%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV839-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 10:59:19 AM UTC 2026
% Result : Unsatisfiable 135.77s 22.93s
% Output : CNFRefutation 135.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 455
% Syntax : Number of formulae : 4220 (2638 unt; 0 typ; 0 def)
% Number of atoms : 23012 (7917 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 81343 (5476 ~;7176 |; 0 &;68691 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 85 ( 82 usr; 13 con; 0-9 aty)
% Number of variables : 16443 ( 0 ^;16443 !; 0 ?;16443 :)
% Comments :
%------------------------------------------------------------------------------
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_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_Complete__Lattice_OInf__class_OInf,type,
c_Complete__Lattice_OInf__class_OInf: $i > $i ).
thf(tp_c_Complete__Lattice_OSup__class_OSup,type,
c_Complete__Lattice_OSup__class_OSup: $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__axioms,type,
c_Complete__Lattice_Ocomplete__lattice__axioms: $i > $i > $i > $i > $o ).
thf(tp_c_Complete__Lattice_Ocomplete__lattice__class_OSUPR,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i > $i > $i ).
thf(tp_c_Finite__Set_Ofinite,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
thf(tp_c_Finite__Set_Ofold1,type,
c_Finite__Set_Ofold1: $i > $i > $i > $i ).
thf(tp_c_Finite__Set_Ofold1Set,type,
c_Finite__Set_Ofold1Set: $i > $i > $i > $i ).
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_Olinorder__class_OMax,type,
c_Finite__Set_Olinorder__class_OMax: $i > $i > $i ).
thf(tp_c_Finite__Set_Olinorder__class_OMin,type,
c_Finite__Set_Olinorder__class_OMin: $i > $i > $i ).
thf(tp_c_Finite__Set_Osetsum,type,
c_Finite__Set_Osetsum: $i > $i > $i > $i > $i ).
thf(tp_c_HOL_Ominus__class_Ominus,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(tp_c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(tp_c_HOL_Ouminus__class_Ouminus,type,
c_HOL_Ouminus__class_Ouminus: $i > $i > $i ).
thf(tp_c_Hoare__Mirabelle_Ohoare__derivs,type,
c_Hoare__Mirabelle_Ohoare__derivs: $i > $i > $i > $o ).
thf(tp_c_Hoare__Mirabelle_Otriple_Otriple,type,
c_Hoare__Mirabelle_Otriple_Otriple: $i > $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_Nitpick_Ofold__graph_H,type,
c_Nitpick_Ofold__graph_H: $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Nitpick_Osko__Nitpick__XEx1__def__1__3,type,
c_Nitpick_Osko__Nitpick__XEx1__def__1__3: $i > $i > $i ).
thf(tp_c_Orderings_Obot__class_Obot,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(tp_c_SetInterval_Oord__class_OatLeastAtMost,type,
c_SetInterval_Oord__class_OatLeastAtMost: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord__class_OatLeastLessThan,type,
c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i > $i ).
thf(tp_c_SetInterval_Oord__class_OgreaterThanAtMost,type,
c_SetInterval_Oord__class_OgreaterThanAtMost: $i > $i > $i > $i ).
thf(tp_c_Set_Ocontents,type,
c_Set_Ocontents: $i > $i > $i ).
thf(tp_c_Set_Oinsert,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(tp_c_The,type,
c_The: $i > $i > $i ).
thf(tp_c_fequal,type,
c_fequal: $i > $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $i ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i ).
thf(tp_class_Complete__Lattice_Ocomplete__lattice,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(tp_class_Finite__Set_Ofinite_Ofinite,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
thf(tp_class_HOL_Ominus,type,
class_HOL_Ominus: $i > $o ).
thf(tp_class_HOL_Oord,type,
class_HOL_Oord: $i > $o ).
thf(tp_class_HOL_Ouminus,type,
class_HOL_Ouminus: $i > $o ).
thf(tp_class_Lattices_Oboolean__algebra,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(tp_class_Lattices_Obounded__lattice,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(tp_class_Lattices_Olattice,type,
class_Lattices_Olattice: $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_Ogroup__add,type,
class_OrderedGroup_Ogroup__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_t_a,type,
t_a: $i ).
thf(tp_t_b,type,
t_b: $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_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_A,type,
v_A: $i ).
thf(tp_v_G,type,
v_G: $i ).
thf(tp_v_Ga,type,
v_Ga: $i ).
thf(tp_v_P,type,
v_P: $i ).
thf(tp_v_sko__Hoare__Mirabelle__Xconseq12__1,type,
v_sko__Hoare__Mirabelle__Xconseq12__1: $i > $i > $i > $i > $i ).
thf(tp_v_sko__Hoare__Mirabelle__Xconseq12__2,type,
v_sko__Hoare__Mirabelle__Xconseq12__2: $i > $i > $i > $i > $i ).
thf(tp_v_sko__Hoare__Mirabelle__Xconseq12__3,type,
v_sko__Hoare__Mirabelle__Xconseq12__3: $i > $i > $i > $i > $i ).
thf(tp_v_sko__Hoare__Mirabelle__Xconseq1__1,type,
v_sko__Hoare__Mirabelle__Xconseq1__1: $i > $i > $i ).
thf(tp_v_sko__Hoare__Mirabelle__Xconseq1__2,type,
v_sko__Hoare__Mirabelle__Xconseq1__2: $i > $i > $i ).
thf(tp_v_sko__Hoare__Mirabelle__Xconseq2__1,type,
v_sko__Hoare__Mirabelle__Xconseq2__1: $i > $i > $i ).
thf(tp_v_sko__Hoare__Mirabelle__Xconseq2__2,type,
v_sko__Hoare__Mirabelle__Xconseq2__2: $i > $i > $i ).
thf(tp_v_sko__Hoare__Mirabelle__Xescape__1,type,
v_sko__Hoare__Mirabelle__Xescape__1: $i > $i > $i > $i > $i ).
thf(tp_v_sko__Hoare__Mirabelle__Xescape__2,type,
v_sko__Hoare__Mirabelle__Xescape__2: $i > $i > $i > $i > $i ).
thf(tp_v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1: $i > $i > $i > $i > $i ).
thf(tp_v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2: $i > $i > $i > $i > $i ).
thf(tp_v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1: $i > $i > $i > $i > $i ).
thf(tp_v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2: $i > $i > $i > $i > $i ).
thf(tp_v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_v_x,type,
v_x: $i ).
thf(1,axiom,
! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(2,axiom,
! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(3,axiom,
class_HOL_Oord @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(4,axiom,
class_HOL_Ominus @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
thf(5,axiom,
class_HOL_Ouminus @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ouminus) ).
thf(6,axiom,
class_Orderings_Obot @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(7,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(8,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(9,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(10,axiom,
class_Finite__Set_Ofinite_Ofinite @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
thf(11,axiom,
class_Lattices_Oboolean__algebra @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
thf(12,axiom,
class_Lattices_Obounded__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(13,axiom,
class_Lattices_Oupper__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(14,axiom,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
thf(15,axiom,
class_HOL_Oord @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(16,axiom,
class_HOL_Ominus @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ominus) ).
thf(17,axiom,
class_Orderings_Obot @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(18,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(19,axiom,
class_Lattices_Olattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(20,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(21,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(22,axiom,
class_Lattices_Oupper__semilattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
thf(23,axiom,
! [T_2: $i,T_1: $i] :
( ( class_HOL_Oord @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_HOL_Oord @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(24,axiom,
! [T_2: $i,T_1: $i] :
( ( class_HOL_Ominus @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_HOL_Ominus @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).
thf(25,axiom,
! [T_2: $i,T_1: $i] :
( ( class_HOL_Ouminus @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_HOL_Ouminus @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ouminus) ).
thf(26,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Obot @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(27,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(28,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Olattice @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(29,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(30,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ T_1 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ T_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
thf(31,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Oboolean__algebra @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
thf(32,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Obounded__lattice @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(35,axiom,
! [T_b: $i,V_f: $i,V_x: $i,V_g: $i,T_a: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_b ) @ ( hAPP @ V_f @ V_x ) ) @ ( hAPP @ V_g @ V_x ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ T_b ) ) @ V_f ) @ V_g ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(36,axiom,
! [V_G: $i,V_ts: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ V_ts ) @ V_G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_asm_0) ).
thf(37,axiom,
! [V_y: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_A @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(38,axiom,
! [V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
!= ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(39,axiom,
! [V_xa: $i,V_x: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_xa @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_xa @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(40,axiom,
! [V_x: $i,V_y: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_y @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(41,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(42,axiom,
! [T_a: $i,V_A: $i,V_b: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(43,axiom,
! [T_a: $i,V_A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(44,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Obot @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Orderings_Obot__class_Obot @ T_a ) ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(45,axiom,
! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(46,axiom,
! [V_x: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_x @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a )
= ( c_Set_Oinsert @ V_x @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(47,axiom,
! [V_A: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ( V_y = V_x )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(48,axiom,
! [T_a: $i,V_B: $i,V_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(49,axiom,
! [V_G: $i,T_a: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty_0) ).
thf(50,axiom,
! [T_a: $i,V_x: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(51,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(52,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(53,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(54,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(55,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(56,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_a = V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(57,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_a = V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(58,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_b = V_d ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(59,axiom,
! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_b = V_d ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(60,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/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_0) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_1) ).
thf(62,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/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_2) ).
thf(63,axiom,
! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(64,axiom,
! [T_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(65,axiom,
! [T_a: $i,V_a: $i,V_A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Set_Oinsert @ V_a @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(66,axiom,
! [V_G: $i,V_ts: $i,T_a: $i,V_G_H: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_G_H @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G_H @ V_ts @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut_0) ).
thf(67,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/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_OSkip_0) ).
thf(68,axiom,
! [V_x: $i,V_A: $i,T_a: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(69,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_z ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_z ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(70,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(71,axiom,
! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(72,axiom,
! [T_a: $i,V_A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(73,axiom,
! [T_a: $i,V_A: $i,V_C: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(74,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 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_P ) @ V_Q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(75,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(76,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(77,axiom,
! [V_Q: $i,V_x: $i,T_a: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_P ) @ V_Q ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(78,axiom,
! [V_G: $i,V_ts: $i,T_a: $i,V_ts_H: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ V_ts ) @ V_ts_H ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts_H @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_weaken_0) ).
thf(79,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(80,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/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).
thf(81,axiom,
! [T_a: $i,V_a: $i,V_C: $i,V_D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ V_C @ T_a ) ) @ ( c_Set_Oinsert @ V_a @ V_D @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(82,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(83,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/sandbox/benchmark/theBenchmark.p',cls_Comp_0) ).
thf(84,axiom,
! [T_a: $i,V_A: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).
thf(85,axiom,
! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ V_G @ V_P @ V_Q @ V_c ) ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ V_G @ V_P @ V_Q @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_escape_0) ).
thf(86,axiom,
! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_Q_H: $i] :
( ( 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_Q @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ V_Q @ V_Q_H ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ V_Q @ V_Q_H ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ V_c @ V_Q_H @ 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/sandbox/benchmark/theBenchmark.p',cls_conseq2_1) ).
thf(87,axiom,
! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_P_H: $i,V_Q_H: $i] :
( ( 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_Q @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ V_P @ V_P_H @ V_Q @ V_Q_H ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ V_P @ V_P_H @ V_Q @ V_Q_H ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P_H @ V_c @ V_Q_H @ 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/sandbox/benchmark/theBenchmark.p',cls_conseq12_2) ).
thf(88,axiom,
! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_P_H: $i] :
( ( 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_H @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ V_P @ V_P_H ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ V_P @ V_P_H ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P_H @ 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/sandbox/benchmark/theBenchmark.p',cls_conseq1_1) ).
thf(89,axiom,
! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_x: $i,V_xa: $i] :
( ( 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_Q @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ V_G @ V_P @ V_Q @ V_c ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ V_G @ V_P @ V_Q @ V_c @ V_x @ V_xa ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_x @ V_c @ V_xa @ 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/sandbox/benchmark/theBenchmark.p',cls_conseq_2) ).
thf(90,axiom,
! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_P_H: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ V_P @ V_P_H ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ V_P @ V_P_H ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P_H @ 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/sandbox/benchmark/theBenchmark.p',cls_conseq1_0) ).
thf(91,axiom,
! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_P_H: $i,V_Q_H: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ V_P @ V_P_H @ V_Q @ V_Q_H ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ V_P @ V_P_H @ V_Q @ V_Q_H ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P_H @ V_c @ V_Q_H @ 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/sandbox/benchmark/theBenchmark.p',cls_conseq12_0) ).
thf(92,axiom,
! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_Q_H: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_H @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ V_Q @ V_Q_H ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ V_Q @ V_Q_H ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ V_c @ V_Q_H @ 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/sandbox/benchmark/theBenchmark.p',cls_conseq2_0) ).
thf(93,axiom,
! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ V_G @ V_P @ V_Q @ V_c ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ V_G @ V_P @ V_Q @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conseq_0) ).
thf(94,axiom,
! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_x: $i,V_xa: $i] :
( ( 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_Q @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ V_G @ V_P @ V_Q @ V_c ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ V_G @ V_P @ V_Q @ V_c @ V_x @ V_xa ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_x @ V_c @ V_xa @ 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/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_2) ).
thf(95,axiom,
! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ V_G @ V_P @ V_Q @ V_c ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ V_G @ V_P @ V_Q @ V_c ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_0) ).
thf(96,axiom,
! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_xa: $i,V_Z_H: $i,V_x: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_xa @ V_Z_H ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ V_G @ V_P @ V_Q @ V_c @ V_x @ V_xa ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_x @ V_Z_H ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ V_G @ V_P @ V_Q @ V_c ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_x @ V_c @ V_xa @ 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/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_1) ).
thf(97,axiom,
! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_Q_H: $i,V_Z_H: $i,V_P_H: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_H @ V_Z_H ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ V_P @ V_P_H @ V_Q @ V_Q_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_H @ V_Z_H ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ V_P @ V_P_H @ V_Q @ V_Q_H ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P_H @ V_c @ V_Q_H @ 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/sandbox/benchmark/theBenchmark.p',cls_conseq12_1) ).
thf(98,axiom,
! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_xa: $i,V_Z_H: $i,V_x: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_xa @ V_Z_H ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ V_G @ V_P @ V_Q @ V_c @ V_x @ V_xa ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_x @ V_Z_H ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ V_G @ V_P @ V_Q @ V_c ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_x @ V_c @ V_xa @ 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/sandbox/benchmark/theBenchmark.p',cls_conseq_1) ).
thf(99,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(100,axiom,
! [T_a: $i,V_A: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(101,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(102,axiom,
! [T_a: $i,V_A: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(103,axiom,
! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(104,axiom,
! [T_a: $i,V_x: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(105,axiom,
! [T_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_1) ).
thf(106,axiom,
! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_0) ).
thf(107,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ T_a ) @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).
thf(108,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/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(109,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 @ ( c_in @ V_x @ V_xa @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(110,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_a @ T_a )
= ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastAtMost__singleton_0) ).
thf(111,axiom,
! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Set_Oinsert @ V_a @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
thf(112,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__singleton_0) ).
thf(113,axiom,
! [V_f: $i,V_a: $i,T_a: $i] :
( ( c_Finite__Set_Ofold1 @ V_f @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__singleton_0) ).
thf(114,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_b = V_a )
| ~ ( hBOOL @ ( c_in @ V_b @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(115,axiom,
! [V_y: $i,V_x: $i,T_a: $i] :
( ( V_y
= ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_3) ).
thf(116,axiom,
! [V_x: $i,T_a: $i] :
( ( c_Set_Ocontents @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_contents__eq_0) ).
thf(117,axiom,
! [V_a: $i,V_b: $i,V_f: $i,T_a: $i] :
( ( V_a = V_b )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ V_f @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1Set__sing_0) ).
thf(118,axiom,
! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
thf(119,axiom,
! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
thf(120,axiom,
! [V_Sup: $i,V_a: $i,V_b: $i,T_a: $i,V_sup: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
= ( hAPP @ ( hAPP @ V_sup @ V_a ) @ V_b ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).
thf(121,axiom,
! [V_Inf: $i,V_a: $i,V_b: $i,T_a: $i,V_inf: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
= ( hAPP @ ( hAPP @ V_inf @ V_a ) @ V_b ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).
thf(122,axiom,
! [V_x: $i,T_a: $i] :
( ( c_The @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OThe__psimp_0) ).
thf(123,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__singleton_0) ).
thf(124,axiom,
! [V_f: $i,V_x: $i,T_a: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ V_f @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1Set__sing_1) ).
thf(125,axiom,
! [V_a: $i,T_b: $i,V_B: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).
thf(126,axiom,
! [V_x: $i,T_a: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_2) ).
thf(127,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ T_a ) @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).
thf(128,axiom,
! [V_Sup: $i,V_a: $i,T_a: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= V_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__singleton_0) ).
thf(129,axiom,
! [V_Inf: $i,V_a: $i,T_a: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= V_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).
thf(130,axiom,
! [V_x: $i,T_a: $i] : ( hBOOL @ ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(131,axiom,
! [T_a: $i,V_a: $i] :
( ( c_Collect @ ( hAPP @ ( c_fequal @ T_a ) @ V_a ) @ T_a )
= ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
thf(132,axiom,
! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__empty_0) ).
thf(133,axiom,
! [T_b: $i] :
( ~ ( class_Orderings_Obot @ T_b )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ T_b ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
thf(134,axiom,
! [T_a: $i,V_b: $i,V_d: $i,V_a: $i,V_c: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_d ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_a @ V_b @ T_a ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_c @ V_d @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_1) ).
thf(135,axiom,
! [T_a: $i,V_x: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ T_a ) @ V_A ) ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
thf(136,axiom,
! [T_a: $i,V_x: $i] :
( ( c_The @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ T_a )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__sym__eq__trivial_0) ).
thf(137,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/sandbox/benchmark/theBenchmark.p',cls_UN__Un_0) ).
thf(138,axiom,
! [T_a: $i,V_i: $i,V_m: $i,V_n: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_i @ V_m @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_i @ V_n @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ V_n @ V_m @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_i ) @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__diff_0) ).
thf(139,axiom,
! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(140,axiom,
! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(141,axiom,
! [T_b: $i,V_A: $i] :
( ~ ( class_HOL_Ouminus @ T_b )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ t_a @ T_b ) ) @ v_x )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ V_A @ v_x ) @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__Compl__def_0) ).
thf(142,axiom,
! [T_a: $i,V_A: $i,V_x: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ T_a ) @ V_A ) ) @ V_x ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__lower_0) ).
thf(143,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/sandbox/benchmark/theBenchmark.p',cls_UN__insert_0) ).
thf(144,axiom,
( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( c_in @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).
thf(145,axiom,
! [V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_HOL_Ouminus__class_Ouminus @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A = V_B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).
thf(146,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a )
!= ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
thf(147,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a )
!= ( c_HOL_Ouminus__class_Ouminus @ V_y @ T_a ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
thf(148,axiom,
! [T_a: $i,V_l: $i,V_m: $i,V_u: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_l @ V_m @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_m @ V_u @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ V_l @ V_u @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_m ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_l ) @ V_m ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I21_J_0) ).
thf(149,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/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).
thf(150,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/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).
thf(151,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 @ ( c_in @ V_x @ V_A @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_0) ).
thf(152,axiom,
! [T_a: $i,V_l: $i,V_m: $i,V_u: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_l @ V_m @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_m @ V_u @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ V_l @ V_u @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_m ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_l ) @ V_m ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I17_J_0) ).
thf(153,axiom,
! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) )
| ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(154,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/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(155,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/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(156,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/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(157,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 @ ( c_in @ V_k @ V_I @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__absorb_0) ).
thf(158,axiom,
! [T_a: $i,V_A: $i,V_x: $i,V_B: $i,V_I: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ V_A @ V_x ) ) @ V_B ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_I @ T_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_I @ V_A @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).
thf(159,axiom,
! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ~ ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).
thf(160,axiom,
! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).
thf(161,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 @ ( c_in @ V_x @ V_A @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I2_J_0) ).
thf(162,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Diff__eq_0) ).
thf(163,axiom,
! [T_a: $i,V_a: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ T_a ) @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ T_a ) @ V_A ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__insert_0) ).
thf(164,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).
thf(165,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).
thf(166,axiom,
! [V_P: $i,T_a: $i] :
( ( c_Collect @ V_P @ T_a )
= V_P ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__def_0) ).
thf(167,axiom,
! [V_c: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_c @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplI_0) ).
thf(168,axiom,
! [V_c: $i,V_A: $i,T_a: $i] :
( ~ ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplD_0) ).
thf(169,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 @ ( c_in @ V_x @ V_B @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
thf(170,axiom,
! [T_b: $i,V_B: $i,V_a: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_b @ tc_bool ) ) @ ( hAPP @ V_B @ V_a ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__upper_0) ).
thf(171,axiom,
! [T_b: $i,V_M: $i,V_i: $i,V_A: $i,T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_b )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_b ) @ ( hAPP @ V_M @ V_i ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_M @ T_a @ T_b ) ) )
| ~ ( hBOOL @ ( c_in @ V_i @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SUPI_0) ).
thf(172,axiom,
! [V_f: $i,V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofold1 @ V_f @ V_A @ T_a )
= ( c_The @ ( c_Finite__Set_Ofold1Set @ V_f @ V_A @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1__def_0) ).
thf(173,axiom,
! [T_b: $i,V_f: $i,V_g: $i] :
( ~ ( class_Lattices_Olattice @ T_b )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_f @ V_g @ ( tc_fun @ t_a @ T_b ) ) @ v_x )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ V_f @ v_x ) @ ( hAPP @ V_g @ v_x ) @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
thf(174,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/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(175,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/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(176,axiom,
! [V_A: $i,T_b: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I4_J_0) ).
thf(177,axiom,
! [V_x: $i,V_S: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_x @ V_S @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_S @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(178,axiom,
! [V_S: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_S @ V_x ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_S @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(179,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
thf(180,axiom,
! [T_a: $i,V_xa: $i,V_y: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_xa @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a ) )
| ( V_xa = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(181,axiom,
! [T_a: $i,V_x: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( V_x_H = V_y_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(182,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/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(183,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/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(184,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/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(185,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/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(186,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(187,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(188,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__partition_0) ).
thf(189,axiom,
! [V_a: $i,V_P: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_a @ ( c_Collect @ V_P @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CollectI_0) ).
thf(190,axiom,
! [V_P: $i,V_a: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( hBOOL @ ( c_in @ V_a @ ( c_Collect @ V_P @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CollectD_0) ).
thf(191,axiom,
! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).
thf(192,axiom,
! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).
thf(193,axiom,
! [V_b: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( c_in @ V_b @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_b @ ( hAPP @ V_B @ V_x ) @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__iff_2) ).
thf(194,axiom,
! [V_b: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_a: $i] :
( ( hBOOL @ ( c_in @ V_b @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) )
| ~ ( hBOOL @ ( c_in @ V_b @ ( hAPP @ V_B @ V_a ) @ T_b ) )
| ~ ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__I_0) ).
thf(195,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/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
thf(196,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/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
thf(197,axiom,
! [T_b: $i,V_A: $i,V_B: $i] :
( ~ ( class_HOL_Ominus @ T_b )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ t_a @ T_b ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ V_A @ v_x ) @ ( hAPP @ V_B @ v_x ) @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).
thf(198,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/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
thf(199,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 @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__lower_0) ).
thf(200,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 @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).
thf(201,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/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(202,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/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(203,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(204,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/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(205,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/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(206,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/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(207,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 @ ( c_in @ V_x @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__iff_2) ).
thf(208,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 @ ( c_in @ V_a @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__I_0) ).
thf(209,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 @ ( c_in @ V_x @ V_B @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
thf(210,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
thf(211,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
thf(212,axiom,
! [V_A: $i,T_a: $i] :
( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__complement_0) ).
thf(213,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__minus_0) ).
thf(214,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a ) @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).
thf(215,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( V_b
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).
thf(216,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( V_a
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
thf(217,axiom,
! [T_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a )
= V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
thf(218,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
thf(219,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 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y_H ) @ V_x_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(220,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 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y_H ) @ V_x_H ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(221,axiom,
! [T_a: $i,V_a: $i,V_x: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(222,axiom,
! [T_a: $i,V_b: $i,V_x: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(223,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(224,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(225,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) @ V_z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(226,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) @ V_z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(227,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(228,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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(229,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(230,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
thf(231,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
thf(232,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(233,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(234,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(235,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i,V_d: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_a ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_a @ V_b @ T_a ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_c @ V_d @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_0) ).
thf(236,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_d ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).
thf(237,axiom,
! [T_a: $i,V_b: $i,V_d: $i,V_a: $i,V_c: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_d ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_1) ).
thf(238,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_0) ).
thf(239,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_2) ).
thf(240,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ V_a @ V_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty_0) ).
thf(241,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_1) ).
thf(242,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_0) ).
thf(243,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_1) ).
thf(244,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_0) ).
thf(245,axiom,
! [T_a: $i,V_A: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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 ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).
thf(246,axiom,
! [T_a: $i,V_A: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).
thf(247,axiom,
! [T_a: $i,V_A: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).
thf(248,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).
thf(249,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/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).
thf(250,axiom,
! [T_a: $i,V_A: $i,V_B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
thf(251,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(252,axiom,
! [T_a: $i,V_A: $i,V_B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(253,axiom,
! [T_a: $i,V_B: $i,V_A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(254,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(255,axiom,
! [T_a: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__anti__mono_0) ).
thf(256,axiom,
! [T_a: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_0) ).
thf(257,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_1) ).
thf(258,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_C: $i,V_D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_D ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
thf(259,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(260,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(261,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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(262,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_C: $i,V_D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(263,axiom,
! [T_a: $i,V_A: $i,V_C: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(264,axiom,
! [T_a: $i,V_B: $i,V_C: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(265,axiom,
! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(266,axiom,
! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(267,axiom,
! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(268,axiom,
! [V_t: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_t @ V_B @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_t @ V_A @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(269,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).
thf(270,axiom,
! [V_a: $i,V_A: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
= V_A )
| ~ ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(271,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 @ ( c_in @ V_x @ V_B @ T_a ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ( V_A = V_B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(272,axiom,
! [V_x: $i,V_B: $i,T_a: $i] : ( hBOOL @ ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(273,axiom,
! [V_a: $i,V_B: $i,T_a: $i] : ( hBOOL @ ( c_in @ V_a @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(274,axiom,
! [V_x: $i,V_A: $i,T_a: $i] : ( hBOOL @ ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(275,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/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(276,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/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(277,axiom,
! [V_a: $i,V_A: $i,T_a: $i,V_b: $i] :
( ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) )
| ( V_a = V_b )
| ~ ( hBOOL @ ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(278,axiom,
! [V_Sup: $i,V_a: $i,V_A: $i,T_a: $i,V_sup: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) )
= ( hAPP @ ( hAPP @ V_sup @ V_a ) @ ( hAPP @ V_Sup @ V_A ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__insert_0) ).
thf(279,axiom,
! [V_Inf: $i,V_a: $i,V_A: $i,T_a: $i,V_inf: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) )
= ( hAPP @ ( hAPP @ V_inf @ V_a ) @ ( hAPP @ V_Inf @ V_A ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).
thf(280,axiom,
! [V_a: $i,V_b: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_a @ V_B @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(281,axiom,
! [V_a: $i,V_b: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(282,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 @ ( c_in @ V_x @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
thf(283,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ T_a ) @ ( 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_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__binary_0) ).
thf(284,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 @ ( c_in @ V_a @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
thf(285,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/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(286,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/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(287,axiom,
! [V_P: $i,V_x: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(288,axiom,
! [V_A: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
thf(289,axiom,
! [V_A: $i,T_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
thf(290,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/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(291,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/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(292,axiom,
! [T_a: $i,V_A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
thf(293,axiom,
! [V_f: $i,T_a: $i,V_x: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__fold1SetE_0) ).
thf(294,axiom,
! [V_P: $i,T_a: $i,V_x: $i] :
( ( ( c_Collect @ V_P @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).
thf(295,axiom,
! [V_a: $i,T_a: $i] :
~ ( hBOOL @ ( c_in @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(296,axiom,
! [V_c: $i,T_a: $i] :
~ ( hBOOL @ ( c_in @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(297,axiom,
! [V_P: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(298,axiom,
! [V_x: $i,T_a: $i] :
~ ( hBOOL @ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(299,axiom,
! [T_a: $i,V_P: $i,V_x: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Collect @ V_P @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Collect__eq_0) ).
thf(300,axiom,
! [V_Sup: $i,T_a: $i,V_bot: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_top: $i] :
( ( ( hAPP @ V_Sup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_bot )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).
thf(301,axiom,
! [V_Inf: $i,T_a: $i,V_top: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_bot: $i] :
( ( ( hAPP @ V_Inf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_top )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_OInf__empty_0) ).
thf(302,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/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(303,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/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(304,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/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(305,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/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(306,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/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(307,axiom,
! [T_a: $i,V_l: $i,V_u: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_l @ V_u @ T_a ) @ ( c_Set_Oinsert @ V_u @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ V_l @ V_u @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_l ) @ V_u ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I6_J_0) ).
thf(308,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) ) @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
thf(309,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
thf(310,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
thf(311,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
thf(312,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(313,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(314,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(315,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_z ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(316,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_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( 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 @ ( c_in @ V_x @ V_B @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_5) ).
thf(317,axiom,
! [T_a: $i,V_l: $i,V_u: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ V_l @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_l @ V_u @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ V_l @ V_u @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_l ) @ V_u ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I5_J_0) ).
thf(318,axiom,
! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( 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 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_COMBK @ ( hAPP @ ( c_COMBC @ ( c_fequal @ tc_Com_Ostate ) @ tc_Com_Ostate @ tc_Com_Ostate @ tc_bool ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ V_G @ V_P @ V_Q @ V_c ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) @ V_c @ ( c_COMBK @ ( hAPP @ V_Q @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ V_G @ V_P @ V_Q @ V_c ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) @ 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/sandbox/benchmark/theBenchmark.p',cls_escape_1) ).
thf(319,axiom,
! [T_a: $i,V_M: $i,V_N: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Finite__Set_Olinorder__class_OMax @ V_M @ T_a ) ) @ ( c_Finite__Set_Olinorder__class_OMax @ V_N @ T_a ) ) )
| ~ ( c_Finite__Set_Ofinite @ V_N @ T_a )
| ( V_M
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_M ) @ V_N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__mono_0) ).
thf(320,axiom,
! [T_a: $i,V_N: $i,V_M: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Finite__Set_Olinorder__class_OMin @ V_N @ T_a ) ) @ ( c_Finite__Set_Olinorder__class_OMin @ V_M @ T_a ) ) )
| ~ ( c_Finite__Set_Ofinite @ V_N @ T_a )
| ( V_M
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_M ) @ V_N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__antimono_0) ).
thf(321,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_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_9) ).
thf(322,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 @ ( c_in @ V_x @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I2_J_0) ).
thf(323,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 @ ( c_in @ V_x @ V_A @ T_a ) )
| ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_1) ).
thf(324,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 @ ( c_in @ V_x @ V_A @ T_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 @ ( c_in @ V_x @ V_B @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_4) ).
thf(325,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_8) ).
thf(326,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 @ ( c_in @ V_a @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1__nat_1) ).
thf(327,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 @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_y @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff1__fold__graph_0) ).
thf(328,axiom,
! [V_f: $i,V_a: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ V_f @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a ) @ V_x ) )
| ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) )
| ~ ( c_Finite__Set_Ofold__graph @ V_f @ V_a @ V_A @ V_x @ T_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold1Set_Ointros_0) ).
thf(329,axiom,
! [T_a: $i,V_A: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMax @ V_A @ T_a ) @ V_A @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__in_0) ).
thf(330,axiom,
! [T_a: $i,V_A: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMin @ V_A @ T_a ) @ V_A @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__in_0) ).
thf(331,axiom,
! [T_a: $i,V_A: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Finite__Set_Olinorder__class_OMin @ V_A @ T_a ) ) @ V_x ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__le_0) ).
thf(332,axiom,
! [T_a: $i,V_x: $i,V_A: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ ( c_Finite__Set_Olinorder__class_OMax @ V_A @ T_a ) ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__ge_0) ).
thf(333,axiom,
( ~ ( class_HOL_Ouminus @ t_b )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ v_A @ ( tc_fun @ t_a @ t_b ) ) @ v_x )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ v_A @ v_x ) @ t_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__Compl__def__raw_0) ).
thf(334,axiom,
! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( c_Complete__Lattice_Ocomplete__lattice__axioms @ ( c_Complete__Lattice_OInf__class_OInf @ T_a ) @ ( c_Complete__Lattice_OSup__class_OSup @ T_a ) @ ( c_lessequals @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice__class_Oaxioms_0) ).
thf(335,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ V_a @ V_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_0) ).
thf(336,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ V_a @ V_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_1) ).
thf(337,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastLessThan @ V_a @ V_b @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_0) ).
thf(338,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ V_a @ V_b @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_1) ).
thf(339,axiom,
! [V_A: $i,V_a: $i,V_B: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).
thf(340,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).
thf(341,axiom,
! [V_A: $i,T_a: $i,T_b: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__empty2_0) ).
thf(342,axiom,
! [V_A: $i,V_c: $i,T_a: $i,T_b: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ ( c_COMBK @ V_c @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= V_c )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__constant_1) ).
thf(343,axiom,
! [T_b: $i,V_c: $i,T_a: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ ( c_COMBK @ V_c @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__constant_0) ).
thf(344,axiom,
! [T_b: $i,V_A: $i,V_M: $i,T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_b )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ ( c_COMBK @ V_M @ T_b @ T_a ) @ T_a @ T_b )
= V_M )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP__const_0) ).
thf(345,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty_0) ).
thf(346,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 @ ( c_in @ V_a @ V_A @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1_1) ).
thf(347,axiom,
! [V_B: $i,V_x: $i,T_b: $i,V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ V_B @ V_x ) @ T_b )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UN_0) ).
thf(348,axiom,
! [T_a: $i,V_l: $i,V_m: $i,V_u: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_l @ V_m @ T_a ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_m @ V_u @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_l @ V_u @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_m ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_l ) @ V_m ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I20_J_0) ).
thf(349,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_d ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_4) ).
thf(350,axiom,
! [T_a: $i,V_c: $i,V_d: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_d ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_3) ).
thf(351,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_0) ).
thf(352,axiom,
! [T_a: $i,V_b: $i,V_d: $i,V_a: $i,V_c: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_d ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_1) ).
thf(353,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 @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_6) ).
thf(354,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 @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).
thf(355,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 @ ( c_in @ V_x @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OinsertI_0) ).
thf(356,axiom,
! [T_a: $i,V_k: $i,V_l: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_k @ V_l @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_l ) @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty_0) ).
thf(357,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 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff_0) ).
thf(358,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(359,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(360,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(361,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(362,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(363,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(364,axiom,
! [T_a: $i,V_k: $i,V_l: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_k @ V_l @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff2_0) ).
thf(365,axiom,
! [T_a: $i,V_k: $i,V_l: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_k @ V_l @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_k @ V_l @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff2_1) ).
thf(366,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(367,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(368,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(369,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(370,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(371,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_d ) )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_d ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_5) ).
thf(372,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_d ) )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_d @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_d ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_6) ).
thf(373,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(374,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(375,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(376,axiom,
! [V_x: $i,T_a: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_1) ).
thf(377,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
thf(378,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
thf(379,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/sandbox/benchmark/theBenchmark.p',cls_finite__Un_1) ).
thf(380,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/sandbox/benchmark/theBenchmark.p',cls_finite__Un_0) ).
thf(381,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/sandbox/benchmark/theBenchmark.p',cls_finite__UnI_0) ).
thf(382,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/sandbox/benchmark/theBenchmark.p',cls_finite__Un_2) ).
thf(383,axiom,
! [T_a: $i,V_a: $i] :
( ( c_The @ ( hAPP @ ( c_COMBC @ ( c_fequal @ T_a ) @ T_a @ T_a @ tc_bool ) @ V_a ) @ T_a )
= V_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__eq__trivial_0) ).
thf(384,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_1) ).
thf(385,axiom,
! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).
thf(386,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff_0) ).
thf(387,axiom,
! [T_a: $i,V_k: $i,V_l: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_k @ V_l @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff_0) ).
thf(388,axiom,
! [T_a: $i,V_k: $i,V_l: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_k @ V_l @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_HOL_Oord__class_Oless @ V_k @ V_l @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff_1) ).
thf(389,axiom,
! [V_A: $i,T_a: $i,V_f: $i,V_z: $i,V_x: $i,T_b: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ V_A @ V_x @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph__imp__finite_0) ).
thf(390,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(391,axiom,
! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__trans_0) ).
thf(392,axiom,
! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubsetD_0) ).
thf(393,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(394,axiom,
! [V_P: $i,T_b: $i,T_c: $i,T_a: $i,V_Q: $i,V_R: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ V_P @ T_b @ T_c @ T_a ) @ V_Q ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(395,axiom,
! [V_P: $i,T_a: $i,T_b: $i,V_Q: $i] :
( ( hAPP @ ( c_COMBK @ V_P @ T_a @ T_b ) @ V_Q )
= V_P ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(396,axiom,
! [V_Sup: $i,V_Inf: $i,V_less__eq: $i,T_a: $i,V_less: $i,V_sup: $i,V_inf: $i,V_top: $i,V_bot: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ V_Sup @ V_Inf @ ( c_COMBC @ V_less__eq @ T_a @ T_a @ tc_bool ) @ ( c_COMBC @ V_less @ T_a @ T_a @ tc_bool ) @ V_sup @ V_inf @ V_top @ V_bot @ T_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice_Odual__complete__lattice_0) ).
thf(397,axiom,
! [T_a: $i,V_b: $i,V_d: $i,V_c: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_d @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_2) ).
thf(398,axiom,
! [T_a: $i,V_A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ T_a )
| ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).
thf(399,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/sandbox/benchmark/theBenchmark.p',cls_less__supI1_0) ).
thf(400,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/sandbox/benchmark/theBenchmark.p',cls_less__supI2_0) ).
thf(401,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
thf(402,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
thf(403,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).
thf(404,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
thf(405,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(406,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(407,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(408,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(409,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(410,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(411,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(412,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(413,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_z ) )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(414,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(415,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(416,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_z ) @ V_y ) )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(417,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(418,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(419,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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(420,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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(421,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_x ) )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(422,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(423,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(424,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(425,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(426,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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(427,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(428,axiom,
! [V_A: $i,T_a: $i] :
~ ( c_HOL_Oord__class_Oless @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).
thf(429,axiom,
! [T_a: $i] : ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
thf(430,axiom,
! [V_x: $i,V_z: $i,V_f: $i,T_a: $i,T_b: $i] :
( ( V_x = V_z )
| ~ ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x @ T_a @ T_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__fold__graphE_0) ).
thf(431,axiom,
! [V_f: $i,V_z: $i,T_a: $i,T_b: $i] : ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_z @ T_a @ T_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OemptyI_0) ).
thf(432,axiom,
! [V_f: $i,V_z: $i,T_a: $i,T_b: $i] : ( c_Nitpick_Ofold__graph_H @ V_f @ V_z @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_z @ T_a @ T_b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I1_J_0) ).
thf(433,axiom,
! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).
thf(434,axiom,
! [V_A: $i,T_a: $i,V_a: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).
thf(435,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/sandbox/benchmark/theBenchmark.p',cls_insert__def_0) ).
thf(436,axiom,
! [T_a: $i,V_a: $i] :
( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ T_a ) @ T_a @ T_a @ tc_bool ) @ V_a ) @ T_a )
= ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__conv_0) ).
thf(437,axiom,
! [T_a: $i,V_l: $i,V_m: $i,V_u: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_l @ V_m @ T_a ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_m @ V_u @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ V_l @ V_u @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_m ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_l ) @ V_m ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I22_J_0) ).
thf(438,axiom,
! [T_a: $i,V_A: $i,V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).
thf(439,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_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).
thf(440,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_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_7) ).
thf(441,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 @ ( c_in @ V_a @ V_A @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1_0) ).
thf(442,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 @ ( c_in @ V_a @ V_A @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1__ring_0) ).
thf(443,axiom,
! [T_a: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_0) ).
thf(444,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset_0) ).
thf(445,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 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).
thf(446,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 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__psubset__trans_0) ).
thf(447,axiom,
! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
thf(448,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_2) ).
thf(449,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 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff__psubset__eq_0) ).
thf(450,axiom,
! [T_b: $i,T_a: $i,V_g: $i,V_f: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ T_b ) ) @ V_g ) @ V_f ) )
| ~ ( c_HOL_Oord__class_Oless @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_1) ).
thf(451,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 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ T_b ) ) @ V_g ) @ V_f ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ T_b ) ) @ V_f ) @ V_g ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_2) ).
thf(452,axiom,
! [T_b: $i,T_a: $i,V_f: $i,V_g: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ T_b ) ) @ V_f ) @ V_g ) )
| ~ ( c_HOL_Oord__class_Oless @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_0) ).
thf(453,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(454,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[453]) ).
thf(455,negated_conjecture,
~ ( c_Hoare__Mirabelle_Ohoare__derivs @ v_Ga @ ( 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/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(456,negated_conjecture,
hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ v_G ) @ v_Ga ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(457,plain,
$false = $false,
inference(unfold_def,[status(thm)],[454]) ).
thf(458,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(459,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(460,plain,
( ( class_HOL_Oord @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(461,plain,
( ( class_HOL_Ominus @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(462,plain,
( ( class_HOL_Ouminus @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(463,plain,
( ( class_Orderings_Obot @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(464,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(465,plain,
( ( class_Lattices_Olattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(466,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(467,plain,
( ( class_Finite__Set_Ofinite_Ofinite @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(468,plain,
( ( class_Lattices_Oboolean__algebra @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(469,plain,
( ( class_Lattices_Obounded__lattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(470,plain,
( ( class_Lattices_Oupper__semilattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(471,plain,
( ( class_Complete__Lattice_Ocomplete__lattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(472,plain,
( ( class_HOL_Oord @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(473,plain,
( ( class_HOL_Ominus @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(474,plain,
( ( class_Orderings_Obot @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(475,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(476,plain,
( ( class_Lattices_Olattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(477,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(478,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(479,plain,
( ( class_Lattices_Oupper__semilattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(480,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)],[23]) ).
thf(481,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_HOL_Ominus @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_HOL_Ominus @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(482,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_HOL_Ouminus @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_HOL_Ouminus @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(483,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)],[26]) ).
thf(484,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)],[27]) ).
thf(485,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)],[28]) ).
thf(486,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)],[29]) ).
thf(487,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)],[30]) ).
thf(488,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Oboolean__algebra @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(489,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)],[32]) ).
thf(490,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(491,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(492,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i,V_g: $i,T_a: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_b ) @ ( hAPP @ V_f @ V_x ) ) @ ( hAPP @ V_g @ V_x ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ T_b ) ) @ V_f ) @ V_g ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(493,plain,
( ( ! [V_G: $i,V_ts: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ V_ts ) @ V_G ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(494,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)],[37]) ).
thf(495,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)],[38]) ).
thf(496,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)],[39]) ).
thf(497,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)],[40]) ).
thf(498,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(499,plain,
( ( ! [T_a: $i,V_A: $i,V_b: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(500,plain,
( ( ! [T_a: $i,V_A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(501,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Obot @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Orderings_Obot__class_Obot @ T_a ) ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(502,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)],[45]) ).
thf(503,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)],[46]) ).
thf(504,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)],[47]) ).
thf(505,plain,
( ( ! [T_a: $i,V_B: $i,V_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(506,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)],[49]) ).
thf(507,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)],[50]) ).
thf(508,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(509,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(510,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(511,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(512,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(513,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)],[56]) ).
thf(514,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)],[57]) ).
thf(515,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)],[58]) ).
thf(516,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)],[59]) ).
thf(517,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)],[60]) ).
thf(518,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)],[61]) ).
thf(519,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)],[62]) ).
thf(520,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( 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)],[63]) ).
thf(521,plain,
( ( ! [T_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(522,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)],[65]) ).
thf(523,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)],[66]) ).
thf(524,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)],[67]) ).
thf(525,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)],[68]) ).
thf(526,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_z ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_z ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(527,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(528,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(529,plain,
( ( ! [T_a: $i,V_A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(530,plain,
( ( ! [T_a: $i,V_A: $i,V_C: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(531,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 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_P ) @ V_Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(532,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(533,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(534,plain,
( ( ! [V_Q: $i,V_x: $i,T_a: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_P ) @ V_Q ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(535,plain,
( ( ! [V_G: $i,V_ts: $i,T_a: $i,V_ts_H: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ V_ts ) @ V_ts_H ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts_H @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(536,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(537,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)],[80]) ).
thf(538,plain,
( ( ! [T_a: $i,V_a: $i,V_C: $i,V_D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ V_C @ T_a ) ) @ ( c_Set_Oinsert @ V_a @ V_D @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(539,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(540,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)],[83]) ).
thf(541,plain,
( ( ! [T_a: $i,V_A: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(542,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ V_G @ V_P @ V_Q @ V_c ) ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ V_G @ V_P @ V_Q @ V_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(543,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_Q_H: $i] :
( ( 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_Q @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ V_Q @ V_Q_H ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ V_Q @ V_Q_H ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ V_c @ V_Q_H @ 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)],[86]) ).
thf(544,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_P_H: $i,V_Q_H: $i] :
( ( 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_Q @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ V_P @ V_P_H @ V_Q @ V_Q_H ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ V_P @ V_P_H @ V_Q @ V_Q_H ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P_H @ V_c @ V_Q_H @ 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)],[87]) ).
thf(545,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_P_H: $i] :
( ( 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_H @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ V_P @ V_P_H ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ V_P @ V_P_H ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P_H @ 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)],[88]) ).
thf(546,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_x: $i,V_xa: $i] :
( ( 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_Q @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ V_G @ V_P @ V_Q @ V_c ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ V_G @ V_P @ V_Q @ V_c @ V_x @ V_xa ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_x @ V_c @ V_xa @ 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)],[89]) ).
thf(547,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_P_H: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ V_P @ V_P_H ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ V_P @ V_P_H ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P_H @ 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)],[90]) ).
thf(548,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_P_H: $i,V_Q_H: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ V_P @ V_P_H @ V_Q @ V_Q_H ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ V_P @ V_P_H @ V_Q @ V_Q_H ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P_H @ V_c @ V_Q_H @ 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)],[91]) ).
thf(549,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_Q_H: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_H @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ V_Q @ V_Q_H ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ V_Q @ V_Q_H ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ V_c @ V_Q_H @ 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)],[92]) ).
thf(550,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ V_G @ V_P @ V_Q @ V_c ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ V_G @ V_P @ V_Q @ V_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(551,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_x: $i,V_xa: $i] :
( ( 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_Q @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ V_G @ V_P @ V_Q @ V_c ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ V_G @ V_P @ V_Q @ V_c @ V_x @ V_xa ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_x @ V_c @ V_xa @ 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)],[94]) ).
thf(552,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ V_G @ V_P @ V_Q @ V_c ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ V_G @ V_P @ V_Q @ V_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(553,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_xa: $i,V_Z_H: $i,V_x: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_xa @ V_Z_H ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ V_G @ V_P @ V_Q @ V_c @ V_x @ V_xa ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_x @ V_Z_H ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ V_G @ V_P @ V_Q @ V_c ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_x @ V_c @ V_xa @ 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)],[96]) ).
thf(554,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_Q_H: $i,V_Z_H: $i,V_P_H: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_H @ V_Z_H ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ V_P @ V_P_H @ V_Q @ V_Q_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_H @ V_Z_H ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ V_P @ V_P_H @ V_Q @ V_Q_H ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P_H @ V_c @ V_Q_H @ 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)],[97]) ).
thf(555,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_xa: $i,V_Z_H: $i,V_x: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_xa @ V_Z_H ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ V_G @ V_P @ V_Q @ V_c @ V_x @ V_xa ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_x @ V_Z_H ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ V_G @ V_P @ V_Q @ V_c ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_x @ V_c @ V_xa @ 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)],[98]) ).
thf(556,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(557,plain,
( ( ! [T_a: $i,V_A: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(558,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(559,plain,
( ( ! [T_a: $i,V_A: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(560,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(561,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(562,plain,
( ( ! [T_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(563,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(564,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ T_a ) @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(565,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)],[108]) ).
thf(566,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 @ ( c_in @ V_x @ V_xa @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(567,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ V_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)],[110]) ).
thf(568,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)],[111]) ).
thf(569,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(570,plain,
( ( ! [V_f: $i,V_a: $i,T_a: $i] :
( ( c_Finite__Set_Ofold1 @ V_f @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_a ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(571,plain,
( ( ! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_b = V_a )
| ~ ( hBOOL @ ( c_in @ V_b @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(572,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( V_y
= ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(573,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_Set_Ocontents @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(574,plain,
( ( ! [V_a: $i,V_b: $i,V_f: $i,T_a: $i] :
( ( V_a = V_b )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ V_f @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(575,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)],[118]) ).
thf(576,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)],[119]) ).
thf(577,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)],[120]) ).
thf(578,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)],[121]) ).
thf(579,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_The @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(580,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(581,plain,
( ( ! [V_f: $i,V_x: $i,T_a: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ V_f @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(582,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)],[125]) ).
thf(583,plain,
( ( ! [V_x: $i,T_a: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(584,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ T_a ) @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(585,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)],[128]) ).
thf(586,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)],[129]) ).
thf(587,plain,
( ( ! [V_x: $i,T_a: $i] : ( hBOOL @ ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(588,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)],[131]) ).
thf(589,plain,
( ( ! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(590,plain,
( ( ! [T_b: $i] :
( ~ ( class_Orderings_Obot @ T_b )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ T_b ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(591,plain,
( ( ! [T_a: $i,V_b: $i,V_d: $i,V_a: $i,V_c: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_d ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_a @ V_b @ T_a ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_c @ V_d @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(592,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ T_a ) @ V_A ) ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(593,plain,
( ( ! [T_a: $i,V_x: $i] :
( ( c_The @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ T_a )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(594,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)],[137]) ).
thf(595,plain,
( ( ! [T_a: $i,V_i: $i,V_m: $i,V_n: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_i @ V_m @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_i @ V_n @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ V_n @ V_m @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_i ) @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(596,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(597,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(598,plain,
( ( ! [T_b: $i,V_A: $i] :
( ~ ( class_HOL_Ouminus @ T_b )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ t_a @ T_b ) ) @ v_x )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ V_A @ v_x ) @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(599,plain,
( ( ! [T_a: $i,V_A: $i,V_x: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ T_a ) @ V_A ) ) @ V_x ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(600,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)],[143]) ).
thf(601,plain,
( ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( c_in @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(602,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_HOL_Ouminus__class_Ouminus @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A = V_B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(603,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a )
!= ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(604,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a )
!= ( c_HOL_Ouminus__class_Ouminus @ V_y @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(605,plain,
( ( ! [T_a: $i,V_l: $i,V_m: $i,V_u: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_l @ V_m @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_m @ V_u @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ V_l @ V_u @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_m ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_l ) @ V_m ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(606,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)],[149]) ).
thf(607,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)],[150]) ).
thf(608,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 @ ( c_in @ V_x @ V_A @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(609,plain,
( ( ! [T_a: $i,V_l: $i,V_m: $i,V_u: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_l @ V_m @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_m @ V_u @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ V_l @ V_u @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_m ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_l ) @ V_m ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(610,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) )
| ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(611,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)],[154]) ).
thf(612,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)],[155]) ).
thf(613,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)],[156]) ).
thf(614,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 @ ( c_in @ V_k @ V_I @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(615,plain,
( ( ! [T_a: $i,V_A: $i,V_x: $i,V_B: $i,V_I: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ V_A @ V_x ) ) @ V_B ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_I @ T_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_I @ V_A @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(616,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ~ ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(617,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(618,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 @ ( c_in @ V_x @ V_A @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(619,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(620,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ T_a ) @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ T_a ) @ V_A ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(621,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)],[164]) ).
thf(622,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)],[165]) ).
thf(623,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( c_Collect @ V_P @ T_a )
= V_P ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(624,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_c @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(625,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ~ ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(626,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 @ ( c_in @ V_x @ V_B @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(627,plain,
( ( ! [T_b: $i,V_B: $i,V_a: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_b @ tc_bool ) ) @ ( hAPP @ V_B @ V_a ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(628,plain,
( ( ! [T_b: $i,V_M: $i,V_i: $i,V_A: $i,T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_b )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_b ) @ ( hAPP @ V_M @ V_i ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_M @ T_a @ T_b ) ) )
| ~ ( hBOOL @ ( c_in @ V_i @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(629,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofold1 @ V_f @ V_A @ T_a )
= ( c_The @ ( c_Finite__Set_Ofold1Set @ V_f @ V_A @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(630,plain,
( ( ! [T_b: $i,V_f: $i,V_g: $i] :
( ~ ( class_Lattices_Olattice @ T_b )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_f @ V_g @ ( tc_fun @ t_a @ T_b ) ) @ v_x )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ V_f @ v_x ) @ ( hAPP @ V_g @ v_x ) @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(631,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)],[174]) ).
thf(632,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)],[175]) ).
thf(633,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)],[176]) ).
thf(634,plain,
( ( ! [V_x: $i,V_S: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_x @ V_S @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_S @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(635,plain,
( ( ! [V_S: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_S @ V_x ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_S @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(636,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)],[179]) ).
thf(637,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)],[180]) ).
thf(638,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)],[181]) ).
thf(639,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)],[182]) ).
thf(640,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)],[183]) ).
thf(641,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)],[184]) ).
thf(642,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)],[185]) ).
thf(643,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)],[186]) ).
thf(644,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)],[187]) ).
thf(645,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(646,plain,
( ( ! [V_a: $i,V_P: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_a @ ( c_Collect @ V_P @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(647,plain,
( ( ! [V_P: $i,V_a: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( hBOOL @ ( c_in @ V_a @ ( c_Collect @ V_P @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(648,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(649,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(650,plain,
( ( ! [V_b: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( c_in @ V_b @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_b @ ( hAPP @ V_B @ V_x ) @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(651,plain,
( ( ! [V_b: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_a: $i] :
( ( hBOOL @ ( c_in @ V_b @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) )
| ~ ( hBOOL @ ( c_in @ V_b @ ( hAPP @ V_B @ V_a ) @ T_b ) )
| ~ ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(652,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)],[195]) ).
thf(653,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)],[196]) ).
thf(654,plain,
( ( ! [T_b: $i,V_A: $i,V_B: $i] :
( ~ ( class_HOL_Ominus @ T_b )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ t_a @ T_b ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ V_A @ v_x ) @ ( hAPP @ V_B @ v_x ) @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(655,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)],[198]) ).
thf(656,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 @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(657,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 @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(658,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)],[201]) ).
thf(659,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)],[202]) ).
thf(660,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)],[203]) ).
thf(661,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)],[204]) ).
thf(662,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)],[205]) ).
thf(663,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)],[206]) ).
thf(664,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 @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(665,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 @ ( c_in @ V_a @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(666,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 @ ( c_in @ V_x @ V_B @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(667,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(668,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(669,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(670,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(671,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(672,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( V_b
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(673,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( V_a
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(674,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a )
= V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(675,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(676,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 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y_H ) @ V_x_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(677,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 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y_H ) @ V_x_H ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(678,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(679,plain,
( ( ! [T_a: $i,V_b: $i,V_x: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(680,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(681,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(682,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) @ V_z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(683,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) @ V_z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(684,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(685,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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(686,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(687,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(688,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(689,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(690,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(691,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(692,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i,V_d: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_a ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_a @ V_b @ T_a ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_c @ V_d @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(693,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_d ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(694,plain,
( ( ! [T_a: $i,V_b: $i,V_d: $i,V_a: $i,V_c: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_d ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(695,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(696,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(697,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ V_a @ V_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(698,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(699,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(700,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(701,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(702,plain,
( ( ! [T_a: $i,V_A: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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 ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(703,plain,
( ( ! [T_a: $i,V_A: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(704,plain,
( ( ! [T_a: $i,V_A: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(705,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)],[248]) ).
thf(706,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)],[249]) ).
thf(707,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( 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)],[250]) ).
thf(708,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(709,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(710,plain,
( ( ! [T_a: $i,V_B: $i,V_A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(711,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(712,plain,
( ( ! [T_a: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(713,plain,
( ( ! [T_a: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(714,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(715,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i,V_D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_D ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(716,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(717,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(718,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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(719,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i,V_D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(720,plain,
( ( ! [T_a: $i,V_A: $i,V_C: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(721,plain,
( ( ! [T_a: $i,V_B: $i,V_C: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(722,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(723,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(724,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(725,plain,
( ( ! [V_t: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_t @ V_B @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_t @ V_A @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(726,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(727,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
= V_A )
| ~ ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(728,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 @ ( c_in @ V_x @ V_B @ T_a ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ( V_A = V_B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(729,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] : ( hBOOL @ ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(730,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i] : ( hBOOL @ ( c_in @ V_a @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(731,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] : ( hBOOL @ ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(732,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)],[275]) ).
thf(733,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)],[276]) ).
thf(734,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i] :
( ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) )
| ( V_a = V_b )
| ~ ( hBOOL @ ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(735,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)],[278]) ).
thf(736,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)],[279]) ).
thf(737,plain,
( ( ! [V_a: $i,V_b: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_a @ V_B @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(738,plain,
( ( ! [V_a: $i,V_b: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(739,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 @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(740,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ T_a ) @ ( 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_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(741,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 @ ( c_in @ V_a @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(742,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)],[285]) ).
thf(743,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)],[286]) ).
thf(744,plain,
( ( ! [V_P: $i,V_x: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(745,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)],[288]) ).
thf(746,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)],[289]) ).
thf(747,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)],[290]) ).
thf(748,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)],[291]) ).
thf(749,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)],[292]) ).
thf(750,plain,
( ( ! [V_f: $i,T_a: $i,V_x: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(751,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)],[294]) ).
thf(752,plain,
( ( ! [V_a: $i,T_a: $i] :
~ ( hBOOL @ ( c_in @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(753,plain,
( ( ! [V_c: $i,T_a: $i] :
~ ( hBOOL @ ( c_in @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(754,plain,
( ( ! [V_P: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(755,plain,
( ( ! [V_x: $i,T_a: $i] :
~ ( hBOOL @ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(756,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)],[299]) ).
thf(757,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)],[300]) ).
thf(758,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)],[301]) ).
thf(759,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)],[302]) ).
thf(760,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)],[303]) ).
thf(761,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)],[304]) ).
thf(762,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)],[305]) ).
thf(763,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)],[306]) ).
thf(764,plain,
( ( ! [T_a: $i,V_l: $i,V_u: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_l @ V_u @ T_a ) @ ( c_Set_Oinsert @ V_u @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ V_l @ V_u @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_l ) @ V_u ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(765,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(766,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(767,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(768,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(769,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(770,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(771,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(772,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_z ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(773,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_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( 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 @ ( c_in @ V_x @ V_B @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(774,plain,
( ( ! [T_a: $i,V_l: $i,V_u: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ V_l @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_l @ V_u @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ V_l @ V_u @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_l ) @ V_u ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(775,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( 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 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_COMBK @ ( hAPP @ ( c_COMBC @ ( c_fequal @ tc_Com_Ostate ) @ tc_Com_Ostate @ tc_Com_Ostate @ tc_bool ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ V_G @ V_P @ V_Q @ V_c ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) @ V_c @ ( c_COMBK @ ( hAPP @ V_Q @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ V_G @ V_P @ V_Q @ V_c ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) @ 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)],[318]) ).
thf(776,plain,
( ( ! [T_a: $i,V_M: $i,V_N: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Finite__Set_Olinorder__class_OMax @ V_M @ T_a ) ) @ ( c_Finite__Set_Olinorder__class_OMax @ V_N @ T_a ) ) )
| ~ ( c_Finite__Set_Ofinite @ V_N @ T_a )
| ( V_M
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_M ) @ V_N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(777,plain,
( ( ! [T_a: $i,V_N: $i,V_M: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Finite__Set_Olinorder__class_OMin @ V_N @ T_a ) ) @ ( c_Finite__Set_Olinorder__class_OMin @ V_M @ T_a ) ) )
| ~ ( c_Finite__Set_Ofinite @ V_N @ T_a )
| ( V_M
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_M ) @ V_N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(778,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_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( 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)],[321]) ).
thf(779,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 @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(780,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 @ ( c_in @ V_x @ V_A @ T_a ) )
| ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( 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)],[323]) ).
thf(781,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 @ ( c_in @ V_x @ V_A @ T_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 @ ( c_in @ V_x @ V_B @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(782,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 @ ( c_in @ V_x @ V_A @ T_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)],[325]) ).
thf(783,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 @ ( c_in @ V_a @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(784,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 @ ( c_in @ V_x @ V_A @ T_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)],[327]) ).
thf(785,plain,
( ( ! [V_f: $i,V_a: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ V_f @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a ) @ V_x ) )
| ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) )
| ~ ( c_Finite__Set_Ofold__graph @ V_f @ V_a @ V_A @ V_x @ T_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(786,plain,
( ( ! [T_a: $i,V_A: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMax @ V_A @ T_a ) @ V_A @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(787,plain,
( ( ! [T_a: $i,V_A: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMin @ V_A @ T_a ) @ V_A @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(788,plain,
( ( ! [T_a: $i,V_A: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Finite__Set_Olinorder__class_OMin @ V_A @ T_a ) ) @ V_x ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(789,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ ( c_Finite__Set_Olinorder__class_OMax @ V_A @ T_a ) ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(790,plain,
( ( ~ ( class_HOL_Ouminus @ t_b )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ v_A @ ( tc_fun @ t_a @ t_b ) ) @ v_x )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ v_A @ v_x ) @ t_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(791,plain,
( ( ! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( c_Complete__Lattice_Ocomplete__lattice__axioms @ ( c_Complete__Lattice_OInf__class_OInf @ T_a ) @ ( c_Complete__Lattice_OSup__class_OSup @ T_a ) @ ( c_lessequals @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(792,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ V_a @ V_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(793,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ V_a @ V_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(794,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastLessThan @ V_a @ V_b @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(795,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ V_a @ V_b @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(796,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)],[339]) ).
thf(797,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)],[340]) ).
thf(798,plain,
( ( ! [V_A: $i,T_a: $i,T_b: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(799,plain,
( ( ! [V_A: $i,V_c: $i,T_a: $i,T_b: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ ( c_COMBK @ V_c @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= V_c )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(800,plain,
( ( ! [T_b: $i,V_c: $i,T_a: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ ( c_COMBK @ V_c @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(801,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)],[344]) ).
thf(802,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(803,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 @ ( c_in @ V_a @ V_A @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(804,plain,
( ( ! [V_B: $i,V_x: $i,T_b: $i,V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ V_B @ V_x ) @ T_b )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_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)],[347]) ).
thf(805,plain,
( ( ! [T_a: $i,V_l: $i,V_m: $i,V_u: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_l @ V_m @ T_a ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_m @ V_u @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_l @ V_u @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_m ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_l ) @ V_m ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(806,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_d ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(807,plain,
( ( ! [T_a: $i,V_c: $i,V_d: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_d ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(808,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(809,plain,
( ( ! [T_a: $i,V_b: $i,V_d: $i,V_a: $i,V_c: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_d ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(810,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 @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(811,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 @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( 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)],[354]) ).
thf(812,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 @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(813,plain,
( ( ! [T_a: $i,V_k: $i,V_l: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_k @ V_l @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_l ) @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(814,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 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(815,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)],[358]) ).
thf(816,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)],[359]) ).
thf(817,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)],[360]) ).
thf(818,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)],[361]) ).
thf(819,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)],[362]) ).
thf(820,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)],[363]) ).
thf(821,plain,
( ( ! [T_a: $i,V_k: $i,V_l: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_k @ V_l @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(822,plain,
( ( ! [T_a: $i,V_k: $i,V_l: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_k @ V_l @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_k @ V_l @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365]) ).
thf(823,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)],[366]) ).
thf(824,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)],[367]) ).
thf(825,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)],[368]) ).
thf(826,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)],[369]) ).
thf(827,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)],[370]) ).
thf(828,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_d ) )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_d ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(829,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_d ) )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_d @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_d ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(830,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)],[373]) ).
thf(831,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)],[374]) ).
thf(832,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)],[375]) ).
thf(833,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)],[376]) ).
thf(834,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(835,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(836,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)],[379]) ).
thf(837,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)],[380]) ).
thf(838,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)],[381]) ).
thf(839,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)],[382]) ).
thf(840,plain,
( ( ! [T_a: $i,V_a: $i] :
( ( c_The @ ( hAPP @ ( c_COMBC @ ( c_fequal @ T_a ) @ T_a @ T_a @ tc_bool ) @ V_a ) @ T_a )
= V_a ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(841,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)],[384]) ).
thf(842,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)],[385]) ).
thf(843,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)],[386]) ).
thf(844,plain,
( ( ! [T_a: $i,V_k: $i,V_l: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_k @ V_l @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(845,plain,
( ( ! [T_a: $i,V_k: $i,V_l: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_k @ V_l @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_HOL_Oord__class_Oless @ V_k @ V_l @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(846,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)],[389]) ).
thf(847,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)],[390]) ).
thf(848,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)],[391]) ).
thf(849,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392]) ).
thf(850,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)],[393]) ).
thf(851,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)],[394]) ).
thf(852,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)],[395]) ).
thf(853,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)],[396]) ).
thf(854,plain,
( ( ! [T_a: $i,V_b: $i,V_d: $i,V_c: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_d @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(855,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)],[398]) ).
thf(856,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)],[399]) ).
thf(857,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)],[400]) ).
thf(858,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401]) ).
thf(859,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(860,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(861,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(862,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405]) ).
thf(863,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406]) ).
thf(864,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407]) ).
thf(865,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[408]) ).
thf(866,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(867,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410]) ).
thf(868,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(869,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412]) ).
thf(870,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_z ) )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(871,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414]) ).
thf(872,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[415]) ).
thf(873,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_z ) @ V_y ) )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416]) ).
thf(874,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417]) ).
thf(875,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418]) ).
thf(876,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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[419]) ).
thf(877,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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(878,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_x ) )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421]) ).
thf(879,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[422]) ).
thf(880,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423]) ).
thf(881,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424]) ).
thf(882,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[425]) ).
thf(883,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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[426]) ).
thf(884,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[427]) ).
thf(885,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)],[428]) ).
thf(886,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)],[429]) ).
thf(887,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)],[430]) ).
thf(888,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)],[431]) ).
thf(889,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)],[432]) ).
thf(890,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)],[433]) ).
thf(891,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)],[434]) ).
thf(892,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)],[435]) ).
thf(893,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)],[436]) ).
thf(894,plain,
( ( ! [T_a: $i,V_l: $i,V_m: $i,V_u: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_l @ V_m @ T_a ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_m @ V_u @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ V_l @ V_u @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_m ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_l ) @ V_m ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(895,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( 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)],[438]) ).
thf(896,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_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(897,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_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(898,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 @ ( c_in @ V_a @ V_A @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441]) ).
thf(899,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 @ ( c_in @ V_a @ V_A @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[442]) ).
thf(900,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(901,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(902,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 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(903,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 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(904,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(905,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(906,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 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(907,plain,
( ( ! [T_b: $i,T_a: $i,V_g: $i,V_f: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ T_b ) ) @ V_g ) @ V_f ) )
| ~ ( c_HOL_Oord__class_Oless @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(908,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 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ T_b ) ) @ V_g ) @ V_f ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ T_b ) ) @ V_f ) @ V_g ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(909,plain,
( ( ! [T_b: $i,T_a: $i,V_f: $i,V_g: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ T_b ) ) @ V_f ) @ V_g ) )
| ~ ( c_HOL_Oord__class_Oless @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452]) ).
thf(910,plain,
( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ v_Ga @ ( 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)],[455]) ).
thf(911,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ v_G ) @ v_Ga ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(912,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[457]) ).
thf(913,plain,
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ v_G ) @ v_Ga ) )
= $true ),
inference(copy,[status(thm)],[911]) ).
thf(914,plain,
( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ v_Ga @ ( 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)],[910]) ).
thf(915,plain,
( ( ! [T_b: $i,T_a: $i,V_f: $i,V_g: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ T_b ) ) @ V_f ) @ V_g ) )
| ~ ( c_HOL_Oord__class_Oless @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[909]) ).
thf(916,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 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ T_b ) ) @ V_g ) @ V_f ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ T_b ) ) @ V_f ) @ V_g ) ) ) )
= $true ),
inference(copy,[status(thm)],[908]) ).
thf(917,plain,
( ( ! [T_b: $i,T_a: $i,V_g: $i,V_f: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ T_b ) ) @ V_g ) @ V_f ) )
| ~ ( c_HOL_Oord__class_Oless @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[907]) ).
thf(918,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 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[906]) ).
thf(919,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[905]) ).
thf(920,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[904]) ).
thf(921,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 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[903]) ).
thf(922,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 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[902]) ).
thf(923,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[901]) ).
thf(924,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[900]) ).
thf(925,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 @ ( c_in @ V_a @ V_A @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[899]) ).
thf(926,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 @ ( c_in @ V_a @ V_A @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[898]) ).
thf(927,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_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[897]) ).
thf(928,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_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[896]) ).
thf(929,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( 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)],[895]) ).
thf(930,plain,
( ( ! [T_a: $i,V_l: $i,V_m: $i,V_u: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_l @ V_m @ T_a ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_m @ V_u @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ V_l @ V_u @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_m ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_l ) @ V_m ) ) ) )
= $true ),
inference(copy,[status(thm)],[894]) ).
thf(931,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)],[893]) ).
thf(932,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)],[892]) ).
thf(933,plain,
( ( ! [V_A: $i,T_a: $i,V_a: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[891]) ).
thf(934,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)],[890]) ).
thf(935,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)],[889]) ).
thf(936,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)],[888]) ).
thf(937,plain,
( ( ! [V_x: $i,V_z: $i,V_f: $i,T_a: $i,T_b: $i] :
( ( V_x = V_z )
| ~ ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[887]) ).
thf(938,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)],[886]) ).
thf(939,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)],[885]) ).
thf(940,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[884]) ).
thf(941,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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[883]) ).
thf(942,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[882]) ).
thf(943,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[881]) ).
thf(944,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[880]) ).
thf(945,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[879]) ).
thf(946,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_x ) )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[878]) ).
thf(947,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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[877]) ).
thf(948,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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[876]) ).
thf(949,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[875]) ).
thf(950,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[874]) ).
thf(951,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_z ) @ V_y ) )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[873]) ).
thf(952,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[872]) ).
thf(953,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[871]) ).
thf(954,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_z ) )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[870]) ).
thf(955,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[869]) ).
thf(956,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[868]) ).
thf(957,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[867]) ).
thf(958,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[866]) ).
thf(959,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[865]) ).
thf(960,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[864]) ).
thf(961,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[863]) ).
thf(962,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[862]) ).
thf(963,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[861]) ).
thf(964,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[860]) ).
thf(965,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[859]) ).
thf(966,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[858]) ).
thf(967,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(copy,[status(thm)],[857]) ).
thf(968,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(copy,[status(thm)],[856]) ).
thf(969,plain,
( ( ! [T_a: $i,V_A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ T_a )
| ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[855]) ).
thf(970,plain,
( ( ! [T_a: $i,V_b: $i,V_d: $i,V_c: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_d @ T_a )
| ( c_HOL_Oord__class_Oless @ V_c @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[854]) ).
thf(971,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)],[853]) ).
thf(972,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)],[852]) ).
thf(973,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)],[851]) ).
thf(974,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[850]) ).
thf(975,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[849]) ).
thf(976,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_HOL_Oord__class_Oless @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[848]) ).
thf(977,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[847]) ).
thf(978,plain,
( ( ! [V_A: $i,T_a: $i,V_f: $i,V_z: $i,V_x: $i,T_b: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofold__graph @ V_f @ V_z @ V_A @ V_x @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[846]) ).
thf(979,plain,
( ( ! [T_a: $i,V_k: $i,V_l: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_k @ V_l @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_HOL_Oord__class_Oless @ V_k @ V_l @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[845]) ).
thf(980,plain,
( ( ! [T_a: $i,V_k: $i,V_l: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_k @ V_l @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[844]) ).
thf(981,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)],[843]) ).
thf(982,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] :
( ( c_Finite__Set_Ofinite @ V_A @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ V_B @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[842]) ).
thf(983,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)],[841]) ).
thf(984,plain,
( ( ! [T_a: $i,V_a: $i] :
( ( c_The @ ( hAPP @ ( c_COMBC @ ( c_fequal @ T_a ) @ T_a @ T_a @ tc_bool ) @ V_a ) @ T_a )
= V_a ) )
= $true ),
inference(copy,[status(thm)],[840]) ).
thf(985,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)],[839]) ).
thf(986,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)],[838]) ).
thf(987,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(copy,[status(thm)],[837]) ).
thf(988,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(copy,[status(thm)],[836]) ).
thf(989,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[835]) ).
thf(990,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[834]) ).
thf(991,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)],[833]) ).
thf(992,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[832]) ).
thf(993,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[831]) ).
thf(994,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[830]) ).
thf(995,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_d ) )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_d @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_d ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[829]) ).
thf(996,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_d ) )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_d ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[828]) ).
thf(997,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[827]) ).
thf(998,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[826]) ).
thf(999,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[825]) ).
thf(1000,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[824]) ).
thf(1001,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[823]) ).
thf(1002,plain,
( ( ! [T_a: $i,V_k: $i,V_l: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_k @ V_l @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_k @ V_l @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[822]) ).
thf(1003,plain,
( ( ! [T_a: $i,V_k: $i,V_l: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_k @ V_l @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[821]) ).
thf(1004,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[820]) ).
thf(1005,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[819]) ).
thf(1006,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[818]) ).
thf(1007,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[817]) ).
thf(1008,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[816]) ).
thf(1009,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[815]) ).
thf(1010,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 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[814]) ).
thf(1011,plain,
( ( ! [T_a: $i,V_k: $i,V_l: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_k @ V_l @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_l ) @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[813]) ).
thf(1012,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 @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[812]) ).
thf(1013,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 @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( 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)],[811]) ).
thf(1014,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 @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[810]) ).
thf(1015,plain,
( ( ! [T_a: $i,V_b: $i,V_d: $i,V_a: $i,V_c: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_d ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[809]) ).
thf(1016,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[808]) ).
thf(1017,plain,
( ( ! [T_a: $i,V_c: $i,V_d: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_d ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[807]) ).
thf(1018,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_d ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[806]) ).
thf(1019,plain,
( ( ! [T_a: $i,V_l: $i,V_m: $i,V_u: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_l @ V_m @ T_a ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_m @ V_u @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_l @ V_u @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_m ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_l ) @ V_m ) ) ) )
= $true ),
inference(copy,[status(thm)],[805]) ).
thf(1020,plain,
( ( ! [V_B: $i,V_x: $i,T_b: $i,V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ V_B @ V_x ) @ T_b )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_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)],[804]) ).
thf(1021,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 @ ( c_in @ V_a @ V_A @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[803]) ).
thf(1022,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[802]) ).
thf(1023,plain,
( ( ! [T_b: $i,V_A: $i,V_M: $i,T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_b )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ ( c_COMBK @ V_M @ T_b @ T_a ) @ T_a @ T_b )
= V_M )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[801]) ).
thf(1024,plain,
( ( ! [T_b: $i,V_c: $i,T_a: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ ( c_COMBK @ V_c @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[800]) ).
thf(1025,plain,
( ( ! [V_A: $i,V_c: $i,T_a: $i,T_b: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ ( c_COMBK @ V_c @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= V_c )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[799]) ).
thf(1026,plain,
( ( ! [V_A: $i,T_a: $i,T_b: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) @ T_b ) @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[798]) ).
thf(1027,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_a: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[797]) ).
thf(1028,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)],[796]) ).
thf(1029,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ V_a @ V_b @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[795]) ).
thf(1030,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastLessThan @ V_a @ V_b @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[794]) ).
thf(1031,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ V_a @ V_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[793]) ).
thf(1032,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ V_a @ V_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[792]) ).
thf(1033,plain,
( ( ! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( c_Complete__Lattice_Ocomplete__lattice__axioms @ ( c_Complete__Lattice_OInf__class_OInf @ T_a ) @ ( c_Complete__Lattice_OSup__class_OSup @ T_a ) @ ( c_lessequals @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[791]) ).
thf(1034,plain,
( ( ~ ( class_HOL_Ouminus @ t_b )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ v_A @ ( tc_fun @ t_a @ t_b ) ) @ v_x )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ v_A @ v_x ) @ t_b ) ) )
= $true ),
inference(copy,[status(thm)],[790]) ).
thf(1035,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ ( c_Finite__Set_Olinorder__class_OMax @ V_A @ T_a ) ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[789]) ).
thf(1036,plain,
( ( ! [T_a: $i,V_A: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Finite__Set_Olinorder__class_OMin @ V_A @ T_a ) ) @ V_x ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[788]) ).
thf(1037,plain,
( ( ! [T_a: $i,V_A: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMin @ V_A @ T_a ) @ V_A @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[787]) ).
thf(1038,plain,
( ( ! [T_a: $i,V_A: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMax @ V_A @ T_a ) @ V_A @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[786]) ).
thf(1039,plain,
( ( ! [V_f: $i,V_a: $i,V_A: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ V_f @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a ) @ V_x ) )
| ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) )
| ~ ( c_Finite__Set_Ofold__graph @ V_f @ V_a @ V_A @ V_x @ T_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[785]) ).
thf(1040,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 @ ( c_in @ V_x @ V_A @ T_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)],[784]) ).
thf(1041,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 @ ( c_in @ V_a @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[783]) ).
thf(1042,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 @ ( c_in @ V_x @ V_A @ T_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)],[782]) ).
thf(1043,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 @ ( c_in @ V_x @ V_A @ T_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 @ ( c_in @ V_x @ V_B @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[781]) ).
thf(1044,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 @ ( c_in @ V_x @ V_A @ T_a ) )
| ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( 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)],[780]) ).
thf(1045,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 @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[779]) ).
thf(1046,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_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( 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)],[778]) ).
thf(1047,plain,
( ( ! [T_a: $i,V_N: $i,V_M: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Finite__Set_Olinorder__class_OMin @ V_N @ T_a ) ) @ ( c_Finite__Set_Olinorder__class_OMin @ V_M @ T_a ) ) )
| ~ ( c_Finite__Set_Ofinite @ V_N @ T_a )
| ( V_M
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_M ) @ V_N ) ) ) )
= $true ),
inference(copy,[status(thm)],[777]) ).
thf(1048,plain,
( ( ! [T_a: $i,V_M: $i,V_N: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Finite__Set_Olinorder__class_OMax @ V_M @ T_a ) ) @ ( c_Finite__Set_Olinorder__class_OMax @ V_N @ T_a ) ) )
| ~ ( c_Finite__Set_Ofinite @ V_N @ T_a )
| ( V_M
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_M ) @ V_N ) ) ) )
= $true ),
inference(copy,[status(thm)],[776]) ).
thf(1049,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( 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 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_COMBK @ ( hAPP @ ( c_COMBC @ ( c_fequal @ tc_Com_Ostate ) @ tc_Com_Ostate @ tc_Com_Ostate @ tc_bool ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ V_G @ V_P @ V_Q @ V_c ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) @ V_c @ ( c_COMBK @ ( hAPP @ V_Q @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ V_G @ V_P @ V_Q @ V_c ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) @ 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)],[775]) ).
thf(1050,plain,
( ( ! [T_a: $i,V_l: $i,V_u: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ V_l @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ V_l @ V_u @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ V_l @ V_u @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_l ) @ V_u ) ) ) )
= $true ),
inference(copy,[status(thm)],[774]) ).
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 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( 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 @ ( c_in @ V_x @ V_B @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[773]) ).
thf(1052,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_z ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[772]) ).
thf(1053,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_z ) ) ) )
= $true ),
inference(copy,[status(thm)],[771]) ).
thf(1054,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[770]) ).
thf(1055,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[769]) ).
thf(1056,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[768]) ).
thf(1057,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[767]) ).
thf(1058,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[766]) ).
thf(1059,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) ) @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[765]) ).
thf(1060,plain,
( ( ! [T_a: $i,V_l: $i,V_u: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_l @ V_u @ T_a ) @ ( c_Set_Oinsert @ V_u @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ V_l @ V_u @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_l ) @ V_u ) ) ) )
= $true ),
inference(copy,[status(thm)],[764]) ).
thf(1061,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(copy,[status(thm)],[763]) ).
thf(1062,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(copy,[status(thm)],[762]) ).
thf(1063,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(copy,[status(thm)],[761]) ).
thf(1064,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(copy,[status(thm)],[760]) ).
thf(1065,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)],[759]) ).
thf(1066,plain,
( ( ! [V_Inf: $i,T_a: $i,V_top: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_bot: $i] :
( ( ( hAPP @ V_Inf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_top )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[758]) ).
thf(1067,plain,
( ( ! [V_Sup: $i,T_a: $i,V_bot: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_top: $i] :
( ( ( hAPP @ V_Sup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_bot )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[757]) ).
thf(1068,plain,
( ( ! [T_a: $i,V_P: $i,V_x: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Collect @ V_P @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[756]) ).
thf(1069,plain,
( ( ! [V_x: $i,T_a: $i] :
~ ( hBOOL @ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[755]) ).
thf(1070,plain,
( ( ! [V_P: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[754]) ).
thf(1071,plain,
( ( ! [V_c: $i,T_a: $i] :
~ ( hBOOL @ ( c_in @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[753]) ).
thf(1072,plain,
( ( ! [V_a: $i,T_a: $i] :
~ ( hBOOL @ ( c_in @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[752]) ).
thf(1073,plain,
( ( ! [V_P: $i,T_a: $i,V_x: $i] :
( ( ( c_Collect @ V_P @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[751]) ).
thf(1074,plain,
( ( ! [V_f: $i,T_a: $i,V_x: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[750]) ).
thf(1075,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)],[749]) ).
thf(1076,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)],[748]) ).
thf(1077,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)],[747]) ).
thf(1078,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)],[746]) ).
thf(1079,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)],[745]) ).
thf(1080,plain,
( ( ! [V_P: $i,V_x: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( hBOOL @ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[744]) ).
thf(1081,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)],[743]) ).
thf(1082,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)],[742]) ).
thf(1083,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 @ ( c_in @ V_a @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[741]) ).
thf(1084,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ T_a ) @ ( 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_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[740]) ).
thf(1085,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 @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[739]) ).
thf(1086,plain,
( ( ! [V_a: $i,V_b: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[738]) ).
thf(1087,plain,
( ( ! [V_a: $i,V_b: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_a @ V_B @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[737]) ).
thf(1088,plain,
( ( ! [V_Inf: $i,V_a: $i,V_A: $i,T_a: $i,V_inf: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) )
= ( hAPP @ ( hAPP @ V_inf @ V_a ) @ ( hAPP @ V_Inf @ V_A ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[736]) ).
thf(1089,plain,
( ( ! [V_Sup: $i,V_a: $i,V_A: $i,T_a: $i,V_sup: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) )
= ( hAPP @ ( hAPP @ V_sup @ V_a ) @ ( hAPP @ V_Sup @ V_A ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[735]) ).
thf(1090,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i,V_b: $i] :
( ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) )
| ( V_a = V_b )
| ~ ( hBOOL @ ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[734]) ).
thf(1091,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)],[733]) ).
thf(1092,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)],[732]) ).
thf(1093,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i] : ( hBOOL @ ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[731]) ).
thf(1094,plain,
( ( ! [V_a: $i,V_B: $i,T_a: $i] : ( hBOOL @ ( c_in @ V_a @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[730]) ).
thf(1095,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] : ( hBOOL @ ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[729]) ).
thf(1096,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 @ ( c_in @ V_x @ V_B @ T_a ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ( V_A = V_B ) ) )
= $true ),
inference(copy,[status(thm)],[728]) ).
thf(1097,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
= V_A )
| ~ ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[727]) ).
thf(1098,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[726]) ).
thf(1099,plain,
( ( ! [V_t: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_t @ V_B @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_t @ V_A @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[725]) ).
thf(1100,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[724]) ).
thf(1101,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[723]) ).
thf(1102,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[722]) ).
thf(1103,plain,
( ( ! [T_a: $i,V_B: $i,V_C: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_C ) ) ) )
= $true ),
inference(copy,[status(thm)],[721]) ).
thf(1104,plain,
( ( ! [T_a: $i,V_A: $i,V_C: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_C ) ) ) )
= $true ),
inference(copy,[status(thm)],[720]) ).
thf(1105,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i,V_D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) ) ) )
= $true ),
inference(copy,[status(thm)],[719]) ).
thf(1106,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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[718]) ).
thf(1107,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[717]) ).
thf(1108,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[716]) ).
thf(1109,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i,V_D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_D ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) ) ) )
= $true ),
inference(copy,[status(thm)],[715]) ).
thf(1110,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) ) ) )
= $true ),
inference(copy,[status(thm)],[714]) ).
thf(1111,plain,
( ( ! [T_a: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[713]) ).
thf(1112,plain,
( ( ! [T_a: $i,V_B: $i,V_A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[712]) ).
thf(1113,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) ) ) )
= $true ),
inference(copy,[status(thm)],[711]) ).
thf(1114,plain,
( ( ! [T_a: $i,V_B: $i,V_A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[710]) ).
thf(1115,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[709]) ).
thf(1116,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) ) ) )
= $true ),
inference(copy,[status(thm)],[708]) ).
thf(1117,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( 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)],[707]) ).
thf(1118,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)],[706]) ).
thf(1119,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)],[705]) ).
thf(1120,plain,
( ( ! [T_a: $i,V_A: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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 ) ) ) )
= $true ),
inference(copy,[status(thm)],[704]) ).
thf(1121,plain,
( ( ! [T_a: $i,V_A: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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 ) ) ) )
= $true ),
inference(copy,[status(thm)],[703]) ).
thf(1122,plain,
( ( ! [T_a: $i,V_A: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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 ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[702]) ).
thf(1123,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[701]) ).
thf(1124,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[700]) ).
thf(1125,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[699]) ).
thf(1126,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[698]) ).
thf(1127,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ V_a @ V_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[697]) ).
thf(1128,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[696]) ).
thf(1129,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[695]) ).
thf(1130,plain,
( ( ! [T_a: $i,V_b: $i,V_d: $i,V_a: $i,V_c: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_d ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[694]) ).
thf(1131,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_c @ V_d @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_d ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[693]) ).
thf(1132,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i,V_d: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_c ) @ V_a ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_a @ V_b @ T_a ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_c @ V_d @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[692]) ).
thf(1133,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[691]) ).
thf(1134,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[690]) ).
thf(1135,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[689]) ).
thf(1136,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[688]) ).
thf(1137,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) ) @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[687]) ).
thf(1138,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[686]) ).
thf(1139,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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[685]) ).
thf(1140,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[684]) ).
thf(1141,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) @ V_z ) ) ) )
= $true ),
inference(copy,[status(thm)],[683]) ).
thf(1142,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) @ V_z ) ) ) )
= $true ),
inference(copy,[status(thm)],[682]) ).
thf(1143,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[681]) ).
thf(1144,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[680]) ).
thf(1145,plain,
( ( ! [T_a: $i,V_b: $i,V_x: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[679]) ).
thf(1146,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_a ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[678]) ).
thf(1147,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 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y_H ) @ V_x_H ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[677]) ).
thf(1148,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 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y_H ) @ V_x_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[676]) ).
thf(1149,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[675]) ).
thf(1150,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a )
= V_b ) ) )
= $true ),
inference(copy,[status(thm)],[674]) ).
thf(1151,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( V_a
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[673]) ).
thf(1152,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( V_b
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[672]) ).
thf(1153,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[671]) ).
thf(1154,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[670]) ).
thf(1155,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A ) )
= $true ),
inference(copy,[status(thm)],[669]) ).
thf(1156,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_C ) ) ) )
= $true ),
inference(copy,[status(thm)],[668]) ).
thf(1157,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[667]) ).
thf(1158,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 @ ( c_in @ V_x @ V_B @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[666]) ).
thf(1159,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 @ ( c_in @ V_a @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[665]) ).
thf(1160,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 @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[664]) ).
thf(1161,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(copy,[status(thm)],[663]) ).
thf(1162,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(copy,[status(thm)],[662]) ).
thf(1163,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)],[661]) ).
thf(1164,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(copy,[status(thm)],[660]) ).
thf(1165,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(copy,[status(thm)],[659]) ).
thf(1166,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)],[658]) ).
thf(1167,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 @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[657]) ).
thf(1168,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 @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[656]) ).
thf(1169,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)],[655]) ).
thf(1170,plain,
( ( ! [T_b: $i,V_A: $i,V_B: $i] :
( ~ ( class_HOL_Ominus @ T_b )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ t_a @ T_b ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ V_A @ v_x ) @ ( hAPP @ V_B @ v_x ) @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[654]) ).
thf(1171,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)],[653]) ).
thf(1172,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)],[652]) ).
thf(1173,plain,
( ( ! [V_b: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_a: $i] :
( ( hBOOL @ ( c_in @ V_b @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) )
| ~ ( hBOOL @ ( c_in @ V_b @ ( hAPP @ V_B @ V_a ) @ T_b ) )
| ~ ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[651]) ).
thf(1174,plain,
( ( ! [V_b: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i,V_x: $i] :
( ( hBOOL @ ( c_in @ V_b @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_b @ ( hAPP @ V_B @ V_x ) @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[650]) ).
thf(1175,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[649]) ).
thf(1176,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[648]) ).
thf(1177,plain,
( ( ! [V_P: $i,V_a: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ~ ( hBOOL @ ( c_in @ V_a @ ( c_Collect @ V_P @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[647]) ).
thf(1178,plain,
( ( ! [V_a: $i,V_P: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_a @ ( c_Collect @ V_P @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[646]) ).
thf(1179,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[645]) ).
thf(1180,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(copy,[status(thm)],[644]) ).
thf(1181,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(copy,[status(thm)],[643]) ).
thf(1182,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(copy,[status(thm)],[642]) ).
thf(1183,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(copy,[status(thm)],[641]) ).
thf(1184,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)],[640]) ).
thf(1185,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)],[639]) ).
thf(1186,plain,
( ( ! [T_a: $i,V_x: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( V_x_H = V_y_H ) ) )
= $true ),
inference(copy,[status(thm)],[638]) ).
thf(1187,plain,
( ( ! [T_a: $i,V_xa: $i,V_y: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_xa @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a ) )
| ( V_xa = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[637]) ).
thf(1188,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)],[636]) ).
thf(1189,plain,
( ( ! [V_S: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_S @ V_x ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_S @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[635]) ).
thf(1190,plain,
( ( ! [V_x: $i,V_S: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_x @ V_S @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_S @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[634]) ).
thf(1191,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)],[633]) ).
thf(1192,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(copy,[status(thm)],[632]) ).
thf(1193,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)],[631]) ).
thf(1194,plain,
( ( ! [T_b: $i,V_f: $i,V_g: $i] :
( ~ ( class_Lattices_Olattice @ T_b )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_f @ V_g @ ( tc_fun @ t_a @ T_b ) ) @ v_x )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ V_f @ v_x ) @ ( hAPP @ V_g @ v_x ) @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[630]) ).
thf(1195,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i] :
( ( c_Finite__Set_Ofold1 @ V_f @ V_A @ T_a )
= ( c_The @ ( c_Finite__Set_Ofold1Set @ V_f @ V_A @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[629]) ).
thf(1196,plain,
( ( ! [T_b: $i,V_M: $i,V_i: $i,V_A: $i,T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_b )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_b ) @ ( hAPP @ V_M @ V_i ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_M @ T_a @ T_b ) ) )
| ~ ( hBOOL @ ( c_in @ V_i @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[628]) ).
thf(1197,plain,
( ( ! [T_b: $i,V_B: $i,V_a: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_b @ tc_bool ) ) @ ( hAPP @ V_B @ V_a ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[627]) ).
thf(1198,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 @ ( c_in @ V_x @ V_B @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[626]) ).
thf(1199,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ~ ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[625]) ).
thf(1200,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_c @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[624]) ).
thf(1201,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( c_Collect @ V_P @ T_a )
= V_P ) )
= $true ),
inference(copy,[status(thm)],[623]) ).
thf(1202,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)],[622]) ).
thf(1203,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)],[621]) ).
thf(1204,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ T_a ) @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ T_a ) @ V_A ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[620]) ).
thf(1205,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[619]) ).
thf(1206,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 @ ( c_in @ V_x @ V_A @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[618]) ).
thf(1207,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[617]) ).
thf(1208,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ~ ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[616]) ).
thf(1209,plain,
( ( ! [T_a: $i,V_A: $i,V_x: $i,V_B: $i,V_I: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( hAPP @ V_A @ V_x ) ) @ V_B ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_I @ T_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_I @ V_A @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[615]) ).
thf(1210,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 @ ( c_in @ V_k @ V_I @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[614]) ).
thf(1211,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(copy,[status(thm)],[613]) ).
thf(1212,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)],[612]) ).
thf(1213,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)],[611]) ).
thf(1214,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) )
| ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[610]) ).
thf(1215,plain,
( ( ! [T_a: $i,V_l: $i,V_m: $i,V_u: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_l @ V_m @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_m @ V_u @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ V_l @ V_u @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_m ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_l ) @ V_m ) ) ) )
= $true ),
inference(copy,[status(thm)],[609]) ).
thf(1216,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 @ ( c_in @ V_x @ V_A @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[608]) ).
thf(1217,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)],[607]) ).
thf(1218,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)],[606]) ).
thf(1219,plain,
( ( ! [T_a: $i,V_l: $i,V_m: $i,V_u: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_l @ V_m @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ V_m @ V_u @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ V_l @ V_u @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_m ) @ V_u ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_l ) @ V_m ) ) ) )
= $true ),
inference(copy,[status(thm)],[605]) ).
thf(1220,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ V_x @ T_a )
!= ( c_HOL_Ouminus__class_Ouminus @ V_y @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[604]) ).
thf(1221,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a )
!= ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[603]) ).
thf(1222,plain,
( ( ! [V_A: $i,T_a: $i,V_B: $i] :
( ( ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_HOL_Ouminus__class_Ouminus @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A = V_B ) ) )
= $true ),
inference(copy,[status(thm)],[602]) ).
thf(1223,plain,
( ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( c_in @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) )
= $true ),
inference(copy,[status(thm)],[601]) ).
thf(1224,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)],[600]) ).
thf(1225,plain,
( ( ! [T_a: $i,V_A: $i,V_x: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ T_a ) @ V_A ) ) @ V_x ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[599]) ).
thf(1226,plain,
( ( ! [T_b: $i,V_A: $i] :
( ~ ( class_HOL_Ouminus @ T_b )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ t_a @ T_b ) ) @ v_x )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ V_A @ v_x ) @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[598]) ).
thf(1227,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[597]) ).
thf(1228,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_c @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[596]) ).
thf(1229,plain,
( ( ! [T_a: $i,V_i: $i,V_m: $i,V_n: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_i @ V_m @ T_a ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_i @ V_n @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ V_n @ V_m @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_i ) @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[595]) ).
thf(1230,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)],[594]) ).
thf(1231,plain,
( ( ! [T_a: $i,V_x: $i] :
( ( c_The @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ T_a )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[593]) ).
thf(1232,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ T_a ) @ V_A ) ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[592]) ).
thf(1233,plain,
( ( ! [T_a: $i,V_b: $i,V_d: $i,V_a: $i,V_c: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_d ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_a @ V_b @ T_a ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ V_c @ V_d @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[591]) ).
thf(1234,plain,
( ( ! [T_b: $i] :
( ~ ( class_Orderings_Obot @ T_b )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ T_b ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[590]) ).
thf(1235,plain,
( ( ! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ T_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[589]) ).
thf(1236,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)],[588]) ).
thf(1237,plain,
( ( ! [V_x: $i,T_a: $i] : ( hBOOL @ ( c_in @ V_x @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[587]) ).
thf(1238,plain,
( ( ! [V_Inf: $i,V_a: $i,T_a: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= V_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[586]) ).
thf(1239,plain,
( ( ! [V_Sup: $i,V_a: $i,T_a: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= V_a )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[585]) ).
thf(1240,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ T_a ) @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[584]) ).
thf(1241,plain,
( ( ! [V_x: $i,T_a: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[583]) ).
thf(1242,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)],[582]) ).
thf(1243,plain,
( ( ! [V_f: $i,V_x: $i,T_a: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ V_f @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[581]) ).
thf(1244,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[580]) ).
thf(1245,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_The @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[579]) ).
thf(1246,plain,
( ( ! [V_Inf: $i,V_a: $i,V_b: $i,T_a: $i,V_inf: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_sup: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
= ( hAPP @ ( hAPP @ V_inf @ V_a ) @ V_b ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[578]) ).
thf(1247,plain,
( ( ! [V_Sup: $i,V_a: $i,V_b: $i,T_a: $i,V_sup: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_bot: $i,V_top: $i] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
= ( hAPP @ ( hAPP @ V_sup @ V_a ) @ V_b ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[577]) ).
thf(1248,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)],[576]) ).
thf(1249,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)],[575]) ).
thf(1250,plain,
( ( ! [V_a: $i,V_b: $i,V_f: $i,T_a: $i] :
( ( V_a = V_b )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ V_f @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[574]) ).
thf(1251,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_Set_Ocontents @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[573]) ).
thf(1252,plain,
( ( ! [V_y: $i,V_x: $i,T_a: $i] :
( ( V_y
= ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[572]) ).
thf(1253,plain,
( ( ! [V_b: $i,V_a: $i,T_a: $i] :
( ( V_b = V_a )
| ~ ( hBOOL @ ( c_in @ V_b @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[571]) ).
thf(1254,plain,
( ( ! [V_f: $i,V_a: $i,T_a: $i] :
( ( c_Finite__Set_Ofold1 @ V_f @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_a ) )
= $true ),
inference(copy,[status(thm)],[570]) ).
thf(1255,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[569]) ).
thf(1256,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)],[568]) ).
thf(1257,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ V_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)],[567]) ).
thf(1258,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 @ ( c_in @ V_x @ V_xa @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[566]) ).
thf(1259,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)],[565]) ).
thf(1260,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ T_a ) @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[564]) ).
thf(1261,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_HOL_Ouminus__class_Ouminus @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[563]) ).
thf(1262,plain,
( ( ! [T_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[562]) ).
thf(1263,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[561]) ).
thf(1264,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[560]) ).
thf(1265,plain,
( ( ! [T_a: $i,V_A: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[559]) ).
thf(1266,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[558]) ).
thf(1267,plain,
( ( ! [T_a: $i,V_A: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[557]) ).
thf(1268,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[556]) ).
thf(1269,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_xa: $i,V_Z_H: $i,V_x: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_xa @ V_Z_H ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ V_G @ V_P @ V_Q @ V_c @ V_x @ V_xa ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_x @ V_Z_H ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ V_G @ V_P @ V_Q @ V_c ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_x @ V_c @ V_xa @ 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)],[555]) ).
thf(1270,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_Q_H: $i,V_Z_H: $i,V_P_H: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_H @ V_Z_H ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ V_P @ V_P_H @ V_Q @ V_Q_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_H @ V_Z_H ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ V_P @ V_P_H @ V_Q @ V_Q_H ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P_H @ V_c @ V_Q_H @ 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)],[554]) ).
thf(1271,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_xa: $i,V_Z_H: $i,V_x: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_xa @ V_Z_H ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ V_G @ V_P @ V_Q @ V_c @ V_x @ V_xa ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_x @ V_Z_H ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ V_G @ V_P @ V_Q @ V_c ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_x @ V_c @ V_xa @ 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)],[553]) ).
thf(1272,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ V_G @ V_P @ V_Q @ V_c ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ V_G @ V_P @ V_Q @ V_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[552]) ).
thf(1273,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_x: $i,V_xa: $i] :
( ( 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_Q @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ V_G @ V_P @ V_Q @ V_c ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ V_G @ V_P @ V_Q @ V_c @ V_x @ V_xa ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_x @ V_c @ V_xa @ 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)],[551]) ).
thf(1274,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ V_G @ V_P @ V_Q @ V_c ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ V_G @ V_P @ V_Q @ V_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[550]) ).
thf(1275,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_Q_H: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_Q_H @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ V_Q @ V_Q_H ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ V_Q @ V_Q_H ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ V_c @ V_Q_H @ 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)],[549]) ).
thf(1276,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_P_H: $i,V_Q_H: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ V_P @ V_P_H @ V_Q @ V_Q_H ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ V_P @ V_P_H @ V_Q @ V_Q_H ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P_H @ V_c @ V_Q_H @ 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)],[548]) ).
thf(1277,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_P_H: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ V_P @ V_P_H ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ V_P @ V_P_H ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P_H @ 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)],[547]) ).
thf(1278,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_x: $i,V_xa: $i] :
( ( 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_Q @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ V_G @ V_P @ V_Q @ V_c ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ V_G @ V_P @ V_Q @ V_c @ V_x @ V_xa ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_x @ V_c @ V_xa @ 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)],[546]) ).
thf(1279,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_P_H: $i] :
( ( 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P_H @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ V_P @ V_P_H ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ V_P @ V_P_H ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P_H @ 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)],[545]) ).
thf(1280,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_P_H: $i,V_Q_H: $i] :
( ( 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_Q @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ V_P @ V_P_H @ V_Q @ V_Q_H ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ V_P @ V_P_H @ V_Q @ V_Q_H ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P_H @ V_c @ V_Q_H @ 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)],[544]) ).
thf(1281,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_Q_H: $i] :
( ( 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_Q @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ V_Q @ V_Q_H ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ V_Q @ V_Q_H ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ V_P @ V_c @ V_Q_H @ 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)],[543]) ).
thf(1282,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ V_G @ V_P @ V_Q @ V_c ) ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ V_G @ V_P @ V_Q @ V_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[542]) ).
thf(1283,plain,
( ( ! [T_a: $i,V_A: $i,V_x: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( 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 ) ) ) )
= $true ),
inference(copy,[status(thm)],[541]) ).
thf(1284,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(copy,[status(thm)],[540]) ).
thf(1285,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[539]) ).
thf(1286,plain,
( ( ! [T_a: $i,V_a: $i,V_C: $i,V_D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_a @ V_C @ T_a ) ) @ ( c_Set_Oinsert @ V_a @ V_D @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C ) @ V_D ) ) ) )
= $true ),
inference(copy,[status(thm)],[538]) ).
thf(1287,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)],[537]) ).
thf(1288,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[536]) ).
thf(1289,plain,
( ( ! [V_G: $i,V_ts: $i,T_a: $i,V_ts_H: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ V_ts ) @ V_ts_H ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts_H @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[535]) ).
thf(1290,plain,
( ( ! [V_Q: $i,V_x: $i,T_a: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_P ) @ V_Q ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[534]) ).
thf(1291,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[533]) ).
thf(1292,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[532]) ).
thf(1293,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 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_P ) @ V_Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[531]) ).
thf(1294,plain,
( ( ! [T_a: $i,V_A: $i,V_C: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[530]) ).
thf(1295,plain,
( ( ! [T_a: $i,V_A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_A ) ) )
= $true ),
inference(copy,[status(thm)],[529]) ).
thf(1296,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[528]) ).
thf(1297,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[527]) ).
thf(1298,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_z ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_z ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[526]) ).
thf(1299,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)],[525]) ).
thf(1300,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)],[524]) ).
thf(1301,plain,
( ( ! [V_G: $i,V_ts: $i,T_a: $i,V_G_H: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_G_H @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G_H @ V_ts @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[523]) ).
thf(1302,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)],[522]) ).
thf(1303,plain,
( ( ! [T_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[521]) ).
thf(1304,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[520]) ).
thf(1305,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)],[519]) ).
thf(1306,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)],[518]) ).
thf(1307,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)],[517]) ).
thf(1308,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)],[516]) ).
thf(1309,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)],[515]) ).
thf(1310,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)],[514]) ).
thf(1311,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)],[513]) ).
thf(1312,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[512]) ).
thf(1313,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[511]) ).
thf(1314,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[510]) ).
thf(1315,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[509]) ).
thf(1316,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ V_A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[508]) ).
thf(1317,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)],[507]) ).
thf(1318,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)],[506]) ).
thf(1319,plain,
( ( ! [T_a: $i,V_B: $i,V_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B ) @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[505]) ).
thf(1320,plain,
( ( ! [V_A: $i,V_x: $i,V_y: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ( V_y = V_x )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[504]) ).
thf(1321,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)],[503]) ).
thf(1322,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)],[502]) ).
thf(1323,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Obot @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_a ) @ ( c_Orderings_Obot__class_Obot @ T_a ) ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[501]) ).
thf(1324,plain,
( ( ! [T_a: $i,V_A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) @ V_A ) ) )
= $true ),
inference(copy,[status(thm)],[500]) ).
thf(1325,plain,
( ( ! [T_a: $i,V_A: $i,V_b: $i,V_B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[499]) ).
thf(1326,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A ) @ V_B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) ) @ V_B ) ) ) )
= $true ),
inference(copy,[status(thm)],[498]) ).
thf(1327,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)],[497]) ).
thf(1328,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)],[496]) ).
thf(1329,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)],[495]) ).
thf(1330,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)],[494]) ).
thf(1331,plain,
( ( ! [V_G: $i,V_ts: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ V_ts ) @ V_G ) ) ) )
= $true ),
inference(copy,[status(thm)],[493]) ).
thf(1332,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i,V_g: $i,T_a: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ T_b ) @ ( hAPP @ V_f @ V_x ) ) @ ( hAPP @ V_g @ V_x ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ T_a @ T_b ) ) @ V_f ) @ V_g ) ) ) )
= $true ),
inference(copy,[status(thm)],[492]) ).
thf(1333,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)],[491]) ).
thf(1334,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)],[490]) ).
thf(1335,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)],[489]) ).
thf(1336,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Lattices_Oboolean__algebra @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(1337,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)],[487]) ).
thf(1338,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)],[486]) ).
thf(1339,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)],[485]) ).
thf(1340,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)],[484]) ).
thf(1341,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)],[483]) ).
thf(1342,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_HOL_Ouminus @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_HOL_Ouminus @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(1343,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_HOL_Ominus @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_HOL_Ominus @ T_1 ) ) )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(1344,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)],[480]) ).
thf(1345,plain,
( ( class_Lattices_Oupper__semilattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[479]) ).
thf(1346,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[478]) ).
thf(1347,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[477]) ).
thf(1348,plain,
( ( class_Lattices_Olattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[476]) ).
thf(1349,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[475]) ).
thf(1350,plain,
( ( class_Orderings_Obot @ tc_nat )
= $true ),
inference(copy,[status(thm)],[474]) ).
thf(1351,plain,
( ( class_HOL_Ominus @ tc_nat )
= $true ),
inference(copy,[status(thm)],[473]) ).
thf(1352,plain,
( ( class_HOL_Oord @ tc_nat )
= $true ),
inference(copy,[status(thm)],[472]) ).
thf(1353,plain,
( ( class_Complete__Lattice_Ocomplete__lattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[471]) ).
thf(1354,plain,
( ( class_Lattices_Oupper__semilattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[470]) ).
thf(1355,plain,
( ( class_Lattices_Obounded__lattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[469]) ).
thf(1356,plain,
( ( class_Lattices_Oboolean__algebra @ tc_bool )
= $true ),
inference(copy,[status(thm)],[468]) ).
thf(1357,plain,
( ( class_Finite__Set_Ofinite_Ofinite @ tc_bool )
= $true ),
inference(copy,[status(thm)],[467]) ).
thf(1358,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[466]) ).
thf(1359,plain,
( ( class_Lattices_Olattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[465]) ).
thf(1360,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[464]) ).
thf(1361,plain,
( ( class_Orderings_Obot @ tc_bool )
= $true ),
inference(copy,[status(thm)],[463]) ).
thf(1362,plain,
( ( class_HOL_Ouminus @ tc_bool )
= $true ),
inference(copy,[status(thm)],[462]) ).
thf(1363,plain,
( ( class_HOL_Ominus @ tc_bool )
= $true ),
inference(copy,[status(thm)],[461]) ).
thf(1364,plain,
( ( class_HOL_Oord @ tc_bool )
= $true ),
inference(copy,[status(thm)],[460]) ).
thf(1365,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[459]) ).
thf(1366,plain,
( ( ! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[458]) ).
thf(1367,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[912]) ).
thf(1368,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Set_Oinsert @ SX0 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_bool ) ) @ SX1 )
!= ( c_Set_Oinsert @ SX2 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_bool ) ) @ SX1 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1329]) ).
thf(1369,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SX0 )
| ( ( c_HOL_Ouminus__class_Ouminus @ SX1 @ SX0 )
!= ( c_HOL_Ouminus__class_Ouminus @ SX2 @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1221]) ).
thf(1370,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Set_Oinsert @ SX0 @ SX1 @ SX2 )
!= ( c_Set_Oinsert @ SX0 @ SX3 @ SX2 ) )
| ( hBOOL @ ( c_in @ SX0 @ SX3 @ SX2 ) )
| ( hBOOL @ ( c_in @ SX0 @ SX1 @ SX2 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1096]) ).
thf(1371,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Collect @ SX0 @ SX1 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX1 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1073]) ).
thf(1372,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Com_Ocom_OSemi @ SX0 @ SX1 )
!= ( c_Com_Ocom_OSemi @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1202]) ).
thf(1373,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SX4 @ SX5 @ SX6 @ SX3 ) )
| ( SX0 = SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1307]) ).
thf(1374,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Set_Oinsert @ SX0 @ SX1 @ SX2 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1322]) ).
thf(1375,plain,
( ( ! [SX0: $i,SX1: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1118]) ).
thf(1376,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Oorder @ SX0 )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SX1 @ SX2 @ SX0 ) )
| ~ ( c_HOL_Oord__class_Oless @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1003]) ).
thf(1377,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_bool ) )
!= ( c_Set_Oinsert @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1302]) ).
thf(1378,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SX0 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SX1 @ SX2 @ SX0 )
!= ( c_Orderings_Obot__class_Obot @ SX0 ) )
| ( SX1
= ( c_Orderings_Obot__class_Obot @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1063]) ).
thf(1379,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_Set_Oinsert @ SX0 @ ( c_Set_Oinsert @ SX1 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) @ SX2 ) @ SX2 )
!= ( c_Set_Oinsert @ SX3 @ ( c_Set_Oinsert @ SX4 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) @ SX2 ) @ SX2 ) )
| ( SX1 = SX3 )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1310]) ).
thf(1380,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SX0 @ SX1 @ ( tc_fun @ SX2 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) )
| ( SX1
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1081]) ).
thf(1381,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX1 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX2 @ SX3 @ SX0 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1186]) ).
thf(1382,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Oorder @ SX0 )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastAtMost @ SX1 @ SX2 @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SX0 ) @ SX1 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1125]) ).
thf(1383,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SX0 @ SX1 @ ( tc_fun @ SX2 @ tc_bool ) )
!= SX1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SX2 @ tc_bool ) ) @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1106]) ).
thf(1384,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Oorder @ SX0 )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SX1 @ SX2 @ SX0 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SX0 ) @ SX1 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1123]) ).
thf(1385,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SX0 @ SX1 @ ( tc_fun @ SX2 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) )
| ( SX0
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1082]) ).
thf(1386,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Com_Ocom_OSemi @ SX0 @ SX1 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(unfold_def,[status(thm)],[1119]) ).
thf(1387,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_Set_Oinsert @ SX0 @ ( c_Set_Oinsert @ SX1 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) @ SX2 ) @ SX2 )
!= ( c_Set_Oinsert @ SX3 @ ( c_Set_Oinsert @ SX4 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) @ SX2 ) @ SX2 ) )
| ( SX0 = SX4 )
| ( SX1 = SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1309]) ).
thf(1388,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SX0 @ SX1 @ SX2 @ ( tc_fun @ SX3 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_bool ) ) )
| ( ( hAPP @ SX1 @ SX4 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX3 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SX4 @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1206]) ).
thf(1389,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX3 @ SX4 @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SX0 ) @ SX4 ) @ SX3 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SX0 ) @ SX2 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1147]) ).
thf(1390,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ SX0 )
| ( ( c_HOL_Ouminus__class_Ouminus @ SX1 @ SX0 )
!= ( c_HOL_Ouminus__class_Ouminus @ SX2 @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1220]) ).
thf(1391,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SX1 @ SX2 @ SX3 @ ( tc_fun @ SX0 @ tc_bool ) ) )
| ( ( hAPP @ SX2 @ SX4 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SX4 @ SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1216]) ).
thf(1392,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Oorder @ SX0 )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ SX1 @ SX2 @ SX0 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1032]) ).
thf(1393,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_Set_Oinsert @ SX0 @ ( c_Set_Oinsert @ SX1 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) @ SX2 ) @ SX2 )
!= ( c_Set_Oinsert @ SX3 @ ( c_Set_Oinsert @ SX4 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) @ SX2 ) @ SX2 ) )
| ( SX1 = SX3 )
| ( SX1 = SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1308]) ).
thf(1394,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Oorder @ SX0 )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastLessThan @ SX1 @ SX2 @ SX0 ) )
| ~ ( c_HOL_Oord__class_Oless @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1030]) ).
thf(1395,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_HOL_Ouminus__class_Ouminus @ SX0 @ ( tc_fun @ SX1 @ tc_bool ) )
!= ( c_HOL_Ouminus__class_Ouminus @ SX2 @ ( tc_fun @ SX1 @ tc_bool ) ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1222]) ).
thf(1396,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SX4 @ SX5 @ SX6 @ SX3 ) )
| ( SX2 = SX6 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1305]) ).
thf(1397,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX3 @ SX4 @ SX0 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SX0 ) @ SX2 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SX0 ) @ SX4 ) @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1148]) ).
thf(1398,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SX0 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SX1 @ SX2 @ SX0 )
!= SX2 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SX0 ) @ SX1 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1139]) ).
thf(1399,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i,SX6: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SX4 @ SX5 @ SX6 @ SX3 ) )
| ( SX1 = SX5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1306]) ).
thf(1400,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Com_Ocom_OSemi @ SX0 @ SX1 )
!= ( c_Com_Ocom_OSemi @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1203]) ).
thf(1401,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX3 @ SX4 @ SX0 ) )
| ( c_HOL_Oord__class_Oless @ SX3 @ SX4 @ SX0 )
| ~ ( c_HOL_Oord__class_Oless @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1004]) ).
thf(1402,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Oorder @ SX0 )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SX1 @ SX2 @ SX0 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[980]) ).
thf(1403,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Set_Oinsert @ SX0 @ SX1 @ SX2 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1258]) ).
thf(1404,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX0 @ tc_bool ) )
!= ( c_Collect @ SX1 @ SX0 ) )
| ~ ( hBOOL @ ( hAPP @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1068]) ).
thf(1405,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX3 @ SX4 @ SX0 ) )
| ( c_HOL_Oord__class_Oless @ SX1 @ SX2 @ SX0 )
| ~ ( c_HOL_Oord__class_Oless @ SX3 @ SX4 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1005]) ).
thf(1406,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX3 @ SX3 @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1187]) ).
thf(1407,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SX0 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SX1 @ SX2 @ SX0 )
!= ( c_Orderings_Obot__class_Obot @ SX0 ) )
| ( SX2
= ( c_Orderings_Obot__class_Obot @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1064]) ).
thf(1408,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_Set_Oinsert @ SX0 @ ( c_Set_Oinsert @ SX1 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) @ SX2 ) @ SX2 )
!= ( c_Set_Oinsert @ SX3 @ ( c_Set_Oinsert @ SX4 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SX2 @ tc_bool ) ) @ SX2 ) @ SX2 ) )
| ( SX0 = SX4 )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1311]) ).
thf(1409,plain,
( ( c_Hoare__Mirabelle_Ohoare__derivs @ v_Ga @ ( 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 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[914]) ).
thf(1410,plain,
! [SV1: $i] :
( ( ! [SY1567: $i,SY1568: $i,SY1569: $i] :
( ~ ( class_HOL_Oord @ SV1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY1567 @ SV1 ) ) @ SY1568 ) @ SY1569 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1568 @ SY1569 @ ( tc_fun @ SY1567 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1411,plain,
! [SV2: $i] :
( ( ! [SY1570: $i,SY1571: $i,SY1572: $i] :
( ~ ( class_HOL_Oord @ SV2 )
| ( c_HOL_Oord__class_Oless @ SY1570 @ SY1571 @ ( tc_fun @ SY1572 @ SV2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY1572 @ SV2 ) ) @ SY1571 ) @ SY1570 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY1572 @ SV2 ) ) @ SY1570 ) @ SY1571 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1412,plain,
! [SV3: $i] :
( ( ! [SY1573: $i,SY1574: $i,SY1575: $i] :
( ~ ( class_HOL_Oord @ SV3 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY1573 @ SV3 ) ) @ SY1574 ) @ SY1575 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1575 @ SY1574 @ ( tc_fun @ SY1573 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1413,plain,
! [SV4: $i] :
( ( ! [SY1576: $i,SY1577: $i] :
( ( SV4 = SY1576 )
| ( c_HOL_Oord__class_Oless @ SV4 @ SY1576 @ ( tc_fun @ SY1577 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY1577 @ tc_bool ) ) @ SV4 ) @ SY1576 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1414,plain,
! [SV5: $i] :
( ( ! [SY1578: $i,SY1579: $i] :
( ( c_HOL_Oord__class_Oless @ SV5 @ SY1578 @ ( tc_fun @ SY1579 @ tc_bool ) )
| ( SV5 = SY1578 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY1579 @ tc_bool ) ) @ SV5 ) @ SY1578 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1415,plain,
! [SV6: $i] :
( ( ! [SY1580: $i,SY1581: $i] :
( ( c_Finite__Set_Ofinite @ SV6 @ SY1580 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY1580 @ tc_bool ) ) @ SV6 ) @ SY1581 ) )
| ~ ( c_Finite__Set_Ofinite @ SY1581 @ SY1580 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1416,plain,
! [SV7: $i] :
( ( ! [SY1582: $i,SY1583: $i,SY1584: $i] :
( ( c_HOL_Oord__class_Oless @ SV7 @ SY1582 @ ( tc_fun @ SY1583 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1584 @ SY1582 @ ( tc_fun @ SY1583 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY1583 @ tc_bool ) ) @ SV7 ) @ SY1584 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1417,plain,
! [SV8: $i] :
( ( ! [SY1585: $i,SY1586: $i,SY1587: $i] :
( ( c_HOL_Oord__class_Oless @ SV8 @ SY1585 @ ( tc_fun @ SY1586 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY1586 @ tc_bool ) ) @ SY1587 ) @ SY1585 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV8 @ SY1587 @ ( tc_fun @ SY1586 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(1418,plain,
! [SV9: $i] :
( ( ! [SY1588: $i,SY1589: $i] :
( ( c_Finite__Set_Ofinite @ SV9 @ SY1588 )
| ~ ( c_Finite__Set_Ofinite @ SY1589 @ SY1588 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY1588 @ tc_bool ) ) @ SV9 ) @ SY1589 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1419,plain,
! [SV10: $i] :
( ( ! [SY1590: $i,SY1591: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV10 @ tc_bool ) ) @ SY1590 ) @ SY1591 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1590 @ SY1591 @ ( tc_fun @ SV10 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1420,plain,
! [SV11: $i] :
( ( ! [SY1592: $i,SY1593: $i,SY1594: $i,SY1595: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV11 )
| ( ( c_Finite__Set_Osetsum @ SY1592 @ ( c_HOL_Ominus__class_Ominus @ SY1593 @ ( c_Set_Oinsert @ SY1594 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1595 @ tc_bool ) ) @ SY1595 ) @ ( tc_fun @ SY1595 @ tc_bool ) ) @ SY1595 @ SV11 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SY1592 @ SY1593 @ SY1595 @ SV11 ) @ ( hAPP @ SY1592 @ SY1594 ) @ SV11 ) )
| ~ ( hBOOL @ ( c_in @ SY1594 @ SY1593 @ SY1595 ) )
| ~ ( c_Finite__Set_Ofinite @ SY1593 @ SY1595 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1421,plain,
! [SV12: $i] :
( ( ! [SY1596: $i,SY1597: $i,SY1598: $i,SY1599: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV12 )
| ( ( c_Finite__Set_Osetsum @ SY1596 @ ( c_HOL_Ominus__class_Ominus @ SY1597 @ ( c_Set_Oinsert @ SY1598 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1599 @ tc_bool ) ) @ SY1599 ) @ ( tc_fun @ SY1599 @ tc_bool ) ) @ SY1599 @ SV12 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SY1596 @ SY1597 @ SY1599 @ SV12 ) @ ( hAPP @ SY1596 @ SY1598 ) @ SV12 ) )
| ~ ( hBOOL @ ( c_in @ SY1598 @ SY1597 @ SY1599 ) )
| ~ ( c_Finite__Set_Ofinite @ SY1597 @ SY1599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1422,plain,
! [SV13: $i] :
( ( ! [SY1600: $i,SY1601: $i,SY1602: $i] :
( ( c_HOL_Oord__class_Oless @ SV13 @ ( c_Set_Oinsert @ SY1600 @ SY1601 @ SY1602 ) @ ( tc_fun @ SY1602 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY1602 @ tc_bool ) ) @ SV13 ) @ SY1601 ) )
| ( hBOOL @ ( c_in @ SY1600 @ SV13 @ SY1602 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV13 @ SY1601 @ ( tc_fun @ SY1602 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1423,plain,
! [SV14: $i] :
( ( ! [SY1603: $i,SY1604: $i,SY1605: $i] :
( ( c_HOL_Oord__class_Oless @ SV14 @ ( c_Set_Oinsert @ SY1603 @ SY1604 @ SY1605 ) @ ( tc_fun @ SY1605 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY1605 @ tc_bool ) ) @ SV14 ) @ SY1604 ) )
| ( hBOOL @ ( c_in @ SY1603 @ SV14 @ SY1605 ) )
| ( hBOOL @ ( c_in @ SY1603 @ SY1604 @ SY1605 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1424,plain,
! [SV15: $i] :
( ( ! [SY1606: $i,SY1607: $i,SY1608: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV15 @ tc_bool ) ) @ SY1606 ) @ SY1607 ) )
| ( hBOOL @ ( c_in @ SY1608 @ SY1606 @ SV15 ) )
| ( hBOOL @ ( c_in @ SY1608 @ SY1607 @ SV15 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1606 @ ( c_Set_Oinsert @ SY1608 @ SY1607 @ SV15 ) @ ( tc_fun @ SV15 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1425,plain,
! [SV16: $i] :
( ( ! [SY1609: $i,SY1610: $i,SY1611: $i] :
( ~ ( class_Orderings_Olinorder @ SV16 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY1609 @ SY1610 @ SV16 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SY1610 @ SY1611 @ SV16 ) @ ( tc_fun @ SV16 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SY1609 @ SY1611 @ SV16 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV16 ) @ SY1610 ) @ SY1611 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV16 ) @ SY1609 ) @ SY1610 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1426,plain,
! [SV17: $i] :
( ( ! [SY1612: $i] :
( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ SV17 ) @ SV17 @ SV17 @ tc_bool ) @ SY1612 ) @ SV17 )
= ( c_Set_Oinsert @ SY1612 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV17 @ tc_bool ) ) @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1427,plain,
! [SV18: $i] :
( ( ! [SY1613: $i,SY1614: $i] :
( ( c_Set_Oinsert @ SV18 @ SY1613 @ SY1614 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ SY1614 ) @ SY1614 @ SY1614 @ tc_bool ) @ SV18 ) @ SY1614 ) @ SY1613 @ ( tc_fun @ SY1614 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1428,plain,
! [SV19: $i] :
( ( ! [SY1615: $i,SY1616: $i] :
( ( c_Finite__Set_Ofinite @ SV19 @ SY1615 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SY1616 @ SV19 @ SY1615 ) @ SY1615 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1429,plain,
! [SV20: $i] :
( ( ! [SY1617: $i,SY1618: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV20 @ SY1617 @ SY1618 ) @ SY1618 )
| ~ ( c_Finite__Set_Ofinite @ SY1617 @ SY1618 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1430,plain,
! [SV21: $i] :
( ( ! [SY1619: $i,SY1620: $i,SY1621: $i] : ( c_Nitpick_Ofold__graph_H @ SV21 @ SY1619 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1620 @ tc_bool ) ) @ SY1619 @ SY1620 @ SY1621 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1431,plain,
! [SV22: $i] :
( ( ! [SY1622: $i,SY1623: $i,SY1624: $i] : ( c_Finite__Set_Ofold__graph @ SV22 @ SY1622 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1623 @ tc_bool ) ) @ SY1622 @ SY1623 @ SY1624 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1432,plain,
! [SV23: $i] :
( ( ! [SY1625: $i,SY1626: $i,SY1627: $i,SY1628: $i] :
( ( SV23 = SY1625 )
| ~ ( c_Finite__Set_Ofold__graph @ SY1626 @ SY1625 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1627 @ tc_bool ) ) @ SV23 @ SY1627 @ SY1628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1433,plain,
! [SV24: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV24 @ tc_bool ) ) @ SV24 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1434,plain,
! [SV25: $i] :
( ( ! [SY1629: $i] :
~ ( c_HOL_Oord__class_Oless @ SV25 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1629 @ tc_bool ) ) @ ( tc_fun @ SY1629 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1435,plain,
! [SV26: $i] :
( ( ! [SY1630: $i,SY1631: $i] :
( ~ ( class_Orderings_Opreorder @ SV26 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV26 ) @ SY1630 ) @ SY1631 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1631 @ SY1630 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1436,plain,
! [SV27: $i] :
( ( ! [SY1632: $i,SY1633: $i] :
( ~ ( class_Orderings_Olinorder @ SV27 )
| ( c_HOL_Oord__class_Oless @ SY1632 @ SY1633 @ SV27 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV27 ) @ SY1633 ) @ SY1632 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1437,plain,
! [SV28: $i] :
( ( ! [SY1634: $i,SY1635: $i] :
( ~ ( class_Orderings_Olinorder @ SV28 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV28 ) @ SY1634 ) @ SY1635 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1635 @ SY1634 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1438,plain,
! [SV29: $i] :
( ( ! [SY1636: $i,SY1637: $i] :
( ~ ( class_Orderings_Olinorder @ SV29 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV29 ) @ SY1636 ) @ SY1637 ) )
| ( c_HOL_Oord__class_Oless @ SY1637 @ SY1636 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1439,plain,
! [SV30: $i] :
( ( ! [SY1638: $i,SY1639: $i] :
( ~ ( class_Orderings_Olinorder @ SV30 )
| ~ ( c_HOL_Oord__class_Oless @ SY1638 @ SY1639 @ SV30 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV30 ) @ SY1639 ) @ SY1638 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1440,plain,
! [SV31: $i] :
( ( ! [SY1640: $i] :
( ~ ( class_Orderings_Olinorder @ SV31 )
| ( c_HOL_Oord__class_Oless @ SY1640 @ SY1640 @ SV31 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV31 ) @ SY1640 ) @ SY1640 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1441,plain,
! [SV32: $i] :
( ( ! [SY1641: $i] :
( ~ ( class_Orderings_Olinorder @ SV32 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV32 ) @ SY1641 ) @ SY1641 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1641 @ SY1641 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1442,plain,
! [SV33: $i] :
( ( ! [SY1642: $i,SY1643: $i] :
( ~ ( class_Orderings_Olinorder @ SV33 )
| ( c_HOL_Oord__class_Oless @ SY1642 @ SY1643 @ SV33 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV33 ) @ SY1643 ) @ SY1642 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1443,plain,
! [SV34: $i] :
( ( ! [SY1644: $i,SY1645: $i] :
( ~ ( class_Orderings_Opreorder @ SV34 )
| ( c_HOL_Oord__class_Oless @ SY1644 @ SY1645 @ SV34 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV34 ) @ SY1645 ) @ SY1644 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV34 ) @ SY1644 ) @ SY1645 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1444,plain,
! [SV35: $i] :
( ( ! [SY1646: $i,SY1647: $i] :
( ~ ( class_Orderings_Oorder @ SV35 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV35 ) @ SY1646 ) @ SY1647 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1646 @ SY1647 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1445,plain,
! [SV36: $i] :
( ( ! [SY1648: $i,SY1649: $i] :
( ~ ( class_Orderings_Opreorder @ SV36 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV36 ) @ SY1648 ) @ SY1649 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1648 @ SY1649 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1446,plain,
! [SV37: $i] :
( ( ! [SY1650: $i,SY1651: $i,SY1652: $i] :
( ~ ( class_Orderings_Oorder @ SV37 )
| ( c_HOL_Oord__class_Oless @ SY1650 @ SY1651 @ SV37 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV37 ) @ SY1650 ) @ SY1652 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1652 @ SY1651 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1447,plain,
! [SV38: $i] :
( ( ! [SY1653: $i,SY1654: $i,SY1655: $i] :
( ~ ( class_Orderings_Oorder @ SV38 )
| ( c_HOL_Oord__class_Oless @ SY1653 @ SY1654 @ SV38 )
| ~ ( c_HOL_Oord__class_Oless @ SY1653 @ SY1655 @ SV38 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV38 ) @ SY1655 ) @ SY1654 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1448,plain,
! [SV39: $i] :
( ( ! [SY1656: $i,SY1657: $i,SY1658: $i] :
( ~ ( class_Orderings_Opreorder @ SV39 )
| ( c_HOL_Oord__class_Oless @ SY1656 @ SY1657 @ SV39 )
| ~ ( c_HOL_Oord__class_Oless @ SY1658 @ SY1657 @ SV39 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV39 ) @ SY1656 ) @ SY1658 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1449,plain,
! [SV40: $i] :
( ( ! [SY1659: $i,SY1660: $i,SY1661: $i] :
( ~ ( class_Orderings_Opreorder @ SV40 )
| ( c_HOL_Oord__class_Oless @ SY1659 @ SY1660 @ SV40 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV40 ) @ SY1661 ) @ SY1660 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1659 @ SY1661 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1450,plain,
! [SV41: $i] :
( ( ! [SY1662: $i,SY1663: $i] :
( ~ ( class_Orderings_Oorder @ SV41 )
| ( c_HOL_Oord__class_Oless @ SY1662 @ SY1663 @ SV41 )
| ( SY1663 = SY1662 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV41 ) @ SY1662 ) @ SY1663 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1451,plain,
! [SV42: $i] :
( ( ! [SY1664: $i,SY1665: $i] :
( ~ ( class_Orderings_Oorder @ SV42 )
| ( c_HOL_Oord__class_Oless @ SY1664 @ SY1665 @ SV42 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV42 ) @ SY1664 ) @ SY1665 ) )
| ( SY1665 = SY1664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1452,plain,
! [SV43: $i] :
( ( ! [SY1666: $i,SY1667: $i] :
( ~ ( class_Orderings_Oorder @ SV43 )
| ( SY1666 = SY1667 )
| ( c_HOL_Oord__class_Oless @ SY1666 @ SY1667 @ SV43 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV43 ) @ SY1666 ) @ SY1667 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1453,plain,
! [SV44: $i] :
( ( ! [SY1668: $i,SY1669: $i] :
( ~ ( class_Orderings_Oorder @ SV44 )
| ( c_HOL_Oord__class_Oless @ SY1668 @ SY1669 @ SV44 )
| ( SY1668 = SY1669 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV44 ) @ SY1668 ) @ SY1669 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1454,plain,
! [SV45: $i] :
( ( ! [SY1670: $i,SY1671: $i] :
( ~ ( class_Orderings_Oorder @ SV45 )
| ( c_HOL_Oord__class_Oless @ SY1670 @ SY1671 @ SV45 )
| ( SY1670 = SY1671 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV45 ) @ SY1670 ) @ SY1671 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1455,plain,
! [SV46: $i] :
( ( ! [SY1672: $i,SY1673: $i] :
( ~ ( class_Orderings_Oorder @ SV46 )
| ( c_HOL_Oord__class_Oless @ SY1672 @ SY1673 @ SV46 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV46 ) @ SY1672 ) @ SY1673 ) )
| ( SY1672 = SY1673 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1456,plain,
! [SV47: $i] :
( ( ! [SY1674: $i,SY1675: $i] :
( ~ ( class_Orderings_Olinorder @ SV47 )
| ( SY1674 = SY1675 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV47 ) @ SY1674 ) @ SY1675 ) )
| ( c_HOL_Oord__class_Oless @ SY1674 @ SY1675 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1457,plain,
! [SV48: $i] :
( ( ! [SY1676: $i,SY1677: $i] :
( ~ ( class_Orderings_Olinorder @ SV48 )
| ( SY1676 = SY1677 )
| ( c_HOL_Oord__class_Oless @ SY1676 @ SY1677 @ SV48 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV48 ) @ SY1676 ) @ SY1677 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1458,plain,
! [SV49: $i] :
( ( ! [SY1678: $i,SY1679: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV49 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SY1678 @ SV49 ) @ SY1679 @ SV49 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SY1679 @ SV49 ) @ SY1678 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1459,plain,
! [SV50: $i] :
( ( ! [SY1680: $i,SY1681: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV50 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SY1680 @ SV50 ) @ SY1681 @ SV50 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SY1681 @ SV50 ) @ SY1680 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1460,plain,
! [SV51: $i] :
( ( ! [SY1682: $i,SY1683: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV51 )
| ( c_HOL_Oord__class_Oless @ SY1682 @ ( c_HOL_Ouminus__class_Ouminus @ SY1683 @ SV51 ) @ SV51 )
| ~ ( c_HOL_Oord__class_Oless @ SY1683 @ ( c_HOL_Ouminus__class_Ouminus @ SY1682 @ SV51 ) @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1461,plain,
! [SV52: $i] :
( ( ! [SY1684: $i,SY1685: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV52 )
| ( c_HOL_Oord__class_Oless @ SY1684 @ ( c_HOL_Ouminus__class_Ouminus @ SY1685 @ SV52 ) @ SV52 )
| ~ ( c_HOL_Oord__class_Oless @ SY1685 @ ( c_HOL_Ouminus__class_Ouminus @ SY1684 @ SV52 ) @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1462,plain,
! [SV53: $i] :
( ( ! [SY1686: $i,SY1687: $i,SY1688: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV53 )
| ( c_HOL_Oord__class_Oless @ SY1686 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1687 @ SY1688 @ SV53 ) @ SV53 )
| ~ ( c_HOL_Oord__class_Oless @ SY1686 @ SY1688 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1463,plain,
! [SV54: $i] :
( ( ! [SY1689: $i,SY1690: $i,SY1691: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV54 )
| ( c_HOL_Oord__class_Oless @ SY1689 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1690 @ SY1691 @ SV54 ) @ SV54 )
| ~ ( c_HOL_Oord__class_Oless @ SY1689 @ SY1690 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1464,plain,
! [SV55: $i] :
( ( ! [SY1692: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV55 )
| ( c_Finite__Set_Ofinite @ SY1692 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1465,plain,
! [SV56: $i] :
( ( ! [SY1693: $i,SY1694: $i,SY1695: $i,SY1696: $i] :
( ~ ( class_Orderings_Oorder @ SV56 )
| ( c_HOL_Oord__class_Oless @ SY1693 @ SY1694 @ SV56 )
| ( c_HOL_Oord__class_Oless @ SY1695 @ SY1696 @ SV56 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV56 ) @ SY1696 ) @ SY1693 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY1696 @ SY1693 @ SV56 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY1695 @ SY1694 @ SV56 ) @ ( tc_fun @ SV56 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1466,plain,
! [SV57: $i] :
( ( ! [SY1697: $i,SY1698: $i,SY1699: $i,SY1700: $i,SY1701: $i,SY1702: $i,SY1703: $i,SY1704: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV57 @ SY1697 @ ( c_COMBC @ SY1698 @ SY1699 @ SY1699 @ tc_bool ) @ ( c_COMBC @ SY1700 @ SY1699 @ SY1699 @ tc_bool ) @ SY1701 @ SY1702 @ SY1703 @ SY1704 @ SY1699 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY1697 @ SV57 @ SY1698 @ SY1700 @ SY1702 @ SY1701 @ SY1704 @ SY1703 @ SY1699 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1467,plain,
! [SV58: $i] :
( ( ! [SY1705: $i,SY1706: $i,SY1707: $i] :
( ( hAPP @ ( c_COMBK @ SV58 @ SY1705 @ SY1706 ) @ SY1707 )
= SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1468,plain,
! [SV59: $i] :
( ( ! [SY1708: $i,SY1709: $i,SY1710: $i,SY1711: $i,SY1712: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV59 @ SY1708 @ SY1709 @ SY1710 ) @ SY1711 ) @ SY1712 )
= ( hAPP @ ( hAPP @ SV59 @ SY1712 ) @ SY1711 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1469,plain,
! [SV60: $i] :
( ( ! [SY1713: $i,SY1714: $i,SY1715: $i] :
( ~ ( class_Orderings_Oorder @ SV60 )
| ( c_HOL_Oord__class_Oless @ SY1713 @ SY1714 @ SV60 )
| ~ ( c_HOL_Oord__class_Oless @ SY1713 @ SY1715 @ SV60 )
| ~ ( c_HOL_Oord__class_Oless @ SY1715 @ SY1714 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1470,plain,
! [SV61: $i] :
( ( ! [SY1716: $i,SY1717: $i,SY1718: $i] :
( ( hBOOL @ ( c_in @ SV61 @ SY1716 @ SY1717 ) )
| ~ ( hBOOL @ ( c_in @ SV61 @ SY1718 @ SY1717 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1718 @ SY1716 @ ( tc_fun @ SY1717 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1471,plain,
! [SV62: $i] :
( ( ! [SY1719: $i,SY1720: $i,SY1721: $i] :
( ( c_HOL_Oord__class_Oless @ SV62 @ SY1719 @ ( tc_fun @ SY1720 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1721 @ SY1719 @ ( tc_fun @ SY1720 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV62 @ SY1721 @ ( tc_fun @ SY1720 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1472,plain,
! [SV63: $i] :
( ( ! [SY1722: $i,SY1723: $i,SY1724: $i] :
( ~ ( class_Orderings_Opreorder @ SV63 )
| ( c_HOL_Oord__class_Oless @ SY1722 @ SY1723 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SY1724 @ SY1723 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SY1722 @ SY1724 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1473,plain,
! [SV64: $i] :
( ( ! [SY1725: $i,SY1726: $i,SY1727: $i,SY1728: $i,SY1729: $i] :
( ( c_Finite__Set_Ofinite @ SV64 @ SY1725 )
| ~ ( c_Finite__Set_Ofold__graph @ SY1726 @ SY1727 @ SV64 @ SY1728 @ SY1725 @ SY1729 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1474,plain,
! [SV65: $i] :
( ( ! [SY1730: $i,SY1731: $i] :
( ~ ( class_Orderings_Oorder @ SV65 )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SY1730 @ SY1731 @ SV65 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV65 @ tc_bool ) ) )
| ( c_HOL_Oord__class_Oless @ SY1730 @ SY1731 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1475,plain,
! [SV66: $i] :
( ( ! [SY1732: $i,SY1733: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV66 @ SY1732 @ ( tc_fun @ SY1733 @ tc_bool ) ) @ SY1733 )
| ~ ( c_Finite__Set_Ofinite @ SV66 @ SY1733 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1476,plain,
! [SV67: $i] :
( ( ! [SY1734: $i,SY1735: $i] :
( ( c_Finite__Set_Ofinite @ SV67 @ SY1734 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV67 @ SY1735 @ ( tc_fun @ SY1734 @ tc_bool ) ) @ SY1734 )
| ~ ( c_Finite__Set_Ofinite @ SY1735 @ SY1734 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1477,plain,
! [SV68: $i] :
( ( ! [SY1736: $i,SY1737: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV68 @ SY1736 @ ( tc_fun @ SY1737 @ tc_bool ) ) @ SY1737 )
| ~ ( c_Finite__Set_Ofinite @ SV68 @ SY1737 )
| ~ ( c_Finite__Set_Ofinite @ SY1736 @ SY1737 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1478,plain,
! [SV69: $i] :
( ( ! [SY1738: $i] :
( ( c_The @ ( hAPP @ ( c_COMBC @ ( c_fequal @ SV69 ) @ SV69 @ SV69 @ tc_bool ) @ SY1738 ) @ SV69 )
= SY1738 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1479,plain,
! [SV70: $i] :
( ( ! [SY1739: $i,SY1740: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV70 @ SY1739 @ ( tc_fun @ SY1740 @ tc_bool ) ) @ SY1740 )
| ~ ( c_Finite__Set_Ofinite @ SY1739 @ SY1740 )
| ~ ( c_Finite__Set_Ofinite @ SV70 @ SY1740 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1480,plain,
! [SV71: $i] :
( ( ! [SY1741: $i,SY1742: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV71 @ SY1741 @ ( tc_fun @ SY1742 @ tc_bool ) ) @ SY1742 )
| ~ ( c_Finite__Set_Ofinite @ SY1741 @ SY1742 )
| ~ ( c_Finite__Set_Ofinite @ SV71 @ SY1742 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1481,plain,
! [SV72: $i] :
( ( ! [SY1743: $i,SY1744: $i] :
( ( c_Finite__Set_Ofinite @ SV72 @ SY1743 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV72 @ SY1744 @ ( tc_fun @ SY1743 @ tc_bool ) ) @ SY1743 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1482,plain,
! [SV73: $i] :
( ( ! [SY1745: $i,SY1746: $i] :
( ( c_Finite__Set_Ofinite @ SV73 @ SY1745 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1746 @ SV73 @ ( tc_fun @ SY1745 @ tc_bool ) ) @ SY1745 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1483,plain,
! [SV74: $i] :
( ( ! [SY1747: $i,SY1748: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV74 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SY1747 @ SV74 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY1748 @ SV74 ) @ SV74 )
| ~ ( c_HOL_Oord__class_Oless @ SY1748 @ SY1747 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1484,plain,
! [SV75: $i] :
( ( ! [SY1749: $i,SY1750: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV75 )
| ( c_HOL_Oord__class_Oless @ SY1749 @ SY1750 @ SV75 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SY1750 @ SV75 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY1749 @ SV75 ) @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1485,plain,
! [SV76: $i] :
( ( ! [SY1751: $i] :
~ ( c_HOL_Oord__class_Oless @ SV76 @ SV76 @ ( tc_fun @ SY1751 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1486,plain,
! [SV77: $i] :
( ( ! [SY1752: $i] :
( ~ ( class_Orderings_Oorder @ SV77 )
| ~ ( c_HOL_Oord__class_Oless @ SY1752 @ SY1752 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1487,plain,
! [SV78: $i] :
( ( ! [SY1753: $i] :
( ~ ( class_Orderings_Olinorder @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ SY1753 @ SY1753 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1488,plain,
! [SV79: $i] :
( ( ! [SY1754: $i] :
( ~ ( class_Orderings_Opreorder @ SV79 )
| ~ ( c_HOL_Oord__class_Oless @ SY1754 @ SY1754 @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1489,plain,
! [SV80: $i] :
( ( ! [SY1755: $i,SY1756: $i,SY1757: $i,SY1758: $i] :
( ~ ( class_Orderings_Oorder @ SV80 )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY1755 @ SY1756 @ SV80 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY1757 @ SY1758 @ SV80 ) @ ( tc_fun @ SV80 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SY1757 ) @ SY1758 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1756 @ SY1758 @ SV80 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SY1756 ) @ SY1758 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SY1757 ) @ SY1755 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1490,plain,
! [SV81: $i] :
( ( ! [SY1759: $i,SY1760: $i,SY1761: $i,SY1762: $i] :
( ~ ( class_Orderings_Oorder @ SV81 )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY1759 @ SY1760 @ SV81 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY1761 @ SY1762 @ SV81 ) @ ( tc_fun @ SV81 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SY1761 ) @ SY1762 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1761 @ SY1759 @ SV81 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SY1760 ) @ SY1762 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SY1761 ) @ SY1759 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1491,plain,
! [SV82: $i] :
( ( ! [SY1763: $i,SY1764: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV82 )
| ( c_HOL_Oord__class_Oless @ SY1763 @ SY1764 @ SV82 )
| ( c_HOL_Oord__class_Oless @ SY1764 @ SY1763 @ SV82 )
| ( SY1764 = SY1763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1492,plain,
! [SV83: $i] :
( ( ! [SY1765: $i,SY1766: $i] :
( ~ ( class_Orderings_Olinorder @ SV83 )
| ( SY1765 = SY1766 )
| ( c_HOL_Oord__class_Oless @ SY1766 @ SY1765 @ SV83 )
| ( c_HOL_Oord__class_Oless @ SY1765 @ SY1766 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1493,plain,
! [SV84: $i] :
( ( ! [SY1767: $i,SY1768: $i] :
( ~ ( class_Orderings_Olinorder @ SV84 )
| ( c_HOL_Oord__class_Oless @ SY1767 @ SY1768 @ SV84 )
| ( c_HOL_Oord__class_Oless @ SY1768 @ SY1767 @ SV84 )
| ( SY1768 = SY1767 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1494,plain,
! [SV85: $i] :
( ( ! [SY1769: $i,SY1770: $i] :
( ~ ( class_Orderings_Olinorder @ SV85 )
| ( c_HOL_Oord__class_Oless @ SY1769 @ SY1770 @ SV85 )
| ( SY1770 = SY1769 )
| ( c_HOL_Oord__class_Oless @ SY1770 @ SY1769 @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1495,plain,
! [SV86: $i] :
( ( ! [SY1771: $i,SY1772: $i] :
( ~ ( class_Orderings_Olinorder @ SV86 )
| ( SY1771 = SY1772 )
| ( c_HOL_Oord__class_Oless @ SY1771 @ SY1772 @ SV86 )
| ( c_HOL_Oord__class_Oless @ SY1772 @ SY1771 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1496,plain,
! [SV87: $i] :
( ( ! [SY1773: $i,SY1774: $i] :
( ~ ( class_Orderings_Oorder @ SV87 )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV87 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SY1773 @ SY1774 @ SV87 ) )
| ( c_HOL_Oord__class_Oless @ SY1773 @ SY1774 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1497,plain,
! [SV88: $i] :
( ( ! [SY1775: $i,SY1776: $i] :
( ~ ( class_Orderings_Oorder @ SV88 )
| ~ ( c_HOL_Oord__class_Oless @ SY1775 @ SY1776 @ SV88 )
| ~ ( c_HOL_Oord__class_Oless @ SY1776 @ SY1775 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1498,plain,
! [SV89: $i] :
( ( ! [SY1777: $i,SY1778: $i] :
( ~ ( class_Orderings_Olinorder @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SY1777 @ SY1778 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SY1778 @ SY1777 @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1499,plain,
! [SV90: $i] :
( ( ! [SY1779: $i,SY1780: $i] :
( ~ ( class_Orderings_Opreorder @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ SY1779 @ SY1780 @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ SY1780 @ SY1779 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1500,plain,
! [SV91: $i] :
( ( ! [SY1781: $i,SY1782: $i] :
( ~ ( class_Orderings_Opreorder @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SY1781 @ SY1782 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SY1782 @ SY1781 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1501,plain,
! [SV92: $i] :
( ( ! [SY1783: $i,SY1784: $i,SY1785: $i,SY1786: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV92 )
| ( ( c_Finite__Set_Osetsum @ SY1783 @ ( c_HOL_Ominus__class_Ominus @ SY1784 @ SY1785 @ ( tc_fun @ SY1786 @ tc_bool ) ) @ SY1786 @ SV92 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SY1783 @ SY1784 @ SY1786 @ SV92 ) @ ( c_Finite__Set_Osetsum @ SY1783 @ SY1785 @ SY1786 @ SV92 ) @ SV92 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY1786 @ tc_bool ) ) @ SY1785 ) @ SY1784 ) )
| ~ ( c_Finite__Set_Ofinite @ SY1784 @ SY1786 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1502,plain,
! [SV93: $i] :
( ( ! [SY1787: $i,SY1788: $i] :
( ~ ( class_Orderings_Oorder @ SV93 )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SY1787 @ SY1788 @ SV93 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV93 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV93 ) @ SY1788 ) @ SY1787 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1503,plain,
! [SV94: $i] :
( ( ! [SY1789: $i,SY1790: $i,SY1791: $i,SY1792: $i,SY1793: $i,SY1794: $i] :
( ( c_Finite__Set_Ofold__graph @ SV94 @ SY1789 @ ( c_Set_Oinsert @ SY1790 @ SY1791 @ SY1792 ) @ ( hAPP @ ( hAPP @ SV94 @ SY1790 ) @ SY1793 ) @ SY1792 @ SY1794 )
| ~ ( c_Finite__Set_Ofold__graph @ SV94 @ SY1789 @ SY1791 @ SY1793 @ SY1792 @ SY1794 )
| ( hBOOL @ ( c_in @ SY1790 @ SY1791 @ SY1792 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1504,plain,
! [SV95: $i] :
( ( ! [SY1795: $i,SY1796: $i,SY1797: $i] :
( ( c_HOL_Oord__class_Oless @ SV95 @ SY1795 @ ( tc_fun @ SY1796 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SY1797 @ SY1795 @ SY1796 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV95 @ ( c_Set_Oinsert @ SY1797 @ SY1795 @ SY1796 ) @ ( tc_fun @ SY1796 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1505,plain,
! [SV96: $i] :
( ( ! [SY1798: $i,SY1799: $i,SY1800: $i] :
( ( c_HOL_Oord__class_Oless @ SV96 @ ( c_Set_Oinsert @ SY1798 @ SY1799 @ SY1800 ) @ ( tc_fun @ SY1800 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SY1798 @ SY1799 @ SY1800 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV96 @ SY1799 @ ( tc_fun @ SY1800 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1506,plain,
! [SV97: $i] :
( ( ! [SY1801: $i,SY1802: $i,SY1803: $i,SY1804: $i] :
( ~ ( class_Orderings_Oorder @ SV97 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV97 ) @ SY1801 ) @ SY1802 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV97 ) @ SY1803 ) @ SY1801 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY1803 @ SY1801 @ SV97 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY1804 @ SY1802 @ SV97 ) @ ( tc_fun @ SV97 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1507,plain,
! [SV98: $i] :
( ( ! [SY1805: $i,SY1806: $i,SY1807: $i,SY1808: $i] :
( ~ ( class_Orderings_Oorder @ SV98 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV98 ) @ SY1805 ) @ SY1806 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV98 ) @ SY1806 ) @ SY1807 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY1806 @ SY1807 @ SV98 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY1805 @ SY1808 @ SV98 ) @ ( tc_fun @ SV98 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1508,plain,
! [SV99: $i] :
( ( ! [SY1809: $i,SY1810: $i,SY1811: $i,SY1812: $i] :
( ~ ( class_Orderings_Oorder @ SV99 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV99 ) @ SY1809 ) @ SY1810 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY1811 @ SY1812 @ SV99 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY1809 @ SY1810 @ SV99 ) @ ( tc_fun @ SV99 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1509,plain,
! [SV100: $i] :
( ( ! [SY1813: $i,SY1814: $i,SY1815: $i,SY1816: $i] :
( ~ ( class_Orderings_Oorder @ SV100 )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY1813 @ SY1814 @ SV100 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY1815 @ SY1816 @ SV100 ) @ ( tc_fun @ SV100 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV100 ) @ SY1815 ) @ SY1816 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV100 ) @ SY1813 ) @ SY1814 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1510,plain,
! [SV101: $i] :
( ( ! [SY1817: $i,SY1818: $i,SY1819: $i] :
( ~ ( class_Orderings_Olinorder @ SV101 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SY1817 @ SY1818 @ SV101 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SY1818 @ SY1819 @ SV101 ) @ ( tc_fun @ SV101 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SY1817 @ SY1819 @ SV101 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV101 ) @ SY1818 ) @ SY1819 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV101 ) @ SY1817 ) @ SY1818 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1511,plain,
! [SV102: $i] :
( ( ! [SY1820: $i,SY1821: $i,SY1822: $i,SY1823: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ SV102 @ SY1820 ) @ SY1821 )
| ~ ( hBOOL @ ( c_in @ SY1820 @ SY1822 @ SY1823 ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY1822 @ SV102 @ SY1823 @ ( tc_fun @ SY1821 @ tc_bool ) ) @ SY1821 )
| ~ ( c_Finite__Set_Ofinite @ SY1822 @ SY1823 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1512,plain,
! [SV103: $i] :
( ( ! [SY1824: $i,SY1825: $i,SY1826: $i,SY1827: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV103 )
| ( ( c_Finite__Set_Osetsum @ SY1824 @ ( c_HOL_Ominus__class_Ominus @ SY1825 @ ( c_Set_Oinsert @ SY1826 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1827 @ tc_bool ) ) @ SY1827 ) @ ( tc_fun @ SY1827 @ tc_bool ) ) @ SY1827 @ SV103 )
= ( c_Finite__Set_Osetsum @ SY1824 @ SY1825 @ SY1827 @ SV103 ) )
| ( hBOOL @ ( c_in @ SY1826 @ SY1825 @ SY1827 ) )
| ~ ( c_Finite__Set_Ofinite @ SY1825 @ SY1827 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1513,plain,
! [SV104: $i] :
( ( ! [SY1828: $i,SY1829: $i] :
( ~ ( class_Orderings_Oorder @ SV104 )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SY1828 @ SY1829 @ SV104 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV104 @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1829 @ SY1828 @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1514,plain,
! [SV105: $i] :
( ( ! [SY1830: $i,SY1831: $i,SY1832: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV105 )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY1830 @ ( c_COMBK @ SY1831 @ SV105 @ SY1832 ) @ SY1832 @ SV105 )
= SY1831 )
| ( SY1830
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1832 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1515,plain,
! [SV106: $i] :
( ( ! [SY1833: $i,SY1834: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV106 @ tc_bool ) ) @ ( c_COMBK @ SY1833 @ ( tc_fun @ SY1834 @ tc_bool ) @ SV106 ) @ SV106 @ ( tc_fun @ SY1834 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1834 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1516,plain,
! [SV107: $i] :
( ( ! [SY1835: $i,SY1836: $i,SY1837: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV107 @ ( c_COMBK @ SY1835 @ ( tc_fun @ SY1836 @ tc_bool ) @ SY1837 ) @ SY1837 @ ( tc_fun @ SY1836 @ tc_bool ) )
= SY1835 )
| ( SV107
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1837 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1517,plain,
! [SV108: $i] :
( ( ! [SY1838: $i,SY1839: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV108 @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1838 @ tc_bool ) ) @ ( tc_fun @ SY1838 @ tc_bool ) @ SY1839 ) @ SY1839 @ ( tc_fun @ SY1838 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1838 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1518,plain,
! [SV109: $i] :
( ( ! [SY1840: $i,SY1841: $i,SY1842: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV109 @ SY1840 @ ( tc_fun @ SY1841 @ tc_bool ) ) @ SY1841 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV109 @ ( c_Set_Oinsert @ SY1842 @ SY1840 @ SY1841 ) @ ( tc_fun @ SY1841 @ tc_bool ) ) @ SY1841 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1519,plain,
! [SV110: $i] :
( ( ! [SY1843: $i,SY1844: $i,SY1845: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV110 @ ( c_Set_Oinsert @ SY1843 @ SY1844 @ SY1845 ) @ ( tc_fun @ SY1845 @ tc_bool ) ) @ SY1845 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV110 @ SY1844 @ ( tc_fun @ SY1845 @ tc_bool ) ) @ SY1845 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1520,plain,
! [SV111: $i] :
( ( ! [SY1846: $i,SY1847: $i] :
( ~ ( class_Orderings_Oorder @ SV111 )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV111 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SY1846 @ SY1847 @ SV111 ) )
| ( c_HOL_Oord__class_Oless @ SY1846 @ SY1847 @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1521,plain,
! [SV112: $i] :
( ( ! [SY1848: $i,SY1849: $i] :
( ~ ( class_Orderings_Oorder @ SV112 )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ SY1848 @ SY1849 @ SV112 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV112 @ tc_bool ) ) )
| ( c_HOL_Oord__class_Oless @ SY1848 @ SY1849 @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1522,plain,
! [SV113: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV113 )
| ( c_Complete__Lattice_Ocomplete__lattice__axioms @ ( c_Complete__Lattice_OInf__class_OInf @ SV113 ) @ ( c_Complete__Lattice_OSup__class_OSup @ SV113 ) @ ( c_lessequals @ SV113 ) @ SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1523,plain,
( ( ( ~ ( class_HOL_Ouminus @ t_b ) )
= $true )
| ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ v_A @ ( tc_fun @ t_a @ t_b ) ) @ v_x )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ v_A @ v_x ) @ t_b ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1034]) ).
thf(1524,plain,
! [SV114: $i] :
( ( ! [SY1850: $i,SY1851: $i] :
( ~ ( class_Orderings_Olinorder @ SV114 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV114 ) @ SY1850 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SY1851 @ SV114 ) ) )
| ~ ( hBOOL @ ( c_in @ SY1850 @ SY1851 @ SV114 ) )
| ~ ( c_Finite__Set_Ofinite @ SY1851 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1525,plain,
! [SV115: $i] :
( ( ! [SY1852: $i,SY1853: $i] :
( ~ ( class_Orderings_Olinorder @ SV115 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV115 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SY1852 @ SV115 ) ) @ SY1853 ) )
| ~ ( hBOOL @ ( c_in @ SY1853 @ SY1852 @ SV115 ) )
| ~ ( c_Finite__Set_Ofinite @ SY1852 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1526,plain,
! [SV116: $i] :
( ( ! [SY1854: $i] :
( ~ ( class_Orderings_Olinorder @ SV116 )
| ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMin @ SY1854 @ SV116 ) @ SY1854 @ SV116 ) )
| ( SY1854
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV116 @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ SY1854 @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1527,plain,
! [SV117: $i] :
( ( ! [SY1855: $i] :
( ~ ( class_Orderings_Olinorder @ SV117 )
| ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMax @ SY1855 @ SV117 ) @ SY1855 @ SV117 ) )
| ( SY1855
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV117 @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ SY1855 @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1528,plain,
! [SV118: $i] :
( ( ! [SY1856: $i,SY1857: $i,SY1858: $i,SY1859: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV118 @ ( c_Set_Oinsert @ SY1856 @ SY1857 @ SY1858 ) @ SY1858 ) @ SY1859 ) )
| ( hBOOL @ ( c_in @ SY1856 @ SY1857 @ SY1858 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV118 @ SY1856 @ SY1857 @ SY1859 @ SY1858 @ SY1858 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1529,plain,
! [SV119: $i] :
( ( ! [SY1860: $i,SY1861: $i,SY1862: $i,SY1863: $i,SY1864: $i,SY1865: $i] :
( ( c_Finite__Set_Ofold__graph @ SV119 @ SY1860 @ SY1861 @ ( hAPP @ ( hAPP @ SV119 @ SY1862 ) @ SY1863 ) @ SY1864 @ SY1865 )
| ~ ( hBOOL @ ( c_in @ SY1862 @ SY1861 @ SY1864 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV119 @ SY1860 @ ( c_HOL_Ominus__class_Ominus @ SY1861 @ ( c_Set_Oinsert @ SY1862 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1864 @ tc_bool ) ) @ SY1864 ) @ ( tc_fun @ SY1864 @ tc_bool ) ) @ SY1863 @ SY1864 @ SY1865 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1530,plain,
! [SV120: $i] :
( ( ! [SY1866: $i,SY1867: $i,SY1868: $i] :
( ( ( c_Finite__Set_Osetsum @ SV120 @ ( c_HOL_Ominus__class_Ominus @ SY1866 @ ( c_Set_Oinsert @ SY1867 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1868 @ tc_bool ) ) @ SY1868 ) @ ( tc_fun @ SY1868 @ tc_bool ) ) @ SY1868 @ tc_nat )
= ( c_Finite__Set_Osetsum @ SV120 @ SY1866 @ SY1868 @ tc_nat ) )
| ( hBOOL @ ( c_in @ SY1867 @ SY1866 @ SY1868 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1531,plain,
! [SV121: $i] :
( ( ! [SY1869: $i,SY1870: $i,SY1871: $i] :
( ( c_HOL_Oord__class_Oless @ SV121 @ ( c_Set_Oinsert @ SY1869 @ SY1870 @ SY1871 ) @ ( tc_fun @ SY1871 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SY1869 @ SV121 @ SY1871 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV121 @ ( c_Set_Oinsert @ SY1869 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1871 @ tc_bool ) ) @ SY1871 ) @ ( tc_fun @ SY1871 @ tc_bool ) ) @ SY1870 @ ( tc_fun @ SY1871 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV121 @ SY1870 @ ( tc_fun @ SY1871 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1532,plain,
! [SV122: $i] :
( ( ! [SY1872: $i,SY1873: $i,SY1874: $i] :
( ( c_HOL_Oord__class_Oless @ SV122 @ ( c_Set_Oinsert @ SY1872 @ SY1873 @ SY1874 ) @ ( tc_fun @ SY1874 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SY1872 @ SV122 @ SY1874 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV122 @ ( c_Set_Oinsert @ SY1872 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1874 @ tc_bool ) ) @ SY1874 ) @ ( tc_fun @ SY1874 @ tc_bool ) ) @ SY1873 @ ( tc_fun @ SY1874 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SY1872 @ SY1873 @ SY1874 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1533,plain,
! [SV123: $i] :
( ( ! [SY1875: $i,SY1876: $i,SY1877: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV123 @ ( c_Set_Oinsert @ SY1875 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1876 @ tc_bool ) ) @ SY1876 ) @ ( tc_fun @ SY1876 @ tc_bool ) ) @ SY1877 @ ( tc_fun @ SY1876 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SY1875 @ SV123 @ SY1876 ) )
| ( hBOOL @ ( c_in @ SY1875 @ SY1877 @ SY1876 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV123 @ ( c_Set_Oinsert @ SY1875 @ SY1877 @ SY1876 ) @ ( tc_fun @ SY1876 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1534,plain,
! [SV124: $i] :
( ( ! [SY1878: $i,SY1879: $i,SY1880: $i,SY1881: $i,SY1882: $i,SY1883: $i] :
( ( c_Nitpick_Ofold__graph_H @ SV124 @ SY1878 @ SY1879 @ ( hAPP @ ( hAPP @ SV124 @ SY1880 ) @ SY1881 ) @ SY1882 @ SY1883 )
| ~ ( c_Nitpick_Ofold__graph_H @ SV124 @ SY1878 @ ( c_HOL_Ominus__class_Ominus @ SY1879 @ ( c_Set_Oinsert @ SY1880 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1882 @ tc_bool ) ) @ SY1882 ) @ ( tc_fun @ SY1882 @ tc_bool ) ) @ SY1881 @ SY1882 @ SY1883 )
| ~ ( hBOOL @ ( c_in @ SY1880 @ SY1879 @ SY1882 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1535,plain,
! [SV125: $i] :
( ( ! [SY1884: $i,SY1885: $i,SY1886: $i] :
( ( c_HOL_Oord__class_Oless @ SV125 @ ( c_Set_Oinsert @ SY1884 @ SY1885 @ SY1886 ) @ ( tc_fun @ SY1886 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY1886 @ tc_bool ) ) @ SV125 ) @ SY1885 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV125 @ ( c_Set_Oinsert @ SY1884 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1886 @ tc_bool ) ) @ SY1886 ) @ ( tc_fun @ SY1886 @ tc_bool ) ) @ SY1885 @ ( tc_fun @ SY1886 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV125 @ SY1885 @ ( tc_fun @ SY1886 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1536,plain,
! [SV126: $i] :
( ( ! [SY1887: $i,SY1888: $i] :
( ~ ( class_Orderings_Olinorder @ SV126 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV126 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SY1887 @ SV126 ) ) @ ( c_Finite__Set_Olinorder__class_OMin @ SY1888 @ SV126 ) ) )
| ~ ( c_Finite__Set_Ofinite @ SY1887 @ SV126 )
| ( SY1888
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV126 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV126 @ tc_bool ) ) @ SY1888 ) @ SY1887 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1537,plain,
! [SV127: $i] :
( ( ! [SY1889: $i,SY1890: $i] :
( ~ ( class_Orderings_Olinorder @ SV127 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV127 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SY1889 @ SV127 ) ) @ ( c_Finite__Set_Olinorder__class_OMax @ SY1890 @ SV127 ) ) )
| ~ ( c_Finite__Set_Ofinite @ SY1890 @ SV127 )
| ( SY1889
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV127 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV127 @ tc_bool ) ) @ SY1889 ) @ SY1890 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1538,plain,
! [SV128: $i] :
( ( ! [SY1891: $i,SY1892: $i,SY1893: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV128 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY1891 @ SY1892 @ SY1893 @ 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 @ SV128 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_COMBK @ ( hAPP @ ( c_COMBC @ ( c_fequal @ tc_Com_Ostate ) @ tc_Com_Ostate @ tc_Com_Ostate @ tc_bool ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ SV128 @ SY1891 @ SY1893 @ SY1892 ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) @ SY1892 @ ( c_COMBK @ ( hAPP @ SY1893 @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ SV128 @ SY1891 @ SY1893 @ SY1892 ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) @ 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_forall_pos,[status(thm)],[1049]) ).
thf(1539,plain,
! [SV129: $i] :
( ( ! [SY1894: $i,SY1895: $i] :
( ~ ( class_Orderings_Olinorder @ SV129 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SY1894 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV129 @ tc_bool ) ) @ SV129 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SY1894 @ SY1895 @ SV129 ) @ ( tc_fun @ SV129 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SY1894 @ SY1895 @ SV129 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV129 ) @ SY1894 ) @ SY1895 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1540,plain,
! [SV130: $i] :
( ( ! [SY1896: $i,SY1897: $i,SY1898: $i] :
( ( c_HOL_Oord__class_Oless @ SV130 @ ( c_Set_Oinsert @ SY1896 @ SY1897 @ SY1898 ) @ ( tc_fun @ SY1898 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY1898 @ tc_bool ) ) @ SV130 ) @ SY1897 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV130 @ ( c_Set_Oinsert @ SY1896 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1898 @ tc_bool ) ) @ SY1898 ) @ ( tc_fun @ SY1898 @ tc_bool ) ) @ SY1897 @ ( tc_fun @ SY1898 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SY1896 @ SY1897 @ SY1898 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1541,plain,
! [SV131: $i] :
( ( ! [SY1899: $i,SY1900: $i,SY1901: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV131 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1899 @ SY1900 @ SV131 ) ) @ SY1901 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ SY1900 ) @ SY1901 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ SY1899 ) @ SY1901 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1542,plain,
! [SV132: $i] :
( ( ! [SY1902: $i,SY1903: $i,SY1904: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV132 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1902 @ SY1903 @ SV132 ) ) @ SY1904 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ SY1903 ) @ SY1904 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ SY1902 ) @ SY1904 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1543,plain,
! [SV133: $i] :
( ( ! [SY1905: $i,SY1906: $i] :
( ~ ( class_Lattices_Olattice @ SV133 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV133 ) @ SY1905 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1906 @ SY1905 @ SV133 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1544,plain,
! [SV134: $i] :
( ( ! [SY1907: $i,SY1908: $i] :
( ~ ( class_Lattices_Olattice @ SV134 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV134 ) @ SY1907 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1907 @ SY1908 @ SV134 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1545,plain,
! [SV135: $i] :
( ( ! [SY1909: $i,SY1910: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV135 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV135 ) @ SY1909 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY1910 @ SV135 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV135 ) @ SY1910 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY1909 @ SV135 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1546,plain,
! [SV136: $i] :
( ( ! [SY1911: $i,SY1912: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV136 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV136 ) @ SY1911 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY1912 @ SV136 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV136 ) @ SY1912 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY1911 @ SV136 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1547,plain,
! [SV137: $i] :
( ( ! [SY1913: $i,SY1914: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV137 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV137 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY1913 @ SV137 ) ) @ SY1914 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV137 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY1914 @ SV137 ) ) @ SY1913 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1548,plain,
! [SV138: $i] :
( ( ! [SY1915: $i,SY1916: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV138 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV138 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY1915 @ SV138 ) ) @ SY1916 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV138 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY1916 @ SV138 ) ) @ SY1915 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1549,plain,
! [SV139: $i] :
( ( ! [SY1917: $i,SY1918: $i] :
( ~ ( class_Orderings_Olinorder @ SV139 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SY1917 @ SY1918 @ SV139 ) @ ( c_Set_Oinsert @ SY1918 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV139 @ tc_bool ) ) @ SV139 ) @ ( tc_fun @ SV139 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SY1917 @ SY1918 @ SV139 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV139 ) @ SY1917 ) @ SY1918 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1550,plain,
! [SV140: $i] :
( ( ! [SY1919: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SV140 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ SV140 ) @ SY1919 @ SV140 )
= SY1919 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1551,plain,
! [SV141: $i] :
( ( ! [SY1920: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SV141 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY1920 @ ( c_Orderings_Obot__class_Obot @ SV141 ) @ SV141 )
= SY1920 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1552,plain,
! [SV142: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV142 @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV142 @ tc_bool ) ) @ ( tc_fun @ SV142 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV142 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1553,plain,
! [SV143: $i] :
( ( ! [SY1921: $i,SY1922: $i,SY1923: $i,SY1924: $i,SY1925: $i,SY1926: $i,SY1927: $i,SY1928: $i] :
( ( ( hAPP @ SV143 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1921 @ tc_bool ) ) )
= SY1922 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV143 @ SY1923 @ SY1924 @ SY1925 @ SY1926 @ SY1927 @ SY1928 @ SY1922 @ SY1921 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1554,plain,
! [SV144: $i] :
( ( ! [SY1929: $i,SY1930: $i,SY1931: $i,SY1932: $i,SY1933: $i,SY1934: $i,SY1935: $i,SY1936: $i] :
( ( ( hAPP @ SV144 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1929 @ tc_bool ) ) )
= SY1930 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY1931 @ SV144 @ SY1932 @ SY1933 @ SY1934 @ SY1935 @ SY1930 @ SY1936 @ SY1929 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1555,plain,
! [SV145: $i] :
( ( ! [SY1937: $i] :
~ ( hBOOL @ ( c_in @ SV145 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1937 @ tc_bool ) ) @ SY1937 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1556,plain,
! [SV146: $i] :
( ( ! [SY1938: $i,SY1939: $i] :
( ( hBOOL @ ( hAPP @ SV146 @ SY1938 ) )
| ~ ( hBOOL @ ( c_in @ SY1938 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1939 @ tc_bool ) ) @ SY1939 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1557,plain,
! [SV147: $i] :
( ( ! [SY1940: $i] :
~ ( hBOOL @ ( c_in @ SV147 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1940 @ tc_bool ) ) @ SY1940 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1558,plain,
! [SV148: $i] :
( ( ! [SY1941: $i] :
~ ( hBOOL @ ( c_in @ SV148 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1941 @ tc_bool ) ) @ SY1941 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1559,plain,
! [SV149: $i] :
( ( ! [SY1942: $i,SY1943: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV149 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1942 @ tc_bool ) ) @ SY1942 ) @ SY1943 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1560,plain,
! [SV150: $i] :
( ( ! [SY1944: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV150 @ tc_bool ) ) @ SY1944 @ ( tc_fun @ SV150 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV150 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1561,plain,
! [SV151: $i] :
( ( ! [SY1945: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV151 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1945 @ tc_bool ) ) @ ( tc_fun @ SY1945 @ tc_bool ) )
= SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1562,plain,
! [SV152: $i] :
( ( ! [SY1946: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV152 @ tc_bool ) ) @ SY1946 @ ( tc_fun @ SV152 @ tc_bool ) )
= SY1946 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1563,plain,
! [SV153: $i] :
( ( ! [SY1947: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV153 @ SV153 @ ( tc_fun @ SY1947 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1947 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1564,plain,
! [SV154: $i] :
( ( ! [SY1948: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV154 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1948 @ tc_bool ) ) @ ( tc_fun @ SY1948 @ tc_bool ) )
= SV154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1565,plain,
! [SV155: $i] :
( ( ! [SY1949: $i,SY1950: $i] :
( ~ ( hBOOL @ ( hAPP @ SV155 @ SY1949 ) )
| ~ ( hBOOL @ ( c_in @ SY1949 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1950 @ tc_bool ) ) @ SY1950 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1566,plain,
! [SV156: $i] :
( ( ! [SY1951: $i,SY1952: $i] :
( ( ( c_Set_Oinsert @ SV156 @ ( c_HOL_Ominus__class_Ominus @ SY1951 @ ( c_Set_Oinsert @ SV156 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1952 @ tc_bool ) ) @ SY1952 ) @ ( tc_fun @ SY1952 @ tc_bool ) ) @ SY1952 )
= SY1951 )
| ~ ( hBOOL @ ( c_in @ SV156 @ SY1951 @ SY1952 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1567,plain,
! [SV157: $i] :
( ( ! [SY1953: $i,SY1954: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV157 )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV157 ) @ ( c_Set_Oinsert @ SY1953 @ ( c_Set_Oinsert @ SY1954 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV157 @ tc_bool ) ) @ SV157 ) @ SV157 ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY1953 @ SY1954 @ SV157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1568,plain,
! [SV158: $i] :
( ( ! [SY1955: $i,SY1956: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV158 @ SY1955 @ SY1956 ) @ ( c_Set_Oinsert @ SV158 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1956 @ tc_bool ) ) @ SY1956 ) @ ( tc_fun @ SY1956 @ tc_bool ) )
= SY1955 )
| ( hBOOL @ ( c_in @ SV158 @ SY1955 @ SY1956 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1569,plain,
! [SV159: $i] :
( ( ! [SY1957: $i,SY1958: $i,SY1959: $i] :
( ( hBOOL @ ( c_in @ SV159 @ ( c_Set_Oinsert @ SY1957 @ SY1958 @ SY1959 ) @ SY1959 ) )
| ~ ( hBOOL @ ( c_in @ SV159 @ SY1958 @ SY1959 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1570,plain,
! [SV160: $i] :
( ( ! [SY1960: $i,SY1961: $i,SY1962: $i] :
( ( hBOOL @ ( c_in @ SV160 @ ( c_Set_Oinsert @ SY1960 @ SY1961 @ SY1962 ) @ SY1962 ) )
| ~ ( hBOOL @ ( c_in @ SV160 @ SY1961 @ SY1962 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1571,plain,
! [SV161: $i] :
( ( ! [SY1963: $i,SY1964: $i,SY1965: $i,SY1966: $i,SY1967: $i,SY1968: $i,SY1969: $i,SY1970: $i,SY1971: $i,SY1972: $i] :
( ( ( hAPP @ SV161 @ ( c_Set_Oinsert @ SY1963 @ SY1964 @ SY1965 ) )
= ( hAPP @ ( hAPP @ SY1966 @ SY1963 ) @ ( hAPP @ SV161 @ SY1964 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV161 @ SY1967 @ SY1968 @ SY1969 @ SY1966 @ SY1970 @ SY1971 @ SY1972 @ SY1965 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1572,plain,
! [SV162: $i] :
( ( ! [SY1973: $i,SY1974: $i,SY1975: $i,SY1976: $i,SY1977: $i,SY1978: $i,SY1979: $i,SY1980: $i,SY1981: $i,SY1982: $i] :
( ( ( hAPP @ SV162 @ ( c_Set_Oinsert @ SY1973 @ SY1974 @ SY1975 ) )
= ( hAPP @ ( hAPP @ SY1976 @ SY1973 ) @ ( hAPP @ SV162 @ SY1974 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY1977 @ SV162 @ SY1978 @ SY1979 @ SY1980 @ SY1976 @ SY1981 @ SY1982 @ SY1975 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1573,plain,
! [SV163: $i] :
( ( ! [SY1983: $i,SY1984: $i,SY1985: $i] :
( ( hBOOL @ ( c_in @ SV163 @ SY1983 @ SY1984 ) )
| ( SV163 = SY1985 )
| ~ ( hBOOL @ ( c_in @ SV163 @ ( c_Set_Oinsert @ SY1985 @ SY1983 @ SY1984 ) @ SY1984 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1574,plain,
! [SV164: $i] :
( ( ! [SY1986: $i,SY1987: $i,SY1988: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV164 @ ( c_Set_Oinsert @ SY1986 @ SY1987 @ SY1988 ) @ ( tc_fun @ SY1988 @ tc_bool ) )
= ( c_Set_Oinsert @ SY1986 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV164 @ SY1987 @ ( tc_fun @ SY1988 @ tc_bool ) ) @ SY1988 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1575,plain,
! [SV165: $i] :
( ( ! [SY1989: $i,SY1990: $i,SY1991: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV165 @ SY1989 @ SY1990 ) @ SY1991 @ ( tc_fun @ SY1990 @ tc_bool ) )
= ( c_Set_Oinsert @ SV165 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1989 @ SY1991 @ ( tc_fun @ SY1990 @ tc_bool ) ) @ SY1990 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1576,plain,
! [SV166: $i] :
( ( ! [SY1992: $i,SY1993: $i] : ( hBOOL @ ( c_in @ SV166 @ ( c_Set_Oinsert @ SV166 @ SY1992 @ SY1993 ) @ SY1993 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1577,plain,
! [SV167: $i] :
( ( ! [SY1994: $i,SY1995: $i] : ( hBOOL @ ( c_in @ SV167 @ ( c_Set_Oinsert @ SV167 @ SY1994 @ SY1995 ) @ SY1995 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1578,plain,
! [SV168: $i] :
( ( ! [SY1996: $i,SY1997: $i] : ( hBOOL @ ( c_in @ SV168 @ ( c_Set_Oinsert @ SV168 @ SY1996 @ SY1997 ) @ SY1997 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1579,plain,
! [SV169: $i] :
( ( ! [SY1998: $i,SY1999: $i] :
( ( ( c_Set_Oinsert @ SV169 @ SY1998 @ SY1999 )
= SY1998 )
| ~ ( hBOOL @ ( c_in @ SV169 @ SY1998 @ SY1999 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1580,plain,
! [SV170: $i] :
( ( ! [SY2000: $i,SY2001: $i,SY2002: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV170 @ ( c_HOL_Ominus__class_Ominus @ SY2000 @ SY2001 @ ( tc_fun @ SY2002 @ tc_bool ) ) @ ( tc_fun @ SY2002 @ tc_bool ) )
= SY2001 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2002 @ tc_bool ) ) @ SV170 ) @ SY2000 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2002 @ tc_bool ) ) @ SY2001 ) @ SV170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1581,plain,
! [SV171: $i] :
( ( ! [SY2003: $i,SY2004: $i,SY2005: $i] :
( ( hBOOL @ ( c_in @ SV171 @ SY2003 @ SY2004 ) )
| ~ ( hBOOL @ ( c_in @ SV171 @ SY2005 @ SY2004 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2004 @ tc_bool ) ) @ SY2005 ) @ SY2003 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1582,plain,
! [SV172: $i] :
( ( ! [SY2006: $i,SY2007: $i,SY2008: $i] :
( ( hBOOL @ ( c_in @ SV172 @ SY2006 @ SY2007 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2007 @ tc_bool ) ) @ SY2008 ) @ SY2006 ) )
| ~ ( hBOOL @ ( c_in @ SV172 @ SY2008 @ SY2007 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1583,plain,
! [SV173: $i] :
( ( ! [SY2009: $i,SY2010: $i,SY2011: $i] :
( ( hBOOL @ ( c_in @ SV173 @ SY2009 @ SY2010 ) )
| ~ ( hBOOL @ ( c_in @ SV173 @ SY2011 @ SY2010 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2010 @ tc_bool ) ) @ SY2011 ) @ SY2009 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1584,plain,
! [SV174: $i] :
( ( ! [SY2012: $i,SY2013: $i,SY2014: $i] :
( ( hBOOL @ ( c_in @ SV174 @ SY2012 @ SY2013 ) )
| ~ ( hBOOL @ ( c_in @ SV174 @ SY2014 @ SY2013 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2013 @ tc_bool ) ) @ SY2014 ) @ SY2012 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1585,plain,
! [SV175: $i] :
( ( ! [SY2015: $i,SY2016: $i,SY2017: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV175 @ tc_bool ) ) @ SY2015 ) @ SY2016 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV175 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2017 @ SY2015 @ ( tc_fun @ SV175 @ tc_bool ) ) ) @ SY2016 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1586,plain,
! [SV176: $i] :
( ( ! [SY2018: $i,SY2019: $i,SY2020: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV176 @ tc_bool ) ) @ SY2018 ) @ SY2019 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV176 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2018 @ SY2020 @ ( tc_fun @ SV176 @ tc_bool ) ) ) @ SY2019 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1587,plain,
! [SV177: $i] :
( ( ! [SY2021: $i,SY2022: $i,SY2023: $i,SY2024: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2021 @ SY2022 @ ( tc_fun @ SV177 @ tc_bool ) ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2023 @ SY2024 @ ( tc_fun @ SV177 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ SY2022 ) @ SY2024 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ SY2021 ) @ SY2023 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1588,plain,
! [SV178: $i] :
( ( ! [SY2025: $i,SY2026: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV178 @ SY2025 @ ( tc_fun @ SY2026 @ tc_bool ) )
= SV178 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2026 @ tc_bool ) ) @ SY2025 ) @ SV178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1589,plain,
! [SV179: $i] :
( ( ! [SY2027: $i,SY2028: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV179 @ SY2027 @ ( tc_fun @ SY2028 @ tc_bool ) )
= SY2027 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2028 @ tc_bool ) ) @ SV179 ) @ SY2027 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1590,plain,
! [SV180: $i] :
( ( ! [SY2029: $i,SY2030: $i,SY2031: $i,SY2032: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY2029 @ SY2030 @ ( tc_fun @ SV180 @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ SY2031 @ SY2032 @ ( tc_fun @ SV180 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ SY2032 ) @ SY2030 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ SY2029 ) @ SY2031 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1591,plain,
! [SV181: $i] :
( ( ! [SY2033: $i,SY2034: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV181 @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SY2033 @ ( tc_fun @ SV181 @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SY2034 @ ( tc_fun @ SV181 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV181 @ tc_bool ) ) @ SY2034 ) @ SY2033 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1592,plain,
! [SV182: $i] :
( ( ! [SY2035: $i,SY2036: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV182 @ tc_bool ) ) @ SY2035 ) @ SY2036 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV182 @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SY2036 @ ( tc_fun @ SV182 @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SY2035 @ ( tc_fun @ SV182 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1593,plain,
! [SV183: $i] :
( ( ! [SY2037: $i,SY2038: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV183 @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SY2037 @ ( tc_fun @ SV183 @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SY2038 @ ( tc_fun @ SV183 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV183 @ tc_bool ) ) @ SY2038 ) @ SY2037 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1594,plain,
! [SV184: $i] :
( ( ! [SY2039: $i,SY2040: $i,SY2041: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV184 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2039 @ SY2040 @ ( tc_fun @ SV184 @ tc_bool ) ) ) @ SY2041 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV184 @ tc_bool ) ) @ SY2040 ) @ SY2041 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV184 @ tc_bool ) ) @ SY2039 ) @ SY2041 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1595,plain,
! [SV185: $i] :
( ( ! [SY2042: $i,SY2043: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV185 @ tc_bool ) ) @ SY2042 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2043 @ SY2042 @ ( tc_fun @ SV185 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1596,plain,
! [SV186: $i] :
( ( ! [SY2044: $i,SY2045: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV186 @ tc_bool ) ) @ SY2044 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2044 @ SY2045 @ ( tc_fun @ SV186 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1597,plain,
! [SV187: $i] :
( ( ! [SY2046: $i,SY2047: $i,SY2048: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV187 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2046 @ SY2047 @ ( tc_fun @ SV187 @ tc_bool ) ) ) @ SY2048 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV187 @ tc_bool ) ) @ SY2047 ) @ SY2048 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV187 @ tc_bool ) ) @ SY2046 ) @ SY2048 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1598,plain,
! [SV188: $i] :
( ( ! [SY2049: $i,SY2050: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV188 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY2049 @ SY2050 @ ( tc_fun @ SV188 @ tc_bool ) ) ) @ SY2049 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1599,plain,
! [SV189: $i] :
( ( ! [SY2051: $i,SY2052: $i,SY2053: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV189 @ tc_bool ) ) @ SY2051 ) @ ( c_Set_Oinsert @ SY2052 @ SY2053 @ SV189 ) ) )
| ~ ( hBOOL @ ( c_in @ SY2052 @ SY2051 @ SV189 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV189 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY2051 @ ( c_Set_Oinsert @ SY2052 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV189 @ tc_bool ) ) @ SV189 ) @ ( tc_fun @ SV189 @ tc_bool ) ) ) @ SY2053 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1600,plain,
! [SV190: $i] :
( ( ! [SY2054: $i,SY2055: $i,SY2056: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV190 @ tc_bool ) ) @ SY2054 ) @ ( c_Set_Oinsert @ SY2055 @ SY2056 @ SV190 ) ) )
| ~ ( hBOOL @ ( c_in @ SY2055 @ SY2054 @ SV190 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV190 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY2054 @ ( c_Set_Oinsert @ SY2055 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV190 @ tc_bool ) ) @ SV190 ) @ ( tc_fun @ SV190 @ tc_bool ) ) ) @ SY2056 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1601,plain,
! [SV191: $i] :
( ( ! [SY2057: $i,SY2058: $i,SY2059: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV191 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY2057 @ ( c_Set_Oinsert @ SY2058 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV191 @ tc_bool ) ) @ SV191 ) @ ( tc_fun @ SV191 @ tc_bool ) ) ) @ SY2059 ) )
| ~ ( hBOOL @ ( c_in @ SY2058 @ SY2057 @ SV191 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV191 @ tc_bool ) ) @ SY2057 ) @ ( c_Set_Oinsert @ SY2058 @ SY2059 @ SV191 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1602,plain,
! [SV192: $i] :
( ( ! [SY2060: $i,SY2061: $i] :
( ~ ( class_Orderings_Oorder @ SV192 )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2060 @ SY2061 @ SV192 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV192 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV192 ) @ SY2060 ) @ SY2061 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1603,plain,
! [SV193: $i] :
( ( ! [SY2062: $i,SY2063: $i] :
( ~ ( class_Orderings_Oorder @ SV193 )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV193 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2062 @ SY2063 @ SV193 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV193 ) @ SY2062 ) @ SY2063 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1604,plain,
! [SV194: $i] :
( ( ! [SY2064: $i,SY2065: $i] :
( ~ ( class_Orderings_Oorder @ SV194 )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ SY2064 @ SY2065 @ SV194 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV194 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV194 ) @ SY2065 ) @ SY2064 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1605,plain,
! [SV195: $i] :
( ( ! [SY2066: $i,SY2067: $i,SY2068: $i,SY2069: $i] :
( ~ ( class_Orderings_Oorder @ SV195 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV195 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2066 @ SY2067 @ SV195 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2068 @ SY2069 @ SV195 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV195 ) @ SY2066 ) @ SY2067 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1606,plain,
! [SV196: $i] :
( ( ! [SY2070: $i,SY2071: $i,SY2072: $i,SY2073: $i] :
( ~ ( class_Orderings_Oorder @ SV196 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV196 ) @ SY2070 ) @ SY2071 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV196 ) @ SY2071 ) @ SY2072 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV196 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2071 @ SY2072 @ SV196 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2070 @ SY2073 @ SV196 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1607,plain,
! [SV197: $i] :
( ( ! [SY2074: $i,SY2075: $i,SY2076: $i,SY2077: $i] :
( ~ ( class_Orderings_Oorder @ SV197 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV197 ) @ SY2074 ) @ SY2075 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV197 ) @ SY2076 ) @ SY2074 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV197 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2076 @ SY2074 @ SV197 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2077 @ SY2075 @ SV197 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1608,plain,
! [SV198: $i] :
( ( ! [SY2078: $i,SY2079: $i,SY2080: $i,SY2081: $i] :
( ~ ( class_Orderings_Oorder @ SV198 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV198 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2078 @ SY2079 @ SV198 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2080 @ SY2081 @ SV198 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV198 ) @ SY2079 ) @ SY2081 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV198 ) @ SY2080 ) @ SY2078 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1609,plain,
! [SV199: $i] :
( ( ! [SY2082: $i,SY2083: $i,SY2084: $i,SY2085: $i] :
( ~ ( class_Orderings_Olinorder @ SV199 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV199 ) @ SY2082 ) @ SY2083 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV199 ) @ SY2084 ) @ SY2083 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV199 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SY2083 @ SY2084 @ SV199 ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SY2082 @ SY2085 @ SV199 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1610,plain,
! [SV200: $i] :
( ( ! [SY2086: $i,SY2087: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV200 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV200 ) @ SY2086 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2087 @ SY2086 @ SV200 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1611,plain,
! [SV201: $i] :
( ( ! [SY2088: $i,SY2089: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV201 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV201 ) @ SY2088 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2088 @ SY2089 @ SV201 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1612,plain,
! [SV202: $i] :
( ( ! [SY2090: $i,SY2091: $i,SY2092: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV202 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2090 @ SY2091 @ SV202 ) ) @ SY2092 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ SY2091 ) @ SY2092 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ SY2090 ) @ SY2092 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1613,plain,
! [SV203: $i] :
( ( ! [SY2093: $i,SY2094: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV203 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV203 ) @ SY2093 ) @ SY2094 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV203 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY2094 @ SV203 ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SY2093 @ SV203 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1614,plain,
! [SV204: $i] :
( ( ! [SY2095: $i,SY2096: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV204 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV204 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY2095 @ SV204 ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SY2096 @ SV204 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV204 ) @ SY2096 ) @ SY2095 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1615,plain,
! [SV205: $i] :
( ( ! [SY2097: $i,SY2098: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV205 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2097 @ SY2098 @ SV205 )
= SY2097 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV205 ) @ SY2098 ) @ SY2097 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1616,plain,
! [SV206: $i] :
( ( ! [SY2099: $i,SY2100: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV206 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2099 @ SY2100 @ SV206 )
= SY2100 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV206 ) @ SY2099 ) @ SY2100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1617,plain,
! [SV207: $i] :
( ( ! [SY2101: $i,SY2102: $i,SY2103: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV207 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV207 ) @ SY2101 ) @ SY2102 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV207 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2103 @ SY2101 @ SV207 ) ) @ SY2102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1618,plain,
! [SV208: $i] :
( ( ! [SY2104: $i,SY2105: $i,SY2106: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV208 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV208 ) @ SY2104 ) @ SY2105 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV208 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2104 @ SY2106 @ SV208 ) ) @ SY2105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1619,plain,
! [SV209: $i] :
( ( ! [SY2107: $i,SY2108: $i,SY2109: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV209 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV209 ) @ SY2107 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2108 @ SY2109 @ SV209 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV209 ) @ SY2107 ) @ SY2109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1620,plain,
! [SV210: $i] :
( ( ! [SY2110: $i,SY2111: $i,SY2112: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV210 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV210 ) @ SY2110 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2111 @ SY2112 @ SV210 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV210 ) @ SY2110 ) @ SY2111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1621,plain,
! [SV211: $i] :
( ( ! [SY2113: $i,SY2114: $i,SY2115: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV211 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV211 ) @ SY2113 ) @ SY2114 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV211 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2115 @ SY2113 @ SV211 ) ) @ SY2114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1622,plain,
! [SV212: $i] :
( ( ! [SY2116: $i,SY2117: $i,SY2118: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV212 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV212 ) @ SY2116 ) @ SY2117 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV212 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2116 @ SY2118 @ SV212 ) ) @ SY2117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1623,plain,
! [SV213: $i] :
( ( ! [SY2119: $i,SY2120: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV213 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ SY2119 @ SY2120 @ SV213 ) @ SV213 )
= ( c_HOL_Ominus__class_Ominus @ SY2120 @ SY2119 @ SV213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1624,plain,
! [SV214: $i] :
( ( ! [SY2121: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV214 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SY2121 @ SV214 ) @ SV214 )
= SY2121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1625,plain,
! [SV215: $i] :
( ( ! [SY2122: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV215 )
| ( SY2122
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SY2122 @ SV215 ) @ SV215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1626,plain,
! [SV216: $i] :
( ( ! [SY2123: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV216 )
| ( SY2123
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SY2123 @ SV216 ) @ SV216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1627,plain,
! [SV217: $i] :
( ( ! [SY2124: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ SV217 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SY2124 @ SV217 ) @ SV217 )
= SY2124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1628,plain,
! [SV218: $i] :
( ( ! [SY2125: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV218 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SY2125 @ SV218 ) @ SV218 )
= SY2125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1629,plain,
! [SV219: $i] :
( ( ! [SY2126: $i] :
( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV219 @ ( tc_fun @ SY2126 @ tc_bool ) ) @ ( tc_fun @ SY2126 @ tc_bool ) )
= SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1630,plain,
! [SV220: $i] :
( ( ! [SY2127: $i,SY2128: $i,SY2129: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV220 @ tc_bool ) ) @ SY2127 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2128 @ SY2129 @ ( tc_fun @ SV220 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV220 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY2127 @ SY2128 @ ( tc_fun @ SV220 @ tc_bool ) ) ) @ SY2129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1631,plain,
! [SV221: $i] :
( ( ! [SY2130: $i,SY2131: $i,SY2132: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV221 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY2130 @ SY2131 @ ( tc_fun @ SV221 @ tc_bool ) ) ) @ SY2132 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV221 @ tc_bool ) ) @ SY2130 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2131 @ SY2132 @ ( tc_fun @ SV221 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1632,plain,
! [SV222: $i] :
( ( ! [SY2133: $i,SY2134: $i,SY2135: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV222 @ SY2133 @ SY2134 ) @ SY2135 @ ( tc_fun @ SY2134 @ tc_bool ) )
= ( c_Set_Oinsert @ SV222 @ ( c_HOL_Ominus__class_Ominus @ SY2133 @ SY2135 @ ( tc_fun @ SY2134 @ tc_bool ) ) @ SY2134 ) )
| ( hBOOL @ ( c_in @ SV222 @ SY2135 @ SY2134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1633,plain,
! [SV223: $i] :
( ( ! [SY2136: $i,SY2137: $i,SY2138: $i,SY2139: $i,SY2140: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV223 @ SY2136 @ SY2137 @ ( tc_fun @ SY2138 @ tc_bool ) ) @ SY2139 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2136 @ SY2140 ) @ SY2139 ) )
| ~ ( hBOOL @ ( c_in @ SY2140 @ SV223 @ SY2137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1634,plain,
! [SV224: $i] :
( ( ! [SY2141: $i,SY2142: $i,SY2143: $i,SY2144: $i,SY2145: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV224 @ SY2141 @ SY2142 @ ( tc_fun @ SY2143 @ tc_bool ) ) @ SY2144 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2141 @ SY2145 ) @ SY2144 ) )
| ~ ( hBOOL @ ( c_in @ SY2145 @ SV224 @ SY2142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1635,plain,
! [SV225: $i] :
( ( ! [SY2146: $i,SY2147: $i] :
( ~ ( class_Lattices_Olattice @ SV225 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2146 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2146 @ SY2147 @ SV225 ) @ SV225 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2146 @ SY2147 @ SV225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1636,plain,
! [SV226: $i] :
( ( ! [SY2148: $i,SY2149: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV226 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2148 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2148 @ SY2149 @ SV226 ) @ SV226 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2148 @ SY2149 @ SV226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1637,plain,
! [SV227: $i] :
( ( ! [SY2150: $i,SY2151: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV227 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV227 @ SY2150 @ ( tc_fun @ SY2151 @ tc_bool ) ) @ ( tc_fun @ SY2151 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV227 @ SY2150 @ ( tc_fun @ SY2151 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1638,plain,
! [SV228: $i] :
( ( ! [SY2152: $i,SY2153: $i] :
( ~ ( class_Lattices_Olattice @ SV228 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2152 @ SY2153 @ SV228 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2153 @ SY2152 @ SV228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1639,plain,
! [SV229: $i] :
( ( ! [SY2154: $i,SY2155: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV229 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2154 @ SY2155 @ SV229 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2155 @ SY2154 @ SV229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1640,plain,
! [SV230: $i] :
( ( ! [SY2156: $i,SY2157: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV230 @ SY2156 @ ( tc_fun @ SY2157 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2156 @ SV230 @ ( tc_fun @ SY2157 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1641,plain,
! [SV231: $i] :
( ( ! [SY2158: $i,SY2159: $i,SY2160: $i,SY2161: $i,SY2162: $i,SY2163: $i,SY2164: $i,SY2165: $i,SY2166: $i,SY2167: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV231 @ SY2158 ) @ ( hAPP @ SY2159 @ SY2160 ) ) )
| ~ ( hBOOL @ ( c_in @ SY2158 @ SY2160 @ SY2161 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY2162 @ SY2159 @ SV231 @ SY2163 @ SY2164 @ SY2165 @ SY2166 @ SY2167 @ SY2161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1642,plain,
! [SV232: $i] :
( ( ! [SY2168: $i,SY2169: $i,SY2170: $i,SY2171: $i,SY2172: $i,SY2173: $i,SY2174: $i,SY2175: $i,SY2176: $i,SY2177: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ ( hAPP @ SY2168 @ SY2169 ) ) @ SY2170 ) )
| ~ ( hBOOL @ ( c_in @ SY2170 @ SY2169 @ SY2171 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY2168 @ SY2172 @ SV232 @ SY2173 @ SY2174 @ SY2175 @ SY2176 @ SY2177 @ SY2171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1643,plain,
! [SV233: $i] :
( ( ! [SY2178: $i,SY2179: $i,SY2180: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV233 @ SY2178 @ ( tc_fun @ SY2179 @ tc_bool ) ) @ SY2180 @ ( tc_fun @ SY2179 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV233 @ SY2180 @ ( tc_fun @ SY2179 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY2178 @ SY2180 @ ( tc_fun @ SY2179 @ tc_bool ) ) @ ( tc_fun @ SY2179 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1644,plain,
! [SV234: $i] :
( ( ! [SY2181: $i,SY2182: $i] :
( ~ ( class_HOL_Ominus @ SV234 )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ SY2181 @ SY2182 @ ( tc_fun @ t_a @ SV234 ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ SY2181 @ v_x ) @ ( hAPP @ SY2182 @ v_x ) @ SV234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1645,plain,
! [SV235: $i] :
( ( ! [SY2183: $i,SY2184: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV235 @ ( c_HOL_Ominus__class_Ominus @ SY2183 @ SV235 @ ( tc_fun @ SY2184 @ tc_bool ) ) @ ( tc_fun @ SY2184 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV235 @ SY2183 @ ( tc_fun @ SY2184 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1646,plain,
! [SV236: $i] :
( ( ! [SY2185: $i,SY2186: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV236 @ SY2185 @ ( tc_fun @ SY2186 @ tc_bool ) ) @ SY2185 @ ( tc_fun @ SY2186 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV236 @ SY2185 @ ( tc_fun @ SY2186 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1647,plain,
! [SV237: $i] :
( ( ! [SY2187: $i,SY2188: $i,SY2189: $i,SY2190: $i,SY2191: $i] :
( ( hBOOL @ ( c_in @ SV237 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2187 @ SY2188 @ SY2189 @ ( tc_fun @ SY2190 @ tc_bool ) ) @ SY2190 ) )
| ~ ( hBOOL @ ( c_in @ SV237 @ ( hAPP @ SY2188 @ SY2191 ) @ SY2190 ) )
| ~ ( hBOOL @ ( c_in @ SY2191 @ SY2187 @ SY2189 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1648,plain,
! [SV238: $i] :
( ( ! [SY2192: $i,SY2193: $i,SY2194: $i,SY2195: $i,SY2196: $i] :
( ( hBOOL @ ( c_in @ SV238 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2192 @ SY2193 @ SY2194 @ ( tc_fun @ SY2195 @ tc_bool ) ) @ SY2195 ) )
| ~ ( hBOOL @ ( c_in @ SV238 @ ( hAPP @ SY2193 @ SY2196 ) @ SY2195 ) )
| ~ ( hBOOL @ ( c_in @ SY2196 @ SY2192 @ SY2194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1649,plain,
! [SV239: $i] :
( ( ! [SY2197: $i,SY2198: $i,SY2199: $i] :
( ( hBOOL @ ( c_in @ SV239 @ ( c_HOL_Ominus__class_Ominus @ SY2197 @ SY2198 @ ( tc_fun @ SY2199 @ tc_bool ) ) @ SY2199 ) )
| ( hBOOL @ ( c_in @ SV239 @ SY2198 @ SY2199 ) )
| ~ ( hBOOL @ ( c_in @ SV239 @ SY2197 @ SY2199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1650,plain,
! [SV240: $i] :
( ( ! [SY2200: $i,SY2201: $i,SY2202: $i] :
( ( hBOOL @ ( c_in @ SV240 @ ( c_HOL_Ominus__class_Ominus @ SY2200 @ SY2201 @ ( tc_fun @ SY2202 @ tc_bool ) ) @ SY2202 ) )
| ( hBOOL @ ( c_in @ SV240 @ SY2201 @ SY2202 ) )
| ~ ( hBOOL @ ( c_in @ SV240 @ SY2200 @ SY2202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1651,plain,
! [SV241: $i] :
( ( ! [SY2203: $i,SY2204: $i] :
( ( hBOOL @ ( hAPP @ SV241 @ SY2203 ) )
| ~ ( hBOOL @ ( c_in @ SY2203 @ ( c_Collect @ SV241 @ SY2204 ) @ SY2204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1652,plain,
! [SV242: $i] :
( ( ! [SY2205: $i,SY2206: $i] :
( ( hBOOL @ ( c_in @ SV242 @ ( c_Collect @ SY2205 @ SY2206 ) @ SY2206 ) )
| ~ ( hBOOL @ ( hAPP @ SY2205 @ SV242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1653,plain,
! [SV243: $i] :
( ( ! [SY2207: $i,SY2208: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV243 @ ( c_HOL_Ominus__class_Ominus @ SY2207 @ SV243 @ ( tc_fun @ SY2208 @ tc_bool ) ) @ ( tc_fun @ SY2208 @ tc_bool ) )
= SY2207 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2208 @ tc_bool ) ) @ SV243 ) @ SY2207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1654,plain,
! [SV244: $i] :
( ( ! [SY2209: $i,SY2210: $i,SY2211: $i] :
( ~ ( class_Lattices_Olattice @ SV244 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2209 @ SY2210 @ SV244 ) @ SY2211 @ SV244 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2209 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2210 @ SY2211 @ SV244 ) @ SV244 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1655,plain,
! [SV245: $i] :
( ( ! [SY2212: $i,SY2213: $i,SY2214: $i] :
( ~ ( class_Lattices_Olattice @ SV245 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2212 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2213 @ SY2214 @ SV245 ) @ SV245 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2213 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2212 @ SY2214 @ SV245 ) @ SV245 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1656,plain,
! [SV246: $i] :
( ( ! [SY2215: $i,SY2216: $i,SY2217: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV246 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2215 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2216 @ SY2217 @ SV246 ) @ SV246 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2216 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2215 @ SY2217 @ SV246 ) @ SV246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1657,plain,
! [SV247: $i] :
( ( ! [SY2218: $i,SY2219: $i,SY2220: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV247 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2218 @ SY2219 @ SV247 ) @ SY2220 @ SV247 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2218 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2219 @ SY2220 @ SV247 ) @ SV247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1658,plain,
! [SV248: $i] :
( ( ! [SY2221: $i,SY2222: $i,SY2223: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV248 @ SY2221 @ ( tc_fun @ SY2222 @ tc_bool ) ) @ SY2223 @ ( tc_fun @ SY2222 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV248 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2221 @ SY2223 @ ( tc_fun @ SY2222 @ tc_bool ) ) @ ( tc_fun @ SY2222 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1659,plain,
! [SV249: $i] :
( ( ! [SY2224: $i,SY2225: $i,SY2226: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV249 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2224 @ SY2225 @ ( tc_fun @ SY2226 @ tc_bool ) ) @ ( tc_fun @ SY2226 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2224 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV249 @ SY2225 @ ( tc_fun @ SY2226 @ tc_bool ) ) @ ( tc_fun @ SY2226 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1660,plain,
! [SV250: $i] :
( ( ! [SY2227: $i,SY2228: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV250 @ SY2227 @ ( tc_fun @ SY2228 @ tc_bool ) ) @ SY2227 @ ( tc_fun @ SY2228 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV250 @ SY2227 @ ( tc_fun @ SY2228 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1661,plain,
! [SV251: $i] :
( ( ! [SY2229: $i,SY2230: $i] :
( ( hBOOL @ ( hAPP @ SV251 @ SY2229 ) )
| ~ ( hBOOL @ ( c_in @ SY2229 @ SV251 @ SY2230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1662,plain,
! [SV252: $i] :
( ( ! [SY2231: $i,SY2232: $i] :
( ( hBOOL @ ( c_in @ SV252 @ SY2231 @ SY2232 ) )
| ~ ( hBOOL @ ( hAPP @ SY2231 @ SV252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1663,plain,
! [SV253: $i] :
( ( ! [SY2233: $i,SY2234: $i,SY2235: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV253 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2233 @ tc_bool ) ) @ SY2234 @ SY2233 @ ( tc_fun @ SY2235 @ tc_bool ) ) @ ( tc_fun @ SY2235 @ tc_bool ) )
= SV253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1664,plain,
! [SV254: $i] :
( ( ! [SY2236: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV254 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2236 @ SY2236 @ SV254 )
= SY2236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1665,plain,
! [SV255: $i] :
( ( ! [SY2237: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 @ SV255 @ ( tc_fun @ SY2237 @ tc_bool ) )
= SV255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1666,plain,
! [SV256: $i] :
( ( ! [SY2238: $i,SY2239: $i] :
( ~ ( class_Lattices_Olattice @ SV256 )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2238 @ SY2239 @ ( tc_fun @ t_a @ SV256 ) ) @ v_x )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SY2238 @ v_x ) @ ( hAPP @ SY2239 @ v_x ) @ SV256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1667,plain,
! [SV257: $i] :
( ( ! [SY2240: $i,SY2241: $i] :
( ( c_Finite__Set_Ofold1 @ SV257 @ SY2240 @ SY2241 )
= ( c_The @ ( c_Finite__Set_Ofold1Set @ SV257 @ SY2240 @ SY2241 ) @ SY2241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1668,plain,
! [SV258: $i] :
( ( ! [SY2242: $i,SY2243: $i,SY2244: $i,SY2245: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV258 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV258 ) @ ( hAPP @ SY2242 @ SY2243 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2244 @ SY2242 @ SY2245 @ SV258 ) ) )
| ~ ( hBOOL @ ( c_in @ SY2243 @ SY2244 @ SY2245 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1669,plain,
! [SV259: $i] :
( ( ! [SY2246: $i,SY2247: $i,SY2248: $i,SY2249: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV259 @ tc_bool ) ) @ ( hAPP @ SY2246 @ SY2247 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2248 @ SY2246 @ SY2249 @ ( tc_fun @ SV259 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( c_in @ SY2247 @ SY2248 @ SY2249 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1670,plain,
! [SV260: $i] :
( ( ! [SY2250: $i,SY2251: $i,SY2252: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV260 @ SY2250 @ SY2251 ) @ SY2252 @ ( tc_fun @ SY2251 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SY2250 @ SY2252 @ ( tc_fun @ SY2251 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SV260 @ SY2252 @ SY2251 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1671,plain,
! [SV261: $i] :
( ( ! [SY2253: $i,SY2254: $i] :
( ~ ( hBOOL @ ( c_in @ SV261 @ SY2253 @ SY2254 ) )
| ~ ( hBOOL @ ( c_in @ SV261 @ ( c_HOL_Ouminus__class_Ouminus @ SY2253 @ ( tc_fun @ SY2254 @ tc_bool ) ) @ SY2254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1672,plain,
! [SV262: $i] :
( ( ! [SY2255: $i,SY2256: $i] :
( ( hBOOL @ ( c_in @ SV262 @ ( c_HOL_Ouminus__class_Ouminus @ SY2255 @ ( tc_fun @ SY2256 @ tc_bool ) ) @ SY2256 ) )
| ( hBOOL @ ( c_in @ SV262 @ SY2255 @ SY2256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1673,plain,
! [SV263: $i] :
( ( ! [SY2257: $i] :
( ( c_Collect @ SV263 @ SY2257 )
= SV263 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1674,plain,
! [SV264: $i] :
( ( ! [SY2258: $i,SY2259: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV264 )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV264 ) @ ( c_Set_Oinsert @ SY2258 @ SY2259 @ SV264 ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2258 @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV264 ) @ SY2259 ) @ SV264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1675,plain,
! [SV265: $i] :
( ( ! [SY2260: $i,SY2261: $i] :
( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ SV265 @ SY2260 @ ( tc_fun @ SY2261 @ tc_bool ) ) @ ( tc_fun @ SY2261 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ SV265 @ ( tc_fun @ SY2261 @ tc_bool ) ) @ SY2260 @ ( tc_fun @ SY2261 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1676,plain,
! [SV266: $i] :
( ( ! [SY2262: $i,SY2263: $i,SY2264: $i] :
( ( hBOOL @ ( c_in @ SV266 @ SY2262 @ SY2263 ) )
| ~ ( hBOOL @ ( c_in @ SV266 @ ( c_HOL_Ominus__class_Ominus @ SY2262 @ SY2264 @ ( tc_fun @ SY2263 @ tc_bool ) ) @ SY2263 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1677,plain,
! [SV267: $i] :
( ( ! [SY2265: $i,SY2266: $i,SY2267: $i] :
( ~ ( hBOOL @ ( c_in @ SV267 @ SY2265 @ SY2266 ) )
| ~ ( hBOOL @ ( c_in @ SV267 @ ( c_HOL_Ominus__class_Ominus @ SY2267 @ SY2265 @ ( tc_fun @ SY2266 @ tc_bool ) ) @ SY2266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1678,plain,
! [SV268: $i] :
( ( ! [SY2268: $i,SY2269: $i,SY2270: $i,SY2271: $i,SY2272: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV268 @ tc_bool ) ) @ ( hAPP @ SY2268 @ SY2269 ) ) @ SY2270 ) )
| ~ ( hBOOL @ ( c_in @ SY2269 @ SY2271 @ SY2272 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV268 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2271 @ SY2268 @ SY2272 @ ( tc_fun @ SV268 @ tc_bool ) ) ) @ SY2270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1679,plain,
! [SV269: $i] :
( ( ! [SY2273: $i,SY2274: $i,SY2275: $i,SY2276: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV269 @ SY2273 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2274 @ SV269 @ SY2275 @ ( tc_fun @ SY2276 @ tc_bool ) ) @ ( tc_fun @ SY2276 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2274 @ SV269 @ SY2275 @ ( tc_fun @ SY2276 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SY2273 @ SY2274 @ SY2275 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1680,plain,
! [SV270: $i] :
( ( ! [SY2277: $i,SY2278: $i,SY2279: $i] :
( ( hBOOL @ ( hAPP @ SV270 @ SY2277 ) )
| ( hBOOL @ ( hAPP @ SY2278 @ SY2277 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2278 @ SV270 @ ( tc_fun @ SY2279 @ tc_bool ) ) @ SY2277 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1681,plain,
! [SV271: $i] :
( ( ! [SY2280: $i,SY2281: $i,SY2282: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV271 @ SY2280 @ ( tc_fun @ SY2281 @ tc_bool ) ) @ SY2282 ) )
| ~ ( hBOOL @ ( hAPP @ SY2280 @ SY2282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1682,plain,
! [SV272: $i] :
( ( ! [SY2283: $i,SY2284: $i,SY2285: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV272 @ SY2283 @ ( tc_fun @ SY2284 @ tc_bool ) ) @ SY2285 ) )
| ~ ( hBOOL @ ( hAPP @ SV272 @ SY2285 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1683,plain,
! [SV273: $i] :
( ( ! [SY2286: $i,SY2287: $i,SY2288: $i] :
( ( hBOOL @ ( c_in @ SV273 @ SY2286 @ SY2287 ) )
| ( hBOOL @ ( c_in @ SV273 @ SY2288 @ SY2287 ) )
| ~ ( hBOOL @ ( c_in @ SV273 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2288 @ SY2286 @ ( tc_fun @ SY2287 @ tc_bool ) ) @ SY2287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1684,plain,
! [SV274: $i] :
( ( ! [SY2289: $i,SY2290: $i,SY2291: $i] :
( ~ ( class_Orderings_Olinorder @ SV274 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SY2289 @ SY2290 @ SV274 ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SY2290 @ SY2291 @ SV274 ) @ ( tc_fun @ SV274 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SY2289 @ SY2291 @ SV274 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV274 ) @ SY2290 ) @ SY2291 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV274 ) @ SY2289 ) @ SY2290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1685,plain,
! [SV275: $i] :
( ( ! [SY2292: $i,SY2293: $i,SY2294: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV275 @ tc_bool ) ) @ SY2292 @ SV275 @ ( tc_fun @ SY2293 @ tc_bool ) ) @ SY2294 @ ( tc_fun @ SY2293 @ tc_bool ) )
= SY2294 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1686,plain,
! [SV276: $i] :
( ( ! [SY2295: $i,SY2296: $i,SY2297: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV276 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2295 @ tc_bool ) ) @ SY2296 @ SY2295 @ ( tc_fun @ SY2297 @ tc_bool ) ) @ ( tc_fun @ SY2297 @ tc_bool ) )
= SV276 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1687,plain,
! [SV277: $i] :
( ( ! [SY2298: $i,SY2299: $i,SY2300: $i] :
( ~ ( class_Orderings_Olinorder @ SV277 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SY2298 @ SY2299 @ SV277 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2299 @ SY2300 @ SV277 ) @ ( tc_fun @ SV277 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2298 @ SY2300 @ SV277 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV277 ) @ SY2299 ) @ SY2300 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV277 ) @ SY2298 ) @ SY2299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1688,plain,
! [SV278: $i] :
( ( ! [SY2301: $i,SY2302: $i,SY2303: $i,SY2304: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ SV278 @ SY2301 @ SY2302 ) @ SY2303 @ SY2302 @ ( tc_fun @ SY2304 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SY2303 @ SV278 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2301 @ SY2303 @ SY2302 @ ( tc_fun @ SY2304 @ tc_bool ) ) @ ( tc_fun @ SY2304 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1689,plain,
! [SV279: $i] :
( ( ! [SY2305: $i,SY2306: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV279 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV279 ) @ ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ SV279 ) @ SY2305 ) ) @ SY2306 ) )
| ~ ( hBOOL @ ( c_in @ SY2306 @ SY2305 @ SV279 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1690,plain,
! [SV280: $i] :
( ( ! [SY2307: $i] :
( ~ ( class_HOL_Ouminus @ SV280 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SY2307 @ ( tc_fun @ t_a @ SV280 ) ) @ v_x )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ SY2307 @ v_x ) @ SV280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1691,plain,
! [SV281: $i] :
( ( ! [SY2308: $i,SY2309: $i,SY2310: $i] :
( ( hBOOL @ ( c_in @ SV281 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2308 @ SY2309 @ ( tc_fun @ SY2310 @ tc_bool ) ) @ SY2310 ) )
| ~ ( hBOOL @ ( c_in @ SV281 @ SY2309 @ SY2310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1692,plain,
! [SV282: $i] :
( ( ! [SY2311: $i,SY2312: $i,SY2313: $i] :
( ( hBOOL @ ( c_in @ SV282 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2311 @ SY2312 @ ( tc_fun @ SY2313 @ tc_bool ) ) @ SY2313 ) )
| ~ ( hBOOL @ ( c_in @ SV282 @ SY2311 @ SY2313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1693,plain,
! [SV283: $i] :
( ( ! [SY2314: $i,SY2315: $i,SY2316: $i] :
( ~ ( class_Orderings_Olinorder @ SV283 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SY2314 @ SY2315 @ SV283 ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SY2314 @ SY2316 @ SV283 ) @ ( tc_fun @ SV283 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SY2316 @ SY2315 @ SV283 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV283 ) @ SY2314 ) @ SY2316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1694,plain,
! [SV284: $i] :
( ( ! [SY2317: $i,SY2318: $i,SY2319: $i,SY2320: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV284 @ SY2317 @ ( tc_fun @ SY2318 @ tc_bool ) ) @ SY2319 @ SY2318 @ ( tc_fun @ SY2320 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV284 @ SY2319 @ SY2318 @ ( tc_fun @ SY2320 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2317 @ SY2319 @ SY2318 @ ( tc_fun @ SY2320 @ tc_bool ) ) @ ( tc_fun @ SY2320 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1695,plain,
! [SV285: $i] :
( ( ! [SY2321: $i] :
( ( c_The @ ( hAPP @ ( c_fequal @ SV285 ) @ SY2321 ) @ SV285 )
= SY2321 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1696,plain,
! [SV286: $i] :
( ( ! [SY2322: $i,SY2323: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV286 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV286 ) @ SY2322 ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV286 ) @ SY2323 ) ) )
| ~ ( hBOOL @ ( c_in @ SY2322 @ SY2323 @ SV286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1697,plain,
! [SV287: $i] :
( ( ! [SY2324: $i,SY2325: $i,SY2326: $i,SY2327: $i] :
( ~ ( class_Orderings_Olinorder @ SV287 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV287 ) @ SY2324 ) @ SY2325 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV287 ) @ SY2324 ) @ SY2326 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV287 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SY2326 @ SY2324 @ SV287 ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SY2327 @ SY2325 @ SV287 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1698,plain,
! [SV288: $i] :
( ( ~ ( class_Orderings_Obot @ SV288 )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ SV288 ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ SV288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1699,plain,
! [SV289: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV289 )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV289 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV289 @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ SV289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1700,plain,
! [SV290: $i] :
( ( ! [SY2328: $i] :
( ( c_Collect @ ( hAPP @ ( c_fequal @ SV290 ) @ SY2328 ) @ SV290 )
= ( c_Set_Oinsert @ SY2328 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV290 @ tc_bool ) ) @ SV290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1701,plain,
! [SV291: $i] :
( ( ! [SY2329: $i] : ( hBOOL @ ( c_in @ SV291 @ ( c_Set_Oinsert @ SV291 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2329 @ tc_bool ) ) @ SY2329 ) @ SY2329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1702,plain,
! [SV292: $i] :
( ( ! [SY2330: $i,SY2331: $i,SY2332: $i,SY2333: $i,SY2334: $i,SY2335: $i,SY2336: $i,SY2337: $i,SY2338: $i] :
( ( ( hAPP @ SV292 @ ( c_Set_Oinsert @ SY2330 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2331 @ tc_bool ) ) @ SY2331 ) )
= SY2330 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV292 @ SY2332 @ SY2333 @ SY2334 @ SY2335 @ SY2336 @ SY2337 @ SY2338 @ SY2331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1703,plain,
! [SV293: $i] :
( ( ! [SY2339: $i,SY2340: $i,SY2341: $i,SY2342: $i,SY2343: $i,SY2344: $i,SY2345: $i,SY2346: $i,SY2347: $i] :
( ( ( hAPP @ SV293 @ ( c_Set_Oinsert @ SY2339 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2340 @ tc_bool ) ) @ SY2340 ) )
= SY2339 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY2341 @ SV293 @ SY2342 @ SY2343 @ SY2344 @ SY2345 @ SY2346 @ SY2347 @ SY2340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1704,plain,
! [SV294: $i] :
( ( ! [SY2348: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV294 )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV294 ) @ ( c_Set_Oinsert @ SY2348 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV294 @ tc_bool ) ) @ SV294 ) )
= SY2348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1705,plain,
! [SV295: $i] :
( ( ! [SY2349: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV295 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2349 @ tc_bool ) ) @ SY2349 ) @ ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ SV295 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2349 @ tc_bool ) ) @ SY2349 ) @ SY2349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1706,plain,
! [SV296: $i] :
( ( ! [SY2350: $i,SY2351: $i,SY2352: $i] :
( ( c_Set_Oinsert @ SV296 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2350 @ tc_bool ) ) @ SY2351 @ SY2350 @ ( tc_fun @ SY2352 @ tc_bool ) ) @ SY2352 )
= ( c_Set_Oinsert @ SV296 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2352 @ tc_bool ) ) @ SY2352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1707,plain,
! [SV297: $i] :
( ( ! [SY2353: $i,SY2354: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV297 @ ( c_Set_Oinsert @ SY2353 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2354 @ tc_bool ) ) @ SY2354 ) @ SY2354 ) @ SY2353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1708,plain,
! [SV298: $i] :
( ( ! [SY2355: $i] :
( ~ ( class_Orderings_Olinorder @ SV298 )
| ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ SY2355 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV298 @ tc_bool ) ) @ SV298 ) @ SV298 )
= SY2355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1709,plain,
! [SV299: $i] :
( ( ! [SY2356: $i] :
( ( c_The @ ( c_Set_Oinsert @ SV299 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2356 @ tc_bool ) ) @ SY2356 ) @ SY2356 )
= SV299 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1710,plain,
! [SV300: $i] :
( ( ! [SY2357: $i,SY2358: $i,SY2359: $i,SY2360: $i,SY2361: $i,SY2362: $i,SY2363: $i,SY2364: $i,SY2365: $i,SY2366: $i] :
( ( ( hAPP @ SV300 @ ( c_Set_Oinsert @ SY2357 @ ( c_Set_Oinsert @ SY2358 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2359 @ tc_bool ) ) @ SY2359 ) @ SY2359 ) )
= ( hAPP @ ( hAPP @ SY2360 @ SY2357 ) @ SY2358 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV300 @ SY2361 @ SY2362 @ SY2363 @ SY2360 @ SY2364 @ SY2365 @ SY2366 @ SY2359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1711,plain,
! [SV301: $i] :
( ( ! [SY2367: $i,SY2368: $i,SY2369: $i,SY2370: $i,SY2371: $i,SY2372: $i,SY2373: $i,SY2374: $i,SY2375: $i,SY2376: $i] :
( ( ( hAPP @ SV301 @ ( c_Set_Oinsert @ SY2367 @ ( c_Set_Oinsert @ SY2368 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2369 @ tc_bool ) ) @ SY2369 ) @ SY2369 ) )
= ( hAPP @ ( hAPP @ SY2370 @ SY2367 ) @ SY2368 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY2371 @ SV301 @ SY2372 @ SY2373 @ SY2374 @ SY2370 @ SY2375 @ SY2376 @ SY2369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1712,plain,
! [SV302: $i] :
( ( ! [SY2377: $i,SY2378: $i,SY2379: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV302 @ ( c_Set_Oinsert @ SY2377 @ SY2378 @ SY2379 ) @ ( tc_fun @ SY2379 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV302 @ ( c_Set_Oinsert @ SY2377 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2379 @ tc_bool ) ) @ SY2379 ) @ ( tc_fun @ SY2379 @ tc_bool ) ) @ SY2378 @ ( tc_fun @ SY2379 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1713,plain,
! [SV303: $i] :
( ( ! [SY2380: $i,SY2381: $i,SY2382: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV303 @ ( c_Set_Oinsert @ SY2380 @ SY2381 @ SY2382 ) @ ( tc_fun @ SY2382 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV303 @ SY2381 @ ( tc_fun @ SY2382 @ tc_bool ) ) @ ( c_Set_Oinsert @ SY2380 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2382 @ tc_bool ) ) @ SY2382 ) @ ( tc_fun @ SY2382 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1714,plain,
! [SV304: $i] :
( ( ! [SY2383: $i,SY2384: $i,SY2385: $i] :
( ( SV304 = SY2383 )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SY2384 @ ( c_Set_Oinsert @ SV304 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2385 @ tc_bool ) ) @ SY2385 ) @ SY2385 ) @ SY2383 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1715,plain,
! [SV305: $i] :
( ( ! [SY2386: $i] :
( ( c_Set_Ocontents @ ( c_Set_Oinsert @ SV305 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2386 @ tc_bool ) ) @ SY2386 ) @ SY2386 )
= SV305 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1716,plain,
! [SV306: $i] :
( ( ! [SY2387: $i,SY2388: $i] :
( ( SV306
= ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ SY2387 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2388 @ tc_bool ) ) @ SY2388 ) @ SY2388 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY2387 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2388 @ tc_bool ) ) @ SY2388 ) @ SV306 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1717,plain,
! [SV307: $i] :
( ( ! [SY2389: $i,SY2390: $i] :
( ( SV307 = SY2389 )
| ~ ( hBOOL @ ( c_in @ SV307 @ ( c_Set_Oinsert @ SY2389 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2390 @ tc_bool ) ) @ SY2390 ) @ SY2390 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1718,plain,
! [SV308: $i] :
( ( ! [SY2391: $i,SY2392: $i] :
( ( c_Finite__Set_Ofold1 @ SV308 @ ( c_Set_Oinsert @ SY2391 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2392 @ tc_bool ) ) @ SY2392 ) @ SY2392 )
= SY2391 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1719,plain,
! [SV309: $i] :
( ( ! [SY2393: $i] :
( ~ ( class_Orderings_Olinorder @ SV309 )
| ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ SY2393 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV309 @ tc_bool ) ) @ SV309 ) @ SV309 )
= SY2393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1720,plain,
! [SV310: $i] :
( ( ! [SY2394: $i,SY2395: $i] :
( ( c_Set_Oinsert @ SV310 @ ( c_HOL_Ominus__class_Ominus @ SY2394 @ ( c_Set_Oinsert @ SV310 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2395 @ tc_bool ) ) @ SY2395 ) @ ( tc_fun @ SY2395 @ tc_bool ) ) @ SY2395 )
= ( c_Set_Oinsert @ SV310 @ SY2394 @ SY2395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1721,plain,
! [SV311: $i] :
( ( ! [SY2396: $i] :
( ~ ( class_Orderings_Oorder @ SV311 )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2396 @ SY2396 @ SV311 )
= ( c_Set_Oinsert @ SY2396 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV311 @ tc_bool ) ) @ SV311 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1722,plain,
! [SV312: $i] :
( ( ! [SY2397: $i,SY2398: $i] :
( ( c_Set_Oinsert @ SV312 @ SY2397 @ SY2398 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV312 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2398 @ tc_bool ) ) @ SY2398 ) @ SY2397 @ ( tc_fun @ SY2398 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1723,plain,
! [SV313: $i] :
( ( ! [SY2399: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV313 )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ SV313 ) @ ( c_Set_Oinsert @ SY2399 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV313 @ tc_bool ) ) @ SV313 ) )
= SY2399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1724,plain,
! [SV314: $i] :
( ( ! [SY2400: $i] :
( ( SV314
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2400 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2400 @ tc_bool ) ) @ SV314 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV314 @ ( tc_fun @ SY2400 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1725,plain,
! [SV315: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV315 @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV315 @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV315 @ tc_bool ) ) @ ( tc_fun @ SV315 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1726,plain,
! [SV316: $i] :
( ( ! [SY2401: $i,SY2402: $i,SY2403: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV316 @ tc_bool ) ) @ ( c_Set_Oinsert @ SY2401 @ SY2402 @ SV316 ) ) @ SY2403 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV316 @ tc_bool ) ) @ SY2402 ) @ SY2403 ) )
| ~ ( hBOOL @ ( c_in @ SY2401 @ SY2403 @ SV316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1727,plain,
! [SV317: $i] :
( ( ! [SY2404: $i,SY2405: $i,SY2406: $i] :
( ( hBOOL @ ( c_in @ SV317 @ SY2404 @ SY2405 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2405 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV317 @ SY2406 @ SY2405 ) ) @ SY2404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1728,plain,
! [SV318: $i] :
( ( ! [SY2407: $i,SY2408: $i,SY2409: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV318 @ tc_bool ) ) @ SY2407 ) @ ( c_Set_Oinsert @ SY2408 @ SY2409 @ SV318 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV318 @ tc_bool ) ) @ SY2407 ) @ SY2409 ) )
| ( hBOOL @ ( c_in @ SY2408 @ SY2407 @ SV318 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1729,plain,
! [SV319: $i] :
( ( ! [SY2410: $i,SY2411: $i,SY2412: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV319 @ tc_bool ) ) @ SY2410 ) @ SY2411 ) )
| ( hBOOL @ ( c_in @ SY2412 @ SY2410 @ SV319 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV319 @ tc_bool ) ) @ SY2410 ) @ ( c_Set_Oinsert @ SY2412 @ SY2411 @ SV319 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1730,plain,
! [SV320: $i] :
( ( ! [SY2413: $i,SY2414: $i,SY2415: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV320 @ tc_bool ) ) @ SY2413 ) @ ( c_Set_Oinsert @ SY2414 @ SY2415 @ SV320 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV320 @ tc_bool ) ) @ SY2413 ) @ SY2415 ) )
| ( hBOOL @ ( c_in @ SY2414 @ SY2413 @ SV320 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1731,plain,
! [SV321: $i] :
( ( ! [SY2416: $i,SY2417: $i,SY2418: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV321 @ tc_bool ) ) @ SY2416 ) @ SY2417 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV321 @ tc_bool ) ) @ SY2416 ) @ ( c_Set_Oinsert @ SY2418 @ SY2417 @ SV321 ) ) )
| ( hBOOL @ ( c_in @ SY2418 @ SY2416 @ SV321 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1732,plain,
! [SV322: $i] :
( ( ! [SY2419: $i,SY2420: $i,SY2421: $i,SY2422: $i,SY2423: $i,SY2424: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV322 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2419 @ SY2420 @ SY2421 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2422 @ SY2423 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV322 @ SY2419 @ SY2421 @ SY2420 @ SY2424 @ SY2422 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2424 @ SY2423 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV322 @ SY2419 @ SY2421 @ SY2420 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV322 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2424 @ SY2420 @ SY2422 @ 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_forall_pos,[status(thm)],[1269]) ).
thf(1733,plain,
! [SV323: $i] :
( ( ! [SY2425: $i,SY2426: $i,SY2427: $i,SY2428: $i,SY2429: $i,SY2430: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV323 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2425 @ SY2426 @ SY2427 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2428 @ SY2429 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SY2425 @ SY2430 @ SY2427 @ SY2428 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2430 @ SY2429 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SY2425 @ SY2430 @ SY2427 @ SY2428 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV323 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2430 @ SY2426 @ SY2428 @ 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_forall_pos,[status(thm)],[1270]) ).
thf(1734,plain,
! [SV324: $i] :
( ( ! [SY2431: $i,SY2432: $i,SY2433: $i,SY2434: $i,SY2435: $i,SY2436: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV324 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2431 @ SY2432 @ SY2433 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2434 @ SY2435 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV324 @ SY2431 @ SY2433 @ SY2432 @ SY2436 @ SY2434 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2436 @ SY2435 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV324 @ SY2431 @ SY2433 @ SY2432 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV324 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2436 @ SY2432 @ SY2434 @ 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_forall_pos,[status(thm)],[1271]) ).
thf(1735,plain,
! [SV325: $i] :
( ( ! [SY2437: $i,SY2438: $i,SY2439: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV325 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2437 @ SY2438 @ SY2439 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2437 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV325 @ SY2437 @ SY2439 @ SY2438 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV325 @ SY2437 @ SY2439 @ SY2438 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1736,plain,
! [SV326: $i] :
( ( ! [SY2440: $i,SY2441: $i,SY2442: $i,SY2443: $i,SY2444: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV326 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2440 @ SY2441 @ SY2442 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2442 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV326 @ SY2440 @ SY2442 @ SY2441 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV326 @ SY2440 @ SY2442 @ SY2441 @ SY2443 @ SY2444 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV326 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2443 @ SY2441 @ SY2444 @ 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_forall_pos,[status(thm)],[1273]) ).
thf(1737,plain,
! [SV327: $i] :
( ( ! [SY2445: $i,SY2446: $i,SY2447: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV327 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2445 @ SY2446 @ SY2447 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2445 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV327 @ SY2445 @ SY2447 @ SY2446 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV327 @ SY2445 @ SY2447 @ SY2446 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1738,plain,
! [SV328: $i] :
( ( ! [SY2448: $i,SY2449: $i,SY2450: $i,SY2451: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV328 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2448 @ SY2449 @ SY2450 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2451 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SY2450 @ SY2451 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SY2450 @ SY2451 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV328 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2448 @ SY2449 @ SY2451 @ 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_forall_pos,[status(thm)],[1275]) ).
thf(1739,plain,
! [SV329: $i] :
( ( ! [SY2452: $i,SY2453: $i,SY2454: $i,SY2455: $i,SY2456: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV329 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2452 @ SY2453 @ SY2454 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2452 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SY2452 @ SY2455 @ SY2454 @ SY2456 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SY2452 @ SY2455 @ SY2454 @ SY2456 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV329 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2455 @ SY2453 @ SY2456 @ 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_forall_pos,[status(thm)],[1276]) ).
thf(1740,plain,
! [SV330: $i] :
( ( ! [SY2457: $i,SY2458: $i,SY2459: $i,SY2460: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV330 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2457 @ SY2458 @ SY2459 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2457 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SY2457 @ SY2460 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SY2457 @ SY2460 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV330 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2460 @ SY2458 @ SY2459 @ 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_forall_pos,[status(thm)],[1277]) ).
thf(1741,plain,
! [SV331: $i] :
( ( ! [SY2461: $i,SY2462: $i,SY2463: $i,SY2464: $i,SY2465: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV331 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2461 @ SY2462 @ SY2463 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2463 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV331 @ SY2461 @ SY2463 @ SY2462 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV331 @ SY2461 @ SY2463 @ SY2462 @ SY2464 @ SY2465 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV331 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2464 @ SY2462 @ SY2465 @ 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_forall_pos,[status(thm)],[1278]) ).
thf(1742,plain,
! [SV332: $i] :
( ( ! [SY2466: $i,SY2467: $i,SY2468: $i,SY2469: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV332 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2466 @ SY2467 @ SY2468 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2469 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SY2466 @ SY2469 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SY2466 @ SY2469 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV332 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2469 @ SY2467 @ SY2468 @ 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_forall_pos,[status(thm)],[1279]) ).
thf(1743,plain,
! [SV333: $i] :
( ( ! [SY2470: $i,SY2471: $i,SY2472: $i,SY2473: $i,SY2474: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV333 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2470 @ SY2471 @ SY2472 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2472 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SY2470 @ SY2473 @ SY2472 @ SY2474 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SY2470 @ SY2473 @ SY2472 @ SY2474 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV333 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2473 @ SY2471 @ SY2474 @ 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_forall_pos,[status(thm)],[1280]) ).
thf(1744,plain,
! [SV334: $i] :
( ( ! [SY2475: $i,SY2476: $i,SY2477: $i,SY2478: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV334 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2475 @ SY2476 @ SY2477 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2477 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SY2477 @ SY2478 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SY2477 @ SY2478 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV334 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2475 @ SY2476 @ SY2478 @ 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_forall_pos,[status(thm)],[1281]) ).
thf(1745,plain,
! [SV335: $i] :
( ( ! [SY2479: $i,SY2480: $i,SY2481: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV335 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2479 @ SY2480 @ SY2481 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2479 @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ SV335 @ SY2479 @ SY2481 @ SY2480 ) ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ SV335 @ SY2479 @ SY2481 @ SY2480 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1746,plain,
! [SV336: $i] :
( ( ! [SY2482: $i,SY2483: $i,SY2484: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV336 @ tc_bool ) ) @ SY2482 ) @ ( c_Set_Oinsert @ SY2483 @ SY2484 @ SV336 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV336 @ tc_bool ) ) @ SY2482 ) @ SY2484 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV336 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY2482 @ ( c_Set_Oinsert @ SY2483 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV336 @ tc_bool ) ) @ SV336 ) @ ( tc_fun @ SV336 @ tc_bool ) ) ) @ SY2484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1747,plain,
! [SV337: $i] :
( ( ! [SY2485: $i,SY2486: $i,SY2487: $i,SY2488: $i,SY2489: $i,SY2490: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2485 @ ( c_Com_Ocom_OSemi @ SY2486 @ SY2487 ) @ SY2488 @ SY2489 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY2489 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2489 ) ) @ SY2489 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2490 @ SY2487 @ SY2488 @ SY2489 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY2489 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2489 ) ) @ SY2489 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2485 @ SY2486 @ SY2490 @ SY2489 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY2489 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2489 ) ) @ SY2489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1748,plain,
! [SV338: $i] :
( ( ! [SY2491: $i,SY2492: $i] :
( ~ ( class_Orderings_Olinorder @ SV338 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV338 ) @ SY2491 ) @ SY2492 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV338 ) @ SY2492 ) @ SY2491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1749,plain,
! [SV339: $i] :
( ( ! [SY2493: $i,SY2494: $i,SY2495: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV339 @ tc_bool ) ) @ ( c_Set_Oinsert @ SY2493 @ SY2494 @ SV339 ) ) @ ( c_Set_Oinsert @ SY2493 @ SY2495 @ SV339 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV339 @ tc_bool ) ) @ SY2494 ) @ SY2495 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1750,plain,
! [SV340: $i] :
( ( ! [SY2496: $i,SY2497: $i,SY2498: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV340 @ ( c_Set_Oinsert @ SY2496 @ SY2497 @ ( tc_Hoare__Mirabelle_Otriple @ SY2498 ) ) @ SY2498 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV340 @ SY2497 @ SY2498 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV340 @ ( c_Set_Oinsert @ SY2496 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY2498 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2498 ) ) @ SY2498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1751,plain,
! [SV341: $i] :
( ( ! [SY2499: $i,SY2500: $i] :
( ( SV341
= ( c_Set_Oinsert @ SY2499 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2500 @ tc_bool ) ) @ SY2500 ) )
| ( SV341
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2500 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2500 @ tc_bool ) ) @ SV341 ) @ ( c_Set_Oinsert @ SY2499 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2500 @ tc_bool ) ) @ SY2500 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1752,plain,
! [SV342: $i] :
( ( ! [SY2501: $i,SY2502: $i,SY2503: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV342 @ SY2501 @ SY2502 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY2502 ) @ tc_bool ) ) @ SY2501 ) @ SY2503 ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV342 @ SY2503 @ SY2502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1753,plain,
! [SV343: $i] :
( ( ! [SY2504: $i,SY2505: $i,SY2506: $i] :
( ( hBOOL @ ( hAPP @ SV343 @ SY2504 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2505 @ tc_bool ) ) @ SY2506 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP @ SY2506 @ SY2504 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1754,plain,
! [SV344: $i] :
( ( ! [SY2507: $i] :
( ~ ( class_Orderings_Opreorder @ SV344 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV344 ) @ SY2507 ) @ SY2507 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1755,plain,
! [SV345: $i] :
( ( ! [SY2508: $i] :
( ~ ( class_Orderings_Oorder @ SV345 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV345 ) @ SY2508 ) @ SY2508 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1756,plain,
! [SV346: $i] :
( ( ! [SY2509: $i,SY2510: $i,SY2511: $i] :
( ( hBOOL @ ( hAPP @ SV346 @ SY2509 ) )
| ~ ( hBOOL @ ( hAPP @ SY2510 @ SY2509 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2511 @ tc_bool ) ) @ SY2510 ) @ SV346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1757,plain,
! [SV347: $i] :
( ( ! [SY2512: $i,SY2513: $i,SY2514: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV347 @ tc_bool ) ) @ SY2512 ) @ SY2513 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV347 @ tc_bool ) ) @ SY2514 ) @ SY2513 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV347 @ tc_bool ) ) @ SY2512 ) @ SY2514 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1758,plain,
! [SV348: $i] :
( ( ! [SY2515: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV348 @ tc_bool ) ) @ SY2515 ) @ SY2515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1759,plain,
! [SV349: $i] :
( ( ! [SY2516: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV349 @ tc_bool ) ) @ SY2516 ) @ SY2516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1760,plain,
! [SV350: $i] :
( ( ! [SY2517: $i,SY2518: $i,SY2519: $i] :
( ~ ( class_Orderings_Opreorder @ SV350 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SY2517 ) @ SY2518 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SY2519 ) @ SY2518 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SY2517 ) @ SY2519 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1761,plain,
! [SV351: $i] :
( ( ! [SY2520: $i,SY2521: $i,SY2522: $i] :
( ~ ( class_Orderings_Oorder @ SV351 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SY2520 ) @ SY2521 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SY2520 ) @ SY2522 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SY2522 ) @ SY2521 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1298]) ).
thf(1762,plain,
! [SV352: $i] :
( ( ! [SY2523: $i,SY2524: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV352 @ SY2523 @ SY2524 ) @ SV352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1763,plain,
! [SV353: $i] :
( ( ! [SY2525: $i,SY2526: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2525 @ c_Com_Ocom_OSKIP @ SY2525 @ SY2526 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY2526 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2526 ) ) @ SY2526 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1764,plain,
! [SV354: $i] :
( ( ! [SY2527: $i,SY2528: $i,SY2529: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV354 @ SY2527 @ SY2528 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV354 @ SY2529 @ SY2528 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY2529 @ SY2527 @ SY2528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1765,plain,
! [SV355: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV355 @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV355 @ tc_bool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV355 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1766,plain,
! [SV356: $i] :
( ( ! [SY2530: $i] :
( ( SV356
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2530 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2530 @ tc_bool ) ) @ SV356 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2530 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1767,plain,
! [SV357: $i] :
( ( ! [SY2531: $i,SY2532: $i] :
( ~ ( class_Orderings_Oorder @ SV357 )
| ( SY2531 = SY2532 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV357 ) @ SY2531 ) @ SY2532 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV357 ) @ SY2532 ) @ SY2531 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1768,plain,
! [SV358: $i] :
( ( ! [SY2533: $i,SY2534: $i] :
( ~ ( class_Orderings_Oorder @ SV358 )
| ( SY2533 = SY2534 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV358 ) @ SY2534 ) @ SY2533 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV358 ) @ SY2533 ) @ SY2534 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1769,plain,
! [SV359: $i] :
( ( ! [SY2535: $i,SY2536: $i] :
( ~ ( class_Orderings_Oorder @ SV359 )
| ( SY2535 = SY2536 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV359 ) @ SY2536 ) @ SY2535 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV359 ) @ SY2535 ) @ SY2536 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1770,plain,
! [SV360: $i] :
( ( ! [SY2537: $i,SY2538: $i] :
( ( SV360 = SY2537 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2538 @ tc_bool ) ) @ SY2537 ) @ SV360 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2538 @ tc_bool ) ) @ SV360 ) @ SY2537 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1771,plain,
! [SV361: $i] :
( ( ! [SY2539: $i,SY2540: $i] :
( ( SV361 = SY2539 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2540 @ tc_bool ) ) @ SY2539 ) @ SV361 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2540 @ tc_bool ) ) @ SV361 ) @ SY2539 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1772,plain,
! [SV362: $i] :
( ( ! [SY2541: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV362 @ tc_bool ) ) @ SY2541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1773,plain,
! [SV363: $i] :
( ( ! [SY2542: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ SV363 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY2542 ) @ tc_bool ) ) @ SY2542 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1774,plain,
! [SV364: $i] :
( ( ! [SY2543: $i,SY2544: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV364 @ tc_bool ) ) @ SY2543 ) @ ( c_Set_Oinsert @ SY2544 @ SY2543 @ SV364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1775,plain,
! [SV365: $i] :
( ( ! [SY2545: $i,SY2546: $i,SY2547: $i] :
( ( hBOOL @ ( hAPP @ SV365 @ SY2545 ) )
| ( SY2546 = SY2545 )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY2546 @ SV365 @ SY2547 ) @ SY2545 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1776,plain,
! [SV366: $i] :
( ( ! [SY2548: $i,SY2549: $i] :
( ( c_Set_Oinsert @ SV366 @ ( c_Set_Oinsert @ SV366 @ SY2548 @ SY2549 ) @ SY2549 )
= ( c_Set_Oinsert @ SV366 @ SY2548 @ SY2549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1777,plain,
! [SV367: $i] :
( ( ! [SY2550: $i] :
( ~ ( class_Orderings_Obot @ SV367 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV367 ) @ ( c_Orderings_Obot__class_Obot @ SV367 ) ) @ SY2550 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1778,plain,
! [SV368: $i] :
( ( ! [SY2551: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV368 @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV368 @ tc_bool ) ) ) @ SY2551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1779,plain,
! [SV369: $i] :
( ( ! [SY2552: $i,SY2553: $i,SY2554: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV369 @ tc_bool ) ) @ SY2552 ) @ ( c_Set_Oinsert @ SY2553 @ SY2554 @ SV369 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV369 @ tc_bool ) ) @ SY2552 ) @ SY2554 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1780,plain,
! [SV370: $i] :
( ( ! [SY2555: $i,SY2556: $i,SY2557: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV370 @ tc_bool ) ) @ SY2555 ) @ SY2556 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV370 @ tc_bool ) ) @ ( c_Set_Oinsert @ SY2557 @ SY2555 @ SV370 ) ) @ SY2556 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1781,plain,
! [SV371: $i] :
( ( ! [SY2558: $i,SY2559: $i,SY2560: $i] :
( ( c_Set_Oinsert @ SV371 @ ( c_Set_Oinsert @ SY2558 @ SY2559 @ SY2560 ) @ SY2560 )
= ( c_Set_Oinsert @ SY2558 @ ( c_Set_Oinsert @ SV371 @ SY2559 @ SY2560 ) @ SY2560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1782,plain,
! [SV372: $i] :
( ( ! [SY2561: $i,SY2562: $i] :
( ( c_Set_Oinsert @ SV372 @ ( c_Set_Oinsert @ SY2561 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2562 @ tc_bool ) ) @ SY2562 ) @ SY2562 )
= ( c_Set_Oinsert @ SY2561 @ ( c_Set_Oinsert @ SV372 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2562 @ tc_bool ) ) @ SY2562 ) @ SY2562 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1783,plain,
! [SV373: $i] :
( ( ! [SY2563: $i,SY2564: $i,SY2565: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV373 @ SY2563 @ SY2564 ) @ SY2565 ) )
| ~ ( hBOOL @ ( hAPP @ SY2563 @ SY2565 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1784,plain,
! [SV374: $i] :
( ( ! [SY2566: $i,SY2567: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV374 @ SY2566 @ SY2567 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY2567 ) @ tc_bool ) ) @ SY2566 ) @ SV374 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1785,plain,
! [SV375: $i] :
( ( ! [SY2568: $i,SY2569: $i,SY2570: $i,SY2571: $i] :
( ~ ( class_HOL_Oord @ SV375 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV375 ) @ ( hAPP @ SY2568 @ SY2569 ) ) @ ( hAPP @ SY2570 @ SY2569 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2571 @ SV375 ) ) @ SY2568 ) @ SY2570 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1786,plain,
! [SV376: $i] :
( ( ! [SY2572: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV376 @ SY2572 ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ SY2572 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1787,plain,
! [SV377: $i] :
( ( ! [SY2573: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV377 @ SY2573 ) )
| ~ ( class_Lattices_Olattice @ SY2573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1788,plain,
! [SV378: $i] :
( ( ! [SY2574: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV378 @ SY2574 ) )
| ~ ( class_Lattices_Obounded__lattice @ SY2574 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1789,plain,
! [SV379: $i] :
( ( ! [SY2575: $i] :
( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ SV379 @ SY2575 ) )
| ~ ( class_Lattices_Oboolean__algebra @ SY2575 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1790,plain,
! [SV380: $i] :
( ( ! [SY2576: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ SV380 @ SY2576 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SY2576 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SV380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1791,plain,
! [SV381: $i] :
( ( ! [SY2577: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ SV381 @ SY2577 ) )
| ~ ( class_Orderings_Opreorder @ SY2577 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1792,plain,
! [SV382: $i] :
( ( ! [SY2578: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ SV382 @ SY2578 ) )
| ~ ( class_Lattices_Olattice @ SY2578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1793,plain,
! [SV383: $i] :
( ( ! [SY2579: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ SV383 @ SY2579 ) )
| ~ ( class_Orderings_Oorder @ SY2579 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1794,plain,
! [SV384: $i] :
( ( ! [SY2580: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ SV384 @ SY2580 ) )
| ~ ( class_Orderings_Obot @ SY2580 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1795,plain,
! [SV385: $i] :
( ( ! [SY2581: $i] :
( ( class_HOL_Ouminus @ ( tc_fun @ SV385 @ SY2581 ) )
| ~ ( class_HOL_Ouminus @ SY2581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1796,plain,
! [SV386: $i] :
( ( ! [SY2582: $i] :
( ( class_HOL_Ominus @ ( tc_fun @ SV386 @ SY2582 ) )
| ~ ( class_HOL_Ominus @ SY2582 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1797,plain,
! [SV387: $i] :
( ( ! [SY2583: $i] :
( ( class_HOL_Oord @ ( tc_fun @ SV387 @ SY2583 ) )
| ~ ( class_HOL_Oord @ SY2583 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1798,plain,
! [SV388: $i] :
( ( ! [SY2584: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV388 ) @ SY2584 ) @ SY2584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1365]) ).
thf(1799,plain,
! [SV389: $i] :
( ( ! [SY2585: $i,SY2586: $i] :
( ( SV389 = SY2585 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY2586 ) @ SV389 ) @ SY2585 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1800,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[1367]) ).
thf(1801,plain,
! [SV390: $i] :
( ( ! [SY2587: $i,SY2588: $i] :
( ( ( c_Set_Oinsert @ SV390 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2587 @ tc_bool ) ) @ SY2587 )
!= ( c_Set_Oinsert @ SY2588 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2587 @ tc_bool ) ) @ SY2587 ) )
| ( SV390 = SY2588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1368]) ).
thf(1802,plain,
! [SV391: $i] :
( ( ! [SY2589: $i,SY2590: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV391 )
| ( ( c_HOL_Ouminus__class_Ouminus @ SY2589 @ SV391 )
!= ( c_HOL_Ouminus__class_Ouminus @ SY2590 @ SV391 ) )
| ( SY2589 = SY2590 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1803,plain,
! [SV392: $i] :
( ( ! [SY2591: $i,SY2592: $i,SY2593: $i] :
( ( ( c_Set_Oinsert @ SV392 @ SY2591 @ SY2592 )
!= ( c_Set_Oinsert @ SV392 @ SY2593 @ SY2592 ) )
| ( hBOOL @ ( c_in @ SV392 @ SY2593 @ SY2592 ) )
| ( hBOOL @ ( c_in @ SV392 @ SY2591 @ SY2592 ) )
| ( SY2591 = SY2593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1804,plain,
! [SV393: $i] :
( ( ! [SY2594: $i,SY2595: $i] :
( ( ( c_Collect @ SV393 @ SY2594 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2594 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ SV393 @ SY2595 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1805,plain,
! [SV394: $i] :
( ( ! [SY2596: $i,SY2597: $i,SY2598: $i] :
( ( ( c_Com_Ocom_OSemi @ SV394 @ SY2596 )
!= ( c_Com_Ocom_OSemi @ SY2597 @ SY2598 ) )
| ( SY2596 = SY2598 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(1806,plain,
! [SV395: $i] :
( ( ! [SY2599: $i,SY2600: $i,SY2601: $i,SY2602: $i,SY2603: $i,SY2604: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV395 @ SY2599 @ SY2600 @ SY2601 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2602 @ SY2603 @ SY2604 @ SY2601 ) )
| ( SV395 = SY2602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1373]) ).
thf(1807,plain,
! [SV396: $i] :
( ( ! [SY2605: $i,SY2606: $i] :
( ( c_Set_Oinsert @ SV396 @ SY2605 @ SY2606 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2606 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1808,plain,
! [SV397: $i] :
( ( ! [SY2607: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ SV397 @ SY2607 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1809,plain,
! [SV398: $i] :
( ( ! [SY2608: $i,SY2609: $i] :
( ~ ( class_Orderings_Oorder @ SV398 )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV398 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SY2608 @ SY2609 @ SV398 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2608 @ SY2609 @ SV398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1810,plain,
! [SV399: $i] :
( ( ! [SY2610: $i,SY2611: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV399 @ tc_bool ) )
!= ( c_Set_Oinsert @ SY2610 @ SY2611 @ SV399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(1811,plain,
! [SV400: $i] :
( ( ! [SY2612: $i,SY2613: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SV400 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2612 @ SY2613 @ SV400 )
!= ( c_Orderings_Obot__class_Obot @ SV400 ) )
| ( SY2612
= ( c_Orderings_Obot__class_Obot @ SV400 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1378]) ).
thf(1812,plain,
! [SV401: $i] :
( ( ! [SY2614: $i,SY2615: $i,SY2616: $i,SY2617: $i] :
( ( ( c_Set_Oinsert @ SV401 @ ( c_Set_Oinsert @ SY2614 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2615 @ tc_bool ) ) @ SY2615 ) @ SY2615 )
!= ( c_Set_Oinsert @ SY2616 @ ( c_Set_Oinsert @ SY2617 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2615 @ tc_bool ) ) @ SY2615 ) @ SY2615 ) )
| ( SY2614 = SY2616 )
| ( SV401 = SY2616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(1813,plain,
! [SV402: $i] :
( ( ! [SY2618: $i,SY2619: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV402 @ SY2618 @ ( tc_fun @ SY2619 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2619 @ tc_bool ) ) )
| ( SY2618
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2619 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1380]) ).
thf(1814,plain,
! [SV403: $i] :
( ( ! [SY2620: $i,SY2621: $i,SY2622: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV403 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2620 @ SY2620 @ SV403 )
!= ( c_HOL_Ominus__class_Ominus @ SY2621 @ SY2622 @ SV403 ) )
| ( SY2621 = SY2622 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1381]) ).
thf(1815,plain,
! [SV404: $i] :
( ( ! [SY2623: $i,SY2624: $i] :
( ~ ( class_Orderings_Oorder @ SV404 )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV404 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2623 @ SY2624 @ SV404 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV404 ) @ SY2623 ) @ SY2624 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1382]) ).
thf(1816,plain,
! [SV405: $i] :
( ( ! [SY2625: $i,SY2626: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV405 @ SY2625 @ ( tc_fun @ SY2626 @ tc_bool ) )
!= SY2625 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2626 @ tc_bool ) ) @ SV405 ) @ SY2625 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1383]) ).
thf(1817,plain,
! [SV406: $i] :
( ( ! [SY2627: $i,SY2628: $i] :
( ~ ( class_Orderings_Oorder @ SV406 )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2627 @ SY2628 @ SV406 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV406 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV406 ) @ SY2627 ) @ SY2628 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1818,plain,
! [SV407: $i] :
( ( ! [SY2629: $i,SY2630: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV407 @ SY2629 @ ( tc_fun @ SY2630 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2630 @ tc_bool ) ) )
| ( SV407
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2630 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1819,plain,
! [SV408: $i] :
( ( ! [SY2631: $i] :
( ( c_Com_Ocom_OSemi @ SV408 @ SY2631 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1820,plain,
! [SV409: $i] :
( ( ! [SY2632: $i,SY2633: $i,SY2634: $i,SY2635: $i] :
( ( ( c_Set_Oinsert @ SV409 @ ( c_Set_Oinsert @ SY2632 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2633 @ tc_bool ) ) @ SY2633 ) @ SY2633 )
!= ( c_Set_Oinsert @ SY2634 @ ( c_Set_Oinsert @ SY2635 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2633 @ tc_bool ) ) @ SY2633 ) @ SY2633 ) )
| ( SV409 = SY2635 )
| ( SY2632 = SY2635 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1387]) ).
thf(1821,plain,
! [SV410: $i] :
( ( ! [SY2636: $i,SY2637: $i,SY2638: $i,SY2639: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV410 @ SY2636 @ SY2637 @ ( tc_fun @ SY2638 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2638 @ tc_bool ) ) )
| ( ( hAPP @ SY2636 @ SY2639 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2638 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SY2639 @ SV410 @ SY2637 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(1822,plain,
! [SV411: $i] :
( ( ! [SY2640: $i,SY2641: $i,SY2642: $i,SY2643: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV411 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2640 @ SY2641 @ SV411 )
!= ( c_HOL_Ominus__class_Ominus @ SY2642 @ SY2643 @ SV411 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV411 ) @ SY2643 ) @ SY2642 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV411 ) @ SY2641 ) @ SY2640 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(1823,plain,
! [SV412: $i] :
( ( ! [SY2644: $i,SY2645: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ SV412 )
| ( ( c_HOL_Ouminus__class_Ouminus @ SY2644 @ SV412 )
!= ( c_HOL_Ouminus__class_Ouminus @ SY2645 @ SV412 ) )
| ( SY2644 = SY2645 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1390]) ).
thf(1824,plain,
! [SV413: $i] :
( ( ! [SY2646: $i,SY2647: $i,SY2648: $i,SY2649: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV413 @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2646 @ SY2647 @ SY2648 @ ( tc_fun @ SV413 @ tc_bool ) ) )
| ( ( hAPP @ SY2647 @ SY2649 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV413 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SY2649 @ SY2646 @ SY2648 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1391]) ).
thf(1825,plain,
! [SV414: $i] :
( ( ! [SY2650: $i,SY2651: $i] :
( ~ ( class_Orderings_Oorder @ SV414 )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ SY2650 @ SY2651 @ SV414 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV414 @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2650 @ SY2651 @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1392]) ).
thf(1826,plain,
! [SV415: $i] :
( ( ! [SY2652: $i,SY2653: $i,SY2654: $i,SY2655: $i] :
( ( ( c_Set_Oinsert @ SV415 @ ( c_Set_Oinsert @ SY2652 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2653 @ tc_bool ) ) @ SY2653 ) @ SY2653 )
!= ( c_Set_Oinsert @ SY2654 @ ( c_Set_Oinsert @ SY2655 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2653 @ tc_bool ) ) @ SY2653 ) @ SY2653 ) )
| ( SY2652 = SY2654 )
| ( SY2652 = SY2655 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1827,plain,
! [SV416: $i] :
( ( ! [SY2656: $i,SY2657: $i] :
( ~ ( class_Orderings_Oorder @ SV416 )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV416 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastLessThan @ SY2656 @ SY2657 @ SV416 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2656 @ SY2657 @ SV416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1828,plain,
! [SV417: $i] :
( ( ! [SY2658: $i,SY2659: $i] :
( ( ( c_HOL_Ouminus__class_Ouminus @ SV417 @ ( tc_fun @ SY2658 @ tc_bool ) )
!= ( c_HOL_Ouminus__class_Ouminus @ SY2659 @ ( tc_fun @ SY2658 @ tc_bool ) ) )
| ( SV417 = SY2659 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1829,plain,
! [SV418: $i] :
( ( ! [SY2660: $i,SY2661: $i,SY2662: $i,SY2663: $i,SY2664: $i,SY2665: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV418 @ SY2660 @ SY2661 @ SY2662 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2663 @ SY2664 @ SY2665 @ SY2662 ) )
| ( SY2661 = SY2665 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1396]) ).
thf(1830,plain,
! [SV419: $i] :
( ( ! [SY2666: $i,SY2667: $i,SY2668: $i,SY2669: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV419 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2666 @ SY2667 @ SV419 )
!= ( c_HOL_Ominus__class_Ominus @ SY2668 @ SY2669 @ SV419 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV419 ) @ SY2667 ) @ SY2666 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV419 ) @ SY2669 ) @ SY2668 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(1831,plain,
! [SV420: $i] :
( ( ! [SY2670: $i,SY2671: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV420 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2670 @ SY2671 @ SV420 )
!= SY2671 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV420 ) @ SY2670 ) @ SY2671 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1832,plain,
! [SV421: $i] :
( ( ! [SY2672: $i,SY2673: $i,SY2674: $i,SY2675: $i,SY2676: $i,SY2677: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV421 @ SY2672 @ SY2673 @ SY2674 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2675 @ SY2676 @ SY2677 @ SY2674 ) )
| ( SY2672 = SY2676 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(1833,plain,
! [SV422: $i] :
( ( ! [SY2678: $i,SY2679: $i,SY2680: $i] :
( ( ( c_Com_Ocom_OSemi @ SV422 @ SY2678 )
!= ( c_Com_Ocom_OSemi @ SY2679 @ SY2680 ) )
| ( SV422 = SY2679 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1400]) ).
thf(1834,plain,
! [SV423: $i] :
( ( ! [SY2681: $i,SY2682: $i,SY2683: $i,SY2684: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV423 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2681 @ SY2682 @ SV423 )
!= ( c_HOL_Ominus__class_Ominus @ SY2683 @ SY2684 @ SV423 ) )
| ( c_HOL_Oord__class_Oless @ SY2683 @ SY2684 @ SV423 )
| ~ ( c_HOL_Oord__class_Oless @ SY2681 @ SY2682 @ SV423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(1835,plain,
! [SV424: $i] :
( ( ! [SY2685: $i,SY2686: $i] :
( ~ ( class_Orderings_Oorder @ SV424 )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SY2685 @ SY2686 @ SV424 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV424 @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2685 @ SY2686 @ SV424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1402]) ).
thf(1836,plain,
! [SV425: $i] :
( ( ! [SY2687: $i,SY2688: $i] :
( ( ( c_Set_Oinsert @ SV425 @ SY2687 @ SY2688 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2688 @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ SV425 @ SY2687 @ SY2688 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(1837,plain,
! [SV426: $i] :
( ( ! [SY2689: $i,SY2690: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV426 @ tc_bool ) )
!= ( c_Collect @ SY2689 @ SV426 ) )
| ~ ( hBOOL @ ( hAPP @ SY2689 @ SY2690 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1838,plain,
! [SV427: $i] :
( ( ! [SY2691: $i,SY2692: $i,SY2693: $i,SY2694: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV427 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2691 @ SY2692 @ SV427 )
!= ( c_HOL_Ominus__class_Ominus @ SY2693 @ SY2694 @ SV427 ) )
| ( c_HOL_Oord__class_Oless @ SY2691 @ SY2692 @ SV427 )
| ~ ( c_HOL_Oord__class_Oless @ SY2693 @ SY2694 @ SV427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1405]) ).
thf(1839,plain,
! [SV428: $i] :
( ( ! [SY2695: $i,SY2696: $i,SY2697: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV428 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2695 @ SY2696 @ SV428 )
!= ( c_HOL_Ominus__class_Ominus @ SY2697 @ SY2697 @ SV428 ) )
| ( SY2695 = SY2696 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1840,plain,
! [SV429: $i] :
( ( ! [SY2698: $i,SY2699: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SV429 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2698 @ SY2699 @ SV429 )
!= ( c_Orderings_Obot__class_Obot @ SV429 ) )
| ( SY2699
= ( c_Orderings_Obot__class_Obot @ SV429 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(1841,plain,
! [SV430: $i] :
( ( ! [SY2700: $i,SY2701: $i,SY2702: $i,SY2703: $i] :
( ( ( c_Set_Oinsert @ SV430 @ ( c_Set_Oinsert @ SY2700 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2701 @ tc_bool ) ) @ SY2701 ) @ SY2701 )
!= ( c_Set_Oinsert @ SY2702 @ ( c_Set_Oinsert @ SY2703 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2701 @ tc_bool ) ) @ SY2701 ) @ SY2701 ) )
| ( SV430 = SY2703 )
| ( SV430 = SY2702 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1842,plain,
! [SV431: $i,SV1: $i] :
( ( ! [SY2704: $i,SY2705: $i] :
( ~ ( class_HOL_Oord @ SV1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV431 @ SV1 ) ) @ SY2704 ) @ SY2705 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2704 @ SY2705 @ ( tc_fun @ SV431 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(1843,plain,
! [SV432: $i,SV2: $i] :
( ( ! [SY2706: $i,SY2707: $i] :
( ~ ( class_HOL_Oord @ SV2 )
| ( c_HOL_Oord__class_Oless @ SV432 @ SY2706 @ ( tc_fun @ SY2707 @ SV2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2707 @ SV2 ) ) @ SY2706 ) @ SV432 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2707 @ SV2 ) ) @ SV432 ) @ SY2706 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(1844,plain,
! [SV433: $i,SV3: $i] :
( ( ! [SY2708: $i,SY2709: $i] :
( ~ ( class_HOL_Oord @ SV3 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV433 @ SV3 ) ) @ SY2708 ) @ SY2709 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2709 @ SY2708 @ ( tc_fun @ SV433 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(1845,plain,
! [SV434: $i,SV4: $i] :
( ( ! [SY2710: $i] :
( ( SV4 = SV434 )
| ( c_HOL_Oord__class_Oless @ SV4 @ SV434 @ ( tc_fun @ SY2710 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2710 @ tc_bool ) ) @ SV4 ) @ SV434 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(1846,plain,
! [SV435: $i,SV5: $i] :
( ( ! [SY2711: $i] :
( ( c_HOL_Oord__class_Oless @ SV5 @ SV435 @ ( tc_fun @ SY2711 @ tc_bool ) )
| ( SV5 = SV435 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2711 @ tc_bool ) ) @ SV5 ) @ SV435 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1414]) ).
thf(1847,plain,
! [SV436: $i,SV6: $i] :
( ( ! [SY2712: $i] :
( ( c_Finite__Set_Ofinite @ SV6 @ SV436 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV436 @ tc_bool ) ) @ SV6 ) @ SY2712 ) )
| ~ ( c_Finite__Set_Ofinite @ SY2712 @ SV436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(1848,plain,
! [SV437: $i,SV7: $i] :
( ( ! [SY2713: $i,SY2714: $i] :
( ( c_HOL_Oord__class_Oless @ SV7 @ SV437 @ ( tc_fun @ SY2713 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2714 @ SV437 @ ( tc_fun @ SY2713 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2713 @ tc_bool ) ) @ SV7 ) @ SY2714 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1416]) ).
thf(1849,plain,
! [SV438: $i,SV8: $i] :
( ( ! [SY2715: $i,SY2716: $i] :
( ( c_HOL_Oord__class_Oless @ SV8 @ SV438 @ ( tc_fun @ SY2715 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2715 @ tc_bool ) ) @ SY2716 ) @ SV438 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV8 @ SY2716 @ ( tc_fun @ SY2715 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(1850,plain,
! [SV439: $i,SV9: $i] :
( ( ! [SY2717: $i] :
( ( c_Finite__Set_Ofinite @ SV9 @ SV439 )
| ~ ( c_Finite__Set_Ofinite @ SY2717 @ SV439 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV439 @ tc_bool ) ) @ SV9 ) @ SY2717 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1418]) ).
thf(1851,plain,
! [SV440: $i,SV10: $i] :
( ( ! [SY2718: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV10 @ tc_bool ) ) @ SV440 ) @ SY2718 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV440 @ SY2718 @ ( tc_fun @ SV10 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1852,plain,
! [SV441: $i,SV11: $i] :
( ( ! [SY2719: $i,SY2720: $i,SY2721: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV11 )
| ( ( c_Finite__Set_Osetsum @ SV441 @ ( c_HOL_Ominus__class_Ominus @ SY2719 @ ( c_Set_Oinsert @ SY2720 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2721 @ tc_bool ) ) @ SY2721 ) @ ( tc_fun @ SY2721 @ tc_bool ) ) @ SY2721 @ SV11 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV441 @ SY2719 @ SY2721 @ SV11 ) @ ( hAPP @ SV441 @ SY2720 ) @ SV11 ) )
| ~ ( hBOOL @ ( c_in @ SY2720 @ SY2719 @ SY2721 ) )
| ~ ( c_Finite__Set_Ofinite @ SY2719 @ SY2721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1853,plain,
! [SV442: $i,SV12: $i] :
( ( ! [SY2722: $i,SY2723: $i,SY2724: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV12 )
| ( ( c_Finite__Set_Osetsum @ SV442 @ ( c_HOL_Ominus__class_Ominus @ SY2722 @ ( c_Set_Oinsert @ SY2723 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2724 @ tc_bool ) ) @ SY2724 ) @ ( tc_fun @ SY2724 @ tc_bool ) ) @ SY2724 @ SV12 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV442 @ SY2722 @ SY2724 @ SV12 ) @ ( hAPP @ SV442 @ SY2723 ) @ SV12 ) )
| ~ ( hBOOL @ ( c_in @ SY2723 @ SY2722 @ SY2724 ) )
| ~ ( c_Finite__Set_Ofinite @ SY2722 @ SY2724 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1854,plain,
! [SV443: $i,SV13: $i] :
( ( ! [SY2725: $i,SY2726: $i] :
( ( c_HOL_Oord__class_Oless @ SV13 @ ( c_Set_Oinsert @ SV443 @ SY2725 @ SY2726 ) @ ( tc_fun @ SY2726 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2726 @ tc_bool ) ) @ SV13 ) @ SY2725 ) )
| ( hBOOL @ ( c_in @ SV443 @ SV13 @ SY2726 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV13 @ SY2725 @ ( tc_fun @ SY2726 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1855,plain,
! [SV444: $i,SV14: $i] :
( ( ! [SY2727: $i,SY2728: $i] :
( ( c_HOL_Oord__class_Oless @ SV14 @ ( c_Set_Oinsert @ SV444 @ SY2727 @ SY2728 ) @ ( tc_fun @ SY2728 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2728 @ tc_bool ) ) @ SV14 ) @ SY2727 ) )
| ( hBOOL @ ( c_in @ SV444 @ SV14 @ SY2728 ) )
| ( hBOOL @ ( c_in @ SV444 @ SY2727 @ SY2728 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1856,plain,
! [SV445: $i,SV15: $i] :
( ( ! [SY2729: $i,SY2730: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV15 @ tc_bool ) ) @ SV445 ) @ SY2729 ) )
| ( hBOOL @ ( c_in @ SY2730 @ SV445 @ SV15 ) )
| ( hBOOL @ ( c_in @ SY2730 @ SY2729 @ SV15 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV445 @ ( c_Set_Oinsert @ SY2730 @ SY2729 @ SV15 ) @ ( tc_fun @ SV15 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1857,plain,
! [SV446: $i,SV16: $i] :
( ( ! [SY2731: $i,SY2732: $i] :
( ~ ( class_Orderings_Olinorder @ SV16 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV446 @ SY2731 @ SV16 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SY2731 @ SY2732 @ SV16 ) @ ( tc_fun @ SV16 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV446 @ SY2732 @ SV16 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV16 ) @ SY2731 ) @ SY2732 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV16 ) @ SV446 ) @ SY2731 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1858,plain,
! [SV447: $i,SV17: $i] :
( ( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ SV17 ) @ SV17 @ SV17 @ tc_bool ) @ SV447 ) @ SV17 )
= ( c_Set_Oinsert @ SV447 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV17 @ tc_bool ) ) @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1426]) ).
thf(1859,plain,
! [SV448: $i,SV18: $i] :
( ( ! [SY2733: $i] :
( ( c_Set_Oinsert @ SV18 @ SV448 @ SY2733 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ SY2733 ) @ SY2733 @ SY2733 @ tc_bool ) @ SV18 ) @ SY2733 ) @ SV448 @ ( tc_fun @ SY2733 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1427]) ).
thf(1860,plain,
! [SV449: $i,SV19: $i] :
( ( ! [SY2734: $i] :
( ( c_Finite__Set_Ofinite @ SV19 @ SV449 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SY2734 @ SV19 @ SV449 ) @ SV449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(1861,plain,
! [SV450: $i,SV20: $i] :
( ( ! [SY2735: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV20 @ SV450 @ SY2735 ) @ SY2735 )
| ~ ( c_Finite__Set_Ofinite @ SV450 @ SY2735 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1862,plain,
! [SV451: $i,SV21: $i] :
( ( ! [SY2736: $i,SY2737: $i] : ( c_Nitpick_Ofold__graph_H @ SV21 @ SV451 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2736 @ tc_bool ) ) @ SV451 @ SY2736 @ SY2737 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1863,plain,
! [SV452: $i,SV22: $i] :
( ( ! [SY2738: $i,SY2739: $i] : ( c_Finite__Set_Ofold__graph @ SV22 @ SV452 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2738 @ tc_bool ) ) @ SV452 @ SY2738 @ SY2739 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(1864,plain,
! [SV453: $i,SV23: $i] :
( ( ! [SY2740: $i,SY2741: $i,SY2742: $i] :
( ( SV23 = SV453 )
| ~ ( c_Finite__Set_Ofold__graph @ SY2740 @ SV453 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2741 @ tc_bool ) ) @ SV23 @ SY2741 @ SY2742 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1865,plain,
! [SV454: $i,SV25: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV25 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV454 @ tc_bool ) ) @ ( tc_fun @ SV454 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1866,plain,
! [SV455: $i,SV26: $i] :
( ( ! [SY2743: $i] :
( ~ ( class_Orderings_Opreorder @ SV26 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV26 ) @ SV455 ) @ SY2743 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2743 @ SV455 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(1867,plain,
! [SV456: $i,SV27: $i] :
( ( ! [SY2744: $i] :
( ~ ( class_Orderings_Olinorder @ SV27 )
| ( c_HOL_Oord__class_Oless @ SV456 @ SY2744 @ SV27 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV27 ) @ SY2744 ) @ SV456 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1436]) ).
thf(1868,plain,
! [SV457: $i,SV28: $i] :
( ( ! [SY2745: $i] :
( ~ ( class_Orderings_Olinorder @ SV28 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV28 ) @ SV457 ) @ SY2745 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2745 @ SV457 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1869,plain,
! [SV458: $i,SV29: $i] :
( ( ! [SY2746: $i] :
( ~ ( class_Orderings_Olinorder @ SV29 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV29 ) @ SV458 ) @ SY2746 ) )
| ( c_HOL_Oord__class_Oless @ SY2746 @ SV458 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1870,plain,
! [SV459: $i,SV30: $i] :
( ( ! [SY2747: $i] :
( ~ ( class_Orderings_Olinorder @ SV30 )
| ~ ( c_HOL_Oord__class_Oless @ SV459 @ SY2747 @ SV30 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV30 ) @ SY2747 ) @ SV459 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(1871,plain,
! [SV460: $i,SV31: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV31 )
| ( c_HOL_Oord__class_Oless @ SV460 @ SV460 @ SV31 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV31 ) @ SV460 ) @ SV460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(1872,plain,
! [SV461: $i,SV32: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV32 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV32 ) @ SV461 ) @ SV461 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV461 @ SV461 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1873,plain,
! [SV462: $i,SV33: $i] :
( ( ! [SY2748: $i] :
( ~ ( class_Orderings_Olinorder @ SV33 )
| ( c_HOL_Oord__class_Oless @ SV462 @ SY2748 @ SV33 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV33 ) @ SY2748 ) @ SV462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1874,plain,
! [SV463: $i,SV34: $i] :
( ( ! [SY2749: $i] :
( ~ ( class_Orderings_Opreorder @ SV34 )
| ( c_HOL_Oord__class_Oless @ SV463 @ SY2749 @ SV34 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV34 ) @ SY2749 ) @ SV463 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV34 ) @ SV463 ) @ SY2749 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(1875,plain,
! [SV464: $i,SV35: $i] :
( ( ! [SY2750: $i] :
( ~ ( class_Orderings_Oorder @ SV35 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV35 ) @ SV464 ) @ SY2750 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV464 @ SY2750 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(1876,plain,
! [SV465: $i,SV36: $i] :
( ( ! [SY2751: $i] :
( ~ ( class_Orderings_Opreorder @ SV36 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV36 ) @ SV465 ) @ SY2751 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV465 @ SY2751 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1877,plain,
! [SV466: $i,SV37: $i] :
( ( ! [SY2752: $i,SY2753: $i] :
( ~ ( class_Orderings_Oorder @ SV37 )
| ( c_HOL_Oord__class_Oless @ SV466 @ SY2752 @ SV37 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV37 ) @ SV466 ) @ SY2753 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2753 @ SY2752 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1878,plain,
! [SV467: $i,SV38: $i] :
( ( ! [SY2754: $i,SY2755: $i] :
( ~ ( class_Orderings_Oorder @ SV38 )
| ( c_HOL_Oord__class_Oless @ SV467 @ SY2754 @ SV38 )
| ~ ( c_HOL_Oord__class_Oless @ SV467 @ SY2755 @ SV38 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV38 ) @ SY2755 ) @ SY2754 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1879,plain,
! [SV468: $i,SV39: $i] :
( ( ! [SY2756: $i,SY2757: $i] :
( ~ ( class_Orderings_Opreorder @ SV39 )
| ( c_HOL_Oord__class_Oless @ SV468 @ SY2756 @ SV39 )
| ~ ( c_HOL_Oord__class_Oless @ SY2757 @ SY2756 @ SV39 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV39 ) @ SV468 ) @ SY2757 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1880,plain,
! [SV469: $i,SV40: $i] :
( ( ! [SY2758: $i,SY2759: $i] :
( ~ ( class_Orderings_Opreorder @ SV40 )
| ( c_HOL_Oord__class_Oless @ SV469 @ SY2758 @ SV40 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV40 ) @ SY2759 ) @ SY2758 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV469 @ SY2759 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(1881,plain,
! [SV470: $i,SV41: $i] :
( ( ! [SY2760: $i] :
( ~ ( class_Orderings_Oorder @ SV41 )
| ( c_HOL_Oord__class_Oless @ SV470 @ SY2760 @ SV41 )
| ( SY2760 = SV470 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV41 ) @ SV470 ) @ SY2760 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1882,plain,
! [SV471: $i,SV42: $i] :
( ( ! [SY2761: $i] :
( ~ ( class_Orderings_Oorder @ SV42 )
| ( c_HOL_Oord__class_Oless @ SV471 @ SY2761 @ SV42 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV42 ) @ SV471 ) @ SY2761 ) )
| ( SY2761 = SV471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1883,plain,
! [SV472: $i,SV43: $i] :
( ( ! [SY2762: $i] :
( ~ ( class_Orderings_Oorder @ SV43 )
| ( SV472 = SY2762 )
| ( c_HOL_Oord__class_Oless @ SV472 @ SY2762 @ SV43 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV43 ) @ SV472 ) @ SY2762 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1884,plain,
! [SV473: $i,SV44: $i] :
( ( ! [SY2763: $i] :
( ~ ( class_Orderings_Oorder @ SV44 )
| ( c_HOL_Oord__class_Oless @ SV473 @ SY2763 @ SV44 )
| ( SV473 = SY2763 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV44 ) @ SV473 ) @ SY2763 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1885,plain,
! [SV474: $i,SV45: $i] :
( ( ! [SY2764: $i] :
( ~ ( class_Orderings_Oorder @ SV45 )
| ( c_HOL_Oord__class_Oless @ SV474 @ SY2764 @ SV45 )
| ( SV474 = SY2764 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV45 ) @ SV474 ) @ SY2764 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1886,plain,
! [SV475: $i,SV46: $i] :
( ( ! [SY2765: $i] :
( ~ ( class_Orderings_Oorder @ SV46 )
| ( c_HOL_Oord__class_Oless @ SV475 @ SY2765 @ SV46 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV46 ) @ SV475 ) @ SY2765 ) )
| ( SV475 = SY2765 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(1887,plain,
! [SV476: $i,SV47: $i] :
( ( ! [SY2766: $i] :
( ~ ( class_Orderings_Olinorder @ SV47 )
| ( SV476 = SY2766 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV47 ) @ SV476 ) @ SY2766 ) )
| ( c_HOL_Oord__class_Oless @ SV476 @ SY2766 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1888,plain,
! [SV477: $i,SV48: $i] :
( ( ! [SY2767: $i] :
( ~ ( class_Orderings_Olinorder @ SV48 )
| ( SV477 = SY2767 )
| ( c_HOL_Oord__class_Oless @ SV477 @ SY2767 @ SV48 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV48 ) @ SV477 ) @ SY2767 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1889,plain,
! [SV478: $i,SV49: $i] :
( ( ! [SY2768: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV49 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV478 @ SV49 ) @ SY2768 @ SV49 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SY2768 @ SV49 ) @ SV478 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(1890,plain,
! [SV479: $i,SV50: $i] :
( ( ! [SY2769: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV50 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV479 @ SV50 ) @ SY2769 @ SV50 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SY2769 @ SV50 ) @ SV479 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1891,plain,
! [SV480: $i,SV51: $i] :
( ( ! [SY2770: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV51 )
| ( c_HOL_Oord__class_Oless @ SV480 @ ( c_HOL_Ouminus__class_Ouminus @ SY2770 @ SV51 ) @ SV51 )
| ~ ( c_HOL_Oord__class_Oless @ SY2770 @ ( c_HOL_Ouminus__class_Ouminus @ SV480 @ SV51 ) @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1892,plain,
! [SV481: $i,SV52: $i] :
( ( ! [SY2771: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV52 )
| ( c_HOL_Oord__class_Oless @ SV481 @ ( c_HOL_Ouminus__class_Ouminus @ SY2771 @ SV52 ) @ SV52 )
| ~ ( c_HOL_Oord__class_Oless @ SY2771 @ ( c_HOL_Ouminus__class_Ouminus @ SV481 @ SV52 ) @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(1893,plain,
! [SV482: $i,SV53: $i] :
( ( ! [SY2772: $i,SY2773: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV53 )
| ( c_HOL_Oord__class_Oless @ SV482 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2772 @ SY2773 @ SV53 ) @ SV53 )
| ~ ( c_HOL_Oord__class_Oless @ SV482 @ SY2773 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(1894,plain,
! [SV483: $i,SV54: $i] :
( ( ! [SY2774: $i,SY2775: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV54 )
| ( c_HOL_Oord__class_Oless @ SV483 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2774 @ SY2775 @ SV54 ) @ SV54 )
| ~ ( c_HOL_Oord__class_Oless @ SV483 @ SY2774 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1895,plain,
! [SV484: $i,SV55: $i] :
( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV55 )
| ( c_Finite__Set_Ofinite @ SV484 @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(1896,plain,
! [SV485: $i,SV56: $i] :
( ( ! [SY2776: $i,SY2777: $i,SY2778: $i] :
( ~ ( class_Orderings_Oorder @ SV56 )
| ( c_HOL_Oord__class_Oless @ SV485 @ SY2776 @ SV56 )
| ( c_HOL_Oord__class_Oless @ SY2777 @ SY2778 @ SV56 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV56 ) @ SY2778 ) @ SV485 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2778 @ SV485 @ SV56 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2777 @ SY2776 @ SV56 ) @ ( tc_fun @ SV56 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1897,plain,
! [SV486: $i,SV57: $i] :
( ( ! [SY2779: $i,SY2780: $i,SY2781: $i,SY2782: $i,SY2783: $i,SY2784: $i,SY2785: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV57 @ SV486 @ ( c_COMBC @ SY2779 @ SY2780 @ SY2780 @ tc_bool ) @ ( c_COMBC @ SY2781 @ SY2780 @ SY2780 @ tc_bool ) @ SY2782 @ SY2783 @ SY2784 @ SY2785 @ SY2780 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV486 @ SV57 @ SY2779 @ SY2781 @ SY2783 @ SY2782 @ SY2785 @ SY2784 @ SY2780 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(1898,plain,
! [SV487: $i,SV58: $i] :
( ( ! [SY2786: $i,SY2787: $i] :
( ( hAPP @ ( c_COMBK @ SV58 @ SV487 @ SY2786 ) @ SY2787 )
= SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(1899,plain,
! [SV488: $i,SV59: $i] :
( ( ! [SY2788: $i,SY2789: $i,SY2790: $i,SY2791: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV59 @ SV488 @ SY2788 @ SY2789 ) @ SY2790 ) @ SY2791 )
= ( hAPP @ ( hAPP @ SV59 @ SY2791 ) @ SY2790 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1900,plain,
! [SV489: $i,SV60: $i] :
( ( ! [SY2792: $i,SY2793: $i] :
( ~ ( class_Orderings_Oorder @ SV60 )
| ( c_HOL_Oord__class_Oless @ SV489 @ SY2792 @ SV60 )
| ~ ( c_HOL_Oord__class_Oless @ SV489 @ SY2793 @ SV60 )
| ~ ( c_HOL_Oord__class_Oless @ SY2793 @ SY2792 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(1901,plain,
! [SV490: $i,SV61: $i] :
( ( ! [SY2794: $i,SY2795: $i] :
( ( hBOOL @ ( c_in @ SV61 @ SV490 @ SY2794 ) )
| ~ ( hBOOL @ ( c_in @ SV61 @ SY2795 @ SY2794 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2795 @ SV490 @ ( tc_fun @ SY2794 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(1902,plain,
! [SV491: $i,SV62: $i] :
( ( ! [SY2796: $i,SY2797: $i] :
( ( c_HOL_Oord__class_Oless @ SV62 @ SV491 @ ( tc_fun @ SY2796 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2797 @ SV491 @ ( tc_fun @ SY2796 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV62 @ SY2797 @ ( tc_fun @ SY2796 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1471]) ).
thf(1903,plain,
! [SV492: $i,SV63: $i] :
( ( ! [SY2798: $i,SY2799: $i] :
( ~ ( class_Orderings_Opreorder @ SV63 )
| ( c_HOL_Oord__class_Oless @ SV492 @ SY2798 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SY2799 @ SY2798 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV492 @ SY2799 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1472]) ).
thf(1904,plain,
! [SV493: $i,SV64: $i] :
( ( ! [SY2800: $i,SY2801: $i,SY2802: $i,SY2803: $i] :
( ( c_Finite__Set_Ofinite @ SV64 @ SV493 )
| ~ ( c_Finite__Set_Ofold__graph @ SY2800 @ SY2801 @ SV64 @ SY2802 @ SV493 @ SY2803 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(1905,plain,
! [SV494: $i,SV65: $i] :
( ( ! [SY2804: $i] :
( ~ ( class_Orderings_Oorder @ SV65 )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV494 @ SY2804 @ SV65 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV65 @ tc_bool ) ) )
| ( c_HOL_Oord__class_Oless @ SV494 @ SY2804 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(1906,plain,
! [SV495: $i,SV66: $i] :
( ( ! [SY2805: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV66 @ SV495 @ ( tc_fun @ SY2805 @ tc_bool ) ) @ SY2805 )
| ~ ( c_Finite__Set_Ofinite @ SV66 @ SY2805 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1907,plain,
! [SV496: $i,SV67: $i] :
( ( ! [SY2806: $i] :
( ( c_Finite__Set_Ofinite @ SV67 @ SV496 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV67 @ SY2806 @ ( tc_fun @ SV496 @ tc_bool ) ) @ SV496 )
| ~ ( c_Finite__Set_Ofinite @ SY2806 @ SV496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(1908,plain,
! [SV497: $i,SV68: $i] :
( ( ! [SY2807: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV68 @ SV497 @ ( tc_fun @ SY2807 @ tc_bool ) ) @ SY2807 )
| ~ ( c_Finite__Set_Ofinite @ SV68 @ SY2807 )
| ~ ( c_Finite__Set_Ofinite @ SV497 @ SY2807 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1909,plain,
! [SV498: $i,SV69: $i] :
( ( ( c_The @ ( hAPP @ ( c_COMBC @ ( c_fequal @ SV69 ) @ SV69 @ SV69 @ tc_bool ) @ SV498 ) @ SV69 )
= SV498 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(1910,plain,
! [SV499: $i,SV70: $i] :
( ( ! [SY2808: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV70 @ SV499 @ ( tc_fun @ SY2808 @ tc_bool ) ) @ SY2808 )
| ~ ( c_Finite__Set_Ofinite @ SV499 @ SY2808 )
| ~ ( c_Finite__Set_Ofinite @ SV70 @ SY2808 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1911,plain,
! [SV500: $i,SV71: $i] :
( ( ! [SY2809: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV71 @ SV500 @ ( tc_fun @ SY2809 @ tc_bool ) ) @ SY2809 )
| ~ ( c_Finite__Set_Ofinite @ SV500 @ SY2809 )
| ~ ( c_Finite__Set_Ofinite @ SV71 @ SY2809 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(1912,plain,
! [SV501: $i,SV72: $i] :
( ( ! [SY2810: $i] :
( ( c_Finite__Set_Ofinite @ SV72 @ SV501 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV72 @ SY2810 @ ( tc_fun @ SV501 @ tc_bool ) ) @ SV501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1481]) ).
thf(1913,plain,
! [SV502: $i,SV73: $i] :
( ( ! [SY2811: $i] :
( ( c_Finite__Set_Ofinite @ SV73 @ SV502 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2811 @ SV73 @ ( tc_fun @ SV502 @ tc_bool ) ) @ SV502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(1914,plain,
! [SV503: $i,SV74: $i] :
( ( ! [SY2812: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV74 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV503 @ SV74 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY2812 @ SV74 ) @ SV74 )
| ~ ( c_HOL_Oord__class_Oless @ SY2812 @ SV503 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1483]) ).
thf(1915,plain,
! [SV504: $i,SV75: $i] :
( ( ! [SY2813: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV75 )
| ( c_HOL_Oord__class_Oless @ SV504 @ SY2813 @ SV75 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SY2813 @ SV75 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV504 @ SV75 ) @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1916,plain,
! [SV505: $i,SV76: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV76 @ SV76 @ ( tc_fun @ SV505 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1485]) ).
thf(1917,plain,
! [SV506: $i,SV77: $i] :
( ( ~ ( class_Orderings_Oorder @ SV77 )
| ~ ( c_HOL_Oord__class_Oless @ SV506 @ SV506 @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(1918,plain,
! [SV507: $i,SV78: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ SV507 @ SV507 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(1919,plain,
! [SV508: $i,SV79: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV79 )
| ~ ( c_HOL_Oord__class_Oless @ SV508 @ SV508 @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(1920,plain,
! [SV509: $i,SV80: $i] :
( ( ! [SY2814: $i,SY2815: $i,SY2816: $i] :
( ~ ( class_Orderings_Oorder @ SV80 )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV509 @ SY2814 @ SV80 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2815 @ SY2816 @ SV80 ) @ ( tc_fun @ SV80 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SY2815 ) @ SY2816 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2814 @ SY2816 @ SV80 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SY2814 ) @ SY2816 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SY2815 ) @ SV509 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(1921,plain,
! [SV510: $i,SV81: $i] :
( ( ! [SY2817: $i,SY2818: $i,SY2819: $i] :
( ~ ( class_Orderings_Oorder @ SV81 )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV510 @ SY2817 @ SV81 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2818 @ SY2819 @ SV81 ) @ ( tc_fun @ SV81 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SY2818 ) @ SY2819 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2818 @ SV510 @ SV81 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SY2817 ) @ SY2819 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SY2818 ) @ SV510 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1922,plain,
! [SV511: $i,SV82: $i] :
( ( ! [SY2820: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV82 )
| ( c_HOL_Oord__class_Oless @ SV511 @ SY2820 @ SV82 )
| ( c_HOL_Oord__class_Oless @ SY2820 @ SV511 @ SV82 )
| ( SY2820 = SV511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(1923,plain,
! [SV512: $i,SV83: $i] :
( ( ! [SY2821: $i] :
( ~ ( class_Orderings_Olinorder @ SV83 )
| ( SV512 = SY2821 )
| ( c_HOL_Oord__class_Oless @ SY2821 @ SV512 @ SV83 )
| ( c_HOL_Oord__class_Oless @ SV512 @ SY2821 @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(1924,plain,
! [SV513: $i,SV84: $i] :
( ( ! [SY2822: $i] :
( ~ ( class_Orderings_Olinorder @ SV84 )
| ( c_HOL_Oord__class_Oless @ SV513 @ SY2822 @ SV84 )
| ( c_HOL_Oord__class_Oless @ SY2822 @ SV513 @ SV84 )
| ( SY2822 = SV513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1925,plain,
! [SV514: $i,SV85: $i] :
( ( ! [SY2823: $i] :
( ~ ( class_Orderings_Olinorder @ SV85 )
| ( c_HOL_Oord__class_Oless @ SV514 @ SY2823 @ SV85 )
| ( SY2823 = SV514 )
| ( c_HOL_Oord__class_Oless @ SY2823 @ SV514 @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1926,plain,
! [SV515: $i,SV86: $i] :
( ( ! [SY2824: $i] :
( ~ ( class_Orderings_Olinorder @ SV86 )
| ( SV515 = SY2824 )
| ( c_HOL_Oord__class_Oless @ SV515 @ SY2824 @ SV86 )
| ( c_HOL_Oord__class_Oless @ SY2824 @ SV515 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(1927,plain,
! [SV516: $i,SV87: $i] :
( ( ! [SY2825: $i] :
( ~ ( class_Orderings_Oorder @ SV87 )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV87 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV516 @ SY2825 @ SV87 ) )
| ( c_HOL_Oord__class_Oless @ SV516 @ SY2825 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(1928,plain,
! [SV517: $i,SV88: $i] :
( ( ! [SY2826: $i] :
( ~ ( class_Orderings_Oorder @ SV88 )
| ~ ( c_HOL_Oord__class_Oless @ SV517 @ SY2826 @ SV88 )
| ~ ( c_HOL_Oord__class_Oless @ SY2826 @ SV517 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(1929,plain,
! [SV518: $i,SV89: $i] :
( ( ! [SY2827: $i] :
( ~ ( class_Orderings_Olinorder @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV518 @ SY2827 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SY2827 @ SV518 @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(1930,plain,
! [SV519: $i,SV90: $i] :
( ( ! [SY2828: $i] :
( ~ ( class_Orderings_Opreorder @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ SV519 @ SY2828 @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ SY2828 @ SV519 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(1931,plain,
! [SV520: $i,SV91: $i] :
( ( ! [SY2829: $i] :
( ~ ( class_Orderings_Opreorder @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV520 @ SY2829 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SY2829 @ SV520 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(1932,plain,
! [SV521: $i,SV92: $i] :
( ( ! [SY2830: $i,SY2831: $i,SY2832: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV92 )
| ( ( c_Finite__Set_Osetsum @ SV521 @ ( c_HOL_Ominus__class_Ominus @ SY2830 @ SY2831 @ ( tc_fun @ SY2832 @ tc_bool ) ) @ SY2832 @ SV92 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV521 @ SY2830 @ SY2832 @ SV92 ) @ ( c_Finite__Set_Osetsum @ SV521 @ SY2831 @ SY2832 @ SV92 ) @ SV92 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2832 @ tc_bool ) ) @ SY2831 ) @ SY2830 ) )
| ~ ( c_Finite__Set_Ofinite @ SY2830 @ SY2832 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1501]) ).
thf(1933,plain,
! [SV522: $i,SV93: $i] :
( ( ! [SY2833: $i] :
( ~ ( class_Orderings_Oorder @ SV93 )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV522 @ SY2833 @ SV93 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV93 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV93 ) @ SY2833 ) @ SV522 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(1934,plain,
! [SV523: $i,SV94: $i] :
( ( ! [SY2834: $i,SY2835: $i,SY2836: $i,SY2837: $i,SY2838: $i] :
( ( c_Finite__Set_Ofold__graph @ SV94 @ SV523 @ ( c_Set_Oinsert @ SY2834 @ SY2835 @ SY2836 ) @ ( hAPP @ ( hAPP @ SV94 @ SY2834 ) @ SY2837 ) @ SY2836 @ SY2838 )
| ~ ( c_Finite__Set_Ofold__graph @ SV94 @ SV523 @ SY2835 @ SY2837 @ SY2836 @ SY2838 )
| ( hBOOL @ ( c_in @ SY2834 @ SY2835 @ SY2836 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(1935,plain,
! [SV524: $i,SV95: $i] :
( ( ! [SY2839: $i,SY2840: $i] :
( ( c_HOL_Oord__class_Oless @ SV95 @ SV524 @ ( tc_fun @ SY2839 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SY2840 @ SV524 @ SY2839 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV95 @ ( c_Set_Oinsert @ SY2840 @ SV524 @ SY2839 ) @ ( tc_fun @ SY2839 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(1936,plain,
! [SV525: $i,SV96: $i] :
( ( ! [SY2841: $i,SY2842: $i] :
( ( c_HOL_Oord__class_Oless @ SV96 @ ( c_Set_Oinsert @ SV525 @ SY2841 @ SY2842 ) @ ( tc_fun @ SY2842 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV525 @ SY2841 @ SY2842 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV96 @ SY2841 @ ( tc_fun @ SY2842 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(1937,plain,
! [SV526: $i,SV97: $i] :
( ( ! [SY2843: $i,SY2844: $i,SY2845: $i] :
( ~ ( class_Orderings_Oorder @ SV97 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV97 ) @ SV526 ) @ SY2843 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV97 ) @ SY2844 ) @ SV526 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2844 @ SV526 @ SV97 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2845 @ SY2843 @ SV97 ) @ ( tc_fun @ SV97 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1938,plain,
! [SV527: $i,SV98: $i] :
( ( ! [SY2846: $i,SY2847: $i,SY2848: $i] :
( ~ ( class_Orderings_Oorder @ SV98 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV98 ) @ SV527 ) @ SY2846 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV98 ) @ SY2846 ) @ SY2847 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2846 @ SY2847 @ SV98 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV527 @ SY2848 @ SV98 ) @ ( tc_fun @ SV98 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(1939,plain,
! [SV528: $i,SV99: $i] :
( ( ! [SY2849: $i,SY2850: $i,SY2851: $i] :
( ~ ( class_Orderings_Oorder @ SV99 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV99 ) @ SV528 ) @ SY2849 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2850 @ SY2851 @ SV99 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV528 @ SY2849 @ SV99 ) @ ( tc_fun @ SV99 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1940,plain,
! [SV529: $i,SV100: $i] :
( ( ! [SY2852: $i,SY2853: $i,SY2854: $i] :
( ~ ( class_Orderings_Oorder @ SV100 )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV529 @ SY2852 @ SV100 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2853 @ SY2854 @ SV100 ) @ ( tc_fun @ SV100 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV100 ) @ SY2853 ) @ SY2854 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV100 ) @ SV529 ) @ SY2852 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(1941,plain,
! [SV530: $i,SV101: $i] :
( ( ! [SY2855: $i,SY2856: $i] :
( ~ ( class_Orderings_Olinorder @ SV101 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV530 @ SY2855 @ SV101 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SY2855 @ SY2856 @ SV101 ) @ ( tc_fun @ SV101 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV530 @ SY2856 @ SV101 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV101 ) @ SY2855 ) @ SY2856 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV101 ) @ SV530 ) @ SY2855 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1942,plain,
! [SV531: $i,SV102: $i] :
( ( ! [SY2857: $i,SY2858: $i,SY2859: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ SV102 @ SV531 ) @ SY2857 )
| ~ ( hBOOL @ ( c_in @ SV531 @ SY2858 @ SY2859 ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2858 @ SV102 @ SY2859 @ ( tc_fun @ SY2857 @ tc_bool ) ) @ SY2857 )
| ~ ( c_Finite__Set_Ofinite @ SY2858 @ SY2859 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(1943,plain,
! [SV532: $i,SV103: $i] :
( ( ! [SY2860: $i,SY2861: $i,SY2862: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV103 )
| ( ( c_Finite__Set_Osetsum @ SV532 @ ( c_HOL_Ominus__class_Ominus @ SY2860 @ ( c_Set_Oinsert @ SY2861 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2862 @ tc_bool ) ) @ SY2862 ) @ ( tc_fun @ SY2862 @ tc_bool ) ) @ SY2862 @ SV103 )
= ( c_Finite__Set_Osetsum @ SV532 @ SY2860 @ SY2862 @ SV103 ) )
| ( hBOOL @ ( c_in @ SY2861 @ SY2860 @ SY2862 ) )
| ~ ( c_Finite__Set_Ofinite @ SY2860 @ SY2862 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(1944,plain,
! [SV533: $i,SV104: $i] :
( ( ! [SY2863: $i] :
( ~ ( class_Orderings_Oorder @ SV104 )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV533 @ SY2863 @ SV104 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV104 @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2863 @ SV533 @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1945,plain,
! [SV534: $i,SV105: $i] :
( ( ! [SY2864: $i,SY2865: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV105 )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV534 @ ( c_COMBK @ SY2864 @ SV105 @ SY2865 ) @ SY2865 @ SV105 )
= SY2864 )
| ( SV534
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2865 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(1946,plain,
! [SV535: $i,SV106: $i] :
( ( ! [SY2866: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV106 @ tc_bool ) ) @ ( c_COMBK @ SV535 @ ( tc_fun @ SY2866 @ tc_bool ) @ SV106 ) @ SV106 @ ( tc_fun @ SY2866 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2866 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(1947,plain,
! [SV536: $i,SV107: $i] :
( ( ! [SY2867: $i,SY2868: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV107 @ ( c_COMBK @ SV536 @ ( tc_fun @ SY2867 @ tc_bool ) @ SY2868 ) @ SY2868 @ ( tc_fun @ SY2867 @ tc_bool ) )
= SV536 )
| ( SV107
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2868 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(1948,plain,
! [SV537: $i,SV108: $i] :
( ( ! [SY2869: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV108 @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV537 @ tc_bool ) ) @ ( tc_fun @ SV537 @ tc_bool ) @ SY2869 ) @ SY2869 @ ( tc_fun @ SV537 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV537 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(1949,plain,
! [SV538: $i,SV109: $i] :
( ( ! [SY2870: $i,SY2871: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV109 @ SV538 @ ( tc_fun @ SY2870 @ tc_bool ) ) @ SY2870 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV109 @ ( c_Set_Oinsert @ SY2871 @ SV538 @ SY2870 ) @ ( tc_fun @ SY2870 @ tc_bool ) ) @ SY2870 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1950,plain,
! [SV539: $i,SV110: $i] :
( ( ! [SY2872: $i,SY2873: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV110 @ ( c_Set_Oinsert @ SV539 @ SY2872 @ SY2873 ) @ ( tc_fun @ SY2873 @ tc_bool ) ) @ SY2873 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV110 @ SY2872 @ ( tc_fun @ SY2873 @ tc_bool ) ) @ SY2873 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(1951,plain,
! [SV540: $i,SV111: $i] :
( ( ! [SY2874: $i] :
( ~ ( class_Orderings_Oorder @ SV111 )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV111 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV540 @ SY2874 @ SV111 ) )
| ( c_HOL_Oord__class_Oless @ SV540 @ SY2874 @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1952,plain,
! [SV541: $i,SV112: $i] :
( ( ! [SY2875: $i] :
( ~ ( class_Orderings_Oorder @ SV112 )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ SV541 @ SY2875 @ SV112 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV112 @ tc_bool ) ) )
| ( c_HOL_Oord__class_Oless @ SV541 @ SY2875 @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(1953,plain,
! [SV113: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV113 ) )
= $true )
| ( ( c_Complete__Lattice_Ocomplete__lattice__axioms @ ( c_Complete__Lattice_OInf__class_OInf @ SV113 ) @ ( c_Complete__Lattice_OSup__class_OSup @ SV113 ) @ ( c_lessequals @ SV113 ) @ SV113 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1522]) ).
thf(1954,plain,
( ( ( class_HOL_Ouminus @ t_b )
= $false )
| ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ v_A @ ( tc_fun @ t_a @ t_b ) ) @ v_x )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ v_A @ v_x ) @ t_b ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1955,plain,
! [SV542: $i,SV114: $i] :
( ( ! [SY2876: $i] :
( ~ ( class_Orderings_Olinorder @ SV114 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV114 ) @ SV542 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SY2876 @ SV114 ) ) )
| ~ ( hBOOL @ ( c_in @ SV542 @ SY2876 @ SV114 ) )
| ~ ( c_Finite__Set_Ofinite @ SY2876 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(1956,plain,
! [SV543: $i,SV115: $i] :
( ( ! [SY2877: $i] :
( ~ ( class_Orderings_Olinorder @ SV115 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV115 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV543 @ SV115 ) ) @ SY2877 ) )
| ~ ( hBOOL @ ( c_in @ SY2877 @ SV543 @ SV115 ) )
| ~ ( c_Finite__Set_Ofinite @ SV543 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(1957,plain,
! [SV544: $i,SV116: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV116 )
| ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMin @ SV544 @ SV116 ) @ SV544 @ SV116 ) )
| ( SV544
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV116 @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV544 @ SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1958,plain,
! [SV545: $i,SV117: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV117 )
| ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMax @ SV545 @ SV117 ) @ SV545 @ SV117 ) )
| ( SV545
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV117 @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV545 @ SV117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1959,plain,
! [SV546: $i,SV118: $i] :
( ( ! [SY2878: $i,SY2879: $i,SY2880: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV118 @ ( c_Set_Oinsert @ SV546 @ SY2878 @ SY2879 ) @ SY2879 ) @ SY2880 ) )
| ( hBOOL @ ( c_in @ SV546 @ SY2878 @ SY2879 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV118 @ SV546 @ SY2878 @ SY2880 @ SY2879 @ SY2879 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1960,plain,
! [SV547: $i,SV119: $i] :
( ( ! [SY2881: $i,SY2882: $i,SY2883: $i,SY2884: $i,SY2885: $i] :
( ( c_Finite__Set_Ofold__graph @ SV119 @ SV547 @ SY2881 @ ( hAPP @ ( hAPP @ SV119 @ SY2882 ) @ SY2883 ) @ SY2884 @ SY2885 )
| ~ ( hBOOL @ ( c_in @ SY2882 @ SY2881 @ SY2884 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV119 @ SV547 @ ( c_HOL_Ominus__class_Ominus @ SY2881 @ ( c_Set_Oinsert @ SY2882 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2884 @ tc_bool ) ) @ SY2884 ) @ ( tc_fun @ SY2884 @ tc_bool ) ) @ SY2883 @ SY2884 @ SY2885 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1961,plain,
! [SV548: $i,SV120: $i] :
( ( ! [SY2886: $i,SY2887: $i] :
( ( ( c_Finite__Set_Osetsum @ SV120 @ ( c_HOL_Ominus__class_Ominus @ SV548 @ ( c_Set_Oinsert @ SY2886 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2887 @ tc_bool ) ) @ SY2887 ) @ ( tc_fun @ SY2887 @ tc_bool ) ) @ SY2887 @ tc_nat )
= ( c_Finite__Set_Osetsum @ SV120 @ SV548 @ SY2887 @ tc_nat ) )
| ( hBOOL @ ( c_in @ SY2886 @ SV548 @ SY2887 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(1962,plain,
! [SV549: $i,SV121: $i] :
( ( ! [SY2888: $i,SY2889: $i] :
( ( c_HOL_Oord__class_Oless @ SV121 @ ( c_Set_Oinsert @ SV549 @ SY2888 @ SY2889 ) @ ( tc_fun @ SY2889 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV549 @ SV121 @ SY2889 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV121 @ ( c_Set_Oinsert @ SV549 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2889 @ tc_bool ) ) @ SY2889 ) @ ( tc_fun @ SY2889 @ tc_bool ) ) @ SY2888 @ ( tc_fun @ SY2889 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV121 @ SY2888 @ ( tc_fun @ SY2889 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1963,plain,
! [SV550: $i,SV122: $i] :
( ( ! [SY2890: $i,SY2891: $i] :
( ( c_HOL_Oord__class_Oless @ SV122 @ ( c_Set_Oinsert @ SV550 @ SY2890 @ SY2891 ) @ ( tc_fun @ SY2891 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV550 @ SV122 @ SY2891 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV122 @ ( c_Set_Oinsert @ SV550 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2891 @ tc_bool ) ) @ SY2891 ) @ ( tc_fun @ SY2891 @ tc_bool ) ) @ SY2890 @ ( tc_fun @ SY2891 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SV550 @ SY2890 @ SY2891 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1964,plain,
! [SV551: $i,SV123: $i] :
( ( ! [SY2892: $i,SY2893: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV123 @ ( c_Set_Oinsert @ SV551 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2892 @ tc_bool ) ) @ SY2892 ) @ ( tc_fun @ SY2892 @ tc_bool ) ) @ SY2893 @ ( tc_fun @ SY2892 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV551 @ SV123 @ SY2892 ) )
| ( hBOOL @ ( c_in @ SV551 @ SY2893 @ SY2892 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV123 @ ( c_Set_Oinsert @ SV551 @ SY2893 @ SY2892 ) @ ( tc_fun @ SY2892 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(1965,plain,
! [SV552: $i,SV124: $i] :
( ( ! [SY2894: $i,SY2895: $i,SY2896: $i,SY2897: $i,SY2898: $i] :
( ( c_Nitpick_Ofold__graph_H @ SV124 @ SV552 @ SY2894 @ ( hAPP @ ( hAPP @ SV124 @ SY2895 ) @ SY2896 ) @ SY2897 @ SY2898 )
| ~ ( c_Nitpick_Ofold__graph_H @ SV124 @ SV552 @ ( c_HOL_Ominus__class_Ominus @ SY2894 @ ( c_Set_Oinsert @ SY2895 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2897 @ tc_bool ) ) @ SY2897 ) @ ( tc_fun @ SY2897 @ tc_bool ) ) @ SY2896 @ SY2897 @ SY2898 )
| ~ ( hBOOL @ ( c_in @ SY2895 @ SY2894 @ SY2897 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(1966,plain,
! [SV553: $i,SV125: $i] :
( ( ! [SY2899: $i,SY2900: $i] :
( ( c_HOL_Oord__class_Oless @ SV125 @ ( c_Set_Oinsert @ SV553 @ SY2899 @ SY2900 ) @ ( tc_fun @ SY2900 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2900 @ tc_bool ) ) @ SV125 ) @ SY2899 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV125 @ ( c_Set_Oinsert @ SV553 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2900 @ tc_bool ) ) @ SY2900 ) @ ( tc_fun @ SY2900 @ tc_bool ) ) @ SY2899 @ ( tc_fun @ SY2900 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV125 @ SY2899 @ ( tc_fun @ SY2900 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(1967,plain,
! [SV554: $i,SV126: $i] :
( ( ! [SY2901: $i] :
( ~ ( class_Orderings_Olinorder @ SV126 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV126 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV554 @ SV126 ) ) @ ( c_Finite__Set_Olinorder__class_OMin @ SY2901 @ SV126 ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV554 @ SV126 )
| ( SY2901
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV126 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV126 @ tc_bool ) ) @ SY2901 ) @ SV554 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(1968,plain,
! [SV555: $i,SV127: $i] :
( ( ! [SY2902: $i] :
( ~ ( class_Orderings_Olinorder @ SV127 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV127 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV555 @ SV127 ) ) @ ( c_Finite__Set_Olinorder__class_OMax @ SY2902 @ SV127 ) ) )
| ~ ( c_Finite__Set_Ofinite @ SY2902 @ SV127 )
| ( SV555
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV127 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV127 @ tc_bool ) ) @ SV555 ) @ SY2902 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1969,plain,
! [SV556: $i,SV128: $i] :
( ( ! [SY2903: $i,SY2904: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV128 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV556 @ SY2903 @ SY2904 @ 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 @ SV128 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_COMBK @ ( hAPP @ ( c_COMBC @ ( c_fequal @ tc_Com_Ostate ) @ tc_Com_Ostate @ tc_Com_Ostate @ tc_bool ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ SV128 @ SV556 @ SY2904 @ SY2903 ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) @ SY2903 @ ( c_COMBK @ ( hAPP @ SY2904 @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ SV128 @ SV556 @ SY2904 @ SY2903 ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) @ 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_forall_pos,[status(thm)],[1538]) ).
thf(1970,plain,
! [SV557: $i,SV129: $i] :
( ( ! [SY2905: $i] :
( ~ ( class_Orderings_Olinorder @ SV129 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV557 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV129 @ tc_bool ) ) @ SV129 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV557 @ SY2905 @ SV129 ) @ ( tc_fun @ SV129 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV557 @ SY2905 @ SV129 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV129 ) @ SV557 ) @ SY2905 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(1971,plain,
! [SV558: $i,SV130: $i] :
( ( ! [SY2906: $i,SY2907: $i] :
( ( c_HOL_Oord__class_Oless @ SV130 @ ( c_Set_Oinsert @ SV558 @ SY2906 @ SY2907 ) @ ( tc_fun @ SY2907 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2907 @ tc_bool ) ) @ SV130 ) @ SY2906 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV130 @ ( c_Set_Oinsert @ SV558 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2907 @ tc_bool ) ) @ SY2907 ) @ ( tc_fun @ SY2907 @ tc_bool ) ) @ SY2906 @ ( tc_fun @ SY2907 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SV558 @ SY2906 @ SY2907 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(1972,plain,
! [SV559: $i,SV131: $i] :
( ( ! [SY2908: $i,SY2909: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV131 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV559 @ SY2908 @ SV131 ) ) @ SY2909 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ SY2908 ) @ SY2909 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ SV559 ) @ SY2909 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(1973,plain,
! [SV560: $i,SV132: $i] :
( ( ! [SY2910: $i,SY2911: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV132 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV560 @ SY2910 @ SV132 ) ) @ SY2911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ SY2910 ) @ SY2911 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ SV560 ) @ SY2911 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(1974,plain,
! [SV561: $i,SV133: $i] :
( ( ! [SY2912: $i] :
( ~ ( class_Lattices_Olattice @ SV133 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV133 ) @ SV561 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2912 @ SV561 @ SV133 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(1975,plain,
! [SV562: $i,SV134: $i] :
( ( ! [SY2913: $i] :
( ~ ( class_Lattices_Olattice @ SV134 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV134 ) @ SV562 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV562 @ SY2913 @ SV134 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(1976,plain,
! [SV563: $i,SV135: $i] :
( ( ! [SY2914: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV135 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV135 ) @ SV563 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY2914 @ SV135 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV135 ) @ SY2914 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV563 @ SV135 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1977,plain,
! [SV564: $i,SV136: $i] :
( ( ! [SY2915: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV136 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV136 ) @ SV564 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY2915 @ SV136 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV136 ) @ SY2915 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV564 @ SV136 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(1978,plain,
! [SV565: $i,SV137: $i] :
( ( ! [SY2916: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV137 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV137 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV565 @ SV137 ) ) @ SY2916 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV137 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY2916 @ SV137 ) ) @ SV565 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(1979,plain,
! [SV566: $i,SV138: $i] :
( ( ! [SY2917: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV138 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV138 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV566 @ SV138 ) ) @ SY2917 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV138 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY2917 @ SV138 ) ) @ SV566 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(1980,plain,
! [SV567: $i,SV139: $i] :
( ( ! [SY2918: $i] :
( ~ ( class_Orderings_Olinorder @ SV139 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV567 @ SY2918 @ SV139 ) @ ( c_Set_Oinsert @ SY2918 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV139 @ tc_bool ) ) @ SV139 ) @ ( tc_fun @ SV139 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV567 @ SY2918 @ SV139 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV139 ) @ SV567 ) @ SY2918 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(1981,plain,
! [SV568: $i,SV140: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV140 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ SV140 ) @ SV568 @ SV140 )
= SV568 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(1982,plain,
! [SV569: $i,SV141: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV141 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV569 @ ( c_Orderings_Obot__class_Obot @ SV141 ) @ SV141 )
= SV569 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1983,plain,
! [SV570: $i,SV143: $i] :
( ( ! [SY2919: $i,SY2920: $i,SY2921: $i,SY2922: $i,SY2923: $i,SY2924: $i,SY2925: $i] :
( ( ( hAPP @ SV143 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV570 @ tc_bool ) ) )
= SY2919 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV143 @ SY2920 @ SY2921 @ SY2922 @ SY2923 @ SY2924 @ SY2925 @ SY2919 @ SV570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(1984,plain,
! [SV571: $i,SV144: $i] :
( ( ! [SY2926: $i,SY2927: $i,SY2928: $i,SY2929: $i,SY2930: $i,SY2931: $i,SY2932: $i] :
( ( ( hAPP @ SV144 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV571 @ tc_bool ) ) )
= SY2926 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY2927 @ SV144 @ SY2928 @ SY2929 @ SY2930 @ SY2931 @ SY2926 @ SY2932 @ SV571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1554]) ).
thf(1985,plain,
! [SV572: $i,SV145: $i] :
( ( ~ ( hBOOL @ ( c_in @ SV145 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV572 @ tc_bool ) ) @ SV572 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(1986,plain,
! [SV573: $i,SV146: $i] :
( ( ! [SY2933: $i] :
( ( hBOOL @ ( hAPP @ SV146 @ SV573 ) )
| ~ ( hBOOL @ ( c_in @ SV573 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2933 @ tc_bool ) ) @ SY2933 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(1987,plain,
! [SV574: $i,SV147: $i] :
( ( ~ ( hBOOL @ ( c_in @ SV147 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV574 @ tc_bool ) ) @ SV574 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(1988,plain,
! [SV575: $i,SV148: $i] :
( ( ~ ( hBOOL @ ( c_in @ SV148 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV575 @ tc_bool ) ) @ SV575 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(1989,plain,
! [SV576: $i,SV149: $i] :
( ( ! [SY2934: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV149 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV576 @ tc_bool ) ) @ SV576 ) @ SY2934 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(1990,plain,
! [SV577: $i,SV150: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV150 @ tc_bool ) ) @ SV577 @ ( tc_fun @ SV150 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV150 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(1991,plain,
! [SV578: $i,SV151: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV151 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV578 @ tc_bool ) ) @ ( tc_fun @ SV578 @ tc_bool ) )
= SV151 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1561]) ).
thf(1992,plain,
! [SV579: $i,SV152: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV152 @ tc_bool ) ) @ SV579 @ ( tc_fun @ SV152 @ tc_bool ) )
= SV579 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1562]) ).
thf(1993,plain,
! [SV580: $i,SV153: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV153 @ SV153 @ ( tc_fun @ SV580 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV580 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(1994,plain,
! [SV581: $i,SV154: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV154 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV581 @ tc_bool ) ) @ ( tc_fun @ SV581 @ tc_bool ) )
= SV154 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(1995,plain,
! [SV582: $i,SV155: $i] :
( ( ! [SY2935: $i] :
( ~ ( hBOOL @ ( hAPP @ SV155 @ SV582 ) )
| ~ ( hBOOL @ ( c_in @ SV582 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2935 @ tc_bool ) ) @ SY2935 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(1996,plain,
! [SV583: $i,SV156: $i] :
( ( ! [SY2936: $i] :
( ( ( c_Set_Oinsert @ SV156 @ ( c_HOL_Ominus__class_Ominus @ SV583 @ ( c_Set_Oinsert @ SV156 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2936 @ tc_bool ) ) @ SY2936 ) @ ( tc_fun @ SY2936 @ tc_bool ) ) @ SY2936 )
= SV583 )
| ~ ( hBOOL @ ( c_in @ SV156 @ SV583 @ SY2936 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(1997,plain,
! [SV584: $i,SV157: $i] :
( ( ! [SY2937: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV157 )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV157 ) @ ( c_Set_Oinsert @ SV584 @ ( c_Set_Oinsert @ SY2937 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV157 @ tc_bool ) ) @ SV157 ) @ SV157 ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV584 @ SY2937 @ SV157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(1998,plain,
! [SV585: $i,SV158: $i] :
( ( ! [SY2938: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV158 @ SV585 @ SY2938 ) @ ( c_Set_Oinsert @ SV158 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2938 @ tc_bool ) ) @ SY2938 ) @ ( tc_fun @ SY2938 @ tc_bool ) )
= SV585 )
| ( hBOOL @ ( c_in @ SV158 @ SV585 @ SY2938 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(1999,plain,
! [SV586: $i,SV159: $i] :
( ( ! [SY2939: $i,SY2940: $i] :
( ( hBOOL @ ( c_in @ SV159 @ ( c_Set_Oinsert @ SV586 @ SY2939 @ SY2940 ) @ SY2940 ) )
| ~ ( hBOOL @ ( c_in @ SV159 @ SY2939 @ SY2940 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1569]) ).
thf(2000,plain,
! [SV587: $i,SV160: $i] :
( ( ! [SY2941: $i,SY2942: $i] :
( ( hBOOL @ ( c_in @ SV160 @ ( c_Set_Oinsert @ SV587 @ SY2941 @ SY2942 ) @ SY2942 ) )
| ~ ( hBOOL @ ( c_in @ SV160 @ SY2941 @ SY2942 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(2001,plain,
! [SV588: $i,SV161: $i] :
( ( ! [SY2943: $i,SY2944: $i,SY2945: $i,SY2946: $i,SY2947: $i,SY2948: $i,SY2949: $i,SY2950: $i,SY2951: $i] :
( ( ( hAPP @ SV161 @ ( c_Set_Oinsert @ SV588 @ SY2943 @ SY2944 ) )
= ( hAPP @ ( hAPP @ SY2945 @ SV588 ) @ ( hAPP @ SV161 @ SY2943 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV161 @ SY2946 @ SY2947 @ SY2948 @ SY2945 @ SY2949 @ SY2950 @ SY2951 @ SY2944 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(2002,plain,
! [SV589: $i,SV162: $i] :
( ( ! [SY2952: $i,SY2953: $i,SY2954: $i,SY2955: $i,SY2956: $i,SY2957: $i,SY2958: $i,SY2959: $i,SY2960: $i] :
( ( ( hAPP @ SV162 @ ( c_Set_Oinsert @ SV589 @ SY2952 @ SY2953 ) )
= ( hAPP @ ( hAPP @ SY2954 @ SV589 ) @ ( hAPP @ SV162 @ SY2952 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY2955 @ SV162 @ SY2956 @ SY2957 @ SY2958 @ SY2954 @ SY2959 @ SY2960 @ SY2953 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(2003,plain,
! [SV590: $i,SV163: $i] :
( ( ! [SY2961: $i,SY2962: $i] :
( ( hBOOL @ ( c_in @ SV163 @ SV590 @ SY2961 ) )
| ( SV163 = SY2962 )
| ~ ( hBOOL @ ( c_in @ SV163 @ ( c_Set_Oinsert @ SY2962 @ SV590 @ SY2961 ) @ SY2961 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(2004,plain,
! [SV591: $i,SV164: $i] :
( ( ! [SY2963: $i,SY2964: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV164 @ ( c_Set_Oinsert @ SV591 @ SY2963 @ SY2964 ) @ ( tc_fun @ SY2964 @ tc_bool ) )
= ( c_Set_Oinsert @ SV591 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV164 @ SY2963 @ ( tc_fun @ SY2964 @ tc_bool ) ) @ SY2964 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(2005,plain,
! [SV592: $i,SV165: $i] :
( ( ! [SY2965: $i,SY2966: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV165 @ SV592 @ SY2965 ) @ SY2966 @ ( tc_fun @ SY2965 @ tc_bool ) )
= ( c_Set_Oinsert @ SV165 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV592 @ SY2966 @ ( tc_fun @ SY2965 @ tc_bool ) ) @ SY2965 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(2006,plain,
! [SV593: $i,SV166: $i] :
( ( ! [SY2967: $i] : ( hBOOL @ ( c_in @ SV166 @ ( c_Set_Oinsert @ SV166 @ SV593 @ SY2967 ) @ SY2967 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(2007,plain,
! [SV594: $i,SV167: $i] :
( ( ! [SY2968: $i] : ( hBOOL @ ( c_in @ SV167 @ ( c_Set_Oinsert @ SV167 @ SV594 @ SY2968 ) @ SY2968 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(2008,plain,
! [SV595: $i,SV168: $i] :
( ( ! [SY2969: $i] : ( hBOOL @ ( c_in @ SV168 @ ( c_Set_Oinsert @ SV168 @ SV595 @ SY2969 ) @ SY2969 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(2009,plain,
! [SV596: $i,SV169: $i] :
( ( ! [SY2970: $i] :
( ( ( c_Set_Oinsert @ SV169 @ SV596 @ SY2970 )
= SV596 )
| ~ ( hBOOL @ ( c_in @ SV169 @ SV596 @ SY2970 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(2010,plain,
! [SV597: $i,SV170: $i] :
( ( ! [SY2971: $i,SY2972: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV170 @ ( c_HOL_Ominus__class_Ominus @ SV597 @ SY2971 @ ( tc_fun @ SY2972 @ tc_bool ) ) @ ( tc_fun @ SY2972 @ tc_bool ) )
= SY2971 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2972 @ tc_bool ) ) @ SV170 ) @ SV597 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2972 @ tc_bool ) ) @ SY2971 ) @ SV170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(2011,plain,
! [SV598: $i,SV171: $i] :
( ( ! [SY2973: $i,SY2974: $i] :
( ( hBOOL @ ( c_in @ SV171 @ SV598 @ SY2973 ) )
| ~ ( hBOOL @ ( c_in @ SV171 @ SY2974 @ SY2973 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2973 @ tc_bool ) ) @ SY2974 ) @ SV598 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(2012,plain,
! [SV599: $i,SV172: $i] :
( ( ! [SY2975: $i,SY2976: $i] :
( ( hBOOL @ ( c_in @ SV172 @ SV599 @ SY2975 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2975 @ tc_bool ) ) @ SY2976 ) @ SV599 ) )
| ~ ( hBOOL @ ( c_in @ SV172 @ SY2976 @ SY2975 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(2013,plain,
! [SV600: $i,SV173: $i] :
( ( ! [SY2977: $i,SY2978: $i] :
( ( hBOOL @ ( c_in @ SV173 @ SV600 @ SY2977 ) )
| ~ ( hBOOL @ ( c_in @ SV173 @ SY2978 @ SY2977 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2977 @ tc_bool ) ) @ SY2978 ) @ SV600 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(2014,plain,
! [SV601: $i,SV174: $i] :
( ( ! [SY2979: $i,SY2980: $i] :
( ( hBOOL @ ( c_in @ SV174 @ SV601 @ SY2979 ) )
| ~ ( hBOOL @ ( c_in @ SV174 @ SY2980 @ SY2979 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2979 @ tc_bool ) ) @ SY2980 ) @ SV601 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(2015,plain,
! [SV602: $i,SV175: $i] :
( ( ! [SY2981: $i,SY2982: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV175 @ tc_bool ) ) @ SV602 ) @ SY2981 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV175 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2982 @ SV602 @ ( tc_fun @ SV175 @ tc_bool ) ) ) @ SY2981 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(2016,plain,
! [SV603: $i,SV176: $i] :
( ( ! [SY2983: $i,SY2984: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV176 @ tc_bool ) ) @ SV603 ) @ SY2983 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV176 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV603 @ SY2984 @ ( tc_fun @ SV176 @ tc_bool ) ) ) @ SY2983 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(2017,plain,
! [SV604: $i,SV177: $i] :
( ( ! [SY2985: $i,SY2986: $i,SY2987: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV604 @ SY2985 @ ( tc_fun @ SV177 @ tc_bool ) ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2986 @ SY2987 @ ( tc_fun @ SV177 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ SY2985 ) @ SY2987 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ SV604 ) @ SY2986 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(2018,plain,
! [SV605: $i,SV178: $i] :
( ( ! [SY2988: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV178 @ SV605 @ ( tc_fun @ SY2988 @ tc_bool ) )
= SV178 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2988 @ tc_bool ) ) @ SV605 ) @ SV178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1588]) ).
thf(2019,plain,
! [SV606: $i,SV179: $i] :
( ( ! [SY2989: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV179 @ SV606 @ ( tc_fun @ SY2989 @ tc_bool ) )
= SV606 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY2989 @ tc_bool ) ) @ SV179 ) @ SV606 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1589]) ).
thf(2020,plain,
! [SV607: $i,SV180: $i] :
( ( ! [SY2990: $i,SY2991: $i,SY2992: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV607 @ SY2990 @ ( tc_fun @ SV180 @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ SY2991 @ SY2992 @ ( tc_fun @ SV180 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ SY2992 ) @ SY2990 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ SV607 ) @ SY2991 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(2021,plain,
! [SV608: $i,SV181: $i] :
( ( ! [SY2993: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV181 @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV608 @ ( tc_fun @ SV181 @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SY2993 @ ( tc_fun @ SV181 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV181 @ tc_bool ) ) @ SY2993 ) @ SV608 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(2022,plain,
! [SV609: $i,SV182: $i] :
( ( ! [SY2994: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV182 @ tc_bool ) ) @ SV609 ) @ SY2994 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV182 @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SY2994 @ ( tc_fun @ SV182 @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV609 @ ( tc_fun @ SV182 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(2023,plain,
! [SV610: $i,SV183: $i] :
( ( ! [SY2995: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV183 @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV610 @ ( tc_fun @ SV183 @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SY2995 @ ( tc_fun @ SV183 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV183 @ tc_bool ) ) @ SY2995 ) @ SV610 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(2024,plain,
! [SV611: $i,SV184: $i] :
( ( ! [SY2996: $i,SY2997: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV184 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV611 @ SY2996 @ ( tc_fun @ SV184 @ tc_bool ) ) ) @ SY2997 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV184 @ tc_bool ) ) @ SY2996 ) @ SY2997 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV184 @ tc_bool ) ) @ SV611 ) @ SY2997 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(2025,plain,
! [SV612: $i,SV185: $i] :
( ( ! [SY2998: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV185 @ tc_bool ) ) @ SV612 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2998 @ SV612 @ ( tc_fun @ SV185 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(2026,plain,
! [SV613: $i,SV186: $i] :
( ( ! [SY2999: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV186 @ tc_bool ) ) @ SV613 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV613 @ SY2999 @ ( tc_fun @ SV186 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(2027,plain,
! [SV614: $i,SV187: $i] :
( ( ! [SY3000: $i,SY3001: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV187 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV614 @ SY3000 @ ( tc_fun @ SV187 @ tc_bool ) ) ) @ SY3001 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV187 @ tc_bool ) ) @ SY3000 ) @ SY3001 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV187 @ tc_bool ) ) @ SV614 ) @ SY3001 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1597]) ).
thf(2028,plain,
! [SV615: $i,SV188: $i] :
( ( ! [SY3002: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV188 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV615 @ SY3002 @ ( tc_fun @ SV188 @ tc_bool ) ) ) @ SV615 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(2029,plain,
! [SV616: $i,SV189: $i] :
( ( ! [SY3003: $i,SY3004: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV189 @ tc_bool ) ) @ SV616 ) @ ( c_Set_Oinsert @ SY3003 @ SY3004 @ SV189 ) ) )
| ~ ( hBOOL @ ( c_in @ SY3003 @ SV616 @ SV189 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV189 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV616 @ ( c_Set_Oinsert @ SY3003 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV189 @ tc_bool ) ) @ SV189 ) @ ( tc_fun @ SV189 @ tc_bool ) ) ) @ SY3004 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1599]) ).
thf(2030,plain,
! [SV617: $i,SV190: $i] :
( ( ! [SY3005: $i,SY3006: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV190 @ tc_bool ) ) @ SV617 ) @ ( c_Set_Oinsert @ SY3005 @ SY3006 @ SV190 ) ) )
| ~ ( hBOOL @ ( c_in @ SY3005 @ SV617 @ SV190 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV190 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV617 @ ( c_Set_Oinsert @ SY3005 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV190 @ tc_bool ) ) @ SV190 ) @ ( tc_fun @ SV190 @ tc_bool ) ) ) @ SY3006 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(2031,plain,
! [SV618: $i,SV191: $i] :
( ( ! [SY3007: $i,SY3008: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV191 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV618 @ ( c_Set_Oinsert @ SY3007 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV191 @ tc_bool ) ) @ SV191 ) @ ( tc_fun @ SV191 @ tc_bool ) ) ) @ SY3008 ) )
| ~ ( hBOOL @ ( c_in @ SY3007 @ SV618 @ SV191 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV191 @ tc_bool ) ) @ SV618 ) @ ( c_Set_Oinsert @ SY3007 @ SY3008 @ SV191 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(2032,plain,
! [SV619: $i,SV192: $i] :
( ( ! [SY3009: $i] :
( ~ ( class_Orderings_Oorder @ SV192 )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV619 @ SY3009 @ SV192 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV192 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV192 ) @ SV619 ) @ SY3009 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(2033,plain,
! [SV620: $i,SV193: $i] :
( ( ! [SY3010: $i] :
( ~ ( class_Orderings_Oorder @ SV193 )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV193 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV620 @ SY3010 @ SV193 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV193 ) @ SV620 ) @ SY3010 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(2034,plain,
! [SV621: $i,SV194: $i] :
( ( ! [SY3011: $i] :
( ~ ( class_Orderings_Oorder @ SV194 )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ SV621 @ SY3011 @ SV194 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV194 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV194 ) @ SY3011 ) @ SV621 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(2035,plain,
! [SV622: $i,SV195: $i] :
( ( ! [SY3012: $i,SY3013: $i,SY3014: $i] :
( ~ ( class_Orderings_Oorder @ SV195 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV195 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV622 @ SY3012 @ SV195 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3013 @ SY3014 @ SV195 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV195 ) @ SV622 ) @ SY3012 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(2036,plain,
! [SV623: $i,SV196: $i] :
( ( ! [SY3015: $i,SY3016: $i,SY3017: $i] :
( ~ ( class_Orderings_Oorder @ SV196 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV196 ) @ SV623 ) @ SY3015 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV196 ) @ SY3015 ) @ SY3016 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV196 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3015 @ SY3016 @ SV196 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV623 @ SY3017 @ SV196 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(2037,plain,
! [SV624: $i,SV197: $i] :
( ( ! [SY3018: $i,SY3019: $i,SY3020: $i] :
( ~ ( class_Orderings_Oorder @ SV197 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV197 ) @ SV624 ) @ SY3018 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV197 ) @ SY3019 ) @ SV624 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV197 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3019 @ SV624 @ SV197 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3020 @ SY3018 @ SV197 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1607]) ).
thf(2038,plain,
! [SV625: $i,SV198: $i] :
( ( ! [SY3021: $i,SY3022: $i,SY3023: $i] :
( ~ ( class_Orderings_Oorder @ SV198 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV198 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV625 @ SY3021 @ SV198 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3022 @ SY3023 @ SV198 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV198 ) @ SY3021 ) @ SY3023 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV198 ) @ SY3022 ) @ SV625 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(2039,plain,
! [SV626: $i,SV199: $i] :
( ( ! [SY3024: $i,SY3025: $i,SY3026: $i] :
( ~ ( class_Orderings_Olinorder @ SV199 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV199 ) @ SV626 ) @ SY3024 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV199 ) @ SY3025 ) @ SY3024 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV199 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SY3024 @ SY3025 @ SV199 ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV626 @ SY3026 @ SV199 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(2040,plain,
! [SV627: $i,SV200: $i] :
( ( ! [SY3027: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV200 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV200 ) @ SV627 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3027 @ SV627 @ SV200 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(2041,plain,
! [SV628: $i,SV201: $i] :
( ( ! [SY3028: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV201 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV201 ) @ SV628 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV628 @ SY3028 @ SV201 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(2042,plain,
! [SV629: $i,SV202: $i] :
( ( ! [SY3029: $i,SY3030: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV202 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV629 @ SY3029 @ SV202 ) ) @ SY3030 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ SY3029 ) @ SY3030 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ SV629 ) @ SY3030 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(2043,plain,
! [SV630: $i,SV203: $i] :
( ( ! [SY3031: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV203 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV203 ) @ SV630 ) @ SY3031 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV203 ) @ ( c_HOL_Ouminus__class_Ouminus @ SY3031 @ SV203 ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV630 @ SV203 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(2044,plain,
! [SV631: $i,SV204: $i] :
( ( ! [SY3032: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV204 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV204 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV631 @ SV204 ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SY3032 @ SV204 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV204 ) @ SY3032 ) @ SV631 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(2045,plain,
! [SV632: $i,SV205: $i] :
( ( ! [SY3033: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV205 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV632 @ SY3033 @ SV205 )
= SV632 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV205 ) @ SY3033 ) @ SV632 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(2046,plain,
! [SV633: $i,SV206: $i] :
( ( ! [SY3034: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV206 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV633 @ SY3034 @ SV206 )
= SY3034 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV206 ) @ SV633 ) @ SY3034 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(2047,plain,
! [SV634: $i,SV207: $i] :
( ( ! [SY3035: $i,SY3036: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV207 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV207 ) @ SV634 ) @ SY3035 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV207 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3036 @ SV634 @ SV207 ) ) @ SY3035 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1617]) ).
thf(2048,plain,
! [SV635: $i,SV208: $i] :
( ( ! [SY3037: $i,SY3038: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV208 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV208 ) @ SV635 ) @ SY3037 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV208 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV635 @ SY3038 @ SV208 ) ) @ SY3037 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(2049,plain,
! [SV636: $i,SV209: $i] :
( ( ! [SY3039: $i,SY3040: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV209 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV209 ) @ SV636 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3039 @ SY3040 @ SV209 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV209 ) @ SV636 ) @ SY3040 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(2050,plain,
! [SV637: $i,SV210: $i] :
( ( ! [SY3041: $i,SY3042: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV210 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV210 ) @ SV637 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3041 @ SY3042 @ SV210 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV210 ) @ SV637 ) @ SY3041 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(2051,plain,
! [SV638: $i,SV211: $i] :
( ( ! [SY3043: $i,SY3044: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV211 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV211 ) @ SV638 ) @ SY3043 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV211 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3044 @ SV638 @ SV211 ) ) @ SY3043 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(2052,plain,
! [SV639: $i,SV212: $i] :
( ( ! [SY3045: $i,SY3046: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV212 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV212 ) @ SV639 ) @ SY3045 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV212 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV639 @ SY3046 @ SV212 ) ) @ SY3045 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(2053,plain,
! [SV640: $i,SV213: $i] :
( ( ! [SY3047: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV213 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ SV640 @ SY3047 @ SV213 ) @ SV213 )
= ( c_HOL_Ominus__class_Ominus @ SY3047 @ SV640 @ SV213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(2054,plain,
! [SV641: $i,SV214: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV214 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV641 @ SV214 ) @ SV214 )
= SV641 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(2055,plain,
! [SV642: $i,SV215: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV215 )
| ( SV642
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV642 @ SV215 ) @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(2056,plain,
! [SV643: $i,SV216: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV216 )
| ( SV643
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV643 @ SV216 ) @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(2057,plain,
! [SV644: $i,SV217: $i] :
( ( ~ ( class_Lattices_Oboolean__algebra @ SV217 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV644 @ SV217 ) @ SV217 )
= SV644 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1627]) ).
thf(2058,plain,
! [SV645: $i,SV218: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV218 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV645 @ SV218 ) @ SV218 )
= SV645 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(2059,plain,
! [SV646: $i,SV219: $i] :
( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV219 @ ( tc_fun @ SV646 @ tc_bool ) ) @ ( tc_fun @ SV646 @ tc_bool ) )
= SV219 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(2060,plain,
! [SV647: $i,SV220: $i] :
( ( ! [SY3048: $i,SY3049: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV220 @ tc_bool ) ) @ SV647 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3048 @ SY3049 @ ( tc_fun @ SV220 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV220 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV647 @ SY3048 @ ( tc_fun @ SV220 @ tc_bool ) ) ) @ SY3049 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(2061,plain,
! [SV648: $i,SV221: $i] :
( ( ! [SY3050: $i,SY3051: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV221 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV648 @ SY3050 @ ( tc_fun @ SV221 @ tc_bool ) ) ) @ SY3051 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV221 @ tc_bool ) ) @ SV648 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3050 @ SY3051 @ ( tc_fun @ SV221 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(2062,plain,
! [SV649: $i,SV222: $i] :
( ( ! [SY3052: $i,SY3053: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV222 @ SV649 @ SY3052 ) @ SY3053 @ ( tc_fun @ SY3052 @ tc_bool ) )
= ( c_Set_Oinsert @ SV222 @ ( c_HOL_Ominus__class_Ominus @ SV649 @ SY3053 @ ( tc_fun @ SY3052 @ tc_bool ) ) @ SY3052 ) )
| ( hBOOL @ ( c_in @ SV222 @ SY3053 @ SY3052 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(2063,plain,
! [SV650: $i,SV223: $i] :
( ( ! [SY3054: $i,SY3055: $i,SY3056: $i,SY3057: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV223 @ SV650 @ SY3054 @ ( tc_fun @ SY3055 @ tc_bool ) ) @ SY3056 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV650 @ SY3057 ) @ SY3056 ) )
| ~ ( hBOOL @ ( c_in @ SY3057 @ SV223 @ SY3054 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(2064,plain,
! [SV651: $i,SV224: $i] :
( ( ! [SY3058: $i,SY3059: $i,SY3060: $i,SY3061: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV224 @ SV651 @ SY3058 @ ( tc_fun @ SY3059 @ tc_bool ) ) @ SY3060 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV651 @ SY3061 ) @ SY3060 ) )
| ~ ( hBOOL @ ( c_in @ SY3061 @ SV224 @ SY3058 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(2065,plain,
! [SV652: $i,SV225: $i] :
( ( ! [SY3062: $i] :
( ~ ( class_Lattices_Olattice @ SV225 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV652 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV652 @ SY3062 @ SV225 ) @ SV225 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV652 @ SY3062 @ SV225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(2066,plain,
! [SV653: $i,SV226: $i] :
( ( ! [SY3063: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV226 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV653 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV653 @ SY3063 @ SV226 ) @ SV226 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV653 @ SY3063 @ SV226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(2067,plain,
! [SV654: $i,SV227: $i] :
( ( ! [SY3064: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV227 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV227 @ SV654 @ ( tc_fun @ SY3064 @ tc_bool ) ) @ ( tc_fun @ SY3064 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV227 @ SV654 @ ( tc_fun @ SY3064 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(2068,plain,
! [SV655: $i,SV228: $i] :
( ( ! [SY3065: $i] :
( ~ ( class_Lattices_Olattice @ SV228 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV655 @ SY3065 @ SV228 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3065 @ SV655 @ SV228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(2069,plain,
! [SV656: $i,SV229: $i] :
( ( ! [SY3066: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV229 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV656 @ SY3066 @ SV229 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3066 @ SV656 @ SV229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(2070,plain,
! [SV657: $i,SV230: $i] :
( ( ! [SY3067: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV230 @ SV657 @ ( tc_fun @ SY3067 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV657 @ SV230 @ ( tc_fun @ SY3067 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(2071,plain,
! [SV658: $i,SV231: $i] :
( ( ! [SY3068: $i,SY3069: $i,SY3070: $i,SY3071: $i,SY3072: $i,SY3073: $i,SY3074: $i,SY3075: $i,SY3076: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV231 @ SV658 ) @ ( hAPP @ SY3068 @ SY3069 ) ) )
| ~ ( hBOOL @ ( c_in @ SV658 @ SY3069 @ SY3070 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3071 @ SY3068 @ SV231 @ SY3072 @ SY3073 @ SY3074 @ SY3075 @ SY3076 @ SY3070 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1641]) ).
thf(2072,plain,
! [SV659: $i,SV232: $i] :
( ( ! [SY3077: $i,SY3078: $i,SY3079: $i,SY3080: $i,SY3081: $i,SY3082: $i,SY3083: $i,SY3084: $i,SY3085: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ ( hAPP @ SV659 @ SY3077 ) ) @ SY3078 ) )
| ~ ( hBOOL @ ( c_in @ SY3078 @ SY3077 @ SY3079 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV659 @ SY3080 @ SV232 @ SY3081 @ SY3082 @ SY3083 @ SY3084 @ SY3085 @ SY3079 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(2073,plain,
! [SV660: $i,SV233: $i] :
( ( ! [SY3086: $i,SY3087: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV233 @ SV660 @ ( tc_fun @ SY3086 @ tc_bool ) ) @ SY3087 @ ( tc_fun @ SY3086 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV233 @ SY3087 @ ( tc_fun @ SY3086 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV660 @ SY3087 @ ( tc_fun @ SY3086 @ tc_bool ) ) @ ( tc_fun @ SY3086 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(2074,plain,
! [SV661: $i,SV234: $i] :
( ( ! [SY3088: $i] :
( ~ ( class_HOL_Ominus @ SV234 )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ SV661 @ SY3088 @ ( tc_fun @ t_a @ SV234 ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ SV661 @ v_x ) @ ( hAPP @ SY3088 @ v_x ) @ SV234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(2075,plain,
! [SV662: $i,SV235: $i] :
( ( ! [SY3089: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV235 @ ( c_HOL_Ominus__class_Ominus @ SV662 @ SV235 @ ( tc_fun @ SY3089 @ tc_bool ) ) @ ( tc_fun @ SY3089 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV235 @ SV662 @ ( tc_fun @ SY3089 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1645]) ).
thf(2076,plain,
! [SV663: $i,SV236: $i] :
( ( ! [SY3090: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV236 @ SV663 @ ( tc_fun @ SY3090 @ tc_bool ) ) @ SV663 @ ( tc_fun @ SY3090 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV236 @ SV663 @ ( tc_fun @ SY3090 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(2077,plain,
! [SV664: $i,SV237: $i] :
( ( ! [SY3091: $i,SY3092: $i,SY3093: $i,SY3094: $i] :
( ( hBOOL @ ( c_in @ SV237 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV664 @ SY3091 @ SY3092 @ ( tc_fun @ SY3093 @ tc_bool ) ) @ SY3093 ) )
| ~ ( hBOOL @ ( c_in @ SV237 @ ( hAPP @ SY3091 @ SY3094 ) @ SY3093 ) )
| ~ ( hBOOL @ ( c_in @ SY3094 @ SV664 @ SY3092 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(2078,plain,
! [SV665: $i,SV238: $i] :
( ( ! [SY3095: $i,SY3096: $i,SY3097: $i,SY3098: $i] :
( ( hBOOL @ ( c_in @ SV238 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV665 @ SY3095 @ SY3096 @ ( tc_fun @ SY3097 @ tc_bool ) ) @ SY3097 ) )
| ~ ( hBOOL @ ( c_in @ SV238 @ ( hAPP @ SY3095 @ SY3098 ) @ SY3097 ) )
| ~ ( hBOOL @ ( c_in @ SY3098 @ SV665 @ SY3096 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(2079,plain,
! [SV666: $i,SV239: $i] :
( ( ! [SY3099: $i,SY3100: $i] :
( ( hBOOL @ ( c_in @ SV239 @ ( c_HOL_Ominus__class_Ominus @ SV666 @ SY3099 @ ( tc_fun @ SY3100 @ tc_bool ) ) @ SY3100 ) )
| ( hBOOL @ ( c_in @ SV239 @ SY3099 @ SY3100 ) )
| ~ ( hBOOL @ ( c_in @ SV239 @ SV666 @ SY3100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(2080,plain,
! [SV667: $i,SV240: $i] :
( ( ! [SY3101: $i,SY3102: $i] :
( ( hBOOL @ ( c_in @ SV240 @ ( c_HOL_Ominus__class_Ominus @ SV667 @ SY3101 @ ( tc_fun @ SY3102 @ tc_bool ) ) @ SY3102 ) )
| ( hBOOL @ ( c_in @ SV240 @ SY3101 @ SY3102 ) )
| ~ ( hBOOL @ ( c_in @ SV240 @ SV667 @ SY3102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(2081,plain,
! [SV668: $i,SV241: $i] :
( ( ! [SY3103: $i] :
( ( hBOOL @ ( hAPP @ SV241 @ SV668 ) )
| ~ ( hBOOL @ ( c_in @ SV668 @ ( c_Collect @ SV241 @ SY3103 ) @ SY3103 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(2082,plain,
! [SV669: $i,SV242: $i] :
( ( ! [SY3104: $i] :
( ( hBOOL @ ( c_in @ SV242 @ ( c_Collect @ SV669 @ SY3104 ) @ SY3104 ) )
| ~ ( hBOOL @ ( hAPP @ SV669 @ SV242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(2083,plain,
! [SV670: $i,SV243: $i] :
( ( ! [SY3105: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV243 @ ( c_HOL_Ominus__class_Ominus @ SV670 @ SV243 @ ( tc_fun @ SY3105 @ tc_bool ) ) @ ( tc_fun @ SY3105 @ tc_bool ) )
= SV670 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY3105 @ tc_bool ) ) @ SV243 ) @ SV670 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(2084,plain,
! [SV671: $i,SV244: $i] :
( ( ! [SY3106: $i,SY3107: $i] :
( ~ ( class_Lattices_Olattice @ SV244 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV671 @ SY3106 @ SV244 ) @ SY3107 @ SV244 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV671 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3106 @ SY3107 @ SV244 ) @ SV244 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(2085,plain,
! [SV672: $i,SV245: $i] :
( ( ! [SY3108: $i,SY3109: $i] :
( ~ ( class_Lattices_Olattice @ SV245 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV672 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3108 @ SY3109 @ SV245 ) @ SV245 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3108 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV672 @ SY3109 @ SV245 ) @ SV245 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(2086,plain,
! [SV673: $i,SV246: $i] :
( ( ! [SY3110: $i,SY3111: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV246 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV673 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3110 @ SY3111 @ SV246 ) @ SV246 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3110 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV673 @ SY3111 @ SV246 ) @ SV246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(2087,plain,
! [SV674: $i,SV247: $i] :
( ( ! [SY3112: $i,SY3113: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV247 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV674 @ SY3112 @ SV247 ) @ SY3113 @ SV247 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV674 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3112 @ SY3113 @ SV247 ) @ SV247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1657]) ).
thf(2088,plain,
! [SV675: $i,SV248: $i] :
( ( ! [SY3114: $i,SY3115: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV248 @ SV675 @ ( tc_fun @ SY3114 @ tc_bool ) ) @ SY3115 @ ( tc_fun @ SY3114 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV248 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV675 @ SY3115 @ ( tc_fun @ SY3114 @ tc_bool ) ) @ ( tc_fun @ SY3114 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(2089,plain,
! [SV676: $i,SV249: $i] :
( ( ! [SY3116: $i,SY3117: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV249 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV676 @ SY3116 @ ( tc_fun @ SY3117 @ tc_bool ) ) @ ( tc_fun @ SY3117 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV676 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV249 @ SY3116 @ ( tc_fun @ SY3117 @ tc_bool ) ) @ ( tc_fun @ SY3117 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1659]) ).
thf(2090,plain,
! [SV677: $i,SV250: $i] :
( ( ! [SY3118: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV250 @ SV677 @ ( tc_fun @ SY3118 @ tc_bool ) ) @ SV677 @ ( tc_fun @ SY3118 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV250 @ SV677 @ ( tc_fun @ SY3118 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(2091,plain,
! [SV678: $i,SV251: $i] :
( ( ! [SY3119: $i] :
( ( hBOOL @ ( hAPP @ SV251 @ SV678 ) )
| ~ ( hBOOL @ ( c_in @ SV678 @ SV251 @ SY3119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(2092,plain,
! [SV679: $i,SV252: $i] :
( ( ! [SY3120: $i] :
( ( hBOOL @ ( c_in @ SV252 @ SV679 @ SY3120 ) )
| ~ ( hBOOL @ ( hAPP @ SV679 @ SV252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1662]) ).
thf(2093,plain,
! [SV680: $i,SV253: $i] :
( ( ! [SY3121: $i,SY3122: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV253 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV680 @ tc_bool ) ) @ SY3121 @ SV680 @ ( tc_fun @ SY3122 @ tc_bool ) ) @ ( tc_fun @ SY3122 @ tc_bool ) )
= SV253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1663]) ).
thf(2094,plain,
! [SV681: $i,SV254: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV254 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV681 @ SV681 @ SV254 )
= SV681 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1664]) ).
thf(2095,plain,
! [SV682: $i,SV255: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV255 @ SV255 @ ( tc_fun @ SV682 @ tc_bool ) )
= SV255 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(2096,plain,
! [SV683: $i,SV256: $i] :
( ( ! [SY3123: $i] :
( ~ ( class_Lattices_Olattice @ SV256 )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV683 @ SY3123 @ ( tc_fun @ t_a @ SV256 ) ) @ v_x )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV683 @ v_x ) @ ( hAPP @ SY3123 @ v_x ) @ SV256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(2097,plain,
! [SV684: $i,SV257: $i] :
( ( ! [SY3124: $i] :
( ( c_Finite__Set_Ofold1 @ SV257 @ SV684 @ SY3124 )
= ( c_The @ ( c_Finite__Set_Ofold1Set @ SV257 @ SV684 @ SY3124 ) @ SY3124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(2098,plain,
! [SV685: $i,SV258: $i] :
( ( ! [SY3125: $i,SY3126: $i,SY3127: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV258 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV258 ) @ ( hAPP @ SV685 @ SY3125 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3126 @ SV685 @ SY3127 @ SV258 ) ) )
| ~ ( hBOOL @ ( c_in @ SY3125 @ SY3126 @ SY3127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(2099,plain,
! [SV686: $i,SV259: $i] :
( ( ! [SY3128: $i,SY3129: $i,SY3130: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV259 @ tc_bool ) ) @ ( hAPP @ SV686 @ SY3128 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3129 @ SV686 @ SY3130 @ ( tc_fun @ SV259 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( c_in @ SY3128 @ SY3129 @ SY3130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(2100,plain,
! [SV687: $i,SV260: $i] :
( ( ! [SY3131: $i,SY3132: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV260 @ SV687 @ SY3131 ) @ SY3132 @ ( tc_fun @ SY3131 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV687 @ SY3132 @ ( tc_fun @ SY3131 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SV260 @ SY3132 @ SY3131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(2101,plain,
! [SV688: $i,SV261: $i] :
( ( ! [SY3133: $i] :
( ~ ( hBOOL @ ( c_in @ SV261 @ SV688 @ SY3133 ) )
| ~ ( hBOOL @ ( c_in @ SV261 @ ( c_HOL_Ouminus__class_Ouminus @ SV688 @ ( tc_fun @ SY3133 @ tc_bool ) ) @ SY3133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1671]) ).
thf(2102,plain,
! [SV689: $i,SV262: $i] :
( ( ! [SY3134: $i] :
( ( hBOOL @ ( c_in @ SV262 @ ( c_HOL_Ouminus__class_Ouminus @ SV689 @ ( tc_fun @ SY3134 @ tc_bool ) ) @ SY3134 ) )
| ( hBOOL @ ( c_in @ SV262 @ SV689 @ SY3134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(2103,plain,
! [SV690: $i,SV263: $i] :
( ( ( c_Collect @ SV263 @ SV690 )
= SV263 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1673]) ).
thf(2104,plain,
! [SV691: $i,SV264: $i] :
( ( ! [SY3135: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV264 )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV264 ) @ ( c_Set_Oinsert @ SV691 @ SY3135 @ SV264 ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV691 @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV264 ) @ SY3135 ) @ SV264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(2105,plain,
! [SV692: $i,SV265: $i] :
( ( ! [SY3136: $i] :
( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ SV265 @ SV692 @ ( tc_fun @ SY3136 @ tc_bool ) ) @ ( tc_fun @ SY3136 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ SV265 @ ( tc_fun @ SY3136 @ tc_bool ) ) @ SV692 @ ( tc_fun @ SY3136 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(2106,plain,
! [SV693: $i,SV266: $i] :
( ( ! [SY3137: $i,SY3138: $i] :
( ( hBOOL @ ( c_in @ SV266 @ SV693 @ SY3137 ) )
| ~ ( hBOOL @ ( c_in @ SV266 @ ( c_HOL_Ominus__class_Ominus @ SV693 @ SY3138 @ ( tc_fun @ SY3137 @ tc_bool ) ) @ SY3137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(2107,plain,
! [SV694: $i,SV267: $i] :
( ( ! [SY3139: $i,SY3140: $i] :
( ~ ( hBOOL @ ( c_in @ SV267 @ SV694 @ SY3139 ) )
| ~ ( hBOOL @ ( c_in @ SV267 @ ( c_HOL_Ominus__class_Ominus @ SY3140 @ SV694 @ ( tc_fun @ SY3139 @ tc_bool ) ) @ SY3139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1677]) ).
thf(2108,plain,
! [SV695: $i,SV268: $i] :
( ( ! [SY3141: $i,SY3142: $i,SY3143: $i,SY3144: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV268 @ tc_bool ) ) @ ( hAPP @ SV695 @ SY3141 ) ) @ SY3142 ) )
| ~ ( hBOOL @ ( c_in @ SY3141 @ SY3143 @ SY3144 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV268 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3143 @ SV695 @ SY3144 @ ( tc_fun @ SV268 @ tc_bool ) ) ) @ SY3142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1678]) ).
thf(2109,plain,
! [SV696: $i,SV269: $i] :
( ( ! [SY3145: $i,SY3146: $i,SY3147: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV269 @ SV696 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3145 @ SV269 @ SY3146 @ ( tc_fun @ SY3147 @ tc_bool ) ) @ ( tc_fun @ SY3147 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3145 @ SV269 @ SY3146 @ ( tc_fun @ SY3147 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SV696 @ SY3145 @ SY3146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1679]) ).
thf(2110,plain,
! [SV697: $i,SV270: $i] :
( ( ! [SY3148: $i,SY3149: $i] :
( ( hBOOL @ ( hAPP @ SV270 @ SV697 ) )
| ( hBOOL @ ( hAPP @ SY3148 @ SV697 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3148 @ SV270 @ ( tc_fun @ SY3149 @ tc_bool ) ) @ SV697 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(2111,plain,
! [SV698: $i,SV271: $i] :
( ( ! [SY3150: $i,SY3151: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV271 @ SV698 @ ( tc_fun @ SY3150 @ tc_bool ) ) @ SY3151 ) )
| ~ ( hBOOL @ ( hAPP @ SV698 @ SY3151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(2112,plain,
! [SV699: $i,SV272: $i] :
( ( ! [SY3152: $i,SY3153: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV272 @ SV699 @ ( tc_fun @ SY3152 @ tc_bool ) ) @ SY3153 ) )
| ~ ( hBOOL @ ( hAPP @ SV272 @ SY3153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(2113,plain,
! [SV700: $i,SV273: $i] :
( ( ! [SY3154: $i,SY3155: $i] :
( ( hBOOL @ ( c_in @ SV273 @ SV700 @ SY3154 ) )
| ( hBOOL @ ( c_in @ SV273 @ SY3155 @ SY3154 ) )
| ~ ( hBOOL @ ( c_in @ SV273 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3155 @ SV700 @ ( tc_fun @ SY3154 @ tc_bool ) ) @ SY3154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(2114,plain,
! [SV701: $i,SV274: $i] :
( ( ! [SY3156: $i,SY3157: $i] :
( ~ ( class_Orderings_Olinorder @ SV274 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV701 @ SY3156 @ SV274 ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SY3156 @ SY3157 @ SV274 ) @ ( tc_fun @ SV274 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV701 @ SY3157 @ SV274 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV274 ) @ SY3156 ) @ SY3157 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV274 ) @ SV701 ) @ SY3156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1684]) ).
thf(2115,plain,
! [SV702: $i,SV275: $i] :
( ( ! [SY3158: $i,SY3159: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV275 @ tc_bool ) ) @ SV702 @ SV275 @ ( tc_fun @ SY3158 @ tc_bool ) ) @ SY3159 @ ( tc_fun @ SY3158 @ tc_bool ) )
= SY3159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1685]) ).
thf(2116,plain,
! [SV703: $i,SV276: $i] :
( ( ! [SY3160: $i,SY3161: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV276 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV703 @ tc_bool ) ) @ SY3160 @ SV703 @ ( tc_fun @ SY3161 @ tc_bool ) ) @ ( tc_fun @ SY3161 @ tc_bool ) )
= SV276 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(2117,plain,
! [SV704: $i,SV277: $i] :
( ( ! [SY3162: $i,SY3163: $i] :
( ~ ( class_Orderings_Olinorder @ SV277 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV704 @ SY3162 @ SV277 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3162 @ SY3163 @ SV277 ) @ ( tc_fun @ SV277 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV704 @ SY3163 @ SV277 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV277 ) @ SY3162 ) @ SY3163 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV277 ) @ SV704 ) @ SY3162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1687]) ).
thf(2118,plain,
! [SV705: $i,SV278: $i] :
( ( ! [SY3164: $i,SY3165: $i,SY3166: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ SV278 @ SV705 @ SY3164 ) @ SY3165 @ SY3164 @ ( tc_fun @ SY3166 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SY3165 @ SV278 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV705 @ SY3165 @ SY3164 @ ( tc_fun @ SY3166 @ tc_bool ) ) @ ( tc_fun @ SY3166 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1688]) ).
thf(2119,plain,
! [SV706: $i,SV279: $i] :
( ( ! [SY3167: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV279 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV279 ) @ ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ SV279 ) @ SV706 ) ) @ SY3167 ) )
| ~ ( hBOOL @ ( c_in @ SY3167 @ SV706 @ SV279 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(2120,plain,
! [SV707: $i,SV280: $i] :
( ( ~ ( class_HOL_Ouminus @ SV280 )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV707 @ ( tc_fun @ t_a @ SV280 ) ) @ v_x )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ SV707 @ v_x ) @ SV280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1690]) ).
thf(2121,plain,
! [SV708: $i,SV281: $i] :
( ( ! [SY3168: $i,SY3169: $i] :
( ( hBOOL @ ( c_in @ SV281 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV708 @ SY3168 @ ( tc_fun @ SY3169 @ tc_bool ) ) @ SY3169 ) )
| ~ ( hBOOL @ ( c_in @ SV281 @ SY3168 @ SY3169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(2122,plain,
! [SV709: $i,SV282: $i] :
( ( ! [SY3170: $i,SY3171: $i] :
( ( hBOOL @ ( c_in @ SV282 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV709 @ SY3170 @ ( tc_fun @ SY3171 @ tc_bool ) ) @ SY3171 ) )
| ~ ( hBOOL @ ( c_in @ SV282 @ SV709 @ SY3171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(2123,plain,
! [SV710: $i,SV283: $i] :
( ( ! [SY3172: $i,SY3173: $i] :
( ~ ( class_Orderings_Olinorder @ SV283 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV710 @ SY3172 @ SV283 ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV710 @ SY3173 @ SV283 ) @ ( tc_fun @ SV283 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SY3173 @ SY3172 @ SV283 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV283 ) @ SV710 ) @ SY3173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(2124,plain,
! [SV711: $i,SV284: $i] :
( ( ! [SY3174: $i,SY3175: $i,SY3176: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV284 @ SV711 @ ( tc_fun @ SY3174 @ tc_bool ) ) @ SY3175 @ SY3174 @ ( tc_fun @ SY3176 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV284 @ SY3175 @ SY3174 @ ( tc_fun @ SY3176 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV711 @ SY3175 @ SY3174 @ ( tc_fun @ SY3176 @ tc_bool ) ) @ ( tc_fun @ SY3176 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1694]) ).
thf(2125,plain,
! [SV712: $i,SV285: $i] :
( ( ( c_The @ ( hAPP @ ( c_fequal @ SV285 ) @ SV712 ) @ SV285 )
= SV712 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(2126,plain,
! [SV713: $i,SV286: $i] :
( ( ! [SY3177: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV286 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV286 ) @ SV713 ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV286 ) @ SY3177 ) ) )
| ~ ( hBOOL @ ( c_in @ SV713 @ SY3177 @ SV286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(2127,plain,
! [SV714: $i,SV287: $i] :
( ( ! [SY3178: $i,SY3179: $i,SY3180: $i] :
( ~ ( class_Orderings_Olinorder @ SV287 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV287 ) @ SV714 ) @ SY3178 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV287 ) @ SV714 ) @ SY3179 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV287 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SY3179 @ SV714 @ SV287 ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SY3180 @ SY3178 @ SV287 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(2128,plain,
! [SV288: $i] :
( ( ( ~ ( class_Orderings_Obot @ SV288 ) )
= $true )
| ( ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ SV288 ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ SV288 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1698]) ).
thf(2129,plain,
! [SV289: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV289 ) )
= $true )
| ( ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV289 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV289 @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ SV289 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1699]) ).
thf(2130,plain,
! [SV715: $i,SV290: $i] :
( ( ( c_Collect @ ( hAPP @ ( c_fequal @ SV290 ) @ SV715 ) @ SV290 )
= ( c_Set_Oinsert @ SV715 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV290 @ tc_bool ) ) @ SV290 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1700]) ).
thf(2131,plain,
! [SV716: $i,SV291: $i] :
( ( hBOOL @ ( c_in @ SV291 @ ( c_Set_Oinsert @ SV291 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV716 @ tc_bool ) ) @ SV716 ) @ SV716 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1701]) ).
thf(2132,plain,
! [SV717: $i,SV292: $i] :
( ( ! [SY3181: $i,SY3182: $i,SY3183: $i,SY3184: $i,SY3185: $i,SY3186: $i,SY3187: $i,SY3188: $i] :
( ( ( hAPP @ SV292 @ ( c_Set_Oinsert @ SV717 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3181 @ tc_bool ) ) @ SY3181 ) )
= SV717 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV292 @ SY3182 @ SY3183 @ SY3184 @ SY3185 @ SY3186 @ SY3187 @ SY3188 @ SY3181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(2133,plain,
! [SV718: $i,SV293: $i] :
( ( ! [SY3189: $i,SY3190: $i,SY3191: $i,SY3192: $i,SY3193: $i,SY3194: $i,SY3195: $i,SY3196: $i] :
( ( ( hAPP @ SV293 @ ( c_Set_Oinsert @ SV718 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3189 @ tc_bool ) ) @ SY3189 ) )
= SV718 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3190 @ SV293 @ SY3191 @ SY3192 @ SY3193 @ SY3194 @ SY3195 @ SY3196 @ SY3189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(2134,plain,
! [SV719: $i,SV294: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV294 )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV294 ) @ ( c_Set_Oinsert @ SV719 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV294 @ tc_bool ) ) @ SV294 ) )
= SV719 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1704]) ).
thf(2135,plain,
! [SV720: $i,SV295: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV295 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV720 @ tc_bool ) ) @ SV720 ) @ ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ SV295 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV720 @ tc_bool ) ) @ SV720 ) @ SV720 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1705]) ).
thf(2136,plain,
! [SV721: $i,SV296: $i] :
( ( ! [SY3197: $i,SY3198: $i] :
( ( c_Set_Oinsert @ SV296 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV721 @ tc_bool ) ) @ SY3197 @ SV721 @ ( tc_fun @ SY3198 @ tc_bool ) ) @ SY3198 )
= ( c_Set_Oinsert @ SV296 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3198 @ tc_bool ) ) @ SY3198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1706]) ).
thf(2137,plain,
! [SV722: $i,SV297: $i] :
( ( ! [SY3199: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV297 @ ( c_Set_Oinsert @ SV722 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3199 @ tc_bool ) ) @ SY3199 ) @ SY3199 ) @ SV722 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1707]) ).
thf(2138,plain,
! [SV723: $i,SV298: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV298 )
| ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ SV723 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV298 @ tc_bool ) ) @ SV298 ) @ SV298 )
= SV723 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(2139,plain,
! [SV724: $i,SV299: $i] :
( ( ( c_The @ ( c_Set_Oinsert @ SV299 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV724 @ tc_bool ) ) @ SV724 ) @ SV724 )
= SV299 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(2140,plain,
! [SV725: $i,SV300: $i] :
( ( ! [SY3200: $i,SY3201: $i,SY3202: $i,SY3203: $i,SY3204: $i,SY3205: $i,SY3206: $i,SY3207: $i,SY3208: $i] :
( ( ( hAPP @ SV300 @ ( c_Set_Oinsert @ SV725 @ ( c_Set_Oinsert @ SY3200 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3201 @ tc_bool ) ) @ SY3201 ) @ SY3201 ) )
= ( hAPP @ ( hAPP @ SY3202 @ SV725 ) @ SY3200 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV300 @ SY3203 @ SY3204 @ SY3205 @ SY3202 @ SY3206 @ SY3207 @ SY3208 @ SY3201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(2141,plain,
! [SV726: $i,SV301: $i] :
( ( ! [SY3209: $i,SY3210: $i,SY3211: $i,SY3212: $i,SY3213: $i,SY3214: $i,SY3215: $i,SY3216: $i,SY3217: $i] :
( ( ( hAPP @ SV301 @ ( c_Set_Oinsert @ SV726 @ ( c_Set_Oinsert @ SY3209 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3210 @ tc_bool ) ) @ SY3210 ) @ SY3210 ) )
= ( hAPP @ ( hAPP @ SY3211 @ SV726 ) @ SY3209 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3212 @ SV301 @ SY3213 @ SY3214 @ SY3215 @ SY3211 @ SY3216 @ SY3217 @ SY3210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1711]) ).
thf(2142,plain,
! [SV727: $i,SV302: $i] :
( ( ! [SY3218: $i,SY3219: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV302 @ ( c_Set_Oinsert @ SV727 @ SY3218 @ SY3219 ) @ ( tc_fun @ SY3219 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV302 @ ( c_Set_Oinsert @ SV727 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3219 @ tc_bool ) ) @ SY3219 ) @ ( tc_fun @ SY3219 @ tc_bool ) ) @ SY3218 @ ( tc_fun @ SY3219 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(2143,plain,
! [SV728: $i,SV303: $i] :
( ( ! [SY3220: $i,SY3221: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV303 @ ( c_Set_Oinsert @ SV728 @ SY3220 @ SY3221 ) @ ( tc_fun @ SY3221 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV303 @ SY3220 @ ( tc_fun @ SY3221 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV728 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3221 @ tc_bool ) ) @ SY3221 ) @ ( tc_fun @ SY3221 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1713]) ).
thf(2144,plain,
! [SV729: $i,SV304: $i] :
( ( ! [SY3222: $i,SY3223: $i] :
( ( SV304 = SV729 )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SY3222 @ ( c_Set_Oinsert @ SV304 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3223 @ tc_bool ) ) @ SY3223 ) @ SY3223 ) @ SV729 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1714]) ).
thf(2145,plain,
! [SV730: $i,SV305: $i] :
( ( ( c_Set_Ocontents @ ( c_Set_Oinsert @ SV305 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV730 @ tc_bool ) ) @ SV730 ) @ SV730 )
= SV305 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(2146,plain,
! [SV731: $i,SV306: $i] :
( ( ! [SY3224: $i] :
( ( SV306
= ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ SV731 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3224 @ tc_bool ) ) @ SY3224 ) @ SY3224 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV731 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3224 @ tc_bool ) ) @ SY3224 ) @ SV306 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(2147,plain,
! [SV732: $i,SV307: $i] :
( ( ! [SY3225: $i] :
( ( SV307 = SV732 )
| ~ ( hBOOL @ ( c_in @ SV307 @ ( c_Set_Oinsert @ SV732 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3225 @ tc_bool ) ) @ SY3225 ) @ SY3225 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1717]) ).
thf(2148,plain,
! [SV733: $i,SV308: $i] :
( ( ! [SY3226: $i] :
( ( c_Finite__Set_Ofold1 @ SV308 @ ( c_Set_Oinsert @ SV733 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3226 @ tc_bool ) ) @ SY3226 ) @ SY3226 )
= SV733 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1718]) ).
thf(2149,plain,
! [SV734: $i,SV309: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV309 )
| ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ SV734 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV309 @ tc_bool ) ) @ SV309 ) @ SV309 )
= SV734 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1719]) ).
thf(2150,plain,
! [SV735: $i,SV310: $i] :
( ( ! [SY3227: $i] :
( ( c_Set_Oinsert @ SV310 @ ( c_HOL_Ominus__class_Ominus @ SV735 @ ( c_Set_Oinsert @ SV310 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3227 @ tc_bool ) ) @ SY3227 ) @ ( tc_fun @ SY3227 @ tc_bool ) ) @ SY3227 )
= ( c_Set_Oinsert @ SV310 @ SV735 @ SY3227 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1720]) ).
thf(2151,plain,
! [SV736: $i,SV311: $i] :
( ( ~ ( class_Orderings_Oorder @ SV311 )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV736 @ SV736 @ SV311 )
= ( c_Set_Oinsert @ SV736 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV311 @ tc_bool ) ) @ SV311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(2152,plain,
! [SV737: $i,SV312: $i] :
( ( ! [SY3228: $i] :
( ( c_Set_Oinsert @ SV312 @ SV737 @ SY3228 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV312 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3228 @ tc_bool ) ) @ SY3228 ) @ SV737 @ ( tc_fun @ SY3228 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1722]) ).
thf(2153,plain,
! [SV738: $i,SV313: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV313 )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ SV313 ) @ ( c_Set_Oinsert @ SV738 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV313 @ tc_bool ) ) @ SV313 ) )
= SV738 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1723]) ).
thf(2154,plain,
! [SV739: $i,SV314: $i] :
( ( ( SV314
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV739 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV739 @ tc_bool ) ) @ SV314 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV314 @ ( tc_fun @ SV739 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(2155,plain,
! [SV740: $i,SV316: $i] :
( ( ! [SY3229: $i,SY3230: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV316 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV740 @ SY3229 @ SV316 ) ) @ SY3230 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV316 @ tc_bool ) ) @ SY3229 ) @ SY3230 ) )
| ~ ( hBOOL @ ( c_in @ SV740 @ SY3230 @ SV316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(2156,plain,
! [SV741: $i,SV317: $i] :
( ( ! [SY3231: $i,SY3232: $i] :
( ( hBOOL @ ( c_in @ SV317 @ SV741 @ SY3231 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY3231 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV317 @ SY3232 @ SY3231 ) ) @ SV741 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1727]) ).
thf(2157,plain,
! [SV742: $i,SV318: $i] :
( ( ! [SY3233: $i,SY3234: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV318 @ tc_bool ) ) @ SV742 ) @ ( c_Set_Oinsert @ SY3233 @ SY3234 @ SV318 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV318 @ tc_bool ) ) @ SV742 ) @ SY3234 ) )
| ( hBOOL @ ( c_in @ SY3233 @ SV742 @ SV318 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(2158,plain,
! [SV743: $i,SV319: $i] :
( ( ! [SY3235: $i,SY3236: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV319 @ tc_bool ) ) @ SV743 ) @ SY3235 ) )
| ( hBOOL @ ( c_in @ SY3236 @ SV743 @ SV319 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV319 @ tc_bool ) ) @ SV743 ) @ ( c_Set_Oinsert @ SY3236 @ SY3235 @ SV319 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1729]) ).
thf(2159,plain,
! [SV744: $i,SV320: $i] :
( ( ! [SY3237: $i,SY3238: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV320 @ tc_bool ) ) @ SV744 ) @ ( c_Set_Oinsert @ SY3237 @ SY3238 @ SV320 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV320 @ tc_bool ) ) @ SV744 ) @ SY3238 ) )
| ( hBOOL @ ( c_in @ SY3237 @ SV744 @ SV320 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1730]) ).
thf(2160,plain,
! [SV745: $i,SV321: $i] :
( ( ! [SY3239: $i,SY3240: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV321 @ tc_bool ) ) @ SV745 ) @ SY3239 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV321 @ tc_bool ) ) @ SV745 ) @ ( c_Set_Oinsert @ SY3240 @ SY3239 @ SV321 ) ) )
| ( hBOOL @ ( c_in @ SY3240 @ SV745 @ SV321 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(2161,plain,
! [SV746: $i,SV322: $i] :
( ( ! [SY3241: $i,SY3242: $i,SY3243: $i,SY3244: $i,SY3245: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV322 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV746 @ SY3241 @ SY3242 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY3243 @ SY3244 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV322 @ SV746 @ SY3242 @ SY3241 @ SY3245 @ SY3243 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3245 @ SY3244 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV322 @ SV746 @ SY3242 @ SY3241 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV322 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3245 @ SY3241 @ SY3243 @ 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_forall_pos,[status(thm)],[1732]) ).
thf(2162,plain,
! [SV747: $i,SV323: $i] :
( ( ! [SY3246: $i,SY3247: $i,SY3248: $i,SY3249: $i,SY3250: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV323 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV747 @ SY3246 @ SY3247 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY3248 @ SY3249 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV747 @ SY3250 @ SY3247 @ SY3248 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3250 @ SY3249 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV747 @ SY3250 @ SY3247 @ SY3248 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV323 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3250 @ SY3246 @ SY3248 @ 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_forall_pos,[status(thm)],[1733]) ).
thf(2163,plain,
! [SV748: $i,SV324: $i] :
( ( ! [SY3251: $i,SY3252: $i,SY3253: $i,SY3254: $i,SY3255: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV324 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV748 @ SY3251 @ SY3252 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY3253 @ SY3254 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV324 @ SV748 @ SY3252 @ SY3251 @ SY3255 @ SY3253 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3255 @ SY3254 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV324 @ SV748 @ SY3252 @ SY3251 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV324 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3255 @ SY3251 @ SY3253 @ 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_forall_pos,[status(thm)],[1734]) ).
thf(2164,plain,
! [SV749: $i,SV325: $i] :
( ( ! [SY3256: $i,SY3257: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV325 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV749 @ SY3256 @ SY3257 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV749 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV325 @ SV749 @ SY3257 @ SY3256 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV325 @ SV749 @ SY3257 @ SY3256 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1735]) ).
thf(2165,plain,
! [SV750: $i,SV326: $i] :
( ( ! [SY3258: $i,SY3259: $i,SY3260: $i,SY3261: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV326 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV750 @ SY3258 @ SY3259 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3259 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV326 @ SV750 @ SY3259 @ SY3258 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV326 @ SV750 @ SY3259 @ SY3258 @ SY3260 @ SY3261 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV326 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3260 @ SY3258 @ SY3261 @ 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_forall_pos,[status(thm)],[1736]) ).
thf(2166,plain,
! [SV751: $i,SV327: $i] :
( ( ! [SY3262: $i,SY3263: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV327 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV751 @ SY3262 @ SY3263 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV751 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV327 @ SV751 @ SY3263 @ SY3262 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV327 @ SV751 @ SY3263 @ SY3262 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(2167,plain,
! [SV752: $i,SV328: $i] :
( ( ! [SY3264: $i,SY3265: $i,SY3266: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV328 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV752 @ SY3264 @ SY3265 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY3266 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SY3265 @ SY3266 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SY3265 @ SY3266 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV328 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV752 @ SY3264 @ SY3266 @ 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_forall_pos,[status(thm)],[1738]) ).
thf(2168,plain,
! [SV753: $i,SV329: $i] :
( ( ! [SY3267: $i,SY3268: $i,SY3269: $i,SY3270: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV329 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV753 @ SY3267 @ SY3268 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV753 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV753 @ SY3269 @ SY3268 @ SY3270 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV753 @ SY3269 @ SY3268 @ SY3270 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV329 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3269 @ SY3267 @ SY3270 @ 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_forall_pos,[status(thm)],[1739]) ).
thf(2169,plain,
! [SV754: $i,SV330: $i] :
( ( ! [SY3271: $i,SY3272: $i,SY3273: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV330 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV754 @ SY3271 @ SY3272 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV754 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV754 @ SY3273 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV754 @ SY3273 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV330 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3273 @ SY3271 @ SY3272 @ 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_forall_pos,[status(thm)],[1740]) ).
thf(2170,plain,
! [SV755: $i,SV331: $i] :
( ( ! [SY3274: $i,SY3275: $i,SY3276: $i,SY3277: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV331 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV755 @ SY3274 @ SY3275 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3275 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV331 @ SV755 @ SY3275 @ SY3274 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV331 @ SV755 @ SY3275 @ SY3274 @ SY3276 @ SY3277 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV331 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3276 @ SY3274 @ SY3277 @ 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_forall_pos,[status(thm)],[1741]) ).
thf(2171,plain,
! [SV756: $i,SV332: $i] :
( ( ! [SY3278: $i,SY3279: $i,SY3280: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV332 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV756 @ SY3278 @ SY3279 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3280 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV756 @ SY3280 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV756 @ SY3280 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV332 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3280 @ SY3278 @ SY3279 @ 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_forall_pos,[status(thm)],[1742]) ).
thf(2172,plain,
! [SV757: $i,SV333: $i] :
( ( ! [SY3281: $i,SY3282: $i,SY3283: $i,SY3284: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV333 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV757 @ SY3281 @ SY3282 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3282 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV757 @ SY3283 @ SY3282 @ SY3284 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV757 @ SY3283 @ SY3282 @ SY3284 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV333 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3283 @ SY3281 @ SY3284 @ 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_forall_pos,[status(thm)],[1743]) ).
thf(2173,plain,
! [SV758: $i,SV334: $i] :
( ( ! [SY3285: $i,SY3286: $i,SY3287: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV334 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV758 @ SY3285 @ SY3286 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3286 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SY3286 @ SY3287 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SY3286 @ SY3287 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV334 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV758 @ SY3285 @ SY3287 @ 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_forall_pos,[status(thm)],[1744]) ).
thf(2174,plain,
! [SV759: $i,SV335: $i] :
( ( ! [SY3288: $i,SY3289: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV335 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV759 @ SY3288 @ SY3289 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV759 @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ SV335 @ SV759 @ SY3289 @ SY3288 ) ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ SV335 @ SV759 @ SY3289 @ SY3288 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(2175,plain,
! [SV760: $i,SV336: $i] :
( ( ! [SY3290: $i,SY3291: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV336 @ tc_bool ) ) @ SV760 ) @ ( c_Set_Oinsert @ SY3290 @ SY3291 @ SV336 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV336 @ tc_bool ) ) @ SV760 ) @ SY3291 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV336 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV760 @ ( c_Set_Oinsert @ SY3290 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV336 @ tc_bool ) ) @ SV336 ) @ ( tc_fun @ SV336 @ tc_bool ) ) ) @ SY3291 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(2176,plain,
! [SV761: $i,SV337: $i] :
( ( ! [SY3292: $i,SY3293: $i,SY3294: $i,SY3295: $i,SY3296: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV761 @ ( c_Com_Ocom_OSemi @ SY3292 @ SY3293 ) @ SY3294 @ SY3295 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3295 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3295 ) ) @ SY3295 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3296 @ SY3293 @ SY3294 @ SY3295 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3295 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3295 ) ) @ SY3295 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV761 @ SY3292 @ SY3296 @ SY3295 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3295 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3295 ) ) @ SY3295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(2177,plain,
! [SV762: $i,SV338: $i] :
( ( ! [SY3297: $i] :
( ~ ( class_Orderings_Olinorder @ SV338 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV338 ) @ SV762 ) @ SY3297 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV338 ) @ SY3297 ) @ SV762 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1748]) ).
thf(2178,plain,
! [SV763: $i,SV339: $i] :
( ( ! [SY3298: $i,SY3299: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV339 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV763 @ SY3298 @ SV339 ) ) @ ( c_Set_Oinsert @ SV763 @ SY3299 @ SV339 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV339 @ tc_bool ) ) @ SY3298 ) @ SY3299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1749]) ).
thf(2179,plain,
! [SV764: $i,SV340: $i] :
( ( ! [SY3300: $i,SY3301: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV340 @ ( c_Set_Oinsert @ SV764 @ SY3300 @ ( tc_Hoare__Mirabelle_Otriple @ SY3301 ) ) @ SY3301 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV340 @ SY3300 @ SY3301 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV340 @ ( c_Set_Oinsert @ SV764 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3301 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3301 ) ) @ SY3301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(2180,plain,
! [SV765: $i,SV341: $i] :
( ( ! [SY3302: $i] :
( ( SV341
= ( c_Set_Oinsert @ SV765 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3302 @ tc_bool ) ) @ SY3302 ) )
| ( SV341
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3302 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY3302 @ tc_bool ) ) @ SV341 ) @ ( c_Set_Oinsert @ SV765 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3302 @ tc_bool ) ) @ SY3302 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(2181,plain,
! [SV766: $i,SV342: $i] :
( ( ! [SY3303: $i,SY3304: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV342 @ SV766 @ SY3303 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3303 ) @ tc_bool ) ) @ SV766 ) @ SY3304 ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV342 @ SY3304 @ SY3303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(2182,plain,
! [SV767: $i,SV343: $i] :
( ( ! [SY3305: $i,SY3306: $i] :
( ( hBOOL @ ( hAPP @ SV343 @ SV767 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY3305 @ tc_bool ) ) @ SY3306 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP @ SY3306 @ SV767 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(2183,plain,
! [SV768: $i,SV344: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV344 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV344 ) @ SV768 ) @ SV768 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(2184,plain,
! [SV769: $i,SV345: $i] :
( ( ~ ( class_Orderings_Oorder @ SV345 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV345 ) @ SV769 ) @ SV769 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(2185,plain,
! [SV770: $i,SV346: $i] :
( ( ! [SY3307: $i,SY3308: $i] :
( ( hBOOL @ ( hAPP @ SV346 @ SV770 ) )
| ~ ( hBOOL @ ( hAPP @ SY3307 @ SV770 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY3308 @ tc_bool ) ) @ SY3307 ) @ SV346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1756]) ).
thf(2186,plain,
! [SV771: $i,SV347: $i] :
( ( ! [SY3309: $i,SY3310: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV347 @ tc_bool ) ) @ SV771 ) @ SY3309 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV347 @ tc_bool ) ) @ SY3310 ) @ SY3309 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV347 @ tc_bool ) ) @ SV771 ) @ SY3310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(2187,plain,
! [SV772: $i,SV348: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV348 @ tc_bool ) ) @ SV772 ) @ SV772 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(2188,plain,
! [SV773: $i,SV349: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV349 @ tc_bool ) ) @ SV773 ) @ SV773 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(2189,plain,
! [SV774: $i,SV350: $i] :
( ( ! [SY3311: $i,SY3312: $i] :
( ~ ( class_Orderings_Opreorder @ SV350 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV774 ) @ SY3311 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SY3312 ) @ SY3311 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV774 ) @ SY3312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1760]) ).
thf(2190,plain,
! [SV775: $i,SV351: $i] :
( ( ! [SY3313: $i,SY3314: $i] :
( ~ ( class_Orderings_Oorder @ SV351 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV775 ) @ SY3313 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV775 ) @ SY3314 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SY3314 ) @ SY3313 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(2191,plain,
! [SV776: $i,SV352: $i] :
( ( ! [SY3315: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV352 @ SV776 @ SY3315 ) @ SV352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(2192,plain,
! [SV777: $i,SV353: $i] :
( ( ! [SY3316: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV777 @ c_Com_Ocom_OSKIP @ SV777 @ SY3316 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3316 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3316 ) ) @ SY3316 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(2193,plain,
! [SV778: $i,SV354: $i] :
( ( ! [SY3317: $i,SY3318: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV354 @ SV778 @ SY3317 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV354 @ SY3318 @ SY3317 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY3318 @ SV778 @ SY3317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(2194,plain,
! [SV779: $i,SV356: $i] :
( ( ( SV356
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV779 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV779 @ tc_bool ) ) @ SV356 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV779 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(2195,plain,
! [SV780: $i,SV357: $i] :
( ( ! [SY3319: $i] :
( ~ ( class_Orderings_Oorder @ SV357 )
| ( SV780 = SY3319 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV357 ) @ SV780 ) @ SY3319 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV357 ) @ SY3319 ) @ SV780 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1767]) ).
thf(2196,plain,
! [SV781: $i,SV358: $i] :
( ( ! [SY3320: $i] :
( ~ ( class_Orderings_Oorder @ SV358 )
| ( SV781 = SY3320 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV358 ) @ SY3320 ) @ SV781 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV358 ) @ SV781 ) @ SY3320 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(2197,plain,
! [SV782: $i,SV359: $i] :
( ( ! [SY3321: $i] :
( ~ ( class_Orderings_Oorder @ SV359 )
| ( SV782 = SY3321 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV359 ) @ SY3321 ) @ SV782 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV359 ) @ SV782 ) @ SY3321 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(2198,plain,
! [SV783: $i,SV360: $i] :
( ( ! [SY3322: $i] :
( ( SV360 = SV783 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY3322 @ tc_bool ) ) @ SV783 ) @ SV360 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY3322 @ tc_bool ) ) @ SV360 ) @ SV783 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(2199,plain,
! [SV784: $i,SV361: $i] :
( ( ! [SY3323: $i] :
( ( SV361 = SV784 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY3323 @ tc_bool ) ) @ SV784 ) @ SV361 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY3323 @ tc_bool ) ) @ SV361 ) @ SV784 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1771]) ).
thf(2200,plain,
! [SV785: $i,SV362: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV362 @ tc_bool ) ) @ SV785 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(2201,plain,
! [SV786: $i,SV363: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV363 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV786 ) @ tc_bool ) ) @ SV786 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(2202,plain,
! [SV787: $i,SV364: $i] :
( ( ! [SY3324: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV364 @ tc_bool ) ) @ SV787 ) @ ( c_Set_Oinsert @ SY3324 @ SV787 @ SV364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(2203,plain,
! [SV788: $i,SV365: $i] :
( ( ! [SY3325: $i,SY3326: $i] :
( ( hBOOL @ ( hAPP @ SV365 @ SV788 ) )
| ( SY3325 = SV788 )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3325 @ SV365 @ SY3326 ) @ SV788 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(2204,plain,
! [SV789: $i,SV366: $i] :
( ( ! [SY3327: $i] :
( ( c_Set_Oinsert @ SV366 @ ( c_Set_Oinsert @ SV366 @ SV789 @ SY3327 ) @ SY3327 )
= ( c_Set_Oinsert @ SV366 @ SV789 @ SY3327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(2205,plain,
! [SV790: $i,SV367: $i] :
( ( ~ ( class_Orderings_Obot @ SV367 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV367 ) @ ( c_Orderings_Obot__class_Obot @ SV367 ) ) @ SV790 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1777]) ).
thf(2206,plain,
! [SV791: $i,SV368: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV368 @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV368 @ tc_bool ) ) ) @ SV791 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(2207,plain,
! [SV792: $i,SV369: $i] :
( ( ! [SY3328: $i,SY3329: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV369 @ tc_bool ) ) @ SV792 ) @ ( c_Set_Oinsert @ SY3328 @ SY3329 @ SV369 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV369 @ tc_bool ) ) @ SV792 ) @ SY3329 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(2208,plain,
! [SV793: $i,SV370: $i] :
( ( ! [SY3330: $i,SY3331: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV370 @ tc_bool ) ) @ SV793 ) @ SY3330 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV370 @ tc_bool ) ) @ ( c_Set_Oinsert @ SY3331 @ SV793 @ SV370 ) ) @ SY3330 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(2209,plain,
! [SV794: $i,SV371: $i] :
( ( ! [SY3332: $i,SY3333: $i] :
( ( c_Set_Oinsert @ SV371 @ ( c_Set_Oinsert @ SV794 @ SY3332 @ SY3333 ) @ SY3333 )
= ( c_Set_Oinsert @ SV794 @ ( c_Set_Oinsert @ SV371 @ SY3332 @ SY3333 ) @ SY3333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1781]) ).
thf(2210,plain,
! [SV795: $i,SV372: $i] :
( ( ! [SY3334: $i] :
( ( c_Set_Oinsert @ SV372 @ ( c_Set_Oinsert @ SV795 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3334 @ tc_bool ) ) @ SY3334 ) @ SY3334 )
= ( c_Set_Oinsert @ SV795 @ ( c_Set_Oinsert @ SV372 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3334 @ tc_bool ) ) @ SY3334 ) @ SY3334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(2211,plain,
! [SV796: $i,SV373: $i] :
( ( ! [SY3335: $i,SY3336: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV373 @ SV796 @ SY3335 ) @ SY3336 ) )
| ~ ( hBOOL @ ( hAPP @ SV796 @ SY3336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(2212,plain,
! [SV797: $i,SV374: $i] :
( ( ! [SY3337: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV374 @ SV797 @ SY3337 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3337 ) @ tc_bool ) ) @ SV797 ) @ SV374 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(2213,plain,
! [SV798: $i,SV375: $i] :
( ( ! [SY3338: $i,SY3339: $i,SY3340: $i] :
( ~ ( class_HOL_Oord @ SV375 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV375 ) @ ( hAPP @ SV798 @ SY3338 ) ) @ ( hAPP @ SY3339 @ SY3338 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY3340 @ SV375 ) ) @ SV798 ) @ SY3339 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(2214,plain,
! [SV799: $i,SV376: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV376 @ SV799 ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV799 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(2215,plain,
! [SV800: $i,SV377: $i] :
( ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV377 @ SV800 ) )
| ~ ( class_Lattices_Olattice @ SV800 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(2216,plain,
! [SV801: $i,SV378: $i] :
( ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV378 @ SV801 ) )
| ~ ( class_Lattices_Obounded__lattice @ SV801 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1788]) ).
thf(2217,plain,
! [SV802: $i,SV379: $i] :
( ( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ SV379 @ SV802 ) )
| ~ ( class_Lattices_Oboolean__algebra @ SV802 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(2218,plain,
! [SV803: $i,SV380: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ SV380 @ SV803 ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SV803 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SV380 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1790]) ).
thf(2219,plain,
! [SV804: $i,SV381: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV381 @ SV804 ) )
| ~ ( class_Orderings_Opreorder @ SV804 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1791]) ).
thf(2220,plain,
! [SV805: $i,SV382: $i] :
( ( ( class_Lattices_Olattice @ ( tc_fun @ SV382 @ SV805 ) )
| ~ ( class_Lattices_Olattice @ SV805 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(2221,plain,
! [SV806: $i,SV383: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV383 @ SV806 ) )
| ~ ( class_Orderings_Oorder @ SV806 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(2222,plain,
! [SV807: $i,SV384: $i] :
( ( ( class_Orderings_Obot @ ( tc_fun @ SV384 @ SV807 ) )
| ~ ( class_Orderings_Obot @ SV807 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(2223,plain,
! [SV808: $i,SV385: $i] :
( ( ( class_HOL_Ouminus @ ( tc_fun @ SV385 @ SV808 ) )
| ~ ( class_HOL_Ouminus @ SV808 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(2224,plain,
! [SV809: $i,SV386: $i] :
( ( ( class_HOL_Ominus @ ( tc_fun @ SV386 @ SV809 ) )
| ~ ( class_HOL_Ominus @ SV809 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(2225,plain,
! [SV810: $i,SV387: $i] :
( ( ( class_HOL_Oord @ ( tc_fun @ SV387 @ SV810 ) )
| ~ ( class_HOL_Oord @ SV810 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(2226,plain,
! [SV811: $i,SV388: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV388 ) @ SV811 ) @ SV811 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(2227,plain,
! [SV812: $i,SV389: $i] :
( ( ! [SY3341: $i] :
( ( SV389 = SV812 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY3341 ) @ SV389 ) @ SV812 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(2228,plain,
! [SV813: $i,SV390: $i] :
( ( ! [SY3342: $i] :
( ( ( c_Set_Oinsert @ SV390 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV813 @ tc_bool ) ) @ SV813 )
!= ( c_Set_Oinsert @ SY3342 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV813 @ tc_bool ) ) @ SV813 ) )
| ( SV390 = SY3342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(2229,plain,
! [SV814: $i,SV391: $i] :
( ( ! [SY3343: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV391 )
| ( ( c_HOL_Ouminus__class_Ouminus @ SV814 @ SV391 )
!= ( c_HOL_Ouminus__class_Ouminus @ SY3343 @ SV391 ) )
| ( SV814 = SY3343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2230,plain,
! [SV815: $i,SV392: $i] :
( ( ! [SY3344: $i,SY3345: $i] :
( ( ( c_Set_Oinsert @ SV392 @ SV815 @ SY3344 )
!= ( c_Set_Oinsert @ SV392 @ SY3345 @ SY3344 ) )
| ( hBOOL @ ( c_in @ SV392 @ SY3345 @ SY3344 ) )
| ( hBOOL @ ( c_in @ SV392 @ SV815 @ SY3344 ) )
| ( SV815 = SY3345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1803]) ).
thf(2231,plain,
! [SV816: $i,SV393: $i] :
( ( ! [SY3346: $i] :
( ( ( c_Collect @ SV393 @ SV816 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV816 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ SV393 @ SY3346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(2232,plain,
! [SV817: $i,SV394: $i] :
( ( ! [SY3347: $i,SY3348: $i] :
( ( ( c_Com_Ocom_OSemi @ SV394 @ SV817 )
!= ( c_Com_Ocom_OSemi @ SY3347 @ SY3348 ) )
| ( SV817 = SY3348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(2233,plain,
! [SV818: $i,SV395: $i] :
( ( ! [SY3349: $i,SY3350: $i,SY3351: $i,SY3352: $i,SY3353: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV395 @ SV818 @ SY3349 @ SY3350 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3351 @ SY3352 @ SY3353 @ SY3350 ) )
| ( SV395 = SY3351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1806]) ).
thf(2234,plain,
! [SV819: $i,SV396: $i] :
( ( ! [SY3354: $i] :
( ( c_Set_Oinsert @ SV396 @ SV819 @ SY3354 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3354 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1807]) ).
thf(2235,plain,
! [SV820: $i,SV397: $i] :
( ( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ SV397 @ SV820 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(2236,plain,
! [SV821: $i,SV398: $i] :
( ( ! [SY3355: $i] :
( ~ ( class_Orderings_Oorder @ SV398 )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV398 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV821 @ SY3355 @ SV398 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV821 @ SY3355 @ SV398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(2237,plain,
! [SV822: $i,SV399: $i] :
( ( ! [SY3356: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV399 @ tc_bool ) )
!= ( c_Set_Oinsert @ SV822 @ SY3356 @ SV399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2238,plain,
! [SV823: $i,SV400: $i] :
( ( ! [SY3357: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SV400 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV823 @ SY3357 @ SV400 )
!= ( c_Orderings_Obot__class_Obot @ SV400 ) )
| ( SV823
= ( c_Orderings_Obot__class_Obot @ SV400 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(2239,plain,
! [SV824: $i,SV401: $i] :
( ( ! [SY3358: $i,SY3359: $i,SY3360: $i] :
( ( ( c_Set_Oinsert @ SV401 @ ( c_Set_Oinsert @ SV824 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3358 @ tc_bool ) ) @ SY3358 ) @ SY3358 )
!= ( c_Set_Oinsert @ SY3359 @ ( c_Set_Oinsert @ SY3360 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3358 @ tc_bool ) ) @ SY3358 ) @ SY3358 ) )
| ( SV824 = SY3359 )
| ( SV401 = SY3359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(2240,plain,
! [SV825: $i,SV402: $i] :
( ( ! [SY3361: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV402 @ SV825 @ ( tc_fun @ SY3361 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3361 @ tc_bool ) ) )
| ( SV825
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3361 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(2241,plain,
! [SV826: $i,SV403: $i] :
( ( ! [SY3362: $i,SY3363: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV403 )
| ( ( c_HOL_Ominus__class_Ominus @ SV826 @ SV826 @ SV403 )
!= ( c_HOL_Ominus__class_Ominus @ SY3362 @ SY3363 @ SV403 ) )
| ( SY3362 = SY3363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1814]) ).
thf(2242,plain,
! [SV827: $i,SV404: $i] :
( ( ! [SY3364: $i] :
( ~ ( class_Orderings_Oorder @ SV404 )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV404 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV827 @ SY3364 @ SV404 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV404 ) @ SV827 ) @ SY3364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1815]) ).
thf(2243,plain,
! [SV828: $i,SV405: $i] :
( ( ! [SY3365: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV405 @ SV828 @ ( tc_fun @ SY3365 @ tc_bool ) )
!= SV828 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY3365 @ tc_bool ) ) @ SV405 ) @ SV828 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1816]) ).
thf(2244,plain,
! [SV829: $i,SV406: $i] :
( ( ! [SY3366: $i] :
( ~ ( class_Orderings_Oorder @ SV406 )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV829 @ SY3366 @ SV406 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV406 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV406 ) @ SV829 ) @ SY3366 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1817]) ).
thf(2245,plain,
! [SV830: $i,SV407: $i] :
( ( ! [SY3367: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV407 @ SV830 @ ( tc_fun @ SY3367 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3367 @ tc_bool ) ) )
| ( SV407
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3367 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1818]) ).
thf(2246,plain,
! [SV831: $i,SV408: $i] :
( ( ( c_Com_Ocom_OSemi @ SV408 @ SV831 )
!= c_Com_Ocom_OSKIP )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(2247,plain,
! [SV832: $i,SV409: $i] :
( ( ! [SY3368: $i,SY3369: $i,SY3370: $i] :
( ( ( c_Set_Oinsert @ SV409 @ ( c_Set_Oinsert @ SV832 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3368 @ tc_bool ) ) @ SY3368 ) @ SY3368 )
!= ( c_Set_Oinsert @ SY3369 @ ( c_Set_Oinsert @ SY3370 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3368 @ tc_bool ) ) @ SY3368 ) @ SY3368 ) )
| ( SV409 = SY3370 )
| ( SV832 = SY3370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1820]) ).
thf(2248,plain,
! [SV833: $i,SV410: $i] :
( ( ! [SY3371: $i,SY3372: $i,SY3373: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV410 @ SV833 @ SY3371 @ ( tc_fun @ SY3372 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3372 @ tc_bool ) ) )
| ( ( hAPP @ SV833 @ SY3373 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3372 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SY3373 @ SV410 @ SY3371 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1821]) ).
thf(2249,plain,
! [SV834: $i,SV411: $i] :
( ( ! [SY3374: $i,SY3375: $i,SY3376: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV411 )
| ( ( c_HOL_Ominus__class_Ominus @ SV834 @ SY3374 @ SV411 )
!= ( c_HOL_Ominus__class_Ominus @ SY3375 @ SY3376 @ SV411 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV411 ) @ SY3376 ) @ SY3375 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV411 ) @ SY3374 ) @ SV834 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1822]) ).
thf(2250,plain,
! [SV835: $i,SV412: $i] :
( ( ! [SY3377: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ SV412 )
| ( ( c_HOL_Ouminus__class_Ouminus @ SV835 @ SV412 )
!= ( c_HOL_Ouminus__class_Ouminus @ SY3377 @ SV412 ) )
| ( SV835 = SY3377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1823]) ).
thf(2251,plain,
! [SV836: $i,SV413: $i] :
( ( ! [SY3378: $i,SY3379: $i,SY3380: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV413 @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV836 @ SY3378 @ SY3379 @ ( tc_fun @ SV413 @ tc_bool ) ) )
| ( ( hAPP @ SY3378 @ SY3380 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV413 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SY3380 @ SV836 @ SY3379 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(2252,plain,
! [SV837: $i,SV414: $i] :
( ( ! [SY3381: $i] :
( ~ ( class_Orderings_Oorder @ SV414 )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ SV837 @ SY3381 @ SV414 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV414 @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV837 @ SY3381 @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(2253,plain,
! [SV838: $i,SV415: $i] :
( ( ! [SY3382: $i,SY3383: $i,SY3384: $i] :
( ( ( c_Set_Oinsert @ SV415 @ ( c_Set_Oinsert @ SV838 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3382 @ tc_bool ) ) @ SY3382 ) @ SY3382 )
!= ( c_Set_Oinsert @ SY3383 @ ( c_Set_Oinsert @ SY3384 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3382 @ tc_bool ) ) @ SY3382 ) @ SY3382 ) )
| ( SV838 = SY3383 )
| ( SV838 = SY3384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2254,plain,
! [SV839: $i,SV416: $i] :
( ( ! [SY3385: $i] :
( ~ ( class_Orderings_Oorder @ SV416 )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV416 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV839 @ SY3385 @ SV416 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV839 @ SY3385 @ SV416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(2255,plain,
! [SV840: $i,SV417: $i] :
( ( ! [SY3386: $i] :
( ( ( c_HOL_Ouminus__class_Ouminus @ SV417 @ ( tc_fun @ SV840 @ tc_bool ) )
!= ( c_HOL_Ouminus__class_Ouminus @ SY3386 @ ( tc_fun @ SV840 @ tc_bool ) ) )
| ( SV417 = SY3386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(2256,plain,
! [SV841: $i,SV418: $i] :
( ( ! [SY3387: $i,SY3388: $i,SY3389: $i,SY3390: $i,SY3391: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV418 @ SV841 @ SY3387 @ SY3388 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3389 @ SY3390 @ SY3391 @ SY3388 ) )
| ( SY3387 = SY3391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(2257,plain,
! [SV842: $i,SV419: $i] :
( ( ! [SY3392: $i,SY3393: $i,SY3394: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV419 )
| ( ( c_HOL_Ominus__class_Ominus @ SV842 @ SY3392 @ SV419 )
!= ( c_HOL_Ominus__class_Ominus @ SY3393 @ SY3394 @ SV419 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV419 ) @ SY3392 ) @ SV842 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV419 ) @ SY3394 ) @ SY3393 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(2258,plain,
! [SV843: $i,SV420: $i] :
( ( ! [SY3395: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV420 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV843 @ SY3395 @ SV420 )
!= SY3395 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV420 ) @ SV843 ) @ SY3395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(2259,plain,
! [SV844: $i,SV421: $i] :
( ( ! [SY3396: $i,SY3397: $i,SY3398: $i,SY3399: $i,SY3400: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV421 @ SV844 @ SY3396 @ SY3397 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3398 @ SY3399 @ SY3400 @ SY3397 ) )
| ( SV844 = SY3399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(2260,plain,
! [SV845: $i,SV422: $i] :
( ( ! [SY3401: $i,SY3402: $i] :
( ( ( c_Com_Ocom_OSemi @ SV422 @ SV845 )
!= ( c_Com_Ocom_OSemi @ SY3401 @ SY3402 ) )
| ( SV422 = SY3401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1833]) ).
thf(2261,plain,
! [SV846: $i,SV423: $i] :
( ( ! [SY3403: $i,SY3404: $i,SY3405: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV423 )
| ( ( c_HOL_Ominus__class_Ominus @ SV846 @ SY3403 @ SV423 )
!= ( c_HOL_Ominus__class_Ominus @ SY3404 @ SY3405 @ SV423 ) )
| ( c_HOL_Oord__class_Oless @ SY3404 @ SY3405 @ SV423 )
| ~ ( c_HOL_Oord__class_Oless @ SV846 @ SY3403 @ SV423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1834]) ).
thf(2262,plain,
! [SV847: $i,SV424: $i] :
( ( ! [SY3406: $i] :
( ~ ( class_Orderings_Oorder @ SV424 )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV847 @ SY3406 @ SV424 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV424 @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV847 @ SY3406 @ SV424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(2263,plain,
! [SV848: $i,SV425: $i] :
( ( ! [SY3407: $i] :
( ( ( c_Set_Oinsert @ SV425 @ SV848 @ SY3407 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3407 @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ SV425 @ SV848 @ SY3407 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1836]) ).
thf(2264,plain,
! [SV849: $i,SV426: $i] :
( ( ! [SY3408: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV426 @ tc_bool ) )
!= ( c_Collect @ SV849 @ SV426 ) )
| ~ ( hBOOL @ ( hAPP @ SV849 @ SY3408 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(2265,plain,
! [SV850: $i,SV427: $i] :
( ( ! [SY3409: $i,SY3410: $i,SY3411: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV427 )
| ( ( c_HOL_Ominus__class_Ominus @ SV850 @ SY3409 @ SV427 )
!= ( c_HOL_Ominus__class_Ominus @ SY3410 @ SY3411 @ SV427 ) )
| ( c_HOL_Oord__class_Oless @ SV850 @ SY3409 @ SV427 )
| ~ ( c_HOL_Oord__class_Oless @ SY3410 @ SY3411 @ SV427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(2266,plain,
! [SV851: $i,SV428: $i] :
( ( ! [SY3412: $i,SY3413: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV428 )
| ( ( c_HOL_Ominus__class_Ominus @ SV851 @ SY3412 @ SV428 )
!= ( c_HOL_Ominus__class_Ominus @ SY3413 @ SY3413 @ SV428 ) )
| ( SV851 = SY3412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(2267,plain,
! [SV852: $i,SV429: $i] :
( ( ! [SY3414: $i] :
( ~ ( class_Lattices_Obounded__lattice @ SV429 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV852 @ SY3414 @ SV429 )
!= ( c_Orderings_Obot__class_Obot @ SV429 ) )
| ( SY3414
= ( c_Orderings_Obot__class_Obot @ SV429 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(2268,plain,
! [SV853: $i,SV430: $i] :
( ( ! [SY3415: $i,SY3416: $i,SY3417: $i] :
( ( ( c_Set_Oinsert @ SV430 @ ( c_Set_Oinsert @ SV853 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3415 @ tc_bool ) ) @ SY3415 ) @ SY3415 )
!= ( c_Set_Oinsert @ SY3416 @ ( c_Set_Oinsert @ SY3417 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3415 @ tc_bool ) ) @ SY3415 ) @ SY3415 ) )
| ( SV430 = SY3417 )
| ( SV430 = SY3416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(2269,plain,
! [SV854: $i,SV431: $i,SV1: $i] :
( ( ! [SY3418: $i] :
( ~ ( class_HOL_Oord @ SV1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV431 @ SV1 ) ) @ SV854 ) @ SY3418 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV854 @ SY3418 @ ( tc_fun @ SV431 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(2270,plain,
! [SV855: $i,SV432: $i,SV2: $i] :
( ( ! [SY3419: $i] :
( ~ ( class_HOL_Oord @ SV2 )
| ( c_HOL_Oord__class_Oless @ SV432 @ SV855 @ ( tc_fun @ SY3419 @ SV2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY3419 @ SV2 ) ) @ SV855 ) @ SV432 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY3419 @ SV2 ) ) @ SV432 ) @ SV855 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1843]) ).
thf(2271,plain,
! [SV856: $i,SV433: $i,SV3: $i] :
( ( ! [SY3420: $i] :
( ~ ( class_HOL_Oord @ SV3 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV433 @ SV3 ) ) @ SV856 ) @ SY3420 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3420 @ SV856 @ ( tc_fun @ SV433 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(2272,plain,
! [SV857: $i,SV434: $i,SV4: $i] :
( ( ( SV4 = SV434 )
| ( c_HOL_Oord__class_Oless @ SV4 @ SV434 @ ( tc_fun @ SV857 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV857 @ tc_bool ) ) @ SV4 ) @ SV434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(2273,plain,
! [SV858: $i,SV435: $i,SV5: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV5 @ SV435 @ ( tc_fun @ SV858 @ tc_bool ) )
| ( SV5 = SV435 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV858 @ tc_bool ) ) @ SV5 ) @ SV435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(2274,plain,
! [SV859: $i,SV436: $i,SV6: $i] :
( ( ( c_Finite__Set_Ofinite @ SV6 @ SV436 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV436 @ tc_bool ) ) @ SV6 ) @ SV859 ) )
| ~ ( c_Finite__Set_Ofinite @ SV859 @ SV436 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(2275,plain,
! [SV860: $i,SV437: $i,SV7: $i] :
( ( ! [SY3421: $i] :
( ( c_HOL_Oord__class_Oless @ SV7 @ SV437 @ ( tc_fun @ SV860 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3421 @ SV437 @ ( tc_fun @ SV860 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV860 @ tc_bool ) ) @ SV7 ) @ SY3421 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(2276,plain,
! [SV861: $i,SV438: $i,SV8: $i] :
( ( ! [SY3422: $i] :
( ( c_HOL_Oord__class_Oless @ SV8 @ SV438 @ ( tc_fun @ SV861 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV861 @ tc_bool ) ) @ SY3422 ) @ SV438 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV8 @ SY3422 @ ( tc_fun @ SV861 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(2277,plain,
! [SV862: $i,SV439: $i,SV9: $i] :
( ( ( c_Finite__Set_Ofinite @ SV9 @ SV439 )
| ~ ( c_Finite__Set_Ofinite @ SV862 @ SV439 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV439 @ tc_bool ) ) @ SV9 ) @ SV862 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(2278,plain,
! [SV863: $i,SV440: $i,SV10: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV10 @ tc_bool ) ) @ SV440 ) @ SV863 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV440 @ SV863 @ ( tc_fun @ SV10 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(2279,plain,
! [SV864: $i,SV441: $i,SV11: $i] :
( ( ! [SY3423: $i,SY3424: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV11 )
| ( ( c_Finite__Set_Osetsum @ SV441 @ ( c_HOL_Ominus__class_Ominus @ SV864 @ ( c_Set_Oinsert @ SY3423 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3424 @ tc_bool ) ) @ SY3424 ) @ ( tc_fun @ SY3424 @ tc_bool ) ) @ SY3424 @ SV11 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV441 @ SV864 @ SY3424 @ SV11 ) @ ( hAPP @ SV441 @ SY3423 ) @ SV11 ) )
| ~ ( hBOOL @ ( c_in @ SY3423 @ SV864 @ SY3424 ) )
| ~ ( c_Finite__Set_Ofinite @ SV864 @ SY3424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(2280,plain,
! [SV865: $i,SV442: $i,SV12: $i] :
( ( ! [SY3425: $i,SY3426: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV12 )
| ( ( c_Finite__Set_Osetsum @ SV442 @ ( c_HOL_Ominus__class_Ominus @ SV865 @ ( c_Set_Oinsert @ SY3425 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3426 @ tc_bool ) ) @ SY3426 ) @ ( tc_fun @ SY3426 @ tc_bool ) ) @ SY3426 @ SV12 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV442 @ SV865 @ SY3426 @ SV12 ) @ ( hAPP @ SV442 @ SY3425 ) @ SV12 ) )
| ~ ( hBOOL @ ( c_in @ SY3425 @ SV865 @ SY3426 ) )
| ~ ( c_Finite__Set_Ofinite @ SV865 @ SY3426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(2281,plain,
! [SV866: $i,SV443: $i,SV13: $i] :
( ( ! [SY3427: $i] :
( ( c_HOL_Oord__class_Oless @ SV13 @ ( c_Set_Oinsert @ SV443 @ SV866 @ SY3427 ) @ ( tc_fun @ SY3427 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY3427 @ tc_bool ) ) @ SV13 ) @ SV866 ) )
| ( hBOOL @ ( c_in @ SV443 @ SV13 @ SY3427 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV13 @ SV866 @ ( tc_fun @ SY3427 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2282,plain,
! [SV867: $i,SV444: $i,SV14: $i] :
( ( ! [SY3428: $i] :
( ( c_HOL_Oord__class_Oless @ SV14 @ ( c_Set_Oinsert @ SV444 @ SV867 @ SY3428 ) @ ( tc_fun @ SY3428 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY3428 @ tc_bool ) ) @ SV14 ) @ SV867 ) )
| ( hBOOL @ ( c_in @ SV444 @ SV14 @ SY3428 ) )
| ( hBOOL @ ( c_in @ SV444 @ SV867 @ SY3428 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(2283,plain,
! [SV868: $i,SV445: $i,SV15: $i] :
( ( ! [SY3429: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV15 @ tc_bool ) ) @ SV445 ) @ SV868 ) )
| ( hBOOL @ ( c_in @ SY3429 @ SV445 @ SV15 ) )
| ( hBOOL @ ( c_in @ SY3429 @ SV868 @ SV15 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV445 @ ( c_Set_Oinsert @ SY3429 @ SV868 @ SV15 ) @ ( tc_fun @ SV15 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2284,plain,
! [SV869: $i,SV446: $i,SV16: $i] :
( ( ! [SY3430: $i] :
( ~ ( class_Orderings_Olinorder @ SV16 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV446 @ SV869 @ SV16 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV869 @ SY3430 @ SV16 ) @ ( tc_fun @ SV16 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV446 @ SY3430 @ SV16 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV16 ) @ SV869 ) @ SY3430 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV16 ) @ SV446 ) @ SV869 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(2285,plain,
! [SV870: $i,SV448: $i,SV18: $i] :
( ( ( c_Set_Oinsert @ SV18 @ SV448 @ SV870 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ SV870 ) @ SV870 @ SV870 @ tc_bool ) @ SV18 ) @ SV870 ) @ SV448 @ ( tc_fun @ SV870 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(2286,plain,
! [SV871: $i,SV449: $i,SV19: $i] :
( ( ( c_Finite__Set_Ofinite @ SV19 @ SV449 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV871 @ SV19 @ SV449 ) @ SV449 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(2287,plain,
! [SV872: $i,SV450: $i,SV20: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV20 @ SV450 @ SV872 ) @ SV872 )
| ~ ( c_Finite__Set_Ofinite @ SV450 @ SV872 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(2288,plain,
! [SV873: $i,SV451: $i,SV21: $i] :
( ( ! [SY3431: $i] : ( c_Nitpick_Ofold__graph_H @ SV21 @ SV451 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV873 @ tc_bool ) ) @ SV451 @ SV873 @ SY3431 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(2289,plain,
! [SV874: $i,SV452: $i,SV22: $i] :
( ( ! [SY3432: $i] : ( c_Finite__Set_Ofold__graph @ SV22 @ SV452 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV874 @ tc_bool ) ) @ SV452 @ SV874 @ SY3432 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(2290,plain,
! [SV875: $i,SV453: $i,SV23: $i] :
( ( ! [SY3433: $i,SY3434: $i] :
( ( SV23 = SV453 )
| ~ ( c_Finite__Set_Ofold__graph @ SV875 @ SV453 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3433 @ tc_bool ) ) @ SV23 @ SY3433 @ SY3434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2291,plain,
! [SV454: $i,SV25: $i] :
( ( c_HOL_Oord__class_Oless @ SV25 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV454 @ tc_bool ) ) @ ( tc_fun @ SV454 @ tc_bool ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1865]) ).
thf(2292,plain,
! [SV876: $i,SV455: $i,SV26: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV26 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV26 ) @ SV455 ) @ SV876 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV876 @ SV455 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(2293,plain,
! [SV877: $i,SV456: $i,SV27: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV27 )
| ( c_HOL_Oord__class_Oless @ SV456 @ SV877 @ SV27 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV27 ) @ SV877 ) @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1867]) ).
thf(2294,plain,
! [SV878: $i,SV457: $i,SV28: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV28 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV28 ) @ SV457 ) @ SV878 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV878 @ SV457 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(2295,plain,
! [SV879: $i,SV458: $i,SV29: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV29 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV29 ) @ SV458 ) @ SV879 ) )
| ( c_HOL_Oord__class_Oless @ SV879 @ SV458 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1869]) ).
thf(2296,plain,
! [SV880: $i,SV459: $i,SV30: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV30 )
| ~ ( c_HOL_Oord__class_Oless @ SV459 @ SV880 @ SV30 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV30 ) @ SV880 ) @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1870]) ).
thf(2297,plain,
! [SV460: $i,SV31: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV31 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV460 @ SV460 @ SV31 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV31 ) @ SV460 ) @ SV460 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1871]) ).
thf(2298,plain,
! [SV461: $i,SV32: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV32 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV32 ) @ SV461 ) @ SV461 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV461 @ SV461 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1872]) ).
thf(2299,plain,
! [SV881: $i,SV462: $i,SV33: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV33 )
| ( c_HOL_Oord__class_Oless @ SV462 @ SV881 @ SV33 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV33 ) @ SV881 ) @ SV462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(2300,plain,
! [SV882: $i,SV463: $i,SV34: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV34 )
| ( c_HOL_Oord__class_Oless @ SV463 @ SV882 @ SV34 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV34 ) @ SV882 ) @ SV463 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV34 ) @ SV463 ) @ SV882 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(2301,plain,
! [SV883: $i,SV464: $i,SV35: $i] :
( ( ~ ( class_Orderings_Oorder @ SV35 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV35 ) @ SV464 ) @ SV883 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV464 @ SV883 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(2302,plain,
! [SV884: $i,SV465: $i,SV36: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV36 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV36 ) @ SV465 ) @ SV884 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV465 @ SV884 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1876]) ).
thf(2303,plain,
! [SV885: $i,SV466: $i,SV37: $i] :
( ( ! [SY3435: $i] :
( ~ ( class_Orderings_Oorder @ SV37 )
| ( c_HOL_Oord__class_Oless @ SV466 @ SV885 @ SV37 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV37 ) @ SV466 ) @ SY3435 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3435 @ SV885 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(2304,plain,
! [SV886: $i,SV467: $i,SV38: $i] :
( ( ! [SY3436: $i] :
( ~ ( class_Orderings_Oorder @ SV38 )
| ( c_HOL_Oord__class_Oless @ SV467 @ SV886 @ SV38 )
| ~ ( c_HOL_Oord__class_Oless @ SV467 @ SY3436 @ SV38 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV38 ) @ SY3436 ) @ SV886 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(2305,plain,
! [SV887: $i,SV468: $i,SV39: $i] :
( ( ! [SY3437: $i] :
( ~ ( class_Orderings_Opreorder @ SV39 )
| ( c_HOL_Oord__class_Oless @ SV468 @ SV887 @ SV39 )
| ~ ( c_HOL_Oord__class_Oless @ SY3437 @ SV887 @ SV39 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV39 ) @ SV468 ) @ SY3437 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(2306,plain,
! [SV888: $i,SV469: $i,SV40: $i] :
( ( ! [SY3438: $i] :
( ~ ( class_Orderings_Opreorder @ SV40 )
| ( c_HOL_Oord__class_Oless @ SV469 @ SV888 @ SV40 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV40 ) @ SY3438 ) @ SV888 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV469 @ SY3438 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(2307,plain,
! [SV889: $i,SV470: $i,SV41: $i] :
( ( ~ ( class_Orderings_Oorder @ SV41 )
| ( c_HOL_Oord__class_Oless @ SV470 @ SV889 @ SV41 )
| ( SV889 = SV470 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV41 ) @ SV470 ) @ SV889 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2308,plain,
! [SV890: $i,SV471: $i,SV42: $i] :
( ( ~ ( class_Orderings_Oorder @ SV42 )
| ( c_HOL_Oord__class_Oless @ SV471 @ SV890 @ SV42 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV42 ) @ SV471 ) @ SV890 ) )
| ( SV890 = SV471 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2309,plain,
! [SV891: $i,SV472: $i,SV43: $i] :
( ( ~ ( class_Orderings_Oorder @ SV43 )
| ( SV472 = SV891 )
| ( c_HOL_Oord__class_Oless @ SV472 @ SV891 @ SV43 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV43 ) @ SV472 ) @ SV891 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2310,plain,
! [SV892: $i,SV473: $i,SV44: $i] :
( ( ~ ( class_Orderings_Oorder @ SV44 )
| ( c_HOL_Oord__class_Oless @ SV473 @ SV892 @ SV44 )
| ( SV473 = SV892 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV44 ) @ SV473 ) @ SV892 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2311,plain,
! [SV893: $i,SV474: $i,SV45: $i] :
( ( ~ ( class_Orderings_Oorder @ SV45 )
| ( c_HOL_Oord__class_Oless @ SV474 @ SV893 @ SV45 )
| ( SV474 = SV893 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV45 ) @ SV474 ) @ SV893 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2312,plain,
! [SV894: $i,SV475: $i,SV46: $i] :
( ( ~ ( class_Orderings_Oorder @ SV46 )
| ( c_HOL_Oord__class_Oless @ SV475 @ SV894 @ SV46 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV46 ) @ SV475 ) @ SV894 ) )
| ( SV475 = SV894 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2313,plain,
! [SV895: $i,SV476: $i,SV47: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV47 )
| ( SV476 = SV895 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV47 ) @ SV476 ) @ SV895 ) )
| ( c_HOL_Oord__class_Oless @ SV476 @ SV895 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(2314,plain,
! [SV896: $i,SV477: $i,SV48: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV48 )
| ( SV477 = SV896 )
| ( c_HOL_Oord__class_Oless @ SV477 @ SV896 @ SV48 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV48 ) @ SV477 ) @ SV896 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(2315,plain,
! [SV897: $i,SV478: $i,SV49: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV49 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV478 @ SV49 ) @ SV897 @ SV49 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV897 @ SV49 ) @ SV478 @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2316,plain,
! [SV898: $i,SV479: $i,SV50: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV50 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV479 @ SV50 ) @ SV898 @ SV50 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV898 @ SV50 ) @ SV479 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1890]) ).
thf(2317,plain,
! [SV899: $i,SV480: $i,SV51: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV51 )
| ( c_HOL_Oord__class_Oless @ SV480 @ ( c_HOL_Ouminus__class_Ouminus @ SV899 @ SV51 ) @ SV51 )
| ~ ( c_HOL_Oord__class_Oless @ SV899 @ ( c_HOL_Ouminus__class_Ouminus @ SV480 @ SV51 ) @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1891]) ).
thf(2318,plain,
! [SV900: $i,SV481: $i,SV52: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV52 )
| ( c_HOL_Oord__class_Oless @ SV481 @ ( c_HOL_Ouminus__class_Ouminus @ SV900 @ SV52 ) @ SV52 )
| ~ ( c_HOL_Oord__class_Oless @ SV900 @ ( c_HOL_Ouminus__class_Ouminus @ SV481 @ SV52 ) @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(2319,plain,
! [SV901: $i,SV482: $i,SV53: $i] :
( ( ! [SY3439: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV53 )
| ( c_HOL_Oord__class_Oless @ SV482 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV901 @ SY3439 @ SV53 ) @ SV53 )
| ~ ( c_HOL_Oord__class_Oless @ SV482 @ SY3439 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2320,plain,
! [SV902: $i,SV483: $i,SV54: $i] :
( ( ! [SY3440: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV54 )
| ( c_HOL_Oord__class_Oless @ SV483 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV902 @ SY3440 @ SV54 ) @ SV54 )
| ~ ( c_HOL_Oord__class_Oless @ SV483 @ SV902 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2321,plain,
! [SV484: $i,SV55: $i] :
( ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV55 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV484 @ SV55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1895]) ).
thf(2322,plain,
! [SV903: $i,SV485: $i,SV56: $i] :
( ( ! [SY3441: $i,SY3442: $i] :
( ~ ( class_Orderings_Oorder @ SV56 )
| ( c_HOL_Oord__class_Oless @ SV485 @ SV903 @ SV56 )
| ( c_HOL_Oord__class_Oless @ SY3441 @ SY3442 @ SV56 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV56 ) @ SY3442 ) @ SV485 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3442 @ SV485 @ SV56 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3441 @ SV903 @ SV56 ) @ ( tc_fun @ SV56 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2323,plain,
! [SV904: $i,SV486: $i,SV57: $i] :
( ( ! [SY3443: $i,SY3444: $i,SY3445: $i,SY3446: $i,SY3447: $i,SY3448: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV57 @ SV486 @ ( c_COMBC @ SV904 @ SY3443 @ SY3443 @ tc_bool ) @ ( c_COMBC @ SY3444 @ SY3443 @ SY3443 @ tc_bool ) @ SY3445 @ SY3446 @ SY3447 @ SY3448 @ SY3443 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV486 @ SV57 @ SV904 @ SY3444 @ SY3446 @ SY3445 @ SY3448 @ SY3447 @ SY3443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1897]) ).
thf(2324,plain,
! [SV905: $i,SV487: $i,SV58: $i] :
( ( ! [SY3449: $i] :
( ( hAPP @ ( c_COMBK @ SV58 @ SV487 @ SV905 ) @ SY3449 )
= SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2325,plain,
! [SV906: $i,SV488: $i,SV59: $i] :
( ( ! [SY3450: $i,SY3451: $i,SY3452: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV59 @ SV488 @ SV906 @ SY3450 ) @ SY3451 ) @ SY3452 )
= ( hAPP @ ( hAPP @ SV59 @ SY3452 ) @ SY3451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1899]) ).
thf(2326,plain,
! [SV907: $i,SV489: $i,SV60: $i] :
( ( ! [SY3453: $i] :
( ~ ( class_Orderings_Oorder @ SV60 )
| ( c_HOL_Oord__class_Oless @ SV489 @ SV907 @ SV60 )
| ~ ( c_HOL_Oord__class_Oless @ SV489 @ SY3453 @ SV60 )
| ~ ( c_HOL_Oord__class_Oless @ SY3453 @ SV907 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(2327,plain,
! [SV908: $i,SV490: $i,SV61: $i] :
( ( ! [SY3454: $i] :
( ( hBOOL @ ( c_in @ SV61 @ SV490 @ SV908 ) )
| ~ ( hBOOL @ ( c_in @ SV61 @ SY3454 @ SV908 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3454 @ SV490 @ ( tc_fun @ SV908 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(2328,plain,
! [SV909: $i,SV491: $i,SV62: $i] :
( ( ! [SY3455: $i] :
( ( c_HOL_Oord__class_Oless @ SV62 @ SV491 @ ( tc_fun @ SV909 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3455 @ SV491 @ ( tc_fun @ SV909 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV62 @ SY3455 @ ( tc_fun @ SV909 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2329,plain,
! [SV910: $i,SV492: $i,SV63: $i] :
( ( ! [SY3456: $i] :
( ~ ( class_Orderings_Opreorder @ SV63 )
| ( c_HOL_Oord__class_Oless @ SV492 @ SV910 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SY3456 @ SV910 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV492 @ SY3456 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(2330,plain,
! [SV911: $i,SV493: $i,SV64: $i] :
( ( ! [SY3457: $i,SY3458: $i,SY3459: $i] :
( ( c_Finite__Set_Ofinite @ SV64 @ SV493 )
| ~ ( c_Finite__Set_Ofold__graph @ SV911 @ SY3457 @ SV64 @ SY3458 @ SV493 @ SY3459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(2331,plain,
! [SV912: $i,SV494: $i,SV65: $i] :
( ( ~ ( class_Orderings_Oorder @ SV65 )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV494 @ SV912 @ SV65 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV65 @ tc_bool ) ) )
| ( c_HOL_Oord__class_Oless @ SV494 @ SV912 @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2332,plain,
! [SV913: $i,SV495: $i,SV66: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV66 @ SV495 @ ( tc_fun @ SV913 @ tc_bool ) ) @ SV913 )
| ~ ( c_Finite__Set_Ofinite @ SV66 @ SV913 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2333,plain,
! [SV914: $i,SV496: $i,SV67: $i] :
( ( ( c_Finite__Set_Ofinite @ SV67 @ SV496 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV67 @ SV914 @ ( tc_fun @ SV496 @ tc_bool ) ) @ SV496 )
| ~ ( c_Finite__Set_Ofinite @ SV914 @ SV496 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(2334,plain,
! [SV915: $i,SV497: $i,SV68: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV68 @ SV497 @ ( tc_fun @ SV915 @ tc_bool ) ) @ SV915 )
| ~ ( c_Finite__Set_Ofinite @ SV68 @ SV915 )
| ~ ( c_Finite__Set_Ofinite @ SV497 @ SV915 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2335,plain,
! [SV916: $i,SV499: $i,SV70: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV70 @ SV499 @ ( tc_fun @ SV916 @ tc_bool ) ) @ SV916 )
| ~ ( c_Finite__Set_Ofinite @ SV499 @ SV916 )
| ~ ( c_Finite__Set_Ofinite @ SV70 @ SV916 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(2336,plain,
! [SV917: $i,SV500: $i,SV71: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV71 @ SV500 @ ( tc_fun @ SV917 @ tc_bool ) ) @ SV917 )
| ~ ( c_Finite__Set_Ofinite @ SV500 @ SV917 )
| ~ ( c_Finite__Set_Ofinite @ SV71 @ SV917 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(2337,plain,
! [SV918: $i,SV501: $i,SV72: $i] :
( ( ( c_Finite__Set_Ofinite @ SV72 @ SV501 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV72 @ SV918 @ ( tc_fun @ SV501 @ tc_bool ) ) @ SV501 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1912]) ).
thf(2338,plain,
! [SV919: $i,SV502: $i,SV73: $i] :
( ( ( c_Finite__Set_Ofinite @ SV73 @ SV502 )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV919 @ SV73 @ ( tc_fun @ SV502 @ tc_bool ) ) @ SV502 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2339,plain,
! [SV920: $i,SV503: $i,SV74: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV74 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV503 @ SV74 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV920 @ SV74 ) @ SV74 )
| ~ ( c_HOL_Oord__class_Oless @ SV920 @ SV503 @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(2340,plain,
! [SV921: $i,SV504: $i,SV75: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV75 )
| ( c_HOL_Oord__class_Oless @ SV504 @ SV921 @ SV75 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV921 @ SV75 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV504 @ SV75 ) @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2341,plain,
! [SV505: $i,SV76: $i] :
( ( c_HOL_Oord__class_Oless @ SV76 @ SV76 @ ( tc_fun @ SV505 @ tc_bool ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1916]) ).
thf(2342,plain,
! [SV506: $i,SV77: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV77 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV506 @ SV506 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1917]) ).
thf(2343,plain,
! [SV507: $i,SV78: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV78 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV507 @ SV507 @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1918]) ).
thf(2344,plain,
! [SV508: $i,SV79: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV79 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV508 @ SV508 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1919]) ).
thf(2345,plain,
! [SV922: $i,SV509: $i,SV80: $i] :
( ( ! [SY3460: $i,SY3461: $i] :
( ~ ( class_Orderings_Oorder @ SV80 )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV509 @ SV922 @ SV80 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3460 @ SY3461 @ SV80 ) @ ( tc_fun @ SV80 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SY3460 ) @ SY3461 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV922 @ SY3461 @ SV80 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV922 ) @ SY3461 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SY3460 ) @ SV509 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(2346,plain,
! [SV923: $i,SV510: $i,SV81: $i] :
( ( ! [SY3462: $i,SY3463: $i] :
( ~ ( class_Orderings_Oorder @ SV81 )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV510 @ SV923 @ SV81 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3462 @ SY3463 @ SV81 ) @ ( tc_fun @ SV81 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SY3462 ) @ SY3463 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3462 @ SV510 @ SV81 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV923 ) @ SY3463 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SY3462 ) @ SV510 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2347,plain,
! [SV924: $i,SV511: $i,SV82: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV82 )
| ( c_HOL_Oord__class_Oless @ SV511 @ SV924 @ SV82 )
| ( c_HOL_Oord__class_Oless @ SV924 @ SV511 @ SV82 )
| ( SV924 = SV511 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2348,plain,
! [SV925: $i,SV512: $i,SV83: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV83 )
| ( SV512 = SV925 )
| ( c_HOL_Oord__class_Oless @ SV925 @ SV512 @ SV83 )
| ( c_HOL_Oord__class_Oless @ SV512 @ SV925 @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2349,plain,
! [SV926: $i,SV513: $i,SV84: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV84 )
| ( c_HOL_Oord__class_Oless @ SV513 @ SV926 @ SV84 )
| ( c_HOL_Oord__class_Oless @ SV926 @ SV513 @ SV84 )
| ( SV926 = SV513 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2350,plain,
! [SV927: $i,SV514: $i,SV85: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV85 )
| ( c_HOL_Oord__class_Oless @ SV514 @ SV927 @ SV85 )
| ( SV927 = SV514 )
| ( c_HOL_Oord__class_Oless @ SV927 @ SV514 @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1925]) ).
thf(2351,plain,
! [SV928: $i,SV515: $i,SV86: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV86 )
| ( SV515 = SV928 )
| ( c_HOL_Oord__class_Oless @ SV515 @ SV928 @ SV86 )
| ( c_HOL_Oord__class_Oless @ SV928 @ SV515 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1926]) ).
thf(2352,plain,
! [SV929: $i,SV516: $i,SV87: $i] :
( ( ~ ( class_Orderings_Oorder @ SV87 )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV87 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV516 @ SV929 @ SV87 ) )
| ( c_HOL_Oord__class_Oless @ SV516 @ SV929 @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2353,plain,
! [SV930: $i,SV517: $i,SV88: $i] :
( ( ~ ( class_Orderings_Oorder @ SV88 )
| ~ ( c_HOL_Oord__class_Oless @ SV517 @ SV930 @ SV88 )
| ~ ( c_HOL_Oord__class_Oless @ SV930 @ SV517 @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2354,plain,
! [SV931: $i,SV518: $i,SV89: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV518 @ SV931 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV931 @ SV518 @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(2355,plain,
! [SV932: $i,SV519: $i,SV90: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ SV519 @ SV932 @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ SV932 @ SV519 @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2356,plain,
! [SV933: $i,SV520: $i,SV91: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV520 @ SV933 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV933 @ SV520 @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2357,plain,
! [SV934: $i,SV521: $i,SV92: $i] :
( ( ! [SY3464: $i,SY3465: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV92 )
| ( ( c_Finite__Set_Osetsum @ SV521 @ ( c_HOL_Ominus__class_Ominus @ SV934 @ SY3464 @ ( tc_fun @ SY3465 @ tc_bool ) ) @ SY3465 @ SV92 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV521 @ SV934 @ SY3465 @ SV92 ) @ ( c_Finite__Set_Osetsum @ SV521 @ SY3464 @ SY3465 @ SV92 ) @ SV92 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY3465 @ tc_bool ) ) @ SY3464 ) @ SV934 ) )
| ~ ( c_Finite__Set_Ofinite @ SV934 @ SY3465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2358,plain,
! [SV935: $i,SV522: $i,SV93: $i] :
( ( ~ ( class_Orderings_Oorder @ SV93 )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV522 @ SV935 @ SV93 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV93 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV93 ) @ SV935 ) @ SV522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2359,plain,
! [SV936: $i,SV523: $i,SV94: $i] :
( ( ! [SY3466: $i,SY3467: $i,SY3468: $i,SY3469: $i] :
( ( c_Finite__Set_Ofold__graph @ SV94 @ SV523 @ ( c_Set_Oinsert @ SV936 @ SY3466 @ SY3467 ) @ ( hAPP @ ( hAPP @ SV94 @ SV936 ) @ SY3468 ) @ SY3467 @ SY3469 )
| ~ ( c_Finite__Set_Ofold__graph @ SV94 @ SV523 @ SY3466 @ SY3468 @ SY3467 @ SY3469 )
| ( hBOOL @ ( c_in @ SV936 @ SY3466 @ SY3467 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2360,plain,
! [SV937: $i,SV524: $i,SV95: $i] :
( ( ! [SY3470: $i] :
( ( c_HOL_Oord__class_Oless @ SV95 @ SV524 @ ( tc_fun @ SV937 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SY3470 @ SV524 @ SV937 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV95 @ ( c_Set_Oinsert @ SY3470 @ SV524 @ SV937 ) @ ( tc_fun @ SV937 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2361,plain,
! [SV938: $i,SV525: $i,SV96: $i] :
( ( ! [SY3471: $i] :
( ( c_HOL_Oord__class_Oless @ SV96 @ ( c_Set_Oinsert @ SV525 @ SV938 @ SY3471 ) @ ( tc_fun @ SY3471 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV525 @ SV938 @ SY3471 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV96 @ SV938 @ ( tc_fun @ SY3471 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2362,plain,
! [SV939: $i,SV526: $i,SV97: $i] :
( ( ! [SY3472: $i,SY3473: $i] :
( ~ ( class_Orderings_Oorder @ SV97 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV97 ) @ SV526 ) @ SV939 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV97 ) @ SY3472 ) @ SV526 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3472 @ SV526 @ SV97 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3473 @ SV939 @ SV97 ) @ ( tc_fun @ SV97 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2363,plain,
! [SV940: $i,SV527: $i,SV98: $i] :
( ( ! [SY3474: $i,SY3475: $i] :
( ~ ( class_Orderings_Oorder @ SV98 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV98 ) @ SV527 ) @ SV940 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV98 ) @ SV940 ) @ SY3474 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV940 @ SY3474 @ SV98 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV527 @ SY3475 @ SV98 ) @ ( tc_fun @ SV98 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2364,plain,
! [SV941: $i,SV528: $i,SV99: $i] :
( ( ! [SY3476: $i,SY3477: $i] :
( ~ ( class_Orderings_Oorder @ SV99 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV99 ) @ SV528 ) @ SV941 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3476 @ SY3477 @ SV99 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV528 @ SV941 @ SV99 ) @ ( tc_fun @ SV99 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2365,plain,
! [SV942: $i,SV529: $i,SV100: $i] :
( ( ! [SY3478: $i,SY3479: $i] :
( ~ ( class_Orderings_Oorder @ SV100 )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV529 @ SV942 @ SV100 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3478 @ SY3479 @ SV100 ) @ ( tc_fun @ SV100 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV100 ) @ SY3478 ) @ SY3479 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV100 ) @ SV529 ) @ SV942 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2366,plain,
! [SV943: $i,SV530: $i,SV101: $i] :
( ( ! [SY3480: $i] :
( ~ ( class_Orderings_Olinorder @ SV101 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV530 @ SV943 @ SV101 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV943 @ SY3480 @ SV101 ) @ ( tc_fun @ SV101 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV530 @ SY3480 @ SV101 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV101 ) @ SV943 ) @ SY3480 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV101 ) @ SV530 ) @ SV943 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(2367,plain,
! [SV944: $i,SV531: $i,SV102: $i] :
( ( ! [SY3481: $i,SY3482: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ SV102 @ SV531 ) @ SV944 )
| ~ ( hBOOL @ ( c_in @ SV531 @ SY3481 @ SY3482 ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3481 @ SV102 @ SY3482 @ ( tc_fun @ SV944 @ tc_bool ) ) @ SV944 )
| ~ ( c_Finite__Set_Ofinite @ SY3481 @ SY3482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2368,plain,
! [SV945: $i,SV532: $i,SV103: $i] :
( ( ! [SY3483: $i,SY3484: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV103 )
| ( ( c_Finite__Set_Osetsum @ SV532 @ ( c_HOL_Ominus__class_Ominus @ SV945 @ ( c_Set_Oinsert @ SY3483 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3484 @ tc_bool ) ) @ SY3484 ) @ ( tc_fun @ SY3484 @ tc_bool ) ) @ SY3484 @ SV103 )
= ( c_Finite__Set_Osetsum @ SV532 @ SV945 @ SY3484 @ SV103 ) )
| ( hBOOL @ ( c_in @ SY3483 @ SV945 @ SY3484 ) )
| ~ ( c_Finite__Set_Ofinite @ SV945 @ SY3484 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2369,plain,
! [SV946: $i,SV533: $i,SV104: $i] :
( ( ~ ( class_Orderings_Oorder @ SV104 )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV533 @ SV946 @ SV104 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV104 @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV946 @ SV533 @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2370,plain,
! [SV947: $i,SV534: $i,SV105: $i] :
( ( ! [SY3485: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV105 )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV534 @ ( c_COMBK @ SV947 @ SV105 @ SY3485 ) @ SY3485 @ SV105 )
= SV947 )
| ( SV534
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3485 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2371,plain,
! [SV948: $i,SV535: $i,SV106: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV106 @ tc_bool ) ) @ ( c_COMBK @ SV535 @ ( tc_fun @ SV948 @ tc_bool ) @ SV106 ) @ SV106 @ ( tc_fun @ SV948 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV948 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2372,plain,
! [SV949: $i,SV536: $i,SV107: $i] :
( ( ! [SY3486: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV107 @ ( c_COMBK @ SV536 @ ( tc_fun @ SV949 @ tc_bool ) @ SY3486 ) @ SY3486 @ ( tc_fun @ SV949 @ tc_bool ) )
= SV536 )
| ( SV107
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3486 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2373,plain,
! [SV950: $i,SV537: $i,SV108: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV108 @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV537 @ tc_bool ) ) @ ( tc_fun @ SV537 @ tc_bool ) @ SV950 ) @ SV950 @ ( tc_fun @ SV537 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV537 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2374,plain,
! [SV951: $i,SV538: $i,SV109: $i] :
( ( ! [SY3487: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV109 @ SV538 @ ( tc_fun @ SV951 @ tc_bool ) ) @ SV951 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV109 @ ( c_Set_Oinsert @ SY3487 @ SV538 @ SV951 ) @ ( tc_fun @ SV951 @ tc_bool ) ) @ SV951 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2375,plain,
! [SV952: $i,SV539: $i,SV110: $i] :
( ( ! [SY3488: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV110 @ ( c_Set_Oinsert @ SV539 @ SV952 @ SY3488 ) @ ( tc_fun @ SY3488 @ tc_bool ) ) @ SY3488 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV110 @ SV952 @ ( tc_fun @ SY3488 @ tc_bool ) ) @ SY3488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2376,plain,
! [SV953: $i,SV540: $i,SV111: $i] :
( ( ~ ( class_Orderings_Oorder @ SV111 )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV111 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV540 @ SV953 @ SV111 ) )
| ( c_HOL_Oord__class_Oless @ SV540 @ SV953 @ SV111 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2377,plain,
! [SV954: $i,SV541: $i,SV112: $i] :
( ( ~ ( class_Orderings_Oorder @ SV112 )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ SV541 @ SV954 @ SV112 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV112 @ tc_bool ) ) )
| ( c_HOL_Oord__class_Oless @ SV541 @ SV954 @ SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2378,plain,
! [SV113: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV113 )
= $false )
| ( ( c_Complete__Lattice_Ocomplete__lattice__axioms @ ( c_Complete__Lattice_OInf__class_OInf @ SV113 ) @ ( c_Complete__Lattice_OSup__class_OSup @ SV113 ) @ ( c_lessequals @ SV113 ) @ SV113 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1953]) ).
thf(2379,plain,
! [SV955: $i,SV542: $i,SV114: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV114 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV114 ) @ SV542 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV955 @ SV114 ) ) )
| ~ ( hBOOL @ ( c_in @ SV542 @ SV955 @ SV114 ) )
| ~ ( c_Finite__Set_Ofinite @ SV955 @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2380,plain,
! [SV956: $i,SV543: $i,SV115: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV115 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV115 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV543 @ SV115 ) ) @ SV956 ) )
| ~ ( hBOOL @ ( c_in @ SV956 @ SV543 @ SV115 ) )
| ~ ( c_Finite__Set_Ofinite @ SV543 @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2381,plain,
! [SV544: $i,SV116: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV116 ) )
= $true )
| ( ( ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMin @ SV544 @ SV116 ) @ SV544 @ SV116 ) )
| ( SV544
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV116 @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV544 @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1957]) ).
thf(2382,plain,
! [SV545: $i,SV117: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV117 ) )
= $true )
| ( ( ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMax @ SV545 @ SV117 ) @ SV545 @ SV117 ) )
| ( SV545
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV117 @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV545 @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1958]) ).
thf(2383,plain,
! [SV957: $i,SV546: $i,SV118: $i] :
( ( ! [SY3489: $i,SY3490: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV118 @ ( c_Set_Oinsert @ SV546 @ SV957 @ SY3489 ) @ SY3489 ) @ SY3490 ) )
| ( hBOOL @ ( c_in @ SV546 @ SV957 @ SY3489 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV118 @ SV546 @ SV957 @ SY3490 @ SY3489 @ SY3489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2384,plain,
! [SV958: $i,SV547: $i,SV119: $i] :
( ( ! [SY3491: $i,SY3492: $i,SY3493: $i,SY3494: $i] :
( ( c_Finite__Set_Ofold__graph @ SV119 @ SV547 @ SV958 @ ( hAPP @ ( hAPP @ SV119 @ SY3491 ) @ SY3492 ) @ SY3493 @ SY3494 )
| ~ ( hBOOL @ ( c_in @ SY3491 @ SV958 @ SY3493 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV119 @ SV547 @ ( c_HOL_Ominus__class_Ominus @ SV958 @ ( c_Set_Oinsert @ SY3491 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3493 @ tc_bool ) ) @ SY3493 ) @ ( tc_fun @ SY3493 @ tc_bool ) ) @ SY3492 @ SY3493 @ SY3494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2385,plain,
! [SV959: $i,SV548: $i,SV120: $i] :
( ( ! [SY3495: $i] :
( ( ( c_Finite__Set_Osetsum @ SV120 @ ( c_HOL_Ominus__class_Ominus @ SV548 @ ( c_Set_Oinsert @ SV959 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3495 @ tc_bool ) ) @ SY3495 ) @ ( tc_fun @ SY3495 @ tc_bool ) ) @ SY3495 @ tc_nat )
= ( c_Finite__Set_Osetsum @ SV120 @ SV548 @ SY3495 @ tc_nat ) )
| ( hBOOL @ ( c_in @ SV959 @ SV548 @ SY3495 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(2386,plain,
! [SV960: $i,SV549: $i,SV121: $i] :
( ( ! [SY3496: $i] :
( ( c_HOL_Oord__class_Oless @ SV121 @ ( c_Set_Oinsert @ SV549 @ SV960 @ SY3496 ) @ ( tc_fun @ SY3496 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV549 @ SV121 @ SY3496 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV121 @ ( c_Set_Oinsert @ SV549 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3496 @ tc_bool ) ) @ SY3496 ) @ ( tc_fun @ SY3496 @ tc_bool ) ) @ SV960 @ ( tc_fun @ SY3496 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV121 @ SV960 @ ( tc_fun @ SY3496 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2387,plain,
! [SV961: $i,SV550: $i,SV122: $i] :
( ( ! [SY3497: $i] :
( ( c_HOL_Oord__class_Oless @ SV122 @ ( c_Set_Oinsert @ SV550 @ SV961 @ SY3497 ) @ ( tc_fun @ SY3497 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV550 @ SV122 @ SY3497 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV122 @ ( c_Set_Oinsert @ SV550 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3497 @ tc_bool ) ) @ SY3497 ) @ ( tc_fun @ SY3497 @ tc_bool ) ) @ SV961 @ ( tc_fun @ SY3497 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SV550 @ SV961 @ SY3497 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2388,plain,
! [SV962: $i,SV551: $i,SV123: $i] :
( ( ! [SY3498: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV123 @ ( c_Set_Oinsert @ SV551 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV962 @ tc_bool ) ) @ SV962 ) @ ( tc_fun @ SV962 @ tc_bool ) ) @ SY3498 @ ( tc_fun @ SV962 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV551 @ SV123 @ SV962 ) )
| ( hBOOL @ ( c_in @ SV551 @ SY3498 @ SV962 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV123 @ ( c_Set_Oinsert @ SV551 @ SY3498 @ SV962 ) @ ( tc_fun @ SV962 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2389,plain,
! [SV963: $i,SV552: $i,SV124: $i] :
( ( ! [SY3499: $i,SY3500: $i,SY3501: $i,SY3502: $i] :
( ( c_Nitpick_Ofold__graph_H @ SV124 @ SV552 @ SV963 @ ( hAPP @ ( hAPP @ SV124 @ SY3499 ) @ SY3500 ) @ SY3501 @ SY3502 )
| ~ ( c_Nitpick_Ofold__graph_H @ SV124 @ SV552 @ ( c_HOL_Ominus__class_Ominus @ SV963 @ ( c_Set_Oinsert @ SY3499 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3501 @ tc_bool ) ) @ SY3501 ) @ ( tc_fun @ SY3501 @ tc_bool ) ) @ SY3500 @ SY3501 @ SY3502 )
| ~ ( hBOOL @ ( c_in @ SY3499 @ SV963 @ SY3501 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2390,plain,
! [SV964: $i,SV553: $i,SV125: $i] :
( ( ! [SY3503: $i] :
( ( c_HOL_Oord__class_Oless @ SV125 @ ( c_Set_Oinsert @ SV553 @ SV964 @ SY3503 ) @ ( tc_fun @ SY3503 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY3503 @ tc_bool ) ) @ SV125 ) @ SV964 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV125 @ ( c_Set_Oinsert @ SV553 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3503 @ tc_bool ) ) @ SY3503 ) @ ( tc_fun @ SY3503 @ tc_bool ) ) @ SV964 @ ( tc_fun @ SY3503 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV125 @ SV964 @ ( tc_fun @ SY3503 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(2391,plain,
! [SV965: $i,SV554: $i,SV126: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV126 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV126 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV554 @ SV126 ) ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV965 @ SV126 ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV554 @ SV126 )
| ( SV965
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV126 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV126 @ tc_bool ) ) @ SV965 ) @ SV554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2392,plain,
! [SV966: $i,SV555: $i,SV127: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV127 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV127 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV555 @ SV127 ) ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV966 @ SV127 ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV966 @ SV127 )
| ( SV555
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV127 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV127 @ tc_bool ) ) @ SV555 ) @ SV966 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2393,plain,
! [SV967: $i,SV556: $i,SV128: $i] :
( ( ! [SY3504: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV128 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV556 @ SV967 @ SY3504 @ 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 @ SV128 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_COMBK @ ( hAPP @ ( c_COMBC @ ( c_fequal @ tc_Com_Ostate ) @ tc_Com_Ostate @ tc_Com_Ostate @ tc_bool ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ SV128 @ SV556 @ SY3504 @ SV967 ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) @ SV967 @ ( c_COMBK @ ( hAPP @ SY3504 @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ SV128 @ SV556 @ SY3504 @ SV967 ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) @ 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_forall_pos,[status(thm)],[1969]) ).
thf(2394,plain,
! [SV968: $i,SV557: $i,SV129: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV129 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV557 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV129 @ tc_bool ) ) @ SV129 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV557 @ SV968 @ SV129 ) @ ( tc_fun @ SV129 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV557 @ SV968 @ SV129 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV129 ) @ SV557 ) @ SV968 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2395,plain,
! [SV969: $i,SV558: $i,SV130: $i] :
( ( ! [SY3505: $i] :
( ( c_HOL_Oord__class_Oless @ SV130 @ ( c_Set_Oinsert @ SV558 @ SV969 @ SY3505 ) @ ( tc_fun @ SY3505 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY3505 @ tc_bool ) ) @ SV130 ) @ SV969 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV130 @ ( c_Set_Oinsert @ SV558 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3505 @ tc_bool ) ) @ SY3505 ) @ ( tc_fun @ SY3505 @ tc_bool ) ) @ SV969 @ ( tc_fun @ SY3505 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SV558 @ SV969 @ SY3505 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2396,plain,
! [SV970: $i,SV559: $i,SV131: $i] :
( ( ! [SY3506: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV131 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV559 @ SV970 @ SV131 ) ) @ SY3506 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ SV970 ) @ SY3506 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ SV559 ) @ SY3506 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2397,plain,
! [SV971: $i,SV560: $i,SV132: $i] :
( ( ! [SY3507: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV132 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV560 @ SV971 @ SV132 ) ) @ SY3507 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ SV971 ) @ SY3507 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ SV560 ) @ SY3507 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2398,plain,
! [SV972: $i,SV561: $i,SV133: $i] :
( ( ~ ( class_Lattices_Olattice @ SV133 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV133 ) @ SV561 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV972 @ SV561 @ SV133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2399,plain,
! [SV973: $i,SV562: $i,SV134: $i] :
( ( ~ ( class_Lattices_Olattice @ SV134 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV134 ) @ SV562 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV562 @ SV973 @ SV134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2400,plain,
! [SV974: $i,SV563: $i,SV135: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV135 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV135 ) @ SV563 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV974 @ SV135 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV135 ) @ SV974 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV563 @ SV135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2401,plain,
! [SV975: $i,SV564: $i,SV136: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV136 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV136 ) @ SV564 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV975 @ SV136 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV136 ) @ SV975 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV564 @ SV136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2402,plain,
! [SV976: $i,SV565: $i,SV137: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV137 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV137 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV565 @ SV137 ) ) @ SV976 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV137 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV976 @ SV137 ) ) @ SV565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2403,plain,
! [SV977: $i,SV566: $i,SV138: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV138 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV138 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV566 @ SV138 ) ) @ SV977 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV138 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV977 @ SV138 ) ) @ SV566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2404,plain,
! [SV978: $i,SV567: $i,SV139: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV139 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV567 @ SV978 @ SV139 ) @ ( c_Set_Oinsert @ SV978 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV139 @ tc_bool ) ) @ SV139 ) @ ( tc_fun @ SV139 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV567 @ SV978 @ SV139 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV139 ) @ SV567 ) @ SV978 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2405,plain,
! [SV568: $i,SV140: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV140 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ SV140 ) @ SV568 @ SV140 )
= SV568 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1981]) ).
thf(2406,plain,
! [SV569: $i,SV141: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV141 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV569 @ ( c_Orderings_Obot__class_Obot @ SV141 ) @ SV141 )
= SV569 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1982]) ).
thf(2407,plain,
! [SV979: $i,SV570: $i,SV143: $i] :
( ( ! [SY3508: $i,SY3509: $i,SY3510: $i,SY3511: $i,SY3512: $i,SY3513: $i] :
( ( ( hAPP @ SV143 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV570 @ tc_bool ) ) )
= SV979 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV143 @ SY3508 @ SY3509 @ SY3510 @ SY3511 @ SY3512 @ SY3513 @ SV979 @ SV570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2408,plain,
! [SV980: $i,SV571: $i,SV144: $i] :
( ( ! [SY3514: $i,SY3515: $i,SY3516: $i,SY3517: $i,SY3518: $i,SY3519: $i] :
( ( ( hAPP @ SV144 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV571 @ tc_bool ) ) )
= SV980 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3514 @ SV144 @ SY3515 @ SY3516 @ SY3517 @ SY3518 @ SV980 @ SY3519 @ SV571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1984]) ).
thf(2409,plain,
! [SV572: $i,SV145: $i] :
( ( hBOOL @ ( c_in @ SV145 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV572 @ tc_bool ) ) @ SV572 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1985]) ).
thf(2410,plain,
! [SV981: $i,SV573: $i,SV146: $i] :
( ( ( hBOOL @ ( hAPP @ SV146 @ SV573 ) )
| ~ ( hBOOL @ ( c_in @ SV573 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV981 @ tc_bool ) ) @ SV981 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2411,plain,
! [SV574: $i,SV147: $i] :
( ( hBOOL @ ( c_in @ SV147 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV574 @ tc_bool ) ) @ SV574 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1987]) ).
thf(2412,plain,
! [SV575: $i,SV148: $i] :
( ( hBOOL @ ( c_in @ SV148 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV575 @ tc_bool ) ) @ SV575 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1988]) ).
thf(2413,plain,
! [SV982: $i,SV576: $i,SV149: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV149 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV576 @ tc_bool ) ) @ SV576 ) @ SV982 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2414,plain,
! [SV983: $i,SV582: $i,SV155: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV155 @ SV582 ) )
| ~ ( hBOOL @ ( c_in @ SV582 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV983 @ tc_bool ) ) @ SV983 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2415,plain,
! [SV984: $i,SV583: $i,SV156: $i] :
( ( ( ( c_Set_Oinsert @ SV156 @ ( c_HOL_Ominus__class_Ominus @ SV583 @ ( c_Set_Oinsert @ SV156 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV984 @ tc_bool ) ) @ SV984 ) @ ( tc_fun @ SV984 @ tc_bool ) ) @ SV984 )
= SV583 )
| ~ ( hBOOL @ ( c_in @ SV156 @ SV583 @ SV984 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2416,plain,
! [SV985: $i,SV584: $i,SV157: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV157 )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV157 ) @ ( c_Set_Oinsert @ SV584 @ ( c_Set_Oinsert @ SV985 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV157 @ tc_bool ) ) @ SV157 ) @ SV157 ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV584 @ SV985 @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2417,plain,
! [SV986: $i,SV585: $i,SV158: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV158 @ SV585 @ SV986 ) @ ( c_Set_Oinsert @ SV158 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV986 @ tc_bool ) ) @ SV986 ) @ ( tc_fun @ SV986 @ tc_bool ) )
= SV585 )
| ( hBOOL @ ( c_in @ SV158 @ SV585 @ SV986 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2418,plain,
! [SV987: $i,SV586: $i,SV159: $i] :
( ( ! [SY3520: $i] :
( ( hBOOL @ ( c_in @ SV159 @ ( c_Set_Oinsert @ SV586 @ SV987 @ SY3520 ) @ SY3520 ) )
| ~ ( hBOOL @ ( c_in @ SV159 @ SV987 @ SY3520 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2419,plain,
! [SV988: $i,SV587: $i,SV160: $i] :
( ( ! [SY3521: $i] :
( ( hBOOL @ ( c_in @ SV160 @ ( c_Set_Oinsert @ SV587 @ SV988 @ SY3521 ) @ SY3521 ) )
| ~ ( hBOOL @ ( c_in @ SV160 @ SV988 @ SY3521 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2420,plain,
! [SV989: $i,SV588: $i,SV161: $i] :
( ( ! [SY3522: $i,SY3523: $i,SY3524: $i,SY3525: $i,SY3526: $i,SY3527: $i,SY3528: $i,SY3529: $i] :
( ( ( hAPP @ SV161 @ ( c_Set_Oinsert @ SV588 @ SV989 @ SY3522 ) )
= ( hAPP @ ( hAPP @ SY3523 @ SV588 ) @ ( hAPP @ SV161 @ SV989 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV161 @ SY3524 @ SY3525 @ SY3526 @ SY3523 @ SY3527 @ SY3528 @ SY3529 @ SY3522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(2421,plain,
! [SV990: $i,SV589: $i,SV162: $i] :
( ( ! [SY3530: $i,SY3531: $i,SY3532: $i,SY3533: $i,SY3534: $i,SY3535: $i,SY3536: $i,SY3537: $i] :
( ( ( hAPP @ SV162 @ ( c_Set_Oinsert @ SV589 @ SV990 @ SY3530 ) )
= ( hAPP @ ( hAPP @ SY3531 @ SV589 ) @ ( hAPP @ SV162 @ SV990 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3532 @ SV162 @ SY3533 @ SY3534 @ SY3535 @ SY3531 @ SY3536 @ SY3537 @ SY3530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2422,plain,
! [SV991: $i,SV590: $i,SV163: $i] :
( ( ! [SY3538: $i] :
( ( hBOOL @ ( c_in @ SV163 @ SV590 @ SV991 ) )
| ( SV163 = SY3538 )
| ~ ( hBOOL @ ( c_in @ SV163 @ ( c_Set_Oinsert @ SY3538 @ SV590 @ SV991 ) @ SV991 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2423,plain,
! [SV992: $i,SV591: $i,SV164: $i] :
( ( ! [SY3539: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV164 @ ( c_Set_Oinsert @ SV591 @ SV992 @ SY3539 ) @ ( tc_fun @ SY3539 @ tc_bool ) )
= ( c_Set_Oinsert @ SV591 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV164 @ SV992 @ ( tc_fun @ SY3539 @ tc_bool ) ) @ SY3539 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2424,plain,
! [SV993: $i,SV592: $i,SV165: $i] :
( ( ! [SY3540: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV165 @ SV592 @ SV993 ) @ SY3540 @ ( tc_fun @ SV993 @ tc_bool ) )
= ( c_Set_Oinsert @ SV165 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV592 @ SY3540 @ ( tc_fun @ SV993 @ tc_bool ) ) @ SV993 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2425,plain,
! [SV994: $i,SV593: $i,SV166: $i] :
( ( hBOOL @ ( c_in @ SV166 @ ( c_Set_Oinsert @ SV166 @ SV593 @ SV994 ) @ SV994 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2426,plain,
! [SV995: $i,SV594: $i,SV167: $i] :
( ( hBOOL @ ( c_in @ SV167 @ ( c_Set_Oinsert @ SV167 @ SV594 @ SV995 ) @ SV995 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2427,plain,
! [SV996: $i,SV595: $i,SV168: $i] :
( ( hBOOL @ ( c_in @ SV168 @ ( c_Set_Oinsert @ SV168 @ SV595 @ SV996 ) @ SV996 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2428,plain,
! [SV997: $i,SV596: $i,SV169: $i] :
( ( ( ( c_Set_Oinsert @ SV169 @ SV596 @ SV997 )
= SV596 )
| ~ ( hBOOL @ ( c_in @ SV169 @ SV596 @ SV997 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2009]) ).
thf(2429,plain,
! [SV998: $i,SV597: $i,SV170: $i] :
( ( ! [SY3541: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV170 @ ( c_HOL_Ominus__class_Ominus @ SV597 @ SV998 @ ( tc_fun @ SY3541 @ tc_bool ) ) @ ( tc_fun @ SY3541 @ tc_bool ) )
= SV998 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY3541 @ tc_bool ) ) @ SV170 ) @ SV597 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY3541 @ tc_bool ) ) @ SV998 ) @ SV170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2010]) ).
thf(2430,plain,
! [SV999: $i,SV598: $i,SV171: $i] :
( ( ! [SY3542: $i] :
( ( hBOOL @ ( c_in @ SV171 @ SV598 @ SV999 ) )
| ~ ( hBOOL @ ( c_in @ SV171 @ SY3542 @ SV999 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV999 @ tc_bool ) ) @ SY3542 ) @ SV598 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2011]) ).
thf(2431,plain,
! [SV1000: $i,SV599: $i,SV172: $i] :
( ( ! [SY3543: $i] :
( ( hBOOL @ ( c_in @ SV172 @ SV599 @ SV1000 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1000 @ tc_bool ) ) @ SY3543 ) @ SV599 ) )
| ~ ( hBOOL @ ( c_in @ SV172 @ SY3543 @ SV1000 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2432,plain,
! [SV1001: $i,SV600: $i,SV173: $i] :
( ( ! [SY3544: $i] :
( ( hBOOL @ ( c_in @ SV173 @ SV600 @ SV1001 ) )
| ~ ( hBOOL @ ( c_in @ SV173 @ SY3544 @ SV1001 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1001 @ tc_bool ) ) @ SY3544 ) @ SV600 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2433,plain,
! [SV1002: $i,SV601: $i,SV174: $i] :
( ( ! [SY3545: $i] :
( ( hBOOL @ ( c_in @ SV174 @ SV601 @ SV1002 ) )
| ~ ( hBOOL @ ( c_in @ SV174 @ SY3545 @ SV1002 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1002 @ tc_bool ) ) @ SY3545 ) @ SV601 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2434,plain,
! [SV1003: $i,SV602: $i,SV175: $i] :
( ( ! [SY3546: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV175 @ tc_bool ) ) @ SV602 ) @ SV1003 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV175 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3546 @ SV602 @ ( tc_fun @ SV175 @ tc_bool ) ) ) @ SV1003 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2015]) ).
thf(2435,plain,
! [SV1004: $i,SV603: $i,SV176: $i] :
( ( ! [SY3547: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV176 @ tc_bool ) ) @ SV603 ) @ SV1004 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV176 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV603 @ SY3547 @ ( tc_fun @ SV176 @ tc_bool ) ) ) @ SV1004 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(2436,plain,
! [SV1005: $i,SV604: $i,SV177: $i] :
( ( ! [SY3548: $i,SY3549: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV604 @ SV1005 @ ( tc_fun @ SV177 @ tc_bool ) ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3548 @ SY3549 @ ( tc_fun @ SV177 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ SV1005 ) @ SY3549 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ SV604 ) @ SY3548 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2017]) ).
thf(2437,plain,
! [SV1006: $i,SV605: $i,SV178: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV178 @ SV605 @ ( tc_fun @ SV1006 @ tc_bool ) )
= SV178 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1006 @ tc_bool ) ) @ SV605 ) @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2018]) ).
thf(2438,plain,
! [SV1007: $i,SV606: $i,SV179: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV179 @ SV606 @ ( tc_fun @ SV1007 @ tc_bool ) )
= SV606 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1007 @ tc_bool ) ) @ SV179 ) @ SV606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2439,plain,
! [SV1008: $i,SV607: $i,SV180: $i] :
( ( ! [SY3550: $i,SY3551: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV607 @ SV1008 @ ( tc_fun @ SV180 @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ SY3550 @ SY3551 @ ( tc_fun @ SV180 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ SY3551 ) @ SV1008 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ SV607 ) @ SY3550 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2440,plain,
! [SV1009: $i,SV608: $i,SV181: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV181 @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV608 @ ( tc_fun @ SV181 @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV1009 @ ( tc_fun @ SV181 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV181 @ tc_bool ) ) @ SV1009 ) @ SV608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2441,plain,
! [SV1010: $i,SV609: $i,SV182: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV182 @ tc_bool ) ) @ SV609 ) @ SV1010 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV182 @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV1010 @ ( tc_fun @ SV182 @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV609 @ ( tc_fun @ SV182 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2442,plain,
! [SV1011: $i,SV610: $i,SV183: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV183 @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV610 @ ( tc_fun @ SV183 @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV1011 @ ( tc_fun @ SV183 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV183 @ tc_bool ) ) @ SV1011 ) @ SV610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2443,plain,
! [SV1012: $i,SV611: $i,SV184: $i] :
( ( ! [SY3552: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV184 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV611 @ SV1012 @ ( tc_fun @ SV184 @ tc_bool ) ) ) @ SY3552 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV184 @ tc_bool ) ) @ SV1012 ) @ SY3552 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV184 @ tc_bool ) ) @ SV611 ) @ SY3552 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2444,plain,
! [SV1013: $i,SV612: $i,SV185: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV185 @ tc_bool ) ) @ SV612 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1013 @ SV612 @ ( tc_fun @ SV185 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2445,plain,
! [SV1014: $i,SV613: $i,SV186: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV186 @ tc_bool ) ) @ SV613 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV613 @ SV1014 @ ( tc_fun @ SV186 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2446,plain,
! [SV1015: $i,SV614: $i,SV187: $i] :
( ( ! [SY3553: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV187 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV614 @ SV1015 @ ( tc_fun @ SV187 @ tc_bool ) ) ) @ SY3553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV187 @ tc_bool ) ) @ SV1015 ) @ SY3553 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV187 @ tc_bool ) ) @ SV614 ) @ SY3553 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2447,plain,
! [SV1016: $i,SV615: $i,SV188: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV188 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV615 @ SV1016 @ ( tc_fun @ SV188 @ tc_bool ) ) ) @ SV615 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2448,plain,
! [SV1017: $i,SV616: $i,SV189: $i] :
( ( ! [SY3554: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV189 @ tc_bool ) ) @ SV616 ) @ ( c_Set_Oinsert @ SV1017 @ SY3554 @ SV189 ) ) )
| ~ ( hBOOL @ ( c_in @ SV1017 @ SV616 @ SV189 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV189 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV616 @ ( c_Set_Oinsert @ SV1017 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV189 @ tc_bool ) ) @ SV189 ) @ ( tc_fun @ SV189 @ tc_bool ) ) ) @ SY3554 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2449,plain,
! [SV1018: $i,SV617: $i,SV190: $i] :
( ( ! [SY3555: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV190 @ tc_bool ) ) @ SV617 ) @ ( c_Set_Oinsert @ SV1018 @ SY3555 @ SV190 ) ) )
| ~ ( hBOOL @ ( c_in @ SV1018 @ SV617 @ SV190 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV190 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV617 @ ( c_Set_Oinsert @ SV1018 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV190 @ tc_bool ) ) @ SV190 ) @ ( tc_fun @ SV190 @ tc_bool ) ) ) @ SY3555 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2030]) ).
thf(2450,plain,
! [SV1019: $i,SV618: $i,SV191: $i] :
( ( ! [SY3556: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV191 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV618 @ ( c_Set_Oinsert @ SV1019 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV191 @ tc_bool ) ) @ SV191 ) @ ( tc_fun @ SV191 @ tc_bool ) ) ) @ SY3556 ) )
| ~ ( hBOOL @ ( c_in @ SV1019 @ SV618 @ SV191 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV191 @ tc_bool ) ) @ SV618 ) @ ( c_Set_Oinsert @ SV1019 @ SY3556 @ SV191 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(2451,plain,
! [SV1020: $i,SV619: $i,SV192: $i] :
( ( ~ ( class_Orderings_Oorder @ SV192 )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV619 @ SV1020 @ SV192 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV192 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV192 ) @ SV619 ) @ SV1020 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2452,plain,
! [SV1021: $i,SV620: $i,SV193: $i] :
( ( ~ ( class_Orderings_Oorder @ SV193 )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV193 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV620 @ SV1021 @ SV193 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV193 ) @ SV620 ) @ SV1021 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2453,plain,
! [SV1022: $i,SV621: $i,SV194: $i] :
( ( ~ ( class_Orderings_Oorder @ SV194 )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ SV621 @ SV1022 @ SV194 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV194 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV194 ) @ SV1022 ) @ SV621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2034]) ).
thf(2454,plain,
! [SV1023: $i,SV622: $i,SV195: $i] :
( ( ! [SY3557: $i,SY3558: $i] :
( ~ ( class_Orderings_Oorder @ SV195 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV195 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV622 @ SV1023 @ SV195 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3557 @ SY3558 @ SV195 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV195 ) @ SV622 ) @ SV1023 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2455,plain,
! [SV1024: $i,SV623: $i,SV196: $i] :
( ( ! [SY3559: $i,SY3560: $i] :
( ~ ( class_Orderings_Oorder @ SV196 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV196 ) @ SV623 ) @ SV1024 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV196 ) @ SV1024 ) @ SY3559 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV196 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1024 @ SY3559 @ SV196 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV623 @ SY3560 @ SV196 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(2456,plain,
! [SV1025: $i,SV624: $i,SV197: $i] :
( ( ! [SY3561: $i,SY3562: $i] :
( ~ ( class_Orderings_Oorder @ SV197 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV197 ) @ SV624 ) @ SV1025 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV197 ) @ SY3561 ) @ SV624 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV197 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3561 @ SV624 @ SV197 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3562 @ SV1025 @ SV197 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2457,plain,
! [SV1026: $i,SV625: $i,SV198: $i] :
( ( ! [SY3563: $i,SY3564: $i] :
( ~ ( class_Orderings_Oorder @ SV198 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV198 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV625 @ SV1026 @ SV198 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3563 @ SY3564 @ SV198 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV198 ) @ SV1026 ) @ SY3564 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV198 ) @ SY3563 ) @ SV625 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2458,plain,
! [SV1027: $i,SV626: $i,SV199: $i] :
( ( ! [SY3565: $i,SY3566: $i] :
( ~ ( class_Orderings_Olinorder @ SV199 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV199 ) @ SV626 ) @ SV1027 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV199 ) @ SY3565 ) @ SV1027 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV199 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1027 @ SY3565 @ SV199 ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV626 @ SY3566 @ SV199 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2459,plain,
! [SV1028: $i,SV627: $i,SV200: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV200 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV200 ) @ SV627 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1028 @ SV627 @ SV200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2460,plain,
! [SV1029: $i,SV628: $i,SV201: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV201 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV201 ) @ SV628 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV628 @ SV1029 @ SV201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2461,plain,
! [SV1030: $i,SV629: $i,SV202: $i] :
( ( ! [SY3567: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV202 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV629 @ SV1030 @ SV202 ) ) @ SY3567 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ SV1030 ) @ SY3567 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ SV629 ) @ SY3567 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2462,plain,
! [SV1031: $i,SV630: $i,SV203: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV203 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV203 ) @ SV630 ) @ SV1031 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV203 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV1031 @ SV203 ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV630 @ SV203 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2463,plain,
! [SV1032: $i,SV631: $i,SV204: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV204 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV204 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV631 @ SV204 ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV1032 @ SV204 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV204 ) @ SV1032 ) @ SV631 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2464,plain,
! [SV1033: $i,SV632: $i,SV205: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV205 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV632 @ SV1033 @ SV205 )
= SV632 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV205 ) @ SV1033 ) @ SV632 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2465,plain,
! [SV1034: $i,SV633: $i,SV206: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV206 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV633 @ SV1034 @ SV206 )
= SV1034 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV206 ) @ SV633 ) @ SV1034 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2466,plain,
! [SV1035: $i,SV634: $i,SV207: $i] :
( ( ! [SY3568: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV207 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV207 ) @ SV634 ) @ SV1035 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV207 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3568 @ SV634 @ SV207 ) ) @ SV1035 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2467,plain,
! [SV1036: $i,SV635: $i,SV208: $i] :
( ( ! [SY3569: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV208 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV208 ) @ SV635 ) @ SV1036 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV208 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV635 @ SY3569 @ SV208 ) ) @ SV1036 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2468,plain,
! [SV1037: $i,SV636: $i,SV209: $i] :
( ( ! [SY3570: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV209 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV209 ) @ SV636 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1037 @ SY3570 @ SV209 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV209 ) @ SV636 ) @ SY3570 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2049]) ).
thf(2469,plain,
! [SV1038: $i,SV637: $i,SV210: $i] :
( ( ! [SY3571: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV210 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV210 ) @ SV637 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1038 @ SY3571 @ SV210 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV210 ) @ SV637 ) @ SV1038 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2470,plain,
! [SV1039: $i,SV638: $i,SV211: $i] :
( ( ! [SY3572: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV211 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV211 ) @ SV638 ) @ SV1039 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV211 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3572 @ SV638 @ SV211 ) ) @ SV1039 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2051]) ).
thf(2471,plain,
! [SV1040: $i,SV639: $i,SV212: $i] :
( ( ! [SY3573: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV212 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV212 ) @ SV639 ) @ SV1040 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV212 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV639 @ SY3573 @ SV212 ) ) @ SV1040 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2472,plain,
! [SV1041: $i,SV640: $i,SV213: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV213 )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ SV640 @ SV1041 @ SV213 ) @ SV213 )
= ( c_HOL_Ominus__class_Ominus @ SV1041 @ SV640 @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2473,plain,
! [SV641: $i,SV214: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV214 ) )
= $true )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV641 @ SV214 ) @ SV214 )
= SV641 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2054]) ).
thf(2474,plain,
! [SV642: $i,SV215: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV215 ) )
= $true )
| ( ( SV642
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV642 @ SV215 ) @ SV215 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2055]) ).
thf(2475,plain,
! [SV643: $i,SV216: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV216 ) )
= $true )
| ( ( SV643
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV643 @ SV216 ) @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2056]) ).
thf(2476,plain,
! [SV644: $i,SV217: $i] :
( ( ( ~ ( class_Lattices_Oboolean__algebra @ SV217 ) )
= $true )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV644 @ SV217 ) @ SV217 )
= SV644 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2057]) ).
thf(2477,plain,
! [SV645: $i,SV218: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV218 ) )
= $true )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV645 @ SV218 ) @ SV218 )
= SV645 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2058]) ).
thf(2478,plain,
! [SV1042: $i,SV647: $i,SV220: $i] :
( ( ! [SY3574: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV220 @ tc_bool ) ) @ SV647 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1042 @ SY3574 @ ( tc_fun @ SV220 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV220 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV647 @ SV1042 @ ( tc_fun @ SV220 @ tc_bool ) ) ) @ SY3574 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2479,plain,
! [SV1043: $i,SV648: $i,SV221: $i] :
( ( ! [SY3575: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV221 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV648 @ SV1043 @ ( tc_fun @ SV221 @ tc_bool ) ) ) @ SY3575 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV221 @ tc_bool ) ) @ SV648 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1043 @ SY3575 @ ( tc_fun @ SV221 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2480,plain,
! [SV1044: $i,SV649: $i,SV222: $i] :
( ( ! [SY3576: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV222 @ SV649 @ SV1044 ) @ SY3576 @ ( tc_fun @ SV1044 @ tc_bool ) )
= ( c_Set_Oinsert @ SV222 @ ( c_HOL_Ominus__class_Ominus @ SV649 @ SY3576 @ ( tc_fun @ SV1044 @ tc_bool ) ) @ SV1044 ) )
| ( hBOOL @ ( c_in @ SV222 @ SY3576 @ SV1044 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2062]) ).
thf(2481,plain,
! [SV1045: $i,SV650: $i,SV223: $i] :
( ( ! [SY3577: $i,SY3578: $i,SY3579: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV223 @ SV650 @ SV1045 @ ( tc_fun @ SY3577 @ tc_bool ) ) @ SY3578 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV650 @ SY3579 ) @ SY3578 ) )
| ~ ( hBOOL @ ( c_in @ SY3579 @ SV223 @ SV1045 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2482,plain,
! [SV1046: $i,SV651: $i,SV224: $i] :
( ( ! [SY3580: $i,SY3581: $i,SY3582: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV224 @ SV651 @ SV1046 @ ( tc_fun @ SY3580 @ tc_bool ) ) @ SY3581 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV651 @ SY3582 ) @ SY3581 ) )
| ~ ( hBOOL @ ( c_in @ SY3582 @ SV224 @ SV1046 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2064]) ).
thf(2483,plain,
! [SV1047: $i,SV652: $i,SV225: $i] :
( ( ~ ( class_Lattices_Olattice @ SV225 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV652 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV652 @ SV1047 @ SV225 ) @ SV225 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV652 @ SV1047 @ SV225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2484,plain,
! [SV1048: $i,SV653: $i,SV226: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV226 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV653 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV653 @ SV1048 @ SV226 ) @ SV226 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV653 @ SV1048 @ SV226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2485,plain,
! [SV1049: $i,SV654: $i,SV227: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV227 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV227 @ SV654 @ ( tc_fun @ SV1049 @ tc_bool ) ) @ ( tc_fun @ SV1049 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV227 @ SV654 @ ( tc_fun @ SV1049 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2486,plain,
! [SV1050: $i,SV655: $i,SV228: $i] :
( ( ~ ( class_Lattices_Olattice @ SV228 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV655 @ SV1050 @ SV228 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1050 @ SV655 @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2487,plain,
! [SV1051: $i,SV656: $i,SV229: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV229 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV656 @ SV1051 @ SV229 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1051 @ SV656 @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2488,plain,
! [SV1052: $i,SV657: $i,SV230: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV230 @ SV657 @ ( tc_fun @ SV1052 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV657 @ SV230 @ ( tc_fun @ SV1052 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(2489,plain,
! [SV1053: $i,SV658: $i,SV231: $i] :
( ( ! [SY3583: $i,SY3584: $i,SY3585: $i,SY3586: $i,SY3587: $i,SY3588: $i,SY3589: $i,SY3590: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV231 @ SV658 ) @ ( hAPP @ SV1053 @ SY3583 ) ) )
| ~ ( hBOOL @ ( c_in @ SV658 @ SY3583 @ SY3584 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3585 @ SV1053 @ SV231 @ SY3586 @ SY3587 @ SY3588 @ SY3589 @ SY3590 @ SY3584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2071]) ).
thf(2490,plain,
! [SV1054: $i,SV659: $i,SV232: $i] :
( ( ! [SY3591: $i,SY3592: $i,SY3593: $i,SY3594: $i,SY3595: $i,SY3596: $i,SY3597: $i,SY3598: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ ( hAPP @ SV659 @ SV1054 ) ) @ SY3591 ) )
| ~ ( hBOOL @ ( c_in @ SY3591 @ SV1054 @ SY3592 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV659 @ SY3593 @ SV232 @ SY3594 @ SY3595 @ SY3596 @ SY3597 @ SY3598 @ SY3592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2491,plain,
! [SV1055: $i,SV660: $i,SV233: $i] :
( ( ! [SY3599: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV233 @ SV660 @ ( tc_fun @ SV1055 @ tc_bool ) ) @ SY3599 @ ( tc_fun @ SV1055 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV233 @ SY3599 @ ( tc_fun @ SV1055 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV660 @ SY3599 @ ( tc_fun @ SV1055 @ tc_bool ) ) @ ( tc_fun @ SV1055 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2492,plain,
! [SV1056: $i,SV661: $i,SV234: $i] :
( ( ~ ( class_HOL_Ominus @ SV234 )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ SV661 @ SV1056 @ ( tc_fun @ t_a @ SV234 ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ SV661 @ v_x ) @ ( hAPP @ SV1056 @ v_x ) @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2493,plain,
! [SV1057: $i,SV662: $i,SV235: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV235 @ ( c_HOL_Ominus__class_Ominus @ SV662 @ SV235 @ ( tc_fun @ SV1057 @ tc_bool ) ) @ ( tc_fun @ SV1057 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV235 @ SV662 @ ( tc_fun @ SV1057 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2494,plain,
! [SV1058: $i,SV663: $i,SV236: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV236 @ SV663 @ ( tc_fun @ SV1058 @ tc_bool ) ) @ SV663 @ ( tc_fun @ SV1058 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV236 @ SV663 @ ( tc_fun @ SV1058 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2076]) ).
thf(2495,plain,
! [SV1059: $i,SV664: $i,SV237: $i] :
( ( ! [SY3600: $i,SY3601: $i,SY3602: $i] :
( ( hBOOL @ ( c_in @ SV237 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV664 @ SV1059 @ SY3600 @ ( tc_fun @ SY3601 @ tc_bool ) ) @ SY3601 ) )
| ~ ( hBOOL @ ( c_in @ SV237 @ ( hAPP @ SV1059 @ SY3602 ) @ SY3601 ) )
| ~ ( hBOOL @ ( c_in @ SY3602 @ SV664 @ SY3600 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2496,plain,
! [SV1060: $i,SV665: $i,SV238: $i] :
( ( ! [SY3603: $i,SY3604: $i,SY3605: $i] :
( ( hBOOL @ ( c_in @ SV238 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV665 @ SV1060 @ SY3603 @ ( tc_fun @ SY3604 @ tc_bool ) ) @ SY3604 ) )
| ~ ( hBOOL @ ( c_in @ SV238 @ ( hAPP @ SV1060 @ SY3605 ) @ SY3604 ) )
| ~ ( hBOOL @ ( c_in @ SY3605 @ SV665 @ SY3603 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2497,plain,
! [SV1061: $i,SV666: $i,SV239: $i] :
( ( ! [SY3606: $i] :
( ( hBOOL @ ( c_in @ SV239 @ ( c_HOL_Ominus__class_Ominus @ SV666 @ SV1061 @ ( tc_fun @ SY3606 @ tc_bool ) ) @ SY3606 ) )
| ( hBOOL @ ( c_in @ SV239 @ SV1061 @ SY3606 ) )
| ~ ( hBOOL @ ( c_in @ SV239 @ SV666 @ SY3606 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2079]) ).
thf(2498,plain,
! [SV1062: $i,SV667: $i,SV240: $i] :
( ( ! [SY3607: $i] :
( ( hBOOL @ ( c_in @ SV240 @ ( c_HOL_Ominus__class_Ominus @ SV667 @ SV1062 @ ( tc_fun @ SY3607 @ tc_bool ) ) @ SY3607 ) )
| ( hBOOL @ ( c_in @ SV240 @ SV1062 @ SY3607 ) )
| ~ ( hBOOL @ ( c_in @ SV240 @ SV667 @ SY3607 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(2499,plain,
! [SV1063: $i,SV668: $i,SV241: $i] :
( ( ( hBOOL @ ( hAPP @ SV241 @ SV668 ) )
| ~ ( hBOOL @ ( c_in @ SV668 @ ( c_Collect @ SV241 @ SV1063 ) @ SV1063 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2500,plain,
! [SV1064: $i,SV669: $i,SV242: $i] :
( ( ( hBOOL @ ( c_in @ SV242 @ ( c_Collect @ SV669 @ SV1064 ) @ SV1064 ) )
| ~ ( hBOOL @ ( hAPP @ SV669 @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2501,plain,
! [SV1065: $i,SV670: $i,SV243: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV243 @ ( c_HOL_Ominus__class_Ominus @ SV670 @ SV243 @ ( tc_fun @ SV1065 @ tc_bool ) ) @ ( tc_fun @ SV1065 @ tc_bool ) )
= SV670 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1065 @ tc_bool ) ) @ SV243 ) @ SV670 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2502,plain,
! [SV1066: $i,SV671: $i,SV244: $i] :
( ( ! [SY3608: $i] :
( ~ ( class_Lattices_Olattice @ SV244 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV671 @ SV1066 @ SV244 ) @ SY3608 @ SV244 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV671 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1066 @ SY3608 @ SV244 ) @ SV244 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2503,plain,
! [SV1067: $i,SV672: $i,SV245: $i] :
( ( ! [SY3609: $i] :
( ~ ( class_Lattices_Olattice @ SV245 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV672 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1067 @ SY3609 @ SV245 ) @ SV245 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1067 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV672 @ SY3609 @ SV245 ) @ SV245 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(2504,plain,
! [SV1068: $i,SV673: $i,SV246: $i] :
( ( ! [SY3610: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV246 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV673 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1068 @ SY3610 @ SV246 ) @ SV246 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1068 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV673 @ SY3610 @ SV246 ) @ SV246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2505,plain,
! [SV1069: $i,SV674: $i,SV247: $i] :
( ( ! [SY3611: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV247 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV674 @ SV1069 @ SV247 ) @ SY3611 @ SV247 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV674 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1069 @ SY3611 @ SV247 ) @ SV247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2506,plain,
! [SV1070: $i,SV675: $i,SV248: $i] :
( ( ! [SY3612: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV248 @ SV675 @ ( tc_fun @ SV1070 @ tc_bool ) ) @ SY3612 @ ( tc_fun @ SV1070 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV248 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV675 @ SY3612 @ ( tc_fun @ SV1070 @ tc_bool ) ) @ ( tc_fun @ SV1070 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2507,plain,
! [SV1071: $i,SV676: $i,SV249: $i] :
( ( ! [SY3613: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV249 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV676 @ SV1071 @ ( tc_fun @ SY3613 @ tc_bool ) ) @ ( tc_fun @ SY3613 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV676 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV249 @ SV1071 @ ( tc_fun @ SY3613 @ tc_bool ) ) @ ( tc_fun @ SY3613 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2508,plain,
! [SV1072: $i,SV677: $i,SV250: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV250 @ SV677 @ ( tc_fun @ SV1072 @ tc_bool ) ) @ SV677 @ ( tc_fun @ SV1072 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV250 @ SV677 @ ( tc_fun @ SV1072 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(2509,plain,
! [SV1073: $i,SV678: $i,SV251: $i] :
( ( ( hBOOL @ ( hAPP @ SV251 @ SV678 ) )
| ~ ( hBOOL @ ( c_in @ SV678 @ SV251 @ SV1073 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2091]) ).
thf(2510,plain,
! [SV1074: $i,SV679: $i,SV252: $i] :
( ( ( hBOOL @ ( c_in @ SV252 @ SV679 @ SV1074 ) )
| ~ ( hBOOL @ ( hAPP @ SV679 @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2092]) ).
thf(2511,plain,
! [SV1075: $i,SV680: $i,SV253: $i] :
( ( ! [SY3614: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV253 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV680 @ tc_bool ) ) @ SV1075 @ SV680 @ ( tc_fun @ SY3614 @ tc_bool ) ) @ ( tc_fun @ SY3614 @ tc_bool ) )
= SV253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2093]) ).
thf(2512,plain,
! [SV681: $i,SV254: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV254 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV681 @ SV681 @ SV254 )
= SV681 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2094]) ).
thf(2513,plain,
! [SV1076: $i,SV683: $i,SV256: $i] :
( ( ~ ( class_Lattices_Olattice @ SV256 )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV683 @ SV1076 @ ( tc_fun @ t_a @ SV256 ) ) @ v_x )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV683 @ v_x ) @ ( hAPP @ SV1076 @ v_x ) @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2514,plain,
! [SV1077: $i,SV684: $i,SV257: $i] :
( ( ( c_Finite__Set_Ofold1 @ SV257 @ SV684 @ SV1077 )
= ( c_The @ ( c_Finite__Set_Ofold1Set @ SV257 @ SV684 @ SV1077 ) @ SV1077 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2515,plain,
! [SV1078: $i,SV685: $i,SV258: $i] :
( ( ! [SY3615: $i,SY3616: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV258 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV258 ) @ ( hAPP @ SV685 @ SV1078 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3615 @ SV685 @ SY3616 @ SV258 ) ) )
| ~ ( hBOOL @ ( c_in @ SV1078 @ SY3615 @ SY3616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2516,plain,
! [SV1079: $i,SV686: $i,SV259: $i] :
( ( ! [SY3617: $i,SY3618: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV259 @ tc_bool ) ) @ ( hAPP @ SV686 @ SV1079 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3617 @ SV686 @ SY3618 @ ( tc_fun @ SV259 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( c_in @ SV1079 @ SY3617 @ SY3618 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2099]) ).
thf(2517,plain,
! [SV1080: $i,SV687: $i,SV260: $i] :
( ( ! [SY3619: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV260 @ SV687 @ SV1080 ) @ SY3619 @ ( tc_fun @ SV1080 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV687 @ SY3619 @ ( tc_fun @ SV1080 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SV260 @ SY3619 @ SV1080 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2518,plain,
! [SV1081: $i,SV688: $i,SV261: $i] :
( ( ~ ( hBOOL @ ( c_in @ SV261 @ SV688 @ SV1081 ) )
| ~ ( hBOOL @ ( c_in @ SV261 @ ( c_HOL_Ouminus__class_Ouminus @ SV688 @ ( tc_fun @ SV1081 @ tc_bool ) ) @ SV1081 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2519,plain,
! [SV1082: $i,SV689: $i,SV262: $i] :
( ( ( hBOOL @ ( c_in @ SV262 @ ( c_HOL_Ouminus__class_Ouminus @ SV689 @ ( tc_fun @ SV1082 @ tc_bool ) ) @ SV1082 ) )
| ( hBOOL @ ( c_in @ SV262 @ SV689 @ SV1082 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2520,plain,
! [SV1083: $i,SV691: $i,SV264: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV264 )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV264 ) @ ( c_Set_Oinsert @ SV691 @ SV1083 @ SV264 ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV691 @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV264 ) @ SV1083 ) @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2104]) ).
thf(2521,plain,
! [SV1084: $i,SV692: $i,SV265: $i] :
( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ SV265 @ SV692 @ ( tc_fun @ SV1084 @ tc_bool ) ) @ ( tc_fun @ SV1084 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ SV265 @ ( tc_fun @ SV1084 @ tc_bool ) ) @ SV692 @ ( tc_fun @ SV1084 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2105]) ).
thf(2522,plain,
! [SV1085: $i,SV693: $i,SV266: $i] :
( ( ! [SY3620: $i] :
( ( hBOOL @ ( c_in @ SV266 @ SV693 @ SV1085 ) )
| ~ ( hBOOL @ ( c_in @ SV266 @ ( c_HOL_Ominus__class_Ominus @ SV693 @ SY3620 @ ( tc_fun @ SV1085 @ tc_bool ) ) @ SV1085 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(2523,plain,
! [SV1086: $i,SV694: $i,SV267: $i] :
( ( ! [SY3621: $i] :
( ~ ( hBOOL @ ( c_in @ SV267 @ SV694 @ SV1086 ) )
| ~ ( hBOOL @ ( c_in @ SV267 @ ( c_HOL_Ominus__class_Ominus @ SY3621 @ SV694 @ ( tc_fun @ SV1086 @ tc_bool ) ) @ SV1086 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2107]) ).
thf(2524,plain,
! [SV1087: $i,SV695: $i,SV268: $i] :
( ( ! [SY3622: $i,SY3623: $i,SY3624: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV268 @ tc_bool ) ) @ ( hAPP @ SV695 @ SV1087 ) ) @ SY3622 ) )
| ~ ( hBOOL @ ( c_in @ SV1087 @ SY3623 @ SY3624 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV268 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3623 @ SV695 @ SY3624 @ ( tc_fun @ SV268 @ tc_bool ) ) ) @ SY3622 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2108]) ).
thf(2525,plain,
! [SV1088: $i,SV696: $i,SV269: $i] :
( ( ! [SY3625: $i,SY3626: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV269 @ SV696 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1088 @ SV269 @ SY3625 @ ( tc_fun @ SY3626 @ tc_bool ) ) @ ( tc_fun @ SY3626 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1088 @ SV269 @ SY3625 @ ( tc_fun @ SY3626 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SV696 @ SV1088 @ SY3625 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2109]) ).
thf(2526,plain,
! [SV1089: $i,SV697: $i,SV270: $i] :
( ( ! [SY3627: $i] :
( ( hBOOL @ ( hAPP @ SV270 @ SV697 ) )
| ( hBOOL @ ( hAPP @ SV1089 @ SV697 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1089 @ SV270 @ ( tc_fun @ SY3627 @ tc_bool ) ) @ SV697 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2110]) ).
thf(2527,plain,
! [SV1090: $i,SV698: $i,SV271: $i] :
( ( ! [SY3628: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV271 @ SV698 @ ( tc_fun @ SV1090 @ tc_bool ) ) @ SY3628 ) )
| ~ ( hBOOL @ ( hAPP @ SV698 @ SY3628 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2111]) ).
thf(2528,plain,
! [SV1091: $i,SV699: $i,SV272: $i] :
( ( ! [SY3629: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV272 @ SV699 @ ( tc_fun @ SV1091 @ tc_bool ) ) @ SY3629 ) )
| ~ ( hBOOL @ ( hAPP @ SV272 @ SY3629 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2112]) ).
thf(2529,plain,
! [SV1092: $i,SV700: $i,SV273: $i] :
( ( ! [SY3630: $i] :
( ( hBOOL @ ( c_in @ SV273 @ SV700 @ SV1092 ) )
| ( hBOOL @ ( c_in @ SV273 @ SY3630 @ SV1092 ) )
| ~ ( hBOOL @ ( c_in @ SV273 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3630 @ SV700 @ ( tc_fun @ SV1092 @ tc_bool ) ) @ SV1092 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2530,plain,
! [SV1093: $i,SV701: $i,SV274: $i] :
( ( ! [SY3631: $i] :
( ~ ( class_Orderings_Olinorder @ SV274 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV701 @ SV1093 @ SV274 ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1093 @ SY3631 @ SV274 ) @ ( tc_fun @ SV274 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV701 @ SY3631 @ SV274 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV274 ) @ SV1093 ) @ SY3631 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV274 ) @ SV701 ) @ SV1093 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2114]) ).
thf(2531,plain,
! [SV1094: $i,SV702: $i,SV275: $i] :
( ( ! [SY3632: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV275 @ tc_bool ) ) @ SV702 @ SV275 @ ( tc_fun @ SV1094 @ tc_bool ) ) @ SY3632 @ ( tc_fun @ SV1094 @ tc_bool ) )
= SY3632 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2115]) ).
thf(2532,plain,
! [SV1095: $i,SV703: $i,SV276: $i] :
( ( ! [SY3633: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV276 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV703 @ tc_bool ) ) @ SV1095 @ SV703 @ ( tc_fun @ SY3633 @ tc_bool ) ) @ ( tc_fun @ SY3633 @ tc_bool ) )
= SV276 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2116]) ).
thf(2533,plain,
! [SV1096: $i,SV704: $i,SV277: $i] :
( ( ! [SY3634: $i] :
( ~ ( class_Orderings_Olinorder @ SV277 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV704 @ SV1096 @ SV277 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1096 @ SY3634 @ SV277 ) @ ( tc_fun @ SV277 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV704 @ SY3634 @ SV277 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV277 ) @ SV1096 ) @ SY3634 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV277 ) @ SV704 ) @ SV1096 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2534,plain,
! [SV1097: $i,SV705: $i,SV278: $i] :
( ( ! [SY3635: $i,SY3636: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ SV278 @ SV705 @ SV1097 ) @ SY3635 @ SV1097 @ ( tc_fun @ SY3636 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SY3635 @ SV278 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV705 @ SY3635 @ SV1097 @ ( tc_fun @ SY3636 @ tc_bool ) ) @ ( tc_fun @ SY3636 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2118]) ).
thf(2535,plain,
! [SV1098: $i,SV706: $i,SV279: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV279 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV279 ) @ ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ SV279 ) @ SV706 ) ) @ SV1098 ) )
| ~ ( hBOOL @ ( c_in @ SV1098 @ SV706 @ SV279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2119]) ).
thf(2536,plain,
! [SV707: $i,SV280: $i] :
( ( ( ~ ( class_HOL_Ouminus @ SV280 ) )
= $true )
| ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV707 @ ( tc_fun @ t_a @ SV280 ) ) @ v_x )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ SV707 @ v_x ) @ SV280 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2120]) ).
thf(2537,plain,
! [SV1099: $i,SV708: $i,SV281: $i] :
( ( ! [SY3637: $i] :
( ( hBOOL @ ( c_in @ SV281 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV708 @ SV1099 @ ( tc_fun @ SY3637 @ tc_bool ) ) @ SY3637 ) )
| ~ ( hBOOL @ ( c_in @ SV281 @ SV1099 @ SY3637 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2121]) ).
thf(2538,plain,
! [SV1100: $i,SV709: $i,SV282: $i] :
( ( ! [SY3638: $i] :
( ( hBOOL @ ( c_in @ SV282 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV709 @ SV1100 @ ( tc_fun @ SY3638 @ tc_bool ) ) @ SY3638 ) )
| ~ ( hBOOL @ ( c_in @ SV282 @ SV709 @ SY3638 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2122]) ).
thf(2539,plain,
! [SV1101: $i,SV710: $i,SV283: $i] :
( ( ! [SY3639: $i] :
( ~ ( class_Orderings_Olinorder @ SV283 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV710 @ SV1101 @ SV283 ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV710 @ SY3639 @ SV283 ) @ ( tc_fun @ SV283 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SY3639 @ SV1101 @ SV283 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV283 ) @ SV710 ) @ SY3639 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2123]) ).
thf(2540,plain,
! [SV1102: $i,SV711: $i,SV284: $i] :
( ( ! [SY3640: $i,SY3641: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV284 @ SV711 @ ( tc_fun @ SV1102 @ tc_bool ) ) @ SY3640 @ SV1102 @ ( tc_fun @ SY3641 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV284 @ SY3640 @ SV1102 @ ( tc_fun @ SY3641 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV711 @ SY3640 @ SV1102 @ ( tc_fun @ SY3641 @ tc_bool ) ) @ ( tc_fun @ SY3641 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2124]) ).
thf(2541,plain,
! [SV1103: $i,SV713: $i,SV286: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV286 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV286 ) @ SV713 ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV286 ) @ SV1103 ) ) )
| ~ ( hBOOL @ ( c_in @ SV713 @ SV1103 @ SV286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2126]) ).
thf(2542,plain,
! [SV1104: $i,SV714: $i,SV287: $i] :
( ( ! [SY3642: $i,SY3643: $i] :
( ~ ( class_Orderings_Olinorder @ SV287 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV287 ) @ SV714 ) @ SV1104 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV287 ) @ SV714 ) @ SY3642 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV287 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SY3642 @ SV714 @ SV287 ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SY3643 @ SV1104 @ SV287 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2127]) ).
thf(2543,plain,
! [SV288: $i] :
( ( ( class_Orderings_Obot @ SV288 )
= $false )
| ( ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ SV288 ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ SV288 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2128]) ).
thf(2544,plain,
! [SV289: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV289 )
= $false )
| ( ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV289 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV289 @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ SV289 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2545,plain,
! [SV1105: $i,SV717: $i,SV292: $i] :
( ( ! [SY3644: $i,SY3645: $i,SY3646: $i,SY3647: $i,SY3648: $i,SY3649: $i,SY3650: $i] :
( ( ( hAPP @ SV292 @ ( c_Set_Oinsert @ SV717 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1105 @ tc_bool ) ) @ SV1105 ) )
= SV717 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV292 @ SY3644 @ SY3645 @ SY3646 @ SY3647 @ SY3648 @ SY3649 @ SY3650 @ SV1105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2132]) ).
thf(2546,plain,
! [SV1106: $i,SV718: $i,SV293: $i] :
( ( ! [SY3651: $i,SY3652: $i,SY3653: $i,SY3654: $i,SY3655: $i,SY3656: $i,SY3657: $i] :
( ( ( hAPP @ SV293 @ ( c_Set_Oinsert @ SV718 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1106 @ tc_bool ) ) @ SV1106 ) )
= SV718 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3651 @ SV293 @ SY3652 @ SY3653 @ SY3654 @ SY3655 @ SY3656 @ SY3657 @ SV1106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2133]) ).
thf(2547,plain,
! [SV719: $i,SV294: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV294 ) )
= $true )
| ( ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV294 ) @ ( c_Set_Oinsert @ SV719 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV294 @ tc_bool ) ) @ SV294 ) )
= SV719 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2134]) ).
thf(2548,plain,
! [SV1107: $i,SV721: $i,SV296: $i] :
( ( ! [SY3658: $i] :
( ( c_Set_Oinsert @ SV296 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV721 @ tc_bool ) ) @ SV1107 @ SV721 @ ( tc_fun @ SY3658 @ tc_bool ) ) @ SY3658 )
= ( c_Set_Oinsert @ SV296 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3658 @ tc_bool ) ) @ SY3658 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2136]) ).
thf(2549,plain,
! [SV1108: $i,SV722: $i,SV297: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV297 @ ( c_Set_Oinsert @ SV722 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1108 @ tc_bool ) ) @ SV1108 ) @ SV1108 ) @ SV722 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2137]) ).
thf(2550,plain,
! [SV723: $i,SV298: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV298 ) )
= $true )
| ( ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ SV723 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV298 @ tc_bool ) ) @ SV298 ) @ SV298 )
= SV723 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2138]) ).
thf(2551,plain,
! [SV1109: $i,SV725: $i,SV300: $i] :
( ( ! [SY3659: $i,SY3660: $i,SY3661: $i,SY3662: $i,SY3663: $i,SY3664: $i,SY3665: $i,SY3666: $i] :
( ( ( hAPP @ SV300 @ ( c_Set_Oinsert @ SV725 @ ( c_Set_Oinsert @ SV1109 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3659 @ tc_bool ) ) @ SY3659 ) @ SY3659 ) )
= ( hAPP @ ( hAPP @ SY3660 @ SV725 ) @ SV1109 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV300 @ SY3661 @ SY3662 @ SY3663 @ SY3660 @ SY3664 @ SY3665 @ SY3666 @ SY3659 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2140]) ).
thf(2552,plain,
! [SV1110: $i,SV726: $i,SV301: $i] :
( ( ! [SY3667: $i,SY3668: $i,SY3669: $i,SY3670: $i,SY3671: $i,SY3672: $i,SY3673: $i,SY3674: $i] :
( ( ( hAPP @ SV301 @ ( c_Set_Oinsert @ SV726 @ ( c_Set_Oinsert @ SV1110 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3667 @ tc_bool ) ) @ SY3667 ) @ SY3667 ) )
= ( hAPP @ ( hAPP @ SY3668 @ SV726 ) @ SV1110 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3669 @ SV301 @ SY3670 @ SY3671 @ SY3672 @ SY3668 @ SY3673 @ SY3674 @ SY3667 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2141]) ).
thf(2553,plain,
! [SV1111: $i,SV727: $i,SV302: $i] :
( ( ! [SY3675: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV302 @ ( c_Set_Oinsert @ SV727 @ SV1111 @ SY3675 ) @ ( tc_fun @ SY3675 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV302 @ ( c_Set_Oinsert @ SV727 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3675 @ tc_bool ) ) @ SY3675 ) @ ( tc_fun @ SY3675 @ tc_bool ) ) @ SV1111 @ ( tc_fun @ SY3675 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2142]) ).
thf(2554,plain,
! [SV1112: $i,SV728: $i,SV303: $i] :
( ( ! [SY3676: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV303 @ ( c_Set_Oinsert @ SV728 @ SV1112 @ SY3676 ) @ ( tc_fun @ SY3676 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV303 @ SV1112 @ ( tc_fun @ SY3676 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV728 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3676 @ tc_bool ) ) @ SY3676 ) @ ( tc_fun @ SY3676 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2143]) ).
thf(2555,plain,
! [SV1113: $i,SV729: $i,SV304: $i] :
( ( ! [SY3677: $i] :
( ( SV304 = SV729 )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV1113 @ ( c_Set_Oinsert @ SV304 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3677 @ tc_bool ) ) @ SY3677 ) @ SY3677 ) @ SV729 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2144]) ).
thf(2556,plain,
! [SV1114: $i,SV731: $i,SV306: $i] :
( ( ( SV306
= ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ SV731 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1114 @ tc_bool ) ) @ SV1114 ) @ SV1114 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV731 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1114 @ tc_bool ) ) @ SV1114 ) @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2146]) ).
thf(2557,plain,
! [SV1115: $i,SV732: $i,SV307: $i] :
( ( ( SV307 = SV732 )
| ~ ( hBOOL @ ( c_in @ SV307 @ ( c_Set_Oinsert @ SV732 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1115 @ tc_bool ) ) @ SV1115 ) @ SV1115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2147]) ).
thf(2558,plain,
! [SV1116: $i,SV733: $i,SV308: $i] :
( ( ( c_Finite__Set_Ofold1 @ SV308 @ ( c_Set_Oinsert @ SV733 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1116 @ tc_bool ) ) @ SV1116 ) @ SV1116 )
= SV733 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2148]) ).
thf(2559,plain,
! [SV734: $i,SV309: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV309 ) )
= $true )
| ( ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ SV734 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV309 @ tc_bool ) ) @ SV309 ) @ SV309 )
= SV734 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2149]) ).
thf(2560,plain,
! [SV1117: $i,SV735: $i,SV310: $i] :
( ( ( c_Set_Oinsert @ SV310 @ ( c_HOL_Ominus__class_Ominus @ SV735 @ ( c_Set_Oinsert @ SV310 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1117 @ tc_bool ) ) @ SV1117 ) @ ( tc_fun @ SV1117 @ tc_bool ) ) @ SV1117 )
= ( c_Set_Oinsert @ SV310 @ SV735 @ SV1117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2150]) ).
thf(2561,plain,
! [SV736: $i,SV311: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV311 ) )
= $true )
| ( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV736 @ SV736 @ SV311 )
= ( c_Set_Oinsert @ SV736 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV311 @ tc_bool ) ) @ SV311 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2151]) ).
thf(2562,plain,
! [SV1118: $i,SV737: $i,SV312: $i] :
( ( ( c_Set_Oinsert @ SV312 @ SV737 @ SV1118 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV312 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1118 @ tc_bool ) ) @ SV1118 ) @ SV737 @ ( tc_fun @ SV1118 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2152]) ).
thf(2563,plain,
! [SV738: $i,SV313: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV313 ) )
= $true )
| ( ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ SV313 ) @ ( c_Set_Oinsert @ SV738 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV313 @ tc_bool ) ) @ SV313 ) )
= SV738 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2153]) ).
thf(2564,plain,
! [SV739: $i,SV314: $i] :
( ( ( SV314
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV739 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV739 @ tc_bool ) ) @ SV314 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV314 @ ( tc_fun @ SV739 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2154]) ).
thf(2565,plain,
! [SV1119: $i,SV740: $i,SV316: $i] :
( ( ! [SY3678: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV316 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV740 @ SV1119 @ SV316 ) ) @ SY3678 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV316 @ tc_bool ) ) @ SV1119 ) @ SY3678 ) )
| ~ ( hBOOL @ ( c_in @ SV740 @ SY3678 @ SV316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2155]) ).
thf(2566,plain,
! [SV1120: $i,SV741: $i,SV317: $i] :
( ( ! [SY3679: $i] :
( ( hBOOL @ ( c_in @ SV317 @ SV741 @ SV1120 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1120 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV317 @ SY3679 @ SV1120 ) ) @ SV741 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2156]) ).
thf(2567,plain,
! [SV1121: $i,SV742: $i,SV318: $i] :
( ( ! [SY3680: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV318 @ tc_bool ) ) @ SV742 ) @ ( c_Set_Oinsert @ SV1121 @ SY3680 @ SV318 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV318 @ tc_bool ) ) @ SV742 ) @ SY3680 ) )
| ( hBOOL @ ( c_in @ SV1121 @ SV742 @ SV318 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2157]) ).
thf(2568,plain,
! [SV1122: $i,SV743: $i,SV319: $i] :
( ( ! [SY3681: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV319 @ tc_bool ) ) @ SV743 ) @ SV1122 ) )
| ( hBOOL @ ( c_in @ SY3681 @ SV743 @ SV319 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV319 @ tc_bool ) ) @ SV743 ) @ ( c_Set_Oinsert @ SY3681 @ SV1122 @ SV319 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2158]) ).
thf(2569,plain,
! [SV1123: $i,SV744: $i,SV320: $i] :
( ( ! [SY3682: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV320 @ tc_bool ) ) @ SV744 ) @ ( c_Set_Oinsert @ SV1123 @ SY3682 @ SV320 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV320 @ tc_bool ) ) @ SV744 ) @ SY3682 ) )
| ( hBOOL @ ( c_in @ SV1123 @ SV744 @ SV320 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2159]) ).
thf(2570,plain,
! [SV1124: $i,SV745: $i,SV321: $i] :
( ( ! [SY3683: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV321 @ tc_bool ) ) @ SV745 ) @ SV1124 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV321 @ tc_bool ) ) @ SV745 ) @ ( c_Set_Oinsert @ SY3683 @ SV1124 @ SV321 ) ) )
| ( hBOOL @ ( c_in @ SY3683 @ SV745 @ SV321 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2160]) ).
thf(2571,plain,
! [SV1125: $i,SV746: $i,SV322: $i] :
( ( ! [SY3684: $i,SY3685: $i,SY3686: $i,SY3687: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV322 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV746 @ SV1125 @ SY3684 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY3685 @ SY3686 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV322 @ SV746 @ SY3684 @ SV1125 @ SY3687 @ SY3685 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3687 @ SY3686 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV322 @ SV746 @ SY3684 @ SV1125 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV322 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3687 @ SV1125 @ SY3685 @ 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_forall_pos,[status(thm)],[2161]) ).
thf(2572,plain,
! [SV1126: $i,SV747: $i,SV323: $i] :
( ( ! [SY3688: $i,SY3689: $i,SY3690: $i,SY3691: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV323 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV747 @ SV1126 @ SY3688 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY3689 @ SY3690 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV747 @ SY3691 @ SY3688 @ SY3689 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3691 @ SY3690 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV747 @ SY3691 @ SY3688 @ SY3689 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV323 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3691 @ SV1126 @ SY3689 @ 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_forall_pos,[status(thm)],[2162]) ).
thf(2573,plain,
! [SV1127: $i,SV748: $i,SV324: $i] :
( ( ! [SY3692: $i,SY3693: $i,SY3694: $i,SY3695: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV324 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV748 @ SV1127 @ SY3692 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY3693 @ SY3694 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV324 @ SV748 @ SY3692 @ SV1127 @ SY3695 @ SY3693 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3695 @ SY3694 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV324 @ SV748 @ SY3692 @ SV1127 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV324 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3695 @ SV1127 @ SY3693 @ 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_forall_pos,[status(thm)],[2163]) ).
thf(2574,plain,
! [SV1128: $i,SV749: $i,SV325: $i] :
( ( ! [SY3696: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV325 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV749 @ SV1128 @ SY3696 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV749 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV325 @ SV749 @ SY3696 @ SV1128 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV325 @ SV749 @ SY3696 @ SV1128 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2164]) ).
thf(2575,plain,
! [SV1129: $i,SV750: $i,SV326: $i] :
( ( ! [SY3697: $i,SY3698: $i,SY3699: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV326 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV750 @ SV1129 @ SY3697 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3697 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV326 @ SV750 @ SY3697 @ SV1129 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV326 @ SV750 @ SY3697 @ SV1129 @ SY3698 @ SY3699 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV326 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3698 @ SV1129 @ SY3699 @ 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_forall_pos,[status(thm)],[2165]) ).
thf(2576,plain,
! [SV1130: $i,SV751: $i,SV327: $i] :
( ( ! [SY3700: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV327 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV751 @ SV1130 @ SY3700 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV751 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV327 @ SV751 @ SY3700 @ SV1130 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV327 @ SV751 @ SY3700 @ SV1130 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2166]) ).
thf(2577,plain,
! [SV1131: $i,SV752: $i,SV328: $i] :
( ( ! [SY3701: $i,SY3702: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV328 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV752 @ SV1131 @ SY3701 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY3702 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SY3701 @ SY3702 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SY3701 @ SY3702 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV328 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV752 @ SV1131 @ SY3702 @ 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_forall_pos,[status(thm)],[2167]) ).
thf(2578,plain,
! [SV1132: $i,SV753: $i,SV329: $i] :
( ( ! [SY3703: $i,SY3704: $i,SY3705: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV329 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV753 @ SV1132 @ SY3703 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV753 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV753 @ SY3704 @ SY3703 @ SY3705 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV753 @ SY3704 @ SY3703 @ SY3705 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV329 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3704 @ SV1132 @ SY3705 @ 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_forall_pos,[status(thm)],[2168]) ).
thf(2579,plain,
! [SV1133: $i,SV754: $i,SV330: $i] :
( ( ! [SY3706: $i,SY3707: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV330 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV754 @ SV1133 @ SY3706 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV754 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV754 @ SY3707 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV754 @ SY3707 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV330 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3707 @ SV1133 @ SY3706 @ 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_forall_pos,[status(thm)],[2169]) ).
thf(2580,plain,
! [SV1134: $i,SV755: $i,SV331: $i] :
( ( ! [SY3708: $i,SY3709: $i,SY3710: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV331 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV755 @ SV1134 @ SY3708 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3708 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV331 @ SV755 @ SY3708 @ SV1134 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV331 @ SV755 @ SY3708 @ SV1134 @ SY3709 @ SY3710 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV331 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3709 @ SV1134 @ SY3710 @ 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_forall_pos,[status(thm)],[2170]) ).
thf(2581,plain,
! [SV1135: $i,SV756: $i,SV332: $i] :
( ( ! [SY3711: $i,SY3712: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV332 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV756 @ SV1135 @ SY3711 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3712 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV756 @ SY3712 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV756 @ SY3712 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV332 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3712 @ SV1135 @ SY3711 @ 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_forall_pos,[status(thm)],[2171]) ).
thf(2582,plain,
! [SV1136: $i,SV757: $i,SV333: $i] :
( ( ! [SY3713: $i,SY3714: $i,SY3715: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV333 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV757 @ SV1136 @ SY3713 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3713 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV757 @ SY3714 @ SY3713 @ SY3715 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV757 @ SY3714 @ SY3713 @ SY3715 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV333 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3714 @ SV1136 @ SY3715 @ 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_forall_pos,[status(thm)],[2172]) ).
thf(2583,plain,
! [SV1137: $i,SV758: $i,SV334: $i] :
( ( ! [SY3716: $i,SY3717: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV334 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV758 @ SV1137 @ SY3716 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3716 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SY3716 @ SY3717 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SY3716 @ SY3717 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV334 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV758 @ SV1137 @ SY3717 @ 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_forall_pos,[status(thm)],[2173]) ).
thf(2584,plain,
! [SV1138: $i,SV759: $i,SV335: $i] :
( ( ! [SY3718: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV335 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV759 @ SV1138 @ SY3718 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV759 @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ SV335 @ SV759 @ SY3718 @ SV1138 ) ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ SV335 @ SV759 @ SY3718 @ SV1138 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2174]) ).
thf(2585,plain,
! [SV1139: $i,SV760: $i,SV336: $i] :
( ( ! [SY3719: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV336 @ tc_bool ) ) @ SV760 ) @ ( c_Set_Oinsert @ SV1139 @ SY3719 @ SV336 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV336 @ tc_bool ) ) @ SV760 ) @ SY3719 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV336 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV760 @ ( c_Set_Oinsert @ SV1139 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV336 @ tc_bool ) ) @ SV336 ) @ ( tc_fun @ SV336 @ tc_bool ) ) ) @ SY3719 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2175]) ).
thf(2586,plain,
! [SV1140: $i,SV761: $i,SV337: $i] :
( ( ! [SY3720: $i,SY3721: $i,SY3722: $i,SY3723: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV761 @ ( c_Com_Ocom_OSemi @ SV1140 @ SY3720 ) @ SY3721 @ SY3722 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3722 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3722 ) ) @ SY3722 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3723 @ SY3720 @ SY3721 @ SY3722 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3722 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3722 ) ) @ SY3722 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV761 @ SV1140 @ SY3723 @ SY3722 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3722 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3722 ) ) @ SY3722 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2176]) ).
thf(2587,plain,
! [SV1141: $i,SV762: $i,SV338: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV338 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV338 ) @ SV762 ) @ SV1141 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV338 ) @ SV1141 ) @ SV762 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2177]) ).
thf(2588,plain,
! [SV1142: $i,SV763: $i,SV339: $i] :
( ( ! [SY3724: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV339 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV763 @ SV1142 @ SV339 ) ) @ ( c_Set_Oinsert @ SV763 @ SY3724 @ SV339 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV339 @ tc_bool ) ) @ SV1142 ) @ SY3724 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2589,plain,
! [SV1143: $i,SV764: $i,SV340: $i] :
( ( ! [SY3725: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV340 @ ( c_Set_Oinsert @ SV764 @ SV1143 @ ( tc_Hoare__Mirabelle_Otriple @ SY3725 ) ) @ SY3725 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV340 @ SV1143 @ SY3725 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV340 @ ( c_Set_Oinsert @ SV764 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3725 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3725 ) ) @ SY3725 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(2590,plain,
! [SV1144: $i,SV765: $i,SV341: $i] :
( ( ( SV341
= ( c_Set_Oinsert @ SV765 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1144 @ tc_bool ) ) @ SV1144 ) )
| ( SV341
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1144 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1144 @ tc_bool ) ) @ SV341 ) @ ( c_Set_Oinsert @ SV765 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1144 @ tc_bool ) ) @ SV1144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2180]) ).
thf(2591,plain,
! [SV1145: $i,SV766: $i,SV342: $i] :
( ( ! [SY3726: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV342 @ SV766 @ SV1145 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1145 ) @ tc_bool ) ) @ SV766 ) @ SY3726 ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV342 @ SY3726 @ SV1145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2181]) ).
thf(2592,plain,
! [SV1146: $i,SV767: $i,SV343: $i] :
( ( ! [SY3727: $i] :
( ( hBOOL @ ( hAPP @ SV343 @ SV767 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1146 @ tc_bool ) ) @ SY3727 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP @ SY3727 @ SV767 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2182]) ).
thf(2593,plain,
! [SV768: $i,SV344: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV344 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV344 ) @ SV768 ) @ SV768 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2183]) ).
thf(2594,plain,
! [SV769: $i,SV345: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV345 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV345 ) @ SV769 ) @ SV769 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2184]) ).
thf(2595,plain,
! [SV1147: $i,SV770: $i,SV346: $i] :
( ( ! [SY3728: $i] :
( ( hBOOL @ ( hAPP @ SV346 @ SV770 ) )
| ~ ( hBOOL @ ( hAPP @ SV1147 @ SV770 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY3728 @ tc_bool ) ) @ SV1147 ) @ SV346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2185]) ).
thf(2596,plain,
! [SV1148: $i,SV771: $i,SV347: $i] :
( ( ! [SY3729: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV347 @ tc_bool ) ) @ SV771 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV347 @ tc_bool ) ) @ SY3729 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV347 @ tc_bool ) ) @ SV771 ) @ SY3729 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2597,plain,
! [SV1149: $i,SV774: $i,SV350: $i] :
( ( ! [SY3730: $i] :
( ~ ( class_Orderings_Opreorder @ SV350 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV774 ) @ SV1149 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SY3730 ) @ SV1149 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV774 ) @ SY3730 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(2598,plain,
! [SV1150: $i,SV775: $i,SV351: $i] :
( ( ! [SY3731: $i] :
( ~ ( class_Orderings_Oorder @ SV351 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV775 ) @ SV1150 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV775 ) @ SY3731 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SY3731 ) @ SV1150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2190]) ).
thf(2599,plain,
! [SV1151: $i,SV776: $i,SV352: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV352 @ SV776 @ SV1151 ) @ SV352 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(2600,plain,
! [SV1152: $i,SV777: $i,SV353: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV777 @ c_Com_Ocom_OSKIP @ SV777 @ SV1152 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1152 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1152 ) ) @ SV1152 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(2601,plain,
! [SV1153: $i,SV778: $i,SV354: $i] :
( ( ! [SY3732: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV354 @ SV778 @ SV1153 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV354 @ SY3732 @ SV1153 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY3732 @ SV778 @ SV1153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2193]) ).
thf(2602,plain,
! [SV779: $i,SV356: $i] :
( ( ( SV356
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV779 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV779 @ tc_bool ) ) @ SV356 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV779 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2194]) ).
thf(2603,plain,
! [SV1154: $i,SV780: $i,SV357: $i] :
( ( ~ ( class_Orderings_Oorder @ SV357 )
| ( SV780 = SV1154 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV357 ) @ SV780 ) @ SV1154 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV357 ) @ SV1154 ) @ SV780 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2195]) ).
thf(2604,plain,
! [SV1155: $i,SV781: $i,SV358: $i] :
( ( ~ ( class_Orderings_Oorder @ SV358 )
| ( SV781 = SV1155 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV358 ) @ SV1155 ) @ SV781 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV358 ) @ SV781 ) @ SV1155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2196]) ).
thf(2605,plain,
! [SV1156: $i,SV782: $i,SV359: $i] :
( ( ~ ( class_Orderings_Oorder @ SV359 )
| ( SV782 = SV1156 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV359 ) @ SV1156 ) @ SV782 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV359 ) @ SV782 ) @ SV1156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2606,plain,
! [SV1157: $i,SV783: $i,SV360: $i] :
( ( ( SV360 = SV783 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1157 @ tc_bool ) ) @ SV783 ) @ SV360 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1157 @ tc_bool ) ) @ SV360 ) @ SV783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2198]) ).
thf(2607,plain,
! [SV1158: $i,SV784: $i,SV361: $i] :
( ( ( SV361 = SV784 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1158 @ tc_bool ) ) @ SV784 ) @ SV361 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1158 @ tc_bool ) ) @ SV361 ) @ SV784 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2199]) ).
thf(2608,plain,
! [SV785: $i,SV362: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV362 @ tc_bool ) ) @ SV785 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2200]) ).
thf(2609,plain,
! [SV1159: $i,SV787: $i,SV364: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV364 @ tc_bool ) ) @ SV787 ) @ ( c_Set_Oinsert @ SV1159 @ SV787 @ SV364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2202]) ).
thf(2610,plain,
! [SV1160: $i,SV788: $i,SV365: $i] :
( ( ! [SY3733: $i] :
( ( hBOOL @ ( hAPP @ SV365 @ SV788 ) )
| ( SV1160 = SV788 )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1160 @ SV365 @ SY3733 ) @ SV788 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2203]) ).
thf(2611,plain,
! [SV1161: $i,SV789: $i,SV366: $i] :
( ( ( c_Set_Oinsert @ SV366 @ ( c_Set_Oinsert @ SV366 @ SV789 @ SV1161 ) @ SV1161 )
= ( c_Set_Oinsert @ SV366 @ SV789 @ SV1161 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2204]) ).
thf(2612,plain,
! [SV790: $i,SV367: $i] :
( ( ( ~ ( class_Orderings_Obot @ SV367 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV367 ) @ ( c_Orderings_Obot__class_Obot @ SV367 ) ) @ SV790 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2205]) ).
thf(2613,plain,
! [SV1162: $i,SV792: $i,SV369: $i] :
( ( ! [SY3734: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV369 @ tc_bool ) ) @ SV792 ) @ ( c_Set_Oinsert @ SV1162 @ SY3734 @ SV369 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV369 @ tc_bool ) ) @ SV792 ) @ SY3734 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(2614,plain,
! [SV1163: $i,SV793: $i,SV370: $i] :
( ( ! [SY3735: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV370 @ tc_bool ) ) @ SV793 ) @ SV1163 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV370 @ tc_bool ) ) @ ( c_Set_Oinsert @ SY3735 @ SV793 @ SV370 ) ) @ SV1163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2208]) ).
thf(2615,plain,
! [SV1164: $i,SV794: $i,SV371: $i] :
( ( ! [SY3736: $i] :
( ( c_Set_Oinsert @ SV371 @ ( c_Set_Oinsert @ SV794 @ SV1164 @ SY3736 ) @ SY3736 )
= ( c_Set_Oinsert @ SV794 @ ( c_Set_Oinsert @ SV371 @ SV1164 @ SY3736 ) @ SY3736 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2209]) ).
thf(2616,plain,
! [SV1165: $i,SV795: $i,SV372: $i] :
( ( ( c_Set_Oinsert @ SV372 @ ( c_Set_Oinsert @ SV795 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1165 @ tc_bool ) ) @ SV1165 ) @ SV1165 )
= ( c_Set_Oinsert @ SV795 @ ( c_Set_Oinsert @ SV372 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1165 @ tc_bool ) ) @ SV1165 ) @ SV1165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2210]) ).
thf(2617,plain,
! [SV1166: $i,SV796: $i,SV373: $i] :
( ( ! [SY3737: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV373 @ SV796 @ SV1166 ) @ SY3737 ) )
| ~ ( hBOOL @ ( hAPP @ SV796 @ SY3737 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2211]) ).
thf(2618,plain,
! [SV1167: $i,SV797: $i,SV374: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV374 @ SV797 @ SV1167 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1167 ) @ tc_bool ) ) @ SV797 ) @ SV374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2212]) ).
thf(2619,plain,
! [SV1168: $i,SV798: $i,SV375: $i] :
( ( ! [SY3738: $i,SY3739: $i] :
( ~ ( class_HOL_Oord @ SV375 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV375 ) @ ( hAPP @ SV798 @ SV1168 ) ) @ ( hAPP @ SY3738 @ SV1168 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY3739 @ SV375 ) ) @ SV798 ) @ SY3738 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2213]) ).
thf(2620,plain,
! [SV799: $i,SV376: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV376 @ SV799 ) )
= $true )
| ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV799 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2214]) ).
thf(2621,plain,
! [SV800: $i,SV377: $i] :
( ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV377 @ SV800 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV800 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2215]) ).
thf(2622,plain,
! [SV801: $i,SV378: $i] :
( ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV378 @ SV801 ) )
= $true )
| ( ( ~ ( class_Lattices_Obounded__lattice @ SV801 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2216]) ).
thf(2623,plain,
! [SV802: $i,SV379: $i] :
( ( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ SV379 @ SV802 ) )
= $true )
| ( ( ~ ( class_Lattices_Oboolean__algebra @ SV802 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2217]) ).
thf(2624,plain,
! [SV803: $i,SV380: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ SV380 @ SV803 ) )
= $true )
| ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV803 )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ SV380 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2218]) ).
thf(2625,plain,
! [SV804: $i,SV381: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV381 @ SV804 ) )
= $true )
| ( ( ~ ( class_Orderings_Opreorder @ SV804 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2219]) ).
thf(2626,plain,
! [SV805: $i,SV382: $i] :
( ( ( class_Lattices_Olattice @ ( tc_fun @ SV382 @ SV805 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV805 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2220]) ).
thf(2627,plain,
! [SV806: $i,SV383: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV383 @ SV806 ) )
= $true )
| ( ( ~ ( class_Orderings_Oorder @ SV806 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2221]) ).
thf(2628,plain,
! [SV807: $i,SV384: $i] :
( ( ( class_Orderings_Obot @ ( tc_fun @ SV384 @ SV807 ) )
= $true )
| ( ( ~ ( class_Orderings_Obot @ SV807 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2222]) ).
thf(2629,plain,
! [SV808: $i,SV385: $i] :
( ( ( class_HOL_Ouminus @ ( tc_fun @ SV385 @ SV808 ) )
= $true )
| ( ( ~ ( class_HOL_Ouminus @ SV808 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2223]) ).
thf(2630,plain,
! [SV809: $i,SV386: $i] :
( ( ( class_HOL_Ominus @ ( tc_fun @ SV386 @ SV809 ) )
= $true )
| ( ( ~ ( class_HOL_Ominus @ SV809 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2224]) ).
thf(2631,plain,
! [SV810: $i,SV387: $i] :
( ( ( class_HOL_Oord @ ( tc_fun @ SV387 @ SV810 ) )
= $true )
| ( ( ~ ( class_HOL_Oord @ SV810 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2225]) ).
thf(2632,plain,
! [SV1169: $i,SV812: $i,SV389: $i] :
( ( ( SV389 = SV812 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV1169 ) @ SV389 ) @ SV812 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(2633,plain,
! [SV1170: $i,SV813: $i,SV390: $i] :
( ( ( ( c_Set_Oinsert @ SV390 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV813 @ tc_bool ) ) @ SV813 )
!= ( c_Set_Oinsert @ SV1170 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV813 @ tc_bool ) ) @ SV813 ) )
| ( SV390 = SV1170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2228]) ).
thf(2634,plain,
! [SV1171: $i,SV814: $i,SV391: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV391 )
| ( ( c_HOL_Ouminus__class_Ouminus @ SV814 @ SV391 )
!= ( c_HOL_Ouminus__class_Ouminus @ SV1171 @ SV391 ) )
| ( SV814 = SV1171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2229]) ).
thf(2635,plain,
! [SV1172: $i,SV815: $i,SV392: $i] :
( ( ! [SY3740: $i] :
( ( ( c_Set_Oinsert @ SV392 @ SV815 @ SV1172 )
!= ( c_Set_Oinsert @ SV392 @ SY3740 @ SV1172 ) )
| ( hBOOL @ ( c_in @ SV392 @ SY3740 @ SV1172 ) )
| ( hBOOL @ ( c_in @ SV392 @ SV815 @ SV1172 ) )
| ( SV815 = SY3740 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2230]) ).
thf(2636,plain,
! [SV1173: $i,SV816: $i,SV393: $i] :
( ( ( ( c_Collect @ SV393 @ SV816 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV816 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ SV393 @ SV1173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2231]) ).
thf(2637,plain,
! [SV1174: $i,SV817: $i,SV394: $i] :
( ( ! [SY3741: $i] :
( ( ( c_Com_Ocom_OSemi @ SV394 @ SV817 )
!= ( c_Com_Ocom_OSemi @ SV1174 @ SY3741 ) )
| ( SV817 = SY3741 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(2638,plain,
! [SV1175: $i,SV818: $i,SV395: $i] :
( ( ! [SY3742: $i,SY3743: $i,SY3744: $i,SY3745: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV395 @ SV818 @ SV1175 @ SY3742 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3743 @ SY3744 @ SY3745 @ SY3742 ) )
| ( SV395 = SY3743 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2233]) ).
thf(2639,plain,
! [SV1176: $i,SV819: $i,SV396: $i] :
( ( ( c_Set_Oinsert @ SV396 @ SV819 @ SV1176 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1176 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2234]) ).
thf(2640,plain,
! [SV820: $i,SV397: $i] :
( ( c_Com_Ocom_OSKIP
= ( c_Com_Ocom_OSemi @ SV397 @ SV820 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2235]) ).
thf(2641,plain,
! [SV1177: $i,SV821: $i,SV398: $i] :
( ( ~ ( class_Orderings_Oorder @ SV398 )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV398 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV821 @ SV1177 @ SV398 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV821 @ SV1177 @ SV398 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(2642,plain,
! [SV1178: $i,SV822: $i,SV399: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV399 @ tc_bool ) )
!= ( c_Set_Oinsert @ SV822 @ SV1178 @ SV399 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2237]) ).
thf(2643,plain,
! [SV1179: $i,SV823: $i,SV400: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV400 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV823 @ SV1179 @ SV400 )
!= ( c_Orderings_Obot__class_Obot @ SV400 ) )
| ( SV823
= ( c_Orderings_Obot__class_Obot @ SV400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2238]) ).
thf(2644,plain,
! [SV1180: $i,SV824: $i,SV401: $i] :
( ( ! [SY3746: $i,SY3747: $i] :
( ( ( c_Set_Oinsert @ SV401 @ ( c_Set_Oinsert @ SV824 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1180 @ tc_bool ) ) @ SV1180 ) @ SV1180 )
!= ( c_Set_Oinsert @ SY3746 @ ( c_Set_Oinsert @ SY3747 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1180 @ tc_bool ) ) @ SV1180 ) @ SV1180 ) )
| ( SV824 = SY3746 )
| ( SV401 = SY3746 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2239]) ).
thf(2645,plain,
! [SV1181: $i,SV825: $i,SV402: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV402 @ SV825 @ ( tc_fun @ SV1181 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1181 @ tc_bool ) ) )
| ( SV825
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1181 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2240]) ).
thf(2646,plain,
! [SV1182: $i,SV826: $i,SV403: $i] :
( ( ! [SY3748: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV403 )
| ( ( c_HOL_Ominus__class_Ominus @ SV826 @ SV826 @ SV403 )
!= ( c_HOL_Ominus__class_Ominus @ SV1182 @ SY3748 @ SV403 ) )
| ( SV1182 = SY3748 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2241]) ).
thf(2647,plain,
! [SV1183: $i,SV827: $i,SV404: $i] :
( ( ~ ( class_Orderings_Oorder @ SV404 )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV404 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV827 @ SV1183 @ SV404 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV404 ) @ SV827 ) @ SV1183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2242]) ).
thf(2648,plain,
! [SV1184: $i,SV828: $i,SV405: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV405 @ SV828 @ ( tc_fun @ SV1184 @ tc_bool ) )
!= SV828 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1184 @ tc_bool ) ) @ SV405 ) @ SV828 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(2649,plain,
! [SV1185: $i,SV829: $i,SV406: $i] :
( ( ~ ( class_Orderings_Oorder @ SV406 )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV829 @ SV1185 @ SV406 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV406 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV406 ) @ SV829 ) @ SV1185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(2650,plain,
! [SV1186: $i,SV830: $i,SV407: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV407 @ SV830 @ ( tc_fun @ SV1186 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1186 @ tc_bool ) ) )
| ( SV407
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1186 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2245]) ).
thf(2651,plain,
! [SV831: $i,SV408: $i] :
( ( ( c_Com_Ocom_OSemi @ SV408 @ SV831 )
= c_Com_Ocom_OSKIP )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2246]) ).
thf(2652,plain,
! [SV1187: $i,SV832: $i,SV409: $i] :
( ( ! [SY3749: $i,SY3750: $i] :
( ( ( c_Set_Oinsert @ SV409 @ ( c_Set_Oinsert @ SV832 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1187 @ tc_bool ) ) @ SV1187 ) @ SV1187 )
!= ( c_Set_Oinsert @ SY3749 @ ( c_Set_Oinsert @ SY3750 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1187 @ tc_bool ) ) @ SV1187 ) @ SV1187 ) )
| ( SV409 = SY3750 )
| ( SV832 = SY3750 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2247]) ).
thf(2653,plain,
! [SV1188: $i,SV833: $i,SV410: $i] :
( ( ! [SY3751: $i,SY3752: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV410 @ SV833 @ SV1188 @ ( tc_fun @ SY3751 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3751 @ tc_bool ) ) )
| ( ( hAPP @ SV833 @ SY3752 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3751 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SY3752 @ SV410 @ SV1188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2248]) ).
thf(2654,plain,
! [SV1189: $i,SV834: $i,SV411: $i] :
( ( ! [SY3753: $i,SY3754: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV411 )
| ( ( c_HOL_Ominus__class_Ominus @ SV834 @ SV1189 @ SV411 )
!= ( c_HOL_Ominus__class_Ominus @ SY3753 @ SY3754 @ SV411 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV411 ) @ SY3754 ) @ SY3753 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV411 ) @ SV1189 ) @ SV834 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2249]) ).
thf(2655,plain,
! [SV1190: $i,SV835: $i,SV412: $i] :
( ( ~ ( class_Lattices_Oboolean__algebra @ SV412 )
| ( ( c_HOL_Ouminus__class_Ouminus @ SV835 @ SV412 )
!= ( c_HOL_Ouminus__class_Ouminus @ SV1190 @ SV412 ) )
| ( SV835 = SV1190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2250]) ).
thf(2656,plain,
! [SV1191: $i,SV836: $i,SV413: $i] :
( ( ! [SY3755: $i,SY3756: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV413 @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV836 @ SV1191 @ SY3755 @ ( tc_fun @ SV413 @ tc_bool ) ) )
| ( ( hAPP @ SV1191 @ SY3756 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV413 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SY3756 @ SV836 @ SY3755 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(2657,plain,
! [SV1192: $i,SV837: $i,SV414: $i] :
( ( ~ ( class_Orderings_Oorder @ SV414 )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ SV837 @ SV1192 @ SV414 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV414 @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV837 @ SV1192 @ SV414 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2252]) ).
thf(2658,plain,
! [SV1193: $i,SV838: $i,SV415: $i] :
( ( ! [SY3757: $i,SY3758: $i] :
( ( ( c_Set_Oinsert @ SV415 @ ( c_Set_Oinsert @ SV838 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SV1193 ) @ SV1193 )
!= ( c_Set_Oinsert @ SY3757 @ ( c_Set_Oinsert @ SY3758 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SV1193 ) @ SV1193 ) )
| ( SV838 = SY3757 )
| ( SV838 = SY3758 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2253]) ).
thf(2659,plain,
! [SV1194: $i,SV839: $i,SV416: $i] :
( ( ~ ( class_Orderings_Oorder @ SV416 )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV416 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV839 @ SV1194 @ SV416 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV839 @ SV1194 @ SV416 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2254]) ).
thf(2660,plain,
! [SV1195: $i,SV840: $i,SV417: $i] :
( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV417 @ ( tc_fun @ SV840 @ tc_bool ) )
!= ( c_HOL_Ouminus__class_Ouminus @ SV1195 @ ( tc_fun @ SV840 @ tc_bool ) ) )
| ( SV417 = SV1195 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2255]) ).
thf(2661,plain,
! [SV1196: $i,SV841: $i,SV418: $i] :
( ( ! [SY3759: $i,SY3760: $i,SY3761: $i,SY3762: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV418 @ SV841 @ SV1196 @ SY3759 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3760 @ SY3761 @ SY3762 @ SY3759 ) )
| ( SV1196 = SY3762 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2256]) ).
thf(2662,plain,
! [SV1197: $i,SV842: $i,SV419: $i] :
( ( ! [SY3763: $i,SY3764: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV419 )
| ( ( c_HOL_Ominus__class_Ominus @ SV842 @ SV1197 @ SV419 )
!= ( c_HOL_Ominus__class_Ominus @ SY3763 @ SY3764 @ SV419 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV419 ) @ SV1197 ) @ SV842 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV419 ) @ SY3764 ) @ SY3763 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2257]) ).
thf(2663,plain,
! [SV1198: $i,SV843: $i,SV420: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV420 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV843 @ SV1198 @ SV420 )
!= SV1198 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV420 ) @ SV843 ) @ SV1198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(2664,plain,
! [SV1199: $i,SV844: $i,SV421: $i] :
( ( ! [SY3765: $i,SY3766: $i,SY3767: $i,SY3768: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV421 @ SV844 @ SV1199 @ SY3765 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3766 @ SY3767 @ SY3768 @ SY3765 ) )
| ( SV844 = SY3767 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2259]) ).
thf(2665,plain,
! [SV1200: $i,SV845: $i,SV422: $i] :
( ( ! [SY3769: $i] :
( ( ( c_Com_Ocom_OSemi @ SV422 @ SV845 )
!= ( c_Com_Ocom_OSemi @ SV1200 @ SY3769 ) )
| ( SV422 = SV1200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2260]) ).
thf(2666,plain,
! [SV1201: $i,SV846: $i,SV423: $i] :
( ( ! [SY3770: $i,SY3771: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV423 )
| ( ( c_HOL_Ominus__class_Ominus @ SV846 @ SV1201 @ SV423 )
!= ( c_HOL_Ominus__class_Ominus @ SY3770 @ SY3771 @ SV423 ) )
| ( c_HOL_Oord__class_Oless @ SY3770 @ SY3771 @ SV423 )
| ~ ( c_HOL_Oord__class_Oless @ SV846 @ SV1201 @ SV423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2261]) ).
thf(2667,plain,
! [SV1202: $i,SV847: $i,SV424: $i] :
( ( ~ ( class_Orderings_Oorder @ SV424 )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV847 @ SV1202 @ SV424 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV424 @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV847 @ SV1202 @ SV424 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2262]) ).
thf(2668,plain,
! [SV1203: $i,SV848: $i,SV425: $i] :
( ( ( ( c_Set_Oinsert @ SV425 @ SV848 @ SV1203 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1203 @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ SV425 @ SV848 @ SV1203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2263]) ).
thf(2669,plain,
! [SV1204: $i,SV849: $i,SV426: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV426 @ tc_bool ) )
!= ( c_Collect @ SV849 @ SV426 ) )
| ~ ( hBOOL @ ( hAPP @ SV849 @ SV1204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2264]) ).
thf(2670,plain,
! [SV1205: $i,SV850: $i,SV427: $i] :
( ( ! [SY3772: $i,SY3773: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV427 )
| ( ( c_HOL_Ominus__class_Ominus @ SV850 @ SV1205 @ SV427 )
!= ( c_HOL_Ominus__class_Ominus @ SY3772 @ SY3773 @ SV427 ) )
| ( c_HOL_Oord__class_Oless @ SV850 @ SV1205 @ SV427 )
| ~ ( c_HOL_Oord__class_Oless @ SY3772 @ SY3773 @ SV427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2265]) ).
thf(2671,plain,
! [SV1206: $i,SV851: $i,SV428: $i] :
( ( ! [SY3774: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV428 )
| ( ( c_HOL_Ominus__class_Ominus @ SV851 @ SV1206 @ SV428 )
!= ( c_HOL_Ominus__class_Ominus @ SY3774 @ SY3774 @ SV428 ) )
| ( SV851 = SV1206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2266]) ).
thf(2672,plain,
! [SV1207: $i,SV852: $i,SV429: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV429 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV852 @ SV1207 @ SV429 )
!= ( c_Orderings_Obot__class_Obot @ SV429 ) )
| ( SV1207
= ( c_Orderings_Obot__class_Obot @ SV429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2267]) ).
thf(2673,plain,
! [SV1208: $i,SV853: $i,SV430: $i] :
( ( ! [SY3775: $i,SY3776: $i] :
( ( ( c_Set_Oinsert @ SV430 @ ( c_Set_Oinsert @ SV853 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1208 @ tc_bool ) ) @ SV1208 ) @ SV1208 )
!= ( c_Set_Oinsert @ SY3775 @ ( c_Set_Oinsert @ SY3776 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1208 @ tc_bool ) ) @ SV1208 ) @ SV1208 ) )
| ( SV430 = SY3776 )
| ( SV430 = SY3775 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2268]) ).
thf(2674,plain,
! [SV1209: $i,SV854: $i,SV431: $i,SV1: $i] :
( ( ~ ( class_HOL_Oord @ SV1 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV431 @ SV1 ) ) @ SV854 ) @ SV1209 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV854 @ SV1209 @ ( tc_fun @ SV431 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2269]) ).
thf(2675,plain,
! [SV1210: $i,SV855: $i,SV432: $i,SV2: $i] :
( ( ~ ( class_HOL_Oord @ SV2 )
| ( c_HOL_Oord__class_Oless @ SV432 @ SV855 @ ( tc_fun @ SV1210 @ SV2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1210 @ SV2 ) ) @ SV855 ) @ SV432 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1210 @ SV2 ) ) @ SV432 ) @ SV855 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2270]) ).
thf(2676,plain,
! [SV1211: $i,SV856: $i,SV433: $i,SV3: $i] :
( ( ~ ( class_HOL_Oord @ SV3 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV433 @ SV3 ) ) @ SV856 ) @ SV1211 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1211 @ SV856 @ ( tc_fun @ SV433 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2271]) ).
thf(2677,plain,
! [SV857: $i,SV434: $i,SV4: $i] :
( ( ( SV4 = SV434 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV4 @ SV434 @ ( tc_fun @ SV857 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV857 @ tc_bool ) ) @ SV4 ) @ SV434 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2272]) ).
thf(2678,plain,
! [SV858: $i,SV435: $i,SV5: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV5 @ SV435 @ ( tc_fun @ SV858 @ tc_bool ) )
= $true )
| ( ( ( SV5 = SV435 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV858 @ tc_bool ) ) @ SV5 ) @ SV435 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2273]) ).
thf(2679,plain,
! [SV859: $i,SV436: $i,SV6: $i] :
( ( ( c_Finite__Set_Ofinite @ SV6 @ SV436 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV436 @ tc_bool ) ) @ SV6 ) @ SV859 ) )
| ~ ( c_Finite__Set_Ofinite @ SV859 @ SV436 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2274]) ).
thf(2680,plain,
! [SV1212: $i,SV860: $i,SV437: $i,SV7: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV7 @ SV437 @ ( tc_fun @ SV860 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1212 @ SV437 @ ( tc_fun @ SV860 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV860 @ tc_bool ) ) @ SV7 ) @ SV1212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2275]) ).
thf(2681,plain,
! [SV1213: $i,SV861: $i,SV438: $i,SV8: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV8 @ SV438 @ ( tc_fun @ SV861 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV861 @ tc_bool ) ) @ SV1213 ) @ SV438 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV8 @ SV1213 @ ( tc_fun @ SV861 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2276]) ).
thf(2682,plain,
! [SV862: $i,SV439: $i,SV9: $i] :
( ( ( c_Finite__Set_Ofinite @ SV9 @ SV439 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV862 @ SV439 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV439 @ tc_bool ) ) @ SV9 ) @ SV862 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2277]) ).
thf(2683,plain,
! [SV863: $i,SV440: $i,SV10: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV10 @ tc_bool ) ) @ SV440 ) @ SV863 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV440 @ SV863 @ ( tc_fun @ SV10 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2278]) ).
thf(2684,plain,
! [SV1214: $i,SV864: $i,SV441: $i,SV11: $i] :
( ( ! [SY3777: $i] :
( ~ ( class_Ring__and__Field_Oring @ SV11 )
| ( ( c_Finite__Set_Osetsum @ SV441 @ ( c_HOL_Ominus__class_Ominus @ SV864 @ ( c_Set_Oinsert @ SV1214 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3777 @ tc_bool ) ) @ SY3777 ) @ ( tc_fun @ SY3777 @ tc_bool ) ) @ SY3777 @ SV11 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV441 @ SV864 @ SY3777 @ SV11 ) @ ( hAPP @ SV441 @ SV1214 ) @ SV11 ) )
| ~ ( hBOOL @ ( c_in @ SV1214 @ SV864 @ SY3777 ) )
| ~ ( c_Finite__Set_Ofinite @ SV864 @ SY3777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2279]) ).
thf(2685,plain,
! [SV1215: $i,SV865: $i,SV442: $i,SV12: $i] :
( ( ! [SY3778: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV12 )
| ( ( c_Finite__Set_Osetsum @ SV442 @ ( c_HOL_Ominus__class_Ominus @ SV865 @ ( c_Set_Oinsert @ SV1215 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3778 @ tc_bool ) ) @ SY3778 ) @ ( tc_fun @ SY3778 @ tc_bool ) ) @ SY3778 @ SV12 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV442 @ SV865 @ SY3778 @ SV12 ) @ ( hAPP @ SV442 @ SV1215 ) @ SV12 ) )
| ~ ( hBOOL @ ( c_in @ SV1215 @ SV865 @ SY3778 ) )
| ~ ( c_Finite__Set_Ofinite @ SV865 @ SY3778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2280]) ).
thf(2686,plain,
! [SV1216: $i,SV866: $i,SV443: $i,SV13: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV13 @ ( c_Set_Oinsert @ SV443 @ SV866 @ SV1216 ) @ ( tc_fun @ SV1216 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1216 @ tc_bool ) ) @ SV13 ) @ SV866 ) )
| ( hBOOL @ ( c_in @ SV443 @ SV13 @ SV1216 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV13 @ SV866 @ ( tc_fun @ SV1216 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2281]) ).
thf(2687,plain,
! [SV1217: $i,SV867: $i,SV444: $i,SV14: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV14 @ ( c_Set_Oinsert @ SV444 @ SV867 @ SV1217 ) @ ( tc_fun @ SV1217 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1217 @ tc_bool ) ) @ SV14 ) @ SV867 ) )
| ( hBOOL @ ( c_in @ SV444 @ SV14 @ SV1217 ) )
| ( hBOOL @ ( c_in @ SV444 @ SV867 @ SV1217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2282]) ).
thf(2688,plain,
! [SV1218: $i,SV868: $i,SV445: $i,SV15: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV15 @ tc_bool ) ) @ SV445 ) @ SV868 ) )
| ( hBOOL @ ( c_in @ SV1218 @ SV445 @ SV15 ) )
| ( hBOOL @ ( c_in @ SV1218 @ SV868 @ SV15 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV445 @ ( c_Set_Oinsert @ SV1218 @ SV868 @ SV15 ) @ ( tc_fun @ SV15 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(2689,plain,
! [SV1219: $i,SV869: $i,SV446: $i,SV16: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV16 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV446 @ SV869 @ SV16 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV869 @ SV1219 @ SV16 ) @ ( tc_fun @ SV16 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV446 @ SV1219 @ SV16 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV16 ) @ SV869 ) @ SV1219 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV16 ) @ SV446 ) @ SV869 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(2690,plain,
! [SV871: $i,SV449: $i,SV19: $i] :
( ( ( c_Finite__Set_Ofinite @ SV19 @ SV449 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV871 @ SV19 @ SV449 ) @ SV449 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2286]) ).
thf(2691,plain,
! [SV872: $i,SV450: $i,SV20: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV20 @ SV450 @ SV872 ) @ SV872 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV450 @ SV872 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2287]) ).
thf(2692,plain,
! [SV1220: $i,SV873: $i,SV451: $i,SV21: $i] :
( ( c_Nitpick_Ofold__graph_H @ SV21 @ SV451 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV873 @ tc_bool ) ) @ SV451 @ SV873 @ SV1220 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2288]) ).
thf(2693,plain,
! [SV1221: $i,SV874: $i,SV452: $i,SV22: $i] :
( ( c_Finite__Set_Ofold__graph @ SV22 @ SV452 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV874 @ tc_bool ) ) @ SV452 @ SV874 @ SV1221 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2289]) ).
thf(2694,plain,
! [SV1222: $i,SV875: $i,SV453: $i,SV23: $i] :
( ( ! [SY3779: $i] :
( ( SV23 = SV453 )
| ~ ( c_Finite__Set_Ofold__graph @ SV875 @ SV453 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1222 @ tc_bool ) ) @ SV23 @ SV1222 @ SY3779 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2290]) ).
thf(2695,plain,
! [SV876: $i,SV455: $i,SV26: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV26 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV26 ) @ SV455 ) @ SV876 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV876 @ SV455 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2292]) ).
thf(2696,plain,
! [SV877: $i,SV456: $i,SV27: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV27 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV456 @ SV877 @ SV27 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV27 ) @ SV877 ) @ SV456 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2293]) ).
thf(2697,plain,
! [SV878: $i,SV457: $i,SV28: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV28 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV28 ) @ SV457 ) @ SV878 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV878 @ SV457 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2294]) ).
thf(2698,plain,
! [SV879: $i,SV458: $i,SV29: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV29 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV29 ) @ SV458 ) @ SV879 ) )
| ( c_HOL_Oord__class_Oless @ SV879 @ SV458 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2295]) ).
thf(2699,plain,
! [SV880: $i,SV459: $i,SV30: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV30 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV459 @ SV880 @ SV30 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV30 ) @ SV880 ) @ SV459 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2296]) ).
thf(2700,plain,
! [SV460: $i,SV31: $i] :
( ( ( class_Orderings_Olinorder @ SV31 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV460 @ SV460 @ SV31 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV31 ) @ SV460 ) @ SV460 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2297]) ).
thf(2701,plain,
! [SV461: $i,SV32: $i] :
( ( ( class_Orderings_Olinorder @ SV32 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV32 ) @ SV461 ) @ SV461 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV461 @ SV461 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2298]) ).
thf(2702,plain,
! [SV881: $i,SV462: $i,SV33: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV33 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV462 @ SV881 @ SV33 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV33 ) @ SV881 ) @ SV462 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2299]) ).
thf(2703,plain,
! [SV882: $i,SV463: $i,SV34: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV34 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV463 @ SV882 @ SV34 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV34 ) @ SV882 ) @ SV463 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV34 ) @ SV463 ) @ SV882 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2300]) ).
thf(2704,plain,
! [SV883: $i,SV464: $i,SV35: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV35 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV35 ) @ SV464 ) @ SV883 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV464 @ SV883 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2301]) ).
thf(2705,plain,
! [SV884: $i,SV465: $i,SV36: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV36 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV36 ) @ SV465 ) @ SV884 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV465 @ SV884 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2302]) ).
thf(2706,plain,
! [SV1223: $i,SV885: $i,SV466: $i,SV37: $i] :
( ( ~ ( class_Orderings_Oorder @ SV37 )
| ( c_HOL_Oord__class_Oless @ SV466 @ SV885 @ SV37 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV37 ) @ SV466 ) @ SV1223 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1223 @ SV885 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(2707,plain,
! [SV1224: $i,SV886: $i,SV467: $i,SV38: $i] :
( ( ~ ( class_Orderings_Oorder @ SV38 )
| ( c_HOL_Oord__class_Oless @ SV467 @ SV886 @ SV38 )
| ~ ( c_HOL_Oord__class_Oless @ SV467 @ SV1224 @ SV38 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV38 ) @ SV1224 ) @ SV886 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2304]) ).
thf(2708,plain,
! [SV1225: $i,SV887: $i,SV468: $i,SV39: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV39 )
| ( c_HOL_Oord__class_Oless @ SV468 @ SV887 @ SV39 )
| ~ ( c_HOL_Oord__class_Oless @ SV1225 @ SV887 @ SV39 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV39 ) @ SV468 ) @ SV1225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2305]) ).
thf(2709,plain,
! [SV1226: $i,SV888: $i,SV469: $i,SV40: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV40 )
| ( c_HOL_Oord__class_Oless @ SV469 @ SV888 @ SV40 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV40 ) @ SV1226 ) @ SV888 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV469 @ SV1226 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2306]) ).
thf(2710,plain,
! [SV889: $i,SV470: $i,SV41: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV41 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV470 @ SV889 @ SV41 )
| ( SV889 = SV470 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV41 ) @ SV470 ) @ SV889 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2307]) ).
thf(2711,plain,
! [SV890: $i,SV471: $i,SV42: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV42 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV471 @ SV890 @ SV42 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV42 ) @ SV471 ) @ SV890 ) )
| ( SV890 = SV471 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2308]) ).
thf(2712,plain,
! [SV891: $i,SV472: $i,SV43: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV43 ) )
= $true )
| ( ( ( SV472 = SV891 )
| ( c_HOL_Oord__class_Oless @ SV472 @ SV891 @ SV43 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV43 ) @ SV472 ) @ SV891 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2309]) ).
thf(2713,plain,
! [SV892: $i,SV473: $i,SV44: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV44 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV473 @ SV892 @ SV44 )
| ( SV473 = SV892 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV44 ) @ SV473 ) @ SV892 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2310]) ).
thf(2714,plain,
! [SV893: $i,SV474: $i,SV45: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV45 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV474 @ SV893 @ SV45 )
| ( SV474 = SV893 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV45 ) @ SV474 ) @ SV893 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2311]) ).
thf(2715,plain,
! [SV894: $i,SV475: $i,SV46: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV46 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV475 @ SV894 @ SV46 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV46 ) @ SV475 ) @ SV894 ) )
| ( SV475 = SV894 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2312]) ).
thf(2716,plain,
! [SV895: $i,SV476: $i,SV47: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV47 ) )
= $true )
| ( ( ( SV476 = SV895 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV47 ) @ SV476 ) @ SV895 ) )
| ( c_HOL_Oord__class_Oless @ SV476 @ SV895 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2313]) ).
thf(2717,plain,
! [SV896: $i,SV477: $i,SV48: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV48 ) )
= $true )
| ( ( ( SV477 = SV896 )
| ( c_HOL_Oord__class_Oless @ SV477 @ SV896 @ SV48 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV48 ) @ SV477 ) @ SV896 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2314]) ).
thf(2718,plain,
! [SV897: $i,SV478: $i,SV49: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV49 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV478 @ SV49 ) @ SV897 @ SV49 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV897 @ SV49 ) @ SV478 @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2315]) ).
thf(2719,plain,
! [SV898: $i,SV479: $i,SV50: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV50 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV479 @ SV50 ) @ SV898 @ SV50 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV898 @ SV50 ) @ SV479 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2316]) ).
thf(2720,plain,
! [SV899: $i,SV480: $i,SV51: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV51 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV480 @ ( c_HOL_Ouminus__class_Ouminus @ SV899 @ SV51 ) @ SV51 )
| ~ ( c_HOL_Oord__class_Oless @ SV899 @ ( c_HOL_Ouminus__class_Ouminus @ SV480 @ SV51 ) @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2317]) ).
thf(2721,plain,
! [SV900: $i,SV481: $i,SV52: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV52 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV481 @ ( c_HOL_Ouminus__class_Ouminus @ SV900 @ SV52 ) @ SV52 )
| ~ ( c_HOL_Oord__class_Oless @ SV900 @ ( c_HOL_Ouminus__class_Ouminus @ SV481 @ SV52 ) @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2318]) ).
thf(2722,plain,
! [SV1227: $i,SV901: $i,SV482: $i,SV53: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV53 )
| ( c_HOL_Oord__class_Oless @ SV482 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV901 @ SV1227 @ SV53 ) @ SV53 )
| ~ ( c_HOL_Oord__class_Oless @ SV482 @ SV1227 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2319]) ).
thf(2723,plain,
! [SV1228: $i,SV902: $i,SV483: $i,SV54: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV54 )
| ( c_HOL_Oord__class_Oless @ SV483 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV902 @ SV1228 @ SV54 ) @ SV54 )
| ~ ( c_HOL_Oord__class_Oless @ SV483 @ SV902 @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2320]) ).
thf(2724,plain,
! [SV484: $i,SV55: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ SV55 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV484 @ SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2321]) ).
thf(2725,plain,
! [SV1229: $i,SV903: $i,SV485: $i,SV56: $i] :
( ( ! [SY3780: $i] :
( ~ ( class_Orderings_Oorder @ SV56 )
| ( c_HOL_Oord__class_Oless @ SV485 @ SV903 @ SV56 )
| ( c_HOL_Oord__class_Oless @ SV1229 @ SY3780 @ SV56 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV56 ) @ SY3780 ) @ SV485 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3780 @ SV485 @ SV56 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1229 @ SV903 @ SV56 ) @ ( tc_fun @ SV56 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2322]) ).
thf(2726,plain,
! [SV1230: $i,SV904: $i,SV486: $i,SV57: $i] :
( ( ! [SY3781: $i,SY3782: $i,SY3783: $i,SY3784: $i,SY3785: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV57 @ SV486 @ ( c_COMBC @ SV904 @ SV1230 @ SV1230 @ tc_bool ) @ ( c_COMBC @ SY3781 @ SV1230 @ SV1230 @ tc_bool ) @ SY3782 @ SY3783 @ SY3784 @ SY3785 @ SV1230 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV486 @ SV57 @ SV904 @ SY3781 @ SY3783 @ SY3782 @ SY3785 @ SY3784 @ SV1230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2323]) ).
thf(2727,plain,
! [SV1231: $i,SV905: $i,SV487: $i,SV58: $i] :
( ( ( hAPP @ ( c_COMBK @ SV58 @ SV487 @ SV905 ) @ SV1231 )
= SV58 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2324]) ).
thf(2728,plain,
! [SV1232: $i,SV906: $i,SV488: $i,SV59: $i] :
( ( ! [SY3786: $i,SY3787: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV59 @ SV488 @ SV906 @ SV1232 ) @ SY3786 ) @ SY3787 )
= ( hAPP @ ( hAPP @ SV59 @ SY3787 ) @ SY3786 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2325]) ).
thf(2729,plain,
! [SV1233: $i,SV907: $i,SV489: $i,SV60: $i] :
( ( ~ ( class_Orderings_Oorder @ SV60 )
| ( c_HOL_Oord__class_Oless @ SV489 @ SV907 @ SV60 )
| ~ ( c_HOL_Oord__class_Oless @ SV489 @ SV1233 @ SV60 )
| ~ ( c_HOL_Oord__class_Oless @ SV1233 @ SV907 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2326]) ).
thf(2730,plain,
! [SV1234: $i,SV908: $i,SV490: $i,SV61: $i] :
( ( ( hBOOL @ ( c_in @ SV61 @ SV490 @ SV908 ) )
| ~ ( hBOOL @ ( c_in @ SV61 @ SV1234 @ SV908 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1234 @ SV490 @ ( tc_fun @ SV908 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2327]) ).
thf(2731,plain,
! [SV1235: $i,SV909: $i,SV491: $i,SV62: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV62 @ SV491 @ ( tc_fun @ SV909 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1235 @ SV491 @ ( tc_fun @ SV909 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV62 @ SV1235 @ ( tc_fun @ SV909 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2328]) ).
thf(2732,plain,
! [SV1236: $i,SV910: $i,SV492: $i,SV63: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV63 )
| ( c_HOL_Oord__class_Oless @ SV492 @ SV910 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV1236 @ SV910 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV492 @ SV1236 @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2329]) ).
thf(2733,plain,
! [SV1237: $i,SV911: $i,SV493: $i,SV64: $i] :
( ( ! [SY3788: $i,SY3789: $i] :
( ( c_Finite__Set_Ofinite @ SV64 @ SV493 )
| ~ ( c_Finite__Set_Ofold__graph @ SV911 @ SV1237 @ SV64 @ SY3788 @ SV493 @ SY3789 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2330]) ).
thf(2734,plain,
! [SV912: $i,SV494: $i,SV65: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV65 ) )
= $true )
| ( ( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV494 @ SV912 @ SV65 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV65 @ tc_bool ) ) )
| ( c_HOL_Oord__class_Oless @ SV494 @ SV912 @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2331]) ).
thf(2735,plain,
! [SV913: $i,SV495: $i,SV66: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV66 @ SV495 @ ( tc_fun @ SV913 @ tc_bool ) ) @ SV913 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV66 @ SV913 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2332]) ).
thf(2736,plain,
! [SV914: $i,SV496: $i,SV67: $i] :
( ( ( c_Finite__Set_Ofinite @ SV67 @ SV496 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV67 @ SV914 @ ( tc_fun @ SV496 @ tc_bool ) ) @ SV496 )
| ~ ( c_Finite__Set_Ofinite @ SV914 @ SV496 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2333]) ).
thf(2737,plain,
! [SV915: $i,SV497: $i,SV68: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV68 @ SV497 @ ( tc_fun @ SV915 @ tc_bool ) ) @ SV915 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV68 @ SV915 )
| ~ ( c_Finite__Set_Ofinite @ SV497 @ SV915 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2334]) ).
thf(2738,plain,
! [SV916: $i,SV499: $i,SV70: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV70 @ SV499 @ ( tc_fun @ SV916 @ tc_bool ) ) @ SV916 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV499 @ SV916 )
| ~ ( c_Finite__Set_Ofinite @ SV70 @ SV916 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2335]) ).
thf(2739,plain,
! [SV917: $i,SV500: $i,SV71: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV71 @ SV500 @ ( tc_fun @ SV917 @ tc_bool ) ) @ SV917 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV500 @ SV917 )
| ~ ( c_Finite__Set_Ofinite @ SV71 @ SV917 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2336]) ).
thf(2740,plain,
! [SV918: $i,SV501: $i,SV72: $i] :
( ( ( c_Finite__Set_Ofinite @ SV72 @ SV501 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV72 @ SV918 @ ( tc_fun @ SV501 @ tc_bool ) ) @ SV501 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2337]) ).
thf(2741,plain,
! [SV919: $i,SV502: $i,SV73: $i] :
( ( ( c_Finite__Set_Ofinite @ SV73 @ SV502 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV919 @ SV73 @ ( tc_fun @ SV502 @ tc_bool ) ) @ SV502 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2338]) ).
thf(2742,plain,
! [SV920: $i,SV503: $i,SV74: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV74 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV503 @ SV74 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV920 @ SV74 ) @ SV74 )
| ~ ( c_HOL_Oord__class_Oless @ SV920 @ SV503 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2339]) ).
thf(2743,plain,
! [SV921: $i,SV504: $i,SV75: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV75 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV504 @ SV921 @ SV75 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV921 @ SV75 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV504 @ SV75 ) @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2340]) ).
thf(2744,plain,
! [SV506: $i,SV77: $i] :
( ( ( class_Orderings_Oorder @ SV77 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV506 @ SV506 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2342]) ).
thf(2745,plain,
! [SV507: $i,SV78: $i] :
( ( ( class_Orderings_Olinorder @ SV78 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV507 @ SV507 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2343]) ).
thf(2746,plain,
! [SV508: $i,SV79: $i] :
( ( ( class_Orderings_Opreorder @ SV79 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV508 @ SV508 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2344]) ).
thf(2747,plain,
! [SV1238: $i,SV922: $i,SV509: $i,SV80: $i] :
( ( ! [SY3790: $i] :
( ~ ( class_Orderings_Oorder @ SV80 )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV509 @ SV922 @ SV80 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1238 @ SY3790 @ SV80 ) @ ( tc_fun @ SV80 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV1238 ) @ SY3790 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV922 @ SY3790 @ SV80 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV922 ) @ SY3790 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV1238 ) @ SV509 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2345]) ).
thf(2748,plain,
! [SV1239: $i,SV923: $i,SV510: $i,SV81: $i] :
( ( ! [SY3791: $i] :
( ~ ( class_Orderings_Oorder @ SV81 )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV510 @ SV923 @ SV81 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1239 @ SY3791 @ SV81 ) @ ( tc_fun @ SV81 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV1239 ) @ SY3791 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1239 @ SV510 @ SV81 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV923 ) @ SY3791 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV1239 ) @ SV510 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2346]) ).
thf(2749,plain,
! [SV924: $i,SV511: $i,SV82: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV82 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV511 @ SV924 @ SV82 )
| ( c_HOL_Oord__class_Oless @ SV924 @ SV511 @ SV82 )
| ( SV924 = SV511 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2347]) ).
thf(2750,plain,
! [SV925: $i,SV512: $i,SV83: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV83 ) )
= $true )
| ( ( ( SV512 = SV925 )
| ( c_HOL_Oord__class_Oless @ SV925 @ SV512 @ SV83 )
| ( c_HOL_Oord__class_Oless @ SV512 @ SV925 @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2348]) ).
thf(2751,plain,
! [SV926: $i,SV513: $i,SV84: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV84 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV513 @ SV926 @ SV84 )
| ( c_HOL_Oord__class_Oless @ SV926 @ SV513 @ SV84 )
| ( SV926 = SV513 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2349]) ).
thf(2752,plain,
! [SV927: $i,SV514: $i,SV85: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV85 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV514 @ SV927 @ SV85 )
| ( SV927 = SV514 )
| ( c_HOL_Oord__class_Oless @ SV927 @ SV514 @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2350]) ).
thf(2753,plain,
! [SV928: $i,SV515: $i,SV86: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV86 ) )
= $true )
| ( ( ( SV515 = SV928 )
| ( c_HOL_Oord__class_Oless @ SV515 @ SV928 @ SV86 )
| ( c_HOL_Oord__class_Oless @ SV928 @ SV515 @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2351]) ).
thf(2754,plain,
! [SV929: $i,SV516: $i,SV87: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV87 ) )
= $true )
| ( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV87 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV516 @ SV929 @ SV87 ) )
| ( c_HOL_Oord__class_Oless @ SV516 @ SV929 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2352]) ).
thf(2755,plain,
! [SV930: $i,SV517: $i,SV88: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV88 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV517 @ SV930 @ SV88 )
| ~ ( c_HOL_Oord__class_Oless @ SV930 @ SV517 @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2353]) ).
thf(2756,plain,
! [SV931: $i,SV518: $i,SV89: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV89 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV518 @ SV931 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV931 @ SV518 @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2354]) ).
thf(2757,plain,
! [SV932: $i,SV519: $i,SV90: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV90 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV519 @ SV932 @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ SV932 @ SV519 @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2355]) ).
thf(2758,plain,
! [SV933: $i,SV520: $i,SV91: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV91 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV520 @ SV933 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV933 @ SV520 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2356]) ).
thf(2759,plain,
! [SV1240: $i,SV934: $i,SV521: $i,SV92: $i] :
( ( ! [SY3792: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV92 )
| ( ( c_Finite__Set_Osetsum @ SV521 @ ( c_HOL_Ominus__class_Ominus @ SV934 @ SV1240 @ ( tc_fun @ SY3792 @ tc_bool ) ) @ SY3792 @ SV92 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV521 @ SV934 @ SY3792 @ SV92 ) @ ( c_Finite__Set_Osetsum @ SV521 @ SV1240 @ SY3792 @ SV92 ) @ SV92 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY3792 @ tc_bool ) ) @ SV1240 ) @ SV934 ) )
| ~ ( c_Finite__Set_Ofinite @ SV934 @ SY3792 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2357]) ).
thf(2760,plain,
! [SV935: $i,SV522: $i,SV93: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV93 ) )
= $true )
| ( ( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV522 @ SV935 @ SV93 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV93 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV93 ) @ SV935 ) @ SV522 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2358]) ).
thf(2761,plain,
! [SV1241: $i,SV936: $i,SV523: $i,SV94: $i] :
( ( ! [SY3793: $i,SY3794: $i,SY3795: $i] :
( ( c_Finite__Set_Ofold__graph @ SV94 @ SV523 @ ( c_Set_Oinsert @ SV936 @ SV1241 @ SY3793 ) @ ( hAPP @ ( hAPP @ SV94 @ SV936 ) @ SY3794 ) @ SY3793 @ SY3795 )
| ~ ( c_Finite__Set_Ofold__graph @ SV94 @ SV523 @ SV1241 @ SY3794 @ SY3793 @ SY3795 )
| ( hBOOL @ ( c_in @ SV936 @ SV1241 @ SY3793 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2359]) ).
thf(2762,plain,
! [SV1242: $i,SV937: $i,SV524: $i,SV95: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV95 @ SV524 @ ( tc_fun @ SV937 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV1242 @ SV524 @ SV937 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV95 @ ( c_Set_Oinsert @ SV1242 @ SV524 @ SV937 ) @ ( tc_fun @ SV937 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2360]) ).
thf(2763,plain,
! [SV1243: $i,SV938: $i,SV525: $i,SV96: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV96 @ ( c_Set_Oinsert @ SV525 @ SV938 @ SV1243 ) @ ( tc_fun @ SV1243 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV525 @ SV938 @ SV1243 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV96 @ SV938 @ ( tc_fun @ SV1243 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2361]) ).
thf(2764,plain,
! [SV1244: $i,SV939: $i,SV526: $i,SV97: $i] :
( ( ! [SY3796: $i] :
( ~ ( class_Orderings_Oorder @ SV97 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV97 ) @ SV526 ) @ SV939 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV97 ) @ SV1244 ) @ SV526 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1244 @ SV526 @ SV97 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3796 @ SV939 @ SV97 ) @ ( tc_fun @ SV97 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2362]) ).
thf(2765,plain,
! [SV1245: $i,SV940: $i,SV527: $i,SV98: $i] :
( ( ! [SY3797: $i] :
( ~ ( class_Orderings_Oorder @ SV98 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV98 ) @ SV527 ) @ SV940 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV98 ) @ SV940 ) @ SV1245 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV940 @ SV1245 @ SV98 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV527 @ SY3797 @ SV98 ) @ ( tc_fun @ SV98 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2363]) ).
thf(2766,plain,
! [SV1246: $i,SV941: $i,SV528: $i,SV99: $i] :
( ( ! [SY3798: $i] :
( ~ ( class_Orderings_Oorder @ SV99 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV99 ) @ SV528 ) @ SV941 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1246 @ SY3798 @ SV99 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV528 @ SV941 @ SV99 ) @ ( tc_fun @ SV99 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2364]) ).
thf(2767,plain,
! [SV1247: $i,SV942: $i,SV529: $i,SV100: $i] :
( ( ! [SY3799: $i] :
( ~ ( class_Orderings_Oorder @ SV100 )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV529 @ SV942 @ SV100 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1247 @ SY3799 @ SV100 ) @ ( tc_fun @ SV100 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV100 ) @ SV1247 ) @ SY3799 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV100 ) @ SV529 ) @ SV942 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2365]) ).
thf(2768,plain,
! [SV1248: $i,SV943: $i,SV530: $i,SV101: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV101 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV530 @ SV943 @ SV101 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV943 @ SV1248 @ SV101 ) @ ( tc_fun @ SV101 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV530 @ SV1248 @ SV101 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV101 ) @ SV943 ) @ SV1248 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV101 ) @ SV530 ) @ SV943 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2366]) ).
thf(2769,plain,
! [SV1249: $i,SV944: $i,SV531: $i,SV102: $i] :
( ( ! [SY3800: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ SV102 @ SV531 ) @ SV944 )
| ~ ( hBOOL @ ( c_in @ SV531 @ SV1249 @ SY3800 ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1249 @ SV102 @ SY3800 @ ( tc_fun @ SV944 @ tc_bool ) ) @ SV944 )
| ~ ( c_Finite__Set_Ofinite @ SV1249 @ SY3800 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2367]) ).
thf(2770,plain,
! [SV1250: $i,SV945: $i,SV532: $i,SV103: $i] :
( ( ! [SY3801: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV103 )
| ( ( c_Finite__Set_Osetsum @ SV532 @ ( c_HOL_Ominus__class_Ominus @ SV945 @ ( c_Set_Oinsert @ SV1250 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3801 @ tc_bool ) ) @ SY3801 ) @ ( tc_fun @ SY3801 @ tc_bool ) ) @ SY3801 @ SV103 )
= ( c_Finite__Set_Osetsum @ SV532 @ SV945 @ SY3801 @ SV103 ) )
| ( hBOOL @ ( c_in @ SV1250 @ SV945 @ SY3801 ) )
| ~ ( c_Finite__Set_Ofinite @ SV945 @ SY3801 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2368]) ).
thf(2771,plain,
! [SV946: $i,SV533: $i,SV104: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV104 ) )
= $true )
| ( ( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV533 @ SV946 @ SV104 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV104 @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV946 @ SV533 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2369]) ).
thf(2772,plain,
! [SV1251: $i,SV947: $i,SV534: $i,SV105: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV105 )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV534 @ ( c_COMBK @ SV947 @ SV105 @ SV1251 ) @ SV1251 @ SV105 )
= SV947 )
| ( SV534
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1251 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2370]) ).
thf(2773,plain,
! [SV1252: $i,SV949: $i,SV536: $i,SV107: $i] :
( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV107 @ ( c_COMBK @ SV536 @ ( tc_fun @ SV949 @ tc_bool ) @ SV1252 ) @ SV1252 @ ( tc_fun @ SV949 @ tc_bool ) )
= SV536 )
| ( SV107
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1252 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2372]) ).
thf(2774,plain,
! [SV1253: $i,SV951: $i,SV538: $i,SV109: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV109 @ SV538 @ ( tc_fun @ SV951 @ tc_bool ) ) @ SV951 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV109 @ ( c_Set_Oinsert @ SV1253 @ SV538 @ SV951 ) @ ( tc_fun @ SV951 @ tc_bool ) ) @ SV951 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2374]) ).
thf(2775,plain,
! [SV1254: $i,SV952: $i,SV539: $i,SV110: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV110 @ ( c_Set_Oinsert @ SV539 @ SV952 @ SV1254 ) @ ( tc_fun @ SV1254 @ tc_bool ) ) @ SV1254 )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV110 @ SV952 @ ( tc_fun @ SV1254 @ tc_bool ) ) @ SV1254 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2375]) ).
thf(2776,plain,
! [SV953: $i,SV540: $i,SV111: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV111 ) )
= $true )
| ( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV111 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV540 @ SV953 @ SV111 ) )
| ( c_HOL_Oord__class_Oless @ SV540 @ SV953 @ SV111 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2376]) ).
thf(2777,plain,
! [SV954: $i,SV541: $i,SV112: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV112 ) )
= $true )
| ( ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ SV541 @ SV954 @ SV112 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV112 @ tc_bool ) ) )
| ( c_HOL_Oord__class_Oless @ SV541 @ SV954 @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2377]) ).
thf(2778,plain,
! [SV955: $i,SV542: $i,SV114: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV114 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV114 ) @ SV542 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV955 @ SV114 ) ) )
| ~ ( hBOOL @ ( c_in @ SV542 @ SV955 @ SV114 ) )
| ~ ( c_Finite__Set_Ofinite @ SV955 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2379]) ).
thf(2779,plain,
! [SV956: $i,SV543: $i,SV115: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV115 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV115 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV543 @ SV115 ) ) @ SV956 ) )
| ~ ( hBOOL @ ( c_in @ SV956 @ SV543 @ SV115 ) )
| ~ ( c_Finite__Set_Ofinite @ SV543 @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2380]) ).
thf(2780,plain,
! [SV544: $i,SV116: $i] :
( ( ( class_Orderings_Olinorder @ SV116 )
= $false )
| ( ( ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMin @ SV544 @ SV116 ) @ SV544 @ SV116 ) )
| ( SV544
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV116 @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV544 @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2381]) ).
thf(2781,plain,
! [SV545: $i,SV117: $i] :
( ( ( class_Orderings_Olinorder @ SV117 )
= $false )
| ( ( ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMax @ SV545 @ SV117 ) @ SV545 @ SV117 ) )
| ( SV545
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV117 @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV545 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2382]) ).
thf(2782,plain,
! [SV1255: $i,SV957: $i,SV546: $i,SV118: $i] :
( ( ! [SY3802: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV118 @ ( c_Set_Oinsert @ SV546 @ SV957 @ SV1255 ) @ SV1255 ) @ SY3802 ) )
| ( hBOOL @ ( c_in @ SV546 @ SV957 @ SV1255 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV118 @ SV546 @ SV957 @ SY3802 @ SV1255 @ SV1255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2383]) ).
thf(2783,plain,
! [SV1256: $i,SV958: $i,SV547: $i,SV119: $i] :
( ( ! [SY3803: $i,SY3804: $i,SY3805: $i] :
( ( c_Finite__Set_Ofold__graph @ SV119 @ SV547 @ SV958 @ ( hAPP @ ( hAPP @ SV119 @ SV1256 ) @ SY3803 ) @ SY3804 @ SY3805 )
| ~ ( hBOOL @ ( c_in @ SV1256 @ SV958 @ SY3804 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV119 @ SV547 @ ( c_HOL_Ominus__class_Ominus @ SV958 @ ( c_Set_Oinsert @ SV1256 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3804 @ tc_bool ) ) @ SY3804 ) @ ( tc_fun @ SY3804 @ tc_bool ) ) @ SY3803 @ SY3804 @ SY3805 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2384]) ).
thf(2784,plain,
! [SV1257: $i,SV959: $i,SV548: $i,SV120: $i] :
( ( ( ( c_Finite__Set_Osetsum @ SV120 @ ( c_HOL_Ominus__class_Ominus @ SV548 @ ( c_Set_Oinsert @ SV959 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1257 @ tc_bool ) ) @ SV1257 ) @ ( tc_fun @ SV1257 @ tc_bool ) ) @ SV1257 @ tc_nat )
= ( c_Finite__Set_Osetsum @ SV120 @ SV548 @ SV1257 @ tc_nat ) )
| ( hBOOL @ ( c_in @ SV959 @ SV548 @ SV1257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2385]) ).
thf(2785,plain,
! [SV1258: $i,SV960: $i,SV549: $i,SV121: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV121 @ ( c_Set_Oinsert @ SV549 @ SV960 @ SV1258 ) @ ( tc_fun @ SV1258 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV549 @ SV121 @ SV1258 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV121 @ ( c_Set_Oinsert @ SV549 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1258 @ tc_bool ) ) @ SV1258 ) @ ( tc_fun @ SV1258 @ tc_bool ) ) @ SV960 @ ( tc_fun @ SV1258 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV121 @ SV960 @ ( tc_fun @ SV1258 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2386]) ).
thf(2786,plain,
! [SV1259: $i,SV961: $i,SV550: $i,SV122: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV122 @ ( c_Set_Oinsert @ SV550 @ SV961 @ SV1259 ) @ ( tc_fun @ SV1259 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV550 @ SV122 @ SV1259 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV122 @ ( c_Set_Oinsert @ SV550 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1259 @ tc_bool ) ) @ SV1259 ) @ ( tc_fun @ SV1259 @ tc_bool ) ) @ SV961 @ ( tc_fun @ SV1259 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SV550 @ SV961 @ SV1259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2387]) ).
thf(2787,plain,
! [SV1260: $i,SV962: $i,SV551: $i,SV123: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV123 @ ( c_Set_Oinsert @ SV551 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV962 @ tc_bool ) ) @ SV962 ) @ ( tc_fun @ SV962 @ tc_bool ) ) @ SV1260 @ ( tc_fun @ SV962 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV551 @ SV123 @ SV962 ) )
| ( hBOOL @ ( c_in @ SV551 @ SV1260 @ SV962 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV123 @ ( c_Set_Oinsert @ SV551 @ SV1260 @ SV962 ) @ ( tc_fun @ SV962 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2388]) ).
thf(2788,plain,
! [SV1261: $i,SV963: $i,SV552: $i,SV124: $i] :
( ( ! [SY3806: $i,SY3807: $i,SY3808: $i] :
( ( c_Nitpick_Ofold__graph_H @ SV124 @ SV552 @ SV963 @ ( hAPP @ ( hAPP @ SV124 @ SV1261 ) @ SY3806 ) @ SY3807 @ SY3808 )
| ~ ( c_Nitpick_Ofold__graph_H @ SV124 @ SV552 @ ( c_HOL_Ominus__class_Ominus @ SV963 @ ( c_Set_Oinsert @ SV1261 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3807 @ tc_bool ) ) @ SY3807 ) @ ( tc_fun @ SY3807 @ tc_bool ) ) @ SY3806 @ SY3807 @ SY3808 )
| ~ ( hBOOL @ ( c_in @ SV1261 @ SV963 @ SY3807 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2389]) ).
thf(2789,plain,
! [SV1262: $i,SV964: $i,SV553: $i,SV125: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV125 @ ( c_Set_Oinsert @ SV553 @ SV964 @ SV1262 ) @ ( tc_fun @ SV1262 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1262 @ tc_bool ) ) @ SV125 ) @ SV964 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV125 @ ( c_Set_Oinsert @ SV553 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1262 @ tc_bool ) ) @ SV1262 ) @ ( tc_fun @ SV1262 @ tc_bool ) ) @ SV964 @ ( tc_fun @ SV1262 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV125 @ SV964 @ ( tc_fun @ SV1262 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2390]) ).
thf(2790,plain,
! [SV965: $i,SV554: $i,SV126: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV126 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV126 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV554 @ SV126 ) ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV965 @ SV126 ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV554 @ SV126 )
| ( SV965
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV126 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV126 @ tc_bool ) ) @ SV965 ) @ SV554 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2391]) ).
thf(2791,plain,
! [SV966: $i,SV555: $i,SV127: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV127 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV127 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV555 @ SV127 ) ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV966 @ SV127 ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV966 @ SV127 )
| ( SV555
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV127 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV127 @ tc_bool ) ) @ SV555 ) @ SV966 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2392]) ).
thf(2792,plain,
! [SV1263: $i,SV967: $i,SV556: $i,SV128: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV128 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV556 @ SV967 @ SV1263 @ 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 @ SV128 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_COMBK @ ( hAPP @ ( c_COMBC @ ( c_fequal @ tc_Com_Ostate ) @ tc_Com_Ostate @ tc_Com_Ostate @ tc_bool ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ SV128 @ SV556 @ SV1263 @ SV967 ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) @ SV967 @ ( c_COMBK @ ( hAPP @ SV1263 @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ SV128 @ SV556 @ SV1263 @ SV967 ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) @ 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_forall_pos,[status(thm)],[2393]) ).
thf(2793,plain,
! [SV968: $i,SV557: $i,SV129: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV129 ) )
= $true )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV557 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV129 @ tc_bool ) ) @ SV129 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV557 @ SV968 @ SV129 ) @ ( tc_fun @ SV129 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV557 @ SV968 @ SV129 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV129 ) @ SV557 ) @ SV968 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2394]) ).
thf(2794,plain,
! [SV1264: $i,SV969: $i,SV558: $i,SV130: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV130 @ ( c_Set_Oinsert @ SV558 @ SV969 @ SV1264 ) @ ( tc_fun @ SV1264 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1264 @ tc_bool ) ) @ SV130 ) @ SV969 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV130 @ ( c_Set_Oinsert @ SV558 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1264 @ tc_bool ) ) @ SV1264 ) @ ( tc_fun @ SV1264 @ tc_bool ) ) @ SV969 @ ( tc_fun @ SV1264 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SV558 @ SV969 @ SV1264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2395]) ).
thf(2795,plain,
! [SV1265: $i,SV970: $i,SV559: $i,SV131: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV131 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV559 @ SV970 @ SV131 ) ) @ SV1265 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ SV970 ) @ SV1265 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ SV559 ) @ SV1265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2396]) ).
thf(2796,plain,
! [SV1266: $i,SV971: $i,SV560: $i,SV132: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV132 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV560 @ SV971 @ SV132 ) ) @ SV1266 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ SV971 ) @ SV1266 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ SV560 ) @ SV1266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2397]) ).
thf(2797,plain,
! [SV972: $i,SV561: $i,SV133: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV133 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV133 ) @ SV561 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV972 @ SV561 @ SV133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2398]) ).
thf(2798,plain,
! [SV973: $i,SV562: $i,SV134: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV134 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV134 ) @ SV562 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV562 @ SV973 @ SV134 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2399]) ).
thf(2799,plain,
! [SV974: $i,SV563: $i,SV135: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV135 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV135 ) @ SV563 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV974 @ SV135 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV135 ) @ SV974 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV563 @ SV135 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2400]) ).
thf(2800,plain,
! [SV975: $i,SV564: $i,SV136: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV136 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV136 ) @ SV564 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV975 @ SV136 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV136 ) @ SV975 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV564 @ SV136 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2401]) ).
thf(2801,plain,
! [SV976: $i,SV565: $i,SV137: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV137 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV137 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV565 @ SV137 ) ) @ SV976 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV137 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV976 @ SV137 ) ) @ SV565 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2402]) ).
thf(2802,plain,
! [SV977: $i,SV566: $i,SV138: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV138 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV138 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV566 @ SV138 ) ) @ SV977 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV138 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV977 @ SV138 ) ) @ SV566 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2403]) ).
thf(2803,plain,
! [SV978: $i,SV567: $i,SV139: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV139 ) )
= $true )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV567 @ SV978 @ SV139 ) @ ( c_Set_Oinsert @ SV978 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV139 @ tc_bool ) ) @ SV139 ) @ ( tc_fun @ SV139 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV567 @ SV978 @ SV139 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV139 ) @ SV567 ) @ SV978 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2404]) ).
thf(2804,plain,
! [SV568: $i,SV140: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV140 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ SV140 ) @ SV568 @ SV140 )
= SV568 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2405]) ).
thf(2805,plain,
! [SV569: $i,SV141: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV141 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV569 @ ( c_Orderings_Obot__class_Obot @ SV141 ) @ SV141 )
= SV569 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2406]) ).
thf(2806,plain,
! [SV1267: $i,SV979: $i,SV570: $i,SV143: $i] :
( ( ! [SY3809: $i,SY3810: $i,SY3811: $i,SY3812: $i,SY3813: $i] :
( ( ( hAPP @ SV143 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV570 @ tc_bool ) ) )
= SV979 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV143 @ SV1267 @ SY3809 @ SY3810 @ SY3811 @ SY3812 @ SY3813 @ SV979 @ SV570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2407]) ).
thf(2807,plain,
! [SV1268: $i,SV980: $i,SV571: $i,SV144: $i] :
( ( ! [SY3814: $i,SY3815: $i,SY3816: $i,SY3817: $i,SY3818: $i] :
( ( ( hAPP @ SV144 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV571 @ tc_bool ) ) )
= SV980 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1268 @ SV144 @ SY3814 @ SY3815 @ SY3816 @ SY3817 @ SV980 @ SY3818 @ SV571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2408]) ).
thf(2808,plain,
! [SV981: $i,SV573: $i,SV146: $i] :
( ( ( hBOOL @ ( hAPP @ SV146 @ SV573 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV573 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV981 @ tc_bool ) ) @ SV981 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2410]) ).
thf(2809,plain,
! [SV982: $i,SV576: $i,SV149: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV149 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV576 @ tc_bool ) ) @ SV576 ) @ SV982 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2413]) ).
thf(2810,plain,
! [SV983: $i,SV582: $i,SV155: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV155 @ SV582 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV582 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV983 @ tc_bool ) ) @ SV983 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2414]) ).
thf(2811,plain,
! [SV984: $i,SV583: $i,SV156: $i] :
( ( ( ( c_Set_Oinsert @ SV156 @ ( c_HOL_Ominus__class_Ominus @ SV583 @ ( c_Set_Oinsert @ SV156 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV984 @ tc_bool ) ) @ SV984 ) @ ( tc_fun @ SV984 @ tc_bool ) ) @ SV984 )
= SV583 )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV156 @ SV583 @ SV984 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2415]) ).
thf(2812,plain,
! [SV985: $i,SV584: $i,SV157: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV157 ) )
= $true )
| ( ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV157 ) @ ( c_Set_Oinsert @ SV584 @ ( c_Set_Oinsert @ SV985 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV157 @ tc_bool ) ) @ SV157 ) @ SV157 ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV584 @ SV985 @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2416]) ).
thf(2813,plain,
! [SV986: $i,SV585: $i,SV158: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV158 @ SV585 @ SV986 ) @ ( c_Set_Oinsert @ SV158 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV986 @ tc_bool ) ) @ SV986 ) @ ( tc_fun @ SV986 @ tc_bool ) )
= SV585 )
= $true )
| ( ( hBOOL @ ( c_in @ SV158 @ SV585 @ SV986 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2417]) ).
thf(2814,plain,
! [SV1269: $i,SV987: $i,SV586: $i,SV159: $i] :
( ( ( hBOOL @ ( c_in @ SV159 @ ( c_Set_Oinsert @ SV586 @ SV987 @ SV1269 ) @ SV1269 ) )
| ~ ( hBOOL @ ( c_in @ SV159 @ SV987 @ SV1269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2418]) ).
thf(2815,plain,
! [SV1270: $i,SV988: $i,SV587: $i,SV160: $i] :
( ( ( hBOOL @ ( c_in @ SV160 @ ( c_Set_Oinsert @ SV587 @ SV988 @ SV1270 ) @ SV1270 ) )
| ~ ( hBOOL @ ( c_in @ SV160 @ SV988 @ SV1270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2419]) ).
thf(2816,plain,
! [SV1271: $i,SV989: $i,SV588: $i,SV161: $i] :
( ( ! [SY3819: $i,SY3820: $i,SY3821: $i,SY3822: $i,SY3823: $i,SY3824: $i,SY3825: $i] :
( ( ( hAPP @ SV161 @ ( c_Set_Oinsert @ SV588 @ SV989 @ SV1271 ) )
= ( hAPP @ ( hAPP @ SY3819 @ SV588 ) @ ( hAPP @ SV161 @ SV989 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV161 @ SY3820 @ SY3821 @ SY3822 @ SY3819 @ SY3823 @ SY3824 @ SY3825 @ SV1271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2420]) ).
thf(2817,plain,
! [SV1272: $i,SV990: $i,SV589: $i,SV162: $i] :
( ( ! [SY3826: $i,SY3827: $i,SY3828: $i,SY3829: $i,SY3830: $i,SY3831: $i,SY3832: $i] :
( ( ( hAPP @ SV162 @ ( c_Set_Oinsert @ SV589 @ SV990 @ SV1272 ) )
= ( hAPP @ ( hAPP @ SY3826 @ SV589 ) @ ( hAPP @ SV162 @ SV990 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3827 @ SV162 @ SY3828 @ SY3829 @ SY3830 @ SY3826 @ SY3831 @ SY3832 @ SV1272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2421]) ).
thf(2818,plain,
! [SV1273: $i,SV991: $i,SV590: $i,SV163: $i] :
( ( ( hBOOL @ ( c_in @ SV163 @ SV590 @ SV991 ) )
| ( SV163 = SV1273 )
| ~ ( hBOOL @ ( c_in @ SV163 @ ( c_Set_Oinsert @ SV1273 @ SV590 @ SV991 ) @ SV991 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2422]) ).
thf(2819,plain,
! [SV1274: $i,SV992: $i,SV591: $i,SV164: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV164 @ ( c_Set_Oinsert @ SV591 @ SV992 @ SV1274 ) @ ( tc_fun @ SV1274 @ tc_bool ) )
= ( c_Set_Oinsert @ SV591 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV164 @ SV992 @ ( tc_fun @ SV1274 @ tc_bool ) ) @ SV1274 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2423]) ).
thf(2820,plain,
! [SV1275: $i,SV993: $i,SV592: $i,SV165: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV165 @ SV592 @ SV993 ) @ SV1275 @ ( tc_fun @ SV993 @ tc_bool ) )
= ( c_Set_Oinsert @ SV165 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV592 @ SV1275 @ ( tc_fun @ SV993 @ tc_bool ) ) @ SV993 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2424]) ).
thf(2821,plain,
! [SV997: $i,SV596: $i,SV169: $i] :
( ( ( ( c_Set_Oinsert @ SV169 @ SV596 @ SV997 )
= SV596 )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV169 @ SV596 @ SV997 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2428]) ).
thf(2822,plain,
! [SV1276: $i,SV998: $i,SV597: $i,SV170: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV170 @ ( c_HOL_Ominus__class_Ominus @ SV597 @ SV998 @ ( tc_fun @ SV1276 @ tc_bool ) ) @ ( tc_fun @ SV1276 @ tc_bool ) )
= SV998 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV170 ) @ SV597 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV998 ) @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2429]) ).
thf(2823,plain,
! [SV1277: $i,SV999: $i,SV598: $i,SV171: $i] :
( ( ( hBOOL @ ( c_in @ SV171 @ SV598 @ SV999 ) )
| ~ ( hBOOL @ ( c_in @ SV171 @ SV1277 @ SV999 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV999 @ tc_bool ) ) @ SV1277 ) @ SV598 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2430]) ).
thf(2824,plain,
! [SV1278: $i,SV1000: $i,SV599: $i,SV172: $i] :
( ( ( hBOOL @ ( c_in @ SV172 @ SV599 @ SV1000 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1000 @ tc_bool ) ) @ SV1278 ) @ SV599 ) )
| ~ ( hBOOL @ ( c_in @ SV172 @ SV1278 @ SV1000 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2431]) ).
thf(2825,plain,
! [SV1279: $i,SV1001: $i,SV600: $i,SV173: $i] :
( ( ( hBOOL @ ( c_in @ SV173 @ SV600 @ SV1001 ) )
| ~ ( hBOOL @ ( c_in @ SV173 @ SV1279 @ SV1001 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1001 @ tc_bool ) ) @ SV1279 ) @ SV600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2432]) ).
thf(2826,plain,
! [SV1280: $i,SV1002: $i,SV601: $i,SV174: $i] :
( ( ( hBOOL @ ( c_in @ SV174 @ SV601 @ SV1002 ) )
| ~ ( hBOOL @ ( c_in @ SV174 @ SV1280 @ SV1002 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1002 @ tc_bool ) ) @ SV1280 ) @ SV601 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2433]) ).
thf(2827,plain,
! [SV1281: $i,SV1003: $i,SV602: $i,SV175: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV175 @ tc_bool ) ) @ SV602 ) @ SV1003 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV175 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1281 @ SV602 @ ( tc_fun @ SV175 @ tc_bool ) ) ) @ SV1003 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2434]) ).
thf(2828,plain,
! [SV1282: $i,SV1004: $i,SV603: $i,SV176: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV176 @ tc_bool ) ) @ SV603 ) @ SV1004 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV176 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV603 @ SV1282 @ ( tc_fun @ SV176 @ tc_bool ) ) ) @ SV1004 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2435]) ).
thf(2829,plain,
! [SV1283: $i,SV1005: $i,SV604: $i,SV177: $i] :
( ( ! [SY3833: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV604 @ SV1005 @ ( tc_fun @ SV177 @ tc_bool ) ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1283 @ SY3833 @ ( tc_fun @ SV177 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ SV1005 ) @ SY3833 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ SV604 ) @ SV1283 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2436]) ).
thf(2830,plain,
! [SV1006: $i,SV605: $i,SV178: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV178 @ SV605 @ ( tc_fun @ SV1006 @ tc_bool ) )
= SV178 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1006 @ tc_bool ) ) @ SV605 ) @ SV178 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2437]) ).
thf(2831,plain,
! [SV1007: $i,SV606: $i,SV179: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV179 @ SV606 @ ( tc_fun @ SV1007 @ tc_bool ) )
= SV606 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1007 @ tc_bool ) ) @ SV179 ) @ SV606 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2438]) ).
thf(2832,plain,
! [SV1284: $i,SV1008: $i,SV607: $i,SV180: $i] :
( ( ! [SY3834: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV607 @ SV1008 @ ( tc_fun @ SV180 @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1284 @ SY3834 @ ( tc_fun @ SV180 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ SY3834 ) @ SV1008 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ SV607 ) @ SV1284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2439]) ).
thf(2833,plain,
! [SV1009: $i,SV608: $i,SV181: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV181 @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV608 @ ( tc_fun @ SV181 @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV1009 @ ( tc_fun @ SV181 @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV181 @ tc_bool ) ) @ SV1009 ) @ SV608 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2440]) ).
thf(2834,plain,
! [SV1010: $i,SV609: $i,SV182: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV182 @ tc_bool ) ) @ SV609 ) @ SV1010 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV182 @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV1010 @ ( tc_fun @ SV182 @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV609 @ ( tc_fun @ SV182 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2441]) ).
thf(2835,plain,
! [SV1011: $i,SV610: $i,SV183: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV183 @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV610 @ ( tc_fun @ SV183 @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV1011 @ ( tc_fun @ SV183 @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV183 @ tc_bool ) ) @ SV1011 ) @ SV610 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2442]) ).
thf(2836,plain,
! [SV1285: $i,SV1012: $i,SV611: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV184 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV611 @ SV1012 @ ( tc_fun @ SV184 @ tc_bool ) ) ) @ SV1285 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV184 @ tc_bool ) ) @ SV1012 ) @ SV1285 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV184 @ tc_bool ) ) @ SV611 ) @ SV1285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2443]) ).
thf(2837,plain,
! [SV1286: $i,SV1015: $i,SV614: $i,SV187: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV187 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV614 @ SV1015 @ ( tc_fun @ SV187 @ tc_bool ) ) ) @ SV1286 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV187 @ tc_bool ) ) @ SV1015 ) @ SV1286 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV187 @ tc_bool ) ) @ SV614 ) @ SV1286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2446]) ).
thf(2838,plain,
! [SV1287: $i,SV1017: $i,SV616: $i,SV189: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV189 @ tc_bool ) ) @ SV616 ) @ ( c_Set_Oinsert @ SV1017 @ SV1287 @ SV189 ) ) )
| ~ ( hBOOL @ ( c_in @ SV1017 @ SV616 @ SV189 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV189 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV616 @ ( c_Set_Oinsert @ SV1017 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV189 @ tc_bool ) ) @ SV189 ) @ ( tc_fun @ SV189 @ tc_bool ) ) ) @ SV1287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2448]) ).
thf(2839,plain,
! [SV1288: $i,SV1018: $i,SV617: $i,SV190: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV190 @ tc_bool ) ) @ SV617 ) @ ( c_Set_Oinsert @ SV1018 @ SV1288 @ SV190 ) ) )
| ~ ( hBOOL @ ( c_in @ SV1018 @ SV617 @ SV190 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV190 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV617 @ ( c_Set_Oinsert @ SV1018 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV190 @ tc_bool ) ) @ SV190 ) @ ( tc_fun @ SV190 @ tc_bool ) ) ) @ SV1288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2449]) ).
thf(2840,plain,
! [SV1289: $i,SV1019: $i,SV618: $i,SV191: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV191 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV618 @ ( c_Set_Oinsert @ SV1019 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV191 @ tc_bool ) ) @ SV191 ) @ ( tc_fun @ SV191 @ tc_bool ) ) ) @ SV1289 ) )
| ~ ( hBOOL @ ( c_in @ SV1019 @ SV618 @ SV191 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV191 @ tc_bool ) ) @ SV618 ) @ ( c_Set_Oinsert @ SV1019 @ SV1289 @ SV191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2450]) ).
thf(2841,plain,
! [SV1020: $i,SV619: $i,SV192: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV192 ) )
= $true )
| ( ( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV619 @ SV1020 @ SV192 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV192 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV192 ) @ SV619 ) @ SV1020 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2451]) ).
thf(2842,plain,
! [SV1021: $i,SV620: $i,SV193: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV193 ) )
= $true )
| ( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV193 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV620 @ SV1021 @ SV193 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV193 ) @ SV620 ) @ SV1021 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2452]) ).
thf(2843,plain,
! [SV1022: $i,SV621: $i,SV194: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV194 ) )
= $true )
| ( ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ SV621 @ SV1022 @ SV194 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV194 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV194 ) @ SV1022 ) @ SV621 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2453]) ).
thf(2844,plain,
! [SV1290: $i,SV1023: $i,SV622: $i,SV195: $i] :
( ( ! [SY3835: $i] :
( ~ ( class_Orderings_Oorder @ SV195 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV195 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV622 @ SV1023 @ SV195 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1290 @ SY3835 @ SV195 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV195 ) @ SV622 ) @ SV1023 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2454]) ).
thf(2845,plain,
! [SV1291: $i,SV1024: $i,SV623: $i,SV196: $i] :
( ( ! [SY3836: $i] :
( ~ ( class_Orderings_Oorder @ SV196 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV196 ) @ SV623 ) @ SV1024 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV196 ) @ SV1024 ) @ SV1291 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV196 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1024 @ SV1291 @ SV196 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV623 @ SY3836 @ SV196 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2455]) ).
thf(2846,plain,
! [SV1292: $i,SV1025: $i,SV624: $i,SV197: $i] :
( ( ! [SY3837: $i] :
( ~ ( class_Orderings_Oorder @ SV197 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV197 ) @ SV624 ) @ SV1025 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV197 ) @ SV1292 ) @ SV624 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV197 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1292 @ SV624 @ SV197 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3837 @ SV1025 @ SV197 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2456]) ).
thf(2847,plain,
! [SV1293: $i,SV1026: $i,SV625: $i,SV198: $i] :
( ( ! [SY3838: $i] :
( ~ ( class_Orderings_Oorder @ SV198 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV198 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV625 @ SV1026 @ SV198 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1293 @ SY3838 @ SV198 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV198 ) @ SV1026 ) @ SY3838 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV198 ) @ SV1293 ) @ SV625 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2457]) ).
thf(2848,plain,
! [SV1294: $i,SV1027: $i,SV626: $i,SV199: $i] :
( ( ! [SY3839: $i] :
( ~ ( class_Orderings_Olinorder @ SV199 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV199 ) @ SV626 ) @ SV1027 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV199 ) @ SV1294 ) @ SV1027 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV199 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1027 @ SV1294 @ SV199 ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV626 @ SY3839 @ SV199 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2458]) ).
thf(2849,plain,
! [SV1028: $i,SV627: $i,SV200: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV200 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV200 ) @ SV627 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1028 @ SV627 @ SV200 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2459]) ).
thf(2850,plain,
! [SV1029: $i,SV628: $i,SV201: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV201 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV201 ) @ SV628 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV628 @ SV1029 @ SV201 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2460]) ).
thf(2851,plain,
! [SV1295: $i,SV1030: $i,SV629: $i,SV202: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV202 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV629 @ SV1030 @ SV202 ) ) @ SV1295 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ SV1030 ) @ SV1295 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ SV629 ) @ SV1295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2461]) ).
thf(2852,plain,
! [SV1031: $i,SV630: $i,SV203: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV203 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV203 ) @ SV630 ) @ SV1031 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV203 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV1031 @ SV203 ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV630 @ SV203 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2462]) ).
thf(2853,plain,
! [SV1032: $i,SV631: $i,SV204: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV204 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV204 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV631 @ SV204 ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV1032 @ SV204 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV204 ) @ SV1032 ) @ SV631 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2463]) ).
thf(2854,plain,
! [SV1033: $i,SV632: $i,SV205: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV205 ) )
= $true )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV632 @ SV1033 @ SV205 )
= SV632 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV205 ) @ SV1033 ) @ SV632 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2464]) ).
thf(2855,plain,
! [SV1034: $i,SV633: $i,SV206: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV206 ) )
= $true )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV633 @ SV1034 @ SV206 )
= SV1034 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV206 ) @ SV633 ) @ SV1034 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2465]) ).
thf(2856,plain,
! [SV1296: $i,SV1035: $i,SV634: $i,SV207: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV207 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV207 ) @ SV634 ) @ SV1035 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV207 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1296 @ SV634 @ SV207 ) ) @ SV1035 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2466]) ).
thf(2857,plain,
! [SV1297: $i,SV1036: $i,SV635: $i,SV208: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV208 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV208 ) @ SV635 ) @ SV1036 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV208 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV635 @ SV1297 @ SV208 ) ) @ SV1036 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2467]) ).
thf(2858,plain,
! [SV1298: $i,SV1037: $i,SV636: $i,SV209: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV209 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV209 ) @ SV636 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1037 @ SV1298 @ SV209 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV209 ) @ SV636 ) @ SV1298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2468]) ).
thf(2859,plain,
! [SV1299: $i,SV1038: $i,SV637: $i,SV210: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV210 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV210 ) @ SV637 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1038 @ SV1299 @ SV210 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV210 ) @ SV637 ) @ SV1038 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2469]) ).
thf(2860,plain,
! [SV1300: $i,SV1039: $i,SV638: $i,SV211: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV211 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV211 ) @ SV638 ) @ SV1039 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV211 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1300 @ SV638 @ SV211 ) ) @ SV1039 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2470]) ).
thf(2861,plain,
! [SV1301: $i,SV1040: $i,SV639: $i,SV212: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV212 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV212 ) @ SV639 ) @ SV1040 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV212 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV639 @ SV1301 @ SV212 ) ) @ SV1040 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2471]) ).
thf(2862,plain,
! [SV1041: $i,SV640: $i,SV213: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV213 ) )
= $true )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ SV640 @ SV1041 @ SV213 ) @ SV213 )
= ( c_HOL_Ominus__class_Ominus @ SV1041 @ SV640 @ SV213 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2472]) ).
thf(2863,plain,
! [SV641: $i,SV214: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV214 )
= $false )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV641 @ SV214 ) @ SV214 )
= SV641 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2473]) ).
thf(2864,plain,
! [SV642: $i,SV215: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV215 )
= $false )
| ( ( SV642
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV642 @ SV215 ) @ SV215 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2474]) ).
thf(2865,plain,
! [SV643: $i,SV216: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV216 )
= $false )
| ( ( SV643
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV643 @ SV216 ) @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2475]) ).
thf(2866,plain,
! [SV644: $i,SV217: $i] :
( ( ( class_Lattices_Oboolean__algebra @ SV217 )
= $false )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV644 @ SV217 ) @ SV217 )
= SV644 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2476]) ).
thf(2867,plain,
! [SV645: $i,SV218: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV218 )
= $false )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ SV645 @ SV218 ) @ SV218 )
= SV645 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2477]) ).
thf(2868,plain,
! [SV1302: $i,SV1042: $i,SV647: $i,SV220: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV220 @ tc_bool ) ) @ SV647 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1042 @ SV1302 @ ( tc_fun @ SV220 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV220 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV647 @ SV1042 @ ( tc_fun @ SV220 @ tc_bool ) ) ) @ SV1302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2478]) ).
thf(2869,plain,
! [SV1303: $i,SV1043: $i,SV648: $i,SV221: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV221 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV648 @ SV1043 @ ( tc_fun @ SV221 @ tc_bool ) ) ) @ SV1303 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV221 @ tc_bool ) ) @ SV648 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1043 @ SV1303 @ ( tc_fun @ SV221 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2479]) ).
thf(2870,plain,
! [SV1304: $i,SV1044: $i,SV649: $i,SV222: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV222 @ SV649 @ SV1044 ) @ SV1304 @ ( tc_fun @ SV1044 @ tc_bool ) )
= ( c_Set_Oinsert @ SV222 @ ( c_HOL_Ominus__class_Ominus @ SV649 @ SV1304 @ ( tc_fun @ SV1044 @ tc_bool ) ) @ SV1044 ) )
| ( hBOOL @ ( c_in @ SV222 @ SV1304 @ SV1044 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2480]) ).
thf(2871,plain,
! [SV1305: $i,SV1045: $i,SV650: $i,SV223: $i] :
( ( ! [SY3840: $i,SY3841: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV223 @ SV650 @ SV1045 @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SY3840 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV650 @ SY3841 ) @ SY3840 ) )
| ~ ( hBOOL @ ( c_in @ SY3841 @ SV223 @ SV1045 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2481]) ).
thf(2872,plain,
! [SV1306: $i,SV1046: $i,SV651: $i,SV224: $i] :
( ( ! [SY3842: $i,SY3843: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV224 @ SV651 @ SV1046 @ ( tc_fun @ SV1306 @ tc_bool ) ) @ SY3842 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV651 @ SY3843 ) @ SY3842 ) )
| ~ ( hBOOL @ ( c_in @ SY3843 @ SV224 @ SV1046 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2482]) ).
thf(2873,plain,
! [SV1047: $i,SV652: $i,SV225: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV225 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV652 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV652 @ SV1047 @ SV225 ) @ SV225 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV652 @ SV1047 @ SV225 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2483]) ).
thf(2874,plain,
! [SV1048: $i,SV653: $i,SV226: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV226 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV653 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV653 @ SV1048 @ SV226 ) @ SV226 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV653 @ SV1048 @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2484]) ).
thf(2875,plain,
! [SV1050: $i,SV655: $i,SV228: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV228 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV655 @ SV1050 @ SV228 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1050 @ SV655 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2486]) ).
thf(2876,plain,
! [SV1051: $i,SV656: $i,SV229: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV229 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV656 @ SV1051 @ SV229 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1051 @ SV656 @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2487]) ).
thf(2877,plain,
! [SV1307: $i,SV1053: $i,SV658: $i,SV231: $i] :
( ( ! [SY3844: $i,SY3845: $i,SY3846: $i,SY3847: $i,SY3848: $i,SY3849: $i,SY3850: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV231 @ SV658 ) @ ( hAPP @ SV1053 @ SV1307 ) ) )
| ~ ( hBOOL @ ( c_in @ SV658 @ SV1307 @ SY3844 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3845 @ SV1053 @ SV231 @ SY3846 @ SY3847 @ SY3848 @ SY3849 @ SY3850 @ SY3844 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2489]) ).
thf(2878,plain,
! [SV1308: $i,SV1054: $i,SV659: $i,SV232: $i] :
( ( ! [SY3851: $i,SY3852: $i,SY3853: $i,SY3854: $i,SY3855: $i,SY3856: $i,SY3857: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ ( hAPP @ SV659 @ SV1054 ) ) @ SV1308 ) )
| ~ ( hBOOL @ ( c_in @ SV1308 @ SV1054 @ SY3851 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV659 @ SY3852 @ SV232 @ SY3853 @ SY3854 @ SY3855 @ SY3856 @ SY3857 @ SY3851 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2490]) ).
thf(2879,plain,
! [SV1309: $i,SV1055: $i,SV660: $i,SV233: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV233 @ SV660 @ ( tc_fun @ SV1055 @ tc_bool ) ) @ SV1309 @ ( tc_fun @ SV1055 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV233 @ SV1309 @ ( tc_fun @ SV1055 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV660 @ SV1309 @ ( tc_fun @ SV1055 @ tc_bool ) ) @ ( tc_fun @ SV1055 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2491]) ).
thf(2880,plain,
! [SV1056: $i,SV661: $i,SV234: $i] :
( ( ( ~ ( class_HOL_Ominus @ SV234 ) )
= $true )
| ( ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ SV661 @ SV1056 @ ( tc_fun @ t_a @ SV234 ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ SV661 @ v_x ) @ ( hAPP @ SV1056 @ v_x ) @ SV234 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2492]) ).
thf(2881,plain,
! [SV1310: $i,SV1059: $i,SV664: $i,SV237: $i] :
( ( ! [SY3858: $i,SY3859: $i] :
( ( hBOOL @ ( c_in @ SV237 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV664 @ SV1059 @ SV1310 @ ( tc_fun @ SY3858 @ tc_bool ) ) @ SY3858 ) )
| ~ ( hBOOL @ ( c_in @ SV237 @ ( hAPP @ SV1059 @ SY3859 ) @ SY3858 ) )
| ~ ( hBOOL @ ( c_in @ SY3859 @ SV664 @ SV1310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2495]) ).
thf(2882,plain,
! [SV1311: $i,SV1060: $i,SV665: $i,SV238: $i] :
( ( ! [SY3860: $i,SY3861: $i] :
( ( hBOOL @ ( c_in @ SV238 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV665 @ SV1060 @ SV1311 @ ( tc_fun @ SY3860 @ tc_bool ) ) @ SY3860 ) )
| ~ ( hBOOL @ ( c_in @ SV238 @ ( hAPP @ SV1060 @ SY3861 ) @ SY3860 ) )
| ~ ( hBOOL @ ( c_in @ SY3861 @ SV665 @ SV1311 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2496]) ).
thf(2883,plain,
! [SV1312: $i,SV1061: $i,SV666: $i,SV239: $i] :
( ( ( hBOOL @ ( c_in @ SV239 @ ( c_HOL_Ominus__class_Ominus @ SV666 @ SV1061 @ ( tc_fun @ SV1312 @ tc_bool ) ) @ SV1312 ) )
| ( hBOOL @ ( c_in @ SV239 @ SV1061 @ SV1312 ) )
| ~ ( hBOOL @ ( c_in @ SV239 @ SV666 @ SV1312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2497]) ).
thf(2884,plain,
! [SV1313: $i,SV1062: $i,SV667: $i,SV240: $i] :
( ( ( hBOOL @ ( c_in @ SV240 @ ( c_HOL_Ominus__class_Ominus @ SV667 @ SV1062 @ ( tc_fun @ SV1313 @ tc_bool ) ) @ SV1313 ) )
| ( hBOOL @ ( c_in @ SV240 @ SV1062 @ SV1313 ) )
| ~ ( hBOOL @ ( c_in @ SV240 @ SV667 @ SV1313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2498]) ).
thf(2885,plain,
! [SV1063: $i,SV668: $i,SV241: $i] :
( ( ( hBOOL @ ( hAPP @ SV241 @ SV668 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV668 @ ( c_Collect @ SV241 @ SV1063 ) @ SV1063 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2499]) ).
thf(2886,plain,
! [SV1064: $i,SV669: $i,SV242: $i] :
( ( ( hBOOL @ ( c_in @ SV242 @ ( c_Collect @ SV669 @ SV1064 ) @ SV1064 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV669 @ SV242 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2500]) ).
thf(2887,plain,
! [SV1065: $i,SV670: $i,SV243: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV243 @ ( c_HOL_Ominus__class_Ominus @ SV670 @ SV243 @ ( tc_fun @ SV1065 @ tc_bool ) ) @ ( tc_fun @ SV1065 @ tc_bool ) )
= SV670 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1065 @ tc_bool ) ) @ SV243 ) @ SV670 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2501]) ).
thf(2888,plain,
! [SV1314: $i,SV1066: $i,SV671: $i,SV244: $i] :
( ( ~ ( class_Lattices_Olattice @ SV244 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV671 @ SV1066 @ SV244 ) @ SV1314 @ SV244 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV671 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1066 @ SV1314 @ SV244 ) @ SV244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2502]) ).
thf(2889,plain,
! [SV1315: $i,SV1067: $i,SV672: $i,SV245: $i] :
( ( ~ ( class_Lattices_Olattice @ SV245 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV672 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1067 @ SV1315 @ SV245 ) @ SV245 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1067 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV672 @ SV1315 @ SV245 ) @ SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2503]) ).
thf(2890,plain,
! [SV1316: $i,SV1068: $i,SV673: $i,SV246: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV246 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV673 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1068 @ SV1316 @ SV246 ) @ SV246 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1068 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV673 @ SV1316 @ SV246 ) @ SV246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2504]) ).
thf(2891,plain,
! [SV1317: $i,SV1069: $i,SV674: $i,SV247: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV247 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV674 @ SV1069 @ SV247 ) @ SV1317 @ SV247 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV674 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1069 @ SV1317 @ SV247 ) @ SV247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2505]) ).
thf(2892,plain,
! [SV1318: $i,SV1070: $i,SV675: $i,SV248: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV248 @ SV675 @ ( tc_fun @ SV1070 @ tc_bool ) ) @ SV1318 @ ( tc_fun @ SV1070 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV248 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV675 @ SV1318 @ ( tc_fun @ SV1070 @ tc_bool ) ) @ ( tc_fun @ SV1070 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2506]) ).
thf(2893,plain,
! [SV1319: $i,SV1071: $i,SV676: $i,SV249: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV249 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV676 @ SV1071 @ ( tc_fun @ SV1319 @ tc_bool ) ) @ ( tc_fun @ SV1319 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV676 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV249 @ SV1071 @ ( tc_fun @ SV1319 @ tc_bool ) ) @ ( tc_fun @ SV1319 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2507]) ).
thf(2894,plain,
! [SV1073: $i,SV678: $i,SV251: $i] :
( ( ( hBOOL @ ( hAPP @ SV251 @ SV678 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV678 @ SV251 @ SV1073 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2509]) ).
thf(2895,plain,
! [SV1074: $i,SV679: $i,SV252: $i] :
( ( ( hBOOL @ ( c_in @ SV252 @ SV679 @ SV1074 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV679 @ SV252 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2510]) ).
thf(2896,plain,
! [SV1320: $i,SV1075: $i,SV680: $i,SV253: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV253 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV680 @ tc_bool ) ) @ SV1075 @ SV680 @ ( tc_fun @ SV1320 @ tc_bool ) ) @ ( tc_fun @ SV1320 @ tc_bool ) )
= SV253 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2511]) ).
thf(2897,plain,
! [SV681: $i,SV254: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV254 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV681 @ SV681 @ SV254 )
= SV681 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2512]) ).
thf(2898,plain,
! [SV1076: $i,SV683: $i,SV256: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV256 ) )
= $true )
| ( ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV683 @ SV1076 @ ( tc_fun @ t_a @ SV256 ) ) @ v_x )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV683 @ v_x ) @ ( hAPP @ SV1076 @ v_x ) @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2513]) ).
thf(2899,plain,
! [SV1321: $i,SV1078: $i,SV685: $i,SV258: $i] :
( ( ! [SY3862: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV258 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV258 ) @ ( hAPP @ SV685 @ SV1078 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1321 @ SV685 @ SY3862 @ SV258 ) ) )
| ~ ( hBOOL @ ( c_in @ SV1078 @ SV1321 @ SY3862 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2515]) ).
thf(2900,plain,
! [SV1322: $i,SV1079: $i,SV686: $i,SV259: $i] :
( ( ! [SY3863: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV259 @ tc_bool ) ) @ ( hAPP @ SV686 @ SV1079 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1322 @ SV686 @ SY3863 @ ( tc_fun @ SV259 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( c_in @ SV1079 @ SV1322 @ SY3863 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2516]) ).
thf(2901,plain,
! [SV1323: $i,SV1080: $i,SV687: $i,SV260: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV260 @ SV687 @ SV1080 ) @ SV1323 @ ( tc_fun @ SV1080 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV687 @ SV1323 @ ( tc_fun @ SV1080 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SV260 @ SV1323 @ SV1080 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2517]) ).
thf(2902,plain,
! [SV1081: $i,SV688: $i,SV261: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV261 @ SV688 @ SV1081 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV261 @ ( c_HOL_Ouminus__class_Ouminus @ SV688 @ ( tc_fun @ SV1081 @ tc_bool ) ) @ SV1081 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2518]) ).
thf(2903,plain,
! [SV1082: $i,SV689: $i,SV262: $i] :
( ( ( hBOOL @ ( c_in @ SV262 @ ( c_HOL_Ouminus__class_Ouminus @ SV689 @ ( tc_fun @ SV1082 @ tc_bool ) ) @ SV1082 ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV262 @ SV689 @ SV1082 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2519]) ).
thf(2904,plain,
! [SV1083: $i,SV691: $i,SV264: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV264 ) )
= $true )
| ( ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV264 ) @ ( c_Set_Oinsert @ SV691 @ SV1083 @ SV264 ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV691 @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV264 ) @ SV1083 ) @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2520]) ).
thf(2905,plain,
! [SV1324: $i,SV1085: $i,SV693: $i,SV266: $i] :
( ( ( hBOOL @ ( c_in @ SV266 @ SV693 @ SV1085 ) )
| ~ ( hBOOL @ ( c_in @ SV266 @ ( c_HOL_Ominus__class_Ominus @ SV693 @ SV1324 @ ( tc_fun @ SV1085 @ tc_bool ) ) @ SV1085 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2522]) ).
thf(2906,plain,
! [SV1325: $i,SV1086: $i,SV694: $i,SV267: $i] :
( ( ~ ( hBOOL @ ( c_in @ SV267 @ SV694 @ SV1086 ) )
| ~ ( hBOOL @ ( c_in @ SV267 @ ( c_HOL_Ominus__class_Ominus @ SV1325 @ SV694 @ ( tc_fun @ SV1086 @ tc_bool ) ) @ SV1086 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2523]) ).
thf(2907,plain,
! [SV1326: $i,SV1087: $i,SV695: $i,SV268: $i] :
( ( ! [SY3864: $i,SY3865: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV268 @ tc_bool ) ) @ ( hAPP @ SV695 @ SV1087 ) ) @ SV1326 ) )
| ~ ( hBOOL @ ( c_in @ SV1087 @ SY3864 @ SY3865 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV268 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3864 @ SV695 @ SY3865 @ ( tc_fun @ SV268 @ tc_bool ) ) ) @ SV1326 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2524]) ).
thf(2908,plain,
! [SV1327: $i,SV1088: $i,SV696: $i,SV269: $i] :
( ( ! [SY3866: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV269 @ SV696 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1088 @ SV269 @ SV1327 @ ( tc_fun @ SY3866 @ tc_bool ) ) @ ( tc_fun @ SY3866 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1088 @ SV269 @ SV1327 @ ( tc_fun @ SY3866 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SV696 @ SV1088 @ SV1327 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2525]) ).
thf(2909,plain,
! [SV1328: $i,SV1089: $i,SV697: $i,SV270: $i] :
( ( ( hBOOL @ ( hAPP @ SV270 @ SV697 ) )
| ( hBOOL @ ( hAPP @ SV1089 @ SV697 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1089 @ SV270 @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV697 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2526]) ).
thf(2910,plain,
! [SV1329: $i,SV1090: $i,SV698: $i,SV271: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV271 @ SV698 @ ( tc_fun @ SV1090 @ tc_bool ) ) @ SV1329 ) )
| ~ ( hBOOL @ ( hAPP @ SV698 @ SV1329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2527]) ).
thf(2911,plain,
! [SV1330: $i,SV1091: $i,SV699: $i,SV272: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV272 @ SV699 @ ( tc_fun @ SV1091 @ tc_bool ) ) @ SV1330 ) )
| ~ ( hBOOL @ ( hAPP @ SV272 @ SV1330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2528]) ).
thf(2912,plain,
! [SV1331: $i,SV1092: $i,SV700: $i,SV273: $i] :
( ( ( hBOOL @ ( c_in @ SV273 @ SV700 @ SV1092 ) )
| ( hBOOL @ ( c_in @ SV273 @ SV1331 @ SV1092 ) )
| ~ ( hBOOL @ ( c_in @ SV273 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1331 @ SV700 @ ( tc_fun @ SV1092 @ tc_bool ) ) @ SV1092 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2529]) ).
thf(2913,plain,
! [SV1332: $i,SV1093: $i,SV701: $i,SV274: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV274 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV701 @ SV1093 @ SV274 ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1093 @ SV1332 @ SV274 ) @ ( tc_fun @ SV274 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV701 @ SV1332 @ SV274 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV274 ) @ SV1093 ) @ SV1332 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV274 ) @ SV701 ) @ SV1093 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2530]) ).
thf(2914,plain,
! [SV1333: $i,SV1094: $i,SV702: $i,SV275: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV275 @ tc_bool ) ) @ SV702 @ SV275 @ ( tc_fun @ SV1094 @ tc_bool ) ) @ SV1333 @ ( tc_fun @ SV1094 @ tc_bool ) )
= SV1333 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2531]) ).
thf(2915,plain,
! [SV1334: $i,SV1095: $i,SV703: $i,SV276: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV276 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV703 @ tc_bool ) ) @ SV1095 @ SV703 @ ( tc_fun @ SV1334 @ tc_bool ) ) @ ( tc_fun @ SV1334 @ tc_bool ) )
= SV276 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2532]) ).
thf(2916,plain,
! [SV1335: $i,SV1096: $i,SV704: $i,SV277: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV277 )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV704 @ SV1096 @ SV277 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1096 @ SV1335 @ SV277 ) @ ( tc_fun @ SV277 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV704 @ SV1335 @ SV277 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV277 ) @ SV1096 ) @ SV1335 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV277 ) @ SV704 ) @ SV1096 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2533]) ).
thf(2917,plain,
! [SV1336: $i,SV1097: $i,SV705: $i,SV278: $i] :
( ( ! [SY3867: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ SV278 @ SV705 @ SV1097 ) @ SV1336 @ SV1097 @ ( tc_fun @ SY3867 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV1336 @ SV278 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV705 @ SV1336 @ SV1097 @ ( tc_fun @ SY3867 @ tc_bool ) ) @ ( tc_fun @ SY3867 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2534]) ).
thf(2918,plain,
! [SV1098: $i,SV706: $i,SV279: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV279 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV279 ) @ ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ SV279 ) @ SV706 ) ) @ SV1098 ) )
| ~ ( hBOOL @ ( c_in @ SV1098 @ SV706 @ SV279 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2535]) ).
thf(2919,plain,
! [SV707: $i,SV280: $i] :
( ( ( class_HOL_Ouminus @ SV280 )
= $false )
| ( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ SV707 @ ( tc_fun @ t_a @ SV280 ) ) @ v_x )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ SV707 @ v_x ) @ SV280 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2536]) ).
thf(2920,plain,
! [SV1337: $i,SV1099: $i,SV708: $i,SV281: $i] :
( ( ( hBOOL @ ( c_in @ SV281 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV708 @ SV1099 @ ( tc_fun @ SV1337 @ tc_bool ) ) @ SV1337 ) )
| ~ ( hBOOL @ ( c_in @ SV281 @ SV1099 @ SV1337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2537]) ).
thf(2921,plain,
! [SV1338: $i,SV1100: $i,SV709: $i,SV282: $i] :
( ( ( hBOOL @ ( c_in @ SV282 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV709 @ SV1100 @ ( tc_fun @ SV1338 @ tc_bool ) ) @ SV1338 ) )
| ~ ( hBOOL @ ( c_in @ SV282 @ SV709 @ SV1338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2538]) ).
thf(2922,plain,
! [SV1339: $i,SV1101: $i,SV710: $i,SV283: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV283 )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV710 @ SV1101 @ SV283 ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV710 @ SV1339 @ SV283 ) @ ( tc_fun @ SV283 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1339 @ SV1101 @ SV283 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV283 ) @ SV710 ) @ SV1339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2539]) ).
thf(2923,plain,
! [SV1340: $i,SV1102: $i,SV711: $i,SV284: $i] :
( ( ! [SY3868: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV284 @ SV711 @ ( tc_fun @ SV1102 @ tc_bool ) ) @ SV1340 @ SV1102 @ ( tc_fun @ SY3868 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV284 @ SV1340 @ SV1102 @ ( tc_fun @ SY3868 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV711 @ SV1340 @ SV1102 @ ( tc_fun @ SY3868 @ tc_bool ) ) @ ( tc_fun @ SY3868 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2540]) ).
thf(2924,plain,
! [SV1103: $i,SV713: $i,SV286: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV286 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV286 ) @ SV713 ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV286 ) @ SV1103 ) ) )
| ~ ( hBOOL @ ( c_in @ SV713 @ SV1103 @ SV286 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2541]) ).
thf(2925,plain,
! [SV1341: $i,SV1104: $i,SV714: $i,SV287: $i] :
( ( ! [SY3869: $i] :
( ~ ( class_Orderings_Olinorder @ SV287 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV287 ) @ SV714 ) @ SV1104 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV287 ) @ SV714 ) @ SV1341 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV287 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1341 @ SV714 @ SV287 ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SY3869 @ SV1104 @ SV287 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2542]) ).
thf(2926,plain,
! [SV1342: $i,SV1105: $i,SV717: $i,SV292: $i] :
( ( ! [SY3870: $i,SY3871: $i,SY3872: $i,SY3873: $i,SY3874: $i,SY3875: $i] :
( ( ( hAPP @ SV292 @ ( c_Set_Oinsert @ SV717 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1105 @ tc_bool ) ) @ SV1105 ) )
= SV717 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV292 @ SV1342 @ SY3870 @ SY3871 @ SY3872 @ SY3873 @ SY3874 @ SY3875 @ SV1105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2545]) ).
thf(2927,plain,
! [SV1343: $i,SV1106: $i,SV718: $i,SV293: $i] :
( ( ! [SY3876: $i,SY3877: $i,SY3878: $i,SY3879: $i,SY3880: $i,SY3881: $i] :
( ( ( hAPP @ SV293 @ ( c_Set_Oinsert @ SV718 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1106 @ tc_bool ) ) @ SV1106 ) )
= SV718 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1343 @ SV293 @ SY3876 @ SY3877 @ SY3878 @ SY3879 @ SY3880 @ SY3881 @ SV1106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2546]) ).
thf(2928,plain,
! [SV719: $i,SV294: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV294 )
= $false )
| ( ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV294 ) @ ( c_Set_Oinsert @ SV719 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV294 @ tc_bool ) ) @ SV294 ) )
= SV719 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2547]) ).
thf(2929,plain,
! [SV1344: $i,SV1107: $i,SV721: $i,SV296: $i] :
( ( ( c_Set_Oinsert @ SV296 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV721 @ tc_bool ) ) @ SV1107 @ SV721 @ ( tc_fun @ SV1344 @ tc_bool ) ) @ SV1344 )
= ( c_Set_Oinsert @ SV296 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1344 @ tc_bool ) ) @ SV1344 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2548]) ).
thf(2930,plain,
! [SV723: $i,SV298: $i] :
( ( ( class_Orderings_Olinorder @ SV298 )
= $false )
| ( ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ SV723 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV298 @ tc_bool ) ) @ SV298 ) @ SV298 )
= SV723 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2550]) ).
thf(2931,plain,
! [SV1345: $i,SV1109: $i,SV725: $i,SV300: $i] :
( ( ! [SY3882: $i,SY3883: $i,SY3884: $i,SY3885: $i,SY3886: $i,SY3887: $i,SY3888: $i] :
( ( ( hAPP @ SV300 @ ( c_Set_Oinsert @ SV725 @ ( c_Set_Oinsert @ SV1109 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1345 @ tc_bool ) ) @ SV1345 ) @ SV1345 ) )
= ( hAPP @ ( hAPP @ SY3882 @ SV725 ) @ SV1109 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV300 @ SY3883 @ SY3884 @ SY3885 @ SY3882 @ SY3886 @ SY3887 @ SY3888 @ SV1345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2551]) ).
thf(2932,plain,
! [SV1346: $i,SV1110: $i,SV726: $i,SV301: $i] :
( ( ! [SY3889: $i,SY3890: $i,SY3891: $i,SY3892: $i,SY3893: $i,SY3894: $i,SY3895: $i] :
( ( ( hAPP @ SV301 @ ( c_Set_Oinsert @ SV726 @ ( c_Set_Oinsert @ SV1110 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1346 @ tc_bool ) ) @ SV1346 ) @ SV1346 ) )
= ( hAPP @ ( hAPP @ SY3889 @ SV726 ) @ SV1110 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3890 @ SV301 @ SY3891 @ SY3892 @ SY3893 @ SY3889 @ SY3894 @ SY3895 @ SV1346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2552]) ).
thf(2933,plain,
! [SV1347: $i,SV1111: $i,SV727: $i,SV302: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV302 @ ( c_Set_Oinsert @ SV727 @ SV1111 @ SV1347 ) @ ( tc_fun @ SV1347 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV302 @ ( c_Set_Oinsert @ SV727 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1347 @ tc_bool ) ) @ SV1347 ) @ ( tc_fun @ SV1347 @ tc_bool ) ) @ SV1111 @ ( tc_fun @ SV1347 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2553]) ).
thf(2934,plain,
! [SV1348: $i,SV1112: $i,SV728: $i,SV303: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV303 @ ( c_Set_Oinsert @ SV728 @ SV1112 @ SV1348 ) @ ( tc_fun @ SV1348 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV303 @ SV1112 @ ( tc_fun @ SV1348 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV728 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1348 @ tc_bool ) ) @ SV1348 ) @ ( tc_fun @ SV1348 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2554]) ).
thf(2935,plain,
! [SV1349: $i,SV1113: $i,SV729: $i,SV304: $i] :
( ( ( SV304 = SV729 )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV1113 @ ( c_Set_Oinsert @ SV304 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1349 @ tc_bool ) ) @ SV1349 ) @ SV1349 ) @ SV729 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2555]) ).
thf(2936,plain,
! [SV1114: $i,SV731: $i,SV306: $i] :
( ( ( SV306
= ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ SV731 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1114 @ tc_bool ) ) @ SV1114 ) @ SV1114 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV731 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1114 @ tc_bool ) ) @ SV1114 ) @ SV306 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2556]) ).
thf(2937,plain,
! [SV1115: $i,SV732: $i,SV307: $i] :
( ( ( SV307 = SV732 )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV307 @ ( c_Set_Oinsert @ SV732 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1115 @ tc_bool ) ) @ SV1115 ) @ SV1115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2557]) ).
thf(2938,plain,
! [SV734: $i,SV309: $i] :
( ( ( class_Orderings_Olinorder @ SV309 )
= $false )
| ( ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ SV734 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV309 @ tc_bool ) ) @ SV309 ) @ SV309 )
= SV734 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2559]) ).
thf(2939,plain,
! [SV736: $i,SV311: $i] :
( ( ( class_Orderings_Oorder @ SV311 )
= $false )
| ( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV736 @ SV736 @ SV311 )
= ( c_Set_Oinsert @ SV736 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV311 @ tc_bool ) ) @ SV311 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2561]) ).
thf(2940,plain,
! [SV738: $i,SV313: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV313 )
= $false )
| ( ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ SV313 ) @ ( c_Set_Oinsert @ SV738 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV313 @ tc_bool ) ) @ SV313 ) )
= SV738 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2563]) ).
thf(2941,plain,
! [SV314: $i,SV739: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV739 @ tc_bool ) ) @ SV314 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV314 @ ( tc_fun @ SV739 @ tc_bool ) ) ) )
= $false )
| ( ( SV314
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV739 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2564]) ).
thf(2942,plain,
! [SV1350: $i,SV1119: $i,SV740: $i,SV316: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV316 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV740 @ SV1119 @ SV316 ) ) @ SV1350 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV316 @ tc_bool ) ) @ SV1119 ) @ SV1350 ) )
| ~ ( hBOOL @ ( c_in @ SV740 @ SV1350 @ SV316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2565]) ).
thf(2943,plain,
! [SV1351: $i,SV1120: $i,SV741: $i,SV317: $i] :
( ( ( hBOOL @ ( c_in @ SV317 @ SV741 @ SV1120 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1120 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV317 @ SV1351 @ SV1120 ) ) @ SV741 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2566]) ).
thf(2944,plain,
! [SV1352: $i,SV1121: $i,SV742: $i,SV318: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV318 @ tc_bool ) ) @ SV742 ) @ ( c_Set_Oinsert @ SV1121 @ SV1352 @ SV318 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV318 @ tc_bool ) ) @ SV742 ) @ SV1352 ) )
| ( hBOOL @ ( c_in @ SV1121 @ SV742 @ SV318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2567]) ).
thf(2945,plain,
! [SV1353: $i,SV1122: $i,SV743: $i,SV319: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV319 @ tc_bool ) ) @ SV743 ) @ SV1122 ) )
| ( hBOOL @ ( c_in @ SV1353 @ SV743 @ SV319 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV319 @ tc_bool ) ) @ SV743 ) @ ( c_Set_Oinsert @ SV1353 @ SV1122 @ SV319 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2568]) ).
thf(2946,plain,
! [SV1354: $i,SV1123: $i,SV744: $i,SV320: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV320 @ tc_bool ) ) @ SV744 ) @ ( c_Set_Oinsert @ SV1123 @ SV1354 @ SV320 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV320 @ tc_bool ) ) @ SV744 ) @ SV1354 ) )
| ( hBOOL @ ( c_in @ SV1123 @ SV744 @ SV320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2569]) ).
thf(2947,plain,
! [SV1355: $i,SV1124: $i,SV745: $i,SV321: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV321 @ tc_bool ) ) @ SV745 ) @ SV1124 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV321 @ tc_bool ) ) @ SV745 ) @ ( c_Set_Oinsert @ SV1355 @ SV1124 @ SV321 ) ) )
| ( hBOOL @ ( c_in @ SV1355 @ SV745 @ SV321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2570]) ).
thf(2948,plain,
! [SV1356: $i,SV1125: $i,SV746: $i,SV322: $i] :
( ( ! [SY3896: $i,SY3897: $i,SY3898: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV322 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV746 @ SV1125 @ SV1356 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY3896 @ SY3897 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV322 @ SV746 @ SV1356 @ SV1125 @ SY3898 @ SY3896 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3898 @ SY3897 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV322 @ SV746 @ SV1356 @ SV1125 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV322 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3898 @ SV1125 @ SY3896 @ 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_forall_pos,[status(thm)],[2571]) ).
thf(2949,plain,
! [SV1357: $i,SV1126: $i,SV747: $i,SV323: $i] :
( ( ! [SY3899: $i,SY3900: $i,SY3901: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV323 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV747 @ SV1126 @ SV1357 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY3899 @ SY3900 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV747 @ SY3901 @ SV1357 @ SY3899 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3901 @ SY3900 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV747 @ SY3901 @ SV1357 @ SY3899 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV323 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3901 @ SV1126 @ SY3899 @ 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_forall_pos,[status(thm)],[2572]) ).
thf(2950,plain,
! [SV1358: $i,SV1127: $i,SV748: $i,SV324: $i] :
( ( ! [SY3902: $i,SY3903: $i,SY3904: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV324 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV748 @ SV1127 @ SV1358 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY3902 @ SY3903 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV324 @ SV748 @ SV1358 @ SV1127 @ SY3904 @ SY3902 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3904 @ SY3903 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV324 @ SV748 @ SV1358 @ SV1127 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV324 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3904 @ SV1127 @ SY3902 @ 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_forall_pos,[status(thm)],[2573]) ).
thf(2951,plain,
! [SV1359: $i,SV1128: $i,SV749: $i,SV325: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV325 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV749 @ SV1128 @ SV1359 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV749 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV325 @ SV749 @ SV1359 @ SV1128 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV325 @ SV749 @ SV1359 @ SV1128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2574]) ).
thf(2952,plain,
! [SV1360: $i,SV1129: $i,SV750: $i,SV326: $i] :
( ( ! [SY3905: $i,SY3906: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV326 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV750 @ SV1129 @ SV1360 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1360 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV326 @ SV750 @ SV1360 @ SV1129 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV326 @ SV750 @ SV1360 @ SV1129 @ SY3905 @ SY3906 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV326 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3905 @ SV1129 @ SY3906 @ 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_forall_pos,[status(thm)],[2575]) ).
thf(2953,plain,
! [SV1361: $i,SV1130: $i,SV751: $i,SV327: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV327 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV751 @ SV1130 @ SV1361 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV751 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV327 @ SV751 @ SV1361 @ SV1130 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV327 @ SV751 @ SV1361 @ SV1130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2576]) ).
thf(2954,plain,
! [SV1362: $i,SV1131: $i,SV752: $i,SV328: $i] :
( ( ! [SY3907: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV328 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV752 @ SV1131 @ SV1362 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY3907 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SV1362 @ SY3907 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SV1362 @ SY3907 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV328 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV752 @ SV1131 @ SY3907 @ 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_forall_pos,[status(thm)],[2577]) ).
thf(2955,plain,
! [SV1363: $i,SV1132: $i,SV753: $i,SV329: $i] :
( ( ! [SY3908: $i,SY3909: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV329 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV753 @ SV1132 @ SV1363 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV753 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV753 @ SY3908 @ SV1363 @ SY3909 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV753 @ SY3908 @ SV1363 @ SY3909 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV329 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3908 @ SV1132 @ SY3909 @ 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_forall_pos,[status(thm)],[2578]) ).
thf(2956,plain,
! [SV1364: $i,SV1133: $i,SV754: $i,SV330: $i] :
( ( ! [SY3910: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV330 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV754 @ SV1133 @ SV1364 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV754 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV754 @ SY3910 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV754 @ SY3910 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV330 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3910 @ SV1133 @ SV1364 @ 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_forall_pos,[status(thm)],[2579]) ).
thf(2957,plain,
! [SV1365: $i,SV1134: $i,SV755: $i,SV331: $i] :
( ( ! [SY3911: $i,SY3912: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV331 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV755 @ SV1134 @ SV1365 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1365 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV331 @ SV755 @ SV1365 @ SV1134 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV331 @ SV755 @ SV1365 @ SV1134 @ SY3911 @ SY3912 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV331 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3911 @ SV1134 @ SY3912 @ 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_forall_pos,[status(thm)],[2580]) ).
thf(2958,plain,
! [SV1366: $i,SV1135: $i,SV756: $i,SV332: $i] :
( ( ! [SY3913: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV332 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV756 @ SV1135 @ SV1366 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3913 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV756 @ SY3913 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV756 @ SY3913 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV332 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3913 @ SV1135 @ SV1366 @ 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_forall_pos,[status(thm)],[2581]) ).
thf(2959,plain,
! [SV1367: $i,SV1136: $i,SV757: $i,SV333: $i] :
( ( ! [SY3914: $i,SY3915: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV333 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV757 @ SV1136 @ SV1367 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1367 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV757 @ SY3914 @ SV1367 @ SY3915 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV757 @ SY3914 @ SV1367 @ SY3915 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV333 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3914 @ SV1136 @ SY3915 @ 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_forall_pos,[status(thm)],[2582]) ).
thf(2960,plain,
! [SV1368: $i,SV1137: $i,SV758: $i,SV334: $i] :
( ( ! [SY3916: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV334 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV758 @ SV1137 @ SV1368 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1368 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SV1368 @ SY3916 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SV1368 @ SY3916 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV334 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV758 @ SV1137 @ SY3916 @ 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_forall_pos,[status(thm)],[2583]) ).
thf(2961,plain,
! [SV1369: $i,SV1138: $i,SV759: $i,SV335: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV335 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV759 @ SV1138 @ SV1369 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV759 @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ SV335 @ SV759 @ SV1369 @ SV1138 ) ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ SV335 @ SV759 @ SV1369 @ SV1138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2584]) ).
thf(2962,plain,
! [SV1370: $i,SV1139: $i,SV760: $i,SV336: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV336 @ tc_bool ) ) @ SV760 ) @ ( c_Set_Oinsert @ SV1139 @ SV1370 @ SV336 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV336 @ tc_bool ) ) @ SV760 ) @ SV1370 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV336 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV760 @ ( c_Set_Oinsert @ SV1139 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV336 @ tc_bool ) ) @ SV336 ) @ ( tc_fun @ SV336 @ tc_bool ) ) ) @ SV1370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2585]) ).
thf(2963,plain,
! [SV1371: $i,SV1140: $i,SV761: $i,SV337: $i] :
( ( ! [SY3917: $i,SY3918: $i,SY3919: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV761 @ ( c_Com_Ocom_OSemi @ SV1140 @ SV1371 ) @ SY3917 @ SY3918 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3918 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3918 ) ) @ SY3918 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3919 @ SV1371 @ SY3917 @ SY3918 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3918 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3918 ) ) @ SY3918 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV761 @ SV1140 @ SY3919 @ SY3918 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3918 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3918 ) ) @ SY3918 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2586]) ).
thf(2964,plain,
! [SV1141: $i,SV762: $i,SV338: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV338 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV338 ) @ SV762 ) @ SV1141 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV338 ) @ SV1141 ) @ SV762 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2587]) ).
thf(2965,plain,
! [SV1372: $i,SV1142: $i,SV763: $i,SV339: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV339 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV763 @ SV1142 @ SV339 ) ) @ ( c_Set_Oinsert @ SV763 @ SV1372 @ SV339 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV339 @ tc_bool ) ) @ SV1142 ) @ SV1372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2588]) ).
thf(2966,plain,
! [SV1373: $i,SV1143: $i,SV764: $i,SV340: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV340 @ ( c_Set_Oinsert @ SV764 @ SV1143 @ ( tc_Hoare__Mirabelle_Otriple @ SV1373 ) ) @ SV1373 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV340 @ SV1143 @ SV1373 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV340 @ ( c_Set_Oinsert @ SV764 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1373 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1373 ) ) @ SV1373 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2589]) ).
thf(2967,plain,
! [SV1144: $i,SV765: $i,SV341: $i] :
( ( ( SV341
= ( c_Set_Oinsert @ SV765 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1144 @ tc_bool ) ) @ SV1144 ) )
= $true )
| ( ( ( SV341
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1144 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1144 @ tc_bool ) ) @ SV341 ) @ ( c_Set_Oinsert @ SV765 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1144 @ tc_bool ) ) @ SV1144 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2590]) ).
thf(2968,plain,
! [SV1374: $i,SV1145: $i,SV766: $i,SV342: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV342 @ SV766 @ SV1145 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1145 ) @ tc_bool ) ) @ SV766 ) @ SV1374 ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV342 @ SV1374 @ SV1145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2591]) ).
thf(2969,plain,
! [SV1375: $i,SV1146: $i,SV767: $i,SV343: $i] :
( ( ( hBOOL @ ( hAPP @ SV343 @ SV767 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1146 @ tc_bool ) ) @ SV1375 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP @ SV1375 @ SV767 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2592]) ).
thf(2970,plain,
! [SV768: $i,SV344: $i] :
( ( ( class_Orderings_Opreorder @ SV344 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV344 ) @ SV768 ) @ SV768 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2593]) ).
thf(2971,plain,
! [SV769: $i,SV345: $i] :
( ( ( class_Orderings_Oorder @ SV345 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV345 ) @ SV769 ) @ SV769 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2594]) ).
thf(2972,plain,
! [SV1376: $i,SV1147: $i,SV770: $i,SV346: $i] :
( ( ( hBOOL @ ( hAPP @ SV346 @ SV770 ) )
| ~ ( hBOOL @ ( hAPP @ SV1147 @ SV770 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1376 @ tc_bool ) ) @ SV1147 ) @ SV346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2595]) ).
thf(2973,plain,
! [SV1377: $i,SV1148: $i,SV771: $i,SV347: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV347 @ tc_bool ) ) @ SV771 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV347 @ tc_bool ) ) @ SV1377 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV347 @ tc_bool ) ) @ SV771 ) @ SV1377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2596]) ).
thf(2974,plain,
! [SV1378: $i,SV1149: $i,SV774: $i,SV350: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV350 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV774 ) @ SV1149 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV1378 ) @ SV1149 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV774 ) @ SV1378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2597]) ).
thf(2975,plain,
! [SV1379: $i,SV1150: $i,SV775: $i,SV351: $i] :
( ( ~ ( class_Orderings_Oorder @ SV351 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV775 ) @ SV1150 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV775 ) @ SV1379 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV1379 ) @ SV1150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2598]) ).
thf(2976,plain,
! [SV1380: $i,SV1153: $i,SV778: $i,SV354: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV354 @ SV778 @ SV1153 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV354 @ SV1380 @ SV1153 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV1380 @ SV778 @ SV1153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2601]) ).
thf(2977,plain,
! [SV356: $i,SV779: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV779 @ tc_bool ) ) @ SV356 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV779 @ tc_bool ) ) ) )
= $false )
| ( ( SV356
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV779 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2602]) ).
thf(2978,plain,
! [SV1154: $i,SV780: $i,SV357: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV357 ) )
= $true )
| ( ( ( SV780 = SV1154 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV357 ) @ SV780 ) @ SV1154 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV357 ) @ SV1154 ) @ SV780 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2603]) ).
thf(2979,plain,
! [SV1155: $i,SV781: $i,SV358: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV358 ) )
= $true )
| ( ( ( SV781 = SV1155 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV358 ) @ SV1155 ) @ SV781 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV358 ) @ SV781 ) @ SV1155 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2604]) ).
thf(2980,plain,
! [SV1156: $i,SV782: $i,SV359: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV359 ) )
= $true )
| ( ( ( SV782 = SV1156 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV359 ) @ SV1156 ) @ SV782 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV359 ) @ SV782 ) @ SV1156 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2605]) ).
thf(2981,plain,
! [SV1157: $i,SV783: $i,SV360: $i] :
( ( ( SV360 = SV783 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1157 @ tc_bool ) ) @ SV783 ) @ SV360 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1157 @ tc_bool ) ) @ SV360 ) @ SV783 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2606]) ).
thf(2982,plain,
! [SV1158: $i,SV784: $i,SV361: $i] :
( ( ( SV361 = SV784 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1158 @ tc_bool ) ) @ SV784 ) @ SV361 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1158 @ tc_bool ) ) @ SV361 ) @ SV784 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2607]) ).
thf(2983,plain,
! [SV1381: $i,SV1160: $i,SV788: $i,SV365: $i] :
( ( ( hBOOL @ ( hAPP @ SV365 @ SV788 ) )
| ( SV1160 = SV788 )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1160 @ SV365 @ SV1381 ) @ SV788 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2610]) ).
thf(2984,plain,
! [SV790: $i,SV367: $i] :
( ( ( class_Orderings_Obot @ SV367 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV367 ) @ ( c_Orderings_Obot__class_Obot @ SV367 ) ) @ SV790 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2612]) ).
thf(2985,plain,
! [SV1382: $i,SV1162: $i,SV792: $i,SV369: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV369 @ tc_bool ) ) @ SV792 ) @ ( c_Set_Oinsert @ SV1162 @ SV1382 @ SV369 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV369 @ tc_bool ) ) @ SV792 ) @ SV1382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2613]) ).
thf(2986,plain,
! [SV1383: $i,SV1163: $i,SV793: $i,SV370: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV370 @ tc_bool ) ) @ SV793 ) @ SV1163 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV370 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV1383 @ SV793 @ SV370 ) ) @ SV1163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2614]) ).
thf(2987,plain,
! [SV1384: $i,SV1164: $i,SV794: $i,SV371: $i] :
( ( ( c_Set_Oinsert @ SV371 @ ( c_Set_Oinsert @ SV794 @ SV1164 @ SV1384 ) @ SV1384 )
= ( c_Set_Oinsert @ SV794 @ ( c_Set_Oinsert @ SV371 @ SV1164 @ SV1384 ) @ SV1384 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2615]) ).
thf(2988,plain,
! [SV1385: $i,SV1166: $i,SV796: $i,SV373: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV373 @ SV796 @ SV1166 ) @ SV1385 ) )
| ~ ( hBOOL @ ( hAPP @ SV796 @ SV1385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2617]) ).
thf(2989,plain,
! [SV1167: $i,SV797: $i,SV374: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV374 @ SV797 @ SV1167 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1167 ) @ tc_bool ) ) @ SV797 ) @ SV374 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2618]) ).
thf(2990,plain,
! [SV1386: $i,SV1168: $i,SV798: $i,SV375: $i] :
( ( ! [SY3920: $i] :
( ~ ( class_HOL_Oord @ SV375 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV375 ) @ ( hAPP @ SV798 @ SV1168 ) ) @ ( hAPP @ SV1386 @ SV1168 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SY3920 @ SV375 ) ) @ SV798 ) @ SV1386 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(2991,plain,
! [SV376: $i,SV799: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV799 )
= $false )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV376 @ SV799 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2620]) ).
thf(2992,plain,
! [SV377: $i,SV800: $i] :
( ( ( class_Lattices_Olattice @ SV800 )
= $false )
| ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV377 @ SV800 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2621]) ).
thf(2993,plain,
! [SV378: $i,SV801: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV801 )
= $false )
| ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV378 @ SV801 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2622]) ).
thf(2994,plain,
! [SV379: $i,SV802: $i] :
( ( ( class_Lattices_Oboolean__algebra @ SV802 )
= $false )
| ( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ SV379 @ SV802 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2623]) ).
thf(2995,plain,
! [SV380: $i,SV803: $i] :
( ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV803 ) )
= $true )
| ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV380 ) )
= $true )
| ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ SV380 @ SV803 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2624]) ).
thf(2996,plain,
! [SV381: $i,SV804: $i] :
( ( ( class_Orderings_Opreorder @ SV804 )
= $false )
| ( ( class_Orderings_Opreorder @ ( tc_fun @ SV381 @ SV804 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2625]) ).
thf(2997,plain,
! [SV382: $i,SV805: $i] :
( ( ( class_Lattices_Olattice @ SV805 )
= $false )
| ( ( class_Lattices_Olattice @ ( tc_fun @ SV382 @ SV805 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2626]) ).
thf(2998,plain,
! [SV383: $i,SV806: $i] :
( ( ( class_Orderings_Oorder @ SV806 )
= $false )
| ( ( class_Orderings_Oorder @ ( tc_fun @ SV383 @ SV806 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2627]) ).
thf(2999,plain,
! [SV384: $i,SV807: $i] :
( ( ( class_Orderings_Obot @ SV807 )
= $false )
| ( ( class_Orderings_Obot @ ( tc_fun @ SV384 @ SV807 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2628]) ).
thf(3000,plain,
! [SV385: $i,SV808: $i] :
( ( ( class_HOL_Ouminus @ SV808 )
= $false )
| ( ( class_HOL_Ouminus @ ( tc_fun @ SV385 @ SV808 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2629]) ).
thf(3001,plain,
! [SV386: $i,SV809: $i] :
( ( ( class_HOL_Ominus @ SV809 )
= $false )
| ( ( class_HOL_Ominus @ ( tc_fun @ SV386 @ SV809 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2630]) ).
thf(3002,plain,
! [SV387: $i,SV810: $i] :
( ( ( class_HOL_Oord @ SV810 )
= $false )
| ( ( class_HOL_Oord @ ( tc_fun @ SV387 @ SV810 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2631]) ).
thf(3003,plain,
! [SV1169: $i,SV812: $i,SV389: $i] :
( ( ( SV389 = SV812 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV1169 ) @ SV389 ) @ SV812 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2632]) ).
thf(3004,plain,
! [SV1170: $i,SV813: $i,SV390: $i] :
( ( ( ( c_Set_Oinsert @ SV390 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV813 @ tc_bool ) ) @ SV813 )
!= ( c_Set_Oinsert @ SV1170 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV813 @ tc_bool ) ) @ SV813 ) )
= $true )
| ( ( SV390 = SV1170 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2633]) ).
thf(3005,plain,
! [SV1171: $i,SV814: $i,SV391: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV391 ) )
= $true )
| ( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV814 @ SV391 )
!= ( c_HOL_Ouminus__class_Ouminus @ SV1171 @ SV391 ) )
| ( SV814 = SV1171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2634]) ).
thf(3006,plain,
! [SV1387: $i,SV1172: $i,SV815: $i,SV392: $i] :
( ( ( ( c_Set_Oinsert @ SV392 @ SV815 @ SV1172 )
!= ( c_Set_Oinsert @ SV392 @ SV1387 @ SV1172 ) )
| ( hBOOL @ ( c_in @ SV392 @ SV1387 @ SV1172 ) )
| ( hBOOL @ ( c_in @ SV392 @ SV815 @ SV1172 ) )
| ( SV815 = SV1387 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2635]) ).
thf(3007,plain,
! [SV1173: $i,SV816: $i,SV393: $i] :
( ( ( ( c_Collect @ SV393 @ SV816 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV816 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV393 @ SV1173 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2636]) ).
thf(3008,plain,
! [SV1388: $i,SV1174: $i,SV817: $i,SV394: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV394 @ SV817 )
!= ( c_Com_Ocom_OSemi @ SV1174 @ SV1388 ) )
| ( SV817 = SV1388 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2637]) ).
thf(3009,plain,
! [SV1389: $i,SV1175: $i,SV818: $i,SV395: $i] :
( ( ! [SY3921: $i,SY3922: $i,SY3923: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV395 @ SV818 @ SV1175 @ SV1389 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3921 @ SY3922 @ SY3923 @ SV1389 ) )
| ( SV395 = SY3921 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2638]) ).
thf(3010,plain,
! [SV1176: $i,SV819: $i,SV396: $i] :
( ( ( c_Set_Oinsert @ SV396 @ SV819 @ SV1176 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1176 @ tc_bool ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2639]) ).
thf(3011,plain,
! [SV1177: $i,SV821: $i,SV398: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV398 ) )
= $true )
| ( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV398 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV821 @ SV1177 @ SV398 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV821 @ SV1177 @ SV398 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2641]) ).
thf(3012,plain,
! [SV1178: $i,SV822: $i,SV399: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV399 @ tc_bool ) )
= ( c_Set_Oinsert @ SV822 @ SV1178 @ SV399 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2642]) ).
thf(3013,plain,
! [SV1179: $i,SV823: $i,SV400: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV400 ) )
= $true )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV823 @ SV1179 @ SV400 )
!= ( c_Orderings_Obot__class_Obot @ SV400 ) )
| ( SV823
= ( c_Orderings_Obot__class_Obot @ SV400 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2643]) ).
thf(3014,plain,
! [SV1390: $i,SV1180: $i,SV824: $i,SV401: $i] :
( ( ! [SY3924: $i] :
( ( ( c_Set_Oinsert @ SV401 @ ( c_Set_Oinsert @ SV824 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1180 @ tc_bool ) ) @ SV1180 ) @ SV1180 )
!= ( c_Set_Oinsert @ SV1390 @ ( c_Set_Oinsert @ SY3924 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1180 @ tc_bool ) ) @ SV1180 ) @ SV1180 ) )
| ( SV824 = SV1390 )
| ( SV401 = SV1390 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2644]) ).
thf(3015,plain,
! [SV1181: $i,SV825: $i,SV402: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV402 @ SV825 @ ( tc_fun @ SV1181 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1181 @ tc_bool ) ) )
= $true )
| ( ( SV825
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1181 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2645]) ).
thf(3016,plain,
! [SV1391: $i,SV1182: $i,SV826: $i,SV403: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV403 )
| ( ( c_HOL_Ominus__class_Ominus @ SV826 @ SV826 @ SV403 )
!= ( c_HOL_Ominus__class_Ominus @ SV1182 @ SV1391 @ SV403 ) )
| ( SV1182 = SV1391 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2646]) ).
thf(3017,plain,
! [SV1183: $i,SV827: $i,SV404: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV404 ) )
= $true )
| ( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV404 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV827 @ SV1183 @ SV404 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV404 ) @ SV827 ) @ SV1183 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2647]) ).
thf(3018,plain,
! [SV1184: $i,SV828: $i,SV405: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV405 @ SV828 @ ( tc_fun @ SV1184 @ tc_bool ) )
!= SV828 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1184 @ tc_bool ) ) @ SV405 ) @ SV828 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2648]) ).
thf(3019,plain,
! [SV1185: $i,SV829: $i,SV406: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV406 ) )
= $true )
| ( ( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV829 @ SV1185 @ SV406 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV406 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV406 ) @ SV829 ) @ SV1185 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2649]) ).
thf(3020,plain,
! [SV1186: $i,SV830: $i,SV407: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV407 @ SV830 @ ( tc_fun @ SV1186 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1186 @ tc_bool ) ) )
= $true )
| ( ( SV407
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1186 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2650]) ).
thf(3021,plain,
! [SV1392: $i,SV1187: $i,SV832: $i,SV409: $i] :
( ( ! [SY3925: $i] :
( ( ( c_Set_Oinsert @ SV409 @ ( c_Set_Oinsert @ SV832 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1187 @ tc_bool ) ) @ SV1187 ) @ SV1187 )
!= ( c_Set_Oinsert @ SV1392 @ ( c_Set_Oinsert @ SY3925 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1187 @ tc_bool ) ) @ SV1187 ) @ SV1187 ) )
| ( SV409 = SY3925 )
| ( SV832 = SY3925 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2652]) ).
thf(3022,plain,
! [SV1393: $i,SV1188: $i,SV833: $i,SV410: $i] :
( ( ! [SY3926: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV410 @ SV833 @ SV1188 @ ( tc_fun @ SV1393 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1393 @ tc_bool ) ) )
| ( ( hAPP @ SV833 @ SY3926 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1393 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SY3926 @ SV410 @ SV1188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2653]) ).
thf(3023,plain,
! [SV1394: $i,SV1189: $i,SV834: $i,SV411: $i] :
( ( ! [SY3927: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV411 )
| ( ( c_HOL_Ominus__class_Ominus @ SV834 @ SV1189 @ SV411 )
!= ( c_HOL_Ominus__class_Ominus @ SV1394 @ SY3927 @ SV411 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV411 ) @ SY3927 ) @ SV1394 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV411 ) @ SV1189 ) @ SV834 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2654]) ).
thf(3024,plain,
! [SV1190: $i,SV835: $i,SV412: $i] :
( ( ( ~ ( class_Lattices_Oboolean__algebra @ SV412 ) )
= $true )
| ( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV835 @ SV412 )
!= ( c_HOL_Ouminus__class_Ouminus @ SV1190 @ SV412 ) )
| ( SV835 = SV1190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2655]) ).
thf(3025,plain,
! [SV1395: $i,SV1191: $i,SV836: $i,SV413: $i] :
( ( ! [SY3928: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV413 @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV836 @ SV1191 @ SV1395 @ ( tc_fun @ SV413 @ tc_bool ) ) )
| ( ( hAPP @ SV1191 @ SY3928 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV413 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SY3928 @ SV836 @ SV1395 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2656]) ).
thf(3026,plain,
! [SV1192: $i,SV837: $i,SV414: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV414 ) )
= $true )
| ( ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ SV837 @ SV1192 @ SV414 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV414 @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV837 @ SV1192 @ SV414 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2657]) ).
thf(3027,plain,
! [SV1396: $i,SV1193: $i,SV838: $i,SV415: $i] :
( ( ! [SY3929: $i] :
( ( ( c_Set_Oinsert @ SV415 @ ( c_Set_Oinsert @ SV838 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SV1193 ) @ SV1193 )
!= ( c_Set_Oinsert @ SV1396 @ ( c_Set_Oinsert @ SY3929 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SV1193 ) @ SV1193 ) )
| ( SV838 = SV1396 )
| ( SV838 = SY3929 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2658]) ).
thf(3028,plain,
! [SV1194: $i,SV839: $i,SV416: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV416 ) )
= $true )
| ( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV416 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV839 @ SV1194 @ SV416 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV839 @ SV1194 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2659]) ).
thf(3029,plain,
! [SV1195: $i,SV840: $i,SV417: $i] :
( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV417 @ ( tc_fun @ SV840 @ tc_bool ) )
!= ( c_HOL_Ouminus__class_Ouminus @ SV1195 @ ( tc_fun @ SV840 @ tc_bool ) ) )
= $true )
| ( ( SV417 = SV1195 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2660]) ).
thf(3030,plain,
! [SV1397: $i,SV1196: $i,SV841: $i,SV418: $i] :
( ( ! [SY3930: $i,SY3931: $i,SY3932: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV418 @ SV841 @ SV1196 @ SV1397 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3930 @ SY3931 @ SY3932 @ SV1397 ) )
| ( SV1196 = SY3932 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2661]) ).
thf(3031,plain,
! [SV1398: $i,SV1197: $i,SV842: $i,SV419: $i] :
( ( ! [SY3933: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV419 )
| ( ( c_HOL_Ominus__class_Ominus @ SV842 @ SV1197 @ SV419 )
!= ( c_HOL_Ominus__class_Ominus @ SV1398 @ SY3933 @ SV419 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV419 ) @ SV1197 ) @ SV842 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV419 ) @ SY3933 ) @ SV1398 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2662]) ).
thf(3032,plain,
! [SV1198: $i,SV843: $i,SV420: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV420 ) )
= $true )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV843 @ SV1198 @ SV420 )
!= SV1198 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV420 ) @ SV843 ) @ SV1198 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2663]) ).
thf(3033,plain,
! [SV1399: $i,SV1199: $i,SV844: $i,SV421: $i] :
( ( ! [SY3934: $i,SY3935: $i,SY3936: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV421 @ SV844 @ SV1199 @ SV1399 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3934 @ SY3935 @ SY3936 @ SV1399 ) )
| ( SV844 = SY3935 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2664]) ).
thf(3034,plain,
! [SV1400: $i,SV1200: $i,SV845: $i,SV422: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV422 @ SV845 )
!= ( c_Com_Ocom_OSemi @ SV1200 @ SV1400 ) )
| ( SV422 = SV1200 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2665]) ).
thf(3035,plain,
! [SV1401: $i,SV1201: $i,SV846: $i,SV423: $i] :
( ( ! [SY3937: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV423 )
| ( ( c_HOL_Ominus__class_Ominus @ SV846 @ SV1201 @ SV423 )
!= ( c_HOL_Ominus__class_Ominus @ SV1401 @ SY3937 @ SV423 ) )
| ( c_HOL_Oord__class_Oless @ SV1401 @ SY3937 @ SV423 )
| ~ ( c_HOL_Oord__class_Oless @ SV846 @ SV1201 @ SV423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2666]) ).
thf(3036,plain,
! [SV1202: $i,SV847: $i,SV424: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV424 ) )
= $true )
| ( ( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV847 @ SV1202 @ SV424 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV424 @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV847 @ SV1202 @ SV424 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2667]) ).
thf(3037,plain,
! [SV1203: $i,SV848: $i,SV425: $i] :
( ( ( ( c_Set_Oinsert @ SV425 @ SV848 @ SV1203 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1203 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV425 @ SV848 @ SV1203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2668]) ).
thf(3038,plain,
! [SV1204: $i,SV849: $i,SV426: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV426 @ tc_bool ) )
!= ( c_Collect @ SV849 @ SV426 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV849 @ SV1204 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2669]) ).
thf(3039,plain,
! [SV1402: $i,SV1205: $i,SV850: $i,SV427: $i] :
( ( ! [SY3938: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV427 )
| ( ( c_HOL_Ominus__class_Ominus @ SV850 @ SV1205 @ SV427 )
!= ( c_HOL_Ominus__class_Ominus @ SV1402 @ SY3938 @ SV427 ) )
| ( c_HOL_Oord__class_Oless @ SV850 @ SV1205 @ SV427 )
| ~ ( c_HOL_Oord__class_Oless @ SV1402 @ SY3938 @ SV427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2670]) ).
thf(3040,plain,
! [SV1403: $i,SV1206: $i,SV851: $i,SV428: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV428 )
| ( ( c_HOL_Ominus__class_Ominus @ SV851 @ SV1206 @ SV428 )
!= ( c_HOL_Ominus__class_Ominus @ SV1403 @ SV1403 @ SV428 ) )
| ( SV851 = SV1206 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2671]) ).
thf(3041,plain,
! [SV1207: $i,SV852: $i,SV429: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV429 ) )
= $true )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV852 @ SV1207 @ SV429 )
!= ( c_Orderings_Obot__class_Obot @ SV429 ) )
| ( SV1207
= ( c_Orderings_Obot__class_Obot @ SV429 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2672]) ).
thf(3042,plain,
! [SV1404: $i,SV1208: $i,SV853: $i,SV430: $i] :
( ( ! [SY3939: $i] :
( ( ( c_Set_Oinsert @ SV430 @ ( c_Set_Oinsert @ SV853 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1208 @ tc_bool ) ) @ SV1208 ) @ SV1208 )
!= ( c_Set_Oinsert @ SV1404 @ ( c_Set_Oinsert @ SY3939 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1208 @ tc_bool ) ) @ SV1208 ) @ SV1208 ) )
| ( SV430 = SY3939 )
| ( SV430 = SV1404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2673]) ).
thf(3043,plain,
! [SV1209: $i,SV854: $i,SV431: $i,SV1: $i] :
( ( ( ~ ( class_HOL_Oord @ SV1 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV431 @ SV1 ) ) @ SV854 ) @ SV1209 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV854 @ SV1209 @ ( tc_fun @ SV431 @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2674]) ).
thf(3044,plain,
! [SV1210: $i,SV855: $i,SV432: $i,SV2: $i] :
( ( ( ~ ( class_HOL_Oord @ SV2 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV432 @ SV855 @ ( tc_fun @ SV1210 @ SV2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1210 @ SV2 ) ) @ SV855 ) @ SV432 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1210 @ SV2 ) ) @ SV432 ) @ SV855 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2675]) ).
thf(3045,plain,
! [SV1211: $i,SV856: $i,SV433: $i,SV3: $i] :
( ( ( ~ ( class_HOL_Oord @ SV3 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV433 @ SV3 ) ) @ SV856 ) @ SV1211 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1211 @ SV856 @ ( tc_fun @ SV433 @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2676]) ).
thf(3046,plain,
! [SV857: $i,SV434: $i,SV4: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV4 @ SV434 @ ( tc_fun @ SV857 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV857 @ tc_bool ) ) @ SV4 ) @ SV434 ) ) )
= $true )
| ( ( SV4 = SV434 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2677]) ).
thf(3047,plain,
! [SV858: $i,SV435: $i,SV5: $i] :
( ( ( SV5 = SV435 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV858 @ tc_bool ) ) @ SV5 ) @ SV435 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV5 @ SV435 @ ( tc_fun @ SV858 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2678]) ).
thf(3048,plain,
! [SV859: $i,SV6: $i,SV436: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV436 @ tc_bool ) ) @ SV6 ) @ SV859 ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV859 @ SV436 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV6 @ SV436 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2679]) ).
thf(3049,plain,
! [SV1212: $i,SV860: $i,SV437: $i,SV7: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV7 @ SV437 @ ( tc_fun @ SV860 @ tc_bool ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1212 @ SV437 @ ( tc_fun @ SV860 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV860 @ tc_bool ) ) @ SV7 ) @ SV1212 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2680]) ).
thf(3050,plain,
! [SV1213: $i,SV861: $i,SV438: $i,SV8: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV8 @ SV438 @ ( tc_fun @ SV861 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV861 @ tc_bool ) ) @ SV1213 ) @ SV438 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV8 @ SV1213 @ ( tc_fun @ SV861 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2681]) ).
thf(3051,plain,
! [SV9: $i,SV439: $i,SV862: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV862 @ SV439 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV439 @ tc_bool ) ) @ SV9 ) @ SV862 ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV9 @ SV439 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2682]) ).
thf(3052,plain,
! [SV10: $i,SV863: $i,SV440: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV440 @ SV863 @ ( tc_fun @ SV10 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV10 @ tc_bool ) ) @ SV440 ) @ SV863 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2683]) ).
thf(3053,plain,
! [SV1405: $i,SV1214: $i,SV864: $i,SV441: $i,SV11: $i] :
( ( ~ ( class_Ring__and__Field_Oring @ SV11 )
| ( ( c_Finite__Set_Osetsum @ SV441 @ ( c_HOL_Ominus__class_Ominus @ SV864 @ ( c_Set_Oinsert @ SV1214 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1405 @ tc_bool ) ) @ SV1405 ) @ ( tc_fun @ SV1405 @ tc_bool ) ) @ SV1405 @ SV11 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV441 @ SV864 @ SV1405 @ SV11 ) @ ( hAPP @ SV441 @ SV1214 ) @ SV11 ) )
| ~ ( hBOOL @ ( c_in @ SV1214 @ SV864 @ SV1405 ) )
| ~ ( c_Finite__Set_Ofinite @ SV864 @ SV1405 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2684]) ).
thf(3054,plain,
! [SV1406: $i,SV1215: $i,SV865: $i,SV442: $i,SV12: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV12 )
| ( ( c_Finite__Set_Osetsum @ SV442 @ ( c_HOL_Ominus__class_Ominus @ SV865 @ ( c_Set_Oinsert @ SV1215 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1406 @ tc_bool ) ) @ SV1406 ) @ ( tc_fun @ SV1406 @ tc_bool ) ) @ SV1406 @ SV12 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV442 @ SV865 @ SV1406 @ SV12 ) @ ( hAPP @ SV442 @ SV1215 ) @ SV12 ) )
| ~ ( hBOOL @ ( c_in @ SV1215 @ SV865 @ SV1406 ) )
| ~ ( c_Finite__Set_Ofinite @ SV865 @ SV1406 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2685]) ).
thf(3055,plain,
! [SV1216: $i,SV866: $i,SV443: $i,SV13: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV13 @ ( c_Set_Oinsert @ SV443 @ SV866 @ SV1216 ) @ ( tc_fun @ SV1216 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1216 @ tc_bool ) ) @ SV13 ) @ SV866 ) )
| ( hBOOL @ ( c_in @ SV443 @ SV13 @ SV1216 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV13 @ SV866 @ ( tc_fun @ SV1216 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2686]) ).
thf(3056,plain,
! [SV1217: $i,SV867: $i,SV444: $i,SV14: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV14 @ ( c_Set_Oinsert @ SV444 @ SV867 @ SV1217 ) @ ( tc_fun @ SV1217 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1217 @ tc_bool ) ) @ SV14 ) @ SV867 ) )
| ( hBOOL @ ( c_in @ SV444 @ SV14 @ SV1217 ) )
| ( hBOOL @ ( c_in @ SV444 @ SV867 @ SV1217 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2687]) ).
thf(3057,plain,
! [SV1218: $i,SV868: $i,SV445: $i,SV15: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV15 @ tc_bool ) ) @ SV445 ) @ SV868 ) )
= $true )
| ( ( ( hBOOL @ ( c_in @ SV1218 @ SV445 @ SV15 ) )
| ( hBOOL @ ( c_in @ SV1218 @ SV868 @ SV15 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV445 @ ( c_Set_Oinsert @ SV1218 @ SV868 @ SV15 ) @ ( tc_fun @ SV15 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2688]) ).
thf(3058,plain,
! [SV1219: $i,SV869: $i,SV446: $i,SV16: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV16 ) )
= $true )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV446 @ SV869 @ SV16 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV869 @ SV1219 @ SV16 ) @ ( tc_fun @ SV16 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV446 @ SV1219 @ SV16 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV16 ) @ SV869 ) @ SV1219 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV16 ) @ SV446 ) @ SV869 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2689]) ).
thf(3059,plain,
! [SV449: $i,SV19: $i,SV871: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV871 @ SV19 @ SV449 ) @ SV449 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV19 @ SV449 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2690]) ).
thf(3060,plain,
! [SV20: $i,SV872: $i,SV450: $i] :
( ( ( c_Finite__Set_Ofinite @ SV450 @ SV872 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ SV20 @ SV450 @ SV872 ) @ SV872 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2691]) ).
thf(3061,plain,
! [SV1407: $i,SV1222: $i,SV875: $i,SV453: $i,SV23: $i] :
( ( ( SV23 = SV453 )
| ~ ( c_Finite__Set_Ofold__graph @ SV875 @ SV453 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1222 @ tc_bool ) ) @ SV23 @ SV1222 @ SV1407 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2694]) ).
thf(3062,plain,
! [SV876: $i,SV455: $i,SV26: $i] :
( ( ( class_Orderings_Opreorder @ SV26 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV26 ) @ SV455 ) @ SV876 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV876 @ SV455 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2695]) ).
thf(3063,plain,
! [SV877: $i,SV456: $i,SV27: $i] :
( ( ( class_Orderings_Olinorder @ SV27 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV456 @ SV877 @ SV27 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV27 ) @ SV877 ) @ SV456 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2696]) ).
thf(3064,plain,
! [SV878: $i,SV457: $i,SV28: $i] :
( ( ( class_Orderings_Olinorder @ SV28 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV28 ) @ SV457 ) @ SV878 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV878 @ SV457 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2697]) ).
thf(3065,plain,
! [SV879: $i,SV458: $i,SV29: $i] :
( ( ( class_Orderings_Olinorder @ SV29 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV29 ) @ SV458 ) @ SV879 ) )
| ( c_HOL_Oord__class_Oless @ SV879 @ SV458 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2698]) ).
thf(3066,plain,
! [SV880: $i,SV459: $i,SV30: $i] :
( ( ( class_Orderings_Olinorder @ SV30 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV459 @ SV880 @ SV30 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV30 ) @ SV880 ) @ SV459 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2699]) ).
thf(3067,plain,
! [SV31: $i,SV460: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV460 @ SV460 @ SV31 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV31 ) @ SV460 ) @ SV460 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2700]) ).
thf(3068,plain,
! [SV461: $i,SV32: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV32 ) @ SV461 ) @ SV461 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV461 @ SV461 @ SV32 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2701]) ).
thf(3069,plain,
! [SV881: $i,SV462: $i,SV33: $i] :
( ( ( class_Orderings_Olinorder @ SV33 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV462 @ SV881 @ SV33 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV33 ) @ SV881 ) @ SV462 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2702]) ).
thf(3070,plain,
! [SV882: $i,SV463: $i,SV34: $i] :
( ( ( class_Orderings_Opreorder @ SV34 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV463 @ SV882 @ SV34 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV34 ) @ SV882 ) @ SV463 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV34 ) @ SV463 ) @ SV882 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2703]) ).
thf(3071,plain,
! [SV883: $i,SV464: $i,SV35: $i] :
( ( ( class_Orderings_Oorder @ SV35 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV35 ) @ SV464 ) @ SV883 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV464 @ SV883 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2704]) ).
thf(3072,plain,
! [SV884: $i,SV465: $i,SV36: $i] :
( ( ( class_Orderings_Opreorder @ SV36 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV36 ) @ SV465 ) @ SV884 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV465 @ SV884 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2705]) ).
thf(3073,plain,
! [SV1223: $i,SV885: $i,SV466: $i,SV37: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV37 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV466 @ SV885 @ SV37 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV37 ) @ SV466 ) @ SV1223 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1223 @ SV885 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2706]) ).
thf(3074,plain,
! [SV1224: $i,SV886: $i,SV467: $i,SV38: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV38 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV467 @ SV886 @ SV38 )
| ~ ( c_HOL_Oord__class_Oless @ SV467 @ SV1224 @ SV38 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV38 ) @ SV1224 ) @ SV886 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2707]) ).
thf(3075,plain,
! [SV1225: $i,SV887: $i,SV468: $i,SV39: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV39 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV468 @ SV887 @ SV39 )
| ~ ( c_HOL_Oord__class_Oless @ SV1225 @ SV887 @ SV39 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV39 ) @ SV468 ) @ SV1225 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2708]) ).
thf(3076,plain,
! [SV1226: $i,SV888: $i,SV469: $i,SV40: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV40 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV469 @ SV888 @ SV40 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV40 ) @ SV1226 ) @ SV888 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV469 @ SV1226 @ SV40 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2709]) ).
thf(3077,plain,
! [SV889: $i,SV470: $i,SV41: $i] :
( ( ( class_Orderings_Oorder @ SV41 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV470 @ SV889 @ SV41 )
| ( SV889 = SV470 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV41 ) @ SV470 ) @ SV889 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2710]) ).
thf(3078,plain,
! [SV890: $i,SV471: $i,SV42: $i] :
( ( ( class_Orderings_Oorder @ SV42 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV471 @ SV890 @ SV42 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV42 ) @ SV471 ) @ SV890 ) )
| ( SV890 = SV471 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2711]) ).
thf(3079,plain,
! [SV891: $i,SV472: $i,SV43: $i] :
( ( ( class_Orderings_Oorder @ SV43 )
= $false )
| ( ( ( SV472 = SV891 )
| ( c_HOL_Oord__class_Oless @ SV472 @ SV891 @ SV43 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV43 ) @ SV472 ) @ SV891 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2712]) ).
thf(3080,plain,
! [SV892: $i,SV473: $i,SV44: $i] :
( ( ( class_Orderings_Oorder @ SV44 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV473 @ SV892 @ SV44 )
| ( SV473 = SV892 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV44 ) @ SV473 ) @ SV892 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2713]) ).
thf(3081,plain,
! [SV893: $i,SV474: $i,SV45: $i] :
( ( ( class_Orderings_Oorder @ SV45 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV474 @ SV893 @ SV45 )
| ( SV474 = SV893 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV45 ) @ SV474 ) @ SV893 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2714]) ).
thf(3082,plain,
! [SV894: $i,SV475: $i,SV46: $i] :
( ( ( class_Orderings_Oorder @ SV46 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV475 @ SV894 @ SV46 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV46 ) @ SV475 ) @ SV894 ) )
| ( SV475 = SV894 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2715]) ).
thf(3083,plain,
! [SV895: $i,SV476: $i,SV47: $i] :
( ( ( class_Orderings_Olinorder @ SV47 )
= $false )
| ( ( ( SV476 = SV895 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV47 ) @ SV476 ) @ SV895 ) )
| ( c_HOL_Oord__class_Oless @ SV476 @ SV895 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2716]) ).
thf(3084,plain,
! [SV896: $i,SV477: $i,SV48: $i] :
( ( ( class_Orderings_Olinorder @ SV48 )
= $false )
| ( ( ( SV477 = SV896 )
| ( c_HOL_Oord__class_Oless @ SV477 @ SV896 @ SV48 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV48 ) @ SV477 ) @ SV896 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2717]) ).
thf(3085,plain,
! [SV897: $i,SV478: $i,SV49: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV49 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV478 @ SV49 ) @ SV897 @ SV49 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV897 @ SV49 ) @ SV478 @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2718]) ).
thf(3086,plain,
! [SV898: $i,SV479: $i,SV50: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV50 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV479 @ SV50 ) @ SV898 @ SV50 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV898 @ SV50 ) @ SV479 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2719]) ).
thf(3087,plain,
! [SV899: $i,SV480: $i,SV51: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV51 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV480 @ ( c_HOL_Ouminus__class_Ouminus @ SV899 @ SV51 ) @ SV51 )
| ~ ( c_HOL_Oord__class_Oless @ SV899 @ ( c_HOL_Ouminus__class_Ouminus @ SV480 @ SV51 ) @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2720]) ).
thf(3088,plain,
! [SV900: $i,SV481: $i,SV52: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV52 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV481 @ ( c_HOL_Ouminus__class_Ouminus @ SV900 @ SV52 ) @ SV52 )
| ~ ( c_HOL_Oord__class_Oless @ SV900 @ ( c_HOL_Ouminus__class_Ouminus @ SV481 @ SV52 ) @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2721]) ).
thf(3089,plain,
! [SV1227: $i,SV901: $i,SV482: $i,SV53: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV53 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV482 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV901 @ SV1227 @ SV53 ) @ SV53 )
| ~ ( c_HOL_Oord__class_Oless @ SV482 @ SV1227 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2722]) ).
thf(3090,plain,
! [SV1228: $i,SV902: $i,SV483: $i,SV54: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV54 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV483 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV902 @ SV1228 @ SV54 ) @ SV54 )
| ~ ( c_HOL_Oord__class_Oless @ SV483 @ SV902 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2723]) ).
thf(3091,plain,
! [SV1408: $i,SV1229: $i,SV903: $i,SV485: $i,SV56: $i] :
( ( ~ ( class_Orderings_Oorder @ SV56 )
| ( c_HOL_Oord__class_Oless @ SV485 @ SV903 @ SV56 )
| ( c_HOL_Oord__class_Oless @ SV1229 @ SV1408 @ SV56 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV56 ) @ SV1408 ) @ SV485 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1408 @ SV485 @ SV56 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1229 @ SV903 @ SV56 ) @ ( tc_fun @ SV56 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2725]) ).
thf(3092,plain,
! [SV1409: $i,SV1230: $i,SV904: $i,SV486: $i,SV57: $i] :
( ( ! [SY3940: $i,SY3941: $i,SY3942: $i,SY3943: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV57 @ SV486 @ ( c_COMBC @ SV904 @ SV1230 @ SV1230 @ tc_bool ) @ ( c_COMBC @ SV1409 @ SV1230 @ SV1230 @ tc_bool ) @ SY3940 @ SY3941 @ SY3942 @ SY3943 @ SV1230 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV486 @ SV57 @ SV904 @ SV1409 @ SY3941 @ SY3940 @ SY3943 @ SY3942 @ SV1230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2726]) ).
thf(3093,plain,
! [SV1410: $i,SV1232: $i,SV906: $i,SV488: $i,SV59: $i] :
( ( ! [SY3944: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV59 @ SV488 @ SV906 @ SV1232 ) @ SV1410 ) @ SY3944 )
= ( hAPP @ ( hAPP @ SV59 @ SY3944 ) @ SV1410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2728]) ).
thf(3094,plain,
! [SV1233: $i,SV907: $i,SV489: $i,SV60: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV60 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV489 @ SV907 @ SV60 )
| ~ ( c_HOL_Oord__class_Oless @ SV489 @ SV1233 @ SV60 )
| ~ ( c_HOL_Oord__class_Oless @ SV1233 @ SV907 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2729]) ).
thf(3095,plain,
! [SV1234: $i,SV908: $i,SV490: $i,SV61: $i] :
( ( ( hBOOL @ ( c_in @ SV61 @ SV490 @ SV908 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV61 @ SV1234 @ SV908 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1234 @ SV490 @ ( tc_fun @ SV908 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2730]) ).
thf(3096,plain,
! [SV1235: $i,SV909: $i,SV491: $i,SV62: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV62 @ SV491 @ ( tc_fun @ SV909 @ tc_bool ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1235 @ SV491 @ ( tc_fun @ SV909 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV62 @ SV1235 @ ( tc_fun @ SV909 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2731]) ).
thf(3097,plain,
! [SV1236: $i,SV910: $i,SV492: $i,SV63: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV63 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV492 @ SV910 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV1236 @ SV910 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV492 @ SV1236 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2732]) ).
thf(3098,plain,
! [SV1411: $i,SV1237: $i,SV911: $i,SV493: $i,SV64: $i] :
( ( ! [SY3945: $i] :
( ( c_Finite__Set_Ofinite @ SV64 @ SV493 )
| ~ ( c_Finite__Set_Ofold__graph @ SV911 @ SV1237 @ SV64 @ SV1411 @ SV493 @ SY3945 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2733]) ).
thf(3099,plain,
! [SV912: $i,SV494: $i,SV65: $i] :
( ( ( class_Orderings_Oorder @ SV65 )
= $false )
| ( ( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV494 @ SV912 @ SV65 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV65 @ tc_bool ) ) )
| ( c_HOL_Oord__class_Oless @ SV494 @ SV912 @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2734]) ).
thf(3100,plain,
! [SV495: $i,SV913: $i,SV66: $i] :
( ( ( c_Finite__Set_Ofinite @ SV66 @ SV913 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV66 @ SV495 @ ( tc_fun @ SV913 @ tc_bool ) ) @ SV913 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2735]) ).
thf(3101,plain,
! [SV496: $i,SV914: $i,SV67: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV67 @ SV914 @ ( tc_fun @ SV496 @ tc_bool ) ) @ SV496 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV914 @ SV496 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV67 @ SV496 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2736]) ).
thf(3102,plain,
! [SV497: $i,SV915: $i,SV68: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV68 @ SV915 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV497 @ SV915 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV68 @ SV497 @ ( tc_fun @ SV915 @ tc_bool ) ) @ SV915 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2737]) ).
thf(3103,plain,
! [SV70: $i,SV916: $i,SV499: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV499 @ SV916 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV70 @ SV916 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV70 @ SV499 @ ( tc_fun @ SV916 @ tc_bool ) ) @ SV916 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2738]) ).
thf(3104,plain,
! [SV71: $i,SV917: $i,SV500: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV500 @ SV917 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV71 @ SV917 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV71 @ SV500 @ ( tc_fun @ SV917 @ tc_bool ) ) @ SV917 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2739]) ).
thf(3105,plain,
! [SV501: $i,SV918: $i,SV72: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV72 @ SV918 @ ( tc_fun @ SV501 @ tc_bool ) ) @ SV501 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV72 @ SV501 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2740]) ).
thf(3106,plain,
! [SV502: $i,SV73: $i,SV919: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV919 @ SV73 @ ( tc_fun @ SV502 @ tc_bool ) ) @ SV502 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV73 @ SV502 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2741]) ).
thf(3107,plain,
! [SV920: $i,SV503: $i,SV74: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV74 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV503 @ SV74 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV920 @ SV74 ) @ SV74 )
| ~ ( c_HOL_Oord__class_Oless @ SV920 @ SV503 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2742]) ).
thf(3108,plain,
! [SV921: $i,SV504: $i,SV75: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV75 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV504 @ SV921 @ SV75 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV921 @ SV75 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV504 @ SV75 ) @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2743]) ).
thf(3109,plain,
! [SV77: $i,SV506: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV506 @ SV506 @ SV77 )
= $false )
| ( ( class_Orderings_Oorder @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2744]) ).
thf(3110,plain,
! [SV78: $i,SV507: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV507 @ SV507 @ SV78 )
= $false )
| ( ( class_Orderings_Olinorder @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2745]) ).
thf(3111,plain,
! [SV79: $i,SV508: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV508 @ SV508 @ SV79 )
= $false )
| ( ( class_Orderings_Opreorder @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2746]) ).
thf(3112,plain,
! [SV1412: $i,SV1238: $i,SV922: $i,SV509: $i,SV80: $i] :
( ( ~ ( class_Orderings_Oorder @ SV80 )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV509 @ SV922 @ SV80 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1238 @ SV1412 @ SV80 ) @ ( tc_fun @ SV80 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV1238 ) @ SV1412 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV922 @ SV1412 @ SV80 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV922 ) @ SV1412 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV1238 ) @ SV509 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2747]) ).
thf(3113,plain,
! [SV1413: $i,SV1239: $i,SV923: $i,SV510: $i,SV81: $i] :
( ( ~ ( class_Orderings_Oorder @ SV81 )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV510 @ SV923 @ SV81 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1239 @ SV1413 @ SV81 ) @ ( tc_fun @ SV81 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV1239 ) @ SV1413 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1239 @ SV510 @ SV81 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV923 ) @ SV1413 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV1239 ) @ SV510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2748]) ).
thf(3114,plain,
! [SV924: $i,SV511: $i,SV82: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV82 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV511 @ SV924 @ SV82 )
| ( c_HOL_Oord__class_Oless @ SV924 @ SV511 @ SV82 )
| ( SV924 = SV511 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2749]) ).
thf(3115,plain,
! [SV925: $i,SV512: $i,SV83: $i] :
( ( ( class_Orderings_Olinorder @ SV83 )
= $false )
| ( ( ( SV512 = SV925 )
| ( c_HOL_Oord__class_Oless @ SV925 @ SV512 @ SV83 )
| ( c_HOL_Oord__class_Oless @ SV512 @ SV925 @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2750]) ).
thf(3116,plain,
! [SV926: $i,SV513: $i,SV84: $i] :
( ( ( class_Orderings_Olinorder @ SV84 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV513 @ SV926 @ SV84 )
| ( c_HOL_Oord__class_Oless @ SV926 @ SV513 @ SV84 )
| ( SV926 = SV513 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2751]) ).
thf(3117,plain,
! [SV927: $i,SV514: $i,SV85: $i] :
( ( ( class_Orderings_Olinorder @ SV85 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV514 @ SV927 @ SV85 )
| ( SV927 = SV514 )
| ( c_HOL_Oord__class_Oless @ SV927 @ SV514 @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2752]) ).
thf(3118,plain,
! [SV928: $i,SV515: $i,SV86: $i] :
( ( ( class_Orderings_Olinorder @ SV86 )
= $false )
| ( ( ( SV515 = SV928 )
| ( c_HOL_Oord__class_Oless @ SV515 @ SV928 @ SV86 )
| ( c_HOL_Oord__class_Oless @ SV928 @ SV515 @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2753]) ).
thf(3119,plain,
! [SV929: $i,SV516: $i,SV87: $i] :
( ( ( class_Orderings_Oorder @ SV87 )
= $false )
| ( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV87 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV516 @ SV929 @ SV87 ) )
| ( c_HOL_Oord__class_Oless @ SV516 @ SV929 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2754]) ).
thf(3120,plain,
! [SV930: $i,SV517: $i,SV88: $i] :
( ( ( class_Orderings_Oorder @ SV88 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV517 @ SV930 @ SV88 )
| ~ ( c_HOL_Oord__class_Oless @ SV930 @ SV517 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2755]) ).
thf(3121,plain,
! [SV931: $i,SV518: $i,SV89: $i] :
( ( ( class_Orderings_Olinorder @ SV89 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV518 @ SV931 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV931 @ SV518 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2756]) ).
thf(3122,plain,
! [SV932: $i,SV519: $i,SV90: $i] :
( ( ( class_Orderings_Opreorder @ SV90 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV519 @ SV932 @ SV90 )
| ~ ( c_HOL_Oord__class_Oless @ SV932 @ SV519 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2757]) ).
thf(3123,plain,
! [SV933: $i,SV520: $i,SV91: $i] :
( ( ( class_Orderings_Opreorder @ SV91 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV520 @ SV933 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV933 @ SV520 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2758]) ).
thf(3124,plain,
! [SV1414: $i,SV1240: $i,SV934: $i,SV521: $i,SV92: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV92 )
| ( ( c_Finite__Set_Osetsum @ SV521 @ ( c_HOL_Ominus__class_Ominus @ SV934 @ SV1240 @ ( tc_fun @ SV1414 @ tc_bool ) ) @ SV1414 @ SV92 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV521 @ SV934 @ SV1414 @ SV92 ) @ ( c_Finite__Set_Osetsum @ SV521 @ SV1240 @ SV1414 @ SV92 ) @ SV92 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1414 @ tc_bool ) ) @ SV1240 ) @ SV934 ) )
| ~ ( c_Finite__Set_Ofinite @ SV934 @ SV1414 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2759]) ).
thf(3125,plain,
! [SV935: $i,SV522: $i,SV93: $i] :
( ( ( class_Orderings_Oorder @ SV93 )
= $false )
| ( ( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV522 @ SV935 @ SV93 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV93 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV93 ) @ SV935 ) @ SV522 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2760]) ).
thf(3126,plain,
! [SV1415: $i,SV1241: $i,SV936: $i,SV523: $i,SV94: $i] :
( ( ! [SY3946: $i,SY3947: $i] :
( ( c_Finite__Set_Ofold__graph @ SV94 @ SV523 @ ( c_Set_Oinsert @ SV936 @ SV1241 @ SV1415 ) @ ( hAPP @ ( hAPP @ SV94 @ SV936 ) @ SY3946 ) @ SV1415 @ SY3947 )
| ~ ( c_Finite__Set_Ofold__graph @ SV94 @ SV523 @ SV1241 @ SY3946 @ SV1415 @ SY3947 )
| ( hBOOL @ ( c_in @ SV936 @ SV1241 @ SV1415 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2761]) ).
thf(3127,plain,
! [SV1242: $i,SV937: $i,SV524: $i,SV95: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV95 @ SV524 @ ( tc_fun @ SV937 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1242 @ SV524 @ SV937 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV95 @ ( c_Set_Oinsert @ SV1242 @ SV524 @ SV937 ) @ ( tc_fun @ SV937 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2762]) ).
thf(3128,plain,
! [SV1243: $i,SV938: $i,SV525: $i,SV96: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV96 @ ( c_Set_Oinsert @ SV525 @ SV938 @ SV1243 ) @ ( tc_fun @ SV1243 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV525 @ SV938 @ SV1243 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV96 @ SV938 @ ( tc_fun @ SV1243 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2763]) ).
thf(3129,plain,
! [SV1416: $i,SV1244: $i,SV939: $i,SV526: $i,SV97: $i] :
( ( ~ ( class_Orderings_Oorder @ SV97 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV97 ) @ SV526 ) @ SV939 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV97 ) @ SV1244 ) @ SV526 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1244 @ SV526 @ SV97 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1416 @ SV939 @ SV97 ) @ ( tc_fun @ SV97 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2764]) ).
thf(3130,plain,
! [SV1417: $i,SV1245: $i,SV940: $i,SV527: $i,SV98: $i] :
( ( ~ ( class_Orderings_Oorder @ SV98 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV98 ) @ SV527 ) @ SV940 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV98 ) @ SV940 ) @ SV1245 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV940 @ SV1245 @ SV98 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV527 @ SV1417 @ SV98 ) @ ( tc_fun @ SV98 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2765]) ).
thf(3131,plain,
! [SV1418: $i,SV1246: $i,SV941: $i,SV528: $i,SV99: $i] :
( ( ~ ( class_Orderings_Oorder @ SV99 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV99 ) @ SV528 ) @ SV941 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1246 @ SV1418 @ SV99 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV528 @ SV941 @ SV99 ) @ ( tc_fun @ SV99 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2766]) ).
thf(3132,plain,
! [SV1419: $i,SV1247: $i,SV942: $i,SV529: $i,SV100: $i] :
( ( ~ ( class_Orderings_Oorder @ SV100 )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV529 @ SV942 @ SV100 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1247 @ SV1419 @ SV100 ) @ ( tc_fun @ SV100 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV100 ) @ SV1247 ) @ SV1419 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV100 ) @ SV529 ) @ SV942 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2767]) ).
thf(3133,plain,
! [SV1248: $i,SV943: $i,SV530: $i,SV101: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV101 ) )
= $true )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV530 @ SV943 @ SV101 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV943 @ SV1248 @ SV101 ) @ ( tc_fun @ SV101 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV530 @ SV1248 @ SV101 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV101 ) @ SV943 ) @ SV1248 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV101 ) @ SV530 ) @ SV943 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2768]) ).
thf(3134,plain,
! [SV1420: $i,SV1249: $i,SV944: $i,SV531: $i,SV102: $i] :
( ( ( c_Finite__Set_Ofinite @ ( hAPP @ SV102 @ SV531 ) @ SV944 )
| ~ ( hBOOL @ ( c_in @ SV531 @ SV1249 @ SV1420 ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1249 @ SV102 @ SV1420 @ ( tc_fun @ SV944 @ tc_bool ) ) @ SV944 )
| ~ ( c_Finite__Set_Ofinite @ SV1249 @ SV1420 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2769]) ).
thf(3135,plain,
! [SV1421: $i,SV1250: $i,SV945: $i,SV532: $i,SV103: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV103 )
| ( ( c_Finite__Set_Osetsum @ SV532 @ ( c_HOL_Ominus__class_Ominus @ SV945 @ ( c_Set_Oinsert @ SV1250 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1421 @ tc_bool ) ) @ SV1421 ) @ ( tc_fun @ SV1421 @ tc_bool ) ) @ SV1421 @ SV103 )
= ( c_Finite__Set_Osetsum @ SV532 @ SV945 @ SV1421 @ SV103 ) )
| ( hBOOL @ ( c_in @ SV1250 @ SV945 @ SV1421 ) )
| ~ ( c_Finite__Set_Ofinite @ SV945 @ SV1421 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2770]) ).
thf(3136,plain,
! [SV946: $i,SV533: $i,SV104: $i] :
( ( ( class_Orderings_Oorder @ SV104 )
= $false )
| ( ( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV533 @ SV946 @ SV104 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV104 @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV946 @ SV533 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2771]) ).
thf(3137,plain,
! [SV1251: $i,SV947: $i,SV534: $i,SV105: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV105 ) )
= $true )
| ( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV534 @ ( c_COMBK @ SV947 @ SV105 @ SV1251 ) @ SV1251 @ SV105 )
= SV947 )
| ( SV534
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1251 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2772]) ).
thf(3138,plain,
! [SV1252: $i,SV949: $i,SV536: $i,SV107: $i] :
( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV107 @ ( c_COMBK @ SV536 @ ( tc_fun @ SV949 @ tc_bool ) @ SV1252 ) @ SV1252 @ ( tc_fun @ SV949 @ tc_bool ) )
= SV536 )
= $true )
| ( ( SV107
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1252 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2773]) ).
thf(3139,plain,
! [SV1253: $i,SV951: $i,SV538: $i,SV109: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV109 @ SV538 @ ( tc_fun @ SV951 @ tc_bool ) ) @ SV951 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV109 @ ( c_Set_Oinsert @ SV1253 @ SV538 @ SV951 ) @ ( tc_fun @ SV951 @ tc_bool ) ) @ SV951 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2774]) ).
thf(3140,plain,
! [SV1254: $i,SV952: $i,SV539: $i,SV110: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV110 @ ( c_Set_Oinsert @ SV539 @ SV952 @ SV1254 ) @ ( tc_fun @ SV1254 @ tc_bool ) ) @ SV1254 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV110 @ SV952 @ ( tc_fun @ SV1254 @ tc_bool ) ) @ SV1254 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2775]) ).
thf(3141,plain,
! [SV953: $i,SV540: $i,SV111: $i] :
( ( ( class_Orderings_Oorder @ SV111 )
= $false )
| ( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV111 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV540 @ SV953 @ SV111 ) )
| ( c_HOL_Oord__class_Oless @ SV540 @ SV953 @ SV111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2776]) ).
thf(3142,plain,
! [SV954: $i,SV541: $i,SV112: $i] :
( ( ( class_Orderings_Oorder @ SV112 )
= $false )
| ( ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ SV541 @ SV954 @ SV112 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV112 @ tc_bool ) ) )
| ( c_HOL_Oord__class_Oless @ SV541 @ SV954 @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2777]) ).
thf(3143,plain,
! [SV955: $i,SV542: $i,SV114: $i] :
( ( ( class_Orderings_Olinorder @ SV114 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV114 ) @ SV542 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV955 @ SV114 ) ) )
| ~ ( hBOOL @ ( c_in @ SV542 @ SV955 @ SV114 ) )
| ~ ( c_Finite__Set_Ofinite @ SV955 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2778]) ).
thf(3144,plain,
! [SV956: $i,SV543: $i,SV115: $i] :
( ( ( class_Orderings_Olinorder @ SV115 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV115 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV543 @ SV115 ) ) @ SV956 ) )
| ~ ( hBOOL @ ( c_in @ SV956 @ SV543 @ SV115 ) )
| ~ ( c_Finite__Set_Ofinite @ SV543 @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2779]) ).
thf(3145,plain,
! [SV116: $i,SV544: $i] :
( ( ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMin @ SV544 @ SV116 ) @ SV544 @ SV116 ) )
= $true )
| ( ( ( SV544
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV116 @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV544 @ SV116 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2780]) ).
thf(3146,plain,
! [SV117: $i,SV545: $i] :
( ( ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMax @ SV545 @ SV117 ) @ SV545 @ SV117 ) )
= $true )
| ( ( ( SV545
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV117 @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV545 @ SV117 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2781]) ).
thf(3147,plain,
! [SV1422: $i,SV1255: $i,SV957: $i,SV546: $i,SV118: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV118 @ ( c_Set_Oinsert @ SV546 @ SV957 @ SV1255 ) @ SV1255 ) @ SV1422 ) )
| ( hBOOL @ ( c_in @ SV546 @ SV957 @ SV1255 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV118 @ SV546 @ SV957 @ SV1422 @ SV1255 @ SV1255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2782]) ).
thf(3148,plain,
! [SV1423: $i,SV1256: $i,SV958: $i,SV547: $i,SV119: $i] :
( ( ! [SY3948: $i,SY3949: $i] :
( ( c_Finite__Set_Ofold__graph @ SV119 @ SV547 @ SV958 @ ( hAPP @ ( hAPP @ SV119 @ SV1256 ) @ SV1423 ) @ SY3948 @ SY3949 )
| ~ ( hBOOL @ ( c_in @ SV1256 @ SV958 @ SY3948 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV119 @ SV547 @ ( c_HOL_Ominus__class_Ominus @ SV958 @ ( c_Set_Oinsert @ SV1256 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3948 @ tc_bool ) ) @ SY3948 ) @ ( tc_fun @ SY3948 @ tc_bool ) ) @ SV1423 @ SY3948 @ SY3949 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2783]) ).
thf(3149,plain,
! [SV1257: $i,SV959: $i,SV548: $i,SV120: $i] :
( ( ( ( c_Finite__Set_Osetsum @ SV120 @ ( c_HOL_Ominus__class_Ominus @ SV548 @ ( c_Set_Oinsert @ SV959 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1257 @ tc_bool ) ) @ SV1257 ) @ ( tc_fun @ SV1257 @ tc_bool ) ) @ SV1257 @ tc_nat )
= ( c_Finite__Set_Osetsum @ SV120 @ SV548 @ SV1257 @ tc_nat ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV959 @ SV548 @ SV1257 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2784]) ).
thf(3150,plain,
! [SV1258: $i,SV960: $i,SV549: $i,SV121: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV121 @ ( c_Set_Oinsert @ SV549 @ SV960 @ SV1258 ) @ ( tc_fun @ SV1258 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV549 @ SV121 @ SV1258 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV121 @ ( c_Set_Oinsert @ SV549 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1258 @ tc_bool ) ) @ SV1258 ) @ ( tc_fun @ SV1258 @ tc_bool ) ) @ SV960 @ ( tc_fun @ SV1258 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV121 @ SV960 @ ( tc_fun @ SV1258 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2785]) ).
thf(3151,plain,
! [SV1259: $i,SV961: $i,SV550: $i,SV122: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV122 @ ( c_Set_Oinsert @ SV550 @ SV961 @ SV1259 ) @ ( tc_fun @ SV1259 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV550 @ SV122 @ SV1259 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV122 @ ( c_Set_Oinsert @ SV550 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1259 @ tc_bool ) ) @ SV1259 ) @ ( tc_fun @ SV1259 @ tc_bool ) ) @ SV961 @ ( tc_fun @ SV1259 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SV550 @ SV961 @ SV1259 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2786]) ).
thf(3152,plain,
! [SV1260: $i,SV962: $i,SV551: $i,SV123: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV123 @ ( c_Set_Oinsert @ SV551 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV962 @ tc_bool ) ) @ SV962 ) @ ( tc_fun @ SV962 @ tc_bool ) ) @ SV1260 @ ( tc_fun @ SV962 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV551 @ SV123 @ SV962 ) )
| ( hBOOL @ ( c_in @ SV551 @ SV1260 @ SV962 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV123 @ ( c_Set_Oinsert @ SV551 @ SV1260 @ SV962 ) @ ( tc_fun @ SV962 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2787]) ).
thf(3153,plain,
! [SV1424: $i,SV1261: $i,SV963: $i,SV552: $i,SV124: $i] :
( ( ! [SY3950: $i,SY3951: $i] :
( ( c_Nitpick_Ofold__graph_H @ SV124 @ SV552 @ SV963 @ ( hAPP @ ( hAPP @ SV124 @ SV1261 ) @ SV1424 ) @ SY3950 @ SY3951 )
| ~ ( c_Nitpick_Ofold__graph_H @ SV124 @ SV552 @ ( c_HOL_Ominus__class_Ominus @ SV963 @ ( c_Set_Oinsert @ SV1261 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3950 @ tc_bool ) ) @ SY3950 ) @ ( tc_fun @ SY3950 @ tc_bool ) ) @ SV1424 @ SY3950 @ SY3951 )
| ~ ( hBOOL @ ( c_in @ SV1261 @ SV963 @ SY3950 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2788]) ).
thf(3154,plain,
! [SV1262: $i,SV964: $i,SV553: $i,SV125: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV125 @ ( c_Set_Oinsert @ SV553 @ SV964 @ SV1262 ) @ ( tc_fun @ SV1262 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1262 @ tc_bool ) ) @ SV125 ) @ SV964 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV125 @ ( c_Set_Oinsert @ SV553 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1262 @ tc_bool ) ) @ SV1262 ) @ ( tc_fun @ SV1262 @ tc_bool ) ) @ SV964 @ ( tc_fun @ SV1262 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV125 @ SV964 @ ( tc_fun @ SV1262 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2789]) ).
thf(3155,plain,
! [SV965: $i,SV554: $i,SV126: $i] :
( ( ( class_Orderings_Olinorder @ SV126 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV126 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV554 @ SV126 ) ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV965 @ SV126 ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV554 @ SV126 )
| ( SV965
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV126 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV126 @ tc_bool ) ) @ SV965 ) @ SV554 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2790]) ).
thf(3156,plain,
! [SV966: $i,SV555: $i,SV127: $i] :
( ( ( class_Orderings_Olinorder @ SV127 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV127 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV555 @ SV127 ) ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV966 @ SV127 ) ) )
| ~ ( c_Finite__Set_Ofinite @ SV966 @ SV127 )
| ( SV555
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV127 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV127 @ tc_bool ) ) @ SV555 ) @ SV966 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2791]) ).
thf(3157,plain,
! [SV1263: $i,SV967: $i,SV556: $i,SV128: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV128 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV556 @ SV967 @ SV1263 @ 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 )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV128 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_COMBK @ ( hAPP @ ( c_COMBC @ ( c_fequal @ tc_Com_Ostate ) @ tc_Com_Ostate @ tc_Com_Ostate @ tc_bool ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ SV128 @ SV556 @ SV1263 @ SV967 ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) @ SV967 @ ( c_COMBK @ ( hAPP @ SV1263 @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ SV128 @ SV556 @ SV1263 @ SV967 ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) @ 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_or_pos,[status(thm)],[2792]) ).
thf(3158,plain,
! [SV968: $i,SV557: $i,SV129: $i] :
( ( ( class_Orderings_Olinorder @ SV129 )
= $false )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV557 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV129 @ tc_bool ) ) @ SV129 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV557 @ SV968 @ SV129 ) @ ( tc_fun @ SV129 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV557 @ SV968 @ SV129 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV129 ) @ SV557 ) @ SV968 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2793]) ).
thf(3159,plain,
! [SV1264: $i,SV969: $i,SV558: $i,SV130: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV130 @ ( c_Set_Oinsert @ SV558 @ SV969 @ SV1264 ) @ ( tc_fun @ SV1264 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1264 @ tc_bool ) ) @ SV130 ) @ SV969 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV130 @ ( c_Set_Oinsert @ SV558 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1264 @ tc_bool ) ) @ SV1264 ) @ ( tc_fun @ SV1264 @ tc_bool ) ) @ SV969 @ ( tc_fun @ SV1264 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SV558 @ SV969 @ SV1264 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2794]) ).
thf(3160,plain,
! [SV1265: $i,SV970: $i,SV559: $i,SV131: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV131 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV559 @ SV970 @ SV131 ) ) @ SV1265 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ SV970 ) @ SV1265 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ SV559 ) @ SV1265 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2795]) ).
thf(3161,plain,
! [SV1266: $i,SV971: $i,SV560: $i,SV132: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV132 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV560 @ SV971 @ SV132 ) ) @ SV1266 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ SV971 ) @ SV1266 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ SV560 ) @ SV1266 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2796]) ).
thf(3162,plain,
! [SV972: $i,SV561: $i,SV133: $i] :
( ( ( class_Lattices_Olattice @ SV133 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV133 ) @ SV561 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV972 @ SV561 @ SV133 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2797]) ).
thf(3163,plain,
! [SV973: $i,SV562: $i,SV134: $i] :
( ( ( class_Lattices_Olattice @ SV134 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV134 ) @ SV562 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV562 @ SV973 @ SV134 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2798]) ).
thf(3164,plain,
! [SV974: $i,SV563: $i,SV135: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV135 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV135 ) @ SV563 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV974 @ SV135 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV135 ) @ SV974 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV563 @ SV135 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2799]) ).
thf(3165,plain,
! [SV975: $i,SV564: $i,SV136: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV136 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV136 ) @ SV564 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV975 @ SV136 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV136 ) @ SV975 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV564 @ SV136 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2800]) ).
thf(3166,plain,
! [SV976: $i,SV565: $i,SV137: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV137 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV137 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV565 @ SV137 ) ) @ SV976 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV137 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV976 @ SV137 ) ) @ SV565 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2801]) ).
thf(3167,plain,
! [SV977: $i,SV566: $i,SV138: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV138 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV138 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV566 @ SV138 ) ) @ SV977 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV138 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV977 @ SV138 ) ) @ SV566 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2802]) ).
thf(3168,plain,
! [SV978: $i,SV567: $i,SV139: $i] :
( ( ( class_Orderings_Olinorder @ SV139 )
= $false )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV567 @ SV978 @ SV139 ) @ ( c_Set_Oinsert @ SV978 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV139 @ tc_bool ) ) @ SV139 ) @ ( tc_fun @ SV139 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV567 @ SV978 @ SV139 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV139 ) @ SV567 ) @ SV978 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2803]) ).
thf(3169,plain,
! [SV1425: $i,SV1267: $i,SV979: $i,SV570: $i,SV143: $i] :
( ( ! [SY3952: $i,SY3953: $i,SY3954: $i,SY3955: $i] :
( ( ( hAPP @ SV143 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV570 @ tc_bool ) ) )
= SV979 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV143 @ SV1267 @ SV1425 @ SY3952 @ SY3953 @ SY3954 @ SY3955 @ SV979 @ SV570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2806]) ).
thf(3170,plain,
! [SV1426: $i,SV1268: $i,SV980: $i,SV571: $i,SV144: $i] :
( ( ! [SY3956: $i,SY3957: $i,SY3958: $i,SY3959: $i] :
( ( ( hAPP @ SV144 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV571 @ tc_bool ) ) )
= SV980 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1268 @ SV144 @ SV1426 @ SY3956 @ SY3957 @ SY3958 @ SV980 @ SY3959 @ SV571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2807]) ).
thf(3171,plain,
! [SV146: $i,SV981: $i,SV573: $i] :
( ( ( hBOOL @ ( c_in @ SV573 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV981 @ tc_bool ) ) @ SV981 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV146 @ SV573 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2808]) ).
thf(3172,plain,
! [SV983: $i,SV582: $i,SV155: $i] :
( ( ( hBOOL @ ( hAPP @ SV155 @ SV582 ) )
= $false )
| ( ( ~ ( hBOOL @ ( c_in @ SV582 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV983 @ tc_bool ) ) @ SV983 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2810]) ).
thf(3173,plain,
! [SV984: $i,SV583: $i,SV156: $i] :
( ( ( hBOOL @ ( c_in @ SV156 @ SV583 @ SV984 ) )
= $false )
| ( ( ( c_Set_Oinsert @ SV156 @ ( c_HOL_Ominus__class_Ominus @ SV583 @ ( c_Set_Oinsert @ SV156 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV984 @ tc_bool ) ) @ SV984 ) @ ( tc_fun @ SV984 @ tc_bool ) ) @ SV984 )
= SV583 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2811]) ).
thf(3174,plain,
! [SV985: $i,SV584: $i,SV157: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV157 )
= $false )
| ( ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV157 ) @ ( c_Set_Oinsert @ SV584 @ ( c_Set_Oinsert @ SV985 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV157 @ tc_bool ) ) @ SV157 ) @ SV157 ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV584 @ SV985 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2812]) ).
thf(3175,plain,
! [SV1269: $i,SV987: $i,SV586: $i,SV159: $i] :
( ( ( hBOOL @ ( c_in @ SV159 @ ( c_Set_Oinsert @ SV586 @ SV987 @ SV1269 ) @ SV1269 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV159 @ SV987 @ SV1269 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2814]) ).
thf(3176,plain,
! [SV1270: $i,SV988: $i,SV587: $i,SV160: $i] :
( ( ( hBOOL @ ( c_in @ SV160 @ ( c_Set_Oinsert @ SV587 @ SV988 @ SV1270 ) @ SV1270 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV160 @ SV988 @ SV1270 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2815]) ).
thf(3177,plain,
! [SV1427: $i,SV1271: $i,SV989: $i,SV588: $i,SV161: $i] :
( ( ! [SY3960: $i,SY3961: $i,SY3962: $i,SY3963: $i,SY3964: $i,SY3965: $i] :
( ( ( hAPP @ SV161 @ ( c_Set_Oinsert @ SV588 @ SV989 @ SV1271 ) )
= ( hAPP @ ( hAPP @ SV1427 @ SV588 ) @ ( hAPP @ SV161 @ SV989 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV161 @ SY3960 @ SY3961 @ SY3962 @ SV1427 @ SY3963 @ SY3964 @ SY3965 @ SV1271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2816]) ).
thf(3178,plain,
! [SV1428: $i,SV1272: $i,SV990: $i,SV589: $i,SV162: $i] :
( ( ! [SY3966: $i,SY3967: $i,SY3968: $i,SY3969: $i,SY3970: $i,SY3971: $i] :
( ( ( hAPP @ SV162 @ ( c_Set_Oinsert @ SV589 @ SV990 @ SV1272 ) )
= ( hAPP @ ( hAPP @ SV1428 @ SV589 ) @ ( hAPP @ SV162 @ SV990 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3966 @ SV162 @ SY3967 @ SY3968 @ SY3969 @ SV1428 @ SY3970 @ SY3971 @ SV1272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2817]) ).
thf(3179,plain,
! [SV1273: $i,SV991: $i,SV590: $i,SV163: $i] :
( ( ( hBOOL @ ( c_in @ SV163 @ SV590 @ SV991 ) )
= $true )
| ( ( ( SV163 = SV1273 )
| ~ ( hBOOL @ ( c_in @ SV163 @ ( c_Set_Oinsert @ SV1273 @ SV590 @ SV991 ) @ SV991 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2818]) ).
thf(3180,plain,
! [SV997: $i,SV596: $i,SV169: $i] :
( ( ( hBOOL @ ( c_in @ SV169 @ SV596 @ SV997 ) )
= $false )
| ( ( ( c_Set_Oinsert @ SV169 @ SV596 @ SV997 )
= SV596 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2821]) ).
thf(3181,plain,
! [SV1276: $i,SV998: $i,SV597: $i,SV170: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV170 @ ( c_HOL_Ominus__class_Ominus @ SV597 @ SV998 @ ( tc_fun @ SV1276 @ tc_bool ) ) @ ( tc_fun @ SV1276 @ tc_bool ) )
= SV998 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV170 ) @ SV597 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV998 ) @ SV170 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2822]) ).
thf(3182,plain,
! [SV1277: $i,SV999: $i,SV598: $i,SV171: $i] :
( ( ( hBOOL @ ( c_in @ SV171 @ SV598 @ SV999 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV171 @ SV1277 @ SV999 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV999 @ tc_bool ) ) @ SV1277 ) @ SV598 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2823]) ).
thf(3183,plain,
! [SV1278: $i,SV1000: $i,SV599: $i,SV172: $i] :
( ( ( hBOOL @ ( c_in @ SV172 @ SV599 @ SV1000 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1000 @ tc_bool ) ) @ SV1278 ) @ SV599 ) )
| ~ ( hBOOL @ ( c_in @ SV172 @ SV1278 @ SV1000 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2824]) ).
thf(3184,plain,
! [SV1279: $i,SV1001: $i,SV600: $i,SV173: $i] :
( ( ( hBOOL @ ( c_in @ SV173 @ SV600 @ SV1001 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV173 @ SV1279 @ SV1001 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1001 @ tc_bool ) ) @ SV1279 ) @ SV600 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2825]) ).
thf(3185,plain,
! [SV1280: $i,SV1002: $i,SV601: $i,SV174: $i] :
( ( ( hBOOL @ ( c_in @ SV174 @ SV601 @ SV1002 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV174 @ SV1280 @ SV1002 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1002 @ tc_bool ) ) @ SV1280 ) @ SV601 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2826]) ).
thf(3186,plain,
! [SV1281: $i,SV1003: $i,SV602: $i,SV175: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV175 @ tc_bool ) ) @ SV602 ) @ SV1003 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV175 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1281 @ SV602 @ ( tc_fun @ SV175 @ tc_bool ) ) ) @ SV1003 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2827]) ).
thf(3187,plain,
! [SV1282: $i,SV1004: $i,SV603: $i,SV176: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV176 @ tc_bool ) ) @ SV603 ) @ SV1004 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV176 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV603 @ SV1282 @ ( tc_fun @ SV176 @ tc_bool ) ) ) @ SV1004 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2828]) ).
thf(3188,plain,
! [SV1429: $i,SV1283: $i,SV1005: $i,SV604: $i,SV177: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV604 @ SV1005 @ ( tc_fun @ SV177 @ tc_bool ) ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1283 @ SV1429 @ ( tc_fun @ SV177 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ SV1005 ) @ SV1429 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ SV604 ) @ SV1283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2829]) ).
thf(3189,plain,
! [SV178: $i,SV605: $i,SV1006: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1006 @ tc_bool ) ) @ SV605 ) @ SV178 ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV178 @ SV605 @ ( tc_fun @ SV1006 @ tc_bool ) )
= SV178 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2830]) ).
thf(3190,plain,
! [SV606: $i,SV179: $i,SV1007: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1007 @ tc_bool ) ) @ SV179 ) @ SV606 ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV179 @ SV606 @ ( tc_fun @ SV1007 @ tc_bool ) )
= SV606 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2831]) ).
thf(3191,plain,
! [SV1430: $i,SV1284: $i,SV1008: $i,SV607: $i,SV180: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV607 @ SV1008 @ ( tc_fun @ SV180 @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1284 @ SV1430 @ ( tc_fun @ SV180 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ SV1430 ) @ SV1008 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ SV607 ) @ SV1284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2832]) ).
thf(3192,plain,
! [SV608: $i,SV1009: $i,SV181: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV181 @ tc_bool ) ) @ SV1009 ) @ SV608 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV181 @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV608 @ ( tc_fun @ SV181 @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV1009 @ ( tc_fun @ SV181 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2833]) ).
thf(3193,plain,
! [SV609: $i,SV1010: $i,SV182: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV182 @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV1010 @ ( tc_fun @ SV182 @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV609 @ ( tc_fun @ SV182 @ tc_bool ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV182 @ tc_bool ) ) @ SV609 ) @ SV1010 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2834]) ).
thf(3194,plain,
! [SV610: $i,SV1011: $i,SV183: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV183 @ tc_bool ) ) @ SV1011 ) @ SV610 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV183 @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV610 @ ( tc_fun @ SV183 @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV1011 @ ( tc_fun @ SV183 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2835]) ).
thf(3195,plain,
! [SV1285: $i,SV1012: $i,SV611: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV184 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV611 @ SV1012 @ ( tc_fun @ SV184 @ tc_bool ) ) ) @ SV1285 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV184 @ tc_bool ) ) @ SV1012 ) @ SV1285 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV184 @ tc_bool ) ) @ SV611 ) @ SV1285 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2836]) ).
thf(3196,plain,
! [SV1286: $i,SV1015: $i,SV614: $i,SV187: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV187 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV614 @ SV1015 @ ( tc_fun @ SV187 @ tc_bool ) ) ) @ SV1286 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV187 @ tc_bool ) ) @ SV1015 ) @ SV1286 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV187 @ tc_bool ) ) @ SV614 ) @ SV1286 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2837]) ).
thf(3197,plain,
! [SV1287: $i,SV1017: $i,SV616: $i,SV189: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV189 @ tc_bool ) ) @ SV616 ) @ ( c_Set_Oinsert @ SV1017 @ SV1287 @ SV189 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1017 @ SV616 @ SV189 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV189 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV616 @ ( c_Set_Oinsert @ SV1017 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV189 @ tc_bool ) ) @ SV189 ) @ ( tc_fun @ SV189 @ tc_bool ) ) ) @ SV1287 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2838]) ).
thf(3198,plain,
! [SV1288: $i,SV1018: $i,SV617: $i,SV190: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV190 @ tc_bool ) ) @ SV617 ) @ ( c_Set_Oinsert @ SV1018 @ SV1288 @ SV190 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1018 @ SV617 @ SV190 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV190 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV617 @ ( c_Set_Oinsert @ SV1018 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV190 @ tc_bool ) ) @ SV190 ) @ ( tc_fun @ SV190 @ tc_bool ) ) ) @ SV1288 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2839]) ).
thf(3199,plain,
! [SV1289: $i,SV1019: $i,SV618: $i,SV191: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV191 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV618 @ ( c_Set_Oinsert @ SV1019 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV191 @ tc_bool ) ) @ SV191 ) @ ( tc_fun @ SV191 @ tc_bool ) ) ) @ SV1289 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1019 @ SV618 @ SV191 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV191 @ tc_bool ) ) @ SV618 ) @ ( c_Set_Oinsert @ SV1019 @ SV1289 @ SV191 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2840]) ).
thf(3200,plain,
! [SV1020: $i,SV619: $i,SV192: $i] :
( ( ( class_Orderings_Oorder @ SV192 )
= $false )
| ( ( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV619 @ SV1020 @ SV192 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV192 @ tc_bool ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV192 ) @ SV619 ) @ SV1020 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2841]) ).
thf(3201,plain,
! [SV1021: $i,SV620: $i,SV193: $i] :
( ( ( class_Orderings_Oorder @ SV193 )
= $false )
| ( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV193 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV620 @ SV1021 @ SV193 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV193 ) @ SV620 ) @ SV1021 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2842]) ).
thf(3202,plain,
! [SV1022: $i,SV621: $i,SV194: $i] :
( ( ( class_Orderings_Oorder @ SV194 )
= $false )
| ( ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ SV621 @ SV1022 @ SV194 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV194 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV194 ) @ SV1022 ) @ SV621 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2843]) ).
thf(3203,plain,
! [SV1431: $i,SV1290: $i,SV1023: $i,SV622: $i,SV195: $i] :
( ( ~ ( class_Orderings_Oorder @ SV195 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV195 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV622 @ SV1023 @ SV195 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1290 @ SV1431 @ SV195 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV195 ) @ SV622 ) @ SV1023 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2844]) ).
thf(3204,plain,
! [SV1432: $i,SV1291: $i,SV1024: $i,SV623: $i,SV196: $i] :
( ( ~ ( class_Orderings_Oorder @ SV196 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV196 ) @ SV623 ) @ SV1024 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV196 ) @ SV1024 ) @ SV1291 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV196 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1024 @ SV1291 @ SV196 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV623 @ SV1432 @ SV196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2845]) ).
thf(3205,plain,
! [SV1433: $i,SV1292: $i,SV1025: $i,SV624: $i,SV197: $i] :
( ( ~ ( class_Orderings_Oorder @ SV197 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV197 ) @ SV624 ) @ SV1025 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV197 ) @ SV1292 ) @ SV624 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV197 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1292 @ SV624 @ SV197 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1433 @ SV1025 @ SV197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2846]) ).
thf(3206,plain,
! [SV1434: $i,SV1293: $i,SV1026: $i,SV625: $i,SV198: $i] :
( ( ~ ( class_Orderings_Oorder @ SV198 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV198 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV625 @ SV1026 @ SV198 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1293 @ SV1434 @ SV198 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV198 ) @ SV1026 ) @ SV1434 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV198 ) @ SV1293 ) @ SV625 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2847]) ).
thf(3207,plain,
! [SV1435: $i,SV1294: $i,SV1027: $i,SV626: $i,SV199: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV199 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV199 ) @ SV626 ) @ SV1027 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV199 ) @ SV1294 ) @ SV1027 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV199 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1027 @ SV1294 @ SV199 ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV626 @ SV1435 @ SV199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2848]) ).
thf(3208,plain,
! [SV1028: $i,SV627: $i,SV200: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV200 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV200 ) @ SV627 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1028 @ SV627 @ SV200 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2849]) ).
thf(3209,plain,
! [SV1029: $i,SV628: $i,SV201: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV201 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV201 ) @ SV628 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV628 @ SV1029 @ SV201 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2850]) ).
thf(3210,plain,
! [SV1295: $i,SV1030: $i,SV629: $i,SV202: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV202 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV629 @ SV1030 @ SV202 ) ) @ SV1295 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ SV1030 ) @ SV1295 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ SV629 ) @ SV1295 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2851]) ).
thf(3211,plain,
! [SV1031: $i,SV630: $i,SV203: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV203 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV203 ) @ SV630 ) @ SV1031 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV203 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV1031 @ SV203 ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV630 @ SV203 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2852]) ).
thf(3212,plain,
! [SV1032: $i,SV631: $i,SV204: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV204 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV204 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV631 @ SV204 ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV1032 @ SV204 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV204 ) @ SV1032 ) @ SV631 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2853]) ).
thf(3213,plain,
! [SV1033: $i,SV632: $i,SV205: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV205 )
= $false )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV632 @ SV1033 @ SV205 )
= SV632 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV205 ) @ SV1033 ) @ SV632 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2854]) ).
thf(3214,plain,
! [SV1034: $i,SV633: $i,SV206: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV206 )
= $false )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV633 @ SV1034 @ SV206 )
= SV1034 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV206 ) @ SV633 ) @ SV1034 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2855]) ).
thf(3215,plain,
! [SV1296: $i,SV1035: $i,SV634: $i,SV207: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV207 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV207 ) @ SV634 ) @ SV1035 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV207 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1296 @ SV634 @ SV207 ) ) @ SV1035 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2856]) ).
thf(3216,plain,
! [SV1297: $i,SV1036: $i,SV635: $i,SV208: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV208 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV208 ) @ SV635 ) @ SV1036 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV208 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV635 @ SV1297 @ SV208 ) ) @ SV1036 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2857]) ).
thf(3217,plain,
! [SV1298: $i,SV1037: $i,SV636: $i,SV209: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV209 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV209 ) @ SV636 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1037 @ SV1298 @ SV209 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV209 ) @ SV636 ) @ SV1298 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2858]) ).
thf(3218,plain,
! [SV1299: $i,SV1038: $i,SV637: $i,SV210: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV210 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV210 ) @ SV637 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1038 @ SV1299 @ SV210 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV210 ) @ SV637 ) @ SV1038 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2859]) ).
thf(3219,plain,
! [SV1300: $i,SV1039: $i,SV638: $i,SV211: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV211 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV211 ) @ SV638 ) @ SV1039 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV211 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1300 @ SV638 @ SV211 ) ) @ SV1039 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2860]) ).
thf(3220,plain,
! [SV1301: $i,SV1040: $i,SV639: $i,SV212: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV212 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV212 ) @ SV639 ) @ SV1040 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV212 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV639 @ SV1301 @ SV212 ) ) @ SV1040 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2861]) ).
thf(3221,plain,
! [SV1041: $i,SV640: $i,SV213: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV213 )
= $false )
| ( ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ SV640 @ SV1041 @ SV213 ) @ SV213 )
= ( c_HOL_Ominus__class_Ominus @ SV1041 @ SV640 @ SV213 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2862]) ).
thf(3222,plain,
! [SV1302: $i,SV1042: $i,SV647: $i,SV220: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV220 @ tc_bool ) ) @ SV647 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1042 @ SV1302 @ ( tc_fun @ SV220 @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV220 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV647 @ SV1042 @ ( tc_fun @ SV220 @ tc_bool ) ) ) @ SV1302 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2868]) ).
thf(3223,plain,
! [SV1303: $i,SV1043: $i,SV648: $i,SV221: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV221 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV648 @ SV1043 @ ( tc_fun @ SV221 @ tc_bool ) ) ) @ SV1303 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV221 @ tc_bool ) ) @ SV648 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1043 @ SV1303 @ ( tc_fun @ SV221 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2869]) ).
thf(3224,plain,
! [SV1304: $i,SV1044: $i,SV649: $i,SV222: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV222 @ SV649 @ SV1044 ) @ SV1304 @ ( tc_fun @ SV1044 @ tc_bool ) )
= ( c_Set_Oinsert @ SV222 @ ( c_HOL_Ominus__class_Ominus @ SV649 @ SV1304 @ ( tc_fun @ SV1044 @ tc_bool ) ) @ SV1044 ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV222 @ SV1304 @ SV1044 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2870]) ).
thf(3225,plain,
! [SV1436: $i,SV1305: $i,SV1045: $i,SV650: $i,SV223: $i] :
( ( ! [SY3972: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV223 @ SV650 @ SV1045 @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1436 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV650 @ SY3972 ) @ SV1436 ) )
| ~ ( hBOOL @ ( c_in @ SY3972 @ SV223 @ SV1045 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2871]) ).
thf(3226,plain,
! [SV1437: $i,SV1306: $i,SV1046: $i,SV651: $i,SV224: $i] :
( ( ! [SY3973: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV224 @ SV651 @ SV1046 @ ( tc_fun @ SV1306 @ tc_bool ) ) @ SV1437 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV651 @ SY3973 ) @ SV1437 ) )
| ~ ( hBOOL @ ( c_in @ SY3973 @ SV224 @ SV1046 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2872]) ).
thf(3227,plain,
! [SV1047: $i,SV652: $i,SV225: $i] :
( ( ( class_Lattices_Olattice @ SV225 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV652 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV652 @ SV1047 @ SV225 ) @ SV225 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV652 @ SV1047 @ SV225 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2873]) ).
thf(3228,plain,
! [SV1048: $i,SV653: $i,SV226: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV226 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV653 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV653 @ SV1048 @ SV226 ) @ SV226 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV653 @ SV1048 @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2874]) ).
thf(3229,plain,
! [SV1050: $i,SV655: $i,SV228: $i] :
( ( ( class_Lattices_Olattice @ SV228 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV655 @ SV1050 @ SV228 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1050 @ SV655 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2875]) ).
thf(3230,plain,
! [SV1051: $i,SV656: $i,SV229: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV229 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV656 @ SV1051 @ SV229 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1051 @ SV656 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2876]) ).
thf(3231,plain,
! [SV1438: $i,SV1307: $i,SV1053: $i,SV658: $i,SV231: $i] :
( ( ! [SY3974: $i,SY3975: $i,SY3976: $i,SY3977: $i,SY3978: $i,SY3979: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV231 @ SV658 ) @ ( hAPP @ SV1053 @ SV1307 ) ) )
| ~ ( hBOOL @ ( c_in @ SV658 @ SV1307 @ SV1438 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3974 @ SV1053 @ SV231 @ SY3975 @ SY3976 @ SY3977 @ SY3978 @ SY3979 @ SV1438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2877]) ).
thf(3232,plain,
! [SV1439: $i,SV1308: $i,SV1054: $i,SV659: $i,SV232: $i] :
( ( ! [SY3980: $i,SY3981: $i,SY3982: $i,SY3983: $i,SY3984: $i,SY3985: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ ( hAPP @ SV659 @ SV1054 ) ) @ SV1308 ) )
| ~ ( hBOOL @ ( c_in @ SV1308 @ SV1054 @ SV1439 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV659 @ SY3980 @ SV232 @ SY3981 @ SY3982 @ SY3983 @ SY3984 @ SY3985 @ SV1439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2878]) ).
thf(3233,plain,
! [SV1056: $i,SV661: $i,SV234: $i] :
( ( ( class_HOL_Ominus @ SV234 )
= $false )
| ( ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ SV661 @ SV1056 @ ( tc_fun @ t_a @ SV234 ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ SV661 @ v_x ) @ ( hAPP @ SV1056 @ v_x ) @ SV234 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2880]) ).
thf(3234,plain,
! [SV1440: $i,SV1310: $i,SV1059: $i,SV664: $i,SV237: $i] :
( ( ! [SY3986: $i] :
( ( hBOOL @ ( c_in @ SV237 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV664 @ SV1059 @ SV1310 @ ( tc_fun @ SV1440 @ tc_bool ) ) @ SV1440 ) )
| ~ ( hBOOL @ ( c_in @ SV237 @ ( hAPP @ SV1059 @ SY3986 ) @ SV1440 ) )
| ~ ( hBOOL @ ( c_in @ SY3986 @ SV664 @ SV1310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2881]) ).
thf(3235,plain,
! [SV1441: $i,SV1311: $i,SV1060: $i,SV665: $i,SV238: $i] :
( ( ! [SY3987: $i] :
( ( hBOOL @ ( c_in @ SV238 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV665 @ SV1060 @ SV1311 @ ( tc_fun @ SV1441 @ tc_bool ) ) @ SV1441 ) )
| ~ ( hBOOL @ ( c_in @ SV238 @ ( hAPP @ SV1060 @ SY3987 ) @ SV1441 ) )
| ~ ( hBOOL @ ( c_in @ SY3987 @ SV665 @ SV1311 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2882]) ).
thf(3236,plain,
! [SV1312: $i,SV1061: $i,SV666: $i,SV239: $i] :
( ( ( hBOOL @ ( c_in @ SV239 @ ( c_HOL_Ominus__class_Ominus @ SV666 @ SV1061 @ ( tc_fun @ SV1312 @ tc_bool ) ) @ SV1312 ) )
= $true )
| ( ( ( hBOOL @ ( c_in @ SV239 @ SV1061 @ SV1312 ) )
| ~ ( hBOOL @ ( c_in @ SV239 @ SV666 @ SV1312 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2883]) ).
thf(3237,plain,
! [SV1313: $i,SV1062: $i,SV667: $i,SV240: $i] :
( ( ( hBOOL @ ( c_in @ SV240 @ ( c_HOL_Ominus__class_Ominus @ SV667 @ SV1062 @ ( tc_fun @ SV1313 @ tc_bool ) ) @ SV1313 ) )
= $true )
| ( ( ( hBOOL @ ( c_in @ SV240 @ SV1062 @ SV1313 ) )
| ~ ( hBOOL @ ( c_in @ SV240 @ SV667 @ SV1313 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2884]) ).
thf(3238,plain,
! [SV1063: $i,SV241: $i,SV668: $i] :
( ( ( hBOOL @ ( c_in @ SV668 @ ( c_Collect @ SV241 @ SV1063 ) @ SV1063 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV241 @ SV668 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2885]) ).
thf(3239,plain,
! [SV1064: $i,SV242: $i,SV669: $i] :
( ( ( hBOOL @ ( hAPP @ SV669 @ SV242 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV242 @ ( c_Collect @ SV669 @ SV1064 ) @ SV1064 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2886]) ).
thf(3240,plain,
! [SV670: $i,SV243: $i,SV1065: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1065 @ tc_bool ) ) @ SV243 ) @ SV670 ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV243 @ ( c_HOL_Ominus__class_Ominus @ SV670 @ SV243 @ ( tc_fun @ SV1065 @ tc_bool ) ) @ ( tc_fun @ SV1065 @ tc_bool ) )
= SV670 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2887]) ).
thf(3241,plain,
! [SV1314: $i,SV1066: $i,SV671: $i,SV244: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV244 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV671 @ SV1066 @ SV244 ) @ SV1314 @ SV244 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV671 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1066 @ SV1314 @ SV244 ) @ SV244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2888]) ).
thf(3242,plain,
! [SV1315: $i,SV1067: $i,SV672: $i,SV245: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV245 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV672 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1067 @ SV1315 @ SV245 ) @ SV245 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1067 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV672 @ SV1315 @ SV245 ) @ SV245 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2889]) ).
thf(3243,plain,
! [SV1316: $i,SV1068: $i,SV673: $i,SV246: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV246 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV673 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1068 @ SV1316 @ SV246 ) @ SV246 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1068 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV673 @ SV1316 @ SV246 ) @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2890]) ).
thf(3244,plain,
! [SV1317: $i,SV1069: $i,SV674: $i,SV247: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV247 ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV674 @ SV1069 @ SV247 ) @ SV1317 @ SV247 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV674 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1069 @ SV1317 @ SV247 ) @ SV247 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2891]) ).
thf(3245,plain,
! [SV1073: $i,SV251: $i,SV678: $i] :
( ( ( hBOOL @ ( c_in @ SV678 @ SV251 @ SV1073 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV251 @ SV678 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2894]) ).
thf(3246,plain,
! [SV1074: $i,SV252: $i,SV679: $i] :
( ( ( hBOOL @ ( hAPP @ SV679 @ SV252 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV252 @ SV679 @ SV1074 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2895]) ).
thf(3247,plain,
! [SV1076: $i,SV683: $i,SV256: $i] :
( ( ( class_Lattices_Olattice @ SV256 )
= $false )
| ( ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV683 @ SV1076 @ ( tc_fun @ t_a @ SV256 ) ) @ v_x )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV683 @ v_x ) @ ( hAPP @ SV1076 @ v_x ) @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2898]) ).
thf(3248,plain,
! [SV1442: $i,SV1321: $i,SV1078: $i,SV685: $i,SV258: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV258 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV258 ) @ ( hAPP @ SV685 @ SV1078 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1321 @ SV685 @ SV1442 @ SV258 ) ) )
| ~ ( hBOOL @ ( c_in @ SV1078 @ SV1321 @ SV1442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2899]) ).
thf(3249,plain,
! [SV1443: $i,SV1322: $i,SV1079: $i,SV686: $i,SV259: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV259 @ tc_bool ) ) @ ( hAPP @ SV686 @ SV1079 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1322 @ SV686 @ SV1443 @ ( tc_fun @ SV259 @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( c_in @ SV1079 @ SV1322 @ SV1443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2900]) ).
thf(3250,plain,
! [SV1323: $i,SV1080: $i,SV687: $i,SV260: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV260 @ SV687 @ SV1080 ) @ SV1323 @ ( tc_fun @ SV1080 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV687 @ SV1323 @ ( tc_fun @ SV1080 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV260 @ SV1323 @ SV1080 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2901]) ).
thf(3251,plain,
! [SV1081: $i,SV688: $i,SV261: $i] :
( ( ( hBOOL @ ( c_in @ SV261 @ SV688 @ SV1081 ) )
= $false )
| ( ( ~ ( hBOOL @ ( c_in @ SV261 @ ( c_HOL_Ouminus__class_Ouminus @ SV688 @ ( tc_fun @ SV1081 @ tc_bool ) ) @ SV1081 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2902]) ).
thf(3252,plain,
! [SV1083: $i,SV691: $i,SV264: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV264 )
= $false )
| ( ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV264 ) @ ( c_Set_Oinsert @ SV691 @ SV1083 @ SV264 ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV691 @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV264 ) @ SV1083 ) @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2904]) ).
thf(3253,plain,
! [SV1324: $i,SV1085: $i,SV693: $i,SV266: $i] :
( ( ( hBOOL @ ( c_in @ SV266 @ SV693 @ SV1085 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV266 @ ( c_HOL_Ominus__class_Ominus @ SV693 @ SV1324 @ ( tc_fun @ SV1085 @ tc_bool ) ) @ SV1085 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2905]) ).
thf(3254,plain,
! [SV1325: $i,SV1086: $i,SV694: $i,SV267: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV267 @ SV694 @ SV1086 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV267 @ ( c_HOL_Ominus__class_Ominus @ SV1325 @ SV694 @ ( tc_fun @ SV1086 @ tc_bool ) ) @ SV1086 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2906]) ).
thf(3255,plain,
! [SV1444: $i,SV1326: $i,SV1087: $i,SV695: $i,SV268: $i] :
( ( ! [SY3988: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV268 @ tc_bool ) ) @ ( hAPP @ SV695 @ SV1087 ) ) @ SV1326 ) )
| ~ ( hBOOL @ ( c_in @ SV1087 @ SV1444 @ SY3988 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV268 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1444 @ SV695 @ SY3988 @ ( tc_fun @ SV268 @ tc_bool ) ) ) @ SV1326 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2907]) ).
thf(3256,plain,
! [SV1445: $i,SV1327: $i,SV1088: $i,SV696: $i,SV269: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV269 @ SV696 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1088 @ SV269 @ SV1327 @ ( tc_fun @ SV1445 @ tc_bool ) ) @ ( tc_fun @ SV1445 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1088 @ SV269 @ SV1327 @ ( tc_fun @ SV1445 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SV696 @ SV1088 @ SV1327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2908]) ).
thf(3257,plain,
! [SV1328: $i,SV1089: $i,SV697: $i,SV270: $i] :
( ( ( hBOOL @ ( hAPP @ SV270 @ SV697 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV1089 @ SV697 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1089 @ SV270 @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV697 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2909]) ).
thf(3258,plain,
! [SV1329: $i,SV1090: $i,SV698: $i,SV271: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV271 @ SV698 @ ( tc_fun @ SV1090 @ tc_bool ) ) @ SV1329 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV698 @ SV1329 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2910]) ).
thf(3259,plain,
! [SV1330: $i,SV1091: $i,SV699: $i,SV272: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV272 @ SV699 @ ( tc_fun @ SV1091 @ tc_bool ) ) @ SV1330 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV272 @ SV1330 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2911]) ).
thf(3260,plain,
! [SV1331: $i,SV1092: $i,SV700: $i,SV273: $i] :
( ( ( hBOOL @ ( c_in @ SV273 @ SV700 @ SV1092 ) )
= $true )
| ( ( ( hBOOL @ ( c_in @ SV273 @ SV1331 @ SV1092 ) )
| ~ ( hBOOL @ ( c_in @ SV273 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1331 @ SV700 @ ( tc_fun @ SV1092 @ tc_bool ) ) @ SV1092 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2912]) ).
thf(3261,plain,
! [SV1332: $i,SV1093: $i,SV701: $i,SV274: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV274 ) )
= $true )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV701 @ SV1093 @ SV274 ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1093 @ SV1332 @ SV274 ) @ ( tc_fun @ SV274 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV701 @ SV1332 @ SV274 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV274 ) @ SV1093 ) @ SV1332 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV274 ) @ SV701 ) @ SV1093 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2913]) ).
thf(3262,plain,
! [SV1335: $i,SV1096: $i,SV704: $i,SV277: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV277 ) )
= $true )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV704 @ SV1096 @ SV277 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1096 @ SV1335 @ SV277 ) @ ( tc_fun @ SV277 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV704 @ SV1335 @ SV277 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV277 ) @ SV1096 ) @ SV1335 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV277 ) @ SV704 ) @ SV1096 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2916]) ).
thf(3263,plain,
! [SV1446: $i,SV1336: $i,SV1097: $i,SV705: $i,SV278: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ SV278 @ SV705 @ SV1097 ) @ SV1336 @ SV1097 @ ( tc_fun @ SV1446 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV1336 @ SV278 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV705 @ SV1336 @ SV1097 @ ( tc_fun @ SV1446 @ tc_bool ) ) @ ( tc_fun @ SV1446 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2917]) ).
thf(3264,plain,
! [SV1098: $i,SV706: $i,SV279: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV279 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV279 ) @ ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ SV279 ) @ SV706 ) ) @ SV1098 ) )
| ~ ( hBOOL @ ( c_in @ SV1098 @ SV706 @ SV279 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2918]) ).
thf(3265,plain,
! [SV1337: $i,SV1099: $i,SV708: $i,SV281: $i] :
( ( ( hBOOL @ ( c_in @ SV281 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV708 @ SV1099 @ ( tc_fun @ SV1337 @ tc_bool ) ) @ SV1337 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV281 @ SV1099 @ SV1337 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2920]) ).
thf(3266,plain,
! [SV1338: $i,SV1100: $i,SV709: $i,SV282: $i] :
( ( ( hBOOL @ ( c_in @ SV282 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV709 @ SV1100 @ ( tc_fun @ SV1338 @ tc_bool ) ) @ SV1338 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV282 @ SV709 @ SV1338 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2921]) ).
thf(3267,plain,
! [SV1339: $i,SV1101: $i,SV710: $i,SV283: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV283 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV710 @ SV1101 @ SV283 ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV710 @ SV1339 @ SV283 ) @ ( tc_fun @ SV283 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1339 @ SV1101 @ SV283 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV283 ) @ SV710 ) @ SV1339 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2922]) ).
thf(3268,plain,
! [SV1447: $i,SV1340: $i,SV1102: $i,SV711: $i,SV284: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV284 @ SV711 @ ( tc_fun @ SV1102 @ tc_bool ) ) @ SV1340 @ SV1102 @ ( tc_fun @ SV1447 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV284 @ SV1340 @ SV1102 @ ( tc_fun @ SV1447 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV711 @ SV1340 @ SV1102 @ ( tc_fun @ SV1447 @ tc_bool ) ) @ ( tc_fun @ SV1447 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2923]) ).
thf(3269,plain,
! [SV1103: $i,SV713: $i,SV286: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV286 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV286 ) @ SV713 ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV286 ) @ SV1103 ) ) )
| ~ ( hBOOL @ ( c_in @ SV713 @ SV1103 @ SV286 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2924]) ).
thf(3270,plain,
! [SV1448: $i,SV1341: $i,SV1104: $i,SV714: $i,SV287: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV287 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV287 ) @ SV714 ) @ SV1104 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV287 ) @ SV714 ) @ SV1341 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV287 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1341 @ SV714 @ SV287 ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1448 @ SV1104 @ SV287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2925]) ).
thf(3271,plain,
! [SV1449: $i,SV1342: $i,SV1105: $i,SV717: $i,SV292: $i] :
( ( ! [SY3989: $i,SY3990: $i,SY3991: $i,SY3992: $i,SY3993: $i] :
( ( ( hAPP @ SV292 @ ( c_Set_Oinsert @ SV717 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1105 @ tc_bool ) ) @ SV1105 ) )
= SV717 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV292 @ SV1342 @ SV1449 @ SY3989 @ SY3990 @ SY3991 @ SY3992 @ SY3993 @ SV1105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2926]) ).
thf(3272,plain,
! [SV1450: $i,SV1343: $i,SV1106: $i,SV718: $i,SV293: $i] :
( ( ! [SY3994: $i,SY3995: $i,SY3996: $i,SY3997: $i,SY3998: $i] :
( ( ( hAPP @ SV293 @ ( c_Set_Oinsert @ SV718 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1106 @ tc_bool ) ) @ SV1106 ) )
= SV718 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1343 @ SV293 @ SV1450 @ SY3994 @ SY3995 @ SY3996 @ SY3997 @ SY3998 @ SV1106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2927]) ).
thf(3273,plain,
! [SV1451: $i,SV1345: $i,SV1109: $i,SV725: $i,SV300: $i] :
( ( ! [SY3999: $i,SY4000: $i,SY4001: $i,SY4002: $i,SY4003: $i,SY4004: $i] :
( ( ( hAPP @ SV300 @ ( c_Set_Oinsert @ SV725 @ ( c_Set_Oinsert @ SV1109 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1345 @ tc_bool ) ) @ SV1345 ) @ SV1345 ) )
= ( hAPP @ ( hAPP @ SV1451 @ SV725 ) @ SV1109 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV300 @ SY3999 @ SY4000 @ SY4001 @ SV1451 @ SY4002 @ SY4003 @ SY4004 @ SV1345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2931]) ).
thf(3274,plain,
! [SV1452: $i,SV1346: $i,SV1110: $i,SV726: $i,SV301: $i] :
( ( ! [SY4005: $i,SY4006: $i,SY4007: $i,SY4008: $i,SY4009: $i,SY4010: $i] :
( ( ( hAPP @ SV301 @ ( c_Set_Oinsert @ SV726 @ ( c_Set_Oinsert @ SV1110 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1346 @ tc_bool ) ) @ SV1346 ) @ SV1346 ) )
= ( hAPP @ ( hAPP @ SV1452 @ SV726 ) @ SV1110 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY4005 @ SV301 @ SY4006 @ SY4007 @ SY4008 @ SV1452 @ SY4009 @ SY4010 @ SV1346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2932]) ).
thf(3275,plain,
! [SV1349: $i,SV1113: $i,SV729: $i,SV304: $i] :
( ( ( SV304 = SV729 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV1113 @ ( c_Set_Oinsert @ SV304 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1349 @ tc_bool ) ) @ SV1349 ) @ SV1349 ) @ SV729 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2935]) ).
thf(3276,plain,
! [SV306: $i,SV1114: $i,SV731: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV731 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1114 @ tc_bool ) ) @ SV1114 ) @ SV306 ) )
= $false )
| ( ( SV306
= ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ SV731 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1114 @ tc_bool ) ) @ SV1114 ) @ SV1114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2936]) ).
thf(3277,plain,
! [SV1115: $i,SV732: $i,SV307: $i] :
( ( ( hBOOL @ ( c_in @ SV307 @ ( c_Set_Oinsert @ SV732 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1115 @ tc_bool ) ) @ SV1115 ) @ SV1115 ) )
= $false )
| ( ( SV307 = SV732 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2937]) ).
thf(3278,plain,
! [SV1350: $i,SV1119: $i,SV740: $i,SV316: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV316 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV740 @ SV1119 @ SV316 ) ) @ SV1350 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV316 @ tc_bool ) ) @ SV1119 ) @ SV1350 ) )
| ~ ( hBOOL @ ( c_in @ SV740 @ SV1350 @ SV316 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2942]) ).
thf(3279,plain,
! [SV1351: $i,SV1120: $i,SV741: $i,SV317: $i] :
( ( ( hBOOL @ ( c_in @ SV317 @ SV741 @ SV1120 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1120 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV317 @ SV1351 @ SV1120 ) ) @ SV741 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2943]) ).
thf(3280,plain,
! [SV1352: $i,SV1121: $i,SV742: $i,SV318: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV318 @ tc_bool ) ) @ SV742 ) @ ( c_Set_Oinsert @ SV1121 @ SV1352 @ SV318 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV318 @ tc_bool ) ) @ SV742 ) @ SV1352 ) )
| ( hBOOL @ ( c_in @ SV1121 @ SV742 @ SV318 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2944]) ).
thf(3281,plain,
! [SV1353: $i,SV1122: $i,SV743: $i,SV319: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV319 @ tc_bool ) ) @ SV743 ) @ SV1122 ) )
= $true )
| ( ( ( hBOOL @ ( c_in @ SV1353 @ SV743 @ SV319 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV319 @ tc_bool ) ) @ SV743 ) @ ( c_Set_Oinsert @ SV1353 @ SV1122 @ SV319 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2945]) ).
thf(3282,plain,
! [SV1354: $i,SV1123: $i,SV744: $i,SV320: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV320 @ tc_bool ) ) @ SV744 ) @ ( c_Set_Oinsert @ SV1123 @ SV1354 @ SV320 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV320 @ tc_bool ) ) @ SV744 ) @ SV1354 ) )
| ( hBOOL @ ( c_in @ SV1123 @ SV744 @ SV320 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2946]) ).
thf(3283,plain,
! [SV1355: $i,SV1124: $i,SV745: $i,SV321: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV321 @ tc_bool ) ) @ SV745 ) @ SV1124 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV321 @ tc_bool ) ) @ SV745 ) @ ( c_Set_Oinsert @ SV1355 @ SV1124 @ SV321 ) ) )
| ( hBOOL @ ( c_in @ SV1355 @ SV745 @ SV321 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2947]) ).
thf(3284,plain,
! [SV1453: $i,SV1356: $i,SV1125: $i,SV746: $i,SV322: $i] :
( ( ! [SY4011: $i,SY4012: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV322 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV746 @ SV1125 @ SV1356 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV1453 @ SY4011 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV322 @ SV746 @ SV1356 @ SV1125 @ SY4012 @ SV1453 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4012 @ SY4011 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV322 @ SV746 @ SV1356 @ SV1125 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV322 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY4012 @ SV1125 @ SV1453 @ 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_forall_pos,[status(thm)],[2948]) ).
thf(3285,plain,
! [SV1454: $i,SV1357: $i,SV1126: $i,SV747: $i,SV323: $i] :
( ( ! [SY4013: $i,SY4014: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV323 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV747 @ SV1126 @ SV1357 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV1454 @ SY4013 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV747 @ SY4014 @ SV1357 @ SV1454 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4014 @ SY4013 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV747 @ SY4014 @ SV1357 @ SV1454 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV323 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY4014 @ SV1126 @ SV1454 @ 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_forall_pos,[status(thm)],[2949]) ).
thf(3286,plain,
! [SV1455: $i,SV1358: $i,SV1127: $i,SV748: $i,SV324: $i] :
( ( ! [SY4015: $i,SY4016: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV324 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV748 @ SV1127 @ SV1358 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV1455 @ SY4015 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV324 @ SV748 @ SV1358 @ SV1127 @ SY4016 @ SV1455 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4016 @ SY4015 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV324 @ SV748 @ SV1358 @ SV1127 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV324 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY4016 @ SV1127 @ SV1455 @ 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_forall_pos,[status(thm)],[2950]) ).
thf(3287,plain,
! [SV1359: $i,SV1128: $i,SV749: $i,SV325: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV325 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV749 @ SV1128 @ SV1359 @ 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 )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV749 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV325 @ SV749 @ SV1359 @ SV1128 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV325 @ SV749 @ SV1359 @ SV1128 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2951]) ).
thf(3288,plain,
! [SV1456: $i,SV1360: $i,SV1129: $i,SV750: $i,SV326: $i] :
( ( ! [SY4017: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV326 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV750 @ SV1129 @ SV1360 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1360 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV326 @ SV750 @ SV1360 @ SV1129 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV326 @ SV750 @ SV1360 @ SV1129 @ SV1456 @ SY4017 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV326 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1456 @ SV1129 @ SY4017 @ 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_forall_pos,[status(thm)],[2952]) ).
thf(3289,plain,
! [SV1361: $i,SV1130: $i,SV751: $i,SV327: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV327 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV751 @ SV1130 @ SV1361 @ 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 )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV751 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV327 @ SV751 @ SV1361 @ SV1130 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV327 @ SV751 @ SV1361 @ SV1130 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2953]) ).
thf(3290,plain,
! [SV1457: $i,SV1362: $i,SV1131: $i,SV752: $i,SV328: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV328 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV752 @ SV1131 @ SV1362 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV1457 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SV1362 @ SV1457 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SV1362 @ SV1457 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV328 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV752 @ SV1131 @ SV1457 @ 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_forall_pos,[status(thm)],[2954]) ).
thf(3291,plain,
! [SV1458: $i,SV1363: $i,SV1132: $i,SV753: $i,SV329: $i] :
( ( ! [SY4018: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV329 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV753 @ SV1132 @ SV1363 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV753 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV753 @ SV1458 @ SV1363 @ SY4018 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV753 @ SV1458 @ SV1363 @ SY4018 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV329 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1458 @ SV1132 @ SY4018 @ 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_forall_pos,[status(thm)],[2955]) ).
thf(3292,plain,
! [SV1459: $i,SV1364: $i,SV1133: $i,SV754: $i,SV330: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV330 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV754 @ SV1133 @ SV1364 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV754 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV754 @ SV1459 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV754 @ SV1459 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV330 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1459 @ SV1133 @ SV1364 @ 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_forall_pos,[status(thm)],[2956]) ).
thf(3293,plain,
! [SV1460: $i,SV1365: $i,SV1134: $i,SV755: $i,SV331: $i] :
( ( ! [SY4019: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV331 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV755 @ SV1134 @ SV1365 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1365 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV331 @ SV755 @ SV1365 @ SV1134 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV331 @ SV755 @ SV1365 @ SV1134 @ SV1460 @ SY4019 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV331 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1460 @ SV1134 @ SY4019 @ 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_forall_pos,[status(thm)],[2957]) ).
thf(3294,plain,
! [SV1461: $i,SV1366: $i,SV1135: $i,SV756: $i,SV332: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV332 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV756 @ SV1135 @ SV1366 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1461 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV756 @ SV1461 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV756 @ SV1461 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV332 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1461 @ SV1135 @ SV1366 @ 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_forall_pos,[status(thm)],[2958]) ).
thf(3295,plain,
! [SV1462: $i,SV1367: $i,SV1136: $i,SV757: $i,SV333: $i] :
( ( ! [SY4020: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV333 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV757 @ SV1136 @ SV1367 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1367 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV757 @ SV1462 @ SV1367 @ SY4020 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV757 @ SV1462 @ SV1367 @ SY4020 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV333 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1462 @ SV1136 @ SY4020 @ 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_forall_pos,[status(thm)],[2959]) ).
thf(3296,plain,
! [SV1463: $i,SV1368: $i,SV1137: $i,SV758: $i,SV334: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV334 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV758 @ SV1137 @ SV1368 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1368 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SV1368 @ SV1463 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SV1368 @ SV1463 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV334 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV758 @ SV1137 @ SV1463 @ 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_forall_pos,[status(thm)],[2960]) ).
thf(3297,plain,
! [SV1369: $i,SV1138: $i,SV759: $i,SV335: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV335 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV759 @ SV1138 @ SV1369 @ 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 )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV759 @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ SV335 @ SV759 @ SV1369 @ SV1138 ) ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ SV335 @ SV759 @ SV1369 @ SV1138 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2961]) ).
thf(3298,plain,
! [SV1370: $i,SV1139: $i,SV760: $i,SV336: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV336 @ tc_bool ) ) @ SV760 ) @ ( c_Set_Oinsert @ SV1139 @ SV1370 @ SV336 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV336 @ tc_bool ) ) @ SV760 ) @ SV1370 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV336 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV760 @ ( c_Set_Oinsert @ SV1139 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV336 @ tc_bool ) ) @ SV336 ) @ ( tc_fun @ SV336 @ tc_bool ) ) ) @ SV1370 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2962]) ).
thf(3299,plain,
! [SV1464: $i,SV1371: $i,SV1140: $i,SV761: $i,SV337: $i] :
( ( ! [SY4021: $i,SY4022: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV761 @ ( c_Com_Ocom_OSemi @ SV1140 @ SV1371 ) @ SV1464 @ SY4021 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY4021 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY4021 ) ) @ SY4021 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY4022 @ SV1371 @ SV1464 @ SY4021 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY4021 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY4021 ) ) @ SY4021 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV761 @ SV1140 @ SY4022 @ SY4021 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY4021 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY4021 ) ) @ SY4021 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2963]) ).
thf(3300,plain,
! [SV1141: $i,SV762: $i,SV338: $i] :
( ( ( class_Orderings_Olinorder @ SV338 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV338 ) @ SV762 ) @ SV1141 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV338 ) @ SV1141 ) @ SV762 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2964]) ).
thf(3301,plain,
! [SV1372: $i,SV1142: $i,SV763: $i,SV339: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV339 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV763 @ SV1142 @ SV339 ) ) @ ( c_Set_Oinsert @ SV763 @ SV1372 @ SV339 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV339 @ tc_bool ) ) @ SV1142 ) @ SV1372 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2965]) ).
thf(3302,plain,
! [SV1373: $i,SV1143: $i,SV764: $i,SV340: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV340 @ ( c_Set_Oinsert @ SV764 @ SV1143 @ ( tc_Hoare__Mirabelle_Otriple @ SV1373 ) ) @ SV1373 )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV340 @ SV1143 @ SV1373 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV340 @ ( c_Set_Oinsert @ SV764 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1373 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1373 ) ) @ SV1373 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2966]) ).
thf(3303,plain,
! [SV765: $i,SV1144: $i,SV341: $i] :
( ( ( SV341
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1144 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1144 @ tc_bool ) ) @ SV341 ) @ ( c_Set_Oinsert @ SV765 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1144 @ tc_bool ) ) @ SV1144 ) ) ) )
= $true )
| ( ( SV341
= ( c_Set_Oinsert @ SV765 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1144 @ tc_bool ) ) @ SV1144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2967]) ).
thf(3304,plain,
! [SV1374: $i,SV1145: $i,SV766: $i,SV342: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV342 @ SV766 @ SV1145 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1145 ) @ tc_bool ) ) @ SV766 ) @ SV1374 ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV342 @ SV1374 @ SV1145 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2968]) ).
thf(3305,plain,
! [SV1375: $i,SV1146: $i,SV767: $i,SV343: $i] :
( ( ( hBOOL @ ( hAPP @ SV343 @ SV767 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1146 @ tc_bool ) ) @ SV1375 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP @ SV1375 @ SV767 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2969]) ).
thf(3306,plain,
! [SV1376: $i,SV1147: $i,SV770: $i,SV346: $i] :
( ( ( hBOOL @ ( hAPP @ SV346 @ SV770 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1147 @ SV770 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1376 @ tc_bool ) ) @ SV1147 ) @ SV346 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2972]) ).
thf(3307,plain,
! [SV1377: $i,SV1148: $i,SV771: $i,SV347: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV347 @ tc_bool ) ) @ SV771 ) @ SV1148 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV347 @ tc_bool ) ) @ SV1377 ) @ SV1148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV347 @ tc_bool ) ) @ SV771 ) @ SV1377 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2973]) ).
thf(3308,plain,
! [SV1378: $i,SV1149: $i,SV774: $i,SV350: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV350 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV774 ) @ SV1149 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV1378 ) @ SV1149 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV774 ) @ SV1378 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2974]) ).
thf(3309,plain,
! [SV1379: $i,SV1150: $i,SV775: $i,SV351: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV351 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV775 ) @ SV1150 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV775 ) @ SV1379 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV1379 ) @ SV1150 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2975]) ).
thf(3310,plain,
! [SV1380: $i,SV1153: $i,SV778: $i,SV354: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV354 @ SV778 @ SV1153 )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV354 @ SV1380 @ SV1153 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV1380 @ SV778 @ SV1153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2976]) ).
thf(3311,plain,
! [SV1154: $i,SV780: $i,SV357: $i] :
( ( ( class_Orderings_Oorder @ SV357 )
= $false )
| ( ( ( SV780 = SV1154 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV357 ) @ SV780 ) @ SV1154 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV357 ) @ SV1154 ) @ SV780 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2978]) ).
thf(3312,plain,
! [SV1155: $i,SV781: $i,SV358: $i] :
( ( ( class_Orderings_Oorder @ SV358 )
= $false )
| ( ( ( SV781 = SV1155 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV358 ) @ SV1155 ) @ SV781 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV358 ) @ SV781 ) @ SV1155 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2979]) ).
thf(3313,plain,
! [SV1156: $i,SV782: $i,SV359: $i] :
( ( ( class_Orderings_Oorder @ SV359 )
= $false )
| ( ( ( SV782 = SV1156 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV359 ) @ SV1156 ) @ SV782 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV359 ) @ SV782 ) @ SV1156 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2980]) ).
thf(3314,plain,
! [SV360: $i,SV783: $i,SV1157: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1157 @ tc_bool ) ) @ SV783 ) @ SV360 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1157 @ tc_bool ) ) @ SV360 ) @ SV783 ) ) )
= $true )
| ( ( SV360 = SV783 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2981]) ).
thf(3315,plain,
! [SV361: $i,SV784: $i,SV1158: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1158 @ tc_bool ) ) @ SV784 ) @ SV361 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1158 @ tc_bool ) ) @ SV361 ) @ SV784 ) ) )
= $true )
| ( ( SV361 = SV784 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2982]) ).
thf(3316,plain,
! [SV1381: $i,SV1160: $i,SV788: $i,SV365: $i] :
( ( ( hBOOL @ ( hAPP @ SV365 @ SV788 ) )
= $true )
| ( ( ( SV1160 = SV788 )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1160 @ SV365 @ SV1381 ) @ SV788 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2983]) ).
thf(3317,plain,
! [SV1382: $i,SV1162: $i,SV792: $i,SV369: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV369 @ tc_bool ) ) @ SV792 ) @ ( c_Set_Oinsert @ SV1162 @ SV1382 @ SV369 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV369 @ tc_bool ) ) @ SV792 ) @ SV1382 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2985]) ).
thf(3318,plain,
! [SV1383: $i,SV1163: $i,SV793: $i,SV370: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV370 @ tc_bool ) ) @ SV793 ) @ SV1163 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV370 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV1383 @ SV793 @ SV370 ) ) @ SV1163 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2986]) ).
thf(3319,plain,
! [SV1385: $i,SV1166: $i,SV796: $i,SV373: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV373 @ SV796 @ SV1166 ) @ SV1385 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV796 @ SV1385 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2988]) ).
thf(3320,plain,
! [SV374: $i,SV797: $i,SV1167: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1167 ) @ tc_bool ) ) @ SV797 ) @ SV374 ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV374 @ SV797 @ SV1167 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2989]) ).
thf(3321,plain,
! [SV1465: $i,SV1386: $i,SV1168: $i,SV798: $i,SV375: $i] :
( ( ~ ( class_HOL_Oord @ SV375 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV375 ) @ ( hAPP @ SV798 @ SV1168 ) ) @ ( hAPP @ SV1386 @ SV1168 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1465 @ SV375 ) ) @ SV798 ) @ SV1386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2990]) ).
thf(3322,plain,
! [SV380: $i,SV803: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ SV803 )
= $false )
| ( ( ~ ( class_Finite__Set_Ofinite_Ofinite @ SV380 ) )
= $true )
| ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ SV380 @ SV803 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2995]) ).
thf(3323,plain,
! [SV812: $i,SV389: $i,SV1169: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV1169 ) @ SV389 ) @ SV812 ) )
= $false )
| ( ( SV389 = SV812 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3003]) ).
thf(3324,plain,
! [SV1170: $i,SV813: $i,SV390: $i] :
( ( ( ( c_Set_Oinsert @ SV390 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV813 @ tc_bool ) ) @ SV813 )
= ( c_Set_Oinsert @ SV1170 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV813 @ tc_bool ) ) @ SV813 ) )
= $false )
| ( ( SV390 = SV1170 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3004]) ).
thf(3325,plain,
! [SV1171: $i,SV814: $i,SV391: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV391 )
= $false )
| ( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV814 @ SV391 )
!= ( c_HOL_Ouminus__class_Ouminus @ SV1171 @ SV391 ) )
| ( SV814 = SV1171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3005]) ).
thf(3326,plain,
! [SV1387: $i,SV1172: $i,SV815: $i,SV392: $i] :
( ( ( ( c_Set_Oinsert @ SV392 @ SV815 @ SV1172 )
!= ( c_Set_Oinsert @ SV392 @ SV1387 @ SV1172 ) )
= $true )
| ( ( ( hBOOL @ ( c_in @ SV392 @ SV1387 @ SV1172 ) )
| ( hBOOL @ ( c_in @ SV392 @ SV815 @ SV1172 ) )
| ( SV815 = SV1387 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3006]) ).
thf(3327,plain,
! [SV1173: $i,SV816: $i,SV393: $i] :
( ( ( ( c_Collect @ SV393 @ SV816 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV816 @ tc_bool ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV393 @ SV1173 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3007]) ).
thf(3328,plain,
! [SV1388: $i,SV1174: $i,SV817: $i,SV394: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV394 @ SV817 )
!= ( c_Com_Ocom_OSemi @ SV1174 @ SV1388 ) )
= $true )
| ( ( SV817 = SV1388 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3008]) ).
thf(3329,plain,
! [SV1466: $i,SV1389: $i,SV1175: $i,SV818: $i,SV395: $i] :
( ( ! [SY4023: $i,SY4024: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV395 @ SV818 @ SV1175 @ SV1389 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1466 @ SY4023 @ SY4024 @ SV1389 ) )
| ( SV395 = SV1466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3009]) ).
thf(3330,plain,
! [SV1177: $i,SV821: $i,SV398: $i] :
( ( ( class_Orderings_Oorder @ SV398 )
= $false )
| ( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV398 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV821 @ SV1177 @ SV398 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV821 @ SV1177 @ SV398 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3011]) ).
thf(3331,plain,
! [SV1179: $i,SV823: $i,SV400: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV400 )
= $false )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV823 @ SV1179 @ SV400 )
!= ( c_Orderings_Obot__class_Obot @ SV400 ) )
| ( SV823
= ( c_Orderings_Obot__class_Obot @ SV400 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3013]) ).
thf(3332,plain,
! [SV1467: $i,SV1390: $i,SV1180: $i,SV824: $i,SV401: $i] :
( ( ( ( c_Set_Oinsert @ SV401 @ ( c_Set_Oinsert @ SV824 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1180 @ tc_bool ) ) @ SV1180 ) @ SV1180 )
!= ( c_Set_Oinsert @ SV1390 @ ( c_Set_Oinsert @ SV1467 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1180 @ tc_bool ) ) @ SV1180 ) @ SV1180 ) )
| ( SV824 = SV1390 )
| ( SV401 = SV1390 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3014]) ).
thf(3333,plain,
! [SV1181: $i,SV825: $i,SV402: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV402 @ SV825 @ ( tc_fun @ SV1181 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1181 @ tc_bool ) ) )
= $false )
| ( ( SV825
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1181 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3015]) ).
thf(3334,plain,
! [SV1391: $i,SV1182: $i,SV826: $i,SV403: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV403 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV826 @ SV826 @ SV403 )
!= ( c_HOL_Ominus__class_Ominus @ SV1182 @ SV1391 @ SV403 ) )
| ( SV1182 = SV1391 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3016]) ).
thf(3335,plain,
! [SV1183: $i,SV827: $i,SV404: $i] :
( ( ( class_Orderings_Oorder @ SV404 )
= $false )
| ( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV404 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV827 @ SV1183 @ SV404 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV404 ) @ SV827 ) @ SV1183 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3017]) ).
thf(3336,plain,
! [SV1184: $i,SV828: $i,SV405: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV405 @ SV828 @ ( tc_fun @ SV1184 @ tc_bool ) )
= SV828 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1184 @ tc_bool ) ) @ SV405 ) @ SV828 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3018]) ).
thf(3337,plain,
! [SV1185: $i,SV829: $i,SV406: $i] :
( ( ( class_Orderings_Oorder @ SV406 )
= $false )
| ( ( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV829 @ SV1185 @ SV406 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV406 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV406 ) @ SV829 ) @ SV1185 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3019]) ).
thf(3338,plain,
! [SV1186: $i,SV830: $i,SV407: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV407 @ SV830 @ ( tc_fun @ SV1186 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1186 @ tc_bool ) ) )
= $false )
| ( ( SV407
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1186 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3020]) ).
thf(3339,plain,
! [SV1468: $i,SV1392: $i,SV1187: $i,SV832: $i,SV409: $i] :
( ( ( ( c_Set_Oinsert @ SV409 @ ( c_Set_Oinsert @ SV832 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1187 @ tc_bool ) ) @ SV1187 ) @ SV1187 )
!= ( c_Set_Oinsert @ SV1392 @ ( c_Set_Oinsert @ SV1468 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1187 @ tc_bool ) ) @ SV1187 ) @ SV1187 ) )
| ( SV409 = SV1468 )
| ( SV832 = SV1468 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3021]) ).
thf(3340,plain,
! [SV1469: $i,SV1393: $i,SV1188: $i,SV833: $i,SV410: $i] :
( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV410 @ SV833 @ SV1188 @ ( tc_fun @ SV1393 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1393 @ tc_bool ) ) )
| ( ( hAPP @ SV833 @ SV1469 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1393 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SV1469 @ SV410 @ SV1188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3022]) ).
thf(3341,plain,
! [SV1470: $i,SV1394: $i,SV1189: $i,SV834: $i,SV411: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV411 )
| ( ( c_HOL_Ominus__class_Ominus @ SV834 @ SV1189 @ SV411 )
!= ( c_HOL_Ominus__class_Ominus @ SV1394 @ SV1470 @ SV411 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV411 ) @ SV1470 ) @ SV1394 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV411 ) @ SV1189 ) @ SV834 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3023]) ).
thf(3342,plain,
! [SV1190: $i,SV835: $i,SV412: $i] :
( ( ( class_Lattices_Oboolean__algebra @ SV412 )
= $false )
| ( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV835 @ SV412 )
!= ( c_HOL_Ouminus__class_Ouminus @ SV1190 @ SV412 ) )
| ( SV835 = SV1190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3024]) ).
thf(3343,plain,
! [SV1471: $i,SV1395: $i,SV1191: $i,SV836: $i,SV413: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV413 @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV836 @ SV1191 @ SV1395 @ ( tc_fun @ SV413 @ tc_bool ) ) )
| ( ( hAPP @ SV1191 @ SV1471 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV413 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SV1471 @ SV836 @ SV1395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3025]) ).
thf(3344,plain,
! [SV1192: $i,SV837: $i,SV414: $i] :
( ( ( class_Orderings_Oorder @ SV414 )
= $false )
| ( ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ SV837 @ SV1192 @ SV414 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV414 @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV837 @ SV1192 @ SV414 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3026]) ).
thf(3345,plain,
! [SV1472: $i,SV1396: $i,SV1193: $i,SV838: $i,SV415: $i] :
( ( ( ( c_Set_Oinsert @ SV415 @ ( c_Set_Oinsert @ SV838 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SV1193 ) @ SV1193 )
!= ( c_Set_Oinsert @ SV1396 @ ( c_Set_Oinsert @ SV1472 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SV1193 ) @ SV1193 ) )
| ( SV838 = SV1396 )
| ( SV838 = SV1472 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3027]) ).
thf(3346,plain,
! [SV1194: $i,SV839: $i,SV416: $i] :
( ( ( class_Orderings_Oorder @ SV416 )
= $false )
| ( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV416 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV839 @ SV1194 @ SV416 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV839 @ SV1194 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3028]) ).
thf(3347,plain,
! [SV1195: $i,SV840: $i,SV417: $i] :
( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV417 @ ( tc_fun @ SV840 @ tc_bool ) )
= ( c_HOL_Ouminus__class_Ouminus @ SV1195 @ ( tc_fun @ SV840 @ tc_bool ) ) )
= $false )
| ( ( SV417 = SV1195 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3029]) ).
thf(3348,plain,
! [SV1473: $i,SV1397: $i,SV1196: $i,SV841: $i,SV418: $i] :
( ( ! [SY4025: $i,SY4026: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV418 @ SV841 @ SV1196 @ SV1397 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1473 @ SY4025 @ SY4026 @ SV1397 ) )
| ( SV1196 = SY4026 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3030]) ).
thf(3349,plain,
! [SV1474: $i,SV1398: $i,SV1197: $i,SV842: $i,SV419: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV419 )
| ( ( c_HOL_Ominus__class_Ominus @ SV842 @ SV1197 @ SV419 )
!= ( c_HOL_Ominus__class_Ominus @ SV1398 @ SV1474 @ SV419 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV419 ) @ SV1197 ) @ SV842 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV419 ) @ SV1474 ) @ SV1398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3031]) ).
thf(3350,plain,
! [SV1198: $i,SV843: $i,SV420: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV420 )
= $false )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV843 @ SV1198 @ SV420 )
!= SV1198 )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV420 ) @ SV843 ) @ SV1198 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3032]) ).
thf(3351,plain,
! [SV1475: $i,SV1399: $i,SV1199: $i,SV844: $i,SV421: $i] :
( ( ! [SY4027: $i,SY4028: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV421 @ SV844 @ SV1199 @ SV1399 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1475 @ SY4027 @ SY4028 @ SV1399 ) )
| ( SV844 = SY4027 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3033]) ).
thf(3352,plain,
! [SV1400: $i,SV1200: $i,SV845: $i,SV422: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV422 @ SV845 )
!= ( c_Com_Ocom_OSemi @ SV1200 @ SV1400 ) )
= $true )
| ( ( SV422 = SV1200 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3034]) ).
thf(3353,plain,
! [SV1476: $i,SV1401: $i,SV1201: $i,SV846: $i,SV423: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV423 )
| ( ( c_HOL_Ominus__class_Ominus @ SV846 @ SV1201 @ SV423 )
!= ( c_HOL_Ominus__class_Ominus @ SV1401 @ SV1476 @ SV423 ) )
| ( c_HOL_Oord__class_Oless @ SV1401 @ SV1476 @ SV423 )
| ~ ( c_HOL_Oord__class_Oless @ SV846 @ SV1201 @ SV423 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3035]) ).
thf(3354,plain,
! [SV1202: $i,SV847: $i,SV424: $i] :
( ( ( class_Orderings_Oorder @ SV424 )
= $false )
| ( ( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV847 @ SV1202 @ SV424 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV424 @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV847 @ SV1202 @ SV424 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3036]) ).
thf(3355,plain,
! [SV1203: $i,SV848: $i,SV425: $i] :
( ( ( ( c_Set_Oinsert @ SV425 @ SV848 @ SV1203 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1203 @ tc_bool ) ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV425 @ SV848 @ SV1203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3037]) ).
thf(3356,plain,
! [SV1204: $i,SV849: $i,SV426: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV426 @ tc_bool ) )
= ( c_Collect @ SV849 @ SV426 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV849 @ SV1204 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3038]) ).
thf(3357,plain,
! [SV1477: $i,SV1402: $i,SV1205: $i,SV850: $i,SV427: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV427 )
| ( ( c_HOL_Ominus__class_Ominus @ SV850 @ SV1205 @ SV427 )
!= ( c_HOL_Ominus__class_Ominus @ SV1402 @ SV1477 @ SV427 ) )
| ( c_HOL_Oord__class_Oless @ SV850 @ SV1205 @ SV427 )
| ~ ( c_HOL_Oord__class_Oless @ SV1402 @ SV1477 @ SV427 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3039]) ).
thf(3358,plain,
! [SV1403: $i,SV1206: $i,SV851: $i,SV428: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV428 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV851 @ SV1206 @ SV428 )
!= ( c_HOL_Ominus__class_Ominus @ SV1403 @ SV1403 @ SV428 ) )
| ( SV851 = SV1206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3040]) ).
thf(3359,plain,
! [SV1207: $i,SV852: $i,SV429: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV429 )
= $false )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV852 @ SV1207 @ SV429 )
!= ( c_Orderings_Obot__class_Obot @ SV429 ) )
| ( SV1207
= ( c_Orderings_Obot__class_Obot @ SV429 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3041]) ).
thf(3360,plain,
! [SV1478: $i,SV1404: $i,SV1208: $i,SV853: $i,SV430: $i] :
( ( ( ( c_Set_Oinsert @ SV430 @ ( c_Set_Oinsert @ SV853 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1208 @ tc_bool ) ) @ SV1208 ) @ SV1208 )
!= ( c_Set_Oinsert @ SV1404 @ ( c_Set_Oinsert @ SV1478 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1208 @ tc_bool ) ) @ SV1208 ) @ SV1208 ) )
| ( SV430 = SV1478 )
| ( SV430 = SV1404 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3042]) ).
thf(3361,plain,
! [SV1209: $i,SV854: $i,SV431: $i,SV1: $i] :
( ( ( class_HOL_Oord @ SV1 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV431 @ SV1 ) ) @ SV854 ) @ SV1209 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV854 @ SV1209 @ ( tc_fun @ SV431 @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3043]) ).
thf(3362,plain,
! [SV1210: $i,SV855: $i,SV432: $i,SV2: $i] :
( ( ( class_HOL_Oord @ SV2 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV432 @ SV855 @ ( tc_fun @ SV1210 @ SV2 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1210 @ SV2 ) ) @ SV855 ) @ SV432 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1210 @ SV2 ) ) @ SV432 ) @ SV855 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3044]) ).
thf(3363,plain,
! [SV1211: $i,SV856: $i,SV433: $i,SV3: $i] :
( ( ( class_HOL_Oord @ SV3 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV433 @ SV3 ) ) @ SV856 ) @ SV1211 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1211 @ SV856 @ ( tc_fun @ SV433 @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3045]) ).
thf(3364,plain,
! [SV434: $i,SV4: $i,SV857: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV857 @ tc_bool ) ) @ SV4 ) @ SV434 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV4 @ SV434 @ ( tc_fun @ SV857 @ tc_bool ) )
= $true )
| ( ( SV4 = SV434 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3046]) ).
thf(3365,plain,
! [SV435: $i,SV5: $i,SV858: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV858 @ tc_bool ) ) @ SV5 ) @ SV435 ) )
= $false )
| ( ( SV5 = SV435 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV5 @ SV435 @ ( tc_fun @ SV858 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3047]) ).
thf(3366,plain,
! [SV859: $i,SV6: $i,SV436: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV436 @ tc_bool ) ) @ SV6 ) @ SV859 ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV859 @ SV436 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV6 @ SV436 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3048]) ).
thf(3367,plain,
! [SV7: $i,SV860: $i,SV437: $i,SV1212: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1212 @ SV437 @ ( tc_fun @ SV860 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV860 @ tc_bool ) ) @ SV7 ) @ SV1212 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV7 @ SV437 @ ( tc_fun @ SV860 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3049]) ).
thf(3368,plain,
! [SV8: $i,SV438: $i,SV1213: $i,SV861: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV861 @ tc_bool ) ) @ SV1213 ) @ SV438 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV8 @ SV1213 @ ( tc_fun @ SV861 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV8 @ SV438 @ ( tc_fun @ SV861 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3050]) ).
thf(3369,plain,
! [SV9: $i,SV439: $i,SV862: $i] :
( ( ( c_Finite__Set_Ofinite @ SV862 @ SV439 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV439 @ tc_bool ) ) @ SV9 ) @ SV862 ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV9 @ SV439 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3051]) ).
thf(3370,plain,
! [SV1405: $i,SV1214: $i,SV864: $i,SV441: $i,SV11: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring @ SV11 ) )
= $true )
| ( ( ( ( c_Finite__Set_Osetsum @ SV441 @ ( c_HOL_Ominus__class_Ominus @ SV864 @ ( c_Set_Oinsert @ SV1214 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1405 @ tc_bool ) ) @ SV1405 ) @ ( tc_fun @ SV1405 @ tc_bool ) ) @ SV1405 @ SV11 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV441 @ SV864 @ SV1405 @ SV11 ) @ ( hAPP @ SV441 @ SV1214 ) @ SV11 ) )
| ~ ( hBOOL @ ( c_in @ SV1214 @ SV864 @ SV1405 ) )
| ~ ( c_Finite__Set_Ofinite @ SV864 @ SV1405 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3053]) ).
thf(3371,plain,
! [SV1406: $i,SV1215: $i,SV865: $i,SV442: $i,SV12: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV12 ) )
= $true )
| ( ( ( ( c_Finite__Set_Osetsum @ SV442 @ ( c_HOL_Ominus__class_Ominus @ SV865 @ ( c_Set_Oinsert @ SV1215 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1406 @ tc_bool ) ) @ SV1406 ) @ ( tc_fun @ SV1406 @ tc_bool ) ) @ SV1406 @ SV12 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV442 @ SV865 @ SV1406 @ SV12 ) @ ( hAPP @ SV442 @ SV1215 ) @ SV12 ) )
| ~ ( hBOOL @ ( c_in @ SV1215 @ SV865 @ SV1406 ) )
| ~ ( c_Finite__Set_Ofinite @ SV865 @ SV1406 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3054]) ).
thf(3372,plain,
! [SV443: $i,SV866: $i,SV13: $i,SV1216: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1216 @ tc_bool ) ) @ SV13 ) @ SV866 ) ) )
= $true )
| ( ( ( hBOOL @ ( c_in @ SV443 @ SV13 @ SV1216 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV13 @ SV866 @ ( tc_fun @ SV1216 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV13 @ ( c_Set_Oinsert @ SV443 @ SV866 @ SV1216 ) @ ( tc_fun @ SV1216 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3055]) ).
thf(3373,plain,
! [SV444: $i,SV867: $i,SV14: $i,SV1217: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1217 @ tc_bool ) ) @ SV14 ) @ SV867 ) ) )
= $true )
| ( ( ( hBOOL @ ( c_in @ SV444 @ SV14 @ SV1217 ) )
| ( hBOOL @ ( c_in @ SV444 @ SV867 @ SV1217 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV14 @ ( c_Set_Oinsert @ SV444 @ SV867 @ SV1217 ) @ ( tc_fun @ SV1217 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3056]) ).
thf(3374,plain,
! [SV868: $i,SV15: $i,SV445: $i,SV1218: $i] :
( ( ( hBOOL @ ( c_in @ SV1218 @ SV445 @ SV15 ) )
= $true )
| ( ( ( hBOOL @ ( c_in @ SV1218 @ SV868 @ SV15 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV445 @ ( c_Set_Oinsert @ SV1218 @ SV868 @ SV15 ) @ ( tc_fun @ SV15 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV15 @ tc_bool ) ) @ SV445 ) @ SV868 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3057]) ).
thf(3375,plain,
! [SV1219: $i,SV869: $i,SV446: $i,SV16: $i] :
( ( ( class_Orderings_Olinorder @ SV16 )
= $false )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV446 @ SV869 @ SV16 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV869 @ SV1219 @ SV16 ) @ ( tc_fun @ SV16 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV446 @ SV1219 @ SV16 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV16 ) @ SV869 ) @ SV1219 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV16 ) @ SV446 ) @ SV869 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3058]) ).
thf(3376,plain,
! [SV1407: $i,SV1222: $i,SV875: $i,SV453: $i,SV23: $i] :
( ( ( SV23 = SV453 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofold__graph @ SV875 @ SV453 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1222 @ tc_bool ) ) @ SV23 @ SV1222 @ SV1407 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3061]) ).
thf(3377,plain,
! [SV876: $i,SV455: $i,SV26: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV26 ) @ SV455 ) @ SV876 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV876 @ SV455 @ SV26 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3062]) ).
thf(3378,plain,
! [SV27: $i,SV877: $i,SV456: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV456 @ SV877 @ SV27 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV27 ) @ SV877 ) @ SV456 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3063]) ).
thf(3379,plain,
! [SV878: $i,SV457: $i,SV28: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV28 ) @ SV457 ) @ SV878 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV878 @ SV457 @ SV28 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3064]) ).
thf(3380,plain,
! [SV879: $i,SV458: $i,SV29: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV29 ) @ SV458 ) @ SV879 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV879 @ SV458 @ SV29 )
= $true )
| ( ( class_Orderings_Olinorder @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3065]) ).
thf(3381,plain,
! [SV30: $i,SV880: $i,SV459: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV459 @ SV880 @ SV30 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV30 ) @ SV880 ) @ SV459 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3066]) ).
thf(3382,plain,
! [SV461: $i,SV32: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV32 ) @ SV461 ) @ SV461 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV461 @ SV461 @ SV32 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3068]) ).
thf(3383,plain,
! [SV33: $i,SV881: $i,SV462: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV462 @ SV881 @ SV33 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV33 ) @ SV881 ) @ SV462 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3069]) ).
thf(3384,plain,
! [SV34: $i,SV882: $i,SV463: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV463 @ SV882 @ SV34 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV34 ) @ SV882 ) @ SV463 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV34 ) @ SV463 ) @ SV882 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3070]) ).
thf(3385,plain,
! [SV883: $i,SV464: $i,SV35: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV35 ) @ SV464 ) @ SV883 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV464 @ SV883 @ SV35 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3071]) ).
thf(3386,plain,
! [SV884: $i,SV465: $i,SV36: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV36 ) @ SV465 ) @ SV884 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV465 @ SV884 @ SV36 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3072]) ).
thf(3387,plain,
! [SV1223: $i,SV885: $i,SV466: $i,SV37: $i] :
( ( ( class_Orderings_Oorder @ SV37 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV466 @ SV885 @ SV37 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV37 ) @ SV466 ) @ SV1223 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1223 @ SV885 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3073]) ).
thf(3388,plain,
! [SV1224: $i,SV886: $i,SV467: $i,SV38: $i] :
( ( ( class_Orderings_Oorder @ SV38 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV467 @ SV886 @ SV38 )
| ~ ( c_HOL_Oord__class_Oless @ SV467 @ SV1224 @ SV38 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV38 ) @ SV1224 ) @ SV886 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3074]) ).
thf(3389,plain,
! [SV1225: $i,SV887: $i,SV468: $i,SV39: $i] :
( ( ( class_Orderings_Opreorder @ SV39 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV468 @ SV887 @ SV39 )
| ~ ( c_HOL_Oord__class_Oless @ SV1225 @ SV887 @ SV39 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV39 ) @ SV468 ) @ SV1225 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3075]) ).
thf(3390,plain,
! [SV1226: $i,SV888: $i,SV469: $i,SV40: $i] :
( ( ( class_Orderings_Opreorder @ SV40 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV469 @ SV888 @ SV40 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV40 ) @ SV1226 ) @ SV888 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV469 @ SV1226 @ SV40 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3076]) ).
thf(3391,plain,
! [SV41: $i,SV889: $i,SV470: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV470 @ SV889 @ SV41 )
= $true )
| ( ( ( SV889 = SV470 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV41 ) @ SV470 ) @ SV889 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3077]) ).
thf(3392,plain,
! [SV42: $i,SV890: $i,SV471: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV471 @ SV890 @ SV42 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV42 ) @ SV471 ) @ SV890 ) )
| ( SV890 = SV471 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3078]) ).
thf(3393,plain,
! [SV43: $i,SV891: $i,SV472: $i] :
( ( ( SV472 = SV891 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV472 @ SV891 @ SV43 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV43 ) @ SV472 ) @ SV891 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3079]) ).
thf(3394,plain,
! [SV44: $i,SV892: $i,SV473: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV473 @ SV892 @ SV44 )
= $true )
| ( ( ( SV473 = SV892 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV44 ) @ SV473 ) @ SV892 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3080]) ).
thf(3395,plain,
! [SV45: $i,SV893: $i,SV474: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV474 @ SV893 @ SV45 )
= $true )
| ( ( ( SV474 = SV893 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV45 ) @ SV474 ) @ SV893 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3081]) ).
thf(3396,plain,
! [SV46: $i,SV894: $i,SV475: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV475 @ SV894 @ SV46 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV46 ) @ SV475 ) @ SV894 ) )
| ( SV475 = SV894 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3082]) ).
thf(3397,plain,
! [SV47: $i,SV895: $i,SV476: $i] :
( ( ( SV476 = SV895 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV47 ) @ SV476 ) @ SV895 ) )
| ( c_HOL_Oord__class_Oless @ SV476 @ SV895 @ SV47 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3083]) ).
thf(3398,plain,
! [SV48: $i,SV896: $i,SV477: $i] :
( ( ( SV477 = SV896 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV477 @ SV896 @ SV48 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV48 ) @ SV477 ) @ SV896 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3084]) ).
thf(3399,plain,
! [SV897: $i,SV49: $i,SV478: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV478 @ SV49 ) @ SV897 @ SV49 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV897 @ SV49 ) @ SV478 @ SV49 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3085]) ).
thf(3400,plain,
! [SV898: $i,SV50: $i,SV479: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV479 @ SV50 ) @ SV898 @ SV50 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV898 @ SV50 ) @ SV479 @ SV50 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3086]) ).
thf(3401,plain,
! [SV51: $i,SV899: $i,SV480: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV480 @ ( c_HOL_Ouminus__class_Ouminus @ SV899 @ SV51 ) @ SV51 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV899 @ ( c_HOL_Ouminus__class_Ouminus @ SV480 @ SV51 ) @ SV51 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3087]) ).
thf(3402,plain,
! [SV52: $i,SV900: $i,SV481: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV481 @ ( c_HOL_Ouminus__class_Ouminus @ SV900 @ SV52 ) @ SV52 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV900 @ ( c_HOL_Ouminus__class_Ouminus @ SV481 @ SV52 ) @ SV52 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3088]) ).
thf(3403,plain,
! [SV1227: $i,SV901: $i,SV482: $i,SV53: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV53 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV482 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV901 @ SV1227 @ SV53 ) @ SV53 )
| ~ ( c_HOL_Oord__class_Oless @ SV482 @ SV1227 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3089]) ).
thf(3404,plain,
! [SV1228: $i,SV902: $i,SV483: $i,SV54: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV54 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV483 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV902 @ SV1228 @ SV54 ) @ SV54 )
| ~ ( c_HOL_Oord__class_Oless @ SV483 @ SV902 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3090]) ).
thf(3405,plain,
! [SV1408: $i,SV1229: $i,SV903: $i,SV485: $i,SV56: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV56 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV485 @ SV903 @ SV56 )
| ( c_HOL_Oord__class_Oless @ SV1229 @ SV1408 @ SV56 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV56 ) @ SV1408 ) @ SV485 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1408 @ SV485 @ SV56 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1229 @ SV903 @ SV56 ) @ ( tc_fun @ SV56 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3091]) ).
thf(3406,plain,
! [SV1479: $i,SV1409: $i,SV1230: $i,SV904: $i,SV486: $i,SV57: $i] :
( ( ! [SY4029: $i,SY4030: $i,SY4031: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV57 @ SV486 @ ( c_COMBC @ SV904 @ SV1230 @ SV1230 @ tc_bool ) @ ( c_COMBC @ SV1409 @ SV1230 @ SV1230 @ tc_bool ) @ SV1479 @ SY4029 @ SY4030 @ SY4031 @ SV1230 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV486 @ SV57 @ SV904 @ SV1409 @ SY4029 @ SV1479 @ SY4031 @ SY4030 @ SV1230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3092]) ).
thf(3407,plain,
! [SV1480: $i,SV1410: $i,SV1232: $i,SV906: $i,SV488: $i,SV59: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ SV59 @ SV488 @ SV906 @ SV1232 ) @ SV1410 ) @ SV1480 )
= ( hAPP @ ( hAPP @ SV59 @ SV1480 ) @ SV1410 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3093]) ).
thf(3408,plain,
! [SV1233: $i,SV907: $i,SV489: $i,SV60: $i] :
( ( ( class_Orderings_Oorder @ SV60 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV489 @ SV907 @ SV60 )
| ~ ( c_HOL_Oord__class_Oless @ SV489 @ SV1233 @ SV60 )
| ~ ( c_HOL_Oord__class_Oless @ SV1233 @ SV907 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3094]) ).
thf(3409,plain,
! [SV490: $i,SV908: $i,SV1234: $i,SV61: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV61 @ SV1234 @ SV908 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1234 @ SV490 @ ( tc_fun @ SV908 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV61 @ SV490 @ SV908 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3095]) ).
thf(3410,plain,
! [SV62: $i,SV909: $i,SV491: $i,SV1235: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1235 @ SV491 @ ( tc_fun @ SV909 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV62 @ SV1235 @ ( tc_fun @ SV909 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV62 @ SV491 @ ( tc_fun @ SV909 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3096]) ).
thf(3411,plain,
! [SV1236: $i,SV910: $i,SV492: $i,SV63: $i] :
( ( ( class_Orderings_Opreorder @ SV63 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV492 @ SV910 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV1236 @ SV910 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV492 @ SV1236 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3097]) ).
thf(3412,plain,
! [SV1481: $i,SV1411: $i,SV1237: $i,SV911: $i,SV493: $i,SV64: $i] :
( ( ( c_Finite__Set_Ofinite @ SV64 @ SV493 )
| ~ ( c_Finite__Set_Ofold__graph @ SV911 @ SV1237 @ SV64 @ SV1411 @ SV493 @ SV1481 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3098]) ).
thf(3413,plain,
! [SV65: $i,SV912: $i,SV494: $i] :
( ( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV494 @ SV912 @ SV65 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV65 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV494 @ SV912 @ SV65 )
= $true )
| ( ( class_Orderings_Oorder @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3099]) ).
thf(3414,plain,
! [SV496: $i,SV914: $i,SV67: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV67 @ SV914 @ ( tc_fun @ SV496 @ tc_bool ) ) @ SV496 )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV914 @ SV496 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV67 @ SV496 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3101]) ).
thf(3415,plain,
! [SV497: $i,SV915: $i,SV68: $i] :
( ( ( c_Finite__Set_Ofinite @ SV68 @ SV915 )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV497 @ SV915 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV68 @ SV497 @ ( tc_fun @ SV915 @ tc_bool ) ) @ SV915 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3102]) ).
thf(3416,plain,
! [SV70: $i,SV916: $i,SV499: $i] :
( ( ( c_Finite__Set_Ofinite @ SV499 @ SV916 )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV70 @ SV916 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV70 @ SV499 @ ( tc_fun @ SV916 @ tc_bool ) ) @ SV916 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3103]) ).
thf(3417,plain,
! [SV71: $i,SV917: $i,SV500: $i] :
( ( ( c_Finite__Set_Ofinite @ SV500 @ SV917 )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV71 @ SV917 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV71 @ SV500 @ ( tc_fun @ SV917 @ tc_bool ) ) @ SV917 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3104]) ).
thf(3418,plain,
! [SV920: $i,SV74: $i,SV503: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV503 @ SV74 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV920 @ SV74 ) @ SV74 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV920 @ SV503 @ SV74 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3107]) ).
thf(3419,plain,
! [SV75: $i,SV921: $i,SV504: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV504 @ SV921 @ SV75 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV921 @ SV75 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV504 @ SV75 ) @ SV75 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3108]) ).
thf(3420,plain,
! [SV1412: $i,SV1238: $i,SV922: $i,SV509: $i,SV80: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV80 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV509 @ SV922 @ SV80 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1238 @ SV1412 @ SV80 ) @ ( tc_fun @ SV80 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV1238 ) @ SV1412 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV922 @ SV1412 @ SV80 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV922 ) @ SV1412 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV1238 ) @ SV509 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3112]) ).
thf(3421,plain,
! [SV1413: $i,SV1239: $i,SV923: $i,SV510: $i,SV81: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV81 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV510 @ SV923 @ SV81 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1239 @ SV1413 @ SV81 ) @ ( tc_fun @ SV81 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV1239 ) @ SV1413 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1239 @ SV510 @ SV81 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV923 ) @ SV1413 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV1239 ) @ SV510 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3113]) ).
thf(3422,plain,
! [SV82: $i,SV924: $i,SV511: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV511 @ SV924 @ SV82 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV924 @ SV511 @ SV82 )
| ( SV924 = SV511 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3114]) ).
thf(3423,plain,
! [SV83: $i,SV925: $i,SV512: $i] :
( ( ( SV512 = SV925 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV925 @ SV512 @ SV83 )
| ( c_HOL_Oord__class_Oless @ SV512 @ SV925 @ SV83 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3115]) ).
thf(3424,plain,
! [SV84: $i,SV926: $i,SV513: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV513 @ SV926 @ SV84 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV926 @ SV513 @ SV84 )
| ( SV926 = SV513 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3116]) ).
thf(3425,plain,
! [SV85: $i,SV927: $i,SV514: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV514 @ SV927 @ SV85 )
= $true )
| ( ( ( SV927 = SV514 )
| ( c_HOL_Oord__class_Oless @ SV927 @ SV514 @ SV85 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3117]) ).
thf(3426,plain,
! [SV86: $i,SV928: $i,SV515: $i] :
( ( ( SV515 = SV928 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV515 @ SV928 @ SV86 )
| ( c_HOL_Oord__class_Oless @ SV928 @ SV515 @ SV86 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3118]) ).
thf(3427,plain,
! [SV929: $i,SV516: $i,SV87: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV87 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV516 @ SV929 @ SV87 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV516 @ SV929 @ SV87 )
= $true )
| ( ( class_Orderings_Oorder @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3119]) ).
thf(3428,plain,
! [SV88: $i,SV930: $i,SV517: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV517 @ SV930 @ SV88 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV930 @ SV517 @ SV88 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3120]) ).
thf(3429,plain,
! [SV89: $i,SV931: $i,SV518: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV518 @ SV931 @ SV89 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV931 @ SV518 @ SV89 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3121]) ).
thf(3430,plain,
! [SV90: $i,SV932: $i,SV519: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV519 @ SV932 @ SV90 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV932 @ SV519 @ SV90 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3122]) ).
thf(3431,plain,
! [SV91: $i,SV933: $i,SV520: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV520 @ SV933 @ SV91 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV933 @ SV520 @ SV91 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3123]) ).
thf(3432,plain,
! [SV1414: $i,SV1240: $i,SV934: $i,SV521: $i,SV92: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV92 ) )
= $true )
| ( ( ( ( c_Finite__Set_Osetsum @ SV521 @ ( c_HOL_Ominus__class_Ominus @ SV934 @ SV1240 @ ( tc_fun @ SV1414 @ tc_bool ) ) @ SV1414 @ SV92 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV521 @ SV934 @ SV1414 @ SV92 ) @ ( c_Finite__Set_Osetsum @ SV521 @ SV1240 @ SV1414 @ SV92 ) @ SV92 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1414 @ tc_bool ) ) @ SV1240 ) @ SV934 ) )
| ~ ( c_Finite__Set_Ofinite @ SV934 @ SV1414 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3124]) ).
thf(3433,plain,
! [SV93: $i,SV935: $i,SV522: $i] :
( ( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV522 @ SV935 @ SV93 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV93 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV93 ) @ SV935 ) @ SV522 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3125]) ).
thf(3434,plain,
! [SV1482: $i,SV1415: $i,SV1241: $i,SV936: $i,SV523: $i,SV94: $i] :
( ( ! [SY4032: $i] :
( ( c_Finite__Set_Ofold__graph @ SV94 @ SV523 @ ( c_Set_Oinsert @ SV936 @ SV1241 @ SV1415 ) @ ( hAPP @ ( hAPP @ SV94 @ SV936 ) @ SV1482 ) @ SV1415 @ SY4032 )
| ~ ( c_Finite__Set_Ofold__graph @ SV94 @ SV523 @ SV1241 @ SV1482 @ SV1415 @ SY4032 )
| ( hBOOL @ ( c_in @ SV936 @ SV1241 @ SV1415 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3126]) ).
thf(3435,plain,
! [SV95: $i,SV937: $i,SV524: $i,SV1242: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV1242 @ SV524 @ SV937 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV95 @ ( c_Set_Oinsert @ SV1242 @ SV524 @ SV937 ) @ ( tc_fun @ SV937 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV95 @ SV524 @ ( tc_fun @ SV937 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3127]) ).
thf(3436,plain,
! [SV96: $i,SV1243: $i,SV938: $i,SV525: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV525 @ SV938 @ SV1243 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV96 @ SV938 @ ( tc_fun @ SV1243 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV96 @ ( c_Set_Oinsert @ SV525 @ SV938 @ SV1243 ) @ ( tc_fun @ SV1243 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3128]) ).
thf(3437,plain,
! [SV1416: $i,SV1244: $i,SV939: $i,SV526: $i,SV97: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV97 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV97 ) @ SV526 ) @ SV939 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV97 ) @ SV1244 ) @ SV526 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1244 @ SV526 @ SV97 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1416 @ SV939 @ SV97 ) @ ( tc_fun @ SV97 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3129]) ).
thf(3438,plain,
! [SV1417: $i,SV1245: $i,SV940: $i,SV527: $i,SV98: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV98 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV98 ) @ SV527 ) @ SV940 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV98 ) @ SV940 ) @ SV1245 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV940 @ SV1245 @ SV98 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV527 @ SV1417 @ SV98 ) @ ( tc_fun @ SV98 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3130]) ).
thf(3439,plain,
! [SV1418: $i,SV1246: $i,SV941: $i,SV528: $i,SV99: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV99 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV99 ) @ SV528 ) @ SV941 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1246 @ SV1418 @ SV99 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV528 @ SV941 @ SV99 ) @ ( tc_fun @ SV99 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3131]) ).
thf(3440,plain,
! [SV1419: $i,SV1247: $i,SV942: $i,SV529: $i,SV100: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV100 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV529 @ SV942 @ SV100 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1247 @ SV1419 @ SV100 ) @ ( tc_fun @ SV100 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV100 ) @ SV1247 ) @ SV1419 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV100 ) @ SV529 ) @ SV942 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3132]) ).
thf(3441,plain,
! [SV1248: $i,SV943: $i,SV530: $i,SV101: $i] :
( ( ( class_Orderings_Olinorder @ SV101 )
= $false )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV530 @ SV943 @ SV101 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV943 @ SV1248 @ SV101 ) @ ( tc_fun @ SV101 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV530 @ SV1248 @ SV101 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV101 ) @ SV943 ) @ SV1248 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV101 ) @ SV530 ) @ SV943 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3133]) ).
thf(3442,plain,
! [SV1420: $i,SV1249: $i,SV944: $i,SV531: $i,SV102: $i] :
( ( ( c_Finite__Set_Ofinite @ ( hAPP @ SV102 @ SV531 ) @ SV944 )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV531 @ SV1249 @ SV1420 ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1249 @ SV102 @ SV1420 @ ( tc_fun @ SV944 @ tc_bool ) ) @ SV944 )
| ~ ( c_Finite__Set_Ofinite @ SV1249 @ SV1420 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3134]) ).
thf(3443,plain,
! [SV1421: $i,SV1250: $i,SV945: $i,SV532: $i,SV103: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV103 ) )
= $true )
| ( ( ( ( c_Finite__Set_Osetsum @ SV532 @ ( c_HOL_Ominus__class_Ominus @ SV945 @ ( c_Set_Oinsert @ SV1250 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1421 @ tc_bool ) ) @ SV1421 ) @ ( tc_fun @ SV1421 @ tc_bool ) ) @ SV1421 @ SV103 )
= ( c_Finite__Set_Osetsum @ SV532 @ SV945 @ SV1421 @ SV103 ) )
| ( hBOOL @ ( c_in @ SV1250 @ SV945 @ SV1421 ) )
| ~ ( c_Finite__Set_Ofinite @ SV945 @ SV1421 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3135]) ).
thf(3444,plain,
! [SV104: $i,SV946: $i,SV533: $i] :
( ( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV533 @ SV946 @ SV104 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV104 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV946 @ SV533 @ SV104 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV104 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3136]) ).
thf(3445,plain,
! [SV1251: $i,SV947: $i,SV534: $i,SV105: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV105 )
= $false )
| ( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV534 @ ( c_COMBK @ SV947 @ SV105 @ SV1251 ) @ SV1251 @ SV105 )
= SV947 )
| ( SV534
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1251 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3137]) ).
thf(3446,plain,
! [SV951: $i,SV538: $i,SV1253: $i,SV109: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV109 @ ( c_Set_Oinsert @ SV1253 @ SV538 @ SV951 ) @ ( tc_fun @ SV951 @ tc_bool ) ) @ SV951 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV109 @ SV538 @ ( tc_fun @ SV951 @ tc_bool ) ) @ SV951 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3139]) ).
thf(3447,plain,
! [SV539: $i,SV1254: $i,SV952: $i,SV110: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV110 @ SV952 @ ( tc_fun @ SV1254 @ tc_bool ) ) @ SV1254 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV110 @ ( c_Set_Oinsert @ SV539 @ SV952 @ SV1254 ) @ ( tc_fun @ SV1254 @ tc_bool ) ) @ SV1254 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3140]) ).
thf(3448,plain,
! [SV953: $i,SV540: $i,SV111: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV111 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV540 @ SV953 @ SV111 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV540 @ SV953 @ SV111 )
= $true )
| ( ( class_Orderings_Oorder @ SV111 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3141]) ).
thf(3449,plain,
! [SV112: $i,SV954: $i,SV541: $i] :
( ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ SV541 @ SV954 @ SV112 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV112 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV541 @ SV954 @ SV112 )
= $true )
| ( ( class_Orderings_Oorder @ SV112 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3142]) ).
thf(3450,plain,
! [SV955: $i,SV542: $i,SV114: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV114 ) @ SV542 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV955 @ SV114 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV542 @ SV955 @ SV114 ) )
| ~ ( c_Finite__Set_Ofinite @ SV955 @ SV114 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3143]) ).
thf(3451,plain,
! [SV956: $i,SV543: $i,SV115: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV115 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV543 @ SV115 ) ) @ SV956 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV956 @ SV543 @ SV115 ) )
| ~ ( c_Finite__Set_Ofinite @ SV543 @ SV115 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3144]) ).
thf(3452,plain,
! [SV116: $i,SV544: $i] :
( ( ( SV544
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV116 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV544 @ SV116 ) )
= $true )
| ( ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMin @ SV544 @ SV116 ) @ SV544 @ SV116 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3145]) ).
thf(3453,plain,
! [SV117: $i,SV545: $i] :
( ( ( SV545
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV117 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV545 @ SV117 ) )
= $true )
| ( ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMax @ SV545 @ SV117 ) @ SV545 @ SV117 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3146]) ).
thf(3454,plain,
! [SV1422: $i,SV1255: $i,SV957: $i,SV546: $i,SV118: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV118 @ ( c_Set_Oinsert @ SV546 @ SV957 @ SV1255 ) @ SV1255 ) @ SV1422 ) )
= $true )
| ( ( ( hBOOL @ ( c_in @ SV546 @ SV957 @ SV1255 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV118 @ SV546 @ SV957 @ SV1422 @ SV1255 @ SV1255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3147]) ).
thf(3455,plain,
! [SV1483: $i,SV1423: $i,SV1256: $i,SV958: $i,SV547: $i,SV119: $i] :
( ( ! [SY4033: $i] :
( ( c_Finite__Set_Ofold__graph @ SV119 @ SV547 @ SV958 @ ( hAPP @ ( hAPP @ SV119 @ SV1256 ) @ SV1423 ) @ SV1483 @ SY4033 )
| ~ ( hBOOL @ ( c_in @ SV1256 @ SV958 @ SV1483 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV119 @ SV547 @ ( c_HOL_Ominus__class_Ominus @ SV958 @ ( c_Set_Oinsert @ SV1256 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1483 @ tc_bool ) ) @ SV1483 ) @ ( tc_fun @ SV1483 @ tc_bool ) ) @ SV1423 @ SV1483 @ SY4033 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3148]) ).
thf(3456,plain,
! [SV960: $i,SV1258: $i,SV121: $i,SV549: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV549 @ SV121 @ SV1258 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV121 @ ( c_Set_Oinsert @ SV549 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1258 @ tc_bool ) ) @ SV1258 ) @ ( tc_fun @ SV1258 @ tc_bool ) ) @ SV960 @ ( tc_fun @ SV1258 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV121 @ SV960 @ ( tc_fun @ SV1258 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV121 @ ( c_Set_Oinsert @ SV549 @ SV960 @ SV1258 ) @ ( tc_fun @ SV1258 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3150]) ).
thf(3457,plain,
! [SV961: $i,SV1259: $i,SV122: $i,SV550: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV550 @ SV122 @ SV1259 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV122 @ ( c_Set_Oinsert @ SV550 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1259 @ tc_bool ) ) @ SV1259 ) @ ( tc_fun @ SV1259 @ tc_bool ) ) @ SV961 @ ( tc_fun @ SV1259 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SV550 @ SV961 @ SV1259 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV122 @ ( c_Set_Oinsert @ SV550 @ SV961 @ SV1259 ) @ ( tc_fun @ SV1259 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3151]) ).
thf(3458,plain,
! [SV1260: $i,SV962: $i,SV123: $i,SV551: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV551 @ SV123 @ SV962 ) ) )
= $true )
| ( ( ( hBOOL @ ( c_in @ SV551 @ SV1260 @ SV962 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV123 @ ( c_Set_Oinsert @ SV551 @ SV1260 @ SV962 ) @ ( tc_fun @ SV962 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV123 @ ( c_Set_Oinsert @ SV551 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV962 @ tc_bool ) ) @ SV962 ) @ ( tc_fun @ SV962 @ tc_bool ) ) @ SV1260 @ ( tc_fun @ SV962 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3152]) ).
thf(3459,plain,
! [SV1484: $i,SV1424: $i,SV1261: $i,SV963: $i,SV552: $i,SV124: $i] :
( ( ! [SY4034: $i] :
( ( c_Nitpick_Ofold__graph_H @ SV124 @ SV552 @ SV963 @ ( hAPP @ ( hAPP @ SV124 @ SV1261 ) @ SV1424 ) @ SV1484 @ SY4034 )
| ~ ( c_Nitpick_Ofold__graph_H @ SV124 @ SV552 @ ( c_HOL_Ominus__class_Ominus @ SV963 @ ( c_Set_Oinsert @ SV1261 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1484 @ tc_bool ) ) @ SV1484 ) @ ( tc_fun @ SV1484 @ tc_bool ) ) @ SV1424 @ SV1484 @ SY4034 )
| ~ ( hBOOL @ ( c_in @ SV1261 @ SV963 @ SV1484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3153]) ).
thf(3460,plain,
! [SV553: $i,SV964: $i,SV125: $i,SV1262: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1262 @ tc_bool ) ) @ SV125 ) @ SV964 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV125 @ ( c_Set_Oinsert @ SV553 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1262 @ tc_bool ) ) @ SV1262 ) @ ( tc_fun @ SV1262 @ tc_bool ) ) @ SV964 @ ( tc_fun @ SV1262 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV125 @ SV964 @ ( tc_fun @ SV1262 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV125 @ ( c_Set_Oinsert @ SV553 @ SV964 @ SV1262 ) @ ( tc_fun @ SV1262 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3154]) ).
thf(3461,plain,
! [SV965: $i,SV554: $i,SV126: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV126 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV554 @ SV126 ) ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV965 @ SV126 ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV554 @ SV126 )
| ( SV965
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV126 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV126 @ tc_bool ) ) @ SV965 ) @ SV554 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV126 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3155]) ).
thf(3462,plain,
! [SV966: $i,SV555: $i,SV127: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV127 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV555 @ SV127 ) ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV966 @ SV127 ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV966 @ SV127 )
| ( SV555
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV127 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV127 @ tc_bool ) ) @ SV555 ) @ SV966 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3156]) ).
thf(3463,plain,
! [SV967: $i,SV1263: $i,SV556: $i,SV128: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV128 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_COMBK @ ( hAPP @ ( c_COMBC @ ( c_fequal @ tc_Com_Ostate ) @ tc_Com_Ostate @ tc_Com_Ostate @ tc_bool ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ SV128 @ SV556 @ SV1263 @ SV967 ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) @ SV967 @ ( c_COMBK @ ( hAPP @ SV1263 @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ SV128 @ SV556 @ SV1263 @ SV967 ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) @ 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 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV128 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV556 @ SV967 @ SV1263 @ 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_not_pos,[status(thm)],[3157]) ).
thf(3464,plain,
! [SV968: $i,SV129: $i,SV557: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV557 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV129 @ tc_bool ) ) @ SV129 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV557 @ SV968 @ SV129 ) @ ( tc_fun @ SV129 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV557 @ SV968 @ SV129 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV129 ) @ SV557 ) @ SV968 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3158]) ).
thf(3465,plain,
! [SV558: $i,SV969: $i,SV130: $i,SV1264: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1264 @ tc_bool ) ) @ SV130 ) @ SV969 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV130 @ ( c_Set_Oinsert @ SV558 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1264 @ tc_bool ) ) @ SV1264 ) @ ( tc_fun @ SV1264 @ tc_bool ) ) @ SV969 @ ( tc_fun @ SV1264 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SV558 @ SV969 @ SV1264 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV130 @ ( c_Set_Oinsert @ SV558 @ SV969 @ SV1264 ) @ ( tc_fun @ SV1264 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3159]) ).
thf(3466,plain,
! [SV1265: $i,SV970: $i,SV559: $i,SV131: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV131 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV559 @ SV970 @ SV131 ) ) @ SV1265 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ SV970 ) @ SV1265 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ SV559 ) @ SV1265 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3160]) ).
thf(3467,plain,
! [SV1266: $i,SV971: $i,SV560: $i,SV132: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV132 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV560 @ SV971 @ SV132 ) ) @ SV1266 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ SV971 ) @ SV1266 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ SV560 ) @ SV1266 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3161]) ).
thf(3468,plain,
! [SV974: $i,SV563: $i,SV135: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV135 ) @ SV563 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV974 @ SV135 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV135 ) @ SV974 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV563 @ SV135 ) ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3164]) ).
thf(3469,plain,
! [SV975: $i,SV564: $i,SV136: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV136 ) @ SV564 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV975 @ SV136 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV136 ) @ SV975 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV564 @ SV136 ) ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3165]) ).
thf(3470,plain,
! [SV976: $i,SV565: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV137 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV565 @ SV137 ) ) @ SV976 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV137 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV976 @ SV137 ) ) @ SV565 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3166]) ).
thf(3471,plain,
! [SV977: $i,SV566: $i,SV138: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV138 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV566 @ SV138 ) ) @ SV977 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV138 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV977 @ SV138 ) ) @ SV566 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3167]) ).
thf(3472,plain,
! [SV139: $i,SV978: $i,SV567: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV567 @ SV978 @ SV139 ) @ ( c_Set_Oinsert @ SV978 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV139 @ tc_bool ) ) @ SV139 ) @ ( tc_fun @ SV139 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV567 @ SV978 @ SV139 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV139 ) @ SV567 ) @ SV978 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3168]) ).
thf(3473,plain,
! [SV1485: $i,SV1425: $i,SV1267: $i,SV979: $i,SV570: $i,SV143: $i] :
( ( ! [SY4035: $i,SY4036: $i,SY4037: $i] :
( ( ( hAPP @ SV143 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV570 @ tc_bool ) ) )
= SV979 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV143 @ SV1267 @ SV1425 @ SV1485 @ SY4035 @ SY4036 @ SY4037 @ SV979 @ SV570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3169]) ).
thf(3474,plain,
! [SV1486: $i,SV1426: $i,SV1268: $i,SV980: $i,SV571: $i,SV144: $i] :
( ( ! [SY4038: $i,SY4039: $i,SY4040: $i] :
( ( ( hAPP @ SV144 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV571 @ tc_bool ) ) )
= SV980 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1268 @ SV144 @ SV1426 @ SV1486 @ SY4038 @ SY4039 @ SV980 @ SY4040 @ SV571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3170]) ).
thf(3475,plain,
! [SV155: $i,SV983: $i,SV582: $i] :
( ( ( hBOOL @ ( c_in @ SV582 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV983 @ tc_bool ) ) @ SV983 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV155 @ SV582 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3172]) ).
thf(3476,plain,
! [SV586: $i,SV1269: $i,SV987: $i,SV159: $i] :
( ( ( hBOOL @ ( c_in @ SV159 @ SV987 @ SV1269 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV159 @ ( c_Set_Oinsert @ SV586 @ SV987 @ SV1269 ) @ SV1269 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3175]) ).
thf(3477,plain,
! [SV587: $i,SV1270: $i,SV988: $i,SV160: $i] :
( ( ( hBOOL @ ( c_in @ SV160 @ SV988 @ SV1270 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV160 @ ( c_Set_Oinsert @ SV587 @ SV988 @ SV1270 ) @ SV1270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3176]) ).
thf(3478,plain,
! [SV1487: $i,SV1427: $i,SV1271: $i,SV989: $i,SV588: $i,SV161: $i] :
( ( ! [SY4041: $i,SY4042: $i,SY4043: $i,SY4044: $i,SY4045: $i] :
( ( ( hAPP @ SV161 @ ( c_Set_Oinsert @ SV588 @ SV989 @ SV1271 ) )
= ( hAPP @ ( hAPP @ SV1427 @ SV588 ) @ ( hAPP @ SV161 @ SV989 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV161 @ SV1487 @ SY4041 @ SY4042 @ SV1427 @ SY4043 @ SY4044 @ SY4045 @ SV1271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3177]) ).
thf(3479,plain,
! [SV1488: $i,SV1428: $i,SV1272: $i,SV990: $i,SV589: $i,SV162: $i] :
( ( ! [SY4046: $i,SY4047: $i,SY4048: $i,SY4049: $i,SY4050: $i] :
( ( ( hAPP @ SV162 @ ( c_Set_Oinsert @ SV589 @ SV990 @ SV1272 ) )
= ( hAPP @ ( hAPP @ SV1428 @ SV589 ) @ ( hAPP @ SV162 @ SV990 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1488 @ SV162 @ SY4046 @ SY4047 @ SY4048 @ SV1428 @ SY4049 @ SY4050 @ SV1272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3178]) ).
thf(3480,plain,
! [SV991: $i,SV590: $i,SV1273: $i,SV163: $i] :
( ( ( SV163 = SV1273 )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV163 @ ( c_Set_Oinsert @ SV1273 @ SV590 @ SV991 ) @ SV991 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV163 @ SV590 @ SV991 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3179]) ).
thf(3481,plain,
! [SV998: $i,SV597: $i,SV170: $i,SV1276: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV170 ) @ SV597 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV998 ) @ SV170 ) ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV170 @ ( c_HOL_Ominus__class_Ominus @ SV597 @ SV998 @ ( tc_fun @ SV1276 @ tc_bool ) ) @ ( tc_fun @ SV1276 @ tc_bool ) )
= SV998 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3181]) ).
thf(3482,plain,
! [SV598: $i,SV999: $i,SV1277: $i,SV171: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV171 @ SV1277 @ SV999 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV999 @ tc_bool ) ) @ SV1277 ) @ SV598 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV171 @ SV598 @ SV999 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3182]) ).
thf(3483,plain,
! [SV172: $i,SV599: $i,SV1278: $i,SV1000: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1000 @ tc_bool ) ) @ SV1278 ) @ SV599 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV172 @ SV1278 @ SV1000 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV172 @ SV599 @ SV1000 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3183]) ).
thf(3484,plain,
! [SV600: $i,SV1001: $i,SV1279: $i,SV173: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV173 @ SV1279 @ SV1001 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1001 @ tc_bool ) ) @ SV1279 ) @ SV600 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV173 @ SV600 @ SV1001 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3184]) ).
thf(3485,plain,
! [SV601: $i,SV1002: $i,SV1280: $i,SV174: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV174 @ SV1280 @ SV1002 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1002 @ tc_bool ) ) @ SV1280 ) @ SV601 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV174 @ SV601 @ SV1002 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3185]) ).
thf(3486,plain,
! [SV1003: $i,SV602: $i,SV1281: $i,SV175: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV175 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1281 @ SV602 @ ( tc_fun @ SV175 @ tc_bool ) ) ) @ SV1003 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV175 @ tc_bool ) ) @ SV602 ) @ SV1003 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3186]) ).
thf(3487,plain,
! [SV1004: $i,SV1282: $i,SV603: $i,SV176: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV176 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV603 @ SV1282 @ ( tc_fun @ SV176 @ tc_bool ) ) ) @ SV1004 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV176 @ tc_bool ) ) @ SV603 ) @ SV1004 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3187]) ).
thf(3488,plain,
! [SV1429: $i,SV1283: $i,SV1005: $i,SV604: $i,SV177: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV604 @ SV1005 @ ( tc_fun @ SV177 @ tc_bool ) ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1283 @ SV1429 @ ( tc_fun @ SV177 @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ SV1005 ) @ SV1429 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ SV604 ) @ SV1283 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3188]) ).
thf(3489,plain,
! [SV1430: $i,SV1284: $i,SV1008: $i,SV607: $i,SV180: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV607 @ SV1008 @ ( tc_fun @ SV180 @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1284 @ SV1430 @ ( tc_fun @ SV180 @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ SV1430 ) @ SV1008 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ SV607 ) @ SV1284 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3191]) ).
thf(3490,plain,
! [SV611: $i,SV1285: $i,SV1012: $i,SV184: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV184 @ tc_bool ) ) @ SV1012 ) @ SV1285 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV184 @ tc_bool ) ) @ SV611 ) @ SV1285 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV184 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV611 @ SV1012 @ ( tc_fun @ SV184 @ tc_bool ) ) ) @ SV1285 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3195]) ).
thf(3491,plain,
! [SV614: $i,SV1286: $i,SV1015: $i,SV187: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV187 @ tc_bool ) ) @ SV1015 ) @ SV1286 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV187 @ tc_bool ) ) @ SV614 ) @ SV1286 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV187 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV614 @ SV1015 @ ( tc_fun @ SV187 @ tc_bool ) ) ) @ SV1286 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3196]) ).
thf(3492,plain,
! [SV1287: $i,SV189: $i,SV616: $i,SV1017: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV1017 @ SV616 @ SV189 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV189 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV616 @ ( c_Set_Oinsert @ SV1017 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV189 @ tc_bool ) ) @ SV189 ) @ ( tc_fun @ SV189 @ tc_bool ) ) ) @ SV1287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV189 @ tc_bool ) ) @ SV616 ) @ ( c_Set_Oinsert @ SV1017 @ SV1287 @ SV189 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3197]) ).
thf(3493,plain,
! [SV1288: $i,SV190: $i,SV617: $i,SV1018: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV1018 @ SV617 @ SV190 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV190 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV617 @ ( c_Set_Oinsert @ SV1018 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV190 @ tc_bool ) ) @ SV190 ) @ ( tc_fun @ SV190 @ tc_bool ) ) ) @ SV1288 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV190 @ tc_bool ) ) @ SV617 ) @ ( c_Set_Oinsert @ SV1018 @ SV1288 @ SV190 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3198]) ).
thf(3494,plain,
! [SV1289: $i,SV191: $i,SV618: $i,SV1019: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV1019 @ SV618 @ SV191 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV191 @ tc_bool ) ) @ SV618 ) @ ( c_Set_Oinsert @ SV1019 @ SV1289 @ SV191 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV191 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV618 @ ( c_Set_Oinsert @ SV1019 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV191 @ tc_bool ) ) @ SV191 ) @ ( tc_fun @ SV191 @ tc_bool ) ) ) @ SV1289 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3199]) ).
thf(3495,plain,
! [SV192: $i,SV1020: $i,SV619: $i] :
( ( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV619 @ SV1020 @ SV192 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV192 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV192 ) @ SV619 ) @ SV1020 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3200]) ).
thf(3496,plain,
! [SV1021: $i,SV620: $i,SV193: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV193 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV620 @ SV1021 @ SV193 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV193 ) @ SV620 ) @ SV1021 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3201]) ).
thf(3497,plain,
! [SV194: $i,SV1022: $i,SV621: $i] :
( ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ SV621 @ SV1022 @ SV194 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV194 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV194 ) @ SV1022 ) @ SV621 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3202]) ).
thf(3498,plain,
! [SV1431: $i,SV1290: $i,SV1023: $i,SV622: $i,SV195: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV195 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV195 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV622 @ SV1023 @ SV195 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1290 @ SV1431 @ SV195 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV195 ) @ SV622 ) @ SV1023 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3203]) ).
thf(3499,plain,
! [SV1432: $i,SV1291: $i,SV1024: $i,SV623: $i,SV196: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV196 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV196 ) @ SV623 ) @ SV1024 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV196 ) @ SV1024 ) @ SV1291 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV196 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1024 @ SV1291 @ SV196 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV623 @ SV1432 @ SV196 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3204]) ).
thf(3500,plain,
! [SV1433: $i,SV1292: $i,SV1025: $i,SV624: $i,SV197: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV197 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV197 ) @ SV624 ) @ SV1025 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV197 ) @ SV1292 ) @ SV624 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV197 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1292 @ SV624 @ SV197 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1433 @ SV1025 @ SV197 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3205]) ).
thf(3501,plain,
! [SV1434: $i,SV1293: $i,SV1026: $i,SV625: $i,SV198: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV198 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV198 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV625 @ SV1026 @ SV198 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1293 @ SV1434 @ SV198 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV198 ) @ SV1026 ) @ SV1434 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV198 ) @ SV1293 ) @ SV625 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3206]) ).
thf(3502,plain,
! [SV1435: $i,SV1294: $i,SV1027: $i,SV626: $i,SV199: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV199 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV199 ) @ SV626 ) @ SV1027 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV199 ) @ SV1294 ) @ SV1027 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV199 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1027 @ SV1294 @ SV199 ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV626 @ SV1435 @ SV199 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3207]) ).
thf(3503,plain,
! [SV1295: $i,SV1030: $i,SV629: $i,SV202: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV202 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV629 @ SV1030 @ SV202 ) ) @ SV1295 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ SV1030 ) @ SV1295 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ SV629 ) @ SV1295 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3210]) ).
thf(3504,plain,
! [SV1031: $i,SV630: $i,SV203: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV203 ) @ SV630 ) @ SV1031 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV203 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV1031 @ SV203 ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV630 @ SV203 ) ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3211]) ).
thf(3505,plain,
! [SV1032: $i,SV631: $i,SV204: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV204 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV631 @ SV204 ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV1032 @ SV204 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV204 ) @ SV1032 ) @ SV631 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3212]) ).
thf(3506,plain,
! [SV205: $i,SV1033: $i,SV632: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV632 @ SV1033 @ SV205 )
= SV632 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV205 ) @ SV1033 ) @ SV632 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3213]) ).
thf(3507,plain,
! [SV206: $i,SV1034: $i,SV633: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV633 @ SV1034 @ SV206 )
= SV1034 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV206 ) @ SV633 ) @ SV1034 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV206 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3214]) ).
thf(3508,plain,
! [SV1296: $i,SV1035: $i,SV634: $i,SV207: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV207 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV207 ) @ SV634 ) @ SV1035 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV207 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1296 @ SV634 @ SV207 ) ) @ SV1035 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3215]) ).
thf(3509,plain,
! [SV1297: $i,SV1036: $i,SV635: $i,SV208: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV208 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV208 ) @ SV635 ) @ SV1036 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV208 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV635 @ SV1297 @ SV208 ) ) @ SV1036 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3216]) ).
thf(3510,plain,
! [SV1298: $i,SV1037: $i,SV636: $i,SV209: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV209 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV209 ) @ SV636 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1037 @ SV1298 @ SV209 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV209 ) @ SV636 ) @ SV1298 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3217]) ).
thf(3511,plain,
! [SV1299: $i,SV1038: $i,SV637: $i,SV210: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV210 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV210 ) @ SV637 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1038 @ SV1299 @ SV210 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV210 ) @ SV637 ) @ SV1038 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3218]) ).
thf(3512,plain,
! [SV1300: $i,SV1039: $i,SV638: $i,SV211: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV211 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV211 ) @ SV638 ) @ SV1039 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV211 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1300 @ SV638 @ SV211 ) ) @ SV1039 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3219]) ).
thf(3513,plain,
! [SV1301: $i,SV1040: $i,SV639: $i,SV212: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV212 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV212 ) @ SV639 ) @ SV1040 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV212 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV639 @ SV1301 @ SV212 ) ) @ SV1040 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3220]) ).
thf(3514,plain,
! [SV1302: $i,SV1042: $i,SV647: $i,SV220: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV220 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV647 @ SV1042 @ ( tc_fun @ SV220 @ tc_bool ) ) ) @ SV1302 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV220 @ tc_bool ) ) @ SV647 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1042 @ SV1302 @ ( tc_fun @ SV220 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3222]) ).
thf(3515,plain,
! [SV1303: $i,SV1043: $i,SV648: $i,SV221: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV221 @ tc_bool ) ) @ SV648 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1043 @ SV1303 @ ( tc_fun @ SV221 @ tc_bool ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV221 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV648 @ SV1043 @ ( tc_fun @ SV221 @ tc_bool ) ) ) @ SV1303 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3223]) ).
thf(3516,plain,
! [SV1489: $i,SV1436: $i,SV1305: $i,SV1045: $i,SV650: $i,SV223: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV223 @ SV650 @ SV1045 @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1436 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV650 @ SV1489 ) @ SV1436 ) )
| ~ ( hBOOL @ ( c_in @ SV1489 @ SV223 @ SV1045 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3225]) ).
thf(3517,plain,
! [SV1490: $i,SV1437: $i,SV1306: $i,SV1046: $i,SV651: $i,SV224: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV224 @ SV651 @ SV1046 @ ( tc_fun @ SV1306 @ tc_bool ) ) @ SV1437 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV651 @ SV1490 ) @ SV1437 ) )
| ~ ( hBOOL @ ( c_in @ SV1490 @ SV224 @ SV1046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3226]) ).
thf(3518,plain,
! [SV1491: $i,SV1438: $i,SV1307: $i,SV1053: $i,SV658: $i,SV231: $i] :
( ( ! [SY4051: $i,SY4052: $i,SY4053: $i,SY4054: $i,SY4055: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV231 @ SV658 ) @ ( hAPP @ SV1053 @ SV1307 ) ) )
| ~ ( hBOOL @ ( c_in @ SV658 @ SV1307 @ SV1438 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1491 @ SV1053 @ SV231 @ SY4051 @ SY4052 @ SY4053 @ SY4054 @ SY4055 @ SV1438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3231]) ).
thf(3519,plain,
! [SV1492: $i,SV1439: $i,SV1308: $i,SV1054: $i,SV659: $i,SV232: $i] :
( ( ! [SY4056: $i,SY4057: $i,SY4058: $i,SY4059: $i,SY4060: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ ( hAPP @ SV659 @ SV1054 ) ) @ SV1308 ) )
| ~ ( hBOOL @ ( c_in @ SV1308 @ SV1054 @ SV1439 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV659 @ SV1492 @ SV232 @ SY4056 @ SY4057 @ SY4058 @ SY4059 @ SY4060 @ SV1439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3232]) ).
thf(3520,plain,
! [SV1493: $i,SV1440: $i,SV1310: $i,SV1059: $i,SV664: $i,SV237: $i] :
( ( ( hBOOL @ ( c_in @ SV237 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV664 @ SV1059 @ SV1310 @ ( tc_fun @ SV1440 @ tc_bool ) ) @ SV1440 ) )
| ~ ( hBOOL @ ( c_in @ SV237 @ ( hAPP @ SV1059 @ SV1493 ) @ SV1440 ) )
| ~ ( hBOOL @ ( c_in @ SV1493 @ SV664 @ SV1310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3234]) ).
thf(3521,plain,
! [SV1494: $i,SV1441: $i,SV1311: $i,SV1060: $i,SV665: $i,SV238: $i] :
( ( ( hBOOL @ ( c_in @ SV238 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV665 @ SV1060 @ SV1311 @ ( tc_fun @ SV1441 @ tc_bool ) ) @ SV1441 ) )
| ~ ( hBOOL @ ( c_in @ SV238 @ ( hAPP @ SV1060 @ SV1494 ) @ SV1441 ) )
| ~ ( hBOOL @ ( c_in @ SV1494 @ SV665 @ SV1311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3235]) ).
thf(3522,plain,
! [SV666: $i,SV1312: $i,SV1061: $i,SV239: $i] :
( ( ( hBOOL @ ( c_in @ SV239 @ SV1061 @ SV1312 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV239 @ SV666 @ SV1312 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV239 @ ( c_HOL_Ominus__class_Ominus @ SV666 @ SV1061 @ ( tc_fun @ SV1312 @ tc_bool ) ) @ SV1312 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3236]) ).
thf(3523,plain,
! [SV667: $i,SV1313: $i,SV1062: $i,SV240: $i] :
( ( ( hBOOL @ ( c_in @ SV240 @ SV1062 @ SV1313 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV240 @ SV667 @ SV1313 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV240 @ ( c_HOL_Ominus__class_Ominus @ SV667 @ SV1062 @ ( tc_fun @ SV1313 @ tc_bool ) ) @ SV1313 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3237]) ).
thf(3524,plain,
! [SV1314: $i,SV1066: $i,SV671: $i,SV244: $i] :
( ( ( class_Lattices_Olattice @ SV244 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV671 @ SV1066 @ SV244 ) @ SV1314 @ SV244 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV671 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1066 @ SV1314 @ SV244 ) @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3241]) ).
thf(3525,plain,
! [SV1315: $i,SV1067: $i,SV672: $i,SV245: $i] :
( ( ( class_Lattices_Olattice @ SV245 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV672 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1067 @ SV1315 @ SV245 ) @ SV245 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1067 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV672 @ SV1315 @ SV245 ) @ SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3242]) ).
thf(3526,plain,
! [SV1316: $i,SV1068: $i,SV673: $i,SV246: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV246 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV673 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1068 @ SV1316 @ SV246 ) @ SV246 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1068 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV673 @ SV1316 @ SV246 ) @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3243]) ).
thf(3527,plain,
! [SV1317: $i,SV1069: $i,SV674: $i,SV247: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV247 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV674 @ SV1069 @ SV247 ) @ SV1317 @ SV247 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV674 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1069 @ SV1317 @ SV247 ) @ SV247 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3244]) ).
thf(3528,plain,
! [SV1442: $i,SV1321: $i,SV1078: $i,SV685: $i,SV258: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV258 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV258 ) @ ( hAPP @ SV685 @ SV1078 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1321 @ SV685 @ SV1442 @ SV258 ) ) )
| ~ ( hBOOL @ ( c_in @ SV1078 @ SV1321 @ SV1442 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3248]) ).
thf(3529,plain,
! [SV1443: $i,SV1322: $i,SV1079: $i,SV686: $i,SV259: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV259 @ tc_bool ) ) @ ( hAPP @ SV686 @ SV1079 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1322 @ SV686 @ SV1443 @ ( tc_fun @ SV259 @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1079 @ SV1322 @ SV1443 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3249]) ).
thf(3530,plain,
! [SV687: $i,SV1080: $i,SV1323: $i,SV260: $i] :
( ( ( hBOOL @ ( c_in @ SV260 @ SV1323 @ SV1080 ) )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV260 @ SV687 @ SV1080 ) @ SV1323 @ ( tc_fun @ SV1080 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV687 @ SV1323 @ ( tc_fun @ SV1080 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3250]) ).
thf(3531,plain,
! [SV1081: $i,SV688: $i,SV261: $i] :
( ( ( hBOOL @ ( c_in @ SV261 @ ( c_HOL_Ouminus__class_Ouminus @ SV688 @ ( tc_fun @ SV1081 @ tc_bool ) ) @ SV1081 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV261 @ SV688 @ SV1081 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3251]) ).
thf(3532,plain,
! [SV1085: $i,SV1324: $i,SV693: $i,SV266: $i] :
( ( ( hBOOL @ ( c_in @ SV266 @ ( c_HOL_Ominus__class_Ominus @ SV693 @ SV1324 @ ( tc_fun @ SV1085 @ tc_bool ) ) @ SV1085 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV266 @ SV693 @ SV1085 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3253]) ).
thf(3533,plain,
! [SV1325: $i,SV1086: $i,SV694: $i,SV267: $i] :
( ( ( hBOOL @ ( c_in @ SV267 @ SV694 @ SV1086 ) )
= $false )
| ( ( ~ ( hBOOL @ ( c_in @ SV267 @ ( c_HOL_Ominus__class_Ominus @ SV1325 @ SV694 @ ( tc_fun @ SV1086 @ tc_bool ) ) @ SV1086 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3254]) ).
thf(3534,plain,
! [SV1495: $i,SV1444: $i,SV1326: $i,SV1087: $i,SV695: $i,SV268: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV268 @ tc_bool ) ) @ ( hAPP @ SV695 @ SV1087 ) ) @ SV1326 ) )
| ~ ( hBOOL @ ( c_in @ SV1087 @ SV1444 @ SV1495 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV268 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1444 @ SV695 @ SV1495 @ ( tc_fun @ SV268 @ tc_bool ) ) ) @ SV1326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3255]) ).
thf(3535,plain,
! [SV1445: $i,SV1327: $i,SV1088: $i,SV696: $i,SV269: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV269 @ SV696 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1088 @ SV269 @ SV1327 @ ( tc_fun @ SV1445 @ tc_bool ) ) @ ( tc_fun @ SV1445 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1088 @ SV269 @ SV1327 @ ( tc_fun @ SV1445 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV696 @ SV1088 @ SV1327 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3256]) ).
thf(3536,plain,
! [SV1328: $i,SV270: $i,SV697: $i,SV1089: $i] :
( ( ( hBOOL @ ( hAPP @ SV1089 @ SV697 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1089 @ SV270 @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV697 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV270 @ SV697 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3257]) ).
thf(3537,plain,
! [SV1090: $i,SV271: $i,SV1329: $i,SV698: $i] :
( ( ( hBOOL @ ( hAPP @ SV698 @ SV1329 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV271 @ SV698 @ ( tc_fun @ SV1090 @ tc_bool ) ) @ SV1329 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3258]) ).
thf(3538,plain,
! [SV1091: $i,SV699: $i,SV1330: $i,SV272: $i] :
( ( ( hBOOL @ ( hAPP @ SV272 @ SV1330 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV272 @ SV699 @ ( tc_fun @ SV1091 @ tc_bool ) ) @ SV1330 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3259]) ).
thf(3539,plain,
! [SV700: $i,SV1092: $i,SV1331: $i,SV273: $i] :
( ( ( hBOOL @ ( c_in @ SV273 @ SV1331 @ SV1092 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV273 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1331 @ SV700 @ ( tc_fun @ SV1092 @ tc_bool ) ) @ SV1092 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV273 @ SV700 @ SV1092 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3260]) ).
thf(3540,plain,
! [SV1332: $i,SV1093: $i,SV701: $i,SV274: $i] :
( ( ( class_Orderings_Olinorder @ SV274 )
= $false )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV701 @ SV1093 @ SV274 ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1093 @ SV1332 @ SV274 ) @ ( tc_fun @ SV274 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV701 @ SV1332 @ SV274 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV274 ) @ SV1093 ) @ SV1332 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV274 ) @ SV701 ) @ SV1093 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3261]) ).
thf(3541,plain,
! [SV1335: $i,SV1096: $i,SV704: $i,SV277: $i] :
( ( ( class_Orderings_Olinorder @ SV277 )
= $false )
| ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV704 @ SV1096 @ SV277 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1096 @ SV1335 @ SV277 ) @ ( tc_fun @ SV277 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV704 @ SV1335 @ SV277 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV277 ) @ SV1096 ) @ SV1335 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV277 ) @ SV704 ) @ SV1096 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3262]) ).
thf(3542,plain,
! [SV1098: $i,SV706: $i,SV279: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV279 ) @ ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ SV279 ) @ SV706 ) ) @ SV1098 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1098 @ SV706 @ SV279 ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV279 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3264]) ).
thf(3543,plain,
! [SV708: $i,SV1337: $i,SV1099: $i,SV281: $i] :
( ( ( hBOOL @ ( c_in @ SV281 @ SV1099 @ SV1337 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV281 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV708 @ SV1099 @ ( tc_fun @ SV1337 @ tc_bool ) ) @ SV1337 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3265]) ).
thf(3544,plain,
! [SV1100: $i,SV1338: $i,SV709: $i,SV282: $i] :
( ( ( hBOOL @ ( c_in @ SV282 @ SV709 @ SV1338 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV282 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV709 @ SV1100 @ ( tc_fun @ SV1338 @ tc_bool ) ) @ SV1338 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3266]) ).
thf(3545,plain,
! [SV1339: $i,SV1101: $i,SV710: $i,SV283: $i] :
( ( ( class_Orderings_Olinorder @ SV283 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV710 @ SV1101 @ SV283 ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV710 @ SV1339 @ SV283 ) @ ( tc_fun @ SV283 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1339 @ SV1101 @ SV283 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV283 ) @ SV710 ) @ SV1339 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3267]) ).
thf(3546,plain,
! [SV1103: $i,SV713: $i,SV286: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV286 ) @ SV713 ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV286 ) @ SV1103 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV713 @ SV1103 @ SV286 ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV286 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3269]) ).
thf(3547,plain,
! [SV1448: $i,SV1341: $i,SV1104: $i,SV714: $i,SV287: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV287 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV287 ) @ SV714 ) @ SV1104 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV287 ) @ SV714 ) @ SV1341 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV287 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1341 @ SV714 @ SV287 ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1448 @ SV1104 @ SV287 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3270]) ).
thf(3548,plain,
! [SV1496: $i,SV1449: $i,SV1342: $i,SV1105: $i,SV717: $i,SV292: $i] :
( ( ! [SY4061: $i,SY4062: $i,SY4063: $i,SY4064: $i] :
( ( ( hAPP @ SV292 @ ( c_Set_Oinsert @ SV717 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1105 @ tc_bool ) ) @ SV1105 ) )
= SV717 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV292 @ SV1342 @ SV1449 @ SV1496 @ SY4061 @ SY4062 @ SY4063 @ SY4064 @ SV1105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3271]) ).
thf(3549,plain,
! [SV1497: $i,SV1450: $i,SV1343: $i,SV1106: $i,SV718: $i,SV293: $i] :
( ( ! [SY4065: $i,SY4066: $i,SY4067: $i,SY4068: $i] :
( ( ( hAPP @ SV293 @ ( c_Set_Oinsert @ SV718 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1106 @ tc_bool ) ) @ SV1106 ) )
= SV718 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1343 @ SV293 @ SV1450 @ SV1497 @ SY4065 @ SY4066 @ SY4067 @ SY4068 @ SV1106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3272]) ).
thf(3550,plain,
! [SV1498: $i,SV1451: $i,SV1345: $i,SV1109: $i,SV725: $i,SV300: $i] :
( ( ! [SY4069: $i,SY4070: $i,SY4071: $i,SY4072: $i,SY4073: $i] :
( ( ( hAPP @ SV300 @ ( c_Set_Oinsert @ SV725 @ ( c_Set_Oinsert @ SV1109 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1345 @ tc_bool ) ) @ SV1345 ) @ SV1345 ) )
= ( hAPP @ ( hAPP @ SV1451 @ SV725 ) @ SV1109 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV300 @ SV1498 @ SY4069 @ SY4070 @ SV1451 @ SY4071 @ SY4072 @ SY4073 @ SV1345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3273]) ).
thf(3551,plain,
! [SV1499: $i,SV1452: $i,SV1346: $i,SV1110: $i,SV726: $i,SV301: $i] :
( ( ! [SY4074: $i,SY4075: $i,SY4076: $i,SY4077: $i,SY4078: $i] :
( ( ( hAPP @ SV301 @ ( c_Set_Oinsert @ SV726 @ ( c_Set_Oinsert @ SV1110 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1346 @ tc_bool ) ) @ SV1346 ) @ SV1346 ) )
= ( hAPP @ ( hAPP @ SV1452 @ SV726 ) @ SV1110 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1499 @ SV301 @ SY4074 @ SY4075 @ SY4076 @ SV1452 @ SY4077 @ SY4078 @ SV1346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3274]) ).
thf(3552,plain,
! [SV729: $i,SV1349: $i,SV304: $i,SV1113: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV1113 @ ( c_Set_Oinsert @ SV304 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1349 @ tc_bool ) ) @ SV1349 ) @ SV1349 ) @ SV729 ) )
= $false )
| ( ( SV304 = SV729 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3275]) ).
thf(3553,plain,
! [SV740: $i,SV1350: $i,SV1119: $i,SV316: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV316 @ tc_bool ) ) @ SV1119 ) @ SV1350 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV740 @ SV1350 @ SV316 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV316 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV740 @ SV1119 @ SV316 ) ) @ SV1350 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3278]) ).
thf(3554,plain,
! [SV741: $i,SV1351: $i,SV317: $i,SV1120: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1120 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV317 @ SV1351 @ SV1120 ) ) @ SV741 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV317 @ SV741 @ SV1120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3279]) ).
thf(3555,plain,
! [SV1121: $i,SV1352: $i,SV742: $i,SV318: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV318 @ tc_bool ) ) @ SV742 ) @ SV1352 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV1121 @ SV742 @ SV318 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV318 @ tc_bool ) ) @ SV742 ) @ ( c_Set_Oinsert @ SV1121 @ SV1352 @ SV318 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3280]) ).
thf(3556,plain,
! [SV1122: $i,SV319: $i,SV743: $i,SV1353: $i] :
( ( ( hBOOL @ ( c_in @ SV1353 @ SV743 @ SV319 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV319 @ tc_bool ) ) @ SV743 ) @ ( c_Set_Oinsert @ SV1353 @ SV1122 @ SV319 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV319 @ tc_bool ) ) @ SV743 ) @ SV1122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3281]) ).
thf(3557,plain,
! [SV1123: $i,SV1354: $i,SV744: $i,SV320: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV320 @ tc_bool ) ) @ SV744 ) @ SV1354 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV1123 @ SV744 @ SV320 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV320 @ tc_bool ) ) @ SV744 ) @ ( c_Set_Oinsert @ SV1123 @ SV1354 @ SV320 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3282]) ).
thf(3558,plain,
! [SV1124: $i,SV1355: $i,SV745: $i,SV321: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV321 @ tc_bool ) ) @ SV745 ) @ ( c_Set_Oinsert @ SV1355 @ SV1124 @ SV321 ) ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV1355 @ SV745 @ SV321 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV321 @ tc_bool ) ) @ SV745 ) @ SV1124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3283]) ).
thf(3559,plain,
! [SV1500: $i,SV1453: $i,SV1356: $i,SV1125: $i,SV746: $i,SV322: $i] :
( ( ! [SY4079: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV322 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV746 @ SV1125 @ SV1356 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV1453 @ SV1500 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV322 @ SV746 @ SV1356 @ SV1125 @ SY4079 @ SV1453 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4079 @ SV1500 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV322 @ SV746 @ SV1356 @ SV1125 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV322 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY4079 @ SV1125 @ SV1453 @ 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_forall_pos,[status(thm)],[3284]) ).
thf(3560,plain,
! [SV1501: $i,SV1454: $i,SV1357: $i,SV1126: $i,SV747: $i,SV323: $i] :
( ( ! [SY4080: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV323 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV747 @ SV1126 @ SV1357 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV1454 @ SV1501 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV747 @ SY4080 @ SV1357 @ SV1454 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4080 @ SV1501 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV747 @ SY4080 @ SV1357 @ SV1454 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV323 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY4080 @ SV1126 @ SV1454 @ 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_forall_pos,[status(thm)],[3285]) ).
thf(3561,plain,
! [SV1502: $i,SV1455: $i,SV1358: $i,SV1127: $i,SV748: $i,SV324: $i] :
( ( ! [SY4081: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV324 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV748 @ SV1127 @ SV1358 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV1455 @ SV1502 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV324 @ SV748 @ SV1358 @ SV1127 @ SY4081 @ SV1455 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4081 @ SV1502 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV324 @ SV748 @ SV1358 @ SV1127 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV324 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY4081 @ SV1127 @ SV1455 @ 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_forall_pos,[status(thm)],[3286]) ).
thf(3562,plain,
! [SV1503: $i,SV1456: $i,SV1360: $i,SV1129: $i,SV750: $i,SV326: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV326 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV750 @ SV1129 @ SV1360 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1360 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV326 @ SV750 @ SV1360 @ SV1129 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV326 @ SV750 @ SV1360 @ SV1129 @ SV1456 @ SV1503 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV326 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1456 @ SV1129 @ SV1503 @ 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_forall_pos,[status(thm)],[3288]) ).
thf(3563,plain,
! [SV1457: $i,SV1362: $i,SV1131: $i,SV752: $i,SV328: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV328 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV752 @ SV1131 @ SV1362 @ 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 )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1457 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SV1362 @ SV1457 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SV1362 @ SV1457 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV328 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV752 @ SV1131 @ SV1457 @ 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_or_pos,[status(thm)],[3290]) ).
thf(3564,plain,
! [SV1504: $i,SV1458: $i,SV1363: $i,SV1132: $i,SV753: $i,SV329: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV329 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV753 @ SV1132 @ SV1363 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV753 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV753 @ SV1458 @ SV1363 @ SV1504 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV753 @ SV1458 @ SV1363 @ SV1504 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV329 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1458 @ SV1132 @ SV1504 @ 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_forall_pos,[status(thm)],[3291]) ).
thf(3565,plain,
! [SV1459: $i,SV1364: $i,SV1133: $i,SV754: $i,SV330: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV330 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV754 @ SV1133 @ SV1364 @ 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 )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV754 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV754 @ SV1459 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV754 @ SV1459 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV330 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1459 @ SV1133 @ SV1364 @ 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_or_pos,[status(thm)],[3292]) ).
thf(3566,plain,
! [SV1505: $i,SV1460: $i,SV1365: $i,SV1134: $i,SV755: $i,SV331: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV331 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV755 @ SV1134 @ SV1365 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1365 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV331 @ SV755 @ SV1365 @ SV1134 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV331 @ SV755 @ SV1365 @ SV1134 @ SV1460 @ SV1505 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV331 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1460 @ SV1134 @ SV1505 @ 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_forall_pos,[status(thm)],[3293]) ).
thf(3567,plain,
! [SV1461: $i,SV1366: $i,SV1135: $i,SV756: $i,SV332: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV332 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV756 @ SV1135 @ SV1366 @ 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 )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1461 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV756 @ SV1461 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV756 @ SV1461 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV332 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1461 @ SV1135 @ SV1366 @ 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_or_pos,[status(thm)],[3294]) ).
thf(3568,plain,
! [SV1506: $i,SV1462: $i,SV1367: $i,SV1136: $i,SV757: $i,SV333: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV333 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV757 @ SV1136 @ SV1367 @ 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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1367 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV757 @ SV1462 @ SV1367 @ SV1506 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV757 @ SV1462 @ SV1367 @ SV1506 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV333 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1462 @ SV1136 @ SV1506 @ 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_forall_pos,[status(thm)],[3295]) ).
thf(3569,plain,
! [SV1463: $i,SV1368: $i,SV1137: $i,SV758: $i,SV334: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV334 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV758 @ SV1137 @ SV1368 @ 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 )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1368 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SV1368 @ SV1463 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SV1368 @ SV1463 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV334 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV758 @ SV1137 @ SV1463 @ 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_or_pos,[status(thm)],[3296]) ).
thf(3570,plain,
! [SV1139: $i,SV1370: $i,SV760: $i,SV336: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV336 @ tc_bool ) ) @ SV760 ) @ SV1370 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV336 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV760 @ ( c_Set_Oinsert @ SV1139 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV336 @ tc_bool ) ) @ SV336 ) @ ( tc_fun @ SV336 @ tc_bool ) ) ) @ SV1370 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV336 @ tc_bool ) ) @ SV760 ) @ ( c_Set_Oinsert @ SV1139 @ SV1370 @ SV336 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3298]) ).
thf(3571,plain,
! [SV1507: $i,SV1464: $i,SV1371: $i,SV1140: $i,SV761: $i,SV337: $i] :
( ( ! [SY4082: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV761 @ ( c_Com_Ocom_OSemi @ SV1140 @ SV1371 ) @ SV1464 @ SV1507 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) ) @ SV1507 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY4082 @ SV1371 @ SV1464 @ SV1507 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) ) @ SV1507 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV761 @ SV1140 @ SY4082 @ SV1507 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) ) @ SV1507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3299]) ).
thf(3572,plain,
! [SV1141: $i,SV762: $i,SV338: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV338 ) @ SV762 ) @ SV1141 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV338 ) @ SV1141 ) @ SV762 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV338 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3300]) ).
thf(3573,plain,
! [SV763: $i,SV1372: $i,SV1142: $i,SV339: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV339 @ tc_bool ) ) @ SV1142 ) @ SV1372 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV339 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV763 @ SV1142 @ SV339 ) ) @ ( c_Set_Oinsert @ SV763 @ SV1372 @ SV339 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3301]) ).
thf(3574,plain,
! [SV764: $i,SV1373: $i,SV1143: $i,SV340: $i] :
( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV340 @ SV1143 @ SV1373 ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV340 @ ( c_Set_Oinsert @ SV764 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1373 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1373 ) ) @ SV1373 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV340 @ ( c_Set_Oinsert @ SV764 @ SV1143 @ ( tc_Hoare__Mirabelle_Otriple @ SV1373 ) ) @ SV1373 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3302]) ).
thf(3575,plain,
! [SV765: $i,SV341: $i,SV1144: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1144 @ tc_bool ) ) @ SV341 ) @ ( c_Set_Oinsert @ SV765 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1144 @ tc_bool ) ) @ SV1144 ) ) )
= $false )
| ( ( SV341
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1144 @ tc_bool ) ) )
= $true )
| ( ( SV341
= ( c_Set_Oinsert @ SV765 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1144 @ tc_bool ) ) @ SV1144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3303]) ).
thf(3576,plain,
! [SV342: $i,SV1374: $i,SV766: $i,SV1145: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1145 ) @ tc_bool ) ) @ SV766 ) @ SV1374 ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV342 @ SV1374 @ SV1145 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV342 @ SV766 @ SV1145 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3304]) ).
thf(3577,plain,
! [SV767: $i,SV343: $i,SV1375: $i,SV1146: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1146 @ tc_bool ) ) @ SV1375 ) @ SV343 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1375 @ SV767 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV343 @ SV767 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3305]) ).
thf(3578,plain,
! [SV346: $i,SV1376: $i,SV770: $i,SV1147: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1147 @ SV770 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1376 @ tc_bool ) ) @ SV1147 ) @ SV346 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV346 @ SV770 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3306]) ).
thf(3579,plain,
! [SV771: $i,SV1148: $i,SV1377: $i,SV347: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV347 @ tc_bool ) ) @ SV1377 ) @ SV1148 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV347 @ tc_bool ) ) @ SV771 ) @ SV1377 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV347 @ tc_bool ) ) @ SV771 ) @ SV1148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3307]) ).
thf(3580,plain,
! [SV1378: $i,SV1149: $i,SV774: $i,SV350: $i] :
( ( ( class_Orderings_Opreorder @ SV350 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV774 ) @ SV1149 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV1378 ) @ SV1149 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV774 ) @ SV1378 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3308]) ).
thf(3581,plain,
! [SV1379: $i,SV1150: $i,SV775: $i,SV351: $i] :
( ( ( class_Orderings_Oorder @ SV351 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV775 ) @ SV1150 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV775 ) @ SV1379 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV1379 ) @ SV1150 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3309]) ).
thf(3582,plain,
! [SV778: $i,SV1153: $i,SV1380: $i,SV354: $i] :
( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV354 @ SV1380 @ SV1153 ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV1380 @ SV778 @ SV1153 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV354 @ SV778 @ SV1153 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3310]) ).
thf(3583,plain,
! [SV357: $i,SV1154: $i,SV780: $i] :
( ( ( SV780 = SV1154 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV357 ) @ SV780 ) @ SV1154 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV357 ) @ SV1154 ) @ SV780 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV357 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3311]) ).
thf(3584,plain,
! [SV358: $i,SV1155: $i,SV781: $i] :
( ( ( SV781 = SV1155 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV358 ) @ SV1155 ) @ SV781 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV358 ) @ SV781 ) @ SV1155 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV358 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3312]) ).
thf(3585,plain,
! [SV359: $i,SV1156: $i,SV782: $i] :
( ( ( SV782 = SV1156 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV359 ) @ SV1156 ) @ SV782 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV359 ) @ SV782 ) @ SV1156 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV359 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3313]) ).
thf(3586,plain,
! [SV360: $i,SV783: $i,SV1157: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1157 @ tc_bool ) ) @ SV783 ) @ SV360 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1157 @ tc_bool ) ) @ SV360 ) @ SV783 ) ) )
= $true )
| ( ( SV360 = SV783 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3314]) ).
thf(3587,plain,
! [SV361: $i,SV784: $i,SV1158: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1158 @ tc_bool ) ) @ SV784 ) @ SV361 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1158 @ tc_bool ) ) @ SV361 ) @ SV784 ) ) )
= $true )
| ( ( SV361 = SV784 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3315]) ).
thf(3588,plain,
! [SV1381: $i,SV365: $i,SV788: $i,SV1160: $i] :
( ( ( SV1160 = SV788 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1160 @ SV365 @ SV1381 ) @ SV788 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV365 @ SV788 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3316]) ).
thf(3589,plain,
! [SV1162: $i,SV1382: $i,SV792: $i,SV369: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV369 @ tc_bool ) ) @ SV792 ) @ SV1382 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV369 @ tc_bool ) ) @ SV792 ) @ ( c_Set_Oinsert @ SV1162 @ SV1382 @ SV369 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3317]) ).
thf(3590,plain,
! [SV1163: $i,SV793: $i,SV1383: $i,SV370: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV370 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV1383 @ SV793 @ SV370 ) ) @ SV1163 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV370 @ tc_bool ) ) @ SV793 ) @ SV1163 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3318]) ).
thf(3591,plain,
! [SV1166: $i,SV373: $i,SV1385: $i,SV796: $i] :
( ( ( hBOOL @ ( hAPP @ SV796 @ SV1385 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV373 @ SV796 @ SV1166 ) @ SV1385 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3319]) ).
thf(3592,plain,
! [SV1465: $i,SV1386: $i,SV1168: $i,SV798: $i,SV375: $i] :
( ( ( ~ ( class_HOL_Oord @ SV375 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV375 ) @ ( hAPP @ SV798 @ SV1168 ) ) @ ( hAPP @ SV1386 @ SV1168 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1465 @ SV375 ) ) @ SV798 ) @ SV1386 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3321]) ).
thf(3593,plain,
! [SV803: $i,SV380: $i] :
( ( ( class_Finite__Set_Ofinite_Ofinite @ SV380 )
= $false )
| ( ( class_Finite__Set_Ofinite_Ofinite @ SV803 )
= $false )
| ( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ SV380 @ SV803 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3322]) ).
thf(3594,plain,
! [SV1171: $i,SV391: $i,SV814: $i] :
( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV814 @ SV391 )
!= ( c_HOL_Ouminus__class_Ouminus @ SV1171 @ SV391 ) )
= $true )
| ( ( SV814 = SV1171 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV391 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3325]) ).
thf(3595,plain,
! [SV1387: $i,SV1172: $i,SV815: $i,SV392: $i] :
( ( ( ( c_Set_Oinsert @ SV392 @ SV815 @ SV1172 )
= ( c_Set_Oinsert @ SV392 @ SV1387 @ SV1172 ) )
= $false )
| ( ( ( hBOOL @ ( c_in @ SV392 @ SV1387 @ SV1172 ) )
| ( hBOOL @ ( c_in @ SV392 @ SV815 @ SV1172 ) )
| ( SV815 = SV1387 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3326]) ).
thf(3596,plain,
! [SV816: $i,SV1173: $i,SV393: $i] :
( ( ( hBOOL @ ( hAPP @ SV393 @ SV1173 ) )
= $false )
| ( ( ( c_Collect @ SV393 @ SV816 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV816 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3327]) ).
thf(3597,plain,
! [SV1388: $i,SV1174: $i,SV817: $i,SV394: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV394 @ SV817 )
= ( c_Com_Ocom_OSemi @ SV1174 @ SV1388 ) )
= $false )
| ( ( SV817 = SV1388 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3328]) ).
thf(3598,plain,
! [SV1508: $i,SV1466: $i,SV1389: $i,SV1175: $i,SV818: $i,SV395: $i] :
( ( ! [SY4083: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV395 @ SV818 @ SV1175 @ SV1389 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1466 @ SV1508 @ SY4083 @ SV1389 ) )
| ( SV395 = SV1466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3329]) ).
thf(3599,plain,
! [SV1177: $i,SV821: $i,SV398: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV398 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV821 @ SV1177 @ SV398 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV821 @ SV1177 @ SV398 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV398 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3330]) ).
thf(3600,plain,
! [SV400: $i,SV1179: $i,SV823: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV823 @ SV1179 @ SV400 )
!= ( c_Orderings_Obot__class_Obot @ SV400 ) )
= $true )
| ( ( SV823
= ( c_Orderings_Obot__class_Obot @ SV400 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV400 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3331]) ).
thf(3601,plain,
! [SV1467: $i,SV1390: $i,SV1180: $i,SV824: $i,SV401: $i] :
( ( ( ( c_Set_Oinsert @ SV401 @ ( c_Set_Oinsert @ SV824 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1180 @ tc_bool ) ) @ SV1180 ) @ SV1180 )
!= ( c_Set_Oinsert @ SV1390 @ ( c_Set_Oinsert @ SV1467 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1180 @ tc_bool ) ) @ SV1180 ) @ SV1180 ) )
= $true )
| ( ( ( SV824 = SV1390 )
| ( SV401 = SV1390 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3332]) ).
thf(3602,plain,
! [SV1391: $i,SV1182: $i,SV826: $i,SV403: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV403 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV826 @ SV826 @ SV403 )
!= ( c_HOL_Ominus__class_Ominus @ SV1182 @ SV1391 @ SV403 ) )
| ( SV1182 = SV1391 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3334]) ).
thf(3603,plain,
! [SV1183: $i,SV827: $i,SV404: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV404 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV827 @ SV1183 @ SV404 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV404 ) @ SV827 ) @ SV1183 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV404 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3335]) ).
thf(3604,plain,
! [SV406: $i,SV1185: $i,SV829: $i] :
( ( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV829 @ SV1185 @ SV406 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV406 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV406 ) @ SV829 ) @ SV1185 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV406 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3337]) ).
thf(3605,plain,
! [SV1468: $i,SV1392: $i,SV1187: $i,SV832: $i,SV409: $i] :
( ( ( ( c_Set_Oinsert @ SV409 @ ( c_Set_Oinsert @ SV832 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1187 @ tc_bool ) ) @ SV1187 ) @ SV1187 )
!= ( c_Set_Oinsert @ SV1392 @ ( c_Set_Oinsert @ SV1468 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1187 @ tc_bool ) ) @ SV1187 ) @ SV1187 ) )
= $true )
| ( ( ( SV409 = SV1468 )
| ( SV832 = SV1468 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3339]) ).
thf(3606,plain,
! [SV1469: $i,SV1393: $i,SV1188: $i,SV833: $i,SV410: $i] :
( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV410 @ SV833 @ SV1188 @ ( tc_fun @ SV1393 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1393 @ tc_bool ) ) )
= $true )
| ( ( ( ( hAPP @ SV833 @ SV1469 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1393 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SV1469 @ SV410 @ SV1188 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3340]) ).
thf(3607,plain,
! [SV1470: $i,SV1394: $i,SV1189: $i,SV834: $i,SV411: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV411 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV834 @ SV1189 @ SV411 )
!= ( c_HOL_Ominus__class_Ominus @ SV1394 @ SV1470 @ SV411 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV411 ) @ SV1470 ) @ SV1394 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV411 ) @ SV1189 ) @ SV834 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3341]) ).
thf(3608,plain,
! [SV1190: $i,SV412: $i,SV835: $i] :
( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV835 @ SV412 )
!= ( c_HOL_Ouminus__class_Ouminus @ SV1190 @ SV412 ) )
= $true )
| ( ( SV835 = SV1190 )
= $true )
| ( ( class_Lattices_Oboolean__algebra @ SV412 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3342]) ).
thf(3609,plain,
! [SV1471: $i,SV1395: $i,SV1191: $i,SV836: $i,SV413: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV413 @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV836 @ SV1191 @ SV1395 @ ( tc_fun @ SV413 @ tc_bool ) ) )
= $true )
| ( ( ( ( hAPP @ SV1191 @ SV1471 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV413 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SV1471 @ SV836 @ SV1395 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3343]) ).
thf(3610,plain,
! [SV414: $i,SV1192: $i,SV837: $i] :
( ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ SV837 @ SV1192 @ SV414 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV414 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV837 @ SV1192 @ SV414 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV414 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3344]) ).
thf(3611,plain,
! [SV1472: $i,SV1396: $i,SV1193: $i,SV838: $i,SV415: $i] :
( ( ( ( c_Set_Oinsert @ SV415 @ ( c_Set_Oinsert @ SV838 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SV1193 ) @ SV1193 )
!= ( c_Set_Oinsert @ SV1396 @ ( c_Set_Oinsert @ SV1472 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SV1193 ) @ SV1193 ) )
= $true )
| ( ( ( SV838 = SV1396 )
| ( SV838 = SV1472 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3345]) ).
thf(3612,plain,
! [SV1194: $i,SV839: $i,SV416: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV416 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV839 @ SV1194 @ SV416 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV839 @ SV1194 @ SV416 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV416 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3346]) ).
thf(3613,plain,
! [SV1509: $i,SV1473: $i,SV1397: $i,SV1196: $i,SV841: $i,SV418: $i] :
( ( ! [SY4084: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV418 @ SV841 @ SV1196 @ SV1397 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1473 @ SV1509 @ SY4084 @ SV1397 ) )
| ( SV1196 = SY4084 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3348]) ).
thf(3614,plain,
! [SV1474: $i,SV1398: $i,SV1197: $i,SV842: $i,SV419: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV419 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV842 @ SV1197 @ SV419 )
!= ( c_HOL_Ominus__class_Ominus @ SV1398 @ SV1474 @ SV419 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV419 ) @ SV1197 ) @ SV842 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV419 ) @ SV1474 ) @ SV1398 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3349]) ).
thf(3615,plain,
! [SV420: $i,SV1198: $i,SV843: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV843 @ SV1198 @ SV420 )
!= SV1198 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV420 ) @ SV843 ) @ SV1198 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV420 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3350]) ).
thf(3616,plain,
! [SV1510: $i,SV1475: $i,SV1399: $i,SV1199: $i,SV844: $i,SV421: $i] :
( ( ! [SY4085: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV421 @ SV844 @ SV1199 @ SV1399 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1475 @ SV1510 @ SY4085 @ SV1399 ) )
| ( SV844 = SV1510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3351]) ).
thf(3617,plain,
! [SV1400: $i,SV1200: $i,SV845: $i,SV422: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV422 @ SV845 )
= ( c_Com_Ocom_OSemi @ SV1200 @ SV1400 ) )
= $false )
| ( ( SV422 = SV1200 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3352]) ).
thf(3618,plain,
! [SV1476: $i,SV1401: $i,SV1201: $i,SV846: $i,SV423: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV423 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV846 @ SV1201 @ SV423 )
!= ( c_HOL_Ominus__class_Ominus @ SV1401 @ SV1476 @ SV423 ) )
| ( c_HOL_Oord__class_Oless @ SV1401 @ SV1476 @ SV423 )
| ~ ( c_HOL_Oord__class_Oless @ SV846 @ SV1201 @ SV423 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3353]) ).
thf(3619,plain,
! [SV424: $i,SV1202: $i,SV847: $i] :
( ( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV847 @ SV1202 @ SV424 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV424 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV847 @ SV1202 @ SV424 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV424 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3354]) ).
thf(3620,plain,
! [SV426: $i,SV1204: $i,SV849: $i] :
( ( ( hBOOL @ ( hAPP @ SV849 @ SV1204 ) )
= $false )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV426 @ tc_bool ) )
= ( c_Collect @ SV849 @ SV426 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3356]) ).
thf(3621,plain,
! [SV1477: $i,SV1402: $i,SV1205: $i,SV850: $i,SV427: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV427 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV850 @ SV1205 @ SV427 )
!= ( c_HOL_Ominus__class_Ominus @ SV1402 @ SV1477 @ SV427 ) )
| ( c_HOL_Oord__class_Oless @ SV850 @ SV1205 @ SV427 )
| ~ ( c_HOL_Oord__class_Oless @ SV1402 @ SV1477 @ SV427 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3357]) ).
thf(3622,plain,
! [SV1403: $i,SV1206: $i,SV851: $i,SV428: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV428 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV851 @ SV1206 @ SV428 )
!= ( c_HOL_Ominus__class_Ominus @ SV1403 @ SV1403 @ SV428 ) )
| ( SV851 = SV1206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3358]) ).
thf(3623,plain,
! [SV429: $i,SV1207: $i,SV852: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV852 @ SV1207 @ SV429 )
!= ( c_Orderings_Obot__class_Obot @ SV429 ) )
= $true )
| ( ( SV1207
= ( c_Orderings_Obot__class_Obot @ SV429 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV429 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3359]) ).
thf(3624,plain,
! [SV1478: $i,SV1404: $i,SV1208: $i,SV853: $i,SV430: $i] :
( ( ( ( c_Set_Oinsert @ SV430 @ ( c_Set_Oinsert @ SV853 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1208 @ tc_bool ) ) @ SV1208 ) @ SV1208 )
!= ( c_Set_Oinsert @ SV1404 @ ( c_Set_Oinsert @ SV1478 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1208 @ tc_bool ) ) @ SV1208 ) @ SV1208 ) )
= $true )
| ( ( ( SV430 = SV1478 )
| ( SV430 = SV1404 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3360]) ).
thf(3625,plain,
! [SV1209: $i,SV854: $i,SV1: $i,SV431: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV431 @ SV1 ) ) @ SV854 ) @ SV1209 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV854 @ SV1209 @ ( tc_fun @ SV431 @ SV1 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3361]) ).
thf(3626,plain,
! [SV2: $i,SV1210: $i,SV855: $i,SV432: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV432 @ SV855 @ ( tc_fun @ SV1210 @ SV2 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1210 @ SV2 ) ) @ SV855 ) @ SV432 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1210 @ SV2 ) ) @ SV432 ) @ SV855 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3362]) ).
thf(3627,plain,
! [SV1211: $i,SV856: $i,SV3: $i,SV433: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV433 @ SV3 ) ) @ SV856 ) @ SV1211 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1211 @ SV856 @ ( tc_fun @ SV433 @ SV3 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3363]) ).
thf(3628,plain,
! [SV6: $i,SV436: $i,SV859: $i] :
( ( ( c_Finite__Set_Ofinite @ SV859 @ SV436 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV436 @ tc_bool ) ) @ SV6 ) @ SV859 ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV6 @ SV436 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3366]) ).
thf(3629,plain,
! [SV7: $i,SV860: $i,SV437: $i,SV1212: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1212 @ SV437 @ ( tc_fun @ SV860 @ tc_bool ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV860 @ tc_bool ) ) @ SV7 ) @ SV1212 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV7 @ SV437 @ ( tc_fun @ SV860 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3367]) ).
thf(3630,plain,
! [SV8: $i,SV438: $i,SV1213: $i,SV861: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV861 @ tc_bool ) ) @ SV1213 ) @ SV438 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV8 @ SV1213 @ ( tc_fun @ SV861 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV8 @ SV438 @ ( tc_fun @ SV861 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3368]) ).
thf(3631,plain,
! [SV862: $i,SV9: $i,SV439: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV439 @ tc_bool ) ) @ SV9 ) @ SV862 ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV862 @ SV439 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV9 @ SV439 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3369]) ).
thf(3632,plain,
! [SV1405: $i,SV1214: $i,SV864: $i,SV441: $i,SV11: $i] :
( ( ( class_Ring__and__Field_Oring @ SV11 )
= $false )
| ( ( ( ( c_Finite__Set_Osetsum @ SV441 @ ( c_HOL_Ominus__class_Ominus @ SV864 @ ( c_Set_Oinsert @ SV1214 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1405 @ tc_bool ) ) @ SV1405 ) @ ( tc_fun @ SV1405 @ tc_bool ) ) @ SV1405 @ SV11 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV441 @ SV864 @ SV1405 @ SV11 ) @ ( hAPP @ SV441 @ SV1214 ) @ SV11 ) )
| ~ ( hBOOL @ ( c_in @ SV1214 @ SV864 @ SV1405 ) )
| ~ ( c_Finite__Set_Ofinite @ SV864 @ SV1405 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3370]) ).
thf(3633,plain,
! [SV1406: $i,SV1215: $i,SV865: $i,SV442: $i,SV12: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV12 )
= $false )
| ( ( ( ( c_Finite__Set_Osetsum @ SV442 @ ( c_HOL_Ominus__class_Ominus @ SV865 @ ( c_Set_Oinsert @ SV1215 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1406 @ tc_bool ) ) @ SV1406 ) @ ( tc_fun @ SV1406 @ tc_bool ) ) @ SV1406 @ SV12 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV442 @ SV865 @ SV1406 @ SV12 ) @ ( hAPP @ SV442 @ SV1215 ) @ SV12 ) )
| ~ ( hBOOL @ ( c_in @ SV1215 @ SV865 @ SV1406 ) )
| ~ ( c_Finite__Set_Ofinite @ SV865 @ SV1406 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3371]) ).
thf(3634,plain,
! [SV443: $i,SV866: $i,SV13: $i,SV1216: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1216 @ tc_bool ) ) @ SV13 ) @ SV866 ) )
= $false )
| ( ( ( hBOOL @ ( c_in @ SV443 @ SV13 @ SV1216 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV13 @ SV866 @ ( tc_fun @ SV1216 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV13 @ ( c_Set_Oinsert @ SV443 @ SV866 @ SV1216 ) @ ( tc_fun @ SV1216 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3372]) ).
thf(3635,plain,
! [SV444: $i,SV867: $i,SV14: $i,SV1217: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1217 @ tc_bool ) ) @ SV14 ) @ SV867 ) )
= $false )
| ( ( ( hBOOL @ ( c_in @ SV444 @ SV14 @ SV1217 ) )
| ( hBOOL @ ( c_in @ SV444 @ SV867 @ SV1217 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV14 @ ( c_Set_Oinsert @ SV444 @ SV867 @ SV1217 ) @ ( tc_fun @ SV1217 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3373]) ).
thf(3636,plain,
! [SV445: $i,SV15: $i,SV868: $i,SV1218: $i] :
( ( ( hBOOL @ ( c_in @ SV1218 @ SV868 @ SV15 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV445 @ ( c_Set_Oinsert @ SV1218 @ SV868 @ SV15 ) @ ( tc_fun @ SV15 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV1218 @ SV445 @ SV15 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV15 @ tc_bool ) ) @ SV445 ) @ SV868 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3374]) ).
thf(3637,plain,
! [SV1219: $i,SV16: $i,SV869: $i,SV446: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV446 @ SV869 @ SV16 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV869 @ SV1219 @ SV16 ) @ ( tc_fun @ SV16 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV446 @ SV1219 @ SV16 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV16 ) @ SV869 ) @ SV1219 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV16 ) @ SV446 ) @ SV869 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3375]) ).
thf(3638,plain,
! [SV1407: $i,SV23: $i,SV1222: $i,SV453: $i,SV875: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV875 @ SV453 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1222 @ tc_bool ) ) @ SV23 @ SV1222 @ SV1407 )
= $false )
| ( ( SV23 = SV453 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3376]) ).
thf(3639,plain,
! [SV876: $i,SV455: $i,SV26: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV26 ) @ SV455 ) @ SV876 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV876 @ SV455 @ SV26 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3377]) ).
thf(3640,plain,
! [SV878: $i,SV457: $i,SV28: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV28 ) @ SV457 ) @ SV878 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV878 @ SV457 @ SV28 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3379]) ).
thf(3641,plain,
! [SV30: $i,SV880: $i,SV459: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV459 @ SV880 @ SV30 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV30 ) @ SV880 ) @ SV459 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3381]) ).
thf(3642,plain,
! [SV32: $i,SV461: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV461 @ SV461 @ SV32 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV32 ) @ SV461 ) @ SV461 ) )
= $false )
| ( ( class_Orderings_Olinorder @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3382]) ).
thf(3643,plain,
! [SV463: $i,SV882: $i,SV34: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV34 ) @ SV882 ) @ SV463 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV34 ) @ SV463 ) @ SV882 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV463 @ SV882 @ SV34 )
= $true )
| ( ( class_Orderings_Opreorder @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3384]) ).
thf(3644,plain,
! [SV35: $i,SV883: $i,SV464: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV464 @ SV883 @ SV35 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV35 ) @ SV464 ) @ SV883 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3385]) ).
thf(3645,plain,
! [SV36: $i,SV884: $i,SV465: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV465 @ SV884 @ SV36 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV36 ) @ SV465 ) @ SV884 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3386]) ).
thf(3646,plain,
! [SV1223: $i,SV37: $i,SV885: $i,SV466: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV466 @ SV885 @ SV37 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV37 ) @ SV466 ) @ SV1223 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1223 @ SV885 @ SV37 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3387]) ).
thf(3647,plain,
! [SV1224: $i,SV38: $i,SV886: $i,SV467: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV467 @ SV886 @ SV38 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV467 @ SV1224 @ SV38 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV38 ) @ SV1224 ) @ SV886 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3388]) ).
thf(3648,plain,
! [SV1225: $i,SV39: $i,SV887: $i,SV468: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV468 @ SV887 @ SV39 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1225 @ SV887 @ SV39 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV39 ) @ SV468 ) @ SV1225 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3389]) ).
thf(3649,plain,
! [SV1226: $i,SV40: $i,SV888: $i,SV469: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV469 @ SV888 @ SV40 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV40 ) @ SV1226 ) @ SV888 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV469 @ SV1226 @ SV40 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3390]) ).
thf(3650,plain,
! [SV41: $i,SV470: $i,SV889: $i] :
( ( ( SV889 = SV470 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV41 ) @ SV470 ) @ SV889 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV470 @ SV889 @ SV41 )
= $true )
| ( ( class_Orderings_Oorder @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3391]) ).
thf(3651,plain,
! [SV890: $i,SV471: $i,SV42: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV42 ) @ SV471 ) @ SV890 ) ) )
= $true )
| ( ( SV890 = SV471 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV471 @ SV890 @ SV42 )
= $true )
| ( ( class_Orderings_Oorder @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3392]) ).
thf(3652,plain,
! [SV43: $i,SV891: $i,SV472: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV472 @ SV891 @ SV43 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV43 ) @ SV472 ) @ SV891 ) ) )
= $true )
| ( ( SV472 = SV891 )
= $true )
| ( ( class_Orderings_Oorder @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3393]) ).
thf(3653,plain,
! [SV44: $i,SV892: $i,SV473: $i] :
( ( ( SV473 = SV892 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV44 ) @ SV473 ) @ SV892 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV473 @ SV892 @ SV44 )
= $true )
| ( ( class_Orderings_Oorder @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3394]) ).
thf(3654,plain,
! [SV45: $i,SV893: $i,SV474: $i] :
( ( ( SV474 = SV893 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV45 ) @ SV474 ) @ SV893 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV474 @ SV893 @ SV45 )
= $true )
| ( ( class_Orderings_Oorder @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3395]) ).
thf(3655,plain,
! [SV894: $i,SV475: $i,SV46: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV46 ) @ SV475 ) @ SV894 ) ) )
= $true )
| ( ( SV475 = SV894 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV475 @ SV894 @ SV46 )
= $true )
| ( ( class_Orderings_Oorder @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3396]) ).
thf(3656,plain,
! [SV895: $i,SV476: $i,SV47: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV47 ) @ SV476 ) @ SV895 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV476 @ SV895 @ SV47 )
= $true )
| ( ( SV476 = SV895 )
= $true )
| ( ( class_Orderings_Olinorder @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3397]) ).
thf(3657,plain,
! [SV48: $i,SV896: $i,SV477: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV477 @ SV896 @ SV48 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV48 ) @ SV477 ) @ SV896 ) ) )
= $true )
| ( ( SV477 = SV896 )
= $true )
| ( ( class_Orderings_Olinorder @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3398]) ).
thf(3658,plain,
! [SV478: $i,SV49: $i,SV897: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV897 @ SV49 ) @ SV478 @ SV49 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV478 @ SV49 ) @ SV897 @ SV49 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3399]) ).
thf(3659,plain,
! [SV479: $i,SV50: $i,SV898: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV898 @ SV50 ) @ SV479 @ SV50 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV479 @ SV50 ) @ SV898 @ SV50 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3400]) ).
thf(3660,plain,
! [SV51: $i,SV480: $i,SV899: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV899 @ ( c_HOL_Ouminus__class_Ouminus @ SV480 @ SV51 ) @ SV51 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV480 @ ( c_HOL_Ouminus__class_Ouminus @ SV899 @ SV51 ) @ SV51 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3401]) ).
thf(3661,plain,
! [SV52: $i,SV481: $i,SV900: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV900 @ ( c_HOL_Ouminus__class_Ouminus @ SV481 @ SV52 ) @ SV52 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV481 @ ( c_HOL_Ouminus__class_Ouminus @ SV900 @ SV52 ) @ SV52 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3402]) ).
thf(3662,plain,
! [SV53: $i,SV1227: $i,SV901: $i,SV482: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV482 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV901 @ SV1227 @ SV53 ) @ SV53 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV482 @ SV1227 @ SV53 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3403]) ).
thf(3663,plain,
! [SV54: $i,SV1228: $i,SV902: $i,SV483: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV483 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV902 @ SV1228 @ SV54 ) @ SV54 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV483 @ SV902 @ SV54 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3404]) ).
thf(3664,plain,
! [SV1408: $i,SV1229: $i,SV903: $i,SV485: $i,SV56: $i] :
( ( ( class_Orderings_Oorder @ SV56 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV485 @ SV903 @ SV56 )
| ( c_HOL_Oord__class_Oless @ SV1229 @ SV1408 @ SV56 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV56 ) @ SV1408 ) @ SV485 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1408 @ SV485 @ SV56 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1229 @ SV903 @ SV56 ) @ ( tc_fun @ SV56 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3405]) ).
thf(3665,plain,
! [SV1511: $i,SV1479: $i,SV1409: $i,SV1230: $i,SV904: $i,SV486: $i,SV57: $i] :
( ( ! [SY4086: $i,SY4087: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV57 @ SV486 @ ( c_COMBC @ SV904 @ SV1230 @ SV1230 @ tc_bool ) @ ( c_COMBC @ SV1409 @ SV1230 @ SV1230 @ tc_bool ) @ SV1479 @ SV1511 @ SY4086 @ SY4087 @ SV1230 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV486 @ SV57 @ SV904 @ SV1409 @ SV1511 @ SV1479 @ SY4087 @ SY4086 @ SV1230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3406]) ).
thf(3666,plain,
! [SV1233: $i,SV60: $i,SV907: $i,SV489: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV489 @ SV907 @ SV60 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV489 @ SV1233 @ SV60 )
| ~ ( c_HOL_Oord__class_Oless @ SV1233 @ SV907 @ SV60 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3408]) ).
thf(3667,plain,
! [SV490: $i,SV908: $i,SV1234: $i,SV61: $i] :
( ( ( hBOOL @ ( c_in @ SV61 @ SV1234 @ SV908 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1234 @ SV490 @ ( tc_fun @ SV908 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV61 @ SV490 @ SV908 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3409]) ).
thf(3668,plain,
! [SV62: $i,SV909: $i,SV491: $i,SV1235: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1235 @ SV491 @ ( tc_fun @ SV909 @ tc_bool ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV62 @ SV1235 @ ( tc_fun @ SV909 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV62 @ SV491 @ ( tc_fun @ SV909 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3410]) ).
thf(3669,plain,
! [SV1236: $i,SV63: $i,SV910: $i,SV492: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV492 @ SV910 @ SV63 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1236 @ SV910 @ SV63 )
| ~ ( c_HOL_Oord__class_Oless @ SV492 @ SV1236 @ SV63 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3411]) ).
thf(3670,plain,
! [SV1481: $i,SV1411: $i,SV1237: $i,SV911: $i,SV493: $i,SV64: $i] :
( ( ( c_Finite__Set_Ofinite @ SV64 @ SV493 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofold__graph @ SV911 @ SV1237 @ SV64 @ SV1411 @ SV493 @ SV1481 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3412]) ).
thf(3671,plain,
! [SV67: $i,SV496: $i,SV914: $i] :
( ( ( c_Finite__Set_Ofinite @ SV914 @ SV496 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV67 @ SV914 @ ( tc_fun @ SV496 @ tc_bool ) ) @ SV496 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV67 @ SV496 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3414]) ).
thf(3672,plain,
! [SV68: $i,SV915: $i,SV497: $i] :
( ( ( c_Finite__Set_Ofinite @ SV497 @ SV915 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV68 @ SV915 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ SV68 @ SV497 @ ( tc_fun @ SV915 @ tc_bool ) ) @ SV915 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3415]) ).
thf(3673,plain,
! [SV499: $i,SV916: $i,SV70: $i] :
( ( ( c_Finite__Set_Ofinite @ SV70 @ SV916 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV499 @ SV916 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV70 @ SV499 @ ( tc_fun @ SV916 @ tc_bool ) ) @ SV916 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3416]) ).
thf(3674,plain,
! [SV500: $i,SV917: $i,SV71: $i] :
( ( ( c_Finite__Set_Ofinite @ SV71 @ SV917 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV500 @ SV917 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV71 @ SV500 @ ( tc_fun @ SV917 @ tc_bool ) ) @ SV917 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3417]) ).
thf(3675,plain,
! [SV74: $i,SV503: $i,SV920: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV920 @ SV503 @ SV74 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV503 @ SV74 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV920 @ SV74 ) @ SV74 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3418]) ).
thf(3676,plain,
! [SV504: $i,SV75: $i,SV921: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ SV921 @ SV75 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV504 @ SV75 ) @ SV75 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV504 @ SV921 @ SV75 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3419]) ).
thf(3677,plain,
! [SV1412: $i,SV1238: $i,SV922: $i,SV509: $i,SV80: $i] :
( ( ( class_Orderings_Oorder @ SV80 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV509 @ SV922 @ SV80 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1238 @ SV1412 @ SV80 ) @ ( tc_fun @ SV80 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV1238 ) @ SV1412 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV922 @ SV1412 @ SV80 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV922 ) @ SV1412 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV1238 ) @ SV509 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3420]) ).
thf(3678,plain,
! [SV1413: $i,SV1239: $i,SV923: $i,SV510: $i,SV81: $i] :
( ( ( class_Orderings_Oorder @ SV81 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV510 @ SV923 @ SV81 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1239 @ SV1413 @ SV81 ) @ ( tc_fun @ SV81 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV1239 ) @ SV1413 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1239 @ SV510 @ SV81 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV923 ) @ SV1413 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV1239 ) @ SV510 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3421]) ).
thf(3679,plain,
! [SV82: $i,SV511: $i,SV924: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV924 @ SV511 @ SV82 )
= $true )
| ( ( SV924 = SV511 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV511 @ SV924 @ SV82 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3422]) ).
thf(3680,plain,
! [SV83: $i,SV512: $i,SV925: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV925 @ SV512 @ SV83 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV512 @ SV925 @ SV83 )
= $true )
| ( ( SV512 = SV925 )
= $true )
| ( ( class_Orderings_Olinorder @ SV83 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3423]) ).
thf(3681,plain,
! [SV84: $i,SV513: $i,SV926: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV926 @ SV513 @ SV84 )
= $true )
| ( ( SV926 = SV513 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV513 @ SV926 @ SV84 )
= $true )
| ( ( class_Orderings_Olinorder @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3424]) ).
thf(3682,plain,
! [SV85: $i,SV514: $i,SV927: $i] :
( ( ( SV927 = SV514 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV927 @ SV514 @ SV85 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV514 @ SV927 @ SV85 )
= $true )
| ( ( class_Orderings_Olinorder @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3425]) ).
thf(3683,plain,
! [SV86: $i,SV928: $i,SV515: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV515 @ SV928 @ SV86 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV928 @ SV515 @ SV86 )
= $true )
| ( ( SV515 = SV928 )
= $true )
| ( ( class_Orderings_Olinorder @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3426]) ).
thf(3684,plain,
! [SV88: $i,SV930: $i,SV517: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV517 @ SV930 @ SV88 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV930 @ SV517 @ SV88 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3428]) ).
thf(3685,plain,
! [SV89: $i,SV931: $i,SV518: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV518 @ SV931 @ SV89 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV931 @ SV518 @ SV89 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3429]) ).
thf(3686,plain,
! [SV90: $i,SV932: $i,SV519: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV519 @ SV932 @ SV90 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV932 @ SV519 @ SV90 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3430]) ).
thf(3687,plain,
! [SV91: $i,SV933: $i,SV520: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV520 @ SV933 @ SV91 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV933 @ SV520 @ SV91 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3431]) ).
thf(3688,plain,
! [SV1414: $i,SV1240: $i,SV934: $i,SV521: $i,SV92: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV92 )
= $false )
| ( ( ( ( c_Finite__Set_Osetsum @ SV521 @ ( c_HOL_Ominus__class_Ominus @ SV934 @ SV1240 @ ( tc_fun @ SV1414 @ tc_bool ) ) @ SV1414 @ SV92 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV521 @ SV934 @ SV1414 @ SV92 ) @ ( c_Finite__Set_Osetsum @ SV521 @ SV1240 @ SV1414 @ SV92 ) @ SV92 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1414 @ tc_bool ) ) @ SV1240 ) @ SV934 ) )
| ~ ( c_Finite__Set_Ofinite @ SV934 @ SV1414 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3432]) ).
thf(3689,plain,
! [SV522: $i,SV935: $i,SV93: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV93 ) @ SV935 ) @ SV522 ) )
= $false )
| ( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV522 @ SV935 @ SV93 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV93 @ tc_bool ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3433]) ).
thf(3690,plain,
! [SV1512: $i,SV1482: $i,SV1415: $i,SV1241: $i,SV936: $i,SV523: $i,SV94: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV94 @ SV523 @ ( c_Set_Oinsert @ SV936 @ SV1241 @ SV1415 ) @ ( hAPP @ ( hAPP @ SV94 @ SV936 ) @ SV1482 ) @ SV1415 @ SV1512 )
| ~ ( c_Finite__Set_Ofold__graph @ SV94 @ SV523 @ SV1241 @ SV1482 @ SV1415 @ SV1512 )
| ( hBOOL @ ( c_in @ SV936 @ SV1241 @ SV1415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3434]) ).
thf(3691,plain,
! [SV95: $i,SV937: $i,SV524: $i,SV1242: $i] :
( ( ( hBOOL @ ( c_in @ SV1242 @ SV524 @ SV937 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV95 @ ( c_Set_Oinsert @ SV1242 @ SV524 @ SV937 ) @ ( tc_fun @ SV937 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV95 @ SV524 @ ( tc_fun @ SV937 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3435]) ).
thf(3692,plain,
! [SV96: $i,SV1243: $i,SV938: $i,SV525: $i] :
( ( ( hBOOL @ ( c_in @ SV525 @ SV938 @ SV1243 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV96 @ SV938 @ ( tc_fun @ SV1243 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV96 @ ( c_Set_Oinsert @ SV525 @ SV938 @ SV1243 ) @ ( tc_fun @ SV1243 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3436]) ).
thf(3693,plain,
! [SV1416: $i,SV1244: $i,SV939: $i,SV526: $i,SV97: $i] :
( ( ( class_Orderings_Oorder @ SV97 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV97 ) @ SV526 ) @ SV939 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV97 ) @ SV1244 ) @ SV526 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1244 @ SV526 @ SV97 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1416 @ SV939 @ SV97 ) @ ( tc_fun @ SV97 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3437]) ).
thf(3694,plain,
! [SV1417: $i,SV1245: $i,SV940: $i,SV527: $i,SV98: $i] :
( ( ( class_Orderings_Oorder @ SV98 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV98 ) @ SV527 ) @ SV940 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV98 ) @ SV940 ) @ SV1245 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV940 @ SV1245 @ SV98 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV527 @ SV1417 @ SV98 ) @ ( tc_fun @ SV98 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3438]) ).
thf(3695,plain,
! [SV1418: $i,SV1246: $i,SV941: $i,SV528: $i,SV99: $i] :
( ( ( class_Orderings_Oorder @ SV99 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV99 ) @ SV528 ) @ SV941 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1246 @ SV1418 @ SV99 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV528 @ SV941 @ SV99 ) @ ( tc_fun @ SV99 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3439]) ).
thf(3696,plain,
! [SV1419: $i,SV1247: $i,SV942: $i,SV529: $i,SV100: $i] :
( ( ( class_Orderings_Oorder @ SV100 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV529 @ SV942 @ SV100 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1247 @ SV1419 @ SV100 ) @ ( tc_fun @ SV100 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV100 ) @ SV1247 ) @ SV1419 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV100 ) @ SV529 ) @ SV942 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3440]) ).
thf(3697,plain,
! [SV1248: $i,SV101: $i,SV943: $i,SV530: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV530 @ SV943 @ SV101 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV943 @ SV1248 @ SV101 ) @ ( tc_fun @ SV101 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV530 @ SV1248 @ SV101 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV101 ) @ SV943 ) @ SV1248 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV101 ) @ SV530 ) @ SV943 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3441]) ).
thf(3698,plain,
! [SV944: $i,SV102: $i,SV1420: $i,SV1249: $i,SV531: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV531 @ SV1249 @ SV1420 ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1249 @ SV102 @ SV1420 @ ( tc_fun @ SV944 @ tc_bool ) ) @ SV944 )
| ~ ( c_Finite__Set_Ofinite @ SV1249 @ SV1420 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ SV102 @ SV531 ) @ SV944 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3442]) ).
thf(3699,plain,
! [SV1421: $i,SV1250: $i,SV945: $i,SV532: $i,SV103: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV103 )
= $false )
| ( ( ( ( c_Finite__Set_Osetsum @ SV532 @ ( c_HOL_Ominus__class_Ominus @ SV945 @ ( c_Set_Oinsert @ SV1250 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1421 @ tc_bool ) ) @ SV1421 ) @ ( tc_fun @ SV1421 @ tc_bool ) ) @ SV1421 @ SV103 )
= ( c_Finite__Set_Osetsum @ SV532 @ SV945 @ SV1421 @ SV103 ) )
| ( hBOOL @ ( c_in @ SV1250 @ SV945 @ SV1421 ) )
| ~ ( c_Finite__Set_Ofinite @ SV945 @ SV1421 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3443]) ).
thf(3700,plain,
! [SV104: $i,SV533: $i,SV946: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV946 @ SV533 @ SV104 )
= $false )
| ( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV533 @ SV946 @ SV104 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV104 @ tc_bool ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3444]) ).
thf(3701,plain,
! [SV1251: $i,SV105: $i,SV947: $i,SV534: $i] :
( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV534 @ ( c_COMBK @ SV947 @ SV105 @ SV1251 ) @ SV1251 @ SV105 )
= SV947 )
= $true )
| ( ( SV534
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1251 @ tc_bool ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV105 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3445]) ).
thf(3702,plain,
! [SV114: $i,SV955: $i,SV542: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV542 @ SV955 @ SV114 ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV955 @ SV114 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV114 ) @ SV542 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV955 @ SV114 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3450]) ).
thf(3703,plain,
! [SV115: $i,SV543: $i,SV956: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV956 @ SV543 @ SV115 ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV543 @ SV115 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV115 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV543 @ SV115 ) ) @ SV956 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3451]) ).
thf(3704,plain,
! [SV116: $i,SV544: $i] :
( ( ( c_Finite__Set_Ofinite @ SV544 @ SV116 )
= $false )
| ( ( SV544
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV116 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMin @ SV544 @ SV116 ) @ SV544 @ SV116 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3452]) ).
thf(3705,plain,
! [SV117: $i,SV545: $i] :
( ( ( c_Finite__Set_Ofinite @ SV545 @ SV117 )
= $false )
| ( ( SV545
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV117 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMax @ SV545 @ SV117 ) @ SV545 @ SV117 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3453]) ).
thf(3706,plain,
! [SV1422: $i,SV118: $i,SV1255: $i,SV957: $i,SV546: $i] :
( ( ( hBOOL @ ( c_in @ SV546 @ SV957 @ SV1255 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofold__graph @ SV118 @ SV546 @ SV957 @ SV1422 @ SV1255 @ SV1255 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV118 @ ( c_Set_Oinsert @ SV546 @ SV957 @ SV1255 ) @ SV1255 ) @ SV1422 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3454]) ).
thf(3707,plain,
! [SV1513: $i,SV1483: $i,SV1423: $i,SV1256: $i,SV958: $i,SV547: $i,SV119: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV119 @ SV547 @ SV958 @ ( hAPP @ ( hAPP @ SV119 @ SV1256 ) @ SV1423 ) @ SV1483 @ SV1513 )
| ~ ( hBOOL @ ( c_in @ SV1256 @ SV958 @ SV1483 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV119 @ SV547 @ ( c_HOL_Ominus__class_Ominus @ SV958 @ ( c_Set_Oinsert @ SV1256 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1483 @ tc_bool ) ) @ SV1483 ) @ ( tc_fun @ SV1483 @ tc_bool ) ) @ SV1423 @ SV1483 @ SV1513 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3455]) ).
thf(3708,plain,
! [SV960: $i,SV1258: $i,SV121: $i,SV549: $i] :
( ( ( hBOOL @ ( c_in @ SV549 @ SV121 @ SV1258 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV121 @ ( c_Set_Oinsert @ SV549 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1258 @ tc_bool ) ) @ SV1258 ) @ ( tc_fun @ SV1258 @ tc_bool ) ) @ SV960 @ ( tc_fun @ SV1258 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV121 @ SV960 @ ( tc_fun @ SV1258 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV121 @ ( c_Set_Oinsert @ SV549 @ SV960 @ SV1258 ) @ ( tc_fun @ SV1258 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3456]) ).
thf(3709,plain,
! [SV961: $i,SV1259: $i,SV122: $i,SV550: $i] :
( ( ( hBOOL @ ( c_in @ SV550 @ SV122 @ SV1259 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV122 @ ( c_Set_Oinsert @ SV550 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1259 @ tc_bool ) ) @ SV1259 ) @ ( tc_fun @ SV1259 @ tc_bool ) ) @ SV961 @ ( tc_fun @ SV1259 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SV550 @ SV961 @ SV1259 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV122 @ ( c_Set_Oinsert @ SV550 @ SV961 @ SV1259 ) @ ( tc_fun @ SV1259 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3457]) ).
thf(3710,plain,
! [SV1260: $i,SV962: $i,SV123: $i,SV551: $i] :
( ( ( hBOOL @ ( c_in @ SV551 @ SV123 @ SV962 ) )
= $false )
| ( ( ( hBOOL @ ( c_in @ SV551 @ SV1260 @ SV962 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV123 @ ( c_Set_Oinsert @ SV551 @ SV1260 @ SV962 ) @ ( tc_fun @ SV962 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV123 @ ( c_Set_Oinsert @ SV551 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV962 @ tc_bool ) ) @ SV962 ) @ ( tc_fun @ SV962 @ tc_bool ) ) @ SV1260 @ ( tc_fun @ SV962 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3458]) ).
thf(3711,plain,
! [SV1514: $i,SV1484: $i,SV1424: $i,SV1261: $i,SV963: $i,SV552: $i,SV124: $i] :
( ( ( c_Nitpick_Ofold__graph_H @ SV124 @ SV552 @ SV963 @ ( hAPP @ ( hAPP @ SV124 @ SV1261 ) @ SV1424 ) @ SV1484 @ SV1514 )
| ~ ( c_Nitpick_Ofold__graph_H @ SV124 @ SV552 @ ( c_HOL_Ominus__class_Ominus @ SV963 @ ( c_Set_Oinsert @ SV1261 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1484 @ tc_bool ) ) @ SV1484 ) @ ( tc_fun @ SV1484 @ tc_bool ) ) @ SV1424 @ SV1484 @ SV1514 )
| ~ ( hBOOL @ ( c_in @ SV1261 @ SV963 @ SV1484 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3459]) ).
thf(3712,plain,
! [SV553: $i,SV964: $i,SV125: $i,SV1262: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1262 @ tc_bool ) ) @ SV125 ) @ SV964 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV125 @ ( c_Set_Oinsert @ SV553 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1262 @ tc_bool ) ) @ SV1262 ) @ ( tc_fun @ SV1262 @ tc_bool ) ) @ SV964 @ ( tc_fun @ SV1262 @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ SV125 @ SV964 @ ( tc_fun @ SV1262 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV125 @ ( c_Set_Oinsert @ SV553 @ SV964 @ SV1262 ) @ ( tc_fun @ SV1262 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3460]) ).
thf(3713,plain,
! [SV965: $i,SV126: $i,SV554: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV554 @ SV126 ) )
= $true )
| ( ( ( SV965
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV126 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV126 @ tc_bool ) ) @ SV965 ) @ SV554 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV126 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV554 @ SV126 ) ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV965 @ SV126 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV126 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3461]) ).
thf(3714,plain,
! [SV555: $i,SV127: $i,SV966: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ SV966 @ SV127 ) )
= $true )
| ( ( ( SV555
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV127 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV127 @ tc_bool ) ) @ SV555 ) @ SV966 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV127 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV555 @ SV127 ) ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV966 @ SV127 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3462]) ).
thf(3715,plain,
! [SV968: $i,SV557: $i,SV129: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV129 ) @ SV557 ) @ SV968 ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV557 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV129 @ tc_bool ) ) @ SV129 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV557 @ SV968 @ SV129 ) @ ( tc_fun @ SV129 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV557 @ SV968 @ SV129 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3464]) ).
thf(3716,plain,
! [SV558: $i,SV969: $i,SV130: $i,SV1264: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1264 @ tc_bool ) ) @ SV130 ) @ SV969 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV130 @ ( c_Set_Oinsert @ SV558 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1264 @ tc_bool ) ) @ SV1264 ) @ ( tc_fun @ SV1264 @ tc_bool ) ) @ SV969 @ ( tc_fun @ SV1264 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SV558 @ SV969 @ SV1264 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV130 @ ( c_Set_Oinsert @ SV558 @ SV969 @ SV1264 ) @ ( tc_fun @ SV1264 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3465]) ).
thf(3717,plain,
! [SV1265: $i,SV970: $i,SV559: $i,SV131: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV559 @ SV970 @ SV131 ) ) @ SV1265 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ SV970 ) @ SV1265 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ SV559 ) @ SV1265 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3466]) ).
thf(3718,plain,
! [SV1266: $i,SV971: $i,SV560: $i,SV132: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV560 @ SV971 @ SV132 ) ) @ SV1266 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ SV971 ) @ SV1266 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ SV560 ) @ SV1266 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV132 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3467]) ).
thf(3719,plain,
! [SV563: $i,SV974: $i,SV135: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV135 ) @ SV974 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV563 @ SV135 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV135 ) @ SV563 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV974 @ SV135 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV135 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3468]) ).
thf(3720,plain,
! [SV564: $i,SV975: $i,SV136: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV136 ) @ SV975 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV564 @ SV136 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV136 ) @ SV564 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV975 @ SV136 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3469]) ).
thf(3721,plain,
! [SV565: $i,SV976: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV137 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV976 @ SV137 ) ) @ SV565 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV137 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV565 @ SV137 ) ) @ SV976 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3470]) ).
thf(3722,plain,
! [SV566: $i,SV977: $i,SV138: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV138 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV977 @ SV138 ) ) @ SV566 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV138 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV566 @ SV138 ) ) @ SV977 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3471]) ).
thf(3723,plain,
! [SV978: $i,SV567: $i,SV139: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV139 ) @ SV567 ) @ SV978 ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV567 @ SV978 @ SV139 ) @ ( c_Set_Oinsert @ SV978 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV139 @ tc_bool ) ) @ SV139 ) @ ( tc_fun @ SV139 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV567 @ SV978 @ SV139 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3472]) ).
thf(3724,plain,
! [SV1515: $i,SV1485: $i,SV1425: $i,SV1267: $i,SV979: $i,SV570: $i,SV143: $i] :
( ( ! [SY4088: $i,SY4089: $i] :
( ( ( hAPP @ SV143 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV570 @ tc_bool ) ) )
= SV979 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV143 @ SV1267 @ SV1425 @ SV1485 @ SV1515 @ SY4088 @ SY4089 @ SV979 @ SV570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3473]) ).
thf(3725,plain,
! [SV1516: $i,SV1486: $i,SV1426: $i,SV1268: $i,SV980: $i,SV571: $i,SV144: $i] :
( ( ! [SY4090: $i,SY4091: $i] :
( ( ( hAPP @ SV144 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV571 @ tc_bool ) ) )
= SV980 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1268 @ SV144 @ SV1426 @ SV1486 @ SV1516 @ SY4090 @ SV980 @ SY4091 @ SV571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3474]) ).
thf(3726,plain,
! [SV1517: $i,SV1487: $i,SV1427: $i,SV1271: $i,SV989: $i,SV588: $i,SV161: $i] :
( ( ! [SY4092: $i,SY4093: $i,SY4094: $i,SY4095: $i] :
( ( ( hAPP @ SV161 @ ( c_Set_Oinsert @ SV588 @ SV989 @ SV1271 ) )
= ( hAPP @ ( hAPP @ SV1427 @ SV588 ) @ ( hAPP @ SV161 @ SV989 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV161 @ SV1487 @ SV1517 @ SY4092 @ SV1427 @ SY4093 @ SY4094 @ SY4095 @ SV1271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3478]) ).
thf(3727,plain,
! [SV1518: $i,SV1488: $i,SV1428: $i,SV1272: $i,SV990: $i,SV589: $i,SV162: $i] :
( ( ! [SY4096: $i,SY4097: $i,SY4098: $i,SY4099: $i] :
( ( ( hAPP @ SV162 @ ( c_Set_Oinsert @ SV589 @ SV990 @ SV1272 ) )
= ( hAPP @ ( hAPP @ SV1428 @ SV589 ) @ ( hAPP @ SV162 @ SV990 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1488 @ SV162 @ SV1518 @ SY4096 @ SY4097 @ SV1428 @ SY4098 @ SY4099 @ SV1272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3479]) ).
thf(3728,plain,
! [SV991: $i,SV590: $i,SV1273: $i,SV163: $i] :
( ( ( hBOOL @ ( c_in @ SV163 @ ( c_Set_Oinsert @ SV1273 @ SV590 @ SV991 ) @ SV991 ) )
= $false )
| ( ( SV163 = SV1273 )
= $true )
| ( ( hBOOL @ ( c_in @ SV163 @ SV590 @ SV991 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3480]) ).
thf(3729,plain,
! [SV998: $i,SV597: $i,SV170: $i,SV1276: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV170 ) @ SV597 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV998 ) @ SV170 ) ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV170 @ ( c_HOL_Ominus__class_Ominus @ SV597 @ SV998 @ ( tc_fun @ SV1276 @ tc_bool ) ) @ ( tc_fun @ SV1276 @ tc_bool ) )
= SV998 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3481]) ).
thf(3730,plain,
! [SV598: $i,SV999: $i,SV1277: $i,SV171: $i] :
( ( ( hBOOL @ ( c_in @ SV171 @ SV1277 @ SV999 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV999 @ tc_bool ) ) @ SV1277 ) @ SV598 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV171 @ SV598 @ SV999 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3482]) ).
thf(3731,plain,
! [SV172: $i,SV599: $i,SV1278: $i,SV1000: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1000 @ tc_bool ) ) @ SV1278 ) @ SV599 ) )
= $false )
| ( ( ~ ( hBOOL @ ( c_in @ SV172 @ SV1278 @ SV1000 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV172 @ SV599 @ SV1000 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3483]) ).
thf(3732,plain,
! [SV600: $i,SV1001: $i,SV1279: $i,SV173: $i] :
( ( ( hBOOL @ ( c_in @ SV173 @ SV1279 @ SV1001 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1001 @ tc_bool ) ) @ SV1279 ) @ SV600 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV173 @ SV600 @ SV1001 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3484]) ).
thf(3733,plain,
! [SV601: $i,SV1002: $i,SV1280: $i,SV174: $i] :
( ( ( hBOOL @ ( c_in @ SV174 @ SV1280 @ SV1002 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1002 @ tc_bool ) ) @ SV1280 ) @ SV601 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV174 @ SV601 @ SV1002 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3485]) ).
thf(3734,plain,
! [SV1283: $i,SV604: $i,SV1429: $i,SV1005: $i,SV177: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ SV1005 ) @ SV1429 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ SV604 ) @ SV1283 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV604 @ SV1005 @ ( tc_fun @ SV177 @ tc_bool ) ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1283 @ SV1429 @ ( tc_fun @ SV177 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3488]) ).
thf(3735,plain,
! [SV1284: $i,SV607: $i,SV1008: $i,SV1430: $i,SV180: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ SV1430 ) @ SV1008 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ SV607 ) @ SV1284 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV607 @ SV1008 @ ( tc_fun @ SV180 @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1284 @ SV1430 @ ( tc_fun @ SV180 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3489]) ).
thf(3736,plain,
! [SV611: $i,SV1285: $i,SV1012: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV184 @ tc_bool ) ) @ SV1012 ) @ SV1285 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV184 @ tc_bool ) ) @ SV611 ) @ SV1285 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV184 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV611 @ SV1012 @ ( tc_fun @ SV184 @ tc_bool ) ) ) @ SV1285 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3490]) ).
thf(3737,plain,
! [SV614: $i,SV1286: $i,SV1015: $i,SV187: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV187 @ tc_bool ) ) @ SV1015 ) @ SV1286 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV187 @ tc_bool ) ) @ SV614 ) @ SV1286 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV187 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV614 @ SV1015 @ ( tc_fun @ SV187 @ tc_bool ) ) ) @ SV1286 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3491]) ).
thf(3738,plain,
! [SV1287: $i,SV189: $i,SV616: $i,SV1017: $i] :
( ( ( hBOOL @ ( c_in @ SV1017 @ SV616 @ SV189 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV189 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV616 @ ( c_Set_Oinsert @ SV1017 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV189 @ tc_bool ) ) @ SV189 ) @ ( tc_fun @ SV189 @ tc_bool ) ) ) @ SV1287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV189 @ tc_bool ) ) @ SV616 ) @ ( c_Set_Oinsert @ SV1017 @ SV1287 @ SV189 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3492]) ).
thf(3739,plain,
! [SV1288: $i,SV190: $i,SV617: $i,SV1018: $i] :
( ( ( hBOOL @ ( c_in @ SV1018 @ SV617 @ SV190 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV190 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV617 @ ( c_Set_Oinsert @ SV1018 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV190 @ tc_bool ) ) @ SV190 ) @ ( tc_fun @ SV190 @ tc_bool ) ) ) @ SV1288 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV190 @ tc_bool ) ) @ SV617 ) @ ( c_Set_Oinsert @ SV1018 @ SV1288 @ SV190 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3493]) ).
thf(3740,plain,
! [SV1289: $i,SV191: $i,SV618: $i,SV1019: $i] :
( ( ( hBOOL @ ( c_in @ SV1019 @ SV618 @ SV191 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV191 @ tc_bool ) ) @ SV618 ) @ ( c_Set_Oinsert @ SV1019 @ SV1289 @ SV191 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV191 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV618 @ ( c_Set_Oinsert @ SV1019 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV191 @ tc_bool ) ) @ SV191 ) @ ( tc_fun @ SV191 @ tc_bool ) ) ) @ SV1289 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3494]) ).
thf(3741,plain,
! [SV621: $i,SV1022: $i,SV194: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV194 ) @ SV1022 ) @ SV621 ) )
= $false )
| ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ SV621 @ SV1022 @ SV194 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV194 @ tc_bool ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3497]) ).
thf(3742,plain,
! [SV1431: $i,SV1290: $i,SV1023: $i,SV622: $i,SV195: $i] :
( ( ( class_Orderings_Oorder @ SV195 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV195 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV622 @ SV1023 @ SV195 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1290 @ SV1431 @ SV195 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV195 ) @ SV622 ) @ SV1023 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3498]) ).
thf(3743,plain,
! [SV1432: $i,SV1291: $i,SV1024: $i,SV623: $i,SV196: $i] :
( ( ( class_Orderings_Oorder @ SV196 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV196 ) @ SV623 ) @ SV1024 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV196 ) @ SV1024 ) @ SV1291 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV196 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1024 @ SV1291 @ SV196 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV623 @ SV1432 @ SV196 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3499]) ).
thf(3744,plain,
! [SV1433: $i,SV1292: $i,SV1025: $i,SV624: $i,SV197: $i] :
( ( ( class_Orderings_Oorder @ SV197 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV197 ) @ SV624 ) @ SV1025 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV197 ) @ SV1292 ) @ SV624 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV197 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1292 @ SV624 @ SV197 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1433 @ SV1025 @ SV197 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3500]) ).
thf(3745,plain,
! [SV1434: $i,SV1293: $i,SV1026: $i,SV625: $i,SV198: $i] :
( ( ( class_Orderings_Oorder @ SV198 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV198 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV625 @ SV1026 @ SV198 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1293 @ SV1434 @ SV198 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV198 ) @ SV1026 ) @ SV1434 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV198 ) @ SV1293 ) @ SV625 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3501]) ).
thf(3746,plain,
! [SV1435: $i,SV1294: $i,SV1027: $i,SV626: $i,SV199: $i] :
( ( ( class_Orderings_Olinorder @ SV199 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV199 ) @ SV626 ) @ SV1027 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV199 ) @ SV1294 ) @ SV1027 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV199 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1027 @ SV1294 @ SV199 ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV626 @ SV1435 @ SV199 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3502]) ).
thf(3747,plain,
! [SV1295: $i,SV1030: $i,SV629: $i,SV202: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV629 @ SV1030 @ SV202 ) ) @ SV1295 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ SV1030 ) @ SV1295 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ SV629 ) @ SV1295 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV202 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3503]) ).
thf(3748,plain,
! [SV630: $i,SV1031: $i,SV203: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV203 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV1031 @ SV203 ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV630 @ SV203 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV203 ) @ SV630 ) @ SV1031 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3504]) ).
thf(3749,plain,
! [SV631: $i,SV1032: $i,SV204: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV204 ) @ SV1032 ) @ SV631 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV204 ) @ ( c_HOL_Ouminus__class_Ouminus @ SV631 @ SV204 ) ) @ ( c_HOL_Ouminus__class_Ouminus @ SV1032 @ SV204 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3505]) ).
thf(3750,plain,
! [SV632: $i,SV1033: $i,SV205: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV205 ) @ SV1033 ) @ SV632 ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV632 @ SV1033 @ SV205 )
= SV632 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3506]) ).
thf(3751,plain,
! [SV1034: $i,SV633: $i,SV206: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV206 ) @ SV633 ) @ SV1034 ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV633 @ SV1034 @ SV206 )
= SV1034 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3507]) ).
thf(3752,plain,
! [SV1296: $i,SV1035: $i,SV634: $i,SV207: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV207 ) @ SV634 ) @ SV1035 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV207 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1296 @ SV634 @ SV207 ) ) @ SV1035 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV207 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3508]) ).
thf(3753,plain,
! [SV1297: $i,SV1036: $i,SV635: $i,SV208: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV208 ) @ SV635 ) @ SV1036 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV208 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV635 @ SV1297 @ SV208 ) ) @ SV1036 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV208 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3509]) ).
thf(3754,plain,
! [SV1298: $i,SV1037: $i,SV636: $i,SV209: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV209 ) @ SV636 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1037 @ SV1298 @ SV209 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV209 ) @ SV636 ) @ SV1298 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV209 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3510]) ).
thf(3755,plain,
! [SV1299: $i,SV1038: $i,SV637: $i,SV210: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV210 ) @ SV637 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1038 @ SV1299 @ SV210 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV210 ) @ SV637 ) @ SV1038 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3511]) ).
thf(3756,plain,
! [SV1300: $i,SV1039: $i,SV638: $i,SV211: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV211 ) @ SV638 ) @ SV1039 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV211 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1300 @ SV638 @ SV211 ) ) @ SV1039 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3512]) ).
thf(3757,plain,
! [SV1301: $i,SV1040: $i,SV639: $i,SV212: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV212 ) @ SV639 ) @ SV1040 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV212 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV639 @ SV1301 @ SV212 ) ) @ SV1040 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3513]) ).
thf(3758,plain,
! [SV1489: $i,SV1436: $i,SV1305: $i,SV1045: $i,SV650: $i,SV223: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV223 @ SV650 @ SV1045 @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1436 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV650 @ SV1489 ) @ SV1436 ) )
| ~ ( hBOOL @ ( c_in @ SV1489 @ SV223 @ SV1045 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3516]) ).
thf(3759,plain,
! [SV1490: $i,SV1437: $i,SV1306: $i,SV1046: $i,SV651: $i,SV224: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV224 @ SV651 @ SV1046 @ ( tc_fun @ SV1306 @ tc_bool ) ) @ SV1437 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV651 @ SV1490 ) @ SV1437 ) )
| ~ ( hBOOL @ ( c_in @ SV1490 @ SV224 @ SV1046 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3517]) ).
thf(3760,plain,
! [SV1519: $i,SV1491: $i,SV1438: $i,SV1307: $i,SV1053: $i,SV658: $i,SV231: $i] :
( ( ! [SY4100: $i,SY4101: $i,SY4102: $i,SY4103: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV231 @ SV658 ) @ ( hAPP @ SV1053 @ SV1307 ) ) )
| ~ ( hBOOL @ ( c_in @ SV658 @ SV1307 @ SV1438 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1491 @ SV1053 @ SV231 @ SV1519 @ SY4100 @ SY4101 @ SY4102 @ SY4103 @ SV1438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3518]) ).
thf(3761,plain,
! [SV1520: $i,SV1492: $i,SV1439: $i,SV1308: $i,SV1054: $i,SV659: $i,SV232: $i] :
( ( ! [SY4104: $i,SY4105: $i,SY4106: $i,SY4107: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ ( hAPP @ SV659 @ SV1054 ) ) @ SV1308 ) )
| ~ ( hBOOL @ ( c_in @ SV1308 @ SV1054 @ SV1439 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV659 @ SV1492 @ SV232 @ SV1520 @ SY4104 @ SY4105 @ SY4106 @ SY4107 @ SV1439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3519]) ).
thf(3762,plain,
! [SV1493: $i,SV1440: $i,SV1310: $i,SV1059: $i,SV664: $i,SV237: $i] :
( ( ( hBOOL @ ( c_in @ SV237 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV664 @ SV1059 @ SV1310 @ ( tc_fun @ SV1440 @ tc_bool ) ) @ SV1440 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV237 @ ( hAPP @ SV1059 @ SV1493 ) @ SV1440 ) )
| ~ ( hBOOL @ ( c_in @ SV1493 @ SV664 @ SV1310 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3520]) ).
thf(3763,plain,
! [SV1494: $i,SV1441: $i,SV1311: $i,SV1060: $i,SV665: $i,SV238: $i] :
( ( ( hBOOL @ ( c_in @ SV238 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV665 @ SV1060 @ SV1311 @ ( tc_fun @ SV1441 @ tc_bool ) ) @ SV1441 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV238 @ ( hAPP @ SV1060 @ SV1494 ) @ SV1441 ) )
| ~ ( hBOOL @ ( c_in @ SV1494 @ SV665 @ SV1311 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3521]) ).
thf(3764,plain,
! [SV1061: $i,SV1312: $i,SV666: $i,SV239: $i] :
( ( ( hBOOL @ ( c_in @ SV239 @ SV666 @ SV1312 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV239 @ SV1061 @ SV1312 ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV239 @ ( c_HOL_Ominus__class_Ominus @ SV666 @ SV1061 @ ( tc_fun @ SV1312 @ tc_bool ) ) @ SV1312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3522]) ).
thf(3765,plain,
! [SV1062: $i,SV1313: $i,SV667: $i,SV240: $i] :
( ( ( hBOOL @ ( c_in @ SV240 @ SV667 @ SV1313 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV240 @ SV1062 @ SV1313 ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV240 @ ( c_HOL_Ominus__class_Ominus @ SV667 @ SV1062 @ ( tc_fun @ SV1313 @ tc_bool ) ) @ SV1313 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3523]) ).
thf(3766,plain,
! [SV1442: $i,SV1321: $i,SV1078: $i,SV685: $i,SV258: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV258 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV258 ) @ ( hAPP @ SV685 @ SV1078 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1321 @ SV685 @ SV1442 @ SV258 ) ) )
| ~ ( hBOOL @ ( c_in @ SV1078 @ SV1321 @ SV1442 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3528]) ).
thf(3767,plain,
! [SV686: $i,SV259: $i,SV1443: $i,SV1322: $i,SV1079: $i] :
( ( ( hBOOL @ ( c_in @ SV1079 @ SV1322 @ SV1443 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV259 @ tc_bool ) ) @ ( hAPP @ SV686 @ SV1079 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1322 @ SV686 @ SV1443 @ ( tc_fun @ SV259 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3529]) ).
thf(3768,plain,
! [SV1086: $i,SV694: $i,SV1325: $i,SV267: $i] :
( ( ( hBOOL @ ( c_in @ SV267 @ ( c_HOL_Ominus__class_Ominus @ SV1325 @ SV694 @ ( tc_fun @ SV1086 @ tc_bool ) ) @ SV1086 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV267 @ SV694 @ SV1086 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3533]) ).
thf(3769,plain,
! [SV1495: $i,SV1444: $i,SV1326: $i,SV1087: $i,SV695: $i,SV268: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV268 @ tc_bool ) ) @ ( hAPP @ SV695 @ SV1087 ) ) @ SV1326 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1087 @ SV1444 @ SV1495 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV268 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1444 @ SV695 @ SV1495 @ ( tc_fun @ SV268 @ tc_bool ) ) ) @ SV1326 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3534]) ).
thf(3770,plain,
! [SV1445: $i,SV269: $i,SV1327: $i,SV1088: $i,SV696: $i] :
( ( ( hBOOL @ ( c_in @ SV696 @ SV1088 @ SV1327 ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV269 @ SV696 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1088 @ SV269 @ SV1327 @ ( tc_fun @ SV1445 @ tc_bool ) ) @ ( tc_fun @ SV1445 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1088 @ SV269 @ SV1327 @ ( tc_fun @ SV1445 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3535]) ).
thf(3771,plain,
! [SV697: $i,SV1328: $i,SV270: $i,SV1089: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1089 @ SV270 @ ( tc_fun @ SV1328 @ tc_bool ) ) @ SV697 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1089 @ SV697 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV270 @ SV697 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3536]) ).
thf(3772,plain,
! [SV1092: $i,SV700: $i,SV1331: $i,SV273: $i] :
( ( ( hBOOL @ ( c_in @ SV273 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1331 @ SV700 @ ( tc_fun @ SV1092 @ tc_bool ) ) @ SV1092 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV273 @ SV1331 @ SV1092 ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV273 @ SV700 @ SV1092 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3539]) ).
thf(3773,plain,
! [SV1332: $i,SV274: $i,SV1093: $i,SV701: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV701 @ SV1093 @ SV274 ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1093 @ SV1332 @ SV274 ) @ ( tc_fun @ SV274 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV701 @ SV1332 @ SV274 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV274 ) @ SV1093 ) @ SV1332 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV274 ) @ SV701 ) @ SV1093 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV274 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3540]) ).
thf(3774,plain,
! [SV1335: $i,SV277: $i,SV1096: $i,SV704: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV704 @ SV1096 @ SV277 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1096 @ SV1335 @ SV277 ) @ ( tc_fun @ SV277 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV704 @ SV1335 @ SV277 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV277 ) @ SV1096 ) @ SV1335 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV277 ) @ SV704 ) @ SV1096 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV277 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3541]) ).
thf(3775,plain,
! [SV279: $i,SV706: $i,SV1098: $i] :
( ( ( hBOOL @ ( c_in @ SV1098 @ SV706 @ SV279 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV279 ) @ ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ SV279 ) @ SV706 ) ) @ SV1098 ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3542]) ).
thf(3776,plain,
! [SV1339: $i,SV283: $i,SV1101: $i,SV710: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV710 @ SV1101 @ SV283 ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV710 @ SV1339 @ SV283 ) @ ( tc_fun @ SV283 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1339 @ SV1101 @ SV283 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV283 ) @ SV710 ) @ SV1339 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3545]) ).
thf(3777,plain,
! [SV286: $i,SV1103: $i,SV713: $i] :
( ( ( hBOOL @ ( c_in @ SV713 @ SV1103 @ SV286 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV286 ) @ SV713 ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ SV286 ) @ SV1103 ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV286 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3546]) ).
thf(3778,plain,
! [SV1448: $i,SV1341: $i,SV1104: $i,SV714: $i,SV287: $i] :
( ( ( class_Orderings_Olinorder @ SV287 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV287 ) @ SV714 ) @ SV1104 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV287 ) @ SV714 ) @ SV1341 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV287 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1341 @ SV714 @ SV287 ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1448 @ SV1104 @ SV287 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3547]) ).
thf(3779,plain,
! [SV1521: $i,SV1496: $i,SV1449: $i,SV1342: $i,SV1105: $i,SV717: $i,SV292: $i] :
( ( ! [SY4108: $i,SY4109: $i,SY4110: $i] :
( ( ( hAPP @ SV292 @ ( c_Set_Oinsert @ SV717 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1105 @ tc_bool ) ) @ SV1105 ) )
= SV717 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV292 @ SV1342 @ SV1449 @ SV1496 @ SV1521 @ SY4108 @ SY4109 @ SY4110 @ SV1105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3548]) ).
thf(3780,plain,
! [SV1522: $i,SV1497: $i,SV1450: $i,SV1343: $i,SV1106: $i,SV718: $i,SV293: $i] :
( ( ! [SY4111: $i,SY4112: $i,SY4113: $i] :
( ( ( hAPP @ SV293 @ ( c_Set_Oinsert @ SV718 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1106 @ tc_bool ) ) @ SV1106 ) )
= SV718 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1343 @ SV293 @ SV1450 @ SV1497 @ SV1522 @ SY4111 @ SY4112 @ SY4113 @ SV1106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3549]) ).
thf(3781,plain,
! [SV1523: $i,SV1498: $i,SV1451: $i,SV1345: $i,SV1109: $i,SV725: $i,SV300: $i] :
( ( ! [SY4114: $i,SY4115: $i,SY4116: $i,SY4117: $i] :
( ( ( hAPP @ SV300 @ ( c_Set_Oinsert @ SV725 @ ( c_Set_Oinsert @ SV1109 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1345 @ tc_bool ) ) @ SV1345 ) @ SV1345 ) )
= ( hAPP @ ( hAPP @ SV1451 @ SV725 ) @ SV1109 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV300 @ SV1498 @ SV1523 @ SY4114 @ SV1451 @ SY4115 @ SY4116 @ SY4117 @ SV1345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3550]) ).
thf(3782,plain,
! [SV1524: $i,SV1499: $i,SV1452: $i,SV1346: $i,SV1110: $i,SV726: $i,SV301: $i] :
( ( ! [SY4118: $i,SY4119: $i,SY4120: $i,SY4121: $i] :
( ( ( hAPP @ SV301 @ ( c_Set_Oinsert @ SV726 @ ( c_Set_Oinsert @ SV1110 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1346 @ tc_bool ) ) @ SV1346 ) @ SV1346 ) )
= ( hAPP @ ( hAPP @ SV1452 @ SV726 ) @ SV1110 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1499 @ SV301 @ SV1524 @ SY4118 @ SY4119 @ SV1452 @ SY4120 @ SY4121 @ SV1346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3551]) ).
thf(3783,plain,
! [SV740: $i,SV1350: $i,SV1119: $i,SV316: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV316 @ tc_bool ) ) @ SV1119 ) @ SV1350 ) )
= $false )
| ( ( ~ ( hBOOL @ ( c_in @ SV740 @ SV1350 @ SV316 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV316 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV740 @ SV1119 @ SV316 ) ) @ SV1350 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3553]) ).
thf(3784,plain,
! [SV1121: $i,SV1352: $i,SV742: $i,SV318: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV318 @ tc_bool ) ) @ SV742 ) @ SV1352 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV1121 @ SV742 @ SV318 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV318 @ tc_bool ) ) @ SV742 ) @ ( c_Set_Oinsert @ SV1121 @ SV1352 @ SV318 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3555]) ).
thf(3785,plain,
! [SV1122: $i,SV1353: $i,SV743: $i,SV319: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV319 @ tc_bool ) ) @ SV743 ) @ ( c_Set_Oinsert @ SV1353 @ SV1122 @ SV319 ) ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV1353 @ SV743 @ SV319 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV319 @ tc_bool ) ) @ SV743 ) @ SV1122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3556]) ).
thf(3786,plain,
! [SV1123: $i,SV1354: $i,SV744: $i,SV320: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV320 @ tc_bool ) ) @ SV744 ) @ SV1354 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV1123 @ SV744 @ SV320 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV320 @ tc_bool ) ) @ SV744 ) @ ( c_Set_Oinsert @ SV1123 @ SV1354 @ SV320 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3557]) ).
thf(3787,plain,
! [SV1124: $i,SV1355: $i,SV745: $i,SV321: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV321 @ tc_bool ) ) @ SV745 ) @ ( c_Set_Oinsert @ SV1355 @ SV1124 @ SV321 ) ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV1355 @ SV745 @ SV321 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV321 @ tc_bool ) ) @ SV745 ) @ SV1124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3558]) ).
thf(3788,plain,
! [SV1525: $i,SV1500: $i,SV1453: $i,SV1356: $i,SV1125: $i,SV746: $i,SV322: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV322 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV746 @ SV1125 @ SV1356 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV1453 @ SV1500 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV322 @ SV746 @ SV1356 @ SV1125 @ SV1525 @ SV1453 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1525 @ SV1500 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV322 @ SV746 @ SV1356 @ SV1125 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV322 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1525 @ SV1125 @ SV1453 @ 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_forall_pos,[status(thm)],[3559]) ).
thf(3789,plain,
! [SV1526: $i,SV1501: $i,SV1454: $i,SV1357: $i,SV1126: $i,SV747: $i,SV323: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV323 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV747 @ SV1126 @ SV1357 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV1454 @ SV1501 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV747 @ SV1526 @ SV1357 @ SV1454 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1526 @ SV1501 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV747 @ SV1526 @ SV1357 @ SV1454 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV323 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1526 @ SV1126 @ SV1454 @ 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_forall_pos,[status(thm)],[3560]) ).
thf(3790,plain,
! [SV1527: $i,SV1502: $i,SV1455: $i,SV1358: $i,SV1127: $i,SV748: $i,SV324: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV324 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV748 @ SV1127 @ SV1358 @ 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 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV1455 @ SV1502 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV324 @ SV748 @ SV1358 @ SV1127 @ SV1527 @ SV1455 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1527 @ SV1502 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV324 @ SV748 @ SV1358 @ SV1127 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV324 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1527 @ SV1127 @ SV1455 @ 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_forall_pos,[status(thm)],[3561]) ).
thf(3791,plain,
! [SV1503: $i,SV1456: $i,SV1360: $i,SV1129: $i,SV750: $i,SV326: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV326 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV750 @ SV1129 @ SV1360 @ 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 )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1360 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV326 @ SV750 @ SV1360 @ SV1129 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV326 @ SV750 @ SV1360 @ SV1129 @ SV1456 @ SV1503 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV326 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1456 @ SV1129 @ SV1503 @ 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_or_pos,[status(thm)],[3562]) ).
thf(3792,plain,
! [SV1131: $i,SV752: $i,SV328: $i,SV1362: $i,SV1457: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1457 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SV1362 @ SV1457 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SV1362 @ SV1457 ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV328 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV752 @ SV1131 @ SV1457 @ 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 )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV328 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV752 @ SV1131 @ SV1362 @ 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_or_pos,[status(thm)],[3563]) ).
thf(3793,plain,
! [SV1504: $i,SV1458: $i,SV1363: $i,SV1132: $i,SV753: $i,SV329: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV329 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV753 @ SV1132 @ SV1363 @ 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 )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV753 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV753 @ SV1458 @ SV1363 @ SV1504 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV753 @ SV1458 @ SV1363 @ SV1504 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV329 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1458 @ SV1132 @ SV1504 @ 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_or_pos,[status(thm)],[3564]) ).
thf(3794,plain,
! [SV1364: $i,SV1133: $i,SV330: $i,SV1459: $i,SV754: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV754 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV754 @ SV1459 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV754 @ SV1459 ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV330 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1459 @ SV1133 @ SV1364 @ 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 )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV330 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV754 @ SV1133 @ SV1364 @ 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_or_pos,[status(thm)],[3565]) ).
thf(3795,plain,
! [SV1505: $i,SV1460: $i,SV1365: $i,SV1134: $i,SV755: $i,SV331: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV331 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV755 @ SV1134 @ SV1365 @ 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 )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1365 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV331 @ SV755 @ SV1365 @ SV1134 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV331 @ SV755 @ SV1365 @ SV1134 @ SV1460 @ SV1505 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV331 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1460 @ SV1134 @ SV1505 @ 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_or_pos,[status(thm)],[3566]) ).
thf(3796,plain,
! [SV1366: $i,SV1135: $i,SV332: $i,SV756: $i,SV1461: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1461 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV756 @ SV1461 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV756 @ SV1461 ) ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV332 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1461 @ SV1135 @ SV1366 @ 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 )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV332 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV756 @ SV1135 @ SV1366 @ 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_or_pos,[status(thm)],[3567]) ).
thf(3797,plain,
! [SV1506: $i,SV1462: $i,SV1367: $i,SV1136: $i,SV757: $i,SV333: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV333 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV757 @ SV1136 @ SV1367 @ 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 )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1367 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV757 @ SV1462 @ SV1367 @ SV1506 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV757 @ SV1462 @ SV1367 @ SV1506 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV333 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1462 @ SV1136 @ SV1506 @ 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_or_pos,[status(thm)],[3568]) ).
thf(3798,plain,
! [SV1137: $i,SV758: $i,SV334: $i,SV1463: $i,SV1368: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1368 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SV1368 @ SV1463 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SV1368 @ SV1463 ) ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV334 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV758 @ SV1137 @ SV1463 @ 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 )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV334 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV758 @ SV1137 @ SV1368 @ 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_or_pos,[status(thm)],[3569]) ).
thf(3799,plain,
! [SV1139: $i,SV1370: $i,SV760: $i,SV336: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV336 @ tc_bool ) ) @ SV760 ) @ SV1370 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV336 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV760 @ ( c_Set_Oinsert @ SV1139 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV336 @ tc_bool ) ) @ SV336 ) @ ( tc_fun @ SV336 @ tc_bool ) ) ) @ SV1370 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV336 @ tc_bool ) ) @ SV760 ) @ ( c_Set_Oinsert @ SV1139 @ SV1370 @ SV336 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3570]) ).
thf(3800,plain,
! [SV1528: $i,SV1507: $i,SV1464: $i,SV1371: $i,SV1140: $i,SV761: $i,SV337: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV761 @ ( c_Com_Ocom_OSemi @ SV1140 @ SV1371 ) @ SV1464 @ SV1507 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) ) @ SV1507 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1528 @ SV1371 @ SV1464 @ SV1507 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) ) @ SV1507 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV761 @ SV1140 @ SV1528 @ SV1507 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) ) @ SV1507 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3571]) ).
thf(3801,plain,
! [SV764: $i,SV1373: $i,SV1143: $i,SV340: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV340 @ SV1143 @ SV1373 )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV340 @ ( c_Set_Oinsert @ SV764 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1373 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1373 ) ) @ SV1373 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV340 @ ( c_Set_Oinsert @ SV764 @ SV1143 @ ( tc_Hoare__Mirabelle_Otriple @ SV1373 ) ) @ SV1373 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3574]) ).
thf(3802,plain,
! [SV342: $i,SV1374: $i,SV766: $i,SV1145: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1145 ) @ tc_bool ) ) @ SV766 ) @ SV1374 ) )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV342 @ SV1374 @ SV1145 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV342 @ SV766 @ SV1145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3576]) ).
thf(3803,plain,
! [SV767: $i,SV343: $i,SV1375: $i,SV1146: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1146 @ tc_bool ) ) @ SV1375 ) @ SV343 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1375 @ SV767 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV343 @ SV767 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3577]) ).
thf(3804,plain,
! [SV346: $i,SV1376: $i,SV770: $i,SV1147: $i] :
( ( ( hBOOL @ ( hAPP @ SV1147 @ SV770 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1376 @ tc_bool ) ) @ SV1147 ) @ SV346 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV346 @ SV770 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3578]) ).
thf(3805,plain,
! [SV771: $i,SV1148: $i,SV1377: $i,SV347: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV347 @ tc_bool ) ) @ SV1377 ) @ SV1148 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV347 @ tc_bool ) ) @ SV771 ) @ SV1377 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV347 @ tc_bool ) ) @ SV771 ) @ SV1148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3579]) ).
thf(3806,plain,
! [SV1378: $i,SV1149: $i,SV774: $i,SV350: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV774 ) @ SV1149 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV1378 ) @ SV1149 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV774 ) @ SV1378 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV350 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3580]) ).
thf(3807,plain,
! [SV1379: $i,SV1150: $i,SV775: $i,SV351: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV775 ) @ SV1150 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV775 ) @ SV1379 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV1379 ) @ SV1150 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV351 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3581]) ).
thf(3808,plain,
! [SV778: $i,SV1153: $i,SV1380: $i,SV354: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV354 @ SV1380 @ SV1153 )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV1380 @ SV778 @ SV1153 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV354 @ SV778 @ SV1153 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3582]) ).
thf(3809,plain,
! [SV1154: $i,SV780: $i,SV357: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV357 ) @ SV780 ) @ SV1154 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV357 ) @ SV1154 ) @ SV780 ) ) )
= $true )
| ( ( SV780 = SV1154 )
= $true )
| ( ( class_Orderings_Oorder @ SV357 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3583]) ).
thf(3810,plain,
! [SV781: $i,SV1155: $i,SV358: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV358 ) @ SV1155 ) @ SV781 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV358 ) @ SV781 ) @ SV1155 ) ) )
= $true )
| ( ( SV781 = SV1155 )
= $true )
| ( ( class_Orderings_Oorder @ SV358 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3584]) ).
thf(3811,plain,
! [SV782: $i,SV1156: $i,SV359: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV359 ) @ SV1156 ) @ SV782 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV359 ) @ SV782 ) @ SV1156 ) ) )
= $true )
| ( ( SV782 = SV1156 )
= $true )
| ( ( class_Orderings_Oorder @ SV359 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3585]) ).
thf(3812,plain,
! [SV783: $i,SV360: $i,SV1157: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1157 @ tc_bool ) ) @ SV360 ) @ SV783 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1157 @ tc_bool ) ) @ SV783 ) @ SV360 ) )
= $false )
| ( ( SV360 = SV783 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3586]) ).
thf(3813,plain,
! [SV784: $i,SV361: $i,SV1158: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1158 @ tc_bool ) ) @ SV361 ) @ SV784 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1158 @ tc_bool ) ) @ SV784 ) @ SV361 ) )
= $false )
| ( ( SV361 = SV784 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3587]) ).
thf(3814,plain,
! [SV788: $i,SV1381: $i,SV365: $i,SV1160: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1160 @ SV365 @ SV1381 ) @ SV788 ) )
= $false )
| ( ( SV1160 = SV788 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV365 @ SV788 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3588]) ).
thf(3815,plain,
! [SV1465: $i,SV1386: $i,SV1168: $i,SV798: $i,SV375: $i] :
( ( ( class_HOL_Oord @ SV375 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV375 ) @ ( hAPP @ SV798 @ SV1168 ) ) @ ( hAPP @ SV1386 @ SV1168 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1465 @ SV375 ) ) @ SV798 ) @ SV1386 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3592]) ).
thf(3816,plain,
! [SV1171: $i,SV391: $i,SV814: $i] :
( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV814 @ SV391 )
= ( c_HOL_Ouminus__class_Ouminus @ SV1171 @ SV391 ) )
= $false )
| ( ( SV814 = SV1171 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3594]) ).
thf(3817,plain,
! [SV815: $i,SV1172: $i,SV1387: $i,SV392: $i] :
( ( ( hBOOL @ ( c_in @ SV392 @ SV1387 @ SV1172 ) )
= $true )
| ( ( ( hBOOL @ ( c_in @ SV392 @ SV815 @ SV1172 ) )
| ( SV815 = SV1387 ) )
= $true )
| ( ( ( c_Set_Oinsert @ SV392 @ SV815 @ SV1172 )
= ( c_Set_Oinsert @ SV392 @ SV1387 @ SV1172 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3595]) ).
thf(3818,plain,
! [SV1529: $i,SV1508: $i,SV1466: $i,SV1389: $i,SV1175: $i,SV818: $i,SV395: $i] :
( ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV395 @ SV818 @ SV1175 @ SV1389 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1466 @ SV1508 @ SV1529 @ SV1389 ) )
| ( SV395 = SV1466 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3598]) ).
thf(3819,plain,
! [SV1177: $i,SV821: $i,SV398: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV398 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV821 @ SV1177 @ SV398 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV821 @ SV1177 @ SV398 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV398 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3599]) ).
thf(3820,plain,
! [SV400: $i,SV1179: $i,SV823: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV823 @ SV1179 @ SV400 )
= ( c_Orderings_Obot__class_Obot @ SV400 ) )
= $false )
| ( ( SV823
= ( c_Orderings_Obot__class_Obot @ SV400 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV400 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3600]) ).
thf(3821,plain,
! [SV1467: $i,SV1390: $i,SV1180: $i,SV824: $i,SV401: $i] :
( ( ( ( c_Set_Oinsert @ SV401 @ ( c_Set_Oinsert @ SV824 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1180 @ tc_bool ) ) @ SV1180 ) @ SV1180 )
= ( c_Set_Oinsert @ SV1390 @ ( c_Set_Oinsert @ SV1467 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1180 @ tc_bool ) ) @ SV1180 ) @ SV1180 ) )
= $false )
| ( ( ( SV824 = SV1390 )
| ( SV401 = SV1390 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3601]) ).
thf(3822,plain,
! [SV1391: $i,SV1182: $i,SV403: $i,SV826: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV826 @ SV826 @ SV403 )
!= ( c_HOL_Ominus__class_Ominus @ SV1182 @ SV1391 @ SV403 ) )
= $true )
| ( ( SV1182 = SV1391 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV403 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3602]) ).
thf(3823,plain,
! [SV1183: $i,SV827: $i,SV404: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV404 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV827 @ SV1183 @ SV404 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV404 ) @ SV827 ) @ SV1183 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV404 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3603]) ).
thf(3824,plain,
! [SV406: $i,SV1185: $i,SV829: $i] :
( ( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV829 @ SV1185 @ SV406 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV406 @ tc_bool ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV406 ) @ SV829 ) @ SV1185 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV406 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3604]) ).
thf(3825,plain,
! [SV1468: $i,SV1392: $i,SV1187: $i,SV832: $i,SV409: $i] :
( ( ( ( c_Set_Oinsert @ SV409 @ ( c_Set_Oinsert @ SV832 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1187 @ tc_bool ) ) @ SV1187 ) @ SV1187 )
= ( c_Set_Oinsert @ SV1392 @ ( c_Set_Oinsert @ SV1468 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1187 @ tc_bool ) ) @ SV1187 ) @ SV1187 ) )
= $false )
| ( ( ( SV409 = SV1468 )
| ( SV832 = SV1468 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3605]) ).
thf(3826,plain,
! [SV1469: $i,SV1393: $i,SV1188: $i,SV833: $i,SV410: $i] :
( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV410 @ SV833 @ SV1188 @ ( tc_fun @ SV1393 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1393 @ tc_bool ) ) )
= $false )
| ( ( ( ( hAPP @ SV833 @ SV1469 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1393 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SV1469 @ SV410 @ SV1188 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3606]) ).
thf(3827,plain,
! [SV1470: $i,SV1394: $i,SV1189: $i,SV834: $i,SV411: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV411 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV834 @ SV1189 @ SV411 )
!= ( c_HOL_Ominus__class_Ominus @ SV1394 @ SV1470 @ SV411 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV411 ) @ SV1470 ) @ SV1394 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV411 ) @ SV1189 ) @ SV834 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3607]) ).
thf(3828,plain,
! [SV1190: $i,SV412: $i,SV835: $i] :
( ( ( ( c_HOL_Ouminus__class_Ouminus @ SV835 @ SV412 )
= ( c_HOL_Ouminus__class_Ouminus @ SV1190 @ SV412 ) )
= $false )
| ( ( SV835 = SV1190 )
= $true )
| ( ( class_Lattices_Oboolean__algebra @ SV412 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3608]) ).
thf(3829,plain,
! [SV1471: $i,SV1395: $i,SV1191: $i,SV836: $i,SV413: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV413 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV836 @ SV1191 @ SV1395 @ ( tc_fun @ SV413 @ tc_bool ) ) )
= $false )
| ( ( ( ( hAPP @ SV1191 @ SV1471 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV413 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SV1471 @ SV836 @ SV1395 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3609]) ).
thf(3830,plain,
! [SV414: $i,SV1192: $i,SV837: $i] :
( ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ SV837 @ SV1192 @ SV414 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV414 @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV837 @ SV1192 @ SV414 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV414 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3610]) ).
thf(3831,plain,
! [SV1472: $i,SV1396: $i,SV1193: $i,SV838: $i,SV415: $i] :
( ( ( ( c_Set_Oinsert @ SV415 @ ( c_Set_Oinsert @ SV838 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SV1193 ) @ SV1193 )
= ( c_Set_Oinsert @ SV1396 @ ( c_Set_Oinsert @ SV1472 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SV1193 ) @ SV1193 ) )
= $false )
| ( ( ( SV838 = SV1396 )
| ( SV838 = SV1472 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3611]) ).
thf(3832,plain,
! [SV1194: $i,SV839: $i,SV416: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV416 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV839 @ SV1194 @ SV416 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV839 @ SV1194 @ SV416 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV416 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3612]) ).
thf(3833,plain,
! [SV1530: $i,SV1509: $i,SV1473: $i,SV1397: $i,SV1196: $i,SV841: $i,SV418: $i] :
( ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV418 @ SV841 @ SV1196 @ SV1397 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1473 @ SV1509 @ SV1530 @ SV1397 ) )
| ( SV1196 = SV1530 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3613]) ).
thf(3834,plain,
! [SV1474: $i,SV1398: $i,SV1197: $i,SV842: $i,SV419: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV419 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV842 @ SV1197 @ SV419 )
!= ( c_HOL_Ominus__class_Ominus @ SV1398 @ SV1474 @ SV419 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV419 ) @ SV1197 ) @ SV842 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV419 ) @ SV1474 ) @ SV1398 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3614]) ).
thf(3835,plain,
! [SV420: $i,SV1198: $i,SV843: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV843 @ SV1198 @ SV420 )
= SV1198 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV420 ) @ SV843 ) @ SV1198 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV420 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3615]) ).
thf(3836,plain,
! [SV1531: $i,SV1510: $i,SV1475: $i,SV1399: $i,SV1199: $i,SV844: $i,SV421: $i] :
( ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV421 @ SV844 @ SV1199 @ SV1399 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1475 @ SV1510 @ SV1531 @ SV1399 ) )
| ( SV844 = SV1510 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3616]) ).
thf(3837,plain,
! [SV1476: $i,SV1401: $i,SV1201: $i,SV846: $i,SV423: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV423 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV846 @ SV1201 @ SV423 )
!= ( c_HOL_Ominus__class_Ominus @ SV1401 @ SV1476 @ SV423 ) )
| ( c_HOL_Oord__class_Oless @ SV1401 @ SV1476 @ SV423 )
| ~ ( c_HOL_Oord__class_Oless @ SV846 @ SV1201 @ SV423 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3618]) ).
thf(3838,plain,
! [SV424: $i,SV1202: $i,SV847: $i] :
( ( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV847 @ SV1202 @ SV424 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV424 @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV847 @ SV1202 @ SV424 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV424 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3619]) ).
thf(3839,plain,
! [SV1477: $i,SV1402: $i,SV1205: $i,SV850: $i,SV427: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV427 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV850 @ SV1205 @ SV427 )
!= ( c_HOL_Ominus__class_Ominus @ SV1402 @ SV1477 @ SV427 ) )
| ( c_HOL_Oord__class_Oless @ SV850 @ SV1205 @ SV427 )
| ~ ( c_HOL_Oord__class_Oless @ SV1402 @ SV1477 @ SV427 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3621]) ).
thf(3840,plain,
! [SV1403: $i,SV428: $i,SV1206: $i,SV851: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV851 @ SV1206 @ SV428 )
!= ( c_HOL_Ominus__class_Ominus @ SV1403 @ SV1403 @ SV428 ) )
= $true )
| ( ( SV851 = SV1206 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV428 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3622]) ).
thf(3841,plain,
! [SV429: $i,SV1207: $i,SV852: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV852 @ SV1207 @ SV429 )
= ( c_Orderings_Obot__class_Obot @ SV429 ) )
= $false )
| ( ( SV1207
= ( c_Orderings_Obot__class_Obot @ SV429 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV429 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3623]) ).
thf(3842,plain,
! [SV1478: $i,SV1404: $i,SV1208: $i,SV853: $i,SV430: $i] :
( ( ( ( c_Set_Oinsert @ SV430 @ ( c_Set_Oinsert @ SV853 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1208 @ tc_bool ) ) @ SV1208 ) @ SV1208 )
= ( c_Set_Oinsert @ SV1404 @ ( c_Set_Oinsert @ SV1478 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1208 @ tc_bool ) ) @ SV1208 ) @ SV1208 ) )
= $false )
| ( ( ( SV430 = SV1478 )
| ( SV430 = SV1404 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3624]) ).
thf(3843,plain,
! [SV1: $i,SV431: $i,SV1209: $i,SV854: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV854 @ SV1209 @ ( tc_fun @ SV431 @ SV1 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV431 @ SV1 ) ) @ SV854 ) @ SV1209 ) )
= $true )
| ( ( class_HOL_Oord @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3625]) ).
thf(3844,plain,
! [SV432: $i,SV855: $i,SV2: $i,SV1210: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1210 @ SV2 ) ) @ SV855 ) @ SV432 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1210 @ SV2 ) ) @ SV432 ) @ SV855 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV432 @ SV855 @ ( tc_fun @ SV1210 @ SV2 ) )
= $true )
| ( ( class_HOL_Oord @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3626]) ).
thf(3845,plain,
! [SV1211: $i,SV856: $i,SV3: $i,SV433: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV433 @ SV3 ) ) @ SV856 ) @ SV1211 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1211 @ SV856 @ ( tc_fun @ SV433 @ SV3 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3627]) ).
thf(3846,plain,
! [SV437: $i,SV1212: $i,SV7: $i,SV860: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV860 @ tc_bool ) ) @ SV7 ) @ SV1212 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1212 @ SV437 @ ( tc_fun @ SV860 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV7 @ SV437 @ ( tc_fun @ SV860 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3629]) ).
thf(3847,plain,
! [SV438: $i,SV861: $i,SV1213: $i,SV8: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV8 @ SV1213 @ ( tc_fun @ SV861 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV861 @ tc_bool ) ) @ SV1213 ) @ SV438 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV8 @ SV438 @ ( tc_fun @ SV861 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3630]) ).
thf(3848,plain,
! [SV11: $i,SV1405: $i,SV1214: $i,SV864: $i,SV441: $i] :
( ( ( ( c_Finite__Set_Osetsum @ SV441 @ ( c_HOL_Ominus__class_Ominus @ SV864 @ ( c_Set_Oinsert @ SV1214 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1405 @ tc_bool ) ) @ SV1405 ) @ ( tc_fun @ SV1405 @ tc_bool ) ) @ SV1405 @ SV11 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV441 @ SV864 @ SV1405 @ SV11 ) @ ( hAPP @ SV441 @ SV1214 ) @ SV11 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1214 @ SV864 @ SV1405 ) )
| ~ ( c_Finite__Set_Ofinite @ SV864 @ SV1405 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3632]) ).
thf(3849,plain,
! [SV12: $i,SV1406: $i,SV1215: $i,SV865: $i,SV442: $i] :
( ( ( ( c_Finite__Set_Osetsum @ SV442 @ ( c_HOL_Ominus__class_Ominus @ SV865 @ ( c_Set_Oinsert @ SV1215 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1406 @ tc_bool ) ) @ SV1406 ) @ ( tc_fun @ SV1406 @ tc_bool ) ) @ SV1406 @ SV12 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV442 @ SV865 @ SV1406 @ SV12 ) @ ( hAPP @ SV442 @ SV1215 ) @ SV12 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1215 @ SV865 @ SV1406 ) )
| ~ ( c_Finite__Set_Ofinite @ SV865 @ SV1406 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3633]) ).
thf(3850,plain,
! [SV866: $i,SV1216: $i,SV13: $i,SV443: $i] :
( ( ( hBOOL @ ( c_in @ SV443 @ SV13 @ SV1216 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV13 @ SV866 @ ( tc_fun @ SV1216 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1216 @ tc_bool ) ) @ SV13 ) @ SV866 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV13 @ ( c_Set_Oinsert @ SV443 @ SV866 @ SV1216 ) @ ( tc_fun @ SV1216 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3634]) ).
thf(3851,plain,
! [SV867: $i,SV1217: $i,SV14: $i,SV444: $i] :
( ( ( hBOOL @ ( c_in @ SV444 @ SV14 @ SV1217 ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV444 @ SV867 @ SV1217 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1217 @ tc_bool ) ) @ SV14 ) @ SV867 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV14 @ ( c_Set_Oinsert @ SV444 @ SV867 @ SV1217 ) @ ( tc_fun @ SV1217 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3635]) ).
thf(3852,plain,
! [SV15: $i,SV868: $i,SV1218: $i,SV445: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV445 @ ( c_Set_Oinsert @ SV1218 @ SV868 @ SV15 ) @ ( tc_fun @ SV15 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV1218 @ SV868 @ SV15 ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV1218 @ SV445 @ SV15 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV15 @ tc_bool ) ) @ SV445 ) @ SV868 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3636]) ).
thf(3853,plain,
! [SV446: $i,SV1219: $i,SV869: $i,SV16: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV16 ) @ SV869 ) @ SV1219 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV16 ) @ SV446 ) @ SV869 ) ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV446 @ SV869 @ SV16 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV869 @ SV1219 @ SV16 ) @ ( tc_fun @ SV16 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV446 @ SV1219 @ SV16 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3637]) ).
thf(3854,plain,
! [SV26: $i,SV455: $i,SV876: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV876 @ SV455 @ SV26 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV26 ) @ SV455 ) @ SV876 ) )
= $false )
| ( ( class_Orderings_Opreorder @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3639]) ).
thf(3855,plain,
! [SV28: $i,SV457: $i,SV878: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV878 @ SV457 @ SV28 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV28 ) @ SV457 ) @ SV878 ) )
= $false )
| ( ( class_Orderings_Olinorder @ SV28 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3640]) ).
thf(3856,plain,
! [SV459: $i,SV880: $i,SV30: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV30 ) @ SV880 ) @ SV459 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV459 @ SV880 @ SV30 )
= $false )
| ( ( class_Orderings_Olinorder @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3641]) ).
thf(3857,plain,
! [SV882: $i,SV463: $i,SV34: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV34 ) @ SV463 ) @ SV882 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV34 ) @ SV882 ) @ SV463 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV463 @ SV882 @ SV34 )
= $true )
| ( ( class_Orderings_Opreorder @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3643]) ).
thf(3858,plain,
! [SV885: $i,SV1223: $i,SV466: $i,SV37: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV37 ) @ SV466 ) @ SV1223 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1223 @ SV885 @ SV37 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV466 @ SV885 @ SV37 )
= $true )
| ( ( class_Orderings_Oorder @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3646]) ).
thf(3859,plain,
! [SV886: $i,SV38: $i,SV1224: $i,SV467: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV467 @ SV1224 @ SV38 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV38 ) @ SV1224 ) @ SV886 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV467 @ SV886 @ SV38 )
= $true )
| ( ( class_Orderings_Oorder @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3647]) ).
thf(3860,plain,
! [SV468: $i,SV39: $i,SV887: $i,SV1225: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1225 @ SV887 @ SV39 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV39 ) @ SV468 ) @ SV1225 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV468 @ SV887 @ SV39 )
= $true )
| ( ( class_Orderings_Opreorder @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3648]) ).
thf(3861,plain,
! [SV469: $i,SV888: $i,SV1226: $i,SV40: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV40 ) @ SV1226 ) @ SV888 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV469 @ SV1226 @ SV40 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV469 @ SV888 @ SV40 )
= $true )
| ( ( class_Orderings_Opreorder @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3649]) ).
thf(3862,plain,
! [SV889: $i,SV470: $i,SV41: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV41 ) @ SV470 ) @ SV889 ) )
= $false )
| ( ( SV889 = SV470 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV470 @ SV889 @ SV41 )
= $true )
| ( ( class_Orderings_Oorder @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3650]) ).
thf(3863,plain,
! [SV890: $i,SV471: $i,SV42: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV42 ) @ SV471 ) @ SV890 ) )
= $false )
| ( ( SV890 = SV471 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV471 @ SV890 @ SV42 )
= $true )
| ( ( class_Orderings_Oorder @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3651]) ).
thf(3864,plain,
! [SV891: $i,SV472: $i,SV43: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV43 ) @ SV472 ) @ SV891 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV472 @ SV891 @ SV43 )
= $true )
| ( ( SV472 = SV891 )
= $true )
| ( ( class_Orderings_Oorder @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3652]) ).
thf(3865,plain,
! [SV892: $i,SV473: $i,SV44: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV44 ) @ SV473 ) @ SV892 ) )
= $false )
| ( ( SV473 = SV892 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV473 @ SV892 @ SV44 )
= $true )
| ( ( class_Orderings_Oorder @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3653]) ).
thf(3866,plain,
! [SV893: $i,SV474: $i,SV45: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV45 ) @ SV474 ) @ SV893 ) )
= $false )
| ( ( SV474 = SV893 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV474 @ SV893 @ SV45 )
= $true )
| ( ( class_Orderings_Oorder @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3654]) ).
thf(3867,plain,
! [SV894: $i,SV475: $i,SV46: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV46 ) @ SV475 ) @ SV894 ) )
= $false )
| ( ( SV475 = SV894 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV475 @ SV894 @ SV46 )
= $true )
| ( ( class_Orderings_Oorder @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3655]) ).
thf(3868,plain,
! [SV895: $i,SV476: $i,SV47: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV47 ) @ SV476 ) @ SV895 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV476 @ SV895 @ SV47 )
= $true )
| ( ( SV476 = SV895 )
= $true )
| ( ( class_Orderings_Olinorder @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3656]) ).
thf(3869,plain,
! [SV896: $i,SV477: $i,SV48: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV48 ) @ SV477 ) @ SV896 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV477 @ SV896 @ SV48 )
= $true )
| ( ( SV477 = SV896 )
= $true )
| ( ( class_Orderings_Olinorder @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3657]) ).
thf(3870,plain,
! [SV901: $i,SV53: $i,SV1227: $i,SV482: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV482 @ SV1227 @ SV53 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV482 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV901 @ SV1227 @ SV53 ) @ SV53 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3662]) ).
thf(3871,plain,
! [SV1228: $i,SV54: $i,SV902: $i,SV483: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV483 @ SV902 @ SV54 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV483 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV902 @ SV1228 @ SV54 ) @ SV54 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3663]) ).
thf(3872,plain,
! [SV1408: $i,SV1229: $i,SV56: $i,SV903: $i,SV485: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV485 @ SV903 @ SV56 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1229 @ SV1408 @ SV56 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV56 ) @ SV1408 ) @ SV485 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1408 @ SV485 @ SV56 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1229 @ SV903 @ SV56 ) @ ( tc_fun @ SV56 @ tc_bool ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3664]) ).
thf(3873,plain,
! [SV1532: $i,SV1511: $i,SV1479: $i,SV1409: $i,SV1230: $i,SV904: $i,SV486: $i,SV57: $i] :
( ( ! [SY4122: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV57 @ SV486 @ ( c_COMBC @ SV904 @ SV1230 @ SV1230 @ tc_bool ) @ ( c_COMBC @ SV1409 @ SV1230 @ SV1230 @ tc_bool ) @ SV1479 @ SV1511 @ SV1532 @ SY4122 @ SV1230 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV486 @ SV57 @ SV904 @ SV1409 @ SV1511 @ SV1479 @ SY4122 @ SV1532 @ SV1230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3665]) ).
thf(3874,plain,
! [SV907: $i,SV60: $i,SV1233: $i,SV489: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV489 @ SV1233 @ SV60 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1233 @ SV907 @ SV60 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV489 @ SV907 @ SV60 )
= $true )
| ( ( class_Orderings_Oorder @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3666]) ).
thf(3875,plain,
! [SV61: $i,SV908: $i,SV490: $i,SV1234: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1234 @ SV490 @ ( tc_fun @ SV908 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV61 @ SV1234 @ SV908 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV61 @ SV490 @ SV908 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3667]) ).
thf(3876,plain,
! [SV491: $i,SV909: $i,SV1235: $i,SV62: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV62 @ SV1235 @ ( tc_fun @ SV909 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1235 @ SV491 @ ( tc_fun @ SV909 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV62 @ SV491 @ ( tc_fun @ SV909 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3668]) ).
thf(3877,plain,
! [SV492: $i,SV63: $i,SV910: $i,SV1236: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1236 @ SV910 @ SV63 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV492 @ SV1236 @ SV63 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV492 @ SV910 @ SV63 )
= $true )
| ( ( class_Orderings_Opreorder @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3669]) ).
thf(3878,plain,
! [SV1481: $i,SV493: $i,SV1411: $i,SV64: $i,SV1237: $i,SV911: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV911 @ SV1237 @ SV64 @ SV1411 @ SV493 @ SV1481 )
= $false )
| ( ( c_Finite__Set_Ofinite @ SV64 @ SV493 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3670]) ).
thf(3879,plain,
! [SV1412: $i,SV1238: $i,SV80: $i,SV922: $i,SV509: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV509 @ SV922 @ SV80 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1238 @ SV1412 @ SV80 ) @ ( tc_fun @ SV80 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV1238 ) @ SV1412 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV922 @ SV1412 @ SV80 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV922 ) @ SV1412 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV1238 ) @ SV509 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3677]) ).
thf(3880,plain,
! [SV1413: $i,SV1239: $i,SV81: $i,SV923: $i,SV510: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV510 @ SV923 @ SV81 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1239 @ SV1413 @ SV81 ) @ ( tc_fun @ SV81 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV1239 ) @ SV1413 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1239 @ SV510 @ SV81 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV923 ) @ SV1413 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV1239 ) @ SV510 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3678]) ).
thf(3881,plain,
! [SV88: $i,SV517: $i,SV930: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV930 @ SV517 @ SV88 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV517 @ SV930 @ SV88 )
= $false )
| ( ( class_Orderings_Oorder @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3684]) ).
thf(3882,plain,
! [SV89: $i,SV518: $i,SV931: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV931 @ SV518 @ SV89 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV518 @ SV931 @ SV89 )
= $false )
| ( ( class_Orderings_Olinorder @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3685]) ).
thf(3883,plain,
! [SV90: $i,SV519: $i,SV932: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV932 @ SV519 @ SV90 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV519 @ SV932 @ SV90 )
= $false )
| ( ( class_Orderings_Opreorder @ SV90 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3686]) ).
thf(3884,plain,
! [SV91: $i,SV520: $i,SV933: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV933 @ SV520 @ SV91 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV520 @ SV933 @ SV91 )
= $false )
| ( ( class_Orderings_Opreorder @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3687]) ).
thf(3885,plain,
! [SV92: $i,SV1414: $i,SV1240: $i,SV934: $i,SV521: $i] :
( ( ( ( c_Finite__Set_Osetsum @ SV521 @ ( c_HOL_Ominus__class_Ominus @ SV934 @ SV1240 @ ( tc_fun @ SV1414 @ tc_bool ) ) @ SV1414 @ SV92 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV521 @ SV934 @ SV1414 @ SV92 ) @ ( c_Finite__Set_Osetsum @ SV521 @ SV1240 @ SV1414 @ SV92 ) @ SV92 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1414 @ tc_bool ) ) @ SV1240 ) @ SV934 ) )
| ~ ( c_Finite__Set_Ofinite @ SV934 @ SV1414 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3688]) ).
thf(3886,plain,
! [SV1512: $i,SV1482: $i,SV1415: $i,SV1241: $i,SV936: $i,SV523: $i,SV94: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV94 @ SV523 @ ( c_Set_Oinsert @ SV936 @ SV1241 @ SV1415 ) @ ( hAPP @ ( hAPP @ SV94 @ SV936 ) @ SV1482 ) @ SV1415 @ SV1512 )
= $true )
| ( ( ~ ( c_Finite__Set_Ofold__graph @ SV94 @ SV523 @ SV1241 @ SV1482 @ SV1415 @ SV1512 )
| ( hBOOL @ ( c_in @ SV936 @ SV1241 @ SV1415 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3690]) ).
thf(3887,plain,
! [SV937: $i,SV524: $i,SV1242: $i,SV95: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV95 @ ( c_Set_Oinsert @ SV1242 @ SV524 @ SV937 ) @ ( tc_fun @ SV937 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV1242 @ SV524 @ SV937 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV95 @ SV524 @ ( tc_fun @ SV937 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3691]) ).
thf(3888,plain,
! [SV525: $i,SV1243: $i,SV938: $i,SV96: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV96 @ SV938 @ ( tc_fun @ SV1243 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV525 @ SV938 @ SV1243 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV96 @ ( c_Set_Oinsert @ SV525 @ SV938 @ SV1243 ) @ ( tc_fun @ SV1243 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3692]) ).
thf(3889,plain,
! [SV1416: $i,SV1244: $i,SV939: $i,SV526: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV97 ) @ SV526 ) @ SV939 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV97 ) @ SV1244 ) @ SV526 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1244 @ SV526 @ SV97 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1416 @ SV939 @ SV97 ) @ ( tc_fun @ SV97 @ tc_bool ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3693]) ).
thf(3890,plain,
! [SV1417: $i,SV1245: $i,SV940: $i,SV527: $i,SV98: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV98 ) @ SV527 ) @ SV940 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV98 ) @ SV940 ) @ SV1245 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV940 @ SV1245 @ SV98 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV527 @ SV1417 @ SV98 ) @ ( tc_fun @ SV98 @ tc_bool ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3694]) ).
thf(3891,plain,
! [SV1418: $i,SV1246: $i,SV941: $i,SV528: $i,SV99: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV99 ) @ SV528 ) @ SV941 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1246 @ SV1418 @ SV99 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV528 @ SV941 @ SV99 ) @ ( tc_fun @ SV99 @ tc_bool ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV99 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3695]) ).
thf(3892,plain,
! [SV1419: $i,SV1247: $i,SV100: $i,SV942: $i,SV529: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV529 @ SV942 @ SV100 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1247 @ SV1419 @ SV100 ) @ ( tc_fun @ SV100 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV100 ) @ SV1247 ) @ SV1419 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV100 ) @ SV529 ) @ SV942 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3696]) ).
thf(3893,plain,
! [SV530: $i,SV1248: $i,SV943: $i,SV101: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV101 ) @ SV943 ) @ SV1248 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV101 ) @ SV530 ) @ SV943 ) ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV530 @ SV943 @ SV101 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV943 @ SV1248 @ SV101 ) @ ( tc_fun @ SV101 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV530 @ SV1248 @ SV101 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3697]) ).
thf(3894,plain,
! [SV944: $i,SV102: $i,SV1420: $i,SV1249: $i,SV531: $i] :
( ( ( hBOOL @ ( c_in @ SV531 @ SV1249 @ SV1420 ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1249 @ SV102 @ SV1420 @ ( tc_fun @ SV944 @ tc_bool ) ) @ SV944 )
| ~ ( c_Finite__Set_Ofinite @ SV1249 @ SV1420 ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ SV102 @ SV531 ) @ SV944 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3698]) ).
thf(3895,plain,
! [SV103: $i,SV1421: $i,SV1250: $i,SV945: $i,SV532: $i] :
( ( ( ( c_Finite__Set_Osetsum @ SV532 @ ( c_HOL_Ominus__class_Ominus @ SV945 @ ( c_Set_Oinsert @ SV1250 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1421 @ tc_bool ) ) @ SV1421 ) @ ( tc_fun @ SV1421 @ tc_bool ) ) @ SV1421 @ SV103 )
= ( c_Finite__Set_Osetsum @ SV532 @ SV945 @ SV1421 @ SV103 ) )
= $true )
| ( ( ( hBOOL @ ( c_in @ SV1250 @ SV945 @ SV1421 ) )
| ~ ( c_Finite__Set_Ofinite @ SV945 @ SV1421 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3699]) ).
thf(3896,plain,
! [SV114: $i,SV955: $i,SV542: $i] :
( ( ( hBOOL @ ( c_in @ SV542 @ SV955 @ SV114 ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV955 @ SV114 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV114 ) @ SV542 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV955 @ SV114 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3702]) ).
thf(3897,plain,
! [SV115: $i,SV543: $i,SV956: $i] :
( ( ( hBOOL @ ( c_in @ SV956 @ SV543 @ SV115 ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV543 @ SV115 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV115 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV543 @ SV115 ) ) @ SV956 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3703]) ).
thf(3898,plain,
! [SV1255: $i,SV1422: $i,SV957: $i,SV546: $i,SV118: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV118 @ SV546 @ SV957 @ SV1422 @ SV1255 @ SV1255 )
= $false )
| ( ( hBOOL @ ( c_in @ SV546 @ SV957 @ SV1255 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV118 @ ( c_Set_Oinsert @ SV546 @ SV957 @ SV1255 ) @ SV1255 ) @ SV1422 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3706]) ).
thf(3899,plain,
! [SV1513: $i,SV1483: $i,SV1423: $i,SV1256: $i,SV958: $i,SV547: $i,SV119: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV119 @ SV547 @ SV958 @ ( hAPP @ ( hAPP @ SV119 @ SV1256 ) @ SV1423 ) @ SV1483 @ SV1513 )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1256 @ SV958 @ SV1483 ) )
| ~ ( c_Finite__Set_Ofold__graph @ SV119 @ SV547 @ ( c_HOL_Ominus__class_Ominus @ SV958 @ ( c_Set_Oinsert @ SV1256 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1483 @ tc_bool ) ) @ SV1483 ) @ ( tc_fun @ SV1483 @ tc_bool ) ) @ SV1423 @ SV1483 @ SV1513 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3707]) ).
thf(3900,plain,
! [SV960: $i,SV1258: $i,SV549: $i,SV121: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV121 @ ( c_Set_Oinsert @ SV549 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1258 @ tc_bool ) ) @ SV1258 ) @ ( tc_fun @ SV1258 @ tc_bool ) ) @ SV960 @ ( tc_fun @ SV1258 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV121 @ SV960 @ ( tc_fun @ SV1258 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV549 @ SV121 @ SV1258 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV121 @ ( c_Set_Oinsert @ SV549 @ SV960 @ SV1258 ) @ ( tc_fun @ SV1258 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3708]) ).
thf(3901,plain,
! [SV961: $i,SV1259: $i,SV550: $i,SV122: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV122 @ ( c_Set_Oinsert @ SV550 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1259 @ tc_bool ) ) @ SV1259 ) @ ( tc_fun @ SV1259 @ tc_bool ) ) @ SV961 @ ( tc_fun @ SV1259 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV550 @ SV961 @ SV1259 ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV550 @ SV122 @ SV1259 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV122 @ ( c_Set_Oinsert @ SV550 @ SV961 @ SV1259 ) @ ( tc_fun @ SV1259 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3709]) ).
thf(3902,plain,
! [SV123: $i,SV962: $i,SV1260: $i,SV551: $i] :
( ( ( hBOOL @ ( c_in @ SV551 @ SV1260 @ SV962 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV123 @ ( c_Set_Oinsert @ SV551 @ SV1260 @ SV962 ) @ ( tc_fun @ SV962 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV551 @ SV123 @ SV962 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV123 @ ( c_Set_Oinsert @ SV551 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV962 @ tc_bool ) ) @ SV962 ) @ ( tc_fun @ SV962 @ tc_bool ) ) @ SV1260 @ ( tc_fun @ SV962 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3710]) ).
thf(3903,plain,
! [SV1514: $i,SV1484: $i,SV1424: $i,SV1261: $i,SV963: $i,SV552: $i,SV124: $i] :
( ( ( c_Nitpick_Ofold__graph_H @ SV124 @ SV552 @ SV963 @ ( hAPP @ ( hAPP @ SV124 @ SV1261 ) @ SV1424 ) @ SV1484 @ SV1514 )
= $true )
| ( ( ~ ( c_Nitpick_Ofold__graph_H @ SV124 @ SV552 @ ( c_HOL_Ominus__class_Ominus @ SV963 @ ( c_Set_Oinsert @ SV1261 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1484 @ tc_bool ) ) @ SV1484 ) @ ( tc_fun @ SV1484 @ tc_bool ) ) @ SV1424 @ SV1484 @ SV1514 )
| ~ ( hBOOL @ ( c_in @ SV1261 @ SV963 @ SV1484 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3711]) ).
thf(3904,plain,
! [SV964: $i,SV1262: $i,SV553: $i,SV125: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV125 @ ( c_Set_Oinsert @ SV553 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1262 @ tc_bool ) ) @ SV1262 ) @ ( tc_fun @ SV1262 @ tc_bool ) ) @ SV964 @ ( tc_fun @ SV1262 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV125 @ SV964 @ ( tc_fun @ SV1262 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1262 @ tc_bool ) ) @ SV125 ) @ SV964 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV125 @ ( c_Set_Oinsert @ SV553 @ SV964 @ SV1262 ) @ ( tc_fun @ SV1262 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3712]) ).
thf(3905,plain,
! [SV965: $i,SV126: $i,SV554: $i] :
( ( ( c_Finite__Set_Ofinite @ SV554 @ SV126 )
= $false )
| ( ( ( SV965
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV126 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV126 @ tc_bool ) ) @ SV965 ) @ SV554 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV126 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV554 @ SV126 ) ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV965 @ SV126 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV126 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3713]) ).
thf(3906,plain,
! [SV555: $i,SV127: $i,SV966: $i] :
( ( ( c_Finite__Set_Ofinite @ SV966 @ SV127 )
= $false )
| ( ( ( SV555
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV127 @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV127 @ tc_bool ) ) @ SV555 ) @ SV966 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV127 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV555 @ SV127 ) ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV966 @ SV127 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3714]) ).
thf(3907,plain,
! [SV969: $i,SV1264: $i,SV558: $i,SV130: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV130 @ ( c_Set_Oinsert @ SV558 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1264 @ tc_bool ) ) @ SV1264 ) @ ( tc_fun @ SV1264 @ tc_bool ) ) @ SV969 @ ( tc_fun @ SV1264 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV558 @ SV969 @ SV1264 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1264 @ tc_bool ) ) @ SV130 ) @ SV969 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV130 @ ( c_Set_Oinsert @ SV558 @ SV969 @ SV1264 ) @ ( tc_fun @ SV1264 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3716]) ).
thf(3908,plain,
! [SV559: $i,SV1265: $i,SV970: $i,SV131: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ SV970 ) @ SV1265 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ SV559 ) @ SV1265 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV559 @ SV970 @ SV131 ) ) @ SV1265 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3717]) ).
thf(3909,plain,
! [SV560: $i,SV1266: $i,SV971: $i,SV132: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ SV971 ) @ SV1266 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ SV560 ) @ SV1266 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV560 @ SV971 @ SV132 ) ) @ SV1266 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV132 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3718]) ).
thf(3910,plain,
! [SV1533: $i,SV1515: $i,SV1485: $i,SV1425: $i,SV1267: $i,SV979: $i,SV570: $i,SV143: $i] :
( ( ! [SY4123: $i] :
( ( ( hAPP @ SV143 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV570 @ tc_bool ) ) )
= SV979 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV143 @ SV1267 @ SV1425 @ SV1485 @ SV1515 @ SV1533 @ SY4123 @ SV979 @ SV570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3724]) ).
thf(3911,plain,
! [SV1534: $i,SV1516: $i,SV1486: $i,SV1426: $i,SV1268: $i,SV980: $i,SV571: $i,SV144: $i] :
( ( ! [SY4124: $i] :
( ( ( hAPP @ SV144 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV571 @ tc_bool ) ) )
= SV980 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1268 @ SV144 @ SV1426 @ SV1486 @ SV1516 @ SV1534 @ SV980 @ SY4124 @ SV571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3725]) ).
thf(3912,plain,
! [SV1535: $i,SV1517: $i,SV1487: $i,SV1427: $i,SV1271: $i,SV989: $i,SV588: $i,SV161: $i] :
( ( ! [SY4125: $i,SY4126: $i,SY4127: $i] :
( ( ( hAPP @ SV161 @ ( c_Set_Oinsert @ SV588 @ SV989 @ SV1271 ) )
= ( hAPP @ ( hAPP @ SV1427 @ SV588 ) @ ( hAPP @ SV161 @ SV989 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV161 @ SV1487 @ SV1517 @ SV1535 @ SV1427 @ SY4125 @ SY4126 @ SY4127 @ SV1271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3726]) ).
thf(3913,plain,
! [SV1536: $i,SV1518: $i,SV1488: $i,SV1428: $i,SV1272: $i,SV990: $i,SV589: $i,SV162: $i] :
( ( ! [SY4128: $i,SY4129: $i,SY4130: $i] :
( ( ( hAPP @ SV162 @ ( c_Set_Oinsert @ SV589 @ SV990 @ SV1272 ) )
= ( hAPP @ ( hAPP @ SV1428 @ SV589 ) @ ( hAPP @ SV162 @ SV990 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1488 @ SV162 @ SV1518 @ SV1536 @ SY4128 @ SV1428 @ SY4129 @ SY4130 @ SV1272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3727]) ).
thf(3914,plain,
! [SV597: $i,SV170: $i,SV998: $i,SV1276: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV998 ) @ SV170 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1276 @ tc_bool ) ) @ SV170 ) @ SV597 ) )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV170 @ ( c_HOL_Ominus__class_Ominus @ SV597 @ SV998 @ ( tc_fun @ SV1276 @ tc_bool ) ) @ ( tc_fun @ SV1276 @ tc_bool ) )
= SV998 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3729]) ).
thf(3915,plain,
! [SV171: $i,SV598: $i,SV1277: $i,SV999: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV999 @ tc_bool ) ) @ SV1277 ) @ SV598 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV171 @ SV1277 @ SV999 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV171 @ SV598 @ SV999 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3730]) ).
thf(3916,plain,
! [SV599: $i,SV1000: $i,SV1278: $i,SV172: $i] :
( ( ( hBOOL @ ( c_in @ SV172 @ SV1278 @ SV1000 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1000 @ tc_bool ) ) @ SV1278 ) @ SV599 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV172 @ SV599 @ SV1000 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3731]) ).
thf(3917,plain,
! [SV173: $i,SV600: $i,SV1279: $i,SV1001: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1001 @ tc_bool ) ) @ SV1279 ) @ SV600 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV173 @ SV1279 @ SV1001 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV173 @ SV600 @ SV1001 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3732]) ).
thf(3918,plain,
! [SV174: $i,SV601: $i,SV1280: $i,SV1002: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1002 @ tc_bool ) ) @ SV1280 ) @ SV601 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV174 @ SV1280 @ SV1002 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV174 @ SV601 @ SV1002 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3733]) ).
thf(3919,plain,
! [SV1283: $i,SV604: $i,SV1429: $i,SV1005: $i,SV177: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ SV1005 ) @ SV1429 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ SV604 ) @ SV1283 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV604 @ SV1005 @ ( tc_fun @ SV177 @ tc_bool ) ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1283 @ SV1429 @ ( tc_fun @ SV177 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3734]) ).
thf(3920,plain,
! [SV1284: $i,SV607: $i,SV1008: $i,SV1430: $i,SV180: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ SV1430 ) @ SV1008 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ SV607 ) @ SV1284 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV607 @ SV1008 @ ( tc_fun @ SV180 @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1284 @ SV1430 @ ( tc_fun @ SV180 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3735]) ).
thf(3921,plain,
! [SV1012: $i,SV1285: $i,SV611: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV184 @ tc_bool ) ) @ SV611 ) @ SV1285 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV184 @ tc_bool ) ) @ SV1012 ) @ SV1285 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV184 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV611 @ SV1012 @ ( tc_fun @ SV184 @ tc_bool ) ) ) @ SV1285 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3736]) ).
thf(3922,plain,
! [SV1015: $i,SV1286: $i,SV614: $i,SV187: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV187 @ tc_bool ) ) @ SV614 ) @ SV1286 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV187 @ tc_bool ) ) @ SV1015 ) @ SV1286 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV187 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV614 @ SV1015 @ ( tc_fun @ SV187 @ tc_bool ) ) ) @ SV1286 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3737]) ).
thf(3923,plain,
! [SV1287: $i,SV1017: $i,SV616: $i,SV189: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV189 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV616 @ ( c_Set_Oinsert @ SV1017 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV189 @ tc_bool ) ) @ SV189 ) @ ( tc_fun @ SV189 @ tc_bool ) ) ) @ SV1287 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV1017 @ SV616 @ SV189 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV189 @ tc_bool ) ) @ SV616 ) @ ( c_Set_Oinsert @ SV1017 @ SV1287 @ SV189 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3738]) ).
thf(3924,plain,
! [SV1288: $i,SV1018: $i,SV617: $i,SV190: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV190 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV617 @ ( c_Set_Oinsert @ SV1018 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV190 @ tc_bool ) ) @ SV190 ) @ ( tc_fun @ SV190 @ tc_bool ) ) ) @ SV1288 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV1018 @ SV617 @ SV190 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV190 @ tc_bool ) ) @ SV617 ) @ ( c_Set_Oinsert @ SV1018 @ SV1288 @ SV190 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3739]) ).
thf(3925,plain,
! [SV1289: $i,SV1019: $i,SV618: $i,SV191: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV191 @ tc_bool ) ) @ SV618 ) @ ( c_Set_Oinsert @ SV1019 @ SV1289 @ SV191 ) ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV1019 @ SV618 @ SV191 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV191 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV618 @ ( c_Set_Oinsert @ SV1019 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV191 @ tc_bool ) ) @ SV191 ) @ ( tc_fun @ SV191 @ tc_bool ) ) ) @ SV1289 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3740]) ).
thf(3926,plain,
! [SV1431: $i,SV1290: $i,SV1023: $i,SV622: $i,SV195: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV195 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV622 @ SV1023 @ SV195 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1290 @ SV1431 @ SV195 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV195 ) @ SV622 ) @ SV1023 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV195 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3742]) ).
thf(3927,plain,
! [SV1432: $i,SV1291: $i,SV1024: $i,SV623: $i,SV196: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV196 ) @ SV623 ) @ SV1024 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV196 ) @ SV1024 ) @ SV1291 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV196 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1024 @ SV1291 @ SV196 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV623 @ SV1432 @ SV196 ) ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV196 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3743]) ).
thf(3928,plain,
! [SV1433: $i,SV1292: $i,SV1025: $i,SV624: $i,SV197: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV197 ) @ SV624 ) @ SV1025 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV197 ) @ SV1292 ) @ SV624 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV197 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1292 @ SV624 @ SV197 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1433 @ SV1025 @ SV197 ) ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3744]) ).
thf(3929,plain,
! [SV1434: $i,SV1293: $i,SV1026: $i,SV625: $i,SV198: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV198 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV625 @ SV1026 @ SV198 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1293 @ SV1434 @ SV198 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV198 ) @ SV1026 ) @ SV1434 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV198 ) @ SV1293 ) @ SV625 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3745]) ).
thf(3930,plain,
! [SV1435: $i,SV1294: $i,SV1027: $i,SV626: $i,SV199: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV199 ) @ SV626 ) @ SV1027 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV199 ) @ SV1294 ) @ SV1027 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV199 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1027 @ SV1294 @ SV199 ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV626 @ SV1435 @ SV199 ) ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3746]) ).
thf(3931,plain,
! [SV629: $i,SV1295: $i,SV1030: $i,SV202: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ SV1030 ) @ SV1295 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ SV629 ) @ SV1295 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV629 @ SV1030 @ SV202 ) ) @ SV1295 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV202 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3747]) ).
thf(3932,plain,
! [SV1035: $i,SV634: $i,SV1296: $i,SV207: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV207 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1296 @ SV634 @ SV207 ) ) @ SV1035 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV207 ) @ SV634 ) @ SV1035 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV207 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3752]) ).
thf(3933,plain,
! [SV1036: $i,SV1297: $i,SV635: $i,SV208: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV208 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV635 @ SV1297 @ SV208 ) ) @ SV1036 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV208 ) @ SV635 ) @ SV1036 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3753]) ).
thf(3934,plain,
! [SV1037: $i,SV1298: $i,SV636: $i,SV209: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV209 ) @ SV636 ) @ SV1298 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV209 ) @ SV636 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1037 @ SV1298 @ SV209 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3754]) ).
thf(3935,plain,
! [SV1299: $i,SV1038: $i,SV637: $i,SV210: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV210 ) @ SV637 ) @ SV1038 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV210 ) @ SV637 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1038 @ SV1299 @ SV210 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3755]) ).
thf(3936,plain,
! [SV1039: $i,SV638: $i,SV1300: $i,SV211: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV211 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1300 @ SV638 @ SV211 ) ) @ SV1039 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV211 ) @ SV638 ) @ SV1039 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV211 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3756]) ).
thf(3937,plain,
! [SV1040: $i,SV1301: $i,SV639: $i,SV212: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV212 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV639 @ SV1301 @ SV212 ) ) @ SV1040 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV212 ) @ SV639 ) @ SV1040 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3757]) ).
thf(3938,plain,
! [SV1305: $i,SV1045: $i,SV223: $i,SV1436: $i,SV1489: $i,SV650: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV650 @ SV1489 ) @ SV1436 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1489 @ SV223 @ SV1045 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV223 @ SV650 @ SV1045 @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1436 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3758]) ).
thf(3939,plain,
! [SV1306: $i,SV1046: $i,SV224: $i,SV1437: $i,SV1490: $i,SV651: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV651 @ SV1490 ) @ SV1437 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1490 @ SV224 @ SV1046 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV224 @ SV651 @ SV1046 @ ( tc_fun @ SV1306 @ tc_bool ) ) @ SV1437 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3759]) ).
thf(3940,plain,
! [SV1537: $i,SV1519: $i,SV1491: $i,SV1438: $i,SV1307: $i,SV1053: $i,SV658: $i,SV231: $i] :
( ( ! [SY4131: $i,SY4132: $i,SY4133: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV231 @ SV658 ) @ ( hAPP @ SV1053 @ SV1307 ) ) )
| ~ ( hBOOL @ ( c_in @ SV658 @ SV1307 @ SV1438 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1491 @ SV1053 @ SV231 @ SV1519 @ SV1537 @ SY4131 @ SY4132 @ SY4133 @ SV1438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3760]) ).
thf(3941,plain,
! [SV1538: $i,SV1520: $i,SV1492: $i,SV1439: $i,SV1308: $i,SV1054: $i,SV659: $i,SV232: $i] :
( ( ! [SY4134: $i,SY4135: $i,SY4136: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ ( hAPP @ SV659 @ SV1054 ) ) @ SV1308 ) )
| ~ ( hBOOL @ ( c_in @ SV1308 @ SV1054 @ SV1439 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV659 @ SV1492 @ SV232 @ SV1520 @ SV1538 @ SY4134 @ SY4135 @ SY4136 @ SV1439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3761]) ).
thf(3942,plain,
! [SV1310: $i,SV664: $i,SV1440: $i,SV1493: $i,SV1059: $i,SV237: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV237 @ ( hAPP @ SV1059 @ SV1493 ) @ SV1440 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1493 @ SV664 @ SV1310 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV237 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV664 @ SV1059 @ SV1310 @ ( tc_fun @ SV1440 @ tc_bool ) ) @ SV1440 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3762]) ).
thf(3943,plain,
! [SV1311: $i,SV665: $i,SV1441: $i,SV1494: $i,SV1060: $i,SV238: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV238 @ ( hAPP @ SV1060 @ SV1494 ) @ SV1441 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1494 @ SV665 @ SV1311 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV238 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV665 @ SV1060 @ SV1311 @ ( tc_fun @ SV1441 @ tc_bool ) ) @ SV1441 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3763]) ).
thf(3944,plain,
! [SV1442: $i,SV1321: $i,SV1078: $i,SV685: $i,SV258: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV258 ) @ ( hAPP @ SV685 @ SV1078 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1321 @ SV685 @ SV1442 @ SV258 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1078 @ SV1321 @ SV1442 ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV258 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3766]) ).
thf(3945,plain,
! [SV1326: $i,SV695: $i,SV268: $i,SV1495: $i,SV1444: $i,SV1087: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV1087 @ SV1444 @ SV1495 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV268 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1444 @ SV695 @ SV1495 @ ( tc_fun @ SV268 @ tc_bool ) ) ) @ SV1326 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV268 @ tc_bool ) ) @ ( hAPP @ SV695 @ SV1087 ) ) @ SV1326 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3769]) ).
thf(3946,plain,
! [SV701: $i,SV1332: $i,SV1093: $i,SV274: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV274 ) @ SV1093 ) @ SV1332 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV274 ) @ SV701 ) @ SV1093 ) ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV701 @ SV1093 @ SV274 ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1093 @ SV1332 @ SV274 ) @ ( tc_fun @ SV274 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV701 @ SV1332 @ SV274 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV274 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3773]) ).
thf(3947,plain,
! [SV704: $i,SV1335: $i,SV1096: $i,SV277: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV277 ) @ SV1096 ) @ SV1335 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV277 ) @ SV704 ) @ SV1096 ) ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV704 @ SV1096 @ SV277 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1096 @ SV1335 @ SV277 ) @ ( tc_fun @ SV277 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV704 @ SV1335 @ SV277 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV277 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3774]) ).
thf(3948,plain,
! [SV1101: $i,SV1339: $i,SV710: $i,SV283: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV283 ) @ SV710 ) @ SV1339 ) )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV710 @ SV1101 @ SV283 ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV710 @ SV1339 @ SV283 ) @ ( tc_fun @ SV283 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1339 @ SV1101 @ SV283 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3776]) ).
thf(3949,plain,
! [SV1448: $i,SV1341: $i,SV1104: $i,SV714: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV287 ) @ SV714 ) @ SV1104 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV287 ) @ SV714 ) @ SV1341 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV287 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1341 @ SV714 @ SV287 ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1448 @ SV1104 @ SV287 ) ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV287 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3778]) ).
thf(3950,plain,
! [SV1539: $i,SV1521: $i,SV1496: $i,SV1449: $i,SV1342: $i,SV1105: $i,SV717: $i,SV292: $i] :
( ( ! [SY4137: $i,SY4138: $i] :
( ( ( hAPP @ SV292 @ ( c_Set_Oinsert @ SV717 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1105 @ tc_bool ) ) @ SV1105 ) )
= SV717 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV292 @ SV1342 @ SV1449 @ SV1496 @ SV1521 @ SV1539 @ SY4137 @ SY4138 @ SV1105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3779]) ).
thf(3951,plain,
! [SV1540: $i,SV1522: $i,SV1497: $i,SV1450: $i,SV1343: $i,SV1106: $i,SV718: $i,SV293: $i] :
( ( ! [SY4139: $i,SY4140: $i] :
( ( ( hAPP @ SV293 @ ( c_Set_Oinsert @ SV718 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1106 @ tc_bool ) ) @ SV1106 ) )
= SV718 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1343 @ SV293 @ SV1450 @ SV1497 @ SV1522 @ SV1540 @ SY4139 @ SY4140 @ SV1106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3780]) ).
thf(3952,plain,
! [SV1541: $i,SV1523: $i,SV1498: $i,SV1451: $i,SV1345: $i,SV1109: $i,SV725: $i,SV300: $i] :
( ( ! [SY4141: $i,SY4142: $i,SY4143: $i] :
( ( ( hAPP @ SV300 @ ( c_Set_Oinsert @ SV725 @ ( c_Set_Oinsert @ SV1109 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1345 @ tc_bool ) ) @ SV1345 ) @ SV1345 ) )
= ( hAPP @ ( hAPP @ SV1451 @ SV725 ) @ SV1109 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV300 @ SV1498 @ SV1523 @ SV1541 @ SV1451 @ SY4141 @ SY4142 @ SY4143 @ SV1345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3781]) ).
thf(3953,plain,
! [SV1542: $i,SV1524: $i,SV1499: $i,SV1452: $i,SV1346: $i,SV1110: $i,SV726: $i,SV301: $i] :
( ( ! [SY4144: $i,SY4145: $i,SY4146: $i] :
( ( ( hAPP @ SV301 @ ( c_Set_Oinsert @ SV726 @ ( c_Set_Oinsert @ SV1110 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1346 @ tc_bool ) ) @ SV1346 ) @ SV1346 ) )
= ( hAPP @ ( hAPP @ SV1452 @ SV726 ) @ SV1110 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1499 @ SV301 @ SV1524 @ SV1542 @ SY4144 @ SV1452 @ SY4145 @ SY4146 @ SV1346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3782]) ).
thf(3954,plain,
! [SV1119: $i,SV316: $i,SV1350: $i,SV740: $i] :
( ( ( hBOOL @ ( c_in @ SV740 @ SV1350 @ SV316 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV316 @ tc_bool ) ) @ SV1119 ) @ SV1350 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV316 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV740 @ SV1119 @ SV316 ) ) @ SV1350 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3783]) ).
thf(3955,plain,
! [SV1525: $i,SV1500: $i,SV1453: $i,SV1356: $i,SV1125: $i,SV746: $i,SV322: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV322 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV746 @ SV1125 @ SV1356 @ 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 )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1453 @ SV1500 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV322 @ SV746 @ SV1356 @ SV1125 @ SV1525 @ SV1453 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1525 @ SV1500 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV322 @ SV746 @ SV1356 @ SV1125 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV322 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1525 @ SV1125 @ SV1453 @ 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_or_pos,[status(thm)],[3788]) ).
thf(3956,plain,
! [SV1526: $i,SV1501: $i,SV1454: $i,SV1357: $i,SV1126: $i,SV747: $i,SV323: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV323 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV747 @ SV1126 @ SV1357 @ 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 )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1454 @ SV1501 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV747 @ SV1526 @ SV1357 @ SV1454 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1526 @ SV1501 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV747 @ SV1526 @ SV1357 @ SV1454 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV323 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1526 @ SV1126 @ SV1454 @ 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_or_pos,[status(thm)],[3789]) ).
thf(3957,plain,
! [SV1527: $i,SV1502: $i,SV1455: $i,SV1358: $i,SV1127: $i,SV748: $i,SV324: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV324 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV748 @ SV1127 @ SV1358 @ 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 )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1455 @ SV1502 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV324 @ SV748 @ SV1358 @ SV1127 @ SV1527 @ SV1455 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1527 @ SV1502 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV324 @ SV748 @ SV1358 @ SV1127 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV324 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1527 @ SV1127 @ SV1455 @ 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_or_pos,[status(thm)],[3790]) ).
thf(3958,plain,
! [SV1503: $i,SV1456: $i,SV1129: $i,SV750: $i,SV326: $i,SV1360: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1360 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV326 @ SV750 @ SV1360 @ SV1129 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV326 @ SV750 @ SV1360 @ SV1129 @ SV1456 @ SV1503 ) ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV326 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1456 @ SV1129 @ SV1503 @ 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 )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV326 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV750 @ SV1129 @ SV1360 @ 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_or_pos,[status(thm)],[3791]) ).
thf(3959,plain,
! [SV1362: $i,SV1457: $i,SV1131: $i,SV752: $i,SV328: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV328 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV752 @ SV1131 @ SV1457 @ 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 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1457 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SV1362 @ SV1457 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SV1362 @ SV1457 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV328 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV752 @ SV1131 @ SV1362 @ 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_not_pos,[status(thm)],[3792]) ).
thf(3960,plain,
! [SV1132: $i,SV329: $i,SV1504: $i,SV1363: $i,SV1458: $i,SV753: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV753 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV753 @ SV1458 @ SV1363 @ SV1504 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV753 @ SV1458 @ SV1363 @ SV1504 ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV329 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1458 @ SV1132 @ SV1504 @ 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 )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV329 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV753 @ SV1132 @ SV1363 @ 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_or_pos,[status(thm)],[3793]) ).
thf(3961,plain,
! [SV754: $i,SV1364: $i,SV1133: $i,SV1459: $i,SV330: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV330 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1459 @ SV1133 @ SV1364 @ 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 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV754 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV754 @ SV1459 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV754 @ SV1459 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV330 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV754 @ SV1133 @ SV1364 @ 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_not_pos,[status(thm)],[3794]) ).
thf(3962,plain,
! [SV1505: $i,SV1460: $i,SV1134: $i,SV755: $i,SV331: $i,SV1365: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1365 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV331 @ SV755 @ SV1365 @ SV1134 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV331 @ SV755 @ SV1365 @ SV1134 @ SV1460 @ SV1505 ) ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV331 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1460 @ SV1134 @ SV1505 @ 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 )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV331 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV755 @ SV1134 @ SV1365 @ 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_or_pos,[status(thm)],[3795]) ).
thf(3963,plain,
! [SV1366: $i,SV1135: $i,SV332: $i,SV756: $i,SV1461: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1461 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV756 @ SV1461 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV756 @ SV1461 ) ) )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV332 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1461 @ SV1135 @ SV1366 @ 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 )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV332 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV756 @ SV1135 @ SV1366 @ 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_not_pos,[status(thm)],[3796]) ).
thf(3964,plain,
! [SV1136: $i,SV333: $i,SV1506: $i,SV1462: $i,SV757: $i,SV1367: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1367 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV757 @ SV1462 @ SV1367 @ SV1506 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV757 @ SV1462 @ SV1367 @ SV1506 ) ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV333 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1462 @ SV1136 @ SV1506 @ 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 )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV333 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV757 @ SV1136 @ SV1367 @ 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_or_pos,[status(thm)],[3797]) ).
thf(3965,plain,
! [SV1137: $i,SV758: $i,SV334: $i,SV1463: $i,SV1368: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1368 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SV1368 @ SV1463 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SV1368 @ SV1463 ) ) )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV334 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV758 @ SV1137 @ SV1463 @ 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 )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV334 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV758 @ SV1137 @ SV1368 @ 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_not_pos,[status(thm)],[3798]) ).
thf(3966,plain,
! [SV1370: $i,SV1139: $i,SV760: $i,SV336: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV336 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV760 @ ( c_Set_Oinsert @ SV1139 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV336 @ tc_bool ) ) @ SV336 ) @ ( tc_fun @ SV336 @ tc_bool ) ) ) @ SV1370 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV336 @ tc_bool ) ) @ SV760 ) @ SV1370 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV336 @ tc_bool ) ) @ SV760 ) @ ( c_Set_Oinsert @ SV1139 @ SV1370 @ SV336 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3799]) ).
thf(3967,plain,
! [SV1528: $i,SV1507: $i,SV1464: $i,SV1371: $i,SV1140: $i,SV761: $i,SV337: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV761 @ ( c_Com_Ocom_OSemi @ SV1140 @ SV1371 ) @ SV1464 @ SV1507 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) ) @ SV1507 )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1528 @ SV1371 @ SV1464 @ SV1507 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) ) @ SV1507 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV761 @ SV1140 @ SV1528 @ SV1507 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) ) @ SV1507 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3800]) ).
thf(3968,plain,
! [SV1143: $i,SV1373: $i,SV764: $i,SV340: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV340 @ ( c_Set_Oinsert @ SV764 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1373 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1373 ) ) @ SV1373 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV340 @ SV1143 @ SV1373 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV340 @ ( c_Set_Oinsert @ SV764 @ SV1143 @ ( tc_Hoare__Mirabelle_Otriple @ SV1373 ) ) @ SV1373 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3801]) ).
thf(3969,plain,
! [SV766: $i,SV1145: $i,SV1374: $i,SV342: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV342 @ SV1374 @ SV1145 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1145 ) @ tc_bool ) ) @ SV766 ) @ SV1374 ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV342 @ SV766 @ SV1145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3802]) ).
thf(3970,plain,
! [SV343: $i,SV1146: $i,SV767: $i,SV1375: $i] :
( ( ( hBOOL @ ( hAPP @ SV1375 @ SV767 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1146 @ tc_bool ) ) @ SV1375 ) @ SV343 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV343 @ SV767 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3803]) ).
thf(3971,plain,
! [SV770: $i,SV346: $i,SV1147: $i,SV1376: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1376 @ tc_bool ) ) @ SV1147 ) @ SV346 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1147 @ SV770 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV346 @ SV770 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3804]) ).
thf(3972,plain,
! [SV1148: $i,SV1377: $i,SV771: $i,SV347: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV347 @ tc_bool ) ) @ SV771 ) @ SV1377 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV347 @ tc_bool ) ) @ SV1377 ) @ SV1148 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV347 @ tc_bool ) ) @ SV771 ) @ SV1148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3805]) ).
thf(3973,plain,
! [SV774: $i,SV1149: $i,SV1378: $i,SV350: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV1378 ) @ SV1149 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV774 ) @ SV1378 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV774 ) @ SV1149 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV350 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3806]) ).
thf(3974,plain,
! [SV1150: $i,SV1379: $i,SV775: $i,SV351: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV775 ) @ SV1379 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV1379 ) @ SV1150 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV775 ) @ SV1150 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV351 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3807]) ).
thf(3975,plain,
! [SV354: $i,SV1153: $i,SV778: $i,SV1380: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV1380 @ SV778 @ SV1153 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV354 @ SV1380 @ SV1153 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV354 @ SV778 @ SV1153 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3808]) ).
thf(3976,plain,
! [SV1154: $i,SV780: $i,SV357: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV357 ) @ SV780 ) @ SV1154 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV357 ) @ SV1154 ) @ SV780 ) ) )
= $true )
| ( ( SV780 = SV1154 )
= $true )
| ( ( class_Orderings_Oorder @ SV357 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3809]) ).
thf(3977,plain,
! [SV781: $i,SV1155: $i,SV358: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV358 ) @ SV1155 ) @ SV781 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV358 ) @ SV781 ) @ SV1155 ) ) )
= $true )
| ( ( SV781 = SV1155 )
= $true )
| ( ( class_Orderings_Oorder @ SV358 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3810]) ).
thf(3978,plain,
! [SV782: $i,SV1156: $i,SV359: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV359 ) @ SV1156 ) @ SV782 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV359 ) @ SV782 ) @ SV1156 ) ) )
= $true )
| ( ( SV782 = SV1156 )
= $true )
| ( ( class_Orderings_Oorder @ SV359 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3811]) ).
thf(3979,plain,
! [SV1465: $i,SV1386: $i,SV1168: $i,SV798: $i,SV375: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV375 ) @ ( hAPP @ SV798 @ SV1168 ) ) @ ( hAPP @ SV1386 @ SV1168 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1465 @ SV375 ) ) @ SV798 ) @ SV1386 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV375 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3815]) ).
thf(3980,plain,
! [SV1387: $i,SV1172: $i,SV815: $i,SV392: $i] :
( ( ( hBOOL @ ( c_in @ SV392 @ SV815 @ SV1172 ) )
= $true )
| ( ( SV815 = SV1387 )
= $true )
| ( ( hBOOL @ ( c_in @ SV392 @ SV1387 @ SV1172 ) )
= $true )
| ( ( ( c_Set_Oinsert @ SV392 @ SV815 @ SV1172 )
= ( c_Set_Oinsert @ SV392 @ SV1387 @ SV1172 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3817]) ).
thf(3981,plain,
! [SV1529: $i,SV1508: $i,SV1466: $i,SV1389: $i,SV1175: $i,SV818: $i,SV395: $i] :
( ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV395 @ SV818 @ SV1175 @ SV1389 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1466 @ SV1508 @ SV1529 @ SV1389 ) )
= $true )
| ( ( SV395 = SV1466 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3818]) ).
thf(3982,plain,
! [SV398: $i,SV1177: $i,SV821: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV821 @ SV1177 @ SV398 )
= $false )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV398 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV821 @ SV1177 @ SV398 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV398 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3819]) ).
thf(3983,plain,
! [SV1467: $i,SV1180: $i,SV401: $i,SV1390: $i,SV824: $i] :
( ( ( SV824 = SV1390 )
= $true )
| ( ( SV401 = SV1390 )
= $true )
| ( ( ( c_Set_Oinsert @ SV401 @ ( c_Set_Oinsert @ SV824 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1180 @ tc_bool ) ) @ SV1180 ) @ SV1180 )
= ( c_Set_Oinsert @ SV1390 @ ( c_Set_Oinsert @ SV1467 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1180 @ tc_bool ) ) @ SV1180 ) @ SV1180 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3821]) ).
thf(3984,plain,
! [SV1391: $i,SV1182: $i,SV403: $i,SV826: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV826 @ SV826 @ SV403 )
= ( c_HOL_Ominus__class_Ominus @ SV1182 @ SV1391 @ SV403 ) )
= $false )
| ( ( SV1182 = SV1391 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV403 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3822]) ).
thf(3985,plain,
! [SV1183: $i,SV827: $i,SV404: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV404 ) @ SV827 ) @ SV1183 ) )
= $false )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV404 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV827 @ SV1183 @ SV404 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV404 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3823]) ).
thf(3986,plain,
! [SV1185: $i,SV829: $i,SV406: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV406 ) @ SV829 ) @ SV1185 ) )
= $false )
| ( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV829 @ SV1185 @ SV406 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV406 @ tc_bool ) ) )
= $false )
| ( ( class_Orderings_Oorder @ SV406 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3824]) ).
thf(3987,plain,
! [SV1392: $i,SV1187: $i,SV832: $i,SV1468: $i,SV409: $i] :
( ( ( SV409 = SV1468 )
= $true )
| ( ( SV832 = SV1468 )
= $true )
| ( ( ( c_Set_Oinsert @ SV409 @ ( c_Set_Oinsert @ SV832 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1187 @ tc_bool ) ) @ SV1187 ) @ SV1187 )
= ( c_Set_Oinsert @ SV1392 @ ( c_Set_Oinsert @ SV1468 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1187 @ tc_bool ) ) @ SV1187 ) @ SV1187 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3825]) ).
thf(3988,plain,
! [SV1188: $i,SV410: $i,SV1393: $i,SV1469: $i,SV833: $i] :
( ( ( ( hAPP @ SV833 @ SV1469 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1393 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1469 @ SV410 @ SV1188 ) ) )
= $true )
| ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV410 @ SV833 @ SV1188 @ ( tc_fun @ SV1393 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1393 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3826]) ).
thf(3989,plain,
! [SV1470: $i,SV1394: $i,SV411: $i,SV1189: $i,SV834: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV834 @ SV1189 @ SV411 )
!= ( c_HOL_Ominus__class_Ominus @ SV1394 @ SV1470 @ SV411 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV411 ) @ SV1470 ) @ SV1394 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV411 ) @ SV1189 ) @ SV834 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV411 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3827]) ).
thf(3990,plain,
! [SV1395: $i,SV836: $i,SV413: $i,SV1471: $i,SV1191: $i] :
( ( ( ( hAPP @ SV1191 @ SV1471 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV413 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1471 @ SV836 @ SV1395 ) ) )
= $true )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV413 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV836 @ SV1191 @ SV1395 @ ( tc_fun @ SV413 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3829]) ).
thf(3991,plain,
! [SV414: $i,SV1192: $i,SV837: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV837 @ SV1192 @ SV414 )
= $false )
| ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ SV837 @ SV1192 @ SV414 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV414 @ tc_bool ) ) )
= $false )
| ( ( class_Orderings_Oorder @ SV414 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3830]) ).
thf(3992,plain,
! [SV1193: $i,SV415: $i,SV1472: $i,SV1396: $i,SV838: $i] :
( ( ( SV838 = SV1396 )
= $true )
| ( ( SV838 = SV1472 )
= $true )
| ( ( ( c_Set_Oinsert @ SV415 @ ( c_Set_Oinsert @ SV838 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SV1193 ) @ SV1193 )
= ( c_Set_Oinsert @ SV1396 @ ( c_Set_Oinsert @ SV1472 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1193 @ tc_bool ) ) @ SV1193 ) @ SV1193 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3831]) ).
thf(3993,plain,
! [SV416: $i,SV1194: $i,SV839: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV839 @ SV1194 @ SV416 )
= $false )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV416 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV839 @ SV1194 @ SV416 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV416 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3832]) ).
thf(3994,plain,
! [SV1530: $i,SV1509: $i,SV1473: $i,SV1397: $i,SV1196: $i,SV841: $i,SV418: $i] :
( ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV418 @ SV841 @ SV1196 @ SV1397 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1473 @ SV1509 @ SV1530 @ SV1397 ) )
= $true )
| ( ( SV1196 = SV1530 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3833]) ).
thf(3995,plain,
! [SV1474: $i,SV1398: $i,SV419: $i,SV1197: $i,SV842: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV842 @ SV1197 @ SV419 )
!= ( c_HOL_Ominus__class_Ominus @ SV1398 @ SV1474 @ SV419 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV419 ) @ SV1197 ) @ SV842 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV419 ) @ SV1474 ) @ SV1398 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV419 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3834]) ).
thf(3996,plain,
! [SV1531: $i,SV1510: $i,SV1475: $i,SV1399: $i,SV1199: $i,SV844: $i,SV421: $i] :
( ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV421 @ SV844 @ SV1199 @ SV1399 )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1475 @ SV1510 @ SV1531 @ SV1399 ) )
= $true )
| ( ( SV844 = SV1510 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3836]) ).
thf(3997,plain,
! [SV1476: $i,SV1401: $i,SV423: $i,SV1201: $i,SV846: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV846 @ SV1201 @ SV423 )
!= ( c_HOL_Ominus__class_Ominus @ SV1401 @ SV1476 @ SV423 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1401 @ SV1476 @ SV423 )
| ~ ( c_HOL_Oord__class_Oless @ SV846 @ SV1201 @ SV423 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV423 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3837]) ).
thf(3998,plain,
! [SV424: $i,SV1202: $i,SV847: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV847 @ SV1202 @ SV424 )
= $false )
| ( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV847 @ SV1202 @ SV424 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV424 @ tc_bool ) ) )
= $false )
| ( ( class_Orderings_Oorder @ SV424 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3838]) ).
thf(3999,plain,
! [SV1477: $i,SV1402: $i,SV427: $i,SV1205: $i,SV850: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV850 @ SV1205 @ SV427 )
!= ( c_HOL_Ominus__class_Ominus @ SV1402 @ SV1477 @ SV427 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV850 @ SV1205 @ SV427 )
| ~ ( c_HOL_Oord__class_Oless @ SV1402 @ SV1477 @ SV427 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV427 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3839]) ).
thf(4000,plain,
! [SV1403: $i,SV428: $i,SV1206: $i,SV851: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV851 @ SV1206 @ SV428 )
= ( c_HOL_Ominus__class_Ominus @ SV1403 @ SV1403 @ SV428 ) )
= $false )
| ( ( SV851 = SV1206 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV428 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3840]) ).
thf(4001,plain,
! [SV1208: $i,SV853: $i,SV1404: $i,SV1478: $i,SV430: $i] :
( ( ( SV430 = SV1478 )
= $true )
| ( ( SV430 = SV1404 )
= $true )
| ( ( ( c_Set_Oinsert @ SV430 @ ( c_Set_Oinsert @ SV853 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1208 @ tc_bool ) ) @ SV1208 ) @ SV1208 )
= ( c_Set_Oinsert @ SV1404 @ ( c_Set_Oinsert @ SV1478 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1208 @ tc_bool ) ) @ SV1208 ) @ SV1208 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3842]) ).
thf(4002,plain,
! [SV855: $i,SV432: $i,SV2: $i,SV1210: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1210 @ SV2 ) ) @ SV432 ) @ SV855 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1210 @ SV2 ) ) @ SV855 ) @ SV432 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV432 @ SV855 @ ( tc_fun @ SV1210 @ SV2 ) )
= $true )
| ( ( class_HOL_Oord @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3844]) ).
thf(4003,plain,
! [SV3: $i,SV433: $i,SV856: $i,SV1211: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1211 @ SV856 @ ( tc_fun @ SV433 @ SV3 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV433 @ SV3 ) ) @ SV856 ) @ SV1211 ) )
= $false )
| ( ( class_HOL_Oord @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3845]) ).
thf(4004,plain,
! [SV11: $i,SV441: $i,SV1405: $i,SV864: $i,SV1214: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV1214 @ SV864 @ SV1405 ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV864 @ SV1405 ) )
= $true )
| ( ( ( c_Finite__Set_Osetsum @ SV441 @ ( c_HOL_Ominus__class_Ominus @ SV864 @ ( c_Set_Oinsert @ SV1214 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1405 @ tc_bool ) ) @ SV1405 ) @ ( tc_fun @ SV1405 @ tc_bool ) ) @ SV1405 @ SV11 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV441 @ SV864 @ SV1405 @ SV11 ) @ ( hAPP @ SV441 @ SV1214 ) @ SV11 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3848]) ).
thf(4005,plain,
! [SV12: $i,SV442: $i,SV1406: $i,SV865: $i,SV1215: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV1215 @ SV865 @ SV1406 ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV865 @ SV1406 ) )
= $true )
| ( ( ( c_Finite__Set_Osetsum @ SV442 @ ( c_HOL_Ominus__class_Ominus @ SV865 @ ( c_Set_Oinsert @ SV1215 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1406 @ tc_bool ) ) @ SV1406 ) @ ( tc_fun @ SV1406 @ tc_bool ) ) @ SV1406 @ SV12 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV442 @ SV865 @ SV1406 @ SV12 ) @ ( hAPP @ SV442 @ SV1215 ) @ SV12 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3849]) ).
thf(4006,plain,
! [SV443: $i,SV1216: $i,SV866: $i,SV13: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV13 @ SV866 @ ( tc_fun @ SV1216 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV443 @ SV13 @ SV1216 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1216 @ tc_bool ) ) @ SV13 ) @ SV866 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV13 @ ( c_Set_Oinsert @ SV443 @ SV866 @ SV1216 ) @ ( tc_fun @ SV1216 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3850]) ).
thf(4007,plain,
! [SV446: $i,SV1219: $i,SV869: $i,SV16: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV16 ) @ SV869 ) @ SV1219 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV16 ) @ SV446 ) @ SV869 ) ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV446 @ SV869 @ SV16 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV869 @ SV1219 @ SV16 ) @ ( tc_fun @ SV16 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV446 @ SV1219 @ SV16 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3853]) ).
thf(4008,plain,
! [SV885: $i,SV1223: $i,SV466: $i,SV37: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV37 ) @ SV466 ) @ SV1223 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1223 @ SV885 @ SV37 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV466 @ SV885 @ SV37 )
= $true )
| ( ( class_Orderings_Oorder @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3858]) ).
thf(4009,plain,
! [SV886: $i,SV38: $i,SV1224: $i,SV467: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV467 @ SV1224 @ SV38 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV38 ) @ SV1224 ) @ SV886 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV467 @ SV886 @ SV38 )
= $true )
| ( ( class_Orderings_Oorder @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3859]) ).
thf(4010,plain,
! [SV468: $i,SV39: $i,SV887: $i,SV1225: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1225 @ SV887 @ SV39 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV39 ) @ SV468 ) @ SV1225 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV468 @ SV887 @ SV39 )
= $true )
| ( ( class_Orderings_Opreorder @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3860]) ).
thf(4011,plain,
! [SV469: $i,SV888: $i,SV1226: $i,SV40: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV40 ) @ SV1226 ) @ SV888 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV469 @ SV1226 @ SV40 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV469 @ SV888 @ SV40 )
= $true )
| ( ( class_Orderings_Opreorder @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3861]) ).
thf(4012,plain,
! [SV903: $i,SV485: $i,SV56: $i,SV1408: $i,SV1229: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1229 @ SV1408 @ SV56 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV56 ) @ SV1408 ) @ SV485 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1408 @ SV485 @ SV56 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1229 @ SV903 @ SV56 ) @ ( tc_fun @ SV56 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV485 @ SV903 @ SV56 )
= $true )
| ( ( class_Orderings_Oorder @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3872]) ).
thf(4013,plain,
! [SV1543: $i,SV1532: $i,SV1511: $i,SV1479: $i,SV1409: $i,SV1230: $i,SV904: $i,SV486: $i,SV57: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV57 @ SV486 @ ( c_COMBC @ SV904 @ SV1230 @ SV1230 @ tc_bool ) @ ( c_COMBC @ SV1409 @ SV1230 @ SV1230 @ tc_bool ) @ SV1479 @ SV1511 @ SV1532 @ SV1543 @ SV1230 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV486 @ SV57 @ SV904 @ SV1409 @ SV1511 @ SV1479 @ SV1543 @ SV1532 @ SV1230 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3873]) ).
thf(4014,plain,
! [SV907: $i,SV60: $i,SV1233: $i,SV489: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV489 @ SV1233 @ SV60 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1233 @ SV907 @ SV60 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV489 @ SV907 @ SV60 )
= $true )
| ( ( class_Orderings_Oorder @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3874]) ).
thf(4015,plain,
! [SV492: $i,SV63: $i,SV910: $i,SV1236: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1236 @ SV910 @ SV63 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV492 @ SV1236 @ SV63 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV492 @ SV910 @ SV63 )
= $true )
| ( ( class_Orderings_Opreorder @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3877]) ).
thf(4016,plain,
! [SV509: $i,SV922: $i,SV1412: $i,SV1238: $i,SV80: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV1238 ) @ SV1412 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV922 @ SV1412 @ SV80 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV922 ) @ SV1412 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV1238 ) @ SV509 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV509 @ SV922 @ SV80 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1238 @ SV1412 @ SV80 ) @ ( tc_fun @ SV80 @ tc_bool ) )
= $true )
| ( ( class_Orderings_Oorder @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3879]) ).
thf(4017,plain,
! [SV923: $i,SV510: $i,SV1413: $i,SV1239: $i,SV81: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV1239 ) @ SV1413 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1239 @ SV510 @ SV81 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV923 ) @ SV1413 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV1239 ) @ SV510 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV510 @ SV923 @ SV81 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1239 @ SV1413 @ SV81 ) @ ( tc_fun @ SV81 @ tc_bool ) )
= $true )
| ( ( class_Orderings_Oorder @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3880]) ).
thf(4018,plain,
! [SV92: $i,SV521: $i,SV934: $i,SV1240: $i,SV1414: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1414 @ tc_bool ) ) @ SV1240 ) @ SV934 ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV934 @ SV1414 ) )
= $true )
| ( ( ( c_Finite__Set_Osetsum @ SV521 @ ( c_HOL_Ominus__class_Ominus @ SV934 @ SV1240 @ ( tc_fun @ SV1414 @ tc_bool ) ) @ SV1414 @ SV92 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV521 @ SV934 @ SV1414 @ SV92 ) @ ( c_Finite__Set_Osetsum @ SV521 @ SV1240 @ SV1414 @ SV92 ) @ SV92 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3885]) ).
thf(4019,plain,
! [SV936: $i,SV1512: $i,SV1415: $i,SV1482: $i,SV1241: $i,SV523: $i,SV94: $i] :
( ( ( ~ ( c_Finite__Set_Ofold__graph @ SV94 @ SV523 @ SV1241 @ SV1482 @ SV1415 @ SV1512 ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV936 @ SV1241 @ SV1415 ) )
= $true )
| ( ( c_Finite__Set_Ofold__graph @ SV94 @ SV523 @ ( c_Set_Oinsert @ SV936 @ SV1241 @ SV1415 ) @ ( hAPP @ ( hAPP @ SV94 @ SV936 ) @ SV1482 ) @ SV1415 @ SV1512 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3886]) ).
thf(4020,plain,
! [SV939: $i,SV1416: $i,SV526: $i,SV1244: $i,SV97: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV97 ) @ SV1244 ) @ SV526 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1244 @ SV526 @ SV97 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1416 @ SV939 @ SV97 ) @ ( tc_fun @ SV97 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV97 ) @ SV526 ) @ SV939 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3889]) ).
thf(4021,plain,
! [SV1417: $i,SV527: $i,SV1245: $i,SV940: $i,SV98: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV98 ) @ SV940 ) @ SV1245 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV940 @ SV1245 @ SV98 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV527 @ SV1417 @ SV98 ) @ ( tc_fun @ SV98 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV98 ) @ SV527 ) @ SV940 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3890]) ).
thf(4022,plain,
! [SV941: $i,SV528: $i,SV99: $i,SV1418: $i,SV1246: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1246 @ SV1418 @ SV99 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV528 @ SV941 @ SV99 ) @ ( tc_fun @ SV99 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV99 ) @ SV528 ) @ SV941 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3891]) ).
thf(4023,plain,
! [SV942: $i,SV529: $i,SV1419: $i,SV1247: $i,SV100: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV100 ) @ SV1247 ) @ SV1419 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV100 ) @ SV529 ) @ SV942 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV529 @ SV942 @ SV100 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1247 @ SV1419 @ SV100 ) @ ( tc_fun @ SV100 @ tc_bool ) )
= $true )
| ( ( class_Orderings_Oorder @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3892]) ).
thf(4024,plain,
! [SV530: $i,SV1248: $i,SV943: $i,SV101: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV101 ) @ SV943 ) @ SV1248 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV101 ) @ SV530 ) @ SV943 ) ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV530 @ SV943 @ SV101 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV943 @ SV1248 @ SV101 ) @ ( tc_fun @ SV101 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV530 @ SV1248 @ SV101 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3893]) ).
thf(4025,plain,
! [SV531: $i,SV944: $i,SV1420: $i,SV102: $i,SV1249: $i] :
( ( ( ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1249 @ SV102 @ SV1420 @ ( tc_fun @ SV944 @ tc_bool ) ) @ SV944 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1249 @ SV1420 ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV531 @ SV1249 @ SV1420 ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ SV102 @ SV531 ) @ SV944 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3894]) ).
thf(4026,plain,
! [SV103: $i,SV532: $i,SV1421: $i,SV945: $i,SV1250: $i] :
( ( ( hBOOL @ ( c_in @ SV1250 @ SV945 @ SV1421 ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV945 @ SV1421 ) )
= $true )
| ( ( ( c_Finite__Set_Osetsum @ SV532 @ ( c_HOL_Ominus__class_Ominus @ SV945 @ ( c_Set_Oinsert @ SV1250 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1421 @ tc_bool ) ) @ SV1421 ) @ ( tc_fun @ SV1421 @ tc_bool ) ) @ SV1421 @ SV103 )
= ( c_Finite__Set_Osetsum @ SV532 @ SV945 @ SV1421 @ SV103 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3895]) ).
thf(4027,plain,
! [SV542: $i,SV114: $i,SV955: $i] :
( ( ( c_Finite__Set_Ofinite @ SV955 @ SV114 )
= $false )
| ( ( hBOOL @ ( c_in @ SV542 @ SV955 @ SV114 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV114 ) @ SV542 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV955 @ SV114 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3896]) ).
thf(4028,plain,
! [SV956: $i,SV115: $i,SV543: $i] :
( ( ( c_Finite__Set_Ofinite @ SV543 @ SV115 )
= $false )
| ( ( hBOOL @ ( c_in @ SV956 @ SV543 @ SV115 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV115 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV543 @ SV115 ) ) @ SV956 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3897]) ).
thf(4029,plain,
! [SV1513: $i,SV1423: $i,SV547: $i,SV119: $i,SV1483: $i,SV958: $i,SV1256: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV1256 @ SV958 @ SV1483 ) ) )
= $true )
| ( ( ~ ( c_Finite__Set_Ofold__graph @ SV119 @ SV547 @ ( c_HOL_Ominus__class_Ominus @ SV958 @ ( c_Set_Oinsert @ SV1256 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1483 @ tc_bool ) ) @ SV1483 ) @ ( tc_fun @ SV1483 @ tc_bool ) ) @ SV1423 @ SV1483 @ SV1513 ) )
= $true )
| ( ( c_Finite__Set_Ofold__graph @ SV119 @ SV547 @ SV958 @ ( hAPP @ ( hAPP @ SV119 @ SV1256 ) @ SV1423 ) @ SV1483 @ SV1513 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3899]) ).
thf(4030,plain,
! [SV960: $i,SV1258: $i,SV549: $i,SV121: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV121 @ ( c_Set_Oinsert @ SV549 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1258 @ tc_bool ) ) @ SV1258 ) @ ( tc_fun @ SV1258 @ tc_bool ) ) @ SV960 @ ( tc_fun @ SV1258 @ tc_bool ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV121 @ SV960 @ ( tc_fun @ SV1258 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV549 @ SV121 @ SV1258 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV121 @ ( c_Set_Oinsert @ SV549 @ SV960 @ SV1258 ) @ ( tc_fun @ SV1258 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3900]) ).
thf(4031,plain,
! [SV961: $i,SV1259: $i,SV550: $i,SV122: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV122 @ ( c_Set_Oinsert @ SV550 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1259 @ tc_bool ) ) @ SV1259 ) @ ( tc_fun @ SV1259 @ tc_bool ) ) @ SV961 @ ( tc_fun @ SV1259 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV550 @ SV961 @ SV1259 ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV550 @ SV122 @ SV1259 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV122 @ ( c_Set_Oinsert @ SV550 @ SV961 @ SV1259 ) @ ( tc_fun @ SV1259 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3901]) ).
thf(4032,plain,
! [SV962: $i,SV1260: $i,SV551: $i,SV123: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV123 @ ( c_Set_Oinsert @ SV551 @ SV1260 @ SV962 ) @ ( tc_fun @ SV962 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV551 @ SV1260 @ SV962 ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV551 @ SV123 @ SV962 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV123 @ ( c_Set_Oinsert @ SV551 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV962 @ tc_bool ) ) @ SV962 ) @ ( tc_fun @ SV962 @ tc_bool ) ) @ SV1260 @ ( tc_fun @ SV962 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3902]) ).
thf(4033,plain,
! [SV1514: $i,SV1424: $i,SV1484: $i,SV1261: $i,SV963: $i,SV552: $i,SV124: $i] :
( ( ( ~ ( c_Nitpick_Ofold__graph_H @ SV124 @ SV552 @ ( c_HOL_Ominus__class_Ominus @ SV963 @ ( c_Set_Oinsert @ SV1261 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1484 @ tc_bool ) ) @ SV1484 ) @ ( tc_fun @ SV1484 @ tc_bool ) ) @ SV1424 @ SV1484 @ SV1514 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1261 @ SV963 @ SV1484 ) ) )
= $true )
| ( ( c_Nitpick_Ofold__graph_H @ SV124 @ SV552 @ SV963 @ ( hAPP @ ( hAPP @ SV124 @ SV1261 ) @ SV1424 ) @ SV1484 @ SV1514 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3903]) ).
thf(4034,plain,
! [SV964: $i,SV1262: $i,SV553: $i,SV125: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV125 @ ( c_Set_Oinsert @ SV553 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1262 @ tc_bool ) ) @ SV1262 ) @ ( tc_fun @ SV1262 @ tc_bool ) ) @ SV964 @ ( tc_fun @ SV1262 @ tc_bool ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV125 @ SV964 @ ( tc_fun @ SV1262 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1262 @ tc_bool ) ) @ SV125 ) @ SV964 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV125 @ ( c_Set_Oinsert @ SV553 @ SV964 @ SV1262 ) @ ( tc_fun @ SV1262 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3904]) ).
thf(4035,plain,
! [SV554: $i,SV126: $i,SV965: $i] :
( ( ( SV965
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV126 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV126 @ tc_bool ) ) @ SV965 ) @ SV554 ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV554 @ SV126 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV126 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV554 @ SV126 ) ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV965 @ SV126 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV126 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3905]) ).
thf(4036,plain,
! [SV966: $i,SV127: $i,SV555: $i] :
( ( ( SV555
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV127 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV127 @ tc_bool ) ) @ SV555 ) @ SV966 ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV966 @ SV127 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV127 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV555 @ SV127 ) ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV966 @ SV127 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3906]) ).
thf(4037,plain,
! [SV969: $i,SV1264: $i,SV558: $i,SV130: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV130 @ ( c_Set_Oinsert @ SV558 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1264 @ tc_bool ) ) @ SV1264 ) @ ( tc_fun @ SV1264 @ tc_bool ) ) @ SV969 @ ( tc_fun @ SV1264 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV558 @ SV969 @ SV1264 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1264 @ tc_bool ) ) @ SV130 ) @ SV969 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV130 @ ( c_Set_Oinsert @ SV558 @ SV969 @ SV1264 ) @ ( tc_fun @ SV1264 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3907]) ).
thf(4038,plain,
! [SV559: $i,SV1265: $i,SV970: $i,SV131: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ SV970 ) @ SV1265 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ SV559 ) @ SV1265 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV559 @ SV970 @ SV131 ) ) @ SV1265 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3908]) ).
thf(4039,plain,
! [SV560: $i,SV1266: $i,SV971: $i,SV132: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ SV971 ) @ SV1266 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ SV560 ) @ SV1266 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV560 @ SV971 @ SV132 ) ) @ SV1266 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3909]) ).
thf(4040,plain,
! [SV1544: $i,SV1533: $i,SV1515: $i,SV1485: $i,SV1425: $i,SV1267: $i,SV979: $i,SV570: $i,SV143: $i] :
( ( ( ( hAPP @ SV143 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV570 @ tc_bool ) ) )
= SV979 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV143 @ SV1267 @ SV1425 @ SV1485 @ SV1515 @ SV1533 @ SV1544 @ SV979 @ SV570 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3910]) ).
thf(4041,plain,
! [SV1545: $i,SV1534: $i,SV1516: $i,SV1486: $i,SV1426: $i,SV1268: $i,SV980: $i,SV571: $i,SV144: $i] :
( ( ( ( hAPP @ SV144 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV571 @ tc_bool ) ) )
= SV980 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1268 @ SV144 @ SV1426 @ SV1486 @ SV1516 @ SV1534 @ SV980 @ SV1545 @ SV571 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3911]) ).
thf(4042,plain,
! [SV1546: $i,SV1535: $i,SV1517: $i,SV1487: $i,SV1427: $i,SV1271: $i,SV989: $i,SV588: $i,SV161: $i] :
( ( ! [SY4147: $i,SY4148: $i] :
( ( ( hAPP @ SV161 @ ( c_Set_Oinsert @ SV588 @ SV989 @ SV1271 ) )
= ( hAPP @ ( hAPP @ SV1427 @ SV588 ) @ ( hAPP @ SV161 @ SV989 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV161 @ SV1487 @ SV1517 @ SV1535 @ SV1427 @ SV1546 @ SY4147 @ SY4148 @ SV1271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3912]) ).
thf(4043,plain,
! [SV1547: $i,SV1536: $i,SV1518: $i,SV1488: $i,SV1428: $i,SV1272: $i,SV990: $i,SV589: $i,SV162: $i] :
( ( ! [SY4149: $i,SY4150: $i] :
( ( ( hAPP @ SV162 @ ( c_Set_Oinsert @ SV589 @ SV990 @ SV1272 ) )
= ( hAPP @ ( hAPP @ SV1428 @ SV589 ) @ ( hAPP @ SV162 @ SV990 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1488 @ SV162 @ SV1518 @ SV1536 @ SV1547 @ SV1428 @ SY4149 @ SY4150 @ SV1272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3913]) ).
thf(4044,plain,
! [SV1429: $i,SV1005: $i,SV1283: $i,SV604: $i,SV177: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ SV604 ) @ SV1283 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ SV1005 ) @ SV1429 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV177 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV604 @ SV1005 @ ( tc_fun @ SV177 @ tc_bool ) ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1283 @ SV1429 @ ( tc_fun @ SV177 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3919]) ).
thf(4045,plain,
! [SV1008: $i,SV1430: $i,SV1284: $i,SV607: $i,SV180: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ SV607 ) @ SV1284 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ SV1430 ) @ SV1008 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV180 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV607 @ SV1008 @ ( tc_fun @ SV180 @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1284 @ SV1430 @ ( tc_fun @ SV180 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3920]) ).
thf(4046,plain,
! [SV1432: $i,SV623: $i,SV1291: $i,SV1024: $i,SV196: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV196 ) @ SV1024 ) @ SV1291 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV196 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1024 @ SV1291 @ SV196 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV623 @ SV1432 @ SV196 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV196 ) @ SV623 ) @ SV1024 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV196 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3927]) ).
thf(4047,plain,
! [SV1025: $i,SV1433: $i,SV624: $i,SV1292: $i,SV197: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV197 ) @ SV1292 ) @ SV624 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV197 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1292 @ SV624 @ SV197 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1433 @ SV1025 @ SV197 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV197 ) @ SV624 ) @ SV1025 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3928]) ).
thf(4048,plain,
! [SV625: $i,SV1293: $i,SV1434: $i,SV1026: $i,SV198: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV198 ) @ SV1026 ) @ SV1434 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV198 ) @ SV1293 ) @ SV625 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV198 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV625 @ SV1026 @ SV198 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1293 @ SV1434 @ SV198 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3929]) ).
thf(4049,plain,
! [SV1435: $i,SV626: $i,SV1027: $i,SV1294: $i,SV199: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV199 ) @ SV1294 ) @ SV1027 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV199 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1027 @ SV1294 @ SV199 ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV626 @ SV1435 @ SV199 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV199 ) @ SV626 ) @ SV1027 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3930]) ).
thf(4050,plain,
! [SV629: $i,SV1295: $i,SV1030: $i,SV202: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ SV1030 ) @ SV1295 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ SV629 ) @ SV1295 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV629 @ SV1030 @ SV202 ) ) @ SV1295 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV202 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3931]) ).
thf(4051,plain,
! [SV1305: $i,SV1045: $i,SV223: $i,SV1436: $i,SV1489: $i,SV650: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV650 @ SV1489 ) @ SV1436 ) )
= $false )
| ( ( ~ ( hBOOL @ ( c_in @ SV1489 @ SV223 @ SV1045 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV223 @ SV650 @ SV1045 @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1436 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3938]) ).
thf(4052,plain,
! [SV1306: $i,SV1046: $i,SV224: $i,SV1437: $i,SV1490: $i,SV651: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV651 @ SV1490 ) @ SV1437 ) )
= $false )
| ( ( ~ ( hBOOL @ ( c_in @ SV1490 @ SV224 @ SV1046 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV224 @ SV651 @ SV1046 @ ( tc_fun @ SV1306 @ tc_bool ) ) @ SV1437 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3939]) ).
thf(4053,plain,
! [SV1548: $i,SV1537: $i,SV1519: $i,SV1491: $i,SV1438: $i,SV1307: $i,SV1053: $i,SV658: $i,SV231: $i] :
( ( ! [SY4151: $i,SY4152: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV231 @ SV658 ) @ ( hAPP @ SV1053 @ SV1307 ) ) )
| ~ ( hBOOL @ ( c_in @ SV658 @ SV1307 @ SV1438 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1491 @ SV1053 @ SV231 @ SV1519 @ SV1537 @ SV1548 @ SY4151 @ SY4152 @ SV1438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3940]) ).
thf(4054,plain,
! [SV1549: $i,SV1538: $i,SV1520: $i,SV1492: $i,SV1439: $i,SV1308: $i,SV1054: $i,SV659: $i,SV232: $i] :
( ( ! [SY4153: $i,SY4154: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ ( hAPP @ SV659 @ SV1054 ) ) @ SV1308 ) )
| ~ ( hBOOL @ ( c_in @ SV1308 @ SV1054 @ SV1439 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV659 @ SV1492 @ SV232 @ SV1520 @ SV1538 @ SV1549 @ SY4153 @ SY4154 @ SV1439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3941]) ).
thf(4055,plain,
! [SV1310: $i,SV664: $i,SV1440: $i,SV1493: $i,SV1059: $i,SV237: $i] :
( ( ( hBOOL @ ( c_in @ SV237 @ ( hAPP @ SV1059 @ SV1493 ) @ SV1440 ) )
= $false )
| ( ( ~ ( hBOOL @ ( c_in @ SV1493 @ SV664 @ SV1310 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV237 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV664 @ SV1059 @ SV1310 @ ( tc_fun @ SV1440 @ tc_bool ) ) @ SV1440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3942]) ).
thf(4056,plain,
! [SV1311: $i,SV665: $i,SV1441: $i,SV1494: $i,SV1060: $i,SV238: $i] :
( ( ( hBOOL @ ( c_in @ SV238 @ ( hAPP @ SV1060 @ SV1494 ) @ SV1441 ) )
= $false )
| ( ( ~ ( hBOOL @ ( c_in @ SV1494 @ SV665 @ SV1311 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV238 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV665 @ SV1060 @ SV1311 @ ( tc_fun @ SV1441 @ tc_bool ) ) @ SV1441 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3943]) ).
thf(4057,plain,
! [SV685: $i,SV258: $i,SV1442: $i,SV1321: $i,SV1078: $i] :
( ( ( hBOOL @ ( c_in @ SV1078 @ SV1321 @ SV1442 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV258 ) @ ( hAPP @ SV685 @ SV1078 ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1321 @ SV685 @ SV1442 @ SV258 ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV258 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3944]) ).
thf(4058,plain,
! [SV1326: $i,SV695: $i,SV268: $i,SV1495: $i,SV1444: $i,SV1087: $i] :
( ( ( hBOOL @ ( c_in @ SV1087 @ SV1444 @ SV1495 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV268 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1444 @ SV695 @ SV1495 @ ( tc_fun @ SV268 @ tc_bool ) ) ) @ SV1326 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV268 @ tc_bool ) ) @ ( hAPP @ SV695 @ SV1087 ) ) @ SV1326 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3945]) ).
thf(4059,plain,
! [SV701: $i,SV1332: $i,SV1093: $i,SV274: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV274 ) @ SV1093 ) @ SV1332 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV274 ) @ SV701 ) @ SV1093 ) ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV701 @ SV1093 @ SV274 ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1093 @ SV1332 @ SV274 ) @ ( tc_fun @ SV274 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV701 @ SV1332 @ SV274 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3946]) ).
thf(4060,plain,
! [SV704: $i,SV1335: $i,SV1096: $i,SV277: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV277 ) @ SV1096 ) @ SV1335 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV277 ) @ SV704 ) @ SV1096 ) ) )
= $true )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV704 @ SV1096 @ SV277 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1096 @ SV1335 @ SV277 ) @ ( tc_fun @ SV277 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV704 @ SV1335 @ SV277 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3947]) ).
thf(4061,plain,
! [SV1104: $i,SV1448: $i,SV1341: $i,SV714: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV287 ) @ SV714 ) @ SV1341 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV287 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1341 @ SV714 @ SV287 ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1448 @ SV1104 @ SV287 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV287 ) @ SV714 ) @ SV1104 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV287 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3949]) ).
thf(4062,plain,
! [SV1550: $i,SV1539: $i,SV1521: $i,SV1496: $i,SV1449: $i,SV1342: $i,SV1105: $i,SV717: $i,SV292: $i] :
( ( ! [SY4155: $i] :
( ( ( hAPP @ SV292 @ ( c_Set_Oinsert @ SV717 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1105 @ tc_bool ) ) @ SV1105 ) )
= SV717 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV292 @ SV1342 @ SV1449 @ SV1496 @ SV1521 @ SV1539 @ SV1550 @ SY4155 @ SV1105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3950]) ).
thf(4063,plain,
! [SV1551: $i,SV1540: $i,SV1522: $i,SV1497: $i,SV1450: $i,SV1343: $i,SV1106: $i,SV718: $i,SV293: $i] :
( ( ! [SY4156: $i] :
( ( ( hAPP @ SV293 @ ( c_Set_Oinsert @ SV718 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1106 @ tc_bool ) ) @ SV1106 ) )
= SV718 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1343 @ SV293 @ SV1450 @ SV1497 @ SV1522 @ SV1540 @ SV1551 @ SY4156 @ SV1106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3951]) ).
thf(4064,plain,
! [SV1552: $i,SV1541: $i,SV1523: $i,SV1498: $i,SV1451: $i,SV1345: $i,SV1109: $i,SV725: $i,SV300: $i] :
( ( ! [SY4157: $i,SY4158: $i] :
( ( ( hAPP @ SV300 @ ( c_Set_Oinsert @ SV725 @ ( c_Set_Oinsert @ SV1109 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1345 @ tc_bool ) ) @ SV1345 ) @ SV1345 ) )
= ( hAPP @ ( hAPP @ SV1451 @ SV725 ) @ SV1109 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV300 @ SV1498 @ SV1523 @ SV1541 @ SV1451 @ SV1552 @ SY4157 @ SY4158 @ SV1345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3952]) ).
thf(4065,plain,
! [SV1553: $i,SV1542: $i,SV1524: $i,SV1499: $i,SV1452: $i,SV1346: $i,SV1110: $i,SV726: $i,SV301: $i] :
( ( ! [SY4159: $i,SY4160: $i] :
( ( ( hAPP @ SV301 @ ( c_Set_Oinsert @ SV726 @ ( c_Set_Oinsert @ SV1110 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1346 @ tc_bool ) ) @ SV1346 ) @ SV1346 ) )
= ( hAPP @ ( hAPP @ SV1452 @ SV726 ) @ SV1110 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1499 @ SV301 @ SV1524 @ SV1542 @ SV1553 @ SV1452 @ SY4159 @ SY4160 @ SV1346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3953]) ).
thf(4066,plain,
! [SV1525: $i,SV1125: $i,SV1356: $i,SV746: $i,SV322: $i,SV1500: $i,SV1453: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1453 @ SV1500 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV322 @ SV746 @ SV1356 @ SV1125 @ SV1525 @ SV1453 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1525 @ SV1500 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV322 @ SV746 @ SV1356 @ SV1125 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV322 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1525 @ SV1125 @ SV1453 @ 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 )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV322 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV746 @ SV1125 @ SV1356 @ 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_or_pos,[status(thm)],[3955]) ).
thf(4067,plain,
! [SV1126: $i,SV323: $i,SV1357: $i,SV1526: $i,SV747: $i,SV1501: $i,SV1454: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1454 @ SV1501 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV747 @ SV1526 @ SV1357 @ SV1454 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1526 @ SV1501 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV747 @ SV1526 @ SV1357 @ SV1454 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV323 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1526 @ SV1126 @ SV1454 @ 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 )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV323 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV747 @ SV1126 @ SV1357 @ 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_or_pos,[status(thm)],[3956]) ).
thf(4068,plain,
! [SV1527: $i,SV1127: $i,SV1358: $i,SV748: $i,SV324: $i,SV1502: $i,SV1455: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1455 @ SV1502 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV324 @ SV748 @ SV1358 @ SV1127 @ SV1527 @ SV1455 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1527 @ SV1502 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV324 @ SV748 @ SV1358 @ SV1127 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV324 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1527 @ SV1127 @ SV1455 @ 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 )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV324 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV748 @ SV1127 @ SV1358 @ 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_or_pos,[status(thm)],[3957]) ).
thf(4069,plain,
! [SV1503: $i,SV1456: $i,SV1129: $i,SV750: $i,SV326: $i,SV1360: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1360 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV326 @ SV750 @ SV1360 @ SV1129 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV326 @ SV750 @ SV1360 @ SV1129 @ SV1456 @ SV1503 ) ) )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV326 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1456 @ SV1129 @ SV1503 @ 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 )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV326 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV750 @ SV1129 @ SV1360 @ 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_not_pos,[status(thm)],[3958]) ).
thf(4070,plain,
! [SV1363: $i,SV753: $i,SV1504: $i,SV1132: $i,SV1458: $i,SV329: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV329 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1458 @ SV1132 @ SV1504 @ 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 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV753 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV753 @ SV1458 @ SV1363 @ SV1504 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV753 @ SV1458 @ SV1363 @ SV1504 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV329 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV753 @ SV1132 @ SV1363 @ 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_not_pos,[status(thm)],[3960]) ).
thf(4071,plain,
! [SV1505: $i,SV1460: $i,SV1134: $i,SV755: $i,SV331: $i,SV1365: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1365 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV331 @ SV755 @ SV1365 @ SV1134 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV331 @ SV755 @ SV1365 @ SV1134 @ SV1460 @ SV1505 ) ) )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV331 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1460 @ SV1134 @ SV1505 @ 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 )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV331 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV755 @ SV1134 @ SV1365 @ 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_not_pos,[status(thm)],[3962]) ).
thf(4072,plain,
! [SV756: $i,SV1366: $i,SV1135: $i,SV1461: $i,SV332: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV332 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1461 @ SV1135 @ SV1366 @ 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 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1461 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV756 @ SV1461 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV756 @ SV1461 ) ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV332 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV756 @ SV1135 @ SV1366 @ 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_not_pos,[status(thm)],[3963]) ).
thf(4073,plain,
! [SV1136: $i,SV333: $i,SV1506: $i,SV1462: $i,SV757: $i,SV1367: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1367 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV757 @ SV1462 @ SV1367 @ SV1506 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV757 @ SV1462 @ SV1367 @ SV1506 ) ) )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV333 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1462 @ SV1136 @ SV1506 @ 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 )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV333 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV757 @ SV1136 @ SV1367 @ 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_not_pos,[status(thm)],[3964]) ).
thf(4074,plain,
! [SV1368: $i,SV1463: $i,SV1137: $i,SV758: $i,SV334: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV334 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV758 @ SV1137 @ SV1463 @ 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 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1368 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SV1368 @ SV1463 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SV1368 @ SV1463 ) ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV334 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV758 @ SV1137 @ SV1368 @ 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_not_pos,[status(thm)],[3965]) ).
thf(4075,plain,
! [SV1140: $i,SV761: $i,SV1507: $i,SV1464: $i,SV1371: $i,SV1528: $i,SV337: $i] :
( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1528 @ SV1371 @ SV1464 @ SV1507 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) ) @ SV1507 ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV761 @ SV1140 @ SV1528 @ SV1507 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) ) @ SV1507 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV761 @ ( c_Com_Ocom_OSemi @ SV1140 @ SV1371 ) @ SV1464 @ SV1507 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) ) @ SV1507 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3967]) ).
thf(4076,plain,
! [SV774: $i,SV1149: $i,SV1378: $i,SV350: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV1378 ) @ SV1149 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV774 ) @ SV1378 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV774 ) @ SV1149 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3973]) ).
thf(4077,plain,
! [SV1150: $i,SV1379: $i,SV775: $i,SV351: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV775 ) @ SV1379 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV1379 ) @ SV1150 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV775 ) @ SV1150 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV351 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3974]) ).
thf(4078,plain,
! [SV780: $i,SV1154: $i,SV357: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV357 ) @ SV1154 ) @ SV780 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV357 ) @ SV780 ) @ SV1154 ) )
= $false )
| ( ( SV780 = SV1154 )
= $true )
| ( ( class_Orderings_Oorder @ SV357 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3976]) ).
thf(4079,plain,
! [SV1155: $i,SV781: $i,SV358: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV358 ) @ SV781 ) @ SV1155 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV358 ) @ SV1155 ) @ SV781 ) )
= $false )
| ( ( SV781 = SV1155 )
= $true )
| ( ( class_Orderings_Oorder @ SV358 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3977]) ).
thf(4080,plain,
! [SV1156: $i,SV782: $i,SV359: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV359 ) @ SV782 ) @ SV1156 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV359 ) @ SV1156 ) @ SV782 ) )
= $false )
| ( ( SV782 = SV1156 )
= $true )
| ( ( class_Orderings_Oorder @ SV359 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3978]) ).
thf(4081,plain,
! [SV1168: $i,SV1386: $i,SV798: $i,SV375: $i,SV1465: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1465 @ SV375 ) ) @ SV798 ) @ SV1386 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV375 ) @ ( hAPP @ SV798 @ SV1168 ) ) @ ( hAPP @ SV1386 @ SV1168 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV375 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3979]) ).
thf(4082,plain,
! [SV1529: $i,SV1508: $i,SV1466: $i,SV1389: $i,SV1175: $i,SV818: $i,SV395: $i] :
( ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV395 @ SV818 @ SV1175 @ SV1389 )
= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1466 @ SV1508 @ SV1529 @ SV1389 ) )
= $false )
| ( ( SV395 = SV1466 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3981]) ).
thf(4083,plain,
! [SV1393: $i,SV833: $i,SV1188: $i,SV410: $i,SV1469: $i] :
( ( ( hBOOL @ ( c_in @ SV1469 @ SV410 @ SV1188 ) )
= $false )
| ( ( ( hAPP @ SV833 @ SV1469 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1393 @ tc_bool ) ) )
= $true )
| ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV410 @ SV833 @ SV1188 @ ( tc_fun @ SV1393 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1393 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3988]) ).
thf(4084,plain,
! [SV1470: $i,SV1394: $i,SV411: $i,SV1189: $i,SV834: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV834 @ SV1189 @ SV411 )
= ( c_HOL_Ominus__class_Ominus @ SV1394 @ SV1470 @ SV411 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV411 ) @ SV1470 ) @ SV1394 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV411 ) @ SV1189 ) @ SV834 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV411 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3989]) ).
thf(4085,plain,
! [SV413: $i,SV1191: $i,SV1395: $i,SV836: $i,SV1471: $i] :
( ( ( hBOOL @ ( c_in @ SV1471 @ SV836 @ SV1395 ) )
= $false )
| ( ( ( hAPP @ SV1191 @ SV1471 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV413 @ tc_bool ) ) )
= $true )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV413 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV836 @ SV1191 @ SV1395 @ ( tc_fun @ SV413 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3990]) ).
thf(4086,plain,
! [SV1530: $i,SV1509: $i,SV1473: $i,SV1397: $i,SV1196: $i,SV841: $i,SV418: $i] :
( ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV418 @ SV841 @ SV1196 @ SV1397 )
= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1473 @ SV1509 @ SV1530 @ SV1397 ) )
= $false )
| ( ( SV1196 = SV1530 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3994]) ).
thf(4087,plain,
! [SV1474: $i,SV1398: $i,SV419: $i,SV1197: $i,SV842: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV842 @ SV1197 @ SV419 )
= ( c_HOL_Ominus__class_Ominus @ SV1398 @ SV1474 @ SV419 ) )
= $false )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV419 ) @ SV1197 ) @ SV842 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV419 ) @ SV1474 ) @ SV1398 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV419 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3995]) ).
thf(4088,plain,
! [SV1531: $i,SV1510: $i,SV1475: $i,SV1399: $i,SV1199: $i,SV844: $i,SV421: $i] :
( ( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ SV421 @ SV844 @ SV1199 @ SV1399 )
= ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1475 @ SV1510 @ SV1531 @ SV1399 ) )
= $false )
| ( ( SV844 = SV1510 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3996]) ).
thf(4089,plain,
! [SV1476: $i,SV1401: $i,SV423: $i,SV1201: $i,SV846: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV846 @ SV1201 @ SV423 )
= ( c_HOL_Ominus__class_Ominus @ SV1401 @ SV1476 @ SV423 ) )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1401 @ SV1476 @ SV423 )
| ~ ( c_HOL_Oord__class_Oless @ SV846 @ SV1201 @ SV423 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV423 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3997]) ).
thf(4090,plain,
! [SV1477: $i,SV1402: $i,SV427: $i,SV1205: $i,SV850: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV850 @ SV1205 @ SV427 )
= ( c_HOL_Ominus__class_Ominus @ SV1402 @ SV1477 @ SV427 ) )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV850 @ SV1205 @ SV427 )
| ~ ( c_HOL_Oord__class_Oless @ SV1402 @ SV1477 @ SV427 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV427 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3999]) ).
thf(4091,plain,
! [SV11: $i,SV441: $i,SV1405: $i,SV864: $i,SV1214: $i] :
( ( ( hBOOL @ ( c_in @ SV1214 @ SV864 @ SV1405 ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV864 @ SV1405 ) )
= $true )
| ( ( ( c_Finite__Set_Osetsum @ SV441 @ ( c_HOL_Ominus__class_Ominus @ SV864 @ ( c_Set_Oinsert @ SV1214 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1405 @ tc_bool ) ) @ SV1405 ) @ ( tc_fun @ SV1405 @ tc_bool ) ) @ SV1405 @ SV11 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV441 @ SV864 @ SV1405 @ SV11 ) @ ( hAPP @ SV441 @ SV1214 ) @ SV11 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4004]) ).
thf(4092,plain,
! [SV12: $i,SV442: $i,SV1406: $i,SV865: $i,SV1215: $i] :
( ( ( hBOOL @ ( c_in @ SV1215 @ SV865 @ SV1406 ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV865 @ SV1406 ) )
= $true )
| ( ( ( c_Finite__Set_Osetsum @ SV442 @ ( c_HOL_Ominus__class_Ominus @ SV865 @ ( c_Set_Oinsert @ SV1215 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1406 @ tc_bool ) ) @ SV1406 ) @ ( tc_fun @ SV1406 @ tc_bool ) ) @ SV1406 @ SV12 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV442 @ SV865 @ SV1406 @ SV12 ) @ ( hAPP @ SV442 @ SV1215 ) @ SV12 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4005]) ).
thf(4093,plain,
! [SV1219: $i,SV869: $i,SV446: $i,SV16: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV16 ) @ SV446 ) @ SV869 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV16 ) @ SV869 ) @ SV1219 ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV446 @ SV869 @ SV16 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV869 @ SV1219 @ SV16 ) @ ( tc_fun @ SV16 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV446 @ SV1219 @ SV16 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4007]) ).
thf(4094,plain,
! [SV466: $i,SV37: $i,SV885: $i,SV1223: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1223 @ SV885 @ SV37 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV37 ) @ SV466 ) @ SV1223 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV466 @ SV885 @ SV37 )
= $true )
| ( ( class_Orderings_Oorder @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4008]) ).
thf(4095,plain,
! [SV467: $i,SV886: $i,SV1224: $i,SV38: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV38 ) @ SV1224 ) @ SV886 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV467 @ SV1224 @ SV38 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV467 @ SV886 @ SV38 )
= $true )
| ( ( class_Orderings_Oorder @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4009]) ).
thf(4096,plain,
! [SV887: $i,SV1225: $i,SV468: $i,SV39: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV39 ) @ SV468 ) @ SV1225 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1225 @ SV887 @ SV39 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV468 @ SV887 @ SV39 )
= $true )
| ( ( class_Orderings_Opreorder @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4010]) ).
thf(4097,plain,
! [SV888: $i,SV40: $i,SV1226: $i,SV469: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV469 @ SV1226 @ SV40 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV40 ) @ SV1226 ) @ SV888 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV469 @ SV888 @ SV40 )
= $true )
| ( ( class_Orderings_Opreorder @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4011]) ).
thf(4098,plain,
! [SV903: $i,SV1229: $i,SV485: $i,SV1408: $i,SV56: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV56 ) @ SV1408 ) @ SV485 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1408 @ SV485 @ SV56 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1229 @ SV903 @ SV56 ) @ ( tc_fun @ SV56 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1229 @ SV1408 @ SV56 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV485 @ SV903 @ SV56 )
= $true )
| ( ( class_Orderings_Oorder @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4012]) ).
thf(4099,plain,
! [SV1543: $i,SV1532: $i,SV1511: $i,SV1479: $i,SV1409: $i,SV1230: $i,SV904: $i,SV486: $i,SV57: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV57 @ SV486 @ ( c_COMBC @ SV904 @ SV1230 @ SV1230 @ tc_bool ) @ ( c_COMBC @ SV1409 @ SV1230 @ SV1230 @ tc_bool ) @ SV1479 @ SV1511 @ SV1532 @ SV1543 @ SV1230 )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV486 @ SV57 @ SV904 @ SV1409 @ SV1511 @ SV1479 @ SV1543 @ SV1532 @ SV1230 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4013]) ).
thf(4100,plain,
! [SV489: $i,SV60: $i,SV907: $i,SV1233: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1233 @ SV907 @ SV60 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV489 @ SV1233 @ SV60 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV489 @ SV907 @ SV60 )
= $true )
| ( ( class_Orderings_Oorder @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4014]) ).
thf(4101,plain,
! [SV910: $i,SV63: $i,SV1236: $i,SV492: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV492 @ SV1236 @ SV63 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1236 @ SV910 @ SV63 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV492 @ SV910 @ SV63 )
= $true )
| ( ( class_Orderings_Opreorder @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4015]) ).
thf(4102,plain,
! [SV509: $i,SV922: $i,SV1412: $i,SV1238: $i,SV80: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV1238 ) @ SV1412 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV922 @ SV1412 @ SV80 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV922 ) @ SV1412 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV1238 ) @ SV509 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV509 @ SV922 @ SV80 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1238 @ SV1412 @ SV80 ) @ ( tc_fun @ SV80 @ tc_bool ) )
= $true )
| ( ( class_Orderings_Oorder @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4016]) ).
thf(4103,plain,
! [SV923: $i,SV510: $i,SV1413: $i,SV1239: $i,SV81: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV1239 ) @ SV1413 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1239 @ SV510 @ SV81 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV923 ) @ SV1413 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV1239 ) @ SV510 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV510 @ SV923 @ SV81 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1239 @ SV1413 @ SV81 ) @ ( tc_fun @ SV81 @ tc_bool ) )
= $true )
| ( ( class_Orderings_Oorder @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4017]) ).
thf(4104,plain,
! [SV92: $i,SV521: $i,SV934: $i,SV1240: $i,SV1414: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1414 @ tc_bool ) ) @ SV1240 ) @ SV934 ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV934 @ SV1414 ) )
= $true )
| ( ( ( c_Finite__Set_Osetsum @ SV521 @ ( c_HOL_Ominus__class_Ominus @ SV934 @ SV1240 @ ( tc_fun @ SV1414 @ tc_bool ) ) @ SV1414 @ SV92 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV521 @ SV934 @ SV1414 @ SV92 ) @ ( c_Finite__Set_Osetsum @ SV521 @ SV1240 @ SV1414 @ SV92 ) @ SV92 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4018]) ).
thf(4105,plain,
! [SV936: $i,SV1512: $i,SV1415: $i,SV1482: $i,SV1241: $i,SV523: $i,SV94: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV94 @ SV523 @ SV1241 @ SV1482 @ SV1415 @ SV1512 )
= $false )
| ( ( hBOOL @ ( c_in @ SV936 @ SV1241 @ SV1415 ) )
= $true )
| ( ( c_Finite__Set_Ofold__graph @ SV94 @ SV523 @ ( c_Set_Oinsert @ SV936 @ SV1241 @ SV1415 ) @ ( hAPP @ ( hAPP @ SV94 @ SV936 ) @ SV1482 ) @ SV1415 @ SV1512 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4019]) ).
thf(4106,plain,
! [SV939: $i,SV1416: $i,SV526: $i,SV1244: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV97 ) @ SV1244 ) @ SV526 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1244 @ SV526 @ SV97 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1416 @ SV939 @ SV97 ) @ ( tc_fun @ SV97 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV97 ) @ SV526 ) @ SV939 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4020]) ).
thf(4107,plain,
! [SV1417: $i,SV527: $i,SV1245: $i,SV940: $i,SV98: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV98 ) @ SV940 ) @ SV1245 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV940 @ SV1245 @ SV98 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV527 @ SV1417 @ SV98 ) @ ( tc_fun @ SV98 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV98 ) @ SV527 ) @ SV940 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4021]) ).
thf(4108,plain,
! [SV942: $i,SV529: $i,SV1419: $i,SV1247: $i,SV100: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV100 ) @ SV1247 ) @ SV1419 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV100 ) @ SV529 ) @ SV942 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV529 @ SV942 @ SV100 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1247 @ SV1419 @ SV100 ) @ ( tc_fun @ SV100 @ tc_bool ) )
= $true )
| ( ( class_Orderings_Oorder @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4023]) ).
thf(4109,plain,
! [SV1248: $i,SV943: $i,SV530: $i,SV101: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV101 ) @ SV530 ) @ SV943 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV101 ) @ SV943 ) @ SV1248 ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV530 @ SV943 @ SV101 ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV943 @ SV1248 @ SV101 ) @ ( tc_fun @ SV101 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ SV530 @ SV1248 @ SV101 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4024]) ).
thf(4110,plain,
! [SV531: $i,SV944: $i,SV1420: $i,SV102: $i,SV1249: $i] :
( ( ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1249 @ SV102 @ SV1420 @ ( tc_fun @ SV944 @ tc_bool ) ) @ SV944 )
= $false )
| ( ( ~ ( c_Finite__Set_Ofinite @ SV1249 @ SV1420 ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV531 @ SV1249 @ SV1420 ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ SV102 @ SV531 ) @ SV944 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4025]) ).
thf(4111,plain,
! [SV103: $i,SV532: $i,SV1250: $i,SV1421: $i,SV945: $i] :
( ( ( c_Finite__Set_Ofinite @ SV945 @ SV1421 )
= $false )
| ( ( hBOOL @ ( c_in @ SV1250 @ SV945 @ SV1421 ) )
= $true )
| ( ( ( c_Finite__Set_Osetsum @ SV532 @ ( c_HOL_Ominus__class_Ominus @ SV945 @ ( c_Set_Oinsert @ SV1250 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1421 @ tc_bool ) ) @ SV1421 ) @ ( tc_fun @ SV1421 @ tc_bool ) ) @ SV1421 @ SV103 )
= ( c_Finite__Set_Osetsum @ SV532 @ SV945 @ SV1421 @ SV103 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4026]) ).
thf(4112,plain,
! [SV1513: $i,SV1423: $i,SV547: $i,SV119: $i,SV1483: $i,SV958: $i,SV1256: $i] :
( ( ( hBOOL @ ( c_in @ SV1256 @ SV958 @ SV1483 ) )
= $false )
| ( ( ~ ( c_Finite__Set_Ofold__graph @ SV119 @ SV547 @ ( c_HOL_Ominus__class_Ominus @ SV958 @ ( c_Set_Oinsert @ SV1256 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1483 @ tc_bool ) ) @ SV1483 ) @ ( tc_fun @ SV1483 @ tc_bool ) ) @ SV1423 @ SV1483 @ SV1513 ) )
= $true )
| ( ( c_Finite__Set_Ofold__graph @ SV119 @ SV547 @ SV958 @ ( hAPP @ ( hAPP @ SV119 @ SV1256 ) @ SV1423 ) @ SV1483 @ SV1513 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4029]) ).
thf(4113,plain,
! [SV549: $i,SV1258: $i,SV960: $i,SV121: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV121 @ SV960 @ ( tc_fun @ SV1258 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV121 @ ( c_Set_Oinsert @ SV549 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1258 @ tc_bool ) ) @ SV1258 ) @ ( tc_fun @ SV1258 @ tc_bool ) ) @ SV960 @ ( tc_fun @ SV1258 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV549 @ SV121 @ SV1258 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV121 @ ( c_Set_Oinsert @ SV549 @ SV960 @ SV1258 ) @ ( tc_fun @ SV1258 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4030]) ).
thf(4114,plain,
! [SV1514: $i,SV1424: $i,SV1484: $i,SV1261: $i,SV963: $i,SV552: $i,SV124: $i] :
( ( ( c_Nitpick_Ofold__graph_H @ SV124 @ SV552 @ ( c_HOL_Ominus__class_Ominus @ SV963 @ ( c_Set_Oinsert @ SV1261 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1484 @ tc_bool ) ) @ SV1484 ) @ ( tc_fun @ SV1484 @ tc_bool ) ) @ SV1424 @ SV1484 @ SV1514 )
= $false )
| ( ( ~ ( hBOOL @ ( c_in @ SV1261 @ SV963 @ SV1484 ) ) )
= $true )
| ( ( c_Nitpick_Ofold__graph_H @ SV124 @ SV552 @ SV963 @ ( hAPP @ ( hAPP @ SV124 @ SV1261 ) @ SV1424 ) @ SV1484 @ SV1514 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4033]) ).
thf(4115,plain,
! [SV553: $i,SV1262: $i,SV964: $i,SV125: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV125 @ SV964 @ ( tc_fun @ SV1262 @ tc_bool ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV125 @ ( c_Set_Oinsert @ SV553 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1262 @ tc_bool ) ) @ SV1262 ) @ ( tc_fun @ SV1262 @ tc_bool ) ) @ SV964 @ ( tc_fun @ SV1262 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1262 @ tc_bool ) ) @ SV125 ) @ SV964 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV125 @ ( c_Set_Oinsert @ SV553 @ SV964 @ SV1262 ) @ ( tc_fun @ SV1262 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4034]) ).
thf(4116,plain,
! [SV554: $i,SV965: $i,SV126: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV126 @ tc_bool ) ) @ SV965 ) @ SV554 ) )
= $false )
| ( ( SV965
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV126 @ tc_bool ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV554 @ SV126 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV126 ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV554 @ SV126 ) ) @ ( c_Finite__Set_Olinorder__class_OMin @ SV965 @ SV126 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV126 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4035]) ).
thf(4117,plain,
! [SV966: $i,SV555: $i,SV127: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV127 @ tc_bool ) ) @ SV555 ) @ SV966 ) )
= $false )
| ( ( SV555
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV127 @ tc_bool ) ) )
= $true )
| ( ( c_Finite__Set_Ofinite @ SV966 @ SV127 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV127 ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV555 @ SV127 ) ) @ ( c_Finite__Set_Olinorder__class_OMax @ SV966 @ SV127 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4036]) ).
thf(4118,plain,
! [SV970: $i,SV1265: $i,SV559: $i,SV131: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ SV559 ) @ SV1265 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ SV970 ) @ SV1265 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV131 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV559 @ SV970 @ SV131 ) ) @ SV1265 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4038]) ).
thf(4119,plain,
! [SV971: $i,SV1266: $i,SV560: $i,SV132: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ SV560 ) @ SV1266 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ SV971 ) @ SV1266 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV132 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV560 @ SV971 @ SV132 ) ) @ SV1266 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4039]) ).
thf(4120,plain,
! [SV1544: $i,SV1533: $i,SV1515: $i,SV1485: $i,SV1425: $i,SV1267: $i,SV979: $i,SV570: $i,SV143: $i] :
( ( ( ( hAPP @ SV143 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV570 @ tc_bool ) ) )
= SV979 )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV143 @ SV1267 @ SV1425 @ SV1485 @ SV1515 @ SV1533 @ SV1544 @ SV979 @ SV570 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4040]) ).
thf(4121,plain,
! [SV1545: $i,SV1534: $i,SV1516: $i,SV1486: $i,SV1426: $i,SV1268: $i,SV980: $i,SV571: $i,SV144: $i] :
( ( ( ( hAPP @ SV144 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV571 @ tc_bool ) ) )
= SV980 )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1268 @ SV144 @ SV1426 @ SV1486 @ SV1516 @ SV1534 @ SV980 @ SV1545 @ SV571 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4041]) ).
thf(4122,plain,
! [SV1554: $i,SV1546: $i,SV1535: $i,SV1517: $i,SV1487: $i,SV1427: $i,SV1271: $i,SV989: $i,SV588: $i,SV161: $i] :
( ( ! [SY4161: $i] :
( ( ( hAPP @ SV161 @ ( c_Set_Oinsert @ SV588 @ SV989 @ SV1271 ) )
= ( hAPP @ ( hAPP @ SV1427 @ SV588 ) @ ( hAPP @ SV161 @ SV989 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV161 @ SV1487 @ SV1517 @ SV1535 @ SV1427 @ SV1546 @ SV1554 @ SY4161 @ SV1271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4042]) ).
thf(4123,plain,
! [SV1555: $i,SV1547: $i,SV1536: $i,SV1518: $i,SV1488: $i,SV1428: $i,SV1272: $i,SV990: $i,SV589: $i,SV162: $i] :
( ( ! [SY4162: $i] :
( ( ( hAPP @ SV162 @ ( c_Set_Oinsert @ SV589 @ SV990 @ SV1272 ) )
= ( hAPP @ ( hAPP @ SV1428 @ SV589 ) @ ( hAPP @ SV162 @ SV990 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1488 @ SV162 @ SV1518 @ SV1536 @ SV1547 @ SV1428 @ SV1555 @ SY4162 @ SV1272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4043]) ).
thf(4124,plain,
! [SV1432: $i,SV623: $i,SV1291: $i,SV1024: $i,SV196: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV196 ) @ SV1024 ) @ SV1291 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV196 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1024 @ SV1291 @ SV196 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV623 @ SV1432 @ SV196 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV196 ) @ SV623 ) @ SV1024 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV196 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4046]) ).
thf(4125,plain,
! [SV1025: $i,SV1433: $i,SV624: $i,SV1292: $i,SV197: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV197 ) @ SV1292 ) @ SV624 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV197 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1292 @ SV624 @ SV197 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1433 @ SV1025 @ SV197 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV197 ) @ SV624 ) @ SV1025 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4047]) ).
thf(4126,plain,
! [SV625: $i,SV1293: $i,SV1434: $i,SV1026: $i,SV198: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV198 ) @ SV1026 ) @ SV1434 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV198 ) @ SV1293 ) @ SV625 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV198 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV625 @ SV1026 @ SV198 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1293 @ SV1434 @ SV198 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV198 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4048]) ).
thf(4127,plain,
! [SV1435: $i,SV626: $i,SV1294: $i,SV1027: $i,SV199: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV199 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1027 @ SV1294 @ SV199 ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV626 @ SV1435 @ SV199 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV199 ) @ SV1294 ) @ SV1027 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV199 ) @ SV626 ) @ SV1027 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4049]) ).
thf(4128,plain,
! [SV1030: $i,SV1295: $i,SV629: $i,SV202: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ SV629 ) @ SV1295 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ SV1030 ) @ SV1295 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV202 ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV629 @ SV1030 @ SV202 ) ) @ SV1295 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV202 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4050]) ).
thf(4129,plain,
! [SV1305: $i,SV1436: $i,SV650: $i,SV1045: $i,SV223: $i,SV1489: $i] :
( ( ( hBOOL @ ( c_in @ SV1489 @ SV223 @ SV1045 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV650 @ SV1489 ) @ SV1436 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV223 @ SV650 @ SV1045 @ ( tc_fun @ SV1305 @ tc_bool ) ) @ SV1436 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4051]) ).
thf(4130,plain,
! [SV1306: $i,SV1437: $i,SV651: $i,SV1046: $i,SV224: $i,SV1490: $i] :
( ( ( hBOOL @ ( c_in @ SV1490 @ SV224 @ SV1046 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV651 @ SV1490 ) @ SV1437 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV224 @ SV651 @ SV1046 @ ( tc_fun @ SV1306 @ tc_bool ) ) @ SV1437 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4052]) ).
thf(4131,plain,
! [SV1556: $i,SV1548: $i,SV1537: $i,SV1519: $i,SV1491: $i,SV1438: $i,SV1307: $i,SV1053: $i,SV658: $i,SV231: $i] :
( ( ! [SY4163: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV231 @ SV658 ) @ ( hAPP @ SV1053 @ SV1307 ) ) )
| ~ ( hBOOL @ ( c_in @ SV658 @ SV1307 @ SV1438 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1491 @ SV1053 @ SV231 @ SV1519 @ SV1537 @ SV1548 @ SV1556 @ SY4163 @ SV1438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4053]) ).
thf(4132,plain,
! [SV1557: $i,SV1549: $i,SV1538: $i,SV1520: $i,SV1492: $i,SV1439: $i,SV1308: $i,SV1054: $i,SV659: $i,SV232: $i] :
( ( ! [SY4164: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ ( hAPP @ SV659 @ SV1054 ) ) @ SV1308 ) )
| ~ ( hBOOL @ ( c_in @ SV1308 @ SV1054 @ SV1439 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV659 @ SV1492 @ SV232 @ SV1520 @ SV1538 @ SV1549 @ SV1557 @ SY4164 @ SV1439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4054]) ).
thf(4133,plain,
! [SV1440: $i,SV1059: $i,SV237: $i,SV1310: $i,SV664: $i,SV1493: $i] :
( ( ( hBOOL @ ( c_in @ SV1493 @ SV664 @ SV1310 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV237 @ ( hAPP @ SV1059 @ SV1493 ) @ SV1440 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV237 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV664 @ SV1059 @ SV1310 @ ( tc_fun @ SV1440 @ tc_bool ) ) @ SV1440 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4055]) ).
thf(4134,plain,
! [SV1441: $i,SV1060: $i,SV238: $i,SV1311: $i,SV665: $i,SV1494: $i] :
( ( ( hBOOL @ ( c_in @ SV1494 @ SV665 @ SV1311 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV238 @ ( hAPP @ SV1060 @ SV1494 ) @ SV1441 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV238 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV665 @ SV1060 @ SV1311 @ ( tc_fun @ SV1441 @ tc_bool ) ) @ SV1441 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4056]) ).
thf(4135,plain,
! [SV1087: $i,SV1326: $i,SV1495: $i,SV695: $i,SV1444: $i,SV268: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV268 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1444 @ SV695 @ SV1495 @ ( tc_fun @ SV268 @ tc_bool ) ) ) @ SV1326 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV1087 @ SV1444 @ SV1495 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV268 @ tc_bool ) ) @ ( hAPP @ SV695 @ SV1087 ) ) @ SV1326 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4058]) ).
thf(4136,plain,
! [SV1332: $i,SV1093: $i,SV701: $i,SV274: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV274 ) @ SV701 ) @ SV1093 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV274 ) @ SV1093 ) @ SV1332 ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV701 @ SV1093 @ SV274 ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1093 @ SV1332 @ SV274 ) @ ( tc_fun @ SV274 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ SV701 @ SV1332 @ SV274 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV274 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4059]) ).
thf(4137,plain,
! [SV1335: $i,SV1096: $i,SV704: $i,SV277: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV277 ) @ SV704 ) @ SV1096 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV277 ) @ SV1096 ) @ SV1335 ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV704 @ SV1096 @ SV277 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1096 @ SV1335 @ SV277 ) @ ( tc_fun @ SV277 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV704 @ SV1335 @ SV277 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV277 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4060]) ).
thf(4138,plain,
! [SV1104: $i,SV1448: $i,SV714: $i,SV1341: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV287 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1341 @ SV714 @ SV287 ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ SV1448 @ SV1104 @ SV287 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV287 ) @ SV714 ) @ SV1341 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV287 ) @ SV714 ) @ SV1104 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV287 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4061]) ).
thf(4139,plain,
! [SV1558: $i,SV1550: $i,SV1539: $i,SV1521: $i,SV1496: $i,SV1449: $i,SV1342: $i,SV1105: $i,SV717: $i,SV292: $i] :
( ( ( ( hAPP @ SV292 @ ( c_Set_Oinsert @ SV717 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1105 @ tc_bool ) ) @ SV1105 ) )
= SV717 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV292 @ SV1342 @ SV1449 @ SV1496 @ SV1521 @ SV1539 @ SV1550 @ SV1558 @ SV1105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4062]) ).
thf(4140,plain,
! [SV1559: $i,SV1551: $i,SV1540: $i,SV1522: $i,SV1497: $i,SV1450: $i,SV1343: $i,SV1106: $i,SV718: $i,SV293: $i] :
( ( ( ( hAPP @ SV293 @ ( c_Set_Oinsert @ SV718 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1106 @ tc_bool ) ) @ SV1106 ) )
= SV718 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1343 @ SV293 @ SV1450 @ SV1497 @ SV1522 @ SV1540 @ SV1551 @ SV1559 @ SV1106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4063]) ).
thf(4141,plain,
! [SV1560: $i,SV1552: $i,SV1541: $i,SV1523: $i,SV1498: $i,SV1451: $i,SV1345: $i,SV1109: $i,SV725: $i,SV300: $i] :
( ( ! [SY4165: $i] :
( ( ( hAPP @ SV300 @ ( c_Set_Oinsert @ SV725 @ ( c_Set_Oinsert @ SV1109 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1345 @ tc_bool ) ) @ SV1345 ) @ SV1345 ) )
= ( hAPP @ ( hAPP @ SV1451 @ SV725 ) @ SV1109 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV300 @ SV1498 @ SV1523 @ SV1541 @ SV1451 @ SV1552 @ SV1560 @ SY4165 @ SV1345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4064]) ).
thf(4142,plain,
! [SV1561: $i,SV1553: $i,SV1542: $i,SV1524: $i,SV1499: $i,SV1452: $i,SV1346: $i,SV1110: $i,SV726: $i,SV301: $i] :
( ( ! [SY4166: $i] :
( ( ( hAPP @ SV301 @ ( c_Set_Oinsert @ SV726 @ ( c_Set_Oinsert @ SV1110 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1346 @ tc_bool ) ) @ SV1346 ) @ SV1346 ) )
= ( hAPP @ ( hAPP @ SV1452 @ SV726 ) @ SV1110 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1499 @ SV301 @ SV1524 @ SV1542 @ SV1553 @ SV1452 @ SV1561 @ SY4166 @ SV1346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4065]) ).
thf(4143,plain,
! [SV1453: $i,SV1125: $i,SV1356: $i,SV746: $i,SV322: $i,SV1500: $i,SV1525: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1525 @ SV1500 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV322 @ SV746 @ SV1356 @ SV1125 ) ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV322 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1525 @ SV1125 @ SV1453 @ 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 )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1453 @ SV1500 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV322 @ SV746 @ SV1356 @ SV1125 @ SV1525 @ SV1453 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV322 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV746 @ SV1125 @ SV1356 @ 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_or_pos,[status(thm)],[4066]) ).
thf(4144,plain,
! [SV1126: $i,SV323: $i,SV1454: $i,SV1357: $i,SV747: $i,SV1501: $i,SV1526: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1526 @ SV1501 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV747 @ SV1526 @ SV1357 @ SV1454 ) ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV323 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1526 @ SV1126 @ SV1454 @ 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 )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1454 @ SV1501 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV747 @ SV1526 @ SV1357 @ SV1454 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV323 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV747 @ SV1126 @ SV1357 @ 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_or_pos,[status(thm)],[4067]) ).
thf(4145,plain,
! [SV1455: $i,SV1127: $i,SV1358: $i,SV748: $i,SV324: $i,SV1502: $i,SV1527: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1527 @ SV1502 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV324 @ SV748 @ SV1358 @ SV1127 ) ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV324 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1527 @ SV1127 @ SV1455 @ 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 )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1455 @ SV1502 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV324 @ SV748 @ SV1358 @ SV1127 @ SV1527 @ SV1455 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV324 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV748 @ SV1127 @ SV1358 @ 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_or_pos,[status(thm)],[4068]) ).
thf(4146,plain,
! [SV750: $i,SV1360: $i,SV1503: $i,SV1129: $i,SV1456: $i,SV326: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV326 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1456 @ SV1129 @ SV1503 @ 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 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1360 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV326 @ SV750 @ SV1360 @ SV1129 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV326 @ SV750 @ SV1360 @ SV1129 @ SV1456 @ SV1503 ) ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV326 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV750 @ SV1129 @ SV1360 @ 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_not_pos,[status(thm)],[4069]) ).
thf(4147,plain,
! [SV755: $i,SV1365: $i,SV1505: $i,SV1134: $i,SV1460: $i,SV331: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV331 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1460 @ SV1134 @ SV1505 @ 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 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1365 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV331 @ SV755 @ SV1365 @ SV1134 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV331 @ SV755 @ SV1365 @ SV1134 @ SV1460 @ SV1505 ) ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV331 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV755 @ SV1134 @ SV1365 @ 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_not_pos,[status(thm)],[4071]) ).
thf(4148,plain,
! [SV757: $i,SV1367: $i,SV1506: $i,SV1136: $i,SV1462: $i,SV333: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV333 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1462 @ SV1136 @ SV1506 @ 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 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1367 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV757 @ SV1462 @ SV1367 @ SV1506 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV757 @ SV1462 @ SV1367 @ SV1506 ) ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV333 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV757 @ SV1136 @ SV1367 @ 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_not_pos,[status(thm)],[4073]) ).
thf(4149,plain,
! [SV1140: $i,SV761: $i,SV1507: $i,SV1464: $i,SV1371: $i,SV1528: $i,SV337: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1528 @ SV1371 @ SV1464 @ SV1507 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) ) @ SV1507 )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV761 @ SV1140 @ SV1528 @ SV1507 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) ) @ SV1507 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV761 @ ( c_Com_Ocom_OSemi @ SV1140 @ SV1371 ) @ SV1464 @ SV1507 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) ) @ SV1507 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4075]) ).
thf(4150,plain,
! [SV1149: $i,SV1378: $i,SV774: $i,SV350: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV774 ) @ SV1378 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV1378 ) @ SV1149 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV350 ) @ SV774 ) @ SV1149 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4076]) ).
thf(4151,plain,
! [SV775: $i,SV1150: $i,SV1379: $i,SV351: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV1379 ) @ SV1150 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV775 ) @ SV1379 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV351 ) @ SV775 ) @ SV1150 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV351 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4077]) ).
thf(4152,plain,
! [SV834: $i,SV1189: $i,SV1394: $i,SV1470: $i,SV411: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV411 ) @ SV1470 ) @ SV1394 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV411 ) @ SV1189 ) @ SV834 ) ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV834 @ SV1189 @ SV411 )
= ( c_HOL_Ominus__class_Ominus @ SV1394 @ SV1470 @ SV411 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV411 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4084]) ).
thf(4153,plain,
! [SV1398: $i,SV1474: $i,SV842: $i,SV1197: $i,SV419: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV419 ) @ SV1197 ) @ SV842 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV419 ) @ SV1474 ) @ SV1398 ) ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV842 @ SV1197 @ SV419 )
= ( c_HOL_Ominus__class_Ominus @ SV1398 @ SV1474 @ SV419 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV419 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4087]) ).
thf(4154,plain,
! [SV1201: $i,SV846: $i,SV423: $i,SV1476: $i,SV1401: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1401 @ SV1476 @ SV423 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV846 @ SV1201 @ SV423 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV846 @ SV1201 @ SV423 )
= ( c_HOL_Ominus__class_Ominus @ SV1401 @ SV1476 @ SV423 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV423 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4089]) ).
thf(4155,plain,
! [SV1477: $i,SV1402: $i,SV427: $i,SV1205: $i,SV850: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV850 @ SV1205 @ SV427 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1402 @ SV1477 @ SV427 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV850 @ SV1205 @ SV427 )
= ( c_HOL_Ominus__class_Ominus @ SV1402 @ SV1477 @ SV427 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV427 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4090]) ).
thf(4156,plain,
! [SV11: $i,SV441: $i,SV1214: $i,SV1405: $i,SV864: $i] :
( ( ( c_Finite__Set_Ofinite @ SV864 @ SV1405 )
= $false )
| ( ( hBOOL @ ( c_in @ SV1214 @ SV864 @ SV1405 ) )
= $false )
| ( ( ( c_Finite__Set_Osetsum @ SV441 @ ( c_HOL_Ominus__class_Ominus @ SV864 @ ( c_Set_Oinsert @ SV1214 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1405 @ tc_bool ) ) @ SV1405 ) @ ( tc_fun @ SV1405 @ tc_bool ) ) @ SV1405 @ SV11 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV441 @ SV864 @ SV1405 @ SV11 ) @ ( hAPP @ SV441 @ SV1214 ) @ SV11 ) )
= $true )
| ( ( class_Ring__and__Field_Oring @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4091]) ).
thf(4157,plain,
! [SV12: $i,SV442: $i,SV1215: $i,SV1406: $i,SV865: $i] :
( ( ( c_Finite__Set_Ofinite @ SV865 @ SV1406 )
= $false )
| ( ( hBOOL @ ( c_in @ SV1215 @ SV865 @ SV1406 ) )
= $false )
| ( ( ( c_Finite__Set_Osetsum @ SV442 @ ( c_HOL_Ominus__class_Ominus @ SV865 @ ( c_Set_Oinsert @ SV1215 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1406 @ tc_bool ) ) @ SV1406 ) @ ( tc_fun @ SV1406 @ tc_bool ) ) @ SV1406 @ SV12 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV442 @ SV865 @ SV1406 @ SV12 ) @ ( hAPP @ SV442 @ SV1215 ) @ SV12 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4092]) ).
thf(4158,plain,
! [SV903: $i,SV1229: $i,SV485: $i,SV1408: $i,SV56: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV56 ) @ SV1408 ) @ SV485 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1408 @ SV485 @ SV56 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1229 @ SV903 @ SV56 ) @ ( tc_fun @ SV56 @ tc_bool ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1229 @ SV1408 @ SV56 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV485 @ SV903 @ SV56 )
= $true )
| ( ( class_Orderings_Oorder @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4098]) ).
thf(4159,plain,
! [SV1230: $i,SV1532: $i,SV1543: $i,SV1479: $i,SV1511: $i,SV1409: $i,SV904: $i,SV57: $i,SV486: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV486 @ SV57 @ SV904 @ SV1409 @ SV1511 @ SV1479 @ SV1543 @ SV1532 @ SV1230 )
= $false )
| ( ( c_Complete__Lattice_Ocomplete__lattice @ SV57 @ SV486 @ ( c_COMBC @ SV904 @ SV1230 @ SV1230 @ tc_bool ) @ ( c_COMBC @ SV1409 @ SV1230 @ SV1230 @ tc_bool ) @ SV1479 @ SV1511 @ SV1532 @ SV1543 @ SV1230 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4099]) ).
thf(4160,plain,
! [SV509: $i,SV1238: $i,SV80: $i,SV1412: $i,SV922: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV922 @ SV1412 @ SV80 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV922 ) @ SV1412 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV1238 ) @ SV509 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV1238 ) @ SV1412 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV509 @ SV922 @ SV80 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1238 @ SV1412 @ SV80 ) @ ( tc_fun @ SV80 @ tc_bool ) )
= $true )
| ( ( class_Orderings_Oorder @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4102]) ).
thf(4161,plain,
! [SV1413: $i,SV923: $i,SV81: $i,SV510: $i,SV1239: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1239 @ SV510 @ SV81 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV923 ) @ SV1413 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV1239 ) @ SV510 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV1239 ) @ SV1413 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV510 @ SV923 @ SV81 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1239 @ SV1413 @ SV81 ) @ ( tc_fun @ SV81 @ tc_bool ) )
= $true )
| ( ( class_Orderings_Oorder @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4103]) ).
thf(4162,plain,
! [SV92: $i,SV521: $i,SV1240: $i,SV1414: $i,SV934: $i] :
( ( ( c_Finite__Set_Ofinite @ SV934 @ SV1414 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV1414 @ tc_bool ) ) @ SV1240 ) @ SV934 ) )
= $false )
| ( ( ( c_Finite__Set_Osetsum @ SV521 @ ( c_HOL_Ominus__class_Ominus @ SV934 @ SV1240 @ ( tc_fun @ SV1414 @ tc_bool ) ) @ SV1414 @ SV92 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ SV521 @ SV934 @ SV1414 @ SV92 ) @ ( c_Finite__Set_Osetsum @ SV521 @ SV1240 @ SV1414 @ SV92 ) @ SV92 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4104]) ).
thf(4163,plain,
! [SV939: $i,SV1416: $i,SV97: $i,SV526: $i,SV1244: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1244 @ SV526 @ SV97 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1416 @ SV939 @ SV97 ) @ ( tc_fun @ SV97 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV97 ) @ SV1244 ) @ SV526 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV97 ) @ SV526 ) @ SV939 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4106]) ).
thf(4164,plain,
! [SV1417: $i,SV527: $i,SV98: $i,SV1245: $i,SV940: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV940 @ SV1245 @ SV98 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV527 @ SV1417 @ SV98 ) @ ( tc_fun @ SV98 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV98 ) @ SV940 ) @ SV1245 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV98 ) @ SV527 ) @ SV940 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4107]) ).
thf(4165,plain,
! [SV531: $i,SV944: $i,SV102: $i,SV1420: $i,SV1249: $i] :
( ( ( c_Finite__Set_Ofinite @ SV1249 @ SV1420 )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1249 @ SV102 @ SV1420 @ ( tc_fun @ SV944 @ tc_bool ) ) @ SV944 )
= $false )
| ( ( hBOOL @ ( c_in @ SV531 @ SV1249 @ SV1420 ) )
= $false )
| ( ( c_Finite__Set_Ofinite @ ( hAPP @ SV102 @ SV531 ) @ SV944 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4110]) ).
thf(4166,plain,
! [SV1513: $i,SV1423: $i,SV1483: $i,SV1256: $i,SV958: $i,SV547: $i,SV119: $i] :
( ( ( c_Finite__Set_Ofold__graph @ SV119 @ SV547 @ ( c_HOL_Ominus__class_Ominus @ SV958 @ ( c_Set_Oinsert @ SV1256 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1483 @ tc_bool ) ) @ SV1483 ) @ ( tc_fun @ SV1483 @ tc_bool ) ) @ SV1423 @ SV1483 @ SV1513 )
= $false )
| ( ( hBOOL @ ( c_in @ SV1256 @ SV958 @ SV1483 ) )
= $false )
| ( ( c_Finite__Set_Ofold__graph @ SV119 @ SV547 @ SV958 @ ( hAPP @ ( hAPP @ SV119 @ SV1256 ) @ SV1423 ) @ SV1483 @ SV1513 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4112]) ).
thf(4167,plain,
! [SV1514: $i,SV1424: $i,SV552: $i,SV124: $i,SV1484: $i,SV963: $i,SV1261: $i] :
( ( ( hBOOL @ ( c_in @ SV1261 @ SV963 @ SV1484 ) )
= $false )
| ( ( c_Nitpick_Ofold__graph_H @ SV124 @ SV552 @ ( c_HOL_Ominus__class_Ominus @ SV963 @ ( c_Set_Oinsert @ SV1261 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1484 @ tc_bool ) ) @ SV1484 ) @ ( tc_fun @ SV1484 @ tc_bool ) ) @ SV1424 @ SV1484 @ SV1514 )
= $false )
| ( ( c_Nitpick_Ofold__graph_H @ SV124 @ SV552 @ SV963 @ ( hAPP @ ( hAPP @ SV124 @ SV1261 ) @ SV1424 ) @ SV1484 @ SV1514 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4114]) ).
thf(4168,plain,
! [SV570: $i,SV979: $i,SV1544: $i,SV1533: $i,SV1515: $i,SV1485: $i,SV1425: $i,SV1267: $i,SV143: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV143 @ SV1267 @ SV1425 @ SV1485 @ SV1515 @ SV1533 @ SV1544 @ SV979 @ SV570 )
= $false )
| ( ( ( hAPP @ SV143 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV570 @ tc_bool ) ) )
= SV979 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4120]) ).
thf(4169,plain,
! [SV571: $i,SV1545: $i,SV980: $i,SV1534: $i,SV1516: $i,SV1486: $i,SV1426: $i,SV144: $i,SV1268: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV1268 @ SV144 @ SV1426 @ SV1486 @ SV1516 @ SV1534 @ SV980 @ SV1545 @ SV571 )
= $false )
| ( ( ( hAPP @ SV144 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV571 @ tc_bool ) ) )
= SV980 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4121]) ).
thf(4170,plain,
! [SV1562: $i,SV1554: $i,SV1546: $i,SV1535: $i,SV1517: $i,SV1487: $i,SV1427: $i,SV1271: $i,SV989: $i,SV588: $i,SV161: $i] :
( ( ( ( hAPP @ SV161 @ ( c_Set_Oinsert @ SV588 @ SV989 @ SV1271 ) )
= ( hAPP @ ( hAPP @ SV1427 @ SV588 ) @ ( hAPP @ SV161 @ SV989 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV161 @ SV1487 @ SV1517 @ SV1535 @ SV1427 @ SV1546 @ SV1554 @ SV1562 @ SV1271 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4122]) ).
thf(4171,plain,
! [SV1563: $i,SV1555: $i,SV1547: $i,SV1536: $i,SV1518: $i,SV1488: $i,SV1428: $i,SV1272: $i,SV990: $i,SV589: $i,SV162: $i] :
( ( ( ( hAPP @ SV162 @ ( c_Set_Oinsert @ SV589 @ SV990 @ SV1272 ) )
= ( hAPP @ ( hAPP @ SV1428 @ SV589 ) @ ( hAPP @ SV162 @ SV990 ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1488 @ SV162 @ SV1518 @ SV1536 @ SV1547 @ SV1428 @ SV1555 @ SV1563 @ SV1272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4123]) ).
thf(4172,plain,
! [SV1432: $i,SV623: $i,SV1291: $i,SV1024: $i,SV196: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV196 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1024 @ SV1291 @ SV196 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV623 @ SV1432 @ SV196 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV196 ) @ SV1024 ) @ SV1291 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV196 ) @ SV623 ) @ SV1024 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV196 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4124]) ).
thf(4173,plain,
! [SV1025: $i,SV1433: $i,SV624: $i,SV1292: $i,SV197: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV197 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1292 @ SV624 @ SV197 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1433 @ SV1025 @ SV197 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV197 ) @ SV1292 ) @ SV624 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV197 ) @ SV624 ) @ SV1025 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4125]) ).
thf(4174,plain,
! [SV1434: $i,SV1026: $i,SV625: $i,SV1293: $i,SV198: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV198 ) @ SV1293 ) @ SV625 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV198 ) @ SV1026 ) @ SV1434 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ SV198 @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV625 @ SV1026 @ SV198 ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1293 @ SV1434 @ SV198 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV198 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4126]) ).
thf(4175,plain,
! [SV1564: $i,SV1556: $i,SV1548: $i,SV1537: $i,SV1519: $i,SV1491: $i,SV1438: $i,SV1307: $i,SV1053: $i,SV658: $i,SV231: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV231 @ SV658 ) @ ( hAPP @ SV1053 @ SV1307 ) ) )
| ~ ( hBOOL @ ( c_in @ SV658 @ SV1307 @ SV1438 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1491 @ SV1053 @ SV231 @ SV1519 @ SV1537 @ SV1548 @ SV1556 @ SV1564 @ SV1438 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4131]) ).
thf(4176,plain,
! [SV1565: $i,SV1557: $i,SV1549: $i,SV1538: $i,SV1520: $i,SV1492: $i,SV1439: $i,SV1308: $i,SV1054: $i,SV659: $i,SV232: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ ( hAPP @ SV659 @ SV1054 ) ) @ SV1308 ) )
| ~ ( hBOOL @ ( c_in @ SV1308 @ SV1054 @ SV1439 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV659 @ SV1492 @ SV232 @ SV1520 @ SV1538 @ SV1549 @ SV1557 @ SV1565 @ SV1439 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4132]) ).
thf(4177,plain,
! [SV1558: $i,SV1550: $i,SV1539: $i,SV1521: $i,SV1496: $i,SV1449: $i,SV1342: $i,SV1105: $i,SV717: $i,SV292: $i] :
( ( ( ( hAPP @ SV292 @ ( c_Set_Oinsert @ SV717 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1105 @ tc_bool ) ) @ SV1105 ) )
= SV717 )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV292 @ SV1342 @ SV1449 @ SV1496 @ SV1521 @ SV1539 @ SV1550 @ SV1558 @ SV1105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4139]) ).
thf(4178,plain,
! [SV1559: $i,SV1551: $i,SV1540: $i,SV1522: $i,SV1497: $i,SV1450: $i,SV1343: $i,SV1106: $i,SV718: $i,SV293: $i] :
( ( ( ( hAPP @ SV293 @ ( c_Set_Oinsert @ SV718 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1106 @ tc_bool ) ) @ SV1106 ) )
= SV718 )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1343 @ SV293 @ SV1450 @ SV1497 @ SV1522 @ SV1540 @ SV1551 @ SV1559 @ SV1106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4140]) ).
thf(4179,plain,
! [SV1566: $i,SV1560: $i,SV1552: $i,SV1541: $i,SV1523: $i,SV1498: $i,SV1451: $i,SV1345: $i,SV1109: $i,SV725: $i,SV300: $i] :
( ( ( ( hAPP @ SV300 @ ( c_Set_Oinsert @ SV725 @ ( c_Set_Oinsert @ SV1109 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1345 @ tc_bool ) ) @ SV1345 ) @ SV1345 ) )
= ( hAPP @ ( hAPP @ SV1451 @ SV725 ) @ SV1109 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV300 @ SV1498 @ SV1523 @ SV1541 @ SV1451 @ SV1552 @ SV1560 @ SV1566 @ SV1345 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4141]) ).
thf(4180,plain,
! [SV1567: $i,SV1561: $i,SV1553: $i,SV1542: $i,SV1524: $i,SV1499: $i,SV1452: $i,SV1346: $i,SV1110: $i,SV726: $i,SV301: $i] :
( ( ( ( hAPP @ SV301 @ ( c_Set_Oinsert @ SV726 @ ( c_Set_Oinsert @ SV1110 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1346 @ tc_bool ) ) @ SV1346 ) @ SV1346 ) )
= ( hAPP @ ( hAPP @ SV1452 @ SV726 ) @ SV1110 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1499 @ SV301 @ SV1524 @ SV1542 @ SV1553 @ SV1452 @ SV1561 @ SV1567 @ SV1346 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4142]) ).
thf(4181,plain,
! [SV1453: $i,SV1125: $i,SV1356: $i,SV746: $i,SV322: $i,SV1500: $i,SV1525: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1525 @ SV1500 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV322 @ SV746 @ SV1356 @ SV1125 ) ) )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV322 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1525 @ SV1125 @ SV1453 @ 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 )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1453 @ SV1500 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV322 @ SV746 @ SV1356 @ SV1125 @ SV1525 @ SV1453 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV322 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV746 @ SV1125 @ SV1356 @ 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_not_pos,[status(thm)],[4143]) ).
thf(4182,plain,
! [SV1126: $i,SV323: $i,SV1454: $i,SV1357: $i,SV747: $i,SV1501: $i,SV1526: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1526 @ SV1501 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV747 @ SV1526 @ SV1357 @ SV1454 ) ) )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV323 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1526 @ SV1126 @ SV1454 @ 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 )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1454 @ SV1501 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV747 @ SV1526 @ SV1357 @ SV1454 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV323 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV747 @ SV1126 @ SV1357 @ 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_not_pos,[status(thm)],[4144]) ).
thf(4183,plain,
! [SV1455: $i,SV1127: $i,SV1358: $i,SV748: $i,SV324: $i,SV1502: $i,SV1527: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1527 @ SV1502 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV324 @ SV748 @ SV1358 @ SV1127 ) ) )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV324 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1527 @ SV1127 @ SV1455 @ 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 )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1455 @ SV1502 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV324 @ SV748 @ SV1358 @ SV1127 @ SV1527 @ SV1455 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV324 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV748 @ SV1127 @ SV1358 @ 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_not_pos,[status(thm)],[4145]) ).
thf(4184,plain,
! [SV1464: $i,SV1371: $i,SV1507: $i,SV1528: $i,SV1140: $i,SV761: $i,SV337: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV761 @ SV1140 @ SV1528 @ SV1507 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) ) @ SV1507 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1528 @ SV1371 @ SV1464 @ SV1507 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) ) @ SV1507 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV337 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV761 @ ( c_Com_Ocom_OSemi @ SV1140 @ SV1371 ) @ SV1464 @ SV1507 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1507 ) ) @ SV1507 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4149]) ).
thf(4185,plain,
! [SV1394: $i,SV1470: $i,SV834: $i,SV1189: $i,SV411: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV411 ) @ SV1189 ) @ SV834 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV411 ) @ SV1470 ) @ SV1394 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV834 @ SV1189 @ SV411 )
= ( c_HOL_Ominus__class_Ominus @ SV1394 @ SV1470 @ SV411 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV411 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4152]) ).
thf(4186,plain,
! [SV842: $i,SV1197: $i,SV1398: $i,SV1474: $i,SV419: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV419 ) @ SV1474 ) @ SV1398 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV419 ) @ SV1197 ) @ SV842 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV842 @ SV1197 @ SV419 )
= ( c_HOL_Ominus__class_Ominus @ SV1398 @ SV1474 @ SV419 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV419 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4153]) ).
thf(4187,plain,
! [SV1476: $i,SV1401: $i,SV423: $i,SV1201: $i,SV846: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV846 @ SV1201 @ SV423 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1401 @ SV1476 @ SV423 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV846 @ SV1201 @ SV423 )
= ( c_HOL_Ominus__class_Ominus @ SV1401 @ SV1476 @ SV423 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV423 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4154]) ).
thf(4188,plain,
! [SV1205: $i,SV850: $i,SV427: $i,SV1477: $i,SV1402: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1402 @ SV1477 @ SV427 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV850 @ SV1205 @ SV427 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV850 @ SV1205 @ SV427 )
= ( c_HOL_Ominus__class_Ominus @ SV1402 @ SV1477 @ SV427 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV427 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4155]) ).
thf(4189,plain,
! [SV903: $i,SV1229: $i,SV56: $i,SV485: $i,SV1408: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1408 @ SV485 @ SV56 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1229 @ SV903 @ SV56 ) @ ( tc_fun @ SV56 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV56 ) @ SV1408 ) @ SV485 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1229 @ SV1408 @ SV56 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV485 @ SV903 @ SV56 )
= $true )
| ( ( class_Orderings_Oorder @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4158]) ).
thf(4190,plain,
! [SV509: $i,SV1238: $i,SV80: $i,SV1412: $i,SV922: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV922 @ SV1412 @ SV80 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV922 ) @ SV1412 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV1238 ) @ SV509 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV1238 ) @ SV1412 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV509 @ SV922 @ SV80 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1238 @ SV1412 @ SV80 ) @ ( tc_fun @ SV80 @ tc_bool ) )
= $true )
| ( ( class_Orderings_Oorder @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4160]) ).
thf(4191,plain,
! [SV1413: $i,SV923: $i,SV81: $i,SV510: $i,SV1239: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1239 @ SV510 @ SV81 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV923 ) @ SV1413 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV1239 ) @ SV510 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV1239 ) @ SV1413 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV510 @ SV923 @ SV81 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1239 @ SV1413 @ SV81 ) @ ( tc_fun @ SV81 @ tc_bool ) )
= $true )
| ( ( class_Orderings_Oorder @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4161]) ).
thf(4192,plain,
! [SV1562: $i,SV1554: $i,SV1546: $i,SV1535: $i,SV1517: $i,SV1487: $i,SV1427: $i,SV1271: $i,SV989: $i,SV588: $i,SV161: $i] :
( ( ( ( hAPP @ SV161 @ ( c_Set_Oinsert @ SV588 @ SV989 @ SV1271 ) )
= ( hAPP @ ( hAPP @ SV1427 @ SV588 ) @ ( hAPP @ SV161 @ SV989 ) ) )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV161 @ SV1487 @ SV1517 @ SV1535 @ SV1427 @ SV1546 @ SV1554 @ SV1562 @ SV1271 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4170]) ).
thf(4193,plain,
! [SV1563: $i,SV1555: $i,SV1547: $i,SV1536: $i,SV1518: $i,SV1488: $i,SV1428: $i,SV1272: $i,SV990: $i,SV589: $i,SV162: $i] :
( ( ( ( hAPP @ SV162 @ ( c_Set_Oinsert @ SV589 @ SV990 @ SV1272 ) )
= ( hAPP @ ( hAPP @ SV1428 @ SV589 ) @ ( hAPP @ SV162 @ SV990 ) ) )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1488 @ SV162 @ SV1518 @ SV1536 @ SV1547 @ SV1428 @ SV1555 @ SV1563 @ SV1272 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4171]) ).
thf(4194,plain,
! [SV1564: $i,SV1556: $i,SV1548: $i,SV1537: $i,SV1519: $i,SV1491: $i,SV1438: $i,SV1307: $i,SV1053: $i,SV658: $i,SV231: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV231 @ SV658 ) @ ( hAPP @ SV1053 @ SV1307 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV658 @ SV1307 @ SV1438 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1491 @ SV1053 @ SV231 @ SV1519 @ SV1537 @ SV1548 @ SV1556 @ SV1564 @ SV1438 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4175]) ).
thf(4195,plain,
! [SV1565: $i,SV1557: $i,SV1549: $i,SV1538: $i,SV1520: $i,SV1492: $i,SV1439: $i,SV1308: $i,SV1054: $i,SV659: $i,SV232: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ ( hAPP @ SV659 @ SV1054 ) ) @ SV1308 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1308 @ SV1054 @ SV1439 ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV659 @ SV1492 @ SV232 @ SV1520 @ SV1538 @ SV1549 @ SV1557 @ SV1565 @ SV1439 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4176]) ).
thf(4196,plain,
! [SV717: $i,SV1105: $i,SV1558: $i,SV1550: $i,SV1539: $i,SV1521: $i,SV1496: $i,SV1449: $i,SV1342: $i,SV292: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV292 @ SV1342 @ SV1449 @ SV1496 @ SV1521 @ SV1539 @ SV1550 @ SV1558 @ SV1105 )
= $false )
| ( ( ( hAPP @ SV292 @ ( c_Set_Oinsert @ SV717 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1105 @ tc_bool ) ) @ SV1105 ) )
= SV717 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4177]) ).
thf(4197,plain,
! [SV718: $i,SV1106: $i,SV1559: $i,SV1551: $i,SV1540: $i,SV1522: $i,SV1497: $i,SV1450: $i,SV293: $i,SV1343: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV1343 @ SV293 @ SV1450 @ SV1497 @ SV1522 @ SV1540 @ SV1551 @ SV1559 @ SV1106 )
= $false )
| ( ( ( hAPP @ SV293 @ ( c_Set_Oinsert @ SV718 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1106 @ tc_bool ) ) @ SV1106 ) )
= SV718 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4178]) ).
thf(4198,plain,
! [SV1566: $i,SV1560: $i,SV1552: $i,SV1541: $i,SV1523: $i,SV1498: $i,SV1451: $i,SV1345: $i,SV1109: $i,SV725: $i,SV300: $i] :
( ( ( ( hAPP @ SV300 @ ( c_Set_Oinsert @ SV725 @ ( c_Set_Oinsert @ SV1109 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1345 @ tc_bool ) ) @ SV1345 ) @ SV1345 ) )
= ( hAPP @ ( hAPP @ SV1451 @ SV725 ) @ SV1109 ) )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV300 @ SV1498 @ SV1523 @ SV1541 @ SV1451 @ SV1552 @ SV1560 @ SV1566 @ SV1345 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4179]) ).
thf(4199,plain,
! [SV1567: $i,SV1561: $i,SV1553: $i,SV1542: $i,SV1524: $i,SV1499: $i,SV1452: $i,SV1346: $i,SV1110: $i,SV726: $i,SV301: $i] :
( ( ( ( hAPP @ SV301 @ ( c_Set_Oinsert @ SV726 @ ( c_Set_Oinsert @ SV1110 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1346 @ tc_bool ) ) @ SV1346 ) @ SV1346 ) )
= ( hAPP @ ( hAPP @ SV1452 @ SV726 ) @ SV1110 ) )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1499 @ SV301 @ SV1524 @ SV1542 @ SV1553 @ SV1452 @ SV1561 @ SV1567 @ SV1346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4180]) ).
thf(4200,plain,
! [SV1356: $i,SV746: $i,SV1500: $i,SV1453: $i,SV1125: $i,SV1525: $i,SV322: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV322 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1525 @ SV1125 @ SV1453 @ 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 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1525 @ SV1500 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV322 @ SV746 @ SV1356 @ SV1125 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1453 @ SV1500 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV322 @ SV746 @ SV1356 @ SV1125 @ SV1525 @ SV1453 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV322 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV746 @ SV1125 @ SV1356 @ 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_not_pos,[status(thm)],[4181]) ).
thf(4201,plain,
! [SV1357: $i,SV747: $i,SV1501: $i,SV1454: $i,SV1126: $i,SV1526: $i,SV323: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV323 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1526 @ SV1126 @ SV1454 @ 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 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1526 @ SV1501 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV747 @ SV1526 @ SV1357 @ SV1454 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1454 @ SV1501 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV747 @ SV1526 @ SV1357 @ SV1454 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV323 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV747 @ SV1126 @ SV1357 @ 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_not_pos,[status(thm)],[4182]) ).
thf(4202,plain,
! [SV1358: $i,SV748: $i,SV1502: $i,SV1455: $i,SV1127: $i,SV1527: $i,SV324: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV324 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV1527 @ SV1127 @ SV1455 @ 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 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1527 @ SV1502 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV324 @ SV748 @ SV1358 @ SV1127 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1455 @ SV1502 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV324 @ SV748 @ SV1358 @ SV1127 @ SV1527 @ SV1455 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV324 @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV748 @ SV1127 @ SV1358 @ 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_not_pos,[status(thm)],[4183]) ).
thf(4203,plain,
! [SV509: $i,SV1238: $i,SV1412: $i,SV922: $i,SV80: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV922 ) @ SV1412 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV1238 ) @ SV509 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV922 @ SV1412 @ SV80 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV1238 ) @ SV1412 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV509 @ SV922 @ SV80 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1238 @ SV1412 @ SV80 ) @ ( tc_fun @ SV80 @ tc_bool ) )
= $true )
| ( ( class_Orderings_Oorder @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4190]) ).
thf(4204,plain,
! [SV510: $i,SV1239: $i,SV1413: $i,SV923: $i,SV81: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV923 ) @ SV1413 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV1239 ) @ SV510 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1239 @ SV510 @ SV81 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV1239 ) @ SV1413 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV510 @ SV923 @ SV81 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1239 @ SV1413 @ SV81 ) @ ( tc_fun @ SV81 @ tc_bool ) )
= $true )
| ( ( class_Orderings_Oorder @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4191]) ).
thf(4205,plain,
! [SV989: $i,SV588: $i,SV1271: $i,SV1562: $i,SV1554: $i,SV1546: $i,SV1427: $i,SV1535: $i,SV1517: $i,SV1487: $i,SV161: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV161 @ SV1487 @ SV1517 @ SV1535 @ SV1427 @ SV1546 @ SV1554 @ SV1562 @ SV1271 )
= $false )
| ( ( ( hAPP @ SV161 @ ( c_Set_Oinsert @ SV588 @ SV989 @ SV1271 ) )
= ( hAPP @ ( hAPP @ SV1427 @ SV588 ) @ ( hAPP @ SV161 @ SV989 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4192]) ).
thf(4206,plain,
! [SV990: $i,SV589: $i,SV1272: $i,SV1563: $i,SV1555: $i,SV1428: $i,SV1547: $i,SV1536: $i,SV1518: $i,SV162: $i,SV1488: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV1488 @ SV162 @ SV1518 @ SV1536 @ SV1547 @ SV1428 @ SV1555 @ SV1563 @ SV1272 )
= $false )
| ( ( ( hAPP @ SV162 @ ( c_Set_Oinsert @ SV589 @ SV990 @ SV1272 ) )
= ( hAPP @ ( hAPP @ SV1428 @ SV589 ) @ ( hAPP @ SV162 @ SV990 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4193]) ).
thf(4207,plain,
! [SV1564: $i,SV1556: $i,SV1548: $i,SV1537: $i,SV1519: $i,SV231: $i,SV1053: $i,SV1491: $i,SV1438: $i,SV1307: $i,SV658: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV658 @ SV1307 @ SV1438 ) ) )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1491 @ SV1053 @ SV231 @ SV1519 @ SV1537 @ SV1548 @ SV1556 @ SV1564 @ SV1438 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV231 @ SV658 ) @ ( hAPP @ SV1053 @ SV1307 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4194]) ).
thf(4208,plain,
! [SV1565: $i,SV1557: $i,SV1549: $i,SV1538: $i,SV1520: $i,SV232: $i,SV1492: $i,SV659: $i,SV1439: $i,SV1054: $i,SV1308: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV1308 @ SV1054 @ SV1439 ) ) )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV659 @ SV1492 @ SV232 @ SV1520 @ SV1538 @ SV1549 @ SV1557 @ SV1565 @ SV1439 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ ( hAPP @ SV659 @ SV1054 ) ) @ SV1308 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4195]) ).
thf(4209,plain,
! [SV1109: $i,SV725: $i,SV1345: $i,SV1566: $i,SV1560: $i,SV1552: $i,SV1451: $i,SV1541: $i,SV1523: $i,SV1498: $i,SV300: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV300 @ SV1498 @ SV1523 @ SV1541 @ SV1451 @ SV1552 @ SV1560 @ SV1566 @ SV1345 )
= $false )
| ( ( ( hAPP @ SV300 @ ( c_Set_Oinsert @ SV725 @ ( c_Set_Oinsert @ SV1109 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1345 @ tc_bool ) ) @ SV1345 ) @ SV1345 ) )
= ( hAPP @ ( hAPP @ SV1451 @ SV725 ) @ SV1109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4198]) ).
thf(4210,plain,
! [SV1110: $i,SV726: $i,SV1346: $i,SV1567: $i,SV1561: $i,SV1452: $i,SV1553: $i,SV1542: $i,SV1524: $i,SV301: $i,SV1499: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV1499 @ SV301 @ SV1524 @ SV1542 @ SV1553 @ SV1452 @ SV1561 @ SV1567 @ SV1346 )
= $false )
| ( ( ( hAPP @ SV301 @ ( c_Set_Oinsert @ SV726 @ ( c_Set_Oinsert @ SV1110 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1346 @ tc_bool ) ) @ SV1346 ) @ SV1346 ) )
= ( hAPP @ ( hAPP @ SV1452 @ SV726 ) @ SV1110 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4199]) ).
thf(4211,plain,
! [SV509: $i,SV1238: $i,SV1412: $i,SV922: $i,SV80: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV922 ) @ SV1412 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV1238 ) @ SV509 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV922 @ SV1412 @ SV80 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV1238 ) @ SV1412 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV509 @ SV922 @ SV80 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1238 @ SV1412 @ SV80 ) @ ( tc_fun @ SV80 @ tc_bool ) )
= $true )
| ( ( class_Orderings_Oorder @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4203]) ).
thf(4212,plain,
! [SV510: $i,SV1239: $i,SV1413: $i,SV923: $i,SV81: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV923 ) @ SV1413 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV1239 ) @ SV510 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1239 @ SV510 @ SV81 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV1239 ) @ SV1413 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV510 @ SV923 @ SV81 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1239 @ SV1413 @ SV81 ) @ ( tc_fun @ SV81 @ tc_bool ) )
= $true )
| ( ( class_Orderings_Oorder @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4204]) ).
thf(4213,plain,
! [SV1564: $i,SV1556: $i,SV1548: $i,SV1537: $i,SV1519: $i,SV231: $i,SV1053: $i,SV1491: $i,SV1438: $i,SV1307: $i,SV658: $i] :
( ( ( hBOOL @ ( c_in @ SV658 @ SV1307 @ SV1438 ) )
= $false )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1491 @ SV1053 @ SV231 @ SV1519 @ SV1537 @ SV1548 @ SV1556 @ SV1564 @ SV1438 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV231 @ SV658 ) @ ( hAPP @ SV1053 @ SV1307 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4207]) ).
thf(4214,plain,
! [SV1565: $i,SV1557: $i,SV1549: $i,SV1538: $i,SV1520: $i,SV232: $i,SV1492: $i,SV659: $i,SV1439: $i,SV1054: $i,SV1308: $i] :
( ( ( hBOOL @ ( c_in @ SV1308 @ SV1054 @ SV1439 ) )
= $false )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV659 @ SV1492 @ SV232 @ SV1520 @ SV1538 @ SV1549 @ SV1557 @ SV1565 @ SV1439 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ ( hAPP @ SV659 @ SV1054 ) ) @ SV1308 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4208]) ).
thf(4215,plain,
! [SV1412: $i,SV922: $i,SV509: $i,SV1238: $i,SV80: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV1238 ) @ SV509 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV922 ) @ SV1412 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV922 @ SV1412 @ SV80 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV80 ) @ SV1238 ) @ SV1412 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV509 @ SV922 @ SV80 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1238 @ SV1412 @ SV80 ) @ ( tc_fun @ SV80 @ tc_bool ) )
= $true )
| ( ( class_Orderings_Oorder @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4211]) ).
thf(4216,plain,
! [SV1413: $i,SV923: $i,SV510: $i,SV1239: $i,SV81: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV1239 ) @ SV510 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV923 ) @ SV1413 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1239 @ SV510 @ SV81 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ SV81 ) @ SV1239 ) @ SV1413 ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV510 @ SV923 @ SV81 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1239 @ SV1413 @ SV81 ) @ ( tc_fun @ SV81 @ tc_bool ) )
= $true )
| ( ( class_Orderings_Oorder @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4212]) ).
thf(4217,plain,
! [SV1307: $i,SV658: $i,SV1438: $i,SV1564: $i,SV1556: $i,SV1548: $i,SV1537: $i,SV1519: $i,SV231: $i,SV1053: $i,SV1491: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV1491 @ SV1053 @ SV231 @ SV1519 @ SV1537 @ SV1548 @ SV1556 @ SV1564 @ SV1438 )
= $false )
| ( ( hBOOL @ ( c_in @ SV658 @ SV1307 @ SV1438 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV231 @ SV658 ) @ ( hAPP @ SV1053 @ SV1307 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4213]) ).
thf(4218,plain,
! [SV1054: $i,SV1308: $i,SV1439: $i,SV1565: $i,SV1557: $i,SV1549: $i,SV1538: $i,SV1520: $i,SV232: $i,SV1492: $i,SV659: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV659 @ SV1492 @ SV232 @ SV1520 @ SV1538 @ SV1549 @ SV1557 @ SV1565 @ SV1439 )
= $false )
| ( ( hBOOL @ ( c_in @ SV1308 @ SV1054 @ SV1439 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV232 @ ( hAPP @ SV659 @ SV1054 ) ) @ SV1308 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4214]) ).
thf(4219,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[913,4218,4217,4216,4215,4210,4209,4206,4205,4202,4201,4200,4197,4196,4189,4188,4187,4186,4185,4184,4174,4173,4172,4169,4168,4167,4166,4165,4164,4163,4162,4159,4157,4156,4151,4150,4148,4147,4146,4138,4137,4136,4135,4134,4133,4130,4129,4128,4127,4119,4118,4117,4116,4115,4113,4111,4109,4108,4105,4101,4100,4097,4096,4095,4094,4093,4088,4086,4085,4083,4082,4081,4080,4079,4078,4074,4072,4070,4057,4045,4044,4037,4032,4031,4028,4027,4022,4006,4003,4002,4001,4000,3998,3993,3992,3991,3987,3986,3985,3984,3983,3982,3980,3975,3972,3971,3970,3969,3968,3966,3961,3959,3954,3948,3937,3936,3935,3934,3933,3932,3926,3925,3924,3923,3922,3921,3918,3917,3916,3915,3914,3898,3888,3887,3884,3883,3882,3881,3878,3876,3875,3871,3870,3869,3868,3867,3866,3865,3864,3863,3862,3857,3856,3855,3854,3852,3851,3847,3846,3843,3841,3835,3828,3820,3816,3814,3813,3812,3787,3786,3785,3784,3777,3775,3772,3771,3770,3768,3767,3765,3764,3751,3750,3749,3748,3741,3728,3723,3722,3721,3720,3719,3715,3705,3704,3701,3700,3689,3683,3682,3681,3680,3679,3676,3675,3674,3673,3672,3671,3661,3660,3659,3658,3645,3644,3642,3638,3631,3628,3620,3617,3597,3596,3593,3591,3590,3589,3575,3573,3572,3554,3552,3544,3543,3538,3537,3532,3531,3530,3527,3526,3525,3524,3515,3514,3496,3495,3487,3486,3477,3476,3475,3463,3449,3448,3447,3446,3427,3413,3407,3383,3380,3378,3365,3364,3355,3347,3338,3336,3333,3324,3323,3320,3297,3289,3287,3277,3276,3268,3263,3252,3247,3246,3245,3240,3239,3238,3233,3230,3229,3228,3227,3224,3221,3209,3208,3194,3193,3192,3190,3189,3180,3174,3173,3171,3163,3162,3149,3138,3111,3110,3109,3106,3105,3100,3067,3060,3059,3052,3012,3010,3002,3001,3000,2999,2998,2997,2996,2994,2993,2992,2991,2987,2984,2977,2971,2970,2941,2940,2939,2938,2934,2933,2930,2929,2928,2919,2915,2914,2903,2897,2896,2893,2892,2879,2867,2866,2865,2864,2863,2820,2819,2813,2809,2805,2804,2727,2724,2693,2692,2651,2640,2616,2611,2609,2608,2600,2599,2562,2560,2558,2549,2544,2543,2521,2514,2508,2494,2493,2488,2485,2447,2445,2444,2427,2426,2425,2412,2411,2409,2378,2373,2371,2341,2291,2285,2226,2206,2201,2188,2187,2145,2139,2135,2131,2130,2125,2103,2095,2059,1994,1993,1992,1991,1990,1954,1909,1858,1800,1765,1725,1552,1433,1409,1364,1363,1362,1361,1360,1359,1358,1357,1356,1355,1354,1353,1352,1351,1350,1349,1348,1347,1346,1345,1223]) ).
thf(4220,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[4219]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV839-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.17 % Computer : n016.cluster.edu
% 0.13/0.17 % Model : x86_64 x86_64
% 0.13/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.17 % Memory : 8046.5625MB
% 0.13/0.17 % OS : Linux 6.8.0-71-generic
% 0.13/0.17 % CPULimit : 300
% 0.13/0.17 % WCLimit : 300
% 0.13/0.17 % DateTime : Tue Oct 6 16:50:59 UTC 2026
% 0.13/0.17 % CPUTime :
% 0.13/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 135.77/22.93 ...
% 135.77/22.93
% 135.77/22.93 No.of.Axioms: 454
% 135.77/22.93
% 135.77/22.93 Length.of.Defs: 0
% 135.77/22.93
% 135.77/22.93 Contains.Choice.Funs: false
% 135.77/22.93 ..............................................................................................................................................................
% 135.77/22.93
% 135.77/22.93 ********************************
% 135.77/22.93 * All subproblems solved! *
% 135.77/22.93 ********************************
% 135.77/22.93 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:454,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:297,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:4219,loop_count:0,foatp_calls:1,translation:fof_full)
% 135.77/22.93
% 135.77/22.93 %**** Beginning of derivation protocol ****
% 135.77/22.93 % SZS output start CNFRefutation
% See solution above
% 135.77/22.96
% 135.77/22.96 %**** End of derivation protocol ****
% 135.77/22.96 %**** no. of clauses in derivation: 4220 ****
% 135.77/22.96 %**** clause counter: 4219 ****
% 135.77/22.96
% 135.77/22.96 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:454,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:297,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:4219,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------