5780 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3071]) ).
thf(3744,plain,
! [SV1146: $i,SV548: $i] :
( ( ! [SY5783: $i,SY5784: $i,SY5785: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV548 @ SV1146 @ SY5783 @ SY5784 ) @ SY5785 ) )
| ~ ( hBOOL @ ( hAPP @ SV1146 @ ( hAPP @ SV548 @ SY5785 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3072]) ).
thf(3745,plain,
! [SV1147: $i,SV549: $i] :
( ( ! [SY5786: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV549 @ SV1147 @ SY5786 )
| ! [SY5787: $i] :
~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV549 @ ( c_Set_Oinsert @ SY5787 @ SV1147 @ ( tc_Hoare__Mirabelle_Otriple @ SY5786 ) ) @ SY5786 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3073]) ).
thf(3746,plain,
! [SV1148: $i,SV550: $i] :
( ( ! [SY5788: $i,SY5789: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV550 @ ( c_Set_Oinsert @ SV1148 @ SY5788 @ ( tc_Hoare__Mirabelle_Otriple @ SY5789 ) ) @ SY5789 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV550 @ SY5788 @ SY5789 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV550 @ ( c_Set_Oinsert @ SV1148 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY5789 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY5789 ) ) @ SY5789 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3074]) ).
thf(3747,plain,
! [SV1149: $i,SV551: $i] :
( ( ! [SY5790: $i,SY5791: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV551 @ SV1149 @ ( tc_fun @ SY5790 @ tc_bool ) ) @ SY5791 ) )
| ~ ( hBOOL @ ( hAPP @ SV1149 @ SY5791 ) )
| ~ ( hBOOL @ ( hAPP @ SV551 @ SY5791 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3075]) ).
thf(3748,plain,
! [SV1150: $i,SV552: $i] :
( ( ! [SY5792: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV552 )
| ! [SY5793: $i,SY5794: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV1150 @ SY5792 @ SV552 )
!= ( c_HOL_Ominus__class_Ominus @ SY5793 @ SY5794 @ SV552 ) )
| ( c_HOL_Oord__class_Oless @ SY5793 @ SY5794 @ SV552 )
| ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SY5792 @ SV552 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3076]) ).
thf(3749,plain,
! [SV1151: $i,SV553: $i] :
( ( ! [SY5795: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV553 )
| ! [SY5796: $i,SY5797: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV1151 @ SY5795 @ SV553 )
!= ( c_HOL_Ominus__class_Ominus @ SY5796 @ SY5797 @ SV553 ) )
| ( c_HOL_Oord__class_Oless @ SV1151 @ SY5795 @ SV553 )
| ~ ( c_HOL_Oord__class_Oless @ SY5796 @ SY5797 @ SV553 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3077]) ).
thf(3750,plain,
! [SV1152: $i,SV554: $i] :
( ( ( c_Com_Ocom_OAss @ SV554 @ SV1152 )
!= c_Com_Ocom_OSKIP )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3078]) ).
thf(3751,plain,
! [SV1153: $i,SV555: $i] :
( ( ( c_Collect @ ( hAPP @ ( c_fequal @ SV555 ) @ SV1153 ) @ SV555 )
= ( c_Set_Oinsert @ SV1153 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV555 @ tc_bool ) ) @ SV555 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3079]) ).
thf(3752,plain,
! [SV1154: $i,SV556: $i] :
( ( ( c_Finite__Set_Ofinite @ SV556 @ SV1154 )
| ! [SY5798: $i,SY5799: $i] :
( ~ ( c_Fun_Oinj__on @ SY5798 @ SV556 @ SV1154 @ SY5799 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SY5798 @ SV556 @ SV1154 @ SY5799 ) @ SY5799 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3080]) ).
thf(3753,plain,
! [SV1155: $i,SV557: $i] :
( ( ! [SY5800: $i] :
( ( c_Set_Ovimage @ SV557 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1155 @ tc_bool ) ) @ SY5800 @ SV1155 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5800 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3081]) ).
thf(3754,plain,
! [SV1156: $i,SV558: $i] :
( ( ! [SY5801: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV558 ) @ SV1156 ) @ SY5801 ) )
| ! [SY5802: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY5802 ) @ SV1156 ) @ SY5801 ) )
| ! [SY5803: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY5803 @ SY5802 @ SV558 ) ) @ SV1156 ) @ SY5801 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3082]) ).
thf(3755,plain,
! [SV1157: $i,SV559: $i] :
( ( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_in @ SV559 ) @ SV559 @ ( tc_fun @ SV559 @ tc_bool ) @ tc_bool ) @ SV1157 ) @ SV559 )
= SV1157 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3083]) ).
thf(3756,plain,
! [SV1158: $i,SV560: $i] :
( ( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ SV560 @ SV1158 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3084]) ).
thf(3757,plain,
! [SV561: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV561 ) )
= $true )
| ( ( ! [SY4382: $i,SY4383: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY4382 @ SY4383 @ SV561 )
| ~ ( c_HOL_Oord__class_Oless @ SY4383 @ SY4382 @ SV561 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3085]) ).
thf(3758,plain,
! [SV562: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV562 ) )
= $true )
| ( ( ! [SY4384: $i,SY4385: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY4384 @ SY4385 @ SV562 )
| ~ ( c_HOL_Oord__class_Oless @ SY4385 @ SY4384 @ SV562 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3086]) ).
thf(3759,plain,
! [SV563: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV563 ) )
= $true )
| ( ( ! [SY4386: $i,SY4387: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY4386 @ SY4387 @ SV563 )
| ~ ( c_HOL_Oord__class_Oless @ SY4387 @ SY4386 @ SV563 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3087]) ).
thf(3760,plain,
! [SV564: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV564 ) )
= $true )
| ( ( ! [SY4388: $i,SY4389: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY4388 @ SY4389 @ SV564 )
| ~ ( c_HOL_Oord__class_Oless @ SY4389 @ SY4388 @ SV564 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3088]) ).
thf(3761,plain,
! [SV1159: $i,SV565: $i] :
( ( ! [SY5804: $i] :
( ( hBOOL @ ( hAPP @ SV565 @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ SV1159 @ SV565 @ SY5804 ) ) )
| ! [SY5805: $i] :
( ~ ( hBOOL @ ( hAPP @ SV565 @ SY5805 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5804 ) @ SY5805 ) @ SV1159 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3089]) ).
thf(3762,plain,
! [SV1160: $i,SV566: $i] :
( ( ! [SY5806: $i,SY5807: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV566 @ SV1160 ) @ SY5806 ) )
| ! [SY5808: $i,SY5809: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5807 ) @ SY5806 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SY5808 @ SV566 @ SV1160 @ SY5809 @ SY5807 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3090]) ).
thf(3763,plain,
! [SV1161: $i,SV567: $i] :
( ( ! [SY5810: $i,SY5811: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV567 @ SV1161 ) @ SY5810 ) )
| ! [SY5812: $i,SY5813: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5811 ) @ SV1161 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV567 @ SY5812 @ SY5813 @ SY5810 @ SY5811 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3091]) ).
thf(3764,plain,
! [SV1162: $i,SV568: $i] :
( ( ! [SY5814: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV568 ) @ SV1162 ) @ SY5814 ) )
| ! [SY5815: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV568 ) @ SV1162 ) @ SY5815 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY5815 @ SY5814 @ ( tc_fun @ SV568 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3092]) ).
thf(3765,plain,
! [SV1163: $i,SV569: $i] :
( ( ! [SY5816: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV569 ) @ SV1163 ) @ ( c_Set_Oinsert @ SV1163 @ SY5816 @ SV569 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3093]) ).
thf(3766,plain,
! [SV1164: $i,SV570: $i] :
( ( ! [SY5817: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV570 ) @ SV1164 ) @ ( c_Set_Oinsert @ SV1164 @ SY5817 @ SV570 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3094]) ).
thf(3767,plain,
! [SV1165: $i,SV571: $i] :
( ( ! [SY5818: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV571 ) @ SV1165 ) @ ( c_Set_Oinsert @ SV1165 @ SY5818 @ SV571 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3095]) ).
thf(3768,plain,
! [SV1166: $i,SV572: $i] :
( ( ! [SY5819: $i] :
( ( hBOOL @ ( hAPP @ SV572 @ SV1166 ) )
| ! [SY5820: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5819 ) @ SV1166 ) @ SY5820 ) )
| ~ ( hBOOL @ ( hAPP @ SV572 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY5820 @ SV572 @ SY5819 ) ) )
| ! [V_P: $i] :
~ ( hBOOL @ ( hAPP @ V_P @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY5820 @ V_P @ SY5819 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3096]) ).
thf(3769,plain,
! [SV1167: $i,SV573: $i] :
( ( ! [SY5822: $i] :
( ( hBOOL @ ( hAPP @ SV573 @ SV1167 ) )
| ! [SY5823: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5822 ) @ SV1167 ) @ SY5823 ) )
| ! [V_Q: $i] :
~ ( hBOOL @ ( hAPP @ V_Q @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY5823 @ V_Q @ SY5822 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV573 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY5823 @ SV573 @ SY5822 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3097]) ).
thf(3770,plain,
! [SV1168: $i,SV574: $i] :
( ( ! [SY5825: $i] :
( ( hBOOL @ ( hAPP @ SV574 @ SV1168 ) )
| ! [SY5826: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5825 ) @ SV1168 ) @ SY5826 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5825 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY5826 @ SV574 @ SY5825 ) ) @ SY5826 ) )
| ! [V_P: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5825 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY5826 @ V_P @ SY5825 ) ) @ SY5826 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3098]) ).
thf(3771,plain,
! [SV1169: $i,SV575: $i] :
( ( ! [SY5828: $i] :
( ( hBOOL @ ( hAPP @ SV575 @ SV1169 ) )
| ! [SY5829: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5828 ) @ SV1169 ) @ SY5829 ) )
| ! [V_Q: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5828 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY5829 @ V_Q @ SY5828 ) ) @ SY5829 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5828 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY5829 @ SV575 @ SY5828 ) ) @ SY5829 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3099]) ).
thf(3772,plain,
! [SV1170: $i,SV576: $i] :
( ( ! [SY5831: $i] :
( ( hBOOL @ ( hAPP @ SV576 @ SV1170 ) )
| ! [SY5832: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5831 ) @ SV1170 ) @ SY5832 ) )
| ! [SY4431: $i] :
( ~ ( hBOOL @ ( hAPP @ SV576 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SY5832 @ SY4431 @ SV576 @ SY5831 ) ) )
| ~ ( hBOOL @ ( hAPP @ SY4431 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SY5832 @ SY4431 @ SV576 @ SY5831 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3100]) ).
thf(3773,plain,
! [SV1171: $i,SV577: $i] :
( ( ! [SY5834: $i] :
( ( hBOOL @ ( hAPP @ SV577 @ SV1171 ) )
| ! [SY5835: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5834 ) @ SV1171 ) @ SY5835 ) )
| ! [SY4435: $i] :
( ~ ( hBOOL @ ( hAPP @ SY4435 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SY5835 @ SV577 @ SY4435 @ SY5834 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV577 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SY5835 @ SV577 @ SY4435 @ SY5834 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3101]) ).
thf(3774,plain,
! [SV1172: $i,SV578: $i] :
( ( ! [SY5837: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV578 ) @ SV1172 ) @ SY5837 ) )
| ! [SY5838: $i] :
( ( hBOOL @ ( hAPP @ SY5838 @ SV1172 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV578 ) @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ SY5837 @ SY5838 @ SV578 ) ) @ SY5837 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3102]) ).
thf(3775,plain,
! [SV1173: $i,SV579: $i] :
( ( ! [SY5839: $i] :
( ( hBOOL @ ( hAPP @ SV579 @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1173 @ SV579 @ SY5839 ) ) )
| ! [SY5840: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5839 ) @ SY5840 ) @ SV1173 ) )
| ~ ( hBOOL @ ( hAPP @ SV579 @ SY5840 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3103]) ).
thf(3776,plain,
! [SV1174: $i,SV580: $i] :
( ( ! [SY5841: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV580 @ SV1174 ) @ SY5841 ) )
| ! [SY5842: $i,SY5843: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5842 ) @ SY5841 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV580 @ SV1174 @ SY5843 @ SY5842 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3104]) ).
thf(3777,plain,
! [SV1175: $i,SV581: $i] :
( ( ! [SY5844: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV581 @ SV1175 ) @ SY5844 ) )
| ! [SY5845: $i,SY5846: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5845 ) @ SV1175 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV581 @ SY5846 @ SY5844 @ SY5845 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3105]) ).
thf(3778,plain,
! [SV1176: $i,SV582: $i] :
( ( ! [SY5847: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV582 ) @ SV1176 ) @ SY5847 ) )
| ! [SY5848: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV582 ) @ SV1176 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5848 @ SY5847 @ ( tc_fun @ SV582 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3106]) ).
thf(3779,plain,
! [SV1177: $i,SV583: $i] :
( ( ! [SY5849: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV583 ) @ SV1177 ) @ SY5849 ) )
| ! [SY5850: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV583 ) @ SV1177 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5849 @ SY5850 @ ( tc_fun @ SV583 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3107]) ).
thf(3780,plain,
! [SV1178: $i,SV584: $i] :
( ( ! [SY5851: $i,SY5852: $i] :
( ( ( hAPP @ SV584 @ SV1178 )
!= ( hAPP @ SV584 @ SY5851 ) )
| ! [SY5853: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5852 ) @ SY5851 ) @ SY5853 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5852 ) @ SV1178 ) @ SY5853 ) )
| ( SV1178 = SY5851 )
| ! [SY4460: $i] :
~ ( c_Fun_Oinj__on @ SV584 @ SY5853 @ SY5852 @ SY4460 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3108]) ).
thf(3781,plain,
! [SV1179: $i,SV585: $i] :
( ( ! [SY5855: $i,SY5856: $i] :
( ( ( hAPP @ SV585 @ SV1179 )
!= ( hAPP @ SV585 @ SY5855 ) )
| ! [SY5857: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5856 ) @ SY5855 ) @ SY5857 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5856 ) @ SV1179 ) @ SY5857 ) )
| ! [SY4465: $i] :
~ ( c_Fun_Oinj__on @ SV585 @ SY5857 @ SY5856 @ SY4465 )
| ( SV1179 = SY5855 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3109]) ).
thf(3782,plain,
! [SV1180: $i,SV586: $i] :
( ( ! [SY5859: $i,SY5860: $i] :
( ( ( hAPP @ SV586 @ SV1180 )
!= ( hAPP @ SV586 @ SY5859 ) )
| ! [SY5861: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5860 ) @ SY5859 ) @ SY5861 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5860 ) @ SV1180 ) @ SY5861 ) )
| ! [SY4470: $i] :
~ ( c_Fun_Oinj__on @ SV586 @ SY5861 @ SY5860 @ SY4470 )
| ( SV1180 = SY5859 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3110]) ).
thf(3783,plain,
! [SV1181: $i,SV587: $i] :
( ( ! [SY5863: $i,SY5864: $i] :
( ( ( hAPP @ SV587 @ SV1181 )
!= ( hAPP @ SV587 @ SY5863 ) )
| ! [SY5865: $i] :
( ! [SY4475: $i] :
~ ( c_Fun_Oinj__on @ SV587 @ SY5864 @ SY5865 @ SY4475 )
| ( SV1181 = SY5863 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5865 ) @ SY5863 ) @ SY5864 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5865 ) @ SV1181 ) @ SY5864 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3111]) ).
thf(3784,plain,
! [SV1182: $i,SV588: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV588 @ SV1182 ) )
| ! [SY5867: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5867 ) @ SV1182 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5867 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3112]) ).
thf(3785,plain,
! [SV1183: $i,SV589: $i] :
( ( ! [SY5868: $i] :
( ( ( hAPP @ ( c_COMBC @ ( c_in @ SV589 ) @ SV589 @ ( tc_fun @ SV589 @ tc_bool ) @ tc_bool ) @ SV1183 )
!= ( hAPP @ ( c_COMBC @ ( c_in @ SV589 ) @ SV589 @ ( tc_fun @ SV589 @ tc_bool ) @ tc_bool ) @ SY5868 ) )
| ( SV1183 = SY5868 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3113]) ).
thf(3786,plain,
! [SV1184: $i,SV590: $i] :
( ( ! [SY5869: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV590 ) @ SV1184 ) @ ( c_Collect @ SY5869 @ SV590 ) ) )
| ~ ( hBOOL @ ( hAPP @ SY5869 @ SV1184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3114]) ).
thf(3787,plain,
! [SV1185: $i,SV591: $i] :
( ( ( hBOOL @ ( hAPP @ SV591 @ SV1185 ) )
| ! [SY5870: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5870 ) @ SV1185 ) @ ( c_Collect @ SV591 @ SY5870 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3115]) ).
thf(3788,plain,
! [SV1186: $i,SV592: $i] :
( ( ! [SY5871: $i,SY5872: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV592 ) @ SV1186 ) @ ( c_SetInterval_Oord_OatMost @ SY5871 @ SY5872 @ SV592 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY5871 @ SV1186 ) @ SY5872 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3116]) ).
thf(3789,plain,
! [SV1187: $i,SV593: $i] :
( ( ! [SY5873: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV593 @ SV1187 ) @ SY5873 ) )
| ! [SY5874: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5874 ) @ SV1187 ) @ ( c_SetInterval_Oord_OatMost @ SV593 @ SY5873 @ SY5874 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3117]) ).
thf(3790,plain,
! [SV1188: $i,SV594: $i] :
( ( ! [SY5875: $i,SY5876: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV594 ) @ SV1188 ) @ ( c_HOL_Ominus__class_Ominus @ SY5875 @ SY5876 @ ( tc_fun @ SV594 @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV594 ) @ SV1188 ) @ SY5876 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV594 ) @ SV1188 ) @ SY5875 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3118]) ).
thf(3791,plain,
! [SV1189: $i,SV595: $i] :
( ( ! [SY5877: $i,SY5878: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV595 ) @ SV1189 ) @ ( c_HOL_Ominus__class_Ominus @ SY5877 @ SY5878 @ ( tc_fun @ SV595 @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV595 ) @ SV1189 ) @ SY5878 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV595 ) @ SV1189 ) @ SY5877 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3119]) ).
thf(3792,plain,
! [SV1190: $i,SV596: $i] :
( ( ! [SY5879: $i] :
( ( hBOOL @ ( hAPP @ SV596 @ SV1190 ) )
| ! [SY5880: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5879 ) @ SV1190 ) @ SY5880 ) )
| ! [SY4499: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5879 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SY5880 @ SY4499 @ SV596 @ SY5879 ) ) @ SY5880 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3120]) ).
thf(3793,plain,
! [SV1191: $i,SV597: $i] :
( ( ! [SY5882: $i] :
( ( hBOOL @ ( hAPP @ SV597 @ SV1191 ) )
| ! [SY5883: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5882 ) @ SV1191 ) @ SY5883 ) )
| ! [SY4503: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5882 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SY5883 @ SV597 @ SY4503 @ SY5882 ) ) @ SY5883 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3121]) ).
thf(3794,plain,
! [SV1192: $i,SV598: $i] :
( ( ! [SY5885: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV598 ) @ SV1192 ) @ SY5885 ) )
| ! [SY5886: $i] :
( ( hBOOL @ ( hAPP @ SY5886 @ SV1192 ) )
| ~ ( hBOOL @ ( hAPP @ SY5886 @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ SY5885 @ SY5886 @ SV598 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3122]) ).
thf(3795,plain,
! [SV1193: $i,SV599: $i] :
( ( ! [SY5887: $i,SY5888: $i] :
( ( ( c_Set_Oinsert @ SV599 @ SV1193 @ SY5887 )
!= ( c_Set_Oinsert @ SV599 @ SY5888 @ SY5887 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5887 ) @ SV599 ) @ SY5888 ) )
| ( SV1193 = SY5888 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5887 ) @ SV599 ) @ SV1193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3123]) ).
thf(3796,plain,
! [SV1194: $i,SV600: $i] :
( ( ! [SY5889: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV600 ) @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ SV1194 @ SY5889 @ SV600 ) ) @ SV1194 ) )
| ! [SY5890: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV600 ) @ SY5890 ) @ SV1194 ) )
| ~ ( hBOOL @ ( hAPP @ SY5889 @ SY5890 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3124]) ).
thf(3797,plain,
! [SV1195: $i,SV601: $i] :
( ( ! [SY5891: $i,SY5892: $i,SY5893: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV601 ) @ SV1195 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY5891 @ SY5892 @ SY5893 @ ( tc_fun @ SV601 @ tc_bool ) ) ) )
| ! [SY5894: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV601 ) @ SV1195 ) @ ( hAPP @ SY5892 @ SY5894 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5893 ) @ SY5894 ) @ SY5891 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3125]) ).
thf(3798,plain,
! [SV1196: $i,SV602: $i] :
( ( ! [SY5895: $i,SY5896: $i,SY5897: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV602 ) @ SV1196 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY5895 @ SY5896 @ SY5897 @ ( tc_fun @ SV602 @ tc_bool ) ) ) )
| ! [SY5898: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV602 ) @ SV1196 ) @ ( hAPP @ SY5896 @ SY5898 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5897 ) @ SY5898 ) @ SY5895 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3126]) ).
thf(3799,plain,
! [SV1197: $i,SV603: $i] :
( ( ! [SY5899: $i,SY5900: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV603 ) @ SV1197 ) @ ( c_SetInterval_Oord_OgreaterThan @ SY5899 @ SY5900 @ SV603 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY5899 @ SY5900 ) @ SV1197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3127]) ).
thf(3800,plain,
! [SV1198: $i,SV604: $i] :
( ( ! [SY5901: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV604 @ SV1198 ) @ SY5901 ) )
| ! [SY5902: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5902 ) @ SY5901 ) @ ( c_SetInterval_Oord_OgreaterThan @ SV604 @ SV1198 @ SY5902 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3128]) ).
thf(3801,plain,
! [SV1199: $i,SV605: $i] :
( ( ! [SY5903: $i,SY5904: $i,SY5905: $i] :
( ( hBOOL @ ( hAPP @ SV605 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SV1199 @ SY5903 @ SV605 @ SY5904 @ SY5905 ) ) )
| ! [SY5906: $i] :
( ~ ( hBOOL @ ( hAPP @ SV605 @ SY5906 ) )
| ! [SY5907: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5905 ) @ SY5906 ) @ ( hAPP @ SY5903 @ SY5907 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5904 ) @ SY5907 ) @ SV1199 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3129]) ).
thf(3802,plain,
! [SV1200: $i,SV606: $i] :
( ( ! [SY5908: $i,SY5909: $i,SY5910: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV606 ) @ SV1200 ) @ ( c_Set_Ovimage @ SY5908 @ SY5909 @ SV606 @ SY5910 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5910 ) @ ( hAPP @ SY5908 @ SV1200 ) ) @ SY5909 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3130]) ).
thf(3803,plain,
! [SV1201: $i,SV607: $i] :
( ( ! [SY5911: $i,SY5912: $i,SY5913: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV607 ) @ SV1201 ) @ ( c_Set_Ovimage @ SY5911 @ SY5912 @ SV607 @ SY5913 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5913 ) @ ( hAPP @ SY5911 @ SV1201 ) ) @ SY5912 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3131]) ).
thf(3804,plain,
! [SV1202: $i,SV608: $i] :
( ( ! [SY5914: $i,SY5915: $i,SY5916: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV608 ) @ SV1202 ) @ ( c_Set_Ovimage @ SY5914 @ SY5915 @ SV608 @ SY5916 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5916 ) @ ( hAPP @ SY5914 @ SV1202 ) ) @ SY5915 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3132]) ).
thf(3805,plain,
! [SV1203: $i,SV609: $i] :
( ( ! [SY5917: $i,SY5918: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV609 ) @ ( hAPP @ SV1203 @ SY5917 ) ) @ SY5918 ) )
| ! [SY5919: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5919 ) @ SY5917 ) @ ( c_Set_Ovimage @ SV1203 @ SY5918 @ SY5919 @ SV609 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3133]) ).
thf(3806,plain,
! [SV1204: $i,SV610: $i] :
( ( ! [SY5920: $i,SY5921: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV610 ) @ ( hAPP @ SV1204 @ SY5920 ) ) @ SY5921 ) )
| ! [SY5922: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5922 ) @ SY5920 ) @ ( c_Set_Ovimage @ SV1204 @ SY5921 @ SY5922 @ SV610 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3134]) ).
thf(3807,plain,
! [SV1205: $i,SV611: $i] :
( ( ! [SY5923: $i,SY5924: $i,SY5925: $i,SY5926: $i,SY5927: $i,SY5928: $i,SY5929: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV611 @ ( hAPP @ SV1205 @ SY5923 ) ) @ SY5924 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5925 ) @ SY5924 ) @ SY5923 ) )
| ! [SY5930: $i,SY5931: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1205 @ SY5926 @ SV611 @ SY5927 @ SY5928 @ SY5929 @ SY5930 @ SY5931 @ SY5925 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3135]) ).
thf(3808,plain,
! [SV1206: $i,SV612: $i] :
( ( ! [SY5932: $i,SY5933: $i,SY5934: $i,SY5935: $i,SY5936: $i,SY5937: $i,SY5938: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV612 @ SV1206 ) @ ( hAPP @ SY5932 @ SY5933 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5934 ) @ SV1206 ) @ SY5933 ) )
| ! [SY4573: $i,SY4574: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY5935 @ SY5932 @ SV612 @ SY5936 @ SY5937 @ SY5938 @ SY4573 @ SY4574 @ SY5934 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3136]) ).
thf(3809,plain,
! [SV1207: $i,SV613: $i] :
( ( ! [SY5941: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV613 @ SV1207 ) @ SY5941 ) )
| ! [SY5942: $i,SY5943: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5942 ) @ SV1207 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV613 @ SY5943 @ SY5941 @ SY5942 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3137]) ).
thf(3810,plain,
! [SV1208: $i,SV614: $i] :
( ( ! [SY5944: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV614 @ SV1208 ) @ SY5944 ) )
| ! [SY5945: $i,SY5946: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5945 ) @ SY5944 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV614 @ SV1208 @ SY5946 @ SY5945 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3138]) ).
thf(3811,plain,
! [SV1209: $i,SV615: $i] :
( ( ! [SY5947: $i,SY5948: $i] :
( ( hBOOL @ ( hAPP @ SV615 @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV1209 @ SY5947 @ SV615 @ SY5948 ) ) )
| ! [SY4586: $i] :
( ~ ( hBOOL @ ( hAPP @ SV615 @ SY4586 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5948 ) @ SY4586 ) @ SY5947 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3139]) ).
thf(3812,plain,
! [SV1210: $i,SV616: $i] :
( ( ! [SY5950: $i,SY5951: $i] :
( ( hBOOL @ ( hAPP @ SV616 @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV1210 @ SY5950 @ SV616 @ SY5951 ) ) )
| ! [SY5952: $i] :
( ~ ( hBOOL @ ( hAPP @ SV616 @ SY5952 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5951 ) @ SY5952 ) @ SV1210 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3140]) ).
thf(3813,plain,
! [SV1211: $i,SV617: $i] :
( ( ! [SY5953: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV617 ) @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ SV1211 @ SY5953 @ SV617 ) ) @ SV1211 ) )
| ! [SY5954: $i] :
( ~ ( hBOOL @ ( hAPP @ SY5953 @ SY5954 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV617 ) @ SY5954 ) @ SV1211 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3141]) ).
thf(3814,plain,
! [SV1212: $i,SV618: $i] :
( ( ! [SY5955: $i] :
( ( ( c_Set_Oinsert @ SV618 @ SV1212 @ SY5955 )
= SV1212 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5955 ) @ SV618 ) @ SV1212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3142]) ).
thf(3815,plain,
! [SV1213: $i,SV619: $i] :
( ( ! [SY5956: $i,SY5957: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV619 ) @ SV1213 ) @ ( c_SetInterval_Oord_OlessThan @ SY5956 @ SY5957 @ SV619 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY5956 @ SV1213 ) @ SY5957 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3143]) ).
thf(3816,plain,
! [SV1214: $i,SV620: $i] :
( ( ! [SY5958: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV620 @ SV1214 ) @ SY5958 ) )
| ! [SY5959: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5959 ) @ SV1214 ) @ ( c_SetInterval_Oord_OlessThan @ SV620 @ SY5958 @ SY5959 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3144]) ).
thf(3817,plain,
! [SV1215: $i,SV621: $i] :
( ( ! [SY5960: $i,SY5961: $i,SY5962: $i,SY5963: $i,SY5964: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV621 @ SV1215 @ SY5960 @ ( tc_fun @ SY5961 @ ( tc_fun @ SY5962 @ tc_bool ) ) ) @ SY5963 ) @ SY5964 ) )
| ! [SY5965: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV1215 @ SY5965 ) @ SY5963 ) @ SY5964 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5960 ) @ SY5965 ) @ SV621 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3145]) ).
thf(3818,plain,
! [SV1216: $i,SV622: $i] :
( ( ! [SY5966: $i,SY5967: $i,SY5968: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV622 @ SV1216 @ SY5966 @ ( tc_fun @ SY5967 @ tc_bool ) ) @ SY5968 ) )
| ! [SY5969: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1216 @ SY5969 ) @ SY5968 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5966 ) @ SY5969 ) @ SV622 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3146]) ).
thf(3819,plain,
! [SV1217: $i,SV623: $i] :
( ( ! [SY5970: $i,SY5971: $i,SY5972: $i,SY5973: $i,SY5974: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV623 @ SV1217 @ SY5970 @ ( tc_fun @ SY5971 @ ( tc_fun @ SY5972 @ tc_bool ) ) ) @ SY5973 ) @ SY5974 ) )
| ! [SY5975: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV1217 @ SY5975 ) @ SY5973 ) @ SY5974 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5970 ) @ SY5975 ) @ SV623 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3147]) ).
thf(3820,plain,
! [SV1218: $i,SV624: $i] :
( ( ! [SY5976: $i,SY5977: $i,SY5978: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV624 @ SV1218 @ SY5976 @ ( tc_fun @ SY5977 @ tc_bool ) ) @ SY5978 ) )
| ! [SY5979: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1218 @ SY5979 ) @ SY5978 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5976 ) @ SY5979 ) @ SV624 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3148]) ).
thf(3821,plain,
! [SV1219: $i,SV625: $i] :
( ( ! [SY5980: $i,SY5981: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SV1219 ) @ SY5980 ) )
| ! [SY5982: $i,SY5983: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5981 ) @ SV1219 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SY5982 @ SV625 @ SY5983 @ SY5980 @ SY5981 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3149]) ).
thf(3822,plain,
! [SV1220: $i,SV626: $i] :
( ( ! [SY5984: $i,SY5985: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV626 @ SV1220 ) @ SY5984 ) )
| ! [SY5986: $i,SY5987: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5985 ) @ SY5984 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV626 @ SY5986 @ SV1220 @ SY5987 @ SY5985 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3150]) ).
thf(3823,plain,
! [SV1221: $i,SV627: $i] :
( ( ! [SY5988: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV627 ) @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ SV1221 @ SY5988 @ SV627 ) ) @ SV1221 ) )
| ! [SY5989: $i] :
( ~ ( hBOOL @ ( hAPP @ SY5988 @ SY5989 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV627 ) @ SY5989 ) @ SV1221 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3151]) ).
thf(3824,plain,
! [SV1222: $i,SV628: $i] :
( ( ! [SY5990: $i] :
( ( hBOOL @ ( hAPP @ SV628 @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ SV1222 @ SV628 @ SY5990 ) ) )
| ! [SY5991: $i] :
( ~ ( hBOOL @ ( hAPP @ SV628 @ SY5991 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5990 ) @ SY5991 ) @ SV1222 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3152]) ).
thf(3825,plain,
! [SV1223: $i,SV629: $i] :
( ( ! [SY5992: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV629 ) @ SV1223 ) @ SY5992 ) )
| ! [SY5993: $i,SY5994: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5993 ) @ ( hAPP @ SY5994 @ SV1223 ) ) @ ( c_Set_Oimage @ SY5994 @ SY5992 @ SV629 @ SY5993 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3153]) ).
thf(3826,plain,
! [SV1224: $i,SV630: $i] :
( ( ! [SY5995: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV630 ) @ SV1224 ) @ SY5995 ) )
| ! [SY5996: $i,SY5997: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5996 ) @ ( hAPP @ SY5997 @ SV1224 ) ) @ ( c_Set_Oimage @ SY5997 @ SY5995 @ SV630 @ SY5996 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3154]) ).
thf(3827,plain,
! [SV1225: $i,SV631: $i] :
( ( ! [SY5998: $i,SY5999: $i,SY6000: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV631 ) @ ( hAPP @ SV1225 @ SY5998 ) ) @ ( c_Set_Oimage @ SV1225 @ SY5999 @ SY6000 @ SV631 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6000 ) @ SY5998 ) @ SY5999 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3155]) ).
thf(3828,plain,
! [SV1226: $i,SV632: $i] :
( ( ! [SY6001: $i,SY6002: $i,SY6003: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV632 ) @ ( hAPP @ SV1226 @ SY6001 ) ) @ ( c_Set_Oimage @ SV1226 @ SY6002 @ SY6003 @ SV632 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6003 ) @ SY6001 ) @ SY6002 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3156]) ).
thf(3829,plain,
! [SV1227: $i,SV633: $i] :
( ( ! [SY6004: $i,SY6005: $i] :
( ( ( hAPP @ SV633 @ SV1227 )
= ( c_Option_Ooption_OSome @ ( c_Map_Osko__Map__XdomD__1__1 @ SV1227 @ SV633 @ SY6004 @ SY6005 ) @ SY6005 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6004 ) @ SV1227 ) @ ( c_Map_Odom @ SV633 @ SY6004 @ SY6005 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3157]) ).
thf(3830,plain,
! [SV1228: $i,SV634: $i] :
( ( ! [SY6006: $i,SY6007: $i] :
( ( c_Map_Omap__le @ SV634 @ SV1228 @ SY6006 @ SY6007 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6006 ) @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ SV634 @ SV1228 @ SY6006 @ SY6007 ) ) @ ( c_Map_Odom @ SV634 @ SY6006 @ SY6007 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3158]) ).
thf(3831,plain,
! [SV635: $i] :
( ( ( ( hAPP @ c_Com_Obody @ SV635 )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) )
= $true )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ SV635 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3159]) ).
thf(3832,plain,
! [SV1229: $i,SV636: $i] :
( ( ! [SY6008: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV636 ) ) @ SV1229 ) @ SY6008 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SV636 ) @ tc_Com_Ocom ) ) @ SV1229 ) @ SY6008 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3160]) ).
thf(3833,plain,
! [SV1230: $i,SV637: $i] :
( ( ! [SY6009: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SV637 ) @ tc_Com_Ocom ) ) @ SV1230 ) @ SY6009 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV637 ) ) @ SV1230 ) @ SY6009 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3161]) ).
thf(3834,plain,
! [SV1231: $i,SV638: $i] :
( ( ( c_Option_Othe @ ( c_Option_Ooption_OSome @ SV638 @ SV1231 ) @ SV1231 )
= SV638 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3162]) ).
thf(3835,plain,
! [SV639: $i] :
( ( ( c_Com_OWT @ SV639 )
= $true )
| ( ( ! [SY4669: $i,SY4670: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SY4669 @ SV639 @ SY4670 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3163]) ).
thf(3836,plain,
! [SV640: $i] :
( ( ( c_Com_OWT @ SV640 )
= $true )
| ( ( ! [SY4671: $i,SY4672: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SY4671 @ SY4672 @ SV640 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3164]) ).
thf(3837,plain,
! [SV1232: $i,SV641: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV641 @ SV1232 ) )
| ~ ( c_Com_OWT @ SV1232 )
| ~ ( c_Com_OWT @ SV641 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3165]) ).
thf(3838,plain,
! [SV642: $i] :
( ( ( c_Com_OWT @ SV642 )
= $true )
| ( ( ! [SY4674: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV642 @ SY4674 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3166]) ).
thf(3839,plain,
! [SV643: $i] :
( ( ( c_Com_OWT @ SV643 )
= $true )
| ( ( ! [SY4675: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SY4675 @ SV643 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3167]) ).
thf(3840,plain,
! [SV1233: $i,SV644: $i] :
( ( ! [SY6010: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV644 @ SV1233 @ SY6010 ) )
| ~ ( c_Com_OWT @ SY6010 )
| ~ ( c_Com_OWT @ SV1233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3168]) ).
thf(3841,plain,
! [SV1234: $i,SV645: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OAss @ SV645 @ SV1234 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3169]) ).
thf(3842,plain,
! [SV1235: $i,SV646: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ SV646 @ SV1235 ) )
| ~ ( c_Com_OWT @ SV1235 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3170]) ).
thf(3843,plain,
! [SV647: $i] :
( ( ( c_Com_OWT @ SV647 )
= $true )
| ( ( ! [SY4680: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ SY4680 @ SV647 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3171]) ).
thf(3844,plain,
! [SV1236: $i,SV648: $i] :
( ( ! [SY6011: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ SV648 @ SV1236 @ SY6011 ) )
| ~ ( c_Com_OWT @ SY6011 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3172]) ).
thf(3845,plain,
! [SV649: $i] :
( ( ( c_Com_OWT @ SV649 )
= $true )
| ( ( ! [SY4683: $i,SY4684: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ SY4683 @ SY4684 @ SV649 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3173]) ).
thf(3846,plain,
! [SV1237: $i,SV650: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV650 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ SV1237 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ ( c_Com_OWT @ SV1237 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ tc_Com_Opname ) @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ SV650 ) ) @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) ) )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3174]) ).
thf(3847,plain,
! [SV1238: $i] :
( ( ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ SV1238 )
!= SV1238 )
= $true )
| ( ( ~ c_Hoare__Mirabelle_Ostate__not__singleton ) = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3175]) ).
thf(3848,plain,
! [SV1239: $i,SV651: $i] :
( ( ! [SY6012: $i,SY6013: $i,SY6014: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV651 @ SV1239 @ SY6012 @ SY6013 ) @ SY6014 )
= ( hAPP @ SV651 @ SY6014 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6012 ) @ SY6014 ) @ ( c_Map_Odom @ SV1239 @ SY6012 @ SY6013 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3176]) ).
thf(3849,plain,
! [SV1240: $i,SV652: $i] :
( ( ! [SY6015: $i,SY6016: $i,SY6017: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV652 @ SV1240 @ SY6015 @ SY6016 ) @ SY6017 )
= ( hAPP @ SV1240 @ SY6017 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6015 ) @ SY6017 ) @ ( c_Map_Odom @ SV652 @ SY6015 @ SY6016 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3177]) ).
thf(3850,plain,
! [SV653: $i,SV1241: $i] :
( ( ! [SY6018: $i,SY6019: $i] :
( ( ( hAPP @ SY6018 @ SV1241 )
= ( c_Option_Ooption_ONone @ SY6019 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV653 ) @ SV1241 ) @ ( c_Map_Odom @ SY6018 @ SV653 @ SY6019 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3178]) ).
thf(3851,plain,
! [SV1242: $i,SV654: $i] :
( ( ! [SY6020: $i] :
( ( ( hAPP @ SV654 @ SV1242 )
!= ( c_Option_Ooption_ONone @ SY6020 ) )
| ! [SY6021: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6021 ) @ SV1242 ) @ ( c_Map_Odom @ SV654 @ SY6021 @ SY6020 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3179]) ).
thf(3852,plain,
! [SV1243: $i,SV655: $i] :
( ( ! [SY6022: $i,SY6023: $i] :
( ( ( hAPP @ SV655 @ SV1243 )
!= ( c_Option_Ooption_OSome @ SY6022 @ SY6023 ) )
| ! [SY6024: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6024 ) @ SV1243 ) @ ( c_Map_Odom @ SV655 @ SY6024 @ SY6023 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3180]) ).
thf(3853,plain,
! [SV1244: $i,SV656: $i] :
( ( ! [SY6025: $i] :
( ( ( hAPP @ SV656 @ SV1244 )
= ( hAPP @ SY6025 @ SV1244 ) )
| ! [SY6026: $i,SY6027: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6026 ) @ SV1244 ) @ ( c_Map_Odom @ SV656 @ SY6026 @ SY6027 ) ) )
| ~ ( c_Map_Omap__le @ SV656 @ SY6025 @ SY6026 @ SY6027 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3181]) ).
thf(3854,plain,
! [SV1245: $i,SV657: $i] :
( ( ! [SY6028: $i,SY6029: $i,SY6030: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV657 @ SV1245 @ SY6028 @ SY6029 ) @ SY6030 )
= ( hAPP @ SV1245 @ SY6030 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6028 ) @ SY6030 ) @ ( c_Map_Odom @ SV1245 @ SY6028 @ SY6029 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3182]) ).
thf(3855,plain,
! [SV1246: $i,SV658: $i] :
( ( ( ( hAPP @ c_Com_Obody @ SV658 )
!= ( c_Option_Ooption_OSome @ SV1246 @ tc_Com_Ocom ) )
| ~ c_Com_OWT__bodies
| ( c_Com_OWT @ SV1246 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3183]) ).
thf(3856,plain,
! [SV1247: $i] :
( ( ( ! [SY6031: $i] : ( SV1247 = SY6031 ) )
= $true )
| ( c_Hoare__Mirabelle_Ostate__not__singleton = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3184]) ).
thf(3857,plain,
! [SV1248: $i,SV659: $i] :
( ( ! [SY6032: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV659 ) @ SV1248 ) @ SY6032 ) )
| ~ ( hBOOL @ ( hAPP @ SY6032 @ SV1248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3185]) ).
thf(3858,plain,
! [SV1249: $i,SV660: $i] :
( ( ( hBOOL @ ( hAPP @ SV660 @ SV1249 ) )
| ! [SY6033: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6033 ) @ SV1249 ) @ SV660 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3186]) ).
thf(3859,plain,
! [SV1250: $i,SV661: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV661 @ SV1250 ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV1250 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3187]) ).
thf(3860,plain,
! [SV1251: $i,SV662: $i] :
( ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV662 @ SV1251 ) )
| ~ ( class_Lattices_Olattice @ SV1251 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3188]) ).
thf(3861,plain,
! [SV1252: $i,SV663: $i] :
( ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV663 @ SV1252 ) )
| ~ ( class_Lattices_Olattice @ SV1252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3189]) ).
thf(3862,plain,
! [SV1253: $i,SV664: $i] :
( ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV664 @ SV1253 ) )
| ~ ( class_Lattices_Odistrib__lattice @ SV1253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3190]) ).
thf(3863,plain,
! [SV1254: $i,SV665: $i] :
( ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV665 @ SV1254 ) )
| ~ ( class_Lattices_Obounded__lattice @ SV1254 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3191]) ).
thf(3864,plain,
! [SV1255: $i,SV666: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ SV666 @ SV1255 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SV1255 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SV666 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3192]) ).
thf(3865,plain,
! [SV1256: $i,SV667: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV667 @ SV1256 ) )
| ~ ( class_Orderings_Opreorder @ SV1256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3193]) ).
thf(3866,plain,
! [SV1257: $i,SV668: $i] :
( ( ( class_Lattices_Olattice @ ( tc_fun @ SV668 @ SV1257 ) )
| ~ ( class_Lattices_Olattice @ SV1257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3194]) ).
thf(3867,plain,
! [SV1258: $i,SV669: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV669 @ SV1258 ) )
| ~ ( class_Orderings_Oorder @ SV1258 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3195]) ).
thf(3868,plain,
! [SV1259: $i,SV670: $i] :
( ( ( class_Orderings_Obot @ ( tc_fun @ SV670 @ SV1259 ) )
| ~ ( class_Orderings_Obot @ SV1259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3196]) ).
thf(3869,plain,
! [SV1260: $i,SV671: $i] :
( ( ( class_HOL_Oord @ ( tc_fun @ SV671 @ SV1260 ) )
| ~ ( class_HOL_Oord @ SV1260 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3197]) ).
thf(3870,plain,
! [SV672: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_Option_Ooption @ SV672 ) )
= $true )
| ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV672 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3198]) ).
thf(3871,plain,
! [SV1261: $i,SV673: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV673 ) @ SV1261 ) @ SV1261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3199]) ).
thf(3872,plain,
! [SV1262: $i,SV674: $i] :
( ( ( SV674 = SV1262 )
| ! [SY6034: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY6034 ) @ SV674 ) @ SV1262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3200]) ).
thf(3873,plain,
! [SV1: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV1 )
= $false )
| ( ( ! [SY2704: $i,SY2705: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2704 @ SY2705 @ SV1 ) @ SY2704 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3202]) ).
thf(3874,plain,
! [SV2: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV2 )
= $false )
| ( ( ! [SY2706: $i,SY2707: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2706 @ SY2707 @ SV2 ) @ SY2707 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3203]) ).
thf(3875,plain,
! [SV675: $i,SV3: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV3 ) )
= $true )
| ( ( ! [SY4731: $i,SY4732: $i] :
( ( c_lessequals @ SV675 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4731 @ SY4732 @ SV3 ) @ SV3 )
| ~ ( c_lessequals @ SV675 @ SY4732 @ SV3 )
| ~ ( c_lessequals @ SV675 @ SY4731 @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3204]) ).
thf(3876,plain,
! [SV676: $i,SV4: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV4 ) )
= $true )
| ( ( ! [SY4733: $i,SY4734: $i] :
( ( c_lessequals @ SV676 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4733 @ SY4734 @ SV4 ) @ SV4 )
| ~ ( c_lessequals @ SV676 @ SY4734 @ SV4 )
| ~ ( c_lessequals @ SV676 @ SY4733 @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3205]) ).
thf(3877,plain,
! [SV677: $i,SV5: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV5 ) )
= $true )
| ( ( ! [SY4735: $i,SY4736: $i] :
( ( c_lessequals @ SV677 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4735 @ SY4736 @ SV5 ) @ SV5 )
| ~ ( c_lessequals @ SV677 @ SY4736 @ SV5 )
| ~ ( c_lessequals @ SV677 @ SY4735 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3206]) ).
thf(3878,plain,
! [SV6: $i] :
( ( ( class_Lattices_Olattice @ SV6 )
= $false )
| ( ( ! [SY2717: $i,SY2718: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2717 @ SY2718 @ SV6 ) @ SY2718 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3207]) ).
thf(3879,plain,
! [SV7: $i] :
( ( ( class_Lattices_Olattice @ SV7 )
= $false )
| ( ( ! [SY2719: $i,SY2720: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2719 @ SY2720 @ SV7 ) @ SY2719 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3208]) ).
thf(3880,plain,
! [SV1263: $i,SV678: $i,SV8: $i] :
( ( ! [SY6035: $i,SY6036: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV8 @ SV678 @ ( tc_fun @ SV1263 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY6035 @ SY6036 @ ( tc_fun @ SV1263 @ tc_bool ) ) @ ( tc_fun @ SV1263 @ tc_bool ) )
| ~ ( c_lessequals @ SV678 @ SY6036 @ ( tc_fun @ SV1263 @ tc_bool ) )
| ~ ( c_lessequals @ SV8 @ SY6035 @ ( tc_fun @ SV1263 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3209]) ).
thf(3881,plain,
! [SV679: $i,SV10: $i] :
( ( ( SV10
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV679 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV10 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV679 @ tc_bool ) ) @ ( tc_fun @ SV679 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3210]) ).
thf(3882,plain,
! [SV1264: $i,SV680: $i,SV11: $i] :
( ( ! [SY6037: $i,SY6038: $i,SY6039: $i,SY6040: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV11 @ SV680 @ SV1264 @ SY6037 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SY6038 @ SY6039 @ SY6040 @ SY6037 ) )
| ( SV1264 = SY6040 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3211]) ).
thf(3883,plain,
! [SV1265: $i,SV681: $i,SV12: $i] :
( ( ! [SY6041: $i,SY6042: $i,SY6043: $i] :
( ! [SY6044: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV12 @ SV681 @ SV1265 @ SY6041 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SY6042 @ SY6043 @ SY6044 @ SY6041 ) )
| ( SV681 = SY6043 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3212]) ).
thf(3884,plain,
! [SV1266: $i,SV682: $i,SV13: $i] :
( ( ! [SY6045: $i,SY6046: $i] :
( ! [SY6047: $i,SY6048: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV13 @ SV682 @ SV1266 @ SY6045 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SY6046 @ SY6047 @ SY6048 @ SY6045 ) )
| ( SV13 = SY6046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3213]) ).
thf(3885,plain,
! [SV1267: $i,SV683: $i,SV14: $i] :
( ( ! [SY6049: $i] :
( ( c_Fun_Ofun__upd @ SV14 @ SV683 @ ( hAPP @ SV14 @ SV683 ) @ SV1267 @ SY6049 )
= SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3214]) ).
thf(3886,plain,
! [SV1268: $i,SV684: $i,SV15: $i] :
( ( ! [SY6050: $i,SY6051: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV15 @ SV684 @ SV1268 @ SY6050 @ SY6051 ) @ SV684 )
= SV1268 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3215]) ).
thf(3887,plain,
! [SV1269: $i,SV685: $i,SV16: $i] :
( ( ! [SY6052: $i] :
( ( c_Fun_Ofun__upd @ SV16 @ SV685 @ ( hAPP @ SV16 @ SV685 ) @ SV1269 @ SY6052 )
= SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3216]) ).
thf(3888,plain,
! [SV1270: $i,SV686: $i,SV17: $i] :
( ( ! [SY6053: $i,SY6054: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV17 @ SV686 @ SV1270 @ SY6053 @ SY6054 ) @ SV686 )
= SV1270 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3217]) ).
thf(3889,plain,
! [SV1271: $i,SV687: $i,SV18: $i] :
( ( ! [SY6055: $i] :
( ( c_Fun_Ofun__upd @ SV18 @ SV687 @ ( hAPP @ SV18 @ SV687 ) @ SV1271 @ SY6055 )
= SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3218]) ).
thf(3890,plain,
! [SV1272: $i,SV688: $i,SV19: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV19 @ SV688 @ ( tc_fun @ SV1272 @ tc_bool ) )
!= SV688 )
| ( c_lessequals @ SV19 @ SV688 @ ( tc_fun @ SV1272 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3219]) ).
thf(3891,plain,
! [SV1273: $i,SV689: $i,SV20: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV20 @ SV689 @ ( tc_fun @ SV1273 @ tc_bool ) )
= SV20 )
| ~ ( c_lessequals @ SV689 @ SV20 @ ( tc_fun @ SV1273 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3220]) ).
thf(3892,plain,
! [SV1274: $i,SV690: $i,SV21: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV21 @ SV690 @ ( tc_fun @ SV1274 @ tc_bool ) )
= SV690 )
| ~ ( c_lessequals @ SV21 @ SV690 @ ( tc_fun @ SV1274 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3221]) ).
thf(3893,plain,
! [SV22: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV22 )
= $false )
| ( ( ! [SY2767: $i,SY2768: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2767 @ SY2768 @ SV22 )
= SY2768 )
| ~ ( c_lessequals @ SY2767 @ SY2768 @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3222]) ).
thf(3894,plain,
! [SV23: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV23 )
= $false )
| ( ( ! [SY2769: $i,SY2770: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2769 @ SY2770 @ SV23 )
!= SY2770 )
| ( c_lessequals @ SY2769 @ SY2770 @ SV23 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3223]) ).
thf(3895,plain,
! [SV24: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV24 )
= $false )
| ( ( ! [SY2771: $i,SY2772: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2771 @ SY2772 @ SV24 )
= SY2771 )
| ~ ( c_lessequals @ SY2772 @ SY2771 @ SV24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3224]) ).
thf(3896,plain,
! [SV25: $i] :
( ( ( class_Orderings_Opreorder @ SV25 )
= $false )
| ( ( ! [SY2773: $i,SY2774: $i] :
( ( c_lessequals @ SY2773 @ SY2774 @ SV25 )
| ~ ( c_HOL_Oord__class_Oless @ SY2773 @ SY2774 @ SV25 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3225]) ).
thf(3897,plain,
! [SV26: $i] :
( ( ( class_Orderings_Oorder @ SV26 )
= $false )
| ( ( ! [SY2775: $i,SY2776: $i] :
( ( c_lessequals @ SY2775 @ SY2776 @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ SY2775 @ SY2776 @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3226]) ).
thf(3898,plain,
! [SV691: $i,SV27: $i] :
( ( ( ~ ( class_HOL_Oord @ SV27 ) )
= $true )
| ( ( ! [SY4770: $i,SY4771: $i] :
( ( c_lessequals @ SV691 @ SY4770 @ ( tc_fun @ SY4771 @ SV27 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV691 @ SY4770 @ ( tc_fun @ SY4771 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3227]) ).
thf(3899,plain,
! [SV1275: $i,SV692: $i,SV28: $i] :
( ( ( c_lessequals @ SV28 @ SV692 @ ( tc_fun @ SV1275 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV28 @ SV692 @ ( tc_fun @ SV1275 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3228]) ).
thf(3900,plain,
! [SV29: $i] :
( ( ( class_Lattices_Olattice @ SV29 )
= $false )
| ( ( ! [SY2782: $i,SY2783: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY2782 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2782 @ SY2783 @ SV29 ) @ SV29 )
= SY2782 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3229]) ).
thf(3901,plain,
! [SV30: $i] :
( ( ( class_Orderings_Oorder @ SV30 )
= $false )
| ( ( ! [SY2784: $i,SY2785: $i] :
( ( SY2784 = SY2785 )
| ~ ( c_lessequals @ SY2784 @ SY2785 @ SV30 )
| ~ ( c_lessequals @ SY2785 @ SY2784 @ SV30 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3230]) ).
thf(3902,plain,
! [SV31: $i] :
( ( ( class_Orderings_Oorder @ SV31 )
= $false )
| ( ( ! [SY2786: $i,SY2787: $i] :
( ( SY2786 = SY2787 )
| ~ ( c_lessequals @ SY2787 @ SY2786 @ SV31 )
| ~ ( c_lessequals @ SY2786 @ SY2787 @ SV31 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3231]) ).
thf(3903,plain,
! [SV32: $i] :
( ( ( class_Orderings_Oorder @ SV32 )
= $false )
| ( ( ! [SY2788: $i,SY2789: $i] :
( ( SY2788 = SY2789 )
| ~ ( c_lessequals @ SY2789 @ SY2788 @ SV32 )
| ~ ( c_lessequals @ SY2788 @ SY2789 @ SV32 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3232]) ).
thf(3904,plain,
! [SV693: $i,SV33: $i] :
( ( ( SV33 = SV693 )
= $true )
| ( ( ! [SY4773: $i] :
( ~ ( c_lessequals @ SV693 @ SV33 @ ( tc_fun @ SY4773 @ tc_bool ) )
| ~ ( c_lessequals @ SV33 @ SV693 @ ( tc_fun @ SY4773 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3233]) ).
thf(3905,plain,
! [SV694: $i,SV34: $i] :
( ( ( SV34 = SV694 )
= $true )
| ( ( ! [SY4774: $i] :
( ~ ( c_lessequals @ SV694 @ SV34 @ ( tc_fun @ SY4774 @ tc_bool ) )
| ~ ( c_lessequals @ SV34 @ SV694 @ ( tc_fun @ SY4774 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3234]) ).
thf(3906,plain,
! [SV35: $i] :
( ( ( class_Lattices_Olattice @ SV35 )
= $false )
| ( ( ! [SY2794: $i,SY2795: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2794 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY2794 @ SY2795 @ SV35 ) @ SV35 )
= SY2794 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3235]) ).
thf(3907,plain,
! [SV695: $i,SV36: $i] :
( ( ( ~ ( class_HOL_Oord @ SV36 ) )
= $true )
| ( ( ! [SY4775: $i,SY4776: $i] :
( ( c_HOL_Oord__class_Oless @ SV695 @ SY4775 @ ( tc_fun @ SY4776 @ SV36 ) )
| ( c_lessequals @ SY4775 @ SV695 @ ( tc_fun @ SY4776 @ SV36 ) )
| ~ ( c_lessequals @ SV695 @ SY4775 @ ( tc_fun @ SY4776 @ SV36 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3236]) ).
thf(3908,plain,
! [SV37: $i] :
( ( ( class_Orderings_Opreorder @ SV37 )
= $false )
| ( ( ! [SY2799: $i,SY2800: $i] :
( ( c_HOL_Oord__class_Oless @ SY2799 @ SY2800 @ SV37 )
| ( c_lessequals @ SY2800 @ SY2799 @ SV37 )
| ~ ( c_lessequals @ SY2799 @ SY2800 @ SV37 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3237]) ).
thf(3909,plain,
! [SV696: $i,SV38: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV38 ) )
= $true )
| ( ( ! [SY4777: $i,SY4778: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV696 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4777 @ SY4778 @ SV38 ) @ SV38 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV696 @ SY4777 @ SV38 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV696 @ SY4778 @ SV38 ) @ SV38 ) @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3238]) ).
thf(3910,plain,
! [SV1276: $i,SV697: $i,SV39: $i] :
( ( ! [SY6056: $i,SY6057: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV39 @ SV697 @ ( tc_fun @ SV1276 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY6056 @ SY6057 @ ( tc_fun @ SV1276 @ tc_bool ) ) @ ( tc_fun @ SV1276 @ tc_bool ) )
| ~ ( c_lessequals @ SY6057 @ SV697 @ ( tc_fun @ SV1276 @ tc_bool ) )
| ~ ( c_lessequals @ SV39 @ SY6056 @ ( tc_fun @ SV1276 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3239]) ).
thf(3911,plain,
! [SV1277: $i,SV698: $i,SV40: $i] :
( ( ! [SY6058: $i,SY6059: $i,SY6060: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ SV40 @ SV698 @ SV1277 @ SY6058 @ SY6059 ) @ SV698 @ SY6060 @ SY6058 @ SY6059 )
= ( c_Fun_Ofun__upd @ SV40 @ SV698 @ SY6060 @ SY6058 @ SY6059 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3240]) ).
thf(3912,plain,
! [SV43: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV43 )
= $false )
| ( ( ! [SY2815: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ SV43 ) @ SY2815 @ SV43 )
= SY2815 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3243]) ).
thf(3913,plain,
! [SV44: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV44 )
= $false )
| ( ( ! [SY2816: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2816 @ ( c_Orderings_Obot__class_Obot @ SV44 ) @ SV44 )
= SY2816 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3244]) ).
thf(3914,plain,
! [SV701: $i,SV45: $i] :
( ( ( c_Finite__Set_Ofinite @ SV45 @ SV701 )
= $true )
| ( ( ! [SY4786: $i] :
~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4786 @ SV45 @ ( tc_fun @ SV701 @ tc_bool ) ) @ SV701 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3245]) ).
thf(3915,plain,
! [SV702: $i,SV46: $i] :
( ( ( c_Finite__Set_Ofinite @ SV46 @ SV702 )
= $true )
| ( ( ! [SY4787: $i] :
~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV46 @ SY4787 @ ( tc_fun @ SV702 @ tc_bool ) ) @ SV702 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3246]) ).
thf(3916,plain,
! [SV1278: $i,SV703: $i,SV47: $i] :
( ( ! [SY6061: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV47 @ SV703 @ ( tc_fun @ SV1278 @ tc_bool ) ) @ SY6061 ) )
| ~ ( hBOOL @ ( hAPP @ SV47 @ SY6061 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3247]) ).
thf(3917,plain,
! [SV1279: $i,SV704: $i,SV48: $i] :
( ( ! [SY6062: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV48 @ SV704 @ ( tc_fun @ SV1279 @ tc_bool ) ) @ SY6062 ) )
| ~ ( hBOOL @ ( hAPP @ SV704 @ SY6062 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3248]) ).
thf(3918,plain,
! [SV705: $i,SV49: $i] :
( ( ( hBOOL @ ( hAPP @ SV49 @ SV705 ) )
= $true )
| ( ( ! [SY4792: $i] :
( ( hBOOL @ ( hAPP @ SY4792 @ SV705 ) )
| ! [SY4793: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4792 @ SV49 @ ( tc_fun @ SY4793 @ tc_bool ) ) @ SV705 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3249]) ).
thf(3919,plain,
! [SV1280: $i,SV706: $i,SV50: $i] :
( ( ! [SY6063: $i,SY6064: $i,SY6065: $i] :
( ! [SY6066: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ SV50 @ SV706 @ SV1280 @ SY6063 @ SY6064 ) @ SY6065 @ SY6066 @ SY6063 @ SY6064 )
= ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ SV50 @ SY6065 @ SY6066 @ SY6063 @ SY6064 ) @ SV706 @ SV1280 @ SY6063 @ SY6064 ) )
| ( SV706 = SY6065 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3250]) ).
thf(3920,plain,
! [SV1281: $i,SV707: $i,SV51: $i] :
( ( ! [SY6067: $i,SY6068: $i,SY6069: $i] :
( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ SV51 @ SV707 @ SV1281 @ SY6067 @ ( tc_Option_Ooption @ SY6068 ) ) @ ( c_Fun_Ofun__upd @ SY6069 @ SV707 @ SV1281 @ SY6067 @ ( tc_Option_Ooption @ SY6068 ) ) @ SY6067 @ SY6068 )
| ~ ( c_Map_Omap__le @ SV51 @ SY6069 @ SY6067 @ SY6068 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3251]) ).
thf(3921,plain,
! [SV1282: $i,SV708: $i,SV52: $i] :
( ( ! [SY6070: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV52 @ SV708 @ ( tc_fun @ SV1282 @ tc_bool ) ) @ SY6070 @ ( tc_fun @ SV1282 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV52 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV708 @ SY6070 @ ( tc_fun @ SV1282 @ tc_bool ) ) @ ( tc_fun @ SV1282 @ tc_bool ) ) )
| ~ ( c_lessequals @ SY6070 @ SV52 @ ( tc_fun @ SV1282 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3252]) ).
thf(3922,plain,
! [SV1283: $i,SV709: $i,SV53: $i] :
( ( ! [SY6071: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV53 @ SV709 @ ( tc_fun @ SV1283 @ tc_bool ) ) @ SY6071 @ ( tc_fun @ SV1283 @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ SV53 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV709 @ SY6071 @ ( tc_fun @ SV1283 @ tc_bool ) ) @ ( tc_fun @ SV1283 @ tc_bool ) ) )
| ( c_lessequals @ SY6071 @ SV53 @ ( tc_fun @ SV1283 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3253]) ).
thf(3923,plain,
! [SV1284: $i,SV710: $i,SV54: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV54 @ SV710 @ ( tc_fun @ SV1284 @ tc_bool ) ) @ SV1284 )
| ~ ( c_Finite__Set_Ofinite @ SV710 @ SV1284 )
| ~ ( c_Finite__Set_Ofinite @ SV54 @ SV1284 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3254]) ).
thf(3924,plain,
! [SV1285: $i,SV711: $i,SV55: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV55 @ SV711 @ ( tc_fun @ SV1285 @ tc_bool ) ) @ SV1285 )
| ~ ( c_Finite__Set_Ofinite @ SV711 @ SV1285 )
| ~ ( c_Finite__Set_Ofinite @ SV55 @ SV1285 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3255]) ).
thf(3925,plain,
! [SV1286: $i,SV712: $i,SV56: $i] :
( ( ( SV56 = SV712 )
| ! [SY6072: $i,SY6073: $i] :
~ ( c_Finite__Set_Ofold__graph @ SV1286 @ SV712 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6072 @ tc_bool ) ) @ SV56 @ SY6072 @ SY6073 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3256]) ).
thf(3926,plain,
! [SV1287: $i,SV713: $i,SV57: $i] :
( ( c_lessequals @ SV57 @ ( c_Set_Oinsert @ SV713 @ SV57 @ SV1287 ) @ ( tc_fun @ SV1287 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3257]) ).
thf(3927,plain,
! [SV1288: $i,SV714: $i,SV58: $i] :
( ( ! [SY6074: $i,SY6075: $i] :
( ( ( hAPP @ SV58 @ SV714 )
!= ( c_Option_Ooption_OSome @ SV1288 @ SY6074 ) )
| ( SV714 = SY6075 )
| ! [SY6076: $i,SY6077: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV58 @ SY6075 @ ( c_Option_Ooption_OSome @ SY6076 @ SY6074 ) @ SY6077 @ ( tc_Option_Ooption @ SY6074 ) ) @ SV714 )
= ( c_Option_Ooption_OSome @ SV1288 @ SY6074 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3258]) ).
thf(3928,plain,
! [SV1289: $i,SV715: $i,SV59: $i] :
( ( ! [SY6078: $i,SY6079: $i,SY6080: $i,SY6081: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV59 @ SV715 @ ( c_Option_Ooption_OSome @ SV1289 @ SY6078 ) @ SY6079 @ ( tc_Option_Ooption @ SY6078 ) ) @ SY6080 )
!= ( c_Option_Ooption_OSome @ SY6081 @ SY6078 ) )
| ( ( hAPP @ SV59 @ SY6080 )
= ( c_Option_Ooption_OSome @ SY6081 @ SY6078 ) )
| ( SV1289 = SY6081 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3259]) ).
thf(3929,plain,
! [SV1290: $i,SV716: $i,SV60: $i] :
( ( ! [SY6082: $i,SY6083: $i,SY6084: $i,SY6085: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV60 @ SV716 @ ( c_Option_Ooption_OSome @ SV1290 @ SY6082 ) @ SY6083 @ ( tc_Option_Ooption @ SY6082 ) ) @ SY6084 )
!= ( c_Option_Ooption_OSome @ SY6085 @ SY6082 ) )
| ( ( hAPP @ SV60 @ SY6084 )
= ( c_Option_Ooption_OSome @ SY6085 @ SY6082 ) )
| ( SY6084 = SV716 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3260]) ).
thf(3930,plain,
! [SV61: $i] :
( ( ( class_Orderings_Obot @ SV61 )
= $false )
| ( ( ! [SY2875: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV61 ) @ SY2875 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3261]) ).
thf(3931,plain,
! [SV1291: $i,SV718: $i,SV63: $i] :
( ( ! [SY6086: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV63 @ ( c_Set_Oinsert @ SV718 @ SV1291 @ SY6086 ) @ ( tc_fun @ SY6086 @ tc_bool ) )
= ( c_Set_Oinsert @ SV718 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV63 @ SV1291 @ ( tc_fun @ SY6086 @ tc_bool ) ) @ SY6086 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3263]) ).
thf(3932,plain,
! [SV1292: $i,SV719: $i,SV64: $i] :
( ( ! [SY6087: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV64 @ SV719 @ SV1292 ) @ SY6087 @ ( tc_fun @ SV1292 @ tc_bool ) )
= ( c_Set_Oinsert @ SV64 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV719 @ SY6087 @ ( tc_fun @ SV1292 @ tc_bool ) ) @ SV1292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3264]) ).
thf(3933,plain,
! [SV1293: $i,SV720: $i,SV65: $i] :
( ( ! [SY6088: $i] :
( ( c_lessequals @ SV65 @ ( c_Set_Oinsert @ SV720 @ SV1293 @ SY6088 ) @ ( tc_fun @ SY6088 @ tc_bool ) )
| ~ ( c_lessequals @ SV65 @ SV1293 @ ( tc_fun @ SY6088 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3265]) ).
thf(3934,plain,
! [SV1294: $i,SV721: $i,SV66: $i] :
( ( ( c_lessequals @ SV66 @ SV721 @ ( tc_fun @ SV1294 @ tc_bool ) )
| ! [SY6089: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SY6089 @ SV66 @ SV1294 ) @ SV721 @ ( tc_fun @ SV1294 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3266]) ).
thf(3935,plain,
! [SV1295: $i,SV722: $i,SV67: $i] :
( ( ! [SY6090: $i] :
( ( c_Finite__Set_Ofinite @ SV67 @ SV722 )
| ! [SY6091: $i,SY6092: $i] :
~ ( c_Finite__Set_Ofold__graph @ SV1295 @ SY6090 @ SV67 @ SY6091 @ SV722 @ SY6092 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3267]) ).
thf(3936,plain,
! [SV1296: $i,SV723: $i,SV68: $i] :
( ( ! [SY6093: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV68 @ SV723 @ ( tc_fun @ SV1296 @ tc_bool ) ) @ SY6093 @ ( tc_fun @ SV1296 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV68 @ SY6093 @ ( tc_fun @ SV1296 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV723 @ SY6093 @ ( tc_fun @ SV1296 @ tc_bool ) ) @ ( tc_fun @ SV1296 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3268]) ).
thf(3937,plain,
! [SV1297: $i,SV724: $i,SV69: $i] :
( ( ! [SY6094: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV69 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV724 @ SV1297 @ ( tc_fun @ SY6094 @ tc_bool ) ) @ ( tc_fun @ SY6094 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV69 @ SV724 @ ( tc_fun @ SY6094 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV69 @ SV1297 @ ( tc_fun @ SY6094 @ tc_bool ) ) @ ( tc_fun @ SY6094 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3269]) ).
thf(3938,plain,
! [SV725: $i,SV70: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV70 ) )
= $true )
| ( ( ! [SY4844: $i,SY4845: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV725 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4844 @ SY4845 @ SV70 ) @ SV70 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV725 @ SY4844 @ SV70 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV725 @ SY4845 @ SV70 ) @ SV70 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3270]) ).
thf(3939,plain,
! [SV726: $i,SV71: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV71 ) )
= $true )
| ( ( ! [SY4846: $i,SY4847: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV726 @ SY4846 @ SV71 ) @ SY4847 @ SV71 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV726 @ SY4847 @ SV71 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4846 @ SY4847 @ SV71 ) @ SV71 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3271]) ).
thf(3940,plain,
! [SV727: $i,SV72: $i,SV1298: $i] :
( ( ! [SY6095: $i] :
( ! [SY6096: $i,SY6097: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV1298 @ SY6095 @ ( c_Option_Ooption_OSome @ SV72 @ SY6096 ) @ SY6097 @ ( tc_Option_Ooption @ SY6096 ) ) @ SY6095 )
!= ( c_Option_Ooption_OSome @ SV727 @ SY6096 ) )
| ( SV72 = SV727 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3272]) ).
thf(3941,plain,
! [SV1299: $i,SV728: $i,SV73: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV73 @ SV728 @ ( tc_fun @ SV1299 @ tc_bool ) ) @ SV73 @ ( tc_fun @ SV1299 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3273]) ).
thf(3942,plain,
! [SV1300: $i,SV729: $i,SV74: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV74 @ SV729 @ ( tc_fun @ SV1300 @ tc_bool ) ) @ SV729 @ ( tc_fun @ SV1300 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3274]) ).
thf(3943,plain,
! [SV1301: $i,SV730: $i,SV75: $i] :
( ( ! [SY6098: $i] :
( ( c_lessequals @ SV75 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV730 @ SV1301 @ ( tc_fun @ SY6098 @ tc_bool ) ) @ ( tc_fun @ SY6098 @ tc_bool ) )
| ~ ( c_lessequals @ SV75 @ SV1301 @ ( tc_fun @ SY6098 @ tc_bool ) )
| ~ ( c_lessequals @ SV75 @ SV730 @ ( tc_fun @ SY6098 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3275]) ).
thf(3944,plain,
! [SV1302: $i,SV731: $i,SV76: $i] :
( ( ! [SY6099: $i] :
( ( c_lessequals @ SV76 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV731 @ SV1302 @ ( tc_fun @ SY6099 @ tc_bool ) ) @ ( tc_fun @ SY6099 @ tc_bool ) )
| ~ ( c_lessequals @ SV76 @ SV1302 @ ( tc_fun @ SY6099 @ tc_bool ) )
| ~ ( c_lessequals @ SV76 @ SV731 @ ( tc_fun @ SY6099 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3276]) ).
thf(3945,plain,
! [SV732: $i,SV77: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV77 ) )
= $true )
| ( ( ! [SY4858: $i,SY4859: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV732 @ SY4858 @ SV77 ) @ SY4859 @ SV77 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV732 @ SY4859 @ SV77 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4858 @ SY4859 @ SV77 ) @ SV77 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3277]) ).
thf(3946,plain,
! [SV733: $i,SV78: $i] :
( ( ( ~ ( class_Lattices_Odistrib__lattice @ SV78 ) )
= $true )
| ( ( ! [SY4860: $i,SY4861: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV733 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4860 @ SY4861 @ SV78 ) @ SV78 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV733 @ SY4860 @ SV78 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV733 @ SY4861 @ SV78 ) @ SV78 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3278]) ).
thf(3947,plain,
! [SV1303: $i,SV734: $i,SV79: $i] :
( ( ! [SY6100: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV79 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV734 @ SV1303 @ ( tc_fun @ SY6100 @ tc_bool ) ) @ ( tc_fun @ SY6100 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV79 @ SV734 @ ( tc_fun @ SY6100 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV79 @ SV1303 @ ( tc_fun @ SY6100 @ tc_bool ) ) @ ( tc_fun @ SY6100 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3279]) ).
thf(3948,plain,
! [SV1304: $i,SV735: $i,SV80: $i] :
( ( ! [SY6101: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV80 @ SV735 @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SY6101 @ ( tc_fun @ SV1304 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV80 @ SY6101 @ ( tc_fun @ SV1304 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV735 @ SY6101 @ ( tc_fun @ SV1304 @ tc_bool ) ) @ ( tc_fun @ SV1304 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3280]) ).
thf(3949,plain,
! [SV1305: $i,SV736: $i,SV81: $i] :
( ( ! [SY6102: $i,SY6103: $i,SY6104: $i] :
( ( c_Set_Oimage @ SV81 @ ( c_Set_Oimage @ SV736 @ SV1305 @ SY6102 @ SY6103 ) @ SY6103 @ SY6104 )
= ( c_Set_Oimage @ ( c_COMBB @ SV81 @ SV736 @ SY6103 @ SY6104 @ SY6102 ) @ SV1305 @ SY6102 @ SY6104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3281]) ).
thf(3950,plain,
! [SV737: $i,SV82: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV82 ) )
= $true )
| ( ( ! [SY4870: $i] :
( ( c_lessequals @ SV737 @ SY4870 @ SV82 )
| ! [SY4871: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4871 @ SV737 @ SV82 ) @ SY4870 @ SV82 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3282]) ).
thf(3951,plain,
! [SV738: $i,SV83: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV83 ) )
= $true )
| ( ( ! [SY4872: $i] :
( ( c_lessequals @ SV738 @ SY4872 @ SV83 )
| ! [SY4873: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV738 @ SY4873 @ SV83 ) @ SY4872 @ SV83 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3283]) ).
thf(3952,plain,
! [SV739: $i,SV84: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV84 ) )
= $true )
| ( ( ! [SY4874: $i,SY4875: $i] :
( ( c_lessequals @ SV739 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4874 @ SY4875 @ SV84 ) @ SV84 )
| ~ ( c_lessequals @ SV739 @ SY4875 @ SV84 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3284]) ).
thf(3953,plain,
! [SV740: $i,SV85: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV85 ) )
= $true )
| ( ( ! [SY4876: $i] :
( ! [SY4877: $i] : ( c_lessequals @ SV740 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4876 @ SY4877 @ SV85 ) @ SV85 )
| ~ ( c_lessequals @ SV740 @ SY4876 @ SV85 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3285]) ).
thf(3954,plain,
! [SV741: $i,SV86: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV86 ) )
= $true )
| ( ( ! [SY4878: $i] :
( ( c_lessequals @ SV741 @ SY4878 @ SV86 )
| ! [SY4879: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4879 @ SV741 @ SV86 ) @ SY4878 @ SV86 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3286]) ).
thf(3955,plain,
! [SV742: $i,SV87: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV87 ) )
= $true )
| ( ( ! [SY4880: $i] :
( ( c_lessequals @ SV742 @ SY4880 @ SV87 )
| ! [SY4881: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV742 @ SY4881 @ SV87 ) @ SY4880 @ SV87 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3287]) ).
thf(3956,plain,
! [SV1306: $i,SV743: $i,SV88: $i] :
( ( ( c_lessequals @ SV88 @ SV743 @ ( tc_fun @ SV1306 @ tc_bool ) )
| ! [SY6105: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV88 @ SY6105 @ ( tc_fun @ SV1306 @ tc_bool ) ) @ SV743 @ ( tc_fun @ SV1306 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3288]) ).
thf(3957,plain,
! [SV1307: $i,SV744: $i,SV89: $i] :
( ( ( c_lessequals @ SV89 @ SV744 @ ( tc_fun @ SV1307 @ tc_bool ) )
| ! [SY6106: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY6106 @ SV89 @ ( tc_fun @ SV1307 @ tc_bool ) ) @ SV744 @ ( tc_fun @ SV1307 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3289]) ).
thf(3958,plain,
! [SV745: $i,SV90: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV90 ) )
= $true )
| ( ( ! [SY4886: $i] :
( ( c_lessequals @ SV745 @ SY4886 @ SV90 )
| ! [SY4887: $i] :
( ~ ( c_lessequals @ SV745 @ SY4887 @ SV90 )
| ~ ( c_lessequals @ SY4887 @ SY4886 @ SV90 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3290]) ).
thf(3959,plain,
! [SV746: $i,SV91: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV91 ) )
= $true )
| ( ( ! [SY4888: $i] :
( ( c_HOL_Oord__class_Oless @ SV746 @ SY4888 @ SV91 )
| ! [SY4889: $i] :
( ~ ( c_lessequals @ SV746 @ SY4889 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SY4889 @ SY4888 @ SV91 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3291]) ).
thf(3960,plain,
! [SV747: $i,SV92: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV92 ) )
= $true )
| ( ( ! [SY4890: $i] :
( ( c_HOL_Oord__class_Oless @ SV747 @ SY4890 @ SV92 )
| ! [SY4891: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV747 @ SY4891 @ SV92 )
| ~ ( c_lessequals @ SY4891 @ SY4890 @ SV92 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3292]) ).
thf(3961,plain,
! [SV748: $i,SV93: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV93 ) )
= $true )
| ( ( ! [SY4892: $i] :
( ( c_lessequals @ SV748 @ SY4892 @ SV93 )
| ! [SY4893: $i] :
( ~ ( c_lessequals @ SY4893 @ SY4892 @ SV93 )
| ~ ( c_lessequals @ SV748 @ SY4893 @ SV93 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3293]) ).
thf(3962,plain,
! [SV1308: $i,SV751: $i,SV96: $i] :
( ( ( c_lessequals @ SV96 @ SV751 @ ( tc_fun @ SV1308 @ tc_bool ) )
| ! [SY6107: $i] :
( ~ ( c_lessequals @ SY6107 @ SV751 @ ( tc_fun @ SV1308 @ tc_bool ) )
| ~ ( c_lessequals @ SV96 @ SY6107 @ ( tc_fun @ SV1308 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3296]) ).
thf(3963,plain,
! [SV1309: $i,SV752: $i,SV97: $i] :
( ( ! [SY6108: $i] :
( ( c_Fun_Oinj__on @ SV97 @ SV752 @ SV1309 @ SY6108 )
| ! [SY6109: $i] :
( ~ ( c_lessequals @ SV752 @ SY6109 @ ( tc_fun @ SV1309 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV97 @ SY6109 @ SV1309 @ SY6108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3297]) ).
thf(3964,plain,
! [SV753: $i,SV98: $i] :
( ( ( hBOOL @ ( hAPP @ SV98 @ SV753 ) )
= $true )
| ( ( ! [SY4899: $i] :
( ~ ( hBOOL @ ( hAPP @ SY4899 @ SV753 ) )
| ! [SY2985: $i] :
~ ( c_lessequals @ SY4899 @ SV98 @ ( tc_fun @ SY2985 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3298]) ).
thf(3965,plain,
! [SV99: $i] :
( ( ( class_Orderings_Oorder @ SV99 )
= $false )
| ( ( ! [SY2986: $i] : ( c_lessequals @ SY2986 @ SY2986 @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3299]) ).
thf(3966,plain,
! [SV100: $i] :
( ( ( class_Orderings_Opreorder @ SV100 )
= $false )
| ( ( ! [SY2987: $i] : ( c_lessequals @ SY2987 @ SY2987 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3300]) ).
thf(3967,plain,
! [SV754: $i,SV101: $i] :
( ( ( c_Finite__Set_Ofinite @ SV101 @ SV754 )
= $true )
| ( ( ! [SY4901: $i] :
( ~ ( c_Finite__Set_Ofinite @ SY4901 @ SV754 )
| ~ ( c_lessequals @ SV101 @ SY4901 @ ( tc_fun @ SV754 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3301]) ).
thf(3968,plain,
! [SV1310: $i,SV755: $i,SV102: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV102 @ SV755 @ ( tc_fun @ SV1310 @ tc_bool ) )
| ! [SY6110: $i] :
( ~ ( c_lessequals @ SY6110 @ SV755 @ ( tc_fun @ SV1310 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV102 @ SY6110 @ ( tc_fun @ SV1310 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3302]) ).
thf(3969,plain,
! [SV1311: $i,SV756: $i,SV103: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV103 @ SV756 @ ( tc_fun @ SV1311 @ tc_bool ) )
| ! [SY6111: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY6111 @ SV756 @ ( tc_fun @ SV1311 @ tc_bool ) )
| ~ ( c_lessequals @ SV103 @ SY6111 @ ( tc_fun @ SV1311 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3303]) ).
thf(3970,plain,
! [SV757: $i,SV104: $i] :
( ( ( hBOOL @ ( hAPP @ SV104 @ SV757 ) )
= $true )
| ( ( ! [SY4906: $i] :
( ! [SY2998: $i] :
~ ( c_lessequals @ SY4906 @ SV104 @ ( tc_fun @ SY2998 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SY4906 @ SV757 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3304]) ).
thf(3971,plain,
! [SV758: $i,SV105: $i] :
( ( ( c_Finite__Set_Ofinite @ SV105 @ SV758 )
= $true )
| ( ( ! [SY4908: $i] :
( ~ ( c_lessequals @ SV105 @ SY4908 @ ( tc_fun @ SV758 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY4908 @ SV758 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3305]) ).
thf(3972,plain,
! [SV759: $i,SV106: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV106 ) )
= $true )
| ( ( ! [SY4909: $i] :
( ( c_HOL_Oord__class_Oless @ SV759 @ SY4909 @ SV106 )
| ! [SY4910: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY4910 @ SY4909 @ SV106 )
| ~ ( c_lessequals @ SV759 @ SY4910 @ SV106 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3306]) ).
thf(3973,plain,
! [SV760: $i,SV107: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV107 ) )
= $true )
| ( ( ! [SY4911: $i] :
( ( c_HOL_Oord__class_Oless @ SV760 @ SY4911 @ SV107 )
| ! [SY4912: $i] :
( ~ ( c_lessequals @ SY4912 @ SY4911 @ SV107 )
| ~ ( c_HOL_Oord__class_Oless @ SV760 @ SY4912 @ SV107 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3307]) ).
thf(3974,plain,
! [SV1312: $i,SV761: $i,SV108: $i] :
( ( ! [SY6112: $i,SY6113: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV108 @ SV761 @ ( tc_fun @ SV1312 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY6112 @ SY6113 @ ( tc_fun @ SV1312 @ tc_bool ) ) @ ( tc_fun @ SV1312 @ tc_bool ) )
| ~ ( c_lessequals @ SV761 @ SY6113 @ ( tc_fun @ SV1312 @ tc_bool ) )
| ~ ( c_lessequals @ SV108 @ SY6112 @ ( tc_fun @ SV1312 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3308]) ).
thf(3975,plain,
! [SV1313: $i,SV762: $i,SV109: $i] :
( ( ! [SY6114: $i,SY6115: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV109 @ SV762 @ ( c_Option_Ooption_OSome @ SV1313 @ SY6114 ) @ SY6115 @ ( tc_Option_Ooption @ SY6114 ) ) @ SV762 )
= ( c_Option_Ooption_OSome @ SV1313 @ SY6114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3309]) ).
thf(3976,plain,
! [SV1314: $i,SV763: $i,SV110: $i] :
( ( ! [SY6116: $i] :
( ( ( hAPP @ SV110 @ SV763 )
!= ( c_Option_Ooption_OSome @ SV1314 @ SY6116 ) )
| ! [SY6117: $i] :
( ( c_Fun_Ofun__upd @ SV110 @ SV763 @ ( c_Option_Ooption_OSome @ SV1314 @ SY6116 ) @ SY6117 @ ( tc_Option_Ooption @ SY6116 ) )
= SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3310]) ).
thf(3977,plain,
! [SV1315: $i,SV764: $i,SV111: $i] :
( ( ! [SY6118: $i,SY6119: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV111 @ SV764 @ ( tc_fun @ SV1315 @ tc_bool ) ) @ SY6118 @ SV1315 @ ( tc_fun @ SY6119 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV111 @ SY6118 @ SV1315 @ ( tc_fun @ SY6119 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV764 @ SY6118 @ SV1315 @ ( tc_fun @ SY6119 @ tc_bool ) ) @ ( tc_fun @ SY6119 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3311]) ).
thf(3978,plain,
! [SV1316: $i,SV765: $i,SV112: $i] :
( ( ! [SY6120: $i,SY6121: $i,SY6122: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV112 @ SV765 @ SV1316 @ SY6120 @ SY6121 ) @ SY6122 )
= ( hAPP @ SV112 @ SY6122 ) )
| ( SY6122 = SV765 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3312]) ).
thf(3979,plain,
! [SV1317: $i,SV766: $i,SV113: $i] :
( ( ! [SY6123: $i,SY6124: $i,SY6125: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV113 @ SV766 @ SV1317 @ SY6123 @ SY6124 ) @ SY6125 )
= ( hAPP @ SV113 @ SY6125 ) )
| ( SY6125 = SV766 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3313]) ).
thf(3980,plain,
! [SV1318: $i,SV767: $i,SV114: $i] :
( ( ! [SY6126: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV114 @ ( c_HOL_Ominus__class_Ominus @ SV767 @ SV1318 @ ( tc_fun @ SY6126 @ tc_bool ) ) @ ( tc_fun @ SY6126 @ tc_bool ) )
= SV1318 )
| ~ ( c_lessequals @ SV114 @ SV767 @ ( tc_fun @ SY6126 @ tc_bool ) )
| ~ ( c_lessequals @ SV1318 @ SV114 @ ( tc_fun @ SY6126 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3314]) ).
thf(3981,plain,
! [SV1319: $i,SV768: $i,SV115: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV115 )
| ! [SY6127: $i,SY6128: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV768 @ SV1319 @ SV115 )
!= ( c_HOL_Ominus__class_Ominus @ SY6127 @ SY6128 @ SV115 ) )
| ( c_lessequals @ SY6128 @ SY6127 @ SV115 )
| ~ ( c_lessequals @ SV1319 @ SV768 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3315]) ).
thf(3982,plain,
! [SV1320: $i,SV769: $i,SV116: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV116 )
| ! [SY6129: $i,SY6130: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV769 @ SV1320 @ SV116 )
!= ( c_HOL_Ominus__class_Ominus @ SY6129 @ SY6130 @ SV116 ) )
| ( c_lessequals @ SV1320 @ SV769 @ SV116 )
| ~ ( c_lessequals @ SY6130 @ SY6129 @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3316]) ).
thf(3983,plain,
! [SV1321: $i,SV770: $i,SV117: $i] :
( ( ! [SY6131: $i,SY6132: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV117 @ SV770 @ SV1321 @ SY6131 ) @ ( c_Set_Oimage @ SV117 @ SY6132 @ SV1321 @ SY6131 ) @ ( tc_fun @ SY6131 @ tc_bool ) )
| ~ ( c_lessequals @ SV770 @ SY6132 @ ( tc_fun @ SV1321 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3317]) ).
thf(3984,plain,
! [SV1322: $i,SV771: $i,SV118: $i] :
( ( ~ ( c_lessequals @ SV118 @ SV771 @ ( tc_fun @ SV1322 @ tc_bool ) )
| ! [SY6133: $i,SY6134: $i] : ( c_lessequals @ ( c_Set_Oimage @ SY6133 @ SV118 @ SV1322 @ SY6134 ) @ ( c_Set_Oimage @ SY6133 @ SV771 @ SV1322 @ SY6134 ) @ ( tc_fun @ SY6134 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3318]) ).
thf(3985,plain,
! [SV1323: $i,SV772: $i,SV119: $i] :
( ( ! [SY6135: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV119 @ SV772 @ SV1323 ) @ ( c_Set_Oinsert @ SV119 @ SY6135 @ SV1323 ) @ ( tc_fun @ SV1323 @ tc_bool ) )
| ~ ( c_lessequals @ SV772 @ SY6135 @ ( tc_fun @ SV1323 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3319]) ).
thf(3986,plain,
! [SV121: $i] :
( ( ( class_Orderings_Oorder @ SV121 )
= $false )
| ( ( ! [SY3055: $i,SY3056: $i] :
( ( c_HOL_Oord__class_Oless @ SY3055 @ SY3056 @ SV121 )
| ( SY3056 = SY3055 )
| ~ ( c_lessequals @ SY3055 @ SY3056 @ SV121 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3320]) ).
thf(3987,plain,
! [SV122: $i] :
( ( ( class_Orderings_Oorder @ SV122 )
= $false )
| ( ( ! [SY3057: $i,SY3058: $i] :
( ( c_HOL_Oord__class_Oless @ SY3057 @ SY3058 @ SV122 )
| ~ ( c_lessequals @ SY3057 @ SY3058 @ SV122 )
| ( SY3058 = SY3057 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3321]) ).
thf(3988,plain,
! [SV1324: $i,SV773: $i,SV123: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV123 @ SV773 @ ( tc_fun @ SV1324 @ tc_bool ) )
| ( SV123 = SV773 )
| ~ ( c_lessequals @ SV123 @ SV773 @ ( tc_fun @ SV1324 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3322]) ).
thf(3989,plain,
! [SV124: $i] :
( ( ( class_Orderings_Oorder @ SV124 )
= $false )
| ( ( ! [SY3061: $i,SY3062: $i] :
( ( SY3061 = SY3062 )
| ( c_HOL_Oord__class_Oless @ SY3061 @ SY3062 @ SV124 )
| ~ ( c_lessequals @ SY3061 @ SY3062 @ SV124 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3323]) ).
thf(3990,plain,
! [SV125: $i] :
( ( ( class_Orderings_Oorder @ SV125 )
= $false )
| ( ( ! [SY3063: $i,SY3064: $i] :
( ( c_HOL_Oord__class_Oless @ SY3063 @ SY3064 @ SV125 )
| ( SY3063 = SY3064 )
| ~ ( c_lessequals @ SY3063 @ SY3064 @ SV125 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3324]) ).
thf(3991,plain,
! [SV774: $i,SV126: $i] :
( ( ( SV126 = SV774 )
= $true )
| ( ( ! [SY4950: $i] :
( ( c_HOL_Oord__class_Oless @ SV126 @ SV774 @ ( tc_fun @ SY4950 @ tc_bool ) )
| ~ ( c_lessequals @ SV126 @ SV774 @ ( tc_fun @ SY4950 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3325]) ).
thf(3992,plain,
! [SV127: $i] :
( ( ( class_Orderings_Oorder @ SV127 )
= $false )
| ( ( ! [SY3067: $i,SY3068: $i] :
( ( c_HOL_Oord__class_Oless @ SY3067 @ SY3068 @ SV127 )
| ( SY3067 = SY3068 )
| ~ ( c_lessequals @ SY3067 @ SY3068 @ SV127 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3326]) ).
thf(3993,plain,
! [SV128: $i] :
( ( ( class_Orderings_Oorder @ SV128 )
= $false )
| ( ( ! [SY3069: $i,SY3070: $i] :
( ( c_HOL_Oord__class_Oless @ SY3069 @ SY3070 @ SV128 )
| ~ ( c_lessequals @ SY3069 @ SY3070 @ SV128 )
| ( SY3069 = SY3070 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3327]) ).
thf(3994,plain,
! [SV129: $i] :
( ( ( class_Orderings_Olinorder @ SV129 )
= $false )
| ( ( ! [SY3071: $i,SY3072: $i] :
( ( SY3071 = SY3072 )
| ~ ( c_lessequals @ SY3071 @ SY3072 @ SV129 )
| ( c_HOL_Oord__class_Oless @ SY3071 @ SY3072 @ SV129 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3328]) ).
thf(3995,plain,
! [SV130: $i] :
( ( ( class_Orderings_Olinorder @ SV130 )
= $false )
| ( ( ! [SY3073: $i,SY3074: $i] :
( ( SY3073 = SY3074 )
| ( c_HOL_Oord__class_Oless @ SY3073 @ SY3074 @ SV130 )
| ~ ( c_lessequals @ SY3073 @ SY3074 @ SV130 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3329]) ).
thf(3996,plain,
! [SV1325: $i,SV775: $i,SV131: $i] :
( ( ! [SY6136: $i,SY6137: $i,SY6138: $i,SY6139: $i] :
( ( ( c_Fun_Ofun__upd @ SV131 @ SV775 @ ( c_Option_Ooption_OSome @ SV1325 @ SY6136 ) @ SY6137 @ ( tc_Option_Ooption @ SY6136 ) )
!= ( c_Fun_Ofun__upd @ SY6138 @ SV775 @ ( c_Option_Ooption_OSome @ SY6139 @ SY6136 ) @ SY6137 @ ( tc_Option_Ooption @ SY6136 ) ) )
| ( SV1325 = SY6139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3330]) ).
thf(3997,plain,
! [SV1326: $i,SV776: $i,SV132: $i] :
( ( ! [SY6140: $i,SY6141: $i] :
( ( c_Set_Oimage @ SV132 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV776 @ SV1326 @ ( tc_fun @ SY6140 @ tc_bool ) ) @ SY6140 @ SY6141 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ SV132 @ SV776 @ SY6140 @ SY6141 ) @ ( c_Set_Oimage @ SV132 @ SV1326 @ SY6140 @ SY6141 ) @ ( tc_fun @ SY6141 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3331]) ).
thf(3998,plain,
! [SV133: $i] :
( ( ( class_Orderings_Olinorder @ SV133 )
= $false )
| ( ( ! [SY3085: $i,SY3086: $i] :
( ( c_lessequals @ SY3085 @ SY3086 @ SV133 )
| ( c_lessequals @ SY3086 @ SY3085 @ SV133 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3332]) ).
thf(3999,plain,
! [SV1327: $i,SV777: $i,SV134: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV134 )
| ! [SY6142: $i,SY6143: $i] :
( ( ( c_Finite__Set_Osetsum @ SV777 @ ( c_HOL_Ominus__class_Ominus @ SV1327 @ SY6142 @ ( tc_fun @ SY6143 @ tc_bool ) ) @ SY6143 @ SV134 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV777 @ SV1327 @ SY6143 @ SV134 ) @ ( c_Finite__Set_Osetsum @ SV777 @ SY6142 @ SY6143 @ SV134 ) @ SV134 ) )
| ~ ( c_lessequals @ SY6142 @ SV1327 @ ( tc_fun @ SY6143 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV1327 @ SY6143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3333]) ).
thf(4000,plain,
! [SV1328: $i,SV778: $i,SV135: $i] :
( ( ! [SY6144: $i] :
( ( ( c_Finite__Set_Ocard @ SV135 @ SV778 )
= ( c_Finite__Set_Ocard @ SV1328 @ SY6144 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1328 @ SY6144 )
| ~ ( c_Finite__Set_Ofinite @ SV135 @ SV778 )
| ! [SY6145: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ SY6145 @ SV1328 @ SY6144 @ SV778 ) @ SV135 @ ( tc_fun @ SV778 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY6145 @ SV1328 @ SY6144 @ SV778 )
| ! [SY6146: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ SY6146 @ SV135 @ SV778 @ SY6144 ) @ SV1328 @ ( tc_fun @ SY6144 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY6146 @ SV135 @ SV778 @ SY6144 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3334]) ).
thf(4001,plain,
! [SV1329: $i,SV779: $i,SV136: $i] :
( ( ! [SY6147: $i,SY6148: $i,SY6149: $i,SY6150: $i] :
( ( c_Finite__Set_Ofold__graph @ SV136 @ SV779 @ ( c_Set_Oinsert @ SV1329 @ SY6147 @ SY6148 ) @ ( hAPP @ ( hAPP @ SV136 @ SV1329 ) @ SY6149 ) @ SY6148 @ SY6150 )
| ~ ( c_Finite__Set_Ofold__graph @ SV136 @ SV779 @ SY6147 @ SY6149 @ SY6148 @ SY6150 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6148 ) @ SV1329 ) @ SY6147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3335]) ).
thf(4002,plain,
! [SV1330: $i,SV780: $i,SV137: $i] :
( ( ( c_lessequals @ SV137 @ SV780 @ ( tc_fun @ SV1330 @ tc_bool ) )
| ! [SY6151: $i] :
( ~ ( c_lessequals @ SV137 @ ( c_Set_Oinsert @ SY6151 @ SV780 @ SV1330 ) @ ( tc_fun @ SV1330 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1330 ) @ SY6151 ) @ SV137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3336]) ).
thf(4003,plain,
! [SV1331: $i,SV781: $i,SV138: $i] :
( ( ! [SY6152: $i] :
( ( c_lessequals @ SV138 @ ( c_Set_Oinsert @ SV781 @ SV1331 @ SY6152 ) @ ( tc_fun @ SY6152 @ tc_bool ) )
| ~ ( c_lessequals @ SV138 @ SV1331 @ ( tc_fun @ SY6152 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6152 ) @ SV781 ) @ SV138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3337]) ).
thf(4004,plain,
! [SV1332: $i,SV782: $i,SV139: $i] :
( ( ( c_lessequals @ SV139 @ SV782 @ ( tc_fun @ SV1332 @ tc_bool ) )
| ! [SY6153: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1332 ) @ SY6153 ) @ SV139 ) )
| ~ ( c_lessequals @ SV139 @ ( c_Set_Oinsert @ SY6153 @ SV782 @ SV1332 ) @ ( tc_fun @ SV1332 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3338]) ).
thf(4005,plain,
! [SV1333: $i,SV783: $i,SV140: $i] :
( ( ! [SY6154: $i] :
( ( c_lessequals @ SV140 @ ( c_Set_Oinsert @ SV783 @ SV1333 @ SY6154 ) @ ( tc_fun @ SY6154 @ tc_bool ) )
| ~ ( c_lessequals @ SV140 @ SV1333 @ ( tc_fun @ SY6154 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6154 ) @ SV783 ) @ SV140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3339]) ).
thf(4006,plain,
! [SV1334: $i,SV784: $i,SV141: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV141 ) @ SV784 ) @ SV1334 ) )
| ! [SY6155: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SV784 @ SY6155 @ SV141 ) @ SV1334 @ ( tc_fun @ SV141 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3340]) ).
thf(4007,plain,
! [SV1335: $i,SV785: $i,SV142: $i] :
( ( ! [SY6156: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV142 @ SV785 @ SV1335 ) @ SY6156 @ ( tc_fun @ SV1335 @ tc_bool ) )
| ~ ( c_lessequals @ SV785 @ SY6156 @ ( tc_fun @ SV1335 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1335 ) @ SV142 ) @ SY6156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3341]) ).
thf(4008,plain,
! [SV1336: $i,SV786: $i,SV143: $i] :
( ( ! [SY6157: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV143 ) @ ( hAPP @ SV786 @ SV1336 ) ) @ SY6157 ) )
| ! [SY6158: $i,SY6159: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6158 ) @ SV1336 ) @ SY6159 ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV786 @ SY6159 @ SY6158 @ SV143 ) @ SY6157 @ ( tc_fun @ SV143 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3342]) ).
thf(4009,plain,
! [SV1337: $i,SV787: $i,SV144: $i] :
( ( ! [SY6160: $i,SY6161: $i,SY6162: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ SV144 @ SV787 @ SV1337 @ SY6160 @ SY6161 ) @ SY6162 @ SY6160 @ SY6161 )
= ( c_Set_Oimage @ SV144 @ SY6162 @ SY6160 @ SY6161 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6160 ) @ SV787 ) @ SY6162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3343]) ).
thf(4010,plain,
! [SV1338: $i,SV788: $i,SV145: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV145 )
| ! [SY6163: $i,SY6164: $i] :
( ( c_lessequals @ ( hAPP @ SV788 @ SV1338 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY6163 @ SV788 @ SY6164 @ SV145 ) @ SV145 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6164 ) @ SV1338 ) @ SY6163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3344]) ).
thf(4011,plain,
! [SV1339: $i,SV789: $i,SV146: $i] :
( ( ! [SY6165: $i] :
( ! [SY6166: $i] : ( c_lessequals @ ( hAPP @ SV146 @ SV789 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1339 @ SV146 @ SY6165 @ ( tc_fun @ SY6166 @ tc_bool ) ) @ ( tc_fun @ SY6166 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6165 ) @ SV789 ) @ SV1339 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3345]) ).
thf(4012,plain,
! [SV1340: $i,SV790: $i,SV147: $i] :
( ( ! [SY6167: $i] :
( ( c_lessequals @ ( hAPP @ SV147 @ SV790 ) @ SV1340 @ ( tc_fun @ SY6167 @ tc_bool ) )
| ! [SY6168: $i,SY6169: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6168 ) @ SV790 ) @ SY6169 ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY6169 @ SV147 @ SY6168 @ ( tc_fun @ SY6167 @ tc_bool ) ) @ SV1340 @ ( tc_fun @ SY6167 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3346]) ).
thf(4013,plain,
! [SV1341: $i,SV791: $i,SV148: $i] :
( ( ! [SY6170: $i] :
( ! [SY6171: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV148 @ SV791 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1341 @ SV148 @ SY6170 @ ( tc_fun @ SY6171 @ tc_bool ) ) @ ( tc_fun @ SY6171 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1341 @ SV148 @ SY6170 @ ( tc_fun @ SY6171 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6170 ) @ SV791 ) @ SV1341 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3347]) ).
thf(4014,plain,
! [SV1342: $i,SV792: $i,SV149: $i] :
( ( ( c_Set_Oinsert @ SV149 @ SV792 @ SV1342 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV149 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1342 @ tc_bool ) ) @ SV1342 ) @ SV792 @ ( tc_fun @ SV1342 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3348]) ).
thf(4015,plain,
! [SV1343: $i,SV793: $i,SV150: $i] :
( ( ( SV150
= ( c_Set_Oinsert @ SV793 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1343 @ tc_bool ) ) @ SV1343 ) )
| ( SV150
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1343 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV150 @ ( c_Set_Oinsert @ SV793 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1343 @ tc_bool ) ) @ SV1343 ) @ ( tc_fun @ SV1343 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3349]) ).
thf(4016,plain,
! [SV1344: $i,SV794: $i,SV151: $i] :
( ( ( c_Finite__Set_Ofinite @ SV151 @ SV794 )
| ! [SY6172: $i,SY6173: $i] :
( ~ ( c_lessequals @ SV151 @ ( c_Set_Oimage @ SV1344 @ SY6172 @ SY6173 @ SV794 ) @ ( tc_fun @ SV794 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY6172 @ SY6173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3350]) ).
thf(4017,plain,
! [SV1345: $i,SV795: $i,SV152: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV152 @ SV795 @ SV1345 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1345 @ tc_bool ) ) @ SV1345 @ SV795 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV795 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3351]) ).
thf(4018,plain,
! [SV1346: $i,SV796: $i,SV153: $i] :
( ( ( c_lessequals @ SV153 @ SV796 @ ( tc_fun @ SV1346 @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ SV1346 ) @ SV1346 @ ( tc_fun @ SV1346 @ tc_bool ) @ tc_bool ) @ SV153 ) @ ( hAPP @ ( c_COMBC @ ( c_in @ SV1346 ) @ SV1346 @ ( tc_fun @ SV1346 @ tc_bool ) @ tc_bool ) @ SV796 ) @ ( tc_fun @ SV1346 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3352]) ).
thf(4019,plain,
! [SV1347: $i,SV797: $i,SV154: $i] :
( ( ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ SV154 ) @ SV154 @ ( tc_fun @ SV154 @ tc_bool ) @ tc_bool ) @ SV797 ) @ ( hAPP @ ( c_COMBC @ ( c_in @ SV154 ) @ SV154 @ ( tc_fun @ SV154 @ tc_bool ) @ tc_bool ) @ SV1347 ) @ ( tc_fun @ SV154 @ tc_bool ) )
| ~ ( c_lessequals @ SV797 @ SV1347 @ ( tc_fun @ SV154 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3353]) ).
thf(4020,plain,
! [SV798: $i,SV155: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV155 ) )
= $true )
| ( ( ! [SY5012: $i,SY5013: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV798 @ ( c_COMBK @ SY5012 @ SV155 @ SY5013 ) @ SY5013 @ SV155 )
= SY5012 )
| ( SV798
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5013 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3354]) ).
thf(4021,plain,
! [SV1348: $i,SV799: $i,SV156: $i] :
( ( ! [SY6174: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV156 @ tc_bool ) ) @ SV799 @ SV156 @ ( tc_fun @ SV1348 @ tc_bool ) ) @ SY6174 @ ( tc_fun @ SV1348 @ tc_bool ) )
= SY6174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3355]) ).
thf(4022,plain,
! [SV1349: $i,SV800: $i,SV157: $i] :
( ( ! [SY6175: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV157 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV800 @ tc_bool ) ) @ SV1349 @ SV800 @ ( tc_fun @ SY6175 @ tc_bool ) ) @ ( tc_fun @ SY6175 @ tc_bool ) )
= SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3356]) ).
thf(4023,plain,
! [SV1350: $i,SV801: $i,SV158: $i] :
( ( ! [SY6176: $i,SY6177: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ SV158 @ SV801 @ SV1350 ) @ SY6176 @ SV1350 @ ( tc_fun @ SY6177 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SY6176 @ SV158 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV801 @ SY6176 @ SV1350 @ ( tc_fun @ SY6177 @ tc_bool ) ) @ ( tc_fun @ SY6177 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3357]) ).
thf(4024,plain,
! [SV1351: $i,SV802: $i,SV159: $i] :
( ( ! [SY6178: $i,SY6179: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV159 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV802 @ SV1351 @ ( tc_fun @ SY6178 @ tc_bool ) ) @ SY6178 @ SY6179 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV159 @ SV802 @ SY6178 @ SY6179 ) @ ( c_Set_Oimage @ SV159 @ SV1351 @ SY6178 @ SY6179 ) @ ( tc_fun @ SY6179 @ tc_bool ) ) @ ( tc_fun @ SY6179 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3358]) ).
thf(4025,plain,
! [SV1352: $i,SV803: $i,SV160: $i] :
( ( ! [SY6180: $i,SY6181: $i,SY6182: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV160 @ ( c_COMBB @ SV803 @ SV1352 @ SY6180 @ ( tc_fun @ SY6181 @ tc_bool ) @ SY6182 ) @ SY6182 @ ( tc_fun @ SY6181 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oimage @ SV1352 @ SV160 @ SY6182 @ SY6180 ) @ SV803 @ SY6180 @ ( tc_fun @ SY6181 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3359]) ).
thf(4026,plain,
! [SV1353: $i,SV804: $i,SV161: $i] :
( ( ! [SY6183: $i,SY6184: $i,SY6185: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oimage @ SV161 @ SV804 @ SV1353 @ SY6183 ) @ SY6184 @ SY6183 @ ( tc_fun @ SY6185 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV804 @ ( c_COMBB @ SY6184 @ SV161 @ SY6183 @ ( tc_fun @ SY6185 @ tc_bool ) @ SV1353 ) @ SV1353 @ ( tc_fun @ SY6185 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3360]) ).
thf(4027,plain,
! [SV1354: $i,SV805: $i,SV162: $i] :
( ( ! [SY6186: $i,SY6187: $i] :
( ( ( c_Set_Oimage @ SV162 @ SV805 @ SV1354 @ SY6186 )
!= ( c_Set_Oimage @ SV162 @ SY6187 @ SV1354 @ SY6186 ) )
| ~ ( c_Fun_Oinj__on @ SV162 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV805 @ SY6187 @ ( tc_fun @ SV1354 @ tc_bool ) ) @ SV1354 @ SY6186 )
| ( SV805 = SY6187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3361]) ).
thf(4028,plain,
! [SV1355: $i,SV806: $i,SV163: $i] :
( ( ! [SY6188: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ SV163 @ SV806 @ SV1355 @ SY6188 ) @ SY6188 )
= ( c_Finite__Set_Ocard @ SV806 @ SV1355 ) )
| ~ ( c_Fun_Oinj__on @ SV163 @ SV806 @ SV1355 @ SY6188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3362]) ).
thf(4029,plain,
! [SV1356: $i,SV807: $i,SV164: $i] :
( ( ! [SY6189: $i,SY6190: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV164 @ SV807 @ SV1356 @ SY6189 ) @ ( c_Set_Oimage @ SV164 @ SY6190 @ SV1356 @ SY6189 ) @ ( tc_fun @ SY6189 @ tc_bool ) ) @ ( c_Set_Oimage @ SV164 @ ( c_HOL_Ominus__class_Ominus @ SV807 @ SY6190 @ ( tc_fun @ SV1356 @ tc_bool ) ) @ SV1356 @ SY6189 ) @ ( tc_fun @ SY6189 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3363]) ).
thf(4030,plain,
! [SV1357: $i,SV808: $i,SV165: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV165 @ SV808 @ ( tc_fun @ SV1357 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV165 @ SV808 @ ( tc_fun @ SV1357 @ tc_bool ) ) @ ( tc_fun @ SV1357 @ tc_bool ) )
= SV165 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3364]) ).
thf(4031,plain,
! [SV1358: $i,SV809: $i,SV166: $i] :
( ( ! [SY6191: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV166 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV809 @ SV1358 @ ( tc_fun @ SY6191 @ tc_bool ) ) @ ( tc_fun @ SY6191 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ SV166 @ SV809 @ ( tc_fun @ SY6191 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV166 @ SV1358 @ ( tc_fun @ SY6191 @ tc_bool ) ) @ ( tc_fun @ SY6191 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3365]) ).
thf(4032,plain,
! [SV1359: $i,SV810: $i,SV167: $i] :
( ( ! [SY6192: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV167 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV810 @ SV1359 @ ( tc_fun @ SY6192 @ tc_bool ) ) @ ( tc_fun @ SY6192 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV167 @ SV810 @ ( tc_fun @ SY6192 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV167 @ SV1359 @ ( tc_fun @ SY6192 @ tc_bool ) ) @ ( tc_fun @ SY6192 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3366]) ).
thf(4033,plain,
! [SV1360: $i,SV811: $i,SV168: $i] :
( ( ! [SY6193: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV168 @ ( c_Set_Ovimage @ SV168 @ SV811 @ SV1360 @ SY6193 ) @ SV1360 @ SY6193 ) @ SV811 @ ( tc_fun @ SY6193 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3367]) ).
thf(4034,plain,
! [SV1361: $i,SV812: $i,SV169: $i] :
( ( ! [SY6194: $i,SY6195: $i,SY6196: $i] :
( ( c_Map_Omap__add @ SV169 @ ( c_Fun_Ofun__upd @ SV812 @ SV1361 @ ( c_Option_Ooption_OSome @ SY6194 @ SY6195 ) @ SY6196 @ ( tc_Option_Ooption @ SY6195 ) ) @ SY6196 @ SY6195 )
= ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ SV169 @ SV812 @ SY6196 @ SY6195 ) @ SV1361 @ ( c_Option_Ooption_OSome @ SY6194 @ SY6195 ) @ SY6196 @ ( tc_Option_Ooption @ SY6195 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3368]) ).
thf(4035,plain,
! [SV1362: $i,SV813: $i,SV170: $i] :
( ( ! [SY6197: $i] :
( ( c_Map_Odom @ ( c_Map_Omap__add @ SV170 @ SV813 @ SV1362 @ SY6197 ) @ SV1362 @ SY6197 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Map_Odom @ SV813 @ SV1362 @ SY6197 ) @ ( c_Map_Odom @ SV170 @ SV1362 @ SY6197 ) @ ( tc_fun @ SV1362 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3369]) ).
thf(4036,plain,
! [SV1363: $i,SV814: $i,SV171: $i] :
( ( ! [SY6198: $i] : ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ SV171 @ SV814 @ ( c_Option_Ooption_ONone @ SV1363 ) @ SY6198 @ ( tc_Option_Ooption @ SV1363 ) ) @ SV171 @ SY6198 @ SV1363 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3370]) ).
thf(4037,plain,
! [SV1364: $i,SV815: $i,SV172: $i] :
( ( ! [SY6199: $i] :
( ( c_lessequals @ ( c_Map_Odom @ SV172 @ SV815 @ SV1364 ) @ ( c_Map_Odom @ SY6199 @ SV815 @ SV1364 ) @ ( tc_fun @ SV815 @ tc_bool ) )
| ~ ( c_Map_Omap__le @ SV172 @ SY6199 @ SV815 @ SV1364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3371]) ).
thf(4038,plain,
! [SV174: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV174 )
= $false )
| ( ( ! [SY3225: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3225 @ SY3225 @ SV174 )
= SY3225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3373]) ).
thf(4039,plain,
! [SV1365: $i,SV817: $i,SV175: $i] :
( ( ! [SY6200: $i,SY6201: $i,SY6202: $i] :
( ( hAPP @ ( c_COMBB @ SV175 @ SV817 @ SV1365 @ SY6200 @ SY6201 ) @ SY6202 )
= ( hAPP @ SV175 @ ( hAPP @ SV817 @ SY6202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3374]) ).
thf(4040,plain,
! [SV1366: $i,SV818: $i,SV176: $i] :
( ( ! [SY6203: $i] :
( ( hAPP @ ( c_COMBK @ SV176 @ SV818 @ SV1366 ) @ SY6203 )
= SV176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3375]) ).
thf(4041,plain,
! [SV177: $i] :
( ( ( class_Orderings_Olinorder @ SV177 )
= $false )
| ( ( ! [SY3234: $i,SY3235: $i] :
( ( c_HOL_Oord__class_Oless @ SY3234 @ SY3235 @ SV177 )
| ( c_lessequals @ SY3235 @ SY3234 @ SV177 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3376]) ).
thf(4042,plain,
! [SV178: $i] :
( ( ( class_Orderings_Olinorder @ SV178 )
= $false )
| ( ( ! [SY3236: $i] :
( ~ ( c_lessequals @ SY3236 @ SY3236 @ SV178 )
| ~ ( c_HOL_Oord__class_Oless @ SY3236 @ SY3236 @ SV178 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3377]) ).
thf(4043,plain,
! [SV179: $i] :
( ( ( class_Orderings_Olinorder @ SV179 )
= $false )
| ( ( ! [SY3237: $i] :
( ( c_HOL_Oord__class_Oless @ SY3237 @ SY3237 @ SV179 )
| ( c_lessequals @ SY3237 @ SY3237 @ SV179 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3378]) ).
thf(4044,plain,
! [SV180: $i] :
( ( ( class_Orderings_Olinorder @ SV180 )
= $false )
| ( ( ! [SY3238: $i,SY3239: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY3238 @ SY3239 @ SV180 )
| ~ ( c_lessequals @ SY3239 @ SY3238 @ SV180 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3379]) ).
thf(4045,plain,
! [SV181: $i] :
( ( ( class_Orderings_Olinorder @ SV181 )
= $false )
| ( ( ! [SY3240: $i,SY3241: $i] :
( ( c_HOL_Oord__class_Oless @ SY3241 @ SY3240 @ SV181 )
| ( c_lessequals @ SY3240 @ SY3241 @ SV181 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3380]) ).
thf(4046,plain,
! [SV182: $i] :
( ( ( class_Orderings_Olinorder @ SV182 )
= $false )
| ( ( ! [SY3242: $i,SY3243: $i] :
( ~ ( c_lessequals @ SY3242 @ SY3243 @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ SY3243 @ SY3242 @ SV182 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3381]) ).
thf(4047,plain,
! [SV183: $i] :
( ( ( class_Orderings_Olinorder @ SV183 )
= $false )
| ( ( ! [SY3244: $i,SY3245: $i] :
( ( c_HOL_Oord__class_Oless @ SY3244 @ SY3245 @ SV183 )
| ( c_lessequals @ SY3245 @ SY3244 @ SV183 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3382]) ).
thf(4048,plain,
! [SV819: $i,SV184: $i] :
( ( ( ~ ( class_HOL_Oord @ SV184 ) )
= $true )
| ( ( ! [SY5063: $i,SY5064: $i] :
( ~ ( c_lessequals @ SV819 @ SY5063 @ ( tc_fun @ SY5064 @ SV184 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY5063 @ SV819 @ ( tc_fun @ SY5064 @ SV184 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3383]) ).
thf(4049,plain,
! [SV185: $i] :
( ( ( class_Orderings_Opreorder @ SV185 )
= $false )
| ( ( ! [SY3249: $i,SY3250: $i] :
( ~ ( c_lessequals @ SY3249 @ SY3250 @ SV185 )
| ~ ( c_HOL_Oord__class_Oless @ SY3250 @ SY3249 @ SV185 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3384]) ).
thf(4050,plain,
! [SV1367: $i,SV820: $i,SV186: $i] :
( ( ! [SY6204: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV186 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV820 @ SV1367 @ ( tc_fun @ SY6204 @ tc_bool ) ) @ ( tc_fun @ SY6204 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV820 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV186 @ SV1367 @ ( tc_fun @ SY6204 @ tc_bool ) ) @ ( tc_fun @ SY6204 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3385]) ).
thf(4051,plain,
! [SV1368: $i,SV821: $i,SV187: $i] :
( ( ! [SY6205: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV187 @ SV821 @ ( tc_fun @ SV1368 @ tc_bool ) ) @ SY6205 @ ( tc_fun @ SV1368 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV187 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV821 @ SY6205 @ ( tc_fun @ SV1368 @ tc_bool ) ) @ ( tc_fun @ SV1368 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3386]) ).
thf(4052,plain,
! [SV822: $i,SV188: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV188 ) )
= $true )
| ( ( ! [SY5069: $i,SY5070: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV822 @ SY5069 @ SV188 ) @ SY5070 @ SV188 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV822 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5069 @ SY5070 @ SV188 ) @ SV188 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3387]) ).
thf(4053,plain,
! [SV823: $i,SV189: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV189 ) )
= $true )
| ( ( ! [SY5071: $i,SY5072: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV823 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5071 @ SY5072 @ SV189 ) @ SV189 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY5071 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV823 @ SY5072 @ SV189 ) @ SV189 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3388]) ).
thf(4054,plain,
! [SV824: $i,SV190: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV190 ) )
= $true )
| ( ( ! [SY5073: $i,SY5074: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV824 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5073 @ SY5074 @ SV190 ) @ SV190 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY5073 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV824 @ SY5074 @ SV190 ) @ SV190 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3389]) ).
thf(4055,plain,
! [SV825: $i,SV191: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV191 ) )
= $true )
| ( ( ! [SY5075: $i,SY5076: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV825 @ SY5075 @ SV191 ) @ SY5076 @ SV191 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV825 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5075 @ SY5076 @ SV191 ) @ SV191 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3390]) ).
thf(4056,plain,
! [SV1369: $i,SV826: $i,SV192: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV192 @ SV826 @ ( tc_fun @ SV1369 @ tc_bool ) )
= SV192 )
| ~ ( c_lessequals @ SV192 @ SV826 @ ( tc_fun @ SV1369 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3391]) ).
thf(4057,plain,
! [SV1370: $i,SV827: $i,SV193: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV193 @ SV827 @ ( tc_fun @ SV1370 @ tc_bool ) )
= SV827 )
| ~ ( c_lessequals @ SV827 @ SV193 @ ( tc_fun @ SV1370 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3392]) ).
thf(4058,plain,
! [SV194: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV194 )
= $false )
| ( ( ! [SY3273: $i,SY3274: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3273 @ SY3274 @ SV194 )
= SY3273 )
| ~ ( c_lessequals @ SY3273 @ SY3274 @ SV194 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3393]) ).
thf(4059,plain,
! [SV195: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV195 )
= $false )
| ( ( ! [SY3275: $i,SY3276: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3275 @ SY3276 @ SV195 )
!= SY3275 )
| ( c_lessequals @ SY3275 @ SY3276 @ SV195 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3394]) ).
thf(4060,plain,
! [SV196: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV196 )
= $false )
| ( ( ! [SY3277: $i,SY3278: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3277 @ SY3278 @ SV196 )
= SY3278 )
| ~ ( c_lessequals @ SY3278 @ SY3277 @ SV196 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3395]) ).
thf(4061,plain,
! [SV1371: $i,SV828: $i,SV197: $i] :
( ( ! [SY6206: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV197 @ SV828 @ ( tc_fun @ SV1371 @ tc_bool ) ) @ SY6206 @ ( tc_fun @ SV1371 @ tc_bool ) )
| ~ ( c_lessequals @ SV828 @ SY6206 @ ( tc_fun @ SV1371 @ tc_bool ) )
| ~ ( c_lessequals @ SV197 @ SY6206 @ ( tc_fun @ SV1371 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3396]) ).
thf(4062,plain,
! [SV1372: $i,SV829: $i,SV198: $i] :
( ( c_lessequals @ SV198 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV829 @ SV198 @ ( tc_fun @ SV1372 @ tc_bool ) ) @ ( tc_fun @ SV1372 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3397]) ).
thf(4063,plain,
! [SV1373: $i,SV830: $i,SV199: $i] :
( ( c_lessequals @ SV199 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV199 @ SV830 @ ( tc_fun @ SV1373 @ tc_bool ) ) @ ( tc_fun @ SV1373 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3398]) ).
thf(4064,plain,
! [SV1374: $i,SV831: $i,SV200: $i] :
( ( ! [SY6207: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ SV831 @ ( tc_fun @ SV1374 @ tc_bool ) ) @ SY6207 @ ( tc_fun @ SV1374 @ tc_bool ) )
| ~ ( c_lessequals @ SV831 @ SY6207 @ ( tc_fun @ SV1374 @ tc_bool ) )
| ~ ( c_lessequals @ SV200 @ SY6207 @ ( tc_fun @ SV1374 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3399]) ).
thf(4065,plain,
! [SV832: $i,SV201: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV201 ) )
= $true )
| ( ( ! [SY5085: $i,SY5086: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV832 @ SY5085 @ SV201 ) @ SY5086 @ SV201 )
| ~ ( c_lessequals @ SY5085 @ SY5086 @ SV201 )
| ~ ( c_lessequals @ SV832 @ SY5086 @ SV201 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3400]) ).
thf(4066,plain,
! [SV202: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV202 )
= $false )
| ( ( ! [SY3292: $i,SY3293: $i] : ( c_lessequals @ SY3292 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3292 @ SY3293 @ SV202 ) @ SV202 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3401]) ).
thf(4067,plain,
! [SV203: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV203 )
= $false )
| ( ( ! [SY3294: $i,SY3295: $i] : ( c_lessequals @ SY3294 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3295 @ SY3294 @ SV203 ) @ SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3402]) ).
thf(4068,plain,
! [SV833: $i,SV204: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV204 ) )
= $true )
| ( ( ! [SY5087: $i,SY5088: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV833 @ SY5087 @ SV204 ) @ SY5088 @ SV204 )
| ~ ( c_lessequals @ SY5087 @ SY5088 @ SV204 )
| ~ ( c_lessequals @ SV833 @ SY5088 @ SV204 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3403]) ).
thf(4069,plain,
! [SV834: $i,SV205: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV205 ) )
= $true )
| ( ( ! [SY5089: $i,SY5090: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV834 @ SY5089 @ SV205 ) @ SY5090 @ SV205 )
| ~ ( c_lessequals @ SY5089 @ SY5090 @ SV205 )
| ~ ( c_lessequals @ SV834 @ SY5090 @ SV205 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3404]) ).
thf(4070,plain,
! [SV206: $i] :
( ( ( class_Lattices_Olattice @ SV206 )
= $false )
| ( ( ! [SY3302: $i,SY3303: $i] : ( c_lessequals @ SY3302 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3303 @ SY3302 @ SV206 ) @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3405]) ).
thf(4071,plain,
! [SV207: $i] :
( ( ( class_Lattices_Olattice @ SV207 )
= $false )
| ( ( ! [SY3304: $i,SY3305: $i] : ( c_lessequals @ SY3304 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3304 @ SY3305 @ SV207 ) @ SV207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3406]) ).
thf(4072,plain,
! [SV1375: $i,SV835: $i,SV208: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV208 @ ( c_HOL_Ominus__class_Ominus @ SV835 @ SV208 @ ( tc_fun @ SV1375 @ tc_bool ) ) @ ( tc_fun @ SV1375 @ tc_bool ) )
= SV835 )
| ~ ( c_lessequals @ SV208 @ SV835 @ ( tc_fun @ SV1375 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3407]) ).
thf(4073,plain,
! [SV836: $i,SV209: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV209 ) )
= $true )
| ( ( ! [SY5092: $i,SY5093: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV836 @ SY5092 @ SV209 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV836 @ SY5093 @ SV209 ) @ SV209 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV836 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5092 @ SY5093 @ SV209 ) @ SV209 ) @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3408]) ).
thf(4074,plain,
! [SV1376: $i,SV837: $i,SV210: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV210 @ SV837 @ ( tc_fun @ SV1376 @ tc_bool ) ) @ SV210 @ ( tc_fun @ SV1376 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3409]) ).
thf(4075,plain,
! [SV1377: $i,SV838: $i,SV211: $i] :
( ( ! [SY6208: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV211 @ SV838 @ ( tc_fun @ SV1377 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV838 @ SY6208 @ ( tc_fun @ SV1377 @ tc_bool ) ) @ ( tc_fun @ SV1377 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY6208 @ SV211 @ ( tc_fun @ SV1377 @ tc_bool ) ) @ ( tc_fun @ SV1377 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV211 @ SV838 @ ( tc_fun @ SV1377 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV838 @ SY6208 @ ( tc_fun @ SV1377 @ tc_bool ) ) @ ( tc_fun @ SV1377 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY6208 @ SV211 @ ( tc_fun @ SV1377 @ tc_bool ) ) @ ( tc_fun @ SV1377 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3410]) ).
thf(4076,plain,
! [SV1378: $i,SV839: $i,SV212: $i] :
( ( ! [SY6209: $i] : ( c_Finite__Set_Ofold__graph @ SV212 @ SV839 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1378 @ tc_bool ) ) @ SV839 @ SV1378 @ SY6209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3411]) ).
thf(4077,plain,
! [SV1379: $i,SV840: $i,SV213: $i] :
( ( ! [SY6210: $i] : ( c_Nitpick_Ofold__graph_H @ SV213 @ SV840 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1379 @ tc_bool ) ) @ SV840 @ SV1379 @ SY6210 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3412]) ).
thf(4078,plain,
! [SV1380: $i,SV841: $i,SV214: $i] :
( ( ! [SY6211: $i,SY6212: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ SV214 @ SV841 @ SV1380 @ SY6211 ) @ ( c_Set_Ovimage @ SV214 @ SY6212 @ SV1380 @ SY6211 ) @ ( tc_fun @ SV1380 @ tc_bool ) )
| ~ ( c_lessequals @ SV841 @ SY6212 @ ( tc_fun @ SY6211 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3413]) ).
thf(4079,plain,
! [SV1381: $i,SV842: $i,SV215: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV215 @ SV842 @ ( tc_fun @ SV1381 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1381 @ tc_bool ) ) )
| ( SV842
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1381 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3414]) ).
thf(4080,plain,
! [SV1382: $i,SV843: $i,SV216: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV216 @ SV843 @ ( tc_fun @ SV1382 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1382 @ tc_bool ) ) )
| ( SV216
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1382 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3415]) ).
thf(4081,plain,
! [SV217: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV217 )
= $false )
| ( ( ! [SY3330: $i] :
( ! [SY3331: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3330 @ SY3331 @ SV217 )
!= ( c_Orderings_Obot__class_Obot @ SV217 ) )
| ( SY3330
= ( c_Orderings_Obot__class_Obot @ SV217 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3416]) ).
thf(4082,plain,
! [SV218: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV218 )
= $false )
| ( ( ! [SY3332: $i,SY3333: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3332 @ SY3333 @ SV218 )
!= ( c_Orderings_Obot__class_Obot @ SV218 ) )
| ( SY3333
= ( c_Orderings_Obot__class_Obot @ SV218 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3417]) ).
thf(4083,plain,
! [SV1383: $i,SV844: $i,SV219: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV219 @ SV844 @ ( tc_fun @ SV1383 @ tc_bool ) ) @ SV844 @ ( tc_fun @ SV1383 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV219 @ SV844 @ ( tc_fun @ SV1383 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3418]) ).
thf(4084,plain,
! [SV1384: $i,SV845: $i,SV220: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV220 @ ( c_HOL_Ominus__class_Ominus @ SV845 @ SV220 @ ( tc_fun @ SV1384 @ tc_bool ) ) @ ( tc_fun @ SV1384 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV220 @ SV845 @ ( tc_fun @ SV1384 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3419]) ).
thf(4085,plain,
! [SV1385: $i,SV846: $i,SV221: $i] :
( ( ( c_lessequals @ SV221 @ SV846 @ ( tc_fun @ SV1385 @ tc_bool ) )
| ! [SY6213: $i] :
~ ( c_lessequals @ SV221 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY6213 @ SV846 @ ( tc_fun @ SV1385 @ tc_bool ) ) @ ( tc_fun @ SV1385 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3420]) ).
thf(4086,plain,
! [SV1386: $i,SV847: $i,SV222: $i] :
( ( ( c_lessequals @ SV222 @ SV847 @ ( tc_fun @ SV1386 @ tc_bool ) )
| ! [SY6214: $i] :
~ ( c_lessequals @ SV222 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV847 @ SY6214 @ ( tc_fun @ SV1386 @ tc_bool ) ) @ ( tc_fun @ SV1386 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3421]) ).
thf(4087,plain,
! [SV848: $i,SV223: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV223 ) )
= $true )
| ( ( ! [SY5112: $i] :
( ( c_lessequals @ SV848 @ SY5112 @ SV223 )
| ! [SY5113: $i] :
~ ( c_lessequals @ SV848 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5112 @ SY5113 @ SV223 ) @ SV223 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3422]) ).
thf(4088,plain,
! [SV849: $i,SV224: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV224 ) )
= $true )
| ( ( ! [SY5114: $i] :
( ( c_lessequals @ SV849 @ SY5114 @ SV224 )
| ! [SY5115: $i] :
~ ( c_lessequals @ SV849 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5115 @ SY5114 @ SV224 ) @ SV224 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3423]) ).
thf(4089,plain,
! [SV850: $i,SV225: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV225 ) )
= $true )
| ( ( ! [SY5116: $i,SY5117: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV850 @ SY5116 @ SV225 ) @ SY5117 @ SV225 )
| ~ ( c_lessequals @ SV850 @ SY5117 @ SV225 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3424]) ).
thf(4090,plain,
! [SV851: $i,SV226: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV226 ) )
= $true )
| ( ( ! [SY5118: $i,SY5119: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV851 @ SY5118 @ SV226 ) @ SY5119 @ SV226 )
| ~ ( c_lessequals @ SY5118 @ SY5119 @ SV226 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3425]) ).
thf(4091,plain,
! [SV852: $i,SV227: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV227 ) )
= $true )
| ( ( ! [SY5120: $i] :
( ( c_lessequals @ SV852 @ SY5120 @ SV227 )
| ! [SY5121: $i] :
~ ( c_lessequals @ SV852 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5120 @ SY5121 @ SV227 ) @ SV227 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3426]) ).
thf(4092,plain,
! [SV853: $i,SV228: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV228 ) )
= $true )
| ( ( ! [SY5122: $i] :
( ( c_lessequals @ SV853 @ SY5122 @ SV228 )
| ! [SY5123: $i] :
~ ( c_lessequals @ SV853 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5123 @ SY5122 @ SV228 ) @ SV228 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3427]) ).
thf(4093,plain,
! [SV1387: $i,SV854: $i,SV229: $i] :
( ( ! [SY6215: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV229 @ SV854 @ ( tc_fun @ SV1387 @ tc_bool ) ) @ SY6215 @ ( tc_fun @ SV1387 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV229 @ SY6215 @ ( tc_fun @ SV1387 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV854 @ SY6215 @ ( tc_fun @ SV1387 @ tc_bool ) ) @ ( tc_fun @ SV1387 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3428]) ).
thf(4094,plain,
! [SV1388: $i,SV855: $i,SV230: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV230 @ SV855 @ ( tc_fun @ SV1388 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV855 @ SV230 @ ( tc_fun @ SV1388 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3429]) ).
thf(4095,plain,
! [SV231: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV231 )
= $false )
| ( ( ! [SY3367: $i,SY3368: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3367 @ SY3368 @ SV231 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3368 @ SY3367 @ SV231 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3430]) ).
thf(4096,plain,
! [SV232: $i] :
( ( ( class_Lattices_Olattice @ SV232 )
= $false )
| ( ( ! [SY3369: $i,SY3370: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3369 @ SY3370 @ SV232 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3370 @ SY3369 @ SV232 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3431]) ).
thf(4097,plain,
! [SV1389: $i,SV856: $i,SV233: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV233 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV233 @ SV856 @ ( tc_fun @ SV1389 @ tc_bool ) ) @ ( tc_fun @ SV1389 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV233 @ SV856 @ ( tc_fun @ SV1389 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3432]) ).
thf(4098,plain,
! [SV234: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV234 )
= $false )
| ( ( ! [SY3373: $i,SY3374: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3373 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3373 @ SY3374 @ SV234 ) @ SV234 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3373 @ SY3374 @ SV234 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3433]) ).
thf(4099,plain,
! [SV235: $i] :
( ( ( class_Lattices_Olattice @ SV235 )
= $false )
| ( ( ! [SY3375: $i,SY3376: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY3375 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3375 @ SY3376 @ SV235 ) @ SV235 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3375 @ SY3376 @ SV235 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3434]) ).
thf(4100,plain,
! [SV1390: $i,SV857: $i,SV236: $i] :
( ( ! [SY6216: $i,SY6217: $i] :
( ( c_Set_Ovimage @ SV236 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV857 @ SV1390 @ ( tc_fun @ SY6216 @ tc_bool ) ) @ SY6217 @ SY6216 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ SV236 @ SV857 @ SY6217 @ SY6216 ) @ ( c_Set_Ovimage @ SV236 @ SV1390 @ SY6217 @ SY6216 ) @ ( tc_fun @ SY6217 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3435]) ).
thf(4101,plain,
! [SV1391: $i,SV858: $i,SV237: $i] :
( ( ! [SY6218: $i,SY6219: $i] :
( ( c_Fun_Ofun__upd @ SV237 @ SV858 @ SV1391 @ SY6218 @ SY6219 )
!= SV237 )
| ( ( hAPP @ SV237 @ SV858 )
= SV1391 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3436]) ).
thf(4102,plain,
! [SV1392: $i,SV859: $i,SV238: $i] :
( ( ! [SY6220: $i] :
( ( c_Fun_Oinj__on @ SV238 @ SV859 @ SV1392 @ SY6220 )
| ! [SY6221: $i] :
~ ( c_Fun_Oinj__on @ SV238 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY6221 @ SV859 @ ( tc_fun @ SV1392 @ tc_bool ) ) @ SV1392 @ SY6220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3437]) ).
thf(4103,plain,
! [SV1393: $i,SV860: $i,SV239: $i] :
( ( ! [SY6222: $i] :
( ( c_Fun_Oinj__on @ SV239 @ SV860 @ SV1393 @ SY6222 )
| ! [SY6223: $i] :
~ ( c_Fun_Oinj__on @ SV239 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV860 @ SY6223 @ ( tc_fun @ SV1393 @ tc_bool ) ) @ SV1393 @ SY6222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3438]) ).
thf(4104,plain,
! [SV1394: $i,SV861: $i,SV240: $i] :
( ( ! [SY6224: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV240 @ SV861 @ ( tc_fun @ SV1394 @ tc_bool ) ) @ SY6224 @ ( tc_fun @ SV1394 @ tc_bool ) )
| ~ ( c_lessequals @ SV240 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV861 @ SY6224 @ ( tc_fun @ SV1394 @ tc_bool ) ) @ ( tc_fun @ SV1394 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3439]) ).
thf(4105,plain,
! [SV1395: $i,SV862: $i,SV241: $i] :
( ( ! [SY6225: $i] :
( ( c_lessequals @ SV241 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV862 @ SV1395 @ ( tc_fun @ SY6225 @ tc_bool ) ) @ ( tc_fun @ SY6225 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV241 @ SV862 @ ( tc_fun @ SY6225 @ tc_bool ) ) @ SV1395 @ ( tc_fun @ SY6225 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3440]) ).
thf(4106,plain,
! [SV863: $i,SV242: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV242 ) )
= $true )
| ( ( ! [SY5144: $i] :
( ! [SY5145: $i] : ( c_HOL_Oord__class_Oless @ SV863 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5144 @ SY5145 @ SV242 ) @ SV242 )
| ~ ( c_HOL_Oord__class_Oless @ SV863 @ SY5144 @ SV242 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3441]) ).
thf(4107,plain,
! [SV864: $i,SV243: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV243 ) )
= $true )
| ( ( ! [SY5146: $i,SY5147: $i] :
( ( c_HOL_Oord__class_Oless @ SV864 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5146 @ SY5147 @ SV243 ) @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ SV864 @ SY5147 @ SV243 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3442]) ).
thf(4108,plain,
! [SV1396: $i,SV865: $i,SV244: $i] :
( ( ~ ( class_HOL_Oord @ SV244 )
| ! [SY6226: $i] :
( ( c_lessequals @ ( hAPP @ SV865 @ SV1396 ) @ ( hAPP @ SY6226 @ SV1396 ) @ SV244 )
| ! [SY5150: $i] :
~ ( c_lessequals @ SV865 @ SY6226 @ ( tc_fun @ SY5150 @ SV244 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3443]) ).
thf(4109,plain,
! [SV1397: $i,SV866: $i,SV245: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV245 ) @ SV866 ) @ SV1397 ) )
| ! [SY6228: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV245 ) @ SV866 ) @ SY6228 ) )
| ~ ( c_lessequals @ SY6228 @ SV1397 @ ( tc_fun @ SV245 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3444]) ).
thf(4110,plain,
! [SV1398: $i,SV867: $i,SV246: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV246 ) @ SV867 ) @ SV1398 ) )
| ! [SY6229: $i] :
( ~ ( c_lessequals @ SY6229 @ SV1398 @ ( tc_fun @ SV246 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV246 ) @ SV867 ) @ SY6229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3445]) ).
thf(4111,plain,
! [SV1399: $i,SV868: $i,SV247: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV247 ) @ SV868 ) @ SV1399 ) )
| ! [SY6230: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV247 ) @ SV868 ) @ SY6230 ) )
| ~ ( c_lessequals @ SY6230 @ SV1399 @ ( tc_fun @ SV247 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3446]) ).
thf(4112,plain,
! [SV1400: $i,SV869: $i,SV248: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV248 ) @ SV869 ) @ SV1400 ) )
| ! [SY6231: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV248 ) @ SV869 ) @ SY6231 ) )
| ~ ( c_lessequals @ SY6231 @ SV1400 @ ( tc_fun @ SV248 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3447]) ).
thf(4113,plain,
! [SV1401: $i,SV870: $i,SV249: $i] :
( ( ! [SY6232: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV249 ) @ SV870 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1401 @ SY6232 @ ( tc_fun @ SV249 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV249 ) @ SV870 ) @ SV1401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3448]) ).
thf(4114,plain,
! [SV1402: $i,SV871: $i,SV250: $i] :
( ( ! [SY6233: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV250 ) @ SV871 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1402 @ SY6233 @ ( tc_fun @ SV250 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV250 ) @ SV871 ) @ SY6233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3449]) ).
thf(4115,plain,
! [SV1403: $i,SV872: $i,SV251: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV251 ) @ SV872 ) @ SV1403 ) )
| ! [SY6234: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV251 ) @ SV872 ) @ SY6234 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV251 ) @ SV872 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY6234 @ SV1403 @ ( tc_fun @ SV251 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3450]) ).
thf(4116,plain,
! [SV1404: $i,SV873: $i,SV253: $i] :
( ( ! [SY6235: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV253 ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV873 @ SV1404 @ SY6235 @ SV253 ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV873 @ SV1404 @ ( tc_fun @ SV253 @ tc_bool ) ) ) )
| ! [SY6236: $i] :
( ~ ( hBOOL @ ( hAPP @ SY6235 @ SY6236 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV253 ) @ SY6236 ) @ SV1404 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3451]) ).
thf(4117,plain,
! [SV1405: $i,SV874: $i,SV254: $i] :
( ( ! [SY6237: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV254 ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV874 @ SV1405 @ SY6237 @ SV254 ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV874 @ SV1405 @ ( tc_fun @ SV254 @ tc_bool ) ) ) )
| ! [SY5170: $i] :
( ~ ( hBOOL @ ( hAPP @ SY6237 @ SY5170 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV254 ) @ SY5170 ) @ SV874 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3452]) ).
thf(4118,plain,
! [SV1406: $i,SV875: $i,SV255: $i] :
( ( ( ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ SV255 @ SV875 @ SV1406 ) @ SV1406 )
= ( c_Finite__Set_Ocard @ SV875 @ SV1406 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1406 ) @ SV255 ) @ SV875 ) )
| ~ ( c_Finite__Set_Ofinite @ SV875 @ SV1406 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3453]) ).
thf(4119,plain,
! [SV1407: $i,SV876: $i,SV256: $i] :
( ( ! [SY6239: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV256 @ SV876 @ SV1407 ) @ SY6239 @ SV1407 @ SV876 )
= ( c_Set_Oinsert @ SV256 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV876 @ tc_bool ) ) @ SV876 ) )
| ( SY6239
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1407 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3454]) ).
thf(4120,plain,
! [SV1408: $i,SV877: $i,SV257: $i] :
( ( ! [SY6240: $i,SY6241: $i,SY6242: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ofun__upd @ SV257 @ SV877 @ SV1408 @ SY6240 @ SY6241 ) @ SY6242 @ SY6240 @ SY6241 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6241 ) @ SV1408 ) @ ( c_Set_Oimage @ SV257 @ SY6242 @ SY6240 @ SY6241 ) ) )
| ~ ( c_Fun_Oinj__on @ SV257 @ SY6242 @ SY6240 @ SY6241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3455]) ).
thf(4121,plain,
! [SV1409: $i,SV878: $i,SV258: $i] :
( ( ( c_Set_Oinsert @ SV258 @ SV878 @ SV1409 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ SV1409 ) @ SV1409 @ SV1409 @ tc_bool ) @ SV258 ) @ SV1409 ) @ SV878 @ ( tc_fun @ SV1409 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3456]) ).
thf(4122,plain,
! [SV1410: $i,SV879: $i,SV259: $i] :
( ( ! [SY6243: $i] :
( ( c_lessequals @ SV259 @ ( c_Set_Oinsert @ SV879 @ SV1410 @ SY6243 ) @ ( tc_fun @ SY6243 @ tc_bool ) )
| ~ ( c_lessequals @ SV259 @ SV1410 @ ( tc_fun @ SY6243 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV259 @ ( c_Set_Oinsert @ SV879 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6243 @ tc_bool ) ) @ SY6243 ) @ ( tc_fun @ SY6243 @ tc_bool ) ) @ SV1410 @ ( tc_fun @ SY6243 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3457]) ).
thf(4123,plain,
! [SV1411: $i,SV880: $i,SV260: $i] :
( ( ! [SY6244: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ SV260 @ SV880 @ SV1411 @ SY6244 ) @ SY6244 )
= ( c_Finite__Set_Ocard @ SV880 @ SV1411 ) )
| ~ ( c_Fun_Oinj__on @ SV260 @ SV880 @ SV1411 @ SY6244 )
| ~ ( c_Finite__Set_Ofinite @ SV880 @ SV1411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3458]) ).
thf(4124,plain,
! [SV1412: $i,SV881: $i,SV261: $i] :
( ( ! [SY6245: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ SV261 @ SV881 @ SV1412 @ SY6245 ) @ SY6245 )
!= ( c_Finite__Set_Ocard @ SV881 @ SV1412 ) )
| ~ ( c_Finite__Set_Ofinite @ SV881 @ SV1412 )
| ( c_Fun_Oinj__on @ SV261 @ SV881 @ SV1412 @ SY6245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3459]) ).
thf(4125,plain,
! [SV1413: $i,SV882: $i,SV262: $i] :
( ( ( ( c_Set_Oimage @ SV262 @ SV882 @ SV1413 @ SV1413 )
= SV882 )
| ~ ( c_Fun_Oinj__on @ SV262 @ SV882 @ SV1413 @ SV1413 )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV262 @ SV882 @ SV1413 @ SV1413 ) @ SV882 @ ( tc_fun @ SV1413 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV882 @ SV1413 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3460]) ).
thf(4126,plain,
! [SV1414: $i,SV883: $i,SV263: $i] :
( ( ( c_Fun_Oinj__on @ SV263 @ SV883 @ SV1414 @ SV1414 )
| ~ ( c_lessequals @ SV883 @ ( c_Set_Oimage @ SV263 @ SV883 @ SV1414 @ SV1414 ) @ ( tc_fun @ SV1414 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV883 @ SV1414 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3461]) ).
thf(4127,plain,
! [SV1415: $i,SV884: $i,SV264: $i] :
( ( ! [SY6246: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ SV264 @ SV884 @ SV1415 ) @ SY6246 @ SV1415 @ SV884 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1415 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV884 ) @ SV264 ) @ SY6246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3462]) ).
thf(4128,plain,
! [SV1416: $i,SV885: $i,SV265: $i] :
( ( ! [SY6247: $i] :
( ( c_HOL_Oord__class_Oless @ SV265 @ ( c_Set_Oinsert @ SV885 @ SV1416 @ SY6247 ) @ ( tc_fun @ SY6247 @ tc_bool ) )
| ~ ( c_lessequals @ SV265 @ SV1416 @ ( tc_fun @ SY6247 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6247 ) @ SV885 ) @ SV265 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV265 @ SV1416 @ ( tc_fun @ SY6247 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3463]) ).
thf(4129,plain,
! [SV1417: $i,SV886: $i,SV266: $i] :
( ( ! [SY6248: $i] :
( ( c_HOL_Oord__class_Oless @ SV266 @ ( c_Set_Oinsert @ SV886 @ SV1417 @ SY6248 ) @ ( tc_fun @ SY6248 @ tc_bool ) )
| ~ ( c_lessequals @ SV266 @ SV1417 @ ( tc_fun @ SY6248 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6248 ) @ SV886 ) @ SV266 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6248 ) @ SV886 ) @ SV1417 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3464]) ).
thf(4130,plain,
! [SV1418: $i,SV887: $i,SV267: $i] :
( ( ( c_lessequals @ SV267 @ SV887 @ ( tc_fun @ SV1418 @ tc_bool ) )
| ! [SY6249: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1418 ) @ SY6249 ) @ SV267 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1418 ) @ SY6249 ) @ SV887 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV267 @ ( c_Set_Oinsert @ SY6249 @ SV887 @ SV1418 ) @ ( tc_fun @ SV1418 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3465]) ).
thf(4131,plain,
! [SV1419: $i,SV888: $i,SV268: $i] :
( ( ! [SY6250: $i,SY6251: $i] :
( ( ( c_Set_Oimage @ SV268 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV888 @ SV1419 @ ( tc_fun @ SY6250 @ tc_bool ) ) @ SY6250 @ SY6251 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV268 @ SV888 @ SY6250 @ SY6251 ) @ ( c_Set_Oimage @ SV268 @ SV1419 @ SY6250 @ SY6251 ) @ ( tc_fun @ SY6251 @ tc_bool ) ) )
| ! [SY6252: $i] :
( ~ ( c_lessequals @ SV1419 @ SY6252 @ ( tc_fun @ SY6250 @ tc_bool ) )
| ~ ( c_lessequals @ SV888 @ SY6252 @ ( tc_fun @ SY6250 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV268 @ SY6252 @ SY6250 @ SY6251 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3466]) ).
thf(4132,plain,
! [SV1420: $i,SV889: $i,SV269: $i] :
( ( ! [SY6253: $i,SY6254: $i] :
( ( c_Set_Ovimage @ SV269 @ ( c_Set_Oinsert @ SV889 @ SV1420 @ SY6253 ) @ SY6254 @ SY6253 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ SV269 @ ( c_Set_Oinsert @ SV889 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6253 @ tc_bool ) ) @ SY6253 ) @ SY6254 @ SY6253 ) @ ( c_Set_Ovimage @ SV269 @ SV1420 @ SY6254 @ SY6253 ) @ ( tc_fun @ SY6254 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3467]) ).
thf(4133,plain,
! [SV1421: $i,SV890: $i,SV270: $i] :
( ( ! [SY6255: $i,SY6256: $i] :
( ( ( c_Set_Oimage @ SV270 @ ( c_HOL_Ominus__class_Ominus @ SV890 @ SV1421 @ ( tc_fun @ SY6255 @ tc_bool ) ) @ SY6255 @ SY6256 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV270 @ SV890 @ SY6255 @ SY6256 ) @ ( c_Set_Oimage @ SV270 @ SV1421 @ SY6255 @ SY6256 ) @ ( tc_fun @ SY6256 @ tc_bool ) ) )
| ! [SY6257: $i] :
( ~ ( c_lessequals @ SV1421 @ SY6257 @ ( tc_fun @ SY6255 @ tc_bool ) )
| ~ ( c_lessequals @ SV890 @ SY6257 @ ( tc_fun @ SY6255 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV270 @ SY6257 @ SY6255 @ SY6256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3468]) ).
thf(4134,plain,
! [SV1422: $i,SV891: $i,SV271: $i] :
( ( ! [SY6258: $i,SY6259: $i] :
( ( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ SV271 @ SV891 @ SV1422 @ SY6258 @ ( tc_Option_Ooption @ SY6259 ) ) @ SY6258 @ SY6259 )
= ( c_Set_Oinsert @ SV891 @ ( c_Map_Odom @ SV271 @ SY6258 @ SY6259 ) @ SY6258 ) )
| ( SV1422
= ( c_Option_Ooption_ONone @ SY6259 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3469]) ).
thf(4135,plain,
! [SV1423: $i,SV892: $i,SV272: $i] :
( ( ! [SY6260: $i,SY6261: $i] :
( ! [SY6262: $i] : ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ SV272 @ SV892 @ ( c_Option_Ooption_ONone @ SV1423 ) @ SY6260 @ ( tc_Option_Ooption @ SV1423 ) ) @ ( c_Fun_Ofun__upd @ SY6261 @ SV892 @ ( c_Option_Ooption_OSome @ SY6262 @ SV1423 ) @ SY6260 @ ( tc_Option_Ooption @ SV1423 ) ) @ SY6260 @ SV1423 )
| ~ ( c_Map_Omap__le @ SV272 @ SY6261 @ SY6260 @ SV1423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3470]) ).
thf(4136,plain,
! [SV1424: $i,SV893: $i,SV273: $i] :
( ( ! [SY6263: $i] :
( ( c_HOL_Oord__class_Oless @ SV273 @ ( c_Set_Oinsert @ SV893 @ SV1424 @ SY6263 ) @ ( tc_fun @ SY6263 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6263 ) @ SV893 ) @ SV273 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV273 @ ( c_Set_Oinsert @ SV893 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6263 @ tc_bool ) ) @ SY6263 ) @ ( tc_fun @ SY6263 @ tc_bool ) ) @ SV1424 @ ( tc_fun @ SY6263 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6263 ) @ SV893 ) @ SV1424 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3471]) ).
thf(4137,plain,
! [SV894: $i,SV274: $i] :
( ( ( c_Com_Ocom_OWhile @ SV274 @ SV894 )
= c_Com_Ocom_OSKIP )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3472]) ).
thf(4138,plain,
! [SV1425: $i,SV895: $i,SV275: $i] :
( ( ( c_Com_Ocom_OBODY @ SV275 )
!= ( c_Com_Ocom_OWhile @ SV895 @ SV1425 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3473]) ).
thf(4139,plain,
! [SV1426: $i,SV896: $i,SV276: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV276 @ SV896 @ ( tc_fun @ SV1426 @ tc_bool ) ) @ SV1426 )
| ~ ( c_Finite__Set_Ofinite @ SV276 @ SV1426 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3474]) ).
thf(4140,plain,
! [SV1427: $i,SV897: $i,SV277: $i] :
( ( ! [SY6264: $i] :
( ( c_Com_Ocom_OBODY @ SV277 )
!= ( c_Com_Ocom_OLocal @ SV897 @ SV1427 @ SY6264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3475]) ).
thf(4141,plain,
! [SV1428: $i,SV898: $i,SV278: $i] :
( ( ! [SY6265: $i,SY6266: $i] :
( ( c_Fun_Oinj__on @ SV278 @ ( c_HOL_Ominus__class_Ominus @ SV898 @ SV1428 @ ( tc_fun @ SY6265 @ tc_bool ) ) @ SY6265 @ SY6266 )
| ~ ( c_Fun_Oinj__on @ SV278 @ SV898 @ SY6265 @ SY6266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3476]) ).
thf(4142,plain,
! [SV1429: $i,SV899: $i,SV279: $i] :
( ( ! [SY6267: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV279 @ tc_bool ) )
!= ( c_Set_Oimage @ SV899 @ SV1429 @ SY6267 @ SV279 ) )
| ( SV1429
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6267 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3477]) ).
thf(4143,plain,
! [SV1430: $i,SV900: $i,SV280: $i] :
( ( ! [SY6268: $i,SY6269: $i] :
( ( c_Com_Ocom_OWhile @ SV280 @ SV900 )
!= ( c_Com_Ocom_OLocal @ SV1430 @ SY6268 @ SY6269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3478]) ).
thf(4144,plain,
! [SV1431: $i,SV901: $i,SV281: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV281 @ SV901 ) ) @ SV1431 ) @ SV1431 ) )
| ( hBOOL @ ( hAPP @ SV281 @ SV1431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3479]) ).
thf(4145,plain,
! [SV1432: $i,SV902: $i,SV282: $i] :
( ( ! [SY6270: $i,SY6271: $i] :
( ( c_Set_Ovimage @ SV282 @ ( c_HOL_Ominus__class_Ominus @ SV902 @ SV1432 @ ( tc_fun @ SY6270 @ tc_bool ) ) @ SY6271 @ SY6270 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Ovimage @ SV282 @ SV902 @ SY6271 @ SY6270 ) @ ( c_Set_Ovimage @ SV282 @ SV1432 @ SY6271 @ SY6270 ) @ ( tc_fun @ SY6271 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3480]) ).
thf(4146,plain,
! [SV1433: $i,SV903: $i,SV283: $i] :
( ( ! [SY6272: $i] :
( ( c_HOL_Oord__class_Oless @ SV283 @ ( c_Set_Oinsert @ SV903 @ SV1433 @ SY6272 ) @ ( tc_fun @ SY6272 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6272 ) @ SV903 ) @ SV283 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV283 @ ( c_Set_Oinsert @ SV903 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6272 @ tc_bool ) ) @ SY6272 ) @ ( tc_fun @ SY6272 @ tc_bool ) ) @ SV1433 @ ( tc_fun @ SY6272 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV283 @ SV1433 @ ( tc_fun @ SY6272 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3481]) ).
thf(4147,plain,
! [SV1434: $i,SV905: $i,SV285: $i] :
( ( ( c_Com_Ocom_OAss @ SV285 @ SV905 )
!= ( c_Com_Ocom_OBODY @ SV1434 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3483]) ).
thf(4148,plain,
! [SV1435: $i,SV906: $i,SV286: $i] :
( ( ! [SY6273: $i] :
( ( ( c_Com_Ocom_OSemi @ SV286 @ SV906 )
!= ( c_Com_Ocom_OSemi @ SV1435 @ SY6273 ) )
| ( SV906 = SY6273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3484]) ).
thf(4149,plain,
! [SV1436: $i,SV907: $i,SV287: $i] :
( ( ! [SY6274: $i] :
( ( c_Com_Ocom_OSemi @ SV287 @ SV907 )
!= ( c_Com_Ocom_OSemi @ SV1436 @ SY6274 ) )
| ( SV287 = SV1436 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3485]) ).
thf(4150,plain,
! [SV1437: $i,SV908: $i,SV288: $i] :
( ( ! [SY6275: $i] :
( ( c_Com_Ocom_OSemi @ SV288 @ SV908 )
!= ( c_Com_Ocom_OWhile @ SV1437 @ SY6275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3486]) ).
thf(4151,plain,
! [SV1438: $i,SV909: $i,SV289: $i] :
( ( ! [SY6276: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV289 @ ( c_Set_Oinsert @ SV909 @ SV1438 @ SY6276 ) @ ( tc_fun @ SY6276 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV289 @ SV1438 @ ( tc_fun @ SY6276 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV909 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6276 @ tc_bool ) ) @ SY6276 ) @ ( tc_fun @ SY6276 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3487]) ).
thf(4152,plain,
! [SV1439: $i,SV910: $i,SV290: $i] :
( ( ! [SY6277: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV290 @ ( c_Set_Oinsert @ SV910 @ SV1439 @ SY6277 ) @ ( tc_fun @ SY6277 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV290 @ ( c_Set_Oinsert @ SV910 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6277 @ tc_bool ) ) @ SY6277 ) @ ( tc_fun @ SY6277 @ tc_bool ) ) @ SV1439 @ ( tc_fun @ SY6277 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3488]) ).
thf(4153,plain,
! [SV1440: $i,SV911: $i,SV291: $i] :
( ( ! [SY6278: $i,SY6279: $i] :
( ( c_Com_Ocom_OSemi @ SV291 @ SV911 )
!= ( c_Com_Ocom_OCond @ SV1440 @ SY6278 @ SY6279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3489]) ).
thf(4154,plain,
! [SV912: $i,SV292: $i] :
( ( ( c_Finite__Set_Ofinite @ SV292 @ SV912 )
= $true )
| ( ( ! [SY5247: $i] :
( ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV292 @ SY5247 @ ( tc_fun @ SV912 @ tc_bool ) ) @ SV912 )
| ~ ( c_Finite__Set_Ofinite @ SY5247 @ SV912 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3490]) ).
thf(4155,plain,
! [SV1441: $i,SV913: $i,SV293: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV293 @ SV913 @ ( tc_fun @ SV1441 @ tc_bool ) ) @ SV1441 )
| ~ ( c_Finite__Set_Ofinite @ SV293 @ SV1441 )
| ~ ( c_Finite__Set_Ofinite @ SV913 @ SV1441 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3491]) ).
thf(4156,plain,
! [SV1442: $i,SV914: $i,SV294: $i] :
( ( ( c_Set_Oinsert @ SV294 @ SV914 @ SV1442 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1442 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3492]) ).
thf(4157,plain,
! [SV1443: $i,SV915: $i,SV295: $i] :
( ( ! [SY6280: $i,SY6281: $i] :
( ( c_Com_Ocom_OSemi @ SV295 @ SV915 )
!= ( c_Com_Ocom_OLocal @ SV1443 @ SY6280 @ SY6281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3493]) ).
thf(4158,plain,
! [SV1444: $i,SV916: $i,SV296: $i] :
( ( ! [SY6282: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV296 ) @ SV916 ) @ ( c_Set_Ovimage @ SV1444 @ ( c_Set_Oinsert @ ( hAPP @ SV1444 @ SV916 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6282 @ tc_bool ) ) @ SY6282 ) @ SV296 @ SY6282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3494]) ).
thf(4159,plain,
! [SV1445: $i,SV917: $i,SV297: $i] :
( ( ! [SY6283: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV297 @ SV917 @ SV1445 ) @ ( c_Set_Oinsert @ SV297 @ SY6283 @ SV1445 ) @ ( tc_fun @ SV1445 @ tc_bool ) )
= ( c_Set_Oinsert @ SV297 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV917 @ SY6283 @ ( tc_fun @ SV1445 @ tc_bool ) ) @ SV1445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3495]) ).
thf(4160,plain,
! [SV1446: $i,SV918: $i,SV298: $i] :
( ( ! [SY6284: $i] :
( ( c_Map_Omap__le @ SV298 @ SV918 @ SV1446 @ SY6284 )
| ! [SY6285: $i] :
~ ( c_Map_Omap__le @ ( c_Map_Omap__add @ SY6285 @ SV298 @ SV1446 @ SY6284 ) @ SV918 @ SV1446 @ SY6284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3496]) ).
thf(4161,plain,
! [SV1447: $i,SV919: $i,SV299: $i] :
( ( ( c_Set_Oinsert @ SV299 @ ( c_Set_Oinsert @ SV299 @ SV919 @ SV1447 ) @ SV1447 )
= ( c_Set_Oinsert @ SV299 @ SV919 @ SV1447 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3497]) ).
thf(4162,plain,
! [SV1448: $i,SV920: $i,SV300: $i] :
( ( ( c_Finite__Set_Ofinite @ ( hAPP @ SV300 @ SV920 ) @ SV1448 )
| ! [SY6286: $i,SY6287: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6286 ) @ SV920 ) @ SY6287 ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY6287 @ SV300 @ SY6286 @ ( tc_fun @ SV1448 @ tc_bool ) ) @ SV1448 )
| ~ ( c_Finite__Set_Ofinite @ SY6287 @ SY6286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3498]) ).
thf(4163,plain,
! [SV1449: $i,SV921: $i,SV301: $i] :
( ( c_Map_Omap__le @ SV301 @ SV301 @ SV921 @ SV1449 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3499]) ).
thf(4164,plain,
! [SV1450: $i,SV922: $i,SV302: $i] :
( ( ! [SY6288: $i] :
( ( c_Map_Omap__le @ SV302 @ SV922 @ SV1450 @ SY6288 )
| ! [SY6289: $i] :
( ~ ( c_Map_Omap__le @ SY6289 @ SV922 @ SV1450 @ SY6288 )
| ~ ( c_Map_Omap__le @ SV302 @ SY6289 @ SV1450 @ SY6288 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3500]) ).
thf(4165,plain,
! [SV1451: $i,SV923: $i,SV303: $i] :
( ( ! [SY6290: $i,SY6291: $i] :
( ( c_Com_Ocom_OLocal @ SV303 @ SV923 @ SV1451 )
!= ( c_Com_Ocom_OAss @ SY6290 @ SY6291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3501]) ).
thf(4166,plain,
! [SV924: $i,SV304: $i] :
( ( ( hBOOL @ ( hAPP @ SV304 @ SV924 ) )
= $true )
| ( ( ! [SY5271: $i] :
( ( SY5271 = SV924 )
| ! [SY5272: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY5271 @ SV304 @ SY5272 ) @ SV924 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3502]) ).
thf(4167,plain,
! [SV1452: $i,SV925: $i,SV305: $i] :
( ( ! [SY6292: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV305 @ SV925 @ SV1452 @ ( tc_fun @ SY6292 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6292 @ tc_bool ) ) )
| ! [SY6293: $i] :
( ( ( hAPP @ SV925 @ SY6293 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6292 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1452 ) @ SY6293 ) @ SV305 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3503]) ).
thf(4168,plain,
! [SV1453: $i,SV926: $i,SV306: $i] :
( ( ( c_Com_Ocom_OBODY @ SV306 )
!= ( c_Com_Ocom_OAss @ SV926 @ SV1453 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3504]) ).
thf(4169,plain,
! [SV1454: $i,SV927: $i,SV307: $i] :
( ( ! [SY6294: $i,SY6295: $i] :
( ( c_Com_Ocom_OCond @ SV307 @ SV927 @ SV1454 )
!= ( c_Com_Ocom_OWhile @ SY6294 @ SY6295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3505]) ).
thf(4170,plain,
! [SV1455: $i,SV928: $i,SV308: $i] :
( ( ! [SY6296: $i,SY6297: $i,SY6298: $i] :
( ( c_Com_Ocom_OCond @ SV308 @ SV928 @ SV1455 )
!= ( c_Com_Ocom_OLocal @ SY6296 @ SY6297 @ SY6298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3506]) ).
thf(4171,plain,
! [SV309: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV309 )
= $false )
| ( ( ! [SY3605: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3605 @ ( c_Orderings_Obot__class_Obot @ SV309 ) @ SV309 )
= ( c_Orderings_Obot__class_Obot @ SV309 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3507]) ).
thf(4172,plain,
! [SV310: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV310 )
= $false )
| ( ( ! [SY3606: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ SV310 ) @ SY3606 @ SV310 )
= ( c_Orderings_Obot__class_Obot @ SV310 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3508]) ).
thf(4173,plain,
! [SV931: $i,SV313: $i] :
( ( ( c_Finite__Set_Ofinite @ SV313 @ SV931 )
= $true )
| ( ( ! [SY5284: $i] :
~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SY5284 @ SV313 @ SV931 ) @ SV931 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3511]) ).
thf(4174,plain,
! [SV1456: $i,SV932: $i,SV314: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV314 @ SV932 @ SV1456 ) @ SV1456 )
| ~ ( c_Finite__Set_Ofinite @ SV932 @ SV1456 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3512]) ).
thf(4175,plain,
! [SV1457: $i,SV933: $i,SV316: $i] :
( ( ! [SY6299: $i,SY6300: $i] :
( ( c_Com_Ocom_OCond @ SV316 @ SV933 @ SV1457 )
!= ( c_Com_Ocom_OSemi @ SY6299 @ SY6300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3513]) ).
thf(4176,plain,
! [SV934: $i,SV317: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV317 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ SV934 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
= $true )
| ( ( ~ ( c_Com_OWT @ SV934 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV317 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ SV317 ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3514]) ).
thf(4177,plain,
! [SV1458: $i,SV935: $i,SV318: $i] :
( ( ! [SY6301: $i,SY6302: $i,SY6303: $i,SY6304: $i,SY6305: $i,SY6306: $i] :
( ( ( hAPP @ SV318 @ ( c_Set_Oinsert @ SV935 @ ( c_Set_Oinsert @ SV1458 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6301 @ tc_bool ) ) @ SY6301 ) @ SY6301 ) )
= ( hAPP @ ( hAPP @ SY6302 @ SV935 ) @ SV1458 ) )
| ! [SY3626: $i,SY3627: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY6303 @ SV318 @ SY6304 @ SY6305 @ SY6306 @ SY6302 @ SY3626 @ SY3627 @ SY6301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3515]) ).
thf(4178,plain,
! [SV1459: $i,SV936: $i,SV319: $i] :
( ( ! [SY6309: $i,SY6310: $i,SY6311: $i,SY6312: $i,SY6313: $i,SY6314: $i] :
( ( ( hAPP @ SV319 @ ( c_Set_Oinsert @ SV936 @ ( c_Set_Oinsert @ SV1459 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6309 @ tc_bool ) ) @ SY6309 ) @ SY6309 ) )
= ( hAPP @ ( hAPP @ SY6310 @ SV936 ) @ SV1459 ) )
| ! [SY3636: $i,SY3637: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV319 @ SY6311 @ SY6312 @ SY6313 @ SY6310 @ SY6314 @ SY3636 @ SY3637 @ SY6309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3516]) ).
thf(4179,plain,
! [SV1460: $i,SV937: $i,SV320: $i] :
( ( ! [SY6317: $i,SY6318: $i,SY6319: $i] :
( ( ( c_Com_Ocom_OCond @ SV320 @ SV937 @ SV1460 )
!= ( c_Com_Ocom_OCond @ SY6317 @ SY6318 @ SY6319 ) )
| ( SV1460 = SY6319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3517]) ).
thf(4180,plain,
! [SV1461: $i,SV938: $i,SV321: $i] :
( ( ! [SY6320: $i,SY6321: $i] :
( ! [SY6322: $i] :
( ( c_Com_Ocom_OCond @ SV321 @ SV938 @ SV1461 )
!= ( c_Com_Ocom_OCond @ SY6320 @ SY6321 @ SY6322 ) )
| ( SV938 = SY6321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3518]) ).
thf(4181,plain,
! [SV1462: $i,SV939: $i,SV322: $i] :
( ( ! [SY6323: $i] :
( ! [SY6324: $i,SY6325: $i] :
( ( c_Com_Ocom_OCond @ SV322 @ SV939 @ SV1462 )
!= ( c_Com_Ocom_OCond @ SY6323 @ SY6324 @ SY6325 ) )
| ( SV322 = SY6323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3519]) ).
thf(4182,plain,
! [SV940: $i,SV323: $i] :
( ( ( c_Option_Ooption_OSome @ SV323 @ SV940 )
= ( c_Option_Ooption_ONone @ SV940 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3520]) ).
thf(4183,plain,
! [SV941: $i,SV324: $i] :
( ( ( c_Option_Ooption_OSome @ SV324 @ SV941 )
= ( c_Option_Ooption_ONone @ SV941 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3521]) ).
thf(4184,plain,
! [SV1463: $i,SV942: $i,SV325: $i] :
( ( ( ( c_Option_Ooption_OSome @ SV325 @ SV942 )
!= ( c_Option_Ooption_OSome @ SV1463 @ SV942 ) )
| ( SV325 = SV1463 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3522]) ).
thf(4185,plain,
! [SV1464: $i,SV945: $i,SV328: $i] :
( ( ! [SY6326: $i] :
( ( c_Com_Ocom_OAss @ SV328 @ SV945 )
!= ( c_Com_Ocom_OWhile @ SV1464 @ SY6326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3525]) ).
thf(4186,plain,
! [SV1465: $i,SV946: $i,SV329: $i] :
( ( ! [SY6327: $i,SY6328: $i] :
( ( c_Map_Omap__add @ SV329 @ ( c_Map_Omap__add @ SV946 @ SV1465 @ SY6327 @ SY6328 ) @ SY6327 @ SY6328 )
= ( c_Map_Omap__add @ ( c_Map_Omap__add @ SV329 @ SV946 @ SY6327 @ SY6328 ) @ SV1465 @ SY6327 @ SY6328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3526]) ).
thf(4187,plain,
! [SV1466: $i,SV947: $i,SV330: $i] :
( ( ! [SY6329: $i,SY6330: $i] :
( ( c_Com_Ocom_OAss @ SV330 @ SV947 )
!= ( c_Com_Ocom_OLocal @ SV1466 @ SY6329 @ SY6330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3527]) ).
thf(4188,plain,
! [SV948: $i,SV331: $i] :
( ( c_HOL_Oord__class_Oless @ SV331 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV948 @ tc_bool ) ) @ ( tc_fun @ SV948 @ tc_bool ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3528]) ).
thf(4189,plain,
! [SV1467: $i,SV949: $i,SV332: $i] :
( ( ! [SY6331: $i] :
( ( c_Com_Ocom_OCond @ SV332 @ SV949 @ SV1467 )
!= ( c_Com_Ocom_OBODY @ SY6331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3529]) ).
thf(4190,plain,
! [SV1468: $i,SV950: $i,SV333: $i] :
( ( ! [SY6332: $i] :
( ( c_Com_Ocom_OBODY @ SV333 )
!= ( c_Com_Ocom_OCond @ SV950 @ SV1468 @ SY6332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3530]) ).
thf(4191,plain,
! [SV951: $i,SV334: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV334 ) )
= $true )
| ( ( ! [SY5332: $i,SY5333: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV951 @ SY5332 @ SV334 ) @ SY5333 @ SV334 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV951 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5332 @ SY5333 @ SV334 ) @ SV334 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3531]) ).
thf(4192,plain,
! [SV952: $i,SV335: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV335 ) )
= $true )
| ( ( ! [SY5334: $i,SY5335: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV952 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5334 @ SY5335 @ SV335 ) @ SV335 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY5334 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV952 @ SY5335 @ SV335 ) @ SV335 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3532]) ).
thf(4193,plain,
! [SV953: $i,SV336: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV336 ) )
= $true )
| ( ( ! [SY5336: $i,SY5337: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV953 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5336 @ SY5337 @ SV336 ) @ SV336 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY5336 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV953 @ SY5337 @ SV336 ) @ SV336 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3533]) ).
thf(4194,plain,
! [SV954: $i,SV337: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV337 ) )
= $true )
| ( ( ! [SY5338: $i,SY5339: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV954 @ SY5338 @ SV337 ) @ SY5339 @ SV337 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV954 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5338 @ SY5339 @ SV337 ) @ SV337 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3534]) ).
thf(4195,plain,
! [SV1469: $i,SV955: $i,SV338: $i] :
( ( ! [SY6333: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV338 @ SV955 @ ( tc_fun @ SV1469 @ tc_bool ) ) @ SY6333 @ ( tc_fun @ SV1469 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV338 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV955 @ SY6333 @ ( tc_fun @ SV1469 @ tc_bool ) ) @ ( tc_fun @ SV1469 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3535]) ).
thf(4196,plain,
! [SV1470: $i,SV956: $i,SV339: $i] :
( ( ! [SY6334: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV339 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV956 @ SV1470 @ ( tc_fun @ SY6334 @ tc_bool ) ) @ ( tc_fun @ SY6334 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV956 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV339 @ SV1470 @ ( tc_fun @ SY6334 @ tc_bool ) ) @ ( tc_fun @ SY6334 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3536]) ).
thf(4197,plain,
! [SV1471: $i,SV957: $i,SV340: $i] :
( ( ! [SY6335: $i,SY6336: $i] :
( ( c_Com_Ocom_OLocal @ SV340 @ SV957 @ SV1471 )
!= ( c_Com_Ocom_OWhile @ SY6335 @ SY6336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3537]) ).
thf(4198,plain,
! [SV1472: $i,SV958: $i,SV341: $i] :
( ( ! [SY6337: $i,SY6338: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV341 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV958 @ ( c_Com_Ocom_OBODY @ SV1472 ) @ SY6337 @ SY6338 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY6338 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY6338 ) ) @ SY6338 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV341 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV958 @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SV1472 ) @ tc_Com_Ocom ) @ SY6337 @ SY6338 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY6338 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY6338 ) ) @ SY6338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3538]) ).
thf(4199,plain,
! [SV1473: $i,SV959: $i,SV342: $i] :
( ( ! [SY6339: $i,SY6340: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV342 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV959 @ ( c_Com_Ocom_OBODY @ SV1473 ) @ SY6339 @ SY6340 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY6340 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY6340 ) ) @ SY6340 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV959 @ ( c_Com_Ocom_OBODY @ SV1473 ) @ SY6339 @ SY6340 ) @ SV342 @ ( tc_Hoare__Mirabelle_Otriple @ SY6340 ) ) @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV959 @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SV1473 ) @ tc_Com_Ocom ) @ SY6339 @ SY6340 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY6340 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY6340 ) ) @ SY6340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3539]) ).
thf(4200,plain,
! [SV1474: $i,SV960: $i,SV343: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV343 )
| ! [SY6341: $i,SY6342: $i] :
( ( ( c_Finite__Set_Osetsum @ SV960 @ ( c_HOL_Ominus__class_Ominus @ SV1474 @ ( c_Set_Oinsert @ SY6341 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6342 @ tc_bool ) ) @ SY6342 ) @ ( tc_fun @ SY6342 @ tc_bool ) ) @ SY6342 @ SV343 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV960 @ SV1474 @ SY6342 @ SV343 ) @ ( hAPP @ SV960 @ SY6341 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6342 ) @ SY6341 ) @ SV1474 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1474 @ SY6342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3540]) ).
thf(4201,plain,
! [SV1475: $i,SV961: $i,SV344: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV344 )
| ! [SY6343: $i,SY6344: $i] :
( ( ( c_Finite__Set_Osetsum @ SV961 @ ( c_HOL_Ominus__class_Ominus @ SV1475 @ ( c_Set_Oinsert @ SY6343 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6344 @ tc_bool ) ) @ SY6344 ) @ ( tc_fun @ SY6344 @ tc_bool ) ) @ SY6344 @ SV344 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV961 @ SV1475 @ SY6344 @ SV344 ) @ ( hAPP @ SV961 @ SY6343 ) @ SV344 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6344 ) @ SY6343 ) @ SV1475 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1475 @ SY6344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3541]) ).
thf(4202,plain,
! [SV345: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OBODY @ SV345 ) )
= $false )
| ( ( ( hAPP @ c_Com_Obody @ SV345 )
= ( c_Option_Ooption_OSome @ ( c_Com_Osko__Com__XWTs__elim__cases__7__1 @ SV345 ) @ tc_Com_Ocom ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3542]) ).
thf(4203,plain,
! [SV1476: $i,SV962: $i,SV346: $i] :
( ( ! [SY6345: $i] :
( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ SV346 @ SV962 @ ( c_Option_Ooption_ONone @ SV1476 ) @ SY6345 @ ( tc_Option_Ooption @ SV1476 ) ) @ SY6345 @ SV1476 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ SV346 @ SY6345 @ SV1476 ) @ ( c_Set_Oinsert @ SV962 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6345 @ tc_bool ) ) @ SY6345 ) @ ( tc_fun @ SY6345 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3543]) ).
thf(4204,plain,
! [SV1477: $i,SV963: $i,SV347: $i] :
( ( ! [SY6346: $i,SY6347: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV347 @ ( c_HOL_Ominus__class_Ominus @ SV963 @ SV1477 @ ( tc_fun @ SY6346 @ tc_bool ) ) @ SY6346 @ SY6347 ) @ ( c_Set_Oimage @ SV347 @ ( c_HOL_Ominus__class_Ominus @ SV1477 @ SV963 @ ( tc_fun @ SY6346 @ tc_bool ) ) @ SY6346 @ SY6347 ) @ ( tc_fun @ SY6347 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6347 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SV347 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV963 @ SV1477 @ ( tc_fun @ SY6346 @ tc_bool ) ) @ SY6346 @ SY6347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3544]) ).
thf(4205,plain,
! [SV1478: $i,SV964: $i,SV348: $i] :
( ( ! [SY6348: $i,SY6349: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV348 @ ( c_HOL_Ominus__class_Ominus @ SV964 @ SV1478 @ ( tc_fun @ SY6348 @ tc_bool ) ) @ SY6348 @ SY6349 ) @ ( c_Set_Oimage @ SV348 @ ( c_HOL_Ominus__class_Ominus @ SV1478 @ SV964 @ ( tc_fun @ SY6348 @ tc_bool ) ) @ SY6348 @ SY6349 ) @ ( tc_fun @ SY6349 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6349 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SV348 @ SV1478 @ SY6348 @ SY6349 )
| ~ ( c_Fun_Oinj__on @ SV348 @ SV964 @ SY6348 @ SY6349 )
| ( c_Fun_Oinj__on @ SV348 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV964 @ SV1478 @ ( tc_fun @ SY6348 @ tc_bool ) ) @ SY6348 @ SY6349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3545]) ).
thf(4206,plain,
! [SV1479: $i,SV965: $i,SV349: $i] :
( ( ! [SY6350: $i] :
( ( c_HOL_Oord__class_Oless @ SV349 @ ( c_Set_Oinsert @ SV965 @ SV1479 @ SY6350 ) @ ( tc_fun @ SY6350 @ tc_bool ) )
| ~ ( c_lessequals @ SV349 @ SV1479 @ ( tc_fun @ SY6350 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV349 @ ( c_Set_Oinsert @ SV965 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6350 @ tc_bool ) ) @ SY6350 ) @ ( tc_fun @ SY6350 @ tc_bool ) ) @ SV1479 @ ( tc_fun @ SY6350 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6350 ) @ SV965 ) @ SV1479 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3546]) ).
thf(4207,plain,
! [SV1480: $i,SV966: $i,SV350: $i] :
( ( ! [SY6351: $i,SY6352: $i,SY6353: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ SV350 @ SV966 @ SV1480 @ SY6351 @ SY6352 ) @ SY6353 @ SY6351 @ SY6352 )
= ( c_Set_Oinsert @ SV1480 @ ( c_Set_Oimage @ SV350 @ ( c_HOL_Ominus__class_Ominus @ SY6353 @ ( c_Set_Oinsert @ SV966 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6351 @ tc_bool ) ) @ SY6351 ) @ ( tc_fun @ SY6351 @ tc_bool ) ) @ SY6351 @ SY6352 ) @ SY6352 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6351 ) @ SV966 ) @ SY6353 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3547]) ).
thf(4208,plain,
! [SV1481: $i,SV967: $i,SV351: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV351 )
| ! [SY6354: $i,SY6355: $i] :
( ( ( c_Finite__Set_Osetsum @ SV967 @ ( c_HOL_Ominus__class_Ominus @ SV1481 @ ( c_Set_Oinsert @ SY6354 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6355 @ tc_bool ) ) @ SY6355 ) @ ( tc_fun @ SY6355 @ tc_bool ) ) @ SY6355 @ SV351 )
= ( c_Finite__Set_Osetsum @ SV967 @ SV1481 @ SY6355 @ SV351 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6355 ) @ SY6354 ) @ SV1481 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1481 @ SY6355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3548]) ).
thf(4209,plain,
! [SV1482: $i,SV968: $i,SV352: $i] :
( ( ( ( c_Finite__Set_Ocard @ ( c_HOL_Ominus__class_Ominus @ SV352 @ ( c_Set_Oinsert @ SV968 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1482 @ tc_bool ) ) @ SV1482 ) @ ( tc_fun @ SV1482 @ tc_bool ) ) @ SV1482 )
= ( c_Finite__Set_Ocard @ SV352 @ SV1482 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1482 ) @ SV968 ) @ SV352 ) )
| ~ ( c_Finite__Set_Ofinite @ SV352 @ SV1482 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3549]) ).
thf(4210,plain,
! [SV1483: $i,SV969: $i,SV353: $i] :
( ( ! [SY6356: $i,SY6357: $i,SY6358: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV969 @ ( c_Com_Ocom_OSemi @ SV1483 @ SY6356 ) @ SY6357 @ SY6358 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY6358 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY6358 ) ) @ SY6358 )
| ! [SY6359: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY6359 @ SY6356 @ SY6357 @ SY6358 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY6358 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY6358 ) ) @ SY6358 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV969 @ SV1483 @ SY6359 @ SY6358 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY6358 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY6358 ) ) @ SY6358 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3550]) ).
thf(4211,plain,
! [SV1484: $i,SV970: $i,SV354: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV354 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV970 @ c_Com_Ocom_OSKIP @ SV970 @ SV1484 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1484 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1484 ) ) @ SV1484 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3551]) ).
thf(4212,plain,
! [SV1485: $i,SV971: $i,SV355: $i] :
( ( ! [SY6360: $i,SY6361: $i,SY6362: $i] :
( ( ( c_Map_Omap__add @ ( c_Fun_Ofun__upd @ SV355 @ SV971 @ ( c_Option_Ooption_OSome @ SV1485 @ SY6360 ) @ SY6361 @ ( tc_Option_Ooption @ SY6360 ) ) @ SY6362 @ SY6361 @ SY6360 )
= ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ SV355 @ SY6362 @ SY6361 @ SY6360 ) @ SV971 @ ( c_Option_Ooption_OSome @ SV1485 @ SY6360 ) @ SY6361 @ ( tc_Option_Ooption @ SY6360 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6361 ) @ SV971 ) @ ( c_Map_Odom @ SY6362 @ SY6361 @ SY6360 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3552]) ).
thf(4213,plain,
! [SV1486: $i,SV972: $i,SV356: $i] :
( ( ! [SY6363: $i] :
( ( c_HOL_Oord__class_Oless @ SV356 @ ( c_Set_Oinsert @ SV972 @ SV1486 @ SY6363 ) @ ( tc_fun @ SY6363 @ tc_bool ) )
| ~ ( c_lessequals @ SV356 @ SV1486 @ ( tc_fun @ SY6363 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV356 @ ( c_Set_Oinsert @ SV972 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6363 @ tc_bool ) ) @ SY6363 ) @ ( tc_fun @ SY6363 @ tc_bool ) ) @ SV1486 @ ( tc_fun @ SY6363 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV356 @ SV1486 @ ( tc_fun @ SY6363 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3553]) ).
thf(4214,plain,
! [SV1487: $i,SV973: $i,SV357: $i] :
( ( ! [SY6364: $i] :
( ( c_Set_Ovimage @ SV357 @ SV973 @ SV1487 @ SY6364 )
= ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_in @ SY6364 ) @ SV357 @ SY6364 @ ( tc_fun @ ( tc_fun @ SY6364 @ tc_bool ) @ tc_bool ) @ SV1487 ) @ SV1487 @ ( tc_fun @ SY6364 @ tc_bool ) @ tc_bool ) @ SV973 ) @ SV1487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3554]) ).
thf(4215,plain,
! [SV1488: $i,SV974: $i,SV358: $i] :
( ( ! [SY6365: $i,SY6366: $i,SY6367: $i,SY6368: $i] :
( ( c_Nitpick_Ofold__graph_H @ SV358 @ SV974 @ SV1488 @ ( hAPP @ ( hAPP @ SV358 @ SY6365 ) @ SY6366 ) @ SY6367 @ SY6368 )
| ~ ( c_Nitpick_Ofold__graph_H @ SV358 @ SV974 @ ( c_HOL_Ominus__class_Ominus @ SV1488 @ ( c_Set_Oinsert @ SY6365 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6367 @ tc_bool ) ) @ SY6367 ) @ ( tc_fun @ SY6367 @ tc_bool ) ) @ SY6366 @ SY6367 @ SY6368 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6367 ) @ SY6365 ) @ SV1488 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3555]) ).
thf(4216,plain,
! [SV1489: $i,SV975: $i,SV359: $i] :
( ( ! [SY6369: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV359 @ ( c_Set_Oinsert @ SV975 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1489 @ tc_bool ) ) @ SV1489 ) @ ( tc_fun @ SV1489 @ tc_bool ) ) @ SY6369 @ ( tc_fun @ SV1489 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1489 ) @ SV975 ) @ SV359 ) )
| ~ ( c_lessequals @ SV359 @ ( c_Set_Oinsert @ SV975 @ SY6369 @ SV1489 ) @ ( tc_fun @ SV1489 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3556]) ).
thf(4217,plain,
! [SV1490: $i,SV976: $i,SV360: $i] :
( ( ! [SY6370: $i] :
( ( c_lessequals @ SV360 @ ( c_Set_Oinsert @ SV976 @ SV1490 @ SY6370 ) @ ( tc_fun @ SY6370 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6370 ) @ SV976 ) @ SV360 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV360 @ ( c_Set_Oinsert @ SV976 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6370 @ tc_bool ) ) @ SY6370 ) @ ( tc_fun @ SY6370 @ tc_bool ) ) @ SV1490 @ ( tc_fun @ SY6370 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3557]) ).
thf(4218,plain,
! [SV1491: $i,SV977: $i,SV361: $i] :
( ( ! [SY6371: $i] :
( ( c_lessequals @ SV361 @ ( c_Set_Oinsert @ SV977 @ SV1491 @ SY6371 ) @ ( tc_fun @ SY6371 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6371 ) @ SV977 ) @ SV361 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV361 @ ( c_Set_Oinsert @ SV977 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6371 @ tc_bool ) ) @ SY6371 ) @ ( tc_fun @ SY6371 @ tc_bool ) ) @ SV1491 @ ( tc_fun @ SY6371 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3558]) ).
thf(4219,plain,
! [SV1492: $i,SV978: $i,SV362: $i] :
( ( ! [SY6372: $i] :
( ( ( c_Finite__Set_Osetsum @ SV362 @ ( c_HOL_Ominus__class_Ominus @ SV978 @ ( c_Set_Oinsert @ SV1492 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6372 @ tc_bool ) ) @ SY6372 ) @ ( tc_fun @ SY6372 @ tc_bool ) ) @ SY6372 @ tc_nat )
= ( c_Finite__Set_Osetsum @ SV362 @ SV978 @ SY6372 @ tc_nat ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6372 ) @ SV1492 ) @ SV978 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3559]) ).
thf(4220,plain,
! [SV1493: $i,SV979: $i,SV363: $i] :
( ( ! [SY6373: $i,SY6374: $i,SY6375: $i,SY6376: $i] :
( ( c_Finite__Set_Ofold__graph @ SV363 @ SV979 @ SV1493 @ ( hAPP @ ( hAPP @ SV363 @ SY6373 ) @ SY6374 ) @ SY6375 @ SY6376 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6375 ) @ SY6373 ) @ SV1493 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV363 @ SV979 @ ( c_HOL_Ominus__class_Ominus @ SV1493 @ ( c_Set_Oinsert @ SY6373 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6375 @ tc_bool ) ) @ SY6375 ) @ ( tc_fun @ SY6375 @ tc_bool ) ) @ SY6374 @ SY6375 @ SY6376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3560]) ).
thf(4221,plain,
! [SV1494: $i,SV980: $i,SV364: $i] :
( ( ! [SY6377: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV364 @ SV980 @ SV1494 ) @ SY6377 @ SV1494 @ SV980 )
= ( c_Set_Oinsert @ SV364 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV980 @ tc_bool ) ) @ SV980 ) )
| ! [SY6378: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1494 ) @ SY6378 ) @ SY6377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3561]) ).
thf(4222,plain,
! [SV1495: $i,SV981: $i,SV365: $i] :
( ( ! [SY6379: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV365 @ ( c_Set_Oinsert @ SV981 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1495 @ tc_bool ) ) @ SV1495 ) @ ( tc_fun @ SV1495 @ tc_bool ) ) @ SY6379 @ ( tc_fun @ SV1495 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1495 ) @ SV981 ) @ SV365 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1495 ) @ SV981 ) @ SY6379 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV365 @ ( c_Set_Oinsert @ SV981 @ SY6379 @ SV1495 ) @ ( tc_fun @ SV1495 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3562]) ).
thf(4223,plain,
! [SV1496: $i,SV982: $i,SV366: $i] :
( ( ( ( hAPP @ SV366 @ SV982 )
!= ( c_Option_Ooption_ONone @ SV1496 ) )
| ! [SY6380: $i,SY6381: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ SV366 @ SY6380 @ SV1496 ) @ ( c_Set_Oinsert @ SV982 @ SY6381 @ SY6380 ) @ ( tc_fun @ SY6380 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ SV366 @ SY6380 @ SV1496 ) @ SY6381 @ ( tc_fun @ SY6380 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3563]) ).
thf(4224,plain,
! [SV1497: $i,SV983: $i,SV367: $i] :
( ( ! [SY6382: $i] :
( ( c_Com_Ocom_OAss @ SV367 @ SV983 )
!= ( c_Com_Ocom_OSemi @ SV1497 @ SY6382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3564]) ).
thf(4225,plain,
! [SV984: $i,SV368: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV368 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ SV984 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ SV984 ) ) @ SV368 @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SV984 ) @ tc_Com_Ocom ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3565]) ).
thf(4226,plain,
! [SV1498: $i,SV985: $i,SV369: $i] :
( ( ! [SY6383: $i,SY6384: $i,SY6385: $i] :
( ( c_Com_Ocom_OLocal @ SV369 @ SV985 @ SV1498 )
!= ( c_Com_Ocom_OCond @ SY6383 @ SY6384 @ SY6385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3566]) ).
thf(4227,plain,
! [SV1499: $i,SV986: $i,SV370: $i] :
( ( ! [SY6386: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV370 @ SV986 @ SV1499 ) @ SY6386 @ ( tc_fun @ SV1499 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV986 @ SY6386 @ ( tc_fun @ SV1499 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1499 ) @ SV370 ) @ SY6386 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3567]) ).
thf(4228,plain,
! [SV1500: $i,SV987: $i,SV371: $i] :
( ( ! [SY6387: $i] :
( ( c_Fun_Oinj__on @ SV371 @ SV987 @ SV1500 @ SY6387 )
| ! [SY6388: $i] :
~ ( c_Fun_Oinj__on @ SV371 @ ( c_Set_Oinsert @ SY6388 @ SV987 @ SV1500 ) @ SV1500 @ SY6387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3568]) ).
thf(4229,plain,
! [SV1501: $i,SV988: $i,SV372: $i] :
( ( ( c_Com_Ocom_OBODY @ SV372 )
!= ( c_Com_Ocom_OSemi @ SV988 @ SV1501 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3569]) ).
thf(4230,plain,
! [SV989: $i,SV373: $i] :
( ( ( SV373 = SV989 )
= $true )
| ( ( ! [SY5429: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5429 ) @ SV373 ) @ ( c_Set_Oinsert @ SV989 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5429 @ tc_bool ) ) @ SY5429 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3570]) ).
thf(4231,plain,
! [SV1502: $i,SV990: $i,SV374: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV374 @ SV990 @ ( tc_fun @ SV1502 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1502 @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ SV374 @ SV990 @ ( tc_fun @ SV1502 @ tc_bool ) )
= SV374 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3571]) ).
thf(4232,plain,
! [SV991: $i,SV375: $i] :
( ( ( hBOOL @ ( hAPP @ SV375 @ SV991 ) )
= $true )
| ( ( ! [SY5431: $i,SY5432: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5431 ) @ SV991 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5432 @ ( c_Collect @ SV375 @ SY5431 ) @ ( tc_fun @ SY5431 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3572]) ).
thf(4233,plain,
! [SV992: $i,SV376: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV376 ) )
= $true )
| ( ( ! [SY5433: $i] :
( ( c_HOL_Oord__class_Oless @ SV992 @ SY5433 @ SV376 )
| ! [SY5434: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY5434 @ SY5433 @ SV376 )
| ~ ( c_HOL_Oord__class_Oless @ SV992 @ SY5434 @ SV376 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3573]) ).
thf(4234,plain,
! [SV1503: $i,SV993: $i,SV377: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV377 @ SV993 @ ( tc_fun @ SV1503 @ tc_bool ) )
| ! [SY6389: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY6389 @ SV993 @ ( tc_fun @ SV1503 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV377 @ SY6389 @ ( tc_fun @ SV1503 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3574]) ).
thf(4235,plain,
! [SV994: $i,SV378: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV378 ) )
= $true )
| ( ( ! [SY5437: $i] :
( ( c_HOL_Oord__class_Oless @ SV994 @ SY5437 @ SV378 )
| ! [SY5438: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV994 @ SY5438 @ SV378 )
| ~ ( c_HOL_Oord__class_Oless @ SY5438 @ SY5437 @ SV378 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3575]) ).
thf(4236,plain,
! [SV1504: $i,SV995: $i,SV379: $i] :
( ( ! [SY6390: $i,SY6391: $i] :
( ( c_Fun_Oinj__on @ SV379 @ ( c_Set_Oinsert @ SV995 @ SV1504 @ SY6390 ) @ SY6390 @ SY6391 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6391 ) @ ( hAPP @ SV379 @ SV995 ) ) @ ( c_Set_Oimage @ SV379 @ ( c_HOL_Ominus__class_Ominus @ SV1504 @ ( c_Set_Oinsert @ SV995 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6390 @ tc_bool ) ) @ SY6390 ) @ ( tc_fun @ SY6390 @ tc_bool ) ) @ SY6390 @ SY6391 ) ) )
| ~ ( c_Fun_Oinj__on @ SV379 @ SV1504 @ SY6390 @ SY6391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3576]) ).
thf(4237,plain,
! [SV1505: $i,SV996: $i,SV380: $i] :
( ( ! [SY6392: $i] :
( ( c_Set_Oinsert @ SV380 @ ( c_Set_Oinsert @ SV996 @ SV1505 @ SY6392 ) @ SY6392 )
= ( c_Set_Oinsert @ SV996 @ ( c_Set_Oinsert @ SV380 @ SV1505 @ SY6392 ) @ SY6392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3577]) ).
thf(4238,plain,
! [SV1506: $i,SV997: $i,SV381: $i] :
( ( ! [SY6393: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV381 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV997 @ tc_bool ) ) @ SV1506 @ SV997 @ ( tc_fun @ SY6393 @ tc_bool ) ) @ ( tc_fun @ SY6393 @ tc_bool ) )
= SV381 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3578]) ).
thf(4239,plain,
! [SV1507: $i,SV998: $i,SV382: $i] :
( ( ! [SY6394: $i,SY6395: $i,SY6396: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV382 @ SV998 @ SV1507 @ SY6394 ) @ SY6395 ) @ SY6396 )
= ( hAPP @ ( hAPP @ SV382 @ SY6396 ) @ SY6395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3579]) ).
thf(4240,plain,
! [SV1508: $i,SV999: $i,SV383: $i] :
( ( ( c_Com_Ocom_OSemi @ SV383 @ SV999 )
!= ( c_Com_Ocom_OBODY @ SV1508 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3580]) ).
thf(4241,plain,
! [SV1509: $i,SV1000: $i,SV384: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV384 @ SV1000 @ ( tc_fun @ SV1509 @ tc_bool ) ) @ SV1000 @ ( tc_fun @ SV1509 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV384 @ SV1000 @ ( tc_fun @ SV1509 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3581]) ).
thf(4242,plain,
! [SV1001: $i,SV385: $i] :
( ( ( c_Option_Ooption_ONone @ SV385 )
= ( c_Option_Ooption_OSome @ SV1001 @ SV385 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3582]) ).
thf(4243,plain,
! [SV1002: $i,SV386: $i] :
( ( ( c_Option_Ooption_ONone @ SV386 )
= ( c_Option_Ooption_OSome @ SV1002 @ SV386 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3583]) ).
thf(4244,plain,
! [SV1510: $i,SV1003: $i,SV387: $i] :
( ( ! [SY6397: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV387 @ SV1003 ) ) @ SV1510 ) @ SY6397 ) )
| ! [SY6398: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV387 @ SV1003 ) ) @ SY6398 ) @ SY6397 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1003 ) @ SV1510 ) @ SY6398 ) )
| ~ ( hBOOL @ ( hAPP @ SV387 @ SV1510 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3584]) ).
thf(4245,plain,
! [SV1511: $i,SV1004: $i,SV388: $i] :
( ( ( c_Set_Oinsert @ SV388 @ ( c_Set_Oinsert @ SV1004 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1511 @ tc_bool ) ) @ SV1511 ) @ SV1511 )
= ( c_Set_Oinsert @ SV1004 @ ( c_Set_Oinsert @ SV388 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1511 @ tc_bool ) ) @ SV1511 ) @ SV1511 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3585]) ).
thf(4246,plain,
! [SV1005: $i,SV389: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV389 ) )
= $true )
| ( ( ! [SY5456: $i] :
( ! [SY5457: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV1005 @ SY5456 @ SV389 )
!= ( c_HOL_Ominus__class_Ominus @ SY5457 @ SY5457 @ SV389 ) )
| ( SV1005 = SY5456 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3586]) ).
thf(4247,plain,
! [SV1006: $i,SV390: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV390 ) )
= $true )
| ( ( ! [SY5458: $i,SY5459: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV1006 @ SV1006 @ SV390 )
!= ( c_HOL_Ominus__class_Ominus @ SY5458 @ SY5459 @ SV390 ) )
| ( SY5458 = SY5459 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3587]) ).
thf(4248,plain,
! [SV1512: $i,SV1007: $i,SV391: $i] :
( ( ( c_Set_Oimage @ SV391 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1007 @ tc_bool ) ) @ SV1007 @ SV1512 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1512 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3588]) ).
thf(4249,plain,
! [SV1513: $i,SV1008: $i,SV392: $i] :
( ( ! [SY6399: $i,SY6400: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV392 @ SV1008 @ SV1513 ) ) @ SY6399 ) @ SY6400 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1008 ) @ SY6399 ) @ SY6400 ) )
| ~ ( hBOOL @ ( hAPP @ SV392 @ SY6399 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3589]) ).
thf(4250,plain,
! [SV1514: $i,SV1009: $i,SV393: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV393 @ SV1009 ) )
| ! [SY6401: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1514 ) @ SV1009 ) @ SY6401 ) )
| ! [SY6402: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV393 @ SV1514 @ SY6402 ) ) @ SV1009 ) @ SY6401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3590]) ).
thf(4251,plain,
! [SV1515: $i,SV1010: $i,SV394: $i] :
( ( ! [SY6403: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV394 @ SV1010 ) ) @ SV1515 ) @ SY6403 ) )
| ! [SY6404: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1010 ) @ SY6404 ) @ SY6403 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV394 ) @ SV1515 ) @ SY6404 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3591]) ).
thf(4252,plain,
! [SV1516: $i,SV1011: $i,SV395: $i] :
( ( c_Fun_Oinj__on @ SV395 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1011 @ tc_bool ) ) @ SV1011 @ SV1516 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3592]) ).
thf(4253,plain,
! [SV1517: $i,SV1012: $i,SV396: $i] :
( ( ! [SY6405: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Map_Odom @ SV396 @ SV1012 @ SV1517 ) @ ( c_Map_Odom @ SY6405 @ SV1012 @ SV1517 ) @ ( tc_fun @ SV1012 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1012 @ tc_bool ) ) )
| ( ( c_Map_Omap__add @ SV396 @ SY6405 @ SV1012 @ SV1517 )
= ( c_Map_Omap__add @ SY6405 @ SV396 @ SV1012 @ SV1517 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3593]) ).
thf(4254,plain,
! [SV1518: $i,SV1013: $i,SV397: $i] :
( ( ! [SY6406: $i] :
( ( ( hAPP @ SV397 @ SV1013 )
!= ( c_Option_Ooption_OSome @ SV1518 @ SY6406 ) )
| ! [SY5475: $i] :
( ( c_Set_Oinsert @ SV1013 @ ( c_Map_Odom @ SV397 @ SY5475 @ SY6406 ) @ SY5475 )
= ( c_Map_Odom @ SV397 @ SY5475 @ SY6406 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3594]) ).
thf(4255,plain,
! [SV1519: $i,SV1014: $i,SV398: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV398 @ SV1014 @ ( tc_fun @ SV1519 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1014 @ SV398 @ ( tc_fun @ SV1519 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3595]) ).
thf(4256,plain,
! [SV399: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV399 )
= $false )
| ( ( ! [SY3886: $i,SY3887: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3886 @ SY3887 @ SV399 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3887 @ SY3886 @ SV399 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3596]) ).
thf(4257,plain,
! [SV400: $i] :
( ( ( class_Lattices_Olattice @ SV400 )
= $false )
| ( ( ! [SY3888: $i,SY3889: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY3888 @ SY3889 @ SV400 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY3889 @ SY3888 @ SV400 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3597]) ).
thf(4258,plain,
! [SV1520: $i,SV1015: $i,SV401: $i] :
( ( ! [SY6408: $i,SY6409: $i,SY6410: $i,SY6411: $i,SY6412: $i,SY6413: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV401 @ SV1015 @ ( c_COMBC @ SV1520 @ SY6408 @ SY6408 @ tc_bool ) @ ( c_COMBC @ SY6409 @ SY6408 @ SY6408 @ tc_bool ) @ SY6410 @ SY6411 @ SY6412 @ SY6413 @ SY6408 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1015 @ SV401 @ SV1520 @ SY6409 @ SY6411 @ SY6410 @ SY6413 @ SY6412 @ SY6408 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3598]) ).
thf(4259,plain,
! [SV1521: $i,SV1016: $i,SV402: $i] :
( ( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCond @ SV402 @ SV1016 @ SV1521 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3599]) ).
thf(4260,plain,
! [SV1522: $i,SV1017: $i,SV403: $i] :
( ( ( c_Set_Oinsert @ SV403 @ ( c_HOL_Ominus__class_Ominus @ SV1017 @ ( c_Set_Oinsert @ SV403 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1522 @ tc_bool ) ) @ SV1522 ) @ ( tc_fun @ SV1522 @ tc_bool ) ) @ SV1522 )
= ( c_Set_Oinsert @ SV403 @ SV1017 @ SV1522 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3600]) ).
thf(4261,plain,
! [SV1523: $i,SV1018: $i,SV404: $i] :
( ( ( ( c_Set_Oinsert @ SV404 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1018 @ tc_bool ) ) @ SV1018 )
!= ( c_Set_Oinsert @ SV1523 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1018 @ tc_bool ) ) @ SV1018 ) )
| ( SV404 = SV1523 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3601]) ).
thf(4262,plain,
! [SV1524: $i,SV1019: $i,SV405: $i] :
( ( ! [SY6414: $i,SY6415: $i,SY6416: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV405 @ SV1019 @ SV1524 @ SY6414 ) @ SY6415 )
!= ( c_Option_Ooption_OSome @ SY6416 @ SY6414 ) )
| ( ( hAPP @ SV405 @ SY6415 )
= ( c_Option_Ooption_OSome @ SY6416 @ SY6414 ) )
| ( ( hAPP @ SV1019 @ SY6415 )
= ( c_Option_Ooption_OSome @ SY6416 @ SY6414 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3602]) ).
thf(4263,plain,
! [SV1525: $i,SV1020: $i,SV406: $i] :
( ( ! [SY6417: $i] :
( ( ( hAPP @ SV406 @ SV1020 )
!= ( c_Option_Ooption_OSome @ SV1525 @ SY6417 ) )
| ! [SY6418: $i] :
( ( ( hAPP @ SY6418 @ SV1020 )
!= ( c_Option_Ooption_ONone @ SY6417 ) )
| ! [SY6419: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SV406 @ SY6418 @ SY6419 @ SY6417 ) @ SV1020 )
= ( c_Option_Ooption_OSome @ SV1525 @ SY6417 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3603]) ).
thf(4264,plain,
! [SV1526: $i,SV1021: $i,SV407: $i] :
( ( ! [SY6420: $i,SY6421: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV407 @ SV1021 @ SV1526 @ SY6420 ) @ SY6421 )
!= ( c_Option_Ooption_ONone @ SY6420 ) )
| ( ( hAPP @ SV407 @ SY6421 )
= ( c_Option_Ooption_ONone @ SY6420 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3604]) ).
thf(4265,plain,
! [SV1527: $i,SV1022: $i,SV408: $i] :
( ( ! [SY6422: $i,SY6423: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV408 @ SV1022 @ SV1527 @ SY6422 ) @ SY6423 )
!= ( c_Option_Ooption_ONone @ SY6422 ) )
| ( ( hAPP @ SV1022 @ SY6423 )
= ( c_Option_Ooption_ONone @ SY6422 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3605]) ).
thf(4266,plain,
! [SV1528: $i,SV1023: $i,SV409: $i] :
( ( ( ( c_Set_Oinsert @ SV409 @ SV1023 @ SV1528 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1528 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1528 ) @ SV409 ) @ SV1023 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3606]) ).
thf(4267,plain,
! [SV1529: $i,SV1024: $i,SV410: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ SV1024 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1529 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1529 ) ) @ SV1529 )
| ! [SY6424: $i] :
~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ SV1024 @ SY6424 @ ( tc_Hoare__Mirabelle_Otriple @ SV1529 ) ) @ SV1529 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3607]) ).
thf(4268,plain,
! [SV1530: $i,SV1025: $i,SV411: $i] :
( ( ! [SY6425: $i] :
( ( c_Com_Ocom_OLocal @ SV411 @ SV1025 @ SV1530 )
!= ( c_Com_Ocom_OBODY @ SY6425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3608]) ).
thf(4269,plain,
! [SV1531: $i,SV1026: $i,SV412: $i] :
( ( ! [SY6426: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV412 @ SV1026 @ SV1531 ) @ SY6426 ) )
| ~ ( hBOOL @ ( hAPP @ SV1026 @ SY6426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3609]) ).
thf(4270,plain,
! [SV1532: $i,SV1027: $i,SV413: $i] :
( ( ! [SY6427: $i] :
( ! [SY6428: $i] :
( ( c_Set_Oinsert @ ( hAPP @ SV413 @ SV1027 ) @ ( c_Set_Oimage @ SV413 @ SV1532 @ SY6427 @ SY6428 ) @ SY6428 )
= ( c_Set_Oimage @ SV413 @ SV1532 @ SY6427 @ SY6428 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6427 ) @ SV1027 ) @ SV1532 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3610]) ).
thf(4271,plain,
! [SV1533: $i,SV1028: $i,SV414: $i] :
( ( ! [SY6429: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV414 @ ( c_Set_Oinsert @ SV1028 @ SV1533 @ SY6429 ) @ ( tc_fun @ SY6429 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV414 @ SV1533 @ ( tc_fun @ SY6429 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6429 ) @ SV1028 ) @ SV414 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3611]) ).
thf(4272,plain,
! [SV1534: $i,SV1029: $i,SV415: $i] :
( ( ! [SY6430: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV415 @ SV1029 @ SV1534 ) @ SY6430 @ ( tc_fun @ SV1534 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1029 @ SY6430 @ ( tc_fun @ SV1534 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1534 ) @ SV415 ) @ SY6430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3612]) ).
thf(4273,plain,
! [SV1535: $i,SV1030: $i,SV416: $i] :
( ( ! [SY6431: $i,SY6432: $i] :
( ( c_Com_Ocom_OLocal @ SV416 @ SV1030 @ SV1535 )
!= ( c_Com_Ocom_OSemi @ SY6431 @ SY6432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3613]) ).
thf(4274,plain,
! [SV1031: $i,SV417: $i] :
( ( ( ( c_Com_Ocom_OBODY @ SV417 )
!= ( c_Com_Ocom_OBODY @ SV1031 ) )
= $true )
| ( ( SV417 = SV1031 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3614]) ).
thf(4275,plain,
! [SV1536: $i,SV1032: $i,SV418: $i] :
( ( ! [SY6433: $i] :
( ( c_Com_Ocom_OWhile @ SV418 @ SV1032 )
!= ( c_Com_Ocom_OWhile @ SV1536 @ SY6433 ) )
| ( SV418 = SV1536 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3615]) ).
thf(4276,plain,
! [SV1537: $i,SV1033: $i,SV419: $i] :
( ( ! [SY6434: $i] :
( ( ( c_Com_Ocom_OWhile @ SV419 @ SV1033 )
!= ( c_Com_Ocom_OWhile @ SV1537 @ SY6434 ) )
| ( SV1033 = SY6434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3616]) ).
thf(4277,plain,
! [SV1538: $i,SV1034: $i,SV420: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV420 @ tc_bool ) )
= ( c_Set_Oimage @ SV1034 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1538 @ tc_bool ) ) @ SV1538 @ SV420 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3617]) ).
thf(4278,plain,
! [SV1539: $i,SV1035: $i,SV421: $i] :
( ( ( c_Com_Ocom_OCond @ SV421 @ SV1035 @ SV1539 )
!= c_Com_Ocom_OSKIP )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3618]) ).
thf(4279,plain,
! [SV1540: $i,SV1036: $i,SV422: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV422 @ ( c_HOL_Ominus__class_Ominus @ SV1036 @ SV422 @ ( tc_fun @ SV1540 @ tc_bool ) ) @ ( tc_fun @ SV1540 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1540 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3619]) ).
thf(4280,plain,
! [SV1541: $i,SV1037: $i,SV423: $i] :
( ( ! [SY6435: $i,SY6436: $i] :
( ( c_Com_Ocom_OWhile @ SV423 @ SV1037 )
!= ( c_Com_Ocom_OCond @ SV1541 @ SY6435 @ SY6436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3620]) ).
thf(4281,plain,
! [SV424: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ SV424 )
= $false )
| ( ( ! [SY3964: $i] : ( c_Finite__Set_Ofinite @ SY3964 @ SV424 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3621]) ).
thf(4282,plain,
! [SV1542: $i,SV1038: $i,SV425: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV425 ) @ SV1038 ) @ SV1542 ) )
| ! [SY6437: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV425 ) @ SV1038 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1542 @ ( c_Collect @ SY6437 @ SV425 ) @ ( tc_fun @ SV425 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3622]) ).
thf(4283,plain,
! [SV1543: $i,SV1039: $i,SV426: $i] :
( ( ( ( hAPP @ SV426 @ SV1039 )
!= ( c_Option_Ooption_ONone @ SV1543 ) )
| ! [SY6438: $i] :
( ( ( hAPP @ SY6438 @ SV1039 )
!= ( c_Option_Ooption_ONone @ SV1543 ) )
| ! [SY6439: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SV426 @ SY6438 @ SY6439 @ SV1543 ) @ SV1039 )
= ( c_Option_Ooption_ONone @ SV1543 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3623]) ).
thf(4284,plain,
! [SV1544: $i,SV1040: $i,SV427: $i] :
( ( ! [SY6440: $i] :
( ( ( hAPP @ SV427 @ SV1040 )
!= ( c_Option_Ooption_OSome @ SV1544 @ SY6440 ) )
| ! [SY6441: $i,SY6442: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SY6441 @ SV427 @ SY6442 @ SY6440 ) @ SV1040 )
= ( c_Option_Ooption_OSome @ SV1544 @ SY6440 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3624]) ).
thf(4285,plain,
! [SV1545: $i,SV1041: $i,SV428: $i] :
( ( ! [SY6443: $i] :
( ( ( hAPP @ SV428 @ SV1041 )
!= ( c_Option_Ooption_OSome @ SV1545 @ SY6443 ) )
| ! [SY6444: $i,SY6445: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SY6444 @ SV428 @ SY6445 @ SY6443 ) @ SV1041 )
= ( c_Option_Ooption_OSome @ SV1545 @ SY6443 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3625]) ).
thf(4286,plain,
! [SV1546: $i,SV1042: $i,SV429: $i] :
( ( ! [SY6446: $i,SY6447: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV429 ) @ ( hAPP @ SV1042 @ SV1546 ) ) @ ( c_Set_Oimage @ SV1042 @ ( c_HOL_Ominus__class_Ominus @ SY6446 @ ( c_Set_Oinsert @ SV1546 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6447 @ tc_bool ) ) @ SY6447 ) @ ( tc_fun @ SY6447 @ tc_bool ) ) @ SY6447 @ SV429 ) ) )
| ~ ( c_Fun_Oinj__on @ SV1042 @ ( c_Set_Oinsert @ SV1546 @ SY6446 @ SY6447 ) @ SY6447 @ SV429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3626]) ).
thf(4287,plain,
! [SV1547: $i,SV1043: $i,SV430: $i] :
( ( ! [SY6448: $i,SY6449: $i] :
( ( c_Com_Ocom_OCond @ SV430 @ SV1043 @ SV1547 )
!= ( c_Com_Ocom_OAss @ SY6448 @ SY6449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3627]) ).
thf(4288,plain,
! [SV1548: $i,SV1044: $i,SV432: $i] :
( ( ! [SY6450: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV432 @ SV1044 @ SV1548 ) @ SY6450 @ ( tc_fun @ SV1548 @ tc_bool ) )
= ( c_Set_Oinsert @ SV432 @ ( c_HOL_Ominus__class_Ominus @ SV1044 @ SY6450 @ ( tc_fun @ SV1548 @ tc_bool ) ) @ SV1548 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1548 ) @ SV432 ) @ SY6450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3629]) ).
thf(4289,plain,
! [SV1045: $i,SV433: $i] :
( ( ( hBOOL @ ( hAPP @ SV433 @ SV1045 ) )
= $true )
| ( ( ! [SY5549: $i,SY5550: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5549 @ SV433 @ ( tc_fun @ SY5550 @ tc_bool ) ) @ SV1045 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3630]) ).
thf(4290,plain,
! [SV1046: $i,SV434: $i] :
( ( ( hBOOL @ ( hAPP @ SV434 @ SV1046 ) )
= $true )
| ( ( ! [SY5551: $i,SY5552: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV434 @ SY5551 @ ( tc_fun @ SY5552 @ tc_bool ) ) @ SV1046 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3631]) ).
thf(4291,plain,
! [SV1549: $i,SV1047: $i,SV435: $i] :
( ( ! [SY6451: $i] : ( c_Map_Omap__le @ SV435 @ ( c_Map_Omap__add @ SV1047 @ SV435 @ SV1549 @ SY6451 ) @ SV1549 @ SY6451 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3632]) ).
thf(4292,plain,
! [SV1550: $i,SV1048: $i,SV436: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV436 @ SV1048 @ SV1550 ) @ ( c_Set_Oinsert @ SV436 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1550 @ tc_bool ) ) @ SV1550 ) @ ( tc_fun @ SV1550 @ tc_bool ) )
= SV1048 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1550 ) @ SV436 ) @ SV1048 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3633]) ).
thf(4293,plain,
! [SV1551: $i,SV1049: $i,SV437: $i] :
( ( ! [SY6452: $i,SY6453: $i] :
( ( c_Set_Ovimage @ SV437 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1049 @ SV1551 @ ( tc_fun @ SY6452 @ tc_bool ) ) @ SY6453 @ SY6452 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Ovimage @ SV437 @ SV1049 @ SY6453 @ SY6452 ) @ ( c_Set_Ovimage @ SV437 @ SV1551 @ SY6453 @ SY6452 ) @ ( tc_fun @ SY6453 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3634]) ).
thf(4294,plain,
! [SV1050: $i,SV438: $i] :
( ( ( SV438 = SV1050 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ SV1050 ) @ SV438 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3635]) ).
thf(4295,plain,
! [SV1552: $i,SV1051: $i,SV439: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV439 @ SV1051 @ ( tc_fun @ SV1552 @ tc_bool ) ) @ SV1552 )
| ~ ( c_Finite__Set_Ofinite @ SV1051 @ SV1552 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3636]) ).
thf(4296,plain,
! [SV1553: $i,SV1052: $i,SV440: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV440 @ SV1052 @ ( tc_fun @ SV1553 @ tc_bool ) ) @ SV1553 )
| ~ ( c_Finite__Set_Ofinite @ SV440 @ SV1553 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3637]) ).
thf(4297,plain,
! [SV1554: $i,SV1053: $i,SV441: $i] :
( ( ! [SY6454: $i,SY6455: $i] :
( ( c_Map_Omap__le @ ( c_Map_Omap__add @ SV441 @ SV1053 @ SV1554 @ SY6454 ) @ SY6455 @ SV1554 @ SY6454 )
| ~ ( c_Map_Omap__le @ SV441 @ ( c_Map_Omap__add @ SV441 @ SV1053 @ SV1554 @ SY6454 ) @ SV1554 @ SY6454 )
| ~ ( c_Map_Omap__le @ SV1053 @ SY6455 @ SV1554 @ SY6454 )
| ~ ( c_Map_Omap__le @ SV441 @ SY6455 @ SV1554 @ SY6454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3638]) ).
thf(4298,plain,
! [SV1555: $i,SV1054: $i,SV442: $i] :
( ( ( hBOOL @ ( hAPP @ SV442 @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1054 @ SV442 @ SV1555 ) ) )
| ! [SY6456: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1555 ) @ SY6456 ) @ SV1054 ) )
| ! [SY6457: $i] :
( ~ ( hBOOL @ ( hAPP @ SV442 @ SY6457 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1555 ) @ SY6457 ) @ SV1054 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3639]) ).
thf(4299,plain,
! [SV1556: $i,SV1055: $i,SV443: $i] :
( ( ! [SY6458: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ SV1055 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1556 @ SY6458 @ ( tc_fun @ SV443 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ SV1055 ) @ SY6458 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ SV1055 ) @ SV1556 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3640]) ).
thf(4300,plain,
! [SV1557: $i,SV1056: $i,SV444: $i] :
( ( ! [SY6459: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ SV1056 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1557 @ SY6459 @ ( tc_fun @ SV444 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ SV1056 ) @ SY6459 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ SV1056 ) @ SV1557 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3641]) ).
thf(4301,plain,
! [SV1558: $i,SV1057: $i,SV445: $i] :
( ( ( hBOOL @ ( hAPP @ SV445 @ SV1057 ) )
| ! [SY6460: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1558 ) @ SV1057 ) @ SY6460 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1558 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6460 @ SV445 @ SV1558 ) ) @ SY6460 ) )
| ! [SY6461: $i] :
~ ( hBOOL @ ( hAPP @ SY6461 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6460 @ SY6461 @ SV1558 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3642]) ).
thf(4302,plain,
! [SV1559: $i,SV1058: $i,SV446: $i] :
( ( ( hBOOL @ ( hAPP @ SV446 @ SV1058 ) )
| ! [SY6462: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1559 ) @ SV1058 ) @ SY6462 ) )
| ! [SY6463: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1559 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6462 @ SY6463 @ SV1559 ) ) @ SY6462 ) )
| ~ ( hBOOL @ ( hAPP @ SV446 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6462 @ SV446 @ SV1559 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3643]) ).
thf(4303,plain,
! [SV1560: $i,SV1059: $i,SV447: $i] :
( ( ( hBOOL @ ( hAPP @ SV447 @ SV1059 ) )
| ! [SY6464: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1560 ) @ SV1059 ) @ SY6464 ) )
| ~ ( hBOOL @ ( hAPP @ SV447 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6464 @ SV447 @ SV1560 ) ) )
| ! [SY6465: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1560 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6464 @ SY6465 @ SV1560 ) ) @ SY6464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3644]) ).
thf(4304,plain,
! [SV1561: $i,SV1060: $i,SV448: $i] :
( ( ( hBOOL @ ( hAPP @ SV448 @ SV1060 ) )
| ! [SY6466: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1561 ) @ SV1060 ) @ SY6466 ) )
| ! [SY6467: $i] :
~ ( hBOOL @ ( hAPP @ SY6467 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6466 @ SY6467 @ SV1561 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1561 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6466 @ SV448 @ SV1561 ) ) @ SY6466 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3645]) ).
thf(4305,plain,
! [SV1562: $i,SV1061: $i,SV449: $i] :
( ( ! [SY6468: $i,SY6469: $i,SY6470: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV449 ) @ SV1061 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV1562 @ SY6468 @ SY6469 @ SY6470 @ SV449 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY6468 @ SV1061 ) @ SY6470 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1562 @ SY6469 ) @ SV1061 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3646]) ).
thf(4306,plain,
! [SV1563: $i,SV1062: $i,SV450: $i] :
( ( ! [SY6471: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV450 ) @ SV1062 ) @ ( c_Set_Oinsert @ SV1563 @ SY6471 @ SV450 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV450 ) @ SV1062 ) @ SY6471 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3647]) ).
thf(4307,plain,
! [SV1564: $i,SV1063: $i,SV451: $i] :
( ( ! [SY6472: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV451 ) @ SV1063 ) @ ( c_Set_Oinsert @ SV1564 @ SY6472 @ SV451 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV451 ) @ SV1063 ) @ SY6472 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3648]) ).
thf(4308,plain,
! [SV1565: $i,SV1064: $i,SV452: $i] :
( ( ! [SY6473: $i,SY6474: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV452 ) @ SV1064 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV1565 @ SY6473 @ SY6474 @ SV452 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1565 @ SV1064 ) @ SY6474 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1565 @ SY6473 ) @ SV1064 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3649]) ).
thf(4309,plain,
! [SV1566: $i,SV1065: $i,SV453: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV453 ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1065 @ SV1566 @ SV453 ) ) @ SV1065 ) )
| ! [SY6475: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV453 ) @ SY6475 ) @ SV1065 ) )
| ~ ( hBOOL @ ( hAPP @ SV1566 @ SY6475 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3650]) ).
thf(4310,plain,
! [SV1066: $i,SV454: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV454 ) @ SV1066 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV454 @ tc_bool ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3651]) ).
thf(4311,plain,
! [SV1067: $i,SV455: $i] :
( ( ( hBOOL @ ( hAPP @ SV455 @ SV1067 ) )
= $true )
| ( ( ! [SY5596: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5596 ) @ SV1067 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5596 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3652]) ).
thf(4312,plain,
! [SV1068: $i,SV456: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV456 ) @ SV1068 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV456 @ tc_bool ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3653]) ).
thf(4313,plain,
! [SV1069: $i,SV457: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV457 ) @ SV1069 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV457 @ tc_bool ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3654]) ).
thf(4314,plain,
! [SV1567: $i,SV1070: $i,SV458: $i] :
( ( ! [SY6476: $i,SY6477: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV458 ) @ SV1070 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV1567 @ SY6476 @ SY6477 @ SV458 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1567 @ SV1070 ) @ SY6477 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1567 @ SY6476 ) @ SV1070 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3655]) ).
thf(4315,plain,
! [SV1568: $i,SV1071: $i,SV459: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV459 ) @ SV1071 ) @ SV1568 ) )
| ! [SY6478: $i] :
( ( SV1071 = SY6478 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV459 ) @ SV1071 ) @ ( c_Set_Oinsert @ SY6478 @ SV1568 @ SV459 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3656]) ).
thf(4316,plain,
! [SV1569: $i,SV1072: $i,SV460: $i] :
( ( ! [SY6479: $i,SY6480: $i,SY6481: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV460 ) @ SV1072 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV1569 @ SY6479 @ SY6480 @ SY6481 @ SV460 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1569 @ SV1072 ) @ SY6481 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY6479 @ SY6480 ) @ SV1072 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3657]) ).
thf(4317,plain,
! [SV1570: $i,SV1073: $i,SV461: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV461 ) @ SV1073 ) @ SV1570 ) )
| ! [SY6482: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV461 ) @ SV1073 ) @ ( c_HOL_Ominus__class_Ominus @ SY6482 @ SV1570 @ ( tc_fun @ SV461 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3658]) ).
thf(4318,plain,
! [SV1571: $i,SV1074: $i,SV462: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV462 ) @ SV1074 ) @ SV1571 ) )
| ! [SY6483: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV462 ) @ SV1074 ) @ ( c_HOL_Ominus__class_Ominus @ SV1571 @ SY6483 @ ( tc_fun @ SV462 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3659]) ).
thf(4319,plain,
! [SV1572: $i,SV1075: $i,SV463: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1075 @ SV1572 @ SV463 ) ) @ SV1075 ) )
| ! [SY5611: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ SY5611 ) @ SV1075 ) )
| ! [SY6485: $i] :
( ~ ( hBOOL @ ( hAPP @ SV1572 @ SY6485 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ SY6485 ) @ SV1075 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3660]) ).
thf(4320,plain,
! [SV1573: $i,SV1076: $i,SV464: $i] :
( ( ( hBOOL @ ( hAPP @ SV464 @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ SV1076 @ SV464 @ SV1573 ) ) )
| ! [SY6486: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1573 ) @ SY6486 ) @ SV1076 ) )
| ~ ( hBOOL @ ( hAPP @ SV464 @ SY6486 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3661]) ).
thf(4321,plain,
! [SV1574: $i,SV1077: $i,SV465: $i] :
( ( ! [SY6487: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV465 @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1077 @ SV1574 @ SY6487 @ ( tc_fun @ SV465 @ tc_bool ) ) )
| ! [SY6488: $i] :
( ( ( hAPP @ SV1574 @ SY6488 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV465 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6487 ) @ SY6488 ) @ SV1077 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3662]) ).
thf(4322,plain,
! [SV1575: $i,SV1079: $i,SV467: $i] :
( ( ! [SY6489: $i,SY6490: $i] :
( ( c_Com_Ocom_OAss @ SV467 @ SV1079 )
!= ( c_Com_Ocom_OCond @ SV1575 @ SY6489 @ SY6490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3664]) ).
thf(4323,plain,
! [SV1081: $i,SV469: $i] :
( ( c_Com_Ocom_OSKIP
= ( c_Com_Ocom_OWhile @ SV469 @ SV1081 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3666]) ).
thf(4324,plain,
! [SV1576: $i,SV1082: $i,SV470: $i] :
( ( ! [SY6491: $i] :
( ( ( c_Map_Omap__add @ SV470 @ SV1082 @ SV1576 @ SY6491 )
= ( c_Map_Omap__add @ SV1082 @ SV470 @ SV1576 @ SY6491 ) )
| ~ ( c_Map_Omap__le @ SV470 @ ( c_Map_Omap__add @ SV470 @ SV1082 @ SV1576 @ SY6491 ) @ SV1576 @ SY6491 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3667]) ).
thf(4325,plain,
! [SV1577: $i,SV1083: $i,SV471: $i] :
( ( ! [SY6492: $i] :
( ( ( c_Map_Omap__add @ SV471 @ SV1083 @ SV1577 @ SY6492 )
!= ( c_Map_Omap__add @ SV1083 @ SV471 @ SV1577 @ SY6492 ) )
| ( c_Map_Omap__le @ SV471 @ ( c_Map_Omap__add @ SV471 @ SV1083 @ SV1577 @ SY6492 ) @ SV1577 @ SY6492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3668]) ).
thf(4326,plain,
! [SV1084: $i,SV472: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV472 @ tc_bool ) ) @ SV1084 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3669]) ).
thf(4327,plain,
! [SV1578: $i,SV1085: $i,SV473: $i] :
( ( ! [SY6493: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV473 @ ( c_HOL_Ominus__class_Ominus @ SV1085 @ SV1578 @ ( tc_fun @ SY6493 @ tc_bool ) ) @ ( tc_fun @ SY6493 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV473 @ SV1085 @ ( tc_fun @ SY6493 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV473 @ SV1578 @ ( tc_fun @ SY6493 @ tc_bool ) ) @ ( tc_fun @ SY6493 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3670]) ).
thf(4328,plain,
! [SV1579: $i,SV1086: $i,SV474: $i] :
( ( ! [SY6494: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ SV474 @ SV1086 @ ( tc_fun @ SV1579 @ tc_bool ) ) @ SY6494 @ ( tc_fun @ SV1579 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV474 @ SY6494 @ ( tc_fun @ SV1579 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1086 @ SY6494 @ ( tc_fun @ SV1579 @ tc_bool ) ) @ ( tc_fun @ SV1579 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3671]) ).
thf(4329,plain,
! [SV1580: $i,SV1087: $i,SV475: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV475 @ SV1087 @ ( tc_fun @ SV1580 @ tc_bool ) )
| ! [SY6495: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1580 ) @ SY6495 ) @ SV1087 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV475 @ ( c_Set_Oinsert @ SY6495 @ SV1087 @ SV1580 ) @ ( tc_fun @ SV1580 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3672]) ).
thf(4330,plain,
! [SV1581: $i,SV1088: $i,SV476: $i] :
( ( ! [SY6496: $i] :
( ( c_HOL_Oord__class_Oless @ SV476 @ ( c_Set_Oinsert @ SV1088 @ SV1581 @ SY6496 ) @ ( tc_fun @ SY6496 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6496 ) @ SV1088 ) @ SV1581 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV476 @ SV1581 @ ( tc_fun @ SY6496 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3673]) ).
thf(4331,plain,
! [SV1582: $i,SV1089: $i,SV477: $i] :
( ( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OLocal @ SV477 @ SV1089 @ SV1582 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3674]) ).
thf(4332,plain,
! [SV1583: $i,SV1090: $i,SV478: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV478 ) @ SV1090 ) @ SV1583 ) )
| ! [SY6497: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV478 ) @ SV1090 ) @ SY6497 ) )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY6497 @ SV1583 @ ( tc_fun @ SV478 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV478 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3675]) ).
thf(4333,plain,
! [SV1584: $i,SV1091: $i,SV479: $i] :
( ( ! [SY6498: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV479 @ SV1091 @ ( tc_fun @ SV1584 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY6498 @ SV1091 @ ( tc_fun @ SV1584 @ tc_bool ) ) @ ( tc_fun @ SV1584 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV479 @ SV1091 @ ( tc_fun @ SV1584 @ tc_bool ) ) @ SY6498 @ ( tc_fun @ SV1584 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3676]) ).
thf(4334,plain,
! [SV1092: $i,SV480: $i] :
( ( c_HOL_Oord__class_Oless @ SV480 @ SV480 @ ( tc_fun @ SV1092 @ tc_bool ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3677]) ).
thf(4335,plain,
! [SV481: $i] :
( ( ( class_Orderings_Oorder @ SV481 )
= $false )
| ( ( ! [SY4130: $i] :
~ ( c_HOL_Oord__class_Oless @ SY4130 @ SY4130 @ SV481 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3678]) ).
thf(4336,plain,
! [SV482: $i] :
( ( ( class_Orderings_Olinorder @ SV482 )
= $false )
| ( ( ! [SY4131: $i] :
~ ( c_HOL_Oord__class_Oless @ SY4131 @ SY4131 @ SV482 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3679]) ).
thf(4337,plain,
! [SV483: $i] :
( ( ( class_Orderings_Opreorder @ SV483 )
= $false )
| ( ( ! [SY4132: $i] :
~ ( c_HOL_Oord__class_Oless @ SY4132 @ SY4132 @ SV483 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3680]) ).
thf(4338,plain,
! [SV1585: $i,SV484: $i] :
( ( ( ( c_Collect @ SV484 @ SV1585 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1585 @ tc_bool ) ) )
= $true )
| ( ( ! [SY4134: $i] :
~ ( hBOOL @ ( hAPP @ SV484 @ SY4134 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3681]) ).
thf(4339,plain,
! [SV1586: $i,SV1093: $i,SV486: $i] :
( ( ! [SY6499: $i] :
( ( c_Com_Ocom_OSemi @ SV486 @ SV1093 )
!= ( c_Com_Ocom_OAss @ SV1586 @ SY6499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3682]) ).
thf(4340,plain,
! [SV487: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV487 )
= $false )
| ( ( ! [SY4138: $i,SY4139: $i] :
( ( c_HOL_Oord__class_Oless @ SY4138 @ SY4139 @ SV487 )
| ( SY4139 = SY4138 )
| ( c_HOL_Oord__class_Oless @ SY4139 @ SY4138 @ SV487 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3683]) ).
thf(4341,plain,
! [SV488: $i] :
( ( ( class_Orderings_Olinorder @ SV488 )
= $false )
| ( ( ! [SY4140: $i,SY4141: $i] :
( ( SY4140 = SY4141 )
| ( c_HOL_Oord__class_Oless @ SY4141 @ SY4140 @ SV488 )
| ( c_HOL_Oord__class_Oless @ SY4140 @ SY4141 @ SV488 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3684]) ).
thf(4342,plain,
! [SV1094: $i,SV489: $i] :
( ( ( SV489 = SV1094 )
= $true )
| ( ( ! [SY5640: $i,SY5641: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY5640 ) @ SY5641 ) @ SV489 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY5640 ) @ SY5641 ) @ SV1094 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3685]) ).
thf(4343,plain,
! [SV1095: $i,SV490: $i] :
( ( ( SV490 = SV1095 )
= $true )
| ( ( ! [SY5642: $i,SY5643: $i] :
( ~ ( c_Map_Omap__le @ SV1095 @ SV490 @ SY5642 @ SY5643 )
| ~ ( c_Map_Omap__le @ SV490 @ SV1095 @ SY5642 @ SY5643 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3686]) ).
thf(4344,plain,
! [SV491: $i] :
( ( ( class_Orderings_Olinorder @ SV491 )
= $false )
| ( ( ! [SY4148: $i,SY4149: $i] :
( ( c_HOL_Oord__class_Oless @ SY4148 @ SY4149 @ SV491 )
| ( SY4149 = SY4148 )
| ( c_HOL_Oord__class_Oless @ SY4149 @ SY4148 @ SV491 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3687]) ).
thf(4345,plain,
! [SV492: $i] :
( ( ( class_Orderings_Olinorder @ SV492 )
= $false )
| ( ( ! [SY4150: $i,SY4151: $i] :
( ( c_HOL_Oord__class_Oless @ SY4150 @ SY4151 @ SV492 )
| ( SY4151 = SY4150 )
| ( c_HOL_Oord__class_Oless @ SY4151 @ SY4150 @ SV492 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3688]) ).
thf(4346,plain,
! [SV493: $i] :
( ( ( class_Orderings_Olinorder @ SV493 )
= $false )
| ( ( ! [SY4152: $i,SY4153: $i] :
( ( SY4152 = SY4153 )
| ( c_HOL_Oord__class_Oless @ SY4152 @ SY4153 @ SV493 )
| ( c_HOL_Oord__class_Oless @ SY4153 @ SY4152 @ SV493 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3689]) ).
thf(4347,plain,
! [SV1587: $i,SV1096: $i,SV494: $i] :
( ( ( c_Com_Ocom_OLocal @ SV494 @ SV1096 @ SV1587 )
!= c_Com_Ocom_OSKIP )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3690]) ).
thf(4348,plain,
! [SV1097: $i,SV495: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV495 ) )
= $true )
| ( ( ! [SY5645: $i,SY5646: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1097 @ SY5645 @ SV495 ) @ SY5646 @ SV495 )
| ~ ( c_HOL_Oord__class_Oless @ SY5645 @ SY5646 @ SV495 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3691]) ).
thf(4349,plain,
! [SV1098: $i,SV496: $i] :
( ( ( ~ ( class_Lattices_Olower__semilattice @ SV496 ) )
= $true )
| ( ( ! [SY5647: $i,SY5648: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1098 @ SY5647 @ SV496 ) @ SY5648 @ SV496 )
| ~ ( c_HOL_Oord__class_Oless @ SV1098 @ SY5648 @ SV496 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3692]) ).
thf(4350,plain,
! [SV1588: $i,SV1099: $i,SV497: $i] :
( ( ! [SY6500: $i] : ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV497 @ SV1099 @ SV1588 @ SY6500 ) @ SY6500 )
| ~ ( c_Finite__Set_Ofinite @ SV1099 @ SV1588 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3693]) ).
thf(4351,plain,
! [SV1589: $i,SV1100: $i,SV498: $i] :
( ( ! [SY6501: $i] :
( ( ( hAPP @ SV498 @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ SV498 @ SV1100 @ SV1589 @ SY6501 ) )
!= ( hAPP @ SV1100 @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ SV498 @ SV1100 @ SV1589 @ SY6501 ) ) )
| ( c_Map_Omap__le @ SV498 @ SV1100 @ SV1589 @ SY6501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3694]) ).
thf(4352,plain,
! [SV1590: $i,SV1101: $i,SV499: $i] :
( ( ! [SY6502: $i,SY6503: $i] :
( ( ( c_Set_Oinsert @ SV499 @ ( c_Set_Oinsert @ SV1101 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1590 @ tc_bool ) ) @ SV1590 ) @ SV1590 )
!= ( c_Set_Oinsert @ SY6502 @ ( c_Set_Oinsert @ SY6503 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1590 @ tc_bool ) ) @ SV1590 ) @ SV1590 ) )
| ( SV499 = SY6503 )
| ( SV499 = SY6502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3695]) ).
thf(4353,plain,
! [SV1591: $i,SV1102: $i,SV500: $i] :
( ( ! [SY6504: $i] :
( ! [SY6505: $i] :
( ( c_Set_Oinsert @ SV500 @ ( c_Set_Oinsert @ SV1102 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1591 @ tc_bool ) ) @ SV1591 ) @ SV1591 )
!= ( c_Set_Oinsert @ SY6504 @ ( c_Set_Oinsert @ SY6505 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1591 @ tc_bool ) ) @ SV1591 ) @ SV1591 ) )
| ( SV1102 = SY6504 )
| ( SV500 = SY6504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3696]) ).
thf(4354,plain,
! [SV1592: $i,SV1103: $i,SV501: $i] :
( ( ! [SY6506: $i,SY6507: $i] :
( ( ( c_Set_Oinsert @ SV501 @ ( c_Set_Oinsert @ SV1103 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1592 @ tc_bool ) ) @ SV1592 ) @ SV1592 )
!= ( c_Set_Oinsert @ SY6506 @ ( c_Set_Oinsert @ SY6507 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1592 @ tc_bool ) ) @ SV1592 ) @ SV1592 ) )
| ( SV501 = SY6507 )
| ( SV1103 = SY6507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3697]) ).
thf(4355,plain,
! [SV1593: $i,SV1104: $i,SV502: $i] :
( ( ! [SY6508: $i,SY6509: $i] :
( ( ( c_Set_Oinsert @ SV502 @ ( c_Set_Oinsert @ SV1104 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1593 @ tc_bool ) ) @ SV1593 ) @ SV1593 )
!= ( c_Set_Oinsert @ SY6508 @ ( c_Set_Oinsert @ SY6509 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1593 @ tc_bool ) ) @ SV1593 ) @ SV1593 ) )
| ( SV1104 = SY6508 )
| ( SV1104 = SY6509 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3698]) ).
thf(4356,plain,
! [SV1594: $i,SV1105: $i,SV503: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV503 ) @ SV1105 ) @ SV1594 ) )
| ! [SY6510: $i] :
( ( hBOOL @ ( hAPP @ SY6510 @ SV1105 ) )
| ! [SY6511: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY6510 @ SY6511 @ SV503 ) ) @ SV1105 ) @ SV1594 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3699]) ).
thf(4357,plain,
! [SV1595: $i,SV1106: $i,SV504: $i] :
( ( ! [SY6512: $i,SY6513: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV504 @ SV1106 @ SV1595 ) ) @ SY6512 ) @ SY6513 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1595 ) @ SY6512 ) @ SY6513 ) )
| ( hBOOL @ ( hAPP @ SV504 @ SY6512 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3700]) ).
thf(4358,plain,
! [SV1107: $i,SV505: $i] :
( ( c_Com_Ocom_OSKIP
= ( c_Com_Ocom_OAss @ SV505 @ SV1107 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3701]) ).
thf(4359,plain,
! [SV1596: $i,SV1108: $i,SV506: $i] :
( ( ! [SY6514: $i,SY6515: $i,SY6516: $i,SY6517: $i,SY6518: $i,SY6519: $i] :
( ( ( hAPP @ SV506 @ ( c_Set_Oinsert @ SV1108 @ SV1596 @ SY6514 ) )
= ( hAPP @ ( hAPP @ SY6515 @ SV1108 ) @ ( hAPP @ SV506 @ SV1596 ) ) )
| ! [SY4201: $i,SY4202: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY6516 @ SV506 @ SY6517 @ SY6518 @ SY6519 @ SY6515 @ SY4201 @ SY4202 @ SY6514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3702]) ).
thf(4360,plain,
! [SV1597: $i,SV1109: $i,SV507: $i] :
( ( ! [SY6522: $i,SY6523: $i,SY6524: $i,SY6525: $i,SY6526: $i,SY6527: $i] :
( ( ( hAPP @ SV507 @ ( c_Set_Oinsert @ SV1109 @ SV1597 @ SY6522 ) )
= ( hAPP @ ( hAPP @ SY6523 @ SV1109 ) @ ( hAPP @ SV507 @ SV1597 ) ) )
| ! [SY4211: $i,SY4212: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV507 @ SY6524 @ SY6525 @ SY6526 @ SY6523 @ SY6527 @ SY4211 @ SY4212 @ SY6522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3703]) ).
thf(4361,plain,
! [SV1598: $i,SV1110: $i,SV508: $i] :
( ( ! [SY6530: $i] :
( ( c_Com_Ocom_OWhile @ SV508 @ SV1110 )
!= ( c_Com_Ocom_OAss @ SV1598 @ SY6530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3704]) ).
thf(4362,plain,
! [SV1599: $i,SV1111: $i,SV509: $i] :
( ( ! [SY6531: $i,SY6532: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SV1111 @ SV1599 @ SY6531 @ SY6532 @ SV509 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1111 @ SV1599 @ SY6532 @ ( tc_fun @ SV509 @ tc_bool ) ) ) )
| ! [SY6533: $i] :
( ~ ( hBOOL @ ( hAPP @ SY6531 @ SY6533 ) )
| ! [SY6534: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ SY6533 ) @ ( hAPP @ SV1599 @ SY6534 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6532 ) @ SY6534 ) @ SV1111 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3705]) ).
thf(4363,plain,
! [SV1600: $i,SV1112: $i,SV510: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV510 @ tc_bool ) )
!= ( c_Set_Oinsert @ SV1112 @ SV1600 @ SV510 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3706]) ).
thf(4364,plain,
! [SV1601: $i,SV1113: $i,SV511: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV511 @ SV1113 @ SV1601 )
| ! [SY6535: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV511 @ SY6535 @ SV1601 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY6535 @ SV1113 @ SV1601 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3707]) ).
thf(4365,plain,
! [SV1602: $i,SV1114: $i,SV512: $i] :
( ( ! [SY6536: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV512 @ SV1114 @ SV1602 ) @ SY6536 @ ( tc_fun @ SV1602 @ tc_bool ) )
= ( c_Set_Oinsert @ SV512 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1114 @ SY6536 @ ( tc_fun @ SV1602 @ tc_bool ) ) @ SV1602 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1602 ) @ SV512 ) @ SY6536 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3708]) ).
thf(4366,plain,
! [SV1603: $i,SV1115: $i,SV513: $i] :
( ( ! [SY6537: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV513 @ ( c_Set_Oinsert @ SV1115 @ SV1603 @ SY6537 ) @ ( tc_fun @ SY6537 @ tc_bool ) )
= ( c_Set_Oinsert @ SV1115 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV513 @ SV1603 @ ( tc_fun @ SY6537 @ tc_bool ) ) @ SY6537 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6537 ) @ SV1115 ) @ SV513 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3709]) ).
thf(4367,plain,
! [SV1604: $i,SV1116: $i,SV514: $i] :
( ( ! [SY6538: $i,SY6539: $i] :
( ( c_Set_Oimage @ SV514 @ ( c_Set_Oinsert @ SV1116 @ SV1604 @ SY6538 ) @ SY6538 @ SY6539 )
= ( c_Set_Oinsert @ ( hAPP @ SV514 @ SV1116 ) @ ( c_Set_Oimage @ SV514 @ SV1604 @ SY6538 @ SY6539 ) @ SY6539 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3710]) ).
thf(4368,plain,
! [SV1605: $i,SV1117: $i,SV515: $i] :
( ( ! [SY6540: $i,SY6541: $i,SY6542: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV515 @ SV1117 @ SV1605 @ SY6540 ) @ SY6541 )
!= ( c_Option_Ooption_OSome @ SY6542 @ SY6540 ) )
| ( ( hAPP @ SV1117 @ SY6541 )
= ( c_Option_Ooption_ONone @ SY6540 ) )
| ( ( hAPP @ SV1117 @ SY6541 )
= ( c_Option_Ooption_OSome @ SY6542 @ SY6540 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3711]) ).
thf(4369,plain,
! [SV1606: $i,SV1118: $i,SV516: $i] :
( ( ( ( hAPP @ SV516 @ SV1118 )
= SV1606 )
| ! [SY6543: $i,SY6544: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6543 ) @ SV1118 ) @ ( c_Set_Ovimage @ SV516 @ ( c_Set_Oinsert @ SV1606 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6544 @ tc_bool ) ) @ SY6544 ) @ SY6543 @ SY6544 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3712]) ).
thf(4370,plain,
! [SV1607: $i,SV1119: $i,SV517: $i] :
( ( ! [SY6545: $i] :
( ( ( c_Com_Ocom_OAss @ SV517 @ SV1119 )
!= ( c_Com_Ocom_OAss @ SV1607 @ SY6545 ) )
| ( SV1119 = SY6545 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3713]) ).
thf(4371,plain,
! [SV1608: $i,SV1120: $i,SV518: $i] :
( ( ! [SY6546: $i] :
( ( c_Com_Ocom_OAss @ SV518 @ SV1120 )
!= ( c_Com_Ocom_OAss @ SV1608 @ SY6546 ) )
| ( SV518 = SV1608 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3714]) ).
thf(4372,plain,
! [SV1609: $i,SV1121: $i,SV519: $i] :
( ( ! [SY6547: $i] :
( ( c_Set_Oinsert @ SV519 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1121 @ tc_bool ) ) @ SV1609 @ SV1121 @ ( tc_fun @ SY6547 @ tc_bool ) ) @ SY6547 )
= ( c_Set_Oinsert @ SV519 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6547 @ tc_bool ) ) @ SY6547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3715]) ).
thf(4373,plain,
! [SV1122: $i,SV520: $i] :
( ( ( c_Com_Ocom_OSemi @ SV520 @ SV1122 )
= c_Com_Ocom_OSKIP )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3716]) ).
thf(4374,plain,
! [SV1123: $i,SV521: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV521 @ tc_bool ) )
!= ( c_Collect @ SV1123 @ SV521 ) )
= $true )
| ( ( ! [SY5719: $i] :
~ ( hBOOL @ ( hAPP @ SV1123 @ SY5719 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3717]) ).
thf(4375,plain,
! [SV1610: $i,SV1124: $i,SV522: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV522 @ SV1124 @ SV1610 ) @ SV522 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3718]) ).
thf(4376,plain,
! [SV523: $i] :
( ( ( class_Lattices_Olattice @ SV523 )
= $false )
| ( ( ! [SY4260: $i,SY4261: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY4260 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4260 @ SY4261 @ SV523 ) @ SV523 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY4260 @ SY4261 @ SV523 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3719]) ).
thf(4377,plain,
! [SV524: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV524 )
= $false )
| ( ( ! [SY4262: $i,SY4263: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY4262 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4262 @ SY4263 @ SV524 ) @ SV524 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY4262 @ SY4263 @ SV524 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3720]) ).
thf(4378,plain,
! [SV1611: $i,SV1125: $i,SV525: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV525 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV525 @ SV1125 @ ( tc_fun @ SV1611 @ tc_bool ) ) @ ( tc_fun @ SV1611 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV525 @ SV1125 @ ( tc_fun @ SV1611 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3721]) ).
thf(4379,plain,
! [SV1612: $i,SV1126: $i,SV526: $i] :
( ( ! [SY6548: $i,SY6549: $i,SY6550: $i] :
( ( ( c_Com_Ocom_OLocal @ SV526 @ SV1126 @ SV1612 )
!= ( c_Com_Ocom_OLocal @ SY6548 @ SY6549 @ SY6550 ) )
| ( SV1612 = SY6550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3722]) ).
thf(4380,plain,
! [SV1613: $i,SV1127: $i,SV527: $i] :
( ( ! [SY6551: $i,SY6552: $i] :
( ! [SY6553: $i] :
( ( c_Com_Ocom_OLocal @ SV527 @ SV1127 @ SV1613 )
!= ( c_Com_Ocom_OLocal @ SY6551 @ SY6552 @ SY6553 ) )
| ( SV1127 = SY6552 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3723]) ).
thf(4381,plain,
! [SV1614: $i,SV1128: $i,SV528: $i] :
( ( ! [SY6554: $i] :
( ! [SY6555: $i,SY6556: $i] :
( ( c_Com_Ocom_OLocal @ SV528 @ SV1128 @ SV1614 )
!= ( c_Com_Ocom_OLocal @ SY6554 @ SY6555 @ SY6556 ) )
| ( SV528 = SY6554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3724]) ).
thf(4382,plain,
! [SV1615: $i,SV1129: $i,SV529: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV529 @ SV1129 @ ( tc_fun @ SV1615 @ tc_bool ) ) @ SV1615 )
| ! [SY6557: $i] :
~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV529 @ ( c_Set_Oinsert @ SY6557 @ SV1129 @ SV1615 ) @ ( tc_fun @ SV1615 @ tc_bool ) ) @ SV1615 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3725]) ).
thf(4383,plain,
! [SV1616: $i,SV1130: $i,SV530: $i] :
( ( ! [SY6558: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV530 @ ( c_Set_Oinsert @ SV1130 @ SV1616 @ SY6558 ) @ ( tc_fun @ SY6558 @ tc_bool ) ) @ SY6558 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV530 @ SV1616 @ ( tc_fun @ SY6558 @ tc_bool ) ) @ SY6558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3726]) ).
thf(4384,plain,
! [SV1617: $i,SV1131: $i,SV531: $i] :
( ( ! [SY6559: $i] :
( ( c_Com_Ocom_OWhile @ SV531 @ SV1131 )
!= ( c_Com_Ocom_OSemi @ SV1617 @ SY6559 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3727]) ).
thf(4385,plain,
! [SV1618: $i,SV1132: $i,SV532: $i] :
( ( ! [SY6560: $i,SY6561: $i,SY6562: $i,SY6563: $i] :
( ( ( hAPP @ SV532 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1132 @ tc_bool ) ) )
= SV1618 )
| ! [SY6564: $i,SY6565: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY6560 @ SV532 @ SY6561 @ SY6562 @ SY6563 @ SY6564 @ SV1618 @ SY6565 @ SV1132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3728]) ).
thf(4386,plain,
! [SV1619: $i,SV1133: $i,SV533: $i] :
( ( ! [SY6566: $i,SY6567: $i,SY6568: $i,SY6569: $i] :
( ( ( hAPP @ SV533 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1133 @ tc_bool ) ) )
= SV1619 )
| ! [SY6570: $i,SY6571: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV533 @ SY6566 @ SY6567 @ SY6568 @ SY6569 @ SY6570 @ SY6571 @ SV1619 @ SV1133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3729]) ).
thf(4387,plain,
! [SV1134: $i,SV534: $i] :
( ( ( hBOOL @ ( hAPP @ SV534 @ SV1134 ) )
= $true )
| ( ( ! [SY5754: $i] :
( ( SY5754 = SV1134 )
| ! [SY5755: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV534 @ SY5755 ) ) @ SV1134 ) @ SY5754 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3730]) ).
thf(4388,plain,
! [SV1620: $i,SV1135: $i,SV535: $i] :
( ( ( ( c_Set_Oinsert @ SV535 @ ( c_HOL_Ominus__class_Ominus @ SV1135 @ ( c_Set_Oinsert @ SV535 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1620 @ tc_bool ) ) @ SV1620 ) @ ( tc_fun @ SV1620 @ tc_bool ) ) @ SV1620 )
= SV1135 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1620 ) @ SV535 ) @ SV1135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3731]) ).
thf(4389,plain,
! [SV536: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV536 )
= $false )
| ( ( ! [SY4311: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SY4311 @ SY4311 @ SV536 )
= SY4311 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3732]) ).
thf(4390,plain,
! [SV1621: $i,SV1137: $i,SV538: $i] :
( ( ! [SY6572: $i] :
( ( c_Set_Oimage @ SV538 @ SV1137 @ SV1621 @ SY6572 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6572 @ tc_bool ) ) )
| ( SV1137
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1621 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3734]) ).
thf(4391,plain,
! [SV1622: $i,SV1139: $i,SV540: $i] :
( ( ! [SY6573: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ SV1139 @ ( tc_fun @ SV1622 @ tc_bool ) ) @ SY6573 @ ( tc_fun @ SV1622 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ ( c_HOL_Ominus__class_Ominus @ SV1139 @ SY6573 @ ( tc_fun @ SV1622 @ tc_bool ) ) @ ( tc_fun @ SV1622 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3736]) ).
thf(4392,plain,
! [SV1623: $i,SV1140: $i,SV541: $i] :
( ( ! [SY6574: $i,SY6575: $i,SY6576: $i,SY6577: $i,SY6578: $i] :
( ( ( hAPP @ SV541 @ ( c_Set_Oinsert @ SV1140 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1623 @ tc_bool ) ) @ SV1623 ) )
= SV1140 )
| ! [SY6579: $i,SY6580: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY6574 @ SV541 @ SY6575 @ SY6576 @ SY6577 @ SY6578 @ SY6579 @ SY6580 @ SV1623 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3737]) ).
thf(4393,plain,
! [SV1624: $i,SV1141: $i,SV542: $i] :
( ( ! [SY6581: $i,SY6582: $i,SY6583: $i,SY6584: $i,SY6585: $i] :
( ( ( hAPP @ SV542 @ ( c_Set_Oinsert @ SV1141 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1624 @ tc_bool ) ) @ SV1624 ) )
= SV1141 )
| ! [SY6586: $i,SY6587: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV542 @ SY6581 @ SY6582 @ SY6583 @ SY6584 @ SY6585 @ SY6586 @ SY6587 @ SV1624 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3738]) ).
thf(4394,plain,
! [SV1625: $i,SV1143: $i,SV544: $i] :
( ( ( c_Com_Ocom_OWhile @ SV544 @ SV1143 )
!= ( c_Com_Ocom_OBODY @ SV1625 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3740]) ).
thf(4395,plain,
! [SV1626: $i,SV1144: $i,SV545: $i] :
( ( ! [SY6588: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1144 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1626 @ ( c_Collect @ SY6588 @ SV545 ) @ ( tc_fun @ SV545 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SY6588 @ SV1144 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1144 ) @ SV1626 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3741]) ).
thf(4396,plain,
! [SV1627: $i,SV1145: $i,SV547: $i] :
( ( ( hBOOL @ ( hAPP @ SV547 @ ( hAPP @ SV1145 @ SV1627 ) ) )
| ! [SY6589: $i,SY6590: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV1145 @ SV547 @ SY6589 @ SY6590 ) @ SV1627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3743]) ).
thf(4397,plain,
! [SV1628: $i,SV1146: $i,SV548: $i] :
( ( ! [SY6591: $i,SY6592: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV548 @ SV1146 @ SV1628 @ SY6591 ) @ SY6592 ) )
| ~ ( hBOOL @ ( hAPP @ SV1146 @ ( hAPP @ SV548 @ SY6592 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3744]) ).
thf(4398,plain,
! [SV1629: $i,SV1147: $i,SV549: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV549 @ SV1147 @ SV1629 )
| ! [SY6593: $i] :
~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV549 @ ( c_Set_Oinsert @ SY6593 @ SV1147 @ ( tc_Hoare__Mirabelle_Otriple @ SV1629 ) ) @ SV1629 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3745]) ).
thf(4399,plain,
! [SV1630: $i,SV1148: $i,SV550: $i] :
( ( ! [SY6594: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV550 @ ( c_Set_Oinsert @ SV1148 @ SV1630 @ ( tc_Hoare__Mirabelle_Otriple @ SY6594 ) ) @ SY6594 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV550 @ SV1630 @ SY6594 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV550 @ ( c_Set_Oinsert @ SV1148 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY6594 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY6594 ) ) @ SY6594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3746]) ).
thf(4400,plain,
! [SV1631: $i,SV1149: $i,SV551: $i] :
( ( ! [SY6595: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV551 @ SV1149 @ ( tc_fun @ SV1631 @ tc_bool ) ) @ SY6595 ) )
| ~ ( hBOOL @ ( hAPP @ SV1149 @ SY6595 ) )
| ~ ( hBOOL @ ( hAPP @ SV551 @ SY6595 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3747]) ).
thf(4401,plain,
! [SV1632: $i,SV1150: $i,SV552: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV552 )
| ! [SY6596: $i,SY6597: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV1150 @ SV1632 @ SV552 )
!= ( c_HOL_Ominus__class_Ominus @ SY6596 @ SY6597 @ SV552 ) )
| ( c_HOL_Oord__class_Oless @ SY6596 @ SY6597 @ SV552 )
| ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SV1632 @ SV552 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3748]) ).
thf(4402,plain,
! [SV1633: $i,SV1151: $i,SV553: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV553 )
| ! [SY6598: $i,SY6599: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV1151 @ SV1633 @ SV553 )
!= ( c_HOL_Ominus__class_Ominus @ SY6598 @ SY6599 @ SV553 ) )
| ( c_HOL_Oord__class_Oless @ SV1151 @ SV1633 @ SV553 )
| ~ ( c_HOL_Oord__class_Oless @ SY6598 @ SY6599 @ SV553 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3749]) ).
thf(4403,plain,
! [SV1152: $i,SV554: $i] :
( ( ( c_Com_Ocom_OAss @ SV554 @ SV1152 )
= c_Com_Ocom_OSKIP )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3750]) ).
thf(4404,plain,
! [SV1154: $i,SV556: $i] :
( ( ( c_Finite__Set_Ofinite @ SV556 @ SV1154 )
= $true )
| ( ( ! [SY5798: $i,SY5799: $i] :
( ~ ( c_Fun_Oinj__on @ SY5798 @ SV556 @ SV1154 @ SY5799 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SY5798 @ SV556 @ SV1154 @ SY5799 ) @ SY5799 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3752]) ).
thf(4405,plain,
! [SV1634: $i,SV1155: $i,SV557: $i] :
( ( ( c_Set_Ovimage @ SV557 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1155 @ tc_bool ) ) @ SV1634 @ SV1155 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1634 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3753]) ).
thf(4406,plain,
! [SV1635: $i,SV1156: $i,SV558: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV558 ) @ SV1156 ) @ SV1635 ) )
| ! [SY6600: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY6600 ) @ SV1156 ) @ SV1635 ) )
| ! [SY6601: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY6601 @ SY6600 @ SV558 ) ) @ SV1156 ) @ SV1635 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3754]) ).
thf(4407,plain,
! [SV1158: $i,SV560: $i] :
( ( c_Com_Ocom_OSKIP
= ( c_Com_Ocom_OSemi @ SV560 @ SV1158 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3756]) ).
thf(4408,plain,
! [SV561: $i] :
( ( ( class_Orderings_Oorder @ SV561 )
= $false )
| ( ( ! [SY4382: $i,SY4383: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY4382 @ SY4383 @ SV561 )
| ~ ( c_HOL_Oord__class_Oless @ SY4383 @ SY4382 @ SV561 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3757]) ).
thf(4409,plain,
! [SV562: $i] :
( ( ( class_Orderings_Olinorder @ SV562 )
= $false )
| ( ( ! [SY4384: $i,SY4385: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY4384 @ SY4385 @ SV562 )
| ~ ( c_HOL_Oord__class_Oless @ SY4385 @ SY4384 @ SV562 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3758]) ).
thf(4410,plain,
! [SV563: $i] :
( ( ( class_Orderings_Opreorder @ SV563 )
= $false )
| ( ( ! [SY4386: $i,SY4387: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY4386 @ SY4387 @ SV563 )
| ~ ( c_HOL_Oord__class_Oless @ SY4387 @ SY4386 @ SV563 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3759]) ).
thf(4411,plain,
! [SV564: $i] :
( ( ( class_Orderings_Opreorder @ SV564 )
= $false )
| ( ( ! [SY4388: $i,SY4389: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY4388 @ SY4389 @ SV564 )
| ~ ( c_HOL_Oord__class_Oless @ SY4389 @ SY4388 @ SV564 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3760]) ).
thf(4412,plain,
! [SV1636: $i,SV1159: $i,SV565: $i] :
( ( ( hBOOL @ ( hAPP @ SV565 @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ SV1159 @ SV565 @ SV1636 ) ) )
| ! [SY6602: $i] :
( ~ ( hBOOL @ ( hAPP @ SV565 @ SY6602 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1636 ) @ SY6602 ) @ SV1159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3761]) ).
thf(4413,plain,
! [SV1637: $i,SV1160: $i,SV566: $i] :
( ( ! [SY6603: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV566 @ SV1160 ) @ SV1637 ) )
| ! [SY6604: $i,SY6605: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6603 ) @ SV1637 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SY6604 @ SV566 @ SV1160 @ SY6605 @ SY6603 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3762]) ).
thf(4414,plain,
! [SV1638: $i,SV1161: $i,SV567: $i] :
( ( ! [SY6606: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV567 @ SV1161 ) @ SV1638 ) )
| ! [SY6607: $i,SY6608: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6606 ) @ SV1161 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV567 @ SY6607 @ SY6608 @ SV1638 @ SY6606 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3763]) ).
thf(4415,plain,
! [SV1639: $i,SV1162: $i,SV568: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV568 ) @ SV1162 ) @ SV1639 ) )
| ! [SY6609: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV568 ) @ SV1162 ) @ SY6609 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY6609 @ SV1639 @ ( tc_fun @ SV568 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3764]) ).
thf(4416,plain,
! [SV1640: $i,SV1163: $i,SV569: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV569 ) @ SV1163 ) @ ( c_Set_Oinsert @ SV1163 @ SV1640 @ SV569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3765]) ).
thf(4417,plain,
! [SV1641: $i,SV1164: $i,SV570: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV570 ) @ SV1164 ) @ ( c_Set_Oinsert @ SV1164 @ SV1641 @ SV570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3766]) ).
thf(4418,plain,
! [SV1642: $i,SV1165: $i,SV571: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV571 ) @ SV1165 ) @ ( c_Set_Oinsert @ SV1165 @ SV1642 @ SV571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3767]) ).
thf(4419,plain,
! [SV1643: $i,SV1166: $i,SV572: $i] :
( ( ( hBOOL @ ( hAPP @ SV572 @ SV1166 ) )
| ! [SY6610: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1643 ) @ SV1166 ) @ SY6610 ) )
| ~ ( hBOOL @ ( hAPP @ SV572 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6610 @ SV572 @ SV1643 ) ) )
| ! [SY6611: $i] :
~ ( hBOOL @ ( hAPP @ SY6611 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6610 @ SY6611 @ SV1643 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3768]) ).
thf(4420,plain,
! [SV1644: $i,SV1167: $i,SV573: $i] :
( ( ( hBOOL @ ( hAPP @ SV573 @ SV1167 ) )
| ! [SY6612: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1644 ) @ SV1167 ) @ SY6612 ) )
| ! [SY6613: $i] :
~ ( hBOOL @ ( hAPP @ SY6613 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6612 @ SY6613 @ SV1644 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV573 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6612 @ SV573 @ SV1644 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3769]) ).
thf(4421,plain,
! [SV1645: $i,SV1168: $i,SV574: $i] :
( ( ( hBOOL @ ( hAPP @ SV574 @ SV1168 ) )
| ! [SY6614: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1645 ) @ SV1168 ) @ SY6614 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1645 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6614 @ SV574 @ SV1645 ) ) @ SY6614 ) )
| ! [SY6615: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1645 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6614 @ SY6615 @ SV1645 ) ) @ SY6614 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3770]) ).
thf(4422,plain,
! [SV1646: $i,SV1169: $i,SV575: $i] :
( ( ( hBOOL @ ( hAPP @ SV575 @ SV1169 ) )
| ! [SY6616: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1646 ) @ SV1169 ) @ SY6616 ) )
| ! [SY6617: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1646 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6616 @ SY6617 @ SV1646 ) ) @ SY6616 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1646 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6616 @ SV575 @ SV1646 ) ) @ SY6616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3771]) ).
thf(4423,plain,
! [SV1647: $i,SV1170: $i,SV576: $i] :
( ( ( hBOOL @ ( hAPP @ SV576 @ SV1170 ) )
| ! [SY6618: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1647 ) @ SV1170 ) @ SY6618 ) )
| ! [SY6619: $i] :
( ~ ( hBOOL @ ( hAPP @ SV576 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SY6618 @ SY6619 @ SV576 @ SV1647 ) ) )
| ~ ( hBOOL @ ( hAPP @ SY6619 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SY6618 @ SY6619 @ SV576 @ SV1647 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3772]) ).
thf(4424,plain,
! [SV1648: $i,SV1171: $i,SV577: $i] :
( ( ( hBOOL @ ( hAPP @ SV577 @ SV1171 ) )
| ! [SY6620: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1648 ) @ SV1171 ) @ SY6620 ) )
| ! [SY6621: $i] :
( ~ ( hBOOL @ ( hAPP @ SY6621 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SY6620 @ SV577 @ SY6621 @ SV1648 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV577 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SY6620 @ SV577 @ SY6621 @ SV1648 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3773]) ).
thf(4425,plain,
! [SV1649: $i,SV1172: $i,SV578: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV578 ) @ SV1172 ) @ SV1649 ) )
| ! [SY6622: $i] :
( ( hBOOL @ ( hAPP @ SY6622 @ SV1172 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV578 ) @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ SV1649 @ SY6622 @ SV578 ) ) @ SV1649 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3774]) ).
thf(4426,plain,
! [SV1650: $i,SV1173: $i,SV579: $i] :
( ( ( hBOOL @ ( hAPP @ SV579 @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1173 @ SV579 @ SV1650 ) ) )
| ! [SY6623: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1650 ) @ SY6623 ) @ SV1173 ) )
| ~ ( hBOOL @ ( hAPP @ SV579 @ SY6623 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3775]) ).
thf(4427,plain,
! [SV1651: $i,SV1174: $i,SV580: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV580 @ SV1174 ) @ SV1651 ) )
| ! [SY6624: $i,SY6625: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6624 ) @ SV1651 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV580 @ SV1174 @ SY6625 @ SY6624 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3776]) ).
thf(4428,plain,
! [SV1652: $i,SV1175: $i,SV581: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV581 @ SV1175 ) @ SV1652 ) )
| ! [SY6626: $i,SY6627: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6626 ) @ SV1175 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV581 @ SY6627 @ SV1652 @ SY6626 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3777]) ).
thf(4429,plain,
! [SV1653: $i,SV1176: $i,SV582: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV582 ) @ SV1176 ) @ SV1653 ) )
| ! [SY6628: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV582 ) @ SV1176 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY6628 @ SV1653 @ ( tc_fun @ SV582 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3778]) ).
thf(4430,plain,
! [SV1654: $i,SV1177: $i,SV583: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV583 ) @ SV1177 ) @ SV1654 ) )
| ! [SY6629: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV583 ) @ SV1177 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1654 @ SY6629 @ ( tc_fun @ SV583 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3779]) ).
thf(4431,plain,
! [SV1655: $i,SV1178: $i,SV584: $i] :
( ( ! [SY6630: $i] :
( ( ( hAPP @ SV584 @ SV1178 )
!= ( hAPP @ SV584 @ SV1655 ) )
| ! [SY6631: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6630 ) @ SV1655 ) @ SY6631 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6630 ) @ SV1178 ) @ SY6631 ) )
| ( SV1178 = SV1655 )
| ! [SY4460: $i] :
~ ( c_Fun_Oinj__on @ SV584 @ SY6631 @ SY6630 @ SY4460 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3780]) ).
thf(4432,plain,
! [SV1656: $i,SV1179: $i,SV585: $i] :
( ( ! [SY6633: $i] :
( ( ( hAPP @ SV585 @ SV1179 )
!= ( hAPP @ SV585 @ SV1656 ) )
| ! [SY6634: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6633 ) @ SV1656 ) @ SY6634 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6633 ) @ SV1179 ) @ SY6634 ) )
| ! [SY4465: $i] :
~ ( c_Fun_Oinj__on @ SV585 @ SY6634 @ SY6633 @ SY4465 )
| ( SV1179 = SV1656 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3781]) ).
thf(4433,plain,
! [SV1657: $i,SV1180: $i,SV586: $i] :
( ( ! [SY6636: $i] :
( ( ( hAPP @ SV586 @ SV1180 )
!= ( hAPP @ SV586 @ SV1657 ) )
| ! [SY6637: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6636 ) @ SV1657 ) @ SY6637 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6636 ) @ SV1180 ) @ SY6637 ) )
| ! [SY4470: $i] :
~ ( c_Fun_Oinj__on @ SV586 @ SY6637 @ SY6636 @ SY4470 )
| ( SV1180 = SV1657 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3782]) ).
thf(4434,plain,
! [SV1658: $i,SV1181: $i,SV587: $i] :
( ( ! [SY6639: $i] :
( ( ( hAPP @ SV587 @ SV1181 )
!= ( hAPP @ SV587 @ SV1658 ) )
| ! [SY6640: $i] :
( ! [SY4475: $i] :
~ ( c_Fun_Oinj__on @ SV587 @ SY6639 @ SY6640 @ SY4475 )
| ( SV1181 = SV1658 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6640 ) @ SV1658 ) @ SY6639 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6640 ) @ SV1181 ) @ SY6639 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3783]) ).
thf(4435,plain,
! [SV1182: $i,SV588: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV588 @ SV1182 ) ) )
= $true )
| ( ( ! [SY5867: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5867 ) @ SV1182 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5867 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3784]) ).
thf(4436,plain,
! [SV1659: $i,SV1183: $i,SV589: $i] :
( ( ( ( hAPP @ ( c_COMBC @ ( c_in @ SV589 ) @ SV589 @ ( tc_fun @ SV589 @ tc_bool ) @ tc_bool ) @ SV1183 )
!= ( hAPP @ ( c_COMBC @ ( c_in @ SV589 ) @ SV589 @ ( tc_fun @ SV589 @ tc_bool ) @ tc_bool ) @ SV1659 ) )
| ( SV1183 = SV1659 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3785]) ).
thf(4437,plain,
! [SV1660: $i,SV1184: $i,SV590: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV590 ) @ SV1184 ) @ ( c_Collect @ SV1660 @ SV590 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV1660 @ SV1184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3786]) ).
thf(4438,plain,
! [SV1185: $i,SV591: $i] :
( ( ( hBOOL @ ( hAPP @ SV591 @ SV1185 ) )
= $true )
| ( ( ! [SY5870: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5870 ) @ SV1185 ) @ ( c_Collect @ SV591 @ SY5870 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3787]) ).
thf(4439,plain,
! [SV1661: $i,SV1186: $i,SV592: $i] :
( ( ! [SY6642: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV592 ) @ SV1186 ) @ ( c_SetInterval_Oord_OatMost @ SV1661 @ SY6642 @ SV592 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1661 @ SV1186 ) @ SY6642 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3788]) ).
thf(4440,plain,
! [SV1662: $i,SV1187: $i,SV593: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV593 @ SV1187 ) @ SV1662 ) )
| ! [SY6643: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6643 ) @ SV1187 ) @ ( c_SetInterval_Oord_OatMost @ SV593 @ SV1662 @ SY6643 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3789]) ).
thf(4441,plain,
! [SV1663: $i,SV1188: $i,SV594: $i] :
( ( ! [SY6644: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV594 ) @ SV1188 ) @ ( c_HOL_Ominus__class_Ominus @ SV1663 @ SY6644 @ ( tc_fun @ SV594 @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV594 ) @ SV1188 ) @ SY6644 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV594 ) @ SV1188 ) @ SV1663 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3790]) ).
thf(4442,plain,
! [SV1664: $i,SV1189: $i,SV595: $i] :
( ( ! [SY6645: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV595 ) @ SV1189 ) @ ( c_HOL_Ominus__class_Ominus @ SV1664 @ SY6645 @ ( tc_fun @ SV595 @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV595 ) @ SV1189 ) @ SY6645 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV595 ) @ SV1189 ) @ SV1664 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3791]) ).
thf(4443,plain,
! [SV1665: $i,SV1190: $i,SV596: $i] :
( ( ( hBOOL @ ( hAPP @ SV596 @ SV1190 ) )
| ! [SY6646: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1665 ) @ SV1190 ) @ SY6646 ) )
| ! [SY6647: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1665 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SY6646 @ SY6647 @ SV596 @ SV1665 ) ) @ SY6646 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3792]) ).
thf(4444,plain,
! [SV1666: $i,SV1191: $i,SV597: $i] :
( ( ( hBOOL @ ( hAPP @ SV597 @ SV1191 ) )
| ! [SY6648: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1666 ) @ SV1191 ) @ SY6648 ) )
| ! [SY6649: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1666 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SY6648 @ SV597 @ SY6649 @ SV1666 ) ) @ SY6648 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3793]) ).
thf(4445,plain,
! [SV1667: $i,SV1192: $i,SV598: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV598 ) @ SV1192 ) @ SV1667 ) )
| ! [SY6650: $i] :
( ( hBOOL @ ( hAPP @ SY6650 @ SV1192 ) )
| ~ ( hBOOL @ ( hAPP @ SY6650 @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ SV1667 @ SY6650 @ SV598 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3794]) ).
thf(4446,plain,
! [SV1668: $i,SV1193: $i,SV599: $i] :
( ( ! [SY6651: $i] :
( ( ( c_Set_Oinsert @ SV599 @ SV1193 @ SV1668 )
!= ( c_Set_Oinsert @ SV599 @ SY6651 @ SV1668 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1668 ) @ SV599 ) @ SY6651 ) )
| ( SV1193 = SY6651 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1668 ) @ SV599 ) @ SV1193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3795]) ).
thf(4447,plain,
! [SV1669: $i,SV1194: $i,SV600: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV600 ) @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ SV1194 @ SV1669 @ SV600 ) ) @ SV1194 ) )
| ! [SY6652: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV600 ) @ SY6652 ) @ SV1194 ) )
| ~ ( hBOOL @ ( hAPP @ SV1669 @ SY6652 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3796]) ).
thf(4448,plain,
! [SV1670: $i,SV1195: $i,SV601: $i] :
( ( ! [SY6653: $i,SY6654: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV601 ) @ SV1195 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1670 @ SY6653 @ SY6654 @ ( tc_fun @ SV601 @ tc_bool ) ) ) )
| ! [SY6655: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV601 ) @ SV1195 ) @ ( hAPP @ SY6653 @ SY6655 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6654 ) @ SY6655 ) @ SV1670 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3797]) ).
thf(4449,plain,
! [SV1671: $i,SV1196: $i,SV602: $i] :
( ( ! [SY6656: $i,SY6657: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV602 ) @ SV1196 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1671 @ SY6656 @ SY6657 @ ( tc_fun @ SV602 @ tc_bool ) ) ) )
| ! [SY6658: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV602 ) @ SV1196 ) @ ( hAPP @ SY6656 @ SY6658 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6657 ) @ SY6658 ) @ SV1671 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3798]) ).
thf(4450,plain,
! [SV1672: $i,SV1197: $i,SV603: $i] :
( ( ! [SY6659: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV603 ) @ SV1197 ) @ ( c_SetInterval_Oord_OgreaterThan @ SV1672 @ SY6659 @ SV603 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1672 @ SY6659 ) @ SV1197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3799]) ).
thf(4451,plain,
! [SV1673: $i,SV1198: $i,SV604: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV604 @ SV1198 ) @ SV1673 ) )
| ! [SY6660: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6660 ) @ SV1673 ) @ ( c_SetInterval_Oord_OgreaterThan @ SV604 @ SV1198 @ SY6660 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3800]) ).
thf(4452,plain,
! [SV1674: $i,SV1199: $i,SV605: $i] :
( ( ! [SY6661: $i,SY6662: $i] :
( ( hBOOL @ ( hAPP @ SV605 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SV1199 @ SV1674 @ SV605 @ SY6661 @ SY6662 ) ) )
| ! [SY6663: $i] :
( ~ ( hBOOL @ ( hAPP @ SV605 @ SY6663 ) )
| ! [SY6664: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6662 ) @ SY6663 ) @ ( hAPP @ SV1674 @ SY6664 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6661 ) @ SY6664 ) @ SV1199 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3801]) ).
thf(4453,plain,
! [SV1675: $i,SV1200: $i,SV606: $i] :
( ( ! [SY6665: $i,SY6666: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV606 ) @ SV1200 ) @ ( c_Set_Ovimage @ SV1675 @ SY6665 @ SV606 @ SY6666 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6666 ) @ ( hAPP @ SV1675 @ SV1200 ) ) @ SY6665 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3802]) ).
thf(4454,plain,
! [SV1676: $i,SV1201: $i,SV607: $i] :
( ( ! [SY6667: $i,SY6668: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV607 ) @ SV1201 ) @ ( c_Set_Ovimage @ SV1676 @ SY6667 @ SV607 @ SY6668 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6668 ) @ ( hAPP @ SV1676 @ SV1201 ) ) @ SY6667 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3803]) ).
thf(4455,plain,
! [SV1677: $i,SV1202: $i,SV608: $i] :
( ( ! [SY6669: $i,SY6670: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV608 ) @ SV1202 ) @ ( c_Set_Ovimage @ SV1677 @ SY6669 @ SV608 @ SY6670 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6670 ) @ ( hAPP @ SV1677 @ SV1202 ) ) @ SY6669 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3804]) ).
thf(4456,plain,
! [SV1678: $i,SV1203: $i,SV609: $i] :
( ( ! [SY6671: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV609 ) @ ( hAPP @ SV1203 @ SV1678 ) ) @ SY6671 ) )
| ! [SY6672: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6672 ) @ SV1678 ) @ ( c_Set_Ovimage @ SV1203 @ SY6671 @ SY6672 @ SV609 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3805]) ).
thf(4457,plain,
! [SV1679: $i,SV1204: $i,SV610: $i] :
( ( ! [SY6673: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV610 ) @ ( hAPP @ SV1204 @ SV1679 ) ) @ SY6673 ) )
| ! [SY6674: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6674 ) @ SV1679 ) @ ( c_Set_Ovimage @ SV1204 @ SY6673 @ SY6674 @ SV610 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3806]) ).
thf(4458,plain,
! [SV1680: $i,SV1205: $i,SV611: $i] :
( ( ! [SY6675: $i,SY6676: $i,SY6677: $i,SY6678: $i,SY6679: $i,SY6680: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV611 @ ( hAPP @ SV1205 @ SV1680 ) ) @ SY6675 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6676 ) @ SY6675 ) @ SV1680 ) )
| ! [SY5930: $i,SY5931: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1205 @ SY6677 @ SV611 @ SY6678 @ SY6679 @ SY6680 @ SY5930 @ SY5931 @ SY6676 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3807]) ).
thf(4459,plain,
! [SV1681: $i,SV1206: $i,SV612: $i] :
( ( ! [SY6683: $i,SY6684: $i,SY6685: $i,SY6686: $i,SY6687: $i,SY6688: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV612 @ SV1206 ) @ ( hAPP @ SV1681 @ SY6683 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6684 ) @ SV1206 ) @ SY6683 ) )
| ! [SY6689: $i,SY6690: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY6685 @ SV1681 @ SV612 @ SY6686 @ SY6687 @ SY6688 @ SY6689 @ SY6690 @ SY6684 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3808]) ).
thf(4460,plain,
! [SV1682: $i,SV1207: $i,SV613: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV613 @ SV1207 ) @ SV1682 ) )
| ! [SY6691: $i,SY6692: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6691 ) @ SV1207 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV613 @ SY6692 @ SV1682 @ SY6691 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3809]) ).
thf(4461,plain,
! [SV1683: $i,SV1208: $i,SV614: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV614 @ SV1208 ) @ SV1683 ) )
| ! [SY6693: $i,SY6694: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6693 ) @ SV1683 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV614 @ SV1208 @ SY6694 @ SY6693 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3810]) ).
thf(4462,plain,
! [SV1684: $i,SV1209: $i,SV615: $i] :
( ( ! [SY6695: $i] :
( ( hBOOL @ ( hAPP @ SV615 @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV1209 @ SV1684 @ SV615 @ SY6695 ) ) )
| ! [SY6696: $i] :
( ~ ( hBOOL @ ( hAPP @ SV615 @ SY6696 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6695 ) @ SY6696 ) @ SV1684 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3811]) ).
thf(4463,plain,
! [SV1685: $i,SV1210: $i,SV616: $i] :
( ( ! [SY6697: $i] :
( ( hBOOL @ ( hAPP @ SV616 @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV1210 @ SV1685 @ SV616 @ SY6697 ) ) )
| ! [SY5952: $i] :
( ~ ( hBOOL @ ( hAPP @ SV616 @ SY5952 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6697 ) @ SY5952 ) @ SV1210 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3812]) ).
thf(4464,plain,
! [SV1686: $i,SV1211: $i,SV617: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV617 ) @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ SV1211 @ SV1686 @ SV617 ) ) @ SV1211 ) )
| ! [SY6699: $i] :
( ~ ( hBOOL @ ( hAPP @ SV1686 @ SY6699 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV617 ) @ SY6699 ) @ SV1211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3813]) ).
thf(4465,plain,
! [SV1687: $i,SV1212: $i,SV618: $i] :
( ( ( ( c_Set_Oinsert @ SV618 @ SV1212 @ SV1687 )
= SV1212 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1687 ) @ SV618 ) @ SV1212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3814]) ).
thf(4466,plain,
! [SV1688: $i,SV1213: $i,SV619: $i] :
( ( ! [SY6700: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV619 ) @ SV1213 ) @ ( c_SetInterval_Oord_OlessThan @ SV1688 @ SY6700 @ SV619 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1688 @ SV1213 ) @ SY6700 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3815]) ).
thf(4467,plain,
! [SV1689: $i,SV1214: $i,SV620: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV620 @ SV1214 ) @ SV1689 ) )
| ! [SY6701: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6701 ) @ SV1214 ) @ ( c_SetInterval_Oord_OlessThan @ SV620 @ SV1689 @ SY6701 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3816]) ).
thf(4468,plain,
! [SV1690: $i,SV1215: $i,SV621: $i] :
( ( ! [SY6702: $i,SY6703: $i,SY6704: $i,SY6705: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV621 @ SV1215 @ SV1690 @ ( tc_fun @ SY6702 @ ( tc_fun @ SY6703 @ tc_bool ) ) ) @ SY6704 ) @ SY6705 ) )
| ! [SY6706: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV1215 @ SY6706 ) @ SY6704 ) @ SY6705 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1690 ) @ SY6706 ) @ SV621 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3817]) ).
thf(4469,plain,
! [SV1691: $i,SV1216: $i,SV622: $i] :
( ( ! [SY6707: $i,SY6708: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV622 @ SV1216 @ SV1691 @ ( tc_fun @ SY6707 @ tc_bool ) ) @ SY6708 ) )
| ! [SY6709: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1216 @ SY6709 ) @ SY6708 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1691 ) @ SY6709 ) @ SV622 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3818]) ).
thf(4470,plain,
! [SV1692: $i,SV1217: $i,SV623: $i] :
( ( ! [SY6710: $i,SY6711: $i,SY6712: $i,SY6713: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV623 @ SV1217 @ SV1692 @ ( tc_fun @ SY6710 @ ( tc_fun @ SY6711 @ tc_bool ) ) ) @ SY6712 ) @ SY6713 ) )
| ! [SY6714: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV1217 @ SY6714 ) @ SY6712 ) @ SY6713 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1692 ) @ SY6714 ) @ SV623 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3819]) ).
thf(4471,plain,
! [SV1693: $i,SV1218: $i,SV624: $i] :
( ( ! [SY6715: $i,SY6716: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV624 @ SV1218 @ SV1693 @ ( tc_fun @ SY6715 @ tc_bool ) ) @ SY6716 ) )
| ! [SY6717: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1218 @ SY6717 ) @ SY6716 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1693 ) @ SY6717 ) @ SV624 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3820]) ).
thf(4472,plain,
! [SV1694: $i,SV1219: $i,SV625: $i] :
( ( ! [SY6718: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SV1219 ) @ SV1694 ) )
| ! [SY6719: $i,SY6720: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6718 ) @ SV1219 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SY6719 @ SV625 @ SY6720 @ SV1694 @ SY6718 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3821]) ).
thf(4473,plain,
! [SV1695: $i,SV1220: $i,SV626: $i] :
( ( ! [SY6721: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV626 @ SV1220 ) @ SV1695 ) )
| ! [SY6722: $i,SY6723: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6721 ) @ SV1695 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV626 @ SY6722 @ SV1220 @ SY6723 @ SY6721 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3822]) ).
thf(4474,plain,
! [SV1696: $i,SV1221: $i,SV627: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV627 ) @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ SV1221 @ SV1696 @ SV627 ) ) @ SV1221 ) )
| ! [SY6724: $i] :
( ~ ( hBOOL @ ( hAPP @ SV1696 @ SY6724 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV627 ) @ SY6724 ) @ SV1221 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3823]) ).
thf(4475,plain,
! [SV1697: $i,SV1222: $i,SV628: $i] :
( ( ( hBOOL @ ( hAPP @ SV628 @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ SV1222 @ SV628 @ SV1697 ) ) )
| ! [SY6725: $i] :
( ~ ( hBOOL @ ( hAPP @ SV628 @ SY6725 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1697 ) @ SY6725 ) @ SV1222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3824]) ).
thf(4476,plain,
! [SV1698: $i,SV1223: $i,SV629: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV629 ) @ SV1223 ) @ SV1698 ) )
| ! [SY6726: $i,SY6727: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6726 ) @ ( hAPP @ SY6727 @ SV1223 ) ) @ ( c_Set_Oimage @ SY6727 @ SV1698 @ SV629 @ SY6726 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3825]) ).
thf(4477,plain,
! [SV1699: $i,SV1224: $i,SV630: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV630 ) @ SV1224 ) @ SV1699 ) )
| ! [SY6728: $i,SY6729: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6728 ) @ ( hAPP @ SY6729 @ SV1224 ) ) @ ( c_Set_Oimage @ SY6729 @ SV1699 @ SV630 @ SY6728 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3826]) ).
thf(4478,plain,
! [SV1700: $i,SV1225: $i,SV631: $i] :
( ( ! [SY6730: $i,SY6731: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV631 ) @ ( hAPP @ SV1225 @ SV1700 ) ) @ ( c_Set_Oimage @ SV1225 @ SY6730 @ SY6731 @ SV631 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6731 ) @ SV1700 ) @ SY6730 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3827]) ).
thf(4479,plain,
! [SV1701: $i,SV1226: $i,SV632: $i] :
( ( ! [SY6732: $i,SY6733: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV632 ) @ ( hAPP @ SV1226 @ SV1701 ) ) @ ( c_Set_Oimage @ SV1226 @ SY6732 @ SY6733 @ SV632 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6733 ) @ SV1701 ) @ SY6732 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3828]) ).
thf(4480,plain,
! [SV1702: $i,SV1227: $i,SV633: $i] :
( ( ! [SY6734: $i] :
( ( ( hAPP @ SV633 @ SV1227 )
= ( c_Option_Ooption_OSome @ ( c_Map_Osko__Map__XdomD__1__1 @ SV1227 @ SV633 @ SV1702 @ SY6734 ) @ SY6734 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1702 ) @ SV1227 ) @ ( c_Map_Odom @ SV633 @ SV1702 @ SY6734 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3829]) ).
thf(4481,plain,
! [SV1703: $i,SV1228: $i,SV634: $i] :
( ( ! [SY6735: $i] :
( ( c_Map_Omap__le @ SV634 @ SV1228 @ SV1703 @ SY6735 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1703 ) @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ SV634 @ SV1228 @ SV1703 @ SY6735 ) ) @ ( c_Map_Odom @ SV634 @ SV1703 @ SY6735 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3830]) ).
thf(4482,plain,
! [SV1704: $i,SV1229: $i,SV636: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV636 ) ) @ SV1229 ) @ SV1704 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SV636 ) @ tc_Com_Ocom ) ) @ SV1229 ) @ SV1704 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3832]) ).
thf(4483,plain,
! [SV1705: $i,SV1230: $i,SV637: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SV637 ) @ tc_Com_Ocom ) ) @ SV1230 ) @ SV1705 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV637 ) ) @ SV1230 ) @ SV1705 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3833]) ).
thf(4484,plain,
! [SV639: $i,SV1706: $i] :
( ( ( ! [SY6736: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV1706 @ SV639 @ SY6736 ) ) )
= $true )
| ( ( c_Com_OWT @ SV639 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3835]) ).
thf(4485,plain,
! [SV640: $i,SV1707: $i] :
( ( ( ! [SY6737: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV1707 @ SY6737 @ SV640 ) ) )
= $true )
| ( ( c_Com_OWT @ SV640 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3836]) ).
thf(4486,plain,
! [SV1232: $i,SV641: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV641 @ SV1232 ) )
= $true )
| ( ( ~ ( c_Com_OWT @ SV1232 )
| ~ ( c_Com_OWT @ SV641 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3837]) ).
thf(4487,plain,
! [SV1708: $i,SV642: $i] :
( ( ( ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV642 @ SV1708 ) ) )
= $true )
| ( ( c_Com_OWT @ SV642 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3838]) ).
thf(4488,plain,
! [SV643: $i,SV1709: $i] :
( ( ( ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV1709 @ SV643 ) ) )
= $true )
| ( ( c_Com_OWT @ SV643 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3839]) ).
thf(4489,plain,
! [SV1710: $i,SV1233: $i,SV644: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV644 @ SV1233 @ SV1710 ) )
| ~ ( c_Com_OWT @ SV1710 )
| ~ ( c_Com_OWT @ SV1233 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3840]) ).
thf(4490,plain,
! [SV1235: $i,SV646: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ SV646 @ SV1235 ) )
= $true )
| ( ( ~ ( c_Com_OWT @ SV1235 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3842]) ).
thf(4491,plain,
! [SV647: $i,SV1711: $i] :
( ( ( ~ ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ SV1711 @ SV647 ) ) )
= $true )
| ( ( c_Com_OWT @ SV647 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3843]) ).
thf(4492,plain,
! [SV1712: $i,SV1236: $i,SV648: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ SV648 @ SV1236 @ SV1712 ) )
| ~ ( c_Com_OWT @ SV1712 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3844]) ).
thf(4493,plain,
! [SV649: $i,SV1713: $i] :
( ( ( ! [SY6738: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ SV1713 @ SY6738 @ SV649 ) ) )
= $true )
| ( ( c_Com_OWT @ SV649 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3845]) ).
thf(4494,plain,
! [SV1237: $i,SV650: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV650 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ SV1237 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
= $true )
| ( ( ~ ( c_Com_OWT @ SV1237 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ tc_Com_Opname ) @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ SV650 ) ) @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) ) )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3846]) ).
thf(4495,plain,
! [SV1238: $i] :
( ( ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ SV1238 )
= SV1238 )
= $false )
| ( ( ~ c_Hoare__Mirabelle_Ostate__not__singleton ) = $true ) ),
inference(extcnf_not_pos,[status(thm)],[3847]) ).
thf(4496,plain,
! [SV1714: $i,SV1239: $i,SV651: $i] :
( ( ! [SY6739: $i,SY6740: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV651 @ SV1239 @ SV1714 @ SY6739 ) @ SY6740 )
= ( hAPP @ SV651 @ SY6740 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1714 ) @ SY6740 ) @ ( c_Map_Odom @ SV1239 @ SV1714 @ SY6739 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3848]) ).
thf(4497,plain,
! [SV1715: $i,SV1240: $i,SV652: $i] :
( ( ! [SY6741: $i,SY6742: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV652 @ SV1240 @ SV1715 @ SY6741 ) @ SY6742 )
= ( hAPP @ SV1240 @ SY6742 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1715 ) @ SY6742 ) @ ( c_Map_Odom @ SV652 @ SV1715 @ SY6741 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3849]) ).
thf(4498,plain,
! [SV653: $i,SV1241: $i,SV1716: $i] :
( ( ! [SY6743: $i] :
( ( ( hAPP @ SV1716 @ SV1241 )
= ( c_Option_Ooption_ONone @ SY6743 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV653 ) @ SV1241 ) @ ( c_Map_Odom @ SV1716 @ SV653 @ SY6743 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3850]) ).
thf(4499,plain,
! [SV1717: $i,SV1242: $i,SV654: $i] :
( ( ( ( hAPP @ SV654 @ SV1242 )
!= ( c_Option_Ooption_ONone @ SV1717 ) )
| ! [SY6744: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6744 ) @ SV1242 ) @ ( c_Map_Odom @ SV654 @ SY6744 @ SV1717 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3851]) ).
thf(4500,plain,
! [SV1718: $i,SV1243: $i,SV655: $i] :
( ( ! [SY6745: $i] :
( ( ( hAPP @ SV655 @ SV1243 )
!= ( c_Option_Ooption_OSome @ SV1718 @ SY6745 ) )
| ! [SY6024: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6024 ) @ SV1243 ) @ ( c_Map_Odom @ SV655 @ SY6024 @ SY6745 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3852]) ).
thf(4501,plain,
! [SV1719: $i,SV1244: $i,SV656: $i] :
( ( ( ( hAPP @ SV656 @ SV1244 )
= ( hAPP @ SV1719 @ SV1244 ) )
| ! [SY6747: $i,SY6748: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6747 ) @ SV1244 ) @ ( c_Map_Odom @ SV656 @ SY6747 @ SY6748 ) ) )
| ~ ( c_Map_Omap__le @ SV656 @ SV1719 @ SY6747 @ SY6748 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3853]) ).
thf(4502,plain,
! [SV1720: $i,SV1245: $i,SV657: $i] :
( ( ! [SY6749: $i,SY6750: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV657 @ SV1245 @ SV1720 @ SY6749 ) @ SY6750 )
= ( hAPP @ SV1245 @ SY6750 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1720 ) @ SY6750 ) @ ( c_Map_Odom @ SV1245 @ SV1720 @ SY6749 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3854]) ).
thf(4503,plain,
! [SV1246: $i,SV658: $i] :
( ( ( ( hAPP @ c_Com_Obody @ SV658 )
!= ( c_Option_Ooption_OSome @ SV1246 @ tc_Com_Ocom ) )
= $true )
| ( ( ~ c_Com_OWT__bodies
| ( c_Com_OWT @ SV1246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3855]) ).
thf(4504,plain,
! [SV1721: $i,SV1247: $i] :
( ( ( SV1247 = SV1721 )
= $true )
| ( c_Hoare__Mirabelle_Ostate__not__singleton = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3856]) ).
thf(4505,plain,
! [SV1722: $i,SV1248: $i,SV659: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV659 ) @ SV1248 ) @ SV1722 ) )
| ~ ( hBOOL @ ( hAPP @ SV1722 @ SV1248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3857]) ).
thf(4506,plain,
! [SV1249: $i,SV660: $i] :
( ( ( hBOOL @ ( hAPP @ SV660 @ SV1249 ) )
= $true )
| ( ( ! [SY6033: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6033 ) @ SV1249 ) @ SV660 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3858]) ).
thf(4507,plain,
! [SV1250: $i,SV661: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV661 @ SV1250 ) )
= $true )
| ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV1250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3859]) ).
thf(4508,plain,
! [SV1251: $i,SV662: $i] :
( ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV662 @ SV1251 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV1251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3860]) ).
thf(4509,plain,
! [SV1252: $i,SV663: $i] :
( ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV663 @ SV1252 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV1252 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3861]) ).
thf(4510,plain,
! [SV1253: $i,SV664: $i] :
( ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV664 @ SV1253 ) )
= $true )
| ( ( ~ ( class_Lattices_Odistrib__lattice @ SV1253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3862]) ).
thf(4511,plain,
! [SV1254: $i,SV665: $i] :
( ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV665 @ SV1254 ) )
= $true )
| ( ( ~ ( class_Lattices_Obounded__lattice @ SV1254 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3863]) ).
thf(4512,plain,
! [SV1255: $i,SV666: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ SV666 @ SV1255 ) )
= $true )
| ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV1255 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SV666 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3864]) ).
thf(4513,plain,
! [SV1256: $i,SV667: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV667 @ SV1256 ) )
= $true )
| ( ( ~ ( class_Orderings_Opreorder @ SV1256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3865]) ).
thf(4514,plain,
! [SV1257: $i,SV668: $i] :
( ( ( class_Lattices_Olattice @ ( tc_fun @ SV668 @ SV1257 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV1257 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3866]) ).
thf(4515,plain,
! [SV1258: $i,SV669: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV669 @ SV1258 ) )
= $true )
| ( ( ~ ( class_Orderings_Oorder @ SV1258 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3867]) ).
thf(4516,plain,
! [SV1259: $i,SV670: $i] :
( ( ( class_Orderings_Obot @ ( tc_fun @ SV670 @ SV1259 ) )
= $true )
| ( ( ~ ( class_Orderings_Obot @ SV1259 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3868]) ).
thf(4517,plain,
! [SV1260: $i,SV671: $i] :
( ( ( class_HOL_Oord @ ( tc_fun @ SV671 @ SV1260 ) )
= $true )
| ( ( ~ ( class_HOL_Oord @ SV1260 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3869]) ).
thf(4518,plain,
! [SV672: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ SV672 )
= $false )
| ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_Option_Ooption @ SV672 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3870]) ).
thf(4519,plain,
! [SV1262: $i,SV674: $i] :
( ( ( SV674 = SV1262 )
= $true )
| ( ( ! [SY6034: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY6034 ) @ SV674 ) @ SV1262 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3872]) ).
thf(4520,plain,
! [SV1: $i,SV1723: $i] :
( ( ( ! [SY6751: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1723 @ SY6751 @ SV1 ) @ SV1723 @ SV1 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3873]) ).
thf(4521,plain,
! [SV2: $i,SV1724: $i] :
( ( ( ! [SY6752: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1724 @ SY6752 @ SV2 ) @ SY6752 @ SV2 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3874]) ).
thf(4522,plain,
! [SV675: $i,SV3: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV3 )
= $false )
| ( ( ! [SY4731: $i,SY4732: $i] :
( ( c_lessequals @ SV675 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4731 @ SY4732 @ SV3 ) @ SV3 )
| ~ ( c_lessequals @ SV675 @ SY4732 @ SV3 )
| ~ ( c_lessequals @ SV675 @ SY4731 @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3875]) ).
thf(4523,plain,
! [SV676: $i,SV4: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV4 )
= $false )
| ( ( ! [SY4733: $i,SY4734: $i] :
( ( c_lessequals @ SV676 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4733 @ SY4734 @ SV4 ) @ SV4 )
| ~ ( c_lessequals @ SV676 @ SY4734 @ SV4 )
| ~ ( c_lessequals @ SV676 @ SY4733 @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3876]) ).
thf(4524,plain,
! [SV677: $i,SV5: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV5 )
= $false )
| ( ( ! [SY4735: $i,SY4736: $i] :
( ( c_lessequals @ SV677 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4735 @ SY4736 @ SV5 ) @ SV5 )
| ~ ( c_lessequals @ SV677 @ SY4736 @ SV5 )
| ~ ( c_lessequals @ SV677 @ SY4735 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3877]) ).
thf(4525,plain,
! [SV6: $i,SV1725: $i] :
( ( ( ! [SY6753: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1725 @ SY6753 @ SV6 ) @ SY6753 @ SV6 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3878]) ).
thf(4526,plain,
! [SV7: $i,SV1726: $i] :
( ( ( ! [SY6754: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1726 @ SY6754 @ SV7 ) @ SV1726 @ SV7 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3879]) ).
thf(4527,plain,
! [SV1727: $i,SV1263: $i,SV678: $i,SV8: $i] :
( ( ! [SY6755: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV8 @ SV678 @ ( tc_fun @ SV1263 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1727 @ SY6755 @ ( tc_fun @ SV1263 @ tc_bool ) ) @ ( tc_fun @ SV1263 @ tc_bool ) )
| ~ ( c_lessequals @ SV678 @ SY6755 @ ( tc_fun @ SV1263 @ tc_bool ) )
| ~ ( c_lessequals @ SV8 @ SV1727 @ ( tc_fun @ SV1263 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3880]) ).
thf(4528,plain,
! [SV679: $i,SV10: $i] :
( ( ( c_lessequals @ SV10 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV679 @ tc_bool ) ) @ ( tc_fun @ SV679 @ tc_bool ) )
= $false )
| ( ( SV10
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV679 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3881]) ).
thf(4529,plain,
! [SV1728: $i,SV1264: $i,SV680: $i,SV11: $i] :
( ( ! [SY6756: $i,SY6757: $i,SY6758: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV11 @ SV680 @ SV1264 @ SV1728 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SY6756 @ SY6757 @ SY6758 @ SV1728 ) )
| ( SV1264 = SY6758 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3882]) ).
thf(4530,plain,
! [SV1729: $i,SV1265: $i,SV681: $i,SV12: $i] :
( ( ! [SY6759: $i,SY6760: $i] :
( ! [SY6761: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV12 @ SV681 @ SV1265 @ SV1729 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SY6759 @ SY6760 @ SY6761 @ SV1729 ) )
| ( SV681 = SY6760 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3883]) ).
thf(4531,plain,
! [SV1730: $i,SV1266: $i,SV682: $i,SV13: $i] :
( ( ! [SY6762: $i] :
( ! [SY6763: $i,SY6764: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV13 @ SV682 @ SV1266 @ SV1730 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SY6762 @ SY6763 @ SY6764 @ SV1730 ) )
| ( SV13 = SY6762 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3884]) ).
thf(4532,plain,
! [SV1731: $i,SV1267: $i,SV683: $i,SV14: $i] :
( ( ( c_Fun_Ofun__upd @ SV14 @ SV683 @ ( hAPP @ SV14 @ SV683 ) @ SV1267 @ SV1731 )
= SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3885]) ).
thf(4533,plain,
! [SV1732: $i,SV1268: $i,SV684: $i,SV15: $i] :
( ( ! [SY6765: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV15 @ SV684 @ SV1268 @ SV1732 @ SY6765 ) @ SV684 )
= SV1268 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3886]) ).
thf(4534,plain,
! [SV1733: $i,SV1269: $i,SV685: $i,SV16: $i] :
( ( ( c_Fun_Ofun__upd @ SV16 @ SV685 @ ( hAPP @ SV16 @ SV685 ) @ SV1269 @ SV1733 )
= SV16 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3887]) ).
thf(4535,plain,
! [SV1734: $i,SV1270: $i,SV686: $i,SV17: $i] :
( ( ! [SY6766: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV17 @ SV686 @ SV1270 @ SV1734 @ SY6766 ) @ SV686 )
= SV1270 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3888]) ).
thf(4536,plain,
! [SV1735: $i,SV1271: $i,SV687: $i,SV18: $i] :
( ( ( c_Fun_Ofun__upd @ SV18 @ SV687 @ ( hAPP @ SV18 @ SV687 ) @ SV1271 @ SV1735 )
= SV18 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3889]) ).
thf(4537,plain,
! [SV1272: $i,SV688: $i,SV19: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV19 @ SV688 @ ( tc_fun @ SV1272 @ tc_bool ) )
!= SV688 )
= $true )
| ( ( c_lessequals @ SV19 @ SV688 @ ( tc_fun @ SV1272 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3890]) ).
thf(4538,plain,
! [SV1273: $i,SV689: $i,SV20: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV20 @ SV689 @ ( tc_fun @ SV1273 @ tc_bool ) )
= SV20 )
= $true )
| ( ( ~ ( c_lessequals @ SV689 @ SV20 @ ( tc_fun @ SV1273 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3891]) ).
thf(4539,plain,
! [SV1274: $i,SV690: $i,SV21: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV21 @ SV690 @ ( tc_fun @ SV1274 @ tc_bool ) )
= SV690 )
= $true )
| ( ( ~ ( c_lessequals @ SV21 @ SV690 @ ( tc_fun @ SV1274 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3892]) ).
thf(4540,plain,
! [SV22: $i,SV1736: $i] :
( ( ( ! [SY6767: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1736 @ SY6767 @ SV22 )
= SY6767 )
| ~ ( c_lessequals @ SV1736 @ SY6767 @ SV22 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3893]) ).
thf(4541,plain,
! [SV23: $i,SV1737: $i] :
( ( ( ! [SY6768: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1737 @ SY6768 @ SV23 )
!= SY6768 )
| ( c_lessequals @ SV1737 @ SY6768 @ SV23 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3894]) ).
thf(4542,plain,
! [SV24: $i,SV1738: $i] :
( ( ( ! [SY6769: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1738 @ SY6769 @ SV24 )
= SV1738 )
| ~ ( c_lessequals @ SY6769 @ SV1738 @ SV24 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3895]) ).
thf(4543,plain,
! [SV25: $i,SV1739: $i] :
( ( ( ! [SY6770: $i] :
( ( c_lessequals @ SV1739 @ SY6770 @ SV25 )
| ~ ( c_HOL_Oord__class_Oless @ SV1739 @ SY6770 @ SV25 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3896]) ).
thf(4544,plain,
! [SV26: $i,SV1740: $i] :
( ( ( ! [SY6771: $i] :
( ( c_lessequals @ SV1740 @ SY6771 @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ SV1740 @ SY6771 @ SV26 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3897]) ).
thf(4545,plain,
! [SV691: $i,SV27: $i] :
( ( ( class_HOL_Oord @ SV27 )
= $false )
| ( ( ! [SY4770: $i,SY4771: $i] :
( ( c_lessequals @ SV691 @ SY4770 @ ( tc_fun @ SY4771 @ SV27 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV691 @ SY4770 @ ( tc_fun @ SY4771 @ SV27 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3898]) ).
thf(4546,plain,
! [SV1275: $i,SV692: $i,SV28: $i] :
( ( ( c_lessequals @ SV28 @ SV692 @ ( tc_fun @ SV1275 @ tc_bool ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV28 @ SV692 @ ( tc_fun @ SV1275 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3899]) ).
thf(4547,plain,
! [SV29: $i,SV1741: $i] :
( ( ( ! [SY6772: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1741 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1741 @ SY6772 @ SV29 ) @ SV29 )
= SV1741 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3900]) ).
thf(4548,plain,
! [SV30: $i,SV1742: $i] :
( ( ( ! [SY6773: $i] :
( ( SV1742 = SY6773 )
| ~ ( c_lessequals @ SV1742 @ SY6773 @ SV30 )
| ~ ( c_lessequals @ SY6773 @ SV1742 @ SV30 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3901]) ).
thf(4549,plain,
! [SV31: $i,SV1743: $i] :
( ( ( ! [SY6774: $i] :
( ( SV1743 = SY6774 )
| ~ ( c_lessequals @ SY6774 @ SV1743 @ SV31 )
| ~ ( c_lessequals @ SV1743 @ SY6774 @ SV31 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3902]) ).
thf(4550,plain,
! [SV32: $i,SV1744: $i] :
( ( ( ! [SY6775: $i] :
( ( SV1744 = SY6775 )
| ~ ( c_lessequals @ SY6775 @ SV1744 @ SV32 )
| ~ ( c_lessequals @ SV1744 @ SY6775 @ SV32 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3903]) ).
thf(4551,plain,
! [SV1745: $i,SV33: $i,SV693: $i] :
( ( ( ~ ( c_lessequals @ SV693 @ SV33 @ ( tc_fun @ SV1745 @ tc_bool ) )
| ~ ( c_lessequals @ SV33 @ SV693 @ ( tc_fun @ SV1745 @ tc_bool ) ) )
= $true )
| ( ( SV33 = SV693 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3904]) ).
thf(4552,plain,
! [SV1746: $i,SV34: $i,SV694: $i] :
( ( ( ~ ( c_lessequals @ SV694 @ SV34 @ ( tc_fun @ SV1746 @ tc_bool ) )
| ~ ( c_lessequals @ SV34 @ SV694 @ ( tc_fun @ SV1746 @ tc_bool ) ) )
= $true )
| ( ( SV34 = SV694 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3905]) ).
thf(4553,plain,
! [SV35: $i,SV1747: $i] :
( ( ( ! [SY6776: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1747 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1747 @ SY6776 @ SV35 ) @ SV35 )
= SV1747 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3906]) ).
thf(4554,plain,
! [SV695: $i,SV36: $i] :
( ( ( class_HOL_Oord @ SV36 )
= $false )
| ( ( ! [SY4775: $i,SY4776: $i] :
( ( c_HOL_Oord__class_Oless @ SV695 @ SY4775 @ ( tc_fun @ SY4776 @ SV36 ) )
| ( c_lessequals @ SY4775 @ SV695 @ ( tc_fun @ SY4776 @ SV36 ) )
| ~ ( c_lessequals @ SV695 @ SY4775 @ ( tc_fun @ SY4776 @ SV36 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3907]) ).
thf(4555,plain,
! [SV37: $i,SV1748: $i] :
( ( ( ! [SY6777: $i] :
( ( c_HOL_Oord__class_Oless @ SV1748 @ SY6777 @ SV37 )
| ( c_lessequals @ SY6777 @ SV1748 @ SV37 )
| ~ ( c_lessequals @ SV1748 @ SY6777 @ SV37 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3908]) ).
thf(4556,plain,
! [SV696: $i,SV38: $i] :
( ( ( class_Lattices_Olattice @ SV38 )
= $false )
| ( ( ! [SY4777: $i,SY4778: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV696 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4777 @ SY4778 @ SV38 ) @ SV38 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV696 @ SY4777 @ SV38 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV696 @ SY4778 @ SV38 ) @ SV38 ) @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3909]) ).
thf(4557,plain,
! [SV1749: $i,SV1276: $i,SV697: $i,SV39: $i] :
( ( ! [SY6778: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV39 @ SV697 @ ( tc_fun @ SV1276 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1749 @ SY6778 @ ( tc_fun @ SV1276 @ tc_bool ) ) @ ( tc_fun @ SV1276 @ tc_bool ) )
| ~ ( c_lessequals @ SY6778 @ SV697 @ ( tc_fun @ SV1276 @ tc_bool ) )
| ~ ( c_lessequals @ SV39 @ SV1749 @ ( tc_fun @ SV1276 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3910]) ).
thf(4558,plain,
! [SV1750: $i,SV1277: $i,SV698: $i,SV40: $i] :
( ( ! [SY6779: $i,SY6780: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ SV40 @ SV698 @ SV1277 @ SV1750 @ SY6779 ) @ SV698 @ SY6780 @ SV1750 @ SY6779 )
= ( c_Fun_Ofun__upd @ SV40 @ SV698 @ SY6780 @ SV1750 @ SY6779 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3911]) ).
thf(4559,plain,
! [SV1751: $i,SV43: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ SV43 ) @ SV1751 @ SV43 )
= SV1751 )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3912]) ).
thf(4560,plain,
! [SV44: $i,SV1752: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1752 @ ( c_Orderings_Obot__class_Obot @ SV44 ) @ SV44 )
= SV1752 )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3913]) ).
thf(4561,plain,
! [SV701: $i,SV45: $i,SV1753: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1753 @ SV45 @ ( tc_fun @ SV701 @ tc_bool ) ) @ SV701 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV45 @ SV701 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3914]) ).
thf(4562,plain,
! [SV702: $i,SV1754: $i,SV46: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV46 @ SV1754 @ ( tc_fun @ SV702 @ tc_bool ) ) @ SV702 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV46 @ SV702 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3915]) ).
thf(4563,plain,
! [SV1755: $i,SV1278: $i,SV703: $i,SV47: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV47 @ SV703 @ ( tc_fun @ SV1278 @ tc_bool ) ) @ SV1755 ) )
| ~ ( hBOOL @ ( hAPP @ SV47 @ SV1755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3916]) ).
thf(4564,plain,
! [SV1756: $i,SV1279: $i,SV704: $i,SV48: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV48 @ SV704 @ ( tc_fun @ SV1279 @ tc_bool ) ) @ SV1756 ) )
| ~ ( hBOOL @ ( hAPP @ SV704 @ SV1756 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3917]) ).
thf(4565,plain,
! [SV49: $i,SV705: $i,SV1757: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV1757 @ SV705 ) )
| ! [SY6781: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1757 @ SV49 @ ( tc_fun @ SY6781 @ tc_bool ) ) @ SV705 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV49 @ SV705 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3918]) ).
thf(4566,plain,
! [SV1758: $i,SV1280: $i,SV706: $i,SV50: $i] :
( ( ! [SY6782: $i,SY6783: $i] :
( ! [SY6784: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ SV50 @ SV706 @ SV1280 @ SV1758 @ SY6782 ) @ SY6783 @ SY6784 @ SV1758 @ SY6782 )
= ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ SV50 @ SY6783 @ SY6784 @ SV1758 @ SY6782 ) @ SV706 @ SV1280 @ SV1758 @ SY6782 ) )
| ( SV706 = SY6783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3919]) ).
thf(4567,plain,
! [SV1759: $i,SV1281: $i,SV707: $i,SV51: $i] :
( ( ! [SY6785: $i,SY6786: $i] :
( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ SV51 @ SV707 @ SV1281 @ SV1759 @ ( tc_Option_Ooption @ SY6785 ) ) @ ( c_Fun_Ofun__upd @ SY6786 @ SV707 @ SV1281 @ SV1759 @ ( tc_Option_Ooption @ SY6785 ) ) @ SV1759 @ SY6785 )
| ~ ( c_Map_Omap__le @ SV51 @ SY6786 @ SV1759 @ SY6785 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3920]) ).
thf(4568,plain,
! [SV1760: $i,SV1282: $i,SV708: $i,SV52: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV52 @ SV708 @ ( tc_fun @ SV1282 @ tc_bool ) ) @ SV1760 @ ( tc_fun @ SV1282 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV52 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV708 @ SV1760 @ ( tc_fun @ SV1282 @ tc_bool ) ) @ ( tc_fun @ SV1282 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV1760 @ SV52 @ ( tc_fun @ SV1282 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3921]) ).
thf(4569,plain,
! [SV1761: $i,SV1283: $i,SV709: $i,SV53: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV53 @ SV709 @ ( tc_fun @ SV1283 @ tc_bool ) ) @ SV1761 @ ( tc_fun @ SV1283 @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ SV53 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV709 @ SV1761 @ ( tc_fun @ SV1283 @ tc_bool ) ) @ ( tc_fun @ SV1283 @ tc_bool ) ) )
| ( c_lessequals @ SV1761 @ SV53 @ ( tc_fun @ SV1283 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3922]) ).
thf(4570,plain,
! [SV1284: $i,SV710: $i,SV54: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV54 @ SV710 @ ( tc_fun @ SV1284 @ tc_bool ) ) @ SV1284 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV710 @ SV1284 )
| ~ ( c_Finite__Set_Ofinite @ SV54 @ SV1284 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3923]) ).
thf(4571,plain,
! [SV1285: $i,SV711: $i,SV55: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV55 @ SV711 @ ( tc_fun @ SV1285 @ tc_bool ) ) @ SV1285 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV711 @ SV1285 )
| ~ ( c_Finite__Set_Ofinite @ SV55 @ SV1285 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3924]) ).
thf(4572,plain,
! [SV1286: $i,SV712: $i,SV56: $i] :
( ( ( SV56 = SV712 )
= $true )
| ( ( ! [SY6072: $i,SY6073: $i] :
~ ( c_Finite__Set_Ofold__graph @ SV1286 @ SV712 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6072 @ tc_bool ) ) @ SV56 @ SY6072 @ SY6073 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3925]) ).
thf(4573,plain,
! [SV1762: $i,SV1288: $i,SV714: $i,SV58: $i] :
( ( ! [SY6787: $i] :
( ( ( hAPP @ SV58 @ SV714 )
!= ( c_Option_Ooption_OSome @ SV1288 @ SV1762 ) )
| ( SV714 = SY6787 )
| ! [SY6788: $i,SY6789: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV58 @ SY6787 @ ( c_Option_Ooption_OSome @ SY6788 @ SV1762 ) @ SY6789 @ ( tc_Option_Ooption @ SV1762 ) ) @ SV714 )
= ( c_Option_Ooption_OSome @ SV1288 @ SV1762 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3927]) ).
thf(4574,plain,
! [SV1763: $i,SV1289: $i,SV715: $i,SV59: $i] :
( ( ! [SY6790: $i,SY6791: $i,SY6792: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV59 @ SV715 @ ( c_Option_Ooption_OSome @ SV1289 @ SV1763 ) @ SY6790 @ ( tc_Option_Ooption @ SV1763 ) ) @ SY6791 )
!= ( c_Option_Ooption_OSome @ SY6792 @ SV1763 ) )
| ( ( hAPP @ SV59 @ SY6791 )
= ( c_Option_Ooption_OSome @ SY6792 @ SV1763 ) )
| ( SV1289 = SY6792 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3928]) ).
thf(4575,plain,
! [SV1764: $i,SV1290: $i,SV716: $i,SV60: $i] :
( ( ! [SY6793: $i,SY6794: $i,SY6795: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV60 @ SV716 @ ( c_Option_Ooption_OSome @ SV1290 @ SV1764 ) @ SY6793 @ ( tc_Option_Ooption @ SV1764 ) ) @ SY6794 )
!= ( c_Option_Ooption_OSome @ SY6795 @ SV1764 ) )
| ( ( hAPP @ SV60 @ SY6794 )
= ( c_Option_Ooption_OSome @ SY6795 @ SV1764 ) )
| ( SY6794 = SV716 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3929]) ).
thf(4576,plain,
! [SV1765: $i,SV61: $i] :
( ( ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV61 ) @ SV1765 @ SV61 )
= $true )
| ( ( class_Orderings_Obot @ SV61 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3930]) ).
thf(4577,plain,
! [SV1766: $i,SV1291: $i,SV718: $i,SV63: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV63 @ ( c_Set_Oinsert @ SV718 @ SV1291 @ SV1766 ) @ ( tc_fun @ SV1766 @ tc_bool ) )
= ( c_Set_Oinsert @ SV718 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV63 @ SV1291 @ ( tc_fun @ SV1766 @ tc_bool ) ) @ SV1766 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3931]) ).
thf(4578,plain,
! [SV1767: $i,SV1292: $i,SV719: $i,SV64: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV64 @ SV719 @ SV1292 ) @ SV1767 @ ( tc_fun @ SV1292 @ tc_bool ) )
= ( c_Set_Oinsert @ SV64 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV719 @ SV1767 @ ( tc_fun @ SV1292 @ tc_bool ) ) @ SV1292 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3932]) ).
thf(4579,plain,
! [SV1768: $i,SV1293: $i,SV720: $i,SV65: $i] :
( ( ( c_lessequals @ SV65 @ ( c_Set_Oinsert @ SV720 @ SV1293 @ SV1768 ) @ ( tc_fun @ SV1768 @ tc_bool ) )
| ~ ( c_lessequals @ SV65 @ SV1293 @ ( tc_fun @ SV1768 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3933]) ).
thf(4580,plain,
! [SV1294: $i,SV721: $i,SV66: $i] :
( ( ( c_lessequals @ SV66 @ SV721 @ ( tc_fun @ SV1294 @ tc_bool ) )
= $true )
| ( ( ! [SY6089: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SY6089 @ SV66 @ SV1294 ) @ SV721 @ ( tc_fun @ SV1294 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3934]) ).
thf(4581,plain,
! [SV1769: $i,SV1295: $i,SV722: $i,SV67: $i] :
( ( ( c_Finite__Set_Ofinite @ SV67 @ SV722 )
| ! [SY6796: $i,SY6797: $i] :
~ ( c_Finite__Set_Ofold__graph @ SV1295 @ SV1769 @ SV67 @ SY6796 @ SV722 @ SY6797 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3935]) ).
thf(4582,plain,
! [SV1770: $i,SV1296: $i,SV723: $i,SV68: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV68 @ SV723 @ ( tc_fun @ SV1296 @ tc_bool ) ) @ SV1770 @ ( tc_fun @ SV1296 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV68 @ SV1770 @ ( tc_fun @ SV1296 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV723 @ SV1770 @ ( tc_fun @ SV1296 @ tc_bool ) ) @ ( tc_fun @ SV1296 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3936]) ).
thf(4583,plain,
! [SV1771: $i,SV1297: $i,SV724: $i,SV69: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV69 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV724 @ SV1297 @ ( tc_fun @ SV1771 @ tc_bool ) ) @ ( tc_fun @ SV1771 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV69 @ SV724 @ ( tc_fun @ SV1771 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV69 @ SV1297 @ ( tc_fun @ SV1771 @ tc_bool ) ) @ ( tc_fun @ SV1771 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3937]) ).
thf(4584,plain,
! [SV725: $i,SV70: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV70 )
= $false )
| ( ( ! [SY4844: $i,SY4845: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV725 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4844 @ SY4845 @ SV70 ) @ SV70 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV725 @ SY4844 @ SV70 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV725 @ SY4845 @ SV70 ) @ SV70 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3938]) ).
thf(4585,plain,
! [SV726: $i,SV71: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV71 )
= $false )
| ( ( ! [SY4846: $i,SY4847: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV726 @ SY4846 @ SV71 ) @ SY4847 @ SV71 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV726 @ SY4847 @ SV71 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4846 @ SY4847 @ SV71 ) @ SV71 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3939]) ).
thf(4586,plain,
! [SV727: $i,SV72: $i,SV1772: $i,SV1298: $i] :
( ( ! [SY6798: $i,SY6799: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV1298 @ SV1772 @ ( c_Option_Ooption_OSome @ SV72 @ SY6798 ) @ SY6799 @ ( tc_Option_Ooption @ SY6798 ) ) @ SV1772 )
!= ( c_Option_Ooption_OSome @ SV727 @ SY6798 ) )
| ( SV72 = SV727 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3940]) ).
thf(4587,plain,
! [SV1773: $i,SV1301: $i,SV730: $i,SV75: $i] :
( ( ( c_lessequals @ SV75 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV730 @ SV1301 @ ( tc_fun @ SV1773 @ tc_bool ) ) @ ( tc_fun @ SV1773 @ tc_bool ) )
| ~ ( c_lessequals @ SV75 @ SV1301 @ ( tc_fun @ SV1773 @ tc_bool ) )
| ~ ( c_lessequals @ SV75 @ SV730 @ ( tc_fun @ SV1773 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3943]) ).
thf(4588,plain,
! [SV1774: $i,SV1302: $i,SV731: $i,SV76: $i] :
( ( ( c_lessequals @ SV76 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV731 @ SV1302 @ ( tc_fun @ SV1774 @ tc_bool ) ) @ ( tc_fun @ SV1774 @ tc_bool ) )
| ~ ( c_lessequals @ SV76 @ SV1302 @ ( tc_fun @ SV1774 @ tc_bool ) )
| ~ ( c_lessequals @ SV76 @ SV731 @ ( tc_fun @ SV1774 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3944]) ).
thf(4589,plain,
! [SV732: $i,SV77: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV77 )
= $false )
| ( ( ! [SY4858: $i,SY4859: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV732 @ SY4858 @ SV77 ) @ SY4859 @ SV77 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV732 @ SY4859 @ SV77 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4858 @ SY4859 @ SV77 ) @ SV77 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3945]) ).
thf(4590,plain,
! [SV733: $i,SV78: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV78 )
= $false )
| ( ( ! [SY4860: $i,SY4861: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV733 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY4860 @ SY4861 @ SV78 ) @ SV78 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV733 @ SY4860 @ SV78 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV733 @ SY4861 @ SV78 ) @ SV78 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3946]) ).
thf(4591,plain,
! [SV1775: $i,SV1303: $i,SV734: $i,SV79: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV79 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV734 @ SV1303 @ ( tc_fun @ SV1775 @ tc_bool ) ) @ ( tc_fun @ SV1775 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV79 @ SV734 @ ( tc_fun @ SV1775 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV79 @ SV1303 @ ( tc_fun @ SV1775 @ tc_bool ) ) @ ( tc_fun @ SV1775 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3947]) ).
thf(4592,plain,
! [SV1776: $i,SV1304: $i,SV735: $i,SV80: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV80 @ SV735 @ ( tc_fun @ SV1304 @ tc_bool ) ) @ SV1776 @ ( tc_fun @ SV1304 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV80 @ SV1776 @ ( tc_fun @ SV1304 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV735 @ SV1776 @ ( tc_fun @ SV1304 @ tc_bool ) ) @ ( tc_fun @ SV1304 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3948]) ).
thf(4593,plain,
! [SV1777: $i,SV1305: $i,SV736: $i,SV81: $i] :
( ( ! [SY6800: $i,SY6801: $i] :
( ( c_Set_Oimage @ SV81 @ ( c_Set_Oimage @ SV736 @ SV1305 @ SV1777 @ SY6800 ) @ SY6800 @ SY6801 )
= ( c_Set_Oimage @ ( c_COMBB @ SV81 @ SV736 @ SY6800 @ SY6801 @ SV1777 ) @ SV1305 @ SV1777 @ SY6801 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3949]) ).
thf(4594,plain,
! [SV737: $i,SV82: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV82 )
= $false )
| ( ( ! [SY4870: $i] :
( ( c_lessequals @ SV737 @ SY4870 @ SV82 )
| ! [SY4871: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4871 @ SV737 @ SV82 ) @ SY4870 @ SV82 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3950]) ).
thf(4595,plain,
! [SV738: $i,SV83: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV83 )
= $false )
| ( ( ! [SY4872: $i] :
( ( c_lessequals @ SV738 @ SY4872 @ SV83 )
| ! [SY4873: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV738 @ SY4873 @ SV83 ) @ SY4872 @ SV83 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3951]) ).
thf(4596,plain,
! [SV739: $i,SV84: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV84 )
= $false )
| ( ( ! [SY4874: $i,SY4875: $i] :
( ( c_lessequals @ SV739 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4874 @ SY4875 @ SV84 ) @ SV84 )
| ~ ( c_lessequals @ SV739 @ SY4875 @ SV84 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3952]) ).
thf(4597,plain,
! [SV740: $i,SV85: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV85 )
= $false )
| ( ( ! [SY4876: $i] :
( ! [SY4877: $i] : ( c_lessequals @ SV740 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4876 @ SY4877 @ SV85 ) @ SV85 )
| ~ ( c_lessequals @ SV740 @ SY4876 @ SV85 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3953]) ).
thf(4598,plain,
! [SV741: $i,SV86: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV86 )
= $false )
| ( ( ! [SY4878: $i] :
( ( c_lessequals @ SV741 @ SY4878 @ SV86 )
| ! [SY4879: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4879 @ SV741 @ SV86 ) @ SY4878 @ SV86 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3954]) ).
thf(4599,plain,
! [SV742: $i,SV87: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV87 )
= $false )
| ( ( ! [SY4880: $i] :
( ( c_lessequals @ SV742 @ SY4880 @ SV87 )
| ! [SY4881: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV742 @ SY4881 @ SV87 ) @ SY4880 @ SV87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3955]) ).
thf(4600,plain,
! [SV1306: $i,SV743: $i,SV88: $i] :
( ( ( c_lessequals @ SV88 @ SV743 @ ( tc_fun @ SV1306 @ tc_bool ) )
= $true )
| ( ( ! [SY6105: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV88 @ SY6105 @ ( tc_fun @ SV1306 @ tc_bool ) ) @ SV743 @ ( tc_fun @ SV1306 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3956]) ).
thf(4601,plain,
! [SV1307: $i,SV744: $i,SV89: $i] :
( ( ( c_lessequals @ SV89 @ SV744 @ ( tc_fun @ SV1307 @ tc_bool ) )
= $true )
| ( ( ! [SY6106: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY6106 @ SV89 @ ( tc_fun @ SV1307 @ tc_bool ) ) @ SV744 @ ( tc_fun @ SV1307 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3957]) ).
thf(4602,plain,
! [SV745: $i,SV90: $i] :
( ( ( class_Orderings_Oorder @ SV90 )
= $false )
| ( ( ! [SY4886: $i] :
( ( c_lessequals @ SV745 @ SY4886 @ SV90 )
| ! [SY4887: $i] :
( ~ ( c_lessequals @ SV745 @ SY4887 @ SV90 )
| ~ ( c_lessequals @ SY4887 @ SY4886 @ SV90 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3958]) ).
thf(4603,plain,
! [SV746: $i,SV91: $i] :
( ( ( class_Orderings_Oorder @ SV91 )
= $false )
| ( ( ! [SY4888: $i] :
( ( c_HOL_Oord__class_Oless @ SV746 @ SY4888 @ SV91 )
| ! [SY4889: $i] :
( ~ ( c_lessequals @ SV746 @ SY4889 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SY4889 @ SY4888 @ SV91 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3959]) ).
thf(4604,plain,
! [SV747: $i,SV92: $i] :
( ( ( class_Orderings_Oorder @ SV92 )
= $false )
| ( ( ! [SY4890: $i] :
( ( c_HOL_Oord__class_Oless @ SV747 @ SY4890 @ SV92 )
| ! [SY4891: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV747 @ SY4891 @ SV92 )
| ~ ( c_lessequals @ SY4891 @ SY4890 @ SV92 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3960]) ).
thf(4605,plain,
! [SV748: $i,SV93: $i] :
( ( ( class_Orderings_Opreorder @ SV93 )
= $false )
| ( ( ! [SY4892: $i] :
( ( c_lessequals @ SV748 @ SY4892 @ SV93 )
| ! [SY4893: $i] :
( ~ ( c_lessequals @ SY4893 @ SY4892 @ SV93 )
| ~ ( c_lessequals @ SV748 @ SY4893 @ SV93 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3961]) ).
thf(4606,plain,
! [SV1308: $i,SV751: $i,SV96: $i] :
( ( ( c_lessequals @ SV96 @ SV751 @ ( tc_fun @ SV1308 @ tc_bool ) )
= $true )
| ( ( ! [SY6107: $i] :
( ~ ( c_lessequals @ SY6107 @ SV751 @ ( tc_fun @ SV1308 @ tc_bool ) )
| ~ ( c_lessequals @ SV96 @ SY6107 @ ( tc_fun @ SV1308 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3962]) ).
thf(4607,plain,
! [SV1778: $i,SV1309: $i,SV752: $i,SV97: $i] :
( ( ( c_Fun_Oinj__on @ SV97 @ SV752 @ SV1309 @ SV1778 )
| ! [SY6802: $i] :
( ~ ( c_lessequals @ SV752 @ SY6802 @ ( tc_fun @ SV1309 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV97 @ SY6802 @ SV1309 @ SV1778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3963]) ).
thf(4608,plain,
! [SV98: $i,SV753: $i,SV1779: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1779 @ SV753 ) )
| ! [SY6803: $i] :
~ ( c_lessequals @ SV1779 @ SV98 @ ( tc_fun @ SY6803 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV98 @ SV753 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3964]) ).
thf(4609,plain,
! [SV99: $i,SV1780: $i] :
( ( ( c_lessequals @ SV1780 @ SV1780 @ SV99 )
= $true )
| ( ( class_Orderings_Oorder @ SV99 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3965]) ).
thf(4610,plain,
! [SV100: $i,SV1781: $i] :
( ( ( c_lessequals @ SV1781 @ SV1781 @ SV100 )
= $true )
| ( ( class_Orderings_Opreorder @ SV100 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3966]) ).
thf(4611,plain,
! [SV101: $i,SV754: $i,SV1782: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV1782 @ SV754 )
| ~ ( c_lessequals @ SV101 @ SV1782 @ ( tc_fun @ SV754 @ tc_bool ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV101 @ SV754 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3967]) ).
thf(4612,plain,
! [SV1310: $i,SV755: $i,SV102: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV102 @ SV755 @ ( tc_fun @ SV1310 @ tc_bool ) )
= $true )
| ( ( ! [SY6110: $i] :
( ~ ( c_lessequals @ SY6110 @ SV755 @ ( tc_fun @ SV1310 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV102 @ SY6110 @ ( tc_fun @ SV1310 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3968]) ).
thf(4613,plain,
! [SV1311: $i,SV756: $i,SV103: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV103 @ SV756 @ ( tc_fun @ SV1311 @ tc_bool ) )
= $true )
| ( ( ! [SY6111: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY6111 @ SV756 @ ( tc_fun @ SV1311 @ tc_bool ) )
| ~ ( c_lessequals @ SV103 @ SY6111 @ ( tc_fun @ SV1311 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3969]) ).
thf(4614,plain,
! [SV757: $i,SV104: $i,SV1783: $i] :
( ( ( ! [SY6804: $i] :
~ ( c_lessequals @ SV1783 @ SV104 @ ( tc_fun @ SY6804 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SV1783 @ SV757 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV104 @ SV757 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3970]) ).
thf(4615,plain,
! [SV758: $i,SV1784: $i,SV105: $i] :
( ( ( ~ ( c_lessequals @ SV105 @ SV1784 @ ( tc_fun @ SV758 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV1784 @ SV758 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV105 @ SV758 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3971]) ).
thf(4616,plain,
! [SV759: $i,SV106: $i] :
( ( ( class_Orderings_Opreorder @ SV106 )
= $false )
| ( ( ! [SY4909: $i] :
( ( c_HOL_Oord__class_Oless @ SV759 @ SY4909 @ SV106 )
| ! [SY4910: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY4910 @ SY4909 @ SV106 )
| ~ ( c_lessequals @ SV759 @ SY4910 @ SV106 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3972]) ).
thf(4617,plain,
! [SV760: $i,SV107: $i] :
( ( ( class_Orderings_Opreorder @ SV107 )
= $false )
| ( ( ! [SY4911: $i] :
( ( c_HOL_Oord__class_Oless @ SV760 @ SY4911 @ SV107 )
| ! [SY4912: $i] :
( ~ ( c_lessequals @ SY4912 @ SY4911 @ SV107 )
| ~ ( c_HOL_Oord__class_Oless @ SV760 @ SY4912 @ SV107 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3973]) ).
thf(4618,plain,
! [SV1785: $i,SV1312: $i,SV761: $i,SV108: $i] :
( ( ! [SY6805: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV108 @ SV761 @ ( tc_fun @ SV1312 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1785 @ SY6805 @ ( tc_fun @ SV1312 @ tc_bool ) ) @ ( tc_fun @ SV1312 @ tc_bool ) )
| ~ ( c_lessequals @ SV761 @ SY6805 @ ( tc_fun @ SV1312 @ tc_bool ) )
| ~ ( c_lessequals @ SV108 @ SV1785 @ ( tc_fun @ SV1312 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3974]) ).
thf(4619,plain,
! [SV1786: $i,SV1313: $i,SV762: $i,SV109: $i] :
( ( ! [SY6806: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV109 @ SV762 @ ( c_Option_Ooption_OSome @ SV1313 @ SV1786 ) @ SY6806 @ ( tc_Option_Ooption @ SV1786 ) ) @ SV762 )
= ( c_Option_Ooption_OSome @ SV1313 @ SV1786 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3975]) ).
thf(4620,plain,
! [SV1787: $i,SV1314: $i,SV763: $i,SV110: $i] :
( ( ( ( hAPP @ SV110 @ SV763 )
!= ( c_Option_Ooption_OSome @ SV1314 @ SV1787 ) )
| ! [SY6807: $i] :
( ( c_Fun_Ofun__upd @ SV110 @ SV763 @ ( c_Option_Ooption_OSome @ SV1314 @ SV1787 ) @ SY6807 @ ( tc_Option_Ooption @ SV1787 ) )
= SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3976]) ).
thf(4621,plain,
! [SV1788: $i,SV1315: $i,SV764: $i,SV111: $i] :
( ( ! [SY6808: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV111 @ SV764 @ ( tc_fun @ SV1315 @ tc_bool ) ) @ SV1788 @ SV1315 @ ( tc_fun @ SY6808 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV111 @ SV1788 @ SV1315 @ ( tc_fun @ SY6808 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV764 @ SV1788 @ SV1315 @ ( tc_fun @ SY6808 @ tc_bool ) ) @ ( tc_fun @ SY6808 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3977]) ).
thf(4622,plain,
! [SV1789: $i,SV1316: $i,SV765: $i,SV112: $i] :
( ( ! [SY6809: $i,SY6810: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV112 @ SV765 @ SV1316 @ SV1789 @ SY6809 ) @ SY6810 )
= ( hAPP @ SV112 @ SY6810 ) )
| ( SY6810 = SV765 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3978]) ).
thf(4623,plain,
! [SV1790: $i,SV1317: $i,SV766: $i,SV113: $i] :
( ( ! [SY6811: $i,SY6812: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV113 @ SV766 @ SV1317 @ SV1790 @ SY6811 ) @ SY6812 )
= ( hAPP @ SV113 @ SY6812 ) )
| ( SY6812 = SV766 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3979]) ).
thf(4624,plain,
! [SV1791: $i,SV1318: $i,SV767: $i,SV114: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV114 @ ( c_HOL_Ominus__class_Ominus @ SV767 @ SV1318 @ ( tc_fun @ SV1791 @ tc_bool ) ) @ ( tc_fun @ SV1791 @ tc_bool ) )
= SV1318 )
| ~ ( c_lessequals @ SV114 @ SV767 @ ( tc_fun @ SV1791 @ tc_bool ) )
| ~ ( c_lessequals @ SV1318 @ SV114 @ ( tc_fun @ SV1791 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3980]) ).
thf(4625,plain,
! [SV1319: $i,SV768: $i,SV115: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV115 ) )
= $true )
| ( ( ! [SY6127: $i,SY6128: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV768 @ SV1319 @ SV115 )
!= ( c_HOL_Ominus__class_Ominus @ SY6127 @ SY6128 @ SV115 ) )
| ( c_lessequals @ SY6128 @ SY6127 @ SV115 )
| ~ ( c_lessequals @ SV1319 @ SV768 @ SV115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3981]) ).
thf(4626,plain,
! [SV1320: $i,SV769: $i,SV116: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV116 ) )
= $true )
| ( ( ! [SY6129: $i,SY6130: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV769 @ SV1320 @ SV116 )
!= ( c_HOL_Ominus__class_Ominus @ SY6129 @ SY6130 @ SV116 ) )
| ( c_lessequals @ SV1320 @ SV769 @ SV116 )
| ~ ( c_lessequals @ SY6130 @ SY6129 @ SV116 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3982]) ).
thf(4627,plain,
! [SV1792: $i,SV1321: $i,SV770: $i,SV117: $i] :
( ( ! [SY6813: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV117 @ SV770 @ SV1321 @ SV1792 ) @ ( c_Set_Oimage @ SV117 @ SY6813 @ SV1321 @ SV1792 ) @ ( tc_fun @ SV1792 @ tc_bool ) )
| ~ ( c_lessequals @ SV770 @ SY6813 @ ( tc_fun @ SV1321 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3983]) ).
thf(4628,plain,
! [SV1322: $i,SV771: $i,SV118: $i] :
( ( ( ~ ( c_lessequals @ SV118 @ SV771 @ ( tc_fun @ SV1322 @ tc_bool ) ) )
= $true )
| ( ( ! [SY6133: $i,SY6134: $i] : ( c_lessequals @ ( c_Set_Oimage @ SY6133 @ SV118 @ SV1322 @ SY6134 ) @ ( c_Set_Oimage @ SY6133 @ SV771 @ SV1322 @ SY6134 ) @ ( tc_fun @ SY6134 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3984]) ).
thf(4629,plain,
! [SV1793: $i,SV1323: $i,SV772: $i,SV119: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV119 @ SV772 @ SV1323 ) @ ( c_Set_Oinsert @ SV119 @ SV1793 @ SV1323 ) @ ( tc_fun @ SV1323 @ tc_bool ) )
| ~ ( c_lessequals @ SV772 @ SV1793 @ ( tc_fun @ SV1323 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3985]) ).
thf(4630,plain,
! [SV121: $i,SV1794: $i] :
( ( ( ! [SY6814: $i] :
( ( c_HOL_Oord__class_Oless @ SV1794 @ SY6814 @ SV121 )
| ( SY6814 = SV1794 )
| ~ ( c_lessequals @ SV1794 @ SY6814 @ SV121 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV121 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3986]) ).
thf(4631,plain,
! [SV122: $i,SV1795: $i] :
( ( ( ! [SY6815: $i] :
( ( c_HOL_Oord__class_Oless @ SV1795 @ SY6815 @ SV122 )
| ~ ( c_lessequals @ SV1795 @ SY6815 @ SV122 )
| ( SY6815 = SV1795 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV122 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3987]) ).
thf(4632,plain,
! [SV1324: $i,SV773: $i,SV123: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV123 @ SV773 @ ( tc_fun @ SV1324 @ tc_bool ) )
= $true )
| ( ( ( SV123 = SV773 )
| ~ ( c_lessequals @ SV123 @ SV773 @ ( tc_fun @ SV1324 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3988]) ).
thf(4633,plain,
! [SV124: $i,SV1796: $i] :
( ( ( ! [SY6816: $i] :
( ( SV1796 = SY6816 )
| ( c_HOL_Oord__class_Oless @ SV1796 @ SY6816 @ SV124 )
| ~ ( c_lessequals @ SV1796 @ SY6816 @ SV124 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3989]) ).
thf(4634,plain,
! [SV125: $i,SV1797: $i] :
( ( ( ! [SY6817: $i] :
( ( c_HOL_Oord__class_Oless @ SV1797 @ SY6817 @ SV125 )
| ( SV1797 = SY6817 )
| ~ ( c_lessequals @ SV1797 @ SY6817 @ SV125 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3990]) ).
thf(4635,plain,
! [SV1798: $i,SV774: $i,SV126: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV126 @ SV774 @ ( tc_fun @ SV1798 @ tc_bool ) )
| ~ ( c_lessequals @ SV126 @ SV774 @ ( tc_fun @ SV1798 @ tc_bool ) ) )
= $true )
| ( ( SV126 = SV774 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3991]) ).
thf(4636,plain,
! [SV127: $i,SV1799: $i] :
( ( ( ! [SY6818: $i] :
( ( c_HOL_Oord__class_Oless @ SV1799 @ SY6818 @ SV127 )
| ( SV1799 = SY6818 )
| ~ ( c_lessequals @ SV1799 @ SY6818 @ SV127 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV127 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3992]) ).
thf(4637,plain,
! [SV128: $i,SV1800: $i] :
( ( ( ! [SY6819: $i] :
( ( c_HOL_Oord__class_Oless @ SV1800 @ SY6819 @ SV128 )
| ~ ( c_lessequals @ SV1800 @ SY6819 @ SV128 )
| ( SV1800 = SY6819 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV128 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3993]) ).
thf(4638,plain,
! [SV129: $i,SV1801: $i] :
( ( ( ! [SY6820: $i] :
( ( SV1801 = SY6820 )
| ~ ( c_lessequals @ SV1801 @ SY6820 @ SV129 )
| ( c_HOL_Oord__class_Oless @ SV1801 @ SY6820 @ SV129 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV129 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3994]) ).
thf(4639,plain,
! [SV130: $i,SV1802: $i] :
( ( ( ! [SY6821: $i] :
( ( SV1802 = SY6821 )
| ( c_HOL_Oord__class_Oless @ SV1802 @ SY6821 @ SV130 )
| ~ ( c_lessequals @ SV1802 @ SY6821 @ SV130 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV130 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3995]) ).
thf(4640,plain,
! [SV1803: $i,SV1325: $i,SV775: $i,SV131: $i] :
( ( ! [SY6822: $i,SY6823: $i,SY6824: $i] :
( ( ( c_Fun_Ofun__upd @ SV131 @ SV775 @ ( c_Option_Ooption_OSome @ SV1325 @ SV1803 ) @ SY6822 @ ( tc_Option_Ooption @ SV1803 ) )
!= ( c_Fun_Ofun__upd @ SY6823 @ SV775 @ ( c_Option_Ooption_OSome @ SY6824 @ SV1803 ) @ SY6822 @ ( tc_Option_Ooption @ SV1803 ) ) )
| ( SV1325 = SY6824 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3996]) ).
thf(4641,plain,
! [SV1804: $i,SV1326: $i,SV776: $i,SV132: $i] :
( ( ! [SY6825: $i] :
( ( c_Set_Oimage @ SV132 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV776 @ SV1326 @ ( tc_fun @ SV1804 @ tc_bool ) ) @ SV1804 @ SY6825 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ SV132 @ SV776 @ SV1804 @ SY6825 ) @ ( c_Set_Oimage @ SV132 @ SV1326 @ SV1804 @ SY6825 ) @ ( tc_fun @ SY6825 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3997]) ).
thf(4642,plain,
! [SV133: $i,SV1805: $i] :
( ( ( ! [SY6826: $i] :
( ( c_lessequals @ SV1805 @ SY6826 @ SV133 )
| ( c_lessequals @ SY6826 @ SV1805 @ SV133 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV133 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3998]) ).
thf(4643,plain,
! [SV1327: $i,SV777: $i,SV134: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV134 ) )
= $true )
| ( ( ! [SY6142: $i,SY6143: $i] :
( ( ( c_Finite__Set_Osetsum @ SV777 @ ( c_HOL_Ominus__class_Ominus @ SV1327 @ SY6142 @ ( tc_fun @ SY6143 @ tc_bool ) ) @ SY6143 @ SV134 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV777 @ SV1327 @ SY6143 @ SV134 ) @ ( c_Finite__Set_Osetsum @ SV777 @ SY6142 @ SY6143 @ SV134 ) @ SV134 ) )
| ~ ( c_lessequals @ SY6142 @ SV1327 @ ( tc_fun @ SY6143 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV1327 @ SY6143 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3999]) ).
thf(4644,plain,
! [SV1806: $i,SV1328: $i,SV778: $i,SV135: $i] :
( ( ( ( c_Finite__Set_Ocard @ SV135 @ SV778 )
= ( c_Finite__Set_Ocard @ SV1328 @ SV1806 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1328 @ SV1806 )
| ~ ( c_Finite__Set_Ofinite @ SV135 @ SV778 )
| ! [SY6827: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ SY6827 @ SV1328 @ SV1806 @ SV778 ) @ SV135 @ ( tc_fun @ SV778 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY6827 @ SV1328 @ SV1806 @ SV778 )
| ! [SY6828: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ SY6828 @ SV135 @ SV778 @ SV1806 ) @ SV1328 @ ( tc_fun @ SV1806 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY6828 @ SV135 @ SV778 @ SV1806 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4000]) ).
thf(4645,plain,
! [SV1807: $i,SV1329: $i,SV779: $i,SV136: $i] :
( ( ! [SY6829: $i,SY6830: $i,SY6831: $i] :
( ( c_Finite__Set_Ofold__graph @ SV136 @ SV779 @ ( c_Set_Oinsert @ SV1329 @ SV1807 @ SY6829 ) @ ( hAPP @ ( hAPP @ SV136 @ SV1329 ) @ SY6830 ) @ SY6829 @ SY6831 )
| ~ ( c_Finite__Set_Ofold__graph @ SV136 @ SV779 @ SV1807 @ SY6830 @ SY6829 @ SY6831 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6829 ) @ SV1329 ) @ SV1807 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4001]) ).
thf(4646,plain,
! [SV1330: $i,SV780: $i,SV137: $i] :
( ( ( c_lessequals @ SV137 @ SV780 @ ( tc_fun @ SV1330 @ tc_bool ) )
= $true )
| ( ( ! [SY6151: $i] :
( ~ ( c_lessequals @ SV137 @ ( c_Set_Oinsert @ SY6151 @ SV780 @ SV1330 ) @ ( tc_fun @ SV1330 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1330 ) @ SY6151 ) @ SV137 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4002]) ).
thf(4647,plain,
! [SV1808: $i,SV1331: $i,SV781: $i,SV138: $i] :
( ( ( c_lessequals @ SV138 @ ( c_Set_Oinsert @ SV781 @ SV1331 @ SV1808 ) @ ( tc_fun @ SV1808 @ tc_bool ) )
| ~ ( c_lessequals @ SV138 @ SV1331 @ ( tc_fun @ SV1808 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1808 ) @ SV781 ) @ SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4003]) ).
thf(4648,plain,
! [SV1332: $i,SV782: $i,SV139: $i] :
( ( ( c_lessequals @ SV139 @ SV782 @ ( tc_fun @ SV1332 @ tc_bool ) )
= $true )
| ( ( ! [SY6153: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1332 ) @ SY6153 ) @ SV139 ) )
| ~ ( c_lessequals @ SV139 @ ( c_Set_Oinsert @ SY6153 @ SV782 @ SV1332 ) @ ( tc_fun @ SV1332 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4004]) ).
thf(4649,plain,
! [SV1809: $i,SV1333: $i,SV783: $i,SV140: $i] :
( ( ( c_lessequals @ SV140 @ ( c_Set_Oinsert @ SV783 @ SV1333 @ SV1809 ) @ ( tc_fun @ SV1809 @ tc_bool ) )
| ~ ( c_lessequals @ SV140 @ SV1333 @ ( tc_fun @ SV1809 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1809 ) @ SV783 ) @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4005]) ).
thf(4650,plain,
! [SV1334: $i,SV784: $i,SV141: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV141 ) @ SV784 ) @ SV1334 ) )
= $true )
| ( ( ! [SY6155: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SV784 @ SY6155 @ SV141 ) @ SV1334 @ ( tc_fun @ SV141 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4006]) ).
thf(4651,plain,
! [SV1810: $i,SV1335: $i,SV785: $i,SV142: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV142 @ SV785 @ SV1335 ) @ SV1810 @ ( tc_fun @ SV1335 @ tc_bool ) )
| ~ ( c_lessequals @ SV785 @ SV1810 @ ( tc_fun @ SV1335 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1335 ) @ SV142 ) @ SV1810 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4007]) ).
thf(4652,plain,
! [SV1811: $i,SV1336: $i,SV786: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV143 ) @ ( hAPP @ SV786 @ SV1336 ) ) @ SV1811 ) )
| ! [SY6832: $i,SY6833: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6832 ) @ SV1336 ) @ SY6833 ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV786 @ SY6833 @ SY6832 @ SV143 ) @ SV1811 @ ( tc_fun @ SV143 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4008]) ).
thf(4653,plain,
! [SV1812: $i,SV1337: $i,SV787: $i,SV144: $i] :
( ( ! [SY6834: $i,SY6835: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ SV144 @ SV787 @ SV1337 @ SV1812 @ SY6834 ) @ SY6835 @ SV1812 @ SY6834 )
= ( c_Set_Oimage @ SV144 @ SY6835 @ SV1812 @ SY6834 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1812 ) @ SV787 ) @ SY6835 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4009]) ).
thf(4654,plain,
! [SV1338: $i,SV788: $i,SV145: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV145 ) )
= $true )
| ( ( ! [SY6163: $i,SY6164: $i] :
( ( c_lessequals @ ( hAPP @ SV788 @ SV1338 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY6163 @ SV788 @ SY6164 @ SV145 ) @ SV145 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6164 ) @ SV1338 ) @ SY6163 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4010]) ).
thf(4655,plain,
! [SV1813: $i,SV1339: $i,SV789: $i,SV146: $i] :
( ( ! [SY6836: $i] : ( c_lessequals @ ( hAPP @ SV146 @ SV789 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1339 @ SV146 @ SV1813 @ ( tc_fun @ SY6836 @ tc_bool ) ) @ ( tc_fun @ SY6836 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1813 ) @ SV789 ) @ SV1339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4011]) ).
thf(4656,plain,
! [SV1814: $i,SV1340: $i,SV790: $i,SV147: $i] :
( ( ( c_lessequals @ ( hAPP @ SV147 @ SV790 ) @ SV1340 @ ( tc_fun @ SV1814 @ tc_bool ) )
| ! [SY6837: $i,SY6838: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6837 ) @ SV790 ) @ SY6838 ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY6838 @ SV147 @ SY6837 @ ( tc_fun @ SV1814 @ tc_bool ) ) @ SV1340 @ ( tc_fun @ SV1814 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4012]) ).
thf(4657,plain,
! [SV1815: $i,SV1341: $i,SV791: $i,SV148: $i] :
( ( ! [SY6839: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV148 @ SV791 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1341 @ SV148 @ SV1815 @ ( tc_fun @ SY6839 @ tc_bool ) ) @ ( tc_fun @ SY6839 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1341 @ SV148 @ SV1815 @ ( tc_fun @ SY6839 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1815 ) @ SV791 ) @ SV1341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4013]) ).
thf(4658,plain,
! [SV1343: $i,SV793: $i,SV150: $i] :
( ( ( SV150
= ( c_Set_Oinsert @ SV793 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1343 @ tc_bool ) ) @ SV1343 ) )
= $true )
| ( ( ( SV150
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1343 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV150 @ ( c_Set_Oinsert @ SV793 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1343 @ tc_bool ) ) @ SV1343 ) @ ( tc_fun @ SV1343 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4015]) ).
thf(4659,plain,
! [SV1344: $i,SV794: $i,SV151: $i] :
( ( ( c_Finite__Set_Ofinite @ SV151 @ SV794 )
= $true )
| ( ( ! [SY6172: $i,SY6173: $i] :
( ~ ( c_lessequals @ SV151 @ ( c_Set_Oimage @ SV1344 @ SY6172 @ SY6173 @ SV794 ) @ ( tc_fun @ SV794 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SY6172 @ SY6173 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4016]) ).
thf(4660,plain,
! [SV1346: $i,SV796: $i,SV153: $i] :
( ( ( c_lessequals @ SV153 @ SV796 @ ( tc_fun @ SV1346 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ SV1346 ) @ SV1346 @ ( tc_fun @ SV1346 @ tc_bool ) @ tc_bool ) @ SV153 ) @ ( hAPP @ ( c_COMBC @ ( c_in @ SV1346 ) @ SV1346 @ ( tc_fun @ SV1346 @ tc_bool ) @ tc_bool ) @ SV796 ) @ ( tc_fun @ SV1346 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4018]) ).
thf(4661,plain,
! [SV1347: $i,SV797: $i,SV154: $i] :
( ( ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ SV154 ) @ SV154 @ ( tc_fun @ SV154 @ tc_bool ) @ tc_bool ) @ SV797 ) @ ( hAPP @ ( c_COMBC @ ( c_in @ SV154 ) @ SV154 @ ( tc_fun @ SV154 @ tc_bool ) @ tc_bool ) @ SV1347 ) @ ( tc_fun @ SV154 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV797 @ SV1347 @ ( tc_fun @ SV154 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4019]) ).
thf(4662,plain,
! [SV798: $i,SV155: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV155 )
= $false )
| ( ( ! [SY5012: $i,SY5013: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV798 @ ( c_COMBK @ SY5012 @ SV155 @ SY5013 ) @ SY5013 @ SV155 )
= SY5012 )
| ( SV798
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5013 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4020]) ).
thf(4663,plain,
! [SV1816: $i,SV1348: $i,SV799: $i,SV156: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV156 @ tc_bool ) ) @ SV799 @ SV156 @ ( tc_fun @ SV1348 @ tc_bool ) ) @ SV1816 @ ( tc_fun @ SV1348 @ tc_bool ) )
= SV1816 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4021]) ).
thf(4664,plain,
! [SV1817: $i,SV1349: $i,SV800: $i,SV157: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV157 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV800 @ tc_bool ) ) @ SV1349 @ SV800 @ ( tc_fun @ SV1817 @ tc_bool ) ) @ ( tc_fun @ SV1817 @ tc_bool ) )
= SV157 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4022]) ).
thf(4665,plain,
! [SV1818: $i,SV1350: $i,SV801: $i,SV158: $i] :
( ( ! [SY6840: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ SV158 @ SV801 @ SV1350 ) @ SV1818 @ SV1350 @ ( tc_fun @ SY6840 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV1818 @ SV158 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV801 @ SV1818 @ SV1350 @ ( tc_fun @ SY6840 @ tc_bool ) ) @ ( tc_fun @ SY6840 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4023]) ).
thf(4666,plain,
! [SV1819: $i,SV1351: $i,SV802: $i,SV159: $i] :
( ( ! [SY6841: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV159 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV802 @ SV1351 @ ( tc_fun @ SV1819 @ tc_bool ) ) @ SV1819 @ SY6841 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV159 @ SV802 @ SV1819 @ SY6841 ) @ ( c_Set_Oimage @ SV159 @ SV1351 @ SV1819 @ SY6841 ) @ ( tc_fun @ SY6841 @ tc_bool ) ) @ ( tc_fun @ SY6841 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4024]) ).
thf(4667,plain,
! [SV1820: $i,SV1352: $i,SV803: $i,SV160: $i] :
( ( ! [SY6842: $i,SY6843: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV160 @ ( c_COMBB @ SV803 @ SV1352 @ SV1820 @ ( tc_fun @ SY6842 @ tc_bool ) @ SY6843 ) @ SY6843 @ ( tc_fun @ SY6842 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oimage @ SV1352 @ SV160 @ SY6843 @ SV1820 ) @ SV803 @ SV1820 @ ( tc_fun @ SY6842 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4025]) ).
thf(4668,plain,
! [SV1821: $i,SV1353: $i,SV804: $i,SV161: $i] :
( ( ! [SY6844: $i,SY6845: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oimage @ SV161 @ SV804 @ SV1353 @ SV1821 ) @ SY6844 @ SV1821 @ ( tc_fun @ SY6845 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV804 @ ( c_COMBB @ SY6844 @ SV161 @ SV1821 @ ( tc_fun @ SY6845 @ tc_bool ) @ SV1353 ) @ SV1353 @ ( tc_fun @ SY6845 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4026]) ).
thf(4669,plain,
! [SV1822: $i,SV1354: $i,SV805: $i,SV162: $i] :
( ( ! [SY6846: $i] :
( ( ( c_Set_Oimage @ SV162 @ SV805 @ SV1354 @ SV1822 )
!= ( c_Set_Oimage @ SV162 @ SY6846 @ SV1354 @ SV1822 ) )
| ~ ( c_Fun_Oinj__on @ SV162 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV805 @ SY6846 @ ( tc_fun @ SV1354 @ tc_bool ) ) @ SV1354 @ SV1822 )
| ( SV805 = SY6846 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4027]) ).
thf(4670,plain,
! [SV1823: $i,SV1355: $i,SV806: $i,SV163: $i] :
( ( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ SV163 @ SV806 @ SV1355 @ SV1823 ) @ SV1823 )
= ( c_Finite__Set_Ocard @ SV806 @ SV1355 ) )
| ~ ( c_Fun_Oinj__on @ SV163 @ SV806 @ SV1355 @ SV1823 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4028]) ).
thf(4671,plain,
! [SV1824: $i,SV1356: $i,SV807: $i,SV164: $i] :
( ( ! [SY6847: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV164 @ SV807 @ SV1356 @ SV1824 ) @ ( c_Set_Oimage @ SV164 @ SY6847 @ SV1356 @ SV1824 ) @ ( tc_fun @ SV1824 @ tc_bool ) ) @ ( c_Set_Oimage @ SV164 @ ( c_HOL_Ominus__class_Ominus @ SV807 @ SY6847 @ ( tc_fun @ SV1356 @ tc_bool ) ) @ SV1356 @ SV1824 ) @ ( tc_fun @ SV1824 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4029]) ).
thf(4672,plain,
! [SV1825: $i,SV1358: $i,SV809: $i,SV166: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV166 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV809 @ SV1358 @ ( tc_fun @ SV1825 @ tc_bool ) ) @ ( tc_fun @ SV1825 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ SV166 @ SV809 @ ( tc_fun @ SV1825 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV166 @ SV1358 @ ( tc_fun @ SV1825 @ tc_bool ) ) @ ( tc_fun @ SV1825 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4031]) ).
thf(4673,plain,
! [SV1826: $i,SV1359: $i,SV810: $i,SV167: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV167 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV810 @ SV1359 @ ( tc_fun @ SV1826 @ tc_bool ) ) @ ( tc_fun @ SV1826 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV167 @ SV810 @ ( tc_fun @ SV1826 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV167 @ SV1359 @ ( tc_fun @ SV1826 @ tc_bool ) ) @ ( tc_fun @ SV1826 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4032]) ).
thf(4674,plain,
! [SV1827: $i,SV1360: $i,SV811: $i,SV168: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV168 @ ( c_Set_Ovimage @ SV168 @ SV811 @ SV1360 @ SV1827 ) @ SV1360 @ SV1827 ) @ SV811 @ ( tc_fun @ SV1827 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4033]) ).
thf(4675,plain,
! [SV1828: $i,SV1361: $i,SV812: $i,SV169: $i] :
( ( ! [SY6848: $i,SY6849: $i] :
( ( c_Map_Omap__add @ SV169 @ ( c_Fun_Ofun__upd @ SV812 @ SV1361 @ ( c_Option_Ooption_OSome @ SV1828 @ SY6848 ) @ SY6849 @ ( tc_Option_Ooption @ SY6848 ) ) @ SY6849 @ SY6848 )
= ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ SV169 @ SV812 @ SY6849 @ SY6848 ) @ SV1361 @ ( c_Option_Ooption_OSome @ SV1828 @ SY6848 ) @ SY6849 @ ( tc_Option_Ooption @ SY6848 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4034]) ).
thf(4676,plain,
! [SV1829: $i,SV1362: $i,SV813: $i,SV170: $i] :
( ( ( c_Map_Odom @ ( c_Map_Omap__add @ SV170 @ SV813 @ SV1362 @ SV1829 ) @ SV1362 @ SV1829 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Map_Odom @ SV813 @ SV1362 @ SV1829 ) @ ( c_Map_Odom @ SV170 @ SV1362 @ SV1829 ) @ ( tc_fun @ SV1362 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4035]) ).
thf(4677,plain,
! [SV1830: $i,SV1363: $i,SV814: $i,SV171: $i] :
( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ SV171 @ SV814 @ ( c_Option_Ooption_ONone @ SV1363 ) @ SV1830 @ ( tc_Option_Ooption @ SV1363 ) ) @ SV171 @ SV1830 @ SV1363 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4036]) ).
thf(4678,plain,
! [SV1831: $i,SV1364: $i,SV815: $i,SV172: $i] :
( ( ( c_lessequals @ ( c_Map_Odom @ SV172 @ SV815 @ SV1364 ) @ ( c_Map_Odom @ SV1831 @ SV815 @ SV1364 ) @ ( tc_fun @ SV815 @ tc_bool ) )
| ~ ( c_Map_Omap__le @ SV172 @ SV1831 @ SV815 @ SV1364 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4037]) ).
thf(4679,plain,
! [SV174: $i,SV1832: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1832 @ SV1832 @ SV174 )
= SV1832 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV174 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4038]) ).
thf(4680,plain,
! [SV1833: $i,SV1365: $i,SV817: $i,SV175: $i] :
( ( ! [SY6850: $i,SY6851: $i] :
( ( hAPP @ ( c_COMBB @ SV175 @ SV817 @ SV1365 @ SV1833 @ SY6850 ) @ SY6851 )
= ( hAPP @ SV175 @ ( hAPP @ SV817 @ SY6851 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4039]) ).
thf(4681,plain,
! [SV1834: $i,SV1366: $i,SV818: $i,SV176: $i] :
( ( ( hAPP @ ( c_COMBK @ SV176 @ SV818 @ SV1366 ) @ SV1834 )
= SV176 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4040]) ).
thf(4682,plain,
! [SV177: $i,SV1835: $i] :
( ( ( ! [SY6852: $i] :
( ( c_HOL_Oord__class_Oless @ SV1835 @ SY6852 @ SV177 )
| ( c_lessequals @ SY6852 @ SV1835 @ SV177 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV177 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4041]) ).
thf(4683,plain,
! [SV178: $i,SV1836: $i] :
( ( ( ~ ( c_lessequals @ SV1836 @ SV1836 @ SV178 )
| ~ ( c_HOL_Oord__class_Oless @ SV1836 @ SV1836 @ SV178 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV178 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4042]) ).
thf(4684,plain,
! [SV179: $i,SV1837: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV1837 @ SV1837 @ SV179 )
| ( c_lessequals @ SV1837 @ SV1837 @ SV179 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV179 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4043]) ).
thf(4685,plain,
! [SV180: $i,SV1838: $i] :
( ( ( ! [SY6853: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV1838 @ SY6853 @ SV180 )
| ~ ( c_lessequals @ SY6853 @ SV1838 @ SV180 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV180 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4044]) ).
thf(4686,plain,
! [SV181: $i,SV1839: $i] :
( ( ( ! [SY6854: $i] :
( ( c_HOL_Oord__class_Oless @ SY6854 @ SV1839 @ SV181 )
| ( c_lessequals @ SV1839 @ SY6854 @ SV181 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4045]) ).
thf(4687,plain,
! [SV182: $i,SV1840: $i] :
( ( ( ! [SY6855: $i] :
( ~ ( c_lessequals @ SV1840 @ SY6855 @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ SY6855 @ SV1840 @ SV182 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV182 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4046]) ).
thf(4688,plain,
! [SV183: $i,SV1841: $i] :
( ( ( ! [SY6856: $i] :
( ( c_HOL_Oord__class_Oless @ SV1841 @ SY6856 @ SV183 )
| ( c_lessequals @ SY6856 @ SV1841 @ SV183 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV183 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4047]) ).
thf(4689,plain,
! [SV819: $i,SV184: $i] :
( ( ( class_HOL_Oord @ SV184 )
= $false )
| ( ( ! [SY5063: $i,SY5064: $i] :
( ~ ( c_lessequals @ SV819 @ SY5063 @ ( tc_fun @ SY5064 @ SV184 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY5063 @ SV819 @ ( tc_fun @ SY5064 @ SV184 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4048]) ).
thf(4690,plain,
! [SV185: $i,SV1842: $i] :
( ( ( ! [SY6857: $i] :
( ~ ( c_lessequals @ SV1842 @ SY6857 @ SV185 )
| ~ ( c_HOL_Oord__class_Oless @ SY6857 @ SV1842 @ SV185 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV185 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4049]) ).
thf(4691,plain,
! [SV1843: $i,SV1367: $i,SV820: $i,SV186: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV186 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV820 @ SV1367 @ ( tc_fun @ SV1843 @ tc_bool ) ) @ ( tc_fun @ SV1843 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV820 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV186 @ SV1367 @ ( tc_fun @ SV1843 @ tc_bool ) ) @ ( tc_fun @ SV1843 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4050]) ).
thf(4692,plain,
! [SV1844: $i,SV1368: $i,SV821: $i,SV187: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV187 @ SV821 @ ( tc_fun @ SV1368 @ tc_bool ) ) @ SV1844 @ ( tc_fun @ SV1368 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV187 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV821 @ SV1844 @ ( tc_fun @ SV1368 @ tc_bool ) ) @ ( tc_fun @ SV1368 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4051]) ).
thf(4693,plain,
! [SV822: $i,SV188: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV188 )
= $false )
| ( ( ! [SY5069: $i,SY5070: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV822 @ SY5069 @ SV188 ) @ SY5070 @ SV188 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV822 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5069 @ SY5070 @ SV188 ) @ SV188 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4052]) ).
thf(4694,plain,
! [SV823: $i,SV189: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV189 )
= $false )
| ( ( ! [SY5071: $i,SY5072: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV823 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5071 @ SY5072 @ SV189 ) @ SV189 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY5071 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV823 @ SY5072 @ SV189 ) @ SV189 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4053]) ).
thf(4695,plain,
! [SV824: $i,SV190: $i] :
( ( ( class_Lattices_Olattice @ SV190 )
= $false )
| ( ( ! [SY5073: $i,SY5074: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV824 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5073 @ SY5074 @ SV190 ) @ SV190 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY5073 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV824 @ SY5074 @ SV190 ) @ SV190 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4054]) ).
thf(4696,plain,
! [SV825: $i,SV191: $i] :
( ( ( class_Lattices_Olattice @ SV191 )
= $false )
| ( ( ! [SY5075: $i,SY5076: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV825 @ SY5075 @ SV191 ) @ SY5076 @ SV191 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV825 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5075 @ SY5076 @ SV191 ) @ SV191 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4055]) ).
thf(4697,plain,
! [SV1369: $i,SV826: $i,SV192: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV192 @ SV826 @ ( tc_fun @ SV1369 @ tc_bool ) )
= SV192 )
= $true )
| ( ( ~ ( c_lessequals @ SV192 @ SV826 @ ( tc_fun @ SV1369 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4056]) ).
thf(4698,plain,
! [SV1370: $i,SV827: $i,SV193: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV193 @ SV827 @ ( tc_fun @ SV1370 @ tc_bool ) )
= SV827 )
= $true )
| ( ( ~ ( c_lessequals @ SV827 @ SV193 @ ( tc_fun @ SV1370 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4057]) ).
thf(4699,plain,
! [SV194: $i,SV1845: $i] :
( ( ( ! [SY6858: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1845 @ SY6858 @ SV194 )
= SV1845 )
| ~ ( c_lessequals @ SV1845 @ SY6858 @ SV194 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV194 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4058]) ).
thf(4700,plain,
! [SV195: $i,SV1846: $i] :
( ( ( ! [SY6859: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1846 @ SY6859 @ SV195 )
!= SV1846 )
| ( c_lessequals @ SV1846 @ SY6859 @ SV195 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV195 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4059]) ).
thf(4701,plain,
! [SV196: $i,SV1847: $i] :
( ( ( ! [SY6860: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1847 @ SY6860 @ SV196 )
= SY6860 )
| ~ ( c_lessequals @ SY6860 @ SV1847 @ SV196 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV196 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4060]) ).
thf(4702,plain,
! [SV1848: $i,SV1371: $i,SV828: $i,SV197: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV197 @ SV828 @ ( tc_fun @ SV1371 @ tc_bool ) ) @ SV1848 @ ( tc_fun @ SV1371 @ tc_bool ) )
| ~ ( c_lessequals @ SV828 @ SV1848 @ ( tc_fun @ SV1371 @ tc_bool ) )
| ~ ( c_lessequals @ SV197 @ SV1848 @ ( tc_fun @ SV1371 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4061]) ).
thf(4703,plain,
! [SV1849: $i,SV1374: $i,SV831: $i,SV200: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ SV831 @ ( tc_fun @ SV1374 @ tc_bool ) ) @ SV1849 @ ( tc_fun @ SV1374 @ tc_bool ) )
| ~ ( c_lessequals @ SV831 @ SV1849 @ ( tc_fun @ SV1374 @ tc_bool ) )
| ~ ( c_lessequals @ SV200 @ SV1849 @ ( tc_fun @ SV1374 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4064]) ).
thf(4704,plain,
! [SV832: $i,SV201: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV201 )
= $false )
| ( ( ! [SY5085: $i,SY5086: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV832 @ SY5085 @ SV201 ) @ SY5086 @ SV201 )
| ~ ( c_lessequals @ SY5085 @ SY5086 @ SV201 )
| ~ ( c_lessequals @ SV832 @ SY5086 @ SV201 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4065]) ).
thf(4705,plain,
! [SV202: $i,SV1850: $i] :
( ( ( ! [SY6861: $i] : ( c_lessequals @ SV1850 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1850 @ SY6861 @ SV202 ) @ SV202 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV202 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4066]) ).
thf(4706,plain,
! [SV203: $i,SV1851: $i] :
( ( ( ! [SY6862: $i] : ( c_lessequals @ SV1851 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY6862 @ SV1851 @ SV203 ) @ SV203 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV203 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4067]) ).
thf(4707,plain,
! [SV833: $i,SV204: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV204 )
= $false )
| ( ( ! [SY5087: $i,SY5088: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV833 @ SY5087 @ SV204 ) @ SY5088 @ SV204 )
| ~ ( c_lessequals @ SY5087 @ SY5088 @ SV204 )
| ~ ( c_lessequals @ SV833 @ SY5088 @ SV204 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4068]) ).
thf(4708,plain,
! [SV834: $i,SV205: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV205 )
= $false )
| ( ( ! [SY5089: $i,SY5090: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV834 @ SY5089 @ SV205 ) @ SY5090 @ SV205 )
| ~ ( c_lessequals @ SY5089 @ SY5090 @ SV205 )
| ~ ( c_lessequals @ SV834 @ SY5090 @ SV205 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4069]) ).
thf(4709,plain,
! [SV206: $i,SV1852: $i] :
( ( ( ! [SY6863: $i] : ( c_lessequals @ SV1852 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY6863 @ SV1852 @ SV206 ) @ SV206 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV206 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4070]) ).
thf(4710,plain,
! [SV207: $i,SV1853: $i] :
( ( ( ! [SY6864: $i] : ( c_lessequals @ SV1853 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1853 @ SY6864 @ SV207 ) @ SV207 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV207 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4071]) ).
thf(4711,plain,
! [SV1375: $i,SV835: $i,SV208: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV208 @ ( c_HOL_Ominus__class_Ominus @ SV835 @ SV208 @ ( tc_fun @ SV1375 @ tc_bool ) ) @ ( tc_fun @ SV1375 @ tc_bool ) )
= SV835 )
= $true )
| ( ( ~ ( c_lessequals @ SV208 @ SV835 @ ( tc_fun @ SV1375 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4072]) ).
thf(4712,plain,
! [SV836: $i,SV209: $i] :
( ( ( class_Lattices_Olattice @ SV209 )
= $false )
| ( ( ! [SY5092: $i,SY5093: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV836 @ SY5092 @ SV209 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV836 @ SY5093 @ SV209 ) @ SV209 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV836 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5092 @ SY5093 @ SV209 ) @ SV209 ) @ SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4073]) ).
thf(4713,plain,
! [SV1854: $i,SV1377: $i,SV838: $i,SV211: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV211 @ SV838 @ ( tc_fun @ SV1377 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV838 @ SV1854 @ ( tc_fun @ SV1377 @ tc_bool ) ) @ ( tc_fun @ SV1377 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1854 @ SV211 @ ( tc_fun @ SV1377 @ tc_bool ) ) @ ( tc_fun @ SV1377 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV211 @ SV838 @ ( tc_fun @ SV1377 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV838 @ SV1854 @ ( tc_fun @ SV1377 @ tc_bool ) ) @ ( tc_fun @ SV1377 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1854 @ SV211 @ ( tc_fun @ SV1377 @ tc_bool ) ) @ ( tc_fun @ SV1377 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4075]) ).
thf(4714,plain,
! [SV1855: $i,SV1378: $i,SV839: $i,SV212: $i] :
( ( c_Finite__Set_Ofold__graph @ SV212 @ SV839 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1378 @ tc_bool ) ) @ SV839 @ SV1378 @ SV1855 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4076]) ).
thf(4715,plain,
! [SV1856: $i,SV1379: $i,SV840: $i,SV213: $i] :
( ( c_Nitpick_Ofold__graph_H @ SV213 @ SV840 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1379 @ tc_bool ) ) @ SV840 @ SV1379 @ SV1856 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4077]) ).
thf(4716,plain,
! [SV1857: $i,SV1380: $i,SV841: $i,SV214: $i] :
( ( ! [SY6865: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ SV214 @ SV841 @ SV1380 @ SV1857 ) @ ( c_Set_Ovimage @ SV214 @ SY6865 @ SV1380 @ SV1857 ) @ ( tc_fun @ SV1380 @ tc_bool ) )
| ~ ( c_lessequals @ SV841 @ SY6865 @ ( tc_fun @ SV1857 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4078]) ).
thf(4717,plain,
! [SV1381: $i,SV842: $i,SV215: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV215 @ SV842 @ ( tc_fun @ SV1381 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1381 @ tc_bool ) ) )
= $true )
| ( ( SV842
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1381 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4079]) ).
thf(4718,plain,
! [SV1382: $i,SV843: $i,SV216: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV216 @ SV843 @ ( tc_fun @ SV1382 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1382 @ tc_bool ) ) )
= $true )
| ( ( SV216
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1382 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4080]) ).
thf(4719,plain,
! [SV217: $i,SV1858: $i] :
( ( ( ! [SY6866: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1858 @ SY6866 @ SV217 )
!= ( c_Orderings_Obot__class_Obot @ SV217 ) )
| ( SV1858
= ( c_Orderings_Obot__class_Obot @ SV217 ) ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV217 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4081]) ).
thf(4720,plain,
! [SV218: $i,SV1859: $i] :
( ( ( ! [SY6867: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1859 @ SY6867 @ SV218 )
!= ( c_Orderings_Obot__class_Obot @ SV218 ) )
| ( SY6867
= ( c_Orderings_Obot__class_Obot @ SV218 ) ) ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV218 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4082]) ).
thf(4721,plain,
! [SV1385: $i,SV846: $i,SV221: $i] :
( ( ( c_lessequals @ SV221 @ SV846 @ ( tc_fun @ SV1385 @ tc_bool ) )
= $true )
| ( ( ! [SY6213: $i] :
~ ( c_lessequals @ SV221 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY6213 @ SV846 @ ( tc_fun @ SV1385 @ tc_bool ) ) @ ( tc_fun @ SV1385 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4085]) ).
thf(4722,plain,
! [SV1386: $i,SV847: $i,SV222: $i] :
( ( ( c_lessequals @ SV222 @ SV847 @ ( tc_fun @ SV1386 @ tc_bool ) )
= $true )
| ( ( ! [SY6214: $i] :
~ ( c_lessequals @ SV222 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV847 @ SY6214 @ ( tc_fun @ SV1386 @ tc_bool ) ) @ ( tc_fun @ SV1386 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4086]) ).
thf(4723,plain,
! [SV848: $i,SV223: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV223 )
= $false )
| ( ( ! [SY5112: $i] :
( ( c_lessequals @ SV848 @ SY5112 @ SV223 )
| ! [SY5113: $i] :
~ ( c_lessequals @ SV848 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5112 @ SY5113 @ SV223 ) @ SV223 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4087]) ).
thf(4724,plain,
! [SV849: $i,SV224: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV224 )
= $false )
| ( ( ! [SY5114: $i] :
( ( c_lessequals @ SV849 @ SY5114 @ SV224 )
| ! [SY5115: $i] :
~ ( c_lessequals @ SV849 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5115 @ SY5114 @ SV224 ) @ SV224 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4088]) ).
thf(4725,plain,
! [SV850: $i,SV225: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV225 )
= $false )
| ( ( ! [SY5116: $i,SY5117: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV850 @ SY5116 @ SV225 ) @ SY5117 @ SV225 )
| ~ ( c_lessequals @ SV850 @ SY5117 @ SV225 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4089]) ).
thf(4726,plain,
! [SV851: $i,SV226: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV226 )
= $false )
| ( ( ! [SY5118: $i,SY5119: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV851 @ SY5118 @ SV226 ) @ SY5119 @ SV226 )
| ~ ( c_lessequals @ SY5118 @ SY5119 @ SV226 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4090]) ).
thf(4727,plain,
! [SV852: $i,SV227: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV227 )
= $false )
| ( ( ! [SY5120: $i] :
( ( c_lessequals @ SV852 @ SY5120 @ SV227 )
| ! [SY5121: $i] :
~ ( c_lessequals @ SV852 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5120 @ SY5121 @ SV227 ) @ SV227 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4091]) ).
thf(4728,plain,
! [SV853: $i,SV228: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV228 )
= $false )
| ( ( ! [SY5122: $i] :
( ( c_lessequals @ SV853 @ SY5122 @ SV228 )
| ! [SY5123: $i] :
~ ( c_lessequals @ SV853 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5123 @ SY5122 @ SV228 ) @ SV228 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4092]) ).
thf(4729,plain,
! [SV1860: $i,SV1387: $i,SV854: $i,SV229: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV229 @ SV854 @ ( tc_fun @ SV1387 @ tc_bool ) ) @ SV1860 @ ( tc_fun @ SV1387 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV229 @ SV1860 @ ( tc_fun @ SV1387 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV854 @ SV1860 @ ( tc_fun @ SV1387 @ tc_bool ) ) @ ( tc_fun @ SV1387 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4093]) ).
thf(4730,plain,
! [SV231: $i,SV1861: $i] :
( ( ( ! [SY6868: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1861 @ SY6868 @ SV231 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY6868 @ SV1861 @ SV231 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV231 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4095]) ).
thf(4731,plain,
! [SV232: $i,SV1862: $i] :
( ( ( ! [SY6869: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1862 @ SY6869 @ SV232 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY6869 @ SV1862 @ SV232 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV232 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4096]) ).
thf(4732,plain,
! [SV234: $i,SV1863: $i] :
( ( ( ! [SY6870: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1863 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1863 @ SY6870 @ SV234 ) @ SV234 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1863 @ SY6870 @ SV234 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV234 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4098]) ).
thf(4733,plain,
! [SV235: $i,SV1864: $i] :
( ( ( ! [SY6871: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1864 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1864 @ SY6871 @ SV235 ) @ SV235 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1864 @ SY6871 @ SV235 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV235 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4099]) ).
thf(4734,plain,
! [SV1865: $i,SV1390: $i,SV857: $i,SV236: $i] :
( ( ! [SY6872: $i] :
( ( c_Set_Ovimage @ SV236 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV857 @ SV1390 @ ( tc_fun @ SV1865 @ tc_bool ) ) @ SY6872 @ SV1865 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ SV236 @ SV857 @ SY6872 @ SV1865 ) @ ( c_Set_Ovimage @ SV236 @ SV1390 @ SY6872 @ SV1865 ) @ ( tc_fun @ SY6872 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4100]) ).
thf(4735,plain,
! [SV1391: $i,SV858: $i,SV237: $i] :
( ( ( ! [SY6218: $i,SY6219: $i] :
( ( c_Fun_Ofun__upd @ SV237 @ SV858 @ SV1391 @ SY6218 @ SY6219 )
!= SV237 ) )
= $true )
| ( ( ( hAPP @ SV237 @ SV858 )
= SV1391 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4101]) ).
thf(4736,plain,
! [SV1866: $i,SV1392: $i,SV859: $i,SV238: $i] :
( ( ( c_Fun_Oinj__on @ SV238 @ SV859 @ SV1392 @ SV1866 )
| ! [SY6873: $i] :
~ ( c_Fun_Oinj__on @ SV238 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY6873 @ SV859 @ ( tc_fun @ SV1392 @ tc_bool ) ) @ SV1392 @ SV1866 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4102]) ).
thf(4737,plain,
! [SV1867: $i,SV1393: $i,SV860: $i,SV239: $i] :
( ( ( c_Fun_Oinj__on @ SV239 @ SV860 @ SV1393 @ SV1867 )
| ! [SY6874: $i] :
~ ( c_Fun_Oinj__on @ SV239 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV860 @ SY6874 @ ( tc_fun @ SV1393 @ tc_bool ) ) @ SV1393 @ SV1867 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4103]) ).
thf(4738,plain,
! [SV1868: $i,SV1394: $i,SV861: $i,SV240: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV240 @ SV861 @ ( tc_fun @ SV1394 @ tc_bool ) ) @ SV1868 @ ( tc_fun @ SV1394 @ tc_bool ) )
| ~ ( c_lessequals @ SV240 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV861 @ SV1868 @ ( tc_fun @ SV1394 @ tc_bool ) ) @ ( tc_fun @ SV1394 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4104]) ).
thf(4739,plain,
! [SV1869: $i,SV1395: $i,SV862: $i,SV241: $i] :
( ( ( c_lessequals @ SV241 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV862 @ SV1395 @ ( tc_fun @ SV1869 @ tc_bool ) ) @ ( tc_fun @ SV1869 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV241 @ SV862 @ ( tc_fun @ SV1869 @ tc_bool ) ) @ SV1395 @ ( tc_fun @ SV1869 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4105]) ).
thf(4740,plain,
! [SV863: $i,SV242: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV242 )
= $false )
| ( ( ! [SY5144: $i] :
( ! [SY5145: $i] : ( c_HOL_Oord__class_Oless @ SV863 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5144 @ SY5145 @ SV242 ) @ SV242 )
| ~ ( c_HOL_Oord__class_Oless @ SV863 @ SY5144 @ SV242 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4106]) ).
thf(4741,plain,
! [SV864: $i,SV243: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV243 )
= $false )
| ( ( ! [SY5146: $i,SY5147: $i] :
( ( c_HOL_Oord__class_Oless @ SV864 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY5146 @ SY5147 @ SV243 ) @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ SV864 @ SY5147 @ SV243 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4107]) ).
thf(4742,plain,
! [SV1396: $i,SV865: $i,SV244: $i] :
( ( ( ~ ( class_HOL_Oord @ SV244 ) )
= $true )
| ( ( ! [SY6226: $i] :
( ( c_lessequals @ ( hAPP @ SV865 @ SV1396 ) @ ( hAPP @ SY6226 @ SV1396 ) @ SV244 )
| ! [SY5150: $i] :
~ ( c_lessequals @ SV865 @ SY6226 @ ( tc_fun @ SY5150 @ SV244 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4108]) ).
thf(4743,plain,
! [SV1397: $i,SV866: $i,SV245: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV245 ) @ SV866 ) @ SV1397 ) )
= $true )
| ( ( ! [SY6228: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV245 ) @ SV866 ) @ SY6228 ) )
| ~ ( c_lessequals @ SY6228 @ SV1397 @ ( tc_fun @ SV245 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4109]) ).
thf(4744,plain,
! [SV1398: $i,SV867: $i,SV246: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV246 ) @ SV867 ) @ SV1398 ) )
= $true )
| ( ( ! [SY6229: $i] :
( ~ ( c_lessequals @ SY6229 @ SV1398 @ ( tc_fun @ SV246 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV246 ) @ SV867 ) @ SY6229 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4110]) ).
thf(4745,plain,
! [SV1399: $i,SV868: $i,SV247: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV247 ) @ SV868 ) @ SV1399 ) )
= $true )
| ( ( ! [SY6230: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV247 ) @ SV868 ) @ SY6230 ) )
| ~ ( c_lessequals @ SY6230 @ SV1399 @ ( tc_fun @ SV247 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4111]) ).
thf(4746,plain,
! [SV1400: $i,SV869: $i,SV248: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV248 ) @ SV869 ) @ SV1400 ) )
= $true )
| ( ( ! [SY6231: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV248 ) @ SV869 ) @ SY6231 ) )
| ~ ( c_lessequals @ SY6231 @ SV1400 @ ( tc_fun @ SV248 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4112]) ).
thf(4747,plain,
! [SV1401: $i,SV870: $i,SV249: $i] :
( ( ( ! [SY6232: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV249 ) @ SV870 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1401 @ SY6232 @ ( tc_fun @ SV249 @ tc_bool ) ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV249 ) @ SV870 ) @ SV1401 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4113]) ).
thf(4748,plain,
! [SV1870: $i,SV1402: $i,SV871: $i,SV250: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV250 ) @ SV871 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1402 @ SV1870 @ ( tc_fun @ SV250 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV250 ) @ SV871 ) @ SV1870 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4114]) ).
thf(4749,plain,
! [SV1403: $i,SV872: $i,SV251: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV251 ) @ SV872 ) @ SV1403 ) )
= $true )
| ( ( ! [SY6234: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV251 ) @ SV872 ) @ SY6234 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV251 ) @ SV872 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY6234 @ SV1403 @ ( tc_fun @ SV251 @ tc_bool ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4115]) ).
thf(4750,plain,
! [SV1871: $i,SV1404: $i,SV873: $i,SV253: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV253 ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV873 @ SV1404 @ SV1871 @ SV253 ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV873 @ SV1404 @ ( tc_fun @ SV253 @ tc_bool ) ) ) )
| ! [SY6875: $i] :
( ~ ( hBOOL @ ( hAPP @ SV1871 @ SY6875 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV253 ) @ SY6875 ) @ SV1404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4116]) ).
thf(4751,plain,
! [SV1872: $i,SV1405: $i,SV874: $i,SV254: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV254 ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV874 @ SV1405 @ SV1872 @ SV254 ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV874 @ SV1405 @ ( tc_fun @ SV254 @ tc_bool ) ) ) )
| ! [SY6876: $i] :
( ~ ( hBOOL @ ( hAPP @ SV1872 @ SY6876 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV254 ) @ SY6876 ) @ SV874 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4117]) ).
thf(4752,plain,
! [SV1406: $i,SV875: $i,SV255: $i] :
( ( ( ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ SV255 @ SV875 @ SV1406 ) @ SV1406 )
= ( c_Finite__Set_Ocard @ SV875 @ SV1406 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1406 ) @ SV255 ) @ SV875 ) )
| ~ ( c_Finite__Set_Ofinite @ SV875 @ SV1406 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4118]) ).
thf(4753,plain,
! [SV1873: $i,SV1407: $i,SV876: $i,SV256: $i] :
( ( ( ( c_Set_Oimage @ ( c_COMBK @ SV256 @ SV876 @ SV1407 ) @ SV1873 @ SV1407 @ SV876 )
= ( c_Set_Oinsert @ SV256 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV876 @ tc_bool ) ) @ SV876 ) )
| ( SV1873
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1407 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4119]) ).
thf(4754,plain,
! [SV1874: $i,SV1408: $i,SV877: $i,SV257: $i] :
( ( ! [SY6877: $i,SY6878: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ofun__upd @ SV257 @ SV877 @ SV1408 @ SV1874 @ SY6877 ) @ SY6878 @ SV1874 @ SY6877 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6877 ) @ SV1408 ) @ ( c_Set_Oimage @ SV257 @ SY6878 @ SV1874 @ SY6877 ) ) )
| ~ ( c_Fun_Oinj__on @ SV257 @ SY6878 @ SV1874 @ SY6877 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4120]) ).
thf(4755,plain,
! [SV1875: $i,SV1410: $i,SV879: $i,SV259: $i] :
( ( ( c_lessequals @ SV259 @ ( c_Set_Oinsert @ SV879 @ SV1410 @ SV1875 ) @ ( tc_fun @ SV1875 @ tc_bool ) )
| ~ ( c_lessequals @ SV259 @ SV1410 @ ( tc_fun @ SV1875 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV259 @ ( c_Set_Oinsert @ SV879 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1875 @ tc_bool ) ) @ SV1875 ) @ ( tc_fun @ SV1875 @ tc_bool ) ) @ SV1410 @ ( tc_fun @ SV1875 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4122]) ).
thf(4756,plain,
! [SV1876: $i,SV1411: $i,SV880: $i,SV260: $i] :
( ( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ SV260 @ SV880 @ SV1411 @ SV1876 ) @ SV1876 )
= ( c_Finite__Set_Ocard @ SV880 @ SV1411 ) )
| ~ ( c_Fun_Oinj__on @ SV260 @ SV880 @ SV1411 @ SV1876 )
| ~ ( c_Finite__Set_Ofinite @ SV880 @ SV1411 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4123]) ).
thf(4757,plain,
! [SV1877: $i,SV1412: $i,SV881: $i,SV261: $i] :
( ( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ SV261 @ SV881 @ SV1412 @ SV1877 ) @ SV1877 )
!= ( c_Finite__Set_Ocard @ SV881 @ SV1412 ) )
| ~ ( c_Finite__Set_Ofinite @ SV881 @ SV1412 )
| ( c_Fun_Oinj__on @ SV261 @ SV881 @ SV1412 @ SV1877 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4124]) ).
thf(4758,plain,
! [SV1413: $i,SV882: $i,SV262: $i] :
( ( ( ( c_Set_Oimage @ SV262 @ SV882 @ SV1413 @ SV1413 )
= SV882 )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV262 @ SV882 @ SV1413 @ SV1413 )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV262 @ SV882 @ SV1413 @ SV1413 ) @ SV882 @ ( tc_fun @ SV1413 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV882 @ SV1413 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4125]) ).
thf(4759,plain,
! [SV1414: $i,SV883: $i,SV263: $i] :
( ( ( c_Fun_Oinj__on @ SV263 @ SV883 @ SV1414 @ SV1414 )
= $true )
| ( ( ~ ( c_lessequals @ SV883 @ ( c_Set_Oimage @ SV263 @ SV883 @ SV1414 @ SV1414 ) @ ( tc_fun @ SV1414 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV883 @ SV1414 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4126]) ).
thf(4760,plain,
! [SV1878: $i,SV1415: $i,SV884: $i,SV264: $i] :
( ( ( ( c_Set_Ovimage @ ( c_COMBK @ SV264 @ SV884 @ SV1415 ) @ SV1878 @ SV1415 @ SV884 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1415 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV884 ) @ SV264 ) @ SV1878 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4127]) ).
thf(4761,plain,
! [SV1879: $i,SV1416: $i,SV885: $i,SV265: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV265 @ ( c_Set_Oinsert @ SV885 @ SV1416 @ SV1879 ) @ ( tc_fun @ SV1879 @ tc_bool ) )
| ~ ( c_lessequals @ SV265 @ SV1416 @ ( tc_fun @ SV1879 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1879 ) @ SV885 ) @ SV265 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV265 @ SV1416 @ ( tc_fun @ SV1879 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4128]) ).
thf(4762,plain,
! [SV1880: $i,SV1417: $i,SV886: $i,SV266: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV266 @ ( c_Set_Oinsert @ SV886 @ SV1417 @ SV1880 ) @ ( tc_fun @ SV1880 @ tc_bool ) )
| ~ ( c_lessequals @ SV266 @ SV1417 @ ( tc_fun @ SV1880 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1880 ) @ SV886 ) @ SV266 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1880 ) @ SV886 ) @ SV1417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4129]) ).
thf(4763,plain,
! [SV1418: $i,SV887: $i,SV267: $i] :
( ( ( c_lessequals @ SV267 @ SV887 @ ( tc_fun @ SV1418 @ tc_bool ) )
= $true )
| ( ( ! [SY6249: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1418 ) @ SY6249 ) @ SV267 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1418 ) @ SY6249 ) @ SV887 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV267 @ ( c_Set_Oinsert @ SY6249 @ SV887 @ SV1418 ) @ ( tc_fun @ SV1418 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4130]) ).
thf(4764,plain,
! [SV1881: $i,SV1419: $i,SV888: $i,SV268: $i] :
( ( ! [SY6879: $i] :
( ( ( c_Set_Oimage @ SV268 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV888 @ SV1419 @ ( tc_fun @ SV1881 @ tc_bool ) ) @ SV1881 @ SY6879 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV268 @ SV888 @ SV1881 @ SY6879 ) @ ( c_Set_Oimage @ SV268 @ SV1419 @ SV1881 @ SY6879 ) @ ( tc_fun @ SY6879 @ tc_bool ) ) )
| ! [SY6880: $i] :
( ~ ( c_lessequals @ SV1419 @ SY6880 @ ( tc_fun @ SV1881 @ tc_bool ) )
| ~ ( c_lessequals @ SV888 @ SY6880 @ ( tc_fun @ SV1881 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV268 @ SY6880 @ SV1881 @ SY6879 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4131]) ).
thf(4765,plain,
! [SV1882: $i,SV1420: $i,SV889: $i,SV269: $i] :
( ( ! [SY6881: $i] :
( ( c_Set_Ovimage @ SV269 @ ( c_Set_Oinsert @ SV889 @ SV1420 @ SV1882 ) @ SY6881 @ SV1882 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ SV269 @ ( c_Set_Oinsert @ SV889 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1882 @ tc_bool ) ) @ SV1882 ) @ SY6881 @ SV1882 ) @ ( c_Set_Ovimage @ SV269 @ SV1420 @ SY6881 @ SV1882 ) @ ( tc_fun @ SY6881 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4132]) ).
thf(4766,plain,
! [SV1883: $i,SV1421: $i,SV890: $i,SV270: $i] :
( ( ! [SY6882: $i] :
( ( ( c_Set_Oimage @ SV270 @ ( c_HOL_Ominus__class_Ominus @ SV890 @ SV1421 @ ( tc_fun @ SV1883 @ tc_bool ) ) @ SV1883 @ SY6882 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV270 @ SV890 @ SV1883 @ SY6882 ) @ ( c_Set_Oimage @ SV270 @ SV1421 @ SV1883 @ SY6882 ) @ ( tc_fun @ SY6882 @ tc_bool ) ) )
| ! [SY6883: $i] :
( ~ ( c_lessequals @ SV1421 @ SY6883 @ ( tc_fun @ SV1883 @ tc_bool ) )
| ~ ( c_lessequals @ SV890 @ SY6883 @ ( tc_fun @ SV1883 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV270 @ SY6883 @ SV1883 @ SY6882 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4133]) ).
thf(4767,plain,
! [SV1884: $i,SV1422: $i,SV891: $i,SV271: $i] :
( ( ! [SY6884: $i] :
( ( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ SV271 @ SV891 @ SV1422 @ SV1884 @ ( tc_Option_Ooption @ SY6884 ) ) @ SV1884 @ SY6884 )
= ( c_Set_Oinsert @ SV891 @ ( c_Map_Odom @ SV271 @ SV1884 @ SY6884 ) @ SV1884 ) )
| ( SV1422
= ( c_Option_Ooption_ONone @ SY6884 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4134]) ).
thf(4768,plain,
! [SV1885: $i,SV1423: $i,SV892: $i,SV272: $i] :
( ( ! [SY6885: $i] :
( ! [SY6886: $i] : ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ SV272 @ SV892 @ ( c_Option_Ooption_ONone @ SV1423 ) @ SV1885 @ ( tc_Option_Ooption @ SV1423 ) ) @ ( c_Fun_Ofun__upd @ SY6885 @ SV892 @ ( c_Option_Ooption_OSome @ SY6886 @ SV1423 ) @ SV1885 @ ( tc_Option_Ooption @ SV1423 ) ) @ SV1885 @ SV1423 )
| ~ ( c_Map_Omap__le @ SV272 @ SY6885 @ SV1885 @ SV1423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4135]) ).
thf(4769,plain,
! [SV1886: $i,SV1424: $i,SV893: $i,SV273: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV273 @ ( c_Set_Oinsert @ SV893 @ SV1424 @ SV1886 ) @ ( tc_fun @ SV1886 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1886 ) @ SV893 ) @ SV273 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV273 @ ( c_Set_Oinsert @ SV893 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1886 @ tc_bool ) ) @ SV1886 ) @ ( tc_fun @ SV1886 @ tc_bool ) ) @ SV1424 @ ( tc_fun @ SV1886 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1886 ) @ SV893 ) @ SV1424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4136]) ).
thf(4770,plain,
! [SV1425: $i,SV895: $i,SV275: $i] :
( ( ( c_Com_Ocom_OBODY @ SV275 )
= ( c_Com_Ocom_OWhile @ SV895 @ SV1425 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4138]) ).
thf(4771,plain,
! [SV1426: $i,SV896: $i,SV276: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV276 @ SV896 @ ( tc_fun @ SV1426 @ tc_bool ) ) @ SV1426 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV276 @ SV1426 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4139]) ).
thf(4772,plain,
! [SV1887: $i,SV1427: $i,SV897: $i,SV277: $i] :
( ( ( c_Com_Ocom_OBODY @ SV277 )
!= ( c_Com_Ocom_OLocal @ SV897 @ SV1427 @ SV1887 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4140]) ).
thf(4773,plain,
! [SV1888: $i,SV1428: $i,SV898: $i,SV278: $i] :
( ( ! [SY6887: $i] :
( ( c_Fun_Oinj__on @ SV278 @ ( c_HOL_Ominus__class_Ominus @ SV898 @ SV1428 @ ( tc_fun @ SV1888 @ tc_bool ) ) @ SV1888 @ SY6887 )
| ~ ( c_Fun_Oinj__on @ SV278 @ SV898 @ SV1888 @ SY6887 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4141]) ).
thf(4774,plain,
! [SV1889: $i,SV1429: $i,SV899: $i,SV279: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV279 @ tc_bool ) )
!= ( c_Set_Oimage @ SV899 @ SV1429 @ SV1889 @ SV279 ) )
| ( SV1429
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1889 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4142]) ).
thf(4775,plain,
! [SV1890: $i,SV1430: $i,SV900: $i,SV280: $i] :
( ( ! [SY6888: $i] :
( ( c_Com_Ocom_OWhile @ SV280 @ SV900 )
!= ( c_Com_Ocom_OLocal @ SV1430 @ SV1890 @ SY6888 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4143]) ).
thf(4776,plain,
! [SV1431: $i,SV901: $i,SV281: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV281 @ SV901 ) ) @ SV1431 ) @ SV1431 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV281 @ SV1431 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4144]) ).
thf(4777,plain,
! [SV1891: $i,SV1432: $i,SV902: $i,SV282: $i] :
( ( ! [SY6889: $i] :
( ( c_Set_Ovimage @ SV282 @ ( c_HOL_Ominus__class_Ominus @ SV902 @ SV1432 @ ( tc_fun @ SV1891 @ tc_bool ) ) @ SY6889 @ SV1891 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Ovimage @ SV282 @ SV902 @ SY6889 @ SV1891 ) @ ( c_Set_Ovimage @ SV282 @ SV1432 @ SY6889 @ SV1891 ) @ ( tc_fun @ SY6889 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4145]) ).
thf(4778,plain,
! [SV1892: $i,SV1433: $i,SV903: $i,SV283: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV283 @ ( c_Set_Oinsert @ SV903 @ SV1433 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1892 ) @ SV903 ) @ SV283 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV283 @ ( c_Set_Oinsert @ SV903 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1892 @ tc_bool ) ) @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) ) @ SV1433 @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV283 @ SV1433 @ ( tc_fun @ SV1892 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4146]) ).
thf(4779,plain,
! [SV1434: $i,SV905: $i,SV285: $i] :
( ( ( c_Com_Ocom_OAss @ SV285 @ SV905 )
= ( c_Com_Ocom_OBODY @ SV1434 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4147]) ).
thf(4780,plain,
! [SV1893: $i,SV1435: $i,SV906: $i,SV286: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV286 @ SV906 )
!= ( c_Com_Ocom_OSemi @ SV1435 @ SV1893 ) )
| ( SV906 = SV1893 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4148]) ).
thf(4781,plain,
! [SV1436: $i,SV907: $i,SV287: $i] :
( ( ( ! [SY6274: $i] :
( ( c_Com_Ocom_OSemi @ SV287 @ SV907 )
!= ( c_Com_Ocom_OSemi @ SV1436 @ SY6274 ) ) )
= $true )
| ( ( SV287 = SV1436 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4149]) ).
thf(4782,plain,
! [SV1894: $i,SV1437: $i,SV908: $i,SV288: $i] :
( ( ( c_Com_Ocom_OSemi @ SV288 @ SV908 )
!= ( c_Com_Ocom_OWhile @ SV1437 @ SV1894 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4150]) ).
thf(4783,plain,
! [SV1895: $i,SV1438: $i,SV909: $i,SV289: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV289 @ ( c_Set_Oinsert @ SV909 @ SV1438 @ SV1895 ) @ ( tc_fun @ SV1895 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV289 @ SV1438 @ ( tc_fun @ SV1895 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV909 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1895 @ tc_bool ) ) @ SV1895 ) @ ( tc_fun @ SV1895 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4151]) ).
thf(4784,plain,
! [SV1896: $i,SV1439: $i,SV910: $i,SV290: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV290 @ ( c_Set_Oinsert @ SV910 @ SV1439 @ SV1896 ) @ ( tc_fun @ SV1896 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV290 @ ( c_Set_Oinsert @ SV910 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1896 @ tc_bool ) ) @ SV1896 ) @ ( tc_fun @ SV1896 @ tc_bool ) ) @ SV1439 @ ( tc_fun @ SV1896 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4152]) ).
thf(4785,plain,
! [SV1897: $i,SV1440: $i,SV911: $i,SV291: $i] :
( ( ! [SY6890: $i] :
( ( c_Com_Ocom_OSemi @ SV291 @ SV911 )
!= ( c_Com_Ocom_OCond @ SV1440 @ SV1897 @ SY6890 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4153]) ).
thf(4786,plain,
! [SV912: $i,SV1898: $i,SV292: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV292 @ SV1898 @ ( tc_fun @ SV912 @ tc_bool ) ) @ SV912 )
| ~ ( c_Finite__Set_Ofinite @ SV1898 @ SV912 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV292 @ SV912 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4154]) ).
thf(4787,plain,
! [SV1441: $i,SV913: $i,SV293: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV293 @ SV913 @ ( tc_fun @ SV1441 @ tc_bool ) ) @ SV1441 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV293 @ SV1441 )
| ~ ( c_Finite__Set_Ofinite @ SV913 @ SV1441 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4155]) ).
thf(4788,plain,
! [SV1442: $i,SV914: $i,SV294: $i] :
( ( ( c_Set_Oinsert @ SV294 @ SV914 @ SV1442 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1442 @ tc_bool ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4156]) ).
thf(4789,plain,
! [SV1899: $i,SV1443: $i,SV915: $i,SV295: $i] :
( ( ! [SY6891: $i] :
( ( c_Com_Ocom_OSemi @ SV295 @ SV915 )
!= ( c_Com_Ocom_OLocal @ SV1443 @ SV1899 @ SY6891 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4157]) ).
thf(4790,plain,
! [SV1900: $i,SV1444: $i,SV916: $i,SV296: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV296 ) @ SV916 ) @ ( c_Set_Ovimage @ SV1444 @ ( c_Set_Oinsert @ ( hAPP @ SV1444 @ SV916 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1900 @ tc_bool ) ) @ SV1900 ) @ SV296 @ SV1900 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4158]) ).
thf(4791,plain,
! [SV1901: $i,SV1445: $i,SV917: $i,SV297: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV297 @ SV917 @ SV1445 ) @ ( c_Set_Oinsert @ SV297 @ SV1901 @ SV1445 ) @ ( tc_fun @ SV1445 @ tc_bool ) )
= ( c_Set_Oinsert @ SV297 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV917 @ SV1901 @ ( tc_fun @ SV1445 @ tc_bool ) ) @ SV1445 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4159]) ).
thf(4792,plain,
! [SV1902: $i,SV1446: $i,SV918: $i,SV298: $i] :
( ( ( c_Map_Omap__le @ SV298 @ SV918 @ SV1446 @ SV1902 )
| ! [SY6892: $i] :
~ ( c_Map_Omap__le @ ( c_Map_Omap__add @ SY6892 @ SV298 @ SV1446 @ SV1902 ) @ SV918 @ SV1446 @ SV1902 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4160]) ).
thf(4793,plain,
! [SV1448: $i,SV920: $i,SV300: $i] :
( ( ( c_Finite__Set_Ofinite @ ( hAPP @ SV300 @ SV920 ) @ SV1448 )
= $true )
| ( ( ! [SY6286: $i,SY6287: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6286 ) @ SV920 ) @ SY6287 ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY6287 @ SV300 @ SY6286 @ ( tc_fun @ SV1448 @ tc_bool ) ) @ SV1448 )
| ~ ( c_Finite__Set_Ofinite @ SY6287 @ SY6286 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4162]) ).
thf(4794,plain,
! [SV1903: $i,SV1450: $i,SV922: $i,SV302: $i] :
( ( ( c_Map_Omap__le @ SV302 @ SV922 @ SV1450 @ SV1903 )
| ! [SY6893: $i] :
( ~ ( c_Map_Omap__le @ SY6893 @ SV922 @ SV1450 @ SV1903 )
| ~ ( c_Map_Omap__le @ SV302 @ SY6893 @ SV1450 @ SV1903 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4164]) ).
thf(4795,plain,
! [SV1904: $i,SV1451: $i,SV923: $i,SV303: $i] :
( ( ! [SY6894: $i] :
( ( c_Com_Ocom_OLocal @ SV303 @ SV923 @ SV1451 )
!= ( c_Com_Ocom_OAss @ SV1904 @ SY6894 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4165]) ).
thf(4796,plain,
! [SV304: $i,SV924: $i,SV1905: $i] :
( ( ( ( SV1905 = SV924 )
| ! [SY6895: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1905 @ SV304 @ SY6895 ) @ SV924 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV304 @ SV924 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4166]) ).
thf(4797,plain,
! [SV1906: $i,SV1452: $i,SV925: $i,SV305: $i] :
( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV305 @ SV925 @ SV1452 @ ( tc_fun @ SV1906 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1906 @ tc_bool ) ) )
| ! [SY6896: $i] :
( ( ( hAPP @ SV925 @ SY6896 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1906 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1452 ) @ SY6896 ) @ SV305 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4167]) ).
thf(4798,plain,
! [SV1453: $i,SV926: $i,SV306: $i] :
( ( ( c_Com_Ocom_OBODY @ SV306 )
= ( c_Com_Ocom_OAss @ SV926 @ SV1453 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4168]) ).
thf(4799,plain,
! [SV1907: $i,SV1454: $i,SV927: $i,SV307: $i] :
( ( ! [SY6897: $i] :
( ( c_Com_Ocom_OCond @ SV307 @ SV927 @ SV1454 )
!= ( c_Com_Ocom_OWhile @ SV1907 @ SY6897 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4169]) ).
thf(4800,plain,
! [SV1908: $i,SV1455: $i,SV928: $i,SV308: $i] :
( ( ! [SY6898: $i,SY6899: $i] :
( ( c_Com_Ocom_OCond @ SV308 @ SV928 @ SV1455 )
!= ( c_Com_Ocom_OLocal @ SV1908 @ SY6898 @ SY6899 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4170]) ).
thf(4801,plain,
! [SV309: $i,SV1909: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1909 @ ( c_Orderings_Obot__class_Obot @ SV309 ) @ SV309 )
= ( c_Orderings_Obot__class_Obot @ SV309 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV309 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4171]) ).
thf(4802,plain,
! [SV1910: $i,SV310: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ SV310 ) @ SV1910 @ SV310 )
= ( c_Orderings_Obot__class_Obot @ SV310 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV310 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4172]) ).
thf(4803,plain,
! [SV931: $i,SV313: $i,SV1911: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV1911 @ SV313 @ SV931 ) @ SV931 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV313 @ SV931 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4173]) ).
thf(4804,plain,
! [SV1456: $i,SV932: $i,SV314: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV314 @ SV932 @ SV1456 ) @ SV1456 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV932 @ SV1456 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4174]) ).
thf(4805,plain,
! [SV1912: $i,SV1457: $i,SV933: $i,SV316: $i] :
( ( ! [SY6900: $i] :
( ( c_Com_Ocom_OCond @ SV316 @ SV933 @ SV1457 )
!= ( c_Com_Ocom_OSemi @ SV1912 @ SY6900 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4175]) ).
thf(4806,plain,
! [SV317: $i,SV934: $i] :
( ( ( ~ ( c_Com_OWT @ SV934 ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV317 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ SV317 ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV317 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ SV934 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4176]) ).
thf(4807,plain,
! [SV1913: $i,SV1458: $i,SV935: $i,SV318: $i] :
( ( ! [SY6901: $i,SY6902: $i,SY6903: $i,SY6904: $i,SY6905: $i] :
( ( ( hAPP @ SV318 @ ( c_Set_Oinsert @ SV935 @ ( c_Set_Oinsert @ SV1458 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1913 @ tc_bool ) ) @ SV1913 ) @ SV1913 ) )
= ( hAPP @ ( hAPP @ SY6901 @ SV935 ) @ SV1458 ) )
| ! [SY6906: $i,SY6907: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY6902 @ SV318 @ SY6903 @ SY6904 @ SY6905 @ SY6901 @ SY6906 @ SY6907 @ SV1913 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4177]) ).
thf(4808,plain,
! [SV1914: $i,SV1459: $i,SV936: $i,SV319: $i] :
( ( ! [SY6908: $i,SY6909: $i,SY6910: $i,SY6911: $i,SY6912: $i] :
( ( ( hAPP @ SV319 @ ( c_Set_Oinsert @ SV936 @ ( c_Set_Oinsert @ SV1459 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1914 @ tc_bool ) ) @ SV1914 ) @ SV1914 ) )
= ( hAPP @ ( hAPP @ SY6908 @ SV936 ) @ SV1459 ) )
| ! [SY6913: $i,SY6914: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV319 @ SY6909 @ SY6910 @ SY6911 @ SY6908 @ SY6912 @ SY6913 @ SY6914 @ SV1914 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4178]) ).
thf(4809,plain,
! [SV1915: $i,SV1460: $i,SV937: $i,SV320: $i] :
( ( ! [SY6915: $i,SY6916: $i] :
( ( ( c_Com_Ocom_OCond @ SV320 @ SV937 @ SV1460 )
!= ( c_Com_Ocom_OCond @ SV1915 @ SY6915 @ SY6916 ) )
| ( SV1460 = SY6916 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4179]) ).
thf(4810,plain,
! [SV1916: $i,SV1461: $i,SV938: $i,SV321: $i] :
( ( ! [SY6917: $i] :
( ! [SY6918: $i] :
( ( c_Com_Ocom_OCond @ SV321 @ SV938 @ SV1461 )
!= ( c_Com_Ocom_OCond @ SV1916 @ SY6917 @ SY6918 ) )
| ( SV938 = SY6917 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4180]) ).
thf(4811,plain,
! [SV1917: $i,SV1462: $i,SV939: $i,SV322: $i] :
( ( ! [SY6919: $i,SY6920: $i] :
( ( c_Com_Ocom_OCond @ SV322 @ SV939 @ SV1462 )
!= ( c_Com_Ocom_OCond @ SV1917 @ SY6919 @ SY6920 ) )
| ( SV322 = SV1917 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4181]) ).
thf(4812,plain,
! [SV1463: $i,SV942: $i,SV325: $i] :
( ( ( ( c_Option_Ooption_OSome @ SV325 @ SV942 )
!= ( c_Option_Ooption_OSome @ SV1463 @ SV942 ) )
= $true )
| ( ( SV325 = SV1463 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4184]) ).
thf(4813,plain,
! [SV1918: $i,SV1464: $i,SV945: $i,SV328: $i] :
( ( ( c_Com_Ocom_OAss @ SV328 @ SV945 )
!= ( c_Com_Ocom_OWhile @ SV1464 @ SV1918 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4185]) ).
thf(4814,plain,
! [SV1919: $i,SV1465: $i,SV946: $i,SV329: $i] :
( ( ! [SY6921: $i] :
( ( c_Map_Omap__add @ SV329 @ ( c_Map_Omap__add @ SV946 @ SV1465 @ SV1919 @ SY6921 ) @ SV1919 @ SY6921 )
= ( c_Map_Omap__add @ ( c_Map_Omap__add @ SV329 @ SV946 @ SV1919 @ SY6921 ) @ SV1465 @ SV1919 @ SY6921 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4186]) ).
thf(4815,plain,
! [SV1920: $i,SV1466: $i,SV947: $i,SV330: $i] :
( ( ! [SY6922: $i] :
( ( c_Com_Ocom_OAss @ SV330 @ SV947 )
!= ( c_Com_Ocom_OLocal @ SV1466 @ SV1920 @ SY6922 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4187]) ).
thf(4816,plain,
! [SV1921: $i,SV1467: $i,SV949: $i,SV332: $i] :
( ( ( c_Com_Ocom_OCond @ SV332 @ SV949 @ SV1467 )
!= ( c_Com_Ocom_OBODY @ SV1921 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4189]) ).
thf(4817,plain,
! [SV1922: $i,SV1468: $i,SV950: $i,SV333: $i] :
( ( ( c_Com_Ocom_OBODY @ SV333 )
!= ( c_Com_Ocom_OCond @ SV950 @ SV1468 @ SV1922 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4190]) ).
thf(4818,plain,
! [SV951: $i,SV334: $i] :
( ( ( class_Lattices_Olattice @ SV334 )
= $false )
| ( ( ! [SY5332: $i,SY5333: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV951 @ SY5332 @ SV334 ) @ SY5333 @ SV334 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV951 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5332 @ SY5333 @ SV334 ) @ SV334 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4191]) ).
thf(4819,plain,
! [SV952: $i,SV335: $i] :
( ( ( class_Lattices_Olattice @ SV335 )
= $false )
| ( ( ! [SY5334: $i,SY5335: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV952 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5334 @ SY5335 @ SV335 ) @ SV335 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY5334 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV952 @ SY5335 @ SV335 ) @ SV335 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4192]) ).
thf(4820,plain,
! [SV953: $i,SV336: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV336 )
= $false )
| ( ( ! [SY5336: $i,SY5337: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV953 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5336 @ SY5337 @ SV336 ) @ SV336 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY5336 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV953 @ SY5337 @ SV336 ) @ SV336 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4193]) ).
thf(4821,plain,
! [SV954: $i,SV337: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV337 )
= $false )
| ( ( ! [SY5338: $i,SY5339: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV954 @ SY5338 @ SV337 ) @ SY5339 @ SV337 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV954 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY5338 @ SY5339 @ SV337 ) @ SV337 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4194]) ).
thf(4822,plain,
! [SV1923: $i,SV1469: $i,SV955: $i,SV338: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV338 @ SV955 @ ( tc_fun @ SV1469 @ tc_bool ) ) @ SV1923 @ ( tc_fun @ SV1469 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV338 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV955 @ SV1923 @ ( tc_fun @ SV1469 @ tc_bool ) ) @ ( tc_fun @ SV1469 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4195]) ).
thf(4823,plain,
! [SV1924: $i,SV1470: $i,SV956: $i,SV339: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV339 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV956 @ SV1470 @ ( tc_fun @ SV1924 @ tc_bool ) ) @ ( tc_fun @ SV1924 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV956 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV339 @ SV1470 @ ( tc_fun @ SV1924 @ tc_bool ) ) @ ( tc_fun @ SV1924 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4196]) ).
thf(4824,plain,
! [SV1925: $i,SV1471: $i,SV957: $i,SV340: $i] :
( ( ! [SY6923: $i] :
( ( c_Com_Ocom_OLocal @ SV340 @ SV957 @ SV1471 )
!= ( c_Com_Ocom_OWhile @ SV1925 @ SY6923 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4197]) ).
thf(4825,plain,
! [SV1926: $i,SV1472: $i,SV958: $i,SV341: $i] :
( ( ! [SY6924: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV341 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV958 @ ( c_Com_Ocom_OBODY @ SV1472 ) @ SV1926 @ SY6924 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY6924 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY6924 ) ) @ SY6924 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV341 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV958 @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SV1472 ) @ tc_Com_Ocom ) @ SV1926 @ SY6924 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY6924 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY6924 ) ) @ SY6924 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4198]) ).
thf(4826,plain,
! [SV1927: $i,SV1473: $i,SV959: $i,SV342: $i] :
( ( ! [SY6925: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV342 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV959 @ ( c_Com_Ocom_OBODY @ SV1473 ) @ SV1927 @ SY6925 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY6925 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY6925 ) ) @ SY6925 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV959 @ ( c_Com_Ocom_OBODY @ SV1473 ) @ SV1927 @ SY6925 ) @ SV342 @ ( tc_Hoare__Mirabelle_Otriple @ SY6925 ) ) @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV959 @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SV1473 ) @ tc_Com_Ocom ) @ SV1927 @ SY6925 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY6925 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY6925 ) ) @ SY6925 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4199]) ).
thf(4827,plain,
! [SV1474: $i,SV960: $i,SV343: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV343 ) )
= $true )
| ( ( ! [SY6341: $i,SY6342: $i] :
( ( ( c_Finite__Set_Osetsum @ SV960 @ ( c_HOL_Ominus__class_Ominus @ SV1474 @ ( c_Set_Oinsert @ SY6341 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6342 @ tc_bool ) ) @ SY6342 ) @ ( tc_fun @ SY6342 @ tc_bool ) ) @ SY6342 @ SV343 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV960 @ SV1474 @ SY6342 @ SV343 ) @ ( hAPP @ SV960 @ SY6341 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6342 ) @ SY6341 ) @ SV1474 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1474 @ SY6342 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4200]) ).
thf(4828,plain,
! [SV1475: $i,SV961: $i,SV344: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV344 ) )
= $true )
| ( ( ! [SY6343: $i,SY6344: $i] :
( ( ( c_Finite__Set_Osetsum @ SV961 @ ( c_HOL_Ominus__class_Ominus @ SV1475 @ ( c_Set_Oinsert @ SY6343 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6344 @ tc_bool ) ) @ SY6344 ) @ ( tc_fun @ SY6344 @ tc_bool ) ) @ SY6344 @ SV344 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV961 @ SV1475 @ SY6344 @ SV344 ) @ ( hAPP @ SV961 @ SY6343 ) @ SV344 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6344 ) @ SY6343 ) @ SV1475 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1475 @ SY6344 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4201]) ).
thf(4829,plain,
! [SV1928: $i,SV1476: $i,SV962: $i,SV346: $i] :
( ( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ SV346 @ SV962 @ ( c_Option_Ooption_ONone @ SV1476 ) @ SV1928 @ ( tc_Option_Ooption @ SV1476 ) ) @ SV1928 @ SV1476 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ SV346 @ SV1928 @ SV1476 ) @ ( c_Set_Oinsert @ SV962 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1928 @ tc_bool ) ) @ SV1928 ) @ ( tc_fun @ SV1928 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4203]) ).
thf(4830,plain,
! [SV1929: $i,SV1477: $i,SV963: $i,SV347: $i] :
( ( ! [SY6926: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV347 @ ( c_HOL_Ominus__class_Ominus @ SV963 @ SV1477 @ ( tc_fun @ SV1929 @ tc_bool ) ) @ SV1929 @ SY6926 ) @ ( c_Set_Oimage @ SV347 @ ( c_HOL_Ominus__class_Ominus @ SV1477 @ SV963 @ ( tc_fun @ SV1929 @ tc_bool ) ) @ SV1929 @ SY6926 ) @ ( tc_fun @ SY6926 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6926 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SV347 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV963 @ SV1477 @ ( tc_fun @ SV1929 @ tc_bool ) ) @ SV1929 @ SY6926 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4204]) ).
thf(4831,plain,
! [SV1930: $i,SV1478: $i,SV964: $i,SV348: $i] :
( ( ! [SY6927: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV348 @ ( c_HOL_Ominus__class_Ominus @ SV964 @ SV1478 @ ( tc_fun @ SV1930 @ tc_bool ) ) @ SV1930 @ SY6927 ) @ ( c_Set_Oimage @ SV348 @ ( c_HOL_Ominus__class_Ominus @ SV1478 @ SV964 @ ( tc_fun @ SV1930 @ tc_bool ) ) @ SV1930 @ SY6927 ) @ ( tc_fun @ SY6927 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6927 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SV348 @ SV1478 @ SV1930 @ SY6927 )
| ~ ( c_Fun_Oinj__on @ SV348 @ SV964 @ SV1930 @ SY6927 )
| ( c_Fun_Oinj__on @ SV348 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV964 @ SV1478 @ ( tc_fun @ SV1930 @ tc_bool ) ) @ SV1930 @ SY6927 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4205]) ).
thf(4832,plain,
! [SV1931: $i,SV1479: $i,SV965: $i,SV349: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV349 @ ( c_Set_Oinsert @ SV965 @ SV1479 @ SV1931 ) @ ( tc_fun @ SV1931 @ tc_bool ) )
| ~ ( c_lessequals @ SV349 @ SV1479 @ ( tc_fun @ SV1931 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV349 @ ( c_Set_Oinsert @ SV965 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1931 @ tc_bool ) ) @ SV1931 ) @ ( tc_fun @ SV1931 @ tc_bool ) ) @ SV1479 @ ( tc_fun @ SV1931 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1931 ) @ SV965 ) @ SV1479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4206]) ).
thf(4833,plain,
! [SV1932: $i,SV1480: $i,SV966: $i,SV350: $i] :
( ( ! [SY6928: $i,SY6929: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ SV350 @ SV966 @ SV1480 @ SV1932 @ SY6928 ) @ SY6929 @ SV1932 @ SY6928 )
= ( c_Set_Oinsert @ SV1480 @ ( c_Set_Oimage @ SV350 @ ( c_HOL_Ominus__class_Ominus @ SY6929 @ ( c_Set_Oinsert @ SV966 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1932 @ tc_bool ) ) @ SV1932 ) @ ( tc_fun @ SV1932 @ tc_bool ) ) @ SV1932 @ SY6928 ) @ SY6928 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1932 ) @ SV966 ) @ SY6929 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4207]) ).
thf(4834,plain,
! [SV1481: $i,SV967: $i,SV351: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV351 ) )
= $true )
| ( ( ! [SY6354: $i,SY6355: $i] :
( ( ( c_Finite__Set_Osetsum @ SV967 @ ( c_HOL_Ominus__class_Ominus @ SV1481 @ ( c_Set_Oinsert @ SY6354 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6355 @ tc_bool ) ) @ SY6355 ) @ ( tc_fun @ SY6355 @ tc_bool ) ) @ SY6355 @ SV351 )
= ( c_Finite__Set_Osetsum @ SV967 @ SV1481 @ SY6355 @ SV351 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6355 ) @ SY6354 ) @ SV1481 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1481 @ SY6355 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4208]) ).
thf(4835,plain,
! [SV1482: $i,SV968: $i,SV352: $i] :
( ( ( ( c_Finite__Set_Ocard @ ( c_HOL_Ominus__class_Ominus @ SV352 @ ( c_Set_Oinsert @ SV968 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1482 @ tc_bool ) ) @ SV1482 ) @ ( tc_fun @ SV1482 @ tc_bool ) ) @ SV1482 )
= ( c_Finite__Set_Ocard @ SV352 @ SV1482 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1482 ) @ SV968 ) @ SV352 ) )
| ~ ( c_Finite__Set_Ofinite @ SV352 @ SV1482 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4209]) ).
thf(4836,plain,
! [SV1933: $i,SV1483: $i,SV969: $i,SV353: $i] :
( ( ! [SY6930: $i,SY6931: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV969 @ ( c_Com_Ocom_OSemi @ SV1483 @ SV1933 ) @ SY6930 @ SY6931 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY6931 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY6931 ) ) @ SY6931 )
| ! [SY6932: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY6932 @ SV1933 @ SY6930 @ SY6931 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY6931 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY6931 ) ) @ SY6931 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV969 @ SV1483 @ SY6932 @ SY6931 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY6931 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY6931 ) ) @ SY6931 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4210]) ).
thf(4837,plain,
! [SV1934: $i,SV1485: $i,SV971: $i,SV355: $i] :
( ( ! [SY6933: $i,SY6934: $i] :
( ( ( c_Map_Omap__add @ ( c_Fun_Ofun__upd @ SV355 @ SV971 @ ( c_Option_Ooption_OSome @ SV1485 @ SV1934 ) @ SY6933 @ ( tc_Option_Ooption @ SV1934 ) ) @ SY6934 @ SY6933 @ SV1934 )
= ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ SV355 @ SY6934 @ SY6933 @ SV1934 ) @ SV971 @ ( c_Option_Ooption_OSome @ SV1485 @ SV1934 ) @ SY6933 @ ( tc_Option_Ooption @ SV1934 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6933 ) @ SV971 ) @ ( c_Map_Odom @ SY6934 @ SY6933 @ SV1934 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4212]) ).
thf(4838,plain,
! [SV1935: $i,SV1486: $i,SV972: $i,SV356: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV356 @ ( c_Set_Oinsert @ SV972 @ SV1486 @ SV1935 ) @ ( tc_fun @ SV1935 @ tc_bool ) )
| ~ ( c_lessequals @ SV356 @ SV1486 @ ( tc_fun @ SV1935 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV356 @ ( c_Set_Oinsert @ SV972 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1935 @ tc_bool ) ) @ SV1935 ) @ ( tc_fun @ SV1935 @ tc_bool ) ) @ SV1486 @ ( tc_fun @ SV1935 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV356 @ SV1486 @ ( tc_fun @ SV1935 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4213]) ).
thf(4839,plain,
! [SV1936: $i,SV1487: $i,SV973: $i,SV357: $i] :
( ( ( c_Set_Ovimage @ SV357 @ SV973 @ SV1487 @ SV1936 )
= ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_COMBB @ ( c_in @ SV1936 ) @ SV357 @ SV1936 @ ( tc_fun @ ( tc_fun @ SV1936 @ tc_bool ) @ tc_bool ) @ SV1487 ) @ SV1487 @ ( tc_fun @ SV1936 @ tc_bool ) @ tc_bool ) @ SV973 ) @ SV1487 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4214]) ).
thf(4840,plain,
! [SV1937: $i,SV1488: $i,SV974: $i,SV358: $i] :
( ( ! [SY6935: $i,SY6936: $i,SY6937: $i] :
( ( c_Nitpick_Ofold__graph_H @ SV358 @ SV974 @ SV1488 @ ( hAPP @ ( hAPP @ SV358 @ SV1937 ) @ SY6935 ) @ SY6936 @ SY6937 )
| ~ ( c_Nitpick_Ofold__graph_H @ SV358 @ SV974 @ ( c_HOL_Ominus__class_Ominus @ SV1488 @ ( c_Set_Oinsert @ SV1937 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6936 @ tc_bool ) ) @ SY6936 ) @ ( tc_fun @ SY6936 @ tc_bool ) ) @ SY6935 @ SY6936 @ SY6937 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6936 ) @ SV1937 ) @ SV1488 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4215]) ).
thf(4841,plain,
! [SV1938: $i,SV1489: $i,SV975: $i,SV359: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV359 @ ( c_Set_Oinsert @ SV975 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1489 @ tc_bool ) ) @ SV1489 ) @ ( tc_fun @ SV1489 @ tc_bool ) ) @ SV1938 @ ( tc_fun @ SV1489 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1489 ) @ SV975 ) @ SV359 ) )
| ~ ( c_lessequals @ SV359 @ ( c_Set_Oinsert @ SV975 @ SV1938 @ SV1489 ) @ ( tc_fun @ SV1489 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4216]) ).
thf(4842,plain,
! [SV1939: $i,SV1490: $i,SV976: $i,SV360: $i] :
( ( ( c_lessequals @ SV360 @ ( c_Set_Oinsert @ SV976 @ SV1490 @ SV1939 ) @ ( tc_fun @ SV1939 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1939 ) @ SV976 ) @ SV360 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV360 @ ( c_Set_Oinsert @ SV976 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1939 @ tc_bool ) ) @ SV1939 ) @ ( tc_fun @ SV1939 @ tc_bool ) ) @ SV1490 @ ( tc_fun @ SV1939 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4217]) ).
thf(4843,plain,
! [SV1940: $i,SV1491: $i,SV977: $i,SV361: $i] :
( ( ( c_lessequals @ SV361 @ ( c_Set_Oinsert @ SV977 @ SV1491 @ SV1940 ) @ ( tc_fun @ SV1940 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1940 ) @ SV977 ) @ SV361 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV361 @ ( c_Set_Oinsert @ SV977 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1940 @ tc_bool ) ) @ SV1940 ) @ ( tc_fun @ SV1940 @ tc_bool ) ) @ SV1491 @ ( tc_fun @ SV1940 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4218]) ).
thf(4844,plain,
! [SV1941: $i,SV1492: $i,SV978: $i,SV362: $i] :
( ( ( ( c_Finite__Set_Osetsum @ SV362 @ ( c_HOL_Ominus__class_Ominus @ SV978 @ ( c_Set_Oinsert @ SV1492 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1941 @ tc_bool ) ) @ SV1941 ) @ ( tc_fun @ SV1941 @ tc_bool ) ) @ SV1941 @ tc_nat )
= ( c_Finite__Set_Osetsum @ SV362 @ SV978 @ SV1941 @ tc_nat ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1941 ) @ SV1492 ) @ SV978 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4219]) ).
thf(4845,plain,
! [SV1942: $i,SV1493: $i,SV979: $i,SV363: $i] :
( ( ! [SY6938: $i,SY6939: $i,SY6940: $i] :
( ( c_Finite__Set_Ofold__graph @ SV363 @ SV979 @ SV1493 @ ( hAPP @ ( hAPP @ SV363 @ SV1942 ) @ SY6938 ) @ SY6939 @ SY6940 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6939 ) @ SV1942 ) @ SV1493 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV363 @ SV979 @ ( c_HOL_Ominus__class_Ominus @ SV1493 @ ( c_Set_Oinsert @ SV1942 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6939 @ tc_bool ) ) @ SY6939 ) @ ( tc_fun @ SY6939 @ tc_bool ) ) @ SY6938 @ SY6939 @ SY6940 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4220]) ).
thf(4846,plain,
! [SV1943: $i,SV1494: $i,SV980: $i,SV364: $i] :
( ( ( ( c_Set_Oimage @ ( c_COMBK @ SV364 @ SV980 @ SV1494 ) @ SV1943 @ SV1494 @ SV980 )
= ( c_Set_Oinsert @ SV364 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV980 @ tc_bool ) ) @ SV980 ) )
| ! [SY6941: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1494 ) @ SY6941 ) @ SV1943 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4221]) ).
thf(4847,plain,
! [SV1944: $i,SV1495: $i,SV981: $i,SV365: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV365 @ ( c_Set_Oinsert @ SV981 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1495 @ tc_bool ) ) @ SV1495 ) @ ( tc_fun @ SV1495 @ tc_bool ) ) @ SV1944 @ ( tc_fun @ SV1495 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1495 ) @ SV981 ) @ SV365 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1495 ) @ SV981 ) @ SV1944 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV365 @ ( c_Set_Oinsert @ SV981 @ SV1944 @ SV1495 ) @ ( tc_fun @ SV1495 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4222]) ).
thf(4848,plain,
! [SV1496: $i,SV982: $i,SV366: $i] :
( ( ( ( hAPP @ SV366 @ SV982 )
!= ( c_Option_Ooption_ONone @ SV1496 ) )
= $true )
| ( ( ! [SY6380: $i,SY6381: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ SV366 @ SY6380 @ SV1496 ) @ ( c_Set_Oinsert @ SV982 @ SY6381 @ SY6380 ) @ ( tc_fun @ SY6380 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ SV366 @ SY6380 @ SV1496 ) @ SY6381 @ ( tc_fun @ SY6380 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4223]) ).
thf(4849,plain,
! [SV1945: $i,SV1497: $i,SV983: $i,SV367: $i] :
( ( ( c_Com_Ocom_OAss @ SV367 @ SV983 )
!= ( c_Com_Ocom_OSemi @ SV1497 @ SV1945 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4224]) ).
thf(4850,plain,
! [SV368: $i,SV984: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ SV984 ) ) @ SV368 @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SV984 ) @ tc_Com_Ocom ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV368 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ SV984 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4225]) ).
thf(4851,plain,
! [SV1946: $i,SV1498: $i,SV985: $i,SV369: $i] :
( ( ! [SY6942: $i,SY6943: $i] :
( ( c_Com_Ocom_OLocal @ SV369 @ SV985 @ SV1498 )
!= ( c_Com_Ocom_OCond @ SV1946 @ SY6942 @ SY6943 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4226]) ).
thf(4852,plain,
! [SV1947: $i,SV1499: $i,SV986: $i,SV370: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV370 @ SV986 @ SV1499 ) @ SV1947 @ ( tc_fun @ SV1499 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV986 @ SV1947 @ ( tc_fun @ SV1499 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1499 ) @ SV370 ) @ SV1947 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4227]) ).
thf(4853,plain,
! [SV1948: $i,SV1500: $i,SV987: $i,SV371: $i] :
( ( ( c_Fun_Oinj__on @ SV371 @ SV987 @ SV1500 @ SV1948 )
| ! [SY6944: $i] :
~ ( c_Fun_Oinj__on @ SV371 @ ( c_Set_Oinsert @ SY6944 @ SV987 @ SV1500 ) @ SV1500 @ SV1948 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4228]) ).
thf(4854,plain,
! [SV1501: $i,SV988: $i,SV372: $i] :
( ( ( c_Com_Ocom_OBODY @ SV372 )
= ( c_Com_Ocom_OSemi @ SV988 @ SV1501 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4229]) ).
thf(4855,plain,
! [SV989: $i,SV373: $i,SV1949: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1949 ) @ SV373 ) @ ( c_Set_Oinsert @ SV989 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1949 @ tc_bool ) ) @ SV1949 ) ) ) )
= $true )
| ( ( SV373 = SV989 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4230]) ).
thf(4856,plain,
! [SV1502: $i,SV990: $i,SV374: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV374 @ SV990 @ ( tc_fun @ SV1502 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1502 @ tc_bool ) ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV374 @ SV990 @ ( tc_fun @ SV1502 @ tc_bool ) )
= SV374 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4231]) ).
thf(4857,plain,
! [SV375: $i,SV991: $i,SV1950: $i] :
( ( ( ! [SY6945: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1950 ) @ SV991 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY6945 @ ( c_Collect @ SV375 @ SV1950 ) @ ( tc_fun @ SV1950 @ tc_bool ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV375 @ SV991 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4232]) ).
thf(4858,plain,
! [SV992: $i,SV376: $i] :
( ( ( class_Orderings_Opreorder @ SV376 )
= $false )
| ( ( ! [SY5433: $i] :
( ( c_HOL_Oord__class_Oless @ SV992 @ SY5433 @ SV376 )
| ! [SY5434: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY5434 @ SY5433 @ SV376 )
| ~ ( c_HOL_Oord__class_Oless @ SV992 @ SY5434 @ SV376 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4233]) ).
thf(4859,plain,
! [SV1503: $i,SV993: $i,SV377: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV377 @ SV993 @ ( tc_fun @ SV1503 @ tc_bool ) )
= $true )
| ( ( ! [SY6389: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY6389 @ SV993 @ ( tc_fun @ SV1503 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV377 @ SY6389 @ ( tc_fun @ SV1503 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4234]) ).
thf(4860,plain,
! [SV994: $i,SV378: $i] :
( ( ( class_Orderings_Oorder @ SV378 )
= $false )
| ( ( ! [SY5437: $i] :
( ( c_HOL_Oord__class_Oless @ SV994 @ SY5437 @ SV378 )
| ! [SY5438: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV994 @ SY5438 @ SV378 )
| ~ ( c_HOL_Oord__class_Oless @ SY5438 @ SY5437 @ SV378 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4235]) ).
thf(4861,plain,
! [SV1951: $i,SV1504: $i,SV995: $i,SV379: $i] :
( ( ! [SY6946: $i] :
( ( c_Fun_Oinj__on @ SV379 @ ( c_Set_Oinsert @ SV995 @ SV1504 @ SV1951 ) @ SV1951 @ SY6946 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6946 ) @ ( hAPP @ SV379 @ SV995 ) ) @ ( c_Set_Oimage @ SV379 @ ( c_HOL_Ominus__class_Ominus @ SV1504 @ ( c_Set_Oinsert @ SV995 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1951 @ tc_bool ) ) @ SV1951 ) @ ( tc_fun @ SV1951 @ tc_bool ) ) @ SV1951 @ SY6946 ) ) )
| ~ ( c_Fun_Oinj__on @ SV379 @ SV1504 @ SV1951 @ SY6946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4236]) ).
thf(4862,plain,
! [SV1952: $i,SV1505: $i,SV996: $i,SV380: $i] :
( ( ( c_Set_Oinsert @ SV380 @ ( c_Set_Oinsert @ SV996 @ SV1505 @ SV1952 ) @ SV1952 )
= ( c_Set_Oinsert @ SV996 @ ( c_Set_Oinsert @ SV380 @ SV1505 @ SV1952 ) @ SV1952 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4237]) ).
thf(4863,plain,
! [SV1953: $i,SV1506: $i,SV997: $i,SV381: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV381 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV997 @ tc_bool ) ) @ SV1506 @ SV997 @ ( tc_fun @ SV1953 @ tc_bool ) ) @ ( tc_fun @ SV1953 @ tc_bool ) )
= SV381 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4238]) ).
thf(4864,plain,
! [SV1954: $i,SV1507: $i,SV998: $i,SV382: $i] :
( ( ! [SY6947: $i,SY6948: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV382 @ SV998 @ SV1507 @ SV1954 ) @ SY6947 ) @ SY6948 )
= ( hAPP @ ( hAPP @ SV382 @ SY6948 ) @ SY6947 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4239]) ).
thf(4865,plain,
! [SV1508: $i,SV999: $i,SV383: $i] :
( ( ( c_Com_Ocom_OSemi @ SV383 @ SV999 )
= ( c_Com_Ocom_OBODY @ SV1508 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4240]) ).
thf(4866,plain,
! [SV1955: $i,SV1510: $i,SV1003: $i,SV387: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV387 @ SV1003 ) ) @ SV1510 ) @ SV1955 ) )
| ! [SY6949: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV387 @ SV1003 ) ) @ SY6949 ) @ SV1955 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1003 ) @ SV1510 ) @ SY6949 ) )
| ~ ( hBOOL @ ( hAPP @ SV387 @ SV1510 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4244]) ).
thf(4867,plain,
! [SV1005: $i,SV389: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV389 )
= $false )
| ( ( ! [SY5456: $i] :
( ! [SY5457: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV1005 @ SY5456 @ SV389 )
!= ( c_HOL_Ominus__class_Ominus @ SY5457 @ SY5457 @ SV389 ) )
| ( SV1005 = SY5456 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4246]) ).
thf(4868,plain,
! [SV1006: $i,SV390: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV390 )
= $false )
| ( ( ! [SY5458: $i,SY5459: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV1006 @ SV1006 @ SV390 )
!= ( c_HOL_Ominus__class_Ominus @ SY5458 @ SY5459 @ SV390 ) )
| ( SY5458 = SY5459 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4247]) ).
thf(4869,plain,
! [SV1956: $i,SV1513: $i,SV1008: $i,SV392: $i] :
( ( ! [SY6950: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV392 @ SV1008 @ SV1513 ) ) @ SV1956 ) @ SY6950 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1008 ) @ SV1956 ) @ SY6950 ) )
| ~ ( hBOOL @ ( hAPP @ SV392 @ SV1956 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4249]) ).
thf(4870,plain,
! [SV1514: $i,SV1009: $i,SV393: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV393 @ SV1009 ) ) )
= $true )
| ( ( ! [SY6401: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1514 ) @ SV1009 ) @ SY6401 ) )
| ! [SY6402: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV393 @ SV1514 @ SY6402 ) ) @ SV1009 ) @ SY6401 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4250]) ).
thf(4871,plain,
! [SV1957: $i,SV1515: $i,SV1010: $i,SV394: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV394 @ SV1010 ) ) @ SV1515 ) @ SV1957 ) )
| ! [SY6951: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1010 ) @ SY6951 ) @ SV1957 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV394 ) @ SV1515 ) @ SY6951 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4251]) ).
thf(4872,plain,
! [SV1958: $i,SV1517: $i,SV1012: $i,SV396: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Map_Odom @ SV396 @ SV1012 @ SV1517 ) @ ( c_Map_Odom @ SV1958 @ SV1012 @ SV1517 ) @ ( tc_fun @ SV1012 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1012 @ tc_bool ) ) )
| ( ( c_Map_Omap__add @ SV396 @ SV1958 @ SV1012 @ SV1517 )
= ( c_Map_Omap__add @ SV1958 @ SV396 @ SV1012 @ SV1517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4253]) ).
thf(4873,plain,
! [SV1959: $i,SV1518: $i,SV1013: $i,SV397: $i] :
( ( ( ( hAPP @ SV397 @ SV1013 )
!= ( c_Option_Ooption_OSome @ SV1518 @ SV1959 ) )
| ! [SY6952: $i] :
( ( c_Set_Oinsert @ SV1013 @ ( c_Map_Odom @ SV397 @ SY6952 @ SV1959 ) @ SY6952 )
= ( c_Map_Odom @ SV397 @ SY6952 @ SV1959 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4254]) ).
thf(4874,plain,
! [SV399: $i,SV1960: $i] :
( ( ( ! [SY6953: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1960 @ SY6953 @ SV399 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY6953 @ SV1960 @ SV399 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV399 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4256]) ).
thf(4875,plain,
! [SV400: $i,SV1961: $i] :
( ( ( ! [SY6954: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1961 @ SY6954 @ SV400 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SY6954 @ SV1961 @ SV400 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV400 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4257]) ).
thf(4876,plain,
! [SV1962: $i,SV1520: $i,SV1015: $i,SV401: $i] :
( ( ! [SY6955: $i,SY6956: $i,SY6957: $i,SY6958: $i,SY6959: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV401 @ SV1015 @ ( c_COMBC @ SV1520 @ SV1962 @ SV1962 @ tc_bool ) @ ( c_COMBC @ SY6955 @ SV1962 @ SV1962 @ tc_bool ) @ SY6956 @ SY6957 @ SY6958 @ SY6959 @ SV1962 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1015 @ SV401 @ SV1520 @ SY6955 @ SY6957 @ SY6956 @ SY6959 @ SY6958 @ SV1962 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4258]) ).
thf(4877,plain,
! [SV1521: $i,SV1016: $i,SV402: $i] :
( ( c_Com_Ocom_OSKIP
= ( c_Com_Ocom_OCond @ SV402 @ SV1016 @ SV1521 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4259]) ).
thf(4878,plain,
! [SV1523: $i,SV1018: $i,SV404: $i] :
( ( ( ( c_Set_Oinsert @ SV404 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1018 @ tc_bool ) ) @ SV1018 )
!= ( c_Set_Oinsert @ SV1523 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1018 @ tc_bool ) ) @ SV1018 ) )
= $true )
| ( ( SV404 = SV1523 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4261]) ).
thf(4879,plain,
! [SV1963: $i,SV1524: $i,SV1019: $i,SV405: $i] :
( ( ! [SY6960: $i,SY6961: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV405 @ SV1019 @ SV1524 @ SV1963 ) @ SY6960 )
!= ( c_Option_Ooption_OSome @ SY6961 @ SV1963 ) )
| ( ( hAPP @ SV405 @ SY6960 )
= ( c_Option_Ooption_OSome @ SY6961 @ SV1963 ) )
| ( ( hAPP @ SV1019 @ SY6960 )
= ( c_Option_Ooption_OSome @ SY6961 @ SV1963 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4262]) ).
thf(4880,plain,
! [SV1964: $i,SV1525: $i,SV1020: $i,SV406: $i] :
( ( ( ( hAPP @ SV406 @ SV1020 )
!= ( c_Option_Ooption_OSome @ SV1525 @ SV1964 ) )
| ! [SY6962: $i] :
( ( ( hAPP @ SY6962 @ SV1020 )
!= ( c_Option_Ooption_ONone @ SV1964 ) )
| ! [SY6963: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SV406 @ SY6962 @ SY6963 @ SV1964 ) @ SV1020 )
= ( c_Option_Ooption_OSome @ SV1525 @ SV1964 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4263]) ).
thf(4881,plain,
! [SV1965: $i,SV1526: $i,SV1021: $i,SV407: $i] :
( ( ! [SY6964: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV407 @ SV1021 @ SV1526 @ SV1965 ) @ SY6964 )
!= ( c_Option_Ooption_ONone @ SV1965 ) )
| ( ( hAPP @ SV407 @ SY6964 )
= ( c_Option_Ooption_ONone @ SV1965 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4264]) ).
thf(4882,plain,
! [SV1966: $i,SV1527: $i,SV1022: $i,SV408: $i] :
( ( ! [SY6965: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV408 @ SV1022 @ SV1527 @ SV1966 ) @ SY6965 )
!= ( c_Option_Ooption_ONone @ SV1966 ) )
| ( ( hAPP @ SV1022 @ SY6965 )
= ( c_Option_Ooption_ONone @ SV1966 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4265]) ).
thf(4883,plain,
! [SV1528: $i,SV1023: $i,SV409: $i] :
( ( ( ( c_Set_Oinsert @ SV409 @ SV1023 @ SV1528 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1528 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1528 ) @ SV409 ) @ SV1023 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4266]) ).
thf(4884,plain,
! [SV1529: $i,SV1024: $i,SV410: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ SV1024 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1529 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1529 ) ) @ SV1529 )
= $true )
| ( ( ! [SY6424: $i] :
~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ SV1024 @ SY6424 @ ( tc_Hoare__Mirabelle_Otriple @ SV1529 ) ) @ SV1529 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4267]) ).
thf(4885,plain,
! [SV1967: $i,SV1530: $i,SV1025: $i,SV411: $i] :
( ( ( c_Com_Ocom_OLocal @ SV411 @ SV1025 @ SV1530 )
!= ( c_Com_Ocom_OBODY @ SV1967 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4268]) ).
thf(4886,plain,
! [SV1968: $i,SV1531: $i,SV1026: $i,SV412: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV412 @ SV1026 @ SV1531 ) @ SV1968 ) )
| ~ ( hBOOL @ ( hAPP @ SV1026 @ SV1968 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4269]) ).
thf(4887,plain,
! [SV1969: $i,SV1532: $i,SV1027: $i,SV413: $i] :
( ( ! [SY6966: $i] :
( ( c_Set_Oinsert @ ( hAPP @ SV413 @ SV1027 ) @ ( c_Set_Oimage @ SV413 @ SV1532 @ SV1969 @ SY6966 ) @ SY6966 )
= ( c_Set_Oimage @ SV413 @ SV1532 @ SV1969 @ SY6966 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1969 ) @ SV1027 ) @ SV1532 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4270]) ).
thf(4888,plain,
! [SV1970: $i,SV1533: $i,SV1028: $i,SV414: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV414 @ ( c_Set_Oinsert @ SV1028 @ SV1533 @ SV1970 ) @ ( tc_fun @ SV1970 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV414 @ SV1533 @ ( tc_fun @ SV1970 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1970 ) @ SV1028 ) @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4271]) ).
thf(4889,plain,
! [SV1971: $i,SV1534: $i,SV1029: $i,SV415: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV415 @ SV1029 @ SV1534 ) @ SV1971 @ ( tc_fun @ SV1534 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1029 @ SV1971 @ ( tc_fun @ SV1534 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1534 ) @ SV415 ) @ SV1971 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4272]) ).
thf(4890,plain,
! [SV1972: $i,SV1535: $i,SV1030: $i,SV416: $i] :
( ( ! [SY6967: $i] :
( ( c_Com_Ocom_OLocal @ SV416 @ SV1030 @ SV1535 )
!= ( c_Com_Ocom_OSemi @ SV1972 @ SY6967 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4273]) ).
thf(4891,plain,
! [SV1031: $i,SV417: $i] :
( ( ( ( c_Com_Ocom_OBODY @ SV417 )
= ( c_Com_Ocom_OBODY @ SV1031 ) )
= $false )
| ( ( SV417 = SV1031 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4274]) ).
thf(4892,plain,
! [SV1536: $i,SV1032: $i,SV418: $i] :
( ( ( ! [SY6433: $i] :
( ( c_Com_Ocom_OWhile @ SV418 @ SV1032 )
!= ( c_Com_Ocom_OWhile @ SV1536 @ SY6433 ) ) )
= $true )
| ( ( SV418 = SV1536 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4275]) ).
thf(4893,plain,
! [SV1973: $i,SV1537: $i,SV1033: $i,SV419: $i] :
( ( ( ( c_Com_Ocom_OWhile @ SV419 @ SV1033 )
!= ( c_Com_Ocom_OWhile @ SV1537 @ SV1973 ) )
| ( SV1033 = SV1973 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4276]) ).
thf(4894,plain,
! [SV1539: $i,SV1035: $i,SV421: $i] :
( ( ( c_Com_Ocom_OCond @ SV421 @ SV1035 @ SV1539 )
= c_Com_Ocom_OSKIP )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4278]) ).
thf(4895,plain,
! [SV1974: $i,SV1541: $i,SV1037: $i,SV423: $i] :
( ( ! [SY6968: $i] :
( ( c_Com_Ocom_OWhile @ SV423 @ SV1037 )
!= ( c_Com_Ocom_OCond @ SV1541 @ SV1974 @ SY6968 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4280]) ).
thf(4896,plain,
! [SV424: $i,SV1975: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1975 @ SV424 )
= $true )
| ( ( class_Finite__Set_Ofinite_Ofinite @ SV424 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4281]) ).
thf(4897,plain,
! [SV1542: $i,SV1038: $i,SV425: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV425 ) @ SV1038 ) @ SV1542 ) )
= $true )
| ( ( ! [SY6437: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV425 ) @ SV1038 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1542 @ ( c_Collect @ SY6437 @ SV425 ) @ ( tc_fun @ SV425 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4282]) ).
thf(4898,plain,
! [SV1543: $i,SV1039: $i,SV426: $i] :
( ( ( ( hAPP @ SV426 @ SV1039 )
!= ( c_Option_Ooption_ONone @ SV1543 ) )
= $true )
| ( ( ! [SY6438: $i] :
( ( ( hAPP @ SY6438 @ SV1039 )
!= ( c_Option_Ooption_ONone @ SV1543 ) )
| ! [SY6439: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SV426 @ SY6438 @ SY6439 @ SV1543 ) @ SV1039 )
= ( c_Option_Ooption_ONone @ SV1543 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4283]) ).
thf(4899,plain,
! [SV1976: $i,SV1544: $i,SV1040: $i,SV427: $i] :
( ( ( ( hAPP @ SV427 @ SV1040 )
!= ( c_Option_Ooption_OSome @ SV1544 @ SV1976 ) )
| ! [SY6969: $i,SY6970: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SY6969 @ SV427 @ SY6970 @ SV1976 ) @ SV1040 )
= ( c_Option_Ooption_OSome @ SV1544 @ SV1976 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4284]) ).
thf(4900,plain,
! [SV1977: $i,SV1545: $i,SV1041: $i,SV428: $i] :
( ( ( ( hAPP @ SV428 @ SV1041 )
!= ( c_Option_Ooption_OSome @ SV1545 @ SV1977 ) )
| ! [SY6971: $i,SY6972: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SY6971 @ SV428 @ SY6972 @ SV1977 ) @ SV1041 )
= ( c_Option_Ooption_OSome @ SV1545 @ SV1977 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4285]) ).
thf(4901,plain,
! [SV1978: $i,SV1546: $i,SV1042: $i,SV429: $i] :
( ( ! [SY6973: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV429 ) @ ( hAPP @ SV1042 @ SV1546 ) ) @ ( c_Set_Oimage @ SV1042 @ ( c_HOL_Ominus__class_Ominus @ SV1978 @ ( c_Set_Oinsert @ SV1546 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6973 @ tc_bool ) ) @ SY6973 ) @ ( tc_fun @ SY6973 @ tc_bool ) ) @ SY6973 @ SV429 ) ) )
| ~ ( c_Fun_Oinj__on @ SV1042 @ ( c_Set_Oinsert @ SV1546 @ SV1978 @ SY6973 ) @ SY6973 @ SV429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4286]) ).
thf(4902,plain,
! [SV1979: $i,SV1547: $i,SV1043: $i,SV430: $i] :
( ( ! [SY6974: $i] :
( ( c_Com_Ocom_OCond @ SV430 @ SV1043 @ SV1547 )
!= ( c_Com_Ocom_OAss @ SV1979 @ SY6974 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4287]) ).
thf(4903,plain,
! [SV1980: $i,SV1548: $i,SV1044: $i,SV432: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV432 @ SV1044 @ SV1548 ) @ SV1980 @ ( tc_fun @ SV1548 @ tc_bool ) )
= ( c_Set_Oinsert @ SV432 @ ( c_HOL_Ominus__class_Ominus @ SV1044 @ SV1980 @ ( tc_fun @ SV1548 @ tc_bool ) ) @ SV1548 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1548 ) @ SV432 ) @ SV1980 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4288]) ).
thf(4904,plain,
! [SV1045: $i,SV433: $i,SV1981: $i] :
( ( ( ! [SY6975: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1981 @ SV433 @ ( tc_fun @ SY6975 @ tc_bool ) ) @ SV1045 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV433 @ SV1045 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4289]) ).
thf(4905,plain,
! [SV1046: $i,SV1982: $i,SV434: $i] :
( ( ( ! [SY6976: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV434 @ SV1982 @ ( tc_fun @ SY6976 @ tc_bool ) ) @ SV1046 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV434 @ SV1046 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4290]) ).
thf(4906,plain,
! [SV1983: $i,SV1549: $i,SV1047: $i,SV435: $i] :
( ( c_Map_Omap__le @ SV435 @ ( c_Map_Omap__add @ SV1047 @ SV435 @ SV1549 @ SV1983 ) @ SV1549 @ SV1983 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4291]) ).
thf(4907,plain,
! [SV1550: $i,SV1048: $i,SV436: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV436 @ SV1048 @ SV1550 ) @ ( c_Set_Oinsert @ SV436 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1550 @ tc_bool ) ) @ SV1550 ) @ ( tc_fun @ SV1550 @ tc_bool ) )
= SV1048 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1550 ) @ SV436 ) @ SV1048 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4292]) ).
thf(4908,plain,
! [SV1984: $i,SV1551: $i,SV1049: $i,SV437: $i] :
( ( ! [SY6977: $i] :
( ( c_Set_Ovimage @ SV437 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1049 @ SV1551 @ ( tc_fun @ SV1984 @ tc_bool ) ) @ SY6977 @ SV1984 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Ovimage @ SV437 @ SV1049 @ SY6977 @ SV1984 ) @ ( c_Set_Ovimage @ SV437 @ SV1551 @ SY6977 @ SV1984 ) @ ( tc_fun @ SY6977 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4293]) ).
thf(4909,plain,
! [SV438: $i,SV1050: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ SV1050 ) @ SV438 ) )
= $false )
| ( ( SV438 = SV1050 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4294]) ).
thf(4910,plain,
! [SV1552: $i,SV1051: $i,SV439: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV439 @ SV1051 @ ( tc_fun @ SV1552 @ tc_bool ) ) @ SV1552 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1051 @ SV1552 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4295]) ).
thf(4911,plain,
! [SV1553: $i,SV1052: $i,SV440: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV440 @ SV1052 @ ( tc_fun @ SV1553 @ tc_bool ) ) @ SV1553 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV440 @ SV1553 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4296]) ).
thf(4912,plain,
! [SV1985: $i,SV1554: $i,SV1053: $i,SV441: $i] :
( ( ! [SY6978: $i] :
( ( c_Map_Omap__le @ ( c_Map_Omap__add @ SV441 @ SV1053 @ SV1554 @ SV1985 ) @ SY6978 @ SV1554 @ SV1985 )
| ~ ( c_Map_Omap__le @ SV441 @ ( c_Map_Omap__add @ SV441 @ SV1053 @ SV1554 @ SV1985 ) @ SV1554 @ SV1985 )
| ~ ( c_Map_Omap__le @ SV1053 @ SY6978 @ SV1554 @ SV1985 )
| ~ ( c_Map_Omap__le @ SV441 @ SY6978 @ SV1554 @ SV1985 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4297]) ).
thf(4913,plain,
! [SV1555: $i,SV1054: $i,SV442: $i] :
( ( ( hBOOL @ ( hAPP @ SV442 @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1054 @ SV442 @ SV1555 ) ) )
= $true )
| ( ( ! [SY6456: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1555 ) @ SY6456 ) @ SV1054 ) )
| ! [SY6457: $i] :
( ~ ( hBOOL @ ( hAPP @ SV442 @ SY6457 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1555 ) @ SY6457 ) @ SV1054 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4298]) ).
thf(4914,plain,
! [SV1986: $i,SV1556: $i,SV1055: $i,SV443: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ SV1055 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1556 @ SV1986 @ ( tc_fun @ SV443 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ SV1055 ) @ SV1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ SV1055 ) @ SV1556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4299]) ).
thf(4915,plain,
! [SV1987: $i,SV1557: $i,SV1056: $i,SV444: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ SV1056 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1557 @ SV1987 @ ( tc_fun @ SV444 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ SV1056 ) @ SV1987 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ SV1056 ) @ SV1557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4300]) ).
thf(4916,plain,
! [SV1558: $i,SV1057: $i,SV445: $i] :
( ( ( hBOOL @ ( hAPP @ SV445 @ SV1057 ) )
= $true )
| ( ( ! [SY6460: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1558 ) @ SV1057 ) @ SY6460 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1558 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6460 @ SV445 @ SV1558 ) ) @ SY6460 ) )
| ! [SY6461: $i] :
~ ( hBOOL @ ( hAPP @ SY6461 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6460 @ SY6461 @ SV1558 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4301]) ).
thf(4917,plain,
! [SV1559: $i,SV1058: $i,SV446: $i] :
( ( ( hBOOL @ ( hAPP @ SV446 @ SV1058 ) )
= $true )
| ( ( ! [SY6462: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1559 ) @ SV1058 ) @ SY6462 ) )
| ! [SY6463: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1559 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6462 @ SY6463 @ SV1559 ) ) @ SY6462 ) )
| ~ ( hBOOL @ ( hAPP @ SV446 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6462 @ SV446 @ SV1559 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4302]) ).
thf(4918,plain,
! [SV1560: $i,SV1059: $i,SV447: $i] :
( ( ( hBOOL @ ( hAPP @ SV447 @ SV1059 ) )
= $true )
| ( ( ! [SY6464: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1560 ) @ SV1059 ) @ SY6464 ) )
| ~ ( hBOOL @ ( hAPP @ SV447 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6464 @ SV447 @ SV1560 ) ) )
| ! [SY6465: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1560 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6464 @ SY6465 @ SV1560 ) ) @ SY6464 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4303]) ).
thf(4919,plain,
! [SV1561: $i,SV1060: $i,SV448: $i] :
( ( ( hBOOL @ ( hAPP @ SV448 @ SV1060 ) )
= $true )
| ( ( ! [SY6466: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1561 ) @ SV1060 ) @ SY6466 ) )
| ! [SY6467: $i] :
~ ( hBOOL @ ( hAPP @ SY6467 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6466 @ SY6467 @ SV1561 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1561 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6466 @ SV448 @ SV1561 ) ) @ SY6466 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4304]) ).
thf(4920,plain,
! [SV1988: $i,SV1562: $i,SV1061: $i,SV449: $i] :
( ( ! [SY6979: $i,SY6980: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV449 ) @ SV1061 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV1562 @ SV1988 @ SY6979 @ SY6980 @ SV449 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1988 @ SV1061 ) @ SY6980 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1562 @ SY6979 ) @ SV1061 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4305]) ).
thf(4921,plain,
! [SV1989: $i,SV1563: $i,SV1062: $i,SV450: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV450 ) @ SV1062 ) @ ( c_Set_Oinsert @ SV1563 @ SV1989 @ SV450 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV450 ) @ SV1062 ) @ SV1989 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4306]) ).
thf(4922,plain,
! [SV1990: $i,SV1564: $i,SV1063: $i,SV451: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV451 ) @ SV1063 ) @ ( c_Set_Oinsert @ SV1564 @ SV1990 @ SV451 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV451 ) @ SV1063 ) @ SV1990 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4307]) ).
thf(4923,plain,
! [SV1991: $i,SV1565: $i,SV1064: $i,SV452: $i] :
( ( ! [SY6981: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV452 ) @ SV1064 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV1565 @ SV1991 @ SY6981 @ SV452 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1565 @ SV1064 ) @ SY6981 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1565 @ SV1991 ) @ SV1064 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4308]) ).
thf(4924,plain,
! [SV1566: $i,SV1065: $i,SV453: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV453 ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1065 @ SV1566 @ SV453 ) ) @ SV1065 ) )
= $true )
| ( ( ! [SY6475: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV453 ) @ SY6475 ) @ SV1065 ) )
| ~ ( hBOOL @ ( hAPP @ SV1566 @ SY6475 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4309]) ).
thf(4925,plain,
! [SV455: $i,SV1067: $i,SV1992: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1992 ) @ SV1067 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1992 @ tc_bool ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV455 @ SV1067 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4311]) ).
thf(4926,plain,
! [SV1993: $i,SV1567: $i,SV1070: $i,SV458: $i] :
( ( ! [SY6982: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV458 ) @ SV1070 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV1567 @ SV1993 @ SY6982 @ SV458 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1567 @ SV1070 ) @ SY6982 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1567 @ SV1993 ) @ SV1070 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4314]) ).
thf(4927,plain,
! [SV1568: $i,SV1071: $i,SV459: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV459 ) @ SV1071 ) @ SV1568 ) )
= $true )
| ( ( ! [SY6478: $i] :
( ( SV1071 = SY6478 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV459 ) @ SV1071 ) @ ( c_Set_Oinsert @ SY6478 @ SV1568 @ SV459 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4315]) ).
thf(4928,plain,
! [SV1994: $i,SV1569: $i,SV1072: $i,SV460: $i] :
( ( ! [SY6983: $i,SY6984: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV460 ) @ SV1072 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV1569 @ SV1994 @ SY6983 @ SY6984 @ SV460 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1569 @ SV1072 ) @ SY6984 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1994 @ SY6983 ) @ SV1072 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4316]) ).
thf(4929,plain,
! [SV1570: $i,SV1073: $i,SV461: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV461 ) @ SV1073 ) @ SV1570 ) ) )
= $true )
| ( ( ! [SY6482: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV461 ) @ SV1073 ) @ ( c_HOL_Ominus__class_Ominus @ SY6482 @ SV1570 @ ( tc_fun @ SV461 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4317]) ).
thf(4930,plain,
! [SV1571: $i,SV1074: $i,SV462: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV462 ) @ SV1074 ) @ SV1571 ) )
= $true )
| ( ( ! [SY6483: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV462 ) @ SV1074 ) @ ( c_HOL_Ominus__class_Ominus @ SV1571 @ SY6483 @ ( tc_fun @ SV462 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4318]) ).
thf(4931,plain,
! [SV1572: $i,SV1075: $i,SV463: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1075 @ SV1572 @ SV463 ) ) @ SV1075 ) )
= $true )
| ( ( ! [SY5611: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ SY5611 ) @ SV1075 ) )
| ! [SY6485: $i] :
( ~ ( hBOOL @ ( hAPP @ SV1572 @ SY6485 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ SY6485 ) @ SV1075 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4319]) ).
thf(4932,plain,
! [SV1573: $i,SV1076: $i,SV464: $i] :
( ( ( hBOOL @ ( hAPP @ SV464 @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ SV1076 @ SV464 @ SV1573 ) ) )
= $true )
| ( ( ! [SY6486: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1573 ) @ SY6486 ) @ SV1076 ) )
| ~ ( hBOOL @ ( hAPP @ SV464 @ SY6486 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4320]) ).
thf(4933,plain,
! [SV1995: $i,SV1574: $i,SV1077: $i,SV465: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV465 @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1077 @ SV1574 @ SV1995 @ ( tc_fun @ SV465 @ tc_bool ) ) )
| ! [SY6985: $i] :
( ( ( hAPP @ SV1574 @ SY6985 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV465 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1995 ) @ SY6985 ) @ SV1077 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4321]) ).
thf(4934,plain,
! [SV1996: $i,SV1575: $i,SV1079: $i,SV467: $i] :
( ( ! [SY6986: $i] :
( ( c_Com_Ocom_OAss @ SV467 @ SV1079 )
!= ( c_Com_Ocom_OCond @ SV1575 @ SV1996 @ SY6986 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4322]) ).
thf(4935,plain,
! [SV1997: $i,SV1576: $i,SV1082: $i,SV470: $i] :
( ( ( ( c_Map_Omap__add @ SV470 @ SV1082 @ SV1576 @ SV1997 )
= ( c_Map_Omap__add @ SV1082 @ SV470 @ SV1576 @ SV1997 ) )
| ~ ( c_Map_Omap__le @ SV470 @ ( c_Map_Omap__add @ SV470 @ SV1082 @ SV1576 @ SV1997 ) @ SV1576 @ SV1997 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4324]) ).
thf(4936,plain,
! [SV1998: $i,SV1577: $i,SV1083: $i,SV471: $i] :
( ( ( ( c_Map_Omap__add @ SV471 @ SV1083 @ SV1577 @ SV1998 )
!= ( c_Map_Omap__add @ SV1083 @ SV471 @ SV1577 @ SV1998 ) )
| ( c_Map_Omap__le @ SV471 @ ( c_Map_Omap__add @ SV471 @ SV1083 @ SV1577 @ SV1998 ) @ SV1577 @ SV1998 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4325]) ).
thf(4937,plain,
! [SV1999: $i,SV1578: $i,SV1085: $i,SV473: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV473 @ ( c_HOL_Ominus__class_Ominus @ SV1085 @ SV1578 @ ( tc_fun @ SV1999 @ tc_bool ) ) @ ( tc_fun @ SV1999 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV473 @ SV1085 @ ( tc_fun @ SV1999 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV473 @ SV1578 @ ( tc_fun @ SV1999 @ tc_bool ) ) @ ( tc_fun @ SV1999 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4327]) ).
thf(4938,plain,
! [SV2000: $i,SV1579: $i,SV1086: $i,SV474: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ SV474 @ SV1086 @ ( tc_fun @ SV1579 @ tc_bool ) ) @ SV2000 @ ( tc_fun @ SV1579 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV474 @ SV2000 @ ( tc_fun @ SV1579 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1086 @ SV2000 @ ( tc_fun @ SV1579 @ tc_bool ) ) @ ( tc_fun @ SV1579 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4328]) ).
thf(4939,plain,
! [SV1580: $i,SV1087: $i,SV475: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV475 @ SV1087 @ ( tc_fun @ SV1580 @ tc_bool ) )
= $true )
| ( ( ! [SY6495: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1580 ) @ SY6495 ) @ SV1087 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV475 @ ( c_Set_Oinsert @ SY6495 @ SV1087 @ SV1580 ) @ ( tc_fun @ SV1580 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4329]) ).
thf(4940,plain,
! [SV2001: $i,SV1581: $i,SV1088: $i,SV476: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV476 @ ( c_Set_Oinsert @ SV1088 @ SV1581 @ SV2001 ) @ ( tc_fun @ SV2001 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2001 ) @ SV1088 ) @ SV1581 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV476 @ SV1581 @ ( tc_fun @ SV2001 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4330]) ).
thf(4941,plain,
! [SV1582: $i,SV1089: $i,SV477: $i] :
( ( c_Com_Ocom_OSKIP
= ( c_Com_Ocom_OLocal @ SV477 @ SV1089 @ SV1582 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4331]) ).
thf(4942,plain,
! [SV1583: $i,SV1090: $i,SV478: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV478 ) @ SV1090 ) @ SV1583 ) ) )
= $true )
| ( ( ! [SY6497: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV478 ) @ SV1090 ) @ SY6497 ) )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY6497 @ SV1583 @ ( tc_fun @ SV478 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV478 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4332]) ).
thf(4943,plain,
! [SV2002: $i,SV1584: $i,SV1091: $i,SV479: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV479 @ SV1091 @ ( tc_fun @ SV1584 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2002 @ SV1091 @ ( tc_fun @ SV1584 @ tc_bool ) ) @ ( tc_fun @ SV1584 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV479 @ SV1091 @ ( tc_fun @ SV1584 @ tc_bool ) ) @ SV2002 @ ( tc_fun @ SV1584 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4333]) ).
thf(4944,plain,
! [SV481: $i,SV2003: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2003 @ SV2003 @ SV481 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV481 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4335]) ).
thf(4945,plain,
! [SV482: $i,SV2004: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2004 @ SV2004 @ SV482 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV482 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4336]) ).
thf(4946,plain,
! [SV483: $i,SV2005: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2005 @ SV2005 @ SV483 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV483 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4337]) ).
thf(4947,plain,
! [SV1585: $i,SV484: $i] :
( ( ( ( c_Collect @ SV484 @ SV1585 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1585 @ tc_bool ) ) )
= $false )
| ( ( ! [SY4134: $i] :
~ ( hBOOL @ ( hAPP @ SV484 @ SY4134 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4338]) ).
thf(4948,plain,
! [SV2006: $i,SV1586: $i,SV1093: $i,SV486: $i] :
( ( ( c_Com_Ocom_OSemi @ SV486 @ SV1093 )
!= ( c_Com_Ocom_OAss @ SV1586 @ SV2006 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4339]) ).
thf(4949,plain,
! [SV487: $i,SV2007: $i] :
( ( ( ! [SY6987: $i] :
( ( c_HOL_Oord__class_Oless @ SV2007 @ SY6987 @ SV487 )
| ( SY6987 = SV2007 )
| ( c_HOL_Oord__class_Oless @ SY6987 @ SV2007 @ SV487 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV487 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4340]) ).
thf(4950,plain,
! [SV488: $i,SV2008: $i] :
( ( ( ! [SY6988: $i] :
( ( SV2008 = SY6988 )
| ( c_HOL_Oord__class_Oless @ SY6988 @ SV2008 @ SV488 )
| ( c_HOL_Oord__class_Oless @ SV2008 @ SY6988 @ SV488 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV488 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4341]) ).
thf(4951,plain,
! [SV1094: $i,SV489: $i,SV2009: $i] :
( ( ( ! [SY6989: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV2009 ) @ SY6989 ) @ SV489 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV2009 ) @ SY6989 ) @ SV1094 ) ) ) )
= $true )
| ( ( SV489 = SV1094 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4342]) ).
thf(4952,plain,
! [SV2010: $i,SV490: $i,SV1095: $i] :
( ( ( ! [SY6990: $i] :
( ~ ( c_Map_Omap__le @ SV1095 @ SV490 @ SV2010 @ SY6990 )
| ~ ( c_Map_Omap__le @ SV490 @ SV1095 @ SV2010 @ SY6990 ) ) )
= $true )
| ( ( SV490 = SV1095 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4343]) ).
thf(4953,plain,
! [SV491: $i,SV2011: $i] :
( ( ( ! [SY6991: $i] :
( ( c_HOL_Oord__class_Oless @ SV2011 @ SY6991 @ SV491 )
| ( SY6991 = SV2011 )
| ( c_HOL_Oord__class_Oless @ SY6991 @ SV2011 @ SV491 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV491 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4344]) ).
thf(4954,plain,
! [SV492: $i,SV2012: $i] :
( ( ( ! [SY6992: $i] :
( ( c_HOL_Oord__class_Oless @ SV2012 @ SY6992 @ SV492 )
| ( SY6992 = SV2012 )
| ( c_HOL_Oord__class_Oless @ SY6992 @ SV2012 @ SV492 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV492 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4345]) ).
thf(4955,plain,
! [SV493: $i,SV2013: $i] :
( ( ( ! [SY6993: $i] :
( ( SV2013 = SY6993 )
| ( c_HOL_Oord__class_Oless @ SV2013 @ SY6993 @ SV493 )
| ( c_HOL_Oord__class_Oless @ SY6993 @ SV2013 @ SV493 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV493 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4346]) ).
thf(4956,plain,
! [SV1587: $i,SV1096: $i,SV494: $i] :
( ( ( c_Com_Ocom_OLocal @ SV494 @ SV1096 @ SV1587 )
= c_Com_Ocom_OSKIP )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4347]) ).
thf(4957,plain,
! [SV1097: $i,SV495: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV495 )
= $false )
| ( ( ! [SY5645: $i,SY5646: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1097 @ SY5645 @ SV495 ) @ SY5646 @ SV495 )
| ~ ( c_HOL_Oord__class_Oless @ SY5645 @ SY5646 @ SV495 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4348]) ).
thf(4958,plain,
! [SV1098: $i,SV496: $i] :
( ( ( class_Lattices_Olower__semilattice @ SV496 )
= $false )
| ( ( ! [SY5647: $i,SY5648: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1098 @ SY5647 @ SV496 ) @ SY5648 @ SV496 )
| ~ ( c_HOL_Oord__class_Oless @ SV1098 @ SY5648 @ SV496 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4349]) ).
thf(4959,plain,
! [SV1588: $i,SV1099: $i,SV497: $i] :
( ( ( ! [SY6500: $i] : ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV497 @ SV1099 @ SV1588 @ SY6500 ) @ SY6500 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1099 @ SV1588 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4350]) ).
thf(4960,plain,
! [SV2014: $i,SV1589: $i,SV1100: $i,SV498: $i] :
( ( ( ( hAPP @ SV498 @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ SV498 @ SV1100 @ SV1589 @ SV2014 ) )
!= ( hAPP @ SV1100 @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ SV498 @ SV1100 @ SV1589 @ SV2014 ) ) )
| ( c_Map_Omap__le @ SV498 @ SV1100 @ SV1589 @ SV2014 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4351]) ).
thf(4961,plain,
! [SV2015: $i,SV1590: $i,SV1101: $i,SV499: $i] :
( ( ! [SY6994: $i] :
( ( ( c_Set_Oinsert @ SV499 @ ( c_Set_Oinsert @ SV1101 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1590 @ tc_bool ) ) @ SV1590 ) @ SV1590 )
!= ( c_Set_Oinsert @ SV2015 @ ( c_Set_Oinsert @ SY6994 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1590 @ tc_bool ) ) @ SV1590 ) @ SV1590 ) )
| ( SV499 = SY6994 )
| ( SV499 = SV2015 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4352]) ).
thf(4962,plain,
! [SV2016: $i,SV1591: $i,SV1102: $i,SV500: $i] :
( ( ! [SY6995: $i] :
( ( c_Set_Oinsert @ SV500 @ ( c_Set_Oinsert @ SV1102 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1591 @ tc_bool ) ) @ SV1591 ) @ SV1591 )
!= ( c_Set_Oinsert @ SV2016 @ ( c_Set_Oinsert @ SY6995 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1591 @ tc_bool ) ) @ SV1591 ) @ SV1591 ) )
| ( SV1102 = SV2016 )
| ( SV500 = SV2016 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4353]) ).
thf(4963,plain,
! [SV2017: $i,SV1592: $i,SV1103: $i,SV501: $i] :
( ( ! [SY6996: $i] :
( ( ( c_Set_Oinsert @ SV501 @ ( c_Set_Oinsert @ SV1103 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1592 @ tc_bool ) ) @ SV1592 ) @ SV1592 )
!= ( c_Set_Oinsert @ SV2017 @ ( c_Set_Oinsert @ SY6996 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1592 @ tc_bool ) ) @ SV1592 ) @ SV1592 ) )
| ( SV501 = SY6996 )
| ( SV1103 = SY6996 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4354]) ).
thf(4964,plain,
! [SV2018: $i,SV1593: $i,SV1104: $i,SV502: $i] :
( ( ! [SY6997: $i] :
( ( ( c_Set_Oinsert @ SV502 @ ( c_Set_Oinsert @ SV1104 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1593 @ tc_bool ) ) @ SV1593 ) @ SV1593 )
!= ( c_Set_Oinsert @ SV2018 @ ( c_Set_Oinsert @ SY6997 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1593 @ tc_bool ) ) @ SV1593 ) @ SV1593 ) )
| ( SV1104 = SV2018 )
| ( SV1104 = SY6997 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4355]) ).
thf(4965,plain,
! [SV1594: $i,SV1105: $i,SV503: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV503 ) @ SV1105 ) @ SV1594 ) )
= $true )
| ( ( ! [SY6510: $i] :
( ( hBOOL @ ( hAPP @ SY6510 @ SV1105 ) )
| ! [SY6511: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY6510 @ SY6511 @ SV503 ) ) @ SV1105 ) @ SV1594 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4356]) ).
thf(4966,plain,
! [SV2019: $i,SV1595: $i,SV1106: $i,SV504: $i] :
( ( ! [SY6998: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV504 @ SV1106 @ SV1595 ) ) @ SV2019 ) @ SY6998 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1595 ) @ SV2019 ) @ SY6998 ) )
| ( hBOOL @ ( hAPP @ SV504 @ SV2019 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4357]) ).
thf(4967,plain,
! [SV2020: $i,SV1596: $i,SV1108: $i,SV506: $i] :
( ( ! [SY6999: $i,SY7000: $i,SY7001: $i,SY7002: $i,SY7003: $i] :
( ( ( hAPP @ SV506 @ ( c_Set_Oinsert @ SV1108 @ SV1596 @ SV2020 ) )
= ( hAPP @ ( hAPP @ SY6999 @ SV1108 ) @ ( hAPP @ SV506 @ SV1596 ) ) )
| ! [SY7004: $i,SY7005: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY7000 @ SV506 @ SY7001 @ SY7002 @ SY7003 @ SY6999 @ SY7004 @ SY7005 @ SV2020 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4359]) ).
thf(4968,plain,
! [SV2021: $i,SV1597: $i,SV1109: $i,SV507: $i] :
( ( ! [SY7006: $i,SY7007: $i,SY7008: $i,SY7009: $i,SY7010: $i] :
( ( ( hAPP @ SV507 @ ( c_Set_Oinsert @ SV1109 @ SV1597 @ SV2021 ) )
= ( hAPP @ ( hAPP @ SY7006 @ SV1109 ) @ ( hAPP @ SV507 @ SV1597 ) ) )
| ! [SY7011: $i,SY7012: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV507 @ SY7007 @ SY7008 @ SY7009 @ SY7006 @ SY7010 @ SY7011 @ SY7012 @ SV2021 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4360]) ).
thf(4969,plain,
! [SV2022: $i,SV1598: $i,SV1110: $i,SV508: $i] :
( ( ( c_Com_Ocom_OWhile @ SV508 @ SV1110 )
!= ( c_Com_Ocom_OAss @ SV1598 @ SV2022 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4361]) ).
thf(4970,plain,
! [SV2023: $i,SV1599: $i,SV1111: $i,SV509: $i] :
( ( ! [SY7013: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SV1111 @ SV1599 @ SV2023 @ SY7013 @ SV509 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1111 @ SV1599 @ SY7013 @ ( tc_fun @ SV509 @ tc_bool ) ) ) )
| ! [SY7014: $i] :
( ~ ( hBOOL @ ( hAPP @ SV2023 @ SY7014 ) )
| ! [SY6534: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ SY7014 ) @ ( hAPP @ SV1599 @ SY6534 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7013 ) @ SY6534 ) @ SV1111 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4362]) ).
thf(4971,plain,
! [SV1600: $i,SV1112: $i,SV510: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV510 @ tc_bool ) )
= ( c_Set_Oinsert @ SV1112 @ SV1600 @ SV510 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4363]) ).
thf(4972,plain,
! [SV1601: $i,SV1113: $i,SV511: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV511 @ SV1113 @ SV1601 )
= $true )
| ( ( ! [SY6535: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV511 @ SY6535 @ SV1601 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY6535 @ SV1113 @ SV1601 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4364]) ).
thf(4973,plain,
! [SV2024: $i,SV1602: $i,SV1114: $i,SV512: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV512 @ SV1114 @ SV1602 ) @ SV2024 @ ( tc_fun @ SV1602 @ tc_bool ) )
= ( c_Set_Oinsert @ SV512 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1114 @ SV2024 @ ( tc_fun @ SV1602 @ tc_bool ) ) @ SV1602 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1602 ) @ SV512 ) @ SV2024 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4365]) ).
thf(4974,plain,
! [SV2025: $i,SV1603: $i,SV1115: $i,SV513: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV513 @ ( c_Set_Oinsert @ SV1115 @ SV1603 @ SV2025 ) @ ( tc_fun @ SV2025 @ tc_bool ) )
= ( c_Set_Oinsert @ SV1115 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV513 @ SV1603 @ ( tc_fun @ SV2025 @ tc_bool ) ) @ SV2025 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2025 ) @ SV1115 ) @ SV513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4366]) ).
thf(4975,plain,
! [SV2026: $i,SV1604: $i,SV1116: $i,SV514: $i] :
( ( ! [SY7016: $i] :
( ( c_Set_Oimage @ SV514 @ ( c_Set_Oinsert @ SV1116 @ SV1604 @ SV2026 ) @ SV2026 @ SY7016 )
= ( c_Set_Oinsert @ ( hAPP @ SV514 @ SV1116 ) @ ( c_Set_Oimage @ SV514 @ SV1604 @ SV2026 @ SY7016 ) @ SY7016 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4367]) ).
thf(4976,plain,
! [SV2027: $i,SV1605: $i,SV1117: $i,SV515: $i] :
( ( ! [SY7017: $i,SY7018: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV515 @ SV1117 @ SV1605 @ SV2027 ) @ SY7017 )
!= ( c_Option_Ooption_OSome @ SY7018 @ SV2027 ) )
| ( ( hAPP @ SV1117 @ SY7017 )
= ( c_Option_Ooption_ONone @ SV2027 ) )
| ( ( hAPP @ SV1117 @ SY7017 )
= ( c_Option_Ooption_OSome @ SY7018 @ SV2027 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4368]) ).
thf(4977,plain,
! [SV1606: $i,SV1118: $i,SV516: $i] :
( ( ( ( hAPP @ SV516 @ SV1118 )
= SV1606 )
= $true )
| ( ( ! [SY6543: $i,SY6544: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6543 ) @ SV1118 ) @ ( c_Set_Ovimage @ SV516 @ ( c_Set_Oinsert @ SV1606 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6544 @ tc_bool ) ) @ SY6544 ) @ SY6543 @ SY6544 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4369]) ).
thf(4978,plain,
! [SV2028: $i,SV1607: $i,SV1119: $i,SV517: $i] :
( ( ( ( c_Com_Ocom_OAss @ SV517 @ SV1119 )
!= ( c_Com_Ocom_OAss @ SV1607 @ SV2028 ) )
| ( SV1119 = SV2028 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4370]) ).
thf(4979,plain,
! [SV1608: $i,SV1120: $i,SV518: $i] :
( ( ( ! [SY6546: $i] :
( ( c_Com_Ocom_OAss @ SV518 @ SV1120 )
!= ( c_Com_Ocom_OAss @ SV1608 @ SY6546 ) ) )
= $true )
| ( ( SV518 = SV1608 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4371]) ).
thf(4980,plain,
! [SV2029: $i,SV1609: $i,SV1121: $i,SV519: $i] :
( ( ( c_Set_Oinsert @ SV519 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1121 @ tc_bool ) ) @ SV1609 @ SV1121 @ ( tc_fun @ SV2029 @ tc_bool ) ) @ SV2029 )
= ( c_Set_Oinsert @ SV519 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2029 @ tc_bool ) ) @ SV2029 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4372]) ).
thf(4981,plain,
! [SV1123: $i,SV521: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV521 @ tc_bool ) )
= ( c_Collect @ SV1123 @ SV521 ) )
= $false )
| ( ( ! [SY5719: $i] :
~ ( hBOOL @ ( hAPP @ SV1123 @ SY5719 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4374]) ).
thf(4982,plain,
! [SV523: $i,SV2030: $i] :
( ( ( ! [SY7019: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV2030 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2030 @ SY7019 @ SV523 ) @ SV523 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV2030 @ SY7019 @ SV523 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV523 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4376]) ).
thf(4983,plain,
! [SV524: $i,SV2031: $i] :
( ( ( ! [SY7020: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV2031 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2031 @ SY7020 @ SV524 ) @ SV524 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV2031 @ SY7020 @ SV524 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV524 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4377]) ).
thf(4984,plain,
! [SV2032: $i,SV1612: $i,SV1126: $i,SV526: $i] :
( ( ! [SY7021: $i,SY7022: $i] :
( ( ( c_Com_Ocom_OLocal @ SV526 @ SV1126 @ SV1612 )
!= ( c_Com_Ocom_OLocal @ SV2032 @ SY7021 @ SY7022 ) )
| ( SV1612 = SY7022 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4379]) ).
thf(4985,plain,
! [SV2033: $i,SV1613: $i,SV1127: $i,SV527: $i] :
( ( ! [SY7023: $i] :
( ! [SY7024: $i] :
( ( c_Com_Ocom_OLocal @ SV527 @ SV1127 @ SV1613 )
!= ( c_Com_Ocom_OLocal @ SV2033 @ SY7023 @ SY7024 ) )
| ( SV1127 = SY7023 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4380]) ).
thf(4986,plain,
! [SV2034: $i,SV1614: $i,SV1128: $i,SV528: $i] :
( ( ! [SY7025: $i,SY7026: $i] :
( ( c_Com_Ocom_OLocal @ SV528 @ SV1128 @ SV1614 )
!= ( c_Com_Ocom_OLocal @ SV2034 @ SY7025 @ SY7026 ) )
| ( SV528 = SV2034 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4381]) ).
thf(4987,plain,
! [SV1615: $i,SV1129: $i,SV529: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV529 @ SV1129 @ ( tc_fun @ SV1615 @ tc_bool ) ) @ SV1615 )
= $true )
| ( ( ! [SY6557: $i] :
~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV529 @ ( c_Set_Oinsert @ SY6557 @ SV1129 @ SV1615 ) @ ( tc_fun @ SV1615 @ tc_bool ) ) @ SV1615 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4382]) ).
thf(4988,plain,
! [SV2035: $i,SV1616: $i,SV1130: $i,SV530: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV530 @ ( c_Set_Oinsert @ SV1130 @ SV1616 @ SV2035 ) @ ( tc_fun @ SV2035 @ tc_bool ) ) @ SV2035 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV530 @ SV1616 @ ( tc_fun @ SV2035 @ tc_bool ) ) @ SV2035 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4383]) ).
thf(4989,plain,
! [SV2036: $i,SV1617: $i,SV1131: $i,SV531: $i] :
( ( ( c_Com_Ocom_OWhile @ SV531 @ SV1131 )
!= ( c_Com_Ocom_OSemi @ SV1617 @ SV2036 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4384]) ).
thf(4990,plain,
! [SV2037: $i,SV1618: $i,SV1132: $i,SV532: $i] :
( ( ! [SY7027: $i,SY7028: $i,SY7029: $i] :
( ( ( hAPP @ SV532 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1132 @ tc_bool ) ) )
= SV1618 )
| ! [SY7030: $i,SY7031: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2037 @ SV532 @ SY7027 @ SY7028 @ SY7029 @ SY7030 @ SV1618 @ SY7031 @ SV1132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4385]) ).
thf(4991,plain,
! [SV2038: $i,SV1619: $i,SV1133: $i,SV533: $i] :
( ( ! [SY7032: $i,SY7033: $i,SY7034: $i] :
( ( ( hAPP @ SV533 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1133 @ tc_bool ) ) )
= SV1619 )
| ! [SY7035: $i,SY7036: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV533 @ SV2038 @ SY7032 @ SY7033 @ SY7034 @ SY7035 @ SY7036 @ SV1619 @ SV1133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4386]) ).
thf(4992,plain,
! [SV534: $i,SV1134: $i,SV2039: $i] :
( ( ( ( SV2039 = SV1134 )
| ! [SY7037: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV534 @ SY7037 ) ) @ SV1134 ) @ SV2039 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV534 @ SV1134 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4387]) ).
thf(4993,plain,
! [SV1620: $i,SV1135: $i,SV535: $i] :
( ( ( ( c_Set_Oinsert @ SV535 @ ( c_HOL_Ominus__class_Ominus @ SV1135 @ ( c_Set_Oinsert @ SV535 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1620 @ tc_bool ) ) @ SV1620 ) @ ( tc_fun @ SV1620 @ tc_bool ) ) @ SV1620 )
= SV1135 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1620 ) @ SV535 ) @ SV1135 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4388]) ).
thf(4994,plain,
! [SV536: $i,SV2040: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV2040 @ SV2040 @ SV536 )
= SV2040 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV536 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4389]) ).
thf(4995,plain,
! [SV1621: $i,SV1137: $i,SV538: $i] :
( ( ( ! [SY6572: $i] :
( ( c_Set_Oimage @ SV538 @ SV1137 @ SV1621 @ SY6572 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6572 @ tc_bool ) ) ) )
= $true )
| ( ( SV1137
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1621 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4390]) ).
thf(4996,plain,
! [SV2041: $i,SV1622: $i,SV1139: $i,SV540: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ SV1139 @ ( tc_fun @ SV1622 @ tc_bool ) ) @ SV2041 @ ( tc_fun @ SV1622 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV540 @ ( c_HOL_Ominus__class_Ominus @ SV1139 @ SV2041 @ ( tc_fun @ SV1622 @ tc_bool ) ) @ ( tc_fun @ SV1622 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4391]) ).
thf(4997,plain,
! [SV2042: $i,SV1623: $i,SV1140: $i,SV541: $i] :
( ( ! [SY7038: $i,SY7039: $i,SY7040: $i,SY7041: $i] :
( ( ( hAPP @ SV541 @ ( c_Set_Oinsert @ SV1140 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1623 @ tc_bool ) ) @ SV1623 ) )
= SV1140 )
| ! [SY7042: $i,SY7043: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2042 @ SV541 @ SY7038 @ SY7039 @ SY7040 @ SY7041 @ SY7042 @ SY7043 @ SV1623 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4392]) ).
thf(4998,plain,
! [SV2043: $i,SV1624: $i,SV1141: $i,SV542: $i] :
( ( ! [SY7044: $i,SY7045: $i,SY7046: $i,SY7047: $i] :
( ( ( hAPP @ SV542 @ ( c_Set_Oinsert @ SV1141 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1624 @ tc_bool ) ) @ SV1624 ) )
= SV1141 )
| ! [SY7048: $i,SY7049: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV542 @ SV2043 @ SY7044 @ SY7045 @ SY7046 @ SY7047 @ SY7048 @ SY7049 @ SV1624 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4393]) ).
thf(4999,plain,
! [SV1625: $i,SV1143: $i,SV544: $i] :
( ( ( c_Com_Ocom_OWhile @ SV544 @ SV1143 )
= ( c_Com_Ocom_OBODY @ SV1625 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4394]) ).
thf(5000,plain,
! [SV2044: $i,SV1626: $i,SV1144: $i,SV545: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1144 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1626 @ ( c_Collect @ SV2044 @ SV545 ) @ ( tc_fun @ SV545 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ SV2044 @ SV1144 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1144 ) @ SV1626 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4395]) ).
thf(5001,plain,
! [SV1627: $i,SV1145: $i,SV547: $i] :
( ( ( hBOOL @ ( hAPP @ SV547 @ ( hAPP @ SV1145 @ SV1627 ) ) )
= $true )
| ( ( ! [SY6589: $i,SY6590: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV1145 @ SV547 @ SY6589 @ SY6590 ) @ SV1627 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4396]) ).
thf(5002,plain,
! [SV2045: $i,SV1628: $i,SV1146: $i,SV548: $i] :
( ( ! [SY7050: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV548 @ SV1146 @ SV1628 @ SV2045 ) @ SY7050 ) )
| ~ ( hBOOL @ ( hAPP @ SV1146 @ ( hAPP @ SV548 @ SY7050 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4397]) ).
thf(5003,plain,
! [SV1629: $i,SV1147: $i,SV549: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV549 @ SV1147 @ SV1629 )
= $true )
| ( ( ! [SY6593: $i] :
~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV549 @ ( c_Set_Oinsert @ SY6593 @ SV1147 @ ( tc_Hoare__Mirabelle_Otriple @ SV1629 ) ) @ SV1629 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4398]) ).
thf(5004,plain,
! [SV2046: $i,SV1630: $i,SV1148: $i,SV550: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV550 @ ( c_Set_Oinsert @ SV1148 @ SV1630 @ ( tc_Hoare__Mirabelle_Otriple @ SV2046 ) ) @ SV2046 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV550 @ SV1630 @ SV2046 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV550 @ ( c_Set_Oinsert @ SV1148 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2046 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2046 ) ) @ SV2046 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4399]) ).
thf(5005,plain,
! [SV2047: $i,SV1631: $i,SV1149: $i,SV551: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV551 @ SV1149 @ ( tc_fun @ SV1631 @ tc_bool ) ) @ SV2047 ) )
| ~ ( hBOOL @ ( hAPP @ SV1149 @ SV2047 ) )
| ~ ( hBOOL @ ( hAPP @ SV551 @ SV2047 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4400]) ).
thf(5006,plain,
! [SV1632: $i,SV1150: $i,SV552: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV552 ) )
= $true )
| ( ( ! [SY6596: $i,SY6597: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV1150 @ SV1632 @ SV552 )
!= ( c_HOL_Ominus__class_Ominus @ SY6596 @ SY6597 @ SV552 ) )
| ( c_HOL_Oord__class_Oless @ SY6596 @ SY6597 @ SV552 )
| ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SV1632 @ SV552 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4401]) ).
thf(5007,plain,
! [SV1633: $i,SV1151: $i,SV553: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV553 ) )
= $true )
| ( ( ! [SY6598: $i,SY6599: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV1151 @ SV1633 @ SV553 )
!= ( c_HOL_Ominus__class_Ominus @ SY6598 @ SY6599 @ SV553 ) )
| ( c_HOL_Oord__class_Oless @ SV1151 @ SV1633 @ SV553 )
| ~ ( c_HOL_Oord__class_Oless @ SY6598 @ SY6599 @ SV553 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4402]) ).
thf(5008,plain,
! [SV1154: $i,SV556: $i,SV2048: $i] :
( ( ( ! [SY7051: $i] :
( ~ ( c_Fun_Oinj__on @ SV2048 @ SV556 @ SV1154 @ SY7051 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV2048 @ SV556 @ SV1154 @ SY7051 ) @ SY7051 ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV556 @ SV1154 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4404]) ).
thf(5009,plain,
! [SV1635: $i,SV1156: $i,SV558: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV558 ) @ SV1156 ) @ SV1635 ) )
= $true )
| ( ( ! [SY6600: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SY6600 ) @ SV1156 ) @ SV1635 ) )
| ! [SY6601: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY6601 @ SY6600 @ SV558 ) ) @ SV1156 ) @ SV1635 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4406]) ).
thf(5010,plain,
! [SV561: $i,SV2049: $i] :
( ( ( ! [SY7052: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV2049 @ SY7052 @ SV561 )
| ~ ( c_HOL_Oord__class_Oless @ SY7052 @ SV2049 @ SV561 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV561 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4408]) ).
thf(5011,plain,
! [SV562: $i,SV2050: $i] :
( ( ( ! [SY7053: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV2050 @ SY7053 @ SV562 )
| ~ ( c_HOL_Oord__class_Oless @ SY7053 @ SV2050 @ SV562 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV562 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4409]) ).
thf(5012,plain,
! [SV563: $i,SV2051: $i] :
( ( ( ! [SY7054: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV2051 @ SY7054 @ SV563 )
| ~ ( c_HOL_Oord__class_Oless @ SY7054 @ SV2051 @ SV563 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV563 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4410]) ).
thf(5013,plain,
! [SV564: $i,SV2052: $i] :
( ( ( ! [SY7055: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV2052 @ SY7055 @ SV564 )
| ~ ( c_HOL_Oord__class_Oless @ SY7055 @ SV2052 @ SV564 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV564 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4411]) ).
thf(5014,plain,
! [SV1636: $i,SV1159: $i,SV565: $i] :
( ( ( hBOOL @ ( hAPP @ SV565 @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ SV1159 @ SV565 @ SV1636 ) ) )
= $true )
| ( ( ! [SY6602: $i] :
( ~ ( hBOOL @ ( hAPP @ SV565 @ SY6602 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1636 ) @ SY6602 ) @ SV1159 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4412]) ).
thf(5015,plain,
! [SV2053: $i,SV1637: $i,SV1160: $i,SV566: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV566 @ SV1160 ) @ SV1637 ) )
| ! [SY7056: $i,SY7057: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2053 ) @ SV1637 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SY7056 @ SV566 @ SV1160 @ SY7057 @ SV2053 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4413]) ).
thf(5016,plain,
! [SV2054: $i,SV1638: $i,SV1161: $i,SV567: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV567 @ SV1161 ) @ SV1638 ) )
| ! [SY7058: $i,SY7059: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2054 ) @ SV1161 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV567 @ SY7058 @ SY7059 @ SV1638 @ SV2054 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4414]) ).
thf(5017,plain,
! [SV1639: $i,SV1162: $i,SV568: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV568 ) @ SV1162 ) @ SV1639 ) )
= $true )
| ( ( ! [SY6609: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV568 ) @ SV1162 ) @ SY6609 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY6609 @ SV1639 @ ( tc_fun @ SV568 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4415]) ).
thf(5018,plain,
! [SV1643: $i,SV1166: $i,SV572: $i] :
( ( ( hBOOL @ ( hAPP @ SV572 @ SV1166 ) )
= $true )
| ( ( ! [SY6610: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1643 ) @ SV1166 ) @ SY6610 ) )
| ~ ( hBOOL @ ( hAPP @ SV572 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6610 @ SV572 @ SV1643 ) ) )
| ! [SY6611: $i] :
~ ( hBOOL @ ( hAPP @ SY6611 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6610 @ SY6611 @ SV1643 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4419]) ).
thf(5019,plain,
! [SV1644: $i,SV1167: $i,SV573: $i] :
( ( ( hBOOL @ ( hAPP @ SV573 @ SV1167 ) )
= $true )
| ( ( ! [SY6612: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1644 ) @ SV1167 ) @ SY6612 ) )
| ! [SY6613: $i] :
~ ( hBOOL @ ( hAPP @ SY6613 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6612 @ SY6613 @ SV1644 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV573 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6612 @ SV573 @ SV1644 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4420]) ).
thf(5020,plain,
! [SV1645: $i,SV1168: $i,SV574: $i] :
( ( ( hBOOL @ ( hAPP @ SV574 @ SV1168 ) )
= $true )
| ( ( ! [SY6614: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1645 ) @ SV1168 ) @ SY6614 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1645 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6614 @ SV574 @ SV1645 ) ) @ SY6614 ) )
| ! [SY6615: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1645 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6614 @ SY6615 @ SV1645 ) ) @ SY6614 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4421]) ).
thf(5021,plain,
! [SV1646: $i,SV1169: $i,SV575: $i] :
( ( ( hBOOL @ ( hAPP @ SV575 @ SV1169 ) )
= $true )
| ( ( ! [SY6616: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1646 ) @ SV1169 ) @ SY6616 ) )
| ! [SY6617: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1646 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6616 @ SY6617 @ SV1646 ) ) @ SY6616 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1646 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SY6616 @ SV575 @ SV1646 ) ) @ SY6616 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4422]) ).
thf(5022,plain,
! [SV1647: $i,SV1170: $i,SV576: $i] :
( ( ( hBOOL @ ( hAPP @ SV576 @ SV1170 ) )
= $true )
| ( ( ! [SY6618: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1647 ) @ SV1170 ) @ SY6618 ) )
| ! [SY6619: $i] :
( ~ ( hBOOL @ ( hAPP @ SV576 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SY6618 @ SY6619 @ SV576 @ SV1647 ) ) )
| ~ ( hBOOL @ ( hAPP @ SY6619 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SY6618 @ SY6619 @ SV576 @ SV1647 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4423]) ).
thf(5023,plain,
! [SV1648: $i,SV1171: $i,SV577: $i] :
( ( ( hBOOL @ ( hAPP @ SV577 @ SV1171 ) )
= $true )
| ( ( ! [SY6620: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1648 ) @ SV1171 ) @ SY6620 ) )
| ! [SY6621: $i] :
( ~ ( hBOOL @ ( hAPP @ SY6621 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SY6620 @ SV577 @ SY6621 @ SV1648 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV577 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SY6620 @ SV577 @ SY6621 @ SV1648 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4424]) ).
thf(5024,plain,
! [SV1649: $i,SV1172: $i,SV578: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV578 ) @ SV1172 ) @ SV1649 ) ) )
= $true )
| ( ( ! [SY6622: $i] :
( ( hBOOL @ ( hAPP @ SY6622 @ SV1172 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV578 ) @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ SV1649 @ SY6622 @ SV578 ) ) @ SV1649 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4425]) ).
thf(5025,plain,
! [SV1650: $i,SV1173: $i,SV579: $i] :
( ( ( hBOOL @ ( hAPP @ SV579 @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1173 @ SV579 @ SV1650 ) ) )
= $true )
| ( ( ! [SY6623: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1650 ) @ SY6623 ) @ SV1173 ) )
| ~ ( hBOOL @ ( hAPP @ SV579 @ SY6623 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4426]) ).
thf(5026,plain,
! [SV1651: $i,SV1174: $i,SV580: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV580 @ SV1174 ) @ SV1651 ) )
= $true )
| ( ( ! [SY6624: $i,SY6625: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6624 ) @ SV1651 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV580 @ SV1174 @ SY6625 @ SY6624 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4427]) ).
thf(5027,plain,
! [SV1652: $i,SV1175: $i,SV581: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV581 @ SV1175 ) @ SV1652 ) )
= $true )
| ( ( ! [SY6626: $i,SY6627: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6626 ) @ SV1175 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV581 @ SY6627 @ SV1652 @ SY6626 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4428]) ).
thf(5028,plain,
! [SV1653: $i,SV1176: $i,SV582: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV582 ) @ SV1176 ) @ SV1653 ) )
= $true )
| ( ( ! [SY6628: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV582 ) @ SV1176 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY6628 @ SV1653 @ ( tc_fun @ SV582 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4429]) ).
thf(5029,plain,
! [SV1654: $i,SV1177: $i,SV583: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV583 ) @ SV1177 ) @ SV1654 ) )
= $true )
| ( ( ! [SY6629: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV583 ) @ SV1177 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1654 @ SY6629 @ ( tc_fun @ SV583 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4430]) ).
thf(5030,plain,
! [SV2055: $i,SV1655: $i,SV1178: $i,SV584: $i] :
( ( ( ( hAPP @ SV584 @ SV1178 )
!= ( hAPP @ SV584 @ SV1655 ) )
| ! [SY7060: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2055 ) @ SV1655 ) @ SY7060 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2055 ) @ SV1178 ) @ SY7060 ) )
| ( SV1178 = SV1655 )
| ! [SY7061: $i] :
~ ( c_Fun_Oinj__on @ SV584 @ SY7060 @ SV2055 @ SY7061 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4431]) ).
thf(5031,plain,
! [SV2056: $i,SV1656: $i,SV1179: $i,SV585: $i] :
( ( ( ( hAPP @ SV585 @ SV1179 )
!= ( hAPP @ SV585 @ SV1656 ) )
| ! [SY7062: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2056 ) @ SV1656 ) @ SY7062 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2056 ) @ SV1179 ) @ SY7062 ) )
| ! [SY7063: $i] :
~ ( c_Fun_Oinj__on @ SV585 @ SY7062 @ SV2056 @ SY7063 )
| ( SV1179 = SV1656 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4432]) ).
thf(5032,plain,
! [SV2057: $i,SV1657: $i,SV1180: $i,SV586: $i] :
( ( ( ( hAPP @ SV586 @ SV1180 )
!= ( hAPP @ SV586 @ SV1657 ) )
| ! [SY7064: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2057 ) @ SV1657 ) @ SY7064 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2057 ) @ SV1180 ) @ SY7064 ) )
| ! [SY7065: $i] :
~ ( c_Fun_Oinj__on @ SV586 @ SY7064 @ SV2057 @ SY7065 )
| ( SV1180 = SV1657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4433]) ).
thf(5033,plain,
! [SV2058: $i,SV1658: $i,SV1181: $i,SV587: $i] :
( ( ( ( hAPP @ SV587 @ SV1181 )
!= ( hAPP @ SV587 @ SV1658 ) )
| ! [SY7066: $i] :
( ! [SY7067: $i] :
~ ( c_Fun_Oinj__on @ SV587 @ SV2058 @ SY7066 @ SY7067 )
| ( SV1181 = SV1658 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7066 ) @ SV1658 ) @ SV2058 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7066 ) @ SV1181 ) @ SV2058 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4434]) ).
thf(5034,plain,
! [SV1182: $i,SV588: $i] :
( ( ( hBOOL @ ( hAPP @ SV588 @ SV1182 ) )
= $false )
| ( ( ! [SY5867: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY5867 ) @ SV1182 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY5867 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4435]) ).
thf(5035,plain,
! [SV1659: $i,SV1183: $i,SV589: $i] :
( ( ( ( hAPP @ ( c_COMBC @ ( c_in @ SV589 ) @ SV589 @ ( tc_fun @ SV589 @ tc_bool ) @ tc_bool ) @ SV1183 )
!= ( hAPP @ ( c_COMBC @ ( c_in @ SV589 ) @ SV589 @ ( tc_fun @ SV589 @ tc_bool ) @ tc_bool ) @ SV1659 ) )
= $true )
| ( ( SV1183 = SV1659 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4436]) ).
thf(5036,plain,
! [SV1660: $i,SV1184: $i,SV590: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV590 ) @ SV1184 ) @ ( c_Collect @ SV1660 @ SV590 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1660 @ SV1184 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4437]) ).
thf(5037,plain,
! [SV591: $i,SV1185: $i,SV2059: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2059 ) @ SV1185 ) @ ( c_Collect @ SV591 @ SV2059 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV591 @ SV1185 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4438]) ).
thf(5038,plain,
! [SV2060: $i,SV1661: $i,SV1186: $i,SV592: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV592 ) @ SV1186 ) @ ( c_SetInterval_Oord_OatMost @ SV1661 @ SV2060 @ SV592 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1661 @ SV1186 ) @ SV2060 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4439]) ).
thf(5039,plain,
! [SV1662: $i,SV1187: $i,SV593: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV593 @ SV1187 ) @ SV1662 ) )
= $true )
| ( ( ! [SY6643: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6643 ) @ SV1187 ) @ ( c_SetInterval_Oord_OatMost @ SV593 @ SV1662 @ SY6643 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4440]) ).
thf(5040,plain,
! [SV2061: $i,SV1663: $i,SV1188: $i,SV594: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV594 ) @ SV1188 ) @ ( c_HOL_Ominus__class_Ominus @ SV1663 @ SV2061 @ ( tc_fun @ SV594 @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV594 ) @ SV1188 ) @ SV2061 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV594 ) @ SV1188 ) @ SV1663 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4441]) ).
thf(5041,plain,
! [SV2062: $i,SV1664: $i,SV1189: $i,SV595: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV595 ) @ SV1189 ) @ ( c_HOL_Ominus__class_Ominus @ SV1664 @ SV2062 @ ( tc_fun @ SV595 @ tc_bool ) ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV595 ) @ SV1189 ) @ SV2062 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV595 ) @ SV1189 ) @ SV1664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4442]) ).
thf(5042,plain,
! [SV1665: $i,SV1190: $i,SV596: $i] :
( ( ( hBOOL @ ( hAPP @ SV596 @ SV1190 ) )
= $true )
| ( ( ! [SY6646: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1665 ) @ SV1190 ) @ SY6646 ) )
| ! [SY6647: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1665 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SY6646 @ SY6647 @ SV596 @ SV1665 ) ) @ SY6646 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4443]) ).
thf(5043,plain,
! [SV1666: $i,SV1191: $i,SV597: $i] :
( ( ( hBOOL @ ( hAPP @ SV597 @ SV1191 ) )
= $true )
| ( ( ! [SY6648: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1666 ) @ SV1191 ) @ SY6648 ) )
| ! [SY6649: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1666 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SY6648 @ SV597 @ SY6649 @ SV1666 ) ) @ SY6648 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4444]) ).
thf(5044,plain,
! [SV1667: $i,SV1192: $i,SV598: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV598 ) @ SV1192 ) @ SV1667 ) ) )
= $true )
| ( ( ! [SY6650: $i] :
( ( hBOOL @ ( hAPP @ SY6650 @ SV1192 ) )
| ~ ( hBOOL @ ( hAPP @ SY6650 @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ SV1667 @ SY6650 @ SV598 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4445]) ).
thf(5045,plain,
! [SV2063: $i,SV1668: $i,SV1193: $i,SV599: $i] :
( ( ( ( c_Set_Oinsert @ SV599 @ SV1193 @ SV1668 )
!= ( c_Set_Oinsert @ SV599 @ SV2063 @ SV1668 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1668 ) @ SV599 ) @ SV2063 ) )
| ( SV1193 = SV2063 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1668 ) @ SV599 ) @ SV1193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4446]) ).
thf(5046,plain,
! [SV1669: $i,SV1194: $i,SV600: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV600 ) @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ SV1194 @ SV1669 @ SV600 ) ) @ SV1194 ) )
= $true )
| ( ( ! [SY6652: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV600 ) @ SY6652 ) @ SV1194 ) )
| ~ ( hBOOL @ ( hAPP @ SV1669 @ SY6652 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4447]) ).
thf(5047,plain,
! [SV2064: $i,SV1670: $i,SV1195: $i,SV601: $i] :
( ( ! [SY7068: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV601 ) @ SV1195 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1670 @ SV2064 @ SY7068 @ ( tc_fun @ SV601 @ tc_bool ) ) ) )
| ! [SY7069: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV601 ) @ SV1195 ) @ ( hAPP @ SV2064 @ SY7069 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7068 ) @ SY7069 ) @ SV1670 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4448]) ).
thf(5048,plain,
! [SV2065: $i,SV1671: $i,SV1196: $i,SV602: $i] :
( ( ! [SY7070: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV602 ) @ SV1196 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1671 @ SV2065 @ SY7070 @ ( tc_fun @ SV602 @ tc_bool ) ) ) )
| ! [SY7071: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV602 ) @ SV1196 ) @ ( hAPP @ SV2065 @ SY7071 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7070 ) @ SY7071 ) @ SV1671 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4449]) ).
thf(5049,plain,
! [SV2066: $i,SV1672: $i,SV1197: $i,SV603: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV603 ) @ SV1197 ) @ ( c_SetInterval_Oord_OgreaterThan @ SV1672 @ SV2066 @ SV603 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1672 @ SV2066 ) @ SV1197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4450]) ).
thf(5050,plain,
! [SV1673: $i,SV1198: $i,SV604: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV604 @ SV1198 ) @ SV1673 ) )
= $true )
| ( ( ! [SY6660: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6660 ) @ SV1673 ) @ ( c_SetInterval_Oord_OgreaterThan @ SV604 @ SV1198 @ SY6660 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4451]) ).
thf(5051,plain,
! [SV2067: $i,SV1674: $i,SV1199: $i,SV605: $i] :
( ( ! [SY7072: $i] :
( ( hBOOL @ ( hAPP @ SV605 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SV1199 @ SV1674 @ SV605 @ SV2067 @ SY7072 ) ) )
| ! [SY7073: $i] :
( ~ ( hBOOL @ ( hAPP @ SV605 @ SY7073 ) )
| ! [SY7074: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7072 ) @ SY7073 ) @ ( hAPP @ SV1674 @ SY7074 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2067 ) @ SY7074 ) @ SV1199 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4452]) ).
thf(5052,plain,
! [SV2068: $i,SV1675: $i,SV1200: $i,SV606: $i] :
( ( ! [SY7075: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV606 ) @ SV1200 ) @ ( c_Set_Ovimage @ SV1675 @ SV2068 @ SV606 @ SY7075 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7075 ) @ ( hAPP @ SV1675 @ SV1200 ) ) @ SV2068 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4453]) ).
thf(5053,plain,
! [SV2069: $i,SV1676: $i,SV1201: $i,SV607: $i] :
( ( ! [SY7076: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV607 ) @ SV1201 ) @ ( c_Set_Ovimage @ SV1676 @ SV2069 @ SV607 @ SY7076 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7076 ) @ ( hAPP @ SV1676 @ SV1201 ) ) @ SV2069 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4454]) ).
thf(5054,plain,
! [SV2070: $i,SV1677: $i,SV1202: $i,SV608: $i] :
( ( ! [SY7077: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV608 ) @ SV1202 ) @ ( c_Set_Ovimage @ SV1677 @ SV2070 @ SV608 @ SY7077 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7077 ) @ ( hAPP @ SV1677 @ SV1202 ) ) @ SV2070 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4455]) ).
thf(5055,plain,
! [SV2071: $i,SV1678: $i,SV1203: $i,SV609: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV609 ) @ ( hAPP @ SV1203 @ SV1678 ) ) @ SV2071 ) )
| ! [SY7078: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7078 ) @ SV1678 ) @ ( c_Set_Ovimage @ SV1203 @ SV2071 @ SY7078 @ SV609 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4456]) ).
thf(5056,plain,
! [SV2072: $i,SV1679: $i,SV1204: $i,SV610: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV610 ) @ ( hAPP @ SV1204 @ SV1679 ) ) @ SV2072 ) )
| ! [SY7079: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7079 ) @ SV1679 ) @ ( c_Set_Ovimage @ SV1204 @ SV2072 @ SY7079 @ SV610 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4457]) ).
thf(5057,plain,
! [SV2073: $i,SV1680: $i,SV1205: $i,SV611: $i] :
( ( ! [SY7080: $i,SY7081: $i,SY7082: $i,SY7083: $i,SY7084: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV611 @ ( hAPP @ SV1205 @ SV1680 ) ) @ SV2073 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7080 ) @ SV2073 ) @ SV1680 ) )
| ! [SY5930: $i,SY5931: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1205 @ SY7081 @ SV611 @ SY7082 @ SY7083 @ SY7084 @ SY5930 @ SY5931 @ SY7080 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4458]) ).
thf(5058,plain,
! [SV2074: $i,SV1681: $i,SV1206: $i,SV612: $i] :
( ( ! [SY7087: $i,SY7088: $i,SY7089: $i,SY7090: $i,SY7091: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV612 @ SV1206 ) @ ( hAPP @ SV1681 @ SV2074 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7087 ) @ SV1206 ) @ SV2074 ) )
| ! [SY6689: $i,SY6690: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY7088 @ SV1681 @ SV612 @ SY7089 @ SY7090 @ SY7091 @ SY6689 @ SY6690 @ SY7087 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4459]) ).
thf(5059,plain,
! [SV1682: $i,SV1207: $i,SV613: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV613 @ SV1207 ) @ SV1682 ) )
= $true )
| ( ( ! [SY6691: $i,SY6692: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6691 ) @ SV1207 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV613 @ SY6692 @ SV1682 @ SY6691 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4460]) ).
thf(5060,plain,
! [SV1683: $i,SV1208: $i,SV614: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV614 @ SV1208 ) @ SV1683 ) )
= $true )
| ( ( ! [SY6693: $i,SY6694: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6693 ) @ SV1683 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV614 @ SV1208 @ SY6694 @ SY6693 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4461]) ).
thf(5061,plain,
! [SV2075: $i,SV1684: $i,SV1209: $i,SV615: $i] :
( ( ( hBOOL @ ( hAPP @ SV615 @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV1209 @ SV1684 @ SV615 @ SV2075 ) ) )
| ! [SY7094: $i] :
( ~ ( hBOOL @ ( hAPP @ SV615 @ SY7094 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2075 ) @ SY7094 ) @ SV1684 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4462]) ).
thf(5062,plain,
! [SV2076: $i,SV1685: $i,SV1210: $i,SV616: $i] :
( ( ( hBOOL @ ( hAPP @ SV616 @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV1210 @ SV1685 @ SV616 @ SV2076 ) ) )
| ! [SY7095: $i] :
( ~ ( hBOOL @ ( hAPP @ SV616 @ SY7095 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2076 ) @ SY7095 ) @ SV1210 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4463]) ).
thf(5063,plain,
! [SV1686: $i,SV1211: $i,SV617: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV617 ) @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ SV1211 @ SV1686 @ SV617 ) ) @ SV1211 ) )
= $true )
| ( ( ! [SY6699: $i] :
( ~ ( hBOOL @ ( hAPP @ SV1686 @ SY6699 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV617 ) @ SY6699 ) @ SV1211 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4464]) ).
thf(5064,plain,
! [SV1687: $i,SV1212: $i,SV618: $i] :
( ( ( ( c_Set_Oinsert @ SV618 @ SV1212 @ SV1687 )
= SV1212 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1687 ) @ SV618 ) @ SV1212 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4465]) ).
thf(5065,plain,
! [SV2077: $i,SV1688: $i,SV1213: $i,SV619: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV619 ) @ SV1213 ) @ ( c_SetInterval_Oord_OlessThan @ SV1688 @ SV2077 @ SV619 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1688 @ SV1213 ) @ SV2077 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4466]) ).
thf(5066,plain,
! [SV1689: $i,SV1214: $i,SV620: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV620 @ SV1214 ) @ SV1689 ) )
= $true )
| ( ( ! [SY6701: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6701 ) @ SV1214 ) @ ( c_SetInterval_Oord_OlessThan @ SV620 @ SV1689 @ SY6701 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4467]) ).
thf(5067,plain,
! [SV2078: $i,SV1690: $i,SV1215: $i,SV621: $i] :
( ( ! [SY7096: $i,SY7097: $i,SY7098: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV621 @ SV1215 @ SV1690 @ ( tc_fun @ SV2078 @ ( tc_fun @ SY7096 @ tc_bool ) ) ) @ SY7097 ) @ SY7098 ) )
| ! [SY6706: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV1215 @ SY6706 ) @ SY7097 ) @ SY7098 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1690 ) @ SY6706 ) @ SV621 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4468]) ).
thf(5068,plain,
! [SV2079: $i,SV1691: $i,SV1216: $i,SV622: $i] :
( ( ! [SY7100: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV622 @ SV1216 @ SV1691 @ ( tc_fun @ SV2079 @ tc_bool ) ) @ SY7100 ) )
| ! [SY6709: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1216 @ SY6709 ) @ SY7100 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1691 ) @ SY6709 ) @ SV622 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4469]) ).
thf(5069,plain,
! [SV2080: $i,SV1692: $i,SV1217: $i,SV623: $i] :
( ( ! [SY7102: $i,SY7103: $i,SY7104: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV623 @ SV1217 @ SV1692 @ ( tc_fun @ SV2080 @ ( tc_fun @ SY7102 @ tc_bool ) ) ) @ SY7103 ) @ SY7104 ) )
| ! [SY6714: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV1217 @ SY6714 ) @ SY7103 ) @ SY7104 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1692 ) @ SY6714 ) @ SV623 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4470]) ).
thf(5070,plain,
! [SV2081: $i,SV1693: $i,SV1218: $i,SV624: $i] :
( ( ! [SY7106: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV624 @ SV1218 @ SV1693 @ ( tc_fun @ SV2081 @ tc_bool ) ) @ SY7106 ) )
| ! [SY6717: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1218 @ SY6717 ) @ SY7106 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1693 ) @ SY6717 ) @ SV624 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4471]) ).
thf(5071,plain,
! [SV2082: $i,SV1694: $i,SV1219: $i,SV625: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SV1219 ) @ SV1694 ) )
| ! [SY7108: $i,SY7109: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2082 ) @ SV1219 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SY7108 @ SV625 @ SY7109 @ SV1694 @ SV2082 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4472]) ).
thf(5072,plain,
! [SV2083: $i,SV1695: $i,SV1220: $i,SV626: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV626 @ SV1220 ) @ SV1695 ) )
| ! [SY7110: $i,SY7111: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2083 ) @ SV1695 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV626 @ SY7110 @ SV1220 @ SY7111 @ SV2083 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4473]) ).
thf(5073,plain,
! [SV1696: $i,SV1221: $i,SV627: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV627 ) @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ SV1221 @ SV1696 @ SV627 ) ) @ SV1221 ) )
= $true )
| ( ( ! [SY6724: $i] :
( ~ ( hBOOL @ ( hAPP @ SV1696 @ SY6724 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV627 ) @ SY6724 ) @ SV1221 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4474]) ).
thf(5074,plain,
! [SV1697: $i,SV1222: $i,SV628: $i] :
( ( ( hBOOL @ ( hAPP @ SV628 @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ SV1222 @ SV628 @ SV1697 ) ) )
= $true )
| ( ( ! [SY6725: $i] :
( ~ ( hBOOL @ ( hAPP @ SV628 @ SY6725 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1697 ) @ SY6725 ) @ SV1222 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4475]) ).
thf(5075,plain,
! [SV1698: $i,SV1223: $i,SV629: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV629 ) @ SV1223 ) @ SV1698 ) ) )
= $true )
| ( ( ! [SY6726: $i,SY6727: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6726 ) @ ( hAPP @ SY6727 @ SV1223 ) ) @ ( c_Set_Oimage @ SY6727 @ SV1698 @ SV629 @ SY6726 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4476]) ).
thf(5076,plain,
! [SV1699: $i,SV1224: $i,SV630: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV630 ) @ SV1224 ) @ SV1699 ) ) )
= $true )
| ( ( ! [SY6728: $i,SY6729: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6728 ) @ ( hAPP @ SY6729 @ SV1224 ) ) @ ( c_Set_Oimage @ SY6729 @ SV1699 @ SV630 @ SY6728 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4477]) ).
thf(5077,plain,
! [SV2084: $i,SV1700: $i,SV1225: $i,SV631: $i] :
( ( ! [SY7112: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV631 ) @ ( hAPP @ SV1225 @ SV1700 ) ) @ ( c_Set_Oimage @ SV1225 @ SV2084 @ SY7112 @ SV631 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7112 ) @ SV1700 ) @ SV2084 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4478]) ).
thf(5078,plain,
! [SV2085: $i,SV1701: $i,SV1226: $i,SV632: $i] :
( ( ! [SY7113: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV632 ) @ ( hAPP @ SV1226 @ SV1701 ) ) @ ( c_Set_Oimage @ SV1226 @ SV2085 @ SY7113 @ SV632 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7113 ) @ SV1701 ) @ SV2085 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4479]) ).
thf(5079,plain,
! [SV2086: $i,SV1702: $i,SV1227: $i,SV633: $i] :
( ( ( ( hAPP @ SV633 @ SV1227 )
= ( c_Option_Ooption_OSome @ ( c_Map_Osko__Map__XdomD__1__1 @ SV1227 @ SV633 @ SV1702 @ SV2086 ) @ SV2086 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1702 ) @ SV1227 ) @ ( c_Map_Odom @ SV633 @ SV1702 @ SV2086 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4480]) ).
thf(5080,plain,
! [SV2087: $i,SV1703: $i,SV1228: $i,SV634: $i] :
( ( ( c_Map_Omap__le @ SV634 @ SV1228 @ SV1703 @ SV2087 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1703 ) @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ SV634 @ SV1228 @ SV1703 @ SV2087 ) ) @ ( c_Map_Odom @ SV634 @ SV1703 @ SV2087 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4481]) ).
thf(5081,plain,
! [SV1704: $i,SV1229: $i,SV636: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV636 ) ) @ SV1229 ) @ SV1704 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SV636 ) @ tc_Com_Ocom ) ) @ SV1229 ) @ SV1704 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4482]) ).
thf(5082,plain,
! [SV1705: $i,SV1230: $i,SV637: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SV637 ) @ tc_Com_Ocom ) ) @ SV1230 ) @ SV1705 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV637 ) ) @ SV1230 ) @ SV1705 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4483]) ).
thf(5083,plain,
! [SV2088: $i,SV639: $i,SV1706: $i] :
( ( ( ~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV1706 @ SV639 @ SV2088 ) ) )
= $true )
| ( ( c_Com_OWT @ SV639 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4484]) ).
thf(5084,plain,
! [SV640: $i,SV2089: $i,SV1707: $i] :
( ( ( ~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV1707 @ SV2089 @ SV640 ) ) )
= $true )
| ( ( c_Com_OWT @ SV640 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4485]) ).
thf(5085,plain,
! [SV641: $i,SV1232: $i] :
( ( ( ~ ( c_Com_OWT @ SV1232 ) )
= $true )
| ( ( ~ ( c_Com_OWT @ SV641 ) )
= $true )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV641 @ SV1232 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4486]) ).
thf(5086,plain,
! [SV1708: $i,SV642: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV642 @ SV1708 ) )
= $false )
| ( ( c_Com_OWT @ SV642 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4487]) ).
thf(5087,plain,
! [SV643: $i,SV1709: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV1709 @ SV643 ) )
= $false )
| ( ( c_Com_OWT @ SV643 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4488]) ).
thf(5088,plain,
! [SV1710: $i,SV1233: $i,SV644: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV644 @ SV1233 @ SV1710 ) )
= $true )
| ( ( ~ ( c_Com_OWT @ SV1710 )
| ~ ( c_Com_OWT @ SV1233 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4489]) ).
thf(5089,plain,
! [SV646: $i,SV1235: $i] :
( ( ( c_Com_OWT @ SV1235 )
= $false )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ SV646 @ SV1235 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4490]) ).
thf(5090,plain,
! [SV647: $i,SV1711: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ SV1711 @ SV647 ) )
= $false )
| ( ( c_Com_OWT @ SV647 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4491]) ).
thf(5091,plain,
! [SV1712: $i,SV1236: $i,SV648: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ SV648 @ SV1236 @ SV1712 ) )
= $true )
| ( ( ~ ( c_Com_OWT @ SV1712 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4492]) ).
thf(5092,plain,
! [SV649: $i,SV2090: $i,SV1713: $i] :
( ( ( ~ ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ SV1713 @ SV2090 @ SV649 ) ) )
= $true )
| ( ( c_Com_OWT @ SV649 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4493]) ).
thf(5093,plain,
! [SV650: $i,SV1237: $i] :
( ( ( ~ ( c_Com_OWT @ SV1237 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ tc_Com_Opname ) @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ SV650 ) ) @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) ) )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV650 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ SV1237 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4494]) ).
thf(5094,plain,
! [SV1238: $i] :
( ( c_Hoare__Mirabelle_Ostate__not__singleton = $false )
| ( ( ( v_sko__Hoare__Mirabelle__Xsingle__stateE__1 @ SV1238 )
= SV1238 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4495]) ).
thf(5095,plain,
! [SV2091: $i,SV1714: $i,SV1239: $i,SV651: $i] :
( ( ! [SY7114: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV651 @ SV1239 @ SV1714 @ SV2091 ) @ SY7114 )
= ( hAPP @ SV651 @ SY7114 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1714 ) @ SY7114 ) @ ( c_Map_Odom @ SV1239 @ SV1714 @ SV2091 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4496]) ).
thf(5096,plain,
! [SV2092: $i,SV1715: $i,SV1240: $i,SV652: $i] :
( ( ! [SY7115: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV652 @ SV1240 @ SV1715 @ SV2092 ) @ SY7115 )
= ( hAPP @ SV1240 @ SY7115 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1715 ) @ SY7115 ) @ ( c_Map_Odom @ SV652 @ SV1715 @ SV2092 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4497]) ).
thf(5097,plain,
! [SV653: $i,SV2093: $i,SV1241: $i,SV1716: $i] :
( ( ( ( hAPP @ SV1716 @ SV1241 )
= ( c_Option_Ooption_ONone @ SV2093 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV653 ) @ SV1241 ) @ ( c_Map_Odom @ SV1716 @ SV653 @ SV2093 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4498]) ).
thf(5098,plain,
! [SV1717: $i,SV1242: $i,SV654: $i] :
( ( ( ( hAPP @ SV654 @ SV1242 )
!= ( c_Option_Ooption_ONone @ SV1717 ) )
= $true )
| ( ( ! [SY6744: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6744 ) @ SV1242 ) @ ( c_Map_Odom @ SV654 @ SY6744 @ SV1717 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4499]) ).
thf(5099,plain,
! [SV2094: $i,SV1718: $i,SV1243: $i,SV655: $i] :
( ( ( ( hAPP @ SV655 @ SV1243 )
!= ( c_Option_Ooption_OSome @ SV1718 @ SV2094 ) )
| ! [SY7116: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7116 ) @ SV1243 ) @ ( c_Map_Odom @ SV655 @ SY7116 @ SV2094 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4500]) ).
thf(5100,plain,
! [SV1719: $i,SV1244: $i,SV656: $i] :
( ( ( ( hAPP @ SV656 @ SV1244 )
= ( hAPP @ SV1719 @ SV1244 ) )
= $true )
| ( ( ! [SY6747: $i,SY6748: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6747 ) @ SV1244 ) @ ( c_Map_Odom @ SV656 @ SY6747 @ SY6748 ) ) )
| ~ ( c_Map_Omap__le @ SV656 @ SV1719 @ SY6747 @ SY6748 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4501]) ).
thf(5101,plain,
! [SV2095: $i,SV1720: $i,SV1245: $i,SV657: $i] :
( ( ! [SY7117: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV657 @ SV1245 @ SV1720 @ SV2095 ) @ SY7117 )
= ( hAPP @ SV1245 @ SY7117 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1720 ) @ SY7117 ) @ ( c_Map_Odom @ SV1245 @ SV1720 @ SV2095 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4502]) ).
thf(5102,plain,
! [SV1246: $i,SV658: $i] :
( ( ( ( hAPP @ c_Com_Obody @ SV658 )
= ( c_Option_Ooption_OSome @ SV1246 @ tc_Com_Ocom ) )
= $false )
| ( ( ~ c_Com_OWT__bodies
| ( c_Com_OWT @ SV1246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4503]) ).
thf(5103,plain,
! [SV1722: $i,SV1248: $i,SV659: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV659 ) @ SV1248 ) @ SV1722 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1722 @ SV1248 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4505]) ).
thf(5104,plain,
! [SV660: $i,SV1249: $i,SV2096: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2096 ) @ SV1249 ) @ SV660 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV660 @ SV1249 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4506]) ).
thf(5105,plain,
! [SV661: $i,SV1250: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV1250 )
= $false )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV661 @ SV1250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4507]) ).
thf(5106,plain,
! [SV662: $i,SV1251: $i] :
( ( ( class_Lattices_Olattice @ SV1251 )
= $false )
| ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV662 @ SV1251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4508]) ).
thf(5107,plain,
! [SV663: $i,SV1252: $i] :
( ( ( class_Lattices_Olattice @ SV1252 )
= $false )
| ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ SV663 @ SV1252 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4509]) ).
thf(5108,plain,
! [SV664: $i,SV1253: $i] :
( ( ( class_Lattices_Odistrib__lattice @ SV1253 )
= $false )
| ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ SV664 @ SV1253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4510]) ).
thf(5109,plain,
! [SV665: $i,SV1254: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV1254 )
= $false )
| ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV665 @ SV1254 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4511]) ).
thf(5110,plain,
! [SV666: $i,SV1255: $i] :
( ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV1255 ) )
= $true )
| ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV666 ) )
= $true )
| ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ SV666 @ SV1255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4512]) ).
thf(5111,plain,
! [SV667: $i,SV1256: $i] :
( ( ( class_Orderings_Opreorder @ SV1256 )
= $false )
| ( ( class_Orderings_Opreorder @ ( tc_fun @ SV667 @ SV1256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4513]) ).
thf(5112,plain,
! [SV668: $i,SV1257: $i] :
( ( ( class_Lattices_Olattice @ SV1257 )
= $false )
| ( ( class_Lattices_Olattice @ ( tc_fun @ SV668 @ SV1257 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4514]) ).
thf(5113,plain,
! [SV669: $i,SV1258: $i] :
( ( ( class_Orderings_Oorder @ SV1258 )
= $false )
| ( ( class_Orderings_Oorder @ ( tc_fun @ SV669 @ SV1258 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4515]) ).
thf(5114,plain,
! [SV670: $i,SV1259: $i] :
( ( ( class_Orderings_Obot @ SV1259 )
= $false )
| ( ( class_Orderings_Obot @ ( tc_fun @ SV670 @ SV1259 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4516]) ).
thf(5115,plain,
! [SV671: $i,SV1260: $i] :
( ( ( class_HOL_Oord @ SV1260 )
= $false )
| ( ( class_HOL_Oord @ ( tc_fun @ SV671 @ SV1260 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4517]) ).
thf(5116,plain,
! [SV1262: $i,SV674: $i,SV2097: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV2097 ) @ SV674 ) @ SV1262 ) ) )
= $true )
| ( ( SV674 = SV1262 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4519]) ).
thf(5117,plain,
! [SV1: $i,SV2098: $i,SV1723: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1723 @ SV2098 @ SV1 ) @ SV1723 @ SV1 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4520]) ).
thf(5118,plain,
! [SV2: $i,SV2099: $i,SV1724: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1724 @ SV2099 @ SV2 ) @ SV2099 @ SV2 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4521]) ).
thf(5119,plain,
! [SV3: $i,SV2100: $i,SV675: $i] :
( ( ( ! [SY7118: $i] :
( ( c_lessequals @ SV675 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2100 @ SY7118 @ SV3 ) @ SV3 )
| ~ ( c_lessequals @ SV675 @ SY7118 @ SV3 )
| ~ ( c_lessequals @ SV675 @ SV2100 @ SV3 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4522]) ).
thf(5120,plain,
! [SV4: $i,SV2101: $i,SV676: $i] :
( ( ( ! [SY7119: $i] :
( ( c_lessequals @ SV676 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2101 @ SY7119 @ SV4 ) @ SV4 )
| ~ ( c_lessequals @ SV676 @ SY7119 @ SV4 )
| ~ ( c_lessequals @ SV676 @ SV2101 @ SV4 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4523]) ).
thf(5121,plain,
! [SV5: $i,SV2102: $i,SV677: $i] :
( ( ( ! [SY7120: $i] :
( ( c_lessequals @ SV677 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2102 @ SY7120 @ SV5 ) @ SV5 )
| ~ ( c_lessequals @ SV677 @ SY7120 @ SV5 )
| ~ ( c_lessequals @ SV677 @ SV2102 @ SV5 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4524]) ).
thf(5122,plain,
! [SV6: $i,SV2103: $i,SV1725: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1725 @ SV2103 @ SV6 ) @ SV2103 @ SV6 )
= $true )
| ( ( class_Lattices_Olattice @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4525]) ).
thf(5123,plain,
! [SV7: $i,SV2104: $i,SV1726: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1726 @ SV2104 @ SV7 ) @ SV1726 @ SV7 )
= $true )
| ( ( class_Lattices_Olattice @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4526]) ).
thf(5124,plain,
! [SV2105: $i,SV1727: $i,SV1263: $i,SV678: $i,SV8: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV8 @ SV678 @ ( tc_fun @ SV1263 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1727 @ SV2105 @ ( tc_fun @ SV1263 @ tc_bool ) ) @ ( tc_fun @ SV1263 @ tc_bool ) )
| ~ ( c_lessequals @ SV678 @ SV2105 @ ( tc_fun @ SV1263 @ tc_bool ) )
| ~ ( c_lessequals @ SV8 @ SV1727 @ ( tc_fun @ SV1263 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4527]) ).
thf(5125,plain,
! [SV2106: $i,SV1728: $i,SV1264: $i,SV680: $i,SV11: $i] :
( ( ! [SY7121: $i,SY7122: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV11 @ SV680 @ SV1264 @ SV1728 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV2106 @ SY7121 @ SY7122 @ SV1728 ) )
| ( SV1264 = SY7122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4529]) ).
thf(5126,plain,
! [SV2107: $i,SV1729: $i,SV1265: $i,SV681: $i,SV12: $i] :
( ( ! [SY7123: $i] :
( ! [SY7124: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV12 @ SV681 @ SV1265 @ SV1729 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV2107 @ SY7123 @ SY7124 @ SV1729 ) )
| ( SV681 = SY7123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4530]) ).
thf(5127,plain,
! [SV2108: $i,SV1730: $i,SV1266: $i,SV682: $i,SV13: $i] :
( ( ! [SY7125: $i,SY7126: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV13 @ SV682 @ SV1266 @ SV1730 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV2108 @ SY7125 @ SY7126 @ SV1730 ) )
| ( SV13 = SV2108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4531]) ).
thf(5128,plain,
! [SV2109: $i,SV1732: $i,SV1268: $i,SV684: $i,SV15: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV15 @ SV684 @ SV1268 @ SV1732 @ SV2109 ) @ SV684 )
= SV1268 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4533]) ).
thf(5129,plain,
! [SV2110: $i,SV1734: $i,SV1270: $i,SV686: $i,SV17: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV17 @ SV686 @ SV1270 @ SV1734 @ SV2110 ) @ SV686 )
= SV1270 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4535]) ).
thf(5130,plain,
! [SV1272: $i,SV688: $i,SV19: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV19 @ SV688 @ ( tc_fun @ SV1272 @ tc_bool ) )
= SV688 )
= $false )
| ( ( c_lessequals @ SV19 @ SV688 @ ( tc_fun @ SV1272 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4537]) ).
thf(5131,plain,
! [SV1273: $i,SV20: $i,SV689: $i] :
( ( ( c_lessequals @ SV689 @ SV20 @ ( tc_fun @ SV1273 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV20 @ SV689 @ ( tc_fun @ SV1273 @ tc_bool ) )
= SV20 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4538]) ).
thf(5132,plain,
! [SV1274: $i,SV690: $i,SV21: $i] :
( ( ( c_lessequals @ SV21 @ SV690 @ ( tc_fun @ SV1274 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV21 @ SV690 @ ( tc_fun @ SV1274 @ tc_bool ) )
= SV690 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4539]) ).
thf(5133,plain,
! [SV22: $i,SV2111: $i,SV1736: $i] :
( ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1736 @ SV2111 @ SV22 )
= SV2111 )
| ~ ( c_lessequals @ SV1736 @ SV2111 @ SV22 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4540]) ).
thf(5134,plain,
! [SV23: $i,SV2112: $i,SV1737: $i] :
( ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1737 @ SV2112 @ SV23 )
!= SV2112 )
| ( c_lessequals @ SV1737 @ SV2112 @ SV23 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4541]) ).
thf(5135,plain,
! [SV24: $i,SV2113: $i,SV1738: $i] :
( ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1738 @ SV2113 @ SV24 )
= SV1738 )
| ~ ( c_lessequals @ SV2113 @ SV1738 @ SV24 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4542]) ).
thf(5136,plain,
! [SV25: $i,SV2114: $i,SV1739: $i] :
( ( ( ( c_lessequals @ SV1739 @ SV2114 @ SV25 )
| ~ ( c_HOL_Oord__class_Oless @ SV1739 @ SV2114 @ SV25 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV25 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4543]) ).
thf(5137,plain,
! [SV26: $i,SV2115: $i,SV1740: $i] :
( ( ( ( c_lessequals @ SV1740 @ SV2115 @ SV26 )
| ~ ( c_HOL_Oord__class_Oless @ SV1740 @ SV2115 @ SV26 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV26 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4544]) ).
thf(5138,plain,
! [SV27: $i,SV2116: $i,SV691: $i] :
( ( ( ! [SY7127: $i] :
( ( c_lessequals @ SV691 @ SV2116 @ ( tc_fun @ SY7127 @ SV27 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV691 @ SV2116 @ ( tc_fun @ SY7127 @ SV27 ) ) ) )
= $true )
| ( ( class_HOL_Oord @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4545]) ).
thf(5139,plain,
! [SV1275: $i,SV692: $i,SV28: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV28 @ SV692 @ ( tc_fun @ SV1275 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV28 @ SV692 @ ( tc_fun @ SV1275 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4546]) ).
thf(5140,plain,
! [SV29: $i,SV2117: $i,SV1741: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1741 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1741 @ SV2117 @ SV29 ) @ SV29 )
= SV1741 )
= $true )
| ( ( class_Lattices_Olattice @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4547]) ).
thf(5141,plain,
! [SV30: $i,SV2118: $i,SV1742: $i] :
( ( ( ( SV1742 = SV2118 )
| ~ ( c_lessequals @ SV1742 @ SV2118 @ SV30 )
| ~ ( c_lessequals @ SV2118 @ SV1742 @ SV30 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4548]) ).
thf(5142,plain,
! [SV31: $i,SV2119: $i,SV1743: $i] :
( ( ( ( SV1743 = SV2119 )
| ~ ( c_lessequals @ SV2119 @ SV1743 @ SV31 )
| ~ ( c_lessequals @ SV1743 @ SV2119 @ SV31 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV31 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4549]) ).
thf(5143,plain,
! [SV32: $i,SV2120: $i,SV1744: $i] :
( ( ( ( SV1744 = SV2120 )
| ~ ( c_lessequals @ SV2120 @ SV1744 @ SV32 )
| ~ ( c_lessequals @ SV1744 @ SV2120 @ SV32 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV32 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4550]) ).
thf(5144,plain,
! [SV1745: $i,SV33: $i,SV693: $i] :
( ( ( ~ ( c_lessequals @ SV693 @ SV33 @ ( tc_fun @ SV1745 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV33 @ SV693 @ ( tc_fun @ SV1745 @ tc_bool ) ) )
= $true )
| ( ( SV33 = SV693 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4551]) ).
thf(5145,plain,
! [SV1746: $i,SV34: $i,SV694: $i] :
( ( ( ~ ( c_lessequals @ SV694 @ SV34 @ ( tc_fun @ SV1746 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV34 @ SV694 @ ( tc_fun @ SV1746 @ tc_bool ) ) )
= $true )
| ( ( SV34 = SV694 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4552]) ).
thf(5146,plain,
! [SV35: $i,SV2121: $i,SV1747: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1747 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1747 @ SV2121 @ SV35 ) @ SV35 )
= SV1747 )
= $true )
| ( ( class_Lattices_Olattice @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4553]) ).
thf(5147,plain,
! [SV36: $i,SV2122: $i,SV695: $i] :
( ( ( ! [SY7128: $i] :
( ( c_HOL_Oord__class_Oless @ SV695 @ SV2122 @ ( tc_fun @ SY7128 @ SV36 ) )
| ( c_lessequals @ SV2122 @ SV695 @ ( tc_fun @ SY7128 @ SV36 ) )
| ~ ( c_lessequals @ SV695 @ SV2122 @ ( tc_fun @ SY7128 @ SV36 ) ) ) )
= $true )
| ( ( class_HOL_Oord @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4554]) ).
thf(5148,plain,
! [SV37: $i,SV2123: $i,SV1748: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV1748 @ SV2123 @ SV37 )
| ( c_lessequals @ SV2123 @ SV1748 @ SV37 )
| ~ ( c_lessequals @ SV1748 @ SV2123 @ SV37 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4555]) ).
thf(5149,plain,
! [SV38: $i,SV2124: $i,SV696: $i] :
( ( ( ! [SY7129: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV696 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2124 @ SY7129 @ SV38 ) @ SV38 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV696 @ SV2124 @ SV38 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV696 @ SY7129 @ SV38 ) @ SV38 ) @ SV38 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4556]) ).
thf(5150,plain,
! [SV2125: $i,SV1749: $i,SV1276: $i,SV697: $i,SV39: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV39 @ SV697 @ ( tc_fun @ SV1276 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1749 @ SV2125 @ ( tc_fun @ SV1276 @ tc_bool ) ) @ ( tc_fun @ SV1276 @ tc_bool ) )
| ~ ( c_lessequals @ SV2125 @ SV697 @ ( tc_fun @ SV1276 @ tc_bool ) )
| ~ ( c_lessequals @ SV39 @ SV1749 @ ( tc_fun @ SV1276 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4557]) ).
thf(5151,plain,
! [SV2126: $i,SV1750: $i,SV1277: $i,SV698: $i,SV40: $i] :
( ( ! [SY7130: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ SV40 @ SV698 @ SV1277 @ SV1750 @ SV2126 ) @ SV698 @ SY7130 @ SV1750 @ SV2126 )
= ( c_Fun_Ofun__upd @ SV40 @ SV698 @ SY7130 @ SV1750 @ SV2126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4558]) ).
thf(5152,plain,
! [SV701: $i,SV45: $i,SV1753: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1753 @ SV45 @ ( tc_fun @ SV701 @ tc_bool ) ) @ SV701 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV45 @ SV701 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4561]) ).
thf(5153,plain,
! [SV702: $i,SV1754: $i,SV46: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV46 @ SV1754 @ ( tc_fun @ SV702 @ tc_bool ) ) @ SV702 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV46 @ SV702 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4562]) ).
thf(5154,plain,
! [SV1755: $i,SV1278: $i,SV703: $i,SV47: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV47 @ SV703 @ ( tc_fun @ SV1278 @ tc_bool ) ) @ SV1755 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV47 @ SV1755 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4563]) ).
thf(5155,plain,
! [SV1756: $i,SV1279: $i,SV704: $i,SV48: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV48 @ SV704 @ ( tc_fun @ SV1279 @ tc_bool ) ) @ SV1756 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV704 @ SV1756 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4564]) ).
thf(5156,plain,
! [SV49: $i,SV705: $i,SV1757: $i] :
( ( ( hBOOL @ ( hAPP @ SV1757 @ SV705 ) )
= $true )
| ( ( ! [SY6781: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1757 @ SV49 @ ( tc_fun @ SY6781 @ tc_bool ) ) @ SV705 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV49 @ SV705 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4565]) ).
thf(5157,plain,
! [SV2127: $i,SV1758: $i,SV1280: $i,SV706: $i,SV50: $i] :
( ( ! [SY7131: $i] :
( ! [SY7132: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ SV50 @ SV706 @ SV1280 @ SV1758 @ SV2127 ) @ SY7131 @ SY7132 @ SV1758 @ SV2127 )
= ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ SV50 @ SY7131 @ SY7132 @ SV1758 @ SV2127 ) @ SV706 @ SV1280 @ SV1758 @ SV2127 ) )
| ( SV706 = SY7131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4566]) ).
thf(5158,plain,
! [SV2128: $i,SV1759: $i,SV1281: $i,SV707: $i,SV51: $i] :
( ( ! [SY7133: $i] :
( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ SV51 @ SV707 @ SV1281 @ SV1759 @ ( tc_Option_Ooption @ SV2128 ) ) @ ( c_Fun_Ofun__upd @ SY7133 @ SV707 @ SV1281 @ SV1759 @ ( tc_Option_Ooption @ SV2128 ) ) @ SV1759 @ SV2128 )
| ~ ( c_Map_Omap__le @ SV51 @ SY7133 @ SV1759 @ SV2128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4567]) ).
thf(5159,plain,
! [SV1760: $i,SV1282: $i,SV708: $i,SV52: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV52 @ SV708 @ ( tc_fun @ SV1282 @ tc_bool ) ) @ SV1760 @ ( tc_fun @ SV1282 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV52 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV708 @ SV1760 @ ( tc_fun @ SV1282 @ tc_bool ) ) @ ( tc_fun @ SV1282 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1760 @ SV52 @ ( tc_fun @ SV1282 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4568]) ).
thf(5160,plain,
! [SV1761: $i,SV1283: $i,SV709: $i,SV53: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV53 @ SV709 @ ( tc_fun @ SV1283 @ tc_bool ) ) @ SV1761 @ ( tc_fun @ SV1283 @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ SV53 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV709 @ SV1761 @ ( tc_fun @ SV1283 @ tc_bool ) ) @ ( tc_fun @ SV1283 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV1761 @ SV53 @ ( tc_fun @ SV1283 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4569]) ).
thf(5161,plain,
! [SV54: $i,SV1284: $i,SV710: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV710 @ SV1284 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV54 @ SV1284 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV54 @ SV710 @ ( tc_fun @ SV1284 @ tc_bool ) ) @ SV1284 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4570]) ).
thf(5162,plain,
! [SV55: $i,SV1285: $i,SV711: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV711 @ SV1285 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV55 @ SV1285 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV55 @ SV711 @ ( tc_fun @ SV1285 @ tc_bool ) ) @ SV1285 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4571]) ).
thf(5163,plain,
! [SV56: $i,SV2129: $i,SV712: $i,SV1286: $i] :
( ( ( ! [SY7134: $i] :
~ ( c_Finite__Set_Ofold__graph @ SV1286 @ SV712 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2129 @ tc_bool ) ) @ SV56 @ SV2129 @ SY7134 ) )
= $true )
| ( ( SV56 = SV712 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4572]) ).
thf(5164,plain,
! [SV2130: $i,SV1762: $i,SV1288: $i,SV714: $i,SV58: $i] :
( ( ( ( hAPP @ SV58 @ SV714 )
!= ( c_Option_Ooption_OSome @ SV1288 @ SV1762 ) )
| ( SV714 = SV2130 )
| ! [SY7135: $i,SY7136: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV58 @ SV2130 @ ( c_Option_Ooption_OSome @ SY7135 @ SV1762 ) @ SY7136 @ ( tc_Option_Ooption @ SV1762 ) ) @ SV714 )
= ( c_Option_Ooption_OSome @ SV1288 @ SV1762 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4573]) ).
thf(5165,plain,
! [SV2131: $i,SV1763: $i,SV1289: $i,SV715: $i,SV59: $i] :
( ( ! [SY7137: $i,SY7138: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV59 @ SV715 @ ( c_Option_Ooption_OSome @ SV1289 @ SV1763 ) @ SV2131 @ ( tc_Option_Ooption @ SV1763 ) ) @ SY7137 )
!= ( c_Option_Ooption_OSome @ SY7138 @ SV1763 ) )
| ( ( hAPP @ SV59 @ SY7137 )
= ( c_Option_Ooption_OSome @ SY7138 @ SV1763 ) )
| ( SV1289 = SY7138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4574]) ).
thf(5166,plain,
! [SV2132: $i,SV1764: $i,SV1290: $i,SV716: $i,SV60: $i] :
( ( ! [SY7139: $i,SY7140: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV60 @ SV716 @ ( c_Option_Ooption_OSome @ SV1290 @ SV1764 ) @ SV2132 @ ( tc_Option_Ooption @ SV1764 ) ) @ SY7139 )
!= ( c_Option_Ooption_OSome @ SY7140 @ SV1764 ) )
| ( ( hAPP @ SV60 @ SY7139 )
= ( c_Option_Ooption_OSome @ SY7140 @ SV1764 ) )
| ( SY7139 = SV716 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4575]) ).
thf(5167,plain,
! [SV1768: $i,SV1293: $i,SV720: $i,SV65: $i] :
( ( ( c_lessequals @ SV65 @ ( c_Set_Oinsert @ SV720 @ SV1293 @ SV1768 ) @ ( tc_fun @ SV1768 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV65 @ SV1293 @ ( tc_fun @ SV1768 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4579]) ).
thf(5168,plain,
! [SV721: $i,SV1294: $i,SV66: $i,SV2133: $i] :
( ( ( ~ ( c_lessequals @ ( c_Set_Oinsert @ SV2133 @ SV66 @ SV1294 ) @ SV721 @ ( tc_fun @ SV1294 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV66 @ SV721 @ ( tc_fun @ SV1294 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4580]) ).
thf(5169,plain,
! [SV1769: $i,SV1295: $i,SV722: $i,SV67: $i] :
( ( ( c_Finite__Set_Ofinite @ SV67 @ SV722 )
= $true )
| ( ( ! [SY6796: $i,SY6797: $i] :
~ ( c_Finite__Set_Ofold__graph @ SV1295 @ SV1769 @ SV67 @ SY6796 @ SV722 @ SY6797 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4581]) ).
thf(5170,plain,
! [SV70: $i,SV2134: $i,SV725: $i] :
( ( ( ! [SY7141: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV725 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2134 @ SY7141 @ SV70 ) @ SV70 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV725 @ SV2134 @ SV70 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV725 @ SY7141 @ SV70 ) @ SV70 ) ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4584]) ).
thf(5171,plain,
! [SV71: $i,SV2135: $i,SV726: $i] :
( ( ( ! [SY7142: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV726 @ SV2135 @ SV71 ) @ SY7142 @ SV71 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV726 @ SY7142 @ SV71 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2135 @ SY7142 @ SV71 ) @ SV71 ) ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4585]) ).
thf(5172,plain,
! [SV727: $i,SV72: $i,SV1772: $i,SV1298: $i] :
( ( ( ! [SY6798: $i,SY6799: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV1298 @ SV1772 @ ( c_Option_Ooption_OSome @ SV72 @ SY6798 ) @ SY6799 @ ( tc_Option_Ooption @ SY6798 ) ) @ SV1772 )
!= ( c_Option_Ooption_OSome @ SV727 @ SY6798 ) ) )
= $true )
| ( ( SV72 = SV727 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4586]) ).
thf(5173,plain,
! [SV1773: $i,SV1301: $i,SV730: $i,SV75: $i] :
( ( ( c_lessequals @ SV75 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV730 @ SV1301 @ ( tc_fun @ SV1773 @ tc_bool ) ) @ ( tc_fun @ SV1773 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV75 @ SV1301 @ ( tc_fun @ SV1773 @ tc_bool ) )
| ~ ( c_lessequals @ SV75 @ SV730 @ ( tc_fun @ SV1773 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4587]) ).
thf(5174,plain,
! [SV1774: $i,SV1302: $i,SV731: $i,SV76: $i] :
( ( ( c_lessequals @ SV76 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV731 @ SV1302 @ ( tc_fun @ SV1774 @ tc_bool ) ) @ ( tc_fun @ SV1774 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV76 @ SV1302 @ ( tc_fun @ SV1774 @ tc_bool ) )
| ~ ( c_lessequals @ SV76 @ SV731 @ ( tc_fun @ SV1774 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4588]) ).
thf(5175,plain,
! [SV77: $i,SV2136: $i,SV732: $i] :
( ( ( ! [SY7143: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV732 @ SV2136 @ SV77 ) @ SY7143 @ SV77 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV732 @ SY7143 @ SV77 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2136 @ SY7143 @ SV77 ) @ SV77 ) ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4589]) ).
thf(5176,plain,
! [SV78: $i,SV2137: $i,SV733: $i] :
( ( ( ! [SY7144: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV733 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2137 @ SY7144 @ SV78 ) @ SV78 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV733 @ SV2137 @ SV78 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV733 @ SY7144 @ SV78 ) @ SV78 ) ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4590]) ).
thf(5177,plain,
! [SV2138: $i,SV1777: $i,SV1305: $i,SV736: $i,SV81: $i] :
( ( ! [SY7145: $i] :
( ( c_Set_Oimage @ SV81 @ ( c_Set_Oimage @ SV736 @ SV1305 @ SV1777 @ SV2138 ) @ SV2138 @ SY7145 )
= ( c_Set_Oimage @ ( c_COMBB @ SV81 @ SV736 @ SV2138 @ SY7145 @ SV1777 ) @ SV1305 @ SV1777 @ SY7145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4593]) ).
thf(5178,plain,
! [SV82: $i,SV2139: $i,SV737: $i] :
( ( ( ( c_lessequals @ SV737 @ SV2139 @ SV82 )
| ! [SY7146: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY7146 @ SV737 @ SV82 ) @ SV2139 @ SV82 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4594]) ).
thf(5179,plain,
! [SV83: $i,SV2140: $i,SV738: $i] :
( ( ( ( c_lessequals @ SV738 @ SV2140 @ SV83 )
| ! [SY7147: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV738 @ SY7147 @ SV83 ) @ SV2140 @ SV83 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV83 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4595]) ).
thf(5180,plain,
! [SV84: $i,SV2141: $i,SV739: $i] :
( ( ( ! [SY7148: $i] :
( ( c_lessequals @ SV739 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2141 @ SY7148 @ SV84 ) @ SV84 )
| ~ ( c_lessequals @ SV739 @ SY7148 @ SV84 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4596]) ).
thf(5181,plain,
! [SV85: $i,SV2142: $i,SV740: $i] :
( ( ( ! [SY7149: $i] : ( c_lessequals @ SV740 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2142 @ SY7149 @ SV85 ) @ SV85 )
| ~ ( c_lessequals @ SV740 @ SV2142 @ SV85 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4597]) ).
thf(5182,plain,
! [SV86: $i,SV2143: $i,SV741: $i] :
( ( ( ( c_lessequals @ SV741 @ SV2143 @ SV86 )
| ! [SY7150: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY7150 @ SV741 @ SV86 ) @ SV2143 @ SV86 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4598]) ).
thf(5183,plain,
! [SV87: $i,SV2144: $i,SV742: $i] :
( ( ( ( c_lessequals @ SV742 @ SV2144 @ SV87 )
| ! [SY7151: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV742 @ SY7151 @ SV87 ) @ SV2144 @ SV87 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV87 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4599]) ).
thf(5184,plain,
! [SV743: $i,SV1306: $i,SV2145: $i,SV88: $i] :
( ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV88 @ SV2145 @ ( tc_fun @ SV1306 @ tc_bool ) ) @ SV743 @ ( tc_fun @ SV1306 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV88 @ SV743 @ ( tc_fun @ SV1306 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4600]) ).
thf(5185,plain,
! [SV744: $i,SV1307: $i,SV89: $i,SV2146: $i] :
( ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2146 @ SV89 @ ( tc_fun @ SV1307 @ tc_bool ) ) @ SV744 @ ( tc_fun @ SV1307 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV89 @ SV744 @ ( tc_fun @ SV1307 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4601]) ).
thf(5186,plain,
! [SV90: $i,SV2147: $i,SV745: $i] :
( ( ( ( c_lessequals @ SV745 @ SV2147 @ SV90 )
| ! [SY7152: $i] :
( ~ ( c_lessequals @ SV745 @ SY7152 @ SV90 )
| ~ ( c_lessequals @ SY7152 @ SV2147 @ SV90 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4602]) ).
thf(5187,plain,
! [SV91: $i,SV2148: $i,SV746: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV746 @ SV2148 @ SV91 )
| ! [SY7153: $i] :
( ~ ( c_lessequals @ SV746 @ SY7153 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SY7153 @ SV2148 @ SV91 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4603]) ).
thf(5188,plain,
! [SV92: $i,SV2149: $i,SV747: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV747 @ SV2149 @ SV92 )
| ! [SY7154: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV747 @ SY7154 @ SV92 )
| ~ ( c_lessequals @ SY7154 @ SV2149 @ SV92 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV92 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4604]) ).
thf(5189,plain,
! [SV93: $i,SV2150: $i,SV748: $i] :
( ( ( ( c_lessequals @ SV748 @ SV2150 @ SV93 )
| ! [SY7155: $i] :
( ~ ( c_lessequals @ SY7155 @ SV2150 @ SV93 )
| ~ ( c_lessequals @ SV748 @ SY7155 @ SV93 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4605]) ).
thf(5190,plain,
! [SV96: $i,SV1308: $i,SV751: $i,SV2151: $i] :
( ( ( ~ ( c_lessequals @ SV2151 @ SV751 @ ( tc_fun @ SV1308 @ tc_bool ) )
| ~ ( c_lessequals @ SV96 @ SV2151 @ ( tc_fun @ SV1308 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV96 @ SV751 @ ( tc_fun @ SV1308 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4606]) ).
thf(5191,plain,
! [SV1778: $i,SV1309: $i,SV752: $i,SV97: $i] :
( ( ( c_Fun_Oinj__on @ SV97 @ SV752 @ SV1309 @ SV1778 )
= $true )
| ( ( ! [SY6802: $i] :
( ~ ( c_lessequals @ SV752 @ SY6802 @ ( tc_fun @ SV1309 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV97 @ SY6802 @ SV1309 @ SV1778 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4607]) ).
thf(5192,plain,
! [SV98: $i,SV753: $i,SV1779: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1779 @ SV753 ) ) )
= $true )
| ( ( ! [SY6803: $i] :
~ ( c_lessequals @ SV1779 @ SV98 @ ( tc_fun @ SY6803 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV98 @ SV753 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4608]) ).
thf(5193,plain,
! [SV101: $i,SV754: $i,SV1782: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV1782 @ SV754 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV101 @ SV1782 @ ( tc_fun @ SV754 @ tc_bool ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV101 @ SV754 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4611]) ).
thf(5194,plain,
! [SV102: $i,SV1310: $i,SV755: $i,SV2152: $i] :
( ( ( ~ ( c_lessequals @ SV2152 @ SV755 @ ( tc_fun @ SV1310 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV102 @ SV2152 @ ( tc_fun @ SV1310 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV102 @ SV755 @ ( tc_fun @ SV1310 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4612]) ).
thf(5195,plain,
! [SV103: $i,SV1311: $i,SV756: $i,SV2153: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2153 @ SV756 @ ( tc_fun @ SV1311 @ tc_bool ) )
| ~ ( c_lessequals @ SV103 @ SV2153 @ ( tc_fun @ SV1311 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV103 @ SV756 @ ( tc_fun @ SV1311 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4613]) ).
thf(5196,plain,
! [SV757: $i,SV104: $i,SV1783: $i] :
( ( ( ! [SY6804: $i] :
~ ( c_lessequals @ SV1783 @ SV104 @ ( tc_fun @ SY6804 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1783 @ SV757 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV104 @ SV757 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4614]) ).
thf(5197,plain,
! [SV758: $i,SV1784: $i,SV105: $i] :
( ( ( ~ ( c_lessequals @ SV105 @ SV1784 @ ( tc_fun @ SV758 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1784 @ SV758 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV105 @ SV758 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4615]) ).
thf(5198,plain,
! [SV106: $i,SV2154: $i,SV759: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV759 @ SV2154 @ SV106 )
| ! [SY7156: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY7156 @ SV2154 @ SV106 )
| ~ ( c_lessequals @ SV759 @ SY7156 @ SV106 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV106 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4616]) ).
thf(5199,plain,
! [SV107: $i,SV2155: $i,SV760: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV760 @ SV2155 @ SV107 )
| ! [SY7157: $i] :
( ~ ( c_lessequals @ SY7157 @ SV2155 @ SV107 )
| ~ ( c_HOL_Oord__class_Oless @ SV760 @ SY7157 @ SV107 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV107 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4617]) ).
thf(5200,plain,
! [SV2156: $i,SV1785: $i,SV1312: $i,SV761: $i,SV108: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV108 @ SV761 @ ( tc_fun @ SV1312 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1785 @ SV2156 @ ( tc_fun @ SV1312 @ tc_bool ) ) @ ( tc_fun @ SV1312 @ tc_bool ) )
| ~ ( c_lessequals @ SV761 @ SV2156 @ ( tc_fun @ SV1312 @ tc_bool ) )
| ~ ( c_lessequals @ SV108 @ SV1785 @ ( tc_fun @ SV1312 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4618]) ).
thf(5201,plain,
! [SV2157: $i,SV1786: $i,SV1313: $i,SV762: $i,SV109: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV109 @ SV762 @ ( c_Option_Ooption_OSome @ SV1313 @ SV1786 ) @ SV2157 @ ( tc_Option_Ooption @ SV1786 ) ) @ SV762 )
= ( c_Option_Ooption_OSome @ SV1313 @ SV1786 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4619]) ).
thf(5202,plain,
! [SV1787: $i,SV1314: $i,SV763: $i,SV110: $i] :
( ( ( ( hAPP @ SV110 @ SV763 )
!= ( c_Option_Ooption_OSome @ SV1314 @ SV1787 ) )
= $true )
| ( ( ! [SY6807: $i] :
( ( c_Fun_Ofun__upd @ SV110 @ SV763 @ ( c_Option_Ooption_OSome @ SV1314 @ SV1787 ) @ SY6807 @ ( tc_Option_Ooption @ SV1787 ) )
= SV110 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4620]) ).
thf(5203,plain,
! [SV2158: $i,SV1788: $i,SV1315: $i,SV764: $i,SV111: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV111 @ SV764 @ ( tc_fun @ SV1315 @ tc_bool ) ) @ SV1788 @ SV1315 @ ( tc_fun @ SV2158 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV111 @ SV1788 @ SV1315 @ ( tc_fun @ SV2158 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV764 @ SV1788 @ SV1315 @ ( tc_fun @ SV2158 @ tc_bool ) ) @ ( tc_fun @ SV2158 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4621]) ).
thf(5204,plain,
! [SV2159: $i,SV1789: $i,SV1316: $i,SV765: $i,SV112: $i] :
( ( ! [SY7158: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV112 @ SV765 @ SV1316 @ SV1789 @ SV2159 ) @ SY7158 )
= ( hAPP @ SV112 @ SY7158 ) )
| ( SY7158 = SV765 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4622]) ).
thf(5205,plain,
! [SV2160: $i,SV1790: $i,SV1317: $i,SV766: $i,SV113: $i] :
( ( ! [SY7159: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV113 @ SV766 @ SV1317 @ SV1790 @ SV2160 ) @ SY7159 )
= ( hAPP @ SV113 @ SY7159 ) )
| ( SY7159 = SV766 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4623]) ).
thf(5206,plain,
! [SV1791: $i,SV1318: $i,SV767: $i,SV114: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV114 @ ( c_HOL_Ominus__class_Ominus @ SV767 @ SV1318 @ ( tc_fun @ SV1791 @ tc_bool ) ) @ ( tc_fun @ SV1791 @ tc_bool ) )
= SV1318 )
= $true )
| ( ( ~ ( c_lessequals @ SV114 @ SV767 @ ( tc_fun @ SV1791 @ tc_bool ) )
| ~ ( c_lessequals @ SV1318 @ SV114 @ ( tc_fun @ SV1791 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4624]) ).
thf(5207,plain,
! [SV1319: $i,SV768: $i,SV115: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV115 )
= $false )
| ( ( ! [SY6127: $i,SY6128: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV768 @ SV1319 @ SV115 )
!= ( c_HOL_Ominus__class_Ominus @ SY6127 @ SY6128 @ SV115 ) )
| ( c_lessequals @ SY6128 @ SY6127 @ SV115 )
| ~ ( c_lessequals @ SV1319 @ SV768 @ SV115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4625]) ).
thf(5208,plain,
! [SV1320: $i,SV769: $i,SV116: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV116 )
= $false )
| ( ( ! [SY6129: $i,SY6130: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV769 @ SV1320 @ SV116 )
!= ( c_HOL_Ominus__class_Ominus @ SY6129 @ SY6130 @ SV116 ) )
| ( c_lessequals @ SV1320 @ SV769 @ SV116 )
| ~ ( c_lessequals @ SY6130 @ SY6129 @ SV116 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4626]) ).
thf(5209,plain,
! [SV2161: $i,SV1792: $i,SV1321: $i,SV770: $i,SV117: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV117 @ SV770 @ SV1321 @ SV1792 ) @ ( c_Set_Oimage @ SV117 @ SV2161 @ SV1321 @ SV1792 ) @ ( tc_fun @ SV1792 @ tc_bool ) )
| ~ ( c_lessequals @ SV770 @ SV2161 @ ( tc_fun @ SV1321 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4627]) ).
thf(5210,plain,
! [SV1322: $i,SV771: $i,SV118: $i] :
( ( ( c_lessequals @ SV118 @ SV771 @ ( tc_fun @ SV1322 @ tc_bool ) )
= $false )
| ( ( ! [SY6133: $i,SY6134: $i] : ( c_lessequals @ ( c_Set_Oimage @ SY6133 @ SV118 @ SV1322 @ SY6134 ) @ ( c_Set_Oimage @ SY6133 @ SV771 @ SV1322 @ SY6134 ) @ ( tc_fun @ SY6134 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4628]) ).
thf(5211,plain,
! [SV1793: $i,SV1323: $i,SV772: $i,SV119: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV119 @ SV772 @ SV1323 ) @ ( c_Set_Oinsert @ SV119 @ SV1793 @ SV1323 ) @ ( tc_fun @ SV1323 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV772 @ SV1793 @ ( tc_fun @ SV1323 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4629]) ).
thf(5212,plain,
! [SV121: $i,SV2162: $i,SV1794: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV1794 @ SV2162 @ SV121 )
| ( SV2162 = SV1794 )
| ~ ( c_lessequals @ SV1794 @ SV2162 @ SV121 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV121 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4630]) ).
thf(5213,plain,
! [SV122: $i,SV2163: $i,SV1795: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV1795 @ SV2163 @ SV122 )
| ~ ( c_lessequals @ SV1795 @ SV2163 @ SV122 )
| ( SV2163 = SV1795 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV122 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4631]) ).
thf(5214,plain,
! [SV1324: $i,SV773: $i,SV123: $i] :
( ( ( SV123 = SV773 )
= $true )
| ( ( ~ ( c_lessequals @ SV123 @ SV773 @ ( tc_fun @ SV1324 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV123 @ SV773 @ ( tc_fun @ SV1324 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4632]) ).
thf(5215,plain,
! [SV124: $i,SV2164: $i,SV1796: $i] :
( ( ( ( SV1796 = SV2164 )
| ( c_HOL_Oord__class_Oless @ SV1796 @ SV2164 @ SV124 )
| ~ ( c_lessequals @ SV1796 @ SV2164 @ SV124 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4633]) ).
thf(5216,plain,
! [SV125: $i,SV2165: $i,SV1797: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV1797 @ SV2165 @ SV125 )
| ( SV1797 = SV2165 )
| ~ ( c_lessequals @ SV1797 @ SV2165 @ SV125 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4634]) ).
thf(5217,plain,
! [SV1798: $i,SV774: $i,SV126: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV126 @ SV774 @ ( tc_fun @ SV1798 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV126 @ SV774 @ ( tc_fun @ SV1798 @ tc_bool ) ) )
= $true )
| ( ( SV126 = SV774 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4635]) ).
thf(5218,plain,
! [SV127: $i,SV2166: $i,SV1799: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV1799 @ SV2166 @ SV127 )
| ( SV1799 = SV2166 )
| ~ ( c_lessequals @ SV1799 @ SV2166 @ SV127 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV127 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4636]) ).
thf(5219,plain,
! [SV128: $i,SV2167: $i,SV1800: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV1800 @ SV2167 @ SV128 )
| ~ ( c_lessequals @ SV1800 @ SV2167 @ SV128 )
| ( SV1800 = SV2167 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV128 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4637]) ).
thf(5220,plain,
! [SV129: $i,SV2168: $i,SV1801: $i] :
( ( ( ( SV1801 = SV2168 )
| ~ ( c_lessequals @ SV1801 @ SV2168 @ SV129 )
| ( c_HOL_Oord__class_Oless @ SV1801 @ SV2168 @ SV129 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV129 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4638]) ).
thf(5221,plain,
! [SV130: $i,SV2169: $i,SV1802: $i] :
( ( ( ( SV1802 = SV2169 )
| ( c_HOL_Oord__class_Oless @ SV1802 @ SV2169 @ SV130 )
| ~ ( c_lessequals @ SV1802 @ SV2169 @ SV130 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV130 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4639]) ).
thf(5222,plain,
! [SV2170: $i,SV1803: $i,SV1325: $i,SV775: $i,SV131: $i] :
( ( ! [SY7160: $i,SY7161: $i] :
( ( ( c_Fun_Ofun__upd @ SV131 @ SV775 @ ( c_Option_Ooption_OSome @ SV1325 @ SV1803 ) @ SV2170 @ ( tc_Option_Ooption @ SV1803 ) )
!= ( c_Fun_Ofun__upd @ SY7160 @ SV775 @ ( c_Option_Ooption_OSome @ SY7161 @ SV1803 ) @ SV2170 @ ( tc_Option_Ooption @ SV1803 ) ) )
| ( SV1325 = SY7161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4640]) ).
thf(5223,plain,
! [SV2171: $i,SV1804: $i,SV1326: $i,SV776: $i,SV132: $i] :
( ( ( c_Set_Oimage @ SV132 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV776 @ SV1326 @ ( tc_fun @ SV1804 @ tc_bool ) ) @ SV1804 @ SV2171 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ SV132 @ SV776 @ SV1804 @ SV2171 ) @ ( c_Set_Oimage @ SV132 @ SV1326 @ SV1804 @ SV2171 ) @ ( tc_fun @ SV2171 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4641]) ).
thf(5224,plain,
! [SV133: $i,SV2172: $i,SV1805: $i] :
( ( ( ( c_lessequals @ SV1805 @ SV2172 @ SV133 )
| ( c_lessequals @ SV2172 @ SV1805 @ SV133 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV133 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4642]) ).
thf(5225,plain,
! [SV1327: $i,SV777: $i,SV134: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV134 )
= $false )
| ( ( ! [SY6142: $i,SY6143: $i] :
( ( ( c_Finite__Set_Osetsum @ SV777 @ ( c_HOL_Ominus__class_Ominus @ SV1327 @ SY6142 @ ( tc_fun @ SY6143 @ tc_bool ) ) @ SY6143 @ SV134 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV777 @ SV1327 @ SY6143 @ SV134 ) @ ( c_Finite__Set_Osetsum @ SV777 @ SY6142 @ SY6143 @ SV134 ) @ SV134 ) )
| ~ ( c_lessequals @ SY6142 @ SV1327 @ ( tc_fun @ SY6143 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV1327 @ SY6143 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4643]) ).
thf(5226,plain,
! [SV1806: $i,SV1328: $i,SV778: $i,SV135: $i] :
( ( ( ( c_Finite__Set_Ocard @ SV135 @ SV778 )
= ( c_Finite__Set_Ocard @ SV1328 @ SV1806 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1328 @ SV1806 )
| ~ ( c_Finite__Set_Ofinite @ SV135 @ SV778 )
| ! [SY6827: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ SY6827 @ SV1328 @ SV1806 @ SV778 ) @ SV135 @ ( tc_fun @ SV778 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY6827 @ SV1328 @ SV1806 @ SV778 )
| ! [SY6828: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ SY6828 @ SV135 @ SV778 @ SV1806 ) @ SV1328 @ ( tc_fun @ SV1806 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY6828 @ SV135 @ SV778 @ SV1806 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4644]) ).
thf(5227,plain,
! [SV2173: $i,SV1807: $i,SV1329: $i,SV779: $i,SV136: $i] :
( ( ! [SY7162: $i,SY7163: $i] :
( ( c_Finite__Set_Ofold__graph @ SV136 @ SV779 @ ( c_Set_Oinsert @ SV1329 @ SV1807 @ SV2173 ) @ ( hAPP @ ( hAPP @ SV136 @ SV1329 ) @ SY7162 ) @ SV2173 @ SY7163 )
| ~ ( c_Finite__Set_Ofold__graph @ SV136 @ SV779 @ SV1807 @ SY7162 @ SV2173 @ SY7163 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2173 ) @ SV1329 ) @ SV1807 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4645]) ).
thf(5228,plain,
! [SV1330: $i,SV780: $i,SV2174: $i,SV137: $i] :
( ( ( ~ ( c_lessequals @ SV137 @ ( c_Set_Oinsert @ SV2174 @ SV780 @ SV1330 ) @ ( tc_fun @ SV1330 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1330 ) @ SV2174 ) @ SV137 ) ) )
= $true )
| ( ( c_lessequals @ SV137 @ SV780 @ ( tc_fun @ SV1330 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4646]) ).
thf(5229,plain,
! [SV1808: $i,SV1331: $i,SV781: $i,SV138: $i] :
( ( ( c_lessequals @ SV138 @ ( c_Set_Oinsert @ SV781 @ SV1331 @ SV1808 ) @ ( tc_fun @ SV1808 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV138 @ SV1331 @ ( tc_fun @ SV1808 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1808 ) @ SV781 ) @ SV138 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4647]) ).
thf(5230,plain,
! [SV782: $i,SV139: $i,SV2175: $i,SV1332: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1332 ) @ SV2175 ) @ SV139 ) )
| ~ ( c_lessequals @ SV139 @ ( c_Set_Oinsert @ SV2175 @ SV782 @ SV1332 ) @ ( tc_fun @ SV1332 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV139 @ SV782 @ ( tc_fun @ SV1332 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4648]) ).
thf(5231,plain,
! [SV1809: $i,SV1333: $i,SV783: $i,SV140: $i] :
( ( ( c_lessequals @ SV140 @ ( c_Set_Oinsert @ SV783 @ SV1333 @ SV1809 ) @ ( tc_fun @ SV1809 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV140 @ SV1333 @ ( tc_fun @ SV1809 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1809 ) @ SV783 ) @ SV140 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4649]) ).
thf(5232,plain,
! [SV1334: $i,SV141: $i,SV2176: $i,SV784: $i] :
( ( ( ~ ( c_lessequals @ ( c_Set_Oinsert @ SV784 @ SV2176 @ SV141 ) @ SV1334 @ ( tc_fun @ SV141 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV141 ) @ SV784 ) @ SV1334 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4650]) ).
thf(5233,plain,
! [SV1810: $i,SV1335: $i,SV785: $i,SV142: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV142 @ SV785 @ SV1335 ) @ SV1810 @ ( tc_fun @ SV1335 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV785 @ SV1810 @ ( tc_fun @ SV1335 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1335 ) @ SV142 ) @ SV1810 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4651]) ).
thf(5234,plain,
! [SV1811: $i,SV1336: $i,SV786: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV143 ) @ ( hAPP @ SV786 @ SV1336 ) ) @ SV1811 ) )
= $true )
| ( ( ! [SY6832: $i,SY6833: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6832 ) @ SV1336 ) @ SY6833 ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV786 @ SY6833 @ SY6832 @ SV143 ) @ SV1811 @ ( tc_fun @ SV143 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4652]) ).
thf(5235,plain,
! [SV2177: $i,SV1812: $i,SV1337: $i,SV787: $i,SV144: $i] :
( ( ! [SY7164: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ SV144 @ SV787 @ SV1337 @ SV1812 @ SV2177 ) @ SY7164 @ SV1812 @ SV2177 )
= ( c_Set_Oimage @ SV144 @ SY7164 @ SV1812 @ SV2177 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1812 ) @ SV787 ) @ SY7164 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4653]) ).
thf(5236,plain,
! [SV1338: $i,SV788: $i,SV145: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV145 )
= $false )
| ( ( ! [SY6163: $i,SY6164: $i] :
( ( c_lessequals @ ( hAPP @ SV788 @ SV1338 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY6163 @ SV788 @ SY6164 @ SV145 ) @ SV145 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6164 ) @ SV1338 ) @ SY6163 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4654]) ).
thf(5237,plain,
! [SV1813: $i,SV1339: $i,SV789: $i,SV146: $i] :
( ( ( ! [SY6836: $i] : ( c_lessequals @ ( hAPP @ SV146 @ SV789 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1339 @ SV146 @ SV1813 @ ( tc_fun @ SY6836 @ tc_bool ) ) @ ( tc_fun @ SY6836 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1813 ) @ SV789 ) @ SV1339 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4655]) ).
thf(5238,plain,
! [SV1814: $i,SV1340: $i,SV790: $i,SV147: $i] :
( ( ( c_lessequals @ ( hAPP @ SV147 @ SV790 ) @ SV1340 @ ( tc_fun @ SV1814 @ tc_bool ) )
= $true )
| ( ( ! [SY6837: $i,SY6838: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6837 ) @ SV790 ) @ SY6838 ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY6838 @ SV147 @ SY6837 @ ( tc_fun @ SV1814 @ tc_bool ) ) @ SV1340 @ ( tc_fun @ SV1814 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4656]) ).
thf(5239,plain,
! [SV1815: $i,SV1341: $i,SV791: $i,SV148: $i] :
( ( ( ! [SY6839: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV148 @ SV791 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1341 @ SV148 @ SV1815 @ ( tc_fun @ SY6839 @ tc_bool ) ) @ ( tc_fun @ SY6839 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1341 @ SV148 @ SV1815 @ ( tc_fun @ SY6839 @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1815 ) @ SV791 ) @ SV1341 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4657]) ).
thf(5240,plain,
! [SV793: $i,SV1343: $i,SV150: $i] :
( ( ( SV150
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1343 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV150 @ ( c_Set_Oinsert @ SV793 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1343 @ tc_bool ) ) @ SV1343 ) @ ( tc_fun @ SV1343 @ tc_bool ) ) )
= $true )
| ( ( SV150
= ( c_Set_Oinsert @ SV793 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1343 @ tc_bool ) ) @ SV1343 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4658]) ).
thf(5241,plain,
! [SV794: $i,SV2178: $i,SV1344: $i,SV151: $i] :
( ( ( ! [SY7165: $i] :
( ~ ( c_lessequals @ SV151 @ ( c_Set_Oimage @ SV1344 @ SV2178 @ SY7165 @ SV794 ) @ ( tc_fun @ SV794 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV2178 @ SY7165 ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV151 @ SV794 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4659]) ).
thf(5242,plain,
! [SV796: $i,SV153: $i,SV1346: $i] :
( ( ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ SV1346 ) @ SV1346 @ ( tc_fun @ SV1346 @ tc_bool ) @ tc_bool ) @ SV153 ) @ ( hAPP @ ( c_COMBC @ ( c_in @ SV1346 ) @ SV1346 @ ( tc_fun @ SV1346 @ tc_bool ) @ tc_bool ) @ SV796 ) @ ( tc_fun @ SV1346 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV153 @ SV796 @ ( tc_fun @ SV1346 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4660]) ).
thf(5243,plain,
! [SV154: $i,SV1347: $i,SV797: $i] :
( ( ( c_lessequals @ SV797 @ SV1347 @ ( tc_fun @ SV154 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( c_COMBC @ ( c_in @ SV154 ) @ SV154 @ ( tc_fun @ SV154 @ tc_bool ) @ tc_bool ) @ SV797 ) @ ( hAPP @ ( c_COMBC @ ( c_in @ SV154 ) @ SV154 @ ( tc_fun @ SV154 @ tc_bool ) @ tc_bool ) @ SV1347 ) @ ( tc_fun @ SV154 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4661]) ).
thf(5244,plain,
! [SV155: $i,SV2179: $i,SV798: $i] :
( ( ( ! [SY7166: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV798 @ ( c_COMBK @ SV2179 @ SV155 @ SY7166 ) @ SY7166 @ SV155 )
= SV2179 )
| ( SV798
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY7166 @ tc_bool ) ) ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV155 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4662]) ).
thf(5245,plain,
! [SV2180: $i,SV1818: $i,SV1350: $i,SV801: $i,SV158: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ SV158 @ SV801 @ SV1350 ) @ SV1818 @ SV1350 @ ( tc_fun @ SV2180 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV1818 @ SV158 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV801 @ SV1818 @ SV1350 @ ( tc_fun @ SV2180 @ tc_bool ) ) @ ( tc_fun @ SV2180 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4665]) ).
thf(5246,plain,
! [SV2181: $i,SV1819: $i,SV1351: $i,SV802: $i,SV159: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV159 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV802 @ SV1351 @ ( tc_fun @ SV1819 @ tc_bool ) ) @ SV1819 @ SV2181 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV159 @ SV802 @ SV1819 @ SV2181 ) @ ( c_Set_Oimage @ SV159 @ SV1351 @ SV1819 @ SV2181 ) @ ( tc_fun @ SV2181 @ tc_bool ) ) @ ( tc_fun @ SV2181 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4666]) ).
thf(5247,plain,
! [SV2182: $i,SV1820: $i,SV1352: $i,SV803: $i,SV160: $i] :
( ( ! [SY7167: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV160 @ ( c_COMBB @ SV803 @ SV1352 @ SV1820 @ ( tc_fun @ SV2182 @ tc_bool ) @ SY7167 ) @ SY7167 @ ( tc_fun @ SV2182 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oimage @ SV1352 @ SV160 @ SY7167 @ SV1820 ) @ SV803 @ SV1820 @ ( tc_fun @ SV2182 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4667]) ).
thf(5248,plain,
! [SV2183: $i,SV1821: $i,SV1353: $i,SV804: $i,SV161: $i] :
( ( ! [SY7168: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oimage @ SV161 @ SV804 @ SV1353 @ SV1821 ) @ SV2183 @ SV1821 @ ( tc_fun @ SY7168 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV804 @ ( c_COMBB @ SV2183 @ SV161 @ SV1821 @ ( tc_fun @ SY7168 @ tc_bool ) @ SV1353 ) @ SV1353 @ ( tc_fun @ SY7168 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4668]) ).
thf(5249,plain,
! [SV2184: $i,SV1822: $i,SV1354: $i,SV805: $i,SV162: $i] :
( ( ( ( c_Set_Oimage @ SV162 @ SV805 @ SV1354 @ SV1822 )
!= ( c_Set_Oimage @ SV162 @ SV2184 @ SV1354 @ SV1822 ) )
| ~ ( c_Fun_Oinj__on @ SV162 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV805 @ SV2184 @ ( tc_fun @ SV1354 @ tc_bool ) ) @ SV1354 @ SV1822 )
| ( SV805 = SV2184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4669]) ).
thf(5250,plain,
! [SV1823: $i,SV1355: $i,SV806: $i,SV163: $i] :
( ( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ SV163 @ SV806 @ SV1355 @ SV1823 ) @ SV1823 )
= ( c_Finite__Set_Ocard @ SV806 @ SV1355 ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV163 @ SV806 @ SV1355 @ SV1823 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4670]) ).
thf(5251,plain,
! [SV2185: $i,SV1824: $i,SV1356: $i,SV807: $i,SV164: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV164 @ SV807 @ SV1356 @ SV1824 ) @ ( c_Set_Oimage @ SV164 @ SV2185 @ SV1356 @ SV1824 ) @ ( tc_fun @ SV1824 @ tc_bool ) ) @ ( c_Set_Oimage @ SV164 @ ( c_HOL_Ominus__class_Ominus @ SV807 @ SV2185 @ ( tc_fun @ SV1356 @ tc_bool ) ) @ SV1356 @ SV1824 ) @ ( tc_fun @ SV1824 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4671]) ).
thf(5252,plain,
! [SV2186: $i,SV1828: $i,SV1361: $i,SV812: $i,SV169: $i] :
( ( ! [SY7169: $i] :
( ( c_Map_Omap__add @ SV169 @ ( c_Fun_Ofun__upd @ SV812 @ SV1361 @ ( c_Option_Ooption_OSome @ SV1828 @ SV2186 ) @ SY7169 @ ( tc_Option_Ooption @ SV2186 ) ) @ SY7169 @ SV2186 )
= ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ SV169 @ SV812 @ SY7169 @ SV2186 ) @ SV1361 @ ( c_Option_Ooption_OSome @ SV1828 @ SV2186 ) @ SY7169 @ ( tc_Option_Ooption @ SV2186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4675]) ).
thf(5253,plain,
! [SV1831: $i,SV1364: $i,SV815: $i,SV172: $i] :
( ( ( c_lessequals @ ( c_Map_Odom @ SV172 @ SV815 @ SV1364 ) @ ( c_Map_Odom @ SV1831 @ SV815 @ SV1364 ) @ ( tc_fun @ SV815 @ tc_bool ) )
= $true )
| ( ( ~ ( c_Map_Omap__le @ SV172 @ SV1831 @ SV815 @ SV1364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4678]) ).
thf(5254,plain,
! [SV2187: $i,SV1833: $i,SV1365: $i,SV817: $i,SV175: $i] :
( ( ! [SY7170: $i] :
( ( hAPP @ ( c_COMBB @ SV175 @ SV817 @ SV1365 @ SV1833 @ SV2187 ) @ SY7170 )
= ( hAPP @ SV175 @ ( hAPP @ SV817 @ SY7170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4680]) ).
thf(5255,plain,
! [SV177: $i,SV2188: $i,SV1835: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV1835 @ SV2188 @ SV177 )
| ( c_lessequals @ SV2188 @ SV1835 @ SV177 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV177 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4682]) ).
thf(5256,plain,
! [SV178: $i,SV1836: $i] :
( ( ( ~ ( c_lessequals @ SV1836 @ SV1836 @ SV178 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1836 @ SV1836 @ SV178 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4683]) ).
thf(5257,plain,
! [SV179: $i,SV1837: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1837 @ SV1837 @ SV179 )
= $true )
| ( ( c_lessequals @ SV1837 @ SV1837 @ SV179 )
= $true )
| ( ( class_Orderings_Olinorder @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4684]) ).
thf(5258,plain,
! [SV180: $i,SV2189: $i,SV1838: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1838 @ SV2189 @ SV180 )
| ~ ( c_lessequals @ SV2189 @ SV1838 @ SV180 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV180 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4685]) ).
thf(5259,plain,
! [SV181: $i,SV1839: $i,SV2190: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV2190 @ SV1839 @ SV181 )
| ( c_lessequals @ SV1839 @ SV2190 @ SV181 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4686]) ).
thf(5260,plain,
! [SV182: $i,SV2191: $i,SV1840: $i] :
( ( ( ~ ( c_lessequals @ SV1840 @ SV2191 @ SV182 )
| ~ ( c_HOL_Oord__class_Oless @ SV2191 @ SV1840 @ SV182 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV182 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4687]) ).
thf(5261,plain,
! [SV183: $i,SV2192: $i,SV1841: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV1841 @ SV2192 @ SV183 )
| ( c_lessequals @ SV2192 @ SV1841 @ SV183 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV183 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4688]) ).
thf(5262,plain,
! [SV184: $i,SV2193: $i,SV819: $i] :
( ( ( ! [SY7171: $i] :
( ~ ( c_lessequals @ SV819 @ SV2193 @ ( tc_fun @ SY7171 @ SV184 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV2193 @ SV819 @ ( tc_fun @ SY7171 @ SV184 ) ) ) )
= $true )
| ( ( class_HOL_Oord @ SV184 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4689]) ).
thf(5263,plain,
! [SV185: $i,SV2194: $i,SV1842: $i] :
( ( ( ~ ( c_lessequals @ SV1842 @ SV2194 @ SV185 )
| ~ ( c_HOL_Oord__class_Oless @ SV2194 @ SV1842 @ SV185 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV185 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4690]) ).
thf(5264,plain,
! [SV188: $i,SV2195: $i,SV822: $i] :
( ( ( ! [SY7172: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV822 @ SV2195 @ SV188 ) @ SY7172 @ SV188 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV822 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2195 @ SY7172 @ SV188 ) @ SV188 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV188 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4693]) ).
thf(5265,plain,
! [SV189: $i,SV2196: $i,SV823: $i] :
( ( ( ! [SY7173: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV823 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2196 @ SY7173 @ SV189 ) @ SV189 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV2196 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV823 @ SY7173 @ SV189 ) @ SV189 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV189 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4694]) ).
thf(5266,plain,
! [SV190: $i,SV2197: $i,SV824: $i] :
( ( ( ! [SY7174: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV824 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2197 @ SY7174 @ SV190 ) @ SV190 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV2197 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV824 @ SY7174 @ SV190 ) @ SV190 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV190 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4695]) ).
thf(5267,plain,
! [SV191: $i,SV2198: $i,SV825: $i] :
( ( ( ! [SY7175: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV825 @ SV2198 @ SV191 ) @ SY7175 @ SV191 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV825 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2198 @ SY7175 @ SV191 ) @ SV191 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV191 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4696]) ).
thf(5268,plain,
! [SV1369: $i,SV826: $i,SV192: $i] :
( ( ( c_lessequals @ SV192 @ SV826 @ ( tc_fun @ SV1369 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV192 @ SV826 @ ( tc_fun @ SV1369 @ tc_bool ) )
= SV192 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4697]) ).
thf(5269,plain,
! [SV1370: $i,SV193: $i,SV827: $i] :
( ( ( c_lessequals @ SV827 @ SV193 @ ( tc_fun @ SV1370 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV193 @ SV827 @ ( tc_fun @ SV1370 @ tc_bool ) )
= SV827 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4698]) ).
thf(5270,plain,
! [SV194: $i,SV2199: $i,SV1845: $i] :
( ( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1845 @ SV2199 @ SV194 )
= SV1845 )
| ~ ( c_lessequals @ SV1845 @ SV2199 @ SV194 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV194 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4699]) ).
thf(5271,plain,
! [SV195: $i,SV2200: $i,SV1846: $i] :
( ( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1846 @ SV2200 @ SV195 )
!= SV1846 )
| ( c_lessequals @ SV1846 @ SV2200 @ SV195 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV195 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4700]) ).
thf(5272,plain,
! [SV196: $i,SV2201: $i,SV1847: $i] :
( ( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1847 @ SV2201 @ SV196 )
= SV2201 )
| ~ ( c_lessequals @ SV2201 @ SV1847 @ SV196 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV196 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4701]) ).
thf(5273,plain,
! [SV1848: $i,SV1371: $i,SV828: $i,SV197: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV197 @ SV828 @ ( tc_fun @ SV1371 @ tc_bool ) ) @ SV1848 @ ( tc_fun @ SV1371 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV828 @ SV1848 @ ( tc_fun @ SV1371 @ tc_bool ) )
| ~ ( c_lessequals @ SV197 @ SV1848 @ ( tc_fun @ SV1371 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4702]) ).
thf(5274,plain,
! [SV1849: $i,SV1374: $i,SV831: $i,SV200: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ SV831 @ ( tc_fun @ SV1374 @ tc_bool ) ) @ SV1849 @ ( tc_fun @ SV1374 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV831 @ SV1849 @ ( tc_fun @ SV1374 @ tc_bool ) )
| ~ ( c_lessequals @ SV200 @ SV1849 @ ( tc_fun @ SV1374 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4703]) ).
thf(5275,plain,
! [SV201: $i,SV2202: $i,SV832: $i] :
( ( ( ! [SY7176: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV832 @ SV2202 @ SV201 ) @ SY7176 @ SV201 )
| ~ ( c_lessequals @ SV2202 @ SY7176 @ SV201 )
| ~ ( c_lessequals @ SV832 @ SY7176 @ SV201 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV201 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4704]) ).
thf(5276,plain,
! [SV202: $i,SV2203: $i,SV1850: $i] :
( ( ( c_lessequals @ SV1850 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1850 @ SV2203 @ SV202 ) @ SV202 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV202 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4705]) ).
thf(5277,plain,
! [SV203: $i,SV2204: $i,SV1851: $i] :
( ( ( c_lessequals @ SV1851 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2204 @ SV1851 @ SV203 ) @ SV203 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV203 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4706]) ).
thf(5278,plain,
! [SV204: $i,SV2205: $i,SV833: $i] :
( ( ( ! [SY7177: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV833 @ SV2205 @ SV204 ) @ SY7177 @ SV204 )
| ~ ( c_lessequals @ SV2205 @ SY7177 @ SV204 )
| ~ ( c_lessequals @ SV833 @ SY7177 @ SV204 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV204 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4707]) ).
thf(5279,plain,
! [SV205: $i,SV2206: $i,SV834: $i] :
( ( ( ! [SY7178: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV834 @ SV2206 @ SV205 ) @ SY7178 @ SV205 )
| ~ ( c_lessequals @ SV2206 @ SY7178 @ SV205 )
| ~ ( c_lessequals @ SV834 @ SY7178 @ SV205 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV205 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4708]) ).
thf(5280,plain,
! [SV206: $i,SV2207: $i,SV1852: $i] :
( ( ( c_lessequals @ SV1852 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2207 @ SV1852 @ SV206 ) @ SV206 )
= $true )
| ( ( class_Lattices_Olattice @ SV206 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4709]) ).
thf(5281,plain,
! [SV207: $i,SV2208: $i,SV1853: $i] :
( ( ( c_lessequals @ SV1853 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1853 @ SV2208 @ SV207 ) @ SV207 )
= $true )
| ( ( class_Lattices_Olattice @ SV207 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4710]) ).
thf(5282,plain,
! [SV1375: $i,SV835: $i,SV208: $i] :
( ( ( c_lessequals @ SV208 @ SV835 @ ( tc_fun @ SV1375 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV208 @ ( c_HOL_Ominus__class_Ominus @ SV835 @ SV208 @ ( tc_fun @ SV1375 @ tc_bool ) ) @ ( tc_fun @ SV1375 @ tc_bool ) )
= SV835 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4711]) ).
thf(5283,plain,
! [SV209: $i,SV2209: $i,SV836: $i] :
( ( ( ! [SY7179: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV836 @ SV2209 @ SV209 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV836 @ SY7179 @ SV209 ) @ SV209 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV836 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2209 @ SY7179 @ SV209 ) @ SV209 ) @ SV209 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV209 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4712]) ).
thf(5284,plain,
! [SV2210: $i,SV1857: $i,SV1380: $i,SV841: $i,SV214: $i] :
( ( ( c_lessequals @ ( c_Set_Ovimage @ SV214 @ SV841 @ SV1380 @ SV1857 ) @ ( c_Set_Ovimage @ SV214 @ SV2210 @ SV1380 @ SV1857 ) @ ( tc_fun @ SV1380 @ tc_bool ) )
| ~ ( c_lessequals @ SV841 @ SV2210 @ ( tc_fun @ SV1857 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4716]) ).
thf(5285,plain,
! [SV1381: $i,SV842: $i,SV215: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV215 @ SV842 @ ( tc_fun @ SV1381 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1381 @ tc_bool ) ) )
= $false )
| ( ( SV842
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1381 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4717]) ).
thf(5286,plain,
! [SV1382: $i,SV843: $i,SV216: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV216 @ SV843 @ ( tc_fun @ SV1382 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1382 @ tc_bool ) ) )
= $false )
| ( ( SV216
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1382 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4718]) ).
thf(5287,plain,
! [SV217: $i,SV1858: $i] :
( ( ( ! [SY6866: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1858 @ SY6866 @ SV217 )
!= ( c_Orderings_Obot__class_Obot @ SV217 ) ) )
= $true )
| ( ( SV1858
= ( c_Orderings_Obot__class_Obot @ SV217 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV217 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4719]) ).
thf(5288,plain,
! [SV218: $i,SV2211: $i,SV1859: $i] :
( ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1859 @ SV2211 @ SV218 )
!= ( c_Orderings_Obot__class_Obot @ SV218 ) )
| ( SV2211
= ( c_Orderings_Obot__class_Obot @ SV218 ) ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV218 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4720]) ).
thf(5289,plain,
! [SV1385: $i,SV846: $i,SV2212: $i,SV221: $i] :
( ( ( ~ ( c_lessequals @ SV221 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2212 @ SV846 @ ( tc_fun @ SV1385 @ tc_bool ) ) @ ( tc_fun @ SV1385 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV221 @ SV846 @ ( tc_fun @ SV1385 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4721]) ).
thf(5290,plain,
! [SV1386: $i,SV2213: $i,SV847: $i,SV222: $i] :
( ( ( ~ ( c_lessequals @ SV222 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV847 @ SV2213 @ ( tc_fun @ SV1386 @ tc_bool ) ) @ ( tc_fun @ SV1386 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV222 @ SV847 @ ( tc_fun @ SV1386 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4722]) ).
thf(5291,plain,
! [SV223: $i,SV2214: $i,SV848: $i] :
( ( ( ( c_lessequals @ SV848 @ SV2214 @ SV223 )
| ! [SY7180: $i] :
~ ( c_lessequals @ SV848 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2214 @ SY7180 @ SV223 ) @ SV223 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV223 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4723]) ).
thf(5292,plain,
! [SV224: $i,SV2215: $i,SV849: $i] :
( ( ( ( c_lessequals @ SV849 @ SV2215 @ SV224 )
| ! [SY7181: $i] :
~ ( c_lessequals @ SV849 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY7181 @ SV2215 @ SV224 ) @ SV224 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV224 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4724]) ).
thf(5293,plain,
! [SV225: $i,SV2216: $i,SV850: $i] :
( ( ( ! [SY7182: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV850 @ SV2216 @ SV225 ) @ SY7182 @ SV225 )
| ~ ( c_lessequals @ SV850 @ SY7182 @ SV225 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV225 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4725]) ).
thf(5294,plain,
! [SV226: $i,SV2217: $i,SV851: $i] :
( ( ( ! [SY7183: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV851 @ SV2217 @ SV226 ) @ SY7183 @ SV226 )
| ~ ( c_lessequals @ SV2217 @ SY7183 @ SV226 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV226 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4726]) ).
thf(5295,plain,
! [SV227: $i,SV2218: $i,SV852: $i] :
( ( ( ( c_lessequals @ SV852 @ SV2218 @ SV227 )
| ! [SY7184: $i] :
~ ( c_lessequals @ SV852 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2218 @ SY7184 @ SV227 ) @ SV227 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV227 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4727]) ).
thf(5296,plain,
! [SV228: $i,SV2219: $i,SV853: $i] :
( ( ( ( c_lessequals @ SV853 @ SV2219 @ SV228 )
| ! [SY7185: $i] :
~ ( c_lessequals @ SV853 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY7185 @ SV2219 @ SV228 ) @ SV228 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV228 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4728]) ).
thf(5297,plain,
! [SV231: $i,SV2220: $i,SV1861: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1861 @ SV2220 @ SV231 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV2220 @ SV1861 @ SV231 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV231 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4730]) ).
thf(5298,plain,
! [SV232: $i,SV2221: $i,SV1862: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1862 @ SV2221 @ SV232 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV2221 @ SV1862 @ SV232 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV232 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4731]) ).
thf(5299,plain,
! [SV234: $i,SV2222: $i,SV1863: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1863 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1863 @ SV2222 @ SV234 ) @ SV234 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1863 @ SV2222 @ SV234 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV234 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4732]) ).
thf(5300,plain,
! [SV235: $i,SV2223: $i,SV1864: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1864 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1864 @ SV2223 @ SV235 ) @ SV235 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1864 @ SV2223 @ SV235 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV235 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4733]) ).
thf(5301,plain,
! [SV2224: $i,SV1865: $i,SV1390: $i,SV857: $i,SV236: $i] :
( ( ( c_Set_Ovimage @ SV236 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV857 @ SV1390 @ ( tc_fun @ SV1865 @ tc_bool ) ) @ SV2224 @ SV1865 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ SV236 @ SV857 @ SV2224 @ SV1865 ) @ ( c_Set_Ovimage @ SV236 @ SV1390 @ SV2224 @ SV1865 ) @ ( tc_fun @ SV2224 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4734]) ).
thf(5302,plain,
! [SV2225: $i,SV1391: $i,SV858: $i,SV237: $i] :
( ( ( ! [SY7186: $i] :
( ( c_Fun_Ofun__upd @ SV237 @ SV858 @ SV1391 @ SV2225 @ SY7186 )
!= SV237 ) )
= $true )
| ( ( ( hAPP @ SV237 @ SV858 )
= SV1391 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4735]) ).
thf(5303,plain,
! [SV1866: $i,SV1392: $i,SV859: $i,SV238: $i] :
( ( ( c_Fun_Oinj__on @ SV238 @ SV859 @ SV1392 @ SV1866 )
= $true )
| ( ( ! [SY6873: $i] :
~ ( c_Fun_Oinj__on @ SV238 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY6873 @ SV859 @ ( tc_fun @ SV1392 @ tc_bool ) ) @ SV1392 @ SV1866 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4736]) ).
thf(5304,plain,
! [SV1867: $i,SV1393: $i,SV860: $i,SV239: $i] :
( ( ( c_Fun_Oinj__on @ SV239 @ SV860 @ SV1393 @ SV1867 )
= $true )
| ( ( ! [SY6874: $i] :
~ ( c_Fun_Oinj__on @ SV239 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV860 @ SY6874 @ ( tc_fun @ SV1393 @ tc_bool ) ) @ SV1393 @ SV1867 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4737]) ).
thf(5305,plain,
! [SV1868: $i,SV1394: $i,SV861: $i,SV240: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV240 @ SV861 @ ( tc_fun @ SV1394 @ tc_bool ) ) @ SV1868 @ ( tc_fun @ SV1394 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV240 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV861 @ SV1868 @ ( tc_fun @ SV1394 @ tc_bool ) ) @ ( tc_fun @ SV1394 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4738]) ).
thf(5306,plain,
! [SV1869: $i,SV1395: $i,SV862: $i,SV241: $i] :
( ( ( c_lessequals @ SV241 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV862 @ SV1395 @ ( tc_fun @ SV1869 @ tc_bool ) ) @ ( tc_fun @ SV1869 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV241 @ SV862 @ ( tc_fun @ SV1869 @ tc_bool ) ) @ SV1395 @ ( tc_fun @ SV1869 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4739]) ).
thf(5307,plain,
! [SV242: $i,SV2226: $i,SV863: $i] :
( ( ( ! [SY7187: $i] : ( c_HOL_Oord__class_Oless @ SV863 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2226 @ SY7187 @ SV242 ) @ SV242 )
| ~ ( c_HOL_Oord__class_Oless @ SV863 @ SV2226 @ SV242 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV242 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4740]) ).
thf(5308,plain,
! [SV243: $i,SV2227: $i,SV864: $i] :
( ( ( ! [SY7188: $i] :
( ( c_HOL_Oord__class_Oless @ SV864 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2227 @ SY7188 @ SV243 ) @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ SV864 @ SY7188 @ SV243 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV243 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4741]) ).
thf(5309,plain,
! [SV1396: $i,SV865: $i,SV244: $i] :
( ( ( class_HOL_Oord @ SV244 )
= $false )
| ( ( ! [SY6226: $i] :
( ( c_lessequals @ ( hAPP @ SV865 @ SV1396 ) @ ( hAPP @ SY6226 @ SV1396 ) @ SV244 )
| ! [SY5150: $i] :
~ ( c_lessequals @ SV865 @ SY6226 @ ( tc_fun @ SY5150 @ SV244 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4742]) ).
thf(5310,plain,
! [SV1397: $i,SV2228: $i,SV866: $i,SV245: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV245 ) @ SV866 ) @ SV2228 ) )
| ~ ( c_lessequals @ SV2228 @ SV1397 @ ( tc_fun @ SV245 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV245 ) @ SV866 ) @ SV1397 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4743]) ).
thf(5311,plain,
! [SV867: $i,SV246: $i,SV1398: $i,SV2229: $i] :
( ( ( ~ ( c_lessequals @ SV2229 @ SV1398 @ ( tc_fun @ SV246 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV246 ) @ SV867 ) @ SV2229 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV246 ) @ SV867 ) @ SV1398 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4744]) ).
thf(5312,plain,
! [SV1399: $i,SV2230: $i,SV868: $i,SV247: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV247 ) @ SV868 ) @ SV2230 ) )
| ~ ( c_lessequals @ SV2230 @ SV1399 @ ( tc_fun @ SV247 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV247 ) @ SV868 ) @ SV1399 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4745]) ).
thf(5313,plain,
! [SV1400: $i,SV2231: $i,SV869: $i,SV248: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV248 ) @ SV869 ) @ SV2231 ) )
| ~ ( c_lessequals @ SV2231 @ SV1400 @ ( tc_fun @ SV248 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV248 ) @ SV869 ) @ SV1400 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4746]) ).
thf(5314,plain,
! [SV2232: $i,SV1401: $i,SV870: $i,SV249: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV249 ) @ SV870 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1401 @ SV2232 @ ( tc_fun @ SV249 @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV249 ) @ SV870 ) @ SV1401 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4747]) ).
thf(5315,plain,
! [SV1870: $i,SV1402: $i,SV871: $i,SV250: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV250 ) @ SV871 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1402 @ SV1870 @ ( tc_fun @ SV250 @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV250 ) @ SV871 ) @ SV1870 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4748]) ).
thf(5316,plain,
! [SV1403: $i,SV2233: $i,SV872: $i,SV251: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV251 ) @ SV872 ) @ SV2233 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV251 ) @ SV872 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2233 @ SV1403 @ ( tc_fun @ SV251 @ tc_bool ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV251 ) @ SV872 ) @ SV1403 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4749]) ).
thf(5317,plain,
! [SV1871: $i,SV1404: $i,SV873: $i,SV253: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV253 ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV873 @ SV1404 @ SV1871 @ SV253 ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV873 @ SV1404 @ ( tc_fun @ SV253 @ tc_bool ) ) ) )
= $true )
| ( ( ! [SY6875: $i] :
( ~ ( hBOOL @ ( hAPP @ SV1871 @ SY6875 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV253 ) @ SY6875 ) @ SV1404 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4750]) ).
thf(5318,plain,
! [SV1872: $i,SV1405: $i,SV874: $i,SV254: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV254 ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV874 @ SV1405 @ SV1872 @ SV254 ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV874 @ SV1405 @ ( tc_fun @ SV254 @ tc_bool ) ) ) )
= $true )
| ( ( ! [SY6876: $i] :
( ~ ( hBOOL @ ( hAPP @ SV1872 @ SY6876 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV254 ) @ SY6876 ) @ SV874 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4751]) ).
thf(5319,plain,
! [SV875: $i,SV255: $i,SV1406: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1406 ) @ SV255 ) @ SV875 ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV875 @ SV1406 ) )
= $true )
| ( ( ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ SV255 @ SV875 @ SV1406 ) @ SV1406 )
= ( c_Finite__Set_Ocard @ SV875 @ SV1406 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4752]) ).
thf(5320,plain,
! [SV1873: $i,SV1407: $i,SV876: $i,SV256: $i] :
( ( ( ( c_Set_Oimage @ ( c_COMBK @ SV256 @ SV876 @ SV1407 ) @ SV1873 @ SV1407 @ SV876 )
= ( c_Set_Oinsert @ SV256 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV876 @ tc_bool ) ) @ SV876 ) )
= $true )
| ( ( SV1873
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1407 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4753]) ).
thf(5321,plain,
! [SV2234: $i,SV1874: $i,SV1408: $i,SV877: $i,SV257: $i] :
( ( ! [SY7189: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ofun__upd @ SV257 @ SV877 @ SV1408 @ SV1874 @ SV2234 ) @ SY7189 @ SV1874 @ SV2234 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2234 ) @ SV1408 ) @ ( c_Set_Oimage @ SV257 @ SY7189 @ SV1874 @ SV2234 ) ) )
| ~ ( c_Fun_Oinj__on @ SV257 @ SY7189 @ SV1874 @ SV2234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4754]) ).
thf(5322,plain,
! [SV1875: $i,SV1410: $i,SV879: $i,SV259: $i] :
( ( ( c_lessequals @ SV259 @ ( c_Set_Oinsert @ SV879 @ SV1410 @ SV1875 ) @ ( tc_fun @ SV1875 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV259 @ SV1410 @ ( tc_fun @ SV1875 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV259 @ ( c_Set_Oinsert @ SV879 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1875 @ tc_bool ) ) @ SV1875 ) @ ( tc_fun @ SV1875 @ tc_bool ) ) @ SV1410 @ ( tc_fun @ SV1875 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4755]) ).
thf(5323,plain,
! [SV1876: $i,SV1411: $i,SV880: $i,SV260: $i] :
( ( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ SV260 @ SV880 @ SV1411 @ SV1876 ) @ SV1876 )
= ( c_Finite__Set_Ocard @ SV880 @ SV1411 ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV260 @ SV880 @ SV1411 @ SV1876 )
| ~ ( c_Finite__Set_Ofinite @ SV880 @ SV1411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4756]) ).
thf(5324,plain,
! [SV1877: $i,SV1412: $i,SV881: $i,SV261: $i] :
( ( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ SV261 @ SV881 @ SV1412 @ SV1877 ) @ SV1877 )
!= ( c_Finite__Set_Ocard @ SV881 @ SV1412 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV881 @ SV1412 )
| ( c_Fun_Oinj__on @ SV261 @ SV881 @ SV1412 @ SV1877 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4757]) ).
thf(5325,plain,
! [SV1413: $i,SV882: $i,SV262: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV262 @ SV882 @ SV1413 @ SV1413 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Set_Oimage @ SV262 @ SV882 @ SV1413 @ SV1413 ) @ SV882 @ ( tc_fun @ SV1413 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV882 @ SV1413 ) )
= $true )
| ( ( ( c_Set_Oimage @ SV262 @ SV882 @ SV1413 @ SV1413 )
= SV882 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4758]) ).
thf(5326,plain,
! [SV1414: $i,SV263: $i,SV883: $i] :
( ( ( ~ ( c_lessequals @ SV883 @ ( c_Set_Oimage @ SV263 @ SV883 @ SV1414 @ SV1414 ) @ ( tc_fun @ SV1414 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV883 @ SV1414 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV263 @ SV883 @ SV1414 @ SV1414 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4759]) ).
thf(5327,plain,
! [SV1878: $i,SV1415: $i,SV884: $i,SV264: $i] :
( ( ( ( c_Set_Ovimage @ ( c_COMBK @ SV264 @ SV884 @ SV1415 ) @ SV1878 @ SV1415 @ SV884 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1415 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV884 ) @ SV264 ) @ SV1878 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4760]) ).
thf(5328,plain,
! [SV1879: $i,SV1416: $i,SV885: $i,SV265: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV265 @ ( c_Set_Oinsert @ SV885 @ SV1416 @ SV1879 ) @ ( tc_fun @ SV1879 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV265 @ SV1416 @ ( tc_fun @ SV1879 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1879 ) @ SV885 ) @ SV265 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV265 @ SV1416 @ ( tc_fun @ SV1879 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4761]) ).
thf(5329,plain,
! [SV1880: $i,SV1417: $i,SV886: $i,SV266: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV266 @ ( c_Set_Oinsert @ SV886 @ SV1417 @ SV1880 ) @ ( tc_fun @ SV1880 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV266 @ SV1417 @ ( tc_fun @ SV1880 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1880 ) @ SV886 ) @ SV266 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1880 ) @ SV886 ) @ SV1417 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4762]) ).
thf(5330,plain,
! [SV887: $i,SV267: $i,SV2235: $i,SV1418: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1418 ) @ SV2235 ) @ SV267 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1418 ) @ SV2235 ) @ SV887 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV267 @ ( c_Set_Oinsert @ SV2235 @ SV887 @ SV1418 ) @ ( tc_fun @ SV1418 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV267 @ SV887 @ ( tc_fun @ SV1418 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4763]) ).
thf(5331,plain,
! [SV2236: $i,SV1881: $i,SV1419: $i,SV888: $i,SV268: $i] :
( ( ( ( c_Set_Oimage @ SV268 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV888 @ SV1419 @ ( tc_fun @ SV1881 @ tc_bool ) ) @ SV1881 @ SV2236 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV268 @ SV888 @ SV1881 @ SV2236 ) @ ( c_Set_Oimage @ SV268 @ SV1419 @ SV1881 @ SV2236 ) @ ( tc_fun @ SV2236 @ tc_bool ) ) )
| ! [SY7190: $i] :
( ~ ( c_lessequals @ SV1419 @ SY7190 @ ( tc_fun @ SV1881 @ tc_bool ) )
| ~ ( c_lessequals @ SV888 @ SY7190 @ ( tc_fun @ SV1881 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV268 @ SY7190 @ SV1881 @ SV2236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4764]) ).
thf(5332,plain,
! [SV2237: $i,SV1882: $i,SV1420: $i,SV889: $i,SV269: $i] :
( ( ( c_Set_Ovimage @ SV269 @ ( c_Set_Oinsert @ SV889 @ SV1420 @ SV1882 ) @ SV2237 @ SV1882 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ SV269 @ ( c_Set_Oinsert @ SV889 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1882 @ tc_bool ) ) @ SV1882 ) @ SV2237 @ SV1882 ) @ ( c_Set_Ovimage @ SV269 @ SV1420 @ SV2237 @ SV1882 ) @ ( tc_fun @ SV2237 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4765]) ).
thf(5333,plain,
! [SV2238: $i,SV1883: $i,SV1421: $i,SV890: $i,SV270: $i] :
( ( ( ( c_Set_Oimage @ SV270 @ ( c_HOL_Ominus__class_Ominus @ SV890 @ SV1421 @ ( tc_fun @ SV1883 @ tc_bool ) ) @ SV1883 @ SV2238 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV270 @ SV890 @ SV1883 @ SV2238 ) @ ( c_Set_Oimage @ SV270 @ SV1421 @ SV1883 @ SV2238 ) @ ( tc_fun @ SV2238 @ tc_bool ) ) )
| ! [SY7191: $i] :
( ~ ( c_lessequals @ SV1421 @ SY7191 @ ( tc_fun @ SV1883 @ tc_bool ) )
| ~ ( c_lessequals @ SV890 @ SY7191 @ ( tc_fun @ SV1883 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV270 @ SY7191 @ SV1883 @ SV2238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4766]) ).
thf(5334,plain,
! [SV2239: $i,SV1884: $i,SV1422: $i,SV891: $i,SV271: $i] :
( ( ( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ SV271 @ SV891 @ SV1422 @ SV1884 @ ( tc_Option_Ooption @ SV2239 ) ) @ SV1884 @ SV2239 )
= ( c_Set_Oinsert @ SV891 @ ( c_Map_Odom @ SV271 @ SV1884 @ SV2239 ) @ SV1884 ) )
| ( SV1422
= ( c_Option_Ooption_ONone @ SV2239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4767]) ).
thf(5335,plain,
! [SV2240: $i,SV1885: $i,SV1423: $i,SV892: $i,SV272: $i] :
( ( ! [SY7192: $i] : ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ SV272 @ SV892 @ ( c_Option_Ooption_ONone @ SV1423 ) @ SV1885 @ ( tc_Option_Ooption @ SV1423 ) ) @ ( c_Fun_Ofun__upd @ SV2240 @ SV892 @ ( c_Option_Ooption_OSome @ SY7192 @ SV1423 ) @ SV1885 @ ( tc_Option_Ooption @ SV1423 ) ) @ SV1885 @ SV1423 )
| ~ ( c_Map_Omap__le @ SV272 @ SV2240 @ SV1885 @ SV1423 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4768]) ).
thf(5336,plain,
! [SV1886: $i,SV1424: $i,SV893: $i,SV273: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV273 @ ( c_Set_Oinsert @ SV893 @ SV1424 @ SV1886 ) @ ( tc_fun @ SV1886 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1886 ) @ SV893 ) @ SV273 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV273 @ ( c_Set_Oinsert @ SV893 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1886 @ tc_bool ) ) @ SV1886 ) @ ( tc_fun @ SV1886 @ tc_bool ) ) @ SV1424 @ ( tc_fun @ SV1886 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1886 ) @ SV893 ) @ SV1424 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4769]) ).
thf(5337,plain,
! [SV896: $i,SV1426: $i,SV276: $i] :
( ( ( c_Finite__Set_Ofinite @ SV276 @ SV1426 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV276 @ SV896 @ ( tc_fun @ SV1426 @ tc_bool ) ) @ SV1426 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4771]) ).
thf(5338,plain,
! [SV1887: $i,SV1427: $i,SV897: $i,SV277: $i] :
( ( ( c_Com_Ocom_OBODY @ SV277 )
= ( c_Com_Ocom_OLocal @ SV897 @ SV1427 @ SV1887 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4772]) ).
thf(5339,plain,
! [SV2241: $i,SV1888: $i,SV1428: $i,SV898: $i,SV278: $i] :
( ( ( c_Fun_Oinj__on @ SV278 @ ( c_HOL_Ominus__class_Ominus @ SV898 @ SV1428 @ ( tc_fun @ SV1888 @ tc_bool ) ) @ SV1888 @ SV2241 )
| ~ ( c_Fun_Oinj__on @ SV278 @ SV898 @ SV1888 @ SV2241 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4773]) ).
thf(5340,plain,
! [SV1889: $i,SV1429: $i,SV899: $i,SV279: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV279 @ tc_bool ) )
!= ( c_Set_Oimage @ SV899 @ SV1429 @ SV1889 @ SV279 ) )
= $true )
| ( ( SV1429
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1889 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4774]) ).
thf(5341,plain,
! [SV2242: $i,SV1890: $i,SV1430: $i,SV900: $i,SV280: $i] :
( ( ( c_Com_Ocom_OWhile @ SV280 @ SV900 )
!= ( c_Com_Ocom_OLocal @ SV1430 @ SV1890 @ SV2242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4775]) ).
thf(5342,plain,
! [SV2243: $i,SV1891: $i,SV1432: $i,SV902: $i,SV282: $i] :
( ( ( c_Set_Ovimage @ SV282 @ ( c_HOL_Ominus__class_Ominus @ SV902 @ SV1432 @ ( tc_fun @ SV1891 @ tc_bool ) ) @ SV2243 @ SV1891 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Ovimage @ SV282 @ SV902 @ SV2243 @ SV1891 ) @ ( c_Set_Ovimage @ SV282 @ SV1432 @ SV2243 @ SV1891 ) @ ( tc_fun @ SV2243 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4777]) ).
thf(5343,plain,
! [SV1892: $i,SV1433: $i,SV903: $i,SV283: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV283 @ ( c_Set_Oinsert @ SV903 @ SV1433 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1892 ) @ SV903 ) @ SV283 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV283 @ ( c_Set_Oinsert @ SV903 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1892 @ tc_bool ) ) @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) ) @ SV1433 @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV283 @ SV1433 @ ( tc_fun @ SV1892 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4778]) ).
thf(5344,plain,
! [SV1893: $i,SV1435: $i,SV906: $i,SV286: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV286 @ SV906 )
!= ( c_Com_Ocom_OSemi @ SV1435 @ SV1893 ) )
= $true )
| ( ( SV906 = SV1893 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4780]) ).
thf(5345,plain,
! [SV2244: $i,SV1436: $i,SV907: $i,SV287: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV287 @ SV907 )
!= ( c_Com_Ocom_OSemi @ SV1436 @ SV2244 ) )
= $true )
| ( ( SV287 = SV1436 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4781]) ).
thf(5346,plain,
! [SV1894: $i,SV1437: $i,SV908: $i,SV288: $i] :
( ( ( c_Com_Ocom_OSemi @ SV288 @ SV908 )
= ( c_Com_Ocom_OWhile @ SV1437 @ SV1894 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4782]) ).
thf(5347,plain,
! [SV2245: $i,SV1897: $i,SV1440: $i,SV911: $i,SV291: $i] :
( ( ( c_Com_Ocom_OSemi @ SV291 @ SV911 )
!= ( c_Com_Ocom_OCond @ SV1440 @ SV1897 @ SV2245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4785]) ).
thf(5348,plain,
! [SV912: $i,SV1898: $i,SV292: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV292 @ SV1898 @ ( tc_fun @ SV912 @ tc_bool ) ) @ SV912 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1898 @ SV912 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV292 @ SV912 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4786]) ).
thf(5349,plain,
! [SV913: $i,SV1441: $i,SV293: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV293 @ SV1441 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV913 @ SV1441 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV293 @ SV913 @ ( tc_fun @ SV1441 @ tc_bool ) ) @ SV1441 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4787]) ).
thf(5350,plain,
! [SV2246: $i,SV1899: $i,SV1443: $i,SV915: $i,SV295: $i] :
( ( ( c_Com_Ocom_OSemi @ SV295 @ SV915 )
!= ( c_Com_Ocom_OLocal @ SV1443 @ SV1899 @ SV2246 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4789]) ).
thf(5351,plain,
! [SV1902: $i,SV1446: $i,SV918: $i,SV298: $i] :
( ( ( c_Map_Omap__le @ SV298 @ SV918 @ SV1446 @ SV1902 )
= $true )
| ( ( ! [SY6892: $i] :
~ ( c_Map_Omap__le @ ( c_Map_Omap__add @ SY6892 @ SV298 @ SV1446 @ SV1902 ) @ SV918 @ SV1446 @ SV1902 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4792]) ).
thf(5352,plain,
! [SV1448: $i,SV300: $i,SV920: $i,SV2247: $i] :
( ( ( ! [SY7193: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2247 ) @ SV920 ) @ SY7193 ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY7193 @ SV300 @ SV2247 @ ( tc_fun @ SV1448 @ tc_bool ) ) @ SV1448 )
| ~ ( c_Finite__Set_Ofinite @ SY7193 @ SV2247 ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ SV300 @ SV920 ) @ SV1448 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4793]) ).
thf(5353,plain,
! [SV1903: $i,SV1450: $i,SV922: $i,SV302: $i] :
( ( ( c_Map_Omap__le @ SV302 @ SV922 @ SV1450 @ SV1903 )
= $true )
| ( ( ! [SY6893: $i] :
( ~ ( c_Map_Omap__le @ SY6893 @ SV922 @ SV1450 @ SV1903 )
| ~ ( c_Map_Omap__le @ SV302 @ SY6893 @ SV1450 @ SV1903 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4794]) ).
thf(5354,plain,
! [SV2248: $i,SV1904: $i,SV1451: $i,SV923: $i,SV303: $i] :
( ( ( c_Com_Ocom_OLocal @ SV303 @ SV923 @ SV1451 )
!= ( c_Com_Ocom_OAss @ SV1904 @ SV2248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4795]) ).
thf(5355,plain,
! [SV304: $i,SV924: $i,SV1905: $i] :
( ( ( SV1905 = SV924 )
= $true )
| ( ( ! [SY6895: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1905 @ SV304 @ SY6895 ) @ SV924 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV304 @ SV924 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4796]) ).
thf(5356,plain,
! [SV1906: $i,SV1452: $i,SV925: $i,SV305: $i] :
( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV305 @ SV925 @ SV1452 @ ( tc_fun @ SV1906 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1906 @ tc_bool ) ) )
= $true )
| ( ( ! [SY6896: $i] :
( ( ( hAPP @ SV925 @ SY6896 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1906 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1452 ) @ SY6896 ) @ SV305 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4797]) ).
thf(5357,plain,
! [SV2249: $i,SV1907: $i,SV1454: $i,SV927: $i,SV307: $i] :
( ( ( c_Com_Ocom_OCond @ SV307 @ SV927 @ SV1454 )
!= ( c_Com_Ocom_OWhile @ SV1907 @ SV2249 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4799]) ).
thf(5358,plain,
! [SV2250: $i,SV1908: $i,SV1455: $i,SV928: $i,SV308: $i] :
( ( ! [SY7194: $i] :
( ( c_Com_Ocom_OCond @ SV308 @ SV928 @ SV1455 )
!= ( c_Com_Ocom_OLocal @ SV1908 @ SV2250 @ SY7194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4800]) ).
thf(5359,plain,
! [SV931: $i,SV313: $i,SV1911: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV1911 @ SV313 @ SV931 ) @ SV931 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV313 @ SV931 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4803]) ).
thf(5360,plain,
! [SV314: $i,SV1456: $i,SV932: $i] :
( ( ( c_Finite__Set_Ofinite @ SV932 @ SV1456 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV314 @ SV932 @ SV1456 ) @ SV1456 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4804]) ).
thf(5361,plain,
! [SV2251: $i,SV1912: $i,SV1457: $i,SV933: $i,SV316: $i] :
( ( ( c_Com_Ocom_OCond @ SV316 @ SV933 @ SV1457 )
!= ( c_Com_Ocom_OSemi @ SV1912 @ SV2251 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4805]) ).
thf(5362,plain,
! [SV317: $i,SV934: $i] :
( ( ( c_Com_OWT @ SV934 )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV317 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ SV317 ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV317 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ SV934 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4806]) ).
thf(5363,plain,
! [SV2252: $i,SV1913: $i,SV1458: $i,SV935: $i,SV318: $i] :
( ( ! [SY7195: $i,SY7196: $i,SY7197: $i,SY7198: $i] :
( ( ( hAPP @ SV318 @ ( c_Set_Oinsert @ SV935 @ ( c_Set_Oinsert @ SV1458 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1913 @ tc_bool ) ) @ SV1913 ) @ SV1913 ) )
= ( hAPP @ ( hAPP @ SV2252 @ SV935 ) @ SV1458 ) )
| ! [SY7199: $i,SY7200: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY7195 @ SV318 @ SY7196 @ SY7197 @ SY7198 @ SV2252 @ SY7199 @ SY7200 @ SV1913 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4807]) ).
thf(5364,plain,
! [SV2253: $i,SV1914: $i,SV1459: $i,SV936: $i,SV319: $i] :
( ( ! [SY7201: $i,SY7202: $i,SY7203: $i,SY7204: $i] :
( ( ( hAPP @ SV319 @ ( c_Set_Oinsert @ SV936 @ ( c_Set_Oinsert @ SV1459 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1914 @ tc_bool ) ) @ SV1914 ) @ SV1914 ) )
= ( hAPP @ ( hAPP @ SV2253 @ SV936 ) @ SV1459 ) )
| ! [SY7205: $i,SY7206: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV319 @ SY7201 @ SY7202 @ SY7203 @ SV2253 @ SY7204 @ SY7205 @ SY7206 @ SV1914 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4808]) ).
thf(5365,plain,
! [SV2254: $i,SV1915: $i,SV1460: $i,SV937: $i,SV320: $i] :
( ( ! [SY7207: $i] :
( ( ( c_Com_Ocom_OCond @ SV320 @ SV937 @ SV1460 )
!= ( c_Com_Ocom_OCond @ SV1915 @ SV2254 @ SY7207 ) )
| ( SV1460 = SY7207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4809]) ).
thf(5366,plain,
! [SV2255: $i,SV1916: $i,SV1461: $i,SV938: $i,SV321: $i] :
( ( ! [SY7208: $i] :
( ( c_Com_Ocom_OCond @ SV321 @ SV938 @ SV1461 )
!= ( c_Com_Ocom_OCond @ SV1916 @ SV2255 @ SY7208 ) )
| ( SV938 = SV2255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4810]) ).
thf(5367,plain,
! [SV1917: $i,SV1462: $i,SV939: $i,SV322: $i] :
( ( ( ! [SY6919: $i,SY6920: $i] :
( ( c_Com_Ocom_OCond @ SV322 @ SV939 @ SV1462 )
!= ( c_Com_Ocom_OCond @ SV1917 @ SY6919 @ SY6920 ) ) )
= $true )
| ( ( SV322 = SV1917 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4811]) ).
thf(5368,plain,
! [SV1463: $i,SV942: $i,SV325: $i] :
( ( ( ( c_Option_Ooption_OSome @ SV325 @ SV942 )
= ( c_Option_Ooption_OSome @ SV1463 @ SV942 ) )
= $false )
| ( ( SV325 = SV1463 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4812]) ).
thf(5369,plain,
! [SV1918: $i,SV1464: $i,SV945: $i,SV328: $i] :
( ( ( c_Com_Ocom_OAss @ SV328 @ SV945 )
= ( c_Com_Ocom_OWhile @ SV1464 @ SV1918 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4813]) ).
thf(5370,plain,
! [SV2256: $i,SV1919: $i,SV1465: $i,SV946: $i,SV329: $i] :
( ( ( c_Map_Omap__add @ SV329 @ ( c_Map_Omap__add @ SV946 @ SV1465 @ SV1919 @ SV2256 ) @ SV1919 @ SV2256 )
= ( c_Map_Omap__add @ ( c_Map_Omap__add @ SV329 @ SV946 @ SV1919 @ SV2256 ) @ SV1465 @ SV1919 @ SV2256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4814]) ).
thf(5371,plain,
! [SV2257: $i,SV1920: $i,SV1466: $i,SV947: $i,SV330: $i] :
( ( ( c_Com_Ocom_OAss @ SV330 @ SV947 )
!= ( c_Com_Ocom_OLocal @ SV1466 @ SV1920 @ SV2257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4815]) ).
thf(5372,plain,
! [SV1921: $i,SV1467: $i,SV949: $i,SV332: $i] :
( ( ( c_Com_Ocom_OCond @ SV332 @ SV949 @ SV1467 )
= ( c_Com_Ocom_OBODY @ SV1921 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4816]) ).
thf(5373,plain,
! [SV1922: $i,SV1468: $i,SV950: $i,SV333: $i] :
( ( ( c_Com_Ocom_OBODY @ SV333 )
= ( c_Com_Ocom_OCond @ SV950 @ SV1468 @ SV1922 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4817]) ).
thf(5374,plain,
! [SV334: $i,SV2258: $i,SV951: $i] :
( ( ( ! [SY7209: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV951 @ SV2258 @ SV334 ) @ SY7209 @ SV334 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV951 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2258 @ SY7209 @ SV334 ) @ SV334 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV334 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4818]) ).
thf(5375,plain,
! [SV335: $i,SV2259: $i,SV952: $i] :
( ( ( ! [SY7210: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV952 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2259 @ SY7210 @ SV335 ) @ SV335 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV2259 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV952 @ SY7210 @ SV335 ) @ SV335 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV335 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4819]) ).
thf(5376,plain,
! [SV336: $i,SV2260: $i,SV953: $i] :
( ( ( ! [SY7211: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ SV953 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2260 @ SY7211 @ SV336 ) @ SV336 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV2260 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV953 @ SY7211 @ SV336 ) @ SV336 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV336 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4820]) ).
thf(5377,plain,
! [SV337: $i,SV2261: $i,SV954: $i] :
( ( ( ! [SY7212: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV954 @ SV2261 @ SV337 ) @ SY7212 @ SV337 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV954 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2261 @ SY7212 @ SV337 ) @ SV337 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV337 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4821]) ).
thf(5378,plain,
! [SV2262: $i,SV1925: $i,SV1471: $i,SV957: $i,SV340: $i] :
( ( ( c_Com_Ocom_OLocal @ SV340 @ SV957 @ SV1471 )
!= ( c_Com_Ocom_OWhile @ SV1925 @ SV2262 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4824]) ).
thf(5379,plain,
! [SV2263: $i,SV1926: $i,SV1472: $i,SV958: $i,SV341: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV341 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV958 @ ( c_Com_Ocom_OBODY @ SV1472 ) @ SV1926 @ SV2263 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2263 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2263 ) ) @ SV2263 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV341 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV958 @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SV1472 ) @ tc_Com_Ocom ) @ SV1926 @ SV2263 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2263 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2263 ) ) @ SV2263 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4825]) ).
thf(5380,plain,
! [SV2264: $i,SV1927: $i,SV1473: $i,SV959: $i,SV342: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV342 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV959 @ ( c_Com_Ocom_OBODY @ SV1473 ) @ SV1927 @ SV2264 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2264 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2264 ) ) @ SV2264 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV959 @ ( c_Com_Ocom_OBODY @ SV1473 ) @ SV1927 @ SV2264 ) @ SV342 @ ( tc_Hoare__Mirabelle_Otriple @ SV2264 ) ) @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV959 @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SV1473 ) @ tc_Com_Ocom ) @ SV1927 @ SV2264 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2264 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2264 ) ) @ SV2264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4826]) ).
thf(5381,plain,
! [SV1474: $i,SV960: $i,SV343: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV343 )
= $false )
| ( ( ! [SY6341: $i,SY6342: $i] :
( ( ( c_Finite__Set_Osetsum @ SV960 @ ( c_HOL_Ominus__class_Ominus @ SV1474 @ ( c_Set_Oinsert @ SY6341 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6342 @ tc_bool ) ) @ SY6342 ) @ ( tc_fun @ SY6342 @ tc_bool ) ) @ SY6342 @ SV343 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV960 @ SV1474 @ SY6342 @ SV343 ) @ ( hAPP @ SV960 @ SY6341 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6342 ) @ SY6341 ) @ SV1474 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1474 @ SY6342 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4827]) ).
thf(5382,plain,
! [SV1475: $i,SV961: $i,SV344: $i] :
( ( ( class_Ring__and__Field_Oring @ SV344 )
= $false )
| ( ( ! [SY6343: $i,SY6344: $i] :
( ( ( c_Finite__Set_Osetsum @ SV961 @ ( c_HOL_Ominus__class_Ominus @ SV1475 @ ( c_Set_Oinsert @ SY6343 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6344 @ tc_bool ) ) @ SY6344 ) @ ( tc_fun @ SY6344 @ tc_bool ) ) @ SY6344 @ SV344 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV961 @ SV1475 @ SY6344 @ SV344 ) @ ( hAPP @ SV961 @ SY6343 ) @ SV344 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6344 ) @ SY6343 ) @ SV1475 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1475 @ SY6344 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4828]) ).
thf(5383,plain,
! [SV2265: $i,SV1929: $i,SV1477: $i,SV963: $i,SV347: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV347 @ ( c_HOL_Ominus__class_Ominus @ SV963 @ SV1477 @ ( tc_fun @ SV1929 @ tc_bool ) ) @ SV1929 @ SV2265 ) @ ( c_Set_Oimage @ SV347 @ ( c_HOL_Ominus__class_Ominus @ SV1477 @ SV963 @ ( tc_fun @ SV1929 @ tc_bool ) ) @ SV1929 @ SV2265 ) @ ( tc_fun @ SV2265 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2265 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SV347 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV963 @ SV1477 @ ( tc_fun @ SV1929 @ tc_bool ) ) @ SV1929 @ SV2265 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4830]) ).
thf(5384,plain,
! [SV2266: $i,SV1930: $i,SV1478: $i,SV964: $i,SV348: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV348 @ ( c_HOL_Ominus__class_Ominus @ SV964 @ SV1478 @ ( tc_fun @ SV1930 @ tc_bool ) ) @ SV1930 @ SV2266 ) @ ( c_Set_Oimage @ SV348 @ ( c_HOL_Ominus__class_Ominus @ SV1478 @ SV964 @ ( tc_fun @ SV1930 @ tc_bool ) ) @ SV1930 @ SV2266 ) @ ( tc_fun @ SV2266 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2266 @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ SV348 @ SV1478 @ SV1930 @ SV2266 )
| ~ ( c_Fun_Oinj__on @ SV348 @ SV964 @ SV1930 @ SV2266 )
| ( c_Fun_Oinj__on @ SV348 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV964 @ SV1478 @ ( tc_fun @ SV1930 @ tc_bool ) ) @ SV1930 @ SV2266 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4831]) ).
thf(5385,plain,
! [SV1931: $i,SV1479: $i,SV965: $i,SV349: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV349 @ ( c_Set_Oinsert @ SV965 @ SV1479 @ SV1931 ) @ ( tc_fun @ SV1931 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV349 @ SV1479 @ ( tc_fun @ SV1931 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV349 @ ( c_Set_Oinsert @ SV965 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1931 @ tc_bool ) ) @ SV1931 ) @ ( tc_fun @ SV1931 @ tc_bool ) ) @ SV1479 @ ( tc_fun @ SV1931 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1931 ) @ SV965 ) @ SV1479 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4832]) ).
thf(5386,plain,
! [SV2267: $i,SV1932: $i,SV1480: $i,SV966: $i,SV350: $i] :
( ( ! [SY7213: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ SV350 @ SV966 @ SV1480 @ SV1932 @ SV2267 ) @ SY7213 @ SV1932 @ SV2267 )
= ( c_Set_Oinsert @ SV1480 @ ( c_Set_Oimage @ SV350 @ ( c_HOL_Ominus__class_Ominus @ SY7213 @ ( c_Set_Oinsert @ SV966 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1932 @ tc_bool ) ) @ SV1932 ) @ ( tc_fun @ SV1932 @ tc_bool ) ) @ SV1932 @ SV2267 ) @ SV2267 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1932 ) @ SV966 ) @ SY7213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4833]) ).
thf(5387,plain,
! [SV1481: $i,SV967: $i,SV351: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV351 )
= $false )
| ( ( ! [SY6354: $i,SY6355: $i] :
( ( ( c_Finite__Set_Osetsum @ SV967 @ ( c_HOL_Ominus__class_Ominus @ SV1481 @ ( c_Set_Oinsert @ SY6354 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY6355 @ tc_bool ) ) @ SY6355 ) @ ( tc_fun @ SY6355 @ tc_bool ) ) @ SY6355 @ SV351 )
= ( c_Finite__Set_Osetsum @ SV967 @ SV1481 @ SY6355 @ SV351 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6355 ) @ SY6354 ) @ SV1481 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1481 @ SY6355 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4834]) ).
thf(5388,plain,
! [SV352: $i,SV968: $i,SV1482: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1482 ) @ SV968 ) @ SV352 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV352 @ SV1482 ) )
= $true )
| ( ( ( c_Finite__Set_Ocard @ ( c_HOL_Ominus__class_Ominus @ SV352 @ ( c_Set_Oinsert @ SV968 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1482 @ tc_bool ) ) @ SV1482 ) @ ( tc_fun @ SV1482 @ tc_bool ) ) @ SV1482 )
= ( c_Finite__Set_Ocard @ SV352 @ SV1482 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4835]) ).
thf(5389,plain,
! [SV2268: $i,SV1933: $i,SV1483: $i,SV969: $i,SV353: $i] :
( ( ! [SY7214: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV969 @ ( c_Com_Ocom_OSemi @ SV1483 @ SV1933 ) @ SV2268 @ SY7214 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY7214 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY7214 ) ) @ SY7214 )
| ! [SY7215: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY7215 @ SV1933 @ SV2268 @ SY7214 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY7214 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY7214 ) ) @ SY7214 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV969 @ SV1483 @ SY7215 @ SY7214 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY7214 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY7214 ) ) @ SY7214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4836]) ).
thf(5390,plain,
! [SV2269: $i,SV1934: $i,SV1485: $i,SV971: $i,SV355: $i] :
( ( ! [SY7216: $i] :
( ( ( c_Map_Omap__add @ ( c_Fun_Ofun__upd @ SV355 @ SV971 @ ( c_Option_Ooption_OSome @ SV1485 @ SV1934 ) @ SV2269 @ ( tc_Option_Ooption @ SV1934 ) ) @ SY7216 @ SV2269 @ SV1934 )
= ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ SV355 @ SY7216 @ SV2269 @ SV1934 ) @ SV971 @ ( c_Option_Ooption_OSome @ SV1485 @ SV1934 ) @ SV2269 @ ( tc_Option_Ooption @ SV1934 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2269 ) @ SV971 ) @ ( c_Map_Odom @ SY7216 @ SV2269 @ SV1934 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4837]) ).
thf(5391,plain,
! [SV1935: $i,SV1486: $i,SV972: $i,SV356: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV356 @ ( c_Set_Oinsert @ SV972 @ SV1486 @ SV1935 ) @ ( tc_fun @ SV1935 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV356 @ SV1486 @ ( tc_fun @ SV1935 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV356 @ ( c_Set_Oinsert @ SV972 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1935 @ tc_bool ) ) @ SV1935 ) @ ( tc_fun @ SV1935 @ tc_bool ) ) @ SV1486 @ ( tc_fun @ SV1935 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV356 @ SV1486 @ ( tc_fun @ SV1935 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4838]) ).
thf(5392,plain,
! [SV2270: $i,SV1937: $i,SV1488: $i,SV974: $i,SV358: $i] :
( ( ! [SY7217: $i,SY7218: $i] :
( ( c_Nitpick_Ofold__graph_H @ SV358 @ SV974 @ SV1488 @ ( hAPP @ ( hAPP @ SV358 @ SV1937 ) @ SV2270 ) @ SY7217 @ SY7218 )
| ~ ( c_Nitpick_Ofold__graph_H @ SV358 @ SV974 @ ( c_HOL_Ominus__class_Ominus @ SV1488 @ ( c_Set_Oinsert @ SV1937 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY7217 @ tc_bool ) ) @ SY7217 ) @ ( tc_fun @ SY7217 @ tc_bool ) ) @ SV2270 @ SY7217 @ SY7218 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7217 ) @ SV1937 ) @ SV1488 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4840]) ).
thf(5393,plain,
! [SV1938: $i,SV1489: $i,SV975: $i,SV359: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV359 @ ( c_Set_Oinsert @ SV975 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1489 @ tc_bool ) ) @ SV1489 ) @ ( tc_fun @ SV1489 @ tc_bool ) ) @ SV1938 @ ( tc_fun @ SV1489 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1489 ) @ SV975 ) @ SV359 ) )
| ~ ( c_lessequals @ SV359 @ ( c_Set_Oinsert @ SV975 @ SV1938 @ SV1489 ) @ ( tc_fun @ SV1489 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4841]) ).
thf(5394,plain,
! [SV1939: $i,SV1490: $i,SV976: $i,SV360: $i] :
( ( ( c_lessequals @ SV360 @ ( c_Set_Oinsert @ SV976 @ SV1490 @ SV1939 ) @ ( tc_fun @ SV1939 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1939 ) @ SV976 ) @ SV360 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV360 @ ( c_Set_Oinsert @ SV976 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1939 @ tc_bool ) ) @ SV1939 ) @ ( tc_fun @ SV1939 @ tc_bool ) ) @ SV1490 @ ( tc_fun @ SV1939 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4842]) ).
thf(5395,plain,
! [SV1940: $i,SV1491: $i,SV977: $i,SV361: $i] :
( ( ( c_lessequals @ SV361 @ ( c_Set_Oinsert @ SV977 @ SV1491 @ SV1940 ) @ ( tc_fun @ SV1940 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1940 ) @ SV977 ) @ SV361 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV361 @ ( c_Set_Oinsert @ SV977 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1940 @ tc_bool ) ) @ SV1940 ) @ ( tc_fun @ SV1940 @ tc_bool ) ) @ SV1491 @ ( tc_fun @ SV1940 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4843]) ).
thf(5396,plain,
! [SV1941: $i,SV1492: $i,SV978: $i,SV362: $i] :
( ( ( ( c_Finite__Set_Osetsum @ SV362 @ ( c_HOL_Ominus__class_Ominus @ SV978 @ ( c_Set_Oinsert @ SV1492 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1941 @ tc_bool ) ) @ SV1941 ) @ ( tc_fun @ SV1941 @ tc_bool ) ) @ SV1941 @ tc_nat )
= ( c_Finite__Set_Osetsum @ SV362 @ SV978 @ SV1941 @ tc_nat ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1941 ) @ SV1492 ) @ SV978 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4844]) ).
thf(5397,plain,
! [SV2271: $i,SV1942: $i,SV1493: $i,SV979: $i,SV363: $i] :
( ( ! [SY7219: $i,SY7220: $i] :
( ( c_Finite__Set_Ofold__graph @ SV363 @ SV979 @ SV1493 @ ( hAPP @ ( hAPP @ SV363 @ SV1942 ) @ SV2271 ) @ SY7219 @ SY7220 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7219 ) @ SV1942 ) @ SV1493 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV363 @ SV979 @ ( c_HOL_Ominus__class_Ominus @ SV1493 @ ( c_Set_Oinsert @ SV1942 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY7219 @ tc_bool ) ) @ SY7219 ) @ ( tc_fun @ SY7219 @ tc_bool ) ) @ SV2271 @ SY7219 @ SY7220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4845]) ).
thf(5398,plain,
! [SV1943: $i,SV1494: $i,SV980: $i,SV364: $i] :
( ( ( ( c_Set_Oimage @ ( c_COMBK @ SV364 @ SV980 @ SV1494 ) @ SV1943 @ SV1494 @ SV980 )
= ( c_Set_Oinsert @ SV364 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV980 @ tc_bool ) ) @ SV980 ) )
= $true )
| ( ( ! [SY6941: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1494 ) @ SY6941 ) @ SV1943 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4846]) ).
thf(5399,plain,
! [SV1944: $i,SV1495: $i,SV981: $i,SV365: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV365 @ ( c_Set_Oinsert @ SV981 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1495 @ tc_bool ) ) @ SV1495 ) @ ( tc_fun @ SV1495 @ tc_bool ) ) @ SV1944 @ ( tc_fun @ SV1495 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1495 ) @ SV981 ) @ SV365 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1495 ) @ SV981 ) @ SV1944 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV365 @ ( c_Set_Oinsert @ SV981 @ SV1944 @ SV1495 ) @ ( tc_fun @ SV1495 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4847]) ).
thf(5400,plain,
! [SV1496: $i,SV982: $i,SV366: $i] :
( ( ( ( hAPP @ SV366 @ SV982 )
= ( c_Option_Ooption_ONone @ SV1496 ) )
= $false )
| ( ( ! [SY6380: $i,SY6381: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ SV366 @ SY6380 @ SV1496 ) @ ( c_Set_Oinsert @ SV982 @ SY6381 @ SY6380 ) @ ( tc_fun @ SY6380 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ SV366 @ SY6380 @ SV1496 ) @ SY6381 @ ( tc_fun @ SY6380 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4848]) ).
thf(5401,plain,
! [SV1945: $i,SV1497: $i,SV983: $i,SV367: $i] :
( ( ( c_Com_Ocom_OAss @ SV367 @ SV983 )
= ( c_Com_Ocom_OSemi @ SV1497 @ SV1945 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4849]) ).
thf(5402,plain,
! [SV2272: $i,SV1946: $i,SV1498: $i,SV985: $i,SV369: $i] :
( ( ! [SY7221: $i] :
( ( c_Com_Ocom_OLocal @ SV369 @ SV985 @ SV1498 )
!= ( c_Com_Ocom_OCond @ SV1946 @ SV2272 @ SY7221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4851]) ).
thf(5403,plain,
! [SV1947: $i,SV1499: $i,SV986: $i,SV370: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV370 @ SV986 @ SV1499 ) @ SV1947 @ ( tc_fun @ SV1499 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV986 @ SV1947 @ ( tc_fun @ SV1499 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1499 ) @ SV370 ) @ SV1947 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4852]) ).
thf(5404,plain,
! [SV1948: $i,SV1500: $i,SV987: $i,SV371: $i] :
( ( ( c_Fun_Oinj__on @ SV371 @ SV987 @ SV1500 @ SV1948 )
= $true )
| ( ( ! [SY6944: $i] :
~ ( c_Fun_Oinj__on @ SV371 @ ( c_Set_Oinsert @ SY6944 @ SV987 @ SV1500 ) @ SV1500 @ SV1948 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4853]) ).
thf(5405,plain,
! [SV989: $i,SV373: $i,SV1949: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1949 ) @ SV373 ) @ ( c_Set_Oinsert @ SV989 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1949 @ tc_bool ) ) @ SV1949 ) ) )
= $false )
| ( ( SV373 = SV989 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4855]) ).
thf(5406,plain,
! [SV1502: $i,SV990: $i,SV374: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV374 @ SV990 @ ( tc_fun @ SV1502 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1502 @ tc_bool ) ) )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV374 @ SV990 @ ( tc_fun @ SV1502 @ tc_bool ) )
= SV374 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4856]) ).
thf(5407,plain,
! [SV375: $i,SV2273: $i,SV991: $i,SV1950: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1950 ) @ SV991 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2273 @ ( c_Collect @ SV375 @ SV1950 ) @ ( tc_fun @ SV1950 @ tc_bool ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV375 @ SV991 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4857]) ).
thf(5408,plain,
! [SV376: $i,SV2274: $i,SV992: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV992 @ SV2274 @ SV376 )
| ! [SY7222: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY7222 @ SV2274 @ SV376 )
| ~ ( c_HOL_Oord__class_Oless @ SV992 @ SY7222 @ SV376 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV376 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4858]) ).
thf(5409,plain,
! [SV377: $i,SV1503: $i,SV993: $i,SV2275: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2275 @ SV993 @ ( tc_fun @ SV1503 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV377 @ SV2275 @ ( tc_fun @ SV1503 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV377 @ SV993 @ ( tc_fun @ SV1503 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4859]) ).
thf(5410,plain,
! [SV378: $i,SV2276: $i,SV994: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV994 @ SV2276 @ SV378 )
| ! [SY7223: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV994 @ SY7223 @ SV378 )
| ~ ( c_HOL_Oord__class_Oless @ SY7223 @ SV2276 @ SV378 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV378 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4860]) ).
thf(5411,plain,
! [SV2277: $i,SV1951: $i,SV1504: $i,SV995: $i,SV379: $i] :
( ( ( c_Fun_Oinj__on @ SV379 @ ( c_Set_Oinsert @ SV995 @ SV1504 @ SV1951 ) @ SV1951 @ SV2277 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2277 ) @ ( hAPP @ SV379 @ SV995 ) ) @ ( c_Set_Oimage @ SV379 @ ( c_HOL_Ominus__class_Ominus @ SV1504 @ ( c_Set_Oinsert @ SV995 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1951 @ tc_bool ) ) @ SV1951 ) @ ( tc_fun @ SV1951 @ tc_bool ) ) @ SV1951 @ SV2277 ) ) )
| ~ ( c_Fun_Oinj__on @ SV379 @ SV1504 @ SV1951 @ SV2277 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4861]) ).
thf(5412,plain,
! [SV2278: $i,SV1954: $i,SV1507: $i,SV998: $i,SV382: $i] :
( ( ! [SY7224: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV382 @ SV998 @ SV1507 @ SV1954 ) @ SV2278 ) @ SY7224 )
= ( hAPP @ ( hAPP @ SV382 @ SY7224 ) @ SV2278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4864]) ).
thf(5413,plain,
! [SV1955: $i,SV1510: $i,SV1003: $i,SV387: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV387 @ SV1003 ) ) @ SV1510 ) @ SV1955 ) )
= $true )
| ( ( ! [SY6949: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV387 @ SV1003 ) ) @ SY6949 ) @ SV1955 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1003 ) @ SV1510 ) @ SY6949 ) )
| ~ ( hBOOL @ ( hAPP @ SV387 @ SV1510 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4866]) ).
thf(5414,plain,
! [SV389: $i,SV2279: $i,SV1005: $i] :
( ( ( ! [SY7225: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV1005 @ SV2279 @ SV389 )
!= ( c_HOL_Ominus__class_Ominus @ SY7225 @ SY7225 @ SV389 ) )
| ( SV1005 = SV2279 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV389 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4867]) ).
thf(5415,plain,
! [SV2280: $i,SV390: $i,SV1006: $i] :
( ( ( ! [SY7226: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV1006 @ SV1006 @ SV390 )
!= ( c_HOL_Ominus__class_Ominus @ SV2280 @ SY7226 @ SV390 ) )
| ( SV2280 = SY7226 ) ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV390 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4868]) ).
thf(5416,plain,
! [SV2281: $i,SV1956: $i,SV1513: $i,SV1008: $i,SV392: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV392 @ SV1008 @ SV1513 ) ) @ SV1956 ) @ SV2281 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1008 ) @ SV1956 ) @ SV2281 ) )
| ~ ( hBOOL @ ( hAPP @ SV392 @ SV1956 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4869]) ).
thf(5417,plain,
! [SV1514: $i,SV1009: $i,SV393: $i] :
( ( ( hBOOL @ ( hAPP @ SV393 @ SV1009 ) )
= $false )
| ( ( ! [SY6401: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1514 ) @ SV1009 ) @ SY6401 ) )
| ! [SY6402: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV393 @ SV1514 @ SY6402 ) ) @ SV1009 ) @ SY6401 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4870]) ).
thf(5418,plain,
! [SV1957: $i,SV1515: $i,SV1010: $i,SV394: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV394 @ SV1010 ) ) @ SV1515 ) @ SV1957 ) )
= $true )
| ( ( ! [SY6951: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1010 ) @ SY6951 ) @ SV1957 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV394 ) @ SV1515 ) @ SY6951 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4871]) ).
thf(5419,plain,
! [SV1958: $i,SV1517: $i,SV1012: $i,SV396: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Map_Odom @ SV396 @ SV1012 @ SV1517 ) @ ( c_Map_Odom @ SV1958 @ SV1012 @ SV1517 ) @ ( tc_fun @ SV1012 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1012 @ tc_bool ) ) )
= $true )
| ( ( ( c_Map_Omap__add @ SV396 @ SV1958 @ SV1012 @ SV1517 )
= ( c_Map_Omap__add @ SV1958 @ SV396 @ SV1012 @ SV1517 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4872]) ).
thf(5420,plain,
! [SV1959: $i,SV1518: $i,SV1013: $i,SV397: $i] :
( ( ( ( hAPP @ SV397 @ SV1013 )
!= ( c_Option_Ooption_OSome @ SV1518 @ SV1959 ) )
= $true )
| ( ( ! [SY6952: $i] :
( ( c_Set_Oinsert @ SV1013 @ ( c_Map_Odom @ SV397 @ SY6952 @ SV1959 ) @ SY6952 )
= ( c_Map_Odom @ SV397 @ SY6952 @ SV1959 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4873]) ).
thf(5421,plain,
! [SV399: $i,SV2282: $i,SV1960: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1960 @ SV2282 @ SV399 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV2282 @ SV1960 @ SV399 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV399 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4874]) ).
thf(5422,plain,
! [SV400: $i,SV2283: $i,SV1961: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1961 @ SV2283 @ SV400 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV2283 @ SV1961 @ SV400 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV400 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4875]) ).
thf(5423,plain,
! [SV2284: $i,SV1962: $i,SV1520: $i,SV1015: $i,SV401: $i] :
( ( ! [SY7227: $i,SY7228: $i,SY7229: $i,SY7230: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV401 @ SV1015 @ ( c_COMBC @ SV1520 @ SV1962 @ SV1962 @ tc_bool ) @ ( c_COMBC @ SV2284 @ SV1962 @ SV1962 @ tc_bool ) @ SY7227 @ SY7228 @ SY7229 @ SY7230 @ SV1962 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1015 @ SV401 @ SV1520 @ SV2284 @ SY7228 @ SY7227 @ SY7230 @ SY7229 @ SV1962 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4876]) ).
thf(5424,plain,
! [SV1523: $i,SV1018: $i,SV404: $i] :
( ( ( ( c_Set_Oinsert @ SV404 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1018 @ tc_bool ) ) @ SV1018 )
= ( c_Set_Oinsert @ SV1523 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1018 @ tc_bool ) ) @ SV1018 ) )
= $false )
| ( ( SV404 = SV1523 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4878]) ).
thf(5425,plain,
! [SV2285: $i,SV1963: $i,SV1524: $i,SV1019: $i,SV405: $i] :
( ( ! [SY7231: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV405 @ SV1019 @ SV1524 @ SV1963 ) @ SV2285 )
!= ( c_Option_Ooption_OSome @ SY7231 @ SV1963 ) )
| ( ( hAPP @ SV405 @ SV2285 )
= ( c_Option_Ooption_OSome @ SY7231 @ SV1963 ) )
| ( ( hAPP @ SV1019 @ SV2285 )
= ( c_Option_Ooption_OSome @ SY7231 @ SV1963 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4879]) ).
thf(5426,plain,
! [SV1964: $i,SV1525: $i,SV1020: $i,SV406: $i] :
( ( ( ( hAPP @ SV406 @ SV1020 )
!= ( c_Option_Ooption_OSome @ SV1525 @ SV1964 ) )
= $true )
| ( ( ! [SY6962: $i] :
( ( ( hAPP @ SY6962 @ SV1020 )
!= ( c_Option_Ooption_ONone @ SV1964 ) )
| ! [SY6963: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SV406 @ SY6962 @ SY6963 @ SV1964 ) @ SV1020 )
= ( c_Option_Ooption_OSome @ SV1525 @ SV1964 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4880]) ).
thf(5427,plain,
! [SV2286: $i,SV1965: $i,SV1526: $i,SV1021: $i,SV407: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ SV407 @ SV1021 @ SV1526 @ SV1965 ) @ SV2286 )
!= ( c_Option_Ooption_ONone @ SV1965 ) )
| ( ( hAPP @ SV407 @ SV2286 )
= ( c_Option_Ooption_ONone @ SV1965 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4881]) ).
thf(5428,plain,
! [SV2287: $i,SV1966: $i,SV1527: $i,SV1022: $i,SV408: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ SV408 @ SV1022 @ SV1527 @ SV1966 ) @ SV2287 )
!= ( c_Option_Ooption_ONone @ SV1966 ) )
| ( ( hAPP @ SV1022 @ SV2287 )
= ( c_Option_Ooption_ONone @ SV1966 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4882]) ).
thf(5429,plain,
! [SV1528: $i,SV1023: $i,SV409: $i] :
( ( ( ( c_Set_Oinsert @ SV409 @ SV1023 @ SV1528 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1528 @ tc_bool ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1528 ) @ SV409 ) @ SV1023 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4883]) ).
thf(5430,plain,
! [SV1529: $i,SV2288: $i,SV1024: $i,SV410: $i] :
( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ SV1024 @ SV2288 @ ( tc_Hoare__Mirabelle_Otriple @ SV1529 ) ) @ SV1529 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ SV1024 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1529 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1529 ) ) @ SV1529 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4884]) ).
thf(5431,plain,
! [SV1967: $i,SV1530: $i,SV1025: $i,SV411: $i] :
( ( ( c_Com_Ocom_OLocal @ SV411 @ SV1025 @ SV1530 )
= ( c_Com_Ocom_OBODY @ SV1967 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4885]) ).
thf(5432,plain,
! [SV1968: $i,SV1531: $i,SV1026: $i,SV412: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV412 @ SV1026 @ SV1531 ) @ SV1968 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1026 @ SV1968 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4886]) ).
thf(5433,plain,
! [SV1969: $i,SV1532: $i,SV1027: $i,SV413: $i] :
( ( ( ! [SY6966: $i] :
( ( c_Set_Oinsert @ ( hAPP @ SV413 @ SV1027 ) @ ( c_Set_Oimage @ SV413 @ SV1532 @ SV1969 @ SY6966 ) @ SY6966 )
= ( c_Set_Oimage @ SV413 @ SV1532 @ SV1969 @ SY6966 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1969 ) @ SV1027 ) @ SV1532 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4887]) ).
thf(5434,plain,
! [SV1970: $i,SV1533: $i,SV1028: $i,SV414: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV414 @ ( c_Set_Oinsert @ SV1028 @ SV1533 @ SV1970 ) @ ( tc_fun @ SV1970 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV414 @ SV1533 @ ( tc_fun @ SV1970 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1970 ) @ SV1028 ) @ SV414 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4888]) ).
thf(5435,plain,
! [SV1971: $i,SV1534: $i,SV1029: $i,SV415: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV415 @ SV1029 @ SV1534 ) @ SV1971 @ ( tc_fun @ SV1534 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV1029 @ SV1971 @ ( tc_fun @ SV1534 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1534 ) @ SV415 ) @ SV1971 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4889]) ).
thf(5436,plain,
! [SV2289: $i,SV1972: $i,SV1535: $i,SV1030: $i,SV416: $i] :
( ( ( c_Com_Ocom_OLocal @ SV416 @ SV1030 @ SV1535 )
!= ( c_Com_Ocom_OSemi @ SV1972 @ SV2289 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4890]) ).
thf(5437,plain,
! [SV2290: $i,SV1536: $i,SV1032: $i,SV418: $i] :
( ( ( ( c_Com_Ocom_OWhile @ SV418 @ SV1032 )
!= ( c_Com_Ocom_OWhile @ SV1536 @ SV2290 ) )
= $true )
| ( ( SV418 = SV1536 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4892]) ).
thf(5438,plain,
! [SV1973: $i,SV1537: $i,SV1033: $i,SV419: $i] :
( ( ( ( c_Com_Ocom_OWhile @ SV419 @ SV1033 )
!= ( c_Com_Ocom_OWhile @ SV1537 @ SV1973 ) )
= $true )
| ( ( SV1033 = SV1973 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4893]) ).
thf(5439,plain,
! [SV2291: $i,SV1974: $i,SV1541: $i,SV1037: $i,SV423: $i] :
( ( ( c_Com_Ocom_OWhile @ SV423 @ SV1037 )
!= ( c_Com_Ocom_OCond @ SV1541 @ SV1974 @ SV2291 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4895]) ).
thf(5440,plain,
! [SV2292: $i,SV1542: $i,SV1038: $i,SV425: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV425 ) @ SV1038 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1542 @ ( c_Collect @ SV2292 @ SV425 ) @ ( tc_fun @ SV425 @ tc_bool ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV425 ) @ SV1038 ) @ SV1542 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4897]) ).
thf(5441,plain,
! [SV1543: $i,SV1039: $i,SV426: $i] :
( ( ( ( hAPP @ SV426 @ SV1039 )
= ( c_Option_Ooption_ONone @ SV1543 ) )
= $false )
| ( ( ! [SY6438: $i] :
( ( ( hAPP @ SY6438 @ SV1039 )
!= ( c_Option_Ooption_ONone @ SV1543 ) )
| ! [SY6439: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SV426 @ SY6438 @ SY6439 @ SV1543 ) @ SV1039 )
= ( c_Option_Ooption_ONone @ SV1543 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4898]) ).
thf(5442,plain,
! [SV1976: $i,SV1544: $i,SV1040: $i,SV427: $i] :
( ( ( ( hAPP @ SV427 @ SV1040 )
!= ( c_Option_Ooption_OSome @ SV1544 @ SV1976 ) )
= $true )
| ( ( ! [SY6969: $i,SY6970: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SY6969 @ SV427 @ SY6970 @ SV1976 ) @ SV1040 )
= ( c_Option_Ooption_OSome @ SV1544 @ SV1976 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4899]) ).
thf(5443,plain,
! [SV1977: $i,SV1545: $i,SV1041: $i,SV428: $i] :
( ( ( ( hAPP @ SV428 @ SV1041 )
!= ( c_Option_Ooption_OSome @ SV1545 @ SV1977 ) )
= $true )
| ( ( ! [SY6971: $i,SY6972: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SY6971 @ SV428 @ SY6972 @ SV1977 ) @ SV1041 )
= ( c_Option_Ooption_OSome @ SV1545 @ SV1977 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4900]) ).
thf(5444,plain,
! [SV2293: $i,SV1978: $i,SV1546: $i,SV1042: $i,SV429: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV429 ) @ ( hAPP @ SV1042 @ SV1546 ) ) @ ( c_Set_Oimage @ SV1042 @ ( c_HOL_Ominus__class_Ominus @ SV1978 @ ( c_Set_Oinsert @ SV1546 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2293 @ tc_bool ) ) @ SV2293 ) @ ( tc_fun @ SV2293 @ tc_bool ) ) @ SV2293 @ SV429 ) ) )
| ~ ( c_Fun_Oinj__on @ SV1042 @ ( c_Set_Oinsert @ SV1546 @ SV1978 @ SV2293 ) @ SV2293 @ SV429 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4901]) ).
thf(5445,plain,
! [SV2294: $i,SV1979: $i,SV1547: $i,SV1043: $i,SV430: $i] :
( ( ( c_Com_Ocom_OCond @ SV430 @ SV1043 @ SV1547 )
!= ( c_Com_Ocom_OAss @ SV1979 @ SV2294 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4902]) ).
thf(5446,plain,
! [SV1980: $i,SV1548: $i,SV1044: $i,SV432: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV432 @ SV1044 @ SV1548 ) @ SV1980 @ ( tc_fun @ SV1548 @ tc_bool ) )
= ( c_Set_Oinsert @ SV432 @ ( c_HOL_Ominus__class_Ominus @ SV1044 @ SV1980 @ ( tc_fun @ SV1548 @ tc_bool ) ) @ SV1548 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1548 ) @ SV432 ) @ SV1980 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4903]) ).
thf(5447,plain,
! [SV1045: $i,SV2295: $i,SV433: $i,SV1981: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1981 @ SV433 @ ( tc_fun @ SV2295 @ tc_bool ) ) @ SV1045 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV433 @ SV1045 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4904]) ).
thf(5448,plain,
! [SV1046: $i,SV2296: $i,SV1982: $i,SV434: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV434 @ SV1982 @ ( tc_fun @ SV2296 @ tc_bool ) ) @ SV1046 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV434 @ SV1046 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4905]) ).
thf(5449,plain,
! [SV2297: $i,SV1984: $i,SV1551: $i,SV1049: $i,SV437: $i] :
( ( ( c_Set_Ovimage @ SV437 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1049 @ SV1551 @ ( tc_fun @ SV1984 @ tc_bool ) ) @ SV2297 @ SV1984 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Ovimage @ SV437 @ SV1049 @ SV2297 @ SV1984 ) @ ( c_Set_Ovimage @ SV437 @ SV1551 @ SV2297 @ SV1984 ) @ ( tc_fun @ SV2297 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4908]) ).
thf(5450,plain,
! [SV439: $i,SV1552: $i,SV1051: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1051 @ SV1552 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV439 @ SV1051 @ ( tc_fun @ SV1552 @ tc_bool ) ) @ SV1552 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4910]) ).
thf(5451,plain,
! [SV1052: $i,SV1553: $i,SV440: $i] :
( ( ( c_Finite__Set_Ofinite @ SV440 @ SV1553 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV440 @ SV1052 @ ( tc_fun @ SV1553 @ tc_bool ) ) @ SV1553 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4911]) ).
thf(5452,plain,
! [SV2298: $i,SV1985: $i,SV1554: $i,SV1053: $i,SV441: $i] :
( ( ( c_Map_Omap__le @ ( c_Map_Omap__add @ SV441 @ SV1053 @ SV1554 @ SV1985 ) @ SV2298 @ SV1554 @ SV1985 )
| ~ ( c_Map_Omap__le @ SV441 @ ( c_Map_Omap__add @ SV441 @ SV1053 @ SV1554 @ SV1985 ) @ SV1554 @ SV1985 )
| ~ ( c_Map_Omap__le @ SV1053 @ SV2298 @ SV1554 @ SV1985 )
| ~ ( c_Map_Omap__le @ SV441 @ SV2298 @ SV1554 @ SV1985 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4912]) ).
thf(5453,plain,
! [SV442: $i,SV1054: $i,SV1555: $i] :
( ( ( ! [SY6456: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1555 ) @ SY6456 ) @ SV1054 ) ) )
= $true )
| ( ( ! [SY6457: $i] :
( ~ ( hBOOL @ ( hAPP @ SV442 @ SY6457 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1555 ) @ SY6457 ) @ SV1054 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV442 @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1054 @ SV442 @ SV1555 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4913]) ).
thf(5454,plain,
! [SV1986: $i,SV1556: $i,SV1055: $i,SV443: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ SV1055 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1556 @ SV1986 @ ( tc_fun @ SV443 @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ SV1055 ) @ SV1986 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ SV1055 ) @ SV1556 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4914]) ).
thf(5455,plain,
! [SV1987: $i,SV1557: $i,SV1056: $i,SV444: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ SV1056 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1557 @ SV1987 @ ( tc_fun @ SV444 @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ SV1056 ) @ SV1987 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ SV1056 ) @ SV1557 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4915]) ).
thf(5456,plain,
! [SV445: $i,SV2299: $i,SV1057: $i,SV1558: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1558 ) @ SV1057 ) @ SV2299 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1558 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2299 @ SV445 @ SV1558 ) ) @ SV2299 ) )
| ! [SY7232: $i] :
~ ( hBOOL @ ( hAPP @ SY7232 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2299 @ SY7232 @ SV1558 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV445 @ SV1057 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4916]) ).
thf(5457,plain,
! [SV446: $i,SV2300: $i,SV1058: $i,SV1559: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1559 ) @ SV1058 ) @ SV2300 ) )
| ! [SY7233: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1559 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2300 @ SY7233 @ SV1559 ) ) @ SV2300 ) )
| ~ ( hBOOL @ ( hAPP @ SV446 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2300 @ SV446 @ SV1559 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV446 @ SV1058 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4917]) ).
thf(5458,plain,
! [SV447: $i,SV2301: $i,SV1059: $i,SV1560: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1560 ) @ SV1059 ) @ SV2301 ) )
| ~ ( hBOOL @ ( hAPP @ SV447 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2301 @ SV447 @ SV1560 ) ) )
| ! [SY7234: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1560 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2301 @ SY7234 @ SV1560 ) ) @ SV2301 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV447 @ SV1059 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4918]) ).
thf(5459,plain,
! [SV448: $i,SV2302: $i,SV1060: $i,SV1561: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1561 ) @ SV1060 ) @ SV2302 ) )
| ! [SY7235: $i] :
~ ( hBOOL @ ( hAPP @ SY7235 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2302 @ SY7235 @ SV1561 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1561 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2302 @ SV448 @ SV1561 ) ) @ SV2302 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV448 @ SV1060 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4919]) ).
thf(5460,plain,
! [SV2303: $i,SV1988: $i,SV1562: $i,SV1061: $i,SV449: $i] :
( ( ! [SY7236: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV449 ) @ SV1061 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV1562 @ SV1988 @ SV2303 @ SY7236 @ SV449 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1988 @ SV1061 ) @ SY7236 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1562 @ SV2303 ) @ SV1061 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4920]) ).
thf(5461,plain,
! [SV1989: $i,SV1563: $i,SV1062: $i,SV450: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV450 ) @ SV1062 ) @ ( c_Set_Oinsert @ SV1563 @ SV1989 @ SV450 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV450 ) @ SV1062 ) @ SV1989 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4921]) ).
thf(5462,plain,
! [SV1990: $i,SV1564: $i,SV1063: $i,SV451: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV451 ) @ SV1063 ) @ ( c_Set_Oinsert @ SV1564 @ SV1990 @ SV451 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV451 ) @ SV1063 ) @ SV1990 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4922]) ).
thf(5463,plain,
! [SV2304: $i,SV1991: $i,SV1565: $i,SV1064: $i,SV452: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV452 ) @ SV1064 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV1565 @ SV1991 @ SV2304 @ SV452 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1565 @ SV1064 ) @ SV2304 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1565 @ SV1991 ) @ SV1064 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4923]) ).
thf(5464,plain,
! [SV1566: $i,SV1065: $i,SV2305: $i,SV453: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV453 ) @ SV2305 ) @ SV1065 ) )
| ~ ( hBOOL @ ( hAPP @ SV1566 @ SV2305 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV453 ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1065 @ SV1566 @ SV453 ) ) @ SV1065 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4924]) ).
thf(5465,plain,
! [SV455: $i,SV1067: $i,SV1992: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1992 ) @ SV1067 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1992 @ tc_bool ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV455 @ SV1067 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4925]) ).
thf(5466,plain,
! [SV2306: $i,SV1993: $i,SV1567: $i,SV1070: $i,SV458: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV458 ) @ SV1070 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV1567 @ SV1993 @ SV2306 @ SV458 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1567 @ SV1070 ) @ SV2306 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1567 @ SV1993 ) @ SV1070 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4926]) ).
thf(5467,plain,
! [SV1568: $i,SV459: $i,SV2307: $i,SV1071: $i] :
( ( ( ( SV1071 = SV2307 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV459 ) @ SV1071 ) @ ( c_Set_Oinsert @ SV2307 @ SV1568 @ SV459 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV459 ) @ SV1071 ) @ SV1568 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4927]) ).
thf(5468,plain,
! [SV2308: $i,SV1994: $i,SV1569: $i,SV1072: $i,SV460: $i] :
( ( ! [SY7237: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV460 ) @ SV1072 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV1569 @ SV1994 @ SV2308 @ SY7237 @ SV460 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1569 @ SV1072 ) @ SY7237 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1994 @ SV2308 ) @ SV1072 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4928]) ).
thf(5469,plain,
! [SV1570: $i,SV1073: $i,SV461: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV461 ) @ SV1073 ) @ SV1570 ) )
= $false )
| ( ( ! [SY6482: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV461 ) @ SV1073 ) @ ( c_HOL_Ominus__class_Ominus @ SY6482 @ SV1570 @ ( tc_fun @ SV461 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4929]) ).
thf(5470,plain,
! [SV2309: $i,SV1571: $i,SV1074: $i,SV462: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV462 ) @ SV1074 ) @ ( c_HOL_Ominus__class_Ominus @ SV1571 @ SV2309 @ ( tc_fun @ SV462 @ tc_bool ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV462 ) @ SV1074 ) @ SV1571 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4930]) ).
thf(5471,plain,
! [SV1572: $i,SV1075: $i,SV463: $i] :
( ( ( ! [SY5611: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ SY5611 ) @ SV1075 ) ) )
= $true )
| ( ( ! [SY6485: $i] :
( ~ ( hBOOL @ ( hAPP @ SV1572 @ SY6485 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ SY6485 ) @ SV1075 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1075 @ SV1572 @ SV463 ) ) @ SV1075 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4931]) ).
thf(5472,plain,
! [SV464: $i,SV1076: $i,SV2310: $i,SV1573: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1573 ) @ SV2310 ) @ SV1076 ) )
| ~ ( hBOOL @ ( hAPP @ SV464 @ SV2310 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV464 @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ SV1076 @ SV464 @ SV1573 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4932]) ).
thf(5473,plain,
! [SV1995: $i,SV1574: $i,SV1077: $i,SV465: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV465 @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1077 @ SV1574 @ SV1995 @ ( tc_fun @ SV465 @ tc_bool ) ) )
= $true )
| ( ( ! [SY6985: $i] :
( ( ( hAPP @ SV1574 @ SY6985 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV465 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1995 ) @ SY6985 ) @ SV1077 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4933]) ).
thf(5474,plain,
! [SV2311: $i,SV1996: $i,SV1575: $i,SV1079: $i,SV467: $i] :
( ( ( c_Com_Ocom_OAss @ SV467 @ SV1079 )
!= ( c_Com_Ocom_OCond @ SV1575 @ SV1996 @ SV2311 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4934]) ).
thf(5475,plain,
! [SV1997: $i,SV1576: $i,SV1082: $i,SV470: $i] :
( ( ( ( c_Map_Omap__add @ SV470 @ SV1082 @ SV1576 @ SV1997 )
= ( c_Map_Omap__add @ SV1082 @ SV470 @ SV1576 @ SV1997 ) )
= $true )
| ( ( ~ ( c_Map_Omap__le @ SV470 @ ( c_Map_Omap__add @ SV470 @ SV1082 @ SV1576 @ SV1997 ) @ SV1576 @ SV1997 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4935]) ).
thf(5476,plain,
! [SV1998: $i,SV1577: $i,SV1083: $i,SV471: $i] :
( ( ( ( c_Map_Omap__add @ SV471 @ SV1083 @ SV1577 @ SV1998 )
!= ( c_Map_Omap__add @ SV1083 @ SV471 @ SV1577 @ SV1998 ) )
= $true )
| ( ( c_Map_Omap__le @ SV471 @ ( c_Map_Omap__add @ SV471 @ SV1083 @ SV1577 @ SV1998 ) @ SV1577 @ SV1998 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4936]) ).
thf(5477,plain,
! [SV475: $i,SV1087: $i,SV2312: $i,SV1580: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1580 ) @ SV2312 ) @ SV1087 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV475 @ ( c_Set_Oinsert @ SV2312 @ SV1087 @ SV1580 ) @ ( tc_fun @ SV1580 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV475 @ SV1087 @ ( tc_fun @ SV1580 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4939]) ).
thf(5478,plain,
! [SV2001: $i,SV1581: $i,SV1088: $i,SV476: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV476 @ ( c_Set_Oinsert @ SV1088 @ SV1581 @ SV2001 ) @ ( tc_fun @ SV2001 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2001 ) @ SV1088 ) @ SV1581 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV476 @ SV1581 @ ( tc_fun @ SV2001 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4940]) ).
thf(5479,plain,
! [SV1583: $i,SV1090: $i,SV478: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV478 ) @ SV1090 ) @ SV1583 ) )
= $false )
| ( ( ! [SY6497: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV478 ) @ SV1090 ) @ SY6497 ) )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SY6497 @ SV1583 @ ( tc_fun @ SV478 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV478 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4942]) ).
thf(5480,plain,
! [SV481: $i,SV2003: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2003 @ SV2003 @ SV481 )
= $false )
| ( ( class_Orderings_Oorder @ SV481 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4944]) ).
thf(5481,plain,
! [SV482: $i,SV2004: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2004 @ SV2004 @ SV482 )
= $false )
| ( ( class_Orderings_Olinorder @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4945]) ).
thf(5482,plain,
! [SV483: $i,SV2005: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2005 @ SV2005 @ SV483 )
= $false )
| ( ( class_Orderings_Opreorder @ SV483 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4946]) ).
thf(5483,plain,
! [SV1585: $i,SV2313: $i,SV484: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV484 @ SV2313 ) ) )
= $true )
| ( ( ( c_Collect @ SV484 @ SV1585 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1585 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4947]) ).
thf(5484,plain,
! [SV2006: $i,SV1586: $i,SV1093: $i,SV486: $i] :
( ( ( c_Com_Ocom_OSemi @ SV486 @ SV1093 )
= ( c_Com_Ocom_OAss @ SV1586 @ SV2006 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4948]) ).
thf(5485,plain,
! [SV487: $i,SV2314: $i,SV2007: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV2007 @ SV2314 @ SV487 )
| ( SV2314 = SV2007 )
| ( c_HOL_Oord__class_Oless @ SV2314 @ SV2007 @ SV487 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV487 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4949]) ).
thf(5486,plain,
! [SV488: $i,SV2315: $i,SV2008: $i] :
( ( ( ( SV2008 = SV2315 )
| ( c_HOL_Oord__class_Oless @ SV2315 @ SV2008 @ SV488 )
| ( c_HOL_Oord__class_Oless @ SV2008 @ SV2315 @ SV488 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV488 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4950]) ).
thf(5487,plain,
! [SV1094: $i,SV489: $i,SV2316: $i,SV2009: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV2009 ) @ SV2316 ) @ SV489 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV2009 ) @ SV2316 ) @ SV1094 ) ) )
= $true )
| ( ( SV489 = SV1094 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4951]) ).
thf(5488,plain,
! [SV2317: $i,SV2010: $i,SV490: $i,SV1095: $i] :
( ( ( ~ ( c_Map_Omap__le @ SV1095 @ SV490 @ SV2010 @ SV2317 )
| ~ ( c_Map_Omap__le @ SV490 @ SV1095 @ SV2010 @ SV2317 ) )
= $true )
| ( ( SV490 = SV1095 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4952]) ).
thf(5489,plain,
! [SV491: $i,SV2318: $i,SV2011: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV2011 @ SV2318 @ SV491 )
| ( SV2318 = SV2011 )
| ( c_HOL_Oord__class_Oless @ SV2318 @ SV2011 @ SV491 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV491 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4953]) ).
thf(5490,plain,
! [SV492: $i,SV2319: $i,SV2012: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV2012 @ SV2319 @ SV492 )
| ( SV2319 = SV2012 )
| ( c_HOL_Oord__class_Oless @ SV2319 @ SV2012 @ SV492 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV492 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4954]) ).
thf(5491,plain,
! [SV493: $i,SV2320: $i,SV2013: $i] :
( ( ( ( SV2013 = SV2320 )
| ( c_HOL_Oord__class_Oless @ SV2013 @ SV2320 @ SV493 )
| ( c_HOL_Oord__class_Oless @ SV2320 @ SV2013 @ SV493 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV493 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4955]) ).
thf(5492,plain,
! [SV495: $i,SV2321: $i,SV1097: $i] :
( ( ( ! [SY7238: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1097 @ SV2321 @ SV495 ) @ SY7238 @ SV495 )
| ~ ( c_HOL_Oord__class_Oless @ SV2321 @ SY7238 @ SV495 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV495 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4957]) ).
thf(5493,plain,
! [SV496: $i,SV2322: $i,SV1098: $i] :
( ( ( ! [SY7239: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1098 @ SV2322 @ SV496 ) @ SY7239 @ SV496 )
| ~ ( c_HOL_Oord__class_Oless @ SV1098 @ SY7239 @ SV496 ) ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV496 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4958]) ).
thf(5494,plain,
! [SV2323: $i,SV1588: $i,SV1099: $i,SV497: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV497 @ SV1099 @ SV1588 @ SV2323 ) @ SV2323 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1099 @ SV1588 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4959]) ).
thf(5495,plain,
! [SV2014: $i,SV1589: $i,SV1100: $i,SV498: $i] :
( ( ( ( hAPP @ SV498 @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ SV498 @ SV1100 @ SV1589 @ SV2014 ) )
!= ( hAPP @ SV1100 @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ SV498 @ SV1100 @ SV1589 @ SV2014 ) ) )
= $true )
| ( ( c_Map_Omap__le @ SV498 @ SV1100 @ SV1589 @ SV2014 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4960]) ).
thf(5496,plain,
! [SV2324: $i,SV2015: $i,SV1590: $i,SV1101: $i,SV499: $i] :
( ( ( ( c_Set_Oinsert @ SV499 @ ( c_Set_Oinsert @ SV1101 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1590 @ tc_bool ) ) @ SV1590 ) @ SV1590 )
!= ( c_Set_Oinsert @ SV2015 @ ( c_Set_Oinsert @ SV2324 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1590 @ tc_bool ) ) @ SV1590 ) @ SV1590 ) )
| ( SV499 = SV2324 )
| ( SV499 = SV2015 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4961]) ).
thf(5497,plain,
! [SV2016: $i,SV1591: $i,SV1102: $i,SV500: $i] :
( ( ( ! [SY6995: $i] :
( ( c_Set_Oinsert @ SV500 @ ( c_Set_Oinsert @ SV1102 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1591 @ tc_bool ) ) @ SV1591 ) @ SV1591 )
!= ( c_Set_Oinsert @ SV2016 @ ( c_Set_Oinsert @ SY6995 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1591 @ tc_bool ) ) @ SV1591 ) @ SV1591 ) ) )
= $true )
| ( ( ( SV1102 = SV2016 )
| ( SV500 = SV2016 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4962]) ).
thf(5498,plain,
! [SV2325: $i,SV2017: $i,SV1592: $i,SV1103: $i,SV501: $i] :
( ( ( ( c_Set_Oinsert @ SV501 @ ( c_Set_Oinsert @ SV1103 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1592 @ tc_bool ) ) @ SV1592 ) @ SV1592 )
!= ( c_Set_Oinsert @ SV2017 @ ( c_Set_Oinsert @ SV2325 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1592 @ tc_bool ) ) @ SV1592 ) @ SV1592 ) )
| ( SV501 = SV2325 )
| ( SV1103 = SV2325 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4963]) ).
thf(5499,plain,
! [SV2326: $i,SV2018: $i,SV1593: $i,SV1104: $i,SV502: $i] :
( ( ( ( c_Set_Oinsert @ SV502 @ ( c_Set_Oinsert @ SV1104 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1593 @ tc_bool ) ) @ SV1593 ) @ SV1593 )
!= ( c_Set_Oinsert @ SV2018 @ ( c_Set_Oinsert @ SV2326 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1593 @ tc_bool ) ) @ SV1593 ) @ SV1593 ) )
| ( SV1104 = SV2018 )
| ( SV1104 = SV2326 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4964]) ).
thf(5500,plain,
! [SV1594: $i,SV503: $i,SV1105: $i,SV2327: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV2327 @ SV1105 ) )
| ! [SY7240: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV2327 @ SY7240 @ SV503 ) ) @ SV1105 ) @ SV1594 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV503 ) @ SV1105 ) @ SV1594 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4965]) ).
thf(5501,plain,
! [SV2328: $i,SV2019: $i,SV1595: $i,SV1106: $i,SV504: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV504 @ SV1106 @ SV1595 ) ) @ SV2019 ) @ SV2328 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1595 ) @ SV2019 ) @ SV2328 ) )
| ( hBOOL @ ( hAPP @ SV504 @ SV2019 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4966]) ).
thf(5502,plain,
! [SV2329: $i,SV2020: $i,SV1596: $i,SV1108: $i,SV506: $i] :
( ( ! [SY7241: $i,SY7242: $i,SY7243: $i,SY7244: $i] :
( ( ( hAPP @ SV506 @ ( c_Set_Oinsert @ SV1108 @ SV1596 @ SV2020 ) )
= ( hAPP @ ( hAPP @ SV2329 @ SV1108 ) @ ( hAPP @ SV506 @ SV1596 ) ) )
| ! [SY7245: $i,SY7246: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY7241 @ SV506 @ SY7242 @ SY7243 @ SY7244 @ SV2329 @ SY7245 @ SY7246 @ SV2020 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4967]) ).
thf(5503,plain,
! [SV2330: $i,SV2021: $i,SV1597: $i,SV1109: $i,SV507: $i] :
( ( ! [SY7247: $i,SY7248: $i,SY7249: $i,SY7250: $i] :
( ( ( hAPP @ SV507 @ ( c_Set_Oinsert @ SV1109 @ SV1597 @ SV2021 ) )
= ( hAPP @ ( hAPP @ SV2330 @ SV1109 ) @ ( hAPP @ SV507 @ SV1597 ) ) )
| ! [SY7251: $i,SY7252: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV507 @ SY7247 @ SY7248 @ SY7249 @ SV2330 @ SY7250 @ SY7251 @ SY7252 @ SV2021 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4968]) ).
thf(5504,plain,
! [SV2022: $i,SV1598: $i,SV1110: $i,SV508: $i] :
( ( ( c_Com_Ocom_OWhile @ SV508 @ SV1110 )
= ( c_Com_Ocom_OAss @ SV1598 @ SV2022 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4969]) ).
thf(5505,plain,
! [SV2331: $i,SV2023: $i,SV1599: $i,SV1111: $i,SV509: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SV1111 @ SV1599 @ SV2023 @ SV2331 @ SV509 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1111 @ SV1599 @ SV2331 @ ( tc_fun @ SV509 @ tc_bool ) ) ) )
| ! [SY7253: $i] :
( ~ ( hBOOL @ ( hAPP @ SV2023 @ SY7253 ) )
| ! [SY7254: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ SY7253 ) @ ( hAPP @ SV1599 @ SY7254 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2331 ) @ SY7254 ) @ SV1111 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4970]) ).
thf(5506,plain,
! [SV1113: $i,SV1601: $i,SV2332: $i,SV511: $i] :
( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV511 @ SV2332 @ SV1601 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV2332 @ SV1113 @ SV1601 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV511 @ SV1113 @ SV1601 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4972]) ).
thf(5507,plain,
! [SV2024: $i,SV1602: $i,SV1114: $i,SV512: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV512 @ SV1114 @ SV1602 ) @ SV2024 @ ( tc_fun @ SV1602 @ tc_bool ) )
= ( c_Set_Oinsert @ SV512 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1114 @ SV2024 @ ( tc_fun @ SV1602 @ tc_bool ) ) @ SV1602 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1602 ) @ SV512 ) @ SV2024 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4973]) ).
thf(5508,plain,
! [SV2025: $i,SV1603: $i,SV1115: $i,SV513: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV513 @ ( c_Set_Oinsert @ SV1115 @ SV1603 @ SV2025 ) @ ( tc_fun @ SV2025 @ tc_bool ) )
= ( c_Set_Oinsert @ SV1115 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV513 @ SV1603 @ ( tc_fun @ SV2025 @ tc_bool ) ) @ SV2025 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2025 ) @ SV1115 ) @ SV513 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4974]) ).
thf(5509,plain,
! [SV2333: $i,SV2026: $i,SV1604: $i,SV1116: $i,SV514: $i] :
( ( ( c_Set_Oimage @ SV514 @ ( c_Set_Oinsert @ SV1116 @ SV1604 @ SV2026 ) @ SV2026 @ SV2333 )
= ( c_Set_Oinsert @ ( hAPP @ SV514 @ SV1116 ) @ ( c_Set_Oimage @ SV514 @ SV1604 @ SV2026 @ SV2333 ) @ SV2333 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4975]) ).
thf(5510,plain,
! [SV2334: $i,SV2027: $i,SV1605: $i,SV1117: $i,SV515: $i] :
( ( ! [SY7255: $i] :
( ( ( hAPP @ ( c_Map_Omap__add @ SV515 @ SV1117 @ SV1605 @ SV2027 ) @ SV2334 )
!= ( c_Option_Ooption_OSome @ SY7255 @ SV2027 ) )
| ( ( hAPP @ SV1117 @ SV2334 )
= ( c_Option_Ooption_ONone @ SV2027 ) )
| ( ( hAPP @ SV1117 @ SV2334 )
= ( c_Option_Ooption_OSome @ SY7255 @ SV2027 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4976]) ).
thf(5511,plain,
! [SV1606: $i,SV516: $i,SV1118: $i,SV2335: $i] :
( ( ( ! [SY7256: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2335 ) @ SV1118 ) @ ( c_Set_Ovimage @ SV516 @ ( c_Set_Oinsert @ SV1606 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY7256 @ tc_bool ) ) @ SY7256 ) @ SV2335 @ SY7256 ) ) ) )
= $true )
| ( ( ( hAPP @ SV516 @ SV1118 )
= SV1606 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4977]) ).
thf(5512,plain,
! [SV2028: $i,SV1607: $i,SV1119: $i,SV517: $i] :
( ( ( ( c_Com_Ocom_OAss @ SV517 @ SV1119 )
!= ( c_Com_Ocom_OAss @ SV1607 @ SV2028 ) )
= $true )
| ( ( SV1119 = SV2028 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4978]) ).
thf(5513,plain,
! [SV2336: $i,SV1608: $i,SV1120: $i,SV518: $i] :
( ( ( ( c_Com_Ocom_OAss @ SV518 @ SV1120 )
!= ( c_Com_Ocom_OAss @ SV1608 @ SV2336 ) )
= $true )
| ( ( SV518 = SV1608 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4979]) ).
thf(5514,plain,
! [SV521: $i,SV2337: $i,SV1123: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1123 @ SV2337 ) ) )
= $true )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV521 @ tc_bool ) )
= ( c_Collect @ SV1123 @ SV521 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4981]) ).
thf(5515,plain,
! [SV523: $i,SV2338: $i,SV2030: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV2030 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2030 @ SV2338 @ SV523 ) @ SV523 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV2030 @ SV2338 @ SV523 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV523 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4982]) ).
thf(5516,plain,
! [SV524: $i,SV2339: $i,SV2031: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV2031 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2031 @ SV2339 @ SV524 ) @ SV524 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV2031 @ SV2339 @ SV524 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV524 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4983]) ).
thf(5517,plain,
! [SV2340: $i,SV2032: $i,SV1612: $i,SV1126: $i,SV526: $i] :
( ( ! [SY7257: $i] :
( ( ( c_Com_Ocom_OLocal @ SV526 @ SV1126 @ SV1612 )
!= ( c_Com_Ocom_OLocal @ SV2032 @ SV2340 @ SY7257 ) )
| ( SV1612 = SY7257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4984]) ).
thf(5518,plain,
! [SV2341: $i,SV2033: $i,SV1613: $i,SV1127: $i,SV527: $i] :
( ( ! [SY7258: $i] :
( ( c_Com_Ocom_OLocal @ SV527 @ SV1127 @ SV1613 )
!= ( c_Com_Ocom_OLocal @ SV2033 @ SV2341 @ SY7258 ) )
| ( SV1127 = SV2341 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4985]) ).
thf(5519,plain,
! [SV2034: $i,SV1614: $i,SV1128: $i,SV528: $i] :
( ( ( ! [SY7025: $i,SY7026: $i] :
( ( c_Com_Ocom_OLocal @ SV528 @ SV1128 @ SV1614 )
!= ( c_Com_Ocom_OLocal @ SV2034 @ SY7025 @ SY7026 ) ) )
= $true )
| ( ( SV528 = SV2034 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4986]) ).
thf(5520,plain,
! [SV1615: $i,SV1129: $i,SV2342: $i,SV529: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV529 @ ( c_Set_Oinsert @ SV2342 @ SV1129 @ SV1615 ) @ ( tc_fun @ SV1615 @ tc_bool ) ) @ SV1615 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV529 @ SV1129 @ ( tc_fun @ SV1615 @ tc_bool ) ) @ SV1615 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4987]) ).
thf(5521,plain,
! [SV2035: $i,SV1616: $i,SV1130: $i,SV530: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV530 @ ( c_Set_Oinsert @ SV1130 @ SV1616 @ SV2035 ) @ ( tc_fun @ SV2035 @ tc_bool ) ) @ SV2035 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV530 @ SV1616 @ ( tc_fun @ SV2035 @ tc_bool ) ) @ SV2035 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4988]) ).
thf(5522,plain,
! [SV2036: $i,SV1617: $i,SV1131: $i,SV531: $i] :
( ( ( c_Com_Ocom_OWhile @ SV531 @ SV1131 )
= ( c_Com_Ocom_OSemi @ SV1617 @ SV2036 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4989]) ).
thf(5523,plain,
! [SV2343: $i,SV2037: $i,SV1618: $i,SV1132: $i,SV532: $i] :
( ( ! [SY7259: $i,SY7260: $i] :
( ( ( hAPP @ SV532 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1132 @ tc_bool ) ) )
= SV1618 )
| ! [SY7261: $i,SY7262: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2037 @ SV532 @ SV2343 @ SY7259 @ SY7260 @ SY7261 @ SV1618 @ SY7262 @ SV1132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4990]) ).
thf(5524,plain,
! [SV2344: $i,SV2038: $i,SV1619: $i,SV1133: $i,SV533: $i] :
( ( ! [SY7263: $i,SY7264: $i] :
( ( ( hAPP @ SV533 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1133 @ tc_bool ) ) )
= SV1619 )
| ! [SY7265: $i,SY7266: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV533 @ SV2038 @ SV2344 @ SY7263 @ SY7264 @ SY7265 @ SY7266 @ SV1619 @ SV1133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4991]) ).
thf(5525,plain,
! [SV534: $i,SV1134: $i,SV2039: $i] :
( ( ( SV2039 = SV1134 )
= $true )
| ( ( ! [SY7037: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV534 @ SY7037 ) ) @ SV1134 ) @ SV2039 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV534 @ SV1134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4992]) ).
thf(5526,plain,
! [SV1135: $i,SV535: $i,SV1620: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1620 ) @ SV535 ) @ SV1135 ) )
= $false )
| ( ( ( c_Set_Oinsert @ SV535 @ ( c_HOL_Ominus__class_Ominus @ SV1135 @ ( c_Set_Oinsert @ SV535 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1620 @ tc_bool ) ) @ SV1620 ) @ ( tc_fun @ SV1620 @ tc_bool ) ) @ SV1620 )
= SV1135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4993]) ).
thf(5527,plain,
! [SV2345: $i,SV1621: $i,SV1137: $i,SV538: $i] :
( ( ( ( c_Set_Oimage @ SV538 @ SV1137 @ SV1621 @ SV2345 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2345 @ tc_bool ) ) )
= $true )
| ( ( SV1137
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1621 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4995]) ).
thf(5528,plain,
! [SV2346: $i,SV2042: $i,SV1623: $i,SV1140: $i,SV541: $i] :
( ( ! [SY7267: $i,SY7268: $i,SY7269: $i] :
( ( ( hAPP @ SV541 @ ( c_Set_Oinsert @ SV1140 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1623 @ tc_bool ) ) @ SV1623 ) )
= SV1140 )
| ! [SY7270: $i,SY7271: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2042 @ SV541 @ SV2346 @ SY7267 @ SY7268 @ SY7269 @ SY7270 @ SY7271 @ SV1623 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4997]) ).
thf(5529,plain,
! [SV2347: $i,SV2043: $i,SV1624: $i,SV1141: $i,SV542: $i] :
( ( ! [SY7272: $i,SY7273: $i,SY7274: $i] :
( ( ( hAPP @ SV542 @ ( c_Set_Oinsert @ SV1141 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1624 @ tc_bool ) ) @ SV1624 ) )
= SV1141 )
| ! [SY7275: $i,SY7276: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV542 @ SV2043 @ SV2347 @ SY7272 @ SY7273 @ SY7274 @ SY7275 @ SY7276 @ SV1624 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4998]) ).
thf(5530,plain,
! [SV2044: $i,SV1626: $i,SV1144: $i,SV545: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1144 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1626 @ ( c_Collect @ SV2044 @ SV545 ) @ ( tc_fun @ SV545 @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV2044 @ SV1144 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1144 ) @ SV1626 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5000]) ).
thf(5531,plain,
! [SV1627: $i,SV2348: $i,SV547: $i,SV1145: $i] :
( ( ( ! [SY7277: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV1145 @ SV547 @ SV2348 @ SY7277 ) @ SV1627 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV547 @ ( hAPP @ SV1145 @ SV1627 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5001]) ).
thf(5532,plain,
! [SV2349: $i,SV2045: $i,SV1628: $i,SV1146: $i,SV548: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV548 @ SV1146 @ SV1628 @ SV2045 ) @ SV2349 ) )
| ~ ( hBOOL @ ( hAPP @ SV1146 @ ( hAPP @ SV548 @ SV2349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5002]) ).
thf(5533,plain,
! [SV1629: $i,SV1147: $i,SV2350: $i,SV549: $i] :
( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV549 @ ( c_Set_Oinsert @ SV2350 @ SV1147 @ ( tc_Hoare__Mirabelle_Otriple @ SV1629 ) ) @ SV1629 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV549 @ SV1147 @ SV1629 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5003]) ).
thf(5534,plain,
! [SV2046: $i,SV1630: $i,SV1148: $i,SV550: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV550 @ ( c_Set_Oinsert @ SV1148 @ SV1630 @ ( tc_Hoare__Mirabelle_Otriple @ SV2046 ) ) @ SV2046 )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV550 @ SV1630 @ SV2046 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV550 @ ( c_Set_Oinsert @ SV1148 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2046 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2046 ) ) @ SV2046 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5004]) ).
thf(5535,plain,
! [SV2047: $i,SV1631: $i,SV1149: $i,SV551: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV551 @ SV1149 @ ( tc_fun @ SV1631 @ tc_bool ) ) @ SV2047 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1149 @ SV2047 ) )
| ~ ( hBOOL @ ( hAPP @ SV551 @ SV2047 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5005]) ).
thf(5536,plain,
! [SV1632: $i,SV1150: $i,SV552: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV552 )
= $false )
| ( ( ! [SY6596: $i,SY6597: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV1150 @ SV1632 @ SV552 )
!= ( c_HOL_Ominus__class_Ominus @ SY6596 @ SY6597 @ SV552 ) )
| ( c_HOL_Oord__class_Oless @ SY6596 @ SY6597 @ SV552 )
| ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SV1632 @ SV552 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5006]) ).
thf(5537,plain,
! [SV1633: $i,SV1151: $i,SV553: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV553 )
= $false )
| ( ( ! [SY6598: $i,SY6599: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV1151 @ SV1633 @ SV553 )
!= ( c_HOL_Ominus__class_Ominus @ SY6598 @ SY6599 @ SV553 ) )
| ( c_HOL_Oord__class_Oless @ SV1151 @ SV1633 @ SV553 )
| ~ ( c_HOL_Oord__class_Oless @ SY6598 @ SY6599 @ SV553 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5007]) ).
thf(5538,plain,
! [SV2351: $i,SV1154: $i,SV556: $i,SV2048: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV2048 @ SV556 @ SV1154 @ SV2351 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV2048 @ SV556 @ SV1154 @ SV2351 ) @ SV2351 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV556 @ SV1154 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5008]) ).
thf(5539,plain,
! [SV558: $i,SV1635: $i,SV1156: $i,SV2352: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV2352 ) @ SV1156 ) @ SV1635 ) )
| ! [SY7278: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY7278 @ SV2352 @ SV558 ) ) @ SV1156 ) @ SV1635 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV558 ) @ SV1156 ) @ SV1635 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5009]) ).
thf(5540,plain,
! [SV561: $i,SV2353: $i,SV2049: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2049 @ SV2353 @ SV561 )
| ~ ( c_HOL_Oord__class_Oless @ SV2353 @ SV2049 @ SV561 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV561 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5010]) ).
thf(5541,plain,
! [SV562: $i,SV2354: $i,SV2050: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2050 @ SV2354 @ SV562 )
| ~ ( c_HOL_Oord__class_Oless @ SV2354 @ SV2050 @ SV562 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV562 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5011]) ).
thf(5542,plain,
! [SV563: $i,SV2355: $i,SV2051: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2051 @ SV2355 @ SV563 )
| ~ ( c_HOL_Oord__class_Oless @ SV2355 @ SV2051 @ SV563 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV563 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5012]) ).
thf(5543,plain,
! [SV564: $i,SV2356: $i,SV2052: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2052 @ SV2356 @ SV564 )
| ~ ( c_HOL_Oord__class_Oless @ SV2356 @ SV2052 @ SV564 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV564 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5013]) ).
thf(5544,plain,
! [SV1159: $i,SV1636: $i,SV2357: $i,SV565: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV565 @ SV2357 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1636 ) @ SV2357 ) @ SV1159 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV565 @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ SV1159 @ SV565 @ SV1636 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5014]) ).
thf(5545,plain,
! [SV2053: $i,SV1637: $i,SV1160: $i,SV566: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV566 @ SV1160 ) @ SV1637 ) )
= $true )
| ( ( ! [SY7056: $i,SY7057: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2053 ) @ SV1637 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SY7056 @ SV566 @ SV1160 @ SY7057 @ SV2053 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5015]) ).
thf(5546,plain,
! [SV2054: $i,SV1638: $i,SV1161: $i,SV567: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV567 @ SV1161 ) @ SV1638 ) )
= $true )
| ( ( ! [SY7058: $i,SY7059: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2054 ) @ SV1161 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV567 @ SY7058 @ SY7059 @ SV1638 @ SV2054 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5016]) ).
thf(5547,plain,
! [SV1639: $i,SV2358: $i,SV1162: $i,SV568: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV568 ) @ SV1162 ) @ SV2358 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV2358 @ SV1639 @ ( tc_fun @ SV568 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV568 ) @ SV1162 ) @ SV1639 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5017]) ).
thf(5548,plain,
! [SV572: $i,SV2359: $i,SV1166: $i,SV1643: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1643 ) @ SV1166 ) @ SV2359 ) )
| ~ ( hBOOL @ ( hAPP @ SV572 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2359 @ SV572 @ SV1643 ) ) )
| ! [SY7279: $i] :
~ ( hBOOL @ ( hAPP @ SY7279 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2359 @ SY7279 @ SV1643 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV572 @ SV1166 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5018]) ).
thf(5549,plain,
! [SV573: $i,SV2360: $i,SV1167: $i,SV1644: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1644 ) @ SV1167 ) @ SV2360 ) )
| ! [SY7280: $i] :
~ ( hBOOL @ ( hAPP @ SY7280 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2360 @ SY7280 @ SV1644 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV573 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2360 @ SV573 @ SV1644 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV573 @ SV1167 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5019]) ).
thf(5550,plain,
! [SV574: $i,SV2361: $i,SV1168: $i,SV1645: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1645 ) @ SV1168 ) @ SV2361 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1645 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2361 @ SV574 @ SV1645 ) ) @ SV2361 ) )
| ! [SY7281: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1645 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2361 @ SY7281 @ SV1645 ) ) @ SV2361 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV574 @ SV1168 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5020]) ).
thf(5551,plain,
! [SV575: $i,SV2362: $i,SV1169: $i,SV1646: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1646 ) @ SV1169 ) @ SV2362 ) )
| ! [SY7282: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1646 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2362 @ SY7282 @ SV1646 ) ) @ SV2362 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1646 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2362 @ SV575 @ SV1646 ) ) @ SV2362 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV575 @ SV1169 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5021]) ).
thf(5552,plain,
! [SV576: $i,SV2363: $i,SV1170: $i,SV1647: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1647 ) @ SV1170 ) @ SV2363 ) )
| ! [SY7283: $i] :
( ~ ( hBOOL @ ( hAPP @ SV576 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2363 @ SY7283 @ SV576 @ SV1647 ) ) )
| ~ ( hBOOL @ ( hAPP @ SY7283 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2363 @ SY7283 @ SV576 @ SV1647 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV576 @ SV1170 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5022]) ).
thf(5553,plain,
! [SV577: $i,SV2364: $i,SV1171: $i,SV1648: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1648 ) @ SV1171 ) @ SV2364 ) )
| ! [SY7284: $i] :
( ~ ( hBOOL @ ( hAPP @ SY7284 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2364 @ SV577 @ SY7284 @ SV1648 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV577 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2364 @ SV577 @ SY7284 @ SV1648 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV577 @ SV1171 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5023]) ).
thf(5554,plain,
! [SV1649: $i,SV1172: $i,SV578: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV578 ) @ SV1172 ) @ SV1649 ) )
= $false )
| ( ( ! [SY6622: $i] :
( ( hBOOL @ ( hAPP @ SY6622 @ SV1172 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV578 ) @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ SV1649 @ SY6622 @ SV578 ) ) @ SV1649 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5024]) ).
thf(5555,plain,
! [SV579: $i,SV1173: $i,SV2365: $i,SV1650: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1650 ) @ SV2365 ) @ SV1173 ) )
| ~ ( hBOOL @ ( hAPP @ SV579 @ SV2365 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV579 @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1173 @ SV579 @ SV1650 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5025]) ).
thf(5556,plain,
! [SV1174: $i,SV580: $i,SV1651: $i,SV2366: $i] :
( ( ( ! [SY7285: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2366 ) @ SV1651 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV580 @ SV1174 @ SY7285 @ SV2366 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV580 @ SV1174 ) @ SV1651 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5026]) ).
thf(5557,plain,
! [SV1652: $i,SV581: $i,SV1175: $i,SV2367: $i] :
( ( ( ! [SY7286: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2367 ) @ SV1175 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV581 @ SY7286 @ SV1652 @ SV2367 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV581 @ SV1175 ) @ SV1652 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5027]) ).
thf(5558,plain,
! [SV1653: $i,SV2368: $i,SV1176: $i,SV582: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV582 ) @ SV1176 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2368 @ SV1653 @ ( tc_fun @ SV582 @ tc_bool ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV582 ) @ SV1176 ) @ SV1653 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5028]) ).
thf(5559,plain,
! [SV2369: $i,SV1654: $i,SV1177: $i,SV583: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV583 ) @ SV1177 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1654 @ SV2369 @ ( tc_fun @ SV583 @ tc_bool ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV583 ) @ SV1177 ) @ SV1654 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5029]) ).
thf(5560,plain,
! [SV2055: $i,SV1655: $i,SV1178: $i,SV584: $i] :
( ( ( ( hAPP @ SV584 @ SV1178 )
!= ( hAPP @ SV584 @ SV1655 ) )
= $true )
| ( ( ! [SY7060: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2055 ) @ SV1655 ) @ SY7060 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2055 ) @ SV1178 ) @ SY7060 ) )
| ( SV1178 = SV1655 )
| ! [SY7061: $i] :
~ ( c_Fun_Oinj__on @ SV584 @ SY7060 @ SV2055 @ SY7061 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5030]) ).
thf(5561,plain,
! [SV2056: $i,SV1656: $i,SV1179: $i,SV585: $i] :
( ( ( ( hAPP @ SV585 @ SV1179 )
!= ( hAPP @ SV585 @ SV1656 ) )
= $true )
| ( ( ! [SY7062: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2056 ) @ SV1656 ) @ SY7062 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2056 ) @ SV1179 ) @ SY7062 ) )
| ! [SY7063: $i] :
~ ( c_Fun_Oinj__on @ SV585 @ SY7062 @ SV2056 @ SY7063 )
| ( SV1179 = SV1656 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5031]) ).
thf(5562,plain,
! [SV2057: $i,SV1657: $i,SV1180: $i,SV586: $i] :
( ( ( ( hAPP @ SV586 @ SV1180 )
!= ( hAPP @ SV586 @ SV1657 ) )
= $true )
| ( ( ! [SY7064: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2057 ) @ SV1657 ) @ SY7064 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2057 ) @ SV1180 ) @ SY7064 ) )
| ! [SY7065: $i] :
~ ( c_Fun_Oinj__on @ SV586 @ SY7064 @ SV2057 @ SY7065 )
| ( SV1180 = SV1657 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5032]) ).
thf(5563,plain,
! [SV2058: $i,SV1658: $i,SV1181: $i,SV587: $i] :
( ( ( ( hAPP @ SV587 @ SV1181 )
!= ( hAPP @ SV587 @ SV1658 ) )
= $true )
| ( ( ! [SY7066: $i] :
( ! [SY7067: $i] :
~ ( c_Fun_Oinj__on @ SV587 @ SV2058 @ SY7066 @ SY7067 )
| ( SV1181 = SV1658 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7066 ) @ SV1658 ) @ SV2058 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7066 ) @ SV1181 ) @ SV2058 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5033]) ).
thf(5564,plain,
! [SV588: $i,SV1182: $i,SV2370: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2370 ) @ SV1182 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2370 @ tc_bool ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV588 @ SV1182 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5034]) ).
thf(5565,plain,
! [SV1659: $i,SV1183: $i,SV589: $i] :
( ( ( ( hAPP @ ( c_COMBC @ ( c_in @ SV589 ) @ SV589 @ ( tc_fun @ SV589 @ tc_bool ) @ tc_bool ) @ SV1183 )
= ( hAPP @ ( c_COMBC @ ( c_in @ SV589 ) @ SV589 @ ( tc_fun @ SV589 @ tc_bool ) @ tc_bool ) @ SV1659 ) )
= $false )
| ( ( SV1183 = SV1659 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5035]) ).
thf(5566,plain,
! [SV590: $i,SV1184: $i,SV1660: $i] :
( ( ( hBOOL @ ( hAPP @ SV1660 @ SV1184 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV590 ) @ SV1184 ) @ ( c_Collect @ SV1660 @ SV590 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5036]) ).
thf(5567,plain,
! [SV591: $i,SV1185: $i,SV2059: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2059 ) @ SV1185 ) @ ( c_Collect @ SV591 @ SV2059 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV591 @ SV1185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5037]) ).
thf(5568,plain,
! [SV2060: $i,SV1661: $i,SV1186: $i,SV592: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV592 ) @ SV1186 ) @ ( c_SetInterval_Oord_OatMost @ SV1661 @ SV2060 @ SV592 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1661 @ SV1186 ) @ SV2060 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5038]) ).
thf(5569,plain,
! [SV1662: $i,SV593: $i,SV1187: $i,SV2371: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2371 ) @ SV1187 ) @ ( c_SetInterval_Oord_OatMost @ SV593 @ SV1662 @ SV2371 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV593 @ SV1187 ) @ SV1662 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5039]) ).
thf(5570,plain,
! [SV2061: $i,SV1663: $i,SV1188: $i,SV594: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV594 ) @ SV1188 ) @ ( c_HOL_Ominus__class_Ominus @ SV1663 @ SV2061 @ ( tc_fun @ SV594 @ tc_bool ) ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV594 ) @ SV1188 ) @ SV2061 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV594 ) @ SV1188 ) @ SV1663 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5040]) ).
thf(5571,plain,
! [SV2062: $i,SV1664: $i,SV1189: $i,SV595: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV595 ) @ SV1189 ) @ ( c_HOL_Ominus__class_Ominus @ SV1664 @ SV2062 @ ( tc_fun @ SV595 @ tc_bool ) ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV595 ) @ SV1189 ) @ SV2062 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV595 ) @ SV1189 ) @ SV1664 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5041]) ).
thf(5572,plain,
! [SV596: $i,SV2372: $i,SV1190: $i,SV1665: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1665 ) @ SV1190 ) @ SV2372 ) )
| ! [SY7287: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1665 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2372 @ SY7287 @ SV596 @ SV1665 ) ) @ SV2372 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV596 @ SV1190 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5042]) ).
thf(5573,plain,
! [SV597: $i,SV2373: $i,SV1191: $i,SV1666: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1666 ) @ SV1191 ) @ SV2373 ) )
| ! [SY7288: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1666 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2373 @ SV597 @ SY7288 @ SV1666 ) ) @ SV2373 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV597 @ SV1191 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5043]) ).
thf(5574,plain,
! [SV1667: $i,SV1192: $i,SV598: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV598 ) @ SV1192 ) @ SV1667 ) )
= $false )
| ( ( ! [SY6650: $i] :
( ( hBOOL @ ( hAPP @ SY6650 @ SV1192 ) )
| ~ ( hBOOL @ ( hAPP @ SY6650 @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ SV1667 @ SY6650 @ SV598 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5044]) ).
thf(5575,plain,
! [SV2063: $i,SV1668: $i,SV1193: $i,SV599: $i] :
( ( ( ( c_Set_Oinsert @ SV599 @ SV1193 @ SV1668 )
!= ( c_Set_Oinsert @ SV599 @ SV2063 @ SV1668 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1668 ) @ SV599 ) @ SV2063 ) )
| ( SV1193 = SV2063 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1668 ) @ SV599 ) @ SV1193 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5045]) ).
thf(5576,plain,
! [SV1669: $i,SV1194: $i,SV2374: $i,SV600: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV600 ) @ SV2374 ) @ SV1194 ) )
| ~ ( hBOOL @ ( hAPP @ SV1669 @ SV2374 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV600 ) @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ SV1194 @ SV1669 @ SV600 ) ) @ SV1194 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5046]) ).
thf(5577,plain,
! [SV2375: $i,SV2064: $i,SV1670: $i,SV1195: $i,SV601: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV601 ) @ SV1195 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1670 @ SV2064 @ SV2375 @ ( tc_fun @ SV601 @ tc_bool ) ) ) )
| ! [SY7289: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV601 ) @ SV1195 ) @ ( hAPP @ SV2064 @ SY7289 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2375 ) @ SY7289 ) @ SV1670 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5047]) ).
thf(5578,plain,
! [SV2376: $i,SV2065: $i,SV1671: $i,SV1196: $i,SV602: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV602 ) @ SV1196 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1671 @ SV2065 @ SV2376 @ ( tc_fun @ SV602 @ tc_bool ) ) ) )
| ! [SY7290: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV602 ) @ SV1196 ) @ ( hAPP @ SV2065 @ SY7290 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2376 ) @ SY7290 ) @ SV1671 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5048]) ).
thf(5579,plain,
! [SV2066: $i,SV1672: $i,SV1197: $i,SV603: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV603 ) @ SV1197 ) @ ( c_SetInterval_Oord_OgreaterThan @ SV1672 @ SV2066 @ SV603 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1672 @ SV2066 ) @ SV1197 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5049]) ).
thf(5580,plain,
! [SV1198: $i,SV604: $i,SV1673: $i,SV2377: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2377 ) @ SV1673 ) @ ( c_SetInterval_Oord_OgreaterThan @ SV604 @ SV1198 @ SV2377 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV604 @ SV1198 ) @ SV1673 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5050]) ).
thf(5581,plain,
! [SV2378: $i,SV2067: $i,SV1674: $i,SV1199: $i,SV605: $i] :
( ( ( hBOOL @ ( hAPP @ SV605 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SV1199 @ SV1674 @ SV605 @ SV2067 @ SV2378 ) ) )
| ! [SY7291: $i] :
( ~ ( hBOOL @ ( hAPP @ SV605 @ SY7291 ) )
| ! [SY7292: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2378 ) @ SY7291 ) @ ( hAPP @ SV1674 @ SY7292 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2067 ) @ SY7292 ) @ SV1199 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5051]) ).
thf(5582,plain,
! [SV2379: $i,SV2068: $i,SV1675: $i,SV1200: $i,SV606: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV606 ) @ SV1200 ) @ ( c_Set_Ovimage @ SV1675 @ SV2068 @ SV606 @ SV2379 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2379 ) @ ( hAPP @ SV1675 @ SV1200 ) ) @ SV2068 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5052]) ).
thf(5583,plain,
! [SV2380: $i,SV2069: $i,SV1676: $i,SV1201: $i,SV607: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV607 ) @ SV1201 ) @ ( c_Set_Ovimage @ SV1676 @ SV2069 @ SV607 @ SV2380 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2380 ) @ ( hAPP @ SV1676 @ SV1201 ) ) @ SV2069 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5053]) ).
thf(5584,plain,
! [SV2381: $i,SV2070: $i,SV1677: $i,SV1202: $i,SV608: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV608 ) @ SV1202 ) @ ( c_Set_Ovimage @ SV1677 @ SV2070 @ SV608 @ SV2381 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2381 ) @ ( hAPP @ SV1677 @ SV1202 ) ) @ SV2070 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5054]) ).
thf(5585,plain,
! [SV2071: $i,SV1678: $i,SV1203: $i,SV609: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV609 ) @ ( hAPP @ SV1203 @ SV1678 ) ) @ SV2071 ) )
= $true )
| ( ( ! [SY7078: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7078 ) @ SV1678 ) @ ( c_Set_Ovimage @ SV1203 @ SV2071 @ SY7078 @ SV609 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5055]) ).
thf(5586,plain,
! [SV2072: $i,SV1679: $i,SV1204: $i,SV610: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV610 ) @ ( hAPP @ SV1204 @ SV1679 ) ) @ SV2072 ) )
= $true )
| ( ( ! [SY7079: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7079 ) @ SV1679 ) @ ( c_Set_Ovimage @ SV1204 @ SV2072 @ SY7079 @ SV610 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5056]) ).
thf(5587,plain,
! [SV2382: $i,SV2073: $i,SV1680: $i,SV1205: $i,SV611: $i] :
( ( ! [SY7293: $i,SY7294: $i,SY7295: $i,SY7296: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV611 @ ( hAPP @ SV1205 @ SV1680 ) ) @ SV2073 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2382 ) @ SV2073 ) @ SV1680 ) )
| ! [SY7297: $i,SY7298: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1205 @ SY7293 @ SV611 @ SY7294 @ SY7295 @ SY7296 @ SY7297 @ SY7298 @ SV2382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5057]) ).
thf(5588,plain,
! [SV2383: $i,SV2074: $i,SV1681: $i,SV1206: $i,SV612: $i] :
( ( ! [SY7299: $i,SY7300: $i,SY7301: $i,SY7302: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV612 @ SV1206 ) @ ( hAPP @ SV1681 @ SV2074 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2383 ) @ SV1206 ) @ SV2074 ) )
| ! [SY7303: $i,SY7304: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY7299 @ SV1681 @ SV612 @ SY7300 @ SY7301 @ SY7302 @ SY7303 @ SY7304 @ SV2383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5058]) ).
thf(5589,plain,
! [SV1682: $i,SV613: $i,SV1207: $i,SV2384: $i] :
( ( ( ! [SY7305: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2384 ) @ SV1207 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV613 @ SY7305 @ SV1682 @ SV2384 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV613 @ SV1207 ) @ SV1682 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5059]) ).
thf(5590,plain,
! [SV1208: $i,SV614: $i,SV1683: $i,SV2385: $i] :
( ( ( ! [SY7306: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2385 ) @ SV1683 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV614 @ SV1208 @ SY7306 @ SV2385 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV614 @ SV1208 ) @ SV1683 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5060]) ).
thf(5591,plain,
! [SV2075: $i,SV1684: $i,SV1209: $i,SV615: $i] :
( ( ( hBOOL @ ( hAPP @ SV615 @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV1209 @ SV1684 @ SV615 @ SV2075 ) ) )
= $true )
| ( ( ! [SY7094: $i] :
( ~ ( hBOOL @ ( hAPP @ SV615 @ SY7094 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2075 ) @ SY7094 ) @ SV1684 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5061]) ).
thf(5592,plain,
! [SV2076: $i,SV1685: $i,SV1210: $i,SV616: $i] :
( ( ( hBOOL @ ( hAPP @ SV616 @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV1210 @ SV1685 @ SV616 @ SV2076 ) ) )
= $true )
| ( ( ! [SY7095: $i] :
( ~ ( hBOOL @ ( hAPP @ SV616 @ SY7095 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2076 ) @ SY7095 ) @ SV1210 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5062]) ).
thf(5593,plain,
! [SV1211: $i,SV617: $i,SV2386: $i,SV1686: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1686 @ SV2386 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV617 ) @ SV2386 ) @ SV1211 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV617 ) @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ SV1211 @ SV1686 @ SV617 ) ) @ SV1211 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5063]) ).
thf(5594,plain,
! [SV1212: $i,SV618: $i,SV1687: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1687 ) @ SV618 ) @ SV1212 ) )
= $false )
| ( ( ( c_Set_Oinsert @ SV618 @ SV1212 @ SV1687 )
= SV1212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5064]) ).
thf(5595,plain,
! [SV2077: $i,SV1688: $i,SV1213: $i,SV619: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV619 ) @ SV1213 ) @ ( c_SetInterval_Oord_OlessThan @ SV1688 @ SV2077 @ SV619 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1688 @ SV1213 ) @ SV2077 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5065]) ).
thf(5596,plain,
! [SV1689: $i,SV620: $i,SV1214: $i,SV2387: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2387 ) @ SV1214 ) @ ( c_SetInterval_Oord_OlessThan @ SV620 @ SV1689 @ SV2387 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV620 @ SV1214 ) @ SV1689 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5066]) ).
thf(5597,plain,
! [SV2388: $i,SV2078: $i,SV1690: $i,SV1215: $i,SV621: $i] :
( ( ! [SY7307: $i,SY7308: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV621 @ SV1215 @ SV1690 @ ( tc_fun @ SV2078 @ ( tc_fun @ SV2388 @ tc_bool ) ) ) @ SY7307 ) @ SY7308 ) )
| ! [SY6706: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV1215 @ SY6706 ) @ SY7307 ) @ SY7308 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1690 ) @ SY6706 ) @ SV621 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5067]) ).
thf(5598,plain,
! [SV2389: $i,SV2079: $i,SV1691: $i,SV1216: $i,SV622: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV622 @ SV1216 @ SV1691 @ ( tc_fun @ SV2079 @ tc_bool ) ) @ SV2389 ) )
| ! [SY7310: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1216 @ SY7310 ) @ SV2389 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1691 ) @ SY7310 ) @ SV622 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5068]) ).
thf(5599,plain,
! [SV2390: $i,SV2080: $i,SV1692: $i,SV1217: $i,SV623: $i] :
( ( ! [SY7311: $i,SY7312: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV623 @ SV1217 @ SV1692 @ ( tc_fun @ SV2080 @ ( tc_fun @ SV2390 @ tc_bool ) ) ) @ SY7311 ) @ SY7312 ) )
| ! [SY6714: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV1217 @ SY6714 ) @ SY7311 ) @ SY7312 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1692 ) @ SY6714 ) @ SV623 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5069]) ).
thf(5600,plain,
! [SV2391: $i,SV2081: $i,SV1693: $i,SV1218: $i,SV624: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV624 @ SV1218 @ SV1693 @ ( tc_fun @ SV2081 @ tc_bool ) ) @ SV2391 ) )
| ! [SY7314: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1218 @ SY7314 ) @ SV2391 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1693 ) @ SY7314 ) @ SV624 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5070]) ).
thf(5601,plain,
! [SV2082: $i,SV1694: $i,SV1219: $i,SV625: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SV1219 ) @ SV1694 ) )
= $true )
| ( ( ! [SY7108: $i,SY7109: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2082 ) @ SV1219 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SY7108 @ SV625 @ SY7109 @ SV1694 @ SV2082 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5071]) ).
thf(5602,plain,
! [SV2083: $i,SV1695: $i,SV1220: $i,SV626: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV626 @ SV1220 ) @ SV1695 ) )
= $true )
| ( ( ! [SY7110: $i,SY7111: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2083 ) @ SV1695 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV626 @ SY7110 @ SV1220 @ SY7111 @ SV2083 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5072]) ).
thf(5603,plain,
! [SV1221: $i,SV627: $i,SV2392: $i,SV1696: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1696 @ SV2392 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV627 ) @ SV2392 ) @ SV1221 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV627 ) @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ SV1221 @ SV1696 @ SV627 ) ) @ SV1221 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5073]) ).
thf(5604,plain,
! [SV1222: $i,SV1697: $i,SV2393: $i,SV628: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV628 @ SV2393 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1697 ) @ SV2393 ) @ SV1222 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV628 @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ SV1222 @ SV628 @ SV1697 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5074]) ).
thf(5605,plain,
! [SV1698: $i,SV1223: $i,SV629: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV629 ) @ SV1223 ) @ SV1698 ) )
= $false )
| ( ( ! [SY6726: $i,SY6727: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6726 ) @ ( hAPP @ SY6727 @ SV1223 ) ) @ ( c_Set_Oimage @ SY6727 @ SV1698 @ SV629 @ SY6726 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5075]) ).
thf(5606,plain,
! [SV1699: $i,SV1224: $i,SV630: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV630 ) @ SV1224 ) @ SV1699 ) )
= $false )
| ( ( ! [SY6728: $i,SY6729: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6728 ) @ ( hAPP @ SY6729 @ SV1224 ) ) @ ( c_Set_Oimage @ SY6729 @ SV1699 @ SV630 @ SY6728 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5076]) ).
thf(5607,plain,
! [SV2394: $i,SV2084: $i,SV1700: $i,SV1225: $i,SV631: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV631 ) @ ( hAPP @ SV1225 @ SV1700 ) ) @ ( c_Set_Oimage @ SV1225 @ SV2084 @ SV2394 @ SV631 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2394 ) @ SV1700 ) @ SV2084 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5077]) ).
thf(5608,plain,
! [SV2395: $i,SV2085: $i,SV1701: $i,SV1226: $i,SV632: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV632 ) @ ( hAPP @ SV1226 @ SV1701 ) ) @ ( c_Set_Oimage @ SV1226 @ SV2085 @ SV2395 @ SV632 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2395 ) @ SV1701 ) @ SV2085 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5078]) ).
thf(5609,plain,
! [SV2086: $i,SV1702: $i,SV1227: $i,SV633: $i] :
( ( ( ( hAPP @ SV633 @ SV1227 )
= ( c_Option_Ooption_OSome @ ( c_Map_Osko__Map__XdomD__1__1 @ SV1227 @ SV633 @ SV1702 @ SV2086 ) @ SV2086 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1702 ) @ SV1227 ) @ ( c_Map_Odom @ SV633 @ SV1702 @ SV2086 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5079]) ).
thf(5610,plain,
! [SV2087: $i,SV1703: $i,SV1228: $i,SV634: $i] :
( ( ( c_Map_Omap__le @ SV634 @ SV1228 @ SV1703 @ SV2087 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1703 ) @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ SV634 @ SV1228 @ SV1703 @ SV2087 ) ) @ ( c_Map_Odom @ SV634 @ SV1703 @ SV2087 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5080]) ).
thf(5611,plain,
! [SV1704: $i,SV1229: $i,SV636: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SV636 ) @ tc_Com_Ocom ) ) @ SV1229 ) @ SV1704 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV636 ) ) @ SV1229 ) @ SV1704 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5081]) ).
thf(5612,plain,
! [SV1705: $i,SV1230: $i,SV637: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ SV637 ) ) @ SV1230 ) @ SV1705 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SV637 ) @ tc_Com_Ocom ) ) @ SV1230 ) @ SV1705 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5082]) ).
thf(5613,plain,
! [SV2088: $i,SV639: $i,SV1706: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV1706 @ SV639 @ SV2088 ) )
= $false )
| ( ( c_Com_OWT @ SV639 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5083]) ).
thf(5614,plain,
! [SV640: $i,SV2089: $i,SV1707: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV1707 @ SV2089 @ SV640 ) )
= $false )
| ( ( c_Com_OWT @ SV640 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5084]) ).
thf(5615,plain,
! [SV641: $i,SV1232: $i] :
( ( ( c_Com_OWT @ SV1232 )
= $false )
| ( ( ~ ( c_Com_OWT @ SV641 ) )
= $true )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV641 @ SV1232 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5085]) ).
thf(5616,plain,
! [SV644: $i,SV1233: $i,SV1710: $i] :
( ( ( ~ ( c_Com_OWT @ SV1710 ) )
= $true )
| ( ( ~ ( c_Com_OWT @ SV1233 ) )
= $true )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV644 @ SV1233 @ SV1710 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5088]) ).
thf(5617,plain,
! [SV1236: $i,SV648: $i,SV1712: $i] :
( ( ( c_Com_OWT @ SV1712 )
= $false )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ SV648 @ SV1236 @ SV1712 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5091]) ).
thf(5618,plain,
! [SV649: $i,SV2090: $i,SV1713: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ SV1713 @ SV2090 @ SV649 ) )
= $false )
| ( ( c_Com_OWT @ SV649 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5092]) ).
thf(5619,plain,
! [SV650: $i,SV1237: $i] :
( ( ( c_Com_OWT @ SV1237 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ tc_Com_Opname ) @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ SV650 ) ) @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) ) )
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV650 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ SV1237 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5093]) ).
thf(5620,plain,
! [SV2396: $i,SV2091: $i,SV1714: $i,SV1239: $i,SV651: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ SV651 @ SV1239 @ SV1714 @ SV2091 ) @ SV2396 )
= ( hAPP @ SV651 @ SV2396 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1714 ) @ SV2396 ) @ ( c_Map_Odom @ SV1239 @ SV1714 @ SV2091 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5095]) ).
thf(5621,plain,
! [SV2397: $i,SV2092: $i,SV1715: $i,SV1240: $i,SV652: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ SV652 @ SV1240 @ SV1715 @ SV2092 ) @ SV2397 )
= ( hAPP @ SV1240 @ SV2397 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1715 ) @ SV2397 ) @ ( c_Map_Odom @ SV652 @ SV1715 @ SV2092 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5096]) ).
thf(5622,plain,
! [SV653: $i,SV2093: $i,SV1241: $i,SV1716: $i] :
( ( ( ( hAPP @ SV1716 @ SV1241 )
= ( c_Option_Ooption_ONone @ SV2093 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV653 ) @ SV1241 ) @ ( c_Map_Odom @ SV1716 @ SV653 @ SV2093 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5097]) ).
thf(5623,plain,
! [SV1717: $i,SV1242: $i,SV654: $i] :
( ( ( ( hAPP @ SV654 @ SV1242 )
= ( c_Option_Ooption_ONone @ SV1717 ) )
= $false )
| ( ( ! [SY6744: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY6744 ) @ SV1242 ) @ ( c_Map_Odom @ SV654 @ SY6744 @ SV1717 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5098]) ).
thf(5624,plain,
! [SV2094: $i,SV1718: $i,SV1243: $i,SV655: $i] :
( ( ( ( hAPP @ SV655 @ SV1243 )
!= ( c_Option_Ooption_OSome @ SV1718 @ SV2094 ) )
= $true )
| ( ( ! [SY7116: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7116 ) @ SV1243 ) @ ( c_Map_Odom @ SV655 @ SY7116 @ SV2094 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5099]) ).
thf(5625,plain,
! [SV1719: $i,SV656: $i,SV1244: $i,SV2398: $i] :
( ( ( ! [SY7315: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2398 ) @ SV1244 ) @ ( c_Map_Odom @ SV656 @ SV2398 @ SY7315 ) ) )
| ~ ( c_Map_Omap__le @ SV656 @ SV1719 @ SV2398 @ SY7315 ) ) )
= $true )
| ( ( ( hAPP @ SV656 @ SV1244 )
= ( hAPP @ SV1719 @ SV1244 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5100]) ).
thf(5626,plain,
! [SV2399: $i,SV2095: $i,SV1720: $i,SV1245: $i,SV657: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ SV657 @ SV1245 @ SV1720 @ SV2095 ) @ SV2399 )
= ( hAPP @ SV1245 @ SV2399 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1720 ) @ SV2399 ) @ ( c_Map_Odom @ SV1245 @ SV1720 @ SV2095 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5101]) ).
thf(5627,plain,
! [SV658: $i,SV1246: $i] :
( ( ( ~ c_Com_OWT__bodies ) = $true )
| ( ( c_Com_OWT @ SV1246 )
= $true )
| ( ( ( hAPP @ c_Com_Obody @ SV658 )
= ( c_Option_Ooption_OSome @ SV1246 @ tc_Com_Ocom ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5102]) ).
thf(5628,plain,
! [SV659: $i,SV1248: $i,SV1722: $i] :
( ( ( hBOOL @ ( hAPP @ SV1722 @ SV1248 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV659 ) @ SV1248 ) @ SV1722 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5103]) ).
thf(5629,plain,
! [SV660: $i,SV1249: $i,SV2096: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2096 ) @ SV1249 ) @ SV660 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV660 @ SV1249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5104]) ).
thf(5630,plain,
! [SV666: $i,SV1255: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ SV1255 )
= $false )
| ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV666 ) )
= $true )
| ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ SV666 @ SV1255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5110]) ).
thf(5631,plain,
! [SV1262: $i,SV674: $i,SV2097: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV2097 ) @ SV674 ) @ SV1262 ) )
= $false )
| ( ( SV674 = SV1262 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5116]) ).
thf(5632,plain,
! [SV3: $i,SV2400: $i,SV2100: $i,SV675: $i] :
( ( ( ( c_lessequals @ SV675 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2100 @ SV2400 @ SV3 ) @ SV3 )
| ~ ( c_lessequals @ SV675 @ SV2400 @ SV3 )
| ~ ( c_lessequals @ SV675 @ SV2100 @ SV3 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5119]) ).
thf(5633,plain,
! [SV4: $i,SV2401: $i,SV2101: $i,SV676: $i] :
( ( ( ( c_lessequals @ SV676 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2101 @ SV2401 @ SV4 ) @ SV4 )
| ~ ( c_lessequals @ SV676 @ SV2401 @ SV4 )
| ~ ( c_lessequals @ SV676 @ SV2101 @ SV4 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5120]) ).
thf(5634,plain,
! [SV5: $i,SV2402: $i,SV2102: $i,SV677: $i] :
( ( ( ( c_lessequals @ SV677 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2102 @ SV2402 @ SV5 ) @ SV5 )
| ~ ( c_lessequals @ SV677 @ SV2402 @ SV5 )
| ~ ( c_lessequals @ SV677 @ SV2102 @ SV5 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5121]) ).
thf(5635,plain,
! [SV2105: $i,SV1727: $i,SV1263: $i,SV678: $i,SV8: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV8 @ SV678 @ ( tc_fun @ SV1263 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1727 @ SV2105 @ ( tc_fun @ SV1263 @ tc_bool ) ) @ ( tc_fun @ SV1263 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV678 @ SV2105 @ ( tc_fun @ SV1263 @ tc_bool ) )
| ~ ( c_lessequals @ SV8 @ SV1727 @ ( tc_fun @ SV1263 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5124]) ).
thf(5636,plain,
! [SV2403: $i,SV2106: $i,SV1728: $i,SV1264: $i,SV680: $i,SV11: $i] :
( ( ! [SY7316: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV11 @ SV680 @ SV1264 @ SV1728 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV2106 @ SV2403 @ SY7316 @ SV1728 ) )
| ( SV1264 = SY7316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5125]) ).
thf(5637,plain,
! [SV2404: $i,SV2107: $i,SV1729: $i,SV1265: $i,SV681: $i,SV12: $i] :
( ( ! [SY7317: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV12 @ SV681 @ SV1265 @ SV1729 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV2107 @ SV2404 @ SY7317 @ SV1729 ) )
| ( SV681 = SV2404 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5126]) ).
thf(5638,plain,
! [SV2108: $i,SV1730: $i,SV1266: $i,SV682: $i,SV13: $i] :
( ( ( ! [SY7125: $i,SY7126: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV13 @ SV682 @ SV1266 @ SV1730 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV2108 @ SY7125 @ SY7126 @ SV1730 ) ) )
= $true )
| ( ( SV13 = SV2108 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5127]) ).
thf(5639,plain,
! [SV22: $i,SV2111: $i,SV1736: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1736 @ SV2111 @ SV22 )
= SV2111 )
= $true )
| ( ( ~ ( c_lessequals @ SV1736 @ SV2111 @ SV22 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5133]) ).
thf(5640,plain,
! [SV23: $i,SV2112: $i,SV1737: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1737 @ SV2112 @ SV23 )
!= SV2112 )
= $true )
| ( ( c_lessequals @ SV1737 @ SV2112 @ SV23 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5134]) ).
thf(5641,plain,
! [SV24: $i,SV2113: $i,SV1738: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1738 @ SV2113 @ SV24 )
= SV1738 )
= $true )
| ( ( ~ ( c_lessequals @ SV2113 @ SV1738 @ SV24 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5135]) ).
thf(5642,plain,
! [SV25: $i,SV2114: $i,SV1739: $i] :
( ( ( c_lessequals @ SV1739 @ SV2114 @ SV25 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1739 @ SV2114 @ SV25 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5136]) ).
thf(5643,plain,
! [SV26: $i,SV2115: $i,SV1740: $i] :
( ( ( c_lessequals @ SV1740 @ SV2115 @ SV26 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1740 @ SV2115 @ SV26 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5137]) ).
thf(5644,plain,
! [SV27: $i,SV2405: $i,SV2116: $i,SV691: $i] :
( ( ( ( c_lessequals @ SV691 @ SV2116 @ ( tc_fun @ SV2405 @ SV27 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV691 @ SV2116 @ ( tc_fun @ SV2405 @ SV27 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5138]) ).
thf(5645,plain,
! [SV30: $i,SV2118: $i,SV1742: $i] :
( ( ( SV1742 = SV2118 )
= $true )
| ( ( ~ ( c_lessequals @ SV1742 @ SV2118 @ SV30 )
| ~ ( c_lessequals @ SV2118 @ SV1742 @ SV30 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5141]) ).
thf(5646,plain,
! [SV31: $i,SV2119: $i,SV1743: $i] :
( ( ( SV1743 = SV2119 )
= $true )
| ( ( ~ ( c_lessequals @ SV2119 @ SV1743 @ SV31 )
| ~ ( c_lessequals @ SV1743 @ SV2119 @ SV31 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5142]) ).
thf(5647,plain,
! [SV32: $i,SV2120: $i,SV1744: $i] :
( ( ( SV1744 = SV2120 )
= $true )
| ( ( ~ ( c_lessequals @ SV2120 @ SV1744 @ SV32 )
| ~ ( c_lessequals @ SV1744 @ SV2120 @ SV32 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5143]) ).
thf(5648,plain,
! [SV1745: $i,SV33: $i,SV693: $i] :
( ( ( c_lessequals @ SV693 @ SV33 @ ( tc_fun @ SV1745 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV33 @ SV693 @ ( tc_fun @ SV1745 @ tc_bool ) ) )
= $true )
| ( ( SV33 = SV693 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5144]) ).
thf(5649,plain,
! [SV1746: $i,SV34: $i,SV694: $i] :
( ( ( c_lessequals @ SV694 @ SV34 @ ( tc_fun @ SV1746 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV34 @ SV694 @ ( tc_fun @ SV1746 @ tc_bool ) ) )
= $true )
| ( ( SV34 = SV694 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5145]) ).
thf(5650,plain,
! [SV36: $i,SV2406: $i,SV2122: $i,SV695: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV695 @ SV2122 @ ( tc_fun @ SV2406 @ SV36 ) )
| ( c_lessequals @ SV2122 @ SV695 @ ( tc_fun @ SV2406 @ SV36 ) )
| ~ ( c_lessequals @ SV695 @ SV2122 @ ( tc_fun @ SV2406 @ SV36 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV36 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5147]) ).
thf(5651,plain,
! [SV37: $i,SV2123: $i,SV1748: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1748 @ SV2123 @ SV37 )
= $true )
| ( ( ( c_lessequals @ SV2123 @ SV1748 @ SV37 )
| ~ ( c_lessequals @ SV1748 @ SV2123 @ SV37 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5148]) ).
thf(5652,plain,
! [SV38: $i,SV2407: $i,SV2124: $i,SV696: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV696 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2124 @ SV2407 @ SV38 ) @ SV38 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV696 @ SV2124 @ SV38 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV696 @ SV2407 @ SV38 ) @ SV38 ) @ SV38 )
= $true )
| ( ( class_Lattices_Olattice @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5149]) ).
thf(5653,plain,
! [SV2125: $i,SV1749: $i,SV1276: $i,SV697: $i,SV39: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV39 @ SV697 @ ( tc_fun @ SV1276 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1749 @ SV2125 @ ( tc_fun @ SV1276 @ tc_bool ) ) @ ( tc_fun @ SV1276 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2125 @ SV697 @ ( tc_fun @ SV1276 @ tc_bool ) )
| ~ ( c_lessequals @ SV39 @ SV1749 @ ( tc_fun @ SV1276 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5150]) ).
thf(5654,plain,
! [SV2408: $i,SV2126: $i,SV1750: $i,SV1277: $i,SV698: $i,SV40: $i] :
( ( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ SV40 @ SV698 @ SV1277 @ SV1750 @ SV2126 ) @ SV698 @ SV2408 @ SV1750 @ SV2126 )
= ( c_Fun_Ofun__upd @ SV40 @ SV698 @ SV2408 @ SV1750 @ SV2126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5151]) ).
thf(5655,plain,
! [SV1278: $i,SV703: $i,SV1755: $i,SV47: $i] :
( ( ( hBOOL @ ( hAPP @ SV47 @ SV1755 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV47 @ SV703 @ ( tc_fun @ SV1278 @ tc_bool ) ) @ SV1755 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5154]) ).
thf(5656,plain,
! [SV1279: $i,SV48: $i,SV1756: $i,SV704: $i] :
( ( ( hBOOL @ ( hAPP @ SV704 @ SV1756 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV48 @ SV704 @ ( tc_fun @ SV1279 @ tc_bool ) ) @ SV1756 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5155]) ).
thf(5657,plain,
! [SV705: $i,SV2409: $i,SV49: $i,SV1757: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1757 @ SV49 @ ( tc_fun @ SV2409 @ tc_bool ) ) @ SV705 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1757 @ SV705 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV49 @ SV705 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5156]) ).
thf(5658,plain,
! [SV2410: $i,SV2127: $i,SV1758: $i,SV1280: $i,SV706: $i,SV50: $i] :
( ( ! [SY7318: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ SV50 @ SV706 @ SV1280 @ SV1758 @ SV2127 ) @ SV2410 @ SY7318 @ SV1758 @ SV2127 )
= ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ SV50 @ SV2410 @ SY7318 @ SV1758 @ SV2127 ) @ SV706 @ SV1280 @ SV1758 @ SV2127 ) )
| ( SV706 = SV2410 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5157]) ).
thf(5659,plain,
! [SV2411: $i,SV2128: $i,SV1759: $i,SV1281: $i,SV707: $i,SV51: $i] :
( ( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ SV51 @ SV707 @ SV1281 @ SV1759 @ ( tc_Option_Ooption @ SV2128 ) ) @ ( c_Fun_Ofun__upd @ SV2411 @ SV707 @ SV1281 @ SV1759 @ ( tc_Option_Ooption @ SV2128 ) ) @ SV1759 @ SV2128 )
| ~ ( c_Map_Omap__le @ SV51 @ SV2411 @ SV1759 @ SV2128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5158]) ).
thf(5660,plain,
! [SV708: $i,SV1282: $i,SV52: $i,SV1760: $i] :
( ( ( c_lessequals @ SV1760 @ SV52 @ ( tc_fun @ SV1282 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV52 @ SV708 @ ( tc_fun @ SV1282 @ tc_bool ) ) @ SV1760 @ ( tc_fun @ SV1282 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV52 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV708 @ SV1760 @ ( tc_fun @ SV1282 @ tc_bool ) ) @ ( tc_fun @ SV1282 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5159]) ).
thf(5661,plain,
! [SV1761: $i,SV1283: $i,SV709: $i,SV53: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV53 @ SV709 @ ( tc_fun @ SV1283 @ tc_bool ) ) @ SV1761 @ ( tc_fun @ SV1283 @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV53 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV709 @ SV1761 @ ( tc_fun @ SV1283 @ tc_bool ) ) @ ( tc_fun @ SV1283 @ tc_bool ) ) )
= $false )
| ( ( c_lessequals @ SV1761 @ SV53 @ ( tc_fun @ SV1283 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5160]) ).
thf(5662,plain,
! [SV54: $i,SV1284: $i,SV710: $i] :
( ( ( c_Finite__Set_Ofinite @ SV710 @ SV1284 )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV54 @ SV1284 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV54 @ SV710 @ ( tc_fun @ SV1284 @ tc_bool ) ) @ SV1284 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5161]) ).
thf(5663,plain,
! [SV55: $i,SV1285: $i,SV711: $i] :
( ( ( c_Finite__Set_Ofinite @ SV711 @ SV1285 )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV55 @ SV1285 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV55 @ SV711 @ ( tc_fun @ SV1285 @ tc_bool ) ) @ SV1285 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5162]) ).
thf(5664,plain,
! [SV2412: $i,SV56: $i,SV2129: $i,SV712: $i,SV1286: $i] :
( ( ( ~ ( c_Finite__Set_Ofold__graph @ SV1286 @ SV712 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2129 @ tc_bool ) ) @ SV56 @ SV2129 @ SV2412 ) )
= $true )
| ( ( SV56 = SV712 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5163]) ).
thf(5665,plain,
! [SV2130: $i,SV1762: $i,SV1288: $i,SV714: $i,SV58: $i] :
( ( ( ( hAPP @ SV58 @ SV714 )
!= ( c_Option_Ooption_OSome @ SV1288 @ SV1762 ) )
= $true )
| ( ( ( SV714 = SV2130 )
| ! [SY7135: $i,SY7136: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV58 @ SV2130 @ ( c_Option_Ooption_OSome @ SY7135 @ SV1762 ) @ SY7136 @ ( tc_Option_Ooption @ SV1762 ) ) @ SV714 )
= ( c_Option_Ooption_OSome @ SV1288 @ SV1762 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5164]) ).
thf(5666,plain,
! [SV2413: $i,SV2131: $i,SV1763: $i,SV1289: $i,SV715: $i,SV59: $i] :
( ( ! [SY7319: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV59 @ SV715 @ ( c_Option_Ooption_OSome @ SV1289 @ SV1763 ) @ SV2131 @ ( tc_Option_Ooption @ SV1763 ) ) @ SV2413 )
!= ( c_Option_Ooption_OSome @ SY7319 @ SV1763 ) )
| ( ( hAPP @ SV59 @ SV2413 )
= ( c_Option_Ooption_OSome @ SY7319 @ SV1763 ) )
| ( SV1289 = SY7319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5165]) ).
thf(5667,plain,
! [SV2414: $i,SV2132: $i,SV1764: $i,SV1290: $i,SV716: $i,SV60: $i] :
( ( ! [SY7320: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV60 @ SV716 @ ( c_Option_Ooption_OSome @ SV1290 @ SV1764 ) @ SV2132 @ ( tc_Option_Ooption @ SV1764 ) ) @ SV2414 )
!= ( c_Option_Ooption_OSome @ SY7320 @ SV1764 ) )
| ( ( hAPP @ SV60 @ SV2414 )
= ( c_Option_Ooption_OSome @ SY7320 @ SV1764 ) )
| ( SV2414 = SV716 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5166]) ).
thf(5668,plain,
! [SV720: $i,SV1768: $i,SV1293: $i,SV65: $i] :
( ( ( c_lessequals @ SV65 @ SV1293 @ ( tc_fun @ SV1768 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV65 @ ( c_Set_Oinsert @ SV720 @ SV1293 @ SV1768 ) @ ( tc_fun @ SV1768 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5167]) ).
thf(5669,plain,
! [SV721: $i,SV1294: $i,SV66: $i,SV2133: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV2133 @ SV66 @ SV1294 ) @ SV721 @ ( tc_fun @ SV1294 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV66 @ SV721 @ ( tc_fun @ SV1294 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5168]) ).
thf(5670,plain,
! [SV722: $i,SV2415: $i,SV67: $i,SV1769: $i,SV1295: $i] :
( ( ( ! [SY7321: $i] :
~ ( c_Finite__Set_Ofold__graph @ SV1295 @ SV1769 @ SV67 @ SV2415 @ SV722 @ SY7321 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV67 @ SV722 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5169]) ).
thf(5671,plain,
! [SV70: $i,SV2416: $i,SV2134: $i,SV725: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV725 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2134 @ SV2416 @ SV70 ) @ SV70 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV725 @ SV2134 @ SV70 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV725 @ SV2416 @ SV70 ) @ SV70 ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5170]) ).
thf(5672,plain,
! [SV2417: $i,SV71: $i,SV2135: $i,SV726: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV726 @ SV2135 @ SV71 ) @ SV2417 @ SV71 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV726 @ SV2417 @ SV71 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2135 @ SV2417 @ SV71 ) @ SV71 ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5171]) ).
thf(5673,plain,
! [SV727: $i,SV2418: $i,SV72: $i,SV1772: $i,SV1298: $i] :
( ( ( ! [SY7322: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV1298 @ SV1772 @ ( c_Option_Ooption_OSome @ SV72 @ SV2418 ) @ SY7322 @ ( tc_Option_Ooption @ SV2418 ) ) @ SV1772 )
!= ( c_Option_Ooption_OSome @ SV727 @ SV2418 ) ) )
= $true )
| ( ( SV72 = SV727 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5172]) ).
thf(5674,plain,
! [SV730: $i,SV1773: $i,SV1301: $i,SV75: $i] :
( ( ( ~ ( c_lessequals @ SV75 @ SV1301 @ ( tc_fun @ SV1773 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV75 @ SV730 @ ( tc_fun @ SV1773 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV75 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV730 @ SV1301 @ ( tc_fun @ SV1773 @ tc_bool ) ) @ ( tc_fun @ SV1773 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5173]) ).
thf(5675,plain,
! [SV731: $i,SV1774: $i,SV1302: $i,SV76: $i] :
( ( ( ~ ( c_lessequals @ SV76 @ SV1302 @ ( tc_fun @ SV1774 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV76 @ SV731 @ ( tc_fun @ SV1774 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV76 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV731 @ SV1302 @ ( tc_fun @ SV1774 @ tc_bool ) ) @ ( tc_fun @ SV1774 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5174]) ).
thf(5676,plain,
! [SV2419: $i,SV77: $i,SV2136: $i,SV732: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV732 @ SV2136 @ SV77 ) @ SV2419 @ SV77 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV732 @ SV2419 @ SV77 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2136 @ SV2419 @ SV77 ) @ SV77 ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5175]) ).
thf(5677,plain,
! [SV78: $i,SV2420: $i,SV2137: $i,SV733: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV733 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2137 @ SV2420 @ SV78 ) @ SV78 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV733 @ SV2137 @ SV78 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV733 @ SV2420 @ SV78 ) @ SV78 ) )
= $true )
| ( ( class_Lattices_Odistrib__lattice @ SV78 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5176]) ).
thf(5678,plain,
! [SV2421: $i,SV2138: $i,SV1777: $i,SV1305: $i,SV736: $i,SV81: $i] :
( ( ( c_Set_Oimage @ SV81 @ ( c_Set_Oimage @ SV736 @ SV1305 @ SV1777 @ SV2138 ) @ SV2138 @ SV2421 )
= ( c_Set_Oimage @ ( c_COMBB @ SV81 @ SV736 @ SV2138 @ SV2421 @ SV1777 ) @ SV1305 @ SV1777 @ SV2421 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5177]) ).
thf(5679,plain,
! [SV82: $i,SV2139: $i,SV737: $i] :
( ( ( c_lessequals @ SV737 @ SV2139 @ SV82 )
= $true )
| ( ( ! [SY7146: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY7146 @ SV737 @ SV82 ) @ SV2139 @ SV82 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5178]) ).
thf(5680,plain,
! [SV83: $i,SV2140: $i,SV738: $i] :
( ( ( c_lessequals @ SV738 @ SV2140 @ SV83 )
= $true )
| ( ( ! [SY7147: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV738 @ SY7147 @ SV83 ) @ SV2140 @ SV83 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5179]) ).
thf(5681,plain,
! [SV84: $i,SV2422: $i,SV2141: $i,SV739: $i] :
( ( ( ( c_lessequals @ SV739 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2141 @ SV2422 @ SV84 ) @ SV84 )
| ~ ( c_lessequals @ SV739 @ SV2422 @ SV84 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5180]) ).
thf(5682,plain,
! [SV85: $i,SV2142: $i,SV740: $i] :
( ( ( ! [SY7149: $i] : ( c_lessequals @ SV740 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2142 @ SY7149 @ SV85 ) @ SV85 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV740 @ SV2142 @ SV85 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5181]) ).
thf(5683,plain,
! [SV86: $i,SV2143: $i,SV741: $i] :
( ( ( c_lessequals @ SV741 @ SV2143 @ SV86 )
= $true )
| ( ( ! [SY7150: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY7150 @ SV741 @ SV86 ) @ SV2143 @ SV86 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5182]) ).
thf(5684,plain,
! [SV87: $i,SV2144: $i,SV742: $i] :
( ( ( c_lessequals @ SV742 @ SV2144 @ SV87 )
= $true )
| ( ( ! [SY7151: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV742 @ SY7151 @ SV87 ) @ SV2144 @ SV87 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5183]) ).
thf(5685,plain,
! [SV743: $i,SV1306: $i,SV2145: $i,SV88: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV88 @ SV2145 @ ( tc_fun @ SV1306 @ tc_bool ) ) @ SV743 @ ( tc_fun @ SV1306 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV88 @ SV743 @ ( tc_fun @ SV1306 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5184]) ).
thf(5686,plain,
! [SV744: $i,SV1307: $i,SV89: $i,SV2146: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2146 @ SV89 @ ( tc_fun @ SV1307 @ tc_bool ) ) @ SV744 @ ( tc_fun @ SV1307 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV89 @ SV744 @ ( tc_fun @ SV1307 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5185]) ).
thf(5687,plain,
! [SV90: $i,SV2147: $i,SV745: $i] :
( ( ( c_lessequals @ SV745 @ SV2147 @ SV90 )
= $true )
| ( ( ! [SY7152: $i] :
( ~ ( c_lessequals @ SV745 @ SY7152 @ SV90 )
| ~ ( c_lessequals @ SY7152 @ SV2147 @ SV90 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5186]) ).
thf(5688,plain,
! [SV91: $i,SV2148: $i,SV746: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV746 @ SV2148 @ SV91 )
= $true )
| ( ( ! [SY7153: $i] :
( ~ ( c_lessequals @ SV746 @ SY7153 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SY7153 @ SV2148 @ SV91 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5187]) ).
thf(5689,plain,
! [SV92: $i,SV2149: $i,SV747: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV747 @ SV2149 @ SV92 )
= $true )
| ( ( ! [SY7154: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV747 @ SY7154 @ SV92 )
| ~ ( c_lessequals @ SY7154 @ SV2149 @ SV92 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5188]) ).
thf(5690,plain,
! [SV93: $i,SV2150: $i,SV748: $i] :
( ( ( c_lessequals @ SV748 @ SV2150 @ SV93 )
= $true )
| ( ( ! [SY7155: $i] :
( ~ ( c_lessequals @ SY7155 @ SV2150 @ SV93 )
| ~ ( c_lessequals @ SV748 @ SY7155 @ SV93 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5189]) ).
thf(5691,plain,
! [SV96: $i,SV1308: $i,SV751: $i,SV2151: $i] :
( ( ( ~ ( c_lessequals @ SV2151 @ SV751 @ ( tc_fun @ SV1308 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV96 @ SV2151 @ ( tc_fun @ SV1308 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV96 @ SV751 @ ( tc_fun @ SV1308 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5190]) ).
thf(5692,plain,
! [SV1778: $i,SV97: $i,SV1309: $i,SV2423: $i,SV752: $i] :
( ( ( ~ ( c_lessequals @ SV752 @ SV2423 @ ( tc_fun @ SV1309 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV97 @ SV2423 @ SV1309 @ SV1778 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV97 @ SV752 @ SV1309 @ SV1778 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5191]) ).
thf(5693,plain,
! [SV98: $i,SV753: $i,SV1779: $i] :
( ( ( hBOOL @ ( hAPP @ SV1779 @ SV753 ) )
= $false )
| ( ( ! [SY6803: $i] :
~ ( c_lessequals @ SV1779 @ SV98 @ ( tc_fun @ SY6803 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV98 @ SV753 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5192]) ).
thf(5694,plain,
! [SV101: $i,SV754: $i,SV1782: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1782 @ SV754 )
= $false )
| ( ( ~ ( c_lessequals @ SV101 @ SV1782 @ ( tc_fun @ SV754 @ tc_bool ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV101 @ SV754 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5193]) ).
thf(5695,plain,
! [SV102: $i,SV1310: $i,SV755: $i,SV2152: $i] :
( ( ( ~ ( c_lessequals @ SV2152 @ SV755 @ ( tc_fun @ SV1310 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV102 @ SV2152 @ ( tc_fun @ SV1310 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV102 @ SV755 @ ( tc_fun @ SV1310 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5194]) ).
thf(5696,plain,
! [SV103: $i,SV1311: $i,SV756: $i,SV2153: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2153 @ SV756 @ ( tc_fun @ SV1311 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV103 @ SV2153 @ ( tc_fun @ SV1311 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV103 @ SV756 @ ( tc_fun @ SV1311 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5195]) ).
thf(5697,plain,
! [SV757: $i,SV2424: $i,SV104: $i,SV1783: $i] :
( ( ( ~ ( c_lessequals @ SV1783 @ SV104 @ ( tc_fun @ SV2424 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1783 @ SV757 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV104 @ SV757 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5196]) ).
thf(5698,plain,
! [SV758: $i,SV1784: $i,SV105: $i] :
( ( ( c_lessequals @ SV105 @ SV1784 @ ( tc_fun @ SV758 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1784 @ SV758 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV105 @ SV758 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5197]) ).
thf(5699,plain,
! [SV106: $i,SV2154: $i,SV759: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV759 @ SV2154 @ SV106 )
= $true )
| ( ( ! [SY7156: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY7156 @ SV2154 @ SV106 )
| ~ ( c_lessequals @ SV759 @ SY7156 @ SV106 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5198]) ).
thf(5700,plain,
! [SV107: $i,SV2155: $i,SV760: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV760 @ SV2155 @ SV107 )
= $true )
| ( ( ! [SY7157: $i] :
( ~ ( c_lessequals @ SY7157 @ SV2155 @ SV107 )
| ~ ( c_HOL_Oord__class_Oless @ SV760 @ SY7157 @ SV107 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5199]) ).
thf(5701,plain,
! [SV2156: $i,SV1785: $i,SV1312: $i,SV761: $i,SV108: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV108 @ SV761 @ ( tc_fun @ SV1312 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1785 @ SV2156 @ ( tc_fun @ SV1312 @ tc_bool ) ) @ ( tc_fun @ SV1312 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV761 @ SV2156 @ ( tc_fun @ SV1312 @ tc_bool ) )
| ~ ( c_lessequals @ SV108 @ SV1785 @ ( tc_fun @ SV1312 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5200]) ).
thf(5702,plain,
! [SV1787: $i,SV1314: $i,SV763: $i,SV110: $i] :
( ( ( ( hAPP @ SV110 @ SV763 )
= ( c_Option_Ooption_OSome @ SV1314 @ SV1787 ) )
= $false )
| ( ( ! [SY6807: $i] :
( ( c_Fun_Ofun__upd @ SV110 @ SV763 @ ( c_Option_Ooption_OSome @ SV1314 @ SV1787 ) @ SY6807 @ ( tc_Option_Ooption @ SV1787 ) )
= SV110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5202]) ).
thf(5703,plain,
! [SV2425: $i,SV2159: $i,SV1789: $i,SV1316: $i,SV765: $i,SV112: $i] :
( ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV112 @ SV765 @ SV1316 @ SV1789 @ SV2159 ) @ SV2425 )
= ( hAPP @ SV112 @ SV2425 ) )
| ( SV2425 = SV765 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5204]) ).
thf(5704,plain,
! [SV2426: $i,SV2160: $i,SV1790: $i,SV1317: $i,SV766: $i,SV113: $i] :
( ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV113 @ SV766 @ SV1317 @ SV1790 @ SV2160 ) @ SV2426 )
= ( hAPP @ SV113 @ SV2426 ) )
| ( SV2426 = SV766 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5205]) ).
thf(5705,plain,
! [SV1318: $i,SV1791: $i,SV767: $i,SV114: $i] :
( ( ( ~ ( c_lessequals @ SV114 @ SV767 @ ( tc_fun @ SV1791 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1318 @ SV114 @ ( tc_fun @ SV1791 @ tc_bool ) ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV114 @ ( c_HOL_Ominus__class_Ominus @ SV767 @ SV1318 @ ( tc_fun @ SV1791 @ tc_bool ) ) @ ( tc_fun @ SV1791 @ tc_bool ) )
= SV1318 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5206]) ).
thf(5706,plain,
! [SV2427: $i,SV115: $i,SV1319: $i,SV768: $i] :
( ( ( ! [SY7323: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV768 @ SV1319 @ SV115 )
!= ( c_HOL_Ominus__class_Ominus @ SV2427 @ SY7323 @ SV115 ) )
| ( c_lessequals @ SY7323 @ SV2427 @ SV115 )
| ~ ( c_lessequals @ SV1319 @ SV768 @ SV115 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV115 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5207]) ).
thf(5707,plain,
! [SV2428: $i,SV116: $i,SV1320: $i,SV769: $i] :
( ( ( ! [SY7324: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV769 @ SV1320 @ SV116 )
!= ( c_HOL_Ominus__class_Ominus @ SV2428 @ SY7324 @ SV116 ) )
| ( c_lessequals @ SV1320 @ SV769 @ SV116 )
| ~ ( c_lessequals @ SY7324 @ SV2428 @ SV116 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV116 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5208]) ).
thf(5708,plain,
! [SV2161: $i,SV1792: $i,SV1321: $i,SV770: $i,SV117: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV117 @ SV770 @ SV1321 @ SV1792 ) @ ( c_Set_Oimage @ SV117 @ SV2161 @ SV1321 @ SV1792 ) @ ( tc_fun @ SV1792 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV770 @ SV2161 @ ( tc_fun @ SV1321 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5209]) ).
thf(5709,plain,
! [SV771: $i,SV1322: $i,SV118: $i,SV2429: $i] :
( ( ( ! [SY7325: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV2429 @ SV118 @ SV1322 @ SY7325 ) @ ( c_Set_Oimage @ SV2429 @ SV771 @ SV1322 @ SY7325 ) @ ( tc_fun @ SY7325 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV118 @ SV771 @ ( tc_fun @ SV1322 @ tc_bool ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5210]) ).
thf(5710,plain,
! [SV119: $i,SV1323: $i,SV1793: $i,SV772: $i] :
( ( ( c_lessequals @ SV772 @ SV1793 @ ( tc_fun @ SV1323 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Set_Oinsert @ SV119 @ SV772 @ SV1323 ) @ ( c_Set_Oinsert @ SV119 @ SV1793 @ SV1323 ) @ ( tc_fun @ SV1323 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5211]) ).
thf(5711,plain,
! [SV121: $i,SV2162: $i,SV1794: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1794 @ SV2162 @ SV121 )
= $true )
| ( ( ( SV2162 = SV1794 )
| ~ ( c_lessequals @ SV1794 @ SV2162 @ SV121 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5212]) ).
thf(5712,plain,
! [SV122: $i,SV2163: $i,SV1795: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1795 @ SV2163 @ SV122 )
= $true )
| ( ( ~ ( c_lessequals @ SV1795 @ SV2163 @ SV122 )
| ( SV2163 = SV1795 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5213]) ).
thf(5713,plain,
! [SV1324: $i,SV773: $i,SV123: $i] :
( ( ( c_lessequals @ SV123 @ SV773 @ ( tc_fun @ SV1324 @ tc_bool ) )
= $false )
| ( ( SV123 = SV773 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV123 @ SV773 @ ( tc_fun @ SV1324 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5214]) ).
thf(5714,plain,
! [SV124: $i,SV2164: $i,SV1796: $i] :
( ( ( SV1796 = SV2164 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1796 @ SV2164 @ SV124 )
| ~ ( c_lessequals @ SV1796 @ SV2164 @ SV124 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5215]) ).
thf(5715,plain,
! [SV125: $i,SV2165: $i,SV1797: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1797 @ SV2165 @ SV125 )
= $true )
| ( ( ( SV1797 = SV2165 )
| ~ ( c_lessequals @ SV1797 @ SV2165 @ SV125 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5216]) ).
thf(5716,plain,
! [SV1798: $i,SV774: $i,SV126: $i] :
( ( ( c_lessequals @ SV126 @ SV774 @ ( tc_fun @ SV1798 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV126 @ SV774 @ ( tc_fun @ SV1798 @ tc_bool ) )
= $true )
| ( ( SV126 = SV774 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5217]) ).
thf(5717,plain,
! [SV127: $i,SV2166: $i,SV1799: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1799 @ SV2166 @ SV127 )
= $true )
| ( ( ( SV1799 = SV2166 )
| ~ ( c_lessequals @ SV1799 @ SV2166 @ SV127 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5218]) ).
thf(5718,plain,
! [SV128: $i,SV2167: $i,SV1800: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1800 @ SV2167 @ SV128 )
= $true )
| ( ( ~ ( c_lessequals @ SV1800 @ SV2167 @ SV128 )
| ( SV1800 = SV2167 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5219]) ).
thf(5719,plain,
! [SV129: $i,SV2168: $i,SV1801: $i] :
( ( ( SV1801 = SV2168 )
= $true )
| ( ( ~ ( c_lessequals @ SV1801 @ SV2168 @ SV129 )
| ( c_HOL_Oord__class_Oless @ SV1801 @ SV2168 @ SV129 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5220]) ).
thf(5720,plain,
! [SV130: $i,SV2169: $i,SV1802: $i] :
( ( ( SV1802 = SV2169 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1802 @ SV2169 @ SV130 )
| ~ ( c_lessequals @ SV1802 @ SV2169 @ SV130 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV130 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5221]) ).
thf(5721,plain,
! [SV2430: $i,SV2170: $i,SV1803: $i,SV1325: $i,SV775: $i,SV131: $i] :
( ( ! [SY7326: $i] :
( ( ( c_Fun_Ofun__upd @ SV131 @ SV775 @ ( c_Option_Ooption_OSome @ SV1325 @ SV1803 ) @ SV2170 @ ( tc_Option_Ooption @ SV1803 ) )
!= ( c_Fun_Ofun__upd @ SV2430 @ SV775 @ ( c_Option_Ooption_OSome @ SY7326 @ SV1803 ) @ SV2170 @ ( tc_Option_Ooption @ SV1803 ) ) )
| ( SV1325 = SY7326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5222]) ).
thf(5722,plain,
! [SV133: $i,SV2172: $i,SV1805: $i] :
( ( ( c_lessequals @ SV1805 @ SV2172 @ SV133 )
= $true )
| ( ( c_lessequals @ SV2172 @ SV1805 @ SV133 )
= $true )
| ( ( class_Orderings_Olinorder @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5224]) ).
thf(5723,plain,
! [SV134: $i,SV2431: $i,SV1327: $i,SV777: $i] :
( ( ( ! [SY7327: $i] :
( ( ( c_Finite__Set_Osetsum @ SV777 @ ( c_HOL_Ominus__class_Ominus @ SV1327 @ SV2431 @ ( tc_fun @ SY7327 @ tc_bool ) ) @ SY7327 @ SV134 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV777 @ SV1327 @ SY7327 @ SV134 ) @ ( c_Finite__Set_Osetsum @ SV777 @ SV2431 @ SY7327 @ SV134 ) @ SV134 ) )
| ~ ( c_lessequals @ SV2431 @ SV1327 @ ( tc_fun @ SY7327 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV1327 @ SY7327 ) ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5225]) ).
thf(5724,plain,
! [SV778: $i,SV135: $i,SV1806: $i,SV1328: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV1328 @ SV1806 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV135 @ SV778 )
| ! [SY6827: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ SY6827 @ SV1328 @ SV1806 @ SV778 ) @ SV135 @ ( tc_fun @ SV778 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY6827 @ SV1328 @ SV1806 @ SV778 )
| ! [SY6828: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ SY6828 @ SV135 @ SV778 @ SV1806 ) @ SV1328 @ ( tc_fun @ SV1806 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY6828 @ SV135 @ SV778 @ SV1806 ) ) ) )
= $true )
| ( ( ( c_Finite__Set_Ocard @ SV135 @ SV778 )
= ( c_Finite__Set_Ocard @ SV1328 @ SV1806 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5226]) ).
thf(5725,plain,
! [SV2432: $i,SV2173: $i,SV1807: $i,SV1329: $i,SV779: $i,SV136: $i] :
( ( ! [SY7328: $i] :
( ( c_Finite__Set_Ofold__graph @ SV136 @ SV779 @ ( c_Set_Oinsert @ SV1329 @ SV1807 @ SV2173 ) @ ( hAPP @ ( hAPP @ SV136 @ SV1329 ) @ SV2432 ) @ SV2173 @ SY7328 )
| ~ ( c_Finite__Set_Ofold__graph @ SV136 @ SV779 @ SV1807 @ SV2432 @ SV2173 @ SY7328 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2173 ) @ SV1329 ) @ SV1807 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5227]) ).
thf(5726,plain,
! [SV1330: $i,SV780: $i,SV2174: $i,SV137: $i] :
( ( ( ~ ( c_lessequals @ SV137 @ ( c_Set_Oinsert @ SV2174 @ SV780 @ SV1330 ) @ ( tc_fun @ SV1330 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1330 ) @ SV2174 ) @ SV137 ) )
= $true )
| ( ( c_lessequals @ SV137 @ SV780 @ ( tc_fun @ SV1330 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5228]) ).
thf(5727,plain,
! [SV781: $i,SV1808: $i,SV1331: $i,SV138: $i] :
( ( ( ~ ( c_lessequals @ SV138 @ SV1331 @ ( tc_fun @ SV1808 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1808 ) @ SV781 ) @ SV138 ) )
= $true )
| ( ( c_lessequals @ SV138 @ ( c_Set_Oinsert @ SV781 @ SV1331 @ SV1808 ) @ ( tc_fun @ SV1808 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5229]) ).
thf(5728,plain,
! [SV782: $i,SV139: $i,SV2175: $i,SV1332: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1332 ) @ SV2175 ) @ SV139 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV139 @ ( c_Set_Oinsert @ SV2175 @ SV782 @ SV1332 ) @ ( tc_fun @ SV1332 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV139 @ SV782 @ ( tc_fun @ SV1332 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5230]) ).
thf(5729,plain,
! [SV783: $i,SV1809: $i,SV1333: $i,SV140: $i] :
( ( ( ~ ( c_lessequals @ SV140 @ SV1333 @ ( tc_fun @ SV1809 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1809 ) @ SV783 ) @ SV140 ) )
= $true )
| ( ( c_lessequals @ SV140 @ ( c_Set_Oinsert @ SV783 @ SV1333 @ SV1809 ) @ ( tc_fun @ SV1809 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5231]) ).
thf(5730,plain,
! [SV1334: $i,SV141: $i,SV2176: $i,SV784: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV784 @ SV2176 @ SV141 ) @ SV1334 @ ( tc_fun @ SV141 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV141 ) @ SV784 ) @ SV1334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5232]) ).
thf(5731,plain,
! [SV142: $i,SV1335: $i,SV1810: $i,SV785: $i] :
( ( ( ~ ( c_lessequals @ SV785 @ SV1810 @ ( tc_fun @ SV1335 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1335 ) @ SV142 ) @ SV1810 ) ) )
= $true )
| ( ( c_lessequals @ ( c_Set_Oinsert @ SV142 @ SV785 @ SV1335 ) @ SV1810 @ ( tc_fun @ SV1335 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5233]) ).
thf(5732,plain,
! [SV1811: $i,SV143: $i,SV786: $i,SV1336: $i,SV2433: $i] :
( ( ( ! [SY7329: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2433 ) @ SV1336 ) @ SY7329 ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV786 @ SY7329 @ SV2433 @ SV143 ) @ SV1811 @ ( tc_fun @ SV143 @ tc_bool ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV143 ) @ ( hAPP @ SV786 @ SV1336 ) ) @ SV1811 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5234]) ).
thf(5733,plain,
! [SV2434: $i,SV2177: $i,SV1812: $i,SV1337: $i,SV787: $i,SV144: $i] :
( ( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ SV144 @ SV787 @ SV1337 @ SV1812 @ SV2177 ) @ SV2434 @ SV1812 @ SV2177 )
= ( c_Set_Oimage @ SV144 @ SV2434 @ SV1812 @ SV2177 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1812 ) @ SV787 ) @ SV2434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5235]) ).
thf(5734,plain,
! [SV145: $i,SV2435: $i,SV1338: $i,SV788: $i] :
( ( ( ! [SY7330: $i] :
( ( c_lessequals @ ( hAPP @ SV788 @ SV1338 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV2435 @ SV788 @ SY7330 @ SV145 ) @ SV145 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7330 ) @ SV1338 ) @ SV2435 ) ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV145 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5236]) ).
thf(5735,plain,
! [SV2436: $i,SV1813: $i,SV1339: $i,SV789: $i,SV146: $i] :
( ( ( c_lessequals @ ( hAPP @ SV146 @ SV789 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1339 @ SV146 @ SV1813 @ ( tc_fun @ SV2436 @ tc_bool ) ) @ ( tc_fun @ SV2436 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1813 ) @ SV789 ) @ SV1339 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5237]) ).
thf(5736,plain,
! [SV1340: $i,SV1814: $i,SV147: $i,SV790: $i,SV2437: $i] :
( ( ( ! [SY7331: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2437 ) @ SV790 ) @ SY7331 ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY7331 @ SV147 @ SV2437 @ ( tc_fun @ SV1814 @ tc_bool ) ) @ SV1340 @ ( tc_fun @ SV1814 @ tc_bool ) ) ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ SV147 @ SV790 ) @ SV1340 @ ( tc_fun @ SV1814 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5238]) ).
thf(5737,plain,
! [SV2438: $i,SV1815: $i,SV1341: $i,SV791: $i,SV148: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV148 @ SV791 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1341 @ SV148 @ SV1815 @ ( tc_fun @ SV2438 @ tc_bool ) ) @ ( tc_fun @ SV2438 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1341 @ SV148 @ SV1815 @ ( tc_fun @ SV2438 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1815 ) @ SV791 ) @ SV1341 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5239]) ).
thf(5738,plain,
! [SV1343: $i,SV793: $i,SV150: $i] :
( ( ( c_lessequals @ SV150 @ ( c_Set_Oinsert @ SV793 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1343 @ tc_bool ) ) @ SV1343 ) @ ( tc_fun @ SV1343 @ tc_bool ) )
= $false )
| ( ( SV150
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1343 @ tc_bool ) ) )
= $true )
| ( ( SV150
= ( c_Set_Oinsert @ SV793 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1343 @ tc_bool ) ) @ SV1343 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5240]) ).
thf(5739,plain,
! [SV794: $i,SV2439: $i,SV2178: $i,SV1344: $i,SV151: $i] :
( ( ( ~ ( c_lessequals @ SV151 @ ( c_Set_Oimage @ SV1344 @ SV2178 @ SV2439 @ SV794 ) @ ( tc_fun @ SV794 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV2178 @ SV2439 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV151 @ SV794 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5241]) ).
thf(5740,plain,
! [SV2440: $i,SV155: $i,SV2179: $i,SV798: $i] :
( ( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV798 @ ( c_COMBK @ SV2179 @ SV155 @ SV2440 ) @ SV2440 @ SV155 )
= SV2179 )
| ( SV798
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2440 @ tc_bool ) ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV155 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5244]) ).
thf(5741,plain,
! [SV2441: $i,SV2182: $i,SV1820: $i,SV1352: $i,SV803: $i,SV160: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV160 @ ( c_COMBB @ SV803 @ SV1352 @ SV1820 @ ( tc_fun @ SV2182 @ tc_bool ) @ SV2441 ) @ SV2441 @ ( tc_fun @ SV2182 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oimage @ SV1352 @ SV160 @ SV2441 @ SV1820 ) @ SV803 @ SV1820 @ ( tc_fun @ SV2182 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5247]) ).
thf(5742,plain,
! [SV2442: $i,SV2183: $i,SV1821: $i,SV1353: $i,SV804: $i,SV161: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oimage @ SV161 @ SV804 @ SV1353 @ SV1821 ) @ SV2183 @ SV1821 @ ( tc_fun @ SV2442 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV804 @ ( c_COMBB @ SV2183 @ SV161 @ SV1821 @ ( tc_fun @ SV2442 @ tc_bool ) @ SV1353 ) @ SV1353 @ ( tc_fun @ SV2442 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5248]) ).
thf(5743,plain,
! [SV2184: $i,SV1822: $i,SV1354: $i,SV805: $i,SV162: $i] :
( ( ( ( c_Set_Oimage @ SV162 @ SV805 @ SV1354 @ SV1822 )
!= ( c_Set_Oimage @ SV162 @ SV2184 @ SV1354 @ SV1822 ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV162 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV805 @ SV2184 @ ( tc_fun @ SV1354 @ tc_bool ) ) @ SV1354 @ SV1822 )
| ( SV805 = SV2184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5249]) ).
thf(5744,plain,
! [SV1823: $i,SV1355: $i,SV806: $i,SV163: $i] :
( ( ( c_Fun_Oinj__on @ SV163 @ SV806 @ SV1355 @ SV1823 )
= $false )
| ( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ SV163 @ SV806 @ SV1355 @ SV1823 ) @ SV1823 )
= ( c_Finite__Set_Ocard @ SV806 @ SV1355 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5250]) ).
thf(5745,plain,
! [SV2443: $i,SV2186: $i,SV1828: $i,SV1361: $i,SV812: $i,SV169: $i] :
( ( ( c_Map_Omap__add @ SV169 @ ( c_Fun_Ofun__upd @ SV812 @ SV1361 @ ( c_Option_Ooption_OSome @ SV1828 @ SV2186 ) @ SV2443 @ ( tc_Option_Ooption @ SV2186 ) ) @ SV2443 @ SV2186 )
= ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ SV169 @ SV812 @ SV2443 @ SV2186 ) @ SV1361 @ ( c_Option_Ooption_OSome @ SV1828 @ SV2186 ) @ SV2443 @ ( tc_Option_Ooption @ SV2186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5252]) ).
thf(5746,plain,
! [SV1364: $i,SV815: $i,SV1831: $i,SV172: $i] :
( ( ( c_Map_Omap__le @ SV172 @ SV1831 @ SV815 @ SV1364 )
= $false )
| ( ( c_lessequals @ ( c_Map_Odom @ SV172 @ SV815 @ SV1364 ) @ ( c_Map_Odom @ SV1831 @ SV815 @ SV1364 ) @ ( tc_fun @ SV815 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5253]) ).
thf(5747,plain,
! [SV2444: $i,SV2187: $i,SV1833: $i,SV1365: $i,SV817: $i,SV175: $i] :
( ( ( hAPP @ ( c_COMBB @ SV175 @ SV817 @ SV1365 @ SV1833 @ SV2187 ) @ SV2444 )
= ( hAPP @ SV175 @ ( hAPP @ SV817 @ SV2444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5254]) ).
thf(5748,plain,
! [SV177: $i,SV2188: $i,SV1835: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1835 @ SV2188 @ SV177 )
= $true )
| ( ( c_lessequals @ SV2188 @ SV1835 @ SV177 )
= $true )
| ( ( class_Orderings_Olinorder @ SV177 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5255]) ).
thf(5749,plain,
! [SV178: $i,SV1836: $i] :
( ( ( c_lessequals @ SV1836 @ SV1836 @ SV178 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1836 @ SV1836 @ SV178 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5256]) ).
thf(5750,plain,
! [SV180: $i,SV2189: $i,SV1838: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1838 @ SV2189 @ SV180 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2189 @ SV1838 @ SV180 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV180 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5258]) ).
thf(5751,plain,
! [SV181: $i,SV1839: $i,SV2190: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2190 @ SV1839 @ SV181 )
= $true )
| ( ( c_lessequals @ SV1839 @ SV2190 @ SV181 )
= $true )
| ( ( class_Orderings_Olinorder @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5259]) ).
thf(5752,plain,
! [SV182: $i,SV2191: $i,SV1840: $i] :
( ( ( ~ ( c_lessequals @ SV1840 @ SV2191 @ SV182 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2191 @ SV1840 @ SV182 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5260]) ).
thf(5753,plain,
! [SV183: $i,SV2192: $i,SV1841: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1841 @ SV2192 @ SV183 )
= $true )
| ( ( c_lessequals @ SV2192 @ SV1841 @ SV183 )
= $true )
| ( ( class_Orderings_Olinorder @ SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5261]) ).
thf(5754,plain,
! [SV184: $i,SV2445: $i,SV2193: $i,SV819: $i] :
( ( ( ~ ( c_lessequals @ SV819 @ SV2193 @ ( tc_fun @ SV2445 @ SV184 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV2193 @ SV819 @ ( tc_fun @ SV2445 @ SV184 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV184 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5262]) ).
thf(5755,plain,
! [SV185: $i,SV2194: $i,SV1842: $i] :
( ( ( ~ ( c_lessequals @ SV1842 @ SV2194 @ SV185 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2194 @ SV1842 @ SV185 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5263]) ).
thf(5756,plain,
! [SV2446: $i,SV188: $i,SV2195: $i,SV822: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV822 @ SV2195 @ SV188 ) @ SV2446 @ SV188 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV822 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2195 @ SV2446 @ SV188 ) @ SV188 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV188 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5264]) ).
thf(5757,plain,
! [SV189: $i,SV2447: $i,SV2196: $i,SV823: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV823 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2196 @ SV2447 @ SV189 ) @ SV189 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV2196 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV823 @ SV2447 @ SV189 ) @ SV189 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV189 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5265]) ).
thf(5758,plain,
! [SV190: $i,SV2448: $i,SV2197: $i,SV824: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV824 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2197 @ SV2448 @ SV190 ) @ SV190 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV2197 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV824 @ SV2448 @ SV190 ) @ SV190 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV190 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5266]) ).
thf(5759,plain,
! [SV2449: $i,SV191: $i,SV2198: $i,SV825: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV825 @ SV2198 @ SV191 ) @ SV2449 @ SV191 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV825 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2198 @ SV2449 @ SV191 ) @ SV191 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV191 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5267]) ).
thf(5760,plain,
! [SV194: $i,SV2199: $i,SV1845: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1845 @ SV2199 @ SV194 )
= SV1845 )
= $true )
| ( ( ~ ( c_lessequals @ SV1845 @ SV2199 @ SV194 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5270]) ).
thf(5761,plain,
! [SV195: $i,SV2200: $i,SV1846: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1846 @ SV2200 @ SV195 )
!= SV1846 )
= $true )
| ( ( c_lessequals @ SV1846 @ SV2200 @ SV195 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV195 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5271]) ).
thf(5762,plain,
! [SV196: $i,SV2201: $i,SV1847: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1847 @ SV2201 @ SV196 )
= SV2201 )
= $true )
| ( ( ~ ( c_lessequals @ SV2201 @ SV1847 @ SV196 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV196 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5272]) ).
thf(5763,plain,
! [SV197: $i,SV1371: $i,SV1848: $i,SV828: $i] :
( ( ( ~ ( c_lessequals @ SV828 @ SV1848 @ ( tc_fun @ SV1371 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV197 @ SV1848 @ ( tc_fun @ SV1371 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV197 @ SV828 @ ( tc_fun @ SV1371 @ tc_bool ) ) @ SV1848 @ ( tc_fun @ SV1371 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5273]) ).
thf(5764,plain,
! [SV200: $i,SV1374: $i,SV1849: $i,SV831: $i] :
( ( ( ~ ( c_lessequals @ SV831 @ SV1849 @ ( tc_fun @ SV1374 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV200 @ SV1849 @ ( tc_fun @ SV1374 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ SV831 @ ( tc_fun @ SV1374 @ tc_bool ) ) @ SV1849 @ ( tc_fun @ SV1374 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5274]) ).
thf(5765,plain,
! [SV2450: $i,SV201: $i,SV2202: $i,SV832: $i] :
( ( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV832 @ SV2202 @ SV201 ) @ SV2450 @ SV201 )
| ~ ( c_lessequals @ SV2202 @ SV2450 @ SV201 )
| ~ ( c_lessequals @ SV832 @ SV2450 @ SV201 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV201 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5275]) ).
thf(5766,plain,
! [SV2451: $i,SV204: $i,SV2205: $i,SV833: $i] :
( ( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV833 @ SV2205 @ SV204 ) @ SV2451 @ SV204 )
| ~ ( c_lessequals @ SV2205 @ SV2451 @ SV204 )
| ~ ( c_lessequals @ SV833 @ SV2451 @ SV204 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV204 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5278]) ).
thf(5767,plain,
! [SV2452: $i,SV205: $i,SV2206: $i,SV834: $i] :
( ( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV834 @ SV2206 @ SV205 ) @ SV2452 @ SV205 )
| ~ ( c_lessequals @ SV2206 @ SV2452 @ SV205 )
| ~ ( c_lessequals @ SV834 @ SV2452 @ SV205 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV205 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5279]) ).
thf(5768,plain,
! [SV2453: $i,SV209: $i,SV2209: $i,SV836: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV836 @ SV2209 @ SV209 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV836 @ SV2453 @ SV209 ) @ SV209 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV836 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2209 @ SV2453 @ SV209 ) @ SV209 ) @ SV209 )
= $true )
| ( ( class_Lattices_Olattice @ SV209 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5283]) ).
thf(5769,plain,
! [SV2210: $i,SV1857: $i,SV1380: $i,SV841: $i,SV214: $i] :
( ( ( c_lessequals @ ( c_Set_Ovimage @ SV214 @ SV841 @ SV1380 @ SV1857 ) @ ( c_Set_Ovimage @ SV214 @ SV2210 @ SV1380 @ SV1857 ) @ ( tc_fun @ SV1380 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV841 @ SV2210 @ ( tc_fun @ SV1857 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5284]) ).
thf(5770,plain,
! [SV217: $i,SV2454: $i,SV1858: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1858 @ SV2454 @ SV217 )
!= ( c_Orderings_Obot__class_Obot @ SV217 ) )
= $true )
| ( ( SV1858
= ( c_Orderings_Obot__class_Obot @ SV217 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV217 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5287]) ).
thf(5771,plain,
! [SV218: $i,SV2211: $i,SV1859: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1859 @ SV2211 @ SV218 )
!= ( c_Orderings_Obot__class_Obot @ SV218 ) )
= $true )
| ( ( SV2211
= ( c_Orderings_Obot__class_Obot @ SV218 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV218 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5288]) ).
thf(5772,plain,
! [SV1385: $i,SV846: $i,SV2212: $i,SV221: $i] :
( ( ( c_lessequals @ SV221 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2212 @ SV846 @ ( tc_fun @ SV1385 @ tc_bool ) ) @ ( tc_fun @ SV1385 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV221 @ SV846 @ ( tc_fun @ SV1385 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5289]) ).
thf(5773,plain,
! [SV1386: $i,SV2213: $i,SV847: $i,SV222: $i] :
( ( ( c_lessequals @ SV222 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV847 @ SV2213 @ ( tc_fun @ SV1386 @ tc_bool ) ) @ ( tc_fun @ SV1386 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV222 @ SV847 @ ( tc_fun @ SV1386 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5290]) ).
thf(5774,plain,
! [SV223: $i,SV2214: $i,SV848: $i] :
( ( ( c_lessequals @ SV848 @ SV2214 @ SV223 )
= $true )
| ( ( ! [SY7180: $i] :
~ ( c_lessequals @ SV848 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2214 @ SY7180 @ SV223 ) @ SV223 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV223 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5291]) ).
thf(5775,plain,
! [SV224: $i,SV2215: $i,SV849: $i] :
( ( ( c_lessequals @ SV849 @ SV2215 @ SV224 )
= $true )
| ( ( ! [SY7181: $i] :
~ ( c_lessequals @ SV849 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY7181 @ SV2215 @ SV224 ) @ SV224 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5292]) ).
thf(5776,plain,
! [SV2455: $i,SV225: $i,SV2216: $i,SV850: $i] :
( ( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV850 @ SV2216 @ SV225 ) @ SV2455 @ SV225 )
| ~ ( c_lessequals @ SV850 @ SV2455 @ SV225 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV225 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5293]) ).
thf(5777,plain,
! [SV2456: $i,SV226: $i,SV2217: $i,SV851: $i] :
( ( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV851 @ SV2217 @ SV226 ) @ SV2456 @ SV226 )
| ~ ( c_lessequals @ SV2217 @ SV2456 @ SV226 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV226 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5294]) ).
thf(5778,plain,
! [SV227: $i,SV2218: $i,SV852: $i] :
( ( ( c_lessequals @ SV852 @ SV2218 @ SV227 )
= $true )
| ( ( ! [SY7184: $i] :
~ ( c_lessequals @ SV852 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2218 @ SY7184 @ SV227 ) @ SV227 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5295]) ).
thf(5779,plain,
! [SV228: $i,SV2219: $i,SV853: $i] :
( ( ( c_lessequals @ SV853 @ SV2219 @ SV228 )
= $true )
| ( ( ! [SY7185: $i] :
~ ( c_lessequals @ SV853 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SY7185 @ SV2219 @ SV228 ) @ SV228 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV228 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5296]) ).
thf(5780,plain,
! [SV2457: $i,SV2225: $i,SV1391: $i,SV858: $i,SV237: $i] :
( ( ( ( c_Fun_Ofun__upd @ SV237 @ SV858 @ SV1391 @ SV2225 @ SV2457 )
!= SV237 )
= $true )
| ( ( ( hAPP @ SV237 @ SV858 )
= SV1391 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5302]) ).
thf(5781,plain,
! [SV1866: $i,SV1392: $i,SV859: $i,SV2458: $i,SV238: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV238 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2458 @ SV859 @ ( tc_fun @ SV1392 @ tc_bool ) ) @ SV1392 @ SV1866 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV238 @ SV859 @ SV1392 @ SV1866 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5303]) ).
thf(5782,plain,
! [SV1867: $i,SV1393: $i,SV2459: $i,SV860: $i,SV239: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV239 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV860 @ SV2459 @ ( tc_fun @ SV1393 @ tc_bool ) ) @ SV1393 @ SV1867 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV239 @ SV860 @ SV1393 @ SV1867 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5304]) ).
thf(5783,plain,
! [SV1394: $i,SV1868: $i,SV861: $i,SV240: $i] :
( ( ( c_lessequals @ SV240 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV861 @ SV1868 @ ( tc_fun @ SV1394 @ tc_bool ) ) @ ( tc_fun @ SV1394 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV240 @ SV861 @ ( tc_fun @ SV1394 @ tc_bool ) ) @ SV1868 @ ( tc_fun @ SV1394 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5305]) ).
thf(5784,plain,
! [SV1395: $i,SV1869: $i,SV862: $i,SV241: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV241 @ SV862 @ ( tc_fun @ SV1869 @ tc_bool ) ) @ SV1395 @ ( tc_fun @ SV1869 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV241 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV862 @ SV1395 @ ( tc_fun @ SV1869 @ tc_bool ) ) @ ( tc_fun @ SV1869 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5306]) ).
thf(5785,plain,
! [SV242: $i,SV2226: $i,SV863: $i] :
( ( ( ! [SY7187: $i] : ( c_HOL_Oord__class_Oless @ SV863 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2226 @ SY7187 @ SV242 ) @ SV242 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV863 @ SV2226 @ SV242 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV242 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5307]) ).
thf(5786,plain,
! [SV243: $i,SV2460: $i,SV2227: $i,SV864: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ SV864 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2227 @ SV2460 @ SV243 ) @ SV243 )
| ~ ( c_HOL_Oord__class_Oless @ SV864 @ SV2460 @ SV243 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV243 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5308]) ).
thf(5787,plain,
! [SV244: $i,SV2461: $i,SV1396: $i,SV865: $i] :
( ( ( ( c_lessequals @ ( hAPP @ SV865 @ SV1396 ) @ ( hAPP @ SV2461 @ SV1396 ) @ SV244 )
| ! [SY7332: $i] :
~ ( c_lessequals @ SV865 @ SV2461 @ ( tc_fun @ SY7332 @ SV244 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV244 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5309]) ).
thf(5788,plain,
! [SV1397: $i,SV2228: $i,SV866: $i,SV245: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV245 ) @ SV866 ) @ SV2228 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2228 @ SV1397 @ ( tc_fun @ SV245 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV245 ) @ SV866 ) @ SV1397 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5310]) ).
thf(5789,plain,
! [SV867: $i,SV246: $i,SV1398: $i,SV2229: $i] :
( ( ( ~ ( c_lessequals @ SV2229 @ SV1398 @ ( tc_fun @ SV246 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV246 ) @ SV867 ) @ SV2229 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV246 ) @ SV867 ) @ SV1398 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5311]) ).
thf(5790,plain,
! [SV1399: $i,SV2230: $i,SV868: $i,SV247: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV247 ) @ SV868 ) @ SV2230 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2230 @ SV1399 @ ( tc_fun @ SV247 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV247 ) @ SV868 ) @ SV1399 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5312]) ).
thf(5791,plain,
! [SV1400: $i,SV2231: $i,SV869: $i,SV248: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV248 ) @ SV869 ) @ SV2231 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2231 @ SV1400 @ ( tc_fun @ SV248 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV248 ) @ SV869 ) @ SV1400 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5313]) ).
thf(5792,plain,
! [SV2232: $i,SV1401: $i,SV870: $i,SV249: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV249 ) @ SV870 ) @ SV1401 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV249 ) @ SV870 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1401 @ SV2232 @ ( tc_fun @ SV249 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5314]) ).
thf(5793,plain,
! [SV1402: $i,SV1870: $i,SV871: $i,SV250: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV250 ) @ SV871 ) @ SV1870 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV250 ) @ SV871 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1402 @ SV1870 @ ( tc_fun @ SV250 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5315]) ).
thf(5794,plain,
! [SV1403: $i,SV2233: $i,SV872: $i,SV251: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV251 ) @ SV872 ) @ SV2233 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV251 ) @ SV872 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2233 @ SV1403 @ ( tc_fun @ SV251 @ tc_bool ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV251 ) @ SV872 ) @ SV1403 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5316]) ).
thf(5795,plain,
! [SV873: $i,SV1404: $i,SV253: $i,SV2462: $i,SV1871: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1871 @ SV2462 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV253 ) @ SV2462 ) @ SV1404 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV253 ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV873 @ SV1404 @ SV1871 @ SV253 ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV873 @ SV1404 @ ( tc_fun @ SV253 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5317]) ).
thf(5796,plain,
! [SV1405: $i,SV874: $i,SV254: $i,SV2463: $i,SV1872: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1872 @ SV2463 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV254 ) @ SV2463 ) @ SV874 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV254 ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV874 @ SV1405 @ SV1872 @ SV254 ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV874 @ SV1405 @ ( tc_fun @ SV254 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5318]) ).
thf(5797,plain,
! [SV875: $i,SV255: $i,SV1406: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1406 ) @ SV255 ) @ SV875 ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV875 @ SV1406 ) )
= $true )
| ( ( ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ SV255 @ SV875 @ SV1406 ) @ SV1406 )
= ( c_Finite__Set_Ocard @ SV875 @ SV1406 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5319]) ).
thf(5798,plain,
! [SV2464: $i,SV2234: $i,SV1874: $i,SV1408: $i,SV877: $i,SV257: $i] :
( ( ( c_Fun_Oinj__on @ ( c_Fun_Ofun__upd @ SV257 @ SV877 @ SV1408 @ SV1874 @ SV2234 ) @ SV2464 @ SV1874 @ SV2234 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2234 ) @ SV1408 ) @ ( c_Set_Oimage @ SV257 @ SV2464 @ SV1874 @ SV2234 ) ) )
| ~ ( c_Fun_Oinj__on @ SV257 @ SV2464 @ SV1874 @ SV2234 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5321]) ).
thf(5799,plain,
! [SV879: $i,SV1875: $i,SV1410: $i,SV259: $i] :
( ( ( ~ ( c_lessequals @ SV259 @ SV1410 @ ( tc_fun @ SV1875 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV259 @ ( c_Set_Oinsert @ SV879 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1875 @ tc_bool ) ) @ SV1875 ) @ ( tc_fun @ SV1875 @ tc_bool ) ) @ SV1410 @ ( tc_fun @ SV1875 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV259 @ ( c_Set_Oinsert @ SV879 @ SV1410 @ SV1875 ) @ ( tc_fun @ SV1875 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5322]) ).
thf(5800,plain,
! [SV1876: $i,SV1411: $i,SV880: $i,SV260: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV260 @ SV880 @ SV1411 @ SV1876 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV880 @ SV1411 ) )
= $true )
| ( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ SV260 @ SV880 @ SV1411 @ SV1876 ) @ SV1876 )
= ( c_Finite__Set_Ocard @ SV880 @ SV1411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5323]) ).
thf(5801,plain,
! [SV1877: $i,SV1412: $i,SV881: $i,SV261: $i] :
( ( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ SV261 @ SV881 @ SV1412 @ SV1877 ) @ SV1877 )
= ( c_Finite__Set_Ocard @ SV881 @ SV1412 ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV881 @ SV1412 )
| ( c_Fun_Oinj__on @ SV261 @ SV881 @ SV1412 @ SV1877 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5324]) ).
thf(5802,plain,
! [SV1413: $i,SV882: $i,SV262: $i] :
( ( ( c_Fun_Oinj__on @ SV262 @ SV882 @ SV1413 @ SV1413 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Set_Oimage @ SV262 @ SV882 @ SV1413 @ SV1413 ) @ SV882 @ ( tc_fun @ SV1413 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV882 @ SV1413 ) )
= $true )
| ( ( ( c_Set_Oimage @ SV262 @ SV882 @ SV1413 @ SV1413 )
= SV882 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5325]) ).
thf(5803,plain,
! [SV1414: $i,SV263: $i,SV883: $i] :
( ( ( c_lessequals @ SV883 @ ( c_Set_Oimage @ SV263 @ SV883 @ SV1414 @ SV1414 ) @ ( tc_fun @ SV1414 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV883 @ SV1414 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV263 @ SV883 @ SV1414 @ SV1414 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5326]) ).
thf(5804,plain,
! [SV885: $i,SV1879: $i,SV1416: $i,SV265: $i] :
( ( ( ~ ( c_lessequals @ SV265 @ SV1416 @ ( tc_fun @ SV1879 @ tc_bool ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1879 ) @ SV885 ) @ SV265 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV265 @ SV1416 @ ( tc_fun @ SV1879 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV265 @ ( c_Set_Oinsert @ SV885 @ SV1416 @ SV1879 ) @ ( tc_fun @ SV1879 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5328]) ).
thf(5805,plain,
! [SV886: $i,SV1880: $i,SV1417: $i,SV266: $i] :
( ( ( ~ ( c_lessequals @ SV266 @ SV1417 @ ( tc_fun @ SV1880 @ tc_bool ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1880 ) @ SV886 ) @ SV266 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1880 ) @ SV886 ) @ SV1417 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV266 @ ( c_Set_Oinsert @ SV886 @ SV1417 @ SV1880 ) @ ( tc_fun @ SV1880 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5329]) ).
thf(5806,plain,
! [SV887: $i,SV267: $i,SV2235: $i,SV1418: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1418 ) @ SV2235 ) @ SV267 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1418 ) @ SV2235 ) @ SV887 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV267 @ ( c_Set_Oinsert @ SV2235 @ SV887 @ SV1418 ) @ ( tc_fun @ SV1418 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV267 @ SV887 @ ( tc_fun @ SV1418 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5330]) ).
thf(5807,plain,
! [SV2236: $i,SV1881: $i,SV1419: $i,SV888: $i,SV268: $i] :
( ( ( ( c_Set_Oimage @ SV268 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV888 @ SV1419 @ ( tc_fun @ SV1881 @ tc_bool ) ) @ SV1881 @ SV2236 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV268 @ SV888 @ SV1881 @ SV2236 ) @ ( c_Set_Oimage @ SV268 @ SV1419 @ SV1881 @ SV2236 ) @ ( tc_fun @ SV2236 @ tc_bool ) ) )
= $true )
| ( ( ! [SY7190: $i] :
( ~ ( c_lessequals @ SV1419 @ SY7190 @ ( tc_fun @ SV1881 @ tc_bool ) )
| ~ ( c_lessequals @ SV888 @ SY7190 @ ( tc_fun @ SV1881 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV268 @ SY7190 @ SV1881 @ SV2236 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5331]) ).
thf(5808,plain,
! [SV2238: $i,SV1883: $i,SV1421: $i,SV890: $i,SV270: $i] :
( ( ( ( c_Set_Oimage @ SV270 @ ( c_HOL_Ominus__class_Ominus @ SV890 @ SV1421 @ ( tc_fun @ SV1883 @ tc_bool ) ) @ SV1883 @ SV2238 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV270 @ SV890 @ SV1883 @ SV2238 ) @ ( c_Set_Oimage @ SV270 @ SV1421 @ SV1883 @ SV2238 ) @ ( tc_fun @ SV2238 @ tc_bool ) ) )
= $true )
| ( ( ! [SY7191: $i] :
( ~ ( c_lessequals @ SV1421 @ SY7191 @ ( tc_fun @ SV1883 @ tc_bool ) )
| ~ ( c_lessequals @ SV890 @ SY7191 @ ( tc_fun @ SV1883 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV270 @ SY7191 @ SV1883 @ SV2238 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5333]) ).
thf(5809,plain,
! [SV2239: $i,SV1884: $i,SV1422: $i,SV891: $i,SV271: $i] :
( ( ( ( c_Map_Odom @ ( c_Fun_Ofun__upd @ SV271 @ SV891 @ SV1422 @ SV1884 @ ( tc_Option_Ooption @ SV2239 ) ) @ SV1884 @ SV2239 )
= ( c_Set_Oinsert @ SV891 @ ( c_Map_Odom @ SV271 @ SV1884 @ SV2239 ) @ SV1884 ) )
= $true )
| ( ( SV1422
= ( c_Option_Ooption_ONone @ SV2239 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5334]) ).
thf(5810,plain,
! [SV2240: $i,SV1885: $i,SV1423: $i,SV892: $i,SV272: $i] :
( ( ( ! [SY7192: $i] : ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ SV272 @ SV892 @ ( c_Option_Ooption_ONone @ SV1423 ) @ SV1885 @ ( tc_Option_Ooption @ SV1423 ) ) @ ( c_Fun_Ofun__upd @ SV2240 @ SV892 @ ( c_Option_Ooption_OSome @ SY7192 @ SV1423 ) @ SV1885 @ ( tc_Option_Ooption @ SV1423 ) ) @ SV1885 @ SV1423 ) )
= $true )
| ( ( ~ ( c_Map_Omap__le @ SV272 @ SV2240 @ SV1885 @ SV1423 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5335]) ).
thf(5811,plain,
! [SV1424: $i,SV273: $i,SV893: $i,SV1886: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1886 ) @ SV893 ) @ SV273 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV273 @ ( c_Set_Oinsert @ SV893 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1886 @ tc_bool ) ) @ SV1886 ) @ ( tc_fun @ SV1886 @ tc_bool ) ) @ SV1424 @ ( tc_fun @ SV1886 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1886 ) @ SV893 ) @ SV1424 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV273 @ ( c_Set_Oinsert @ SV893 @ SV1424 @ SV1886 ) @ ( tc_fun @ SV1886 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5336]) ).
thf(5812,plain,
! [SV2241: $i,SV1888: $i,SV1428: $i,SV898: $i,SV278: $i] :
( ( ( c_Fun_Oinj__on @ SV278 @ ( c_HOL_Ominus__class_Ominus @ SV898 @ SV1428 @ ( tc_fun @ SV1888 @ tc_bool ) ) @ SV1888 @ SV2241 )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV278 @ SV898 @ SV1888 @ SV2241 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5339]) ).
thf(5813,plain,
! [SV1889: $i,SV1429: $i,SV899: $i,SV279: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV279 @ tc_bool ) )
= ( c_Set_Oimage @ SV899 @ SV1429 @ SV1889 @ SV279 ) )
= $false )
| ( ( SV1429
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1889 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5340]) ).
thf(5814,plain,
! [SV2242: $i,SV1890: $i,SV1430: $i,SV900: $i,SV280: $i] :
( ( ( c_Com_Ocom_OWhile @ SV280 @ SV900 )
= ( c_Com_Ocom_OLocal @ SV1430 @ SV1890 @ SV2242 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5341]) ).
thf(5815,plain,
! [SV1433: $i,SV283: $i,SV903: $i,SV1892: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1892 ) @ SV903 ) @ SV283 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV283 @ ( c_Set_Oinsert @ SV903 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1892 @ tc_bool ) ) @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) ) @ SV1433 @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV283 @ SV1433 @ ( tc_fun @ SV1892 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV283 @ ( c_Set_Oinsert @ SV903 @ SV1433 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5343]) ).
thf(5816,plain,
! [SV1893: $i,SV1435: $i,SV906: $i,SV286: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV286 @ SV906 )
= ( c_Com_Ocom_OSemi @ SV1435 @ SV1893 ) )
= $false )
| ( ( SV906 = SV1893 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5344]) ).
thf(5817,plain,
! [SV2244: $i,SV1436: $i,SV907: $i,SV287: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV287 @ SV907 )
= ( c_Com_Ocom_OSemi @ SV1436 @ SV2244 ) )
= $false )
| ( ( SV287 = SV1436 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5345]) ).
thf(5818,plain,
! [SV2245: $i,SV1897: $i,SV1440: $i,SV911: $i,SV291: $i] :
( ( ( c_Com_Ocom_OSemi @ SV291 @ SV911 )
= ( c_Com_Ocom_OCond @ SV1440 @ SV1897 @ SV2245 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5347]) ).
thf(5819,plain,
! [SV912: $i,SV1898: $i,SV292: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV292 @ SV1898 @ ( tc_fun @ SV912 @ tc_bool ) ) @ SV912 )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1898 @ SV912 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV292 @ SV912 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5348]) ).
thf(5820,plain,
! [SV913: $i,SV1441: $i,SV293: $i] :
( ( ( c_Finite__Set_Ofinite @ SV293 @ SV1441 )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV913 @ SV1441 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV293 @ SV913 @ ( tc_fun @ SV1441 @ tc_bool ) ) @ SV1441 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5349]) ).
thf(5821,plain,
! [SV2246: $i,SV1899: $i,SV1443: $i,SV915: $i,SV295: $i] :
( ( ( c_Com_Ocom_OSemi @ SV295 @ SV915 )
= ( c_Com_Ocom_OLocal @ SV1443 @ SV1899 @ SV2246 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5350]) ).
thf(5822,plain,
! [SV918: $i,SV1902: $i,SV1446: $i,SV298: $i,SV2465: $i] :
( ( ( ~ ( c_Map_Omap__le @ ( c_Map_Omap__add @ SV2465 @ SV298 @ SV1446 @ SV1902 ) @ SV918 @ SV1446 @ SV1902 ) )
= $true )
| ( ( c_Map_Omap__le @ SV298 @ SV918 @ SV1446 @ SV1902 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5351]) ).
thf(5823,plain,
! [SV1448: $i,SV300: $i,SV2466: $i,SV920: $i,SV2247: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2247 ) @ SV920 ) @ SV2466 ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV2466 @ SV300 @ SV2247 @ ( tc_fun @ SV1448 @ tc_bool ) ) @ SV1448 )
| ~ ( c_Finite__Set_Ofinite @ SV2466 @ SV2247 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ SV300 @ SV920 ) @ SV1448 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5352]) ).
thf(5824,plain,
! [SV302: $i,SV1903: $i,SV1450: $i,SV922: $i,SV2467: $i] :
( ( ( ~ ( c_Map_Omap__le @ SV2467 @ SV922 @ SV1450 @ SV1903 )
| ~ ( c_Map_Omap__le @ SV302 @ SV2467 @ SV1450 @ SV1903 ) )
= $true )
| ( ( c_Map_Omap__le @ SV302 @ SV922 @ SV1450 @ SV1903 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5353]) ).
thf(5825,plain,
! [SV2248: $i,SV1904: $i,SV1451: $i,SV923: $i,SV303: $i] :
( ( ( c_Com_Ocom_OLocal @ SV303 @ SV923 @ SV1451 )
= ( c_Com_Ocom_OAss @ SV1904 @ SV2248 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5354]) ).
thf(5826,plain,
! [SV924: $i,SV2468: $i,SV304: $i,SV1905: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1905 @ SV304 @ SV2468 ) @ SV924 ) ) )
= $true )
| ( ( SV1905 = SV924 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV304 @ SV924 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5355]) ).
thf(5827,plain,
! [SV1906: $i,SV1452: $i,SV925: $i,SV305: $i] :
( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV305 @ SV925 @ SV1452 @ ( tc_fun @ SV1906 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1906 @ tc_bool ) ) )
= $false )
| ( ( ! [SY6896: $i] :
( ( ( hAPP @ SV925 @ SY6896 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1906 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1452 ) @ SY6896 ) @ SV305 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5356]) ).
thf(5828,plain,
! [SV2249: $i,SV1907: $i,SV1454: $i,SV927: $i,SV307: $i] :
( ( ( c_Com_Ocom_OCond @ SV307 @ SV927 @ SV1454 )
= ( c_Com_Ocom_OWhile @ SV1907 @ SV2249 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5357]) ).
thf(5829,plain,
! [SV2469: $i,SV2250: $i,SV1908: $i,SV1455: $i,SV928: $i,SV308: $i] :
( ( ( c_Com_Ocom_OCond @ SV308 @ SV928 @ SV1455 )
!= ( c_Com_Ocom_OLocal @ SV1908 @ SV2250 @ SV2469 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5358]) ).
thf(5830,plain,
! [SV2251: $i,SV1912: $i,SV1457: $i,SV933: $i,SV316: $i] :
( ( ( c_Com_Ocom_OCond @ SV316 @ SV933 @ SV1457 )
= ( c_Com_Ocom_OSemi @ SV1912 @ SV2251 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5361]) ).
thf(5831,plain,
! [SV934: $i,SV317: $i] :
( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV317 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ SV317 ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate ) )
= $true )
| ( ( ~ c_Hoare__Mirabelle_Ostate__not__singleton ) = $true )
| ( ( c_Com_OWT @ SV934 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV317 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ SV934 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5362]) ).
thf(5832,plain,
! [SV2470: $i,SV2252: $i,SV1913: $i,SV1458: $i,SV935: $i,SV318: $i] :
( ( ! [SY7333: $i,SY7334: $i,SY7335: $i] :
( ( ( hAPP @ SV318 @ ( c_Set_Oinsert @ SV935 @ ( c_Set_Oinsert @ SV1458 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1913 @ tc_bool ) ) @ SV1913 ) @ SV1913 ) )
= ( hAPP @ ( hAPP @ SV2252 @ SV935 ) @ SV1458 ) )
| ! [SY7336: $i,SY7337: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2470 @ SV318 @ SY7333 @ SY7334 @ SY7335 @ SV2252 @ SY7336 @ SY7337 @ SV1913 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5363]) ).
thf(5833,plain,
! [SV2471: $i,SV2253: $i,SV1914: $i,SV1459: $i,SV936: $i,SV319: $i] :
( ( ! [SY7338: $i,SY7339: $i,SY7340: $i] :
( ( ( hAPP @ SV319 @ ( c_Set_Oinsert @ SV936 @ ( c_Set_Oinsert @ SV1459 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1914 @ tc_bool ) ) @ SV1914 ) @ SV1914 ) )
= ( hAPP @ ( hAPP @ SV2253 @ SV936 ) @ SV1459 ) )
| ! [SY7341: $i,SY7342: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV319 @ SV2471 @ SY7338 @ SY7339 @ SV2253 @ SY7340 @ SY7341 @ SY7342 @ SV1914 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5364]) ).
thf(5834,plain,
! [SV2472: $i,SV2254: $i,SV1915: $i,SV1460: $i,SV937: $i,SV320: $i] :
( ( ( ( c_Com_Ocom_OCond @ SV320 @ SV937 @ SV1460 )
!= ( c_Com_Ocom_OCond @ SV1915 @ SV2254 @ SV2472 ) )
| ( SV1460 = SV2472 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5365]) ).
thf(5835,plain,
! [SV2255: $i,SV1916: $i,SV1461: $i,SV938: $i,SV321: $i] :
( ( ( ! [SY7208: $i] :
( ( c_Com_Ocom_OCond @ SV321 @ SV938 @ SV1461 )
!= ( c_Com_Ocom_OCond @ SV1916 @ SV2255 @ SY7208 ) ) )
= $true )
| ( ( SV938 = SV2255 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5366]) ).
thf(5836,plain,
! [SV2473: $i,SV1917: $i,SV1462: $i,SV939: $i,SV322: $i] :
( ( ( ! [SY7343: $i] :
( ( c_Com_Ocom_OCond @ SV322 @ SV939 @ SV1462 )
!= ( c_Com_Ocom_OCond @ SV1917 @ SV2473 @ SY7343 ) ) )
= $true )
| ( ( SV322 = SV1917 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5367]) ).
thf(5837,plain,
! [SV2257: $i,SV1920: $i,SV1466: $i,SV947: $i,SV330: $i] :
( ( ( c_Com_Ocom_OAss @ SV330 @ SV947 )
= ( c_Com_Ocom_OLocal @ SV1466 @ SV1920 @ SV2257 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5371]) ).
thf(5838,plain,
! [SV2474: $i,SV334: $i,SV2258: $i,SV951: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV951 @ SV2258 @ SV334 ) @ SV2474 @ SV334 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV951 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2258 @ SV2474 @ SV334 ) @ SV334 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV334 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5374]) ).
thf(5839,plain,
! [SV335: $i,SV2475: $i,SV2259: $i,SV952: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV952 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2259 @ SV2475 @ SV335 ) @ SV335 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV2259 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV952 @ SV2475 @ SV335 ) @ SV335 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV335 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5375]) ).
thf(5840,plain,
! [SV336: $i,SV2476: $i,SV2260: $i,SV953: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV953 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2260 @ SV2476 @ SV336 ) @ SV336 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV2260 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV953 @ SV2476 @ SV336 ) @ SV336 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV336 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5376]) ).
thf(5841,plain,
! [SV2477: $i,SV337: $i,SV2261: $i,SV954: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV954 @ SV2261 @ SV337 ) @ SV2477 @ SV337 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ SV954 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2261 @ SV2477 @ SV337 ) @ SV337 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV337 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5377]) ).
thf(5842,plain,
! [SV2262: $i,SV1925: $i,SV1471: $i,SV957: $i,SV340: $i] :
( ( ( c_Com_Ocom_OLocal @ SV340 @ SV957 @ SV1471 )
= ( c_Com_Ocom_OWhile @ SV1925 @ SV2262 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5378]) ).
thf(5843,plain,
! [SV2263: $i,SV1926: $i,SV1472: $i,SV958: $i,SV341: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV341 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV958 @ ( c_Com_Ocom_OBODY @ SV1472 ) @ SV1926 @ SV2263 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2263 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2263 ) ) @ SV2263 )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV341 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV958 @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SV1472 ) @ tc_Com_Ocom ) @ SV1926 @ SV2263 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2263 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2263 ) ) @ SV2263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5379]) ).
thf(5844,plain,
! [SV2264: $i,SV1927: $i,SV1473: $i,SV959: $i,SV342: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV342 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV959 @ ( c_Com_Ocom_OBODY @ SV1473 ) @ SV1927 @ SV2264 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2264 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2264 ) ) @ SV2264 )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV959 @ ( c_Com_Ocom_OBODY @ SV1473 ) @ SV1927 @ SV2264 ) @ SV342 @ ( tc_Hoare__Mirabelle_Otriple @ SV2264 ) ) @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV959 @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SV1473 ) @ tc_Com_Ocom ) @ SV1927 @ SV2264 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2264 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2264 ) ) @ SV2264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5380]) ).
thf(5845,plain,
! [SV343: $i,SV2478: $i,SV1474: $i,SV960: $i] :
( ( ( ! [SY7344: $i] :
( ( ( c_Finite__Set_Osetsum @ SV960 @ ( c_HOL_Ominus__class_Ominus @ SV1474 @ ( c_Set_Oinsert @ SV2478 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY7344 @ tc_bool ) ) @ SY7344 ) @ ( tc_fun @ SY7344 @ tc_bool ) ) @ SY7344 @ SV343 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV960 @ SV1474 @ SY7344 @ SV343 ) @ ( hAPP @ SV960 @ SV2478 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7344 ) @ SV2478 ) @ SV1474 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1474 @ SY7344 ) ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV343 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5381]) ).
thf(5846,plain,
! [SV344: $i,SV2479: $i,SV1475: $i,SV961: $i] :
( ( ( ! [SY7345: $i] :
( ( ( c_Finite__Set_Osetsum @ SV961 @ ( c_HOL_Ominus__class_Ominus @ SV1475 @ ( c_Set_Oinsert @ SV2479 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY7345 @ tc_bool ) ) @ SY7345 ) @ ( tc_fun @ SY7345 @ tc_bool ) ) @ SY7345 @ SV344 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV961 @ SV1475 @ SY7345 @ SV344 ) @ ( hAPP @ SV961 @ SV2479 ) @ SV344 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7345 ) @ SV2479 ) @ SV1475 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1475 @ SY7345 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV344 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5382]) ).
thf(5847,plain,
! [SV2265: $i,SV1929: $i,SV1477: $i,SV963: $i,SV347: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV347 @ ( c_HOL_Ominus__class_Ominus @ SV963 @ SV1477 @ ( tc_fun @ SV1929 @ tc_bool ) ) @ SV1929 @ SV2265 ) @ ( c_Set_Oimage @ SV347 @ ( c_HOL_Ominus__class_Ominus @ SV1477 @ SV963 @ ( tc_fun @ SV1929 @ tc_bool ) ) @ SV1929 @ SV2265 ) @ ( tc_fun @ SV2265 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2265 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV347 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV963 @ SV1477 @ ( tc_fun @ SV1929 @ tc_bool ) ) @ SV1929 @ SV2265 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5383]) ).
thf(5848,plain,
! [SV2266: $i,SV1930: $i,SV1478: $i,SV964: $i,SV348: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV348 @ ( c_HOL_Ominus__class_Ominus @ SV964 @ SV1478 @ ( tc_fun @ SV1930 @ tc_bool ) ) @ SV1930 @ SV2266 ) @ ( c_Set_Oimage @ SV348 @ ( c_HOL_Ominus__class_Ominus @ SV1478 @ SV964 @ ( tc_fun @ SV1930 @ tc_bool ) ) @ SV1930 @ SV2266 ) @ ( tc_fun @ SV2266 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2266 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV348 @ SV1478 @ SV1930 @ SV2266 )
| ~ ( c_Fun_Oinj__on @ SV348 @ SV964 @ SV1930 @ SV2266 )
| ( c_Fun_Oinj__on @ SV348 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV964 @ SV1478 @ ( tc_fun @ SV1930 @ tc_bool ) ) @ SV1930 @ SV2266 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5384]) ).
thf(5849,plain,
! [SV965: $i,SV1931: $i,SV1479: $i,SV349: $i] :
( ( ( ~ ( c_lessequals @ SV349 @ SV1479 @ ( tc_fun @ SV1931 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV349 @ ( c_Set_Oinsert @ SV965 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1931 @ tc_bool ) ) @ SV1931 ) @ ( tc_fun @ SV1931 @ tc_bool ) ) @ SV1479 @ ( tc_fun @ SV1931 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1931 ) @ SV965 ) @ SV1479 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV349 @ ( c_Set_Oinsert @ SV965 @ SV1479 @ SV1931 ) @ ( tc_fun @ SV1931 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5385]) ).
thf(5850,plain,
! [SV2480: $i,SV2267: $i,SV1932: $i,SV1480: $i,SV966: $i,SV350: $i] :
( ( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ SV350 @ SV966 @ SV1480 @ SV1932 @ SV2267 ) @ SV2480 @ SV1932 @ SV2267 )
= ( c_Set_Oinsert @ SV1480 @ ( c_Set_Oimage @ SV350 @ ( c_HOL_Ominus__class_Ominus @ SV2480 @ ( c_Set_Oinsert @ SV966 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1932 @ tc_bool ) ) @ SV1932 ) @ ( tc_fun @ SV1932 @ tc_bool ) ) @ SV1932 @ SV2267 ) @ SV2267 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1932 ) @ SV966 ) @ SV2480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5386]) ).
thf(5851,plain,
! [SV351: $i,SV2481: $i,SV1481: $i,SV967: $i] :
( ( ( ! [SY7346: $i] :
( ( ( c_Finite__Set_Osetsum @ SV967 @ ( c_HOL_Ominus__class_Ominus @ SV1481 @ ( c_Set_Oinsert @ SV2481 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY7346 @ tc_bool ) ) @ SY7346 ) @ ( tc_fun @ SY7346 @ tc_bool ) ) @ SY7346 @ SV351 )
= ( c_Finite__Set_Osetsum @ SV967 @ SV1481 @ SY7346 @ SV351 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7346 ) @ SV2481 ) @ SV1481 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1481 @ SY7346 ) ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV351 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5387]) ).
thf(5852,plain,
! [SV968: $i,SV1482: $i,SV352: $i] :
( ( ( c_Finite__Set_Ofinite @ SV352 @ SV1482 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1482 ) @ SV968 ) @ SV352 ) )
= $true )
| ( ( ( c_Finite__Set_Ocard @ ( c_HOL_Ominus__class_Ominus @ SV352 @ ( c_Set_Oinsert @ SV968 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1482 @ tc_bool ) ) @ SV1482 ) @ ( tc_fun @ SV1482 @ tc_bool ) ) @ SV1482 )
= ( c_Finite__Set_Ocard @ SV352 @ SV1482 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5388]) ).
thf(5853,plain,
! [SV2482: $i,SV2268: $i,SV1933: $i,SV1483: $i,SV969: $i,SV353: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV969 @ ( c_Com_Ocom_OSemi @ SV1483 @ SV1933 ) @ SV2268 @ SV2482 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) ) @ SV2482 )
| ! [SY7347: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY7347 @ SV1933 @ SV2268 @ SV2482 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) ) @ SV2482 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV969 @ SV1483 @ SY7347 @ SV2482 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) ) @ SV2482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5389]) ).
thf(5854,plain,
! [SV2483: $i,SV2269: $i,SV1934: $i,SV1485: $i,SV971: $i,SV355: $i] :
( ( ( ( c_Map_Omap__add @ ( c_Fun_Ofun__upd @ SV355 @ SV971 @ ( c_Option_Ooption_OSome @ SV1485 @ SV1934 ) @ SV2269 @ ( tc_Option_Ooption @ SV1934 ) ) @ SV2483 @ SV2269 @ SV1934 )
= ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ SV355 @ SV2483 @ SV2269 @ SV1934 ) @ SV971 @ ( c_Option_Ooption_OSome @ SV1485 @ SV1934 ) @ SV2269 @ ( tc_Option_Ooption @ SV1934 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2269 ) @ SV971 ) @ ( c_Map_Odom @ SV2483 @ SV2269 @ SV1934 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5390]) ).
thf(5855,plain,
! [SV972: $i,SV1935: $i,SV1486: $i,SV356: $i] :
( ( ( ~ ( c_lessequals @ SV356 @ SV1486 @ ( tc_fun @ SV1935 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV356 @ ( c_Set_Oinsert @ SV972 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1935 @ tc_bool ) ) @ SV1935 ) @ ( tc_fun @ SV1935 @ tc_bool ) ) @ SV1486 @ ( tc_fun @ SV1935 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV356 @ SV1486 @ ( tc_fun @ SV1935 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV356 @ ( c_Set_Oinsert @ SV972 @ SV1486 @ SV1935 ) @ ( tc_fun @ SV1935 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5391]) ).
thf(5856,plain,
! [SV2484: $i,SV2270: $i,SV1937: $i,SV1488: $i,SV974: $i,SV358: $i] :
( ( ! [SY7348: $i] :
( ( c_Nitpick_Ofold__graph_H @ SV358 @ SV974 @ SV1488 @ ( hAPP @ ( hAPP @ SV358 @ SV1937 ) @ SV2270 ) @ SV2484 @ SY7348 )
| ~ ( c_Nitpick_Ofold__graph_H @ SV358 @ SV974 @ ( c_HOL_Ominus__class_Ominus @ SV1488 @ ( c_Set_Oinsert @ SV1937 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2484 @ tc_bool ) ) @ SV2484 ) @ ( tc_fun @ SV2484 @ tc_bool ) ) @ SV2270 @ SV2484 @ SY7348 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2484 ) @ SV1937 ) @ SV1488 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5392]) ).
thf(5857,plain,
! [SV1938: $i,SV359: $i,SV975: $i,SV1489: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1489 ) @ SV975 ) @ SV359 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV359 @ ( c_Set_Oinsert @ SV975 @ SV1938 @ SV1489 ) @ ( tc_fun @ SV1489 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV359 @ ( c_Set_Oinsert @ SV975 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1489 @ tc_bool ) ) @ SV1489 ) @ ( tc_fun @ SV1489 @ tc_bool ) ) @ SV1938 @ ( tc_fun @ SV1489 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5393]) ).
thf(5858,plain,
! [SV1490: $i,SV360: $i,SV976: $i,SV1939: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1939 ) @ SV976 ) @ SV360 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV360 @ ( c_Set_Oinsert @ SV976 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1939 @ tc_bool ) ) @ SV1939 ) @ ( tc_fun @ SV1939 @ tc_bool ) ) @ SV1490 @ ( tc_fun @ SV1939 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV360 @ ( c_Set_Oinsert @ SV976 @ SV1490 @ SV1939 ) @ ( tc_fun @ SV1939 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5394]) ).
thf(5859,plain,
! [SV1491: $i,SV361: $i,SV977: $i,SV1940: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1940 ) @ SV977 ) @ SV361 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV361 @ ( c_Set_Oinsert @ SV977 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1940 @ tc_bool ) ) @ SV1940 ) @ ( tc_fun @ SV1940 @ tc_bool ) ) @ SV1491 @ ( tc_fun @ SV1940 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV361 @ ( c_Set_Oinsert @ SV977 @ SV1491 @ SV1940 ) @ ( tc_fun @ SV1940 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5395]) ).
thf(5860,plain,
! [SV2485: $i,SV2271: $i,SV1942: $i,SV1493: $i,SV979: $i,SV363: $i] :
( ( ! [SY7349: $i] :
( ( c_Finite__Set_Ofold__graph @ SV363 @ SV979 @ SV1493 @ ( hAPP @ ( hAPP @ SV363 @ SV1942 ) @ SV2271 ) @ SV2485 @ SY7349 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2485 ) @ SV1942 ) @ SV1493 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV363 @ SV979 @ ( c_HOL_Ominus__class_Ominus @ SV1493 @ ( c_Set_Oinsert @ SV1942 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2485 @ tc_bool ) ) @ SV2485 ) @ ( tc_fun @ SV2485 @ tc_bool ) ) @ SV2271 @ SV2485 @ SY7349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5397]) ).
thf(5861,plain,
! [SV980: $i,SV364: $i,SV1943: $i,SV2486: $i,SV1494: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1494 ) @ SV2486 ) @ SV1943 ) ) )
= $true )
| ( ( ( c_Set_Oimage @ ( c_COMBK @ SV364 @ SV980 @ SV1494 ) @ SV1943 @ SV1494 @ SV980 )
= ( c_Set_Oinsert @ SV364 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV980 @ tc_bool ) ) @ SV980 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5398]) ).
thf(5862,plain,
! [SV1944: $i,SV365: $i,SV981: $i,SV1495: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1495 ) @ SV981 ) @ SV365 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1495 ) @ SV981 ) @ SV1944 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV365 @ ( c_Set_Oinsert @ SV981 @ SV1944 @ SV1495 ) @ ( tc_fun @ SV1495 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV365 @ ( c_Set_Oinsert @ SV981 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1495 @ tc_bool ) ) @ SV1495 ) @ ( tc_fun @ SV1495 @ tc_bool ) ) @ SV1944 @ ( tc_fun @ SV1495 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5399]) ).
thf(5863,plain,
! [SV982: $i,SV1496: $i,SV2487: $i,SV366: $i] :
( ( ( ! [SY7350: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ SV366 @ SV2487 @ SV1496 ) @ ( c_Set_Oinsert @ SV982 @ SY7350 @ SV2487 ) @ ( tc_fun @ SV2487 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ SV366 @ SV2487 @ SV1496 ) @ SY7350 @ ( tc_fun @ SV2487 @ tc_bool ) ) ) )
= $true )
| ( ( ( hAPP @ SV366 @ SV982 )
= ( c_Option_Ooption_ONone @ SV1496 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5400]) ).
thf(5864,plain,
! [SV2488: $i,SV2272: $i,SV1946: $i,SV1498: $i,SV985: $i,SV369: $i] :
( ( ( c_Com_Ocom_OLocal @ SV369 @ SV985 @ SV1498 )
!= ( c_Com_Ocom_OCond @ SV1946 @ SV2272 @ SV2488 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5402]) ).
thf(5865,plain,
! [SV986: $i,SV1947: $i,SV370: $i,SV1499: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1499 ) @ SV370 ) @ SV1947 ) )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV370 @ SV986 @ SV1499 ) @ SV1947 @ ( tc_fun @ SV1499 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV986 @ SV1947 @ ( tc_fun @ SV1499 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5403]) ).
thf(5866,plain,
! [SV1948: $i,SV1500: $i,SV987: $i,SV2489: $i,SV371: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV371 @ ( c_Set_Oinsert @ SV2489 @ SV987 @ SV1500 ) @ SV1500 @ SV1948 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV371 @ SV987 @ SV1500 @ SV1948 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5404]) ).
thf(5867,plain,
! [SV375: $i,SV2273: $i,SV991: $i,SV1950: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1950 ) @ SV991 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2273 @ ( c_Collect @ SV375 @ SV1950 ) @ ( tc_fun @ SV1950 @ tc_bool ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV375 @ SV991 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5407]) ).
thf(5868,plain,
! [SV376: $i,SV2274: $i,SV992: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV992 @ SV2274 @ SV376 )
= $true )
| ( ( ! [SY7222: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SY7222 @ SV2274 @ SV376 )
| ~ ( c_HOL_Oord__class_Oless @ SV992 @ SY7222 @ SV376 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV376 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5408]) ).
thf(5869,plain,
! [SV377: $i,SV1503: $i,SV993: $i,SV2275: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2275 @ SV993 @ ( tc_fun @ SV1503 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV377 @ SV2275 @ ( tc_fun @ SV1503 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV377 @ SV993 @ ( tc_fun @ SV1503 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5409]) ).
thf(5870,plain,
! [SV378: $i,SV2276: $i,SV994: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV994 @ SV2276 @ SV378 )
= $true )
| ( ( ! [SY7223: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV994 @ SY7223 @ SV378 )
| ~ ( c_HOL_Oord__class_Oless @ SY7223 @ SV2276 @ SV378 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV378 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5410]) ).
thf(5871,plain,
! [SV2277: $i,SV1951: $i,SV1504: $i,SV995: $i,SV379: $i] :
( ( ( c_Fun_Oinj__on @ SV379 @ ( c_Set_Oinsert @ SV995 @ SV1504 @ SV1951 ) @ SV1951 @ SV2277 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2277 ) @ ( hAPP @ SV379 @ SV995 ) ) @ ( c_Set_Oimage @ SV379 @ ( c_HOL_Ominus__class_Ominus @ SV1504 @ ( c_Set_Oinsert @ SV995 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1951 @ tc_bool ) ) @ SV1951 ) @ ( tc_fun @ SV1951 @ tc_bool ) ) @ SV1951 @ SV2277 ) ) )
| ~ ( c_Fun_Oinj__on @ SV379 @ SV1504 @ SV1951 @ SV2277 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5411]) ).
thf(5872,plain,
! [SV2490: $i,SV2278: $i,SV1954: $i,SV1507: $i,SV998: $i,SV382: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ SV382 @ SV998 @ SV1507 @ SV1954 ) @ SV2278 ) @ SV2490 )
= ( hAPP @ ( hAPP @ SV382 @ SV2490 ) @ SV2278 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5412]) ).
thf(5873,plain,
! [SV1510: $i,SV1955: $i,SV2491: $i,SV1003: $i,SV387: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV387 @ SV1003 ) ) @ SV2491 ) @ SV1955 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1003 ) @ SV1510 ) @ SV2491 ) )
| ~ ( hBOOL @ ( hAPP @ SV387 @ SV1510 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV387 @ SV1003 ) ) @ SV1510 ) @ SV1955 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5413]) ).
thf(5874,plain,
! [SV389: $i,SV2279: $i,SV1005: $i] :
( ( ( ! [SY7225: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV1005 @ SV2279 @ SV389 )
!= ( c_HOL_Ominus__class_Ominus @ SY7225 @ SY7225 @ SV389 ) ) )
= $true )
| ( ( SV1005 = SV2279 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV389 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5414]) ).
thf(5875,plain,
! [SV2492: $i,SV2280: $i,SV390: $i,SV1006: $i] :
( ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1006 @ SV1006 @ SV390 )
!= ( c_HOL_Ominus__class_Ominus @ SV2280 @ SV2492 @ SV390 ) )
| ( SV2280 = SV2492 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV390 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5415]) ).
thf(5876,plain,
! [SV2281: $i,SV1956: $i,SV1513: $i,SV1008: $i,SV392: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV392 @ SV1008 @ SV1513 ) ) @ SV1956 ) @ SV2281 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1008 ) @ SV1956 ) @ SV2281 ) )
| ~ ( hBOOL @ ( hAPP @ SV392 @ SV1956 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5416]) ).
thf(5877,plain,
! [SV393: $i,SV2493: $i,SV1009: $i,SV1514: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1514 ) @ SV1009 ) @ SV2493 ) )
| ! [SY7351: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV393 @ SV1514 @ SY7351 ) ) @ SV1009 ) @ SV2493 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV393 @ SV1009 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5417]) ).
thf(5878,plain,
! [SV1515: $i,SV394: $i,SV1957: $i,SV2494: $i,SV1010: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1010 ) @ SV2494 ) @ SV1957 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV394 ) @ SV1515 ) @ SV2494 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV394 @ SV1010 ) ) @ SV1515 ) @ SV1957 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5418]) ).
thf(5879,plain,
! [SV1958: $i,SV1517: $i,SV1012: $i,SV396: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Map_Odom @ SV396 @ SV1012 @ SV1517 ) @ ( c_Map_Odom @ SV1958 @ SV1012 @ SV1517 ) @ ( tc_fun @ SV1012 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1012 @ tc_bool ) ) )
= $false )
| ( ( ( c_Map_Omap__add @ SV396 @ SV1958 @ SV1012 @ SV1517 )
= ( c_Map_Omap__add @ SV1958 @ SV396 @ SV1012 @ SV1517 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5419]) ).
thf(5880,plain,
! [SV1959: $i,SV1518: $i,SV1013: $i,SV397: $i] :
( ( ( ( hAPP @ SV397 @ SV1013 )
= ( c_Option_Ooption_OSome @ SV1518 @ SV1959 ) )
= $false )
| ( ( ! [SY6952: $i] :
( ( c_Set_Oinsert @ SV1013 @ ( c_Map_Odom @ SV397 @ SY6952 @ SV1959 ) @ SY6952 )
= ( c_Map_Odom @ SV397 @ SY6952 @ SV1959 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5420]) ).
thf(5881,plain,
! [SV2495: $i,SV2284: $i,SV1962: $i,SV1520: $i,SV1015: $i,SV401: $i] :
( ( ! [SY7352: $i,SY7353: $i,SY7354: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV401 @ SV1015 @ ( c_COMBC @ SV1520 @ SV1962 @ SV1962 @ tc_bool ) @ ( c_COMBC @ SV2284 @ SV1962 @ SV1962 @ tc_bool ) @ SV2495 @ SY7352 @ SY7353 @ SY7354 @ SV1962 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1015 @ SV401 @ SV1520 @ SV2284 @ SY7352 @ SV2495 @ SY7354 @ SY7353 @ SV1962 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5423]) ).
thf(5882,plain,
! [SV2496: $i,SV2285: $i,SV1963: $i,SV1524: $i,SV1019: $i,SV405: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ SV405 @ SV1019 @ SV1524 @ SV1963 ) @ SV2285 )
!= ( c_Option_Ooption_OSome @ SV2496 @ SV1963 ) )
| ( ( hAPP @ SV405 @ SV2285 )
= ( c_Option_Ooption_OSome @ SV2496 @ SV1963 ) )
| ( ( hAPP @ SV1019 @ SV2285 )
= ( c_Option_Ooption_OSome @ SV2496 @ SV1963 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5425]) ).
thf(5883,plain,
! [SV1964: $i,SV1525: $i,SV1020: $i,SV406: $i] :
( ( ( ( hAPP @ SV406 @ SV1020 )
= ( c_Option_Ooption_OSome @ SV1525 @ SV1964 ) )
= $false )
| ( ( ! [SY6962: $i] :
( ( ( hAPP @ SY6962 @ SV1020 )
!= ( c_Option_Ooption_ONone @ SV1964 ) )
| ! [SY6963: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SV406 @ SY6962 @ SY6963 @ SV1964 ) @ SV1020 )
= ( c_Option_Ooption_OSome @ SV1525 @ SV1964 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5426]) ).
thf(5884,plain,
! [SV2286: $i,SV1965: $i,SV1526: $i,SV1021: $i,SV407: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ SV407 @ SV1021 @ SV1526 @ SV1965 ) @ SV2286 )
!= ( c_Option_Ooption_ONone @ SV1965 ) )
= $true )
| ( ( ( hAPP @ SV407 @ SV2286 )
= ( c_Option_Ooption_ONone @ SV1965 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5427]) ).
thf(5885,plain,
! [SV2287: $i,SV1966: $i,SV1527: $i,SV1022: $i,SV408: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ SV408 @ SV1022 @ SV1527 @ SV1966 ) @ SV2287 )
!= ( c_Option_Ooption_ONone @ SV1966 ) )
= $true )
| ( ( ( hAPP @ SV1022 @ SV2287 )
= ( c_Option_Ooption_ONone @ SV1966 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5428]) ).
thf(5886,plain,
! [SV1529: $i,SV2288: $i,SV1024: $i,SV410: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ SV1024 @ SV2288 @ ( tc_Hoare__Mirabelle_Otriple @ SV1529 ) ) @ SV1529 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ SV1024 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1529 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1529 ) ) @ SV1529 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5430]) ).
thf(5887,plain,
! [SV1531: $i,SV412: $i,SV1968: $i,SV1026: $i] :
( ( ( hBOOL @ ( hAPP @ SV1026 @ SV1968 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV412 @ SV1026 @ SV1531 ) @ SV1968 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5432]) ).
thf(5888,plain,
! [SV2497: $i,SV1969: $i,SV1532: $i,SV1027: $i,SV413: $i] :
( ( ( ( c_Set_Oinsert @ ( hAPP @ SV413 @ SV1027 ) @ ( c_Set_Oimage @ SV413 @ SV1532 @ SV1969 @ SV2497 ) @ SV2497 )
= ( c_Set_Oimage @ SV413 @ SV1532 @ SV1969 @ SV2497 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1969 ) @ SV1027 ) @ SV1532 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5433]) ).
thf(5889,plain,
! [SV2289: $i,SV1972: $i,SV1535: $i,SV1030: $i,SV416: $i] :
( ( ( c_Com_Ocom_OLocal @ SV416 @ SV1030 @ SV1535 )
= ( c_Com_Ocom_OSemi @ SV1972 @ SV2289 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5436]) ).
thf(5890,plain,
! [SV2290: $i,SV1536: $i,SV1032: $i,SV418: $i] :
( ( ( ( c_Com_Ocom_OWhile @ SV418 @ SV1032 )
= ( c_Com_Ocom_OWhile @ SV1536 @ SV2290 ) )
= $false )
| ( ( SV418 = SV1536 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5437]) ).
thf(5891,plain,
! [SV1973: $i,SV1537: $i,SV1033: $i,SV419: $i] :
( ( ( ( c_Com_Ocom_OWhile @ SV419 @ SV1033 )
= ( c_Com_Ocom_OWhile @ SV1537 @ SV1973 ) )
= $false )
| ( ( SV1033 = SV1973 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5438]) ).
thf(5892,plain,
! [SV2291: $i,SV1974: $i,SV1541: $i,SV1037: $i,SV423: $i] :
( ( ( c_Com_Ocom_OWhile @ SV423 @ SV1037 )
= ( c_Com_Ocom_OCond @ SV1541 @ SV1974 @ SV2291 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5439]) ).
thf(5893,plain,
! [SV2292: $i,SV1542: $i,SV1038: $i,SV425: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV425 ) @ SV1038 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1542 @ ( c_Collect @ SV2292 @ SV425 ) @ ( tc_fun @ SV425 @ tc_bool ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV425 ) @ SV1038 ) @ SV1542 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5440]) ).
thf(5894,plain,
! [SV426: $i,SV1543: $i,SV1039: $i,SV2498: $i] :
( ( ( ( ( hAPP @ SV2498 @ SV1039 )
!= ( c_Option_Ooption_ONone @ SV1543 ) )
| ! [SY7355: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SV426 @ SV2498 @ SY7355 @ SV1543 ) @ SV1039 )
= ( c_Option_Ooption_ONone @ SV1543 ) ) )
= $true )
| ( ( ( hAPP @ SV426 @ SV1039 )
= ( c_Option_Ooption_ONone @ SV1543 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5441]) ).
thf(5895,plain,
! [SV1976: $i,SV1544: $i,SV1040: $i,SV427: $i] :
( ( ( ( hAPP @ SV427 @ SV1040 )
= ( c_Option_Ooption_OSome @ SV1544 @ SV1976 ) )
= $false )
| ( ( ! [SY6969: $i,SY6970: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SY6969 @ SV427 @ SY6970 @ SV1976 ) @ SV1040 )
= ( c_Option_Ooption_OSome @ SV1544 @ SV1976 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5442]) ).
thf(5896,plain,
! [SV1977: $i,SV1545: $i,SV1041: $i,SV428: $i] :
( ( ( ( hAPP @ SV428 @ SV1041 )
= ( c_Option_Ooption_OSome @ SV1545 @ SV1977 ) )
= $false )
| ( ( ! [SY6971: $i,SY6972: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SY6971 @ SV428 @ SY6972 @ SV1977 ) @ SV1041 )
= ( c_Option_Ooption_OSome @ SV1545 @ SV1977 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5443]) ).
thf(5897,plain,
! [SV2293: $i,SV1978: $i,SV1546: $i,SV1042: $i,SV429: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV429 ) @ ( hAPP @ SV1042 @ SV1546 ) ) @ ( c_Set_Oimage @ SV1042 @ ( c_HOL_Ominus__class_Ominus @ SV1978 @ ( c_Set_Oinsert @ SV1546 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2293 @ tc_bool ) ) @ SV2293 ) @ ( tc_fun @ SV2293 @ tc_bool ) ) @ SV2293 @ SV429 ) ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV1042 @ ( c_Set_Oinsert @ SV1546 @ SV1978 @ SV2293 ) @ SV2293 @ SV429 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5444]) ).
thf(5898,plain,
! [SV2294: $i,SV1979: $i,SV1547: $i,SV1043: $i,SV430: $i] :
( ( ( c_Com_Ocom_OCond @ SV430 @ SV1043 @ SV1547 )
= ( c_Com_Ocom_OAss @ SV1979 @ SV2294 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5445]) ).
thf(5899,plain,
! [SV1045: $i,SV2295: $i,SV433: $i,SV1981: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1981 @ SV433 @ ( tc_fun @ SV2295 @ tc_bool ) ) @ SV1045 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV433 @ SV1045 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5447]) ).
thf(5900,plain,
! [SV1046: $i,SV2296: $i,SV1982: $i,SV434: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV434 @ SV1982 @ ( tc_fun @ SV2296 @ tc_bool ) ) @ SV1046 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV434 @ SV1046 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5448]) ).
thf(5901,plain,
! [SV2298: $i,SV1985: $i,SV1554: $i,SV1053: $i,SV441: $i] :
( ( ( c_Map_Omap__le @ ( c_Map_Omap__add @ SV441 @ SV1053 @ SV1554 @ SV1985 ) @ SV2298 @ SV1554 @ SV1985 )
= $true )
| ( ( ~ ( c_Map_Omap__le @ SV441 @ ( c_Map_Omap__add @ SV441 @ SV1053 @ SV1554 @ SV1985 ) @ SV1554 @ SV1985 )
| ~ ( c_Map_Omap__le @ SV1053 @ SV2298 @ SV1554 @ SV1985 )
| ~ ( c_Map_Omap__le @ SV441 @ SV2298 @ SV1554 @ SV1985 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5452]) ).
thf(5902,plain,
! [SV442: $i,SV1054: $i,SV2499: $i,SV1555: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1555 ) @ SV2499 ) @ SV1054 ) ) )
= $true )
| ( ( ! [SY6457: $i] :
( ~ ( hBOOL @ ( hAPP @ SV442 @ SY6457 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1555 ) @ SY6457 ) @ SV1054 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV442 @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1054 @ SV442 @ SV1555 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5453]) ).
thf(5903,plain,
! [SV1556: $i,SV1986: $i,SV1055: $i,SV443: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ SV1055 ) @ SV1986 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ SV1055 ) @ SV1556 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ SV1055 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1556 @ SV1986 @ ( tc_fun @ SV443 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5454]) ).
thf(5904,plain,
! [SV1557: $i,SV1987: $i,SV1056: $i,SV444: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ SV1056 ) @ SV1987 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ SV1056 ) @ SV1557 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ SV1056 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1557 @ SV1987 @ ( tc_fun @ SV444 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5455]) ).
thf(5905,plain,
! [SV445: $i,SV2299: $i,SV1057: $i,SV1558: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1558 ) @ SV1057 ) @ SV2299 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1558 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2299 @ SV445 @ SV1558 ) ) @ SV2299 ) )
| ! [SY7232: $i] :
~ ( hBOOL @ ( hAPP @ SY7232 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2299 @ SY7232 @ SV1558 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV445 @ SV1057 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5456]) ).
thf(5906,plain,
! [SV446: $i,SV2300: $i,SV1058: $i,SV1559: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1559 ) @ SV1058 ) @ SV2300 ) ) )
= $true )
| ( ( ! [SY7233: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1559 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2300 @ SY7233 @ SV1559 ) ) @ SV2300 ) )
| ~ ( hBOOL @ ( hAPP @ SV446 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2300 @ SV446 @ SV1559 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV446 @ SV1058 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5457]) ).
thf(5907,plain,
! [SV447: $i,SV2301: $i,SV1059: $i,SV1560: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1560 ) @ SV1059 ) @ SV2301 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV447 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2301 @ SV447 @ SV1560 ) ) )
| ! [SY7234: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1560 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2301 @ SY7234 @ SV1560 ) ) @ SV2301 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV447 @ SV1059 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5458]) ).
thf(5908,plain,
! [SV448: $i,SV2302: $i,SV1060: $i,SV1561: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1561 ) @ SV1060 ) @ SV2302 ) ) )
= $true )
| ( ( ! [SY7235: $i] :
~ ( hBOOL @ ( hAPP @ SY7235 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2302 @ SY7235 @ SV1561 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1561 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2302 @ SV448 @ SV1561 ) ) @ SV2302 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV448 @ SV1060 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5459]) ).
thf(5909,plain,
! [SV2500: $i,SV2303: $i,SV1988: $i,SV1562: $i,SV1061: $i,SV449: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV449 ) @ SV1061 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV1562 @ SV1988 @ SV2303 @ SV2500 @ SV449 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1988 @ SV1061 ) @ SV2500 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1562 @ SV2303 ) @ SV1061 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5460]) ).
thf(5910,plain,
! [SV1563: $i,SV1989: $i,SV1062: $i,SV450: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV450 ) @ SV1062 ) @ SV1989 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV450 ) @ SV1062 ) @ ( c_Set_Oinsert @ SV1563 @ SV1989 @ SV450 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5461]) ).
thf(5911,plain,
! [SV1564: $i,SV1990: $i,SV1063: $i,SV451: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV451 ) @ SV1063 ) @ SV1990 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV451 ) @ SV1063 ) @ ( c_Set_Oinsert @ SV1564 @ SV1990 @ SV451 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5462]) ).
thf(5912,plain,
! [SV2304: $i,SV1991: $i,SV1565: $i,SV1064: $i,SV452: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV452 ) @ SV1064 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV1565 @ SV1991 @ SV2304 @ SV452 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1565 @ SV1064 ) @ SV2304 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1565 @ SV1991 ) @ SV1064 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5463]) ).
thf(5913,plain,
! [SV1566: $i,SV1065: $i,SV2305: $i,SV453: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV453 ) @ SV2305 ) @ SV1065 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1566 @ SV2305 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV453 ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1065 @ SV1566 @ SV453 ) ) @ SV1065 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5464]) ).
thf(5914,plain,
! [SV2306: $i,SV1993: $i,SV1567: $i,SV1070: $i,SV458: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV458 ) @ SV1070 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV1567 @ SV1993 @ SV2306 @ SV458 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1567 @ SV1070 ) @ SV2306 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1567 @ SV1993 ) @ SV1070 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5466]) ).
thf(5915,plain,
! [SV1568: $i,SV459: $i,SV2307: $i,SV1071: $i] :
( ( ( SV1071 = SV2307 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV459 ) @ SV1071 ) @ ( c_Set_Oinsert @ SV2307 @ SV1568 @ SV459 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV459 ) @ SV1071 ) @ SV1568 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5467]) ).
thf(5916,plain,
! [SV2501: $i,SV2308: $i,SV1994: $i,SV1569: $i,SV1072: $i,SV460: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV460 ) @ SV1072 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV1569 @ SV1994 @ SV2308 @ SV2501 @ SV460 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1569 @ SV1072 ) @ SV2501 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1994 @ SV2308 ) @ SV1072 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5468]) ).
thf(5917,plain,
! [SV1570: $i,SV2502: $i,SV1073: $i,SV461: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV461 ) @ SV1073 ) @ ( c_HOL_Ominus__class_Ominus @ SV2502 @ SV1570 @ ( tc_fun @ SV461 @ tc_bool ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV461 ) @ SV1073 ) @ SV1570 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5469]) ).
thf(5918,plain,
! [SV2309: $i,SV1571: $i,SV1074: $i,SV462: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV462 ) @ SV1074 ) @ ( c_HOL_Ominus__class_Ominus @ SV1571 @ SV2309 @ ( tc_fun @ SV462 @ tc_bool ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV462 ) @ SV1074 ) @ SV1571 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5470]) ).
thf(5919,plain,
! [SV1572: $i,SV1075: $i,SV2503: $i,SV463: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ SV2503 ) @ SV1075 ) ) )
= $true )
| ( ( ! [SY6485: $i] :
( ~ ( hBOOL @ ( hAPP @ SV1572 @ SY6485 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ SY6485 ) @ SV1075 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1075 @ SV1572 @ SV463 ) ) @ SV1075 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5471]) ).
thf(5920,plain,
! [SV464: $i,SV1076: $i,SV2310: $i,SV1573: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1573 ) @ SV2310 ) @ SV1076 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV464 @ SV2310 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV464 @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ SV1076 @ SV464 @ SV1573 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5472]) ).
thf(5921,plain,
! [SV1995: $i,SV1574: $i,SV1077: $i,SV465: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV465 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1077 @ SV1574 @ SV1995 @ ( tc_fun @ SV465 @ tc_bool ) ) )
= $false )
| ( ( ! [SY6985: $i] :
( ( ( hAPP @ SV1574 @ SY6985 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV465 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1995 ) @ SY6985 ) @ SV1077 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5473]) ).
thf(5922,plain,
! [SV2311: $i,SV1996: $i,SV1575: $i,SV1079: $i,SV467: $i] :
( ( ( c_Com_Ocom_OAss @ SV467 @ SV1079 )
= ( c_Com_Ocom_OCond @ SV1575 @ SV1996 @ SV2311 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5474]) ).
thf(5923,plain,
! [SV1997: $i,SV1576: $i,SV1082: $i,SV470: $i] :
( ( ( c_Map_Omap__le @ SV470 @ ( c_Map_Omap__add @ SV470 @ SV1082 @ SV1576 @ SV1997 ) @ SV1576 @ SV1997 )
= $false )
| ( ( ( c_Map_Omap__add @ SV470 @ SV1082 @ SV1576 @ SV1997 )
= ( c_Map_Omap__add @ SV1082 @ SV470 @ SV1576 @ SV1997 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5475]) ).
thf(5924,plain,
! [SV1998: $i,SV1577: $i,SV1083: $i,SV471: $i] :
( ( ( ( c_Map_Omap__add @ SV471 @ SV1083 @ SV1577 @ SV1998 )
= ( c_Map_Omap__add @ SV1083 @ SV471 @ SV1577 @ SV1998 ) )
= $false )
| ( ( c_Map_Omap__le @ SV471 @ ( c_Map_Omap__add @ SV471 @ SV1083 @ SV1577 @ SV1998 ) @ SV1577 @ SV1998 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5476]) ).
thf(5925,plain,
! [SV475: $i,SV1087: $i,SV2312: $i,SV1580: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1580 ) @ SV2312 ) @ SV1087 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV475 @ ( c_Set_Oinsert @ SV2312 @ SV1087 @ SV1580 ) @ ( tc_fun @ SV1580 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV475 @ SV1087 @ ( tc_fun @ SV1580 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5477]) ).
thf(5926,plain,
! [SV476: $i,SV1581: $i,SV1088: $i,SV2001: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2001 ) @ SV1088 ) @ SV1581 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV476 @ SV1581 @ ( tc_fun @ SV2001 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV476 @ ( c_Set_Oinsert @ SV1088 @ SV1581 @ SV2001 ) @ ( tc_fun @ SV2001 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5478]) ).
thf(5927,plain,
! [SV1583: $i,SV2504: $i,SV1090: $i,SV478: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV478 ) @ SV1090 ) @ SV2504 ) )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV2504 @ SV1583 @ ( tc_fun @ SV478 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV478 @ tc_bool ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV478 ) @ SV1090 ) @ SV1583 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5479]) ).
thf(5928,plain,
! [SV1585: $i,SV2313: $i,SV484: $i] :
( ( ( hBOOL @ ( hAPP @ SV484 @ SV2313 ) )
= $false )
| ( ( ( c_Collect @ SV484 @ SV1585 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1585 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5483]) ).
thf(5929,plain,
! [SV487: $i,SV2314: $i,SV2007: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2007 @ SV2314 @ SV487 )
= $true )
| ( ( ( SV2314 = SV2007 )
| ( c_HOL_Oord__class_Oless @ SV2314 @ SV2007 @ SV487 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV487 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5485]) ).
thf(5930,plain,
! [SV488: $i,SV2315: $i,SV2008: $i] :
( ( ( SV2008 = SV2315 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV2315 @ SV2008 @ SV488 )
| ( c_HOL_Oord__class_Oless @ SV2008 @ SV2315 @ SV488 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV488 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5486]) ).
thf(5931,plain,
! [SV1094: $i,SV489: $i,SV2316: $i,SV2009: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV2009 ) @ SV2316 ) @ SV489 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV2009 ) @ SV2316 ) @ SV1094 ) ) )
= $true )
| ( ( SV489 = SV1094 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5487]) ).
thf(5932,plain,
! [SV2317: $i,SV2010: $i,SV490: $i,SV1095: $i] :
( ( ( ~ ( c_Map_Omap__le @ SV1095 @ SV490 @ SV2010 @ SV2317 ) )
= $true )
| ( ( ~ ( c_Map_Omap__le @ SV490 @ SV1095 @ SV2010 @ SV2317 ) )
= $true )
| ( ( SV490 = SV1095 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5488]) ).
thf(5933,plain,
! [SV491: $i,SV2318: $i,SV2011: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2011 @ SV2318 @ SV491 )
= $true )
| ( ( ( SV2318 = SV2011 )
| ( c_HOL_Oord__class_Oless @ SV2318 @ SV2011 @ SV491 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV491 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5489]) ).
thf(5934,plain,
! [SV492: $i,SV2319: $i,SV2012: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2012 @ SV2319 @ SV492 )
= $true )
| ( ( ( SV2319 = SV2012 )
| ( c_HOL_Oord__class_Oless @ SV2319 @ SV2012 @ SV492 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV492 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5490]) ).
thf(5935,plain,
! [SV493: $i,SV2320: $i,SV2013: $i] :
( ( ( SV2013 = SV2320 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV2013 @ SV2320 @ SV493 )
| ( c_HOL_Oord__class_Oless @ SV2320 @ SV2013 @ SV493 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV493 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5491]) ).
thf(5936,plain,
! [SV2505: $i,SV495: $i,SV2321: $i,SV1097: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1097 @ SV2321 @ SV495 ) @ SV2505 @ SV495 )
| ~ ( c_HOL_Oord__class_Oless @ SV2321 @ SV2505 @ SV495 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV495 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5492]) ).
thf(5937,plain,
! [SV2506: $i,SV496: $i,SV2322: $i,SV1098: $i] :
( ( ( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1098 @ SV2322 @ SV496 ) @ SV2506 @ SV496 )
| ~ ( c_HOL_Oord__class_Oless @ SV1098 @ SV2506 @ SV496 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV496 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5493]) ).
thf(5938,plain,
! [SV2323: $i,SV497: $i,SV1588: $i,SV1099: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1099 @ SV1588 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV497 @ SV1099 @ SV1588 @ SV2323 ) @ SV2323 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5494]) ).
thf(5939,plain,
! [SV2014: $i,SV1589: $i,SV1100: $i,SV498: $i] :
( ( ( ( hAPP @ SV498 @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ SV498 @ SV1100 @ SV1589 @ SV2014 ) )
= ( hAPP @ SV1100 @ ( c_Map_Osko__Map__Xmap__le__def__1__1 @ SV498 @ SV1100 @ SV1589 @ SV2014 ) ) )
= $false )
| ( ( c_Map_Omap__le @ SV498 @ SV1100 @ SV1589 @ SV2014 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5495]) ).
thf(5940,plain,
! [SV2324: $i,SV2015: $i,SV1590: $i,SV1101: $i,SV499: $i] :
( ( ( ( c_Set_Oinsert @ SV499 @ ( c_Set_Oinsert @ SV1101 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1590 @ tc_bool ) ) @ SV1590 ) @ SV1590 )
!= ( c_Set_Oinsert @ SV2015 @ ( c_Set_Oinsert @ SV2324 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1590 @ tc_bool ) ) @ SV1590 ) @ SV1590 ) )
= $true )
| ( ( ( SV499 = SV2324 )
| ( SV499 = SV2015 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5496]) ).
thf(5941,plain,
! [SV2507: $i,SV2016: $i,SV1591: $i,SV1102: $i,SV500: $i] :
( ( ( ( c_Set_Oinsert @ SV500 @ ( c_Set_Oinsert @ SV1102 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1591 @ tc_bool ) ) @ SV1591 ) @ SV1591 )
!= ( c_Set_Oinsert @ SV2016 @ ( c_Set_Oinsert @ SV2507 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1591 @ tc_bool ) ) @ SV1591 ) @ SV1591 ) )
= $true )
| ( ( ( SV1102 = SV2016 )
| ( SV500 = SV2016 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5497]) ).
thf(5942,plain,
! [SV2325: $i,SV2017: $i,SV1592: $i,SV1103: $i,SV501: $i] :
( ( ( ( c_Set_Oinsert @ SV501 @ ( c_Set_Oinsert @ SV1103 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1592 @ tc_bool ) ) @ SV1592 ) @ SV1592 )
!= ( c_Set_Oinsert @ SV2017 @ ( c_Set_Oinsert @ SV2325 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1592 @ tc_bool ) ) @ SV1592 ) @ SV1592 ) )
= $true )
| ( ( ( SV501 = SV2325 )
| ( SV1103 = SV2325 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5498]) ).
thf(5943,plain,
! [SV2326: $i,SV2018: $i,SV1593: $i,SV1104: $i,SV502: $i] :
( ( ( ( c_Set_Oinsert @ SV502 @ ( c_Set_Oinsert @ SV1104 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1593 @ tc_bool ) ) @ SV1593 ) @ SV1593 )
!= ( c_Set_Oinsert @ SV2018 @ ( c_Set_Oinsert @ SV2326 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1593 @ tc_bool ) ) @ SV1593 ) @ SV1593 ) )
= $true )
| ( ( ( SV1104 = SV2018 )
| ( SV1104 = SV2326 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5499]) ).
thf(5944,plain,
! [SV1594: $i,SV503: $i,SV1105: $i,SV2327: $i] :
( ( ( hBOOL @ ( hAPP @ SV2327 @ SV1105 ) )
= $true )
| ( ( ! [SY7240: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV2327 @ SY7240 @ SV503 ) ) @ SV1105 ) @ SV1594 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV503 ) @ SV1105 ) @ SV1594 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5500]) ).
thf(5945,plain,
! [SV2328: $i,SV2019: $i,SV1595: $i,SV1106: $i,SV504: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV504 @ SV1106 @ SV1595 ) ) @ SV2019 ) @ SV2328 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1595 ) @ SV2019 ) @ SV2328 ) )
| ( hBOOL @ ( hAPP @ SV504 @ SV2019 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5501]) ).
thf(5946,plain,
! [SV2508: $i,SV2329: $i,SV2020: $i,SV1596: $i,SV1108: $i,SV506: $i] :
( ( ! [SY7356: $i,SY7357: $i,SY7358: $i] :
( ( ( hAPP @ SV506 @ ( c_Set_Oinsert @ SV1108 @ SV1596 @ SV2020 ) )
= ( hAPP @ ( hAPP @ SV2329 @ SV1108 ) @ ( hAPP @ SV506 @ SV1596 ) ) )
| ! [SY7359: $i,SY7360: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2508 @ SV506 @ SY7356 @ SY7357 @ SY7358 @ SV2329 @ SY7359 @ SY7360 @ SV2020 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5502]) ).
thf(5947,plain,
! [SV2509: $i,SV2330: $i,SV2021: $i,SV1597: $i,SV1109: $i,SV507: $i] :
( ( ! [SY7361: $i,SY7362: $i,SY7363: $i] :
( ( ( hAPP @ SV507 @ ( c_Set_Oinsert @ SV1109 @ SV1597 @ SV2021 ) )
= ( hAPP @ ( hAPP @ SV2330 @ SV1109 ) @ ( hAPP @ SV507 @ SV1597 ) ) )
| ! [SY7364: $i,SY7365: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV507 @ SV2509 @ SY7361 @ SY7362 @ SV2330 @ SY7363 @ SY7364 @ SY7365 @ SV2021 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5503]) ).
thf(5948,plain,
! [SV2331: $i,SV2023: $i,SV1599: $i,SV1111: $i,SV509: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SV1111 @ SV1599 @ SV2023 @ SV2331 @ SV509 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1111 @ SV1599 @ SV2331 @ ( tc_fun @ SV509 @ tc_bool ) ) ) )
= $true )
| ( ( ! [SY7253: $i] :
( ~ ( hBOOL @ ( hAPP @ SV2023 @ SY7253 ) )
| ! [SY7254: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ SY7253 ) @ ( hAPP @ SV1599 @ SY7254 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2331 ) @ SY7254 ) @ SV1111 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5505]) ).
thf(5949,plain,
! [SV1113: $i,SV1601: $i,SV2332: $i,SV511: $i] :
( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV511 @ SV2332 @ SV1601 ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV2332 @ SV1113 @ SV1601 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV511 @ SV1113 @ SV1601 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5506]) ).
thf(5950,plain,
! [SV1114: $i,SV2024: $i,SV512: $i,SV1602: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1602 ) @ SV512 ) @ SV2024 ) )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ SV512 @ SV1114 @ SV1602 ) @ SV2024 @ ( tc_fun @ SV1602 @ tc_bool ) )
= ( c_Set_Oinsert @ SV512 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1114 @ SV2024 @ ( tc_fun @ SV1602 @ tc_bool ) ) @ SV1602 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5507]) ).
thf(5951,plain,
! [SV1603: $i,SV513: $i,SV1115: $i,SV2025: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2025 ) @ SV1115 ) @ SV513 ) )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV513 @ ( c_Set_Oinsert @ SV1115 @ SV1603 @ SV2025 ) @ ( tc_fun @ SV2025 @ tc_bool ) )
= ( c_Set_Oinsert @ SV1115 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV513 @ SV1603 @ ( tc_fun @ SV2025 @ tc_bool ) ) @ SV2025 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5508]) ).
thf(5952,plain,
! [SV2510: $i,SV2334: $i,SV2027: $i,SV1605: $i,SV1117: $i,SV515: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ SV515 @ SV1117 @ SV1605 @ SV2027 ) @ SV2334 )
!= ( c_Option_Ooption_OSome @ SV2510 @ SV2027 ) )
| ( ( hAPP @ SV1117 @ SV2334 )
= ( c_Option_Ooption_ONone @ SV2027 ) )
| ( ( hAPP @ SV1117 @ SV2334 )
= ( c_Option_Ooption_OSome @ SV2510 @ SV2027 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5510]) ).
thf(5953,plain,
! [SV2511: $i,SV1606: $i,SV516: $i,SV1118: $i,SV2335: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2335 ) @ SV1118 ) @ ( c_Set_Ovimage @ SV516 @ ( c_Set_Oinsert @ SV1606 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2511 @ tc_bool ) ) @ SV2511 ) @ SV2335 @ SV2511 ) ) ) )
= $true )
| ( ( ( hAPP @ SV516 @ SV1118 )
= SV1606 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5511]) ).
thf(5954,plain,
! [SV2028: $i,SV1607: $i,SV1119: $i,SV517: $i] :
( ( ( ( c_Com_Ocom_OAss @ SV517 @ SV1119 )
= ( c_Com_Ocom_OAss @ SV1607 @ SV2028 ) )
= $false )
| ( ( SV1119 = SV2028 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5512]) ).
thf(5955,plain,
! [SV2336: $i,SV1608: $i,SV1120: $i,SV518: $i] :
( ( ( ( c_Com_Ocom_OAss @ SV518 @ SV1120 )
= ( c_Com_Ocom_OAss @ SV1608 @ SV2336 ) )
= $false )
| ( ( SV518 = SV1608 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5513]) ).
thf(5956,plain,
! [SV521: $i,SV2337: $i,SV1123: $i] :
( ( ( hBOOL @ ( hAPP @ SV1123 @ SV2337 ) )
= $false )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV521 @ tc_bool ) )
= ( c_Collect @ SV1123 @ SV521 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5514]) ).
thf(5957,plain,
! [SV2512: $i,SV2340: $i,SV2032: $i,SV1612: $i,SV1126: $i,SV526: $i] :
( ( ( ( c_Com_Ocom_OLocal @ SV526 @ SV1126 @ SV1612 )
!= ( c_Com_Ocom_OLocal @ SV2032 @ SV2340 @ SV2512 ) )
| ( SV1612 = SV2512 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5517]) ).
thf(5958,plain,
! [SV2341: $i,SV2033: $i,SV1613: $i,SV1127: $i,SV527: $i] :
( ( ( ! [SY7258: $i] :
( ( c_Com_Ocom_OLocal @ SV527 @ SV1127 @ SV1613 )
!= ( c_Com_Ocom_OLocal @ SV2033 @ SV2341 @ SY7258 ) ) )
= $true )
| ( ( SV1127 = SV2341 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5518]) ).
thf(5959,plain,
! [SV2513: $i,SV2034: $i,SV1614: $i,SV1128: $i,SV528: $i] :
( ( ( ! [SY7366: $i] :
( ( c_Com_Ocom_OLocal @ SV528 @ SV1128 @ SV1614 )
!= ( c_Com_Ocom_OLocal @ SV2034 @ SV2513 @ SY7366 ) ) )
= $true )
| ( ( SV528 = SV2034 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5519]) ).
thf(5960,plain,
! [SV1615: $i,SV1129: $i,SV2342: $i,SV529: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV529 @ ( c_Set_Oinsert @ SV2342 @ SV1129 @ SV1615 ) @ ( tc_fun @ SV1615 @ tc_bool ) ) @ SV1615 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV529 @ SV1129 @ ( tc_fun @ SV1615 @ tc_bool ) ) @ SV1615 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5520]) ).
thf(5961,plain,
! [SV1130: $i,SV2035: $i,SV1616: $i,SV530: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV530 @ SV1616 @ ( tc_fun @ SV2035 @ tc_bool ) ) @ SV2035 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV530 @ ( c_Set_Oinsert @ SV1130 @ SV1616 @ SV2035 ) @ ( tc_fun @ SV2035 @ tc_bool ) ) @ SV2035 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5521]) ).
thf(5962,plain,
! [SV2514: $i,SV2343: $i,SV2037: $i,SV1618: $i,SV1132: $i,SV532: $i] :
( ( ! [SY7367: $i] :
( ( ( hAPP @ SV532 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1132 @ tc_bool ) ) )
= SV1618 )
| ! [SY7368: $i,SY7369: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2037 @ SV532 @ SV2343 @ SV2514 @ SY7367 @ SY7368 @ SV1618 @ SY7369 @ SV1132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5523]) ).
thf(5963,plain,
! [SV2515: $i,SV2344: $i,SV2038: $i,SV1619: $i,SV1133: $i,SV533: $i] :
( ( ! [SY7370: $i] :
( ( ( hAPP @ SV533 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1133 @ tc_bool ) ) )
= SV1619 )
| ! [SY7371: $i,SY7372: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV533 @ SV2038 @ SV2344 @ SV2515 @ SY7370 @ SY7371 @ SY7372 @ SV1619 @ SV1133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5524]) ).
thf(5964,plain,
! [SV2039: $i,SV1134: $i,SV2516: $i,SV534: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV534 @ SV2516 ) ) @ SV1134 ) @ SV2039 ) ) )
= $true )
| ( ( SV2039 = SV1134 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV534 @ SV1134 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5525]) ).
thf(5965,plain,
! [SV2345: $i,SV1621: $i,SV1137: $i,SV538: $i] :
( ( ( ( c_Set_Oimage @ SV538 @ SV1137 @ SV1621 @ SV2345 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2345 @ tc_bool ) ) )
= $false )
| ( ( SV1137
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1621 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5527]) ).
thf(5966,plain,
! [SV2517: $i,SV2346: $i,SV2042: $i,SV1623: $i,SV1140: $i,SV541: $i] :
( ( ! [SY7373: $i,SY7374: $i] :
( ( ( hAPP @ SV541 @ ( c_Set_Oinsert @ SV1140 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1623 @ tc_bool ) ) @ SV1623 ) )
= SV1140 )
| ! [SY7375: $i,SY7376: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2042 @ SV541 @ SV2346 @ SV2517 @ SY7373 @ SY7374 @ SY7375 @ SY7376 @ SV1623 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5528]) ).
thf(5967,plain,
! [SV2518: $i,SV2347: $i,SV2043: $i,SV1624: $i,SV1141: $i,SV542: $i] :
( ( ! [SY7377: $i,SY7378: $i] :
( ( ( hAPP @ SV542 @ ( c_Set_Oinsert @ SV1141 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1624 @ tc_bool ) ) @ SV1624 ) )
= SV1141 )
| ! [SY7379: $i,SY7380: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV542 @ SV2043 @ SV2347 @ SV2518 @ SY7377 @ SY7378 @ SY7379 @ SY7380 @ SV1624 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5529]) ).
thf(5968,plain,
! [SV1626: $i,SV545: $i,SV1144: $i,SV2044: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV2044 @ SV1144 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1144 ) @ SV1626 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1144 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1626 @ ( c_Collect @ SV2044 @ SV545 ) @ ( tc_fun @ SV545 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5530]) ).
thf(5969,plain,
! [SV1627: $i,SV2519: $i,SV2348: $i,SV547: $i,SV1145: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV1145 @ SV547 @ SV2348 @ SV2519 ) @ SV1627 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV547 @ ( hAPP @ SV1145 @ SV1627 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5531]) ).
thf(5970,plain,
! [SV2349: $i,SV2045: $i,SV1628: $i,SV1146: $i,SV548: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV548 @ SV1146 @ SV1628 @ SV2045 ) @ SV2349 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1146 @ ( hAPP @ SV548 @ SV2349 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5532]) ).
thf(5971,plain,
! [SV1629: $i,SV1147: $i,SV2350: $i,SV549: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV549 @ ( c_Set_Oinsert @ SV2350 @ SV1147 @ ( tc_Hoare__Mirabelle_Otriple @ SV1629 ) ) @ SV1629 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV549 @ SV1147 @ SV1629 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5533]) ).
thf(5972,plain,
! [SV1148: $i,SV2046: $i,SV1630: $i,SV550: $i] :
( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV550 @ SV1630 @ SV2046 ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV550 @ ( c_Set_Oinsert @ SV1148 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2046 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2046 ) ) @ SV2046 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV550 @ ( c_Set_Oinsert @ SV1148 @ SV1630 @ ( tc_Hoare__Mirabelle_Otriple @ SV2046 ) ) @ SV2046 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5534]) ).
thf(5973,plain,
! [SV1631: $i,SV551: $i,SV2047: $i,SV1149: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1149 @ SV2047 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV551 @ SV2047 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV551 @ SV1149 @ ( tc_fun @ SV1631 @ tc_bool ) ) @ SV2047 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5535]) ).
thf(5974,plain,
! [SV2520: $i,SV552: $i,SV1632: $i,SV1150: $i] :
( ( ( ! [SY7381: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV1150 @ SV1632 @ SV552 )
!= ( c_HOL_Ominus__class_Ominus @ SV2520 @ SY7381 @ SV552 ) )
| ( c_HOL_Oord__class_Oless @ SV2520 @ SY7381 @ SV552 )
| ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SV1632 @ SV552 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV552 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5536]) ).
thf(5975,plain,
! [SV2521: $i,SV553: $i,SV1633: $i,SV1151: $i] :
( ( ( ! [SY7382: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV1151 @ SV1633 @ SV553 )
!= ( c_HOL_Ominus__class_Ominus @ SV2521 @ SY7382 @ SV553 ) )
| ( c_HOL_Oord__class_Oless @ SV1151 @ SV1633 @ SV553 )
| ~ ( c_HOL_Oord__class_Oless @ SV2521 @ SY7382 @ SV553 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV553 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5537]) ).
thf(5976,plain,
! [SV2351: $i,SV1154: $i,SV556: $i,SV2048: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV2048 @ SV556 @ SV1154 @ SV2351 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV2048 @ SV556 @ SV1154 @ SV2351 ) @ SV2351 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV556 @ SV1154 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5538]) ).
thf(5977,plain,
! [SV558: $i,SV1635: $i,SV1156: $i,SV2352: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV2352 ) @ SV1156 ) @ SV1635 ) )
= $true )
| ( ( ! [SY7278: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY7278 @ SV2352 @ SV558 ) ) @ SV1156 ) @ SV1635 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV558 ) @ SV1156 ) @ SV1635 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5539]) ).
thf(5978,plain,
! [SV561: $i,SV2353: $i,SV2049: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2049 @ SV2353 @ SV561 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2353 @ SV2049 @ SV561 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV561 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5540]) ).
thf(5979,plain,
! [SV562: $i,SV2354: $i,SV2050: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2050 @ SV2354 @ SV562 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2354 @ SV2050 @ SV562 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV562 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5541]) ).
thf(5980,plain,
! [SV563: $i,SV2355: $i,SV2051: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2051 @ SV2355 @ SV563 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2355 @ SV2051 @ SV563 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV563 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5542]) ).
thf(5981,plain,
! [SV564: $i,SV2356: $i,SV2052: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2052 @ SV2356 @ SV564 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2356 @ SV2052 @ SV564 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV564 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5543]) ).
thf(5982,plain,
! [SV1159: $i,SV1636: $i,SV2357: $i,SV565: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV565 @ SV2357 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1636 ) @ SV2357 ) @ SV1159 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV565 @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ SV1159 @ SV565 @ SV1636 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5544]) ).
thf(5983,plain,
! [SV1160: $i,SV566: $i,SV2522: $i,SV1637: $i,SV2053: $i] :
( ( ( ! [SY7383: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2053 ) @ SV1637 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV2522 @ SV566 @ SV1160 @ SY7383 @ SV2053 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV566 @ SV1160 ) @ SV1637 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5545]) ).
thf(5984,plain,
! [SV1638: $i,SV2523: $i,SV567: $i,SV1161: $i,SV2054: $i] :
( ( ( ! [SY7384: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2054 ) @ SV1161 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV567 @ SV2523 @ SY7384 @ SV1638 @ SV2054 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV567 @ SV1161 ) @ SV1638 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5546]) ).
thf(5985,plain,
! [SV1639: $i,SV2358: $i,SV1162: $i,SV568: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV568 ) @ SV1162 ) @ SV2358 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2358 @ SV1639 @ ( tc_fun @ SV568 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV568 ) @ SV1162 ) @ SV1639 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5547]) ).
thf(5986,plain,
! [SV572: $i,SV2359: $i,SV1166: $i,SV1643: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1643 ) @ SV1166 ) @ SV2359 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV572 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2359 @ SV572 @ SV1643 ) ) )
| ! [SY7279: $i] :
~ ( hBOOL @ ( hAPP @ SY7279 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2359 @ SY7279 @ SV1643 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV572 @ SV1166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5548]) ).
thf(5987,plain,
! [SV573: $i,SV2360: $i,SV1167: $i,SV1644: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1644 ) @ SV1167 ) @ SV2360 ) ) )
= $true )
| ( ( ! [SY7280: $i] :
~ ( hBOOL @ ( hAPP @ SY7280 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2360 @ SY7280 @ SV1644 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV573 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2360 @ SV573 @ SV1644 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV573 @ SV1167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5549]) ).
thf(5988,plain,
! [SV574: $i,SV2361: $i,SV1168: $i,SV1645: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1645 ) @ SV1168 ) @ SV2361 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1645 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2361 @ SV574 @ SV1645 ) ) @ SV2361 ) )
| ! [SY7281: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1645 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2361 @ SY7281 @ SV1645 ) ) @ SV2361 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV574 @ SV1168 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5550]) ).
thf(5989,plain,
! [SV575: $i,SV2362: $i,SV1169: $i,SV1646: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1646 ) @ SV1169 ) @ SV2362 ) ) )
= $true )
| ( ( ! [SY7282: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1646 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2362 @ SY7282 @ SV1646 ) ) @ SV2362 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1646 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2362 @ SV575 @ SV1646 ) ) @ SV2362 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV575 @ SV1169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5551]) ).
thf(5990,plain,
! [SV576: $i,SV2363: $i,SV1170: $i,SV1647: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1647 ) @ SV1170 ) @ SV2363 ) ) )
= $true )
| ( ( ! [SY7283: $i] :
( ~ ( hBOOL @ ( hAPP @ SV576 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2363 @ SY7283 @ SV576 @ SV1647 ) ) )
| ~ ( hBOOL @ ( hAPP @ SY7283 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2363 @ SY7283 @ SV576 @ SV1647 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV576 @ SV1170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5552]) ).
thf(5991,plain,
! [SV577: $i,SV2364: $i,SV1171: $i,SV1648: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1648 ) @ SV1171 ) @ SV2364 ) ) )
= $true )
| ( ( ! [SY7284: $i] :
( ~ ( hBOOL @ ( hAPP @ SY7284 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2364 @ SV577 @ SY7284 @ SV1648 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV577 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2364 @ SV577 @ SY7284 @ SV1648 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV577 @ SV1171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5553]) ).
thf(5992,plain,
! [SV1649: $i,SV578: $i,SV1172: $i,SV2524: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV2524 @ SV1172 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV578 ) @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ SV1649 @ SV2524 @ SV578 ) ) @ SV1649 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV578 ) @ SV1172 ) @ SV1649 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5554]) ).
thf(5993,plain,
! [SV579: $i,SV1173: $i,SV2365: $i,SV1650: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1650 ) @ SV2365 ) @ SV1173 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV579 @ SV2365 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV579 @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1173 @ SV579 @ SV1650 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5555]) ).
thf(5994,plain,
! [SV2525: $i,SV1174: $i,SV580: $i,SV1651: $i,SV2366: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2366 ) @ SV1651 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV580 @ SV1174 @ SV2525 @ SV2366 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV580 @ SV1174 ) @ SV1651 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5556]) ).
thf(5995,plain,
! [SV1652: $i,SV2526: $i,SV581: $i,SV1175: $i,SV2367: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2367 ) @ SV1175 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV581 @ SV2526 @ SV1652 @ SV2367 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV581 @ SV1175 ) @ SV1652 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5557]) ).
thf(5996,plain,
! [SV1653: $i,SV2368: $i,SV1176: $i,SV582: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV582 ) @ SV1176 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2368 @ SV1653 @ ( tc_fun @ SV582 @ tc_bool ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV582 ) @ SV1176 ) @ SV1653 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5558]) ).
thf(5997,plain,
! [SV2369: $i,SV1654: $i,SV1177: $i,SV583: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV583 ) @ SV1177 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1654 @ SV2369 @ ( tc_fun @ SV583 @ tc_bool ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV583 ) @ SV1177 ) @ SV1654 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5559]) ).
thf(5998,plain,
! [SV2055: $i,SV1655: $i,SV1178: $i,SV584: $i] :
( ( ( ( hAPP @ SV584 @ SV1178 )
= ( hAPP @ SV584 @ SV1655 ) )
= $false )
| ( ( ! [SY7060: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2055 ) @ SV1655 ) @ SY7060 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2055 ) @ SV1178 ) @ SY7060 ) )
| ( SV1178 = SV1655 )
| ! [SY7061: $i] :
~ ( c_Fun_Oinj__on @ SV584 @ SY7060 @ SV2055 @ SY7061 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5560]) ).
thf(5999,plain,
! [SV2056: $i,SV1656: $i,SV1179: $i,SV585: $i] :
( ( ( ( hAPP @ SV585 @ SV1179 )
= ( hAPP @ SV585 @ SV1656 ) )
= $false )
| ( ( ! [SY7062: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2056 ) @ SV1656 ) @ SY7062 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2056 ) @ SV1179 ) @ SY7062 ) )
| ! [SY7063: $i] :
~ ( c_Fun_Oinj__on @ SV585 @ SY7062 @ SV2056 @ SY7063 )
| ( SV1179 = SV1656 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5561]) ).
thf(6000,plain,
! [SV2057: $i,SV1657: $i,SV1180: $i,SV586: $i] :
( ( ( ( hAPP @ SV586 @ SV1180 )
= ( hAPP @ SV586 @ SV1657 ) )
= $false )
| ( ( ! [SY7064: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2057 ) @ SV1657 ) @ SY7064 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2057 ) @ SV1180 ) @ SY7064 ) )
| ! [SY7065: $i] :
~ ( c_Fun_Oinj__on @ SV586 @ SY7064 @ SV2057 @ SY7065 )
| ( SV1180 = SV1657 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5562]) ).
thf(6001,plain,
! [SV2058: $i,SV1658: $i,SV1181: $i,SV587: $i] :
( ( ( ( hAPP @ SV587 @ SV1181 )
= ( hAPP @ SV587 @ SV1658 ) )
= $false )
| ( ( ! [SY7066: $i] :
( ! [SY7067: $i] :
~ ( c_Fun_Oinj__on @ SV587 @ SV2058 @ SY7066 @ SY7067 )
| ( SV1181 = SV1658 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7066 ) @ SV1658 ) @ SV2058 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7066 ) @ SV1181 ) @ SV2058 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5563]) ).
thf(6002,plain,
! [SV588: $i,SV1182: $i,SV2370: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2370 ) @ SV1182 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2370 @ tc_bool ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV588 @ SV1182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5564]) ).
thf(6003,plain,
! [SV592: $i,SV2060: $i,SV1186: $i,SV1661: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1661 @ SV1186 ) @ SV2060 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV592 ) @ SV1186 ) @ ( c_SetInterval_Oord_OatMost @ SV1661 @ SV2060 @ SV592 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5568]) ).
thf(6004,plain,
! [SV1662: $i,SV593: $i,SV1187: $i,SV2371: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2371 ) @ SV1187 ) @ ( c_SetInterval_Oord_OatMost @ SV593 @ SV1662 @ SV2371 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV593 @ SV1187 ) @ SV1662 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5569]) ).
thf(6005,plain,
! [SV1663: $i,SV2061: $i,SV1188: $i,SV594: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV594 ) @ SV1188 ) @ SV2061 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV594 ) @ SV1188 ) @ SV1663 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV594 ) @ SV1188 ) @ ( c_HOL_Ominus__class_Ominus @ SV1663 @ SV2061 @ ( tc_fun @ SV594 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5570]) ).
thf(6006,plain,
! [SV1664: $i,SV2062: $i,SV1189: $i,SV595: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV595 ) @ SV1189 ) @ SV2062 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV595 ) @ SV1189 ) @ SV1664 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV595 ) @ SV1189 ) @ ( c_HOL_Ominus__class_Ominus @ SV1664 @ SV2062 @ ( tc_fun @ SV595 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5571]) ).
thf(6007,plain,
! [SV596: $i,SV2372: $i,SV1190: $i,SV1665: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1665 ) @ SV1190 ) @ SV2372 ) ) )
= $true )
| ( ( ! [SY7287: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1665 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2372 @ SY7287 @ SV596 @ SV1665 ) ) @ SV2372 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV596 @ SV1190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5572]) ).
thf(6008,plain,
! [SV597: $i,SV2373: $i,SV1191: $i,SV1666: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1666 ) @ SV1191 ) @ SV2373 ) ) )
= $true )
| ( ( ! [SY7288: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1666 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2373 @ SV597 @ SY7288 @ SV1666 ) ) @ SV2373 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV597 @ SV1191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5573]) ).
thf(6009,plain,
! [SV598: $i,SV1667: $i,SV1192: $i,SV2527: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV2527 @ SV1192 ) )
| ~ ( hBOOL @ ( hAPP @ SV2527 @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ SV1667 @ SV2527 @ SV598 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV598 ) @ SV1192 ) @ SV1667 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5574]) ).
thf(6010,plain,
! [SV2063: $i,SV1668: $i,SV1193: $i,SV599: $i] :
( ( ( ( c_Set_Oinsert @ SV599 @ SV1193 @ SV1668 )
= ( c_Set_Oinsert @ SV599 @ SV2063 @ SV1668 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1668 ) @ SV599 ) @ SV2063 ) )
| ( SV1193 = SV2063 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1668 ) @ SV599 ) @ SV1193 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5575]) ).
thf(6011,plain,
! [SV1669: $i,SV1194: $i,SV2374: $i,SV600: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV600 ) @ SV2374 ) @ SV1194 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1669 @ SV2374 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV600 ) @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ SV1194 @ SV1669 @ SV600 ) ) @ SV1194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5576]) ).
thf(6012,plain,
! [SV2375: $i,SV2064: $i,SV1670: $i,SV1195: $i,SV601: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV601 ) @ SV1195 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1670 @ SV2064 @ SV2375 @ ( tc_fun @ SV601 @ tc_bool ) ) ) )
= $true )
| ( ( ! [SY7289: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV601 ) @ SV1195 ) @ ( hAPP @ SV2064 @ SY7289 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2375 ) @ SY7289 ) @ SV1670 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5577]) ).
thf(6013,plain,
! [SV2376: $i,SV2065: $i,SV1671: $i,SV1196: $i,SV602: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV602 ) @ SV1196 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1671 @ SV2065 @ SV2376 @ ( tc_fun @ SV602 @ tc_bool ) ) ) )
= $true )
| ( ( ! [SY7290: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV602 ) @ SV1196 ) @ ( hAPP @ SV2065 @ SY7290 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2376 ) @ SY7290 ) @ SV1671 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5578]) ).
thf(6014,plain,
! [SV603: $i,SV1197: $i,SV2066: $i,SV1672: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1672 @ SV2066 ) @ SV1197 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV603 ) @ SV1197 ) @ ( c_SetInterval_Oord_OgreaterThan @ SV1672 @ SV2066 @ SV603 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5579]) ).
thf(6015,plain,
! [SV1198: $i,SV604: $i,SV1673: $i,SV2377: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2377 ) @ SV1673 ) @ ( c_SetInterval_Oord_OgreaterThan @ SV604 @ SV1198 @ SV2377 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV604 @ SV1198 ) @ SV1673 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5580]) ).
thf(6016,plain,
! [SV2378: $i,SV2067: $i,SV1674: $i,SV1199: $i,SV605: $i] :
( ( ( hBOOL @ ( hAPP @ SV605 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SV1199 @ SV1674 @ SV605 @ SV2067 @ SV2378 ) ) )
= $true )
| ( ( ! [SY7291: $i] :
( ~ ( hBOOL @ ( hAPP @ SV605 @ SY7291 ) )
| ! [SY7292: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2378 ) @ SY7291 ) @ ( hAPP @ SV1674 @ SY7292 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2067 ) @ SY7292 ) @ SV1199 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5581]) ).
thf(6017,plain,
! [SV2379: $i,SV2068: $i,SV1675: $i,SV1200: $i,SV606: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV606 ) @ SV1200 ) @ ( c_Set_Ovimage @ SV1675 @ SV2068 @ SV606 @ SV2379 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2379 ) @ ( hAPP @ SV1675 @ SV1200 ) ) @ SV2068 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5582]) ).
thf(6018,plain,
! [SV2380: $i,SV2069: $i,SV1676: $i,SV1201: $i,SV607: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV607 ) @ SV1201 ) @ ( c_Set_Ovimage @ SV1676 @ SV2069 @ SV607 @ SV2380 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2380 ) @ ( hAPP @ SV1676 @ SV1201 ) ) @ SV2069 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5583]) ).
thf(6019,plain,
! [SV2381: $i,SV2070: $i,SV1677: $i,SV1202: $i,SV608: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV608 ) @ SV1202 ) @ ( c_Set_Ovimage @ SV1677 @ SV2070 @ SV608 @ SV2381 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2381 ) @ ( hAPP @ SV1677 @ SV1202 ) ) @ SV2070 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5584]) ).
thf(6020,plain,
! [SV609: $i,SV2071: $i,SV1203: $i,SV1678: $i,SV2528: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2528 ) @ SV1678 ) @ ( c_Set_Ovimage @ SV1203 @ SV2071 @ SV2528 @ SV609 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV609 ) @ ( hAPP @ SV1203 @ SV1678 ) ) @ SV2071 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5585]) ).
thf(6021,plain,
! [SV610: $i,SV2072: $i,SV1204: $i,SV1679: $i,SV2529: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2529 ) @ SV1679 ) @ ( c_Set_Ovimage @ SV1204 @ SV2072 @ SV2529 @ SV610 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV610 ) @ ( hAPP @ SV1204 @ SV1679 ) ) @ SV2072 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5586]) ).
thf(6022,plain,
! [SV2530: $i,SV2382: $i,SV2073: $i,SV1680: $i,SV1205: $i,SV611: $i] :
( ( ! [SY7385: $i,SY7386: $i,SY7387: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV611 @ ( hAPP @ SV1205 @ SV1680 ) ) @ SV2073 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2382 ) @ SV2073 ) @ SV1680 ) )
| ! [SY7388: $i,SY7389: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1205 @ SV2530 @ SV611 @ SY7385 @ SY7386 @ SY7387 @ SY7388 @ SY7389 @ SV2382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5587]) ).
thf(6023,plain,
! [SV2531: $i,SV2383: $i,SV2074: $i,SV1681: $i,SV1206: $i,SV612: $i] :
( ( ! [SY7390: $i,SY7391: $i,SY7392: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV612 @ SV1206 ) @ ( hAPP @ SV1681 @ SV2074 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2383 ) @ SV1206 ) @ SV2074 ) )
| ! [SY7393: $i,SY7394: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2531 @ SV1681 @ SV612 @ SY7390 @ SY7391 @ SY7392 @ SY7393 @ SY7394 @ SV2383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5588]) ).
thf(6024,plain,
! [SV1682: $i,SV2532: $i,SV613: $i,SV1207: $i,SV2384: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2384 ) @ SV1207 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV613 @ SV2532 @ SV1682 @ SV2384 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV613 @ SV1207 ) @ SV1682 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5589]) ).
thf(6025,plain,
! [SV2533: $i,SV1208: $i,SV614: $i,SV1683: $i,SV2385: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2385 ) @ SV1683 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV614 @ SV1208 @ SV2533 @ SV2385 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV614 @ SV1208 ) @ SV1683 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5590]) ).
thf(6026,plain,
! [SV1209: $i,SV1684: $i,SV2075: $i,SV2534: $i,SV615: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV615 @ SV2534 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2075 ) @ SV2534 ) @ SV1684 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV615 @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV1209 @ SV1684 @ SV615 @ SV2075 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5591]) ).
thf(6027,plain,
! [SV1685: $i,SV1210: $i,SV2076: $i,SV2535: $i,SV616: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV616 @ SV2535 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2076 ) @ SV2535 ) @ SV1210 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV616 @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV1210 @ SV1685 @ SV616 @ SV2076 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5592]) ).
thf(6028,plain,
! [SV1211: $i,SV617: $i,SV2386: $i,SV1686: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1686 @ SV2386 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV617 ) @ SV2386 ) @ SV1211 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV617 ) @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ SV1211 @ SV1686 @ SV617 ) ) @ SV1211 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5593]) ).
thf(6029,plain,
! [SV619: $i,SV2077: $i,SV1213: $i,SV1688: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1688 @ SV1213 ) @ SV2077 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV619 ) @ SV1213 ) @ ( c_SetInterval_Oord_OlessThan @ SV1688 @ SV2077 @ SV619 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5595]) ).
thf(6030,plain,
! [SV1689: $i,SV620: $i,SV1214: $i,SV2387: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2387 ) @ SV1214 ) @ ( c_SetInterval_Oord_OlessThan @ SV620 @ SV1689 @ SV2387 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV620 @ SV1214 ) @ SV1689 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5596]) ).
thf(6031,plain,
! [SV2536: $i,SV2388: $i,SV2078: $i,SV1690: $i,SV1215: $i,SV621: $i] :
( ( ! [SY7395: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV621 @ SV1215 @ SV1690 @ ( tc_fun @ SV2078 @ ( tc_fun @ SV2388 @ tc_bool ) ) ) @ SV2536 ) @ SY7395 ) )
| ! [SY7396: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV1215 @ SY7396 ) @ SV2536 ) @ SY7395 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1690 ) @ SY7396 ) @ SV621 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5597]) ).
thf(6032,plain,
! [SV2389: $i,SV2079: $i,SV1691: $i,SV1216: $i,SV622: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV622 @ SV1216 @ SV1691 @ ( tc_fun @ SV2079 @ tc_bool ) ) @ SV2389 ) )
= $true )
| ( ( ! [SY7310: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1216 @ SY7310 ) @ SV2389 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1691 ) @ SY7310 ) @ SV622 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5598]) ).
thf(6033,plain,
! [SV2537: $i,SV2390: $i,SV2080: $i,SV1692: $i,SV1217: $i,SV623: $i] :
( ( ! [SY7397: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV623 @ SV1217 @ SV1692 @ ( tc_fun @ SV2080 @ ( tc_fun @ SV2390 @ tc_bool ) ) ) @ SV2537 ) @ SY7397 ) )
| ! [SY7398: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV1217 @ SY7398 ) @ SV2537 ) @ SY7397 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1692 ) @ SY7398 ) @ SV623 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5599]) ).
thf(6034,plain,
! [SV2391: $i,SV2081: $i,SV1693: $i,SV1218: $i,SV624: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV624 @ SV1218 @ SV1693 @ ( tc_fun @ SV2081 @ tc_bool ) ) @ SV2391 ) )
= $true )
| ( ( ! [SY7314: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1218 @ SY7314 ) @ SV2391 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1693 ) @ SY7314 ) @ SV624 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5600]) ).
thf(6035,plain,
! [SV1694: $i,SV625: $i,SV2538: $i,SV1219: $i,SV2082: $i] :
( ( ( ! [SY7399: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2082 ) @ SV1219 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV2538 @ SV625 @ SY7399 @ SV1694 @ SV2082 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SV1219 ) @ SV1694 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5601]) ).
thf(6036,plain,
! [SV1220: $i,SV2539: $i,SV626: $i,SV1695: $i,SV2083: $i] :
( ( ( ! [SY7400: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2083 ) @ SV1695 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV626 @ SV2539 @ SV1220 @ SY7400 @ SV2083 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV626 @ SV1220 ) @ SV1695 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5602]) ).
thf(6037,plain,
! [SV1221: $i,SV627: $i,SV2392: $i,SV1696: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1696 @ SV2392 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV627 ) @ SV2392 ) @ SV1221 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV627 ) @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ SV1221 @ SV1696 @ SV627 ) ) @ SV1221 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5603]) ).
thf(6038,plain,
! [SV1222: $i,SV1697: $i,SV2393: $i,SV628: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV628 @ SV2393 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1697 ) @ SV2393 ) @ SV1222 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV628 @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ SV1222 @ SV628 @ SV1697 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5604]) ).
thf(6039,plain,
! [SV629: $i,SV1698: $i,SV1223: $i,SV2540: $i] :
( ( ( ! [SY7401: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2540 ) @ ( hAPP @ SY7401 @ SV1223 ) ) @ ( c_Set_Oimage @ SY7401 @ SV1698 @ SV629 @ SV2540 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV629 ) @ SV1223 ) @ SV1698 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5605]) ).
thf(6040,plain,
! [SV630: $i,SV1699: $i,SV1224: $i,SV2541: $i] :
( ( ( ! [SY7402: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2541 ) @ ( hAPP @ SY7402 @ SV1224 ) ) @ ( c_Set_Oimage @ SY7402 @ SV1699 @ SV630 @ SV2541 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV630 ) @ SV1224 ) @ SV1699 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5606]) ).
thf(6041,plain,
! [SV2394: $i,SV2084: $i,SV1700: $i,SV1225: $i,SV631: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV631 ) @ ( hAPP @ SV1225 @ SV1700 ) ) @ ( c_Set_Oimage @ SV1225 @ SV2084 @ SV2394 @ SV631 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2394 ) @ SV1700 ) @ SV2084 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5607]) ).
thf(6042,plain,
! [SV2395: $i,SV2085: $i,SV1701: $i,SV1226: $i,SV632: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV632 ) @ ( hAPP @ SV1226 @ SV1701 ) ) @ ( c_Set_Oimage @ SV1226 @ SV2085 @ SV2395 @ SV632 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2395 ) @ SV1701 ) @ SV2085 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5608]) ).
thf(6043,plain,
! [SV2086: $i,SV633: $i,SV1227: $i,SV1702: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1702 ) @ SV1227 ) @ ( c_Map_Odom @ SV633 @ SV1702 @ SV2086 ) ) )
= $false )
| ( ( ( hAPP @ SV633 @ SV1227 )
= ( c_Option_Ooption_OSome @ ( c_Map_Osko__Map__XdomD__1__1 @ SV1227 @ SV633 @ SV1702 @ SV2086 ) @ SV2086 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5609]) ).
thf(6044,plain,
! [SV1232: $i,SV641: $i] :
( ( ( c_Com_OWT @ SV641 )
= $false )
| ( ( c_Com_OWT @ SV1232 )
= $false )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV641 @ SV1232 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5615]) ).
thf(6045,plain,
! [SV644: $i,SV1233: $i,SV1710: $i] :
( ( ( c_Com_OWT @ SV1710 )
= $false )
| ( ( ~ ( c_Com_OWT @ SV1233 ) )
= $true )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV644 @ SV1233 @ SV1710 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5616]) ).
thf(6046,plain,
! [SV1237: $i,SV650: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ tc_Com_Opname ) @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ SV650 ) ) @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) ) )
= $true )
| ( ( ~ c_Hoare__Mirabelle_Ostate__not__singleton ) = $true )
| ( ( c_Com_OWT @ SV1237 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV650 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ SV1237 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5619]) ).
thf(6047,plain,
! [SV2396: $i,SV2091: $i,SV1714: $i,SV1239: $i,SV651: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ SV651 @ SV1239 @ SV1714 @ SV2091 ) @ SV2396 )
= ( hAPP @ SV651 @ SV2396 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1714 ) @ SV2396 ) @ ( c_Map_Odom @ SV1239 @ SV1714 @ SV2091 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5620]) ).
thf(6048,plain,
! [SV2397: $i,SV2092: $i,SV1715: $i,SV1240: $i,SV652: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ SV652 @ SV1240 @ SV1715 @ SV2092 ) @ SV2397 )
= ( hAPP @ SV1240 @ SV2397 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1715 ) @ SV2397 ) @ ( c_Map_Odom @ SV652 @ SV1715 @ SV2092 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5621]) ).
thf(6049,plain,
! [SV1717: $i,SV654: $i,SV1242: $i,SV2542: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2542 ) @ SV1242 ) @ ( c_Map_Odom @ SV654 @ SV2542 @ SV1717 ) ) ) )
= $true )
| ( ( ( hAPP @ SV654 @ SV1242 )
= ( c_Option_Ooption_ONone @ SV1717 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5623]) ).
thf(6050,plain,
! [SV2094: $i,SV1718: $i,SV1243: $i,SV655: $i] :
( ( ( ( hAPP @ SV655 @ SV1243 )
= ( c_Option_Ooption_OSome @ SV1718 @ SV2094 ) )
= $false )
| ( ( ! [SY7116: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SY7116 ) @ SV1243 ) @ ( c_Map_Odom @ SV655 @ SY7116 @ SV2094 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5624]) ).
thf(6051,plain,
! [SV1719: $i,SV2543: $i,SV656: $i,SV1244: $i,SV2398: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2398 ) @ SV1244 ) @ ( c_Map_Odom @ SV656 @ SV2398 @ SV2543 ) ) )
| ~ ( c_Map_Omap__le @ SV656 @ SV1719 @ SV2398 @ SV2543 ) )
= $true )
| ( ( ( hAPP @ SV656 @ SV1244 )
= ( hAPP @ SV1719 @ SV1244 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5625]) ).
thf(6052,plain,
! [SV2399: $i,SV2095: $i,SV1720: $i,SV1245: $i,SV657: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ SV657 @ SV1245 @ SV1720 @ SV2095 ) @ SV2399 )
= ( hAPP @ SV1245 @ SV2399 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1720 ) @ SV2399 ) @ ( c_Map_Odom @ SV1245 @ SV1720 @ SV2095 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5626]) ).
thf(6053,plain,
! [SV658: $i,SV1246: $i] :
( ( c_Com_OWT__bodies = $false )
| ( ( c_Com_OWT @ SV1246 )
= $true )
| ( ( ( hAPP @ c_Com_Obody @ SV658 )
= ( c_Option_Ooption_OSome @ SV1246 @ tc_Com_Ocom ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5627]) ).
thf(6054,plain,
! [SV1255: $i,SV666: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ SV666 )
= $false )
| ( ( class_Finite__Set_Ofinite_Ofinite @ SV1255 )
= $false )
| ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ SV666 @ SV1255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5630]) ).
thf(6055,plain,
! [SV3: $i,SV2400: $i,SV2100: $i,SV675: $i] :
( ( ( c_lessequals @ SV675 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2100 @ SV2400 @ SV3 ) @ SV3 )
= $true )
| ( ( ~ ( c_lessequals @ SV675 @ SV2400 @ SV3 )
| ~ ( c_lessequals @ SV675 @ SV2100 @ SV3 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5632]) ).
thf(6056,plain,
! [SV4: $i,SV2401: $i,SV2101: $i,SV676: $i] :
( ( ( c_lessequals @ SV676 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2101 @ SV2401 @ SV4 ) @ SV4 )
= $true )
| ( ( ~ ( c_lessequals @ SV676 @ SV2401 @ SV4 )
| ~ ( c_lessequals @ SV676 @ SV2101 @ SV4 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5633]) ).
thf(6057,plain,
! [SV5: $i,SV2402: $i,SV2102: $i,SV677: $i] :
( ( ( c_lessequals @ SV677 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2102 @ SV2402 @ SV5 ) @ SV5 )
= $true )
| ( ( ~ ( c_lessequals @ SV677 @ SV2402 @ SV5 )
| ~ ( c_lessequals @ SV677 @ SV2102 @ SV5 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5634]) ).
thf(6058,plain,
! [SV1727: $i,SV8: $i,SV1263: $i,SV2105: $i,SV678: $i] :
( ( ( ~ ( c_lessequals @ SV678 @ SV2105 @ ( tc_fun @ SV1263 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV8 @ SV1727 @ ( tc_fun @ SV1263 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV8 @ SV678 @ ( tc_fun @ SV1263 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1727 @ SV2105 @ ( tc_fun @ SV1263 @ tc_bool ) ) @ ( tc_fun @ SV1263 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5635]) ).
thf(6059,plain,
! [SV2544: $i,SV2403: $i,SV2106: $i,SV1728: $i,SV1264: $i,SV680: $i,SV11: $i] :
( ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV11 @ SV680 @ SV1264 @ SV1728 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV2106 @ SV2403 @ SV2544 @ SV1728 ) )
| ( SV1264 = SV2544 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5636]) ).
thf(6060,plain,
! [SV2404: $i,SV2107: $i,SV1729: $i,SV1265: $i,SV681: $i,SV12: $i] :
( ( ( ! [SY7317: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV12 @ SV681 @ SV1265 @ SV1729 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV2107 @ SV2404 @ SY7317 @ SV1729 ) ) )
= $true )
| ( ( SV681 = SV2404 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5637]) ).
thf(6061,plain,
! [SV2545: $i,SV2108: $i,SV1730: $i,SV1266: $i,SV682: $i,SV13: $i] :
( ( ( ! [SY7403: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV13 @ SV682 @ SV1266 @ SV1730 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV2108 @ SV2545 @ SY7403 @ SV1730 ) ) )
= $true )
| ( ( SV13 = SV2108 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5638]) ).
thf(6062,plain,
! [SV22: $i,SV2111: $i,SV1736: $i] :
( ( ( c_lessequals @ SV1736 @ SV2111 @ SV22 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1736 @ SV2111 @ SV22 )
= SV2111 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5639]) ).
thf(6063,plain,
! [SV23: $i,SV2112: $i,SV1737: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1737 @ SV2112 @ SV23 )
= SV2112 )
= $false )
| ( ( c_lessequals @ SV1737 @ SV2112 @ SV23 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5640]) ).
thf(6064,plain,
! [SV24: $i,SV1738: $i,SV2113: $i] :
( ( ( c_lessequals @ SV2113 @ SV1738 @ SV24 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1738 @ SV2113 @ SV24 )
= SV1738 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5641]) ).
thf(6065,plain,
! [SV25: $i,SV2114: $i,SV1739: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1739 @ SV2114 @ SV25 )
= $false )
| ( ( c_lessequals @ SV1739 @ SV2114 @ SV25 )
= $true )
| ( ( class_Orderings_Opreorder @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5642]) ).
thf(6066,plain,
! [SV26: $i,SV2115: $i,SV1740: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1740 @ SV2115 @ SV26 )
= $false )
| ( ( c_lessequals @ SV1740 @ SV2115 @ SV26 )
= $true )
| ( ( class_Orderings_Oorder @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5643]) ).
thf(6067,plain,
! [SV27: $i,SV2405: $i,SV2116: $i,SV691: $i] :
( ( ( c_lessequals @ SV691 @ SV2116 @ ( tc_fun @ SV2405 @ SV27 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV691 @ SV2116 @ ( tc_fun @ SV2405 @ SV27 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5644]) ).
thf(6068,plain,
! [SV30: $i,SV2118: $i,SV1742: $i] :
( ( ( ~ ( c_lessequals @ SV1742 @ SV2118 @ SV30 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2118 @ SV1742 @ SV30 ) )
= $true )
| ( ( SV1742 = SV2118 )
= $true )
| ( ( class_Orderings_Oorder @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5645]) ).
thf(6069,plain,
! [SV31: $i,SV1743: $i,SV2119: $i] :
( ( ( ~ ( c_lessequals @ SV2119 @ SV1743 @ SV31 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1743 @ SV2119 @ SV31 ) )
= $true )
| ( ( SV1743 = SV2119 )
= $true )
| ( ( class_Orderings_Oorder @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5646]) ).
thf(6070,plain,
! [SV32: $i,SV1744: $i,SV2120: $i] :
( ( ( ~ ( c_lessequals @ SV2120 @ SV1744 @ SV32 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1744 @ SV2120 @ SV32 ) )
= $true )
| ( ( SV1744 = SV2120 )
= $true )
| ( ( class_Orderings_Oorder @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5647]) ).
thf(6071,plain,
! [SV1745: $i,SV693: $i,SV33: $i] :
( ( ( c_lessequals @ SV33 @ SV693 @ ( tc_fun @ SV1745 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV693 @ SV33 @ ( tc_fun @ SV1745 @ tc_bool ) )
= $false )
| ( ( SV33 = SV693 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5648]) ).
thf(6072,plain,
! [SV1746: $i,SV694: $i,SV34: $i] :
( ( ( c_lessequals @ SV34 @ SV694 @ ( tc_fun @ SV1746 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV694 @ SV34 @ ( tc_fun @ SV1746 @ tc_bool ) )
= $false )
| ( ( SV34 = SV694 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5649]) ).
thf(6073,plain,
! [SV36: $i,SV2406: $i,SV2122: $i,SV695: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV695 @ SV2122 @ ( tc_fun @ SV2406 @ SV36 ) )
= $true )
| ( ( ( c_lessequals @ SV2122 @ SV695 @ ( tc_fun @ SV2406 @ SV36 ) )
| ~ ( c_lessequals @ SV695 @ SV2122 @ ( tc_fun @ SV2406 @ SV36 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5650]) ).
thf(6074,plain,
! [SV37: $i,SV1748: $i,SV2123: $i] :
( ( ( c_lessequals @ SV2123 @ SV1748 @ SV37 )
= $true )
| ( ( ~ ( c_lessequals @ SV1748 @ SV2123 @ SV37 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1748 @ SV2123 @ SV37 )
= $true )
| ( ( class_Orderings_Opreorder @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5651]) ).
thf(6075,plain,
! [SV1749: $i,SV39: $i,SV1276: $i,SV697: $i,SV2125: $i] :
( ( ( ~ ( c_lessequals @ SV2125 @ SV697 @ ( tc_fun @ SV1276 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV39 @ SV1749 @ ( tc_fun @ SV1276 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV39 @ SV697 @ ( tc_fun @ SV1276 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1749 @ SV2125 @ ( tc_fun @ SV1276 @ tc_bool ) ) @ ( tc_fun @ SV1276 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5653]) ).
thf(6076,plain,
! [SV705: $i,SV2409: $i,SV49: $i,SV1757: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1757 @ SV49 @ ( tc_fun @ SV2409 @ tc_bool ) ) @ SV705 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1757 @ SV705 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV49 @ SV705 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5657]) ).
thf(6077,plain,
! [SV2410: $i,SV2127: $i,SV1758: $i,SV1280: $i,SV706: $i,SV50: $i] :
( ( ( ! [SY7318: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ SV50 @ SV706 @ SV1280 @ SV1758 @ SV2127 ) @ SV2410 @ SY7318 @ SV1758 @ SV2127 )
= ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ SV50 @ SV2410 @ SY7318 @ SV1758 @ SV2127 ) @ SV706 @ SV1280 @ SV1758 @ SV2127 ) ) )
= $true )
| ( ( SV706 = SV2410 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5658]) ).
thf(6078,plain,
! [SV2411: $i,SV2128: $i,SV1759: $i,SV1281: $i,SV707: $i,SV51: $i] :
( ( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ SV51 @ SV707 @ SV1281 @ SV1759 @ ( tc_Option_Ooption @ SV2128 ) ) @ ( c_Fun_Ofun__upd @ SV2411 @ SV707 @ SV1281 @ SV1759 @ ( tc_Option_Ooption @ SV2128 ) ) @ SV1759 @ SV2128 )
= $true )
| ( ( ~ ( c_Map_Omap__le @ SV51 @ SV2411 @ SV1759 @ SV2128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5659]) ).
thf(6079,plain,
! [SV710: $i,SV1284: $i,SV54: $i] :
( ( ( c_Finite__Set_Ofinite @ SV54 @ SV1284 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV710 @ SV1284 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV54 @ SV710 @ ( tc_fun @ SV1284 @ tc_bool ) ) @ SV1284 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5662]) ).
thf(6080,plain,
! [SV711: $i,SV1285: $i,SV55: $i] :
( ( ( c_Finite__Set_Ofinite @ SV55 @ SV1285 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV711 @ SV1285 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV55 @ SV711 @ ( tc_fun @ SV1285 @ tc_bool ) ) @ SV1285 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5663]) ).
thf(6081,plain,
! [SV2412: $i,SV56: $i,SV2129: $i,SV712: $i,SV1286: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV1286 @ SV712 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2129 @ tc_bool ) ) @ SV56 @ SV2129 @ SV2412 )
= $false )
| ( ( SV56 = SV712 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5664]) ).
thf(6082,plain,
! [SV2130: $i,SV1762: $i,SV1288: $i,SV714: $i,SV58: $i] :
( ( ( ( hAPP @ SV58 @ SV714 )
= ( c_Option_Ooption_OSome @ SV1288 @ SV1762 ) )
= $false )
| ( ( ( SV714 = SV2130 )
| ! [SY7135: $i,SY7136: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV58 @ SV2130 @ ( c_Option_Ooption_OSome @ SY7135 @ SV1762 ) @ SY7136 @ ( tc_Option_Ooption @ SV1762 ) ) @ SV714 )
= ( c_Option_Ooption_OSome @ SV1288 @ SV1762 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5665]) ).
thf(6083,plain,
! [SV2546: $i,SV2413: $i,SV2131: $i,SV1763: $i,SV1289: $i,SV715: $i,SV59: $i] :
( ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV59 @ SV715 @ ( c_Option_Ooption_OSome @ SV1289 @ SV1763 ) @ SV2131 @ ( tc_Option_Ooption @ SV1763 ) ) @ SV2413 )
!= ( c_Option_Ooption_OSome @ SV2546 @ SV1763 ) )
| ( ( hAPP @ SV59 @ SV2413 )
= ( c_Option_Ooption_OSome @ SV2546 @ SV1763 ) )
| ( SV1289 = SV2546 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5666]) ).
thf(6084,plain,
! [SV2547: $i,SV2414: $i,SV2132: $i,SV1764: $i,SV1290: $i,SV716: $i,SV60: $i] :
( ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV60 @ SV716 @ ( c_Option_Ooption_OSome @ SV1290 @ SV1764 ) @ SV2132 @ ( tc_Option_Ooption @ SV1764 ) ) @ SV2414 )
!= ( c_Option_Ooption_OSome @ SV2547 @ SV1764 ) )
| ( ( hAPP @ SV60 @ SV2414 )
= ( c_Option_Ooption_OSome @ SV2547 @ SV1764 ) )
| ( SV2414 = SV716 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5667]) ).
thf(6085,plain,
! [SV2548: $i,SV722: $i,SV2415: $i,SV67: $i,SV1769: $i,SV1295: $i] :
( ( ( ~ ( c_Finite__Set_Ofold__graph @ SV1295 @ SV1769 @ SV67 @ SV2415 @ SV722 @ SV2548 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV67 @ SV722 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5670]) ).
thf(6086,plain,
! [SV727: $i,SV2549: $i,SV2418: $i,SV72: $i,SV1772: $i,SV1298: $i] :
( ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV1298 @ SV1772 @ ( c_Option_Ooption_OSome @ SV72 @ SV2418 ) @ SV2549 @ ( tc_Option_Ooption @ SV2418 ) ) @ SV1772 )
!= ( c_Option_Ooption_OSome @ SV727 @ SV2418 ) )
= $true )
| ( ( SV72 = SV727 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5673]) ).
thf(6087,plain,
! [SV730: $i,SV1773: $i,SV1301: $i,SV75: $i] :
( ( ( c_lessequals @ SV75 @ SV1301 @ ( tc_fun @ SV1773 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV75 @ SV730 @ ( tc_fun @ SV1773 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV75 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV730 @ SV1301 @ ( tc_fun @ SV1773 @ tc_bool ) ) @ ( tc_fun @ SV1773 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5674]) ).
thf(6088,plain,
! [SV731: $i,SV1774: $i,SV1302: $i,SV76: $i] :
( ( ( c_lessequals @ SV76 @ SV1302 @ ( tc_fun @ SV1774 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV76 @ SV731 @ ( tc_fun @ SV1774 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV76 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV731 @ SV1302 @ ( tc_fun @ SV1774 @ tc_bool ) ) @ ( tc_fun @ SV1774 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5675]) ).
thf(6089,plain,
! [SV2139: $i,SV82: $i,SV737: $i,SV2550: $i] :
( ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2550 @ SV737 @ SV82 ) @ SV2139 @ SV82 ) )
= $true )
| ( ( c_lessequals @ SV737 @ SV2139 @ SV82 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV82 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5679]) ).
thf(6090,plain,
! [SV2140: $i,SV83: $i,SV2551: $i,SV738: $i] :
( ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV738 @ SV2551 @ SV83 ) @ SV2140 @ SV83 ) )
= $true )
| ( ( c_lessequals @ SV738 @ SV2140 @ SV83 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV83 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5680]) ).
thf(6091,plain,
! [SV84: $i,SV2422: $i,SV2141: $i,SV739: $i] :
( ( ( c_lessequals @ SV739 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2141 @ SV2422 @ SV84 ) @ SV84 )
= $true )
| ( ( ~ ( c_lessequals @ SV739 @ SV2422 @ SV84 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5681]) ).
thf(6092,plain,
! [SV85: $i,SV2552: $i,SV2142: $i,SV740: $i] :
( ( ( c_lessequals @ SV740 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2142 @ SV2552 @ SV85 ) @ SV85 )
= $true )
| ( ( ~ ( c_lessequals @ SV740 @ SV2142 @ SV85 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5682]) ).
thf(6093,plain,
! [SV2143: $i,SV86: $i,SV741: $i,SV2553: $i] :
( ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2553 @ SV741 @ SV86 ) @ SV2143 @ SV86 ) )
= $true )
| ( ( c_lessequals @ SV741 @ SV2143 @ SV86 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5683]) ).
thf(6094,plain,
! [SV2144: $i,SV87: $i,SV2554: $i,SV742: $i] :
( ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV742 @ SV2554 @ SV87 ) @ SV2144 @ SV87 ) )
= $true )
| ( ( c_lessequals @ SV742 @ SV2144 @ SV87 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV87 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5684]) ).
thf(6095,plain,
! [SV2147: $i,SV90: $i,SV2555: $i,SV745: $i] :
( ( ( ~ ( c_lessequals @ SV745 @ SV2555 @ SV90 )
| ~ ( c_lessequals @ SV2555 @ SV2147 @ SV90 ) )
= $true )
| ( ( c_lessequals @ SV745 @ SV2147 @ SV90 )
= $true )
| ( ( class_Orderings_Oorder @ SV90 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5687]) ).
thf(6096,plain,
! [SV2148: $i,SV91: $i,SV2556: $i,SV746: $i] :
( ( ( ~ ( c_lessequals @ SV746 @ SV2556 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV2556 @ SV2148 @ SV91 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV746 @ SV2148 @ SV91 )
= $true )
| ( ( class_Orderings_Oorder @ SV91 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5688]) ).
thf(6097,plain,
! [SV2149: $i,SV92: $i,SV2557: $i,SV747: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV747 @ SV2557 @ SV92 )
| ~ ( c_lessequals @ SV2557 @ SV2149 @ SV92 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV747 @ SV2149 @ SV92 )
= $true )
| ( ( class_Orderings_Oorder @ SV92 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5689]) ).
thf(6098,plain,
! [SV748: $i,SV93: $i,SV2150: $i,SV2558: $i] :
( ( ( ~ ( c_lessequals @ SV2558 @ SV2150 @ SV93 )
| ~ ( c_lessequals @ SV748 @ SV2558 @ SV93 ) )
= $true )
| ( ( c_lessequals @ SV748 @ SV2150 @ SV93 )
= $true )
| ( ( class_Orderings_Opreorder @ SV93 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5690]) ).
thf(6099,plain,
! [SV96: $i,SV1308: $i,SV751: $i,SV2151: $i] :
( ( ( c_lessequals @ SV2151 @ SV751 @ ( tc_fun @ SV1308 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV96 @ SV2151 @ ( tc_fun @ SV1308 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV96 @ SV751 @ ( tc_fun @ SV1308 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5691]) ).
thf(6100,plain,
! [SV1778: $i,SV97: $i,SV1309: $i,SV2423: $i,SV752: $i] :
( ( ( ~ ( c_lessequals @ SV752 @ SV2423 @ ( tc_fun @ SV1309 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV97 @ SV2423 @ SV1309 @ SV1778 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV97 @ SV752 @ SV1309 @ SV1778 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5692]) ).
thf(6101,plain,
! [SV753: $i,SV2559: $i,SV98: $i,SV1779: $i] :
( ( ( ~ ( c_lessequals @ SV1779 @ SV98 @ ( tc_fun @ SV2559 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1779 @ SV753 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV98 @ SV753 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5693]) ).
thf(6102,plain,
! [SV754: $i,SV1782: $i,SV101: $i] :
( ( ( c_lessequals @ SV101 @ SV1782 @ ( tc_fun @ SV754 @ tc_bool ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV1782 @ SV754 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV101 @ SV754 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5694]) ).
thf(6103,plain,
! [SV102: $i,SV1310: $i,SV755: $i,SV2152: $i] :
( ( ( c_lessequals @ SV2152 @ SV755 @ ( tc_fun @ SV1310 @ tc_bool ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV102 @ SV2152 @ ( tc_fun @ SV1310 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV102 @ SV755 @ ( tc_fun @ SV1310 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5695]) ).
thf(6104,plain,
! [SV103: $i,SV1311: $i,SV756: $i,SV2153: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2153 @ SV756 @ ( tc_fun @ SV1311 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV103 @ SV2153 @ ( tc_fun @ SV1311 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV103 @ SV756 @ ( tc_fun @ SV1311 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5696]) ).
thf(6105,plain,
! [SV757: $i,SV2424: $i,SV104: $i,SV1783: $i] :
( ( ( c_lessequals @ SV1783 @ SV104 @ ( tc_fun @ SV2424 @ tc_bool ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1783 @ SV757 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV104 @ SV757 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5697]) ).
thf(6106,plain,
! [SV105: $i,SV758: $i,SV1784: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1784 @ SV758 )
= $false )
| ( ( c_lessequals @ SV105 @ SV1784 @ ( tc_fun @ SV758 @ tc_bool ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV105 @ SV758 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5698]) ).
thf(6107,plain,
! [SV759: $i,SV106: $i,SV2154: $i,SV2560: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2560 @ SV2154 @ SV106 )
| ~ ( c_lessequals @ SV759 @ SV2560 @ SV106 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV759 @ SV2154 @ SV106 )
= $true )
| ( ( class_Orderings_Opreorder @ SV106 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5699]) ).
thf(6108,plain,
! [SV760: $i,SV107: $i,SV2155: $i,SV2561: $i] :
( ( ( ~ ( c_lessequals @ SV2561 @ SV2155 @ SV107 )
| ~ ( c_HOL_Oord__class_Oless @ SV760 @ SV2561 @ SV107 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV760 @ SV2155 @ SV107 )
= $true )
| ( ( class_Orderings_Opreorder @ SV107 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5700]) ).
thf(6109,plain,
! [SV1785: $i,SV108: $i,SV1312: $i,SV2156: $i,SV761: $i] :
( ( ( ~ ( c_lessequals @ SV761 @ SV2156 @ ( tc_fun @ SV1312 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV108 @ SV1785 @ ( tc_fun @ SV1312 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV108 @ SV761 @ ( tc_fun @ SV1312 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1785 @ SV2156 @ ( tc_fun @ SV1312 @ tc_bool ) ) @ ( tc_fun @ SV1312 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5701]) ).
thf(6110,plain,
! [SV2562: $i,SV1787: $i,SV1314: $i,SV763: $i,SV110: $i] :
( ( ( ( c_Fun_Ofun__upd @ SV110 @ SV763 @ ( c_Option_Ooption_OSome @ SV1314 @ SV1787 ) @ SV2562 @ ( tc_Option_Ooption @ SV1787 ) )
= SV110 )
= $true )
| ( ( ( hAPP @ SV110 @ SV763 )
= ( c_Option_Ooption_OSome @ SV1314 @ SV1787 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5702]) ).
thf(6111,plain,
! [SV2425: $i,SV2159: $i,SV1789: $i,SV1316: $i,SV765: $i,SV112: $i] :
( ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV112 @ SV765 @ SV1316 @ SV1789 @ SV2159 ) @ SV2425 )
= ( hAPP @ SV112 @ SV2425 ) )
= $true )
| ( ( SV2425 = SV765 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5703]) ).
thf(6112,plain,
! [SV2426: $i,SV2160: $i,SV1790: $i,SV1317: $i,SV766: $i,SV113: $i] :
( ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV113 @ SV766 @ SV1317 @ SV1790 @ SV2160 ) @ SV2426 )
= ( hAPP @ SV113 @ SV2426 ) )
= $true )
| ( ( SV2426 = SV766 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5704]) ).
thf(6113,plain,
! [SV1318: $i,SV1791: $i,SV767: $i,SV114: $i] :
( ( ( c_lessequals @ SV114 @ SV767 @ ( tc_fun @ SV1791 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1318 @ SV114 @ ( tc_fun @ SV1791 @ tc_bool ) ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV114 @ ( c_HOL_Ominus__class_Ominus @ SV767 @ SV1318 @ ( tc_fun @ SV1791 @ tc_bool ) ) @ ( tc_fun @ SV1791 @ tc_bool ) )
= SV1318 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5705]) ).
thf(6114,plain,
! [SV2563: $i,SV2427: $i,SV115: $i,SV1319: $i,SV768: $i] :
( ( ( ( ( c_HOL_Ominus__class_Ominus @ SV768 @ SV1319 @ SV115 )
!= ( c_HOL_Ominus__class_Ominus @ SV2427 @ SV2563 @ SV115 ) )
| ( c_lessequals @ SV2563 @ SV2427 @ SV115 )
| ~ ( c_lessequals @ SV1319 @ SV768 @ SV115 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV115 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5706]) ).
thf(6115,plain,
! [SV2564: $i,SV2428: $i,SV116: $i,SV1320: $i,SV769: $i] :
( ( ( ( ( c_HOL_Ominus__class_Ominus @ SV769 @ SV1320 @ SV116 )
!= ( c_HOL_Ominus__class_Ominus @ SV2428 @ SV2564 @ SV116 ) )
| ( c_lessequals @ SV1320 @ SV769 @ SV116 )
| ~ ( c_lessequals @ SV2564 @ SV2428 @ SV116 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV116 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5707]) ).
thf(6116,plain,
! [SV1792: $i,SV117: $i,SV1321: $i,SV2161: $i,SV770: $i] :
( ( ( c_lessequals @ SV770 @ SV2161 @ ( tc_fun @ SV1321 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Set_Oimage @ SV117 @ SV770 @ SV1321 @ SV1792 ) @ ( c_Set_Oimage @ SV117 @ SV2161 @ SV1321 @ SV1792 ) @ ( tc_fun @ SV1792 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5708]) ).
thf(6117,plain,
! [SV771: $i,SV2565: $i,SV1322: $i,SV118: $i,SV2429: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV2429 @ SV118 @ SV1322 @ SV2565 ) @ ( c_Set_Oimage @ SV2429 @ SV771 @ SV1322 @ SV2565 ) @ ( tc_fun @ SV2565 @ tc_bool ) )
= $true )
| ( ( c_lessequals @ SV118 @ SV771 @ ( tc_fun @ SV1322 @ tc_bool ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5709]) ).
thf(6118,plain,
! [SV121: $i,SV1794: $i,SV2162: $i] :
( ( ( SV2162 = SV1794 )
= $true )
| ( ( ~ ( c_lessequals @ SV1794 @ SV2162 @ SV121 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1794 @ SV2162 @ SV121 )
= $true )
| ( ( class_Orderings_Oorder @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5711]) ).
thf(6119,plain,
! [SV122: $i,SV2163: $i,SV1795: $i] :
( ( ( ~ ( c_lessequals @ SV1795 @ SV2163 @ SV122 ) )
= $true )
| ( ( SV2163 = SV1795 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1795 @ SV2163 @ SV122 )
= $true )
| ( ( class_Orderings_Oorder @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5712]) ).
thf(6120,plain,
! [SV124: $i,SV2164: $i,SV1796: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1796 @ SV2164 @ SV124 )
= $true )
| ( ( ~ ( c_lessequals @ SV1796 @ SV2164 @ SV124 ) )
= $true )
| ( ( SV1796 = SV2164 )
= $true )
| ( ( class_Orderings_Oorder @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5714]) ).
thf(6121,plain,
! [SV125: $i,SV2165: $i,SV1797: $i] :
( ( ( SV1797 = SV2165 )
= $true )
| ( ( ~ ( c_lessequals @ SV1797 @ SV2165 @ SV125 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1797 @ SV2165 @ SV125 )
= $true )
| ( ( class_Orderings_Oorder @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5715]) ).
thf(6122,plain,
! [SV127: $i,SV2166: $i,SV1799: $i] :
( ( ( SV1799 = SV2166 )
= $true )
| ( ( ~ ( c_lessequals @ SV1799 @ SV2166 @ SV127 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1799 @ SV2166 @ SV127 )
= $true )
| ( ( class_Orderings_Oorder @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5717]) ).
thf(6123,plain,
! [SV128: $i,SV2167: $i,SV1800: $i] :
( ( ( ~ ( c_lessequals @ SV1800 @ SV2167 @ SV128 ) )
= $true )
| ( ( SV1800 = SV2167 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1800 @ SV2167 @ SV128 )
= $true )
| ( ( class_Orderings_Oorder @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5718]) ).
thf(6124,plain,
! [SV129: $i,SV2168: $i,SV1801: $i] :
( ( ( ~ ( c_lessequals @ SV1801 @ SV2168 @ SV129 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1801 @ SV2168 @ SV129 )
= $true )
| ( ( SV1801 = SV2168 )
= $true )
| ( ( class_Orderings_Olinorder @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5719]) ).
thf(6125,plain,
! [SV130: $i,SV2169: $i,SV1802: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1802 @ SV2169 @ SV130 )
= $true )
| ( ( ~ ( c_lessequals @ SV1802 @ SV2169 @ SV130 ) )
= $true )
| ( ( SV1802 = SV2169 )
= $true )
| ( ( class_Orderings_Olinorder @ SV130 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5720]) ).
thf(6126,plain,
! [SV2566: $i,SV2430: $i,SV2170: $i,SV1803: $i,SV1325: $i,SV775: $i,SV131: $i] :
( ( ( ( c_Fun_Ofun__upd @ SV131 @ SV775 @ ( c_Option_Ooption_OSome @ SV1325 @ SV1803 ) @ SV2170 @ ( tc_Option_Ooption @ SV1803 ) )
!= ( c_Fun_Ofun__upd @ SV2430 @ SV775 @ ( c_Option_Ooption_OSome @ SV2566 @ SV1803 ) @ SV2170 @ ( tc_Option_Ooption @ SV1803 ) ) )
| ( SV1325 = SV2566 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5721]) ).
thf(6127,plain,
! [SV134: $i,SV2567: $i,SV2431: $i,SV1327: $i,SV777: $i] :
( ( ( ( ( c_Finite__Set_Osetsum @ SV777 @ ( c_HOL_Ominus__class_Ominus @ SV1327 @ SV2431 @ ( tc_fun @ SV2567 @ tc_bool ) ) @ SV2567 @ SV134 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV777 @ SV1327 @ SV2567 @ SV134 ) @ ( c_Finite__Set_Osetsum @ SV777 @ SV2431 @ SV2567 @ SV134 ) @ SV134 ) )
| ~ ( c_lessequals @ SV2431 @ SV1327 @ ( tc_fun @ SV2567 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV1327 @ SV2567 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5723]) ).
thf(6128,plain,
! [SV778: $i,SV135: $i,SV1806: $i,SV1328: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1328 @ SV1806 )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV135 @ SV778 )
| ! [SY6827: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ SY6827 @ SV1328 @ SV1806 @ SV778 ) @ SV135 @ ( tc_fun @ SV778 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY6827 @ SV1328 @ SV1806 @ SV778 )
| ! [SY6828: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ SY6828 @ SV135 @ SV778 @ SV1806 ) @ SV1328 @ ( tc_fun @ SV1806 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY6828 @ SV135 @ SV778 @ SV1806 ) ) ) )
= $true )
| ( ( ( c_Finite__Set_Ocard @ SV135 @ SV778 )
= ( c_Finite__Set_Ocard @ SV1328 @ SV1806 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5724]) ).
thf(6129,plain,
! [SV2568: $i,SV2432: $i,SV2173: $i,SV1807: $i,SV1329: $i,SV779: $i,SV136: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV136 @ SV779 @ ( c_Set_Oinsert @ SV1329 @ SV1807 @ SV2173 ) @ ( hAPP @ ( hAPP @ SV136 @ SV1329 ) @ SV2432 ) @ SV2173 @ SV2568 )
| ~ ( c_Finite__Set_Ofold__graph @ SV136 @ SV779 @ SV1807 @ SV2432 @ SV2173 @ SV2568 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2173 ) @ SV1329 ) @ SV1807 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5725]) ).
thf(6130,plain,
! [SV1330: $i,SV780: $i,SV2174: $i,SV137: $i] :
( ( ( c_lessequals @ SV137 @ ( c_Set_Oinsert @ SV2174 @ SV780 @ SV1330 ) @ ( tc_fun @ SV1330 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1330 ) @ SV2174 ) @ SV137 ) )
= $true )
| ( ( c_lessequals @ SV137 @ SV780 @ ( tc_fun @ SV1330 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5726]) ).
thf(6131,plain,
! [SV781: $i,SV1808: $i,SV1331: $i,SV138: $i] :
( ( ( c_lessequals @ SV138 @ SV1331 @ ( tc_fun @ SV1808 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1808 ) @ SV781 ) @ SV138 ) )
= $true )
| ( ( c_lessequals @ SV138 @ ( c_Set_Oinsert @ SV781 @ SV1331 @ SV1808 ) @ ( tc_fun @ SV1808 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5727]) ).
thf(6132,plain,
! [SV1332: $i,SV782: $i,SV2175: $i,SV139: $i] :
( ( ( c_lessequals @ SV139 @ ( c_Set_Oinsert @ SV2175 @ SV782 @ SV1332 ) @ ( tc_fun @ SV1332 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1332 ) @ SV2175 ) @ SV139 ) )
= $true )
| ( ( c_lessequals @ SV139 @ SV782 @ ( tc_fun @ SV1332 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5728]) ).
thf(6133,plain,
! [SV783: $i,SV1809: $i,SV1333: $i,SV140: $i] :
( ( ( c_lessequals @ SV140 @ SV1333 @ ( tc_fun @ SV1809 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1809 ) @ SV783 ) @ SV140 ) )
= $true )
| ( ( c_lessequals @ SV140 @ ( c_Set_Oinsert @ SV783 @ SV1333 @ SV1809 ) @ ( tc_fun @ SV1809 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5729]) ).
thf(6134,plain,
! [SV142: $i,SV1335: $i,SV1810: $i,SV785: $i] :
( ( ( c_lessequals @ SV785 @ SV1810 @ ( tc_fun @ SV1335 @ tc_bool ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1335 ) @ SV142 ) @ SV1810 ) ) )
= $true )
| ( ( c_lessequals @ ( c_Set_Oinsert @ SV142 @ SV785 @ SV1335 ) @ SV1810 @ ( tc_fun @ SV1335 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5731]) ).
thf(6135,plain,
! [SV1811: $i,SV143: $i,SV786: $i,SV2569: $i,SV1336: $i,SV2433: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2433 ) @ SV1336 ) @ SV2569 ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV786 @ SV2569 @ SV2433 @ SV143 ) @ SV1811 @ ( tc_fun @ SV143 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV143 ) @ ( hAPP @ SV786 @ SV1336 ) ) @ SV1811 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5732]) ).
thf(6136,plain,
! [SV2434: $i,SV2177: $i,SV1812: $i,SV1337: $i,SV787: $i,SV144: $i] :
( ( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ SV144 @ SV787 @ SV1337 @ SV1812 @ SV2177 ) @ SV2434 @ SV1812 @ SV2177 )
= ( c_Set_Oimage @ SV144 @ SV2434 @ SV1812 @ SV2177 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1812 ) @ SV787 ) @ SV2434 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5733]) ).
thf(6137,plain,
! [SV145: $i,SV2570: $i,SV2435: $i,SV1338: $i,SV788: $i] :
( ( ( ( c_lessequals @ ( hAPP @ SV788 @ SV1338 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV2435 @ SV788 @ SV2570 @ SV145 ) @ SV145 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2570 ) @ SV1338 ) @ SV2435 ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV145 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5734]) ).
thf(6138,plain,
! [SV2436: $i,SV146: $i,SV1339: $i,SV789: $i,SV1813: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1813 ) @ SV789 ) @ SV1339 ) )
= $false )
| ( ( c_lessequals @ ( hAPP @ SV146 @ SV789 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1339 @ SV146 @ SV1813 @ ( tc_fun @ SV2436 @ tc_bool ) ) @ ( tc_fun @ SV2436 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5735]) ).
thf(6139,plain,
! [SV1340: $i,SV1814: $i,SV147: $i,SV2571: $i,SV790: $i,SV2437: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2437 ) @ SV790 ) @ SV2571 ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV2571 @ SV147 @ SV2437 @ ( tc_fun @ SV1814 @ tc_bool ) ) @ SV1340 @ ( tc_fun @ SV1814 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ SV147 @ SV790 ) @ SV1340 @ ( tc_fun @ SV1814 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5736]) ).
thf(6140,plain,
! [SV2438: $i,SV148: $i,SV1341: $i,SV791: $i,SV1815: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1815 ) @ SV791 ) @ SV1341 ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV148 @ SV791 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1341 @ SV148 @ SV1815 @ ( tc_fun @ SV2438 @ tc_bool ) ) @ ( tc_fun @ SV2438 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1341 @ SV148 @ SV1815 @ ( tc_fun @ SV2438 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5737]) ).
thf(6141,plain,
! [SV794: $i,SV2439: $i,SV2178: $i,SV1344: $i,SV151: $i] :
( ( ( ~ ( c_lessequals @ SV151 @ ( c_Set_Oimage @ SV1344 @ SV2178 @ SV2439 @ SV794 ) @ ( tc_fun @ SV794 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV2178 @ SV2439 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV151 @ SV794 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5739]) ).
thf(6142,plain,
! [SV2440: $i,SV155: $i,SV2179: $i,SV798: $i] :
( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV798 @ ( c_COMBK @ SV2179 @ SV155 @ SV2440 ) @ SV2440 @ SV155 )
= SV2179 )
= $true )
| ( ( SV798
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2440 @ tc_bool ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV155 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5740]) ).
thf(6143,plain,
! [SV2184: $i,SV1822: $i,SV1354: $i,SV805: $i,SV162: $i] :
( ( ( ( c_Set_Oimage @ SV162 @ SV805 @ SV1354 @ SV1822 )
= ( c_Set_Oimage @ SV162 @ SV2184 @ SV1354 @ SV1822 ) )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV162 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV805 @ SV2184 @ ( tc_fun @ SV1354 @ tc_bool ) ) @ SV1354 @ SV1822 )
| ( SV805 = SV2184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5743]) ).
thf(6144,plain,
! [SV178: $i,SV1836: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1836 @ SV1836 @ SV178 )
= $false )
| ( ( c_lessequals @ SV1836 @ SV1836 @ SV178 )
= $false )
| ( ( class_Orderings_Olinorder @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5749]) ).
thf(6145,plain,
! [SV180: $i,SV2189: $i,SV1838: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1838 @ SV2189 @ SV180 )
= $false )
| ( ( ~ ( c_lessequals @ SV2189 @ SV1838 @ SV180 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5750]) ).
thf(6146,plain,
! [SV182: $i,SV2191: $i,SV1840: $i] :
( ( ( c_lessequals @ SV1840 @ SV2191 @ SV182 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2191 @ SV1840 @ SV182 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5752]) ).
thf(6147,plain,
! [SV184: $i,SV2445: $i,SV2193: $i,SV819: $i] :
( ( ( ~ ( c_lessequals @ SV819 @ SV2193 @ ( tc_fun @ SV2445 @ SV184 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2193 @ SV819 @ ( tc_fun @ SV2445 @ SV184 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5754]) ).
thf(6148,plain,
! [SV185: $i,SV2194: $i,SV1842: $i] :
( ( ( c_lessequals @ SV1842 @ SV2194 @ SV185 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2194 @ SV1842 @ SV185 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5755]) ).
thf(6149,plain,
! [SV194: $i,SV2199: $i,SV1845: $i] :
( ( ( c_lessequals @ SV1845 @ SV2199 @ SV194 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1845 @ SV2199 @ SV194 )
= SV1845 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5760]) ).
thf(6150,plain,
! [SV195: $i,SV2200: $i,SV1846: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1846 @ SV2200 @ SV195 )
= SV1846 )
= $false )
| ( ( c_lessequals @ SV1846 @ SV2200 @ SV195 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5761]) ).
thf(6151,plain,
! [SV196: $i,SV1847: $i,SV2201: $i] :
( ( ( c_lessequals @ SV2201 @ SV1847 @ SV196 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV1847 @ SV2201 @ SV196 )
= SV2201 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV196 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5762]) ).
thf(6152,plain,
! [SV197: $i,SV1371: $i,SV1848: $i,SV828: $i] :
( ( ( c_lessequals @ SV828 @ SV1848 @ ( tc_fun @ SV1371 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV197 @ SV1848 @ ( tc_fun @ SV1371 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV197 @ SV828 @ ( tc_fun @ SV1371 @ tc_bool ) ) @ SV1848 @ ( tc_fun @ SV1371 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5763]) ).
thf(6153,plain,
! [SV200: $i,SV1374: $i,SV1849: $i,SV831: $i] :
( ( ( c_lessequals @ SV831 @ SV1849 @ ( tc_fun @ SV1374 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV200 @ SV1849 @ ( tc_fun @ SV1374 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ SV831 @ ( tc_fun @ SV1374 @ tc_bool ) ) @ SV1849 @ ( tc_fun @ SV1374 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5764]) ).
thf(6154,plain,
! [SV2450: $i,SV201: $i,SV2202: $i,SV832: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV832 @ SV2202 @ SV201 ) @ SV2450 @ SV201 )
= $true )
| ( ( ~ ( c_lessequals @ SV2202 @ SV2450 @ SV201 )
| ~ ( c_lessequals @ SV832 @ SV2450 @ SV201 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5765]) ).
thf(6155,plain,
! [SV2451: $i,SV204: $i,SV2205: $i,SV833: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV833 @ SV2205 @ SV204 ) @ SV2451 @ SV204 )
= $true )
| ( ( ~ ( c_lessequals @ SV2205 @ SV2451 @ SV204 )
| ~ ( c_lessequals @ SV833 @ SV2451 @ SV204 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5766]) ).
thf(6156,plain,
! [SV2452: $i,SV205: $i,SV2206: $i,SV834: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV834 @ SV2206 @ SV205 ) @ SV2452 @ SV205 )
= $true )
| ( ( ~ ( c_lessequals @ SV2206 @ SV2452 @ SV205 )
| ~ ( c_lessequals @ SV834 @ SV2452 @ SV205 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5767]) ).
thf(6157,plain,
! [SV1380: $i,SV214: $i,SV1857: $i,SV2210: $i,SV841: $i] :
( ( ( c_lessequals @ SV841 @ SV2210 @ ( tc_fun @ SV1857 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Set_Ovimage @ SV214 @ SV841 @ SV1380 @ SV1857 ) @ ( c_Set_Ovimage @ SV214 @ SV2210 @ SV1380 @ SV1857 ) @ ( tc_fun @ SV1380 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5769]) ).
thf(6158,plain,
! [SV217: $i,SV2454: $i,SV1858: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1858 @ SV2454 @ SV217 )
= ( c_Orderings_Obot__class_Obot @ SV217 ) )
= $false )
| ( ( SV1858
= ( c_Orderings_Obot__class_Obot @ SV217 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV217 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5770]) ).
thf(6159,plain,
! [SV218: $i,SV2211: $i,SV1859: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1859 @ SV2211 @ SV218 )
= ( c_Orderings_Obot__class_Obot @ SV218 ) )
= $false )
| ( ( SV2211
= ( c_Orderings_Obot__class_Obot @ SV218 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5771]) ).
thf(6160,plain,
! [SV223: $i,SV2572: $i,SV2214: $i,SV848: $i] :
( ( ( ~ ( c_lessequals @ SV848 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2214 @ SV2572 @ SV223 ) @ SV223 ) )
= $true )
| ( ( c_lessequals @ SV848 @ SV2214 @ SV223 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV223 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5774]) ).
thf(6161,plain,
! [SV224: $i,SV2215: $i,SV2573: $i,SV849: $i] :
( ( ( ~ ( c_lessequals @ SV849 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2573 @ SV2215 @ SV224 ) @ SV224 ) )
= $true )
| ( ( c_lessequals @ SV849 @ SV2215 @ SV224 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV224 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5775]) ).
thf(6162,plain,
! [SV2455: $i,SV225: $i,SV2216: $i,SV850: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV850 @ SV2216 @ SV225 ) @ SV2455 @ SV225 )
= $true )
| ( ( ~ ( c_lessequals @ SV850 @ SV2455 @ SV225 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5776]) ).
thf(6163,plain,
! [SV2456: $i,SV226: $i,SV2217: $i,SV851: $i] :
( ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV851 @ SV2217 @ SV226 ) @ SV2456 @ SV226 )
= $true )
| ( ( ~ ( c_lessequals @ SV2217 @ SV2456 @ SV226 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV226 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5777]) ).
thf(6164,plain,
! [SV227: $i,SV2574: $i,SV2218: $i,SV852: $i] :
( ( ( ~ ( c_lessequals @ SV852 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2218 @ SV2574 @ SV227 ) @ SV227 ) )
= $true )
| ( ( c_lessequals @ SV852 @ SV2218 @ SV227 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV227 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5778]) ).
thf(6165,plain,
! [SV228: $i,SV2219: $i,SV2575: $i,SV853: $i] :
( ( ( ~ ( c_lessequals @ SV853 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2575 @ SV2219 @ SV228 ) @ SV228 ) )
= $true )
| ( ( c_lessequals @ SV853 @ SV2219 @ SV228 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV228 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5779]) ).
thf(6166,plain,
! [SV2457: $i,SV2225: $i,SV1391: $i,SV858: $i,SV237: $i] :
( ( ( ( c_Fun_Ofun__upd @ SV237 @ SV858 @ SV1391 @ SV2225 @ SV2457 )
= SV237 )
= $false )
| ( ( ( hAPP @ SV237 @ SV858 )
= SV1391 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5780]) ).
thf(6167,plain,
! [SV1866: $i,SV1392: $i,SV859: $i,SV2458: $i,SV238: $i] :
( ( ( c_Fun_Oinj__on @ SV238 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2458 @ SV859 @ ( tc_fun @ SV1392 @ tc_bool ) ) @ SV1392 @ SV1866 )
= $false )
| ( ( c_Fun_Oinj__on @ SV238 @ SV859 @ SV1392 @ SV1866 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5781]) ).
thf(6168,plain,
! [SV1867: $i,SV1393: $i,SV2459: $i,SV860: $i,SV239: $i] :
( ( ( c_Fun_Oinj__on @ SV239 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV860 @ SV2459 @ ( tc_fun @ SV1393 @ tc_bool ) ) @ SV1393 @ SV1867 )
= $false )
| ( ( c_Fun_Oinj__on @ SV239 @ SV860 @ SV1393 @ SV1867 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5782]) ).
thf(6169,plain,
! [SV242: $i,SV2576: $i,SV2226: $i,SV863: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV863 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2226 @ SV2576 @ SV242 ) @ SV242 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV863 @ SV2226 @ SV242 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV242 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5785]) ).
thf(6170,plain,
! [SV243: $i,SV2460: $i,SV2227: $i,SV864: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV864 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2227 @ SV2460 @ SV243 ) @ SV243 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV864 @ SV2460 @ SV243 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV243 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5786]) ).
thf(6171,plain,
! [SV244: $i,SV2461: $i,SV1396: $i,SV865: $i] :
( ( ( c_lessequals @ ( hAPP @ SV865 @ SV1396 ) @ ( hAPP @ SV2461 @ SV1396 ) @ SV244 )
= $true )
| ( ( ! [SY7332: $i] :
~ ( c_lessequals @ SV865 @ SV2461 @ ( tc_fun @ SY7332 @ SV244 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV244 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5787]) ).
thf(6172,plain,
! [SV1397: $i,SV2228: $i,SV866: $i,SV245: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV245 ) @ SV866 ) @ SV2228 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV2228 @ SV1397 @ ( tc_fun @ SV245 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV245 ) @ SV866 ) @ SV1397 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5788]) ).
thf(6173,plain,
! [SV867: $i,SV246: $i,SV1398: $i,SV2229: $i] :
( ( ( c_lessequals @ SV2229 @ SV1398 @ ( tc_fun @ SV246 @ tc_bool ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV246 ) @ SV867 ) @ SV2229 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV246 ) @ SV867 ) @ SV1398 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5789]) ).
thf(6174,plain,
! [SV1399: $i,SV2230: $i,SV868: $i,SV247: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV247 ) @ SV868 ) @ SV2230 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV2230 @ SV1399 @ ( tc_fun @ SV247 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV247 ) @ SV868 ) @ SV1399 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5790]) ).
thf(6175,plain,
! [SV1400: $i,SV2231: $i,SV869: $i,SV248: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV248 ) @ SV869 ) @ SV2231 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV2231 @ SV1400 @ ( tc_fun @ SV248 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV248 ) @ SV869 ) @ SV1400 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5791]) ).
thf(6176,plain,
! [SV1403: $i,SV2233: $i,SV872: $i,SV251: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV251 ) @ SV872 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2233 @ SV1403 @ ( tc_fun @ SV251 @ tc_bool ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV251 ) @ SV872 ) @ SV2233 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV251 ) @ SV872 ) @ SV1403 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5794]) ).
thf(6177,plain,
! [SV873: $i,SV1404: $i,SV253: $i,SV2462: $i,SV1871: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1871 @ SV2462 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV253 ) @ SV2462 ) @ SV1404 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV253 ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV873 @ SV1404 @ SV1871 @ SV253 ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV873 @ SV1404 @ ( tc_fun @ SV253 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5795]) ).
thf(6178,plain,
! [SV1405: $i,SV874: $i,SV254: $i,SV2463: $i,SV1872: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1872 @ SV2463 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV254 ) @ SV2463 ) @ SV874 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV254 ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV874 @ SV1405 @ SV1872 @ SV254 ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV874 @ SV1405 @ ( tc_fun @ SV254 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5796]) ).
thf(6179,plain,
! [SV255: $i,SV1406: $i,SV875: $i] :
( ( ( c_Finite__Set_Ofinite @ SV875 @ SV1406 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1406 ) @ SV255 ) @ SV875 ) )
= $false )
| ( ( ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ SV255 @ SV875 @ SV1406 ) @ SV1406 )
= ( c_Finite__Set_Ocard @ SV875 @ SV1406 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5797]) ).
thf(6180,plain,
! [SV2464: $i,SV2234: $i,SV1874: $i,SV1408: $i,SV877: $i,SV257: $i] :
( ( ( c_Fun_Oinj__on @ ( c_Fun_Ofun__upd @ SV257 @ SV877 @ SV1408 @ SV1874 @ SV2234 ) @ SV2464 @ SV1874 @ SV2234 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2234 ) @ SV1408 ) @ ( c_Set_Oimage @ SV257 @ SV2464 @ SV1874 @ SV2234 ) ) )
| ~ ( c_Fun_Oinj__on @ SV257 @ SV2464 @ SV1874 @ SV2234 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5798]) ).
thf(6181,plain,
! [SV879: $i,SV1875: $i,SV1410: $i,SV259: $i] :
( ( ( c_lessequals @ SV259 @ SV1410 @ ( tc_fun @ SV1875 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV259 @ ( c_Set_Oinsert @ SV879 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1875 @ tc_bool ) ) @ SV1875 ) @ ( tc_fun @ SV1875 @ tc_bool ) ) @ SV1410 @ ( tc_fun @ SV1875 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV259 @ ( c_Set_Oinsert @ SV879 @ SV1410 @ SV1875 ) @ ( tc_fun @ SV1875 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5799]) ).
thf(6182,plain,
! [SV1876: $i,SV1411: $i,SV880: $i,SV260: $i] :
( ( ( c_Fun_Oinj__on @ SV260 @ SV880 @ SV1411 @ SV1876 )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV880 @ SV1411 ) )
= $true )
| ( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ SV260 @ SV880 @ SV1411 @ SV1876 ) @ SV1876 )
= ( c_Finite__Set_Ocard @ SV880 @ SV1411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5800]) ).
thf(6183,plain,
! [SV1877: $i,SV261: $i,SV1412: $i,SV881: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV881 @ SV1412 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV261 @ SV881 @ SV1412 @ SV1877 )
= $true )
| ( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ SV261 @ SV881 @ SV1412 @ SV1877 ) @ SV1877 )
= ( c_Finite__Set_Ocard @ SV881 @ SV1412 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5801]) ).
thf(6184,plain,
! [SV1413: $i,SV882: $i,SV262: $i] :
( ( ( ~ ( c_lessequals @ ( c_Set_Oimage @ SV262 @ SV882 @ SV1413 @ SV1413 ) @ SV882 @ ( tc_fun @ SV1413 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV882 @ SV1413 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV262 @ SV882 @ SV1413 @ SV1413 )
= $false )
| ( ( ( c_Set_Oimage @ SV262 @ SV882 @ SV1413 @ SV1413 )
= SV882 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5802]) ).
thf(6185,plain,
! [SV263: $i,SV1414: $i,SV883: $i] :
( ( ( c_Finite__Set_Ofinite @ SV883 @ SV1414 )
= $false )
| ( ( c_lessequals @ SV883 @ ( c_Set_Oimage @ SV263 @ SV883 @ SV1414 @ SV1414 ) @ ( tc_fun @ SV1414 @ tc_bool ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV263 @ SV883 @ SV1414 @ SV1414 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5803]) ).
thf(6186,plain,
! [SV885: $i,SV1879: $i,SV1416: $i,SV265: $i] :
( ( ( c_lessequals @ SV265 @ SV1416 @ ( tc_fun @ SV1879 @ tc_bool ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1879 ) @ SV885 ) @ SV265 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV265 @ SV1416 @ ( tc_fun @ SV1879 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV265 @ ( c_Set_Oinsert @ SV885 @ SV1416 @ SV1879 ) @ ( tc_fun @ SV1879 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5804]) ).
thf(6187,plain,
! [SV886: $i,SV1880: $i,SV1417: $i,SV266: $i] :
( ( ( c_lessequals @ SV266 @ SV1417 @ ( tc_fun @ SV1880 @ tc_bool ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1880 ) @ SV886 ) @ SV266 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1880 ) @ SV886 ) @ SV1417 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV266 @ ( c_Set_Oinsert @ SV886 @ SV1417 @ SV1880 ) @ ( tc_fun @ SV1880 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5805]) ).
thf(6188,plain,
! [SV267: $i,SV887: $i,SV2235: $i,SV1418: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1418 ) @ SV2235 ) @ SV887 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV267 @ ( c_Set_Oinsert @ SV2235 @ SV887 @ SV1418 ) @ ( tc_fun @ SV1418 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1418 ) @ SV2235 ) @ SV267 ) )
= $true )
| ( ( c_lessequals @ SV267 @ SV887 @ ( tc_fun @ SV1418 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5806]) ).
thf(6189,plain,
! [SV2236: $i,SV268: $i,SV888: $i,SV1881: $i,SV2577: $i,SV1419: $i] :
( ( ( ~ ( c_lessequals @ SV1419 @ SV2577 @ ( tc_fun @ SV1881 @ tc_bool ) )
| ~ ( c_lessequals @ SV888 @ SV2577 @ ( tc_fun @ SV1881 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV268 @ SV2577 @ SV1881 @ SV2236 ) )
= $true )
| ( ( ( c_Set_Oimage @ SV268 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV888 @ SV1419 @ ( tc_fun @ SV1881 @ tc_bool ) ) @ SV1881 @ SV2236 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV268 @ SV888 @ SV1881 @ SV2236 ) @ ( c_Set_Oimage @ SV268 @ SV1419 @ SV1881 @ SV2236 ) @ ( tc_fun @ SV2236 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5807]) ).
thf(6190,plain,
! [SV2238: $i,SV270: $i,SV890: $i,SV1883: $i,SV2578: $i,SV1421: $i] :
( ( ( ~ ( c_lessequals @ SV1421 @ SV2578 @ ( tc_fun @ SV1883 @ tc_bool ) )
| ~ ( c_lessequals @ SV890 @ SV2578 @ ( tc_fun @ SV1883 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV270 @ SV2578 @ SV1883 @ SV2238 ) )
= $true )
| ( ( ( c_Set_Oimage @ SV270 @ ( c_HOL_Ominus__class_Ominus @ SV890 @ SV1421 @ ( tc_fun @ SV1883 @ tc_bool ) ) @ SV1883 @ SV2238 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV270 @ SV890 @ SV1883 @ SV2238 ) @ ( c_Set_Oimage @ SV270 @ SV1421 @ SV1883 @ SV2238 ) @ ( tc_fun @ SV2238 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5808]) ).
thf(6191,plain,
! [SV2579: $i,SV2240: $i,SV1885: $i,SV1423: $i,SV892: $i,SV272: $i] :
( ( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ SV272 @ SV892 @ ( c_Option_Ooption_ONone @ SV1423 ) @ SV1885 @ ( tc_Option_Ooption @ SV1423 ) ) @ ( c_Fun_Ofun__upd @ SV2240 @ SV892 @ ( c_Option_Ooption_OSome @ SV2579 @ SV1423 ) @ SV1885 @ ( tc_Option_Ooption @ SV1423 ) ) @ SV1885 @ SV1423 )
= $true )
| ( ( ~ ( c_Map_Omap__le @ SV272 @ SV2240 @ SV1885 @ SV1423 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5810]) ).
thf(6192,plain,
! [SV1424: $i,SV273: $i,SV893: $i,SV1886: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1886 ) @ SV893 ) @ SV273 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV273 @ ( c_Set_Oinsert @ SV893 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1886 @ tc_bool ) ) @ SV1886 ) @ ( tc_fun @ SV1886 @ tc_bool ) ) @ SV1424 @ ( tc_fun @ SV1886 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1886 ) @ SV893 ) @ SV1424 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV273 @ ( c_Set_Oinsert @ SV893 @ SV1424 @ SV1886 ) @ ( tc_fun @ SV1886 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5811]) ).
thf(6193,plain,
! [SV1428: $i,SV2241: $i,SV1888: $i,SV898: $i,SV278: $i] :
( ( ( c_Fun_Oinj__on @ SV278 @ SV898 @ SV1888 @ SV2241 )
= $false )
| ( ( c_Fun_Oinj__on @ SV278 @ ( c_HOL_Ominus__class_Ominus @ SV898 @ SV1428 @ ( tc_fun @ SV1888 @ tc_bool ) ) @ SV1888 @ SV2241 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5812]) ).
thf(6194,plain,
! [SV1433: $i,SV283: $i,SV903: $i,SV1892: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1892 ) @ SV903 ) @ SV283 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV283 @ ( c_Set_Oinsert @ SV903 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1892 @ tc_bool ) ) @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) ) @ SV1433 @ ( tc_fun @ SV1892 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV283 @ SV1433 @ ( tc_fun @ SV1892 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV283 @ ( c_Set_Oinsert @ SV903 @ SV1433 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5815]) ).
thf(6195,plain,
! [SV292: $i,SV912: $i,SV1898: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1898 @ SV912 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV292 @ SV1898 @ ( tc_fun @ SV912 @ tc_bool ) ) @ SV912 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV292 @ SV912 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5819]) ).
thf(6196,plain,
! [SV293: $i,SV1441: $i,SV913: $i] :
( ( ( c_Finite__Set_Ofinite @ SV913 @ SV1441 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV293 @ SV1441 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV293 @ SV913 @ ( tc_fun @ SV1441 @ tc_bool ) ) @ SV1441 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5820]) ).
thf(6197,plain,
! [SV918: $i,SV1902: $i,SV1446: $i,SV298: $i,SV2465: $i] :
( ( ( c_Map_Omap__le @ ( c_Map_Omap__add @ SV2465 @ SV298 @ SV1446 @ SV1902 ) @ SV918 @ SV1446 @ SV1902 )
= $false )
| ( ( c_Map_Omap__le @ SV298 @ SV918 @ SV1446 @ SV1902 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5822]) ).
thf(6198,plain,
! [SV1448: $i,SV300: $i,SV2466: $i,SV920: $i,SV2247: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2247 ) @ SV920 ) @ SV2466 ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV2466 @ SV300 @ SV2247 @ ( tc_fun @ SV1448 @ tc_bool ) ) @ SV1448 )
| ~ ( c_Finite__Set_Ofinite @ SV2466 @ SV2247 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ SV300 @ SV920 ) @ SV1448 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5823]) ).
thf(6199,plain,
! [SV302: $i,SV1903: $i,SV1450: $i,SV922: $i,SV2467: $i] :
( ( ( ~ ( c_Map_Omap__le @ SV2467 @ SV922 @ SV1450 @ SV1903 ) )
= $true )
| ( ( ~ ( c_Map_Omap__le @ SV302 @ SV2467 @ SV1450 @ SV1903 ) )
= $true )
| ( ( c_Map_Omap__le @ SV302 @ SV922 @ SV1450 @ SV1903 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5824]) ).
thf(6200,plain,
! [SV924: $i,SV2468: $i,SV304: $i,SV1905: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1905 @ SV304 @ SV2468 ) @ SV924 ) )
= $false )
| ( ( SV1905 = SV924 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV304 @ SV924 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5826]) ).
thf(6201,plain,
! [SV305: $i,SV1452: $i,SV1906: $i,SV2580: $i,SV925: $i] :
( ( ( ( ( hAPP @ SV925 @ SV2580 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1906 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1452 ) @ SV2580 ) @ SV305 ) ) )
= $true )
| ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV305 @ SV925 @ SV1452 @ ( tc_fun @ SV1906 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1906 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5827]) ).
thf(6202,plain,
! [SV2469: $i,SV2250: $i,SV1908: $i,SV1455: $i,SV928: $i,SV308: $i] :
( ( ( c_Com_Ocom_OCond @ SV308 @ SV928 @ SV1455 )
= ( c_Com_Ocom_OLocal @ SV1908 @ SV2250 @ SV2469 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5829]) ).
thf(6203,plain,
! [SV934: $i,SV317: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV317 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ SV317 ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
= $false )
| ( ( ~ c_Hoare__Mirabelle_Ostate__not__singleton ) = $true )
| ( ( c_Com_OWT @ SV934 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV317 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ SV934 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5831]) ).
thf(6204,plain,
! [SV2581: $i,SV2470: $i,SV2252: $i,SV1913: $i,SV1458: $i,SV935: $i,SV318: $i] :
( ( ! [SY7404: $i,SY7405: $i] :
( ( ( hAPP @ SV318 @ ( c_Set_Oinsert @ SV935 @ ( c_Set_Oinsert @ SV1458 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1913 @ tc_bool ) ) @ SV1913 ) @ SV1913 ) )
= ( hAPP @ ( hAPP @ SV2252 @ SV935 ) @ SV1458 ) )
| ! [SY7406: $i,SY7407: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2470 @ SV318 @ SV2581 @ SY7404 @ SY7405 @ SV2252 @ SY7406 @ SY7407 @ SV1913 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5832]) ).
thf(6205,plain,
! [SV2582: $i,SV2471: $i,SV2253: $i,SV1914: $i,SV1459: $i,SV936: $i,SV319: $i] :
( ( ! [SY7408: $i,SY7409: $i] :
( ( ( hAPP @ SV319 @ ( c_Set_Oinsert @ SV936 @ ( c_Set_Oinsert @ SV1459 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1914 @ tc_bool ) ) @ SV1914 ) @ SV1914 ) )
= ( hAPP @ ( hAPP @ SV2253 @ SV936 ) @ SV1459 ) )
| ! [SY7410: $i,SY7411: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV319 @ SV2471 @ SV2582 @ SY7408 @ SV2253 @ SY7409 @ SY7410 @ SY7411 @ SV1914 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5833]) ).
thf(6206,plain,
! [SV2472: $i,SV2254: $i,SV1915: $i,SV1460: $i,SV937: $i,SV320: $i] :
( ( ( ( c_Com_Ocom_OCond @ SV320 @ SV937 @ SV1460 )
!= ( c_Com_Ocom_OCond @ SV1915 @ SV2254 @ SV2472 ) )
= $true )
| ( ( SV1460 = SV2472 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5834]) ).
thf(6207,plain,
! [SV2583: $i,SV2255: $i,SV1916: $i,SV1461: $i,SV938: $i,SV321: $i] :
( ( ( ( c_Com_Ocom_OCond @ SV321 @ SV938 @ SV1461 )
!= ( c_Com_Ocom_OCond @ SV1916 @ SV2255 @ SV2583 ) )
= $true )
| ( ( SV938 = SV2255 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5835]) ).
thf(6208,plain,
! [SV2584: $i,SV2473: $i,SV1917: $i,SV1462: $i,SV939: $i,SV322: $i] :
( ( ( ( c_Com_Ocom_OCond @ SV322 @ SV939 @ SV1462 )
!= ( c_Com_Ocom_OCond @ SV1917 @ SV2473 @ SV2584 ) )
= $true )
| ( ( SV322 = SV1917 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5836]) ).
thf(6209,plain,
! [SV2263: $i,SV1926: $i,SV1472: $i,SV958: $i,SV341: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV341 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV958 @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SV1472 ) @ tc_Com_Ocom ) @ SV1926 @ SV2263 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2263 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2263 ) ) @ SV2263 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV341 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV958 @ ( c_Com_Ocom_OBODY @ SV1472 ) @ SV1926 @ SV2263 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2263 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2263 ) ) @ SV2263 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5843]) ).
thf(6210,plain,
! [SV342: $i,SV2264: $i,SV1927: $i,SV1473: $i,SV959: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV959 @ ( c_Com_Ocom_OBODY @ SV1473 ) @ SV1927 @ SV2264 ) @ SV342 @ ( tc_Hoare__Mirabelle_Otriple @ SV2264 ) ) @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV959 @ ( c_Option_Othe @ ( hAPP @ c_Com_Obody @ SV1473 ) @ tc_Com_Ocom ) @ SV1927 @ SV2264 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2264 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2264 ) ) @ SV2264 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV342 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV959 @ ( c_Com_Ocom_OBODY @ SV1473 ) @ SV1927 @ SV2264 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2264 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2264 ) ) @ SV2264 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5844]) ).
thf(6211,plain,
! [SV343: $i,SV2585: $i,SV2478: $i,SV1474: $i,SV960: $i] :
( ( ( ( ( c_Finite__Set_Osetsum @ SV960 @ ( c_HOL_Ominus__class_Ominus @ SV1474 @ ( c_Set_Oinsert @ SV2478 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2585 @ tc_bool ) ) @ SV2585 ) @ ( tc_fun @ SV2585 @ tc_bool ) ) @ SV2585 @ SV343 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV960 @ SV1474 @ SV2585 @ SV343 ) @ ( hAPP @ SV960 @ SV2478 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2585 ) @ SV2478 ) @ SV1474 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1474 @ SV2585 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV343 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5845]) ).
thf(6212,plain,
! [SV344: $i,SV2586: $i,SV2479: $i,SV1475: $i,SV961: $i] :
( ( ( ( ( c_Finite__Set_Osetsum @ SV961 @ ( c_HOL_Ominus__class_Ominus @ SV1475 @ ( c_Set_Oinsert @ SV2479 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2586 @ tc_bool ) ) @ SV2586 ) @ ( tc_fun @ SV2586 @ tc_bool ) ) @ SV2586 @ SV344 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV961 @ SV1475 @ SV2586 @ SV344 ) @ ( hAPP @ SV961 @ SV2479 ) @ SV344 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2586 ) @ SV2479 ) @ SV1475 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1475 @ SV2586 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV344 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5846]) ).
thf(6213,plain,
! [SV2265: $i,SV1929: $i,SV1477: $i,SV963: $i,SV347: $i] :
( ( ( c_Fun_Oinj__on @ SV347 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV963 @ SV1477 @ ( tc_fun @ SV1929 @ tc_bool ) ) @ SV1929 @ SV2265 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV347 @ ( c_HOL_Ominus__class_Ominus @ SV963 @ SV1477 @ ( tc_fun @ SV1929 @ tc_bool ) ) @ SV1929 @ SV2265 ) @ ( c_Set_Oimage @ SV347 @ ( c_HOL_Ominus__class_Ominus @ SV1477 @ SV963 @ ( tc_fun @ SV1929 @ tc_bool ) ) @ SV1929 @ SV2265 ) @ ( tc_fun @ SV2265 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2265 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5847]) ).
thf(6214,plain,
! [SV2266: $i,SV1930: $i,SV1478: $i,SV964: $i,SV348: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV348 @ ( c_HOL_Ominus__class_Ominus @ SV964 @ SV1478 @ ( tc_fun @ SV1930 @ tc_bool ) ) @ SV1930 @ SV2266 ) @ ( c_Set_Oimage @ SV348 @ ( c_HOL_Ominus__class_Ominus @ SV1478 @ SV964 @ ( tc_fun @ SV1930 @ tc_bool ) ) @ SV1930 @ SV2266 ) @ ( tc_fun @ SV2266 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2266 @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV348 @ SV1478 @ SV1930 @ SV2266 )
| ~ ( c_Fun_Oinj__on @ SV348 @ SV964 @ SV1930 @ SV2266 )
| ( c_Fun_Oinj__on @ SV348 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV964 @ SV1478 @ ( tc_fun @ SV1930 @ tc_bool ) ) @ SV1930 @ SV2266 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5848]) ).
thf(6215,plain,
! [SV965: $i,SV1931: $i,SV1479: $i,SV349: $i] :
( ( ( c_lessequals @ SV349 @ SV1479 @ ( tc_fun @ SV1931 @ tc_bool ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV349 @ ( c_Set_Oinsert @ SV965 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1931 @ tc_bool ) ) @ SV1931 ) @ ( tc_fun @ SV1931 @ tc_bool ) ) @ SV1479 @ ( tc_fun @ SV1931 @ tc_bool ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1931 ) @ SV965 ) @ SV1479 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV349 @ ( c_Set_Oinsert @ SV965 @ SV1479 @ SV1931 ) @ ( tc_fun @ SV1931 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5849]) ).
thf(6216,plain,
! [SV2480: $i,SV2267: $i,SV1932: $i,SV1480: $i,SV966: $i,SV350: $i] :
( ( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ SV350 @ SV966 @ SV1480 @ SV1932 @ SV2267 ) @ SV2480 @ SV1932 @ SV2267 )
= ( c_Set_Oinsert @ SV1480 @ ( c_Set_Oimage @ SV350 @ ( c_HOL_Ominus__class_Ominus @ SV2480 @ ( c_Set_Oinsert @ SV966 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1932 @ tc_bool ) ) @ SV1932 ) @ ( tc_fun @ SV1932 @ tc_bool ) ) @ SV1932 @ SV2267 ) @ SV2267 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1932 ) @ SV966 ) @ SV2480 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5850]) ).
thf(6217,plain,
! [SV351: $i,SV2587: $i,SV2481: $i,SV1481: $i,SV967: $i] :
( ( ( ( ( c_Finite__Set_Osetsum @ SV967 @ ( c_HOL_Ominus__class_Ominus @ SV1481 @ ( c_Set_Oinsert @ SV2481 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2587 @ tc_bool ) ) @ SV2587 ) @ ( tc_fun @ SV2587 @ tc_bool ) ) @ SV2587 @ SV351 )
= ( c_Finite__Set_Osetsum @ SV967 @ SV1481 @ SV2587 @ SV351 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2587 ) @ SV2481 ) @ SV1481 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1481 @ SV2587 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV351 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5851]) ).
thf(6218,plain,
! [SV2482: $i,SV2268: $i,SV1933: $i,SV1483: $i,SV969: $i,SV353: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV969 @ ( c_Com_Ocom_OSemi @ SV1483 @ SV1933 ) @ SV2268 @ SV2482 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) ) @ SV2482 )
= $true )
| ( ( ! [SY7347: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY7347 @ SV1933 @ SV2268 @ SV2482 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) ) @ SV2482 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV969 @ SV1483 @ SY7347 @ SV2482 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) ) @ SV2482 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5853]) ).
thf(6219,plain,
! [SV2483: $i,SV2269: $i,SV1934: $i,SV1485: $i,SV971: $i,SV355: $i] :
( ( ( ( c_Map_Omap__add @ ( c_Fun_Ofun__upd @ SV355 @ SV971 @ ( c_Option_Ooption_OSome @ SV1485 @ SV1934 ) @ SV2269 @ ( tc_Option_Ooption @ SV1934 ) ) @ SV2483 @ SV2269 @ SV1934 )
= ( c_Fun_Ofun__upd @ ( c_Map_Omap__add @ SV355 @ SV2483 @ SV2269 @ SV1934 ) @ SV971 @ ( c_Option_Ooption_OSome @ SV1485 @ SV1934 ) @ SV2269 @ ( tc_Option_Ooption @ SV1934 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2269 ) @ SV971 ) @ ( c_Map_Odom @ SV2483 @ SV2269 @ SV1934 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5854]) ).
thf(6220,plain,
! [SV972: $i,SV1935: $i,SV1486: $i,SV356: $i] :
( ( ( c_lessequals @ SV356 @ SV1486 @ ( tc_fun @ SV1935 @ tc_bool ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV356 @ ( c_Set_Oinsert @ SV972 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1935 @ tc_bool ) ) @ SV1935 ) @ ( tc_fun @ SV1935 @ tc_bool ) ) @ SV1486 @ ( tc_fun @ SV1935 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV356 @ SV1486 @ ( tc_fun @ SV1935 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV356 @ ( c_Set_Oinsert @ SV972 @ SV1486 @ SV1935 ) @ ( tc_fun @ SV1935 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5855]) ).
thf(6221,plain,
! [SV2588: $i,SV2484: $i,SV2270: $i,SV1937: $i,SV1488: $i,SV974: $i,SV358: $i] :
( ( ( c_Nitpick_Ofold__graph_H @ SV358 @ SV974 @ SV1488 @ ( hAPP @ ( hAPP @ SV358 @ SV1937 ) @ SV2270 ) @ SV2484 @ SV2588 )
| ~ ( c_Nitpick_Ofold__graph_H @ SV358 @ SV974 @ ( c_HOL_Ominus__class_Ominus @ SV1488 @ ( c_Set_Oinsert @ SV1937 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2484 @ tc_bool ) ) @ SV2484 ) @ ( tc_fun @ SV2484 @ tc_bool ) ) @ SV2270 @ SV2484 @ SV2588 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2484 ) @ SV1937 ) @ SV1488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5856]) ).
thf(6222,plain,
! [SV1938: $i,SV359: $i,SV975: $i,SV1489: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1489 ) @ SV975 ) @ SV359 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV359 @ ( c_Set_Oinsert @ SV975 @ SV1938 @ SV1489 ) @ ( tc_fun @ SV1489 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV359 @ ( c_Set_Oinsert @ SV975 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1489 @ tc_bool ) ) @ SV1489 ) @ ( tc_fun @ SV1489 @ tc_bool ) ) @ SV1938 @ ( tc_fun @ SV1489 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5857]) ).
thf(6223,plain,
! [SV1490: $i,SV360: $i,SV976: $i,SV1939: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1939 ) @ SV976 ) @ SV360 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV360 @ ( c_Set_Oinsert @ SV976 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1939 @ tc_bool ) ) @ SV1939 ) @ ( tc_fun @ SV1939 @ tc_bool ) ) @ SV1490 @ ( tc_fun @ SV1939 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV360 @ ( c_Set_Oinsert @ SV976 @ SV1490 @ SV1939 ) @ ( tc_fun @ SV1939 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5858]) ).
thf(6224,plain,
! [SV1491: $i,SV361: $i,SV977: $i,SV1940: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1940 ) @ SV977 ) @ SV361 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV361 @ ( c_Set_Oinsert @ SV977 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1940 @ tc_bool ) ) @ SV1940 ) @ ( tc_fun @ SV1940 @ tc_bool ) ) @ SV1491 @ ( tc_fun @ SV1940 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV361 @ ( c_Set_Oinsert @ SV977 @ SV1491 @ SV1940 ) @ ( tc_fun @ SV1940 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5859]) ).
thf(6225,plain,
! [SV2589: $i,SV2485: $i,SV2271: $i,SV1942: $i,SV1493: $i,SV979: $i,SV363: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV363 @ SV979 @ SV1493 @ ( hAPP @ ( hAPP @ SV363 @ SV1942 ) @ SV2271 ) @ SV2485 @ SV2589 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2485 ) @ SV1942 ) @ SV1493 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV363 @ SV979 @ ( c_HOL_Ominus__class_Ominus @ SV1493 @ ( c_Set_Oinsert @ SV1942 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2485 @ tc_bool ) ) @ SV2485 ) @ ( tc_fun @ SV2485 @ tc_bool ) ) @ SV2271 @ SV2485 @ SV2589 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5860]) ).
thf(6226,plain,
! [SV980: $i,SV364: $i,SV1943: $i,SV2486: $i,SV1494: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1494 ) @ SV2486 ) @ SV1943 ) )
= $false )
| ( ( ( c_Set_Oimage @ ( c_COMBK @ SV364 @ SV980 @ SV1494 ) @ SV1943 @ SV1494 @ SV980 )
= ( c_Set_Oinsert @ SV364 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV980 @ tc_bool ) ) @ SV980 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5861]) ).
thf(6227,plain,
! [SV1944: $i,SV365: $i,SV981: $i,SV1495: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1495 ) @ SV981 ) @ SV365 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1495 ) @ SV981 ) @ SV1944 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV365 @ ( c_Set_Oinsert @ SV981 @ SV1944 @ SV1495 ) @ ( tc_fun @ SV1495 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV365 @ ( c_Set_Oinsert @ SV981 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1495 @ tc_bool ) ) @ SV1495 ) @ ( tc_fun @ SV1495 @ tc_bool ) ) @ SV1944 @ ( tc_fun @ SV1495 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5862]) ).
thf(6228,plain,
! [SV2590: $i,SV982: $i,SV1496: $i,SV2487: $i,SV366: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ SV366 @ SV2487 @ SV1496 ) @ ( c_Set_Oinsert @ SV982 @ SV2590 @ SV2487 ) @ ( tc_fun @ SV2487 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Map_Odom @ SV366 @ SV2487 @ SV1496 ) @ SV2590 @ ( tc_fun @ SV2487 @ tc_bool ) ) )
= $true )
| ( ( ( hAPP @ SV366 @ SV982 )
= ( c_Option_Ooption_ONone @ SV1496 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5863]) ).
thf(6229,plain,
! [SV2488: $i,SV2272: $i,SV1946: $i,SV1498: $i,SV985: $i,SV369: $i] :
( ( ( c_Com_Ocom_OLocal @ SV369 @ SV985 @ SV1498 )
= ( c_Com_Ocom_OCond @ SV1946 @ SV2272 @ SV2488 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[5864]) ).
thf(6230,plain,
! [SV1948: $i,SV1500: $i,SV987: $i,SV2489: $i,SV371: $i] :
( ( ( c_Fun_Oinj__on @ SV371 @ ( c_Set_Oinsert @ SV2489 @ SV987 @ SV1500 ) @ SV1500 @ SV1948 )
= $false )
| ( ( c_Fun_Oinj__on @ SV371 @ SV987 @ SV1500 @ SV1948 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5866]) ).
thf(6231,plain,
! [SV992: $i,SV376: $i,SV2274: $i,SV2591: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2591 @ SV2274 @ SV376 )
| ~ ( c_HOL_Oord__class_Oless @ SV992 @ SV2591 @ SV376 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV992 @ SV2274 @ SV376 )
= $true )
| ( ( class_Orderings_Opreorder @ SV376 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5868]) ).
thf(6232,plain,
! [SV377: $i,SV1503: $i,SV993: $i,SV2275: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2275 @ SV993 @ ( tc_fun @ SV1503 @ tc_bool ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV377 @ SV2275 @ ( tc_fun @ SV1503 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV377 @ SV993 @ ( tc_fun @ SV1503 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5869]) ).
thf(6233,plain,
! [SV2276: $i,SV378: $i,SV2592: $i,SV994: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV994 @ SV2592 @ SV378 )
| ~ ( c_HOL_Oord__class_Oless @ SV2592 @ SV2276 @ SV378 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV994 @ SV2276 @ SV378 )
= $true )
| ( ( class_Orderings_Oorder @ SV378 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5870]) ).
thf(6234,plain,
! [SV1951: $i,SV1504: $i,SV995: $i,SV379: $i,SV2277: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2277 ) @ ( hAPP @ SV379 @ SV995 ) ) @ ( c_Set_Oimage @ SV379 @ ( c_HOL_Ominus__class_Ominus @ SV1504 @ ( c_Set_Oinsert @ SV995 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1951 @ tc_bool ) ) @ SV1951 ) @ ( tc_fun @ SV1951 @ tc_bool ) ) @ SV1951 @ SV2277 ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV379 @ SV1504 @ SV1951 @ SV2277 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV379 @ ( c_Set_Oinsert @ SV995 @ SV1504 @ SV1951 ) @ SV1951 @ SV2277 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5871]) ).
thf(6235,plain,
! [SV1510: $i,SV1955: $i,SV2491: $i,SV1003: $i,SV387: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV387 @ SV1003 ) ) @ SV2491 ) @ SV1955 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1003 ) @ SV1510 ) @ SV2491 ) )
| ~ ( hBOOL @ ( hAPP @ SV387 @ SV1510 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV387 @ SV1003 ) ) @ SV1510 ) @ SV1955 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5873]) ).
thf(6236,plain,
! [SV2593: $i,SV389: $i,SV2279: $i,SV1005: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1005 @ SV2279 @ SV389 )
!= ( c_HOL_Ominus__class_Ominus @ SV2593 @ SV2593 @ SV389 ) )
= $true )
| ( ( SV1005 = SV2279 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV389 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5874]) ).
thf(6237,plain,
! [SV2492: $i,SV2280: $i,SV390: $i,SV1006: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1006 @ SV1006 @ SV390 )
!= ( c_HOL_Ominus__class_Ominus @ SV2280 @ SV2492 @ SV390 ) )
= $true )
| ( ( SV2280 = SV2492 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV390 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5875]) ).
thf(6238,plain,
! [SV1513: $i,SV392: $i,SV2281: $i,SV1956: $i,SV1008: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1008 ) @ SV1956 ) @ SV2281 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV392 @ SV1956 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV392 @ SV1008 @ SV1513 ) ) @ SV1956 ) @ SV2281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5876]) ).
thf(6239,plain,
! [SV393: $i,SV2493: $i,SV1009: $i,SV1514: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1514 ) @ SV1009 ) @ SV2493 ) )
= $true )
| ( ( ! [SY7351: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV393 @ SV1514 @ SY7351 ) ) @ SV1009 ) @ SV2493 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV393 @ SV1009 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5877]) ).
thf(6240,plain,
! [SV1515: $i,SV394: $i,SV1957: $i,SV2494: $i,SV1010: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1010 ) @ SV2494 ) @ SV1957 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV394 ) @ SV1515 ) @ SV2494 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV394 @ SV1010 ) ) @ SV1515 ) @ SV1957 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5878]) ).
thf(6241,plain,
! [SV1518: $i,SV1959: $i,SV2594: $i,SV397: $i,SV1013: $i] :
( ( ( ( c_Set_Oinsert @ SV1013 @ ( c_Map_Odom @ SV397 @ SV2594 @ SV1959 ) @ SV2594 )
= ( c_Map_Odom @ SV397 @ SV2594 @ SV1959 ) )
= $true )
| ( ( ( hAPP @ SV397 @ SV1013 )
= ( c_Option_Ooption_OSome @ SV1518 @ SV1959 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5880]) ).
thf(6242,plain,
! [SV2595: $i,SV2495: $i,SV2284: $i,SV1962: $i,SV1520: $i,SV1015: $i,SV401: $i] :
( ( ! [SY7412: $i,SY7413: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV401 @ SV1015 @ ( c_COMBC @ SV1520 @ SV1962 @ SV1962 @ tc_bool ) @ ( c_COMBC @ SV2284 @ SV1962 @ SV1962 @ tc_bool ) @ SV2495 @ SV2595 @ SY7412 @ SY7413 @ SV1962 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1015 @ SV401 @ SV1520 @ SV2284 @ SV2595 @ SV2495 @ SY7413 @ SY7412 @ SV1962 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5881]) ).
thf(6243,plain,
! [SV2496: $i,SV2285: $i,SV1963: $i,SV1524: $i,SV1019: $i,SV405: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ SV405 @ SV1019 @ SV1524 @ SV1963 ) @ SV2285 )
!= ( c_Option_Ooption_OSome @ SV2496 @ SV1963 ) )
= $true )
| ( ( ( ( hAPP @ SV405 @ SV2285 )
= ( c_Option_Ooption_OSome @ SV2496 @ SV1963 ) )
| ( ( hAPP @ SV1019 @ SV2285 )
= ( c_Option_Ooption_OSome @ SV2496 @ SV1963 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5882]) ).
thf(6244,plain,
! [SV1525: $i,SV406: $i,SV1964: $i,SV1020: $i,SV2596: $i] :
( ( ( ( ( hAPP @ SV2596 @ SV1020 )
!= ( c_Option_Ooption_ONone @ SV1964 ) )
| ! [SY7414: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SV406 @ SV2596 @ SY7414 @ SV1964 ) @ SV1020 )
= ( c_Option_Ooption_OSome @ SV1525 @ SV1964 ) ) )
= $true )
| ( ( ( hAPP @ SV406 @ SV1020 )
= ( c_Option_Ooption_OSome @ SV1525 @ SV1964 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5883]) ).
thf(6245,plain,
! [SV2286: $i,SV1965: $i,SV1526: $i,SV1021: $i,SV407: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ SV407 @ SV1021 @ SV1526 @ SV1965 ) @ SV2286 )
= ( c_Option_Ooption_ONone @ SV1965 ) )
= $false )
| ( ( ( hAPP @ SV407 @ SV2286 )
= ( c_Option_Ooption_ONone @ SV1965 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5884]) ).
thf(6246,plain,
! [SV2287: $i,SV1966: $i,SV1527: $i,SV1022: $i,SV408: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ SV408 @ SV1022 @ SV1527 @ SV1966 ) @ SV2287 )
= ( c_Option_Ooption_ONone @ SV1966 ) )
= $false )
| ( ( ( hAPP @ SV1022 @ SV2287 )
= ( c_Option_Ooption_ONone @ SV1966 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5885]) ).
thf(6247,plain,
! [SV2497: $i,SV413: $i,SV1532: $i,SV1027: $i,SV1969: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1969 ) @ SV1027 ) @ SV1532 ) )
= $false )
| ( ( ( c_Set_Oinsert @ ( hAPP @ SV413 @ SV1027 ) @ ( c_Set_Oimage @ SV413 @ SV1532 @ SV1969 @ SV2497 ) @ SV2497 )
= ( c_Set_Oimage @ SV413 @ SV1532 @ SV1969 @ SV2497 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5888]) ).
thf(6248,plain,
! [SV426: $i,SV1543: $i,SV1039: $i,SV2498: $i] :
( ( ( ( hAPP @ SV2498 @ SV1039 )
!= ( c_Option_Ooption_ONone @ SV1543 ) )
= $true )
| ( ( ! [SY7355: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SV426 @ SV2498 @ SY7355 @ SV1543 ) @ SV1039 )
= ( c_Option_Ooption_ONone @ SV1543 ) ) )
= $true )
| ( ( ( hAPP @ SV426 @ SV1039 )
= ( c_Option_Ooption_ONone @ SV1543 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5894]) ).
thf(6249,plain,
! [SV1544: $i,SV1040: $i,SV1976: $i,SV427: $i,SV2597: $i] :
( ( ( ! [SY7415: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SV2597 @ SV427 @ SY7415 @ SV1976 ) @ SV1040 )
= ( c_Option_Ooption_OSome @ SV1544 @ SV1976 ) ) )
= $true )
| ( ( ( hAPP @ SV427 @ SV1040 )
= ( c_Option_Ooption_OSome @ SV1544 @ SV1976 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5895]) ).
thf(6250,plain,
! [SV1545: $i,SV1041: $i,SV1977: $i,SV428: $i,SV2598: $i] :
( ( ( ! [SY7416: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SV2598 @ SV428 @ SY7416 @ SV1977 ) @ SV1041 )
= ( c_Option_Ooption_OSome @ SV1545 @ SV1977 ) ) )
= $true )
| ( ( ( hAPP @ SV428 @ SV1041 )
= ( c_Option_Ooption_OSome @ SV1545 @ SV1977 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5896]) ).
thf(6251,plain,
! [SV2293: $i,SV1978: $i,SV1546: $i,SV1042: $i,SV429: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV429 ) @ ( hAPP @ SV1042 @ SV1546 ) ) @ ( c_Set_Oimage @ SV1042 @ ( c_HOL_Ominus__class_Ominus @ SV1978 @ ( c_Set_Oinsert @ SV1546 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2293 @ tc_bool ) ) @ SV2293 ) @ ( tc_fun @ SV2293 @ tc_bool ) ) @ SV2293 @ SV429 ) ) )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV1042 @ ( c_Set_Oinsert @ SV1546 @ SV1978 @ SV2293 ) @ SV2293 @ SV429 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5897]) ).
thf(6252,plain,
! [SV2298: $i,SV1985: $i,SV1554: $i,SV1053: $i,SV441: $i] :
( ( ( ~ ( c_Map_Omap__le @ SV441 @ ( c_Map_Omap__add @ SV441 @ SV1053 @ SV1554 @ SV1985 ) @ SV1554 @ SV1985 ) )
= $true )
| ( ( ~ ( c_Map_Omap__le @ SV1053 @ SV2298 @ SV1554 @ SV1985 )
| ~ ( c_Map_Omap__le @ SV441 @ SV2298 @ SV1554 @ SV1985 ) )
= $true )
| ( ( c_Map_Omap__le @ ( c_Map_Omap__add @ SV441 @ SV1053 @ SV1554 @ SV1985 ) @ SV2298 @ SV1554 @ SV1985 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5901]) ).
thf(6253,plain,
! [SV442: $i,SV1054: $i,SV2499: $i,SV1555: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1555 ) @ SV2499 ) @ SV1054 ) )
= $false )
| ( ( ! [SY6457: $i] :
( ~ ( hBOOL @ ( hAPP @ SV442 @ SY6457 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1555 ) @ SY6457 ) @ SV1054 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV442 @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1054 @ SV442 @ SV1555 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5902]) ).
thf(6254,plain,
! [SV1556: $i,SV1986: $i,SV1055: $i,SV443: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ SV1055 ) @ SV1986 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ SV1055 ) @ SV1556 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ SV1055 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1556 @ SV1986 @ ( tc_fun @ SV443 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5903]) ).
thf(6255,plain,
! [SV1557: $i,SV1987: $i,SV1056: $i,SV444: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ SV1056 ) @ SV1987 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ SV1056 ) @ SV1557 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ SV1056 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1557 @ SV1987 @ ( tc_fun @ SV444 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5904]) ).
thf(6256,plain,
! [SV445: $i,SV2299: $i,SV1057: $i,SV1558: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1558 ) @ SV1057 ) @ SV2299 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1558 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2299 @ SV445 @ SV1558 ) ) @ SV2299 ) )
| ! [SY7232: $i] :
~ ( hBOOL @ ( hAPP @ SY7232 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2299 @ SY7232 @ SV1558 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV445 @ SV1057 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5905]) ).
thf(6257,plain,
! [SV446: $i,SV2300: $i,SV1058: $i,SV1559: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1559 ) @ SV1058 ) @ SV2300 ) )
= $false )
| ( ( ! [SY7233: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1559 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2300 @ SY7233 @ SV1559 ) ) @ SV2300 ) )
| ~ ( hBOOL @ ( hAPP @ SV446 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2300 @ SV446 @ SV1559 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV446 @ SV1058 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5906]) ).
thf(6258,plain,
! [SV447: $i,SV2301: $i,SV1059: $i,SV1560: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1560 ) @ SV1059 ) @ SV2301 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV447 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2301 @ SV447 @ SV1560 ) ) )
| ! [SY7234: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1560 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2301 @ SY7234 @ SV1560 ) ) @ SV2301 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV447 @ SV1059 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5907]) ).
thf(6259,plain,
! [SV448: $i,SV2302: $i,SV1060: $i,SV1561: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1561 ) @ SV1060 ) @ SV2302 ) )
= $false )
| ( ( ! [SY7235: $i] :
~ ( hBOOL @ ( hAPP @ SY7235 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2302 @ SY7235 @ SV1561 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1561 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2302 @ SV448 @ SV1561 ) ) @ SV2302 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV448 @ SV1060 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5908]) ).
thf(6260,plain,
! [SV2500: $i,SV2303: $i,SV1988: $i,SV1562: $i,SV1061: $i,SV449: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV449 ) @ SV1061 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV1562 @ SV1988 @ SV2303 @ SV2500 @ SV449 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1988 @ SV1061 ) @ SV2500 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1562 @ SV2303 ) @ SV1061 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5909]) ).
thf(6261,plain,
! [SV452: $i,SV1991: $i,SV2304: $i,SV1064: $i,SV1565: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1565 @ SV1064 ) @ SV2304 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1565 @ SV1991 ) @ SV1064 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV452 ) @ SV1064 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV1565 @ SV1991 @ SV2304 @ SV452 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5912]) ).
thf(6262,plain,
! [SV1566: $i,SV1065: $i,SV2305: $i,SV453: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV453 ) @ SV2305 ) @ SV1065 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1566 @ SV2305 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV453 ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1065 @ SV1566 @ SV453 ) ) @ SV1065 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5913]) ).
thf(6263,plain,
! [SV458: $i,SV1993: $i,SV2306: $i,SV1070: $i,SV1567: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1567 @ SV1070 ) @ SV2306 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1567 @ SV1993 ) @ SV1070 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV458 ) @ SV1070 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV1567 @ SV1993 @ SV2306 @ SV458 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5914]) ).
thf(6264,plain,
! [SV1568: $i,SV2307: $i,SV1071: $i,SV459: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV459 ) @ SV1071 ) @ ( c_Set_Oinsert @ SV2307 @ SV1568 @ SV459 ) ) )
= $false )
| ( ( SV1071 = SV2307 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV459 ) @ SV1071 ) @ SV1568 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5915]) ).
thf(6265,plain,
! [SV2501: $i,SV2308: $i,SV1994: $i,SV1569: $i,SV1072: $i,SV460: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV460 ) @ SV1072 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV1569 @ SV1994 @ SV2308 @ SV2501 @ SV460 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1569 @ SV1072 ) @ SV2501 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1994 @ SV2308 ) @ SV1072 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5916]) ).
thf(6266,plain,
! [SV1570: $i,SV2502: $i,SV1073: $i,SV461: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV461 ) @ SV1073 ) @ ( c_HOL_Ominus__class_Ominus @ SV2502 @ SV1570 @ ( tc_fun @ SV461 @ tc_bool ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV461 ) @ SV1073 ) @ SV1570 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5917]) ).
thf(6267,plain,
! [SV1572: $i,SV1075: $i,SV2503: $i,SV463: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ SV2503 ) @ SV1075 ) )
= $false )
| ( ( ! [SY6485: $i] :
( ~ ( hBOOL @ ( hAPP @ SV1572 @ SY6485 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ SY6485 ) @ SV1075 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1075 @ SV1572 @ SV463 ) ) @ SV1075 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5919]) ).
thf(6268,plain,
! [SV464: $i,SV1076: $i,SV2310: $i,SV1573: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1573 ) @ SV2310 ) @ SV1076 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV464 @ SV2310 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV464 @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ SV1076 @ SV464 @ SV1573 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5920]) ).
thf(6269,plain,
! [SV1077: $i,SV1995: $i,SV465: $i,SV2599: $i,SV1574: $i] :
( ( ( ( ( hAPP @ SV1574 @ SV2599 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV465 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1995 ) @ SV2599 ) @ SV1077 ) ) )
= $true )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV465 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1077 @ SV1574 @ SV1995 @ ( tc_fun @ SV465 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5921]) ).
thf(6270,plain,
! [SV475: $i,SV1087: $i,SV2312: $i,SV1580: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1580 ) @ SV2312 ) @ SV1087 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV475 @ ( c_Set_Oinsert @ SV2312 @ SV1087 @ SV1580 ) @ ( tc_fun @ SV1580 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV475 @ SV1087 @ ( tc_fun @ SV1580 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5925]) ).
thf(6271,plain,
! [SV476: $i,SV1581: $i,SV1088: $i,SV2001: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2001 ) @ SV1088 ) @ SV1581 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV476 @ SV1581 @ ( tc_fun @ SV2001 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV476 @ ( c_Set_Oinsert @ SV1088 @ SV1581 @ SV2001 ) @ ( tc_fun @ SV2001 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5926]) ).
thf(6272,plain,
! [SV1583: $i,SV2504: $i,SV1090: $i,SV478: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV478 ) @ SV1090 ) @ SV2504 ) ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV2504 @ SV1583 @ ( tc_fun @ SV478 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV478 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV478 ) @ SV1090 ) @ SV1583 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5927]) ).
thf(6273,plain,
! [SV487: $i,SV2007: $i,SV2314: $i] :
( ( ( SV2314 = SV2007 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV2314 @ SV2007 @ SV487 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV2007 @ SV2314 @ SV487 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV487 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5929]) ).
thf(6274,plain,
! [SV488: $i,SV2008: $i,SV2315: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2315 @ SV2008 @ SV488 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV2008 @ SV2315 @ SV488 )
= $true )
| ( ( SV2008 = SV2315 )
= $true )
| ( ( class_Orderings_Olinorder @ SV488 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5930]) ).
thf(6275,plain,
! [SV1094: $i,SV489: $i,SV2316: $i,SV2009: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV2009 ) @ SV2316 ) @ SV489 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV2009 ) @ SV2316 ) @ SV1094 ) ) )
= $true )
| ( ( SV489 = SV1094 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5931]) ).
thf(6276,plain,
! [SV2317: $i,SV2010: $i,SV490: $i,SV1095: $i] :
( ( ( c_Map_Omap__le @ SV1095 @ SV490 @ SV2010 @ SV2317 )
= $false )
| ( ( ~ ( c_Map_Omap__le @ SV490 @ SV1095 @ SV2010 @ SV2317 ) )
= $true )
| ( ( SV490 = SV1095 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5932]) ).
thf(6277,plain,
! [SV491: $i,SV2011: $i,SV2318: $i] :
( ( ( SV2318 = SV2011 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV2318 @ SV2011 @ SV491 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV2011 @ SV2318 @ SV491 )
= $true )
| ( ( class_Orderings_Olinorder @ SV491 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5933]) ).
thf(6278,plain,
! [SV492: $i,SV2012: $i,SV2319: $i] :
( ( ( SV2319 = SV2012 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV2319 @ SV2012 @ SV492 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV2012 @ SV2319 @ SV492 )
= $true )
| ( ( class_Orderings_Olinorder @ SV492 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5934]) ).
thf(6279,plain,
! [SV493: $i,SV2320: $i,SV2013: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2013 @ SV2320 @ SV493 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV2320 @ SV2013 @ SV493 )
= $true )
| ( ( SV2013 = SV2320 )
= $true )
| ( ( class_Orderings_Olinorder @ SV493 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5935]) ).
thf(6280,plain,
! [SV2505: $i,SV495: $i,SV2321: $i,SV1097: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1097 @ SV2321 @ SV495 ) @ SV2505 @ SV495 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2321 @ SV2505 @ SV495 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV495 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5936]) ).
thf(6281,plain,
! [SV2506: $i,SV496: $i,SV2322: $i,SV1098: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1098 @ SV2322 @ SV496 ) @ SV2506 @ SV496 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1098 @ SV2506 @ SV496 ) )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV496 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5937]) ).
thf(6282,plain,
! [SV2324: $i,SV2015: $i,SV1590: $i,SV1101: $i,SV499: $i] :
( ( ( ( c_Set_Oinsert @ SV499 @ ( c_Set_Oinsert @ SV1101 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1590 @ tc_bool ) ) @ SV1590 ) @ SV1590 )
= ( c_Set_Oinsert @ SV2015 @ ( c_Set_Oinsert @ SV2324 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1590 @ tc_bool ) ) @ SV1590 ) @ SV1590 ) )
= $false )
| ( ( ( SV499 = SV2324 )
| ( SV499 = SV2015 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5940]) ).
thf(6283,plain,
! [SV2507: $i,SV2016: $i,SV1591: $i,SV1102: $i,SV500: $i] :
( ( ( ( c_Set_Oinsert @ SV500 @ ( c_Set_Oinsert @ SV1102 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1591 @ tc_bool ) ) @ SV1591 ) @ SV1591 )
= ( c_Set_Oinsert @ SV2016 @ ( c_Set_Oinsert @ SV2507 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1591 @ tc_bool ) ) @ SV1591 ) @ SV1591 ) )
= $false )
| ( ( ( SV1102 = SV2016 )
| ( SV500 = SV2016 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5941]) ).
thf(6284,plain,
! [SV2325: $i,SV2017: $i,SV1592: $i,SV1103: $i,SV501: $i] :
( ( ( ( c_Set_Oinsert @ SV501 @ ( c_Set_Oinsert @ SV1103 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1592 @ tc_bool ) ) @ SV1592 ) @ SV1592 )
= ( c_Set_Oinsert @ SV2017 @ ( c_Set_Oinsert @ SV2325 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1592 @ tc_bool ) ) @ SV1592 ) @ SV1592 ) )
= $false )
| ( ( ( SV501 = SV2325 )
| ( SV1103 = SV2325 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5942]) ).
thf(6285,plain,
! [SV2326: $i,SV2018: $i,SV1593: $i,SV1104: $i,SV502: $i] :
( ( ( ( c_Set_Oinsert @ SV502 @ ( c_Set_Oinsert @ SV1104 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1593 @ tc_bool ) ) @ SV1593 ) @ SV1593 )
= ( c_Set_Oinsert @ SV2018 @ ( c_Set_Oinsert @ SV2326 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1593 @ tc_bool ) ) @ SV1593 ) @ SV1593 ) )
= $false )
| ( ( ( SV1104 = SV2018 )
| ( SV1104 = SV2326 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5943]) ).
thf(6286,plain,
! [SV1594: $i,SV1105: $i,SV503: $i,SV2600: $i,SV2327: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV2327 @ SV2600 @ SV503 ) ) @ SV1105 ) @ SV1594 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV2327 @ SV1105 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV503 ) @ SV1105 ) @ SV1594 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5944]) ).
thf(6287,plain,
! [SV1106: $i,SV504: $i,SV2328: $i,SV2019: $i,SV1595: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1595 ) @ SV2019 ) @ SV2328 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV504 @ SV2019 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV504 @ SV1106 @ SV1595 ) ) @ SV2019 ) @ SV2328 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5945]) ).
thf(6288,plain,
! [SV2601: $i,SV2508: $i,SV2329: $i,SV2020: $i,SV1596: $i,SV1108: $i,SV506: $i] :
( ( ! [SY7417: $i,SY7418: $i] :
( ( ( hAPP @ SV506 @ ( c_Set_Oinsert @ SV1108 @ SV1596 @ SV2020 ) )
= ( hAPP @ ( hAPP @ SV2329 @ SV1108 ) @ ( hAPP @ SV506 @ SV1596 ) ) )
| ! [SY7419: $i,SY7420: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2508 @ SV506 @ SV2601 @ SY7417 @ SY7418 @ SV2329 @ SY7419 @ SY7420 @ SV2020 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5946]) ).
thf(6289,plain,
! [SV2602: $i,SV2509: $i,SV2330: $i,SV2021: $i,SV1597: $i,SV1109: $i,SV507: $i] :
( ( ! [SY7421: $i,SY7422: $i] :
( ( ( hAPP @ SV507 @ ( c_Set_Oinsert @ SV1109 @ SV1597 @ SV2021 ) )
= ( hAPP @ ( hAPP @ SV2330 @ SV1109 ) @ ( hAPP @ SV507 @ SV1597 ) ) )
| ! [SY7423: $i,SY7424: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV507 @ SV2509 @ SV2602 @ SY7421 @ SV2330 @ SY7422 @ SY7423 @ SY7424 @ SV2021 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5947]) ).
thf(6290,plain,
! [SV1111: $i,SV2331: $i,SV1599: $i,SV509: $i,SV2603: $i,SV2023: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV2023 @ SV2603 ) )
| ! [SY7425: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ SV2603 ) @ ( hAPP @ SV1599 @ SY7425 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2331 ) @ SY7425 ) @ SV1111 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SV1111 @ SV1599 @ SV2023 @ SV2331 @ SV509 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1111 @ SV1599 @ SV2331 @ ( tc_fun @ SV509 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5948]) ).
thf(6291,plain,
! [SV1113: $i,SV1601: $i,SV2332: $i,SV511: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV511 @ SV2332 @ SV1601 )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV2332 @ SV1113 @ SV1601 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV511 @ SV1113 @ SV1601 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5949]) ).
thf(6292,plain,
! [SV2510: $i,SV2334: $i,SV2027: $i,SV1605: $i,SV1117: $i,SV515: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ SV515 @ SV1117 @ SV1605 @ SV2027 ) @ SV2334 )
!= ( c_Option_Ooption_OSome @ SV2510 @ SV2027 ) )
= $true )
| ( ( ( ( hAPP @ SV1117 @ SV2334 )
= ( c_Option_Ooption_ONone @ SV2027 ) )
| ( ( hAPP @ SV1117 @ SV2334 )
= ( c_Option_Ooption_OSome @ SV2510 @ SV2027 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5952]) ).
thf(6293,plain,
! [SV2511: $i,SV1606: $i,SV516: $i,SV1118: $i,SV2335: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2335 ) @ SV1118 ) @ ( c_Set_Ovimage @ SV516 @ ( c_Set_Oinsert @ SV1606 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2511 @ tc_bool ) ) @ SV2511 ) @ SV2335 @ SV2511 ) ) )
= $false )
| ( ( ( hAPP @ SV516 @ SV1118 )
= SV1606 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5953]) ).
thf(6294,plain,
! [SV2512: $i,SV2340: $i,SV2032: $i,SV1612: $i,SV1126: $i,SV526: $i] :
( ( ( ( c_Com_Ocom_OLocal @ SV526 @ SV1126 @ SV1612 )
!= ( c_Com_Ocom_OLocal @ SV2032 @ SV2340 @ SV2512 ) )
= $true )
| ( ( SV1612 = SV2512 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5957]) ).
thf(6295,plain,
! [SV2604: $i,SV2341: $i,SV2033: $i,SV1613: $i,SV1127: $i,SV527: $i] :
( ( ( ( c_Com_Ocom_OLocal @ SV527 @ SV1127 @ SV1613 )
!= ( c_Com_Ocom_OLocal @ SV2033 @ SV2341 @ SV2604 ) )
= $true )
| ( ( SV1127 = SV2341 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5958]) ).
thf(6296,plain,
! [SV2605: $i,SV2513: $i,SV2034: $i,SV1614: $i,SV1128: $i,SV528: $i] :
( ( ( ( c_Com_Ocom_OLocal @ SV528 @ SV1128 @ SV1614 )
!= ( c_Com_Ocom_OLocal @ SV2034 @ SV2513 @ SV2605 ) )
= $true )
| ( ( SV528 = SV2034 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5959]) ).
thf(6297,plain,
! [SV2606: $i,SV2514: $i,SV2343: $i,SV2037: $i,SV1618: $i,SV1132: $i,SV532: $i] :
( ( ( ( hAPP @ SV532 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1132 @ tc_bool ) ) )
= SV1618 )
| ! [SY7426: $i,SY7427: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2037 @ SV532 @ SV2343 @ SV2514 @ SV2606 @ SY7426 @ SV1618 @ SY7427 @ SV1132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5962]) ).
thf(6298,plain,
! [SV2607: $i,SV2515: $i,SV2344: $i,SV2038: $i,SV1619: $i,SV1133: $i,SV533: $i] :
( ( ( ( hAPP @ SV533 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1133 @ tc_bool ) ) )
= SV1619 )
| ! [SY7428: $i,SY7429: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV533 @ SV2038 @ SV2344 @ SV2515 @ SV2607 @ SY7428 @ SY7429 @ SV1619 @ SV1133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5963]) ).
thf(6299,plain,
! [SV2039: $i,SV1134: $i,SV2516: $i,SV534: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV534 @ SV2516 ) ) @ SV1134 ) @ SV2039 ) )
= $false )
| ( ( SV2039 = SV1134 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV534 @ SV1134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5964]) ).
thf(6300,plain,
! [SV2608: $i,SV2517: $i,SV2346: $i,SV2042: $i,SV1623: $i,SV1140: $i,SV541: $i] :
( ( ! [SY7430: $i] :
( ( ( hAPP @ SV541 @ ( c_Set_Oinsert @ SV1140 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1623 @ tc_bool ) ) @ SV1623 ) )
= SV1140 )
| ! [SY7431: $i,SY7432: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2042 @ SV541 @ SV2346 @ SV2517 @ SV2608 @ SY7430 @ SY7431 @ SY7432 @ SV1623 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5966]) ).
thf(6301,plain,
! [SV2609: $i,SV2518: $i,SV2347: $i,SV2043: $i,SV1624: $i,SV1141: $i,SV542: $i] :
( ( ! [SY7433: $i] :
( ( ( hAPP @ SV542 @ ( c_Set_Oinsert @ SV1141 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1624 @ tc_bool ) ) @ SV1624 ) )
= SV1141 )
| ! [SY7434: $i,SY7435: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV542 @ SV2043 @ SV2347 @ SV2518 @ SV2609 @ SY7433 @ SY7434 @ SY7435 @ SV1624 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5967]) ).
thf(6302,plain,
! [SV1626: $i,SV545: $i,SV1144: $i,SV2044: $i] :
( ( ( hBOOL @ ( hAPP @ SV2044 @ SV1144 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1144 ) @ SV1626 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1144 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1626 @ ( c_Collect @ SV2044 @ SV545 ) @ ( tc_fun @ SV545 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5968]) ).
thf(6303,plain,
! [SV1627: $i,SV2519: $i,SV2348: $i,SV547: $i,SV1145: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV1145 @ SV547 @ SV2348 @ SV2519 ) @ SV1627 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV547 @ ( hAPP @ SV1145 @ SV1627 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5969]) ).
thf(6304,plain,
! [SV2045: $i,SV1628: $i,SV2349: $i,SV548: $i,SV1146: $i] :
( ( ( hBOOL @ ( hAPP @ SV1146 @ ( hAPP @ SV548 @ SV2349 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ SV548 @ SV1146 @ SV1628 @ SV2045 ) @ SV2349 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5970]) ).
thf(6305,plain,
! [SV1148: $i,SV2046: $i,SV1630: $i,SV550: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV550 @ SV1630 @ SV2046 )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV550 @ ( c_Set_Oinsert @ SV1148 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2046 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2046 ) ) @ SV2046 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV550 @ ( c_Set_Oinsert @ SV1148 @ SV1630 @ ( tc_Hoare__Mirabelle_Otriple @ SV2046 ) ) @ SV2046 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5972]) ).
thf(6306,plain,
! [SV1631: $i,SV551: $i,SV2047: $i,SV1149: $i] :
( ( ( hBOOL @ ( hAPP @ SV1149 @ SV2047 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV551 @ SV2047 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV551 @ SV1149 @ ( tc_fun @ SV1631 @ tc_bool ) ) @ SV2047 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5973]) ).
thf(6307,plain,
! [SV2610: $i,SV2520: $i,SV552: $i,SV1632: $i,SV1150: $i] :
( ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1150 @ SV1632 @ SV552 )
!= ( c_HOL_Ominus__class_Ominus @ SV2520 @ SV2610 @ SV552 ) )
| ( c_HOL_Oord__class_Oless @ SV2520 @ SV2610 @ SV552 )
| ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SV1632 @ SV552 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV552 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5974]) ).
thf(6308,plain,
! [SV2611: $i,SV2521: $i,SV553: $i,SV1633: $i,SV1151: $i] :
( ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1151 @ SV1633 @ SV553 )
!= ( c_HOL_Ominus__class_Ominus @ SV2521 @ SV2611 @ SV553 ) )
| ( c_HOL_Oord__class_Oless @ SV1151 @ SV1633 @ SV553 )
| ~ ( c_HOL_Oord__class_Oless @ SV2521 @ SV2611 @ SV553 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV553 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5975]) ).
thf(6309,plain,
! [SV2351: $i,SV1154: $i,SV556: $i,SV2048: $i] :
( ( ( c_Fun_Oinj__on @ SV2048 @ SV556 @ SV1154 @ SV2351 )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV2048 @ SV556 @ SV1154 @ SV2351 ) @ SV2351 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV556 @ SV1154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5976]) ).
thf(6310,plain,
! [SV1635: $i,SV1156: $i,SV558: $i,SV2352: $i,SV2612: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV2612 @ SV2352 @ SV558 ) ) @ SV1156 ) @ SV1635 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV2352 ) @ SV1156 ) @ SV1635 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV558 ) @ SV1156 ) @ SV1635 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5977]) ).
thf(6311,plain,
! [SV561: $i,SV2353: $i,SV2049: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2049 @ SV2353 @ SV561 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2353 @ SV2049 @ SV561 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV561 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5978]) ).
thf(6312,plain,
! [SV562: $i,SV2354: $i,SV2050: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2050 @ SV2354 @ SV562 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2354 @ SV2050 @ SV562 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV562 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5979]) ).
thf(6313,plain,
! [SV563: $i,SV2355: $i,SV2051: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2051 @ SV2355 @ SV563 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2355 @ SV2051 @ SV563 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV563 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5980]) ).
thf(6314,plain,
! [SV564: $i,SV2356: $i,SV2052: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2052 @ SV2356 @ SV564 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2356 @ SV2052 @ SV564 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV564 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5981]) ).
thf(6315,plain,
! [SV1159: $i,SV1636: $i,SV2357: $i,SV565: $i] :
( ( ( hBOOL @ ( hAPP @ SV565 @ SV2357 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1636 ) @ SV2357 ) @ SV1159 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV565 @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ SV1159 @ SV565 @ SV1636 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5982]) ).
thf(6316,plain,
! [SV2613: $i,SV1160: $i,SV566: $i,SV2522: $i,SV1637: $i,SV2053: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2053 ) @ SV1637 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV2522 @ SV566 @ SV1160 @ SV2613 @ SV2053 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV566 @ SV1160 ) @ SV1637 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5983]) ).
thf(6317,plain,
! [SV1638: $i,SV2614: $i,SV2523: $i,SV567: $i,SV1161: $i,SV2054: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2054 ) @ SV1161 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV567 @ SV2523 @ SV2614 @ SV1638 @ SV2054 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV567 @ SV1161 ) @ SV1638 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5984]) ).
thf(6318,plain,
! [SV1639: $i,SV2358: $i,SV1162: $i,SV568: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV568 ) @ SV1162 ) @ SV2358 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2358 @ SV1639 @ ( tc_fun @ SV568 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV568 ) @ SV1162 ) @ SV1639 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5985]) ).
thf(6319,plain,
! [SV572: $i,SV2359: $i,SV1166: $i,SV1643: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1643 ) @ SV1166 ) @ SV2359 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV572 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2359 @ SV572 @ SV1643 ) ) )
| ! [SY7279: $i] :
~ ( hBOOL @ ( hAPP @ SY7279 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2359 @ SY7279 @ SV1643 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV572 @ SV1166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5986]) ).
thf(6320,plain,
! [SV573: $i,SV2360: $i,SV1167: $i,SV1644: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1644 ) @ SV1167 ) @ SV2360 ) )
= $false )
| ( ( ! [SY7280: $i] :
~ ( hBOOL @ ( hAPP @ SY7280 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2360 @ SY7280 @ SV1644 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV573 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2360 @ SV573 @ SV1644 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV573 @ SV1167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5987]) ).
thf(6321,plain,
! [SV574: $i,SV2361: $i,SV1168: $i,SV1645: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1645 ) @ SV1168 ) @ SV2361 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1645 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2361 @ SV574 @ SV1645 ) ) @ SV2361 ) )
| ! [SY7281: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1645 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2361 @ SY7281 @ SV1645 ) ) @ SV2361 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV574 @ SV1168 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5988]) ).
thf(6322,plain,
! [SV575: $i,SV2362: $i,SV1169: $i,SV1646: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1646 ) @ SV1169 ) @ SV2362 ) )
= $false )
| ( ( ! [SY7282: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1646 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2362 @ SY7282 @ SV1646 ) ) @ SV2362 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1646 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2362 @ SV575 @ SV1646 ) ) @ SV2362 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV575 @ SV1169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5989]) ).
thf(6323,plain,
! [SV576: $i,SV2363: $i,SV1170: $i,SV1647: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1647 ) @ SV1170 ) @ SV2363 ) )
= $false )
| ( ( ! [SY7283: $i] :
( ~ ( hBOOL @ ( hAPP @ SV576 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2363 @ SY7283 @ SV576 @ SV1647 ) ) )
| ~ ( hBOOL @ ( hAPP @ SY7283 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2363 @ SY7283 @ SV576 @ SV1647 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV576 @ SV1170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5990]) ).
thf(6324,plain,
! [SV577: $i,SV2364: $i,SV1171: $i,SV1648: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1648 ) @ SV1171 ) @ SV2364 ) )
= $false )
| ( ( ! [SY7284: $i] :
( ~ ( hBOOL @ ( hAPP @ SY7284 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2364 @ SV577 @ SY7284 @ SV1648 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV577 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2364 @ SV577 @ SY7284 @ SV1648 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV577 @ SV1171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5991]) ).
thf(6325,plain,
! [SV1649: $i,SV578: $i,SV1172: $i,SV2524: $i] :
( ( ( hBOOL @ ( hAPP @ SV2524 @ SV1172 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV578 ) @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ SV1649 @ SV2524 @ SV578 ) ) @ SV1649 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV578 ) @ SV1172 ) @ SV1649 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5992]) ).
thf(6326,plain,
! [SV579: $i,SV1173: $i,SV2365: $i,SV1650: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1650 ) @ SV2365 ) @ SV1173 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV579 @ SV2365 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV579 @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1173 @ SV579 @ SV1650 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5993]) ).
thf(6327,plain,
! [SV2525: $i,SV1174: $i,SV580: $i,SV1651: $i,SV2366: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2366 ) @ SV1651 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV580 @ SV1174 @ SV2525 @ SV2366 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV580 @ SV1174 ) @ SV1651 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5994]) ).
thf(6328,plain,
! [SV1652: $i,SV2526: $i,SV581: $i,SV1175: $i,SV2367: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2367 ) @ SV1175 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV581 @ SV2526 @ SV1652 @ SV2367 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV581 @ SV1175 ) @ SV1652 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5995]) ).
thf(6329,plain,
! [SV584: $i,SV1178: $i,SV2615: $i,SV1655: $i,SV2055: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2055 ) @ SV1655 ) @ SV2615 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2055 ) @ SV1178 ) @ SV2615 ) )
| ( SV1178 = SV1655 )
| ! [SY7436: $i] :
~ ( c_Fun_Oinj__on @ SV584 @ SV2615 @ SV2055 @ SY7436 ) )
= $true )
| ( ( ( hAPP @ SV584 @ SV1178 )
= ( hAPP @ SV584 @ SV1655 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5998]) ).
thf(6330,plain,
! [SV585: $i,SV1179: $i,SV2616: $i,SV1656: $i,SV2056: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2056 ) @ SV1656 ) @ SV2616 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2056 ) @ SV1179 ) @ SV2616 ) )
| ! [SY7437: $i] :
~ ( c_Fun_Oinj__on @ SV585 @ SV2616 @ SV2056 @ SY7437 )
| ( SV1179 = SV1656 ) )
= $true )
| ( ( ( hAPP @ SV585 @ SV1179 )
= ( hAPP @ SV585 @ SV1656 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5999]) ).
thf(6331,plain,
! [SV586: $i,SV1180: $i,SV2617: $i,SV1657: $i,SV2057: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2057 ) @ SV1657 ) @ SV2617 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2057 ) @ SV1180 ) @ SV2617 ) )
| ! [SY7438: $i] :
~ ( c_Fun_Oinj__on @ SV586 @ SV2617 @ SV2057 @ SY7438 )
| ( SV1180 = SV1657 ) )
= $true )
| ( ( ( hAPP @ SV586 @ SV1180 )
= ( hAPP @ SV586 @ SV1657 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6000]) ).
thf(6332,plain,
! [SV1658: $i,SV1181: $i,SV2618: $i,SV2058: $i,SV587: $i] :
( ( ( ! [SY7439: $i] :
~ ( c_Fun_Oinj__on @ SV587 @ SV2058 @ SV2618 @ SY7439 )
| ( SV1181 = SV1658 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2618 ) @ SV1658 ) @ SV2058 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2618 ) @ SV1181 ) @ SV2058 ) ) )
= $true )
| ( ( ( hAPP @ SV587 @ SV1181 )
= ( hAPP @ SV587 @ SV1658 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6001]) ).
thf(6333,plain,
! [SV2061: $i,SV1663: $i,SV1188: $i,SV594: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV594 ) @ SV1188 ) @ SV1663 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV594 ) @ SV1188 ) @ SV2061 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV594 ) @ SV1188 ) @ ( c_HOL_Ominus__class_Ominus @ SV1663 @ SV2061 @ ( tc_fun @ SV594 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6005]) ).
thf(6334,plain,
! [SV2062: $i,SV1664: $i,SV1189: $i,SV595: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV595 ) @ SV1189 ) @ SV1664 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV595 ) @ SV1189 ) @ SV2062 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV595 ) @ SV1189 ) @ ( c_HOL_Ominus__class_Ominus @ SV1664 @ SV2062 @ ( tc_fun @ SV595 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6006]) ).
thf(6335,plain,
! [SV596: $i,SV2372: $i,SV1190: $i,SV1665: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1665 ) @ SV1190 ) @ SV2372 ) )
= $false )
| ( ( ! [SY7287: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1665 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2372 @ SY7287 @ SV596 @ SV1665 ) ) @ SV2372 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV596 @ SV1190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6007]) ).
thf(6336,plain,
! [SV597: $i,SV2373: $i,SV1191: $i,SV1666: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1666 ) @ SV1191 ) @ SV2373 ) )
= $false )
| ( ( ! [SY7288: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1666 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2373 @ SV597 @ SY7288 @ SV1666 ) ) @ SV2373 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV597 @ SV1191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6008]) ).
thf(6337,plain,
! [SV598: $i,SV1667: $i,SV1192: $i,SV2527: $i] :
( ( ( hBOOL @ ( hAPP @ SV2527 @ SV1192 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV2527 @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ SV1667 @ SV2527 @ SV598 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV598 ) @ SV1192 ) @ SV1667 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6009]) ).
thf(6338,plain,
! [SV1193: $i,SV2063: $i,SV599: $i,SV1668: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1668 ) @ SV599 ) @ SV2063 ) )
= $true )
| ( ( ( SV1193 = SV2063 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1668 ) @ SV599 ) @ SV1193 ) ) )
= $true )
| ( ( ( c_Set_Oinsert @ SV599 @ SV1193 @ SV1668 )
= ( c_Set_Oinsert @ SV599 @ SV2063 @ SV1668 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6010]) ).
thf(6339,plain,
! [SV1669: $i,SV1194: $i,SV2374: $i,SV600: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV600 ) @ SV2374 ) @ SV1194 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1669 @ SV2374 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV600 ) @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ SV1194 @ SV1669 @ SV600 ) ) @ SV1194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6011]) ).
thf(6340,plain,
! [SV1670: $i,SV2375: $i,SV2619: $i,SV2064: $i,SV1195: $i,SV601: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV601 ) @ SV1195 ) @ ( hAPP @ SV2064 @ SV2619 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2375 ) @ SV2619 ) @ SV1670 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV601 ) @ SV1195 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1670 @ SV2064 @ SV2375 @ ( tc_fun @ SV601 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6012]) ).
thf(6341,plain,
! [SV1671: $i,SV2376: $i,SV2620: $i,SV2065: $i,SV1196: $i,SV602: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV602 ) @ SV1196 ) @ ( hAPP @ SV2065 @ SV2620 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2376 ) @ SV2620 ) @ SV1671 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV602 ) @ SV1196 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1671 @ SV2065 @ SV2376 @ ( tc_fun @ SV602 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6013]) ).
thf(6342,plain,
! [SV1199: $i,SV2067: $i,SV1674: $i,SV2378: $i,SV2621: $i,SV605: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV605 @ SV2621 ) )
| ! [SY7440: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2378 ) @ SV2621 ) @ ( hAPP @ SV1674 @ SY7440 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2067 ) @ SY7440 ) @ SV1199 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV605 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SV1199 @ SV1674 @ SV605 @ SV2067 @ SV2378 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6016]) ).
thf(6343,plain,
! [SV606: $i,SV2068: $i,SV1200: $i,SV1675: $i,SV2379: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2379 ) @ ( hAPP @ SV1675 @ SV1200 ) ) @ SV2068 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV606 ) @ SV1200 ) @ ( c_Set_Ovimage @ SV1675 @ SV2068 @ SV606 @ SV2379 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6017]) ).
thf(6344,plain,
! [SV607: $i,SV2069: $i,SV1201: $i,SV1676: $i,SV2380: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2380 ) @ ( hAPP @ SV1676 @ SV1201 ) ) @ SV2069 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV607 ) @ SV1201 ) @ ( c_Set_Ovimage @ SV1676 @ SV2069 @ SV607 @ SV2380 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6018]) ).
thf(6345,plain,
! [SV608: $i,SV2070: $i,SV1202: $i,SV1677: $i,SV2381: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2381 ) @ ( hAPP @ SV1677 @ SV1202 ) ) @ SV2070 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV608 ) @ SV1202 ) @ ( c_Set_Ovimage @ SV1677 @ SV2070 @ SV608 @ SV2381 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6019]) ).
thf(6346,plain,
! [SV609: $i,SV2071: $i,SV1203: $i,SV1678: $i,SV2528: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2528 ) @ SV1678 ) @ ( c_Set_Ovimage @ SV1203 @ SV2071 @ SV2528 @ SV609 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV609 ) @ ( hAPP @ SV1203 @ SV1678 ) ) @ SV2071 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6020]) ).
thf(6347,plain,
! [SV610: $i,SV2072: $i,SV1204: $i,SV1679: $i,SV2529: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2529 ) @ SV1679 ) @ ( c_Set_Ovimage @ SV1204 @ SV2072 @ SV2529 @ SV610 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV610 ) @ ( hAPP @ SV1204 @ SV1679 ) ) @ SV2072 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6021]) ).
thf(6348,plain,
! [SV2622: $i,SV2530: $i,SV2382: $i,SV2073: $i,SV1680: $i,SV1205: $i,SV611: $i] :
( ( ! [SY7441: $i,SY7442: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV611 @ ( hAPP @ SV1205 @ SV1680 ) ) @ SV2073 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2382 ) @ SV2073 ) @ SV1680 ) )
| ! [SY7443: $i,SY7444: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1205 @ SV2530 @ SV611 @ SV2622 @ SY7441 @ SY7442 @ SY7443 @ SY7444 @ SV2382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6022]) ).
thf(6349,plain,
! [SV2623: $i,SV2531: $i,SV2383: $i,SV2074: $i,SV1681: $i,SV1206: $i,SV612: $i] :
( ( ! [SY7445: $i,SY7446: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV612 @ SV1206 ) @ ( hAPP @ SV1681 @ SV2074 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2383 ) @ SV1206 ) @ SV2074 ) )
| ! [SY7447: $i,SY7448: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2531 @ SV1681 @ SV612 @ SV2623 @ SY7445 @ SY7446 @ SY7447 @ SY7448 @ SV2383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6023]) ).
thf(6350,plain,
! [SV1682: $i,SV2532: $i,SV613: $i,SV1207: $i,SV2384: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2384 ) @ SV1207 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV613 @ SV2532 @ SV1682 @ SV2384 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV613 @ SV1207 ) @ SV1682 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6024]) ).
thf(6351,plain,
! [SV2533: $i,SV1208: $i,SV614: $i,SV1683: $i,SV2385: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2385 ) @ SV1683 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV614 @ SV1208 @ SV2533 @ SV2385 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV614 @ SV1208 ) @ SV1683 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6025]) ).
thf(6352,plain,
! [SV1209: $i,SV1684: $i,SV2075: $i,SV2534: $i,SV615: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV615 @ SV2534 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2075 ) @ SV2534 ) @ SV1684 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV615 @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV1209 @ SV1684 @ SV615 @ SV2075 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6026]) ).
thf(6353,plain,
! [SV1685: $i,SV1210: $i,SV2076: $i,SV2535: $i,SV616: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV616 @ SV2535 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2076 ) @ SV2535 ) @ SV1210 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV616 @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV1210 @ SV1685 @ SV616 @ SV2076 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6027]) ).
thf(6354,plain,
! [SV1211: $i,SV617: $i,SV2386: $i,SV1686: $i] :
( ( ( hBOOL @ ( hAPP @ SV1686 @ SV2386 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV617 ) @ SV2386 ) @ SV1211 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV617 ) @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ SV1211 @ SV1686 @ SV617 ) ) @ SV1211 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6028]) ).
thf(6355,plain,
! [SV2624: $i,SV2536: $i,SV2388: $i,SV2078: $i,SV1690: $i,SV1215: $i,SV621: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV621 @ SV1215 @ SV1690 @ ( tc_fun @ SV2078 @ ( tc_fun @ SV2388 @ tc_bool ) ) ) @ SV2536 ) @ SV2624 ) )
| ! [SY7449: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV1215 @ SY7449 ) @ SV2536 ) @ SV2624 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1690 ) @ SY7449 ) @ SV621 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6031]) ).
thf(6356,plain,
! [SV2079: $i,SV622: $i,SV1691: $i,SV2389: $i,SV2625: $i,SV1216: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1216 @ SV2625 ) @ SV2389 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1691 ) @ SV2625 ) @ SV622 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV622 @ SV1216 @ SV1691 @ ( tc_fun @ SV2079 @ tc_bool ) ) @ SV2389 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6032]) ).
thf(6357,plain,
! [SV2626: $i,SV2537: $i,SV2390: $i,SV2080: $i,SV1692: $i,SV1217: $i,SV623: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV623 @ SV1217 @ SV1692 @ ( tc_fun @ SV2080 @ ( tc_fun @ SV2390 @ tc_bool ) ) ) @ SV2537 ) @ SV2626 ) )
| ! [SY7450: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV1217 @ SY7450 ) @ SV2537 ) @ SV2626 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1692 ) @ SY7450 ) @ SV623 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6033]) ).
thf(6358,plain,
! [SV2081: $i,SV624: $i,SV1693: $i,SV2391: $i,SV2627: $i,SV1218: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1218 @ SV2627 ) @ SV2391 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1693 ) @ SV2627 ) @ SV624 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV624 @ SV1218 @ SV1693 @ ( tc_fun @ SV2081 @ tc_bool ) ) @ SV2391 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6034]) ).
thf(6359,plain,
! [SV1694: $i,SV2628: $i,SV625: $i,SV2538: $i,SV1219: $i,SV2082: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2082 ) @ SV1219 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV2538 @ SV625 @ SV2628 @ SV1694 @ SV2082 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SV1219 ) @ SV1694 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6035]) ).
thf(6360,plain,
! [SV2629: $i,SV1220: $i,SV2539: $i,SV626: $i,SV1695: $i,SV2083: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2083 ) @ SV1695 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV626 @ SV2539 @ SV1220 @ SV2629 @ SV2083 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV626 @ SV1220 ) @ SV1695 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6036]) ).
thf(6361,plain,
! [SV1221: $i,SV627: $i,SV2392: $i,SV1696: $i] :
( ( ( hBOOL @ ( hAPP @ SV1696 @ SV2392 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV627 ) @ SV2392 ) @ SV1221 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV627 ) @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ SV1221 @ SV1696 @ SV627 ) ) @ SV1221 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6037]) ).
thf(6362,plain,
! [SV1222: $i,SV1697: $i,SV2393: $i,SV628: $i] :
( ( ( hBOOL @ ( hAPP @ SV628 @ SV2393 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1697 ) @ SV2393 ) @ SV1222 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV628 @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ SV1222 @ SV628 @ SV1697 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6038]) ).
thf(6363,plain,
! [SV629: $i,SV1698: $i,SV1223: $i,SV2630: $i,SV2540: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2540 ) @ ( hAPP @ SV2630 @ SV1223 ) ) @ ( c_Set_Oimage @ SV2630 @ SV1698 @ SV629 @ SV2540 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV629 ) @ SV1223 ) @ SV1698 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6039]) ).
thf(6364,plain,
! [SV630: $i,SV1699: $i,SV1224: $i,SV2631: $i,SV2541: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2541 ) @ ( hAPP @ SV2631 @ SV1224 ) ) @ ( c_Set_Oimage @ SV2631 @ SV1699 @ SV630 @ SV2541 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV630 ) @ SV1224 ) @ SV1699 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6040]) ).
thf(6365,plain,
! [SV1225: $i,SV631: $i,SV2084: $i,SV1700: $i,SV2394: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2394 ) @ SV1700 ) @ SV2084 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV631 ) @ ( hAPP @ SV1225 @ SV1700 ) ) @ ( c_Set_Oimage @ SV1225 @ SV2084 @ SV2394 @ SV631 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6041]) ).
thf(6366,plain,
! [SV1226: $i,SV632: $i,SV2085: $i,SV1701: $i,SV2395: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2395 ) @ SV1701 ) @ SV2085 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV632 ) @ ( hAPP @ SV1226 @ SV1701 ) ) @ ( c_Set_Oimage @ SV1226 @ SV2085 @ SV2395 @ SV632 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6042]) ).
thf(6367,plain,
! [SV644: $i,SV1710: $i,SV1233: $i] :
( ( ( c_Com_OWT @ SV1233 )
= $false )
| ( ( c_Com_OWT @ SV1710 )
= $false )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV644 @ SV1233 @ SV1710 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6045]) ).
thf(6368,plain,
! [SV1237: $i,SV650: $i] :
( ( c_Hoare__Mirabelle_Ostate__not__singleton = $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ tc_Com_Opname ) @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ SV650 ) ) @ ( c_Map_Odom @ c_Com_Obody @ tc_Com_Opname @ tc_Com_Ocom ) ) )
= $true )
| ( ( c_Com_OWT @ SV1237 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV650 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ SV1237 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6046]) ).
thf(6369,plain,
! [SV1717: $i,SV654: $i,SV1242: $i,SV2542: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2542 ) @ SV1242 ) @ ( c_Map_Odom @ SV654 @ SV2542 @ SV1717 ) ) )
= $false )
| ( ( ( hAPP @ SV654 @ SV1242 )
= ( c_Option_Ooption_ONone @ SV1717 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6049]) ).
thf(6370,plain,
! [SV1718: $i,SV2094: $i,SV655: $i,SV1243: $i,SV2632: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2632 ) @ SV1243 ) @ ( c_Map_Odom @ SV655 @ SV2632 @ SV2094 ) ) )
= $true )
| ( ( ( hAPP @ SV655 @ SV1243 )
= ( c_Option_Ooption_OSome @ SV1718 @ SV2094 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6050]) ).
thf(6371,plain,
! [SV1719: $i,SV2543: $i,SV656: $i,SV1244: $i,SV2398: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2398 ) @ SV1244 ) @ ( c_Map_Odom @ SV656 @ SV2398 @ SV2543 ) ) ) )
= $true )
| ( ( ~ ( c_Map_Omap__le @ SV656 @ SV1719 @ SV2398 @ SV2543 ) )
= $true )
| ( ( ( hAPP @ SV656 @ SV1244 )
= ( hAPP @ SV1719 @ SV1244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6051]) ).
thf(6372,plain,
! [SV657: $i,SV2095: $i,SV1245: $i,SV2399: $i,SV1720: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1720 ) @ SV2399 ) @ ( c_Map_Odom @ SV1245 @ SV1720 @ SV2095 ) ) )
= $false )
| ( ( ( hAPP @ ( c_Map_Omap__add @ SV657 @ SV1245 @ SV1720 @ SV2095 ) @ SV2399 )
= ( hAPP @ SV1245 @ SV2399 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6052]) ).
thf(6373,plain,
! [SV2100: $i,SV3: $i,SV2400: $i,SV675: $i] :
( ( ( ~ ( c_lessequals @ SV675 @ SV2400 @ SV3 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV675 @ SV2100 @ SV3 ) )
= $true )
| ( ( c_lessequals @ SV675 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2100 @ SV2400 @ SV3 ) @ SV3 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6055]) ).
thf(6374,plain,
! [SV2101: $i,SV4: $i,SV2401: $i,SV676: $i] :
( ( ( ~ ( c_lessequals @ SV676 @ SV2401 @ SV4 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV676 @ SV2101 @ SV4 ) )
= $true )
| ( ( c_lessequals @ SV676 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2101 @ SV2401 @ SV4 ) @ SV4 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6056]) ).
thf(6375,plain,
! [SV2102: $i,SV5: $i,SV2402: $i,SV677: $i] :
( ( ( ~ ( c_lessequals @ SV677 @ SV2402 @ SV5 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV677 @ SV2102 @ SV5 ) )
= $true )
| ( ( c_lessequals @ SV677 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2102 @ SV2402 @ SV5 ) @ SV5 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6057]) ).
thf(6376,plain,
! [SV1727: $i,SV8: $i,SV1263: $i,SV2105: $i,SV678: $i] :
( ( ( c_lessequals @ SV678 @ SV2105 @ ( tc_fun @ SV1263 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV8 @ SV1727 @ ( tc_fun @ SV1263 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV8 @ SV678 @ ( tc_fun @ SV1263 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1727 @ SV2105 @ ( tc_fun @ SV1263 @ tc_bool ) ) @ ( tc_fun @ SV1263 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6058]) ).
thf(6377,plain,
! [SV2544: $i,SV2403: $i,SV2106: $i,SV1728: $i,SV1264: $i,SV680: $i,SV11: $i] :
( ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV11 @ SV680 @ SV1264 @ SV1728 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV2106 @ SV2403 @ SV2544 @ SV1728 ) )
= $true )
| ( ( SV1264 = SV2544 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6059]) ).
thf(6378,plain,
! [SV2633: $i,SV2404: $i,SV2107: $i,SV1729: $i,SV1265: $i,SV681: $i,SV12: $i] :
( ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV12 @ SV681 @ SV1265 @ SV1729 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV2107 @ SV2404 @ SV2633 @ SV1729 ) )
= $true )
| ( ( SV681 = SV2404 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6060]) ).
thf(6379,plain,
! [SV2634: $i,SV2545: $i,SV2108: $i,SV1730: $i,SV1266: $i,SV682: $i,SV13: $i] :
( ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV13 @ SV682 @ SV1266 @ SV1730 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV2108 @ SV2545 @ SV2634 @ SV1730 ) )
= $true )
| ( ( SV13 = SV2108 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6061]) ).
thf(6380,plain,
! [SV27: $i,SV2405: $i,SV2116: $i,SV691: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV691 @ SV2116 @ ( tc_fun @ SV2405 @ SV27 ) )
= $false )
| ( ( c_lessequals @ SV691 @ SV2116 @ ( tc_fun @ SV2405 @ SV27 ) )
= $true )
| ( ( class_HOL_Oord @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6067]) ).
thf(6381,plain,
! [SV30: $i,SV2118: $i,SV1742: $i] :
( ( ( c_lessequals @ SV1742 @ SV2118 @ SV30 )
= $false )
| ( ( ~ ( c_lessequals @ SV2118 @ SV1742 @ SV30 ) )
= $true )
| ( ( SV1742 = SV2118 )
= $true )
| ( ( class_Orderings_Oorder @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6068]) ).
thf(6382,plain,
! [SV31: $i,SV1743: $i,SV2119: $i] :
( ( ( c_lessequals @ SV2119 @ SV1743 @ SV31 )
= $false )
| ( ( ~ ( c_lessequals @ SV1743 @ SV2119 @ SV31 ) )
= $true )
| ( ( SV1743 = SV2119 )
= $true )
| ( ( class_Orderings_Oorder @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6069]) ).
thf(6383,plain,
! [SV32: $i,SV1744: $i,SV2120: $i] :
( ( ( c_lessequals @ SV2120 @ SV1744 @ SV32 )
= $false )
| ( ( ~ ( c_lessequals @ SV1744 @ SV2120 @ SV32 ) )
= $true )
| ( ( SV1744 = SV2120 )
= $true )
| ( ( class_Orderings_Oorder @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6070]) ).
thf(6384,plain,
! [SV36: $i,SV2406: $i,SV695: $i,SV2122: $i] :
( ( ( c_lessequals @ SV2122 @ SV695 @ ( tc_fun @ SV2406 @ SV36 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV695 @ SV2122 @ ( tc_fun @ SV2406 @ SV36 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV695 @ SV2122 @ ( tc_fun @ SV2406 @ SV36 ) )
= $true )
| ( ( class_HOL_Oord @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6073]) ).
thf(6385,plain,
! [SV37: $i,SV2123: $i,SV1748: $i] :
( ( ( c_lessequals @ SV1748 @ SV2123 @ SV37 )
= $false )
| ( ( c_lessequals @ SV2123 @ SV1748 @ SV37 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1748 @ SV2123 @ SV37 )
= $true )
| ( ( class_Orderings_Opreorder @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6074]) ).
thf(6386,plain,
! [SV1749: $i,SV39: $i,SV1276: $i,SV697: $i,SV2125: $i] :
( ( ( c_lessequals @ SV2125 @ SV697 @ ( tc_fun @ SV1276 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV39 @ SV1749 @ ( tc_fun @ SV1276 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV39 @ SV697 @ ( tc_fun @ SV1276 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1749 @ SV2125 @ ( tc_fun @ SV1276 @ tc_bool ) ) @ ( tc_fun @ SV1276 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6075]) ).
thf(6387,plain,
! [SV2635: $i,SV2410: $i,SV2127: $i,SV1758: $i,SV1280: $i,SV706: $i,SV50: $i] :
( ( ( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ SV50 @ SV706 @ SV1280 @ SV1758 @ SV2127 ) @ SV2410 @ SV2635 @ SV1758 @ SV2127 )
= ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ SV50 @ SV2410 @ SV2635 @ SV1758 @ SV2127 ) @ SV706 @ SV1280 @ SV1758 @ SV2127 ) )
= $true )
| ( ( SV706 = SV2410 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6077]) ).
thf(6388,plain,
! [SV1281: $i,SV707: $i,SV2128: $i,SV1759: $i,SV2411: $i,SV51: $i] :
( ( ( c_Map_Omap__le @ SV51 @ SV2411 @ SV1759 @ SV2128 )
= $false )
| ( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ SV51 @ SV707 @ SV1281 @ SV1759 @ ( tc_Option_Ooption @ SV2128 ) ) @ ( c_Fun_Ofun__upd @ SV2411 @ SV707 @ SV1281 @ SV1759 @ ( tc_Option_Ooption @ SV2128 ) ) @ SV1759 @ SV2128 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6078]) ).
thf(6389,plain,
! [SV1288: $i,SV1762: $i,SV58: $i,SV2130: $i,SV714: $i] :
( ( ( SV714 = SV2130 )
= $true )
| ( ( ! [SY7135: $i,SY7136: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV58 @ SV2130 @ ( c_Option_Ooption_OSome @ SY7135 @ SV1762 ) @ SY7136 @ ( tc_Option_Ooption @ SV1762 ) ) @ SV714 )
= ( c_Option_Ooption_OSome @ SV1288 @ SV1762 ) ) )
= $true )
| ( ( ( hAPP @ SV58 @ SV714 )
= ( c_Option_Ooption_OSome @ SV1288 @ SV1762 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6082]) ).
thf(6390,plain,
! [SV2546: $i,SV2413: $i,SV2131: $i,SV1763: $i,SV1289: $i,SV715: $i,SV59: $i] :
( ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV59 @ SV715 @ ( c_Option_Ooption_OSome @ SV1289 @ SV1763 ) @ SV2131 @ ( tc_Option_Ooption @ SV1763 ) ) @ SV2413 )
!= ( c_Option_Ooption_OSome @ SV2546 @ SV1763 ) )
= $true )
| ( ( ( ( hAPP @ SV59 @ SV2413 )
= ( c_Option_Ooption_OSome @ SV2546 @ SV1763 ) )
| ( SV1289 = SV2546 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6083]) ).
thf(6391,plain,
! [SV2547: $i,SV2414: $i,SV2132: $i,SV1764: $i,SV1290: $i,SV716: $i,SV60: $i] :
( ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV60 @ SV716 @ ( c_Option_Ooption_OSome @ SV1290 @ SV1764 ) @ SV2132 @ ( tc_Option_Ooption @ SV1764 ) ) @ SV2414 )
!= ( c_Option_Ooption_OSome @ SV2547 @ SV1764 ) )
= $true )
| ( ( ( ( hAPP @ SV60 @ SV2414 )
= ( c_Option_Ooption_OSome @ SV2547 @ SV1764 ) )
| ( SV2414 = SV716 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6084]) ).
thf(6392,plain,
! [SV2548: $i,SV722: $i,SV2415: $i,SV67: $i,SV1769: $i,SV1295: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV1295 @ SV1769 @ SV67 @ SV2415 @ SV722 @ SV2548 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV67 @ SV722 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6085]) ).
thf(6393,plain,
! [SV727: $i,SV2549: $i,SV2418: $i,SV72: $i,SV1772: $i,SV1298: $i] :
( ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV1298 @ SV1772 @ ( c_Option_Ooption_OSome @ SV72 @ SV2418 ) @ SV2549 @ ( tc_Option_Ooption @ SV2418 ) ) @ SV1772 )
= ( c_Option_Ooption_OSome @ SV727 @ SV2418 ) )
= $false )
| ( ( SV72 = SV727 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6086]) ).
thf(6394,plain,
! [SV1301: $i,SV1773: $i,SV730: $i,SV75: $i] :
( ( ( c_lessequals @ SV75 @ SV730 @ ( tc_fun @ SV1773 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV75 @ SV1301 @ ( tc_fun @ SV1773 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV75 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV730 @ SV1301 @ ( tc_fun @ SV1773 @ tc_bool ) ) @ ( tc_fun @ SV1773 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6087]) ).
thf(6395,plain,
! [SV1302: $i,SV1774: $i,SV731: $i,SV76: $i] :
( ( ( c_lessequals @ SV76 @ SV731 @ ( tc_fun @ SV1774 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV76 @ SV1302 @ ( tc_fun @ SV1774 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV76 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV731 @ SV1302 @ ( tc_fun @ SV1774 @ tc_bool ) ) @ ( tc_fun @ SV1774 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6088]) ).
thf(6396,plain,
! [SV2139: $i,SV82: $i,SV737: $i,SV2550: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2550 @ SV737 @ SV82 ) @ SV2139 @ SV82 )
= $false )
| ( ( c_lessequals @ SV737 @ SV2139 @ SV82 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6089]) ).
thf(6397,plain,
! [SV2140: $i,SV83: $i,SV2551: $i,SV738: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV738 @ SV2551 @ SV83 ) @ SV2140 @ SV83 )
= $false )
| ( ( c_lessequals @ SV738 @ SV2140 @ SV83 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV83 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6090]) ).
thf(6398,plain,
! [SV2141: $i,SV84: $i,SV2422: $i,SV739: $i] :
( ( ( c_lessequals @ SV739 @ SV2422 @ SV84 )
= $false )
| ( ( c_lessequals @ SV739 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2141 @ SV2422 @ SV84 ) @ SV84 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6091]) ).
thf(6399,plain,
! [SV2552: $i,SV85: $i,SV2142: $i,SV740: $i] :
( ( ( c_lessequals @ SV740 @ SV2142 @ SV85 )
= $false )
| ( ( c_lessequals @ SV740 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2142 @ SV2552 @ SV85 ) @ SV85 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6092]) ).
thf(6400,plain,
! [SV2143: $i,SV86: $i,SV741: $i,SV2553: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2553 @ SV741 @ SV86 ) @ SV2143 @ SV86 )
= $false )
| ( ( c_lessequals @ SV741 @ SV2143 @ SV86 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6093]) ).
thf(6401,plain,
! [SV2144: $i,SV87: $i,SV2554: $i,SV742: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV742 @ SV2554 @ SV87 ) @ SV2144 @ SV87 )
= $false )
| ( ( c_lessequals @ SV742 @ SV2144 @ SV87 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6094]) ).
thf(6402,plain,
! [SV2147: $i,SV90: $i,SV2555: $i,SV745: $i] :
( ( ( ~ ( c_lessequals @ SV745 @ SV2555 @ SV90 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2555 @ SV2147 @ SV90 ) )
= $true )
| ( ( c_lessequals @ SV745 @ SV2147 @ SV90 )
= $true )
| ( ( class_Orderings_Oorder @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6095]) ).
thf(6403,plain,
! [SV2148: $i,SV91: $i,SV2556: $i,SV746: $i] :
( ( ( ~ ( c_lessequals @ SV746 @ SV2556 @ SV91 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2556 @ SV2148 @ SV91 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV746 @ SV2148 @ SV91 )
= $true )
| ( ( class_Orderings_Oorder @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6096]) ).
thf(6404,plain,
! [SV2149: $i,SV92: $i,SV2557: $i,SV747: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV747 @ SV2557 @ SV92 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2557 @ SV2149 @ SV92 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV747 @ SV2149 @ SV92 )
= $true )
| ( ( class_Orderings_Oorder @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6097]) ).
thf(6405,plain,
! [SV748: $i,SV93: $i,SV2150: $i,SV2558: $i] :
( ( ( ~ ( c_lessequals @ SV2558 @ SV2150 @ SV93 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV748 @ SV2558 @ SV93 ) )
= $true )
| ( ( c_lessequals @ SV748 @ SV2150 @ SV93 )
= $true )
| ( ( class_Orderings_Opreorder @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6098]) ).
thf(6406,plain,
! [SV751: $i,SV1308: $i,SV2151: $i,SV96: $i] :
( ( ( c_lessequals @ SV96 @ SV2151 @ ( tc_fun @ SV1308 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV2151 @ SV751 @ ( tc_fun @ SV1308 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV96 @ SV751 @ ( tc_fun @ SV1308 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6099]) ).
thf(6407,plain,
! [SV1778: $i,SV97: $i,SV1309: $i,SV2423: $i,SV752: $i] :
( ( ( c_lessequals @ SV752 @ SV2423 @ ( tc_fun @ SV1309 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV97 @ SV2423 @ SV1309 @ SV1778 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV97 @ SV752 @ SV1309 @ SV1778 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6100]) ).
thf(6408,plain,
! [SV753: $i,SV2559: $i,SV98: $i,SV1779: $i] :
( ( ( c_lessequals @ SV1779 @ SV98 @ ( tc_fun @ SV2559 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1779 @ SV753 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV98 @ SV753 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6101]) ).
thf(6409,plain,
! [SV755: $i,SV1310: $i,SV2152: $i,SV102: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV102 @ SV2152 @ ( tc_fun @ SV1310 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV2152 @ SV755 @ ( tc_fun @ SV1310 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV102 @ SV755 @ ( tc_fun @ SV1310 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6103]) ).
thf(6410,plain,
! [SV756: $i,SV1311: $i,SV2153: $i,SV103: $i] :
( ( ( c_lessequals @ SV103 @ SV2153 @ ( tc_fun @ SV1311 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2153 @ SV756 @ ( tc_fun @ SV1311 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV103 @ SV756 @ ( tc_fun @ SV1311 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6104]) ).
thf(6411,plain,
! [SV2424: $i,SV104: $i,SV757: $i,SV1783: $i] :
( ( ( hBOOL @ ( hAPP @ SV1783 @ SV757 ) )
= $false )
| ( ( c_lessequals @ SV1783 @ SV104 @ ( tc_fun @ SV2424 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV104 @ SV757 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6105]) ).
thf(6412,plain,
! [SV759: $i,SV106: $i,SV2154: $i,SV2560: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2560 @ SV2154 @ SV106 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV759 @ SV2560 @ SV106 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV759 @ SV2154 @ SV106 )
= $true )
| ( ( class_Orderings_Opreorder @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6107]) ).
thf(6413,plain,
! [SV760: $i,SV107: $i,SV2155: $i,SV2561: $i] :
( ( ( ~ ( c_lessequals @ SV2561 @ SV2155 @ SV107 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV760 @ SV2561 @ SV107 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV760 @ SV2155 @ SV107 )
= $true )
| ( ( class_Orderings_Opreorder @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6108]) ).
thf(6414,plain,
! [SV1785: $i,SV108: $i,SV1312: $i,SV2156: $i,SV761: $i] :
( ( ( c_lessequals @ SV761 @ SV2156 @ ( tc_fun @ SV1312 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV108 @ SV1785 @ ( tc_fun @ SV1312 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV108 @ SV761 @ ( tc_fun @ SV1312 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1785 @ SV2156 @ ( tc_fun @ SV1312 @ tc_bool ) ) @ ( tc_fun @ SV1312 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6109]) ).
thf(6415,plain,
! [SV767: $i,SV1791: $i,SV114: $i,SV1318: $i] :
( ( ( c_lessequals @ SV1318 @ SV114 @ ( tc_fun @ SV1791 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV114 @ SV767 @ ( tc_fun @ SV1791 @ tc_bool ) )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV114 @ ( c_HOL_Ominus__class_Ominus @ SV767 @ SV1318 @ ( tc_fun @ SV1791 @ tc_bool ) ) @ ( tc_fun @ SV1791 @ tc_bool ) )
= SV1318 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6113]) ).
thf(6416,plain,
! [SV2563: $i,SV2427: $i,SV115: $i,SV1319: $i,SV768: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV768 @ SV1319 @ SV115 )
!= ( c_HOL_Ominus__class_Ominus @ SV2427 @ SV2563 @ SV115 ) )
= $true )
| ( ( ( c_lessequals @ SV2563 @ SV2427 @ SV115 )
| ~ ( c_lessequals @ SV1319 @ SV768 @ SV115 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6114]) ).
thf(6417,plain,
! [SV2564: $i,SV2428: $i,SV116: $i,SV1320: $i,SV769: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV769 @ SV1320 @ SV116 )
!= ( c_HOL_Ominus__class_Ominus @ SV2428 @ SV2564 @ SV116 ) )
= $true )
| ( ( ( c_lessequals @ SV1320 @ SV769 @ SV116 )
| ~ ( c_lessequals @ SV2564 @ SV2428 @ SV116 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6115]) ).
thf(6418,plain,
! [SV121: $i,SV2162: $i,SV1794: $i] :
( ( ( c_lessequals @ SV1794 @ SV2162 @ SV121 )
= $false )
| ( ( SV2162 = SV1794 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1794 @ SV2162 @ SV121 )
= $true )
| ( ( class_Orderings_Oorder @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6118]) ).
thf(6419,plain,
! [SV122: $i,SV2163: $i,SV1795: $i] :
( ( ( c_lessequals @ SV1795 @ SV2163 @ SV122 )
= $false )
| ( ( SV2163 = SV1795 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1795 @ SV2163 @ SV122 )
= $true )
| ( ( class_Orderings_Oorder @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6119]) ).
thf(6420,plain,
! [SV124: $i,SV2164: $i,SV1796: $i] :
( ( ( c_lessequals @ SV1796 @ SV2164 @ SV124 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1796 @ SV2164 @ SV124 )
= $true )
| ( ( SV1796 = SV2164 )
= $true )
| ( ( class_Orderings_Oorder @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6120]) ).
thf(6421,plain,
! [SV125: $i,SV2165: $i,SV1797: $i] :
( ( ( c_lessequals @ SV1797 @ SV2165 @ SV125 )
= $false )
| ( ( SV1797 = SV2165 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1797 @ SV2165 @ SV125 )
= $true )
| ( ( class_Orderings_Oorder @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6121]) ).
thf(6422,plain,
! [SV127: $i,SV2166: $i,SV1799: $i] :
( ( ( c_lessequals @ SV1799 @ SV2166 @ SV127 )
= $false )
| ( ( SV1799 = SV2166 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1799 @ SV2166 @ SV127 )
= $true )
| ( ( class_Orderings_Oorder @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6122]) ).
thf(6423,plain,
! [SV128: $i,SV2167: $i,SV1800: $i] :
( ( ( c_lessequals @ SV1800 @ SV2167 @ SV128 )
= $false )
| ( ( SV1800 = SV2167 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1800 @ SV2167 @ SV128 )
= $true )
| ( ( class_Orderings_Oorder @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6123]) ).
thf(6424,plain,
! [SV129: $i,SV2168: $i,SV1801: $i] :
( ( ( c_lessequals @ SV1801 @ SV2168 @ SV129 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1801 @ SV2168 @ SV129 )
= $true )
| ( ( SV1801 = SV2168 )
= $true )
| ( ( class_Orderings_Olinorder @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6124]) ).
thf(6425,plain,
! [SV130: $i,SV2169: $i,SV1802: $i] :
( ( ( c_lessequals @ SV1802 @ SV2169 @ SV130 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1802 @ SV2169 @ SV130 )
= $true )
| ( ( SV1802 = SV2169 )
= $true )
| ( ( class_Orderings_Olinorder @ SV130 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6125]) ).
thf(6426,plain,
! [SV2566: $i,SV2430: $i,SV2170: $i,SV1803: $i,SV1325: $i,SV775: $i,SV131: $i] :
( ( ( ( c_Fun_Ofun__upd @ SV131 @ SV775 @ ( c_Option_Ooption_OSome @ SV1325 @ SV1803 ) @ SV2170 @ ( tc_Option_Ooption @ SV1803 ) )
!= ( c_Fun_Ofun__upd @ SV2430 @ SV775 @ ( c_Option_Ooption_OSome @ SV2566 @ SV1803 ) @ SV2170 @ ( tc_Option_Ooption @ SV1803 ) ) )
= $true )
| ( ( SV1325 = SV2566 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6126]) ).
thf(6427,plain,
! [SV134: $i,SV2567: $i,SV2431: $i,SV1327: $i,SV777: $i] :
( ( ( ( c_Finite__Set_Osetsum @ SV777 @ ( c_HOL_Ominus__class_Ominus @ SV1327 @ SV2431 @ ( tc_fun @ SV2567 @ tc_bool ) ) @ SV2567 @ SV134 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV777 @ SV1327 @ SV2567 @ SV134 ) @ ( c_Finite__Set_Osetsum @ SV777 @ SV2431 @ SV2567 @ SV134 ) @ SV134 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV2431 @ SV1327 @ ( tc_fun @ SV2567 @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ SV1327 @ SV2567 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6127]) ).
thf(6428,plain,
! [SV1806: $i,SV1328: $i,SV778: $i,SV135: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV135 @ SV778 ) )
= $true )
| ( ( ! [SY6827: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ SY6827 @ SV1328 @ SV1806 @ SV778 ) @ SV135 @ ( tc_fun @ SV778 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY6827 @ SV1328 @ SV1806 @ SV778 )
| ! [SY6828: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ SY6828 @ SV135 @ SV778 @ SV1806 ) @ SV1328 @ ( tc_fun @ SV1806 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY6828 @ SV135 @ SV778 @ SV1806 ) ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV1328 @ SV1806 )
= $false )
| ( ( ( c_Finite__Set_Ocard @ SV135 @ SV778 )
= ( c_Finite__Set_Ocard @ SV1328 @ SV1806 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6128]) ).
thf(6429,plain,
! [SV2568: $i,SV2432: $i,SV2173: $i,SV1807: $i,SV1329: $i,SV779: $i,SV136: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV136 @ SV779 @ ( c_Set_Oinsert @ SV1329 @ SV1807 @ SV2173 ) @ ( hAPP @ ( hAPP @ SV136 @ SV1329 ) @ SV2432 ) @ SV2173 @ SV2568 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofold__graph @ SV136 @ SV779 @ SV1807 @ SV2432 @ SV2173 @ SV2568 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2173 ) @ SV1329 ) @ SV1807 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6129]) ).
thf(6430,plain,
! [SV785: $i,SV1810: $i,SV142: $i,SV1335: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1335 ) @ SV142 ) @ SV1810 ) )
= $false )
| ( ( c_lessequals @ SV785 @ SV1810 @ ( tc_fun @ SV1335 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Set_Oinsert @ SV142 @ SV785 @ SV1335 ) @ SV1810 @ ( tc_fun @ SV1335 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6134]) ).
thf(6431,plain,
! [SV1811: $i,SV143: $i,SV786: $i,SV2569: $i,SV1336: $i,SV2433: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2433 ) @ SV1336 ) @ SV2569 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Set_Oimage @ SV786 @ SV2569 @ SV2433 @ SV143 ) @ SV1811 @ ( tc_fun @ SV143 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV143 ) @ ( hAPP @ SV786 @ SV1336 ) ) @ SV1811 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6135]) ).
thf(6432,plain,
! [SV145: $i,SV2570: $i,SV2435: $i,SV1338: $i,SV788: $i] :
( ( ( c_lessequals @ ( hAPP @ SV788 @ SV1338 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV2435 @ SV788 @ SV2570 @ SV145 ) @ SV145 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2570 ) @ SV1338 ) @ SV2435 ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6137]) ).
thf(6433,plain,
! [SV1340: $i,SV1814: $i,SV147: $i,SV2571: $i,SV790: $i,SV2437: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2437 ) @ SV790 ) @ SV2571 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV2571 @ SV147 @ SV2437 @ ( tc_fun @ SV1814 @ tc_bool ) ) @ SV1340 @ ( tc_fun @ SV1814 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ SV147 @ SV790 ) @ SV1340 @ ( tc_fun @ SV1814 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6139]) ).
thf(6434,plain,
! [SV794: $i,SV2439: $i,SV2178: $i,SV1344: $i,SV151: $i] :
( ( ( c_lessequals @ SV151 @ ( c_Set_Oimage @ SV1344 @ SV2178 @ SV2439 @ SV794 ) @ ( tc_fun @ SV794 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV2178 @ SV2439 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV151 @ SV794 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6141]) ).
thf(6435,plain,
! [SV1822: $i,SV1354: $i,SV2184: $i,SV805: $i,SV162: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV162 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV805 @ SV2184 @ ( tc_fun @ SV1354 @ tc_bool ) ) @ SV1354 @ SV1822 ) )
= $true )
| ( ( SV805 = SV2184 )
= $true )
| ( ( ( c_Set_Oimage @ SV162 @ SV805 @ SV1354 @ SV1822 )
= ( c_Set_Oimage @ SV162 @ SV2184 @ SV1354 @ SV1822 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6143]) ).
thf(6436,plain,
! [SV180: $i,SV1838: $i,SV2189: $i] :
( ( ( c_lessequals @ SV2189 @ SV1838 @ SV180 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1838 @ SV2189 @ SV180 )
= $false )
| ( ( class_Orderings_Olinorder @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6145]) ).
thf(6437,plain,
! [SV182: $i,SV1840: $i,SV2191: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2191 @ SV1840 @ SV182 )
= $false )
| ( ( c_lessequals @ SV1840 @ SV2191 @ SV182 )
= $false )
| ( ( class_Orderings_Olinorder @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6146]) ).
thf(6438,plain,
! [SV184: $i,SV2445: $i,SV2193: $i,SV819: $i] :
( ( ( c_lessequals @ SV819 @ SV2193 @ ( tc_fun @ SV2445 @ SV184 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2193 @ SV819 @ ( tc_fun @ SV2445 @ SV184 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6147]) ).
thf(6439,plain,
! [SV185: $i,SV1842: $i,SV2194: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2194 @ SV1842 @ SV185 )
= $false )
| ( ( c_lessequals @ SV1842 @ SV2194 @ SV185 )
= $false )
| ( ( class_Orderings_Opreorder @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6148]) ).
thf(6440,plain,
! [SV828: $i,SV1371: $i,SV1848: $i,SV197: $i] :
( ( ( c_lessequals @ SV197 @ SV1848 @ ( tc_fun @ SV1371 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV828 @ SV1848 @ ( tc_fun @ SV1371 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV197 @ SV828 @ ( tc_fun @ SV1371 @ tc_bool ) ) @ SV1848 @ ( tc_fun @ SV1371 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6152]) ).
thf(6441,plain,
! [SV831: $i,SV1374: $i,SV1849: $i,SV200: $i] :
( ( ( c_lessequals @ SV200 @ SV1849 @ ( tc_fun @ SV1374 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV831 @ SV1849 @ ( tc_fun @ SV1374 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ SV831 @ ( tc_fun @ SV1374 @ tc_bool ) ) @ SV1849 @ ( tc_fun @ SV1374 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6153]) ).
thf(6442,plain,
! [SV832: $i,SV201: $i,SV2450: $i,SV2202: $i] :
( ( ( ~ ( c_lessequals @ SV2202 @ SV2450 @ SV201 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV832 @ SV2450 @ SV201 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV832 @ SV2202 @ SV201 ) @ SV2450 @ SV201 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6154]) ).
thf(6443,plain,
! [SV833: $i,SV204: $i,SV2451: $i,SV2205: $i] :
( ( ( ~ ( c_lessequals @ SV2205 @ SV2451 @ SV204 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV833 @ SV2451 @ SV204 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV833 @ SV2205 @ SV204 ) @ SV2451 @ SV204 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6155]) ).
thf(6444,plain,
! [SV834: $i,SV205: $i,SV2452: $i,SV2206: $i] :
( ( ( ~ ( c_lessequals @ SV2206 @ SV2452 @ SV205 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV834 @ SV2452 @ SV205 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV834 @ SV2206 @ SV205 ) @ SV2452 @ SV205 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6156]) ).
thf(6445,plain,
! [SV223: $i,SV2572: $i,SV2214: $i,SV848: $i] :
( ( ( c_lessequals @ SV848 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2214 @ SV2572 @ SV223 ) @ SV223 )
= $false )
| ( ( c_lessequals @ SV848 @ SV2214 @ SV223 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV223 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6160]) ).
thf(6446,plain,
! [SV224: $i,SV2215: $i,SV2573: $i,SV849: $i] :
( ( ( c_lessequals @ SV849 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2573 @ SV2215 @ SV224 ) @ SV224 )
= $false )
| ( ( c_lessequals @ SV849 @ SV2215 @ SV224 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6161]) ).
thf(6447,plain,
! [SV2216: $i,SV225: $i,SV2455: $i,SV850: $i] :
( ( ( c_lessequals @ SV850 @ SV2455 @ SV225 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV850 @ SV2216 @ SV225 ) @ SV2455 @ SV225 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6162]) ).
thf(6448,plain,
! [SV851: $i,SV226: $i,SV2456: $i,SV2217: $i] :
( ( ( c_lessequals @ SV2217 @ SV2456 @ SV226 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV851 @ SV2217 @ SV226 ) @ SV2456 @ SV226 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6163]) ).
thf(6449,plain,
! [SV227: $i,SV2574: $i,SV2218: $i,SV852: $i] :
( ( ( c_lessequals @ SV852 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2218 @ SV2574 @ SV227 ) @ SV227 )
= $false )
| ( ( c_lessequals @ SV852 @ SV2218 @ SV227 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6164]) ).
thf(6450,plain,
! [SV228: $i,SV2219: $i,SV2575: $i,SV853: $i] :
( ( ( c_lessequals @ SV853 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2575 @ SV2219 @ SV228 ) @ SV228 )
= $false )
| ( ( c_lessequals @ SV853 @ SV2219 @ SV228 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV228 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6165]) ).
thf(6451,plain,
! [SV2576: $i,SV242: $i,SV2226: $i,SV863: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV863 @ SV2226 @ SV242 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV863 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2226 @ SV2576 @ SV242 ) @ SV242 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV242 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6169]) ).
thf(6452,plain,
! [SV2227: $i,SV243: $i,SV2460: $i,SV864: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV864 @ SV2460 @ SV243 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV864 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV2227 @ SV2460 @ SV243 ) @ SV243 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV243 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6170]) ).
thf(6453,plain,
! [SV1396: $i,SV244: $i,SV2636: $i,SV2461: $i,SV865: $i] :
( ( ( ~ ( c_lessequals @ SV865 @ SV2461 @ ( tc_fun @ SV2636 @ SV244 ) ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ SV865 @ SV1396 ) @ ( hAPP @ SV2461 @ SV1396 ) @ SV244 )
= $true )
| ( ( class_HOL_Oord @ SV244 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6171]) ).
thf(6454,plain,
! [SV866: $i,SV245: $i,SV1397: $i,SV2228: $i] :
( ( ( c_lessequals @ SV2228 @ SV1397 @ ( tc_fun @ SV245 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV245 ) @ SV866 ) @ SV2228 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV245 ) @ SV866 ) @ SV1397 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6172]) ).
thf(6455,plain,
! [SV1398: $i,SV2229: $i,SV867: $i,SV246: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV246 ) @ SV867 ) @ SV2229 ) )
= $false )
| ( ( c_lessequals @ SV2229 @ SV1398 @ ( tc_fun @ SV246 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV246 ) @ SV867 ) @ SV1398 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6173]) ).
thf(6456,plain,
! [SV868: $i,SV247: $i,SV1399: $i,SV2230: $i] :
( ( ( c_lessequals @ SV2230 @ SV1399 @ ( tc_fun @ SV247 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV247 ) @ SV868 ) @ SV2230 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV247 ) @ SV868 ) @ SV1399 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6174]) ).
thf(6457,plain,
! [SV869: $i,SV248: $i,SV1400: $i,SV2231: $i] :
( ( ( c_lessequals @ SV2231 @ SV1400 @ ( tc_fun @ SV248 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV248 ) @ SV869 ) @ SV2231 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV248 ) @ SV869 ) @ SV1400 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6175]) ).
thf(6458,plain,
! [SV873: $i,SV1404: $i,SV253: $i,SV2462: $i,SV1871: $i] :
( ( ( hBOOL @ ( hAPP @ SV1871 @ SV2462 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV253 ) @ SV2462 ) @ SV1404 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV253 ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV873 @ SV1404 @ SV1871 @ SV253 ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV873 @ SV1404 @ ( tc_fun @ SV253 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6177]) ).
thf(6459,plain,
! [SV1405: $i,SV874: $i,SV254: $i,SV2463: $i,SV1872: $i] :
( ( ( hBOOL @ ( hAPP @ SV1872 @ SV2463 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV254 ) @ SV2463 ) @ SV874 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV254 ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV874 @ SV1405 @ SV1872 @ SV254 ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV874 @ SV1405 @ ( tc_fun @ SV254 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6178]) ).
thf(6460,plain,
! [SV877: $i,SV1874: $i,SV2464: $i,SV257: $i,SV1408: $i,SV2234: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2234 ) @ SV1408 ) @ ( c_Set_Oimage @ SV257 @ SV2464 @ SV1874 @ SV2234 ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV257 @ SV2464 @ SV1874 @ SV2234 ) )
= $true )
| ( ( c_Fun_Oinj__on @ ( c_Fun_Ofun__upd @ SV257 @ SV877 @ SV1408 @ SV1874 @ SV2234 ) @ SV2464 @ SV1874 @ SV2234 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6180]) ).
thf(6461,plain,
! [SV1410: $i,SV1875: $i,SV879: $i,SV259: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV259 @ ( c_Set_Oinsert @ SV879 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1875 @ tc_bool ) ) @ SV1875 ) @ ( tc_fun @ SV1875 @ tc_bool ) ) @ SV1410 @ ( tc_fun @ SV1875 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV259 @ SV1410 @ ( tc_fun @ SV1875 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV259 @ ( c_Set_Oinsert @ SV879 @ SV1410 @ SV1875 ) @ ( tc_fun @ SV1875 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6181]) ).
thf(6462,plain,
! [SV1876: $i,SV260: $i,SV1411: $i,SV880: $i] :
( ( ( c_Finite__Set_Ofinite @ SV880 @ SV1411 )
= $false )
| ( ( c_Fun_Oinj__on @ SV260 @ SV880 @ SV1411 @ SV1876 )
= $false )
| ( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ SV260 @ SV880 @ SV1411 @ SV1876 ) @ SV1876 )
= ( c_Finite__Set_Ocard @ SV880 @ SV1411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6182]) ).
thf(6463,plain,
! [SV1877: $i,SV261: $i,SV1412: $i,SV881: $i] :
( ( ( c_Finite__Set_Ofinite @ SV881 @ SV1412 )
= $false )
| ( ( c_Fun_Oinj__on @ SV261 @ SV881 @ SV1412 @ SV1877 )
= $true )
| ( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ SV261 @ SV881 @ SV1412 @ SV1877 ) @ SV1877 )
= ( c_Finite__Set_Ocard @ SV881 @ SV1412 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6183]) ).
thf(6464,plain,
! [SV1413: $i,SV882: $i,SV262: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV262 @ SV882 @ SV1413 @ SV1413 ) @ SV882 @ ( tc_fun @ SV1413 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV882 @ SV1413 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV262 @ SV882 @ SV1413 @ SV1413 )
= $false )
| ( ( ( c_Set_Oimage @ SV262 @ SV882 @ SV1413 @ SV1413 )
= SV882 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6184]) ).
thf(6465,plain,
! [SV1416: $i,SV265: $i,SV885: $i,SV1879: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1879 ) @ SV885 ) @ SV265 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV265 @ SV1416 @ ( tc_fun @ SV1879 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV265 @ SV1416 @ ( tc_fun @ SV1879 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV265 @ ( c_Set_Oinsert @ SV885 @ SV1416 @ SV1879 ) @ ( tc_fun @ SV1879 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6186]) ).
thf(6466,plain,
! [SV1417: $i,SV266: $i,SV886: $i,SV1880: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1880 ) @ SV886 ) @ SV266 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1880 ) @ SV886 ) @ SV1417 ) )
= $true )
| ( ( c_lessequals @ SV266 @ SV1417 @ ( tc_fun @ SV1880 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV266 @ ( c_Set_Oinsert @ SV886 @ SV1417 @ SV1880 ) @ ( tc_fun @ SV1880 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6187]) ).
thf(6467,plain,
! [SV1418: $i,SV887: $i,SV2235: $i,SV267: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV267 @ ( c_Set_Oinsert @ SV2235 @ SV887 @ SV1418 ) @ ( tc_fun @ SV1418 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1418 ) @ SV2235 ) @ SV887 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1418 ) @ SV2235 ) @ SV267 ) )
= $true )
| ( ( c_lessequals @ SV267 @ SV887 @ ( tc_fun @ SV1418 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6188]) ).
thf(6468,plain,
! [SV2236: $i,SV268: $i,SV888: $i,SV1881: $i,SV2577: $i,SV1419: $i] :
( ( ( ~ ( c_lessequals @ SV1419 @ SV2577 @ ( tc_fun @ SV1881 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV888 @ SV2577 @ ( tc_fun @ SV1881 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV268 @ SV2577 @ SV1881 @ SV2236 ) )
= $true )
| ( ( ( c_Set_Oimage @ SV268 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV888 @ SV1419 @ ( tc_fun @ SV1881 @ tc_bool ) ) @ SV1881 @ SV2236 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV268 @ SV888 @ SV1881 @ SV2236 ) @ ( c_Set_Oimage @ SV268 @ SV1419 @ SV1881 @ SV2236 ) @ ( tc_fun @ SV2236 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6189]) ).
thf(6469,plain,
! [SV2238: $i,SV270: $i,SV890: $i,SV1883: $i,SV2578: $i,SV1421: $i] :
( ( ( ~ ( c_lessequals @ SV1421 @ SV2578 @ ( tc_fun @ SV1883 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV890 @ SV2578 @ ( tc_fun @ SV1883 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV270 @ SV2578 @ SV1883 @ SV2238 ) )
= $true )
| ( ( ( c_Set_Oimage @ SV270 @ ( c_HOL_Ominus__class_Ominus @ SV890 @ SV1421 @ ( tc_fun @ SV1883 @ tc_bool ) ) @ SV1883 @ SV2238 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV270 @ SV890 @ SV1883 @ SV2238 ) @ ( c_Set_Oimage @ SV270 @ SV1421 @ SV1883 @ SV2238 ) @ ( tc_fun @ SV2238 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6190]) ).
thf(6470,plain,
! [SV2579: $i,SV892: $i,SV1423: $i,SV1885: $i,SV2240: $i,SV272: $i] :
( ( ( c_Map_Omap__le @ SV272 @ SV2240 @ SV1885 @ SV1423 )
= $false )
| ( ( c_Map_Omap__le @ ( c_Fun_Ofun__upd @ SV272 @ SV892 @ ( c_Option_Ooption_ONone @ SV1423 ) @ SV1885 @ ( tc_Option_Ooption @ SV1423 ) ) @ ( c_Fun_Ofun__upd @ SV2240 @ SV892 @ ( c_Option_Ooption_OSome @ SV2579 @ SV1423 ) @ SV1885 @ ( tc_Option_Ooption @ SV1423 ) ) @ SV1885 @ SV1423 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6191]) ).
thf(6471,plain,
! [SV1424: $i,SV1886: $i,SV893: $i,SV273: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV273 @ ( c_Set_Oinsert @ SV893 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1886 @ tc_bool ) ) @ SV1886 ) @ ( tc_fun @ SV1886 @ tc_bool ) ) @ SV1424 @ ( tc_fun @ SV1886 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1886 ) @ SV893 ) @ SV1424 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1886 ) @ SV893 ) @ SV273 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV273 @ ( c_Set_Oinsert @ SV893 @ SV1424 @ SV1886 ) @ ( tc_fun @ SV1886 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6192]) ).
thf(6472,plain,
! [SV1433: $i,SV1892: $i,SV903: $i,SV283: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV283 @ ( c_Set_Oinsert @ SV903 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1892 @ tc_bool ) ) @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) ) @ SV1433 @ ( tc_fun @ SV1892 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV283 @ SV1433 @ ( tc_fun @ SV1892 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1892 ) @ SV903 ) @ SV283 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV283 @ ( c_Set_Oinsert @ SV903 @ SV1433 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6194]) ).
thf(6473,plain,
! [SV1448: $i,SV300: $i,SV2466: $i,SV920: $i,SV2247: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2247 ) @ SV920 ) @ SV2466 ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV2466 @ SV300 @ SV2247 @ ( tc_fun @ SV1448 @ tc_bool ) ) @ SV1448 )
| ~ ( c_Finite__Set_Ofinite @ SV2466 @ SV2247 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ SV300 @ SV920 ) @ SV1448 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6198]) ).
thf(6474,plain,
! [SV302: $i,SV1903: $i,SV1450: $i,SV922: $i,SV2467: $i] :
( ( ( c_Map_Omap__le @ SV2467 @ SV922 @ SV1450 @ SV1903 )
= $false )
| ( ( ~ ( c_Map_Omap__le @ SV302 @ SV2467 @ SV1450 @ SV1903 ) )
= $true )
| ( ( c_Map_Omap__le @ SV302 @ SV922 @ SV1450 @ SV1903 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6199]) ).
thf(6475,plain,
! [SV305: $i,SV1452: $i,SV1906: $i,SV2580: $i,SV925: $i] :
( ( ( ( hAPP @ SV925 @ SV2580 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1906 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1452 ) @ SV2580 ) @ SV305 ) ) )
= $true )
| ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV305 @ SV925 @ SV1452 @ ( tc_fun @ SV1906 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1906 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6201]) ).
thf(6476,plain,
! [SV934: $i,SV317: $i] :
( ( c_Hoare__Mirabelle_Ostate__not__singleton = $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV317 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ ( c_Com_Ocom_OBODY @ ( v_sko__Hoare__Mirabelle__XMGF__lemma1__1 @ SV317 ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
= $false )
| ( ( c_Com_OWT @ SV934 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV317 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_OMGT @ SV934 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ tc_Com_Ostate ) ) @ tc_Com_Ostate )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6203]) ).
thf(6477,plain,
! [SV2637: $i,SV2581: $i,SV2470: $i,SV2252: $i,SV1913: $i,SV1458: $i,SV935: $i,SV318: $i] :
( ( ! [SY7451: $i] :
( ( ( hAPP @ SV318 @ ( c_Set_Oinsert @ SV935 @ ( c_Set_Oinsert @ SV1458 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1913 @ tc_bool ) ) @ SV1913 ) @ SV1913 ) )
= ( hAPP @ ( hAPP @ SV2252 @ SV935 ) @ SV1458 ) )
| ! [SY7452: $i,SY7453: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2470 @ SV318 @ SV2581 @ SV2637 @ SY7451 @ SV2252 @ SY7452 @ SY7453 @ SV1913 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6204]) ).
thf(6478,plain,
! [SV2638: $i,SV2582: $i,SV2471: $i,SV2253: $i,SV1914: $i,SV1459: $i,SV936: $i,SV319: $i] :
( ( ! [SY7454: $i] :
( ( ( hAPP @ SV319 @ ( c_Set_Oinsert @ SV936 @ ( c_Set_Oinsert @ SV1459 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1914 @ tc_bool ) ) @ SV1914 ) @ SV1914 ) )
= ( hAPP @ ( hAPP @ SV2253 @ SV936 ) @ SV1459 ) )
| ! [SY7455: $i,SY7456: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV319 @ SV2471 @ SV2582 @ SV2638 @ SV2253 @ SY7454 @ SY7455 @ SY7456 @ SV1914 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6205]) ).
thf(6479,plain,
! [SV2472: $i,SV2254: $i,SV1915: $i,SV1460: $i,SV937: $i,SV320: $i] :
( ( ( ( c_Com_Ocom_OCond @ SV320 @ SV937 @ SV1460 )
= ( c_Com_Ocom_OCond @ SV1915 @ SV2254 @ SV2472 ) )
= $false )
| ( ( SV1460 = SV2472 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6206]) ).
thf(6480,plain,
! [SV2583: $i,SV2255: $i,SV1916: $i,SV1461: $i,SV938: $i,SV321: $i] :
( ( ( ( c_Com_Ocom_OCond @ SV321 @ SV938 @ SV1461 )
= ( c_Com_Ocom_OCond @ SV1916 @ SV2255 @ SV2583 ) )
= $false )
| ( ( SV938 = SV2255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6207]) ).
thf(6481,plain,
! [SV2584: $i,SV2473: $i,SV1917: $i,SV1462: $i,SV939: $i,SV322: $i] :
( ( ( ( c_Com_Ocom_OCond @ SV322 @ SV939 @ SV1462 )
= ( c_Com_Ocom_OCond @ SV1917 @ SV2473 @ SV2584 ) )
= $false )
| ( ( SV322 = SV1917 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6208]) ).
thf(6482,plain,
! [SV343: $i,SV2585: $i,SV2478: $i,SV1474: $i,SV960: $i] :
( ( ( ( c_Finite__Set_Osetsum @ SV960 @ ( c_HOL_Ominus__class_Ominus @ SV1474 @ ( c_Set_Oinsert @ SV2478 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2585 @ tc_bool ) ) @ SV2585 ) @ ( tc_fun @ SV2585 @ tc_bool ) ) @ SV2585 @ SV343 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV960 @ SV1474 @ SV2585 @ SV343 ) @ ( hAPP @ SV960 @ SV2478 ) @ SV343 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2585 ) @ SV2478 ) @ SV1474 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1474 @ SV2585 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV343 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6211]) ).
thf(6483,plain,
! [SV344: $i,SV2586: $i,SV2479: $i,SV1475: $i,SV961: $i] :
( ( ( ( c_Finite__Set_Osetsum @ SV961 @ ( c_HOL_Ominus__class_Ominus @ SV1475 @ ( c_Set_Oinsert @ SV2479 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2586 @ tc_bool ) ) @ SV2586 ) @ ( tc_fun @ SV2586 @ tc_bool ) ) @ SV2586 @ SV344 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV961 @ SV1475 @ SV2586 @ SV344 ) @ ( hAPP @ SV961 @ SV2479 ) @ SV344 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2586 ) @ SV2479 ) @ SV1475 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1475 @ SV2586 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV344 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6212]) ).
thf(6484,plain,
! [SV964: $i,SV2266: $i,SV1930: $i,SV1478: $i,SV348: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV348 @ SV1478 @ SV1930 @ SV2266 ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV348 @ SV964 @ SV1930 @ SV2266 )
| ( c_Fun_Oinj__on @ SV348 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV964 @ SV1478 @ ( tc_fun @ SV1930 @ tc_bool ) ) @ SV1930 @ SV2266 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV348 @ ( c_HOL_Ominus__class_Ominus @ SV964 @ SV1478 @ ( tc_fun @ SV1930 @ tc_bool ) ) @ SV1930 @ SV2266 ) @ ( c_Set_Oimage @ SV348 @ ( c_HOL_Ominus__class_Ominus @ SV1478 @ SV964 @ ( tc_fun @ SV1930 @ tc_bool ) ) @ SV1930 @ SV2266 ) @ ( tc_fun @ SV2266 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2266 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6214]) ).
thf(6485,plain,
! [SV1479: $i,SV1931: $i,SV965: $i,SV349: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV349 @ ( c_Set_Oinsert @ SV965 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1931 @ tc_bool ) ) @ SV1931 ) @ ( tc_fun @ SV1931 @ tc_bool ) ) @ SV1479 @ ( tc_fun @ SV1931 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1931 ) @ SV965 ) @ SV1479 ) )
= $true )
| ( ( c_lessequals @ SV349 @ SV1479 @ ( tc_fun @ SV1931 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV349 @ ( c_Set_Oinsert @ SV965 @ SV1479 @ SV1931 ) @ ( tc_fun @ SV1931 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6215]) ).
thf(6486,plain,
! [SV2267: $i,SV1480: $i,SV350: $i,SV2480: $i,SV966: $i,SV1932: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1932 ) @ SV966 ) @ SV2480 ) )
= $false )
| ( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ SV350 @ SV966 @ SV1480 @ SV1932 @ SV2267 ) @ SV2480 @ SV1932 @ SV2267 )
= ( c_Set_Oinsert @ SV1480 @ ( c_Set_Oimage @ SV350 @ ( c_HOL_Ominus__class_Ominus @ SV2480 @ ( c_Set_Oinsert @ SV966 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1932 @ tc_bool ) ) @ SV1932 ) @ ( tc_fun @ SV1932 @ tc_bool ) ) @ SV1932 @ SV2267 ) @ SV2267 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6216]) ).
thf(6487,plain,
! [SV351: $i,SV2587: $i,SV2481: $i,SV1481: $i,SV967: $i] :
( ( ( ( c_Finite__Set_Osetsum @ SV967 @ ( c_HOL_Ominus__class_Ominus @ SV1481 @ ( c_Set_Oinsert @ SV2481 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2587 @ tc_bool ) ) @ SV2587 ) @ ( tc_fun @ SV2587 @ tc_bool ) ) @ SV2587 @ SV351 )
= ( c_Finite__Set_Osetsum @ SV967 @ SV1481 @ SV2587 @ SV351 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2587 ) @ SV2481 ) @ SV1481 ) )
| ~ ( c_Finite__Set_Ofinite @ SV1481 @ SV2587 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV351 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6217]) ).
thf(6488,plain,
! [SV1483: $i,SV969: $i,SV2482: $i,SV2268: $i,SV1933: $i,SV2639: $i,SV353: $i] :
( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV2639 @ SV1933 @ SV2268 @ SV2482 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) ) @ SV2482 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV969 @ SV1483 @ SV2639 @ SV2482 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) ) @ SV2482 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV969 @ ( c_Com_Ocom_OSemi @ SV1483 @ SV1933 ) @ SV2268 @ SV2482 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) ) @ SV2482 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6218]) ).
thf(6489,plain,
! [SV1486: $i,SV1935: $i,SV972: $i,SV356: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV356 @ ( c_Set_Oinsert @ SV972 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1935 @ tc_bool ) ) @ SV1935 ) @ ( tc_fun @ SV1935 @ tc_bool ) ) @ SV1486 @ ( tc_fun @ SV1935 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV356 @ SV1486 @ ( tc_fun @ SV1935 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV356 @ SV1486 @ ( tc_fun @ SV1935 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV356 @ ( c_Set_Oinsert @ SV972 @ SV1486 @ SV1935 ) @ ( tc_fun @ SV1935 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6220]) ).
thf(6490,plain,
! [SV2588: $i,SV2484: $i,SV2270: $i,SV1937: $i,SV1488: $i,SV974: $i,SV358: $i] :
( ( ( c_Nitpick_Ofold__graph_H @ SV358 @ SV974 @ SV1488 @ ( hAPP @ ( hAPP @ SV358 @ SV1937 ) @ SV2270 ) @ SV2484 @ SV2588 )
= $true )
| ( ( ~ ( c_Nitpick_Ofold__graph_H @ SV358 @ SV974 @ ( c_HOL_Ominus__class_Ominus @ SV1488 @ ( c_Set_Oinsert @ SV1937 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2484 @ tc_bool ) ) @ SV2484 ) @ ( tc_fun @ SV2484 @ tc_bool ) ) @ SV2270 @ SV2484 @ SV2588 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2484 ) @ SV1937 ) @ SV1488 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6221]) ).
thf(6491,plain,
! [SV1489: $i,SV1938: $i,SV975: $i,SV359: $i] :
( ( ( c_lessequals @ SV359 @ ( c_Set_Oinsert @ SV975 @ SV1938 @ SV1489 ) @ ( tc_fun @ SV1489 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1489 ) @ SV975 ) @ SV359 ) )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV359 @ ( c_Set_Oinsert @ SV975 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1489 @ tc_bool ) ) @ SV1489 ) @ ( tc_fun @ SV1489 @ tc_bool ) ) @ SV1938 @ ( tc_fun @ SV1489 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6222]) ).
thf(6492,plain,
! [SV1490: $i,SV1939: $i,SV976: $i,SV360: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV360 @ ( c_Set_Oinsert @ SV976 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1939 @ tc_bool ) ) @ SV1939 ) @ ( tc_fun @ SV1939 @ tc_bool ) ) @ SV1490 @ ( tc_fun @ SV1939 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1939 ) @ SV976 ) @ SV360 ) )
= $false )
| ( ( c_lessequals @ SV360 @ ( c_Set_Oinsert @ SV976 @ SV1490 @ SV1939 ) @ ( tc_fun @ SV1939 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6223]) ).
thf(6493,plain,
! [SV1491: $i,SV1940: $i,SV977: $i,SV361: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV361 @ ( c_Set_Oinsert @ SV977 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1940 @ tc_bool ) ) @ SV1940 ) @ ( tc_fun @ SV1940 @ tc_bool ) ) @ SV1491 @ ( tc_fun @ SV1940 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1940 ) @ SV977 ) @ SV361 ) )
= $false )
| ( ( c_lessequals @ SV361 @ ( c_Set_Oinsert @ SV977 @ SV1491 @ SV1940 ) @ ( tc_fun @ SV1940 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6224]) ).
thf(6494,plain,
! [SV2589: $i,SV2485: $i,SV2271: $i,SV1942: $i,SV1493: $i,SV979: $i,SV363: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV363 @ SV979 @ SV1493 @ ( hAPP @ ( hAPP @ SV363 @ SV1942 ) @ SV2271 ) @ SV2485 @ SV2589 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2485 ) @ SV1942 ) @ SV1493 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV363 @ SV979 @ ( c_HOL_Ominus__class_Ominus @ SV1493 @ ( c_Set_Oinsert @ SV1942 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2485 @ tc_bool ) ) @ SV2485 ) @ ( tc_fun @ SV2485 @ tc_bool ) ) @ SV2271 @ SV2485 @ SV2589 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6225]) ).
thf(6495,plain,
! [SV365: $i,SV1944: $i,SV981: $i,SV1495: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1495 ) @ SV981 ) @ SV1944 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV365 @ ( c_Set_Oinsert @ SV981 @ SV1944 @ SV1495 ) @ ( tc_fun @ SV1495 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1495 ) @ SV981 ) @ SV365 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV365 @ ( c_Set_Oinsert @ SV981 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1495 @ tc_bool ) ) @ SV1495 ) @ ( tc_fun @ SV1495 @ tc_bool ) ) @ SV1944 @ ( tc_fun @ SV1495 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6227]) ).
thf(6496,plain,
! [SV992: $i,SV376: $i,SV2274: $i,SV2591: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV2591 @ SV2274 @ SV376 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV992 @ SV2591 @ SV376 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV992 @ SV2274 @ SV376 )
= $true )
| ( ( class_Orderings_Opreorder @ SV376 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6231]) ).
thf(6497,plain,
! [SV993: $i,SV1503: $i,SV2275: $i,SV377: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV377 @ SV2275 @ ( tc_fun @ SV1503 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2275 @ SV993 @ ( tc_fun @ SV1503 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV377 @ SV993 @ ( tc_fun @ SV1503 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6232]) ).
thf(6498,plain,
! [SV2276: $i,SV378: $i,SV2592: $i,SV994: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV994 @ SV2592 @ SV378 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2592 @ SV2276 @ SV378 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV994 @ SV2276 @ SV378 )
= $true )
| ( ( class_Orderings_Oorder @ SV378 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6233]) ).
thf(6499,plain,
! [SV995: $i,SV2277: $i,SV1951: $i,SV1504: $i,SV379: $i] :
( ( ( c_Fun_Oinj__on @ SV379 @ SV1504 @ SV1951 @ SV2277 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2277 ) @ ( hAPP @ SV379 @ SV995 ) ) @ ( c_Set_Oimage @ SV379 @ ( c_HOL_Ominus__class_Ominus @ SV1504 @ ( c_Set_Oinsert @ SV995 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1951 @ tc_bool ) ) @ SV1951 ) @ ( tc_fun @ SV1951 @ tc_bool ) ) @ SV1951 @ SV2277 ) ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV379 @ ( c_Set_Oinsert @ SV995 @ SV1504 @ SV1951 ) @ SV1951 @ SV2277 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6234]) ).
thf(6500,plain,
! [SV1510: $i,SV1955: $i,SV2491: $i,SV1003: $i,SV387: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV387 @ SV1003 ) ) @ SV2491 ) @ SV1955 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1003 ) @ SV1510 ) @ SV2491 ) )
| ~ ( hBOOL @ ( hAPP @ SV387 @ SV1510 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV387 @ SV1003 ) ) @ SV1510 ) @ SV1955 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6235]) ).
thf(6501,plain,
! [SV2593: $i,SV389: $i,SV2279: $i,SV1005: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1005 @ SV2279 @ SV389 )
= ( c_HOL_Ominus__class_Ominus @ SV2593 @ SV2593 @ SV389 ) )
= $false )
| ( ( SV1005 = SV2279 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV389 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6236]) ).
thf(6502,plain,
! [SV2492: $i,SV2280: $i,SV390: $i,SV1006: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1006 @ SV1006 @ SV390 )
= ( c_HOL_Ominus__class_Ominus @ SV2280 @ SV2492 @ SV390 ) )
= $false )
| ( ( SV2280 = SV2492 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV390 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6237]) ).
thf(6503,plain,
! [SV1513: $i,SV392: $i,SV2281: $i,SV1956: $i,SV1008: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1008 ) @ SV1956 ) @ SV2281 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV392 @ SV1956 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV392 @ SV1008 @ SV1513 ) ) @ SV1956 ) @ SV2281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6238]) ).
thf(6504,plain,
! [SV2493: $i,SV1009: $i,SV2640: $i,SV1514: $i,SV393: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV393 @ SV1514 @ SV2640 ) ) @ SV1009 ) @ SV2493 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1514 ) @ SV1009 ) @ SV2493 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV393 @ SV1009 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6239]) ).
thf(6505,plain,
! [SV1515: $i,SV394: $i,SV1957: $i,SV2494: $i,SV1010: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1010 ) @ SV2494 ) @ SV1957 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV394 ) @ SV1515 ) @ SV2494 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV394 @ SV1010 ) ) @ SV1515 ) @ SV1957 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6240]) ).
thf(6506,plain,
! [SV2641: $i,SV2595: $i,SV2495: $i,SV2284: $i,SV1962: $i,SV1520: $i,SV1015: $i,SV401: $i] :
( ( ! [SY7457: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV401 @ SV1015 @ ( c_COMBC @ SV1520 @ SV1962 @ SV1962 @ tc_bool ) @ ( c_COMBC @ SV2284 @ SV1962 @ SV1962 @ tc_bool ) @ SV2495 @ SV2595 @ SV2641 @ SY7457 @ SV1962 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1015 @ SV401 @ SV1520 @ SV2284 @ SV2595 @ SV2495 @ SY7457 @ SV2641 @ SV1962 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6242]) ).
thf(6507,plain,
! [SV2496: $i,SV2285: $i,SV1963: $i,SV1524: $i,SV1019: $i,SV405: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ SV405 @ SV1019 @ SV1524 @ SV1963 ) @ SV2285 )
= ( c_Option_Ooption_OSome @ SV2496 @ SV1963 ) )
= $false )
| ( ( ( ( hAPP @ SV405 @ SV2285 )
= ( c_Option_Ooption_OSome @ SV2496 @ SV1963 ) )
| ( ( hAPP @ SV1019 @ SV2285 )
= ( c_Option_Ooption_OSome @ SV2496 @ SV1963 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6243]) ).
thf(6508,plain,
! [SV1525: $i,SV406: $i,SV1964: $i,SV1020: $i,SV2596: $i] :
( ( ( ( hAPP @ SV2596 @ SV1020 )
!= ( c_Option_Ooption_ONone @ SV1964 ) )
= $true )
| ( ( ! [SY7414: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SV406 @ SV2596 @ SY7414 @ SV1964 ) @ SV1020 )
= ( c_Option_Ooption_OSome @ SV1525 @ SV1964 ) ) )
= $true )
| ( ( ( hAPP @ SV406 @ SV1020 )
= ( c_Option_Ooption_OSome @ SV1525 @ SV1964 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6244]) ).
thf(6509,plain,
! [SV426: $i,SV1543: $i,SV1039: $i,SV2498: $i] :
( ( ( ( hAPP @ SV2498 @ SV1039 )
= ( c_Option_Ooption_ONone @ SV1543 ) )
= $false )
| ( ( ! [SY7355: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SV426 @ SV2498 @ SY7355 @ SV1543 ) @ SV1039 )
= ( c_Option_Ooption_ONone @ SV1543 ) ) )
= $true )
| ( ( ( hAPP @ SV426 @ SV1039 )
= ( c_Option_Ooption_ONone @ SV1543 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6248]) ).
thf(6510,plain,
! [SV1544: $i,SV1040: $i,SV1976: $i,SV2642: $i,SV427: $i,SV2597: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ SV2597 @ SV427 @ SV2642 @ SV1976 ) @ SV1040 )
= ( c_Option_Ooption_OSome @ SV1544 @ SV1976 ) )
= $true )
| ( ( ( hAPP @ SV427 @ SV1040 )
= ( c_Option_Ooption_OSome @ SV1544 @ SV1976 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6249]) ).
thf(6511,plain,
! [SV1545: $i,SV1041: $i,SV1977: $i,SV2643: $i,SV428: $i,SV2598: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ SV2598 @ SV428 @ SV2643 @ SV1977 ) @ SV1041 )
= ( c_Option_Ooption_OSome @ SV1545 @ SV1977 ) )
= $true )
| ( ( ( hAPP @ SV428 @ SV1041 )
= ( c_Option_Ooption_OSome @ SV1545 @ SV1977 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6250]) ).
thf(6512,plain,
! [SV429: $i,SV2293: $i,SV1978: $i,SV1546: $i,SV1042: $i] :
( ( ( c_Fun_Oinj__on @ SV1042 @ ( c_Set_Oinsert @ SV1546 @ SV1978 @ SV2293 ) @ SV2293 @ SV429 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV429 ) @ ( hAPP @ SV1042 @ SV1546 ) ) @ ( c_Set_Oimage @ SV1042 @ ( c_HOL_Ominus__class_Ominus @ SV1978 @ ( c_Set_Oinsert @ SV1546 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2293 @ tc_bool ) ) @ SV2293 ) @ ( tc_fun @ SV2293 @ tc_bool ) ) @ SV2293 @ SV429 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6251]) ).
thf(6513,plain,
! [SV2298: $i,SV1985: $i,SV1554: $i,SV1053: $i,SV441: $i] :
( ( ( c_Map_Omap__le @ SV441 @ ( c_Map_Omap__add @ SV441 @ SV1053 @ SV1554 @ SV1985 ) @ SV1554 @ SV1985 )
= $false )
| ( ( ~ ( c_Map_Omap__le @ SV1053 @ SV2298 @ SV1554 @ SV1985 )
| ~ ( c_Map_Omap__le @ SV441 @ SV2298 @ SV1554 @ SV1985 ) )
= $true )
| ( ( c_Map_Omap__le @ ( c_Map_Omap__add @ SV441 @ SV1053 @ SV1554 @ SV1985 ) @ SV2298 @ SV1554 @ SV1985 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6252]) ).
thf(6514,plain,
! [SV2499: $i,SV1054: $i,SV1555: $i,SV2644: $i,SV442: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV442 @ SV2644 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1555 ) @ SV2644 ) @ SV1054 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1555 ) @ SV2499 ) @ SV1054 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV442 @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1054 @ SV442 @ SV1555 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6253]) ).
thf(6515,plain,
! [SV1986: $i,SV1556: $i,SV1055: $i,SV443: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ SV1055 ) @ SV1556 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ SV1055 ) @ SV1986 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV443 ) @ SV1055 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1556 @ SV1986 @ ( tc_fun @ SV443 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6254]) ).
thf(6516,plain,
! [SV1987: $i,SV1557: $i,SV1056: $i,SV444: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ SV1056 ) @ SV1557 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ SV1056 ) @ SV1987 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV444 ) @ SV1056 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1557 @ SV1987 @ ( tc_fun @ SV444 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6255]) ).
thf(6517,plain,
! [SV1057: $i,SV445: $i,SV2299: $i,SV1558: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1558 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2299 @ SV445 @ SV1558 ) ) @ SV2299 ) )
= $true )
| ( ( ! [SY7232: $i] :
~ ( hBOOL @ ( hAPP @ SY7232 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2299 @ SY7232 @ SV1558 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1558 ) @ SV1057 ) @ SV2299 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV445 @ SV1057 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6256]) ).
thf(6518,plain,
! [SV1058: $i,SV446: $i,SV2300: $i,SV1559: $i] :
( ( ( ! [SY7233: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1559 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2300 @ SY7233 @ SV1559 ) ) @ SV2300 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV446 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2300 @ SV446 @ SV1559 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1559 ) @ SV1058 ) @ SV2300 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV446 @ SV1058 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6257]) ).
thf(6519,plain,
! [SV1059: $i,SV1560: $i,SV2301: $i,SV447: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV447 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2301 @ SV447 @ SV1560 ) ) ) )
= $true )
| ( ( ! [SY7234: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1560 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2301 @ SY7234 @ SV1560 ) ) @ SV2301 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1560 ) @ SV1059 ) @ SV2301 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV447 @ SV1059 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6258]) ).
thf(6520,plain,
! [SV1060: $i,SV448: $i,SV1561: $i,SV2302: $i] :
( ( ( ! [SY7235: $i] :
~ ( hBOOL @ ( hAPP @ SY7235 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2302 @ SY7235 @ SV1561 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1561 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2302 @ SV448 @ SV1561 ) ) @ SV2302 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1561 ) @ SV1060 ) @ SV2302 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV448 @ SV1060 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6259]) ).
thf(6521,plain,
! [SV449: $i,SV2303: $i,SV1562: $i,SV2500: $i,SV1061: $i,SV1988: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1988 @ SV1061 ) @ SV2500 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1562 @ SV2303 ) @ SV1061 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV449 ) @ SV1061 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV1562 @ SV1988 @ SV2303 @ SV2500 @ SV449 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6260]) ).
thf(6522,plain,
! [SV452: $i,SV1991: $i,SV2304: $i,SV1064: $i,SV1565: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1565 @ SV1064 ) @ SV2304 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1565 @ SV1991 ) @ SV1064 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV452 ) @ SV1064 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV1565 @ SV1991 @ SV2304 @ SV452 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6261]) ).
thf(6523,plain,
! [SV1065: $i,SV453: $i,SV2305: $i,SV1566: $i] :
( ( ( hBOOL @ ( hAPP @ SV1566 @ SV2305 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV453 ) @ SV2305 ) @ SV1065 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV453 ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1065 @ SV1566 @ SV453 ) ) @ SV1065 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6262]) ).
thf(6524,plain,
! [SV458: $i,SV1993: $i,SV2306: $i,SV1070: $i,SV1567: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1567 @ SV1070 ) @ SV2306 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1567 @ SV1993 ) @ SV1070 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV458 ) @ SV1070 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV1567 @ SV1993 @ SV2306 @ SV458 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6263]) ).
thf(6525,plain,
! [SV460: $i,SV2308: $i,SV1994: $i,SV2501: $i,SV1072: $i,SV1569: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1569 @ SV1072 ) @ SV2501 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1994 @ SV2308 ) @ SV1072 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV460 ) @ SV1072 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV1569 @ SV1994 @ SV2308 @ SV2501 @ SV460 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6265]) ).
thf(6526,plain,
! [SV2503: $i,SV1075: $i,SV463: $i,SV2645: $i,SV1572: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1572 @ SV2645 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ SV2645 ) @ SV1075 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ SV2503 ) @ SV1075 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1075 @ SV1572 @ SV463 ) ) @ SV1075 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6267]) ).
thf(6527,plain,
! [SV1076: $i,SV1573: $i,SV2310: $i,SV464: $i] :
( ( ( hBOOL @ ( hAPP @ SV464 @ SV2310 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1573 ) @ SV2310 ) @ SV1076 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV464 @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ SV1076 @ SV464 @ SV1573 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6268]) ).
thf(6528,plain,
! [SV1077: $i,SV1995: $i,SV465: $i,SV2599: $i,SV1574: $i] :
( ( ( ( hAPP @ SV1574 @ SV2599 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV465 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1995 ) @ SV2599 ) @ SV1077 ) ) )
= $true )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV465 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1077 @ SV1574 @ SV1995 @ ( tc_fun @ SV465 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6269]) ).
thf(6529,plain,
! [SV1580: $i,SV1087: $i,SV2312: $i,SV475: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV475 @ ( c_Set_Oinsert @ SV2312 @ SV1087 @ SV1580 ) @ ( tc_fun @ SV1580 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1580 ) @ SV2312 ) @ SV1087 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV475 @ SV1087 @ ( tc_fun @ SV1580 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6270]) ).
thf(6530,plain,
! [SV1088: $i,SV2001: $i,SV1581: $i,SV476: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV476 @ SV1581 @ ( tc_fun @ SV2001 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2001 ) @ SV1088 ) @ SV1581 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV476 @ ( c_Set_Oinsert @ SV1088 @ SV1581 @ SV2001 ) @ ( tc_fun @ SV2001 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6271]) ).
thf(6531,plain,
! [SV1583: $i,SV2504: $i,SV1090: $i,SV478: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV478 ) @ SV1090 ) @ SV2504 ) )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV2504 @ SV1583 @ ( tc_fun @ SV478 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV478 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV478 ) @ SV1090 ) @ SV1583 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6272]) ).
thf(6532,plain,
! [SV489: $i,SV1094: $i,SV2316: $i,SV2009: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV2009 ) @ SV2316 ) @ SV1094 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV2009 ) @ SV2316 ) @ SV489 ) )
= $false )
| ( ( SV489 = SV1094 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6275]) ).
thf(6533,plain,
! [SV2317: $i,SV2010: $i,SV1095: $i,SV490: $i] :
( ( ( c_Map_Omap__le @ SV490 @ SV1095 @ SV2010 @ SV2317 )
= $false )
| ( ( c_Map_Omap__le @ SV1095 @ SV490 @ SV2010 @ SV2317 )
= $false )
| ( ( SV490 = SV1095 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6276]) ).
thf(6534,plain,
! [SV1097: $i,SV495: $i,SV2505: $i,SV2321: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2321 @ SV2505 @ SV495 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1097 @ SV2321 @ SV495 ) @ SV2505 @ SV495 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV495 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6280]) ).
thf(6535,plain,
! [SV2322: $i,SV496: $i,SV2506: $i,SV1098: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1098 @ SV2506 @ SV496 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1098 @ SV2322 @ SV496 ) @ SV2506 @ SV496 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV496 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6281]) ).
thf(6536,plain,
! [SV1590: $i,SV1101: $i,SV2015: $i,SV2324: $i,SV499: $i] :
( ( ( SV499 = SV2324 )
= $true )
| ( ( SV499 = SV2015 )
= $true )
| ( ( ( c_Set_Oinsert @ SV499 @ ( c_Set_Oinsert @ SV1101 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1590 @ tc_bool ) ) @ SV1590 ) @ SV1590 )
= ( c_Set_Oinsert @ SV2015 @ ( c_Set_Oinsert @ SV2324 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1590 @ tc_bool ) ) @ SV1590 ) @ SV1590 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6282]) ).
thf(6537,plain,
! [SV2507: $i,SV1591: $i,SV500: $i,SV2016: $i,SV1102: $i] :
( ( ( SV1102 = SV2016 )
= $true )
| ( ( SV500 = SV2016 )
= $true )
| ( ( ( c_Set_Oinsert @ SV500 @ ( c_Set_Oinsert @ SV1102 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1591 @ tc_bool ) ) @ SV1591 ) @ SV1591 )
= ( c_Set_Oinsert @ SV2016 @ ( c_Set_Oinsert @ SV2507 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1591 @ tc_bool ) ) @ SV1591 ) @ SV1591 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6283]) ).
thf(6538,plain,
! [SV2017: $i,SV1592: $i,SV1103: $i,SV2325: $i,SV501: $i] :
( ( ( SV501 = SV2325 )
= $true )
| ( ( SV1103 = SV2325 )
= $true )
| ( ( ( c_Set_Oinsert @ SV501 @ ( c_Set_Oinsert @ SV1103 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1592 @ tc_bool ) ) @ SV1592 ) @ SV1592 )
= ( c_Set_Oinsert @ SV2017 @ ( c_Set_Oinsert @ SV2325 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1592 @ tc_bool ) ) @ SV1592 ) @ SV1592 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6284]) ).
thf(6539,plain,
! [SV1593: $i,SV502: $i,SV2326: $i,SV2018: $i,SV1104: $i] :
( ( ( SV1104 = SV2018 )
= $true )
| ( ( SV1104 = SV2326 )
= $true )
| ( ( ( c_Set_Oinsert @ SV502 @ ( c_Set_Oinsert @ SV1104 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1593 @ tc_bool ) ) @ SV1593 ) @ SV1593 )
= ( c_Set_Oinsert @ SV2018 @ ( c_Set_Oinsert @ SV2326 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1593 @ tc_bool ) ) @ SV1593 ) @ SV1593 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6285]) ).
thf(6540,plain,
! [SV1594: $i,SV1105: $i,SV503: $i,SV2600: $i,SV2327: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV2327 @ SV2600 @ SV503 ) ) @ SV1105 ) @ SV1594 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV2327 @ SV1105 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV503 ) @ SV1105 ) @ SV1594 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6286]) ).
thf(6541,plain,
! [SV1106: $i,SV504: $i,SV2328: $i,SV2019: $i,SV1595: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1595 ) @ SV2019 ) @ SV2328 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV504 @ SV2019 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV504 @ SV1106 @ SV1595 ) ) @ SV2019 ) @ SV2328 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6287]) ).
thf(6542,plain,
! [SV2646: $i,SV2601: $i,SV2508: $i,SV2329: $i,SV2020: $i,SV1596: $i,SV1108: $i,SV506: $i] :
( ( ! [SY7458: $i] :
( ( ( hAPP @ SV506 @ ( c_Set_Oinsert @ SV1108 @ SV1596 @ SV2020 ) )
= ( hAPP @ ( hAPP @ SV2329 @ SV1108 ) @ ( hAPP @ SV506 @ SV1596 ) ) )
| ! [SY7459: $i,SY7460: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2508 @ SV506 @ SV2601 @ SV2646 @ SY7458 @ SV2329 @ SY7459 @ SY7460 @ SV2020 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6288]) ).
thf(6543,plain,
! [SV2647: $i,SV2602: $i,SV2509: $i,SV2330: $i,SV2021: $i,SV1597: $i,SV1109: $i,SV507: $i] :
( ( ! [SY7461: $i] :
( ( ( hAPP @ SV507 @ ( c_Set_Oinsert @ SV1109 @ SV1597 @ SV2021 ) )
= ( hAPP @ ( hAPP @ SV2330 @ SV1109 ) @ ( hAPP @ SV507 @ SV1597 ) ) )
| ! [SY7462: $i,SY7463: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV507 @ SV2509 @ SV2602 @ SV2647 @ SV2330 @ SY7461 @ SY7462 @ SY7463 @ SV2021 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6289]) ).
thf(6544,plain,
! [SV1111: $i,SV2331: $i,SV1599: $i,SV509: $i,SV2603: $i,SV2023: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV2023 @ SV2603 ) ) )
= $true )
| ( ( ! [SY7425: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ SV2603 ) @ ( hAPP @ SV1599 @ SY7425 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2331 ) @ SY7425 ) @ SV1111 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SV1111 @ SV1599 @ SV2023 @ SV2331 @ SV509 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1111 @ SV1599 @ SV2331 @ ( tc_fun @ SV509 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6290]) ).
thf(6545,plain,
! [SV511: $i,SV1601: $i,SV1113: $i,SV2332: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV2332 @ SV1113 @ SV1601 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV511 @ SV2332 @ SV1601 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV511 @ SV1113 @ SV1601 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6291]) ).
thf(6546,plain,
! [SV2510: $i,SV2334: $i,SV2027: $i,SV1605: $i,SV1117: $i,SV515: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ SV515 @ SV1117 @ SV1605 @ SV2027 ) @ SV2334 )
= ( c_Option_Ooption_OSome @ SV2510 @ SV2027 ) )
= $false )
| ( ( ( ( hAPP @ SV1117 @ SV2334 )
= ( c_Option_Ooption_ONone @ SV2027 ) )
| ( ( hAPP @ SV1117 @ SV2334 )
= ( c_Option_Ooption_OSome @ SV2510 @ SV2027 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6292]) ).
thf(6547,plain,
! [SV2512: $i,SV2340: $i,SV2032: $i,SV1612: $i,SV1126: $i,SV526: $i] :
( ( ( ( c_Com_Ocom_OLocal @ SV526 @ SV1126 @ SV1612 )
= ( c_Com_Ocom_OLocal @ SV2032 @ SV2340 @ SV2512 ) )
= $false )
| ( ( SV1612 = SV2512 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6294]) ).
thf(6548,plain,
! [SV2604: $i,SV2341: $i,SV2033: $i,SV1613: $i,SV1127: $i,SV527: $i] :
( ( ( ( c_Com_Ocom_OLocal @ SV527 @ SV1127 @ SV1613 )
= ( c_Com_Ocom_OLocal @ SV2033 @ SV2341 @ SV2604 ) )
= $false )
| ( ( SV1127 = SV2341 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6295]) ).
thf(6549,plain,
! [SV2605: $i,SV2513: $i,SV2034: $i,SV1614: $i,SV1128: $i,SV528: $i] :
( ( ( ( c_Com_Ocom_OLocal @ SV528 @ SV1128 @ SV1614 )
= ( c_Com_Ocom_OLocal @ SV2034 @ SV2513 @ SV2605 ) )
= $false )
| ( ( SV528 = SV2034 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6296]) ).
thf(6550,plain,
! [SV2606: $i,SV2514: $i,SV2343: $i,SV2037: $i,SV1618: $i,SV1132: $i,SV532: $i] :
( ( ( ( hAPP @ SV532 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1132 @ tc_bool ) ) )
= SV1618 )
= $true )
| ( ( ! [SY7426: $i,SY7427: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2037 @ SV532 @ SV2343 @ SV2514 @ SV2606 @ SY7426 @ SV1618 @ SY7427 @ SV1132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6297]) ).
thf(6551,plain,
! [SV2607: $i,SV2515: $i,SV2344: $i,SV2038: $i,SV1619: $i,SV1133: $i,SV533: $i] :
( ( ( ( hAPP @ SV533 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1133 @ tc_bool ) ) )
= SV1619 )
= $true )
| ( ( ! [SY7428: $i,SY7429: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV533 @ SV2038 @ SV2344 @ SV2515 @ SV2607 @ SY7428 @ SY7429 @ SV1619 @ SV1133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6298]) ).
thf(6552,plain,
! [SV2648: $i,SV2608: $i,SV2517: $i,SV2346: $i,SV2042: $i,SV1623: $i,SV1140: $i,SV541: $i] :
( ( ( ( hAPP @ SV541 @ ( c_Set_Oinsert @ SV1140 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1623 @ tc_bool ) ) @ SV1623 ) )
= SV1140 )
| ! [SY7464: $i,SY7465: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2042 @ SV541 @ SV2346 @ SV2517 @ SV2608 @ SV2648 @ SY7464 @ SY7465 @ SV1623 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6300]) ).
thf(6553,plain,
! [SV2649: $i,SV2609: $i,SV2518: $i,SV2347: $i,SV2043: $i,SV1624: $i,SV1141: $i,SV542: $i] :
( ( ( ( hAPP @ SV542 @ ( c_Set_Oinsert @ SV1141 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1624 @ tc_bool ) ) @ SV1624 ) )
= SV1141 )
| ! [SY7466: $i,SY7467: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV542 @ SV2043 @ SV2347 @ SV2518 @ SV2609 @ SV2649 @ SY7466 @ SY7467 @ SV1624 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6301]) ).
thf(6554,plain,
! [SV2044: $i,SV1626: $i,SV1144: $i,SV545: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1144 ) @ SV1626 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV2044 @ SV1144 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV545 ) @ SV1144 ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1626 @ ( c_Collect @ SV2044 @ SV545 ) @ ( tc_fun @ SV545 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6302]) ).
thf(6555,plain,
! [SV1630: $i,SV2046: $i,SV1148: $i,SV550: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV550 @ ( c_Set_Oinsert @ SV1148 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2046 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2046 ) ) @ SV2046 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV550 @ SV1630 @ SV2046 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV550 @ ( c_Set_Oinsert @ SV1148 @ SV1630 @ ( tc_Hoare__Mirabelle_Otriple @ SV2046 ) ) @ SV2046 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6305]) ).
thf(6556,plain,
! [SV1631: $i,SV1149: $i,SV2047: $i,SV551: $i] :
( ( ( hBOOL @ ( hAPP @ SV551 @ SV2047 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1149 @ SV2047 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV551 @ SV1149 @ ( tc_fun @ SV1631 @ tc_bool ) ) @ SV2047 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6306]) ).
thf(6557,plain,
! [SV2610: $i,SV2520: $i,SV552: $i,SV1632: $i,SV1150: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1150 @ SV1632 @ SV552 )
!= ( c_HOL_Ominus__class_Ominus @ SV2520 @ SV2610 @ SV552 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV2520 @ SV2610 @ SV552 )
| ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SV1632 @ SV552 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV552 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6307]) ).
thf(6558,plain,
! [SV2611: $i,SV2521: $i,SV553: $i,SV1633: $i,SV1151: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1151 @ SV1633 @ SV553 )
!= ( c_HOL_Ominus__class_Ominus @ SV2521 @ SV2611 @ SV553 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1151 @ SV1633 @ SV553 )
| ~ ( c_HOL_Oord__class_Oless @ SV2521 @ SV2611 @ SV553 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV553 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6308]) ).
thf(6559,plain,
! [SV2351: $i,SV1154: $i,SV556: $i,SV2048: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ SV2048 @ SV556 @ SV1154 @ SV2351 ) @ SV2351 )
= $false )
| ( ( c_Fun_Oinj__on @ SV2048 @ SV556 @ SV1154 @ SV2351 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV556 @ SV1154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6309]) ).
thf(6560,plain,
! [SV1635: $i,SV1156: $i,SV558: $i,SV2352: $i,SV2612: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV2612 @ SV2352 @ SV558 ) ) @ SV1156 ) @ SV1635 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV2352 ) @ SV1156 ) @ SV1635 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV558 ) @ SV1156 ) @ SV1635 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6310]) ).
thf(6561,plain,
! [SV561: $i,SV2049: $i,SV2353: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2353 @ SV2049 @ SV561 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2049 @ SV2353 @ SV561 )
= $false )
| ( ( class_Orderings_Oorder @ SV561 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6311]) ).
thf(6562,plain,
! [SV562: $i,SV2050: $i,SV2354: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2354 @ SV2050 @ SV562 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2050 @ SV2354 @ SV562 )
= $false )
| ( ( class_Orderings_Olinorder @ SV562 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6312]) ).
thf(6563,plain,
! [SV563: $i,SV2051: $i,SV2355: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2355 @ SV2051 @ SV563 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2051 @ SV2355 @ SV563 )
= $false )
| ( ( class_Orderings_Opreorder @ SV563 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6313]) ).
thf(6564,plain,
! [SV564: $i,SV2052: $i,SV2356: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2356 @ SV2052 @ SV564 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2052 @ SV2356 @ SV564 )
= $false )
| ( ( class_Orderings_Opreorder @ SV564 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6314]) ).
thf(6565,plain,
! [SV565: $i,SV1159: $i,SV2357: $i,SV1636: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1636 ) @ SV2357 ) @ SV1159 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV565 @ SV2357 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV565 @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ SV1159 @ SV565 @ SV1636 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6315]) ).
thf(6566,plain,
! [SV2613: $i,SV1160: $i,SV566: $i,SV2522: $i,SV1637: $i,SV2053: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2053 ) @ SV1637 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV2522 @ SV566 @ SV1160 @ SV2613 @ SV2053 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV566 @ SV1160 ) @ SV1637 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6316]) ).
thf(6567,plain,
! [SV1638: $i,SV2614: $i,SV2523: $i,SV567: $i,SV1161: $i,SV2054: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2054 ) @ SV1161 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV567 @ SV2523 @ SV2614 @ SV1638 @ SV2054 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV567 @ SV1161 ) @ SV1638 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6317]) ).
thf(6568,plain,
! [SV1162: $i,SV568: $i,SV1639: $i,SV2358: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2358 @ SV1639 @ ( tc_fun @ SV568 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV568 ) @ SV1162 ) @ SV2358 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV568 ) @ SV1162 ) @ SV1639 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6318]) ).
thf(6569,plain,
! [SV1166: $i,SV1643: $i,SV2359: $i,SV572: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV572 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2359 @ SV572 @ SV1643 ) ) ) )
= $true )
| ( ( ! [SY7279: $i] :
~ ( hBOOL @ ( hAPP @ SY7279 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2359 @ SY7279 @ SV1643 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1643 ) @ SV1166 ) @ SV2359 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV572 @ SV1166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6319]) ).
thf(6570,plain,
! [SV1167: $i,SV573: $i,SV1644: $i,SV2360: $i] :
( ( ( ! [SY7280: $i] :
~ ( hBOOL @ ( hAPP @ SY7280 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2360 @ SY7280 @ SV1644 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV573 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2360 @ SV573 @ SV1644 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1644 ) @ SV1167 ) @ SV2360 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV573 @ SV1167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6320]) ).
thf(6571,plain,
! [SV1168: $i,SV574: $i,SV2361: $i,SV1645: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1645 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2361 @ SV574 @ SV1645 ) ) @ SV2361 ) )
= $true )
| ( ( ! [SY7281: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1645 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2361 @ SY7281 @ SV1645 ) ) @ SV2361 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1645 ) @ SV1168 ) @ SV2361 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV574 @ SV1168 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6321]) ).
thf(6572,plain,
! [SV1169: $i,SV575: $i,SV2362: $i,SV1646: $i] :
( ( ( ! [SY7282: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1646 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2362 @ SY7282 @ SV1646 ) ) @ SV2362 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1646 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2362 @ SV575 @ SV1646 ) ) @ SV2362 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1646 ) @ SV1169 ) @ SV2362 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV575 @ SV1169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6322]) ).
thf(6573,plain,
! [SV1170: $i,SV1647: $i,SV2650: $i,SV2363: $i,SV576: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV576 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2363 @ SV2650 @ SV576 @ SV1647 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV2650 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2363 @ SV2650 @ SV576 @ SV1647 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1647 ) @ SV1170 ) @ SV2363 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV576 @ SV1170 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6323]) ).
thf(6574,plain,
! [SV1171: $i,SV1648: $i,SV577: $i,SV2364: $i,SV2651: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV2651 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2364 @ SV577 @ SV2651 @ SV1648 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV577 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2364 @ SV577 @ SV2651 @ SV1648 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1648 ) @ SV1171 ) @ SV2364 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV577 @ SV1171 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6324]) ).
thf(6575,plain,
! [SV1173: $i,SV1650: $i,SV2365: $i,SV579: $i] :
( ( ( hBOOL @ ( hAPP @ SV579 @ SV2365 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1650 ) @ SV2365 ) @ SV1173 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV579 @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1173 @ SV579 @ SV1650 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6326]) ).
thf(6576,plain,
! [SV584: $i,SV1178: $i,SV2615: $i,SV1655: $i,SV2055: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2055 ) @ SV1655 ) @ SV2615 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2055 ) @ SV1178 ) @ SV2615 ) )
| ( SV1178 = SV1655 )
| ! [SY7436: $i] :
~ ( c_Fun_Oinj__on @ SV584 @ SV2615 @ SV2055 @ SY7436 ) )
= $true )
| ( ( ( hAPP @ SV584 @ SV1178 )
= ( hAPP @ SV584 @ SV1655 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6329]) ).
thf(6577,plain,
! [SV585: $i,SV1179: $i,SV2616: $i,SV1656: $i,SV2056: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2056 ) @ SV1656 ) @ SV2616 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2056 ) @ SV1179 ) @ SV2616 ) )
| ! [SY7437: $i] :
~ ( c_Fun_Oinj__on @ SV585 @ SV2616 @ SV2056 @ SY7437 )
| ( SV1179 = SV1656 ) )
= $true )
| ( ( ( hAPP @ SV585 @ SV1179 )
= ( hAPP @ SV585 @ SV1656 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6330]) ).
thf(6578,plain,
! [SV586: $i,SV1180: $i,SV2617: $i,SV1657: $i,SV2057: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2057 ) @ SV1657 ) @ SV2617 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2057 ) @ SV1180 ) @ SV2617 ) )
| ! [SY7438: $i] :
~ ( c_Fun_Oinj__on @ SV586 @ SV2617 @ SV2057 @ SY7438 )
| ( SV1180 = SV1657 ) )
= $true )
| ( ( ( hAPP @ SV586 @ SV1180 )
= ( hAPP @ SV586 @ SV1657 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6331]) ).
thf(6579,plain,
! [SV1658: $i,SV1181: $i,SV2618: $i,SV2058: $i,SV587: $i] :
( ( ( ! [SY7439: $i] :
~ ( c_Fun_Oinj__on @ SV587 @ SV2058 @ SV2618 @ SY7439 ) )
= $true )
| ( ( ( SV1181 = SV1658 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2618 ) @ SV1658 ) @ SV2058 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2618 ) @ SV1181 ) @ SV2058 ) ) )
= $true )
| ( ( ( hAPP @ SV587 @ SV1181 )
= ( hAPP @ SV587 @ SV1658 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6332]) ).
thf(6580,plain,
! [SV1190: $i,SV596: $i,SV2652: $i,SV2372: $i,SV1665: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1665 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2372 @ SV2652 @ SV596 @ SV1665 ) ) @ SV2372 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1665 ) @ SV1190 ) @ SV2372 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV596 @ SV1190 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6335]) ).
thf(6581,plain,
! [SV1191: $i,SV2653: $i,SV597: $i,SV2373: $i,SV1666: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1666 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2373 @ SV597 @ SV2653 @ SV1666 ) ) @ SV2373 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1666 ) @ SV1191 ) @ SV2373 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV597 @ SV1191 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6336]) ).
thf(6582,plain,
! [SV1192: $i,SV598: $i,SV1667: $i,SV2527: $i] :
( ( ( hBOOL @ ( hAPP @ SV2527 @ ( c_ATP__Linkup_Osko__Set__XballE__1__1 @ SV1667 @ SV2527 @ SV598 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV2527 @ SV1192 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV598 ) @ SV1192 ) @ SV1667 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6337]) ).
thf(6583,plain,
! [SV599: $i,SV1668: $i,SV2063: $i,SV1193: $i] :
( ( ( SV1193 = SV2063 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1668 ) @ SV599 ) @ SV1193 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1668 ) @ SV599 ) @ SV2063 ) )
= $true )
| ( ( ( c_Set_Oinsert @ SV599 @ SV1193 @ SV1668 )
= ( c_Set_Oinsert @ SV599 @ SV2063 @ SV1668 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6338]) ).
thf(6584,plain,
! [SV1194: $i,SV600: $i,SV2374: $i,SV1669: $i] :
( ( ( hBOOL @ ( hAPP @ SV1669 @ SV2374 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV600 ) @ SV2374 ) @ SV1194 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV600 ) @ ( c_ATP__Linkup_Osko__Set__XbexI__1__1 @ SV1194 @ SV1669 @ SV600 ) ) @ SV1194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6339]) ).
thf(6585,plain,
! [SV1670: $i,SV2375: $i,SV2619: $i,SV2064: $i,SV1195: $i,SV601: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV601 ) @ SV1195 ) @ ( hAPP @ SV2064 @ SV2619 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2375 ) @ SV2619 ) @ SV1670 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV601 ) @ SV1195 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1670 @ SV2064 @ SV2375 @ ( tc_fun @ SV601 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6340]) ).
thf(6586,plain,
! [SV1671: $i,SV2376: $i,SV2620: $i,SV2065: $i,SV1196: $i,SV602: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV602 ) @ SV1196 ) @ ( hAPP @ SV2065 @ SV2620 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2376 ) @ SV2620 ) @ SV1671 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV602 ) @ SV1196 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1671 @ SV2065 @ SV2376 @ ( tc_fun @ SV602 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6341]) ).
thf(6587,plain,
! [SV1199: $i,SV2067: $i,SV1674: $i,SV2378: $i,SV2621: $i,SV605: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV605 @ SV2621 ) ) )
= $true )
| ( ( ! [SY7440: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2378 ) @ SV2621 ) @ ( hAPP @ SV1674 @ SY7440 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2067 ) @ SY7440 ) @ SV1199 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV605 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SV1199 @ SV1674 @ SV605 @ SV2067 @ SV2378 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6342]) ).
thf(6588,plain,
! [SV2654: $i,SV2622: $i,SV2530: $i,SV2382: $i,SV2073: $i,SV1680: $i,SV1205: $i,SV611: $i] :
( ( ! [SY7468: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV611 @ ( hAPP @ SV1205 @ SV1680 ) ) @ SV2073 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2382 ) @ SV2073 ) @ SV1680 ) )
| ! [SY7469: $i,SY7470: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1205 @ SV2530 @ SV611 @ SV2622 @ SV2654 @ SY7468 @ SY7469 @ SY7470 @ SV2382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6348]) ).
thf(6589,plain,
! [SV2655: $i,SV2623: $i,SV2531: $i,SV2383: $i,SV2074: $i,SV1681: $i,SV1206: $i,SV612: $i] :
( ( ! [SY7471: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV612 @ SV1206 ) @ ( hAPP @ SV1681 @ SV2074 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2383 ) @ SV1206 ) @ SV2074 ) )
| ! [SY7472: $i,SY7473: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2531 @ SV1681 @ SV612 @ SV2623 @ SV2655 @ SY7471 @ SY7472 @ SY7473 @ SV2383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6349]) ).
thf(6590,plain,
! [SV1209: $i,SV1684: $i,SV2075: $i,SV2534: $i,SV615: $i] :
( ( ( hBOOL @ ( hAPP @ SV615 @ SV2534 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2075 ) @ SV2534 ) @ SV1684 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV615 @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV1209 @ SV1684 @ SV615 @ SV2075 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6352]) ).
thf(6591,plain,
! [SV1685: $i,SV1210: $i,SV2076: $i,SV2535: $i,SV616: $i] :
( ( ( hBOOL @ ( hAPP @ SV616 @ SV2535 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2076 ) @ SV2535 ) @ SV1210 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV616 @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV1210 @ SV1685 @ SV616 @ SV2076 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6353]) ).
thf(6592,plain,
! [SV1686: $i,SV1211: $i,SV2386: $i,SV617: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV617 ) @ SV2386 ) @ SV1211 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1686 @ SV2386 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV617 ) @ ( c_ATP__Linkup_Osko__Set__XbexE__1__1 @ SV1211 @ SV1686 @ SV617 ) ) @ SV1211 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6354]) ).
thf(6593,plain,
! [SV2624: $i,SV2536: $i,SV2388: $i,SV2078: $i,SV1690: $i,SV1215: $i,SV621: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV621 @ SV1215 @ SV1690 @ ( tc_fun @ SV2078 @ ( tc_fun @ SV2388 @ tc_bool ) ) ) @ SV2536 ) @ SV2624 ) )
= $true )
| ( ( ! [SY7449: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV1215 @ SY7449 ) @ SV2536 ) @ SV2624 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1690 ) @ SY7449 ) @ SV621 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6355]) ).
thf(6594,plain,
! [SV2079: $i,SV622: $i,SV1691: $i,SV2389: $i,SV2625: $i,SV1216: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1216 @ SV2625 ) @ SV2389 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1691 ) @ SV2625 ) @ SV622 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV622 @ SV1216 @ SV1691 @ ( tc_fun @ SV2079 @ tc_bool ) ) @ SV2389 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6356]) ).
thf(6595,plain,
! [SV2626: $i,SV2537: $i,SV2390: $i,SV2080: $i,SV1692: $i,SV1217: $i,SV623: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV623 @ SV1217 @ SV1692 @ ( tc_fun @ SV2080 @ ( tc_fun @ SV2390 @ tc_bool ) ) ) @ SV2537 ) @ SV2626 ) )
= $true )
| ( ( ! [SY7450: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV1217 @ SY7450 ) @ SV2537 ) @ SV2626 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1692 ) @ SY7450 ) @ SV623 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6357]) ).
thf(6596,plain,
! [SV2081: $i,SV624: $i,SV1693: $i,SV2391: $i,SV2627: $i,SV1218: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1218 @ SV2627 ) @ SV2391 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1693 ) @ SV2627 ) @ SV624 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV624 @ SV1218 @ SV1693 @ ( tc_fun @ SV2081 @ tc_bool ) ) @ SV2391 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6358]) ).
thf(6597,plain,
! [SV1694: $i,SV2628: $i,SV625: $i,SV2538: $i,SV1219: $i,SV2082: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2082 ) @ SV1219 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV2538 @ SV625 @ SV2628 @ SV1694 @ SV2082 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV625 @ SV1219 ) @ SV1694 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6359]) ).
thf(6598,plain,
! [SV2629: $i,SV1220: $i,SV2539: $i,SV626: $i,SV1695: $i,SV2083: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2083 ) @ SV1695 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV626 @ SV2539 @ SV1220 @ SV2629 @ SV2083 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV626 @ SV1220 ) @ SV1695 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6360]) ).
thf(6599,plain,
! [SV1696: $i,SV1221: $i,SV2392: $i,SV627: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV627 ) @ SV2392 ) @ SV1221 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1696 @ SV2392 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV627 ) @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ SV1221 @ SV1696 @ SV627 ) ) @ SV1221 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6361]) ).
thf(6600,plain,
! [SV628: $i,SV1222: $i,SV2393: $i,SV1697: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1697 ) @ SV2393 ) @ SV1222 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV628 @ SV2393 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV628 @ ( c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 @ SV1222 @ SV628 @ SV1697 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6362]) ).
thf(6601,plain,
! [SV1719: $i,SV2543: $i,SV656: $i,SV1244: $i,SV2398: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2398 ) @ SV1244 ) @ ( c_Map_Odom @ SV656 @ SV2398 @ SV2543 ) ) )
= $false )
| ( ( ~ ( c_Map_Omap__le @ SV656 @ SV1719 @ SV2398 @ SV2543 ) )
= $true )
| ( ( ( hAPP @ SV656 @ SV1244 )
= ( hAPP @ SV1719 @ SV1244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6371]) ).
thf(6602,plain,
! [SV2100: $i,SV3: $i,SV2400: $i,SV675: $i] :
( ( ( c_lessequals @ SV675 @ SV2400 @ SV3 )
= $false )
| ( ( ~ ( c_lessequals @ SV675 @ SV2100 @ SV3 ) )
= $true )
| ( ( c_lessequals @ SV675 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2100 @ SV2400 @ SV3 ) @ SV3 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6373]) ).
thf(6603,plain,
! [SV2101: $i,SV4: $i,SV2401: $i,SV676: $i] :
( ( ( c_lessequals @ SV676 @ SV2401 @ SV4 )
= $false )
| ( ( ~ ( c_lessequals @ SV676 @ SV2101 @ SV4 ) )
= $true )
| ( ( c_lessequals @ SV676 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2101 @ SV2401 @ SV4 ) @ SV4 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6374]) ).
thf(6604,plain,
! [SV2102: $i,SV5: $i,SV2402: $i,SV677: $i] :
( ( ( c_lessequals @ SV677 @ SV2402 @ SV5 )
= $false )
| ( ( ~ ( c_lessequals @ SV677 @ SV2102 @ SV5 ) )
= $true )
| ( ( c_lessequals @ SV677 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2102 @ SV2402 @ SV5 ) @ SV5 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6375]) ).
thf(6605,plain,
! [SV2105: $i,SV678: $i,SV1263: $i,SV1727: $i,SV8: $i] :
( ( ( c_lessequals @ SV8 @ SV1727 @ ( tc_fun @ SV1263 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV678 @ SV2105 @ ( tc_fun @ SV1263 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV8 @ SV678 @ ( tc_fun @ SV1263 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1727 @ SV2105 @ ( tc_fun @ SV1263 @ tc_bool ) ) @ ( tc_fun @ SV1263 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6376]) ).
thf(6606,plain,
! [SV2544: $i,SV2403: $i,SV2106: $i,SV1728: $i,SV1264: $i,SV680: $i,SV11: $i] :
( ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV11 @ SV680 @ SV1264 @ SV1728 )
= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV2106 @ SV2403 @ SV2544 @ SV1728 ) )
= $false )
| ( ( SV1264 = SV2544 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6377]) ).
thf(6607,plain,
! [SV2633: $i,SV2404: $i,SV2107: $i,SV1729: $i,SV1265: $i,SV681: $i,SV12: $i] :
( ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV12 @ SV681 @ SV1265 @ SV1729 )
= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV2107 @ SV2404 @ SV2633 @ SV1729 ) )
= $false )
| ( ( SV681 = SV2404 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6378]) ).
thf(6608,plain,
! [SV2634: $i,SV2545: $i,SV2108: $i,SV1730: $i,SV1266: $i,SV682: $i,SV13: $i] :
( ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV13 @ SV682 @ SV1266 @ SV1730 )
= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV2108 @ SV2545 @ SV2634 @ SV1730 ) )
= $false )
| ( ( SV13 = SV2108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6379]) ).
thf(6609,plain,
! [SV30: $i,SV1742: $i,SV2118: $i] :
( ( ( c_lessequals @ SV2118 @ SV1742 @ SV30 )
= $false )
| ( ( c_lessequals @ SV1742 @ SV2118 @ SV30 )
= $false )
| ( ( SV1742 = SV2118 )
= $true )
| ( ( class_Orderings_Oorder @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6381]) ).
thf(6610,plain,
! [SV31: $i,SV2119: $i,SV1743: $i] :
( ( ( c_lessequals @ SV1743 @ SV2119 @ SV31 )
= $false )
| ( ( c_lessequals @ SV2119 @ SV1743 @ SV31 )
= $false )
| ( ( SV1743 = SV2119 )
= $true )
| ( ( class_Orderings_Oorder @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6382]) ).
thf(6611,plain,
! [SV32: $i,SV2120: $i,SV1744: $i] :
( ( ( c_lessequals @ SV1744 @ SV2120 @ SV32 )
= $false )
| ( ( c_lessequals @ SV2120 @ SV1744 @ SV32 )
= $false )
| ( ( SV1744 = SV2120 )
= $true )
| ( ( class_Orderings_Oorder @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6383]) ).
thf(6612,plain,
! [SV36: $i,SV2406: $i,SV2122: $i,SV695: $i] :
( ( ( c_lessequals @ SV695 @ SV2122 @ ( tc_fun @ SV2406 @ SV36 ) )
= $false )
| ( ( c_lessequals @ SV2122 @ SV695 @ ( tc_fun @ SV2406 @ SV36 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV695 @ SV2122 @ ( tc_fun @ SV2406 @ SV36 ) )
= $true )
| ( ( class_HOL_Oord @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6384]) ).
thf(6613,plain,
! [SV697: $i,SV2125: $i,SV1276: $i,SV1749: $i,SV39: $i] :
( ( ( c_lessequals @ SV39 @ SV1749 @ ( tc_fun @ SV1276 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV2125 @ SV697 @ ( tc_fun @ SV1276 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV39 @ SV697 @ ( tc_fun @ SV1276 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1749 @ SV2125 @ ( tc_fun @ SV1276 @ tc_bool ) ) @ ( tc_fun @ SV1276 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6386]) ).
thf(6614,plain,
! [SV1288: $i,SV714: $i,SV1762: $i,SV2656: $i,SV2130: $i,SV58: $i] :
( ( ( ! [SY7474: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ SV58 @ SV2130 @ ( c_Option_Ooption_OSome @ SV2656 @ SV1762 ) @ SY7474 @ ( tc_Option_Ooption @ SV1762 ) ) @ SV714 )
= ( c_Option_Ooption_OSome @ SV1288 @ SV1762 ) ) )
= $true )
| ( ( SV714 = SV2130 )
= $true )
| ( ( ( hAPP @ SV58 @ SV714 )
= ( c_Option_Ooption_OSome @ SV1288 @ SV1762 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6389]) ).
thf(6615,plain,
! [SV2546: $i,SV2413: $i,SV2131: $i,SV1763: $i,SV1289: $i,SV715: $i,SV59: $i] :
( ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV59 @ SV715 @ ( c_Option_Ooption_OSome @ SV1289 @ SV1763 ) @ SV2131 @ ( tc_Option_Ooption @ SV1763 ) ) @ SV2413 )
= ( c_Option_Ooption_OSome @ SV2546 @ SV1763 ) )
= $false )
| ( ( ( ( hAPP @ SV59 @ SV2413 )
= ( c_Option_Ooption_OSome @ SV2546 @ SV1763 ) )
| ( SV1289 = SV2546 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6390]) ).
thf(6616,plain,
! [SV2547: $i,SV2414: $i,SV2132: $i,SV1764: $i,SV1290: $i,SV716: $i,SV60: $i] :
( ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV60 @ SV716 @ ( c_Option_Ooption_OSome @ SV1290 @ SV1764 ) @ SV2132 @ ( tc_Option_Ooption @ SV1764 ) ) @ SV2414 )
= ( c_Option_Ooption_OSome @ SV2547 @ SV1764 ) )
= $false )
| ( ( ( ( hAPP @ SV60 @ SV2414 )
= ( c_Option_Ooption_OSome @ SV2547 @ SV1764 ) )
| ( SV2414 = SV716 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6391]) ).
thf(6617,plain,
! [SV2147: $i,SV90: $i,SV2555: $i,SV745: $i] :
( ( ( c_lessequals @ SV745 @ SV2555 @ SV90 )
= $false )
| ( ( ~ ( c_lessequals @ SV2555 @ SV2147 @ SV90 ) )
= $true )
| ( ( c_lessequals @ SV745 @ SV2147 @ SV90 )
= $true )
| ( ( class_Orderings_Oorder @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6402]) ).
thf(6618,plain,
! [SV2148: $i,SV91: $i,SV2556: $i,SV746: $i] :
( ( ( c_lessequals @ SV746 @ SV2556 @ SV91 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2556 @ SV2148 @ SV91 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV746 @ SV2148 @ SV91 )
= $true )
| ( ( class_Orderings_Oorder @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6403]) ).
thf(6619,plain,
! [SV2149: $i,SV92: $i,SV2557: $i,SV747: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV747 @ SV2557 @ SV92 )
= $false )
| ( ( ~ ( c_lessequals @ SV2557 @ SV2149 @ SV92 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV747 @ SV2149 @ SV92 )
= $true )
| ( ( class_Orderings_Oorder @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6404]) ).
thf(6620,plain,
! [SV748: $i,SV93: $i,SV2150: $i,SV2558: $i] :
( ( ( c_lessequals @ SV2558 @ SV2150 @ SV93 )
= $false )
| ( ( ~ ( c_lessequals @ SV748 @ SV2558 @ SV93 ) )
= $true )
| ( ( c_lessequals @ SV748 @ SV2150 @ SV93 )
= $true )
| ( ( class_Orderings_Opreorder @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6405]) ).
thf(6621,plain,
! [SV752: $i,SV1778: $i,SV1309: $i,SV2423: $i,SV97: $i] :
( ( ( c_Fun_Oinj__on @ SV97 @ SV2423 @ SV1309 @ SV1778 )
= $false )
| ( ( c_lessequals @ SV752 @ SV2423 @ ( tc_fun @ SV1309 @ tc_bool ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV97 @ SV752 @ SV1309 @ SV1778 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6407]) ).
thf(6622,plain,
! [SV759: $i,SV106: $i,SV2154: $i,SV2560: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2560 @ SV2154 @ SV106 )
= $false )
| ( ( ~ ( c_lessequals @ SV759 @ SV2560 @ SV106 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV759 @ SV2154 @ SV106 )
= $true )
| ( ( class_Orderings_Opreorder @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6412]) ).
thf(6623,plain,
! [SV760: $i,SV107: $i,SV2155: $i,SV2561: $i] :
( ( ( c_lessequals @ SV2561 @ SV2155 @ SV107 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV760 @ SV2561 @ SV107 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV760 @ SV2155 @ SV107 )
= $true )
| ( ( class_Orderings_Opreorder @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6413]) ).
thf(6624,plain,
! [SV2156: $i,SV761: $i,SV1312: $i,SV1785: $i,SV108: $i] :
( ( ( c_lessequals @ SV108 @ SV1785 @ ( tc_fun @ SV1312 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV761 @ SV2156 @ ( tc_fun @ SV1312 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV108 @ SV761 @ ( tc_fun @ SV1312 @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV1785 @ SV2156 @ ( tc_fun @ SV1312 @ tc_bool ) ) @ ( tc_fun @ SV1312 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6414]) ).
thf(6625,plain,
! [SV2563: $i,SV2427: $i,SV115: $i,SV1319: $i,SV768: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV768 @ SV1319 @ SV115 )
= ( c_HOL_Ominus__class_Ominus @ SV2427 @ SV2563 @ SV115 ) )
= $false )
| ( ( ( c_lessequals @ SV2563 @ SV2427 @ SV115 )
| ~ ( c_lessequals @ SV1319 @ SV768 @ SV115 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6416]) ).
thf(6626,plain,
! [SV2564: $i,SV2428: $i,SV116: $i,SV1320: $i,SV769: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV769 @ SV1320 @ SV116 )
= ( c_HOL_Ominus__class_Ominus @ SV2428 @ SV2564 @ SV116 ) )
= $false )
| ( ( ( c_lessequals @ SV1320 @ SV769 @ SV116 )
| ~ ( c_lessequals @ SV2564 @ SV2428 @ SV116 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6417]) ).
thf(6627,plain,
! [SV2566: $i,SV2430: $i,SV2170: $i,SV1803: $i,SV1325: $i,SV775: $i,SV131: $i] :
( ( ( ( c_Fun_Ofun__upd @ SV131 @ SV775 @ ( c_Option_Ooption_OSome @ SV1325 @ SV1803 ) @ SV2170 @ ( tc_Option_Ooption @ SV1803 ) )
= ( c_Fun_Ofun__upd @ SV2430 @ SV775 @ ( c_Option_Ooption_OSome @ SV2566 @ SV1803 ) @ SV2170 @ ( tc_Option_Ooption @ SV1803 ) ) )
= $false )
| ( ( SV1325 = SV2566 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6426]) ).
thf(6628,plain,
! [SV134: $i,SV777: $i,SV2567: $i,SV1327: $i,SV2431: $i] :
( ( ( ~ ( c_lessequals @ SV2431 @ SV1327 @ ( tc_fun @ SV2567 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1327 @ SV2567 ) )
= $true )
| ( ( ( c_Finite__Set_Osetsum @ SV777 @ ( c_HOL_Ominus__class_Ominus @ SV1327 @ SV2431 @ ( tc_fun @ SV2567 @ tc_bool ) ) @ SV2567 @ SV134 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV777 @ SV1327 @ SV2567 @ SV134 ) @ ( c_Finite__Set_Osetsum @ SV777 @ SV2431 @ SV2567 @ SV134 ) @ SV134 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6427]) ).
thf(6629,plain,
! [SV1806: $i,SV1328: $i,SV778: $i,SV135: $i] :
( ( ( c_Finite__Set_Ofinite @ SV135 @ SV778 )
= $false )
| ( ( ! [SY6827: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ SY6827 @ SV1328 @ SV1806 @ SV778 ) @ SV135 @ ( tc_fun @ SV778 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY6827 @ SV1328 @ SV1806 @ SV778 )
| ! [SY6828: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ SY6828 @ SV135 @ SV778 @ SV1806 ) @ SV1328 @ ( tc_fun @ SV1806 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY6828 @ SV135 @ SV778 @ SV1806 ) ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV1328 @ SV1806 )
= $false )
| ( ( ( c_Finite__Set_Ocard @ SV135 @ SV778 )
= ( c_Finite__Set_Ocard @ SV1328 @ SV1806 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6428]) ).
thf(6630,plain,
! [SV1329: $i,SV2568: $i,SV2173: $i,SV2432: $i,SV1807: $i,SV779: $i,SV136: $i] :
( ( ( ~ ( c_Finite__Set_Ofold__graph @ SV136 @ SV779 @ SV1807 @ SV2432 @ SV2173 @ SV2568 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2173 ) @ SV1329 ) @ SV1807 ) )
= $true )
| ( ( c_Finite__Set_Ofold__graph @ SV136 @ SV779 @ ( c_Set_Oinsert @ SV1329 @ SV1807 @ SV2173 ) @ ( hAPP @ ( hAPP @ SV136 @ SV1329 ) @ SV2432 ) @ SV2173 @ SV2568 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6429]) ).
thf(6631,plain,
! [SV1811: $i,SV143: $i,SV786: $i,SV2569: $i,SV1336: $i,SV2433: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2433 ) @ SV1336 ) @ SV2569 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Set_Oimage @ SV786 @ SV2569 @ SV2433 @ SV143 ) @ SV1811 @ ( tc_fun @ SV143 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV143 ) @ ( hAPP @ SV786 @ SV1336 ) ) @ SV1811 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6431]) ).
thf(6632,plain,
! [SV145: $i,SV788: $i,SV2435: $i,SV1338: $i,SV2570: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2570 ) @ SV1338 ) @ SV2435 ) )
= $false )
| ( ( c_lessequals @ ( hAPP @ SV788 @ SV1338 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV2435 @ SV788 @ SV2570 @ SV145 ) @ SV145 )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6432]) ).
thf(6633,plain,
! [SV1340: $i,SV1814: $i,SV147: $i,SV2571: $i,SV790: $i,SV2437: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2437 ) @ SV790 ) @ SV2571 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV2571 @ SV147 @ SV2437 @ ( tc_fun @ SV1814 @ tc_bool ) ) @ SV1340 @ ( tc_fun @ SV1814 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ SV147 @ SV790 ) @ SV1340 @ ( tc_fun @ SV1814 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6433]) ).
thf(6634,plain,
! [SV794: $i,SV1344: $i,SV151: $i,SV2439: $i,SV2178: $i] :
( ( ( c_Finite__Set_Ofinite @ SV2178 @ SV2439 )
= $false )
| ( ( c_lessequals @ SV151 @ ( c_Set_Oimage @ SV1344 @ SV2178 @ SV2439 @ SV794 ) @ ( tc_fun @ SV794 @ tc_bool ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV151 @ SV794 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6434]) ).
thf(6635,plain,
! [SV1822: $i,SV1354: $i,SV2184: $i,SV805: $i,SV162: $i] :
( ( ( c_Fun_Oinj__on @ SV162 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV805 @ SV2184 @ ( tc_fun @ SV1354 @ tc_bool ) ) @ SV1354 @ SV1822 )
= $false )
| ( ( SV805 = SV2184 )
= $true )
| ( ( ( c_Set_Oimage @ SV162 @ SV805 @ SV1354 @ SV1822 )
= ( c_Set_Oimage @ SV162 @ SV2184 @ SV1354 @ SV1822 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6435]) ).
thf(6636,plain,
! [SV184: $i,SV2445: $i,SV819: $i,SV2193: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2193 @ SV819 @ ( tc_fun @ SV2445 @ SV184 ) )
= $false )
| ( ( c_lessequals @ SV819 @ SV2193 @ ( tc_fun @ SV2445 @ SV184 ) )
= $false )
| ( ( class_HOL_Oord @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6438]) ).
thf(6637,plain,
! [SV832: $i,SV201: $i,SV2450: $i,SV2202: $i] :
( ( ( c_lessequals @ SV2202 @ SV2450 @ SV201 )
= $false )
| ( ( ~ ( c_lessequals @ SV832 @ SV2450 @ SV201 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV832 @ SV2202 @ SV201 ) @ SV2450 @ SV201 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6442]) ).
thf(6638,plain,
! [SV833: $i,SV204: $i,SV2451: $i,SV2205: $i] :
( ( ( c_lessequals @ SV2205 @ SV2451 @ SV204 )
= $false )
| ( ( ~ ( c_lessequals @ SV833 @ SV2451 @ SV204 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV833 @ SV2205 @ SV204 ) @ SV2451 @ SV204 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6443]) ).
thf(6639,plain,
! [SV834: $i,SV205: $i,SV2452: $i,SV2206: $i] :
( ( ( c_lessequals @ SV2206 @ SV2452 @ SV205 )
= $false )
| ( ( ~ ( c_lessequals @ SV834 @ SV2452 @ SV205 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV834 @ SV2206 @ SV205 ) @ SV2452 @ SV205 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6444]) ).
thf(6640,plain,
! [SV1396: $i,SV244: $i,SV2636: $i,SV2461: $i,SV865: $i] :
( ( ( c_lessequals @ SV865 @ SV2461 @ ( tc_fun @ SV2636 @ SV244 ) )
= $false )
| ( ( c_lessequals @ ( hAPP @ SV865 @ SV1396 ) @ ( hAPP @ SV2461 @ SV1396 ) @ SV244 )
= $true )
| ( ( class_HOL_Oord @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6453]) ).
thf(6641,plain,
! [SV873: $i,SV1871: $i,SV1404: $i,SV2462: $i,SV253: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV253 ) @ SV2462 ) @ SV1404 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1871 @ SV2462 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV253 ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV873 @ SV1404 @ SV1871 @ SV253 ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV873 @ SV1404 @ ( tc_fun @ SV253 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6458]) ).
thf(6642,plain,
! [SV1405: $i,SV1872: $i,SV874: $i,SV2463: $i,SV254: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV254 ) @ SV2463 ) @ SV874 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1872 @ SV2463 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV254 ) @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV874 @ SV1405 @ SV1872 @ SV254 ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV874 @ SV1405 @ ( tc_fun @ SV254 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6459]) ).
thf(6643,plain,
! [SV877: $i,SV1408: $i,SV2234: $i,SV1874: $i,SV2464: $i,SV257: $i] :
( ( ( c_Fun_Oinj__on @ SV257 @ SV2464 @ SV1874 @ SV2234 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2234 ) @ SV1408 ) @ ( c_Set_Oimage @ SV257 @ SV2464 @ SV1874 @ SV2234 ) ) )
= $true )
| ( ( c_Fun_Oinj__on @ ( c_Fun_Ofun__upd @ SV257 @ SV877 @ SV1408 @ SV1874 @ SV2234 ) @ SV2464 @ SV1874 @ SV2234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6460]) ).
thf(6644,plain,
! [SV262: $i,SV1413: $i,SV882: $i] :
( ( ( c_Finite__Set_Ofinite @ SV882 @ SV1413 )
= $false )
| ( ( c_lessequals @ ( c_Set_Oimage @ SV262 @ SV882 @ SV1413 @ SV1413 ) @ SV882 @ ( tc_fun @ SV1413 @ tc_bool ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV262 @ SV882 @ SV1413 @ SV1413 )
= $false )
| ( ( ( c_Set_Oimage @ SV262 @ SV882 @ SV1413 @ SV1413 )
= SV882 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6464]) ).
thf(6645,plain,
! [SV885: $i,SV1879: $i,SV1416: $i,SV265: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV265 @ SV1416 @ ( tc_fun @ SV1879 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1879 ) @ SV885 ) @ SV265 ) )
= $true )
| ( ( c_lessequals @ SV265 @ SV1416 @ ( tc_fun @ SV1879 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV265 @ ( c_Set_Oinsert @ SV885 @ SV1416 @ SV1879 ) @ ( tc_fun @ SV1879 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6465]) ).
thf(6646,plain,
! [SV2236: $i,SV268: $i,SV888: $i,SV1881: $i,SV2577: $i,SV1419: $i] :
( ( ( c_lessequals @ SV1419 @ SV2577 @ ( tc_fun @ SV1881 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV888 @ SV2577 @ ( tc_fun @ SV1881 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV268 @ SV2577 @ SV1881 @ SV2236 ) )
= $true )
| ( ( ( c_Set_Oimage @ SV268 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV888 @ SV1419 @ ( tc_fun @ SV1881 @ tc_bool ) ) @ SV1881 @ SV2236 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV268 @ SV888 @ SV1881 @ SV2236 ) @ ( c_Set_Oimage @ SV268 @ SV1419 @ SV1881 @ SV2236 ) @ ( tc_fun @ SV2236 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6468]) ).
thf(6647,plain,
! [SV2238: $i,SV270: $i,SV890: $i,SV1883: $i,SV2578: $i,SV1421: $i] :
( ( ( c_lessequals @ SV1421 @ SV2578 @ ( tc_fun @ SV1883 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV890 @ SV2578 @ ( tc_fun @ SV1883 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV270 @ SV2578 @ SV1883 @ SV2238 ) )
= $true )
| ( ( ( c_Set_Oimage @ SV270 @ ( c_HOL_Ominus__class_Ominus @ SV890 @ SV1421 @ ( tc_fun @ SV1883 @ tc_bool ) ) @ SV1883 @ SV2238 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV270 @ SV890 @ SV1883 @ SV2238 ) @ ( c_Set_Oimage @ SV270 @ SV1421 @ SV1883 @ SV2238 ) @ ( tc_fun @ SV2238 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6469]) ).
thf(6648,plain,
! [SV1424: $i,SV1886: $i,SV893: $i,SV273: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV273 @ ( c_Set_Oinsert @ SV893 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1886 @ tc_bool ) ) @ SV1886 ) @ ( tc_fun @ SV1886 @ tc_bool ) ) @ SV1424 @ ( tc_fun @ SV1886 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1886 ) @ SV893 ) @ SV1424 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1886 ) @ SV893 ) @ SV273 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV273 @ ( c_Set_Oinsert @ SV893 @ SV1424 @ SV1886 ) @ ( tc_fun @ SV1886 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6471]) ).
thf(6649,plain,
! [SV1433: $i,SV1892: $i,SV903: $i,SV283: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV283 @ ( c_Set_Oinsert @ SV903 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1892 @ tc_bool ) ) @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) ) @ SV1433 @ ( tc_fun @ SV1892 @ tc_bool ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV283 @ SV1433 @ ( tc_fun @ SV1892 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1892 ) @ SV903 ) @ SV283 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV283 @ ( c_Set_Oinsert @ SV903 @ SV1433 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6472]) ).
thf(6650,plain,
! [SV920: $i,SV1448: $i,SV2247: $i,SV300: $i,SV2466: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV2466 @ SV300 @ SV2247 @ ( tc_fun @ SV1448 @ tc_bool ) ) @ SV1448 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV2466 @ SV2247 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2247 ) @ SV920 ) @ SV2466 ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ SV300 @ SV920 ) @ SV1448 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6473]) ).
thf(6651,plain,
! [SV922: $i,SV1903: $i,SV1450: $i,SV2467: $i,SV302: $i] :
( ( ( c_Map_Omap__le @ SV302 @ SV2467 @ SV1450 @ SV1903 )
= $false )
| ( ( c_Map_Omap__le @ SV2467 @ SV922 @ SV1450 @ SV1903 )
= $false )
| ( ( c_Map_Omap__le @ SV302 @ SV922 @ SV1450 @ SV1903 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6474]) ).
thf(6652,plain,
! [SV1906: $i,SV925: $i,SV305: $i,SV2580: $i,SV1452: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1452 ) @ SV2580 ) @ SV305 ) )
= $false )
| ( ( ( hAPP @ SV925 @ SV2580 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1906 @ tc_bool ) ) )
= $true )
| ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV305 @ SV925 @ SV1452 @ ( tc_fun @ SV1906 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1906 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6475]) ).
thf(6653,plain,
! [SV2657: $i,SV2637: $i,SV2581: $i,SV2470: $i,SV2252: $i,SV1913: $i,SV1458: $i,SV935: $i,SV318: $i] :
( ( ( ( hAPP @ SV318 @ ( c_Set_Oinsert @ SV935 @ ( c_Set_Oinsert @ SV1458 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1913 @ tc_bool ) ) @ SV1913 ) @ SV1913 ) )
= ( hAPP @ ( hAPP @ SV2252 @ SV935 ) @ SV1458 ) )
| ! [SY7475: $i,SY7476: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2470 @ SV318 @ SV2581 @ SV2637 @ SV2657 @ SV2252 @ SY7475 @ SY7476 @ SV1913 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6477]) ).
thf(6654,plain,
! [SV2658: $i,SV2638: $i,SV2582: $i,SV2471: $i,SV2253: $i,SV1914: $i,SV1459: $i,SV936: $i,SV319: $i] :
( ( ( ( hAPP @ SV319 @ ( c_Set_Oinsert @ SV936 @ ( c_Set_Oinsert @ SV1459 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1914 @ tc_bool ) ) @ SV1914 ) @ SV1914 ) )
= ( hAPP @ ( hAPP @ SV2253 @ SV936 ) @ SV1459 ) )
| ! [SY7477: $i,SY7478: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV319 @ SV2471 @ SV2582 @ SV2638 @ SV2253 @ SV2658 @ SY7477 @ SY7478 @ SV1914 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6478]) ).
thf(6655,plain,
! [SV343: $i,SV960: $i,SV1474: $i,SV2478: $i,SV2585: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2585 ) @ SV2478 ) @ SV1474 ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1474 @ SV2585 ) )
= $true )
| ( ( ( c_Finite__Set_Osetsum @ SV960 @ ( c_HOL_Ominus__class_Ominus @ SV1474 @ ( c_Set_Oinsert @ SV2478 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2585 @ tc_bool ) ) @ SV2585 ) @ ( tc_fun @ SV2585 @ tc_bool ) ) @ SV2585 @ SV343 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV960 @ SV1474 @ SV2585 @ SV343 ) @ ( hAPP @ SV960 @ SV2478 ) @ SV343 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV343 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6482]) ).
thf(6656,plain,
! [SV344: $i,SV961: $i,SV1475: $i,SV2479: $i,SV2586: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2586 ) @ SV2479 ) @ SV1475 ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1475 @ SV2586 ) )
= $true )
| ( ( ( c_Finite__Set_Osetsum @ SV961 @ ( c_HOL_Ominus__class_Ominus @ SV1475 @ ( c_Set_Oinsert @ SV2479 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2586 @ tc_bool ) ) @ SV2586 ) @ ( tc_fun @ SV2586 @ tc_bool ) ) @ SV2586 @ SV344 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV961 @ SV1475 @ SV2586 @ SV344 ) @ ( hAPP @ SV961 @ SV2479 ) @ SV344 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV344 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6483]) ).
thf(6657,plain,
! [SV964: $i,SV2266: $i,SV1930: $i,SV1478: $i,SV348: $i] :
( ( ( c_Fun_Oinj__on @ SV348 @ SV1478 @ SV1930 @ SV2266 )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV348 @ SV964 @ SV1930 @ SV2266 )
| ( c_Fun_Oinj__on @ SV348 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV964 @ SV1478 @ ( tc_fun @ SV1930 @ tc_bool ) ) @ SV1930 @ SV2266 ) )
= $true )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV348 @ ( c_HOL_Ominus__class_Ominus @ SV964 @ SV1478 @ ( tc_fun @ SV1930 @ tc_bool ) ) @ SV1930 @ SV2266 ) @ ( c_Set_Oimage @ SV348 @ ( c_HOL_Ominus__class_Ominus @ SV1478 @ SV964 @ ( tc_fun @ SV1930 @ tc_bool ) ) @ SV1930 @ SV2266 ) @ ( tc_fun @ SV2266 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2266 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6484]) ).
thf(6658,plain,
! [SV1479: $i,SV1931: $i,SV965: $i,SV349: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV349 @ ( c_Set_Oinsert @ SV965 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1931 @ tc_bool ) ) @ SV1931 ) @ ( tc_fun @ SV1931 @ tc_bool ) ) @ SV1479 @ ( tc_fun @ SV1931 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1931 ) @ SV965 ) @ SV1479 ) )
= $true )
| ( ( c_lessequals @ SV349 @ SV1479 @ ( tc_fun @ SV1931 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV349 @ ( c_Set_Oinsert @ SV965 @ SV1479 @ SV1931 ) @ ( tc_fun @ SV1931 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6485]) ).
thf(6659,plain,
! [SV351: $i,SV967: $i,SV1481: $i,SV2481: $i,SV2587: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2587 ) @ SV2481 ) @ SV1481 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1481 @ SV2587 ) )
= $true )
| ( ( ( c_Finite__Set_Osetsum @ SV967 @ ( c_HOL_Ominus__class_Ominus @ SV1481 @ ( c_Set_Oinsert @ SV2481 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2587 @ tc_bool ) ) @ SV2587 ) @ ( tc_fun @ SV2587 @ tc_bool ) ) @ SV2587 @ SV351 )
= ( c_Finite__Set_Osetsum @ SV967 @ SV1481 @ SV2587 @ SV351 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV351 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6487]) ).
thf(6660,plain,
! [SV1483: $i,SV969: $i,SV2482: $i,SV2268: $i,SV1933: $i,SV2639: $i,SV353: $i] :
( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV2639 @ SV1933 @ SV2268 @ SV2482 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) ) @ SV2482 ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV969 @ SV1483 @ SV2639 @ SV2482 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) ) @ SV2482 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV969 @ ( c_Com_Ocom_OSemi @ SV1483 @ SV1933 ) @ SV2268 @ SV2482 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) ) @ SV2482 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6488]) ).
thf(6661,plain,
! [SV1486: $i,SV1935: $i,SV972: $i,SV356: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV356 @ ( c_Set_Oinsert @ SV972 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1935 @ tc_bool ) ) @ SV1935 ) @ ( tc_fun @ SV1935 @ tc_bool ) ) @ SV1486 @ ( tc_fun @ SV1935 @ tc_bool ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV356 @ SV1486 @ ( tc_fun @ SV1935 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV356 @ SV1486 @ ( tc_fun @ SV1935 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV356 @ ( c_Set_Oinsert @ SV972 @ SV1486 @ SV1935 ) @ ( tc_fun @ SV1935 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6489]) ).
thf(6662,plain,
! [SV2588: $i,SV2270: $i,SV2484: $i,SV1937: $i,SV1488: $i,SV974: $i,SV358: $i] :
( ( ( ~ ( c_Nitpick_Ofold__graph_H @ SV358 @ SV974 @ ( c_HOL_Ominus__class_Ominus @ SV1488 @ ( c_Set_Oinsert @ SV1937 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2484 @ tc_bool ) ) @ SV2484 ) @ ( tc_fun @ SV2484 @ tc_bool ) ) @ SV2270 @ SV2484 @ SV2588 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2484 ) @ SV1937 ) @ SV1488 ) ) )
= $true )
| ( ( c_Nitpick_Ofold__graph_H @ SV358 @ SV974 @ SV1488 @ ( hAPP @ ( hAPP @ SV358 @ SV1937 ) @ SV2270 ) @ SV2484 @ SV2588 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6490]) ).
thf(6663,plain,
! [SV2589: $i,SV2271: $i,SV979: $i,SV363: $i,SV1493: $i,SV1942: $i,SV2485: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2485 ) @ SV1942 ) @ SV1493 ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofold__graph @ SV363 @ SV979 @ ( c_HOL_Ominus__class_Ominus @ SV1493 @ ( c_Set_Oinsert @ SV1942 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2485 @ tc_bool ) ) @ SV2485 ) @ ( tc_fun @ SV2485 @ tc_bool ) ) @ SV2271 @ SV2485 @ SV2589 ) )
= $true )
| ( ( c_Finite__Set_Ofold__graph @ SV363 @ SV979 @ SV1493 @ ( hAPP @ ( hAPP @ SV363 @ SV1942 ) @ SV2271 ) @ SV2485 @ SV2589 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6494]) ).
thf(6664,plain,
! [SV1495: $i,SV1944: $i,SV981: $i,SV365: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV365 @ ( c_Set_Oinsert @ SV981 @ SV1944 @ SV1495 ) @ ( tc_fun @ SV1495 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1495 ) @ SV981 ) @ SV1944 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1495 ) @ SV981 ) @ SV365 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV365 @ ( c_Set_Oinsert @ SV981 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1495 @ tc_bool ) ) @ SV1495 ) @ ( tc_fun @ SV1495 @ tc_bool ) ) @ SV1944 @ ( tc_fun @ SV1495 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6495]) ).
thf(6665,plain,
! [SV992: $i,SV376: $i,SV2274: $i,SV2591: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2591 @ SV2274 @ SV376 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV992 @ SV2591 @ SV376 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV992 @ SV2274 @ SV376 )
= $true )
| ( ( class_Orderings_Opreorder @ SV376 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6496]) ).
thf(6666,plain,
! [SV2276: $i,SV378: $i,SV2592: $i,SV994: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV994 @ SV2592 @ SV378 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2592 @ SV2276 @ SV378 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV994 @ SV2276 @ SV378 )
= $true )
| ( ( class_Orderings_Oorder @ SV378 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6498]) ).
thf(6667,plain,
! [SV1955: $i,SV387: $i,SV2491: $i,SV1510: $i,SV1003: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1003 ) @ SV1510 ) @ SV2491 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV387 @ SV1510 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV387 @ SV1003 ) ) @ SV2491 ) @ SV1955 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV387 @ SV1003 ) ) @ SV1510 ) @ SV1955 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6500]) ).
thf(6668,plain,
! [SV1513: $i,SV2281: $i,SV1008: $i,SV1956: $i,SV392: $i] :
( ( ( hBOOL @ ( hAPP @ SV392 @ SV1956 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1008 ) @ SV1956 ) @ SV2281 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV392 @ SV1008 @ SV1513 ) ) @ SV1956 ) @ SV2281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6503]) ).
thf(6669,plain,
! [SV2493: $i,SV1009: $i,SV2640: $i,SV1514: $i,SV393: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV393 @ SV1514 @ SV2640 ) ) @ SV1009 ) @ SV2493 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1514 ) @ SV1009 ) @ SV2493 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV393 @ SV1009 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6504]) ).
thf(6670,plain,
! [SV1957: $i,SV1010: $i,SV2494: $i,SV1515: $i,SV394: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV394 ) @ SV1515 ) @ SV2494 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1010 ) @ SV2494 ) @ SV1957 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV394 @ SV1010 ) ) @ SV1515 ) @ SV1957 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6505]) ).
thf(6671,plain,
! [SV2659: $i,SV2641: $i,SV2595: $i,SV2495: $i,SV2284: $i,SV1962: $i,SV1520: $i,SV1015: $i,SV401: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV401 @ SV1015 @ ( c_COMBC @ SV1520 @ SV1962 @ SV1962 @ tc_bool ) @ ( c_COMBC @ SV2284 @ SV1962 @ SV1962 @ tc_bool ) @ SV2495 @ SV2595 @ SV2641 @ SV2659 @ SV1962 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1015 @ SV401 @ SV1520 @ SV2284 @ SV2595 @ SV2495 @ SV2659 @ SV2641 @ SV1962 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6506]) ).
thf(6672,plain,
! [SV1524: $i,SV1019: $i,SV1963: $i,SV2496: $i,SV2285: $i,SV405: $i] :
( ( ( ( hAPP @ SV405 @ SV2285 )
= ( c_Option_Ooption_OSome @ SV2496 @ SV1963 ) )
= $true )
| ( ( ( hAPP @ SV1019 @ SV2285 )
= ( c_Option_Ooption_OSome @ SV2496 @ SV1963 ) )
= $true )
| ( ( ( hAPP @ ( c_Map_Omap__add @ SV405 @ SV1019 @ SV1524 @ SV1963 ) @ SV2285 )
= ( c_Option_Ooption_OSome @ SV2496 @ SV1963 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6507]) ).
thf(6673,plain,
! [SV1525: $i,SV406: $i,SV1964: $i,SV1020: $i,SV2596: $i] :
( ( ( ( hAPP @ SV2596 @ SV1020 )
= ( c_Option_Ooption_ONone @ SV1964 ) )
= $false )
| ( ( ! [SY7414: $i] :
( ( hAPP @ ( c_Map_Omap__add @ SV406 @ SV2596 @ SY7414 @ SV1964 ) @ SV1020 )
= ( c_Option_Ooption_OSome @ SV1525 @ SV1964 ) ) )
= $true )
| ( ( ( hAPP @ SV406 @ SV1020 )
= ( c_Option_Ooption_OSome @ SV1525 @ SV1964 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6508]) ).
thf(6674,plain,
! [SV1039: $i,SV1543: $i,SV2660: $i,SV2498: $i,SV426: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ SV426 @ SV2498 @ SV2660 @ SV1543 ) @ SV1039 )
= ( c_Option_Ooption_ONone @ SV1543 ) )
= $true )
| ( ( ( hAPP @ SV2498 @ SV1039 )
= ( c_Option_Ooption_ONone @ SV1543 ) )
= $false )
| ( ( ( hAPP @ SV426 @ SV1039 )
= ( c_Option_Ooption_ONone @ SV1543 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6509]) ).
thf(6675,plain,
! [SV441: $i,SV1985: $i,SV1554: $i,SV2298: $i,SV1053: $i] :
( ( ( ~ ( c_Map_Omap__le @ SV1053 @ SV2298 @ SV1554 @ SV1985 ) )
= $true )
| ( ( ~ ( c_Map_Omap__le @ SV441 @ SV2298 @ SV1554 @ SV1985 ) )
= $true )
| ( ( c_Map_Omap__le @ SV441 @ ( c_Map_Omap__add @ SV441 @ SV1053 @ SV1554 @ SV1985 ) @ SV1554 @ SV1985 )
= $false )
| ( ( c_Map_Omap__le @ ( c_Map_Omap__add @ SV441 @ SV1053 @ SV1554 @ SV1985 ) @ SV2298 @ SV1554 @ SV1985 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6513]) ).
thf(6676,plain,
! [SV2499: $i,SV1054: $i,SV1555: $i,SV2644: $i,SV442: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV442 @ SV2644 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1555 ) @ SV2644 ) @ SV1054 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1555 ) @ SV2499 ) @ SV1054 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV442 @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1054 @ SV442 @ SV1555 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6514]) ).
thf(6677,plain,
! [SV1057: $i,SV445: $i,SV1558: $i,SV2299: $i,SV2661: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV2661 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2299 @ SV2661 @ SV1558 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1558 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2299 @ SV445 @ SV1558 ) ) @ SV2299 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1558 ) @ SV1057 ) @ SV2299 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV445 @ SV1057 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6517]) ).
thf(6678,plain,
! [SV1058: $i,SV446: $i,SV2662: $i,SV2300: $i,SV1559: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1559 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2300 @ SV2662 @ SV1559 ) ) @ SV2300 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV446 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2300 @ SV446 @ SV1559 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1559 ) @ SV1058 ) @ SV2300 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV446 @ SV1058 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6518]) ).
thf(6679,plain,
! [SV1059: $i,SV1560: $i,SV2301: $i,SV447: $i] :
( ( ( hBOOL @ ( hAPP @ SV447 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2301 @ SV447 @ SV1560 ) ) )
= $false )
| ( ( ! [SY7234: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1560 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2301 @ SY7234 @ SV1560 ) ) @ SV2301 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1560 ) @ SV1059 ) @ SV2301 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV447 @ SV1059 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6519]) ).
thf(6680,plain,
! [SV1060: $i,SV448: $i,SV1561: $i,SV2302: $i,SV2663: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV2663 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2302 @ SV2663 @ SV1561 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1561 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2302 @ SV448 @ SV1561 ) ) @ SV2302 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1561 ) @ SV1060 ) @ SV2302 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV448 @ SV1060 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6520]) ).
thf(6681,plain,
! [SV449: $i,SV2303: $i,SV1562: $i,SV2500: $i,SV1061: $i,SV1988: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1988 @ SV1061 ) @ SV2500 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1562 @ SV2303 ) @ SV1061 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV449 ) @ SV1061 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV1562 @ SV1988 @ SV2303 @ SV2500 @ SV449 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6521]) ).
thf(6682,plain,
! [SV452: $i,SV2304: $i,SV1064: $i,SV1991: $i,SV1565: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1565 @ SV1991 ) @ SV1064 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1565 @ SV1064 ) @ SV2304 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV452 ) @ SV1064 ) @ ( c_SetInterval_Oord_OatLeastAtMost @ SV1565 @ SV1991 @ SV2304 @ SV452 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6522]) ).
thf(6683,plain,
! [SV458: $i,SV2306: $i,SV1070: $i,SV1993: $i,SV1567: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1567 @ SV1993 ) @ SV1070 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1567 @ SV1070 ) @ SV2306 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV458 ) @ SV1070 ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ SV1567 @ SV1993 @ SV2306 @ SV458 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6524]) ).
thf(6684,plain,
! [SV460: $i,SV2308: $i,SV1994: $i,SV2501: $i,SV1072: $i,SV1569: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1569 @ SV1072 ) @ SV2501 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1994 @ SV2308 ) @ SV1072 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV460 ) @ SV1072 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV1569 @ SV1994 @ SV2308 @ SV2501 @ SV460 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6525]) ).
thf(6685,plain,
! [SV2503: $i,SV1075: $i,SV463: $i,SV2645: $i,SV1572: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1572 @ SV2645 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ SV2645 ) @ SV1075 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ SV2503 ) @ SV1075 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1075 @ SV1572 @ SV463 ) ) @ SV1075 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6526]) ).
thf(6686,plain,
! [SV465: $i,SV1574: $i,SV1077: $i,SV2599: $i,SV1995: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1995 ) @ SV2599 ) @ SV1077 ) )
= $false )
| ( ( ( hAPP @ SV1574 @ SV2599 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV465 @ tc_bool ) ) )
= $true )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV465 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1077 @ SV1574 @ SV1995 @ ( tc_fun @ SV465 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6528]) ).
thf(6687,plain,
! [SV1090: $i,SV478: $i,SV1583: $i,SV2504: $i] :
( ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ SV2504 @ SV1583 @ ( tc_fun @ SV478 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV478 @ tc_bool ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV478 ) @ SV1090 ) @ SV2504 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV478 ) @ SV1090 ) @ SV1583 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6531]) ).
thf(6688,plain,
! [SV2664: $i,SV2646: $i,SV2601: $i,SV2508: $i,SV2329: $i,SV2020: $i,SV1596: $i,SV1108: $i,SV506: $i] :
( ( ( ( hAPP @ SV506 @ ( c_Set_Oinsert @ SV1108 @ SV1596 @ SV2020 ) )
= ( hAPP @ ( hAPP @ SV2329 @ SV1108 ) @ ( hAPP @ SV506 @ SV1596 ) ) )
| ! [SY7479: $i,SY7480: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2508 @ SV506 @ SV2601 @ SV2646 @ SV2664 @ SV2329 @ SY7479 @ SY7480 @ SV2020 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6542]) ).
thf(6689,plain,
! [SV2665: $i,SV2647: $i,SV2602: $i,SV2509: $i,SV2330: $i,SV2021: $i,SV1597: $i,SV1109: $i,SV507: $i] :
( ( ( ( hAPP @ SV507 @ ( c_Set_Oinsert @ SV1109 @ SV1597 @ SV2021 ) )
= ( hAPP @ ( hAPP @ SV2330 @ SV1109 ) @ ( hAPP @ SV507 @ SV1597 ) ) )
| ! [SY7481: $i,SY7482: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV507 @ SV2509 @ SV2602 @ SV2647 @ SV2330 @ SV2665 @ SY7481 @ SY7482 @ SV2021 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6543]) ).
thf(6690,plain,
! [SV1111: $i,SV2331: $i,SV1599: $i,SV509: $i,SV2603: $i,SV2023: $i] :
( ( ( hBOOL @ ( hAPP @ SV2023 @ SV2603 ) )
= $false )
| ( ( ! [SY7425: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ SV2603 ) @ ( hAPP @ SV1599 @ SY7425 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2331 ) @ SY7425 ) @ SV1111 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SV1111 @ SV1599 @ SV2023 @ SV2331 @ SV509 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1111 @ SV1599 @ SV2331 @ ( tc_fun @ SV509 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6544]) ).
thf(6691,plain,
! [SV1605: $i,SV515: $i,SV2510: $i,SV2027: $i,SV2334: $i,SV1117: $i] :
( ( ( ( hAPP @ SV1117 @ SV2334 )
= ( c_Option_Ooption_ONone @ SV2027 ) )
= $true )
| ( ( ( hAPP @ SV1117 @ SV2334 )
= ( c_Option_Ooption_OSome @ SV2510 @ SV2027 ) )
= $true )
| ( ( ( hAPP @ ( c_Map_Omap__add @ SV515 @ SV1117 @ SV1605 @ SV2027 ) @ SV2334 )
= ( c_Option_Ooption_OSome @ SV2510 @ SV2027 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6546]) ).
thf(6692,plain,
! [SV1132: $i,SV1618: $i,SV2666: $i,SV2606: $i,SV2514: $i,SV2343: $i,SV532: $i,SV2037: $i] :
( ( ( ! [SY7483: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2037 @ SV532 @ SV2343 @ SV2514 @ SV2606 @ SV2666 @ SV1618 @ SY7483 @ SV1132 ) )
= $true )
| ( ( ( hAPP @ SV532 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1132 @ tc_bool ) ) )
= SV1618 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6550]) ).
thf(6693,plain,
! [SV1133: $i,SV1619: $i,SV2667: $i,SV2607: $i,SV2515: $i,SV2344: $i,SV2038: $i,SV533: $i] :
( ( ( ! [SY7484: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV533 @ SV2038 @ SV2344 @ SV2515 @ SV2607 @ SV2667 @ SY7484 @ SV1619 @ SV1133 ) )
= $true )
| ( ( ( hAPP @ SV533 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1133 @ tc_bool ) ) )
= SV1619 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6551]) ).
thf(6694,plain,
! [SV2648: $i,SV2608: $i,SV2517: $i,SV2346: $i,SV2042: $i,SV1623: $i,SV1140: $i,SV541: $i] :
( ( ( ( hAPP @ SV541 @ ( c_Set_Oinsert @ SV1140 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1623 @ tc_bool ) ) @ SV1623 ) )
= SV1140 )
= $true )
| ( ( ! [SY7464: $i,SY7465: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2042 @ SV541 @ SV2346 @ SV2517 @ SV2608 @ SV2648 @ SY7464 @ SY7465 @ SV1623 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6552]) ).
thf(6695,plain,
! [SV2649: $i,SV2609: $i,SV2518: $i,SV2347: $i,SV2043: $i,SV1624: $i,SV1141: $i,SV542: $i] :
( ( ( ( hAPP @ SV542 @ ( c_Set_Oinsert @ SV1141 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1624 @ tc_bool ) ) @ SV1624 ) )
= SV1141 )
= $true )
| ( ( ! [SY7466: $i,SY7467: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV542 @ SV2043 @ SV2347 @ SV2518 @ SV2609 @ SV2649 @ SY7466 @ SY7467 @ SV1624 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6553]) ).
thf(6696,plain,
! [SV2610: $i,SV2520: $i,SV552: $i,SV1632: $i,SV1150: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1150 @ SV1632 @ SV552 )
= ( c_HOL_Ominus__class_Ominus @ SV2520 @ SV2610 @ SV552 ) )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV2520 @ SV2610 @ SV552 )
| ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SV1632 @ SV552 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV552 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6557]) ).
thf(6697,plain,
! [SV2611: $i,SV2521: $i,SV553: $i,SV1633: $i,SV1151: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1151 @ SV1633 @ SV553 )
= ( c_HOL_Ominus__class_Ominus @ SV2521 @ SV2611 @ SV553 ) )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1151 @ SV1633 @ SV553 )
| ~ ( c_HOL_Oord__class_Oless @ SV2521 @ SV2611 @ SV553 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV553 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6558]) ).
thf(6698,plain,
! [SV1166: $i,SV1643: $i,SV2359: $i,SV572: $i] :
( ( ( hBOOL @ ( hAPP @ SV572 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2359 @ SV572 @ SV1643 ) ) )
= $false )
| ( ( ! [SY7279: $i] :
~ ( hBOOL @ ( hAPP @ SY7279 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2359 @ SY7279 @ SV1643 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1643 ) @ SV1166 ) @ SV2359 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV572 @ SV1166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6569]) ).
thf(6699,plain,
! [SV1167: $i,SV573: $i,SV1644: $i,SV2360: $i,SV2668: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV2668 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2360 @ SV2668 @ SV1644 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV573 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2360 @ SV573 @ SV1644 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1644 ) @ SV1167 ) @ SV2360 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV573 @ SV1167 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6570]) ).
thf(6700,plain,
! [SV1168: $i,SV574: $i,SV2669: $i,SV2361: $i,SV1645: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1645 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2361 @ SV2669 @ SV1645 ) ) @ SV2361 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1645 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2361 @ SV574 @ SV1645 ) ) @ SV2361 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1645 ) @ SV1168 ) @ SV2361 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV574 @ SV1168 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6571]) ).
thf(6701,plain,
! [SV1169: $i,SV575: $i,SV2670: $i,SV2362: $i,SV1646: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1646 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2362 @ SV2670 @ SV1646 ) ) @ SV2362 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1646 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2362 @ SV575 @ SV1646 ) ) @ SV2362 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1646 ) @ SV1169 ) @ SV2362 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV575 @ SV1169 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6572]) ).
thf(6702,plain,
! [SV1170: $i,SV1647: $i,SV2650: $i,SV2363: $i,SV576: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV576 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2363 @ SV2650 @ SV576 @ SV1647 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV2650 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2363 @ SV2650 @ SV576 @ SV1647 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1647 ) @ SV1170 ) @ SV2363 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV576 @ SV1170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6573]) ).
thf(6703,plain,
! [SV1171: $i,SV1648: $i,SV577: $i,SV2364: $i,SV2651: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV2651 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2364 @ SV577 @ SV2651 @ SV1648 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV577 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2364 @ SV577 @ SV2651 @ SV1648 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1648 ) @ SV1171 ) @ SV2364 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV577 @ SV1171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6574]) ).
thf(6704,plain,
! [SV584: $i,SV1178: $i,SV2615: $i,SV1655: $i,SV2055: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2055 ) @ SV1655 ) @ SV2615 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2055 ) @ SV1178 ) @ SV2615 ) )
| ( SV1178 = SV1655 )
| ! [SY7436: $i] :
~ ( c_Fun_Oinj__on @ SV584 @ SV2615 @ SV2055 @ SY7436 ) )
= $true )
| ( ( ( hAPP @ SV584 @ SV1178 )
= ( hAPP @ SV584 @ SV1655 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6576]) ).
thf(6705,plain,
! [SV585: $i,SV1179: $i,SV2616: $i,SV1656: $i,SV2056: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2056 ) @ SV1656 ) @ SV2616 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2056 ) @ SV1179 ) @ SV2616 ) )
| ! [SY7437: $i] :
~ ( c_Fun_Oinj__on @ SV585 @ SV2616 @ SV2056 @ SY7437 )
| ( SV1179 = SV1656 ) )
= $true )
| ( ( ( hAPP @ SV585 @ SV1179 )
= ( hAPP @ SV585 @ SV1656 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6577]) ).
thf(6706,plain,
! [SV586: $i,SV1180: $i,SV2617: $i,SV1657: $i,SV2057: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2057 ) @ SV1657 ) @ SV2617 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2057 ) @ SV1180 ) @ SV2617 ) )
| ! [SY7438: $i] :
~ ( c_Fun_Oinj__on @ SV586 @ SV2617 @ SV2057 @ SY7438 )
| ( SV1180 = SV1657 ) )
= $true )
| ( ( ( hAPP @ SV586 @ SV1180 )
= ( hAPP @ SV586 @ SV1657 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6578]) ).
thf(6707,plain,
! [SV1658: $i,SV1181: $i,SV2671: $i,SV2618: $i,SV2058: $i,SV587: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV587 @ SV2058 @ SV2618 @ SV2671 ) )
= $true )
| ( ( ( SV1181 = SV1658 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2618 ) @ SV1658 ) @ SV2058 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2618 ) @ SV1181 ) @ SV2058 ) ) )
= $true )
| ( ( ( hAPP @ SV587 @ SV1181 )
= ( hAPP @ SV587 @ SV1658 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6579]) ).
thf(6708,plain,
! [SV1670: $i,SV2375: $i,SV2619: $i,SV2064: $i,SV1195: $i,SV601: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV601 ) @ SV1195 ) @ ( hAPP @ SV2064 @ SV2619 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2375 ) @ SV2619 ) @ SV1670 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV601 ) @ SV1195 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1670 @ SV2064 @ SV2375 @ ( tc_fun @ SV601 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6585]) ).
thf(6709,plain,
! [SV1671: $i,SV2376: $i,SV2620: $i,SV2065: $i,SV1196: $i,SV602: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV602 ) @ SV1196 ) @ ( hAPP @ SV2065 @ SV2620 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2376 ) @ SV2620 ) @ SV1671 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV602 ) @ SV1196 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1671 @ SV2065 @ SV2376 @ ( tc_fun @ SV602 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6586]) ).
thf(6710,plain,
! [SV1199: $i,SV2067: $i,SV1674: $i,SV2378: $i,SV2621: $i,SV605: $i] :
( ( ( hBOOL @ ( hAPP @ SV605 @ SV2621 ) )
= $false )
| ( ( ! [SY7440: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2378 ) @ SV2621 ) @ ( hAPP @ SV1674 @ SY7440 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2067 ) @ SY7440 ) @ SV1199 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV605 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SV1199 @ SV1674 @ SV605 @ SV2067 @ SV2378 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6587]) ).
thf(6711,plain,
! [SV2672: $i,SV2654: $i,SV2622: $i,SV2530: $i,SV2382: $i,SV2073: $i,SV1680: $i,SV1205: $i,SV611: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV611 @ ( hAPP @ SV1205 @ SV1680 ) ) @ SV2073 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2382 ) @ SV2073 ) @ SV1680 ) )
| ! [SY7485: $i,SY7486: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1205 @ SV2530 @ SV611 @ SV2622 @ SV2654 @ SV2672 @ SY7485 @ SY7486 @ SV2382 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6588]) ).
thf(6712,plain,
! [SV2673: $i,SV2655: $i,SV2623: $i,SV2531: $i,SV2383: $i,SV2074: $i,SV1681: $i,SV1206: $i,SV612: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV612 @ SV1206 ) @ ( hAPP @ SV1681 @ SV2074 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2383 ) @ SV1206 ) @ SV2074 ) )
| ! [SY7487: $i,SY7488: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2531 @ SV1681 @ SV612 @ SV2623 @ SV2655 @ SV2673 @ SY7487 @ SY7488 @ SV2383 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[6589]) ).
thf(6713,plain,
! [SV1209: $i,SV615: $i,SV1684: $i,SV2534: $i,SV2075: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2075 ) @ SV2534 ) @ SV1684 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV615 @ SV2534 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV615 @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV1209 @ SV1684 @ SV615 @ SV2075 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6590]) ).
thf(6714,plain,
! [SV1685: $i,SV616: $i,SV1210: $i,SV2535: $i,SV2076: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2076 ) @ SV2535 ) @ SV1210 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV616 @ SV2535 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV616 @ ( c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 @ SV1210 @ SV1685 @ SV616 @ SV2076 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6591]) ).
thf(6715,plain,
! [SV2388: $i,SV2078: $i,SV621: $i,SV1690: $i,SV2624: $i,SV2536: $i,SV2674: $i,SV1215: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV1215 @ SV2674 ) @ SV2536 ) @ SV2624 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1690 ) @ SV2674 ) @ SV621 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV621 @ SV1215 @ SV1690 @ ( tc_fun @ SV2078 @ ( tc_fun @ SV2388 @ tc_bool ) ) ) @ SV2536 ) @ SV2624 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6593]) ).
thf(6716,plain,
! [SV2079: $i,SV622: $i,SV1691: $i,SV2389: $i,SV2625: $i,SV1216: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1216 @ SV2625 ) @ SV2389 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1691 ) @ SV2625 ) @ SV622 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV622 @ SV1216 @ SV1691 @ ( tc_fun @ SV2079 @ tc_bool ) ) @ SV2389 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6594]) ).
thf(6717,plain,
! [SV2390: $i,SV2080: $i,SV623: $i,SV1692: $i,SV2626: $i,SV2537: $i,SV2675: $i,SV1217: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV1217 @ SV2675 ) @ SV2537 ) @ SV2626 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1692 ) @ SV2675 ) @ SV623 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV623 @ SV1217 @ SV1692 @ ( tc_fun @ SV2080 @ ( tc_fun @ SV2390 @ tc_bool ) ) ) @ SV2537 ) @ SV2626 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6595]) ).
thf(6718,plain,
! [SV2081: $i,SV624: $i,SV1693: $i,SV2391: $i,SV2627: $i,SV1218: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1218 @ SV2627 ) @ SV2391 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1693 ) @ SV2627 ) @ SV624 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV624 @ SV1218 @ SV1693 @ ( tc_fun @ SV2081 @ tc_bool ) ) @ SV2391 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6596]) ).
thf(6719,plain,
! [SV1244: $i,SV2543: $i,SV2398: $i,SV1719: $i,SV656: $i] :
( ( ( c_Map_Omap__le @ SV656 @ SV1719 @ SV2398 @ SV2543 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2398 ) @ SV1244 ) @ ( c_Map_Odom @ SV656 @ SV2398 @ SV2543 ) ) )
= $false )
| ( ( ( hAPP @ SV656 @ SV1244 )
= ( hAPP @ SV1719 @ SV1244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6601]) ).
thf(6720,plain,
! [SV2400: $i,SV3: $i,SV2100: $i,SV675: $i] :
( ( ( c_lessequals @ SV675 @ SV2100 @ SV3 )
= $false )
| ( ( c_lessequals @ SV675 @ SV2400 @ SV3 )
= $false )
| ( ( c_lessequals @ SV675 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2100 @ SV2400 @ SV3 ) @ SV3 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6602]) ).
thf(6721,plain,
! [SV2401: $i,SV4: $i,SV2101: $i,SV676: $i] :
( ( ( c_lessequals @ SV676 @ SV2101 @ SV4 )
= $false )
| ( ( c_lessequals @ SV676 @ SV2401 @ SV4 )
= $false )
| ( ( c_lessequals @ SV676 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2101 @ SV2401 @ SV4 ) @ SV4 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6603]) ).
thf(6722,plain,
! [SV2402: $i,SV5: $i,SV2102: $i,SV677: $i] :
( ( ( c_lessequals @ SV677 @ SV2102 @ SV5 )
= $false )
| ( ( c_lessequals @ SV677 @ SV2402 @ SV5 )
= $false )
| ( ( c_lessequals @ SV677 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV2102 @ SV2402 @ SV5 ) @ SV5 )
= $true )
| ( ( class_Lattices_Olower__semilattice @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6604]) ).
thf(6723,plain,
! [SV1288: $i,SV714: $i,SV2676: $i,SV1762: $i,SV2656: $i,SV2130: $i,SV58: $i] :
( ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV58 @ SV2130 @ ( c_Option_Ooption_OSome @ SV2656 @ SV1762 ) @ SV2676 @ ( tc_Option_Ooption @ SV1762 ) ) @ SV714 )
= ( c_Option_Ooption_OSome @ SV1288 @ SV1762 ) )
= $true )
| ( ( SV714 = SV2130 )
= $true )
| ( ( ( hAPP @ SV58 @ SV714 )
= ( c_Option_Ooption_OSome @ SV1288 @ SV1762 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6614]) ).
thf(6724,plain,
! [SV2131: $i,SV715: $i,SV1289: $i,SV1763: $i,SV2546: $i,SV2413: $i,SV59: $i] :
( ( ( ( hAPP @ SV59 @ SV2413 )
= ( c_Option_Ooption_OSome @ SV2546 @ SV1763 ) )
= $true )
| ( ( SV1289 = SV2546 )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV59 @ SV715 @ ( c_Option_Ooption_OSome @ SV1289 @ SV1763 ) @ SV2131 @ ( tc_Option_Ooption @ SV1763 ) ) @ SV2413 )
= ( c_Option_Ooption_OSome @ SV2546 @ SV1763 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6615]) ).
thf(6725,plain,
! [SV2132: $i,SV1290: $i,SV716: $i,SV1764: $i,SV2547: $i,SV2414: $i,SV60: $i] :
( ( ( ( hAPP @ SV60 @ SV2414 )
= ( c_Option_Ooption_OSome @ SV2547 @ SV1764 ) )
= $true )
| ( ( SV2414 = SV716 )
= $true )
| ( ( ( hAPP @ ( c_Fun_Ofun__upd @ SV60 @ SV716 @ ( c_Option_Ooption_OSome @ SV1290 @ SV1764 ) @ SV2132 @ ( tc_Option_Ooption @ SV1764 ) ) @ SV2414 )
= ( c_Option_Ooption_OSome @ SV2547 @ SV1764 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6616]) ).
thf(6726,plain,
! [SV745: $i,SV90: $i,SV2147: $i,SV2555: $i] :
( ( ( c_lessequals @ SV2555 @ SV2147 @ SV90 )
= $false )
| ( ( c_lessequals @ SV745 @ SV2555 @ SV90 )
= $false )
| ( ( c_lessequals @ SV745 @ SV2147 @ SV90 )
= $true )
| ( ( class_Orderings_Oorder @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6617]) ).
thf(6727,plain,
! [SV746: $i,SV91: $i,SV2148: $i,SV2556: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2556 @ SV2148 @ SV91 )
= $false )
| ( ( c_lessequals @ SV746 @ SV2556 @ SV91 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV746 @ SV2148 @ SV91 )
= $true )
| ( ( class_Orderings_Oorder @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6618]) ).
thf(6728,plain,
! [SV747: $i,SV92: $i,SV2149: $i,SV2557: $i] :
( ( ( c_lessequals @ SV2557 @ SV2149 @ SV92 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV747 @ SV2557 @ SV92 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV747 @ SV2149 @ SV92 )
= $true )
| ( ( class_Orderings_Oorder @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6619]) ).
thf(6729,plain,
! [SV2150: $i,SV93: $i,SV2558: $i,SV748: $i] :
( ( ( c_lessequals @ SV748 @ SV2558 @ SV93 )
= $false )
| ( ( c_lessequals @ SV2558 @ SV2150 @ SV93 )
= $false )
| ( ( c_lessequals @ SV748 @ SV2150 @ SV93 )
= $true )
| ( ( class_Orderings_Opreorder @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6620]) ).
thf(6730,plain,
! [SV2154: $i,SV106: $i,SV2560: $i,SV759: $i] :
( ( ( c_lessequals @ SV759 @ SV2560 @ SV106 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2560 @ SV2154 @ SV106 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV759 @ SV2154 @ SV106 )
= $true )
| ( ( class_Orderings_Opreorder @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6622]) ).
thf(6731,plain,
! [SV2155: $i,SV107: $i,SV2561: $i,SV760: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV760 @ SV2561 @ SV107 )
= $false )
| ( ( c_lessequals @ SV2561 @ SV2155 @ SV107 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV760 @ SV2155 @ SV107 )
= $true )
| ( ( class_Orderings_Opreorder @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6623]) ).
thf(6732,plain,
! [SV768: $i,SV1319: $i,SV115: $i,SV2427: $i,SV2563: $i] :
( ( ( c_lessequals @ SV2563 @ SV2427 @ SV115 )
= $true )
| ( ( ~ ( c_lessequals @ SV1319 @ SV768 @ SV115 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV768 @ SV1319 @ SV115 )
= ( c_HOL_Ominus__class_Ominus @ SV2427 @ SV2563 @ SV115 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6625]) ).
thf(6733,plain,
! [SV2428: $i,SV2564: $i,SV116: $i,SV769: $i,SV1320: $i] :
( ( ( c_lessequals @ SV1320 @ SV769 @ SV116 )
= $true )
| ( ( ~ ( c_lessequals @ SV2564 @ SV2428 @ SV116 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV769 @ SV1320 @ SV116 )
= ( c_HOL_Ominus__class_Ominus @ SV2428 @ SV2564 @ SV116 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6626]) ).
thf(6734,plain,
! [SV134: $i,SV777: $i,SV2567: $i,SV1327: $i,SV2431: $i] :
( ( ( c_lessequals @ SV2431 @ SV1327 @ ( tc_fun @ SV2567 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1327 @ SV2567 ) )
= $true )
| ( ( ( c_Finite__Set_Osetsum @ SV777 @ ( c_HOL_Ominus__class_Ominus @ SV1327 @ SV2431 @ ( tc_fun @ SV2567 @ tc_bool ) ) @ SV2567 @ SV134 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV777 @ SV1327 @ SV2567 @ SV134 ) @ ( c_Finite__Set_Osetsum @ SV777 @ SV2431 @ SV2567 @ SV134 ) @ SV134 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6628]) ).
thf(6735,plain,
! [SV135: $i,SV778: $i,SV1806: $i,SV1328: $i,SV2677: $i] :
( ( ( ~ ( c_lessequals @ ( c_Set_Oimage @ SV2677 @ SV1328 @ SV1806 @ SV778 ) @ SV135 @ ( tc_fun @ SV778 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV2677 @ SV1328 @ SV1806 @ SV778 )
| ! [SY6828: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ SY6828 @ SV135 @ SV778 @ SV1806 ) @ SV1328 @ ( tc_fun @ SV1806 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY6828 @ SV135 @ SV778 @ SV1806 ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV135 @ SV778 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV1328 @ SV1806 )
= $false )
| ( ( ( c_Finite__Set_Ocard @ SV135 @ SV778 )
= ( c_Finite__Set_Ocard @ SV1328 @ SV1806 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6629]) ).
thf(6736,plain,
! [SV1329: $i,SV2568: $i,SV2173: $i,SV2432: $i,SV1807: $i,SV779: $i,SV136: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV136 @ SV779 @ SV1807 @ SV2432 @ SV2173 @ SV2568 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2173 ) @ SV1329 ) @ SV1807 ) )
= $true )
| ( ( c_Finite__Set_Ofold__graph @ SV136 @ SV779 @ ( c_Set_Oinsert @ SV1329 @ SV1807 @ SV2173 ) @ ( hAPP @ ( hAPP @ SV136 @ SV1329 ) @ SV2432 ) @ SV2173 @ SV2568 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6630]) ).
thf(6737,plain,
! [SV1336: $i,SV1811: $i,SV143: $i,SV2433: $i,SV2569: $i,SV786: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV786 @ SV2569 @ SV2433 @ SV143 ) @ SV1811 @ ( tc_fun @ SV143 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2433 ) @ SV1336 ) @ SV2569 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV143 ) @ ( hAPP @ SV786 @ SV1336 ) ) @ SV1811 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6631]) ).
thf(6738,plain,
! [SV790: $i,SV1340: $i,SV1814: $i,SV2437: $i,SV147: $i,SV2571: $i] :
( ( ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV2571 @ SV147 @ SV2437 @ ( tc_fun @ SV1814 @ tc_bool ) ) @ SV1340 @ ( tc_fun @ SV1814 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2437 ) @ SV790 ) @ SV2571 ) )
= $false )
| ( ( c_lessequals @ ( hAPP @ SV147 @ SV790 ) @ SV1340 @ ( tc_fun @ SV1814 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6633]) ).
thf(6739,plain,
! [SV2202: $i,SV201: $i,SV2450: $i,SV832: $i] :
( ( ( c_lessequals @ SV832 @ SV2450 @ SV201 )
= $false )
| ( ( c_lessequals @ SV2202 @ SV2450 @ SV201 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV832 @ SV2202 @ SV201 ) @ SV2450 @ SV201 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6637]) ).
thf(6740,plain,
! [SV2205: $i,SV204: $i,SV2451: $i,SV833: $i] :
( ( ( c_lessequals @ SV833 @ SV2451 @ SV204 )
= $false )
| ( ( c_lessequals @ SV2205 @ SV2451 @ SV204 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV833 @ SV2205 @ SV204 ) @ SV2451 @ SV204 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6638]) ).
thf(6741,plain,
! [SV2206: $i,SV205: $i,SV2452: $i,SV834: $i] :
( ( ( c_lessequals @ SV834 @ SV2452 @ SV205 )
= $false )
| ( ( c_lessequals @ SV2206 @ SV2452 @ SV205 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV834 @ SV2206 @ SV205 ) @ SV2452 @ SV205 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6639]) ).
thf(6742,plain,
! [SV1419: $i,SV2236: $i,SV268: $i,SV1881: $i,SV2577: $i,SV888: $i] :
( ( ( ~ ( c_lessequals @ SV888 @ SV2577 @ ( tc_fun @ SV1881 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV268 @ SV2577 @ SV1881 @ SV2236 ) )
= $true )
| ( ( c_lessequals @ SV1419 @ SV2577 @ ( tc_fun @ SV1881 @ tc_bool ) )
= $false )
| ( ( ( c_Set_Oimage @ SV268 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV888 @ SV1419 @ ( tc_fun @ SV1881 @ tc_bool ) ) @ SV1881 @ SV2236 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV268 @ SV888 @ SV1881 @ SV2236 ) @ ( c_Set_Oimage @ SV268 @ SV1419 @ SV1881 @ SV2236 ) @ ( tc_fun @ SV2236 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6646]) ).
thf(6743,plain,
! [SV1421: $i,SV2238: $i,SV270: $i,SV1883: $i,SV2578: $i,SV890: $i] :
( ( ( ~ ( c_lessequals @ SV890 @ SV2578 @ ( tc_fun @ SV1883 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV270 @ SV2578 @ SV1883 @ SV2238 ) )
= $true )
| ( ( c_lessequals @ SV1421 @ SV2578 @ ( tc_fun @ SV1883 @ tc_bool ) )
= $false )
| ( ( ( c_Set_Oimage @ SV270 @ ( c_HOL_Ominus__class_Ominus @ SV890 @ SV1421 @ ( tc_fun @ SV1883 @ tc_bool ) ) @ SV1883 @ SV2238 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV270 @ SV890 @ SV1883 @ SV2238 ) @ ( c_Set_Oimage @ SV270 @ SV1421 @ SV1883 @ SV2238 ) @ ( tc_fun @ SV2238 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6647]) ).
thf(6744,plain,
! [SV903: $i,SV1892: $i,SV1433: $i,SV283: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV283 @ SV1433 @ ( tc_fun @ SV1892 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV283 @ ( c_Set_Oinsert @ SV903 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1892 @ tc_bool ) ) @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) ) @ SV1433 @ ( tc_fun @ SV1892 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1892 ) @ SV903 ) @ SV283 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV283 @ ( c_Set_Oinsert @ SV903 @ SV1433 @ SV1892 ) @ ( tc_fun @ SV1892 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6649]) ).
thf(6745,plain,
! [SV920: $i,SV1448: $i,SV2247: $i,SV300: $i,SV2466: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV2466 @ SV300 @ SV2247 @ ( tc_fun @ SV1448 @ tc_bool ) ) @ SV1448 )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV2466 @ SV2247 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2247 ) @ SV920 ) @ SV2466 ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ SV300 @ SV920 ) @ SV1448 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6650]) ).
thf(6746,plain,
! [SV2657: $i,SV2637: $i,SV2581: $i,SV2470: $i,SV2252: $i,SV1913: $i,SV1458: $i,SV935: $i,SV318: $i] :
( ( ( ( hAPP @ SV318 @ ( c_Set_Oinsert @ SV935 @ ( c_Set_Oinsert @ SV1458 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1913 @ tc_bool ) ) @ SV1913 ) @ SV1913 ) )
= ( hAPP @ ( hAPP @ SV2252 @ SV935 ) @ SV1458 ) )
= $true )
| ( ( ! [SY7475: $i,SY7476: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2470 @ SV318 @ SV2581 @ SV2637 @ SV2657 @ SV2252 @ SY7475 @ SY7476 @ SV1913 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6653]) ).
thf(6747,plain,
! [SV2658: $i,SV2638: $i,SV2582: $i,SV2471: $i,SV2253: $i,SV1914: $i,SV1459: $i,SV936: $i,SV319: $i] :
( ( ( ( hAPP @ SV319 @ ( c_Set_Oinsert @ SV936 @ ( c_Set_Oinsert @ SV1459 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1914 @ tc_bool ) ) @ SV1914 ) @ SV1914 ) )
= ( hAPP @ ( hAPP @ SV2253 @ SV936 ) @ SV1459 ) )
= $true )
| ( ( ! [SY7477: $i,SY7478: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV319 @ SV2471 @ SV2582 @ SV2638 @ SV2253 @ SV2658 @ SY7477 @ SY7478 @ SV1914 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6654]) ).
thf(6748,plain,
! [SV343: $i,SV960: $i,SV1474: $i,SV2478: $i,SV2585: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2585 ) @ SV2478 ) @ SV1474 ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1474 @ SV2585 ) )
= $true )
| ( ( ( c_Finite__Set_Osetsum @ SV960 @ ( c_HOL_Ominus__class_Ominus @ SV1474 @ ( c_Set_Oinsert @ SV2478 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2585 @ tc_bool ) ) @ SV2585 ) @ ( tc_fun @ SV2585 @ tc_bool ) ) @ SV2585 @ SV343 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV960 @ SV1474 @ SV2585 @ SV343 ) @ ( hAPP @ SV960 @ SV2478 ) @ SV343 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV343 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6655]) ).
thf(6749,plain,
! [SV344: $i,SV961: $i,SV1475: $i,SV2479: $i,SV2586: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2586 ) @ SV2479 ) @ SV1475 ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1475 @ SV2586 ) )
= $true )
| ( ( ( c_Finite__Set_Osetsum @ SV961 @ ( c_HOL_Ominus__class_Ominus @ SV1475 @ ( c_Set_Oinsert @ SV2479 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2586 @ tc_bool ) ) @ SV2586 ) @ ( tc_fun @ SV2586 @ tc_bool ) ) @ SV2586 @ SV344 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV961 @ SV1475 @ SV2586 @ SV344 ) @ ( hAPP @ SV961 @ SV2479 ) @ SV344 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV344 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6656]) ).
thf(6750,plain,
! [SV1478: $i,SV2266: $i,SV1930: $i,SV964: $i,SV348: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV348 @ SV964 @ SV1930 @ SV2266 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV348 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV964 @ SV1478 @ ( tc_fun @ SV1930 @ tc_bool ) ) @ SV1930 @ SV2266 )
= $true )
| ( ( c_Fun_Oinj__on @ SV348 @ SV1478 @ SV1930 @ SV2266 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV348 @ ( c_HOL_Ominus__class_Ominus @ SV964 @ SV1478 @ ( tc_fun @ SV1930 @ tc_bool ) ) @ SV1930 @ SV2266 ) @ ( c_Set_Oimage @ SV348 @ ( c_HOL_Ominus__class_Ominus @ SV1478 @ SV964 @ ( tc_fun @ SV1930 @ tc_bool ) ) @ SV1930 @ SV2266 ) @ ( tc_fun @ SV2266 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2266 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6657]) ).
thf(6751,plain,
! [SV351: $i,SV967: $i,SV2481: $i,SV2587: $i,SV1481: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1481 @ SV2587 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2587 ) @ SV2481 ) @ SV1481 ) )
= $true )
| ( ( ( c_Finite__Set_Osetsum @ SV967 @ ( c_HOL_Ominus__class_Ominus @ SV1481 @ ( c_Set_Oinsert @ SV2481 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2587 @ tc_bool ) ) @ SV2587 ) @ ( tc_fun @ SV2587 @ tc_bool ) ) @ SV2587 @ SV351 )
= ( c_Finite__Set_Osetsum @ SV967 @ SV1481 @ SV2587 @ SV351 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV351 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6659]) ).
thf(6752,plain,
! [SV1483: $i,SV969: $i,SV2482: $i,SV2268: $i,SV1933: $i,SV2639: $i,SV353: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV2639 @ SV1933 @ SV2268 @ SV2482 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) ) @ SV2482 )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV969 @ SV1483 @ SV2639 @ SV2482 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) ) @ SV2482 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV969 @ ( c_Com_Ocom_OSemi @ SV1483 @ SV1933 ) @ SV2268 @ SV2482 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) ) @ SV2482 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6660]) ).
thf(6753,plain,
! [SV972: $i,SV1935: $i,SV1486: $i,SV356: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV356 @ SV1486 @ ( tc_fun @ SV1935 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV356 @ ( c_Set_Oinsert @ SV972 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1935 @ tc_bool ) ) @ SV1935 ) @ ( tc_fun @ SV1935 @ tc_bool ) ) @ SV1486 @ ( tc_fun @ SV1935 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV356 @ SV1486 @ ( tc_fun @ SV1935 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV356 @ ( c_Set_Oinsert @ SV972 @ SV1486 @ SV1935 ) @ ( tc_fun @ SV1935 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6661]) ).
thf(6754,plain,
! [SV2588: $i,SV2270: $i,SV2484: $i,SV1937: $i,SV1488: $i,SV974: $i,SV358: $i] :
( ( ( c_Nitpick_Ofold__graph_H @ SV358 @ SV974 @ ( c_HOL_Ominus__class_Ominus @ SV1488 @ ( c_Set_Oinsert @ SV1937 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2484 @ tc_bool ) ) @ SV2484 ) @ ( tc_fun @ SV2484 @ tc_bool ) ) @ SV2270 @ SV2484 @ SV2588 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2484 ) @ SV1937 ) @ SV1488 ) ) )
= $true )
| ( ( c_Nitpick_Ofold__graph_H @ SV358 @ SV974 @ SV1488 @ ( hAPP @ ( hAPP @ SV358 @ SV1937 ) @ SV2270 ) @ SV2484 @ SV2588 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6662]) ).
thf(6755,plain,
! [SV2589: $i,SV2271: $i,SV979: $i,SV363: $i,SV1493: $i,SV1942: $i,SV2485: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2485 ) @ SV1942 ) @ SV1493 ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofold__graph @ SV363 @ SV979 @ ( c_HOL_Ominus__class_Ominus @ SV1493 @ ( c_Set_Oinsert @ SV1942 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2485 @ tc_bool ) ) @ SV2485 ) @ ( tc_fun @ SV2485 @ tc_bool ) ) @ SV2271 @ SV2485 @ SV2589 ) )
= $true )
| ( ( c_Finite__Set_Ofold__graph @ SV363 @ SV979 @ SV1493 @ ( hAPP @ ( hAPP @ SV363 @ SV1942 ) @ SV2271 ) @ SV2485 @ SV2589 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6663]) ).
thf(6756,plain,
! [SV2274: $i,SV376: $i,SV2591: $i,SV992: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV992 @ SV2591 @ SV376 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2591 @ SV2274 @ SV376 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV992 @ SV2274 @ SV376 )
= $true )
| ( ( class_Orderings_Opreorder @ SV376 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6665]) ).
thf(6757,plain,
! [SV994: $i,SV378: $i,SV2276: $i,SV2592: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2592 @ SV2276 @ SV378 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV994 @ SV2592 @ SV378 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV994 @ SV2276 @ SV378 )
= $true )
| ( ( class_Orderings_Oorder @ SV378 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6666]) ).
thf(6758,plain,
! [SV1955: $i,SV387: $i,SV2491: $i,SV1510: $i,SV1003: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1003 ) @ SV1510 ) @ SV2491 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV387 @ SV1510 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV387 @ SV1003 ) ) @ SV2491 ) @ SV1955 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV387 @ SV1003 ) ) @ SV1510 ) @ SV1955 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6667]) ).
thf(6759,plain,
! [SV2659: $i,SV2641: $i,SV2595: $i,SV2495: $i,SV2284: $i,SV1962: $i,SV1520: $i,SV1015: $i,SV401: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV401 @ SV1015 @ ( c_COMBC @ SV1520 @ SV1962 @ SV1962 @ tc_bool ) @ ( c_COMBC @ SV2284 @ SV1962 @ SV1962 @ tc_bool ) @ SV2495 @ SV2595 @ SV2641 @ SV2659 @ SV1962 )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1015 @ SV401 @ SV1520 @ SV2284 @ SV2595 @ SV2495 @ SV2659 @ SV2641 @ SV1962 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6671]) ).
thf(6760,plain,
! [SV1525: $i,SV1020: $i,SV1964: $i,SV2678: $i,SV2596: $i,SV406: $i] :
( ( ( ( hAPP @ ( c_Map_Omap__add @ SV406 @ SV2596 @ SV2678 @ SV1964 ) @ SV1020 )
= ( c_Option_Ooption_OSome @ SV1525 @ SV1964 ) )
= $true )
| ( ( ( hAPP @ SV2596 @ SV1020 )
= ( c_Option_Ooption_ONone @ SV1964 ) )
= $false )
| ( ( ( hAPP @ SV406 @ SV1020 )
= ( c_Option_Ooption_OSome @ SV1525 @ SV1964 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6673]) ).
thf(6761,plain,
! [SV441: $i,SV1985: $i,SV1554: $i,SV2298: $i,SV1053: $i] :
( ( ( c_Map_Omap__le @ SV1053 @ SV2298 @ SV1554 @ SV1985 )
= $false )
| ( ( ~ ( c_Map_Omap__le @ SV441 @ SV2298 @ SV1554 @ SV1985 ) )
= $true )
| ( ( c_Map_Omap__le @ SV441 @ ( c_Map_Omap__add @ SV441 @ SV1053 @ SV1554 @ SV1985 ) @ SV1554 @ SV1985 )
= $false )
| ( ( c_Map_Omap__le @ ( c_Map_Omap__add @ SV441 @ SV1053 @ SV1554 @ SV1985 ) @ SV2298 @ SV1554 @ SV1985 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6675]) ).
thf(6762,plain,
! [SV2499: $i,SV1054: $i,SV1555: $i,SV2644: $i,SV442: $i] :
( ( ( hBOOL @ ( hAPP @ SV442 @ SV2644 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1555 ) @ SV2644 ) @ SV1054 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1555 ) @ SV2499 ) @ SV1054 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV442 @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1054 @ SV442 @ SV1555 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6676]) ).
thf(6763,plain,
! [SV1057: $i,SV445: $i,SV1558: $i,SV2299: $i,SV2661: $i] :
( ( ( hBOOL @ ( hAPP @ SV2661 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2299 @ SV2661 @ SV1558 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1558 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2299 @ SV445 @ SV1558 ) ) @ SV2299 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1558 ) @ SV1057 ) @ SV2299 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV445 @ SV1057 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6677]) ).
thf(6764,plain,
! [SV1058: $i,SV2662: $i,SV1559: $i,SV2300: $i,SV446: $i] :
( ( ( hBOOL @ ( hAPP @ SV446 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2300 @ SV446 @ SV1559 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1559 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2300 @ SV2662 @ SV1559 ) ) @ SV2300 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1559 ) @ SV1058 ) @ SV2300 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV446 @ SV1058 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6678]) ).
thf(6765,plain,
! [SV1059: $i,SV447: $i,SV2679: $i,SV2301: $i,SV1560: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1560 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2301 @ SV2679 @ SV1560 ) ) @ SV2301 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV447 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2301 @ SV447 @ SV1560 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1560 ) @ SV1059 ) @ SV2301 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV447 @ SV1059 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6679]) ).
thf(6766,plain,
! [SV1060: $i,SV448: $i,SV1561: $i,SV2302: $i,SV2663: $i] :
( ( ( hBOOL @ ( hAPP @ SV2663 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2302 @ SV2663 @ SV1561 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1561 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2302 @ SV448 @ SV1561 ) ) @ SV2302 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1561 ) @ SV1060 ) @ SV2302 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV448 @ SV1060 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6680]) ).
thf(6767,plain,
! [SV449: $i,SV2500: $i,SV1988: $i,SV1061: $i,SV2303: $i,SV1562: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1562 @ SV2303 ) @ SV1061 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1988 @ SV1061 ) @ SV2500 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV449 ) @ SV1061 ) @ ( c_SetInterval_Oord_OatLeastLessThan @ SV1562 @ SV1988 @ SV2303 @ SV2500 @ SV449 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6681]) ).
thf(6768,plain,
! [SV460: $i,SV2501: $i,SV1569: $i,SV1072: $i,SV2308: $i,SV1994: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1994 @ SV2308 ) @ SV1072 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1569 @ SV1072 ) @ SV2501 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV460 ) @ SV1072 ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ SV1569 @ SV1994 @ SV2308 @ SV2501 @ SV460 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6684]) ).
thf(6769,plain,
! [SV2503: $i,SV1075: $i,SV463: $i,SV2645: $i,SV1572: $i] :
( ( ( hBOOL @ ( hAPP @ SV1572 @ SV2645 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ SV2645 ) @ SV1075 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ SV2503 ) @ SV1075 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1075 @ SV1572 @ SV463 ) ) @ SV1075 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6685]) ).
thf(6770,plain,
! [SV2664: $i,SV2646: $i,SV2601: $i,SV2508: $i,SV2329: $i,SV2020: $i,SV1596: $i,SV1108: $i,SV506: $i] :
( ( ( ( hAPP @ SV506 @ ( c_Set_Oinsert @ SV1108 @ SV1596 @ SV2020 ) )
= ( hAPP @ ( hAPP @ SV2329 @ SV1108 ) @ ( hAPP @ SV506 @ SV1596 ) ) )
= $true )
| ( ( ! [SY7479: $i,SY7480: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2508 @ SV506 @ SV2601 @ SV2646 @ SV2664 @ SV2329 @ SY7479 @ SY7480 @ SV2020 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6688]) ).
thf(6771,plain,
! [SV2665: $i,SV2647: $i,SV2602: $i,SV2509: $i,SV2330: $i,SV2021: $i,SV1597: $i,SV1109: $i,SV507: $i] :
( ( ( ( hAPP @ SV507 @ ( c_Set_Oinsert @ SV1109 @ SV1597 @ SV2021 ) )
= ( hAPP @ ( hAPP @ SV2330 @ SV1109 ) @ ( hAPP @ SV507 @ SV1597 ) ) )
= $true )
| ( ( ! [SY7481: $i,SY7482: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV507 @ SV2509 @ SV2602 @ SV2647 @ SV2330 @ SV2665 @ SY7481 @ SY7482 @ SV2021 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6689]) ).
thf(6772,plain,
! [SV2023: $i,SV1111: $i,SV2331: $i,SV2680: $i,SV1599: $i,SV2603: $i,SV509: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ SV2603 ) @ ( hAPP @ SV1599 @ SV2680 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2331 ) @ SV2680 ) @ SV1111 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV2023 @ SV2603 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SV1111 @ SV1599 @ SV2023 @ SV2331 @ SV509 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1111 @ SV1599 @ SV2331 @ ( tc_fun @ SV509 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6690]) ).
thf(6773,plain,
! [SV1132: $i,SV2681: $i,SV1618: $i,SV2666: $i,SV2606: $i,SV2514: $i,SV2343: $i,SV532: $i,SV2037: $i] :
( ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2037 @ SV532 @ SV2343 @ SV2514 @ SV2606 @ SV2666 @ SV1618 @ SV2681 @ SV1132 ) )
= $true )
| ( ( ( hAPP @ SV532 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1132 @ tc_bool ) ) )
= SV1618 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6692]) ).
thf(6774,plain,
! [SV1133: $i,SV1619: $i,SV2682: $i,SV2667: $i,SV2607: $i,SV2515: $i,SV2344: $i,SV2038: $i,SV533: $i] :
( ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV533 @ SV2038 @ SV2344 @ SV2515 @ SV2607 @ SV2667 @ SV2682 @ SV1619 @ SV1133 ) )
= $true )
| ( ( ( hAPP @ SV533 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1133 @ tc_bool ) ) )
= SV1619 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6693]) ).
thf(6775,plain,
! [SV1140: $i,SV1623: $i,SV2683: $i,SV2648: $i,SV2608: $i,SV2517: $i,SV2346: $i,SV541: $i,SV2042: $i] :
( ( ( ! [SY7490: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2042 @ SV541 @ SV2346 @ SV2517 @ SV2608 @ SV2648 @ SV2683 @ SY7490 @ SV1623 ) )
= $true )
| ( ( ( hAPP @ SV541 @ ( c_Set_Oinsert @ SV1140 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1623 @ tc_bool ) ) @ SV1623 ) )
= SV1140 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6694]) ).
thf(6776,plain,
! [SV1141: $i,SV1624: $i,SV2684: $i,SV2649: $i,SV2609: $i,SV2518: $i,SV2347: $i,SV2043: $i,SV542: $i] :
( ( ( ! [SY7491: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV542 @ SV2043 @ SV2347 @ SV2518 @ SV2609 @ SV2649 @ SV2684 @ SY7491 @ SV1624 ) )
= $true )
| ( ( ( hAPP @ SV542 @ ( c_Set_Oinsert @ SV1141 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1624 @ tc_bool ) ) @ SV1624 ) )
= SV1141 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6695]) ).
thf(6777,plain,
! [SV1632: $i,SV1150: $i,SV552: $i,SV2610: $i,SV2520: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2520 @ SV2610 @ SV552 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1150 @ SV1632 @ SV552 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1150 @ SV1632 @ SV552 )
= ( c_HOL_Ominus__class_Ominus @ SV2520 @ SV2610 @ SV552 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV552 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6696]) ).
thf(6778,plain,
! [SV2611: $i,SV2521: $i,SV553: $i,SV1633: $i,SV1151: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1151 @ SV1633 @ SV553 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV2521 @ SV2611 @ SV553 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1151 @ SV1633 @ SV553 )
= ( c_HOL_Ominus__class_Ominus @ SV2521 @ SV2611 @ SV553 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV553 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6697]) ).
thf(6779,plain,
! [SV1166: $i,SV572: $i,SV1643: $i,SV2359: $i,SV2685: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV2685 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2359 @ SV2685 @ SV1643 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV572 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2359 @ SV572 @ SV1643 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1643 ) @ SV1166 ) @ SV2359 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV572 @ SV1166 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6698]) ).
thf(6780,plain,
! [SV1167: $i,SV573: $i,SV1644: $i,SV2360: $i,SV2668: $i] :
( ( ( hBOOL @ ( hAPP @ SV2668 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2360 @ SV2668 @ SV1644 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV573 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2360 @ SV573 @ SV1644 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1644 ) @ SV1167 ) @ SV2360 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV573 @ SV1167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6699]) ).
thf(6781,plain,
! [SV1170: $i,SV1647: $i,SV2650: $i,SV2363: $i,SV576: $i] :
( ( ( hBOOL @ ( hAPP @ SV576 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2363 @ SV2650 @ SV576 @ SV1647 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV2650 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2363 @ SV2650 @ SV576 @ SV1647 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1647 ) @ SV1170 ) @ SV2363 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV576 @ SV1170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6702]) ).
thf(6782,plain,
! [SV1171: $i,SV1648: $i,SV577: $i,SV2364: $i,SV2651: $i] :
( ( ( hBOOL @ ( hAPP @ SV2651 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2364 @ SV577 @ SV2651 @ SV1648 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV577 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2364 @ SV577 @ SV2651 @ SV1648 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1648 ) @ SV1171 ) @ SV2364 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV577 @ SV1171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6703]) ).
thf(6783,plain,
! [SV584: $i,SV1655: $i,SV2615: $i,SV1178: $i,SV2055: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2055 ) @ SV1178 ) @ SV2615 ) ) )
= $true )
| ( ( ( SV1178 = SV1655 )
| ! [SY7436: $i] :
~ ( c_Fun_Oinj__on @ SV584 @ SV2615 @ SV2055 @ SY7436 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2055 ) @ SV1655 ) @ SV2615 ) )
= $false )
| ( ( ( hAPP @ SV584 @ SV1178 )
= ( hAPP @ SV584 @ SV1655 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6704]) ).
thf(6784,plain,
! [SV1656: $i,SV585: $i,SV2616: $i,SV1179: $i,SV2056: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2056 ) @ SV1179 ) @ SV2616 ) ) )
= $true )
| ( ( ! [SY7437: $i] :
~ ( c_Fun_Oinj__on @ SV585 @ SV2616 @ SV2056 @ SY7437 )
| ( SV1179 = SV1656 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2056 ) @ SV1656 ) @ SV2616 ) )
= $false )
| ( ( ( hAPP @ SV585 @ SV1179 )
= ( hAPP @ SV585 @ SV1656 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6705]) ).
thf(6785,plain,
! [SV1657: $i,SV586: $i,SV2617: $i,SV1180: $i,SV2057: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2057 ) @ SV1180 ) @ SV2617 ) ) )
= $true )
| ( ( ! [SY7438: $i] :
~ ( c_Fun_Oinj__on @ SV586 @ SV2617 @ SV2057 @ SY7438 )
| ( SV1180 = SV1657 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2057 ) @ SV1657 ) @ SV2617 ) )
= $false )
| ( ( ( hAPP @ SV586 @ SV1180 )
= ( hAPP @ SV586 @ SV1657 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6706]) ).
thf(6786,plain,
! [SV1658: $i,SV1181: $i,SV2671: $i,SV2618: $i,SV2058: $i,SV587: $i] :
( ( ( c_Fun_Oinj__on @ SV587 @ SV2058 @ SV2618 @ SV2671 )
= $false )
| ( ( ( SV1181 = SV1658 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2618 ) @ SV1658 ) @ SV2058 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2618 ) @ SV1181 ) @ SV2058 ) ) )
= $true )
| ( ( ( hAPP @ SV587 @ SV1181 )
= ( hAPP @ SV587 @ SV1658 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6707]) ).
thf(6787,plain,
! [SV2064: $i,SV1195: $i,SV601: $i,SV1670: $i,SV2619: $i,SV2375: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2375 ) @ SV2619 ) @ SV1670 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV601 ) @ SV1195 ) @ ( hAPP @ SV2064 @ SV2619 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV601 ) @ SV1195 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1670 @ SV2064 @ SV2375 @ ( tc_fun @ SV601 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6708]) ).
thf(6788,plain,
! [SV2065: $i,SV1196: $i,SV602: $i,SV1671: $i,SV2620: $i,SV2376: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2376 ) @ SV2620 ) @ SV1671 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV602 ) @ SV1196 ) @ ( hAPP @ SV2065 @ SV2620 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV602 ) @ SV1196 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1671 @ SV2065 @ SV2376 @ ( tc_fun @ SV602 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6709]) ).
thf(6789,plain,
! [SV605: $i,SV1199: $i,SV2067: $i,SV2686: $i,SV1674: $i,SV2621: $i,SV2378: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2378 ) @ SV2621 ) @ ( hAPP @ SV1674 @ SV2686 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2067 ) @ SV2686 ) @ SV1199 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV605 @ SV2621 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV605 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SV1199 @ SV1674 @ SV605 @ SV2067 @ SV2378 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6710]) ).
thf(6790,plain,
! [SV2672: $i,SV2654: $i,SV2622: $i,SV2530: $i,SV2382: $i,SV2073: $i,SV1680: $i,SV1205: $i,SV611: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV611 @ ( hAPP @ SV1205 @ SV1680 ) ) @ SV2073 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2382 ) @ SV2073 ) @ SV1680 ) )
| ! [SY7485: $i,SY7486: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1205 @ SV2530 @ SV611 @ SV2622 @ SV2654 @ SV2672 @ SY7485 @ SY7486 @ SV2382 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6711]) ).
thf(6791,plain,
! [SV2673: $i,SV2655: $i,SV2623: $i,SV2531: $i,SV2383: $i,SV2074: $i,SV1681: $i,SV1206: $i,SV612: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV612 @ SV1206 ) @ ( hAPP @ SV1681 @ SV2074 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2383 ) @ SV1206 ) @ SV2074 ) )
| ! [SY7487: $i,SY7488: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2531 @ SV1681 @ SV612 @ SV2623 @ SV2655 @ SV2673 @ SY7487 @ SY7488 @ SV2383 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6712]) ).
thf(6792,plain,
! [SV2388: $i,SV2078: $i,SV621: $i,SV1690: $i,SV2624: $i,SV2536: $i,SV2674: $i,SV1215: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV1215 @ SV2674 ) @ SV2536 ) @ SV2624 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1690 ) @ SV2674 ) @ SV621 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV621 @ SV1215 @ SV1690 @ ( tc_fun @ SV2078 @ ( tc_fun @ SV2388 @ tc_bool ) ) ) @ SV2536 ) @ SV2624 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6715]) ).
thf(6793,plain,
! [SV2079: $i,SV2389: $i,SV1216: $i,SV622: $i,SV2625: $i,SV1691: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1691 ) @ SV2625 ) @ SV622 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1216 @ SV2625 ) @ SV2389 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV622 @ SV1216 @ SV1691 @ ( tc_fun @ SV2079 @ tc_bool ) ) @ SV2389 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6716]) ).
thf(6794,plain,
! [SV2390: $i,SV2080: $i,SV623: $i,SV1692: $i,SV2626: $i,SV2537: $i,SV2675: $i,SV1217: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV1217 @ SV2675 ) @ SV2537 ) @ SV2626 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1692 ) @ SV2675 ) @ SV623 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV623 @ SV1217 @ SV1692 @ ( tc_fun @ SV2080 @ ( tc_fun @ SV2390 @ tc_bool ) ) ) @ SV2537 ) @ SV2626 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6717]) ).
thf(6795,plain,
! [SV2081: $i,SV2391: $i,SV1218: $i,SV624: $i,SV2627: $i,SV1693: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1693 ) @ SV2627 ) @ SV624 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1218 @ SV2627 ) @ SV2391 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV624 @ SV1218 @ SV1693 @ ( tc_fun @ SV2081 @ tc_bool ) ) @ SV2391 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6718]) ).
thf(6796,plain,
! [SV2427: $i,SV2563: $i,SV115: $i,SV768: $i,SV1319: $i] :
( ( ( c_lessequals @ SV1319 @ SV768 @ SV115 )
= $false )
| ( ( c_lessequals @ SV2563 @ SV2427 @ SV115 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV768 @ SV1319 @ SV115 )
= ( c_HOL_Ominus__class_Ominus @ SV2427 @ SV2563 @ SV115 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6732]) ).
thf(6797,plain,
! [SV769: $i,SV1320: $i,SV116: $i,SV2428: $i,SV2564: $i] :
( ( ( c_lessequals @ SV2564 @ SV2428 @ SV116 )
= $false )
| ( ( c_lessequals @ SV1320 @ SV769 @ SV116 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV769 @ SV1320 @ SV116 )
= ( c_HOL_Ominus__class_Ominus @ SV2428 @ SV2564 @ SV116 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6733]) ).
thf(6798,plain,
! [SV134: $i,SV777: $i,SV2431: $i,SV2567: $i,SV1327: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1327 @ SV2567 )
= $false )
| ( ( c_lessequals @ SV2431 @ SV1327 @ ( tc_fun @ SV2567 @ tc_bool ) )
= $false )
| ( ( ( c_Finite__Set_Osetsum @ SV777 @ ( c_HOL_Ominus__class_Ominus @ SV1327 @ SV2431 @ ( tc_fun @ SV2567 @ tc_bool ) ) @ SV2567 @ SV134 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV777 @ SV1327 @ SV2567 @ SV134 ) @ ( c_Finite__Set_Osetsum @ SV777 @ SV2431 @ SV2567 @ SV134 ) @ SV134 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6734]) ).
thf(6799,plain,
! [SV135: $i,SV778: $i,SV1806: $i,SV1328: $i,SV2677: $i] :
( ( ( ~ ( c_lessequals @ ( c_Set_Oimage @ SV2677 @ SV1328 @ SV1806 @ SV778 ) @ SV135 @ ( tc_fun @ SV778 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV2677 @ SV1328 @ SV1806 @ SV778 )
| ! [SY6828: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ SY6828 @ SV135 @ SV778 @ SV1806 ) @ SV1328 @ ( tc_fun @ SV1806 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY6828 @ SV135 @ SV778 @ SV1806 ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV135 @ SV778 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV1328 @ SV1806 )
= $false )
| ( ( ( c_Finite__Set_Ocard @ SV135 @ SV778 )
= ( c_Finite__Set_Ocard @ SV1328 @ SV1806 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6735]) ).
thf(6800,plain,
! [SV1419: $i,SV2236: $i,SV268: $i,SV1881: $i,SV2577: $i,SV888: $i] :
( ( ( c_lessequals @ SV888 @ SV2577 @ ( tc_fun @ SV1881 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV268 @ SV2577 @ SV1881 @ SV2236 ) )
= $true )
| ( ( c_lessequals @ SV1419 @ SV2577 @ ( tc_fun @ SV1881 @ tc_bool ) )
= $false )
| ( ( ( c_Set_Oimage @ SV268 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV888 @ SV1419 @ ( tc_fun @ SV1881 @ tc_bool ) ) @ SV1881 @ SV2236 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV268 @ SV888 @ SV1881 @ SV2236 ) @ ( c_Set_Oimage @ SV268 @ SV1419 @ SV1881 @ SV2236 ) @ ( tc_fun @ SV2236 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6742]) ).
thf(6801,plain,
! [SV1421: $i,SV2238: $i,SV270: $i,SV1883: $i,SV2578: $i,SV890: $i] :
( ( ( c_lessequals @ SV890 @ SV2578 @ ( tc_fun @ SV1883 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV270 @ SV2578 @ SV1883 @ SV2238 ) )
= $true )
| ( ( c_lessequals @ SV1421 @ SV2578 @ ( tc_fun @ SV1883 @ tc_bool ) )
= $false )
| ( ( ( c_Set_Oimage @ SV270 @ ( c_HOL_Ominus__class_Ominus @ SV890 @ SV1421 @ ( tc_fun @ SV1883 @ tc_bool ) ) @ SV1883 @ SV2238 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV270 @ SV890 @ SV1883 @ SV2238 ) @ ( c_Set_Oimage @ SV270 @ SV1421 @ SV1883 @ SV2238 ) @ ( tc_fun @ SV2238 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6743]) ).
thf(6802,plain,
! [SV920: $i,SV1448: $i,SV300: $i,SV2247: $i,SV2466: $i] :
( ( ( c_Finite__Set_Ofinite @ SV2466 @ SV2247 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV2466 @ SV300 @ SV2247 @ ( tc_fun @ SV1448 @ tc_bool ) ) @ SV1448 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2247 ) @ SV920 ) @ SV2466 ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ SV300 @ SV920 ) @ SV1448 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6745]) ).
thf(6803,plain,
! [SV1458: $i,SV935: $i,SV1913: $i,SV2687: $i,SV2252: $i,SV2657: $i,SV2637: $i,SV2581: $i,SV318: $i,SV2470: $i] :
( ( ( ! [SY7492: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2470 @ SV318 @ SV2581 @ SV2637 @ SV2657 @ SV2252 @ SV2687 @ SY7492 @ SV1913 ) )
= $true )
| ( ( ( hAPP @ SV318 @ ( c_Set_Oinsert @ SV935 @ ( c_Set_Oinsert @ SV1458 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1913 @ tc_bool ) ) @ SV1913 ) @ SV1913 ) )
= ( hAPP @ ( hAPP @ SV2252 @ SV935 ) @ SV1458 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6746]) ).
thf(6804,plain,
! [SV1459: $i,SV936: $i,SV1914: $i,SV2688: $i,SV2658: $i,SV2253: $i,SV2638: $i,SV2582: $i,SV2471: $i,SV319: $i] :
( ( ( ! [SY7493: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV319 @ SV2471 @ SV2582 @ SV2638 @ SV2253 @ SV2658 @ SV2688 @ SY7493 @ SV1914 ) )
= $true )
| ( ( ( hAPP @ SV319 @ ( c_Set_Oinsert @ SV936 @ ( c_Set_Oinsert @ SV1459 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1914 @ tc_bool ) ) @ SV1914 ) @ SV1914 ) )
= ( hAPP @ ( hAPP @ SV2253 @ SV936 ) @ SV1459 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6747]) ).
thf(6805,plain,
! [SV343: $i,SV960: $i,SV2478: $i,SV2585: $i,SV1474: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1474 @ SV2585 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2585 ) @ SV2478 ) @ SV1474 ) )
= $false )
| ( ( ( c_Finite__Set_Osetsum @ SV960 @ ( c_HOL_Ominus__class_Ominus @ SV1474 @ ( c_Set_Oinsert @ SV2478 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2585 @ tc_bool ) ) @ SV2585 ) @ ( tc_fun @ SV2585 @ tc_bool ) ) @ SV2585 @ SV343 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV960 @ SV1474 @ SV2585 @ SV343 ) @ ( hAPP @ SV960 @ SV2478 ) @ SV343 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV343 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6748]) ).
thf(6806,plain,
! [SV344: $i,SV961: $i,SV2479: $i,SV2586: $i,SV1475: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1475 @ SV2586 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2586 ) @ SV2479 ) @ SV1475 ) )
= $false )
| ( ( ( c_Finite__Set_Osetsum @ SV961 @ ( c_HOL_Ominus__class_Ominus @ SV1475 @ ( c_Set_Oinsert @ SV2479 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2586 @ tc_bool ) ) @ SV2586 ) @ ( tc_fun @ SV2586 @ tc_bool ) ) @ SV2586 @ SV344 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV961 @ SV1475 @ SV2586 @ SV344 ) @ ( hAPP @ SV961 @ SV2479 ) @ SV344 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV344 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6749]) ).
thf(6807,plain,
! [SV1478: $i,SV2266: $i,SV1930: $i,SV964: $i,SV348: $i] :
( ( ( c_Fun_Oinj__on @ SV348 @ SV964 @ SV1930 @ SV2266 )
= $false )
| ( ( c_Fun_Oinj__on @ SV348 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV964 @ SV1478 @ ( tc_fun @ SV1930 @ tc_bool ) ) @ SV1930 @ SV2266 )
= $true )
| ( ( c_Fun_Oinj__on @ SV348 @ SV1478 @ SV1930 @ SV2266 )
= $false )
| ( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV348 @ ( c_HOL_Ominus__class_Ominus @ SV964 @ SV1478 @ ( tc_fun @ SV1930 @ tc_bool ) ) @ SV1930 @ SV2266 ) @ ( c_Set_Oimage @ SV348 @ ( c_HOL_Ominus__class_Ominus @ SV1478 @ SV964 @ ( tc_fun @ SV1930 @ tc_bool ) ) @ SV1930 @ SV2266 ) @ ( tc_fun @ SV2266 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2266 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6750]) ).
thf(6808,plain,
! [SV2268: $i,SV1933: $i,SV2482: $i,SV2639: $i,SV1483: $i,SV969: $i,SV353: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV969 @ SV1483 @ SV2639 @ SV2482 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) ) @ SV2482 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV2639 @ SV1933 @ SV2268 @ SV2482 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) ) @ SV2482 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV969 @ ( c_Com_Ocom_OSemi @ SV1483 @ SV1933 ) @ SV2268 @ SV2482 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV2482 ) ) @ SV2482 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6752]) ).
thf(6809,plain,
! [SV2588: $i,SV2270: $i,SV974: $i,SV358: $i,SV1488: $i,SV1937: $i,SV2484: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2484 ) @ SV1937 ) @ SV1488 ) )
= $false )
| ( ( c_Nitpick_Ofold__graph_H @ SV358 @ SV974 @ ( c_HOL_Ominus__class_Ominus @ SV1488 @ ( c_Set_Oinsert @ SV1937 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2484 @ tc_bool ) ) @ SV2484 ) @ ( tc_fun @ SV2484 @ tc_bool ) ) @ SV2270 @ SV2484 @ SV2588 )
= $false )
| ( ( c_Nitpick_Ofold__graph_H @ SV358 @ SV974 @ SV1488 @ ( hAPP @ ( hAPP @ SV358 @ SV1937 ) @ SV2270 ) @ SV2484 @ SV2588 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6754]) ).
thf(6810,plain,
! [SV2589: $i,SV2271: $i,SV2485: $i,SV1942: $i,SV1493: $i,SV979: $i,SV363: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV363 @ SV979 @ ( c_HOL_Ominus__class_Ominus @ SV1493 @ ( c_Set_Oinsert @ SV1942 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV2485 @ tc_bool ) ) @ SV2485 ) @ ( tc_fun @ SV2485 @ tc_bool ) ) @ SV2271 @ SV2485 @ SV2589 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2485 ) @ SV1942 ) @ SV1493 ) )
= $false )
| ( ( c_Finite__Set_Ofold__graph @ SV363 @ SV979 @ SV1493 @ ( hAPP @ ( hAPP @ SV363 @ SV1942 ) @ SV2271 ) @ SV2485 @ SV2589 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6755]) ).
thf(6811,plain,
! [SV1955: $i,SV2491: $i,SV1003: $i,SV1510: $i,SV387: $i] :
( ( ( hBOOL @ ( hAPP @ SV387 @ SV1510 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ SV1003 ) @ SV1510 ) @ SV2491 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV387 @ SV1003 ) ) @ SV2491 ) @ SV1955 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV387 @ SV1003 ) ) @ SV1510 ) @ SV1955 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6758]) ).
thf(6812,plain,
! [SV1962: $i,SV2641: $i,SV2659: $i,SV2495: $i,SV2595: $i,SV2284: $i,SV1520: $i,SV401: $i,SV1015: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV1015 @ SV401 @ SV1520 @ SV2284 @ SV2595 @ SV2495 @ SV2659 @ SV2641 @ SV1962 )
= $false )
| ( ( c_Complete__Lattice_Ocomplete__lattice @ SV401 @ SV1015 @ ( c_COMBC @ SV1520 @ SV1962 @ SV1962 @ tc_bool ) @ ( c_COMBC @ SV2284 @ SV1962 @ SV1962 @ tc_bool ) @ SV2495 @ SV2595 @ SV2641 @ SV2659 @ SV1962 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6759]) ).
thf(6813,plain,
! [SV1053: $i,SV1985: $i,SV1554: $i,SV2298: $i,SV441: $i] :
( ( ( c_Map_Omap__le @ SV441 @ SV2298 @ SV1554 @ SV1985 )
= $false )
| ( ( c_Map_Omap__le @ SV1053 @ SV2298 @ SV1554 @ SV1985 )
= $false )
| ( ( c_Map_Omap__le @ SV441 @ ( c_Map_Omap__add @ SV441 @ SV1053 @ SV1554 @ SV1985 ) @ SV1554 @ SV1985 )
= $false )
| ( ( c_Map_Omap__le @ ( c_Map_Omap__add @ SV441 @ SV1053 @ SV1554 @ SV1985 ) @ SV2298 @ SV1554 @ SV1985 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6761]) ).
thf(6814,plain,
! [SV2499: $i,SV442: $i,SV1054: $i,SV2644: $i,SV1555: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1555 ) @ SV2644 ) @ SV1054 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV442 @ SV2644 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1555 ) @ SV2499 ) @ SV1054 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV442 @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1054 @ SV442 @ SV1555 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6762]) ).
thf(6815,plain,
! [SV2503: $i,SV1572: $i,SV1075: $i,SV2645: $i,SV463: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ SV2645 ) @ SV1075 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1572 @ SV2645 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ SV2503 ) @ SV1075 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV463 ) @ ( c_ATP__Linkup_Osko__Set__XbexCI__1__1 @ SV1075 @ SV1572 @ SV463 ) ) @ SV1075 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6769]) ).
thf(6816,plain,
! [SV1596: $i,SV1108: $i,SV2020: $i,SV2689: $i,SV2329: $i,SV2664: $i,SV2646: $i,SV2601: $i,SV506: $i,SV2508: $i] :
( ( ( ! [SY7494: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2508 @ SV506 @ SV2601 @ SV2646 @ SV2664 @ SV2329 @ SV2689 @ SY7494 @ SV2020 ) )
= $true )
| ( ( ( hAPP @ SV506 @ ( c_Set_Oinsert @ SV1108 @ SV1596 @ SV2020 ) )
= ( hAPP @ ( hAPP @ SV2329 @ SV1108 ) @ ( hAPP @ SV506 @ SV1596 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6770]) ).
thf(6817,plain,
! [SV1597: $i,SV1109: $i,SV2021: $i,SV2690: $i,SV2665: $i,SV2330: $i,SV2647: $i,SV2602: $i,SV2509: $i,SV507: $i] :
( ( ( ! [SY7495: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV507 @ SV2509 @ SV2602 @ SV2647 @ SV2330 @ SV2665 @ SV2690 @ SY7495 @ SV2021 ) )
= $true )
| ( ( ( hAPP @ SV507 @ ( c_Set_Oinsert @ SV1109 @ SV1597 @ SV2021 ) )
= ( hAPP @ ( hAPP @ SV2330 @ SV1109 ) @ ( hAPP @ SV507 @ SV1597 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6771]) ).
thf(6818,plain,
! [SV2023: $i,SV1111: $i,SV2331: $i,SV2680: $i,SV1599: $i,SV2603: $i,SV509: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ SV2603 ) @ ( hAPP @ SV1599 @ SV2680 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2331 ) @ SV2680 ) @ SV1111 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV2023 @ SV2603 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SV1111 @ SV1599 @ SV2023 @ SV2331 @ SV509 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1111 @ SV1599 @ SV2331 @ ( tc_fun @ SV509 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6772]) ).
thf(6819,plain,
! [SV1132: $i,SV2681: $i,SV1618: $i,SV2666: $i,SV2606: $i,SV2514: $i,SV2343: $i,SV532: $i,SV2037: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV2037 @ SV532 @ SV2343 @ SV2514 @ SV2606 @ SV2666 @ SV1618 @ SV2681 @ SV1132 )
= $false )
| ( ( ( hAPP @ SV532 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1132 @ tc_bool ) ) )
= SV1618 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6773]) ).
thf(6820,plain,
! [SV1133: $i,SV1619: $i,SV2682: $i,SV2667: $i,SV2607: $i,SV2515: $i,SV2344: $i,SV2038: $i,SV533: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV533 @ SV2038 @ SV2344 @ SV2515 @ SV2607 @ SV2667 @ SV2682 @ SV1619 @ SV1133 )
= $false )
| ( ( ( hAPP @ SV533 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1133 @ tc_bool ) ) )
= SV1619 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6774]) ).
thf(6821,plain,
! [SV1140: $i,SV1623: $i,SV2691: $i,SV2683: $i,SV2648: $i,SV2608: $i,SV2517: $i,SV2346: $i,SV541: $i,SV2042: $i] :
( ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2042 @ SV541 @ SV2346 @ SV2517 @ SV2608 @ SV2648 @ SV2683 @ SV2691 @ SV1623 ) )
= $true )
| ( ( ( hAPP @ SV541 @ ( c_Set_Oinsert @ SV1140 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1623 @ tc_bool ) ) @ SV1623 ) )
= SV1140 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6775]) ).
thf(6822,plain,
! [SV1141: $i,SV1624: $i,SV2692: $i,SV2684: $i,SV2649: $i,SV2609: $i,SV2518: $i,SV2347: $i,SV2043: $i,SV542: $i] :
( ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV542 @ SV2043 @ SV2347 @ SV2518 @ SV2609 @ SV2649 @ SV2684 @ SV2692 @ SV1624 ) )
= $true )
| ( ( ( hAPP @ SV542 @ ( c_Set_Oinsert @ SV1141 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1624 @ tc_bool ) ) @ SV1624 ) )
= SV1141 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6776]) ).
thf(6823,plain,
! [SV2610: $i,SV2520: $i,SV552: $i,SV1632: $i,SV1150: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1150 @ SV1632 @ SV552 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV2520 @ SV2610 @ SV552 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1150 @ SV1632 @ SV552 )
= ( c_HOL_Ominus__class_Ominus @ SV2520 @ SV2610 @ SV552 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV552 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6777]) ).
thf(6824,plain,
! [SV1633: $i,SV1151: $i,SV553: $i,SV2611: $i,SV2521: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV2521 @ SV2611 @ SV553 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1151 @ SV1633 @ SV553 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1151 @ SV1633 @ SV553 )
= ( c_HOL_Ominus__class_Ominus @ SV2521 @ SV2611 @ SV553 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV553 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6778]) ).
thf(6825,plain,
! [SV1166: $i,SV572: $i,SV1643: $i,SV2359: $i,SV2685: $i] :
( ( ( hBOOL @ ( hAPP @ SV2685 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2359 @ SV2685 @ SV1643 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV572 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2359 @ SV572 @ SV1643 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1643 ) @ SV1166 ) @ SV2359 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV572 @ SV1166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6779]) ).
thf(6826,plain,
! [SV1167: $i,SV2668: $i,SV1644: $i,SV2360: $i,SV573: $i] :
( ( ( hBOOL @ ( hAPP @ SV573 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2360 @ SV573 @ SV1644 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV2668 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3 @ SV2360 @ SV2668 @ SV1644 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1644 ) @ SV1167 ) @ SV2360 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV573 @ SV1167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6780]) ).
thf(6827,plain,
! [SV1170: $i,SV1647: $i,SV576: $i,SV2363: $i,SV2650: $i] :
( ( ( hBOOL @ ( hAPP @ SV2650 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2363 @ SV2650 @ SV576 @ SV1647 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV576 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2363 @ SV2650 @ SV576 @ SV1647 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1647 ) @ SV1170 ) @ SV2363 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV576 @ SV1170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6781]) ).
thf(6828,plain,
! [SV1171: $i,SV1648: $i,SV2651: $i,SV2364: $i,SV577: $i] :
( ( ( hBOOL @ ( hAPP @ SV577 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2364 @ SV577 @ SV2651 @ SV1648 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV2651 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 @ SV2364 @ SV577 @ SV2651 @ SV1648 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1648 ) @ SV1171 ) @ SV2364 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV577 @ SV1171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6782]) ).
thf(6829,plain,
! [SV584: $i,SV1655: $i,SV2615: $i,SV1178: $i,SV2055: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2055 ) @ SV1178 ) @ SV2615 ) )
= $false )
| ( ( ( SV1178 = SV1655 )
| ! [SY7436: $i] :
~ ( c_Fun_Oinj__on @ SV584 @ SV2615 @ SV2055 @ SY7436 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2055 ) @ SV1655 ) @ SV2615 ) )
= $false )
| ( ( ( hAPP @ SV584 @ SV1178 )
= ( hAPP @ SV584 @ SV1655 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6783]) ).
thf(6830,plain,
! [SV1656: $i,SV585: $i,SV2616: $i,SV1179: $i,SV2056: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2056 ) @ SV1179 ) @ SV2616 ) )
= $false )
| ( ( ! [SY7437: $i] :
~ ( c_Fun_Oinj__on @ SV585 @ SV2616 @ SV2056 @ SY7437 )
| ( SV1179 = SV1656 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2056 ) @ SV1656 ) @ SV2616 ) )
= $false )
| ( ( ( hAPP @ SV585 @ SV1179 )
= ( hAPP @ SV585 @ SV1656 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6784]) ).
thf(6831,plain,
! [SV1657: $i,SV586: $i,SV2617: $i,SV1180: $i,SV2057: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2057 ) @ SV1180 ) @ SV2617 ) )
= $false )
| ( ( ! [SY7438: $i] :
~ ( c_Fun_Oinj__on @ SV586 @ SV2617 @ SV2057 @ SY7438 )
| ( SV1180 = SV1657 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2057 ) @ SV1657 ) @ SV2617 ) )
= $false )
| ( ( ( hAPP @ SV586 @ SV1180 )
= ( hAPP @ SV586 @ SV1657 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6785]) ).
thf(6832,plain,
! [SV2671: $i,SV587: $i,SV2058: $i,SV2618: $i,SV1658: $i,SV1181: $i] :
( ( ( SV1181 = SV1658 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2618 ) @ SV1658 ) @ SV2058 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2618 ) @ SV1181 ) @ SV2058 ) ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV587 @ SV2058 @ SV2618 @ SV2671 )
= $false )
| ( ( ( hAPP @ SV587 @ SV1181 )
= ( hAPP @ SV587 @ SV1658 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6786]) ).
thf(6833,plain,
! [SV605: $i,SV1199: $i,SV2067: $i,SV2686: $i,SV1674: $i,SV2621: $i,SV2378: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2378 ) @ SV2621 ) @ ( hAPP @ SV1674 @ SV2686 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2067 ) @ SV2686 ) @ SV1199 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV605 @ SV2621 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV605 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SV1199 @ SV1674 @ SV605 @ SV2067 @ SV2378 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6789]) ).
thf(6834,plain,
! [SV2672: $i,SV2654: $i,SV2622: $i,SV611: $i,SV2530: $i,SV1205: $i,SV1680: $i,SV2073: $i,SV2382: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2382 ) @ SV2073 ) @ SV1680 ) ) )
= $true )
| ( ( ! [SY7485: $i,SY7486: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1205 @ SV2530 @ SV611 @ SV2622 @ SV2654 @ SV2672 @ SY7485 @ SY7486 @ SV2382 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV611 @ ( hAPP @ SV1205 @ SV1680 ) ) @ SV2073 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6790]) ).
thf(6835,plain,
! [SV2673: $i,SV2655: $i,SV2623: $i,SV612: $i,SV1681: $i,SV2531: $i,SV2074: $i,SV1206: $i,SV2383: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2383 ) @ SV1206 ) @ SV2074 ) ) )
= $true )
| ( ( ! [SY7487: $i,SY7488: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2531 @ SV1681 @ SV612 @ SV2623 @ SV2655 @ SV2673 @ SY7487 @ SY7488 @ SV2383 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV612 @ SV1206 ) @ ( hAPP @ SV1681 @ SV2074 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6791]) ).
thf(6836,plain,
! [SV2388: $i,SV2078: $i,SV621: $i,SV1690: $i,SV2624: $i,SV2536: $i,SV2674: $i,SV1215: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV1215 @ SV2674 ) @ SV2536 ) @ SV2624 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1690 ) @ SV2674 ) @ SV621 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV621 @ SV1215 @ SV1690 @ ( tc_fun @ SV2078 @ ( tc_fun @ SV2388 @ tc_bool ) ) ) @ SV2536 ) @ SV2624 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6792]) ).
thf(6837,plain,
! [SV2390: $i,SV2080: $i,SV623: $i,SV1692: $i,SV2626: $i,SV2537: $i,SV2675: $i,SV1217: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV1217 @ SV2675 ) @ SV2537 ) @ SV2626 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1692 ) @ SV2675 ) @ SV623 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV623 @ SV1217 @ SV1692 @ ( tc_fun @ SV2080 @ ( tc_fun @ SV2390 @ tc_bool ) ) ) @ SV2537 ) @ SV2626 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6794]) ).
thf(6838,plain,
! [SV135: $i,SV778: $i,SV1806: $i,SV1328: $i,SV2677: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV2677 @ SV1328 @ SV1806 @ SV778 ) @ SV135 @ ( tc_fun @ SV778 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV2677 @ SV1328 @ SV1806 @ SV778 )
| ! [SY6828: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ SY6828 @ SV135 @ SV778 @ SV1806 ) @ SV1328 @ ( tc_fun @ SV1806 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY6828 @ SV135 @ SV778 @ SV1806 ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV135 @ SV778 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV1328 @ SV1806 )
= $false )
| ( ( ( c_Finite__Set_Ocard @ SV135 @ SV778 )
= ( c_Finite__Set_Ocard @ SV1328 @ SV1806 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6799]) ).
thf(6839,plain,
! [SV1419: $i,SV888: $i,SV2236: $i,SV1881: $i,SV2577: $i,SV268: $i] :
( ( ( c_Fun_Oinj__on @ SV268 @ SV2577 @ SV1881 @ SV2236 )
= $false )
| ( ( c_lessequals @ SV888 @ SV2577 @ ( tc_fun @ SV1881 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV1419 @ SV2577 @ ( tc_fun @ SV1881 @ tc_bool ) )
= $false )
| ( ( ( c_Set_Oimage @ SV268 @ ( c_Lattices_Olower__semilattice__class_Oinf @ SV888 @ SV1419 @ ( tc_fun @ SV1881 @ tc_bool ) ) @ SV1881 @ SV2236 )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ SV268 @ SV888 @ SV1881 @ SV2236 ) @ ( c_Set_Oimage @ SV268 @ SV1419 @ SV1881 @ SV2236 ) @ ( tc_fun @ SV2236 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6800]) ).
thf(6840,plain,
! [SV1421: $i,SV890: $i,SV2238: $i,SV1883: $i,SV2578: $i,SV270: $i] :
( ( ( c_Fun_Oinj__on @ SV270 @ SV2578 @ SV1883 @ SV2238 )
= $false )
| ( ( c_lessequals @ SV890 @ SV2578 @ ( tc_fun @ SV1883 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV1421 @ SV2578 @ ( tc_fun @ SV1883 @ tc_bool ) )
= $false )
| ( ( ( c_Set_Oimage @ SV270 @ ( c_HOL_Ominus__class_Ominus @ SV890 @ SV1421 @ ( tc_fun @ SV1883 @ tc_bool ) ) @ SV1883 @ SV2238 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV270 @ SV890 @ SV1883 @ SV2238 ) @ ( c_Set_Oimage @ SV270 @ SV1421 @ SV1883 @ SV2238 ) @ ( tc_fun @ SV2238 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6801]) ).
thf(6841,plain,
! [SV1458: $i,SV935: $i,SV1913: $i,SV2693: $i,SV2687: $i,SV2252: $i,SV2657: $i,SV2637: $i,SV2581: $i,SV318: $i,SV2470: $i] :
( ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2470 @ SV318 @ SV2581 @ SV2637 @ SV2657 @ SV2252 @ SV2687 @ SV2693 @ SV1913 ) )
= $true )
| ( ( ( hAPP @ SV318 @ ( c_Set_Oinsert @ SV935 @ ( c_Set_Oinsert @ SV1458 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1913 @ tc_bool ) ) @ SV1913 ) @ SV1913 ) )
= ( hAPP @ ( hAPP @ SV2252 @ SV935 ) @ SV1458 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6803]) ).
thf(6842,plain,
! [SV1459: $i,SV936: $i,SV1914: $i,SV2694: $i,SV2688: $i,SV2658: $i,SV2253: $i,SV2638: $i,SV2582: $i,SV2471: $i,SV319: $i] :
( ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV319 @ SV2471 @ SV2582 @ SV2638 @ SV2253 @ SV2658 @ SV2688 @ SV2694 @ SV1914 ) )
= $true )
| ( ( ( hAPP @ SV319 @ ( c_Set_Oinsert @ SV936 @ ( c_Set_Oinsert @ SV1459 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1914 @ tc_bool ) ) @ SV1914 ) @ SV1914 ) )
= ( hAPP @ ( hAPP @ SV2253 @ SV936 ) @ SV1459 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6804]) ).
thf(6843,plain,
! [SV1596: $i,SV1108: $i,SV2020: $i,SV2695: $i,SV2689: $i,SV2329: $i,SV2664: $i,SV2646: $i,SV2601: $i,SV506: $i,SV2508: $i] :
( ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2508 @ SV506 @ SV2601 @ SV2646 @ SV2664 @ SV2329 @ SV2689 @ SV2695 @ SV2020 ) )
= $true )
| ( ( ( hAPP @ SV506 @ ( c_Set_Oinsert @ SV1108 @ SV1596 @ SV2020 ) )
= ( hAPP @ ( hAPP @ SV2329 @ SV1108 ) @ ( hAPP @ SV506 @ SV1596 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6816]) ).
thf(6844,plain,
! [SV1597: $i,SV1109: $i,SV2021: $i,SV2696: $i,SV2690: $i,SV2665: $i,SV2330: $i,SV2647: $i,SV2602: $i,SV2509: $i,SV507: $i] :
( ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV507 @ SV2509 @ SV2602 @ SV2647 @ SV2330 @ SV2665 @ SV2690 @ SV2696 @ SV2021 ) )
= $true )
| ( ( ( hAPP @ SV507 @ ( c_Set_Oinsert @ SV1109 @ SV1597 @ SV2021 ) )
= ( hAPP @ ( hAPP @ SV2330 @ SV1109 ) @ ( hAPP @ SV507 @ SV1597 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6817]) ).
thf(6845,plain,
! [SV2023: $i,SV1111: $i,SV2331: $i,SV2680: $i,SV1599: $i,SV2603: $i,SV509: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ SV2603 ) @ ( hAPP @ SV1599 @ SV2680 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2331 ) @ SV2680 ) @ SV1111 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV2023 @ SV2603 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SV1111 @ SV1599 @ SV2023 @ SV2331 @ SV509 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1111 @ SV1599 @ SV2331 @ ( tc_fun @ SV509 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6818]) ).
thf(6846,plain,
! [SV1140: $i,SV1623: $i,SV2691: $i,SV2683: $i,SV2648: $i,SV2608: $i,SV2517: $i,SV2346: $i,SV541: $i,SV2042: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV2042 @ SV541 @ SV2346 @ SV2517 @ SV2608 @ SV2648 @ SV2683 @ SV2691 @ SV1623 )
= $false )
| ( ( ( hAPP @ SV541 @ ( c_Set_Oinsert @ SV1140 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1623 @ tc_bool ) ) @ SV1623 ) )
= SV1140 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6821]) ).
thf(6847,plain,
! [SV1141: $i,SV1624: $i,SV2692: $i,SV2684: $i,SV2649: $i,SV2609: $i,SV2518: $i,SV2347: $i,SV2043: $i,SV542: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV542 @ SV2043 @ SV2347 @ SV2518 @ SV2609 @ SV2649 @ SV2684 @ SV2692 @ SV1624 )
= $false )
| ( ( ( hAPP @ SV542 @ ( c_Set_Oinsert @ SV1141 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1624 @ tc_bool ) ) @ SV1624 ) )
= SV1141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6822]) ).
thf(6848,plain,
! [SV2055: $i,SV2615: $i,SV584: $i,SV1655: $i,SV1178: $i] :
( ( ( SV1178 = SV1655 )
= $true )
| ( ( ! [SY7436: $i] :
~ ( c_Fun_Oinj__on @ SV584 @ SV2615 @ SV2055 @ SY7436 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2055 ) @ SV1178 ) @ SV2615 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2055 ) @ SV1655 ) @ SV2615 ) )
= $false )
| ( ( ( hAPP @ SV584 @ SV1178 )
= ( hAPP @ SV584 @ SV1655 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6829]) ).
thf(6849,plain,
! [SV1656: $i,SV1179: $i,SV2056: $i,SV2616: $i,SV585: $i] :
( ( ( ! [SY7437: $i] :
~ ( c_Fun_Oinj__on @ SV585 @ SV2616 @ SV2056 @ SY7437 ) )
= $true )
| ( ( SV1179 = SV1656 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2056 ) @ SV1179 ) @ SV2616 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2056 ) @ SV1656 ) @ SV2616 ) )
= $false )
| ( ( ( hAPP @ SV585 @ SV1179 )
= ( hAPP @ SV585 @ SV1656 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6830]) ).
thf(6850,plain,
! [SV1657: $i,SV1180: $i,SV2057: $i,SV2617: $i,SV586: $i] :
( ( ( ! [SY7438: $i] :
~ ( c_Fun_Oinj__on @ SV586 @ SV2617 @ SV2057 @ SY7438 ) )
= $true )
| ( ( SV1180 = SV1657 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2057 ) @ SV1180 ) @ SV2617 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2057 ) @ SV1657 ) @ SV2617 ) )
= $false )
| ( ( ( hAPP @ SV586 @ SV1180 )
= ( hAPP @ SV586 @ SV1657 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6831]) ).
thf(6851,plain,
! [SV2671: $i,SV587: $i,SV1181: $i,SV2058: $i,SV1658: $i,SV2618: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2618 ) @ SV1658 ) @ SV2058 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2618 ) @ SV1181 ) @ SV2058 ) ) )
= $true )
| ( ( SV1181 = SV1658 )
= $true )
| ( ( c_Fun_Oinj__on @ SV587 @ SV2058 @ SV2618 @ SV2671 )
= $false )
| ( ( ( hAPP @ SV587 @ SV1181 )
= ( hAPP @ SV587 @ SV1658 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[6832]) ).
thf(6852,plain,
! [SV605: $i,SV1199: $i,SV2067: $i,SV2686: $i,SV1674: $i,SV2621: $i,SV2378: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2378 ) @ SV2621 ) @ ( hAPP @ SV1674 @ SV2686 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2067 ) @ SV2686 ) @ SV1199 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV605 @ SV2621 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV605 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SV1199 @ SV1674 @ SV605 @ SV2067 @ SV2378 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6833]) ).
thf(6853,plain,
! [SV2672: $i,SV2654: $i,SV2622: $i,SV611: $i,SV2530: $i,SV1205: $i,SV1680: $i,SV2073: $i,SV2382: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2382 ) @ SV2073 ) @ SV1680 ) )
= $false )
| ( ( ! [SY7485: $i,SY7486: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1205 @ SV2530 @ SV611 @ SV2622 @ SV2654 @ SV2672 @ SY7485 @ SY7486 @ SV2382 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV611 @ ( hAPP @ SV1205 @ SV1680 ) ) @ SV2073 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6834]) ).
thf(6854,plain,
! [SV2673: $i,SV2655: $i,SV2623: $i,SV612: $i,SV1681: $i,SV2531: $i,SV2074: $i,SV1206: $i,SV2383: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2383 ) @ SV1206 ) @ SV2074 ) )
= $false )
| ( ( ! [SY7487: $i,SY7488: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2531 @ SV1681 @ SV612 @ SV2623 @ SV2655 @ SV2673 @ SY7487 @ SY7488 @ SV2383 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV612 @ SV1206 ) @ ( hAPP @ SV1681 @ SV2074 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6835]) ).
thf(6855,plain,
! [SV2388: $i,SV2078: $i,SV2624: $i,SV2536: $i,SV1215: $i,SV621: $i,SV2674: $i,SV1690: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1690 ) @ SV2674 ) @ SV621 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV1215 @ SV2674 ) @ SV2536 ) @ SV2624 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV621 @ SV1215 @ SV1690 @ ( tc_fun @ SV2078 @ ( tc_fun @ SV2388 @ tc_bool ) ) ) @ SV2536 ) @ SV2624 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6836]) ).
thf(6856,plain,
! [SV2390: $i,SV2080: $i,SV2626: $i,SV2537: $i,SV1217: $i,SV623: $i,SV2675: $i,SV1692: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV1692 ) @ SV2675 ) @ SV623 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ SV1217 @ SV2675 ) @ SV2537 ) @ SV2626 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV623 @ SV1217 @ SV1692 @ ( tc_fun @ SV2080 @ ( tc_fun @ SV2390 @ tc_bool ) ) ) @ SV2537 ) @ SV2626 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6837]) ).
thf(6857,plain,
! [SV135: $i,SV778: $i,SV1806: $i,SV1328: $i,SV2677: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV2677 @ SV1328 @ SV1806 @ SV778 ) )
= $true )
| ( ( ! [SY6828: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ SY6828 @ SV135 @ SV778 @ SV1806 ) @ SV1328 @ ( tc_fun @ SV1806 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY6828 @ SV135 @ SV778 @ SV1806 ) ) )
= $true )
| ( ( c_lessequals @ ( c_Set_Oimage @ SV2677 @ SV1328 @ SV1806 @ SV778 ) @ SV135 @ ( tc_fun @ SV778 @ tc_bool ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV135 @ SV778 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV1328 @ SV1806 )
= $false )
| ( ( ( c_Finite__Set_Ocard @ SV135 @ SV778 )
= ( c_Finite__Set_Ocard @ SV1328 @ SV1806 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6838]) ).
thf(6858,plain,
! [SV1458: $i,SV935: $i,SV1913: $i,SV2693: $i,SV2687: $i,SV2252: $i,SV2657: $i,SV2637: $i,SV2581: $i,SV318: $i,SV2470: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV2470 @ SV318 @ SV2581 @ SV2637 @ SV2657 @ SV2252 @ SV2687 @ SV2693 @ SV1913 )
= $false )
| ( ( ( hAPP @ SV318 @ ( c_Set_Oinsert @ SV935 @ ( c_Set_Oinsert @ SV1458 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1913 @ tc_bool ) ) @ SV1913 ) @ SV1913 ) )
= ( hAPP @ ( hAPP @ SV2252 @ SV935 ) @ SV1458 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6841]) ).
thf(6859,plain,
! [SV1459: $i,SV936: $i,SV1914: $i,SV2694: $i,SV2688: $i,SV2658: $i,SV2253: $i,SV2638: $i,SV2582: $i,SV2471: $i,SV319: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV319 @ SV2471 @ SV2582 @ SV2638 @ SV2253 @ SV2658 @ SV2688 @ SV2694 @ SV1914 )
= $false )
| ( ( ( hAPP @ SV319 @ ( c_Set_Oinsert @ SV936 @ ( c_Set_Oinsert @ SV1459 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1914 @ tc_bool ) ) @ SV1914 ) @ SV1914 ) )
= ( hAPP @ ( hAPP @ SV2253 @ SV936 ) @ SV1459 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6842]) ).
thf(6860,plain,
! [SV1596: $i,SV1108: $i,SV2020: $i,SV2695: $i,SV2689: $i,SV2329: $i,SV2664: $i,SV2646: $i,SV2601: $i,SV506: $i,SV2508: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV2508 @ SV506 @ SV2601 @ SV2646 @ SV2664 @ SV2329 @ SV2689 @ SV2695 @ SV2020 )
= $false )
| ( ( ( hAPP @ SV506 @ ( c_Set_Oinsert @ SV1108 @ SV1596 @ SV2020 ) )
= ( hAPP @ ( hAPP @ SV2329 @ SV1108 ) @ ( hAPP @ SV506 @ SV1596 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6843]) ).
thf(6861,plain,
! [SV1597: $i,SV1109: $i,SV2021: $i,SV2696: $i,SV2690: $i,SV2665: $i,SV2330: $i,SV2647: $i,SV2602: $i,SV2509: $i,SV507: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV507 @ SV2509 @ SV2602 @ SV2647 @ SV2330 @ SV2665 @ SV2690 @ SV2696 @ SV2021 )
= $false )
| ( ( ( hAPP @ SV507 @ ( c_Set_Oinsert @ SV1109 @ SV1597 @ SV2021 ) )
= ( hAPP @ ( hAPP @ SV2330 @ SV1109 ) @ ( hAPP @ SV507 @ SV1597 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6844]) ).
thf(6862,plain,
! [SV2023: $i,SV1599: $i,SV2603: $i,SV509: $i,SV1111: $i,SV2680: $i,SV2331: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2331 ) @ SV2680 ) @ SV1111 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ SV2603 ) @ ( hAPP @ SV1599 @ SV2680 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV2023 @ SV2603 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV509 ) @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SV1111 @ SV1599 @ SV2023 @ SV2331 @ SV509 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1111 @ SV1599 @ SV2331 @ ( tc_fun @ SV509 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6845]) ).
thf(6863,plain,
! [SV1655: $i,SV1178: $i,SV2697: $i,SV2055: $i,SV2615: $i,SV584: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV584 @ SV2615 @ SV2055 @ SV2697 ) )
= $true )
| ( ( SV1178 = SV1655 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2055 ) @ SV1178 ) @ SV2615 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2055 ) @ SV1655 ) @ SV2615 ) )
= $false )
| ( ( ( hAPP @ SV584 @ SV1178 )
= ( hAPP @ SV584 @ SV1655 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6848]) ).
thf(6864,plain,
! [SV1656: $i,SV1179: $i,SV2698: $i,SV2056: $i,SV2616: $i,SV585: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV585 @ SV2616 @ SV2056 @ SV2698 ) )
= $true )
| ( ( SV1179 = SV1656 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2056 ) @ SV1179 ) @ SV2616 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2056 ) @ SV1656 ) @ SV2616 ) )
= $false )
| ( ( ( hAPP @ SV585 @ SV1179 )
= ( hAPP @ SV585 @ SV1656 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6849]) ).
thf(6865,plain,
! [SV1657: $i,SV1180: $i,SV2699: $i,SV2057: $i,SV2617: $i,SV586: $i] :
( ( ( ~ ( c_Fun_Oinj__on @ SV586 @ SV2617 @ SV2057 @ SV2699 ) )
= $true )
| ( ( SV1180 = SV1657 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2057 ) @ SV1180 ) @ SV2617 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2057 ) @ SV1657 ) @ SV2617 ) )
= $false )
| ( ( ( hAPP @ SV586 @ SV1180 )
= ( hAPP @ SV586 @ SV1657 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[6850]) ).
thf(6866,plain,
! [SV2671: $i,SV587: $i,SV1181: $i,SV2058: $i,SV1658: $i,SV2618: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2618 ) @ SV1658 ) @ SV2058 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2618 ) @ SV1181 ) @ SV2058 ) ) )
= $true )
| ( ( SV1181 = SV1658 )
= $true )
| ( ( c_Fun_Oinj__on @ SV587 @ SV2058 @ SV2618 @ SV2671 )
= $false )
| ( ( ( hAPP @ SV587 @ SV1181 )
= ( hAPP @ SV587 @ SV1658 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6851]) ).
thf(6867,plain,
! [SV605: $i,SV1674: $i,SV2621: $i,SV2378: $i,SV1199: $i,SV2686: $i,SV2067: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2067 ) @ SV2686 ) @ SV1199 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2378 ) @ SV2621 ) @ ( hAPP @ SV1674 @ SV2686 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV605 @ SV2621 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV605 @ ( c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 @ SV1199 @ SV1674 @ SV605 @ SV2067 @ SV2378 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6852]) ).
thf(6868,plain,
! [SV1680: $i,SV2073: $i,SV2382: $i,SV2700: $i,SV2672: $i,SV2654: $i,SV2622: $i,SV611: $i,SV2530: $i,SV1205: $i] :
( ( ( ! [SY7496: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1205 @ SV2530 @ SV611 @ SV2622 @ SV2654 @ SV2672 @ SV2700 @ SY7496 @ SV2382 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2382 ) @ SV2073 ) @ SV1680 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV611 @ ( hAPP @ SV1205 @ SV1680 ) ) @ SV2073 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6853]) ).
thf(6869,plain,
! [SV2074: $i,SV1206: $i,SV2383: $i,SV2701: $i,SV2673: $i,SV2655: $i,SV2623: $i,SV612: $i,SV1681: $i,SV2531: $i] :
( ( ( ! [SY7497: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2531 @ SV1681 @ SV612 @ SV2623 @ SV2655 @ SV2673 @ SV2701 @ SY7497 @ SV2383 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2383 ) @ SV1206 ) @ SV2074 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV612 @ SV1206 ) @ ( hAPP @ SV1681 @ SV2074 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6854]) ).
thf(6870,plain,
! [SV135: $i,SV778: $i,SV1806: $i,SV1328: $i,SV2677: $i] :
( ( ( c_Fun_Oinj__on @ SV2677 @ SV1328 @ SV1806 @ SV778 )
= $false )
| ( ( ! [SY6828: $i] :
( ~ ( c_lessequals @ ( c_Set_Oimage @ SY6828 @ SV135 @ SV778 @ SV1806 ) @ SV1328 @ ( tc_fun @ SV1806 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SY6828 @ SV135 @ SV778 @ SV1806 ) ) )
= $true )
| ( ( c_lessequals @ ( c_Set_Oimage @ SV2677 @ SV1328 @ SV1806 @ SV778 ) @ SV135 @ ( tc_fun @ SV778 @ tc_bool ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV135 @ SV778 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV1328 @ SV1806 )
= $false )
| ( ( ( c_Finite__Set_Ocard @ SV135 @ SV778 )
= ( c_Finite__Set_Ocard @ SV1328 @ SV1806 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6857]) ).
thf(6871,plain,
! [SV1655: $i,SV1178: $i,SV2697: $i,SV2055: $i,SV2615: $i,SV584: $i] :
( ( ( c_Fun_Oinj__on @ SV584 @ SV2615 @ SV2055 @ SV2697 )
= $false )
| ( ( SV1178 = SV1655 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2055 ) @ SV1178 ) @ SV2615 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2055 ) @ SV1655 ) @ SV2615 ) )
= $false )
| ( ( ( hAPP @ SV584 @ SV1178 )
= ( hAPP @ SV584 @ SV1655 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6863]) ).
thf(6872,plain,
! [SV1656: $i,SV1179: $i,SV2698: $i,SV2056: $i,SV2616: $i,SV585: $i] :
( ( ( c_Fun_Oinj__on @ SV585 @ SV2616 @ SV2056 @ SV2698 )
= $false )
| ( ( SV1179 = SV1656 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2056 ) @ SV1179 ) @ SV2616 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2056 ) @ SV1656 ) @ SV2616 ) )
= $false )
| ( ( ( hAPP @ SV585 @ SV1179 )
= ( hAPP @ SV585 @ SV1656 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6864]) ).
thf(6873,plain,
! [SV1657: $i,SV1180: $i,SV2699: $i,SV2057: $i,SV2617: $i,SV586: $i] :
( ( ( c_Fun_Oinj__on @ SV586 @ SV2617 @ SV2057 @ SV2699 )
= $false )
| ( ( SV1180 = SV1657 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2057 ) @ SV1180 ) @ SV2617 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2057 ) @ SV1657 ) @ SV2617 ) )
= $false )
| ( ( ( hAPP @ SV586 @ SV1180 )
= ( hAPP @ SV586 @ SV1657 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6865]) ).
thf(6874,plain,
! [SV2671: $i,SV587: $i,SV1658: $i,SV2058: $i,SV1181: $i,SV2618: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2618 ) @ SV1181 ) @ SV2058 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2618 ) @ SV1658 ) @ SV2058 ) )
= $false )
| ( ( SV1181 = SV1658 )
= $true )
| ( ( c_Fun_Oinj__on @ SV587 @ SV2058 @ SV2618 @ SV2671 )
= $false )
| ( ( ( hAPP @ SV587 @ SV1181 )
= ( hAPP @ SV587 @ SV1658 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[6866]) ).
thf(6875,plain,
! [SV1680: $i,SV2073: $i,SV2382: $i,SV2702: $i,SV2700: $i,SV2672: $i,SV2654: $i,SV2622: $i,SV611: $i,SV2530: $i,SV1205: $i] :
( ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1205 @ SV2530 @ SV611 @ SV2622 @ SV2654 @ SV2672 @ SV2700 @ SV2702 @ SV2382 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2382 ) @ SV2073 ) @ SV1680 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV611 @ ( hAPP @ SV1205 @ SV1680 ) ) @ SV2073 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6868]) ).
thf(6876,plain,
! [SV2074: $i,SV1206: $i,SV2383: $i,SV2703: $i,SV2701: $i,SV2673: $i,SV2655: $i,SV2623: $i,SV612: $i,SV1681: $i,SV2531: $i] :
( ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV2531 @ SV1681 @ SV612 @ SV2623 @ SV2655 @ SV2673 @ SV2701 @ SV2703 @ SV2383 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2383 ) @ SV1206 ) @ SV2074 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV612 @ SV1206 ) @ ( hAPP @ SV1681 @ SV2074 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6869]) ).
thf(6877,plain,
! [SV2677: $i,SV1328: $i,SV1806: $i,SV778: $i,SV135: $i,SV2704: $i] :
( ( ( ~ ( c_lessequals @ ( c_Set_Oimage @ SV2704 @ SV135 @ SV778 @ SV1806 ) @ SV1328 @ ( tc_fun @ SV1806 @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ SV2704 @ SV135 @ SV778 @ SV1806 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV2677 @ SV1328 @ SV1806 @ SV778 )
= $false )
| ( ( c_lessequals @ ( c_Set_Oimage @ SV2677 @ SV1328 @ SV1806 @ SV778 ) @ SV135 @ ( tc_fun @ SV778 @ tc_bool ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV135 @ SV778 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV1328 @ SV1806 )
= $false )
| ( ( ( c_Finite__Set_Ocard @ SV135 @ SV778 )
= ( c_Finite__Set_Ocard @ SV1328 @ SV1806 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[6870]) ).
thf(6878,plain,
! [SV1680: $i,SV2073: $i,SV2382: $i,SV2702: $i,SV2700: $i,SV2672: $i,SV2654: $i,SV2622: $i,SV611: $i,SV2530: $i,SV1205: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV1205 @ SV2530 @ SV611 @ SV2622 @ SV2654 @ SV2672 @ SV2700 @ SV2702 @ SV2382 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2382 ) @ SV2073 ) @ SV1680 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV611 @ ( hAPP @ SV1205 @ SV1680 ) ) @ SV2073 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6875]) ).
thf(6879,plain,
! [SV2074: $i,SV1206: $i,SV2383: $i,SV2703: $i,SV2701: $i,SV2673: $i,SV2655: $i,SV2623: $i,SV612: $i,SV1681: $i,SV2531: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV2531 @ SV1681 @ SV612 @ SV2623 @ SV2655 @ SV2673 @ SV2701 @ SV2703 @ SV2383 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_in @ SV2383 ) @ SV1206 ) @ SV2074 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV612 @ SV1206 ) @ ( hAPP @ SV1681 @ SV2074 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6876]) ).
thf(6880,plain,
! [SV2677: $i,SV1328: $i,SV1806: $i,SV778: $i,SV135: $i,SV2704: $i] :
( ( ( ~ ( c_lessequals @ ( c_Set_Oimage @ SV2704 @ SV135 @ SV778 @ SV1806 ) @ SV1328 @ ( tc_fun @ SV1806 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Fun_Oinj__on @ SV2704 @ SV135 @ SV778 @ SV1806 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV2677 @ SV1328 @ SV1806 @ SV778 )
= $false )
| ( ( c_lessequals @ ( c_Set_Oimage @ SV2677 @ SV1328 @ SV1806 @ SV778 ) @ SV135 @ ( tc_fun @ SV778 @ tc_bool ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV135 @ SV778 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV1328 @ SV1806 )
= $false )
| ( ( ( c_Finite__Set_Ocard @ SV135 @ SV778 )
= ( c_Finite__Set_Ocard @ SV1328 @ SV1806 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[6877]) ).
thf(6881,plain,
! [SV2677: $i,SV1328: $i,SV1806: $i,SV778: $i,SV135: $i,SV2704: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV2704 @ SV135 @ SV778 @ SV1806 ) @ SV1328 @ ( tc_fun @ SV1806 @ tc_bool ) )
= $false )
| ( ( ~ ( c_Fun_Oinj__on @ SV2704 @ SV135 @ SV778 @ SV1806 ) )
= $true )
| ( ( c_Fun_Oinj__on @ SV2677 @ SV1328 @ SV1806 @ SV778 )
= $false )
| ( ( c_lessequals @ ( c_Set_Oimage @ SV2677 @ SV1328 @ SV1806 @ SV778 ) @ SV135 @ ( tc_fun @ SV778 @ tc_bool ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV135 @ SV778 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV1328 @ SV1806 )
= $false )
| ( ( ( c_Finite__Set_Ocard @ SV135 @ SV778 )
= ( c_Finite__Set_Ocard @ SV1328 @ SV1806 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6880]) ).
thf(6882,plain,
! [SV2677: $i,SV1328: $i,SV1806: $i,SV778: $i,SV135: $i,SV2704: $i] :
( ( ( c_Fun_Oinj__on @ SV2704 @ SV135 @ SV778 @ SV1806 )
= $false )
| ( ( c_lessequals @ ( c_Set_Oimage @ SV2704 @ SV135 @ SV778 @ SV1806 ) @ SV1328 @ ( tc_fun @ SV1806 @ tc_bool ) )
= $false )
| ( ( c_Fun_Oinj__on @ SV2677 @ SV1328 @ SV1806 @ SV778 )
= $false )
| ( ( c_lessequals @ ( c_Set_Oimage @ SV2677 @ SV1328 @ SV1806 @ SV778 ) @ SV135 @ ( tc_fun @ SV778 @ tc_bool ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV135 @ SV778 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV1328 @ SV1806 )
= $false )
| ( ( ( c_Finite__Set_Ocard @ SV135 @ SV778 )
= ( c_Finite__Set_Ocard @ SV1328 @ SV1806 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[6881]) ).
thf(6883,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1819,6882,6879,6878,6874,6873,6872,6871,6867,6862,6861,6860,6859,6858,6856,6855,6847,6846,6840,6839,6828,6827,6826,6825,6824,6823,6820,6819,6815,6814,6813,6812,6811,6810,6809,6808,6807,6806,6805,6802,6798,6797,6796,6795,6793,6788,6787,6768,6767,6766,6765,6764,6763,6760,6757,6756,6753,6751,6744,6741,6740,6739,6738,6737,6736,6731,6730,6729,6728,6727,6726,6725,6724,6723,6722,6721,6720,6719,6714,6713,6701,6700,6691,6687,6686,6683,6682,6674,6672,6670,6669,6668,6664,6658,6652,6651,6648,6645,6644,6643,6642,6641,6640,6636,6635,6634,6632,6627,6624,6621,6613,6612,6611,6610,6609,6608,6607,6606,6605,6600,6599,6598,6597,6592,6584,6583,6582,6581,6580,6575,6568,6567,6566,6565,6564,6563,6562,6561,6560,6559,6556,6555,6554,6549,6548,6547,6545,6541,6540,6539,6538,6537,6536,6535,6534,6533,6532,6530,6529,6527,6523,6516,6515,6512,6511,6510,6502,6501,6499,6497,6493,6492,6491,6486,6481,6480,6479,6476,6470,6467,6466,6463,6462,6461,6457,6456,6455,6454,6452,6451,6450,6449,6448,6447,6446,6445,6441,6440,6439,6437,6436,6430,6425,6424,6423,6422,6421,6420,6419,6418,6415,6411,6410,6409,6408,6406,6401,6400,6399,6398,6397,6396,6395,6394,6393,6392,6388,6387,6385,6380,6372,6370,6369,6368,6367,6366,6365,6364,6363,6351,6350,6347,6346,6345,6344,6343,6334,6333,6328,6327,6325,6304,6303,6299,6293,6279,6278,6277,6274,6273,6266,6264,6247,6246,6245,6241,6230,6229,6228,6226,6219,6213,6210,6209,6202,6200,6197,6196,6195,6193,6185,6179,6176,6168,6167,6166,6159,6158,6157,6151,6150,6149,6144,6142,6140,6138,6136,6133,6132,6131,6130,6117,6116,6112,6111,6110,6106,6102,6081,6080,6079,6076,6072,6071,6066,6065,6064,6063,6062,6054,6053,6048,6047,6044,6043,6030,6029,6015,6014,6004,6003,6002,5997,5996,5971,5965,5961,5960,5956,5955,5954,5951,5950,5939,5938,5928,5924,5923,5922,5918,5911,5910,5900,5899,5898,5893,5892,5891,5890,5889,5887,5886,5879,5872,5867,5865,5852,5842,5841,5840,5839,5838,5837,5830,5828,5825,5821,5818,5817,5816,5814,5813,5809,5793,5792,5784,5783,5773,5772,5768,5759,5758,5757,5756,5753,5751,5748,5747,5746,5745,5744,5742,5741,5738,5730,5722,5716,5713,5710,5686,5685,5678,5677,5676,5672,5671,5669,5668,5661,5660,5656,5655,5654,5652,5631,5629,5628,5622,5618,5617,5614,5613,5612,5611,5610,5594,5567,5566,5565,5526,5522,5516,5515,5509,5504,5484,5482,5481,5480,5465,5451,5450,5449,5446,5435,5434,5431,5429,5424,5422,5421,5406,5405,5401,5396,5373,5372,5370,5369,5368,5360,5359,5346,5342,5338,5337,5332,5327,5320,5301,5300,5299,5298,5297,5286,5285,5282,5281,5280,5277,5276,5269,5268,5257,5251,5246,5245,5243,5242,5223,5203,5201,5153,5152,5146,5140,5139,5132,5131,5130,5129,5128,5123,5122,5118,5117,5115,5114,5113,5112,5111,5109,5108,5107,5106,5105,5094,5090,5089,5087,5086,4999,4996,4994,4980,4971,4956,4943,4941,4938,4937,4909,4907,4906,4896,4894,4891,4877,4865,4863,4862,4854,4850,4839,4829,4823,4822,4802,4801,4798,4791,4790,4788,4784,4783,4779,4776,4770,4729,4715,4714,4713,4692,4691,4681,4679,4677,4676,4674,4673,4672,4664,4663,4610,4609,4592,4591,4583,4582,4578,4577,4576,4560,4559,4536,4534,4532,4528,4518,4504,4418,4417,4416,4407,4405,4403,4378,4375,4373,4358,4334,4326,4323,4313,4312,4310,4279,4277,4260,4255,4252,4248,4245,4243,4242,4241,4211,4202,4188,4183,4182,4163,4161,4137,4121,4097,4094,4084,4083,4074,4063,4062,4030,4017,4014,3942,3941,3926,3871,3841,3834,3831,3755,3751,3742,3739,3735,3733,3665,3663,3628,3524,3523,3510,3509,3482,3372,3295,3294,3262,3242,3241,3201,3009,2839,2776,2644,2533,2524,2519,2518,2517,2516,2515,2514,2513,2512,2511,2510,2509,2508,2507,2506,2505,2504,2503,2502,2501,2500,2484,2469,2188,1822,1821,1820]) ).
thf(6884,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[6883]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV892-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.21 % Computer : n003.cluster.edu
% 0.07/0.21 % Model : x86_64 x86_64
% 0.07/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.21 % Memory : 8046.5625MB
% 0.07/0.21 % OS : Linux 6.8.0-71-generic
% 0.07/0.21 % CPULimit : 300
% 0.07/0.21 % WCLimit : 300
% 0.07/0.21 % DateTime : Tue Oct 6 16:48:55 UTC 2026
% 0.07/0.21 % CPUTime :
% 0.07/0.21 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 243.85/40.94 .....
% 243.85/40.94
% 243.85/40.94 No.of.Axioms: 704
% 243.85/40.94
% 243.85/40.94 Length.of.Defs: 0
% 243.85/40.94
% 243.85/40.94 Contains.Choice.Funs: false
% 243.85/40.94 .............................................................................................................................................................................................................................................................................................................................................................................................................
% 243.85/40.94
% 243.85/40.94 ********************************
% 243.85/40.94 * All subproblems solved! *
% 243.85/40.94 ********************************
% 243.85/40.94 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:704,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:72,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:6883,loop_count:0,foatp_calls:1,translation:fof_full)
% 243.85/40.94
% 243.85/40.94 %**** Beginning of derivation protocol ****
% 243.85/40.94 % SZS output start CNFRefutation
% See solution above
% 243.85/40.97
% 243.85/40.97 %**** End of derivation protocol ****
% 243.85/40.97 %**** no. of clauses in derivation: 6884 ****
% 243.85/40.97 %**** clause counter: 6883 ****
% 243.85/40.97
% 243.85/40.97 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:2,axioms:704,ps:3,u:5,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:72,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:6883,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------