%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV840-1 : 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 : n017.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 10:59:20 AM UTC 2026
% Result : Unsatisfiable 195.52s 32.95s
% Output : CNFRefutation 195.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 470
% Syntax : Number of formulae : 4360 (2935 unt; 0 typ; 0 def)
% Number of atoms : 20285 (8298 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 71933 (4251 ~;5019 |; 0 &;62663 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 36 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 104 ( 101 usr; 20 con; 0-10 aty)
% Number of variables : 19149 ( 0 ^;19149 !; 0 ?;19149 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_COMBB,type,
c_COMBB: $i > $i > $i > $i > $i > $i ).
thf(tp_c_COMBC,type,
c_COMBC: $i > $i > $i > $i > $i ).
thf(tp_c_COMBI,type,
c_COMBI: $i > $i ).
thf(tp_c_COMBK,type,
c_COMBK: $i > $i > $i > $i ).
thf(tp_c_COMBS,type,
c_COMBS: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Collect,type,
c_Collect: $i > $i > $i ).
thf(tp_c_Com_OWT,type,
c_Com_OWT: $i > $o ).
thf(tp_c_Com_Obody,type,
c_Com_Obody: $i ).
thf(tp_c_Com_Ocom_OBODY,type,
c_Com_Ocom_OBODY: $i ).
thf(tp_c_Com_Ocom_OCall,type,
c_Com_Ocom_OCall: $i > $i > $i > $i ).
thf(tp_c_Com_Ocom_OCond,type,
c_Com_Ocom_OCond: $i > $i > $i > $i ).
thf(tp_c_Com_Ocom_OLocal,type,
c_Com_Ocom_OLocal: $i > $i > $i > $i ).
thf(tp_c_Com_Ocom_OSKIP,type,
c_Com_Ocom_OSKIP: $i ).
thf(tp_c_Com_Ocom_OSemi,type,
c_Com_Ocom_OSemi: $i > $i > $i ).
thf(tp_c_Com_Ocom_OWhile,type,
c_Com_Ocom_OWhile: $i > $i > $i ).
thf(tp_c_Com_Ocom_Ocom__case,type,
c_Com_Ocom_Ocom__case: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(tp_c_Complete__Lattice_OInf__class_OInf,type,
c_Complete__Lattice_OInf__class_OInf: $i > $i > $i ).
thf(tp_c_Complete__Lattice_OSup__class_OSup,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i > $i ).
thf(tp_c_Complete__Lattice_Ocomplete__lattice,type,
c_Complete__Lattice_Ocomplete__lattice: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(tp_c_Complete__Lattice_Ocomplete__lattice__class_OSUPR,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i > $i > $i ).
thf(tp_c_Finite__Set_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_Olinorder__class_OMax,type,
c_Finite__Set_Olinorder__class_OMax: $i > $i > $i ).
thf(tp_c_Finite__Set_Olinorder__class_OMin,type,
c_Finite__Set_Olinorder__class_OMin: $i > $i > $i ).
thf(tp_c_Fun_Ocomp,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i > $i ).
thf(tp_c_HOL_Ominus__class_Ominus,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(tp_c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(tp_c_Hoare__Mirabelle_Ohoare__derivs,type,
c_Hoare__Mirabelle_Ohoare__derivs: $i > $i > $i > $o ).
thf(tp_c_Hoare__Mirabelle_Opeek__and,type,
c_Hoare__Mirabelle_Opeek__and: $i > $i > $i > $i ).
thf(tp_c_Hoare__Mirabelle_Otriple_Otriple,type,
c_Hoare__Mirabelle_Otriple_Otriple: $i > $i ).
thf(tp_c_Hoare__Mirabelle_Otriple_Otriple__case,type,
c_Hoare__Mirabelle_Otriple_Otriple__case: $i > $i > $i > $i > $i ).
thf(tp_c_Hoare__Mirabelle_Otriple_Otriple__rec,type,
c_Hoare__Mirabelle_Otriple_Otriple__rec: $i > $i > $i > $i > $i ).
thf(tp_c_Hoare__Mirabelle_Otriple__valid,type,
c_Hoare__Mirabelle_Otriple__valid: $i > $i > $i > $o ).
thf(tp_c_Lattices_Oupper__semilattice__class_Osup,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i > $i ).
thf(tp_c_Natural_Oevalc,type,
c_Natural_Oevalc: $i > $i > $i > $o ).
thf(tp_c_Natural_Oevaln,type,
c_Natural_Oevaln: $i > $i > $i > $i > $o ).
thf(tp_c_Natural_Osko__Natural__Xevaln__elim__cases__6__1,type,
c_Natural_Osko__Natural__Xevaln__elim__cases__6__1: $i > $i > $i > $i > $i ).
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_Not,type,
c_Not: $i ).
thf(tp_c_Option_Ooption_ONone,type,
c_Option_Ooption_ONone: $i > $i ).
thf(tp_c_Option_Ooption_OSome,type,
c_Option_Ooption_OSome: $i > $i > $i ).
thf(tp_c_Option_Othe,type,
c_Option_Othe: $i > $i ).
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_Set_Ocontents,type,
c_Set_Ocontents: $i > $i > $i ).
thf(tp_c_Set_Oimage,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(tp_c_Set_Oinsert,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(tp_c_Suc,type,
c_Suc: $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 > $i > $o ).
thf(tp_class_Complete__Lattice_Ocomplete__lattice,type,
class_Complete__Lattice_Ocomplete__lattice: $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_Int_Onumber__ring,type,
class_Int_Onumber__ring: $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_Oidom,type,
class_Ring__and__Field_Oidom: $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_t_c,type,
t_c: $i ).
thf(tp_tc_Com_Ocom,type,
tc_Com_Ocom: $i ).
thf(tp_tc_Com_Opname,type,
tc_Com_Opname: $i ).
thf(tp_tc_Com_Ostate,type,
tc_Com_Ostate: $i ).
thf(tp_tc_Hoare__Mirabelle_Otriple,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
thf(tp_tc_Option_Ooption,type,
tc_Option_Ooption: $i > $i ).
thf(tp_tc_bool,type,
tc_bool: $i ).
thf(tp_tc_fun,type,
tc_fun: $i > $i > $i ).
thf(tp_tc_nat,type,
tc_nat: $i ).
thf(tp_v_G,type,
v_G: $i ).
thf(tp_v_P,type,
v_P: $i ).
thf(tp_v_Q,type,
v_Q: $i ).
thf(tp_v_R,type,
v_R: $i ).
thf(tp_v_pn,type,
v_pn: $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_Orderings_Obot @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(6,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(7,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(8,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(9,axiom,
class_Lattices_Obounded__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(10,axiom,
class_Lattices_Oupper__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(11,axiom,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
thf(12,axiom,
class_HOL_Oord @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(13,axiom,
class_HOL_Ominus @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ominus) ).
thf(14,axiom,
class_Orderings_Obot @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(15,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(16,axiom,
class_Lattices_Olattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(17,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(18,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(19,axiom,
class_Lattices_Oupper__semilattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
thf(20,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(21,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(22,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(23,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(24,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(25,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(26,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(27,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(28,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(29,axiom,
! [V_pname: $i,V_pname_H: $i] :
( ( ( hAPP @ c_Com_Ocom_OBODY @ V_pname )
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H ) )
| ( V_pname = V_pname_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).
thf(30,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(31,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(32,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(33,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(34,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(35,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(36,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(37,axiom,
! [V_G: $i,T_a: $i,V_P: $i,V_pn: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) @ V_Q ) @ V_G @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_pn ) ) ) @ V_Q ) @ ( 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_BodyN_0) ).
thf(38,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(39,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(40,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(41,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(42,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(43,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(44,axiom,
! [T_a: $i,V_fun1: $i,V_com: $i,V_fun2: $i,V_fun1_H: $i,V_com_H: $i,V_fun2_H: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1 ) @ V_com ) @ V_fun2 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1_H ) @ V_com_H ) @ V_fun2_H ) )
| ( V_fun1 = V_fun1_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_0) ).
thf(45,axiom,
! [T_a: $i,V_fun1: $i,V_com: $i,V_fun2: $i,V_fun1_H: $i,V_com_H: $i,V_fun2_H: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1 ) @ V_com ) @ V_fun2 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1_H ) @ V_com_H ) @ V_fun2_H ) )
| ( V_com = V_com_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_1) ).
thf(46,axiom,
! [T_a: $i,V_fun1: $i,V_com: $i,V_fun2: $i,V_fun1_H: $i,V_com_H: $i,V_fun2_H: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1 ) @ V_com ) @ V_fun2 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1_H ) @ V_com_H ) @ V_fun2_H ) )
| ( V_fun2 = V_fun2_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Oinject_2) ).
thf(47,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(48,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(49,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(50,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(51,axiom,
! [V_G: $i,T_a: $i,V_P: $i,V_c: $i,V_d: $i,V_R: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( c_Com_Ocom_OSemi @ V_c @ V_d ) ) @ V_R ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_Q ) @ V_d ) @ V_R ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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(52,axiom,
! [V_G: $i,T_a: $i,V_P: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ c_Com_Ocom_OSKIP ) @ V_P ) @ ( 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(53,axiom,
! [V_P: $i,V_s: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_P ) ) @ V_s @ V_s1 )
| ~ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_s1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I6_J_0) ).
thf(54,axiom,
! [V_pn: $i,V_s0: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) @ V_s0 @ V_s1 )
| ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_pn ) ) @ V_s0 @ V_s1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OBody_0) ).
thf(55,axiom,
! [V_n: $i,T_a: $i,V_P: $i,V_pn: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_pn ) ) ) @ V_Q ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ V_n ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) @ V_Q ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Body__triple__valid__Suc_1) ).
thf(56,axiom,
! [V_n: $i,T_a: $i,V_P: $i,V_pn: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ V_n ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) @ V_Q ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_pn ) ) ) @ V_Q ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Body__triple__valid__Suc_0) ).
thf(57,axiom,
( ( hAPP @ ( c_COMBK @ v_P @ t_a @ t_b ) @ v_Q )
= v_P ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def__raw_0) ).
thf(58,axiom,
! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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(59,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q_H ) @ ( 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(60,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P_H ) @ V_c ) @ V_Q_H ) @ ( 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(61,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P_H ) @ V_c ) @ V_Q ) @ ( 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(62,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_x ) @ V_c ) @ V_xa ) @ ( 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(63,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P_H ) @ V_c ) @ V_Q ) @ ( 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(64,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P_H ) @ V_c ) @ V_Q_H ) @ ( 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(65,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q_H ) @ ( 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(66,axiom,
! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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(67,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_x ) @ V_c ) @ V_xa ) @ ( 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(68,axiom,
! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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(69,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_x ) @ V_c ) @ V_xa ) @ ( 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(70,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P_H ) @ V_c ) @ V_Q_H ) @ ( 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(71,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_x ) @ V_c ) @ V_xa ) @ ( 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(72,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( 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_Inf__singleton_0) ).
thf(73,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(74,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(75,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(76,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(77,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(78,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(79,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(80,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(81,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(82,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(83,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(84,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(85,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(86,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(87,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(88,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(89,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(90,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(91,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(92,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).
thf(93,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(94,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(95,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(96,axiom,
! [V_A: $i,V_x: $i,T_a: $i] :
( ( V_A
= ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(97,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(98,axiom,
! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__empty_0) ).
thf(99,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(100,axiom,
! [V_pn: $i,V_s0: $i,V_n: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) @ V_s0 @ ( c_Suc @ V_n ) @ V_s1 )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_pn ) ) @ V_s0 @ V_n @ V_s1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OBody_0) ).
thf(101,axiom,
! [V_P: $i,V_s: $i,V_n: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_P ) ) @ V_s @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ V_P @ V_n @ V_s @ V_s1 ) @ V_s1 )
| ~ ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_n @ V_s1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I6_J_1) ).
thf(102,axiom,
! [V_G: $i,T_a: $i,V_P: $i,V_b: $i,V_c: $i,V_d: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( c_Com_Ocom_OCond @ V_b @ V_c @ V_d ) ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ ( c_Hoare__Mirabelle_Opeek__and @ V_P @ ( c_Fun_Ocomp @ c_Not @ V_b @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ T_a ) ) @ V_d ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ ( c_Hoare__Mirabelle_Opeek__and @ V_P @ V_b @ T_a ) ) @ V_c ) @ V_Q ) @ ( 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_OIf_0) ).
thf(103,axiom,
! [V_G: $i,T_a: $i,V_P: $i,V_b: $i,V_c: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) @ ( c_Hoare__Mirabelle_Opeek__and @ V_P @ ( c_Fun_Ocomp @ c_Not @ V_b @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ T_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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ ( c_Hoare__Mirabelle_Opeek__and @ V_P @ V_b @ T_a ) ) @ V_c ) @ V_P ) @ ( 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_Loop_0) ).
thf(104,axiom,
! [T_a: $i,V_x: $i] :
( ( hAPP @ ( c_Option_Othe @ T_a ) @ ( c_Option_Ooption_OSome @ V_x @ T_a ) )
= V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the_Osimps_0) ).
thf(105,axiom,
( ( hAPP @ ( hAPP @ ( c_COMBC @ v_P @ t_a @ t_b @ t_c ) @ v_Q ) @ v_R )
= ( hAPP @ ( hAPP @ v_P @ v_R ) @ v_Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def__raw_0) ).
thf(106,axiom,
( ( hAPP @ ( c_COMBS @ v_P @ v_Q @ t_a @ t_b @ t_c ) @ v_R )
= ( hAPP @ ( hAPP @ v_P @ v_R ) @ ( hAPP @ v_Q @ v_R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBS__def__raw_0) ).
thf(107,axiom,
( ( hAPP @ ( c_COMBB @ v_P @ v_Q @ t_a @ t_b @ t_c ) @ v_R )
= ( hAPP @ v_P @ ( hAPP @ v_Q @ v_R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def__raw_0) ).
thf(108,axiom,
! [V_pn: $i] :
( ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) )
| ( ( hAPP @ c_Com_Obody @ V_pn )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OBody_0) ).
thf(109,axiom,
! [V_G: $i,T_a: $i,V_P: $i,V_pn: $i,V_Q: $i,V_Procs: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ ( hAPP @ V_P @ V_pn ) ) @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) @ ( hAPP @ V_Q @ V_pn ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( hBOOL @ ( c_in @ V_pn @ V_Procs @ tc_Com_Opname ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_G @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ V_Q @ tc_Com_Opname @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ V_Procs @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ V_Q @ tc_Com_Opname @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ V_Procs @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Body1_0) ).
thf(110,axiom,
! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ ( 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 ) ) @ ( 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(111,axiom,
( ( hAPP @ ( c_COMBI @ t_a ) @ v_P )
= v_P ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBI__def__raw_0) ).
thf(112,axiom,
! [V_G: $i,V_ts: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ~ ( c_lessequals @ V_ts @ V_G @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_asm_0) ).
thf(113,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_lessequals @ V_G_H @ V_G @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G_H @ V_ts @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_thin_0) ).
thf(114,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 )
| ~ ( c_lessequals @ V_ts @ V_ts_H @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts_H @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_weaken_0) ).
thf(115,axiom,
! [V_f1: $i,T_b: $i,V_fun1: $i,V_com: $i,V_fun2: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ V_f1 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b ) @ V_fun1 ) @ V_com ) @ V_fun2 ) @ T_b @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ V_f1 @ V_fun1 ) @ V_com ) @ V_fun2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Ocases_0) ).
thf(116,axiom,
! [V_f1: $i,T_b: $i,V_fun1: $i,V_com: $i,V_fun2: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ V_f1 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b ) @ V_fun1 ) @ V_com ) @ V_fun2 ) @ T_b @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ V_f1 @ V_fun1 ) @ V_com ) @ V_fun2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Orecs_0) ).
thf(117,axiom,
! [V_P: $i,V_f1: $i,V_fun1: $i,V_com: $i,V_fun2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ V_f1 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ V_fun1 ) @ V_com ) @ V_fun2 ) @ t_b @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ ( hAPP @ V_f1 @ V_fun1 ) @ V_com ) @ V_fun2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Osplit_0) ).
thf(118,axiom,
! [V_P: $i,V_f1: $i,V_xa: $i,V_xb: $i,V_xc: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ V_f1 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ V_xa ) @ V_xb ) @ V_xc ) @ t_b @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ ( hAPP @ V_f1 @ V_xa ) @ V_xb ) @ V_xc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple_Osplit__asm_0) ).
thf(119,axiom,
! [T_a: $i,V_P: $i,V_pn: $i,V_Q: $i] : ( c_Hoare__Mirabelle_Otriple__valid @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) @ V_Q ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Body__triple__valid__0_0) ).
thf(120,axiom,
! [V_pname_H: $i] :
( c_Com_Ocom_OSKIP
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I18_J_0) ).
thf(121,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_f4: $i,V_f5: $i,V_f6: $i,V_f7: $i,V_f8: $i,V_pname: $i,T_a: $i] :
( ( c_Com_Ocom_Ocom__case @ V_f1 @ V_f2 @ V_f3 @ V_f4 @ V_f5 @ V_f6 @ V_f7 @ V_f8 @ ( hAPP @ c_Com_Ocom_OBODY @ V_pname ) @ T_a )
= ( hAPP @ V_f7 @ V_pname ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I70_J_0) ).
thf(122,axiom,
! [V_pname: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ V_pname )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I62_J_0) ).
thf(123,axiom,
! [V_loc: $i,V_fun: $i,V_com: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I40_J_0) ).
thf(124,axiom,
! [V_com1: $i,V_com2: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I48_J_0) ).
thf(125,axiom,
! [V_pname_H: $i,V_com1: $i,V_com2: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I49_J_0) ).
thf(126,axiom,
! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i,V_pname: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H )
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I63_J_0) ).
thf(127,axiom,
! [V_pname_H: $i,V_fun: $i,V_com: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OWhile @ V_fun @ V_com ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I59_J_0) ).
thf(128,axiom,
! [V_pname_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I41_J_0) ).
thf(129,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(130,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(131,axiom,
! [V_c1: $i,V_b: $i,V_c2: $i] :
( ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I5_J_0) ).
thf(132,axiom,
! [V_c2: $i,V_b: $i,V_c1: $i] :
( ( c_Com_OWT @ V_c2 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I5_J_1) ).
thf(133,axiom,
! [T_a: $i,V_x: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a ) @ T_a )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
thf(134,axiom,
! [V_c2: $i,V_s: $i,V_t: $i,V_c1: $i,V_b: $i] :
( ( c_Natural_Oevalc @ V_c2 @ V_s @ V_t )
| ( c_Natural_Oevalc @ V_c1 @ V_s @ V_t )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) @ V_s @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_2) ).
thf(135,axiom,
! [V_loc: $i,V_fun: $i,V_com: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I42_J_0) ).
thf(136,axiom,
! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(137,axiom,
! [V_c2: $i,V_s: $i,V_n: $i,V_t: $i,V_c1: $i,V_b: $i] :
( ( c_Natural_Oevaln @ V_c2 @ V_s @ V_n @ V_t )
| ( c_Natural_Oevaln @ V_c1 @ V_s @ V_n @ V_t )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I5_J_2) ).
thf(138,axiom,
! [V_x: $i,V_A: $i,T_b: $i,V_f: $i,T_a: $i] :
( ~ ( c_lessequals @ V_x @ V_A @ ( tc_fun @ T_b @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_x @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
thf(139,axiom,
! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).
thf(140,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_y_H @ V_x_H @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(141,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y_H @ V_x_H @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(142,axiom,
! [V_B: $i,V_C: $i,V_A: $i,T_a: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_B @ ( c_HOL_Ominus__class_Ominus @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).
thf(143,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(144,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(145,axiom,
! [V_b: $i,V_s: $i,V_t: $i,V_c: $i,V_n: $i] :
( ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ( V_t = V_s )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s @ V_n @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__WHILE__case_0) ).
thf(146,axiom,
! [V_f: $i,V_g: $i,V_x: $i,V_f_H: $i,V_g_H: $i,V_x_H: $i,T_b: $i,T_a: $i,T_c: $i,T_d: $i,T_e: $i] :
( ( ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) )
!= ( hAPP @ V_f_H @ ( hAPP @ V_g_H @ V_x_H ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ ( c_Fun_Ocomp @ V_f_H @ V_g_H @ T_d @ T_a @ T_e ) @ V_x_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__cong_0) ).
thf(147,axiom,
! [V_a: $i,V_b: $i,T_c: $i,T_b: $i,T_a: $i,V_c: $i,V_d: $i,T_d: $i,V_v: $i] :
( ( ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a )
!= ( c_Fun_Ocomp @ V_c @ V_d @ T_d @ T_b @ T_a ) )
| ( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ V_c @ ( hAPP @ V_d @ V_v ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).
thf(148,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_f4: $i,V_f5: $i,V_f6: $i,V_f7: $i,V_f8: $i,V_fun: $i,V_com1: $i,V_com2: $i,T_a: $i] :
( ( c_Com_Ocom_Ocom__case @ V_f1 @ V_f2 @ V_f3 @ V_f4 @ V_f5 @ V_f6 @ V_f7 @ V_f8 @ ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ V_f5 @ V_fun ) @ V_com1 ) @ V_com2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I68_J_0) ).
thf(149,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_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_0) ).
thf(150,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_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_1) ).
thf(151,axiom,
! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I21_J_0) ).
thf(152,axiom,
! [V_Q: $i,V_x: $i,V_P: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(153,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(154,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(155,axiom,
! [V_Q: $i,V_x: $i,V_P: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(156,axiom,
! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(157,axiom,
! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(158,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 ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(159,axiom,
! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(160,axiom,
! [V_x: $i,T_a: $i] : ( c_lessequals @ V_x @ V_x @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(161,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_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(162,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 ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(163,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(164,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(165,axiom,
! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(166,axiom,
! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(167,axiom,
! [T_a: $i,V_a: $i,V_x: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_a @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(168,axiom,
! [T_a: $i,V_b: $i,V_x: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(169,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(170,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(171,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(172,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(173,axiom,
! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(174,axiom,
! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(175,axiom,
! [V_b: $i,V_s: $i,V_t: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ( V_t = V_s )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__WHILE__case_0) ).
thf(176,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(177,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(178,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(179,axiom,
! [V_fun_H: $i,V_com_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I47_J_0) ).
thf(180,axiom,
! [V_f: $i,V_g: $i,T_c: $i,T_a: $i,T_b: $i,V_r: $i] :
( ( c_Set_Oimage @ ( c_Fun_Ocomp @ V_f @ V_g @ T_c @ T_a @ T_b ) @ V_r @ T_b @ T_a )
= ( c_Set_Oimage @ V_f @ ( c_Set_Oimage @ V_g @ V_r @ T_b @ T_c ) @ T_c @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__compose_0) ).
thf(181,axiom,
! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I20_J_0) ).
thf(182,axiom,
! [V_c0: $i,V_c1: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) )
| ~ ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ V_c0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OSemi_0) ).
thf(183,axiom,
! [V_loc: $i,V_fun: $i,V_com: $i,V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) )
| ( V_loc = V_loc_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_0) ).
thf(184,axiom,
! [V_loc: $i,V_fun: $i,V_com: $i,V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) )
| ( V_fun = V_fun_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_1) ).
thf(185,axiom,
! [V_loc: $i,V_fun: $i,V_com: $i,V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) )
| ( V_com = V_com_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I2_J_2) ).
thf(186,axiom,
! [V_f: $i,V_g: $i,V_A: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Set_Oimage @ V_g @ V_A @ T_c @ T_b ) @ T_b @ T_a )
= ( c_Set_Oimage @ ( c_COMBB @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_A @ T_c @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__image_0) ).
thf(187,axiom,
! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(188,axiom,
! [V_f: $i,V_g: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_c @ T_b @ t_a ) @ v_x )
= ( hAPP @ V_f @ ( hAPP @ V_g @ v_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__def_0) ).
thf(189,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(190,axiom,
! [V_f: $i,V_g: $i,V_h: $i,T_d: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Ocomp @ V_f @ ( c_Fun_Ocomp @ V_g @ V_h @ T_d @ T_c @ T_a ) @ T_c @ T_b @ T_a )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ V_f @ V_g @ T_c @ T_b @ T_d ) @ V_h @ T_d @ T_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__assoc_0) ).
thf(191,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_D @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(192,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_f4: $i,V_f5: $i,V_f6: $i,V_f7: $i,V_f8: $i,V_fun: $i,V_com: $i,T_a: $i] :
( ( c_Com_Ocom_Ocom__case @ V_f1 @ V_f2 @ V_f3 @ V_f4 @ V_f5 @ V_f6 @ V_f7 @ V_f8 @ ( c_Com_Ocom_OWhile @ V_fun @ V_com ) @ T_a )
= ( hAPP @ ( hAPP @ V_f6 @ V_fun ) @ V_com ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I69_J_0) ).
thf(193,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_f4: $i,V_f5: $i,V_f6: $i,V_f7: $i,V_f8: $i,V_loc: $i,V_fun: $i,V_com: $i,T_a: $i] :
( ( c_Com_Ocom_Ocom__case @ V_f1 @ V_f2 @ V_f3 @ V_f4 @ V_f5 @ V_f6 @ V_f7 @ V_f8 @ ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ V_f3 @ V_loc ) @ V_fun ) @ V_com ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I66_J_0) ).
thf(194,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 ) )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_0) ).
thf(195,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 ) )
| ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_1) ).
thf(196,axiom,
! [T_a: $i,V_A: $i,V_x: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ V_A @ T_a ) @ V_x @ T_a )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__lower_0) ).
thf(197,axiom,
! [V_c1: $i,V_c2: $i] :
( ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_0) ).
thf(198,axiom,
! [V_c2: $i,V_c1: $i] :
( ( c_Com_OWT @ V_c2 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I4_J_1) ).
thf(199,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(200,axiom,
! [V_b: $i,V_c0: $i,V_c1: $i,V_s: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c0 @ V_c1 ) @ V_s @ V_s1 )
| ~ ( c_Natural_Oevalc @ V_c1 @ V_s @ V_s1 )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OIfFalse_0) ).
thf(201,axiom,
! [V_c2: $i,V_s: $i,V_t: $i,V_b: $i,V_c1: $i] :
( ( c_Natural_Oevalc @ V_c2 @ V_s @ V_t )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) @ V_s @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_0) ).
thf(202,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(203,axiom,
! [V_Q: $i,V_Z: $i,V_s_H: $i,V_c: $i,V_s: $i,V_n: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_Q @ V_Z ) @ V_s_H ) )
| ~ ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_s_H )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_Z ) @ V_s ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple__valid__def2_0) ).
thf(204,axiom,
! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(205,axiom,
! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(206,axiom,
! [V_s: $i,V_n: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_s ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OSkip_0) ).
thf(207,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= V_B )
| ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(208,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(209,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(210,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(211,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(212,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(213,axiom,
! [V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I11_J_0) ).
thf(214,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
thf(215,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
thf(216,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(217,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(218,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(219,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(220,axiom,
! [V_u: $i,V_t: $i,V_c: $i,V_s: $i] :
( ( V_u = V_t )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_u )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com__det_0) ).
thf(221,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(222,axiom,
! [V_s: $i] : ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ V_s @ V_s ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OSkip_0) ).
thf(223,axiom,
! [V_fun: $i,V_com: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I60_J_0) ).
thf(224,axiom,
! [V_b: $i,V_c0: $i,V_c1: $i,V_s: $i,V_n: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ V_b @ V_c0 @ V_c1 ) @ V_s @ V_n @ V_s1 )
| ~ ( c_Natural_Oevaln @ V_c1 @ V_s @ V_n @ V_s1 )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OIfFalse_0) ).
thf(225,axiom,
! [V_c2: $i,V_s: $i,V_n: $i,V_t: $i,V_b: $i,V_c1: $i] :
( ( c_Natural_Oevaln @ V_c2 @ V_s @ V_n @ V_t )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I5_J_0) ).
thf(226,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_D @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
thf(227,axiom,
! [V_c: $i,V_s: $i,V_n: $i,V_s_H: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ ( c_Suc @ V_n ) @ V_s_H )
| ~ ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_s_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__Suc_0) ).
thf(228,axiom,
! [V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I10_J_0) ).
thf(229,axiom,
! [V_fun: $i,V_com1: $i,V_com2: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I54_J_0) ).
thf(230,axiom,
! [V_pname_H: $i,V_fun: $i,V_com1: $i,V_com2: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I55_J_0) ).
thf(231,axiom,
! [V_fun: $i,V_com: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I58_J_0) ).
thf(232,axiom,
! [V_pname_H: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I19_J_0) ).
thf(233,axiom,
! [V_G: $i,T_a: $i,V_P: $i,V_Q: $i,V_Procs: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ V_Q @ tc_Com_Opname @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ V_Procs @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_G @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ V_Q @ tc_Com_Opname @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ V_Procs @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ V_Q @ tc_Com_Opname @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ V_Procs @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__derivs_OBody_0) ).
thf(234,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(235,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(236,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(237,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(238,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(239,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(240,axiom,
! [V_A: $i,V_b: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(241,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(242,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(243,axiom,
! [V_B: $i,V_a: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(244,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(245,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(246,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(247,axiom,
! [V_f: $i,V_a: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Set_Oinsert @ V_a @ V_B @ T_b ) @ T_b @ T_a )
= ( c_Set_Oinsert @ ( hAPP @ V_f @ V_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(248,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(249,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(250,axiom,
! [V_a: $i,V_C: $i,T_a: $i,V_D: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ V_a @ V_C @ T_a ) @ ( c_Set_Oinsert @ V_a @ V_D @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(251,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(252,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).
thf(253,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__binary_0) ).
thf(254,axiom,
! [V_c: $i,T_a: $i,T_b: $i,V_A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_a @ T_b ) @ V_A @ T_b @ T_a )
= ( c_Set_Oinsert @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
thf(255,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(256,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(257,axiom,
! [T_a: $i,V_f: $i,T_b: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oimage @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
thf(258,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(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 ) )
!= ( 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(260,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(261,axiom,
! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).
thf(262,axiom,
! [T_a: $i,V_f: $i,V_A: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
thf(263,axiom,
! [T_a: $i,V_A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(264,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(265,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(266,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(267,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(268,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(269,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(270,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(271,axiom,
! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(272,axiom,
! [T_a: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(273,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(274,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(275,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(276,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(277,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(278,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(279,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(280,axiom,
! [V_f: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
thf(281,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(282,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(283,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(284,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Obot @ T_a )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(285,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(286,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(287,axiom,
! [T_b: $i,V_f: $i,V_x: $i,V_g: $i,T_a: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ( c_lessequals @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_g @ V_x ) @ T_b )
| ~ ( c_lessequals @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(288,axiom,
! [V_c: $i,V_s: $i,V_t: $i,V_x: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
| ~ ( c_Natural_Oevaln @ V_c @ V_s @ V_x @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eval__eq_1) ).
thf(289,axiom,
! [V_c: $i,V_s: $i,V_t: $i,V_n: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
| ~ ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__evalc_0) ).
thf(290,axiom,
! [V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ V_s @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I1_J_0) ).
thf(291,axiom,
! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
thf(292,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
thf(293,axiom,
! [V_f: $i,V_x: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(294,axiom,
! [V_f: $i,V_x: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(295,axiom,
! [V_x: $i,V_A: $i,T_b: $i,V_f: $i,T_a: $i] :
( ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_b ) )
| ( hBOOL @ ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(296,axiom,
! [V_x: $i,V_A: $i,T_aa: $i,V_f: $i,T_a: $i] :
( ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_aa ) )
| ( hBOOL @ ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_aa @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(297,axiom,
! [V_t: $i,V_s: $i,V_n: $i] :
( ( V_t = V_s )
| ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I1_J_0) ).
thf(298,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(299,axiom,
! [V_n: $i,V_P: $i,V_s: $i,V_s1: $i] :
( ( V_n
= ( c_Suc @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ V_P @ V_n @ V_s @ V_s1 ) ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_n @ V_s1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I6_J_0) ).
thf(300,axiom,
! [V_com1: $i,V_com2: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I50_J_0) ).
thf(301,axiom,
! [V_fun_H: $i,V_com_H: $i,V_fun: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I53_J_0) ).
thf(302,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(303,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(304,axiom,
! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I15_J_0) ).
thf(305,axiom,
! [V_c: $i,V_Y: $i,V_a: $i] :
( ( c_Com_OWT @ V_c )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ V_Y @ V_a @ V_c ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I3_J_0) ).
thf(306,axiom,
! [V_Y: $i,V_a: $i,V_c: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ V_Y @ V_a @ V_c ) )
| ~ ( c_Com_OWT @ V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OLocal_0) ).
thf(307,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(308,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(309,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(310,axiom,
! [V_c: $i,V_b: $i] :
( ( c_Com_OWT @ V_c )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I6_J_0) ).
thf(311,axiom,
! [V_b: $i,V_c: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) )
| ~ ( c_Com_OWT @ V_c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_While_0) ).
thf(312,axiom,
! [V_fun: $i,V_com: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) )
| ( V_com = V_com_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_1) ).
thf(313,axiom,
! [V_fun: $i,V_com: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) )
| ( V_fun = V_fun_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_0) ).
thf(314,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(315,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(316,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(317,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(318,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(319,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(320,axiom,
! [V_loc: $i,V_fun: $i,V_com: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I34_J_0) ).
thf(321,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_f4: $i,V_f5: $i,V_f6: $i,V_f7: $i,V_f8: $i,V_com1: $i,V_com2: $i,T_a: $i] :
( ( c_Com_Ocom_Ocom__case @ V_f1 @ V_f2 @ V_f3 @ V_f4 @ V_f5 @ V_f6 @ V_f7 @ V_f8 @ ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) @ T_a )
= ( hAPP @ ( hAPP @ V_f4 @ V_com1 ) @ V_com2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I67_J_0) ).
thf(322,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(323,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(324,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(325,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(326,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(327,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(328,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(329,axiom,
! [V_fun_H: $i,V_com_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I16_J_0) ).
thf(330,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(331,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(332,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(333,axiom,
! [V_loc: $i,V_fun: $i,V_com: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I38_J_0) ).
thf(334,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(335,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_f4: $i,V_f5: $i,V_f6: $i,V_f7: $i,V_f8: $i,T_a: $i] :
( ( c_Com_Ocom_Ocom__case @ V_f1 @ V_f2 @ V_f3 @ V_f4 @ V_f5 @ V_f6 @ V_f7 @ V_f8 @ c_Com_Ocom_OSKIP @ T_a )
= V_f1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I64_J_0) ).
thf(336,axiom,
! [V_b: $i,V_c0: $i,V_c1: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ V_b @ V_c0 @ V_c1 ) )
| ~ ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ V_c0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OIf_0) ).
thf(337,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(338,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(339,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(340,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ ( 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 ) )
| ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_2) ).
thf(341,axiom,
! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Suc @ V_nat )
!= ( c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(342,axiom,
! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(343,axiom,
! [V_a: $i,V_b: $i,V_v: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a ) @ V_v ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
thf(344,axiom,
! [V_f: $i,V_g: $i,T_b: $i,T_a: $i,T_c: $i,V_x: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__apply_0) ).
thf(345,axiom,
! [V_a: $i,T_a: $i,V_a_H: $i] :
( ( ( c_Option_Ooption_OSome @ V_a @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) )
| ( V_a = V_a_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Oinject_0) ).
thf(346,axiom,
! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i,V_fun: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H )
!= ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I57_J_0) ).
thf(347,axiom,
! [V_xa: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_xa @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__None__eq_1) ).
thf(348,axiom,
! [V_a_H: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_a_H @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osimps_I3_J_0) ).
thf(349,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_c @ V_a @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( 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__subset__iff_0) ).
thf(350,axiom,
! [T_a: $i,V_b: $i,V_d: $i,V_a: $i,V_c: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_b @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( 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__subset__iff_1) ).
thf(351,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ ( 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 ) )
| ~ ( c_lessequals @ V_b @ V_d @ T_a )
| ~ ( c_lessequals @ V_c @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).
thf(352,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
thf(353,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self_0) ).
thf(354,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
thf(355,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
thf(356,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
thf(357,axiom,
! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) )
| ( V_fun = V_fun_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_0) ).
thf(358,axiom,
! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) )
| ( V_com1 = V_com1_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_1) ).
thf(359,axiom,
! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) )
| ( V_com2 = V_com2_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_2) ).
thf(360,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(361,axiom,
! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I45_J_0) ).
thf(362,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(363,axiom,
! [V_c: $i,T_b: $i,T_c: $i,V_f: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ ( c_COMBK @ V_c @ T_b @ T_c ) @ V_f @ T_c @ T_b @ t_a ) @ v_x )
= V_c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_K__record__comp_0) ).
thf(364,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i,V_I: $i,T_b: $i] :
( ( c_lessequals @ ( hAPP @ V_A @ V_x ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_I @ T_b ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_I @ V_A @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).
thf(365,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(366,axiom,
! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I37_J_0) ).
thf(367,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(368,axiom,
! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I52_J_0) ).
thf(369,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(370,axiom,
! [V_n: $i,V_t: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ V_t @ T_a )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ V_n ) @ V_t @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple__valid__Suc_0) ).
thf(371,axiom,
! [V_com1_H: $i,V_com2_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I35_J_0) ).
thf(372,axiom,
! [V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I44_J_0) ).
thf(373,axiom,
! [T_a: $i,V_a: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__insert_0) ).
thf(374,axiom,
! [V_com1: $i,V_com2: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I46_J_0) ).
thf(375,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(376,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(377,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(378,axiom,
! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(379,axiom,
! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(380,axiom,
! [V_b: $i,V_c: $i,V_s: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s @ V_s )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OWhileFalse_0) ).
thf(381,axiom,
! [V_fun_H: $i,V_com_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I39_J_0) ).
thf(382,axiom,
! [V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I17_J_0) ).
thf(383,axiom,
! [V_vname: $i,V_pname: $i,V_fun: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( ( c_Com_Ocom_OCall @ V_vname @ V_pname @ V_fun )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) )
| ( V_vname = V_vname_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_0) ).
thf(384,axiom,
! [V_vname: $i,V_pname: $i,V_fun: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( ( c_Com_Ocom_OCall @ V_vname @ V_pname @ V_fun )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) )
| ( V_pname = V_pname_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_1) ).
thf(385,axiom,
! [V_vname: $i,V_pname: $i,V_fun: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( ( c_Com_Ocom_OCall @ V_vname @ V_pname @ V_fun )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) )
| ( V_fun = V_fun_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I7_J_2) ).
thf(386,axiom,
! [T_a: $i,V_Y: $i] :
( ( c_Set_Oimage @ ( c_COMBI @ T_a ) @ V_Y @ T_a @ T_a )
= V_Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__ident_0) ).
thf(387,axiom,
! [V_loc: $i,V_fun: $i,V_com: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I36_J_0) ).
thf(388,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(389,axiom,
! [V_B: $i,V_a: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( c_lessequals @ ( hAPP @ V_B @ V_a ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__upper_0) ).
thf(390,axiom,
! [T_b: $i,V_M: $i,V_i: $i,V_A: $i,T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_b )
| ( c_lessequals @ ( hAPP @ V_M @ V_i ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_M @ T_a @ T_b ) @ T_b )
| ~ ( hBOOL @ ( c_in @ V_i @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SUPI_0) ).
thf(391,axiom,
! [V_fun: $i,V_com1: $i,V_com2: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I56_J_0) ).
thf(392,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(393,axiom,
! [V_b: $i,V_c: $i,V_s: $i,V_n: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s @ V_n @ V_s )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OWhileFalse_0) ).
thf(394,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).
thf(395,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).
thf(396,axiom,
! [V_A: $i,V_x: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).
thf(397,axiom,
! [V_f: $i,V_x: $i,V_B: $i,T_a: $i,V_A: $i,T_b: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ V_f @ V_x ) @ V_B @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_b ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
thf(398,axiom,
! [V_c: $i,T_b: $i,T_a: $i,V_A: $i,V_x: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_b @ T_a ) @ V_A @ T_a @ T_b )
= ( c_Set_Oinsert @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).
thf(399,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(400,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(401,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(402,axiom,
! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I51_J_0) ).
thf(403,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_f4: $i,V_f5: $i,V_f6: $i,V_f7: $i,V_f8: $i,V_vname: $i,V_pname: $i,V_fun: $i,T_a: $i] :
( ( c_Com_Ocom_Ocom__case @ V_f1 @ V_f2 @ V_f3 @ V_f4 @ V_f5 @ V_f6 @ V_f7 @ V_f8 @ ( c_Com_Ocom_OCall @ V_vname @ V_pname @ V_fun ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ V_f8 @ V_vname ) @ V_pname ) @ V_fun ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I71_J_0) ).
thf(404,axiom,
! [V_b: $i,V_c0: $i,V_c1: $i,V_s: $i,V_n: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ V_b @ V_c0 @ V_c1 ) @ V_s @ V_n @ V_s1 )
| ~ ( c_Natural_Oevaln @ V_c0 @ V_s @ V_n @ V_s1 )
| ~ ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OIfTrue_0) ).
thf(405,axiom,
! [V_b: $i,V_s: $i,V_c1: $i,V_n: $i,V_t: $i,V_c2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ( c_Natural_Oevaln @ V_c1 @ V_s @ V_n @ V_t )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln__elim__cases_I5_J_1) ).
thf(406,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(407,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(408,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(409,axiom,
! [V_P: $i,V_Q: $i,T_b: $i,T_a: $i,T_c: $i,V_R: $i] :
( ( hAPP @ ( c_COMBB @ V_P @ V_Q @ T_b @ T_a @ T_c ) @ V_R )
= ( hAPP @ V_P @ ( hAPP @ V_Q @ V_R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
thf(410,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(411,axiom,
! [T_a: $i,V_P: $i] :
( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
= V_P ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBI__def_0) ).
thf(412,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(413,axiom,
! [V_P: $i,V_Q: $i,T_b: $i,T_c: $i,T_a: $i,V_R: $i] :
( ( hAPP @ ( c_COMBS @ V_P @ V_Q @ T_b @ T_c @ T_a ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ ( hAPP @ V_Q @ V_R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBS__def_0) ).
thf(414,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(415,axiom,
! [V_b: $i,V_c: $i,V_s0: $i,V_n: $i,V_s2: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s0 @ V_n @ V_s2 )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s1 @ V_n @ V_s2 )
| ~ ( c_Natural_Oevaln @ V_c @ V_s0 @ V_n @ V_s1 )
| ~ ( hBOOL @ ( hAPP @ V_b @ V_s0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OWhileTrue_0) ).
thf(416,axiom,
! [T_a: $i,V_y: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Some__eq_1) ).
thf(417,axiom,
! [T_a: $i,V_a_H: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_option_Osimps_I2_J_0) ).
thf(418,axiom,
! [V_b: $i,V_c: $i,V_s0: $i,V_s2: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s0 @ V_s2 )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s1 @ V_s2 )
| ~ ( c_Natural_Oevalc @ V_c @ V_s0 @ V_s1 )
| ~ ( hBOOL @ ( hAPP @ V_b @ V_s0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OWhileTrue_0) ).
thf(419,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(420,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(421,axiom,
! [V_c0: $i,V_c1: $i,V_s0: $i,V_n: $i,V_s2: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_n @ V_s2 )
| ~ ( c_Natural_Oevaln @ V_c1 @ V_s1 @ V_n @ V_s2 )
| ~ ( c_Natural_Oevaln @ V_c0 @ V_s0 @ V_n @ V_s1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evaln_OSemi_0) ).
thf(422,axiom,
c_Com_OWT @ c_Com_Ocom_OSKIP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OSkip_0) ).
thf(423,axiom,
! [V_b: $i,V_c0: $i,V_c1: $i,V_s: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c0 @ V_c1 ) @ V_s @ V_s1 )
| ~ ( c_Natural_Oevalc @ V_c0 @ V_s @ V_s1 )
| ~ ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OIfTrue_0) ).
thf(424,axiom,
! [V_b: $i,V_s: $i,V_c1: $i,V_t: $i,V_c2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ( c_Natural_Oevalc @ V_c1 @ V_s @ V_t )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) @ V_s @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc__elim__cases_I5_J_1) ).
thf(425,axiom,
! [V_f: $i,V_A: $i,T_b: $i,T_a: $i,V_B: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
thf(426,axiom,
! [V_c0: $i,V_c1: $i,V_s0: $i,V_s2: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_s2 )
| ~ ( c_Natural_Oevalc @ V_c1 @ V_s1 @ V_s2 )
| ~ ( c_Natural_Oevalc @ V_c0 @ V_s0 @ V_s1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_evalc_OSemi_0) ).
thf(427,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(428,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(429,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(430,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(431,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(432,axiom,
! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(433,axiom,
! [V_f: $i,V_x: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
= ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(434,axiom,
! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H )
!= ( c_Com_Ocom_OWhile @ V_fun @ V_com ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I61_J_0) ).
thf(435,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(436,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(437,axiom,
! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(438,axiom,
! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I43_J_0) ).
thf(439,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(440,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(441,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(442,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(443,axiom,
! [V_c: $i,T_a: $i,T_b: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_a @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).
thf(444,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
thf(445,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
thf(446,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
thf(447,axiom,
! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
thf(448,axiom,
! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_com_Osimps_I14_J_0) ).
thf(449,axiom,
! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__partition_0) ).
thf(450,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(451,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(452,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(453,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(454,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(455,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(456,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(457,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(458,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(459,axiom,
! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(460,axiom,
! [V_B: $i,V_A: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(461,axiom,
! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(462,axiom,
! [V_P: $i,V_X: $i,V_a: $i] :
( ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ V_P ) )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OCall @ V_X @ V_P @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WTs__elim__cases_I8_J_0) ).
thf(463,axiom,
! [V_X: $i,V_pn: $i,V_a: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OCall @ V_X @ V_pn @ V_a ) )
| ~ ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_WT_OCall_0) ).
thf(464,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(465,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(466,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(467,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(468,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(469,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[468]) ).
thf(470,negated_conjecture,
~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ v_P ) @ ( hAPP @ c_Com_Ocom_OBODY @ v_pn ) ) @ v_Q ) @ v_G @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ v_P ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) ) @ v_Q ) @ ( 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(471,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ v_P ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) ) @ v_Q ) @ ( 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_0) ).
thf(472,plain,
$false = $false,
inference(unfold_def,[status(thm)],[469]) ).
thf(473,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(474,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(475,plain,
( ( class_HOL_Oord @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(476,plain,
( ( class_HOL_Ominus @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(477,plain,
( ( class_Orderings_Obot @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(478,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(479,plain,
( ( class_Lattices_Olattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(480,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(481,plain,
( ( class_Lattices_Obounded__lattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(482,plain,
( ( class_Lattices_Oupper__semilattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(483,plain,
( ( class_Complete__Lattice_Ocomplete__lattice @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(484,plain,
( ( class_HOL_Oord @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(485,plain,
( ( class_HOL_Ominus @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(486,plain,
( ( class_Orderings_Obot @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(487,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(488,plain,
( ( class_Lattices_Olattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(489,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(490,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(491,plain,
( ( class_Lattices_Oupper__semilattice @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(492,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)],[20]) ).
thf(493,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)],[21]) ).
thf(494,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)],[22]) ).
thf(495,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)],[23]) ).
thf(496,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)],[24]) ).
thf(497,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)],[25]) ).
thf(498,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)],[26]) ).
thf(499,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)],[27]) ).
thf(500,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)],[28]) ).
thf(501,plain,
( ( ! [V_pname: $i,V_pname_H: $i] :
( ( ( hAPP @ c_Com_Ocom_OBODY @ V_pname )
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H ) )
| ( V_pname = V_pname_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(502,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)],[30]) ).
thf(503,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)],[31]) ).
thf(504,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)],[32]) ).
thf(505,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)],[33]) ).
thf(506,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)],[34]) ).
thf(507,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)],[35]) ).
thf(508,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)],[36]) ).
thf(509,plain,
( ( ! [V_G: $i,T_a: $i,V_P: $i,V_pn: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) @ V_Q ) @ V_G @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_pn ) ) ) @ V_Q ) @ ( 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)],[37]) ).
thf(510,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)],[38]) ).
thf(511,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)],[39]) ).
thf(512,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)],[40]) ).
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_b = V_c )
| ( V_a = V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
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_a = V_d )
| ( V_b = V_d ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
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_b = V_c )
| ( V_b = V_d ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(516,plain,
( ( ! [T_a: $i,V_fun1: $i,V_com: $i,V_fun2: $i,V_fun1_H: $i,V_com_H: $i,V_fun2_H: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1 ) @ V_com ) @ V_fun2 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1_H ) @ V_com_H ) @ V_fun2_H ) )
| ( V_fun1 = V_fun1_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(517,plain,
( ( ! [T_a: $i,V_fun1: $i,V_com: $i,V_fun2: $i,V_fun1_H: $i,V_com_H: $i,V_fun2_H: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1 ) @ V_com ) @ V_fun2 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1_H ) @ V_com_H ) @ V_fun2_H ) )
| ( V_com = V_com_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(518,plain,
( ( ! [T_a: $i,V_fun1: $i,V_com: $i,V_fun2: $i,V_fun1_H: $i,V_com_H: $i,V_fun2_H: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1 ) @ V_com ) @ V_fun2 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1_H ) @ V_com_H ) @ V_fun2_H ) )
| ( V_fun2 = V_fun2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(519,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)],[47]) ).
thf(520,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)],[48]) ).
thf(521,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)],[49]) ).
thf(522,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)],[50]) ).
thf(523,plain,
( ( ! [V_G: $i,T_a: $i,V_P: $i,V_c: $i,V_d: $i,V_R: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( c_Com_Ocom_OSemi @ V_c @ V_d ) ) @ V_R ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_Q ) @ V_d ) @ V_R ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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)],[51]) ).
thf(524,plain,
( ( ! [V_G: $i,T_a: $i,V_P: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ c_Com_Ocom_OSKIP ) @ V_P ) @ ( 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)],[52]) ).
thf(525,plain,
( ( ! [V_P: $i,V_s: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_P ) ) @ V_s @ V_s1 )
| ~ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_s1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(526,plain,
( ( ! [V_pn: $i,V_s0: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) @ V_s0 @ V_s1 )
| ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_pn ) ) @ V_s0 @ V_s1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(527,plain,
( ( ! [V_n: $i,T_a: $i,V_P: $i,V_pn: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_pn ) ) ) @ V_Q ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ V_n ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) @ V_Q ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(528,plain,
( ( ! [V_n: $i,T_a: $i,V_P: $i,V_pn: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ V_n ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) @ V_Q ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_pn ) ) ) @ V_Q ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(529,plain,
( ( ( hAPP @ ( c_COMBK @ v_P @ t_a @ t_b ) @ v_Q )
= v_P )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(530,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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)],[58]) ).
thf(531,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q_H ) @ ( 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)],[59]) ).
thf(532,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P_H ) @ V_c ) @ V_Q_H ) @ ( 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)],[60]) ).
thf(533,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P_H ) @ V_c ) @ V_Q ) @ ( 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)],[61]) ).
thf(534,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_x ) @ V_c ) @ V_xa ) @ ( 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)],[62]) ).
thf(535,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P_H ) @ V_c ) @ V_Q ) @ ( 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)],[63]) ).
thf(536,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P_H ) @ V_c ) @ V_Q_H ) @ ( 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)],[64]) ).
thf(537,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q_H ) @ ( 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)],[65]) ).
thf(538,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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)],[66]) ).
thf(539,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_x ) @ V_c ) @ V_xa ) @ ( 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(540,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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)],[68]) ).
thf(541,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_x ) @ V_c ) @ V_xa ) @ ( 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)],[69]) ).
thf(542,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P_H ) @ V_c ) @ V_Q_H ) @ ( 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)],[70]) ).
thf(543,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_x ) @ V_c ) @ V_xa ) @ ( 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)],[71]) ).
thf(544,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( 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)],[72]) ).
thf(545,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)],[73]) ).
thf(546,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)],[74]) ).
thf(547,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)],[75]) ).
thf(548,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)],[76]) ).
thf(549,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)],[77]) ).
thf(550,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)],[78]) ).
thf(551,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)],[79]) ).
thf(552,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)],[80]) ).
thf(553,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)],[81]) ).
thf(554,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)],[82]) ).
thf(555,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)],[83]) ).
thf(556,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)],[84]) ).
thf(557,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)],[85]) ).
thf(558,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)],[86]) ).
thf(559,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)],[87]) ).
thf(560,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)],[88]) ).
thf(561,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)],[89]) ).
thf(562,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)],[90]) ).
thf(563,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)],[91]) ).
thf(564,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(565,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)],[93]) ).
thf(566,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)],[94]) ).
thf(567,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)],[95]) ).
thf(568,plain,
( ( ! [V_A: $i,V_x: $i,T_a: $i] :
( ( V_A
= ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(569,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)],[97]) ).
thf(570,plain,
( ( ! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(571,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)],[99]) ).
thf(572,plain,
( ( ! [V_pn: $i,V_s0: $i,V_n: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) @ V_s0 @ ( c_Suc @ V_n ) @ V_s1 )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_pn ) ) @ V_s0 @ V_n @ V_s1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(573,plain,
( ( ! [V_P: $i,V_s: $i,V_n: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_P ) ) @ V_s @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ V_P @ V_n @ V_s @ V_s1 ) @ V_s1 )
| ~ ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_n @ V_s1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(574,plain,
( ( ! [V_G: $i,T_a: $i,V_P: $i,V_b: $i,V_c: $i,V_d: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( c_Com_Ocom_OCond @ V_b @ V_c @ V_d ) ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ ( c_Hoare__Mirabelle_Opeek__and @ V_P @ ( c_Fun_Ocomp @ c_Not @ V_b @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ T_a ) ) @ V_d ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ ( c_Hoare__Mirabelle_Opeek__and @ V_P @ V_b @ T_a ) ) @ V_c ) @ V_Q ) @ ( 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)],[102]) ).
thf(575,plain,
( ( ! [V_G: $i,T_a: $i,V_P: $i,V_b: $i,V_c: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) @ ( c_Hoare__Mirabelle_Opeek__and @ V_P @ ( c_Fun_Ocomp @ c_Not @ V_b @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ T_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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ ( c_Hoare__Mirabelle_Opeek__and @ V_P @ V_b @ T_a ) ) @ V_c ) @ V_P ) @ ( 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)],[103]) ).
thf(576,plain,
( ( ! [T_a: $i,V_x: $i] :
( ( hAPP @ ( c_Option_Othe @ T_a ) @ ( c_Option_Ooption_OSome @ V_x @ T_a ) )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(577,plain,
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ v_P @ t_a @ t_b @ t_c ) @ v_Q ) @ v_R )
= ( hAPP @ ( hAPP @ v_P @ v_R ) @ v_Q ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(578,plain,
( ( ( hAPP @ ( c_COMBS @ v_P @ v_Q @ t_a @ t_b @ t_c ) @ v_R )
= ( hAPP @ ( hAPP @ v_P @ v_R ) @ ( hAPP @ v_Q @ v_R ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(579,plain,
( ( ( hAPP @ ( c_COMBB @ v_P @ v_Q @ t_a @ t_b @ t_c ) @ v_R )
= ( hAPP @ v_P @ ( hAPP @ v_Q @ v_R ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(580,plain,
( ( ! [V_pn: $i] :
( ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) )
| ( ( hAPP @ c_Com_Obody @ V_pn )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(581,plain,
( ( ! [V_G: $i,T_a: $i,V_P: $i,V_pn: $i,V_Q: $i,V_Procs: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ ( hAPP @ V_P @ V_pn ) ) @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) @ ( hAPP @ V_Q @ V_pn ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( hBOOL @ ( c_in @ V_pn @ V_Procs @ tc_Com_Opname ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_G @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ V_Q @ tc_Com_Opname @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ V_Procs @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ V_Q @ tc_Com_Opname @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ V_Procs @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(582,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ ( 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 ) ) @ ( 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)],[110]) ).
thf(583,plain,
( ( ( hAPP @ ( c_COMBI @ t_a ) @ v_P )
= v_P )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(584,plain,
( ( ! [V_G: $i,V_ts: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ~ ( c_lessequals @ V_ts @ V_G @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(585,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_lessequals @ V_G_H @ V_G @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G_H @ V_ts @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(586,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 )
| ~ ( c_lessequals @ V_ts @ V_ts_H @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts_H @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(587,plain,
( ( ! [V_f1: $i,T_b: $i,V_fun1: $i,V_com: $i,V_fun2: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ V_f1 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b ) @ V_fun1 ) @ V_com ) @ V_fun2 ) @ T_b @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ V_f1 @ V_fun1 ) @ V_com ) @ V_fun2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(588,plain,
( ( ! [V_f1: $i,T_b: $i,V_fun1: $i,V_com: $i,V_fun2: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ V_f1 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b ) @ V_fun1 ) @ V_com ) @ V_fun2 ) @ T_b @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ V_f1 @ V_fun1 ) @ V_com ) @ V_fun2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(589,plain,
( ( ! [V_P: $i,V_f1: $i,V_fun1: $i,V_com: $i,V_fun2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ V_f1 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ V_fun1 ) @ V_com ) @ V_fun2 ) @ t_b @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ ( hAPP @ V_f1 @ V_fun1 ) @ V_com ) @ V_fun2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(590,plain,
( ( ! [V_P: $i,V_f1: $i,V_xa: $i,V_xb: $i,V_xc: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ V_f1 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ V_xa ) @ V_xb ) @ V_xc ) @ t_b @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ ( hAPP @ V_f1 @ V_xa ) @ V_xb ) @ V_xc ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(591,plain,
( ( ! [T_a: $i,V_P: $i,V_pn: $i,V_Q: $i] : ( c_Hoare__Mirabelle_Otriple__valid @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) @ V_Q ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(592,plain,
( ( ! [V_pname_H: $i] :
( c_Com_Ocom_OSKIP
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(593,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_f4: $i,V_f5: $i,V_f6: $i,V_f7: $i,V_f8: $i,V_pname: $i,T_a: $i] :
( ( c_Com_Ocom_Ocom__case @ V_f1 @ V_f2 @ V_f3 @ V_f4 @ V_f5 @ V_f6 @ V_f7 @ V_f8 @ ( hAPP @ c_Com_Ocom_OBODY @ V_pname ) @ T_a )
= ( hAPP @ V_f7 @ V_pname ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(594,plain,
( ( ! [V_pname: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ V_pname )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(595,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(596,plain,
( ( ! [V_com1: $i,V_com2: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(597,plain,
( ( ! [V_pname_H: $i,V_com1: $i,V_com2: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(598,plain,
( ( ! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i,V_pname: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H )
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(599,plain,
( ( ! [V_pname_H: $i,V_fun: $i,V_com: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OWhile @ V_fun @ V_com ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(600,plain,
( ( ! [V_pname_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(601,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(602,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)],[130]) ).
thf(603,plain,
( ( ! [V_c1: $i,V_b: $i,V_c2: $i] :
( ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(604,plain,
( ( ! [V_c2: $i,V_b: $i,V_c1: $i] :
( ( c_Com_OWT @ V_c2 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(605,plain,
( ( ! [T_a: $i,V_x: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a ) @ T_a )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(606,plain,
( ( ! [V_c2: $i,V_s: $i,V_t: $i,V_c1: $i,V_b: $i] :
( ( c_Natural_Oevalc @ V_c2 @ V_s @ V_t )
| ( c_Natural_Oevalc @ V_c1 @ V_s @ V_t )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(607,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(608,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(609,plain,
( ( ! [V_c2: $i,V_s: $i,V_n: $i,V_t: $i,V_c1: $i,V_b: $i] :
( ( c_Natural_Oevaln @ V_c2 @ V_s @ V_n @ V_t )
| ( c_Natural_Oevaln @ V_c1 @ V_s @ V_n @ V_t )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(610,plain,
( ( ! [V_x: $i,V_A: $i,T_b: $i,V_f: $i,T_a: $i] :
( ~ ( c_lessequals @ V_x @ V_A @ ( tc_fun @ T_b @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_x @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(611,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(612,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_y_H @ V_x_H @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(613,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y_H @ V_x_H @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(614,plain,
( ( ! [V_B: $i,V_C: $i,V_A: $i,T_a: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_B @ ( c_HOL_Ominus__class_Ominus @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(615,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)],[143]) ).
thf(616,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)],[144]) ).
thf(617,plain,
( ( ! [V_b: $i,V_s: $i,V_t: $i,V_c: $i,V_n: $i] :
( ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ( V_t = V_s )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(618,plain,
( ( ! [V_f: $i,V_g: $i,V_x: $i,V_f_H: $i,V_g_H: $i,V_x_H: $i,T_b: $i,T_a: $i,T_c: $i,T_d: $i,T_e: $i] :
( ( ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) )
!= ( hAPP @ V_f_H @ ( hAPP @ V_g_H @ V_x_H ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ ( c_Fun_Ocomp @ V_f_H @ V_g_H @ T_d @ T_a @ T_e ) @ V_x_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(619,plain,
( ( ! [V_a: $i,V_b: $i,T_c: $i,T_b: $i,T_a: $i,V_c: $i,V_d: $i,T_d: $i,V_v: $i] :
( ( ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a )
!= ( c_Fun_Ocomp @ V_c @ V_d @ T_d @ T_b @ T_a ) )
| ( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ V_c @ ( hAPP @ V_d @ V_v ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(620,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_f4: $i,V_f5: $i,V_f6: $i,V_f7: $i,V_f8: $i,V_fun: $i,V_com1: $i,V_com2: $i,T_a: $i] :
( ( c_Com_Ocom_Ocom__case @ V_f1 @ V_f2 @ V_f3 @ V_f4 @ V_f5 @ V_f6 @ V_f7 @ V_f8 @ ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ V_f5 @ V_fun ) @ V_com1 ) @ V_com2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(621,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_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(622,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_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(623,plain,
( ( ! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(624,plain,
( ( ! [V_Q: $i,V_x: $i,V_P: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(625,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(626,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(627,plain,
( ( ! [V_Q: $i,V_x: $i,V_P: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(628,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(629,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(630,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 ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(631,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(632,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_lessequals @ V_x @ V_x @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(633,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_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(634,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 ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(635,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(636,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(637,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i,V_A: $i] :
( ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(638,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(639,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_a @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(640,plain,
( ( ! [T_a: $i,V_b: $i,V_x: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(641,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(642,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(643,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(644,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(645,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(646,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(647,plain,
( ( ! [V_b: $i,V_s: $i,V_t: $i,V_c: $i] :
( ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ( V_t = V_s )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(648,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)],[176]) ).
thf(649,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)],[177]) ).
thf(650,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)],[178]) ).
thf(651,plain,
( ( ! [V_fun_H: $i,V_com_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(652,plain,
( ( ! [V_f: $i,V_g: $i,T_c: $i,T_a: $i,T_b: $i,V_r: $i] :
( ( c_Set_Oimage @ ( c_Fun_Ocomp @ V_f @ V_g @ T_c @ T_a @ T_b ) @ V_r @ T_b @ T_a )
= ( c_Set_Oimage @ V_f @ ( c_Set_Oimage @ V_g @ V_r @ T_b @ T_c ) @ T_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(653,plain,
( ( ! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(654,plain,
( ( ! [V_c0: $i,V_c1: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) )
| ~ ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ V_c0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(655,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) )
| ( V_loc = V_loc_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(656,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) )
| ( V_fun = V_fun_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(657,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) )
| ( V_com = V_com_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(658,plain,
( ( ! [V_f: $i,V_g: $i,V_A: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Set_Oimage @ V_g @ V_A @ T_c @ T_b ) @ T_b @ T_a )
= ( c_Set_Oimage @ ( c_COMBB @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_A @ T_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(659,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(660,plain,
( ( ! [V_f: $i,V_g: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_c @ T_b @ t_a ) @ v_x )
= ( hAPP @ V_f @ ( hAPP @ V_g @ v_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(661,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)],[189]) ).
thf(662,plain,
( ( ! [V_f: $i,V_g: $i,V_h: $i,T_d: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Ocomp @ V_f @ ( c_Fun_Ocomp @ V_g @ V_h @ T_d @ T_c @ T_a ) @ T_c @ T_b @ T_a )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ V_f @ V_g @ T_c @ T_b @ T_d ) @ V_h @ T_d @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(663,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_D @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(664,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_f4: $i,V_f5: $i,V_f6: $i,V_f7: $i,V_f8: $i,V_fun: $i,V_com: $i,T_a: $i] :
( ( c_Com_Ocom_Ocom__case @ V_f1 @ V_f2 @ V_f3 @ V_f4 @ V_f5 @ V_f6 @ V_f7 @ V_f8 @ ( c_Com_Ocom_OWhile @ V_fun @ V_com ) @ T_a )
= ( hAPP @ ( hAPP @ V_f6 @ V_fun ) @ V_com ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(665,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_f4: $i,V_f5: $i,V_f6: $i,V_f7: $i,V_f8: $i,V_loc: $i,V_fun: $i,V_com: $i,T_a: $i] :
( ( c_Com_Ocom_Ocom__case @ V_f1 @ V_f2 @ V_f3 @ V_f4 @ V_f5 @ V_f6 @ V_f7 @ V_f8 @ ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ V_f3 @ V_loc ) @ V_fun ) @ V_com ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(666,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 ) )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(667,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 ) )
| ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(668,plain,
( ( ! [T_a: $i,V_A: $i,V_x: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ V_A @ T_a ) @ V_x @ T_a )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(669,plain,
( ( ! [V_c1: $i,V_c2: $i] :
( ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(670,plain,
( ( ! [V_c2: $i,V_c1: $i] :
( ( c_Com_OWT @ V_c2 )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(671,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)],[199]) ).
thf(672,plain,
( ( ! [V_b: $i,V_c0: $i,V_c1: $i,V_s: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c0 @ V_c1 ) @ V_s @ V_s1 )
| ~ ( c_Natural_Oevalc @ V_c1 @ V_s @ V_s1 )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(673,plain,
( ( ! [V_c2: $i,V_s: $i,V_t: $i,V_b: $i,V_c1: $i] :
( ( c_Natural_Oevalc @ V_c2 @ V_s @ V_t )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(674,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)],[202]) ).
thf(675,plain,
( ( ! [V_Q: $i,V_Z: $i,V_s_H: $i,V_c: $i,V_s: $i,V_n: $i,V_P: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_Q @ V_Z ) @ V_s_H ) )
| ~ ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_s_H )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_Z ) @ V_s ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ t_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(676,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(677,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(678,plain,
( ( ! [V_s: $i,V_n: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_s ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(679,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= V_B )
| ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(680,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(681,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(682,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(683,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
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_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(685,plain,
( ( ! [V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(686,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(687,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(688,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(689,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(690,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(691,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(692,plain,
( ( ! [V_u: $i,V_t: $i,V_c: $i,V_s: $i] :
( ( V_u = V_t )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_u )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(693,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( V_A = V_B )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(694,plain,
( ( ! [V_s: $i] : ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ V_s @ V_s ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(695,plain,
( ( ! [V_fun: $i,V_com: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(696,plain,
( ( ! [V_b: $i,V_c0: $i,V_c1: $i,V_s: $i,V_n: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ V_b @ V_c0 @ V_c1 ) @ V_s @ V_n @ V_s1 )
| ~ ( c_Natural_Oevaln @ V_c1 @ V_s @ V_n @ V_s1 )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(697,plain,
( ( ! [V_c2: $i,V_s: $i,V_n: $i,V_t: $i,V_b: $i,V_c1: $i] :
( ( c_Natural_Oevaln @ V_c2 @ V_s @ V_n @ V_t )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(698,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_D @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(699,plain,
( ( ! [V_c: $i,V_s: $i,V_n: $i,V_s_H: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ ( c_Suc @ V_n ) @ V_s_H )
| ~ ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_s_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(700,plain,
( ( ! [V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(701,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(702,plain,
( ( ! [V_pname_H: $i,V_fun: $i,V_com1: $i,V_com2: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(703,plain,
( ( ! [V_fun: $i,V_com: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(704,plain,
( ( ! [V_pname_H: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(705,plain,
( ( ! [V_G: $i,T_a: $i,V_P: $i,V_Q: $i,V_Procs: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ V_Q @ tc_Com_Opname @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ V_Procs @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_G @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ V_Q @ tc_Com_Opname @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ V_Procs @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ V_Q @ tc_Com_Opname @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ V_Procs @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(706,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)],[234]) ).
thf(707,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)],[235]) ).
thf(708,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)],[236]) ).
thf(709,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)],[237]) ).
thf(710,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)],[238]) ).
thf(711,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(712,plain,
( ( ! [V_A: $i,V_b: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(713,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)],[241]) ).
thf(714,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)],[242]) ).
thf(715,plain,
( ( ! [V_B: $i,V_a: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(716,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)],[244]) ).
thf(717,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)],[245]) ).
thf(718,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)],[246]) ).
thf(719,plain,
( ( ! [V_f: $i,V_a: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Set_Oinsert @ V_a @ V_B @ T_b ) @ T_b @ T_a )
= ( c_Set_Oinsert @ ( hAPP @ V_f @ V_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(720,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)],[248]) ).
thf(721,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)],[249]) ).
thf(722,plain,
( ( ! [V_a: $i,V_C: $i,T_a: $i,V_D: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ V_a @ V_C @ T_a ) @ ( c_Set_Oinsert @ V_a @ V_D @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(723,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)],[251]) ).
thf(724,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(725,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(726,plain,
( ( ! [V_c: $i,T_a: $i,T_b: $i,V_A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_a @ T_b ) @ V_A @ T_b @ T_a )
= ( c_Set_Oinsert @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(727,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)],[255]) ).
thf(728,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)],[256]) ).
thf(729,plain,
( ( ! [T_a: $i,V_f: $i,T_b: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oimage @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(730,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)],[258]) ).
thf(731,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)],[259]) ).
thf(732,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)],[260]) ).
thf(733,plain,
( ( ! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(734,plain,
( ( ! [T_a: $i,V_f: $i,V_A: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(735,plain,
( ( ! [T_a: $i,V_A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(736,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)],[264]) ).
thf(737,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)],[265]) ).
thf(738,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)],[266]) ).
thf(739,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)],[267]) ).
thf(740,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)],[268]) ).
thf(741,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)],[269]) ).
thf(742,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)],[270]) ).
thf(743,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(744,plain,
( ( ! [T_a: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(745,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)],[273]) ).
thf(746,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)],[274]) ).
thf(747,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)],[275]) ).
thf(748,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)],[276]) ).
thf(749,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)],[277]) ).
thf(750,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)],[278]) ).
thf(751,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)],[279]) ).
thf(752,plain,
( ( ! [V_f: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(753,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)],[281]) ).
thf(754,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)],[282]) ).
thf(755,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)],[283]) ).
thf(756,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Obot @ T_a )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(757,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)],[285]) ).
thf(758,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)],[286]) ).
thf(759,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i,V_g: $i,T_a: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ( c_lessequals @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_g @ V_x ) @ T_b )
| ~ ( c_lessequals @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(760,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i,V_x: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
| ~ ( c_Natural_Oevaln @ V_c @ V_s @ V_x @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(761,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i,V_n: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
| ~ ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(762,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(763,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(764,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(765,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(766,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_b: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(767,plain,
( ( ! [V_x: $i,V_A: $i,T_b: $i,V_f: $i,T_a: $i] :
( ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_b ) )
| ( hBOOL @ ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(768,plain,
( ( ! [V_x: $i,V_A: $i,T_aa: $i,V_f: $i,T_a: $i] :
( ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_aa ) )
| ( hBOOL @ ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_aa @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(769,plain,
( ( ! [V_t: $i,V_s: $i,V_n: $i] :
( ( V_t = V_s )
| ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(770,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)],[298]) ).
thf(771,plain,
( ( ! [V_n: $i,V_P: $i,V_s: $i,V_s1: $i] :
( ( V_n
= ( c_Suc @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ V_P @ V_n @ V_s @ V_s1 ) ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_n @ V_s1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(772,plain,
( ( ! [V_com1: $i,V_com2: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(773,plain,
( ( ! [V_fun_H: $i,V_com_H: $i,V_fun: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(774,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)],[302]) ).
thf(775,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)],[303]) ).
thf(776,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(777,plain,
( ( ! [V_c: $i,V_Y: $i,V_a: $i] :
( ( c_Com_OWT @ V_c )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ V_Y @ V_a @ V_c ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(778,plain,
( ( ! [V_Y: $i,V_a: $i,V_c: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ V_Y @ V_a @ V_c ) )
| ~ ( c_Com_OWT @ V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(779,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)],[307]) ).
thf(780,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)],[308]) ).
thf(781,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)],[309]) ).
thf(782,plain,
( ( ! [V_c: $i,V_b: $i] :
( ( c_Com_OWT @ V_c )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(783,plain,
( ( ! [V_b: $i,V_c: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) )
| ~ ( c_Com_OWT @ V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(784,plain,
( ( ! [V_fun: $i,V_com: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) )
| ( V_com = V_com_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(785,plain,
( ( ! [V_fun: $i,V_com: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) )
| ( V_fun = V_fun_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(786,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)],[314]) ).
thf(787,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)],[315]) ).
thf(788,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)],[316]) ).
thf(789,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)],[317]) ).
thf(790,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)],[318]) ).
thf(791,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)],[319]) ).
thf(792,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(793,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_f4: $i,V_f5: $i,V_f6: $i,V_f7: $i,V_f8: $i,V_com1: $i,V_com2: $i,T_a: $i] :
( ( c_Com_Ocom_Ocom__case @ V_f1 @ V_f2 @ V_f3 @ V_f4 @ V_f5 @ V_f6 @ V_f7 @ V_f8 @ ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) @ T_a )
= ( hAPP @ ( hAPP @ V_f4 @ V_com1 ) @ V_com2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(794,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)],[322]) ).
thf(795,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)],[323]) ).
thf(796,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)],[324]) ).
thf(797,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)],[325]) ).
thf(798,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)],[326]) ).
thf(799,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)],[327]) ).
thf(800,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)],[328]) ).
thf(801,plain,
( ( ! [V_fun_H: $i,V_com_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(802,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)],[330]) ).
thf(803,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)],[331]) ).
thf(804,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)],[332]) ).
thf(805,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(806,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)],[334]) ).
thf(807,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_f4: $i,V_f5: $i,V_f6: $i,V_f7: $i,V_f8: $i,T_a: $i] :
( ( c_Com_Ocom_Ocom__case @ V_f1 @ V_f2 @ V_f3 @ V_f4 @ V_f5 @ V_f6 @ V_f7 @ V_f8 @ c_Com_Ocom_OSKIP @ T_a )
= V_f1 ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(808,plain,
( ( ! [V_b: $i,V_c0: $i,V_c1: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ V_b @ V_c0 @ V_c1 ) )
| ~ ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ V_c0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(809,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)],[337]) ).
thf(810,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)],[338]) ).
thf(811,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)],[339]) ).
thf(812,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ ( 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 ) )
| ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(813,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Suc @ V_nat )
!= ( c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(814,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(815,plain,
( ( ! [V_a: $i,V_b: $i,V_v: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a ) @ V_v ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(816,plain,
( ( ! [V_f: $i,V_g: $i,T_b: $i,T_a: $i,T_c: $i,V_x: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(817,plain,
( ( ! [V_a: $i,T_a: $i,V_a_H: $i] :
( ( ( c_Option_Ooption_OSome @ V_a @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(818,plain,
( ( ! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i,V_fun: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H )
!= ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(819,plain,
( ( ! [V_xa: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_xa @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(820,plain,
( ( ! [V_a_H: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_a_H @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(821,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_c @ V_a @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( 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)],[349]) ).
thf(822,plain,
( ( ! [T_a: $i,V_b: $i,V_d: $i,V_a: $i,V_c: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_b @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( 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(823,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ ( 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 ) )
| ~ ( c_lessequals @ V_b @ V_d @ T_a )
| ~ ( c_lessequals @ V_c @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(824,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(825,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(826,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(827,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(828,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(829,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) )
| ( V_fun = V_fun_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(830,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) )
| ( V_com1 = V_com1_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(831,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) )
| ( V_com2 = V_com2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(832,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)],[360]) ).
thf(833,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(834,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)],[362]) ).
thf(835,plain,
( ( ! [V_c: $i,T_b: $i,T_c: $i,V_f: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ ( c_COMBK @ V_c @ T_b @ T_c ) @ V_f @ T_c @ T_b @ t_a ) @ v_x )
= V_c ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(836,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i,V_I: $i,T_b: $i] :
( ( c_lessequals @ ( hAPP @ V_A @ V_x ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_I @ T_b ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_I @ V_A @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(837,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)],[365]) ).
thf(838,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(839,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)],[367]) ).
thf(840,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(841,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)],[369]) ).
thf(842,plain,
( ( ! [V_n: $i,V_t: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ V_t @ T_a )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ V_n ) @ V_t @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(843,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(844,plain,
( ( ! [V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(845,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373]) ).
thf(846,plain,
( ( ! [V_com1: $i,V_com2: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(847,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)],[375]) ).
thf(848,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)],[376]) ).
thf(849,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( c_Collect @ V_P @ T_a )
= V_P ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(850,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(851,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(852,plain,
( ( ! [V_b: $i,V_c: $i,V_s: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s @ V_s )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(853,plain,
( ( ! [V_fun_H: $i,V_com_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(854,plain,
( ( ! [V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(855,plain,
( ( ! [V_vname: $i,V_pname: $i,V_fun: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( ( c_Com_Ocom_OCall @ V_vname @ V_pname @ V_fun )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) )
| ( V_vname = V_vname_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(856,plain,
( ( ! [V_vname: $i,V_pname: $i,V_fun: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( ( c_Com_Ocom_OCall @ V_vname @ V_pname @ V_fun )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) )
| ( V_pname = V_pname_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(857,plain,
( ( ! [V_vname: $i,V_pname: $i,V_fun: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( ( c_Com_Ocom_OCall @ V_vname @ V_pname @ V_fun )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) )
| ( V_fun = V_fun_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385]) ).
thf(858,plain,
( ( ! [T_a: $i,V_Y: $i] :
( ( c_Set_Oimage @ ( c_COMBI @ T_a ) @ V_Y @ T_a @ T_a )
= V_Y ) )
= $true ),
inference(unfold_def,[status(thm)],[386]) ).
thf(859,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(860,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)],[388]) ).
thf(861,plain,
( ( ! [V_B: $i,V_a: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( c_lessequals @ ( hAPP @ V_B @ V_a ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(862,plain,
( ( ! [T_b: $i,V_M: $i,V_i: $i,V_A: $i,T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_b )
| ( c_lessequals @ ( hAPP @ V_M @ V_i ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_M @ T_a @ T_b ) @ T_b )
| ~ ( hBOOL @ ( c_in @ V_i @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(863,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(864,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)],[392]) ).
thf(865,plain,
( ( ! [V_b: $i,V_c: $i,V_s: $i,V_n: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s @ V_n @ V_s )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393]) ).
thf(866,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(867,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(868,plain,
( ( ! [V_A: $i,V_x: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(869,plain,
( ( ! [V_f: $i,V_x: $i,V_B: $i,T_a: $i,V_A: $i,T_b: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ V_f @ V_x ) @ V_B @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_b ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(870,plain,
( ( ! [V_c: $i,T_b: $i,T_a: $i,V_A: $i,V_x: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_b @ T_a ) @ V_A @ T_a @ T_b )
= ( c_Set_Oinsert @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(871,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)],[399]) ).
thf(872,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)],[400]) ).
thf(873,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)],[401]) ).
thf(874,plain,
( ( ! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(875,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_f4: $i,V_f5: $i,V_f6: $i,V_f7: $i,V_f8: $i,V_vname: $i,V_pname: $i,V_fun: $i,T_a: $i] :
( ( c_Com_Ocom_Ocom__case @ V_f1 @ V_f2 @ V_f3 @ V_f4 @ V_f5 @ V_f6 @ V_f7 @ V_f8 @ ( c_Com_Ocom_OCall @ V_vname @ V_pname @ V_fun ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ V_f8 @ V_vname ) @ V_pname ) @ V_fun ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(876,plain,
( ( ! [V_b: $i,V_c0: $i,V_c1: $i,V_s: $i,V_n: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ V_b @ V_c0 @ V_c1 ) @ V_s @ V_n @ V_s1 )
| ~ ( c_Natural_Oevaln @ V_c0 @ V_s @ V_n @ V_s1 )
| ~ ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(877,plain,
( ( ! [V_b: $i,V_s: $i,V_c1: $i,V_n: $i,V_t: $i,V_c2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ( c_Natural_Oevaln @ V_c1 @ V_s @ V_n @ V_t )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405]) ).
thf(878,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)],[406]) ).
thf(879,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)],[407]) ).
thf(880,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)],[408]) ).
thf(881,plain,
( ( ! [V_P: $i,V_Q: $i,T_b: $i,T_a: $i,T_c: $i,V_R: $i] :
( ( hAPP @ ( c_COMBB @ V_P @ V_Q @ T_b @ T_a @ T_c ) @ V_R )
= ( hAPP @ V_P @ ( hAPP @ V_Q @ V_R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(882,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)],[410]) ).
thf(883,plain,
( ( ! [T_a: $i,V_P: $i] :
( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
= V_P ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(884,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)],[412]) ).
thf(885,plain,
( ( ! [V_P: $i,V_Q: $i,T_b: $i,T_c: $i,T_a: $i,V_R: $i] :
( ( hAPP @ ( c_COMBS @ V_P @ V_Q @ T_b @ T_c @ T_a ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ ( hAPP @ V_Q @ V_R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(886,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)],[414]) ).
thf(887,plain,
( ( ! [V_b: $i,V_c: $i,V_s0: $i,V_n: $i,V_s2: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s0 @ V_n @ V_s2 )
| ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s1 @ V_n @ V_s2 )
| ~ ( c_Natural_Oevaln @ V_c @ V_s0 @ V_n @ V_s1 )
| ~ ( hBOOL @ ( hAPP @ V_b @ V_s0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[415]) ).
thf(888,plain,
( ( ! [T_a: $i,V_y: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416]) ).
thf(889,plain,
( ( ! [T_a: $i,V_a_H: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417]) ).
thf(890,plain,
( ( ! [V_b: $i,V_c: $i,V_s0: $i,V_s2: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s0 @ V_s2 )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s1 @ V_s2 )
| ~ ( c_Natural_Oevalc @ V_c @ V_s0 @ V_s1 )
| ~ ( hBOOL @ ( hAPP @ V_b @ V_s0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418]) ).
thf(891,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)],[419]) ).
thf(892,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)],[420]) ).
thf(893,plain,
( ( ! [V_c0: $i,V_c1: $i,V_s0: $i,V_n: $i,V_s2: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_n @ V_s2 )
| ~ ( c_Natural_Oevaln @ V_c1 @ V_s1 @ V_n @ V_s2 )
| ~ ( c_Natural_Oevaln @ V_c0 @ V_s0 @ V_n @ V_s1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421]) ).
thf(894,plain,
( ( c_Com_OWT @ c_Com_Ocom_OSKIP )
= $true ),
inference(unfold_def,[status(thm)],[422]) ).
thf(895,plain,
( ( ! [V_b: $i,V_c0: $i,V_c1: $i,V_s: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c0 @ V_c1 ) @ V_s @ V_s1 )
| ~ ( c_Natural_Oevalc @ V_c0 @ V_s @ V_s1 )
| ~ ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423]) ).
thf(896,plain,
( ( ! [V_b: $i,V_s: $i,V_c1: $i,V_t: $i,V_c2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ( c_Natural_Oevalc @ V_c1 @ V_s @ V_t )
| ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) @ V_s @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424]) ).
thf(897,plain,
( ( ! [V_f: $i,V_A: $i,T_b: $i,T_a: $i,V_B: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[425]) ).
thf(898,plain,
( ( ! [V_c0: $i,V_c1: $i,V_s0: $i,V_s2: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_s2 )
| ~ ( c_Natural_Oevalc @ V_c1 @ V_s1 @ V_s2 )
| ~ ( c_Natural_Oevalc @ V_c0 @ V_s0 @ V_s1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[426]) ).
thf(899,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)],[427]) ).
thf(900,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)],[428]) ).
thf(901,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[429]) ).
thf(902,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[430]) ).
thf(903,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(904,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[432]) ).
thf(905,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_a: $i,T_b: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
= ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[433]) ).
thf(906,plain,
( ( ! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H )
!= ( c_Com_Ocom_OWhile @ V_fun @ V_com ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(907,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)],[435]) ).
thf(908,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)],[436]) ).
thf(909,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i,V_A: $i] :
( ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(910,plain,
( ( ! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(unfold_def,[status(thm)],[438]) ).
thf(911,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)],[439]) ).
thf(912,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)],[440]) ).
thf(913,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)],[441]) ).
thf(914,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)],[442]) ).
thf(915,plain,
( ( ! [V_c: $i,T_a: $i,T_b: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_a @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(916,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(917,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(918,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(919,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(920,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(921,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(922,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)],[450]) ).
thf(923,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(924,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452]) ).
thf(925,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453]) ).
thf(926,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454]) ).
thf(927,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455]) ).
thf(928,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(929,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(930,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(931,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[459]) ).
thf(932,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(933,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461]) ).
thf(934,plain,
( ( ! [V_P: $i,V_X: $i,V_a: $i] :
( ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ V_P ) )
| ~ ( c_Com_OWT @ ( c_Com_Ocom_OCall @ V_X @ V_P @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[462]) ).
thf(935,plain,
( ( ! [V_X: $i,V_pn: $i,V_a: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OCall @ V_X @ V_pn @ V_a ) )
| ~ ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(936,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)],[464]) ).
thf(937,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)],[465]) ).
thf(938,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)],[466]) ).
thf(939,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)],[467]) ).
thf(940,plain,
( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ v_P ) @ ( hAPP @ c_Com_Ocom_OBODY @ v_pn ) ) @ v_Q ) @ v_G @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ v_P ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) ) @ v_Q ) @ ( 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)],[470]) ).
thf(941,plain,
( ( c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ v_P ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) ) @ v_Q ) @ ( 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)],[471]) ).
thf(942,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[472]) ).
thf(943,plain,
( ( ! [V_X: $i,V_Y: $i] :
( ( V_X = V_Y )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[473]) ).
thf(944,plain,
( ( ! [V_pname: $i,V_pname_H: $i] :
( ( ( hAPP @ c_Com_Ocom_OBODY @ V_pname )
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H ) )
| ( V_pname = V_pname_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[501]) ).
thf(945,plain,
( ( ! [V_a: $i,T_a: $i,V_b: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
!= ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_a = V_b ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[503]) ).
thf(946,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( c_Set_Oinsert @ V_a @ V_A @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[506]) ).
thf(947,plain,
( ( ! [V_A: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ! [V_y: $i] :
( ( V_y = V_x )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[508]) ).
thf(948,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_a = V_c ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[512]) ).
thf(949,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i] :
( ! [V_d: $i] :
( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_a = V_c ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[513]) ).
thf(950,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_a = V_d )
| ( V_b = V_d ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[514]) ).
thf(951,plain,
( ( ! [V_a: $i,V_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ( ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
!= ( c_Set_Oinsert @ V_c @ ( c_Set_Oinsert @ V_d @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
| ( V_b = V_c )
| ( V_b = V_d ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[515]) ).
thf(952,plain,
( ( ! [T_a: $i,V_fun1: $i,V_com: $i,V_fun2: $i,V_fun1_H: $i] :
( ! [V_com_H: $i,V_fun2_H: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1 ) @ V_com ) @ V_fun2 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1_H ) @ V_com_H ) @ V_fun2_H ) )
| ( V_fun1 = V_fun1_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[516]) ).
thf(953,plain,
( ( ! [T_a: $i,V_fun1: $i,V_com: $i,V_fun2: $i,V_fun1_H: $i,V_com_H: $i] :
( ! [V_fun2_H: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1 ) @ V_com ) @ V_fun2 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1_H ) @ V_com_H ) @ V_fun2_H ) )
| ( V_com = V_com_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[517]) ).
thf(954,plain,
( ( ! [T_a: $i,V_fun1: $i,V_com: $i,V_fun2: $i,V_fun1_H: $i,V_com_H: $i,V_fun2_H: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1 ) @ V_com ) @ V_fun2 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1_H ) @ V_com_H ) @ V_fun2_H ) )
| ( V_fun2 = V_fun2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[518]) ).
thf(955,plain,
( ( ! [T_a: $i,V_a: $i,V_A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Set_Oinsert @ V_a @ V_A @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[519]) ).
thf(956,plain,
( ( ! [V_G: $i,V_ts: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ! [V_G_H: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_G_H @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G_H @ V_ts @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[520]) ).
thf(957,plain,
( ( ! [V_G: $i,T_a: $i,V_P: $i,V_c: $i,V_d: $i,V_R: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( c_Com_Ocom_OSemi @ V_c @ V_d ) ) @ V_R ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ! [V_Q: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_Q ) @ V_d ) @ V_R ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[523]) ).
thf(958,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [V_Q_H: $i] :
( ~ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q_H ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[531]) ).
thf(959,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [V_P_H: $i,V_Q_H: $i] :
( ~ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P_H ) @ V_c ) @ V_Q_H ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[532]) ).
thf(960,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [V_P_H: $i] :
( ~ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P_H ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[533]) ).
thf(961,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [V_x: $i,V_xa: $i] :
( ~ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_x ) @ V_c ) @ V_xa ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[534]) ).
thf(962,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [V_P_H: $i] :
( ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P_H ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[535]) ).
thf(963,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [V_P_H: $i,V_Q_H: $i] :
( ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P_H ) @ V_c ) @ V_Q_H ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[536]) ).
thf(964,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [V_Q_H: $i] :
( ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q_H ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[537]) ).
thf(965,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [V_x: $i,V_xa: $i] :
( ~ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_x ) @ V_c ) @ V_xa ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[539]) ).
thf(966,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_xa: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [V_Z_H: $i,V_x: $i] :
( ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_x ) @ V_c ) @ V_xa ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[541]) ).
thf(967,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [V_Z_H: $i,V_P_H: $i] :
( ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P_H ) @ V_c ) @ V_Q_H ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[542]) ).
thf(968,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_xa: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [V_Z_H: $i,V_x: $i] :
( ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_x ) @ V_c ) @ V_xa ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[543]) ).
thf(969,plain,
( ( ! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ! [V_a: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[544]) ).
thf(970,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(extcnf_combined,[status(esa)],[546]) ).
thf(971,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_a: $i] :
( ( 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(extcnf_combined,[status(esa)],[547]) ).
thf(972,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_a: $i] :
( ( 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(extcnf_combined,[status(esa)],[549]) ).
thf(973,plain,
( ( ! [V_b: $i,V_a: $i] :
( ( V_b = V_a )
| ! [T_a: $i] :
~ ( 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(extcnf_combined,[status(esa)],[551]) ).
thf(974,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( V_a = V_b )
| ! [V_f: $i,T_a: $i] :
~ ( 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(extcnf_combined,[status(esa)],[554]) ).
thf(975,plain,
( ( ! [V_Sup: $i,V_a: $i,V_b: $i,T_a: $i,V_sup: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
= ( hAPP @ ( hAPP @ V_sup @ V_a ) @ V_b ) )
| ! [V_bot: $i,V_top: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[557]) ).
thf(976,plain,
( ( ! [V_Inf: $i,V_a: $i,V_b: $i,T_a: $i,V_inf: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_sup: $i] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
= ( hAPP @ ( hAPP @ V_inf @ V_a ) @ V_b ) )
| ! [V_bot: $i,V_top: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[558]) ).
thf(977,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_a: $i] :
( ( 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(extcnf_combined,[status(esa)],[560]) ).
thf(978,plain,
( ( ! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ! [V_a: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[564]) ).
thf(979,plain,
( ( ! [V_Sup: $i,V_a: $i,T_a: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= V_a )
| ! [V_bot: $i,V_top: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[565]) ).
thf(980,plain,
( ( ! [V_Inf: $i,V_a: $i,T_a: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= V_a )
| ! [V_bot: $i,V_top: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[566]) ).
thf(981,plain,
( ( ! [V_pn: $i] :
( ( ( hAPP @ c_Com_Obody @ V_pn )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) )
| ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[580]) ).
thf(982,plain,
( ( ! [V_G: $i,T_a: $i,V_P: $i,V_pn: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ ( hAPP @ V_P @ V_pn ) ) @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) @ ( hAPP @ V_Q @ V_pn ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ! [V_Procs: $i] :
( ~ ( hBOOL @ ( c_in @ V_pn @ V_Procs @ tc_Com_Opname ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_G @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ V_Q @ tc_Com_Opname @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ V_Procs @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ V_Q @ tc_Com_Opname @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ V_Procs @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[581]) ).
thf(983,plain,
( ( ! [V_G: $i,V_ts: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ! [V_G_H: $i] :
( ~ ( c_lessequals @ V_G_H @ V_G @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G_H @ V_ts @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[585]) ).
thf(984,plain,
( ( ! [V_G: $i,V_ts: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ! [V_ts_H: $i] :
( ~ ( c_lessequals @ V_ts @ V_ts_H @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts_H @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[586]) ).
thf(985,plain,
( ( ! [V_pname_H: $i] :
( c_Com_Ocom_OSKIP
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[592]) ).
thf(986,plain,
( ( ! [V_pname: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ V_pname )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[594]) ).
thf(987,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[595]) ).
thf(988,plain,
( ( ! [V_com1: $i,V_com2: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[596]) ).
thf(989,plain,
( ( ! [V_pname_H: $i,V_com1: $i,V_com2: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[597]) ).
thf(990,plain,
( ( ! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i,V_pname: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H )
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[598]) ).
thf(991,plain,
( ( ! [V_pname_H: $i,V_fun: $i,V_com: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OWhile @ V_fun @ V_com ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[599]) ).
thf(992,plain,
( ( ! [V_pname_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[600]) ).
thf(993,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[601]) ).
thf(994,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[602]) ).
thf(995,plain,
( ( ! [V_c1: $i] :
( ( c_Com_OWT @ V_c1 )
| ! [V_b: $i,V_c2: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[603]) ).
thf(996,plain,
( ( ! [V_c2: $i] :
( ( c_Com_OWT @ V_c2 )
| ! [V_b: $i,V_c1: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[604]) ).
thf(997,plain,
( ( ! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ! [V_x: $i,V_A: $i] :
( ( c_lessequals @ V_x @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a ) @ T_a )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[605]) ).
thf(998,plain,
( ( ! [V_c2: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c2 @ V_s @ V_t )
| ! [V_c1: $i] :
( ( c_Natural_Oevalc @ V_c1 @ V_s @ V_t )
| ! [V_b: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) @ V_s @ V_t ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[606]) ).
thf(999,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[607]) ).
thf(1000,plain,
( ( ! [V_c2: $i,V_s: $i,V_n: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c2 @ V_s @ V_n @ V_t )
| ! [V_c1: $i] :
( ( c_Natural_Oevaln @ V_c1 @ V_s @ V_n @ V_t )
| ! [V_b: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[609]) ).
thf(1001,plain,
( ( ! [V_x: $i,V_A: $i,T_b: $i] :
( ~ ( c_lessequals @ V_x @ V_A @ ( tc_fun @ T_b @ tc_bool ) )
| ! [V_f: $i,T_a: $i] : ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_x @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[610]) ).
thf(1002,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ! [V_x_H: $i,V_y_H: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_y_H @ V_x_H @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[612]) ).
thf(1003,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ! [V_x_H: $i,V_y_H: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y_H @ V_x_H @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[613]) ).
thf(1004,plain,
( ( ! [V_b: $i,V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ( V_t = V_s )
| ! [V_c: $i,V_n: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[617]) ).
thf(1005,plain,
( ( ! [V_f: $i,V_g: $i,V_x: $i,V_f_H: $i,V_g_H: $i,V_x_H: $i,T_b: $i,T_a: $i,T_c: $i] :
( ( ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) )
!= ( hAPP @ V_f_H @ ( hAPP @ V_g_H @ V_x_H ) ) )
| ! [T_d: $i,T_e: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ ( c_Fun_Ocomp @ V_f_H @ V_g_H @ T_d @ T_a @ T_e ) @ V_x_H ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[618]) ).
thf(1006,plain,
( ( ! [V_a: $i,V_b: $i,T_c: $i,T_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ! [T_d: $i] :
( ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a )
!= ( c_Fun_Ocomp @ V_c @ V_d @ T_d @ T_b @ T_a ) )
| ! [V_v: $i] :
( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ V_c @ ( hAPP @ V_d @ V_v ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[619]) ).
thf(1007,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[621]) ).
thf(1008,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_lessequals @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[622]) ).
thf(1009,plain,
( ( ! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_combined,[status(esa)],[623]) ).
thf(1010,plain,
( ( ! [V_Q: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ! [V_P: $i] :
( ! [T_a: $i] :
~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[624]) ).
thf(1011,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[625]) ).
thf(1012,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[626]) ).
thf(1013,plain,
( ( ! [V_Q: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ! [V_P: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i] :
~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[627]) ).
thf(1014,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
( ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[628]) ).
thf(1015,plain,
( ( ! [V_t: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_t @ V_B @ T_a ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( c_in @ V_t @ V_A @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[630]) ).
thf(1016,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[631]) ).
thf(1017,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[633]) ).
thf(1018,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[634]) ).
thf(1019,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
( ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[635]) ).
thf(1020,plain,
( ( ! [T_a: $i,V_z: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
( ( c_lessequals @ V_z @ V_x @ T_a )
| ! [V_y: $i] :
( ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[636]) ).
thf(1021,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_A: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[637]) ).
thf(1022,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[638]) ).
thf(1023,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_lessequals @ V_a @ V_x @ T_a )
| ! [V_b: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[639]) ).
thf(1024,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_lessequals @ V_b @ V_x @ T_a )
| ! [V_a: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[640]) ).
thf(1025,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_a: $i] :
( ! [V_b: $i] : ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[641]) ).
thf(1026,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[642]) ).
thf(1027,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[643]) ).
thf(1028,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_y @ V_z @ T_a )
| ! [V_x: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[644]) ).
thf(1029,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[645]) ).
thf(1030,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(extcnf_combined,[status(esa)],[646]) ).
thf(1031,plain,
( ( ! [V_b: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ! [V_t: $i] :
( ( V_t = V_s )
| ! [V_c: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s @ V_t ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[647]) ).
thf(1032,plain,
( ( ! [V_fun_H: $i,V_com_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[651]) ).
thf(1033,plain,
( ( ! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[653]) ).
thf(1034,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_loc_H: $i] :
( ! [V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) )
| ( V_loc = V_loc_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[655]) ).
thf(1035,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_loc_H: $i,V_fun_H: $i] :
( ! [V_com_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) )
| ( V_fun = V_fun_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[656]) ).
thf(1036,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) )
| ( V_com = V_com_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[657]) ).
thf(1037,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_combined,[status(esa)],[661]) ).
thf(1038,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[666]) ).
thf(1039,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) )
| ( c_lessequals @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[667]) ).
thf(1040,plain,
( ( ! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ! [V_A: $i,V_x: $i] :
( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ V_A @ T_a ) @ V_x @ T_a )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[668]) ).
thf(1041,plain,
( ( ! [V_c1: $i] :
( ( c_Com_OWT @ V_c1 )
| ! [V_c2: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[669]) ).
thf(1042,plain,
( ( ! [V_c2: $i] :
( ( c_Com_OWT @ V_c2 )
| ! [V_c1: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[670]) ).
thf(1043,plain,
( ( ! [V_c2: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c2 @ V_s @ V_t )
| ! [V_b: $i] :
( ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ! [V_c1: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) @ V_s @ V_t ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[673]) ).
thf(1044,plain,
( ( ! [V_Q: $i,V_Z: $i,V_s_H: $i,V_c: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_Q @ V_Z ) @ V_s_H ) )
| ! [V_n: $i] :
( ~ ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_s_H )
| ! [V_P: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_Z ) @ V_s ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ t_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[675]) ).
thf(1045,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[676]) ).
thf(1046,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[677]) ).
thf(1047,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= V_B )
| ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[679]) ).
thf(1048,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[682]) ).
thf(1049,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[683]) ).
thf(1050,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[684]) ).
thf(1051,plain,
( ( ! [V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_combined,[status(esa)],[685]) ).
thf(1052,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[686]) ).
thf(1053,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[687]) ).
thf(1054,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[688]) ).
thf(1055,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[689]) ).
thf(1056,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[690]) ).
thf(1057,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( V_A = V_B )
| ! [T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[691]) ).
thf(1058,plain,
( ( ! [V_u: $i,V_t: $i] :
( ( V_u = V_t )
| ! [V_c: $i,V_s: $i] :
( ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_u )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[692]) ).
thf(1059,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( V_A = V_B )
| ! [T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[693]) ).
thf(1060,plain,
( ( ! [V_fun: $i,V_com: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[695]) ).
thf(1061,plain,
( ( ! [V_c2: $i,V_s: $i,V_n: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c2 @ V_s @ V_n @ V_t )
| ! [V_b: $i] :
( ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ! [V_c1: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[697]) ).
thf(1062,plain,
( ( ! [V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[700]) ).
thf(1063,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[701]) ).
thf(1064,plain,
( ( ! [V_pname_H: $i,V_fun: $i,V_com1: $i,V_com2: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[702]) ).
thf(1065,plain,
( ( ! [V_fun: $i,V_com: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[703]) ).
thf(1066,plain,
( ( ! [V_pname_H: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_combined,[status(esa)],[704]) ).
thf(1067,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 ) )
| ( V_A = V_B )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[707]) ).
thf(1068,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[711]) ).
thf(1069,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) )
| ! [V_b: $i] :
( ( V_a = V_b )
| ~ ( hBOOL @ ( c_in @ V_a @ ( c_Set_Oinsert @ V_b @ V_A @ T_a ) @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[716]) ).
thf(1070,plain,
( ( ! [V_Sup: $i,V_a: $i,V_A: $i,T_a: $i,V_sup: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) )
= ( hAPP @ ( hAPP @ V_sup @ V_a ) @ ( hAPP @ V_Sup @ V_A ) ) )
| ! [V_bot: $i,V_top: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[717]) ).
thf(1071,plain,
( ( ! [V_Inf: $i,V_a: $i,V_A: $i,T_a: $i,V_inf: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_sup: $i] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) )
= ( hAPP @ ( hAPP @ V_inf @ V_a ) @ ( hAPP @ V_Inf @ V_A ) ) )
| ! [V_bot: $i,V_top: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[718]) ).
thf(1072,plain,
( ( ! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[725]) ).
thf(1073,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[730]) ).
thf(1074,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[731]) ).
thf(1075,plain,
( ( ! [V_P: $i,V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[732]) ).
thf(1076,plain,
( ( ! [T_a: $i,V_f: $i,V_A: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[734]) ).
thf(1077,plain,
( ( ! [V_P: $i] :
( ! [T_a: $i] :
( ( c_Collect @ V_P @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ! [V_x: $i] :
~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[742]) ).
thf(1078,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( c_in @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[747]) ).
thf(1079,plain,
( ( ! [T_a: $i,V_P: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Collect @ V_P @ T_a ) )
| ! [V_x: $i] :
~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[749]) ).
thf(1080,plain,
( ( ! [V_Sup: $i,T_a: $i,V_bot: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i] :
( ( ( hAPP @ V_Sup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_bot )
| ! [V_sup: $i,V_top: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[750]) ).
thf(1081,plain,
( ( ! [V_Inf: $i,T_a: $i,V_top: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_inf: $i] :
( ( ( hAPP @ V_Inf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_top )
| ! [V_sup: $i,V_bot: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[751]) ).
thf(1082,plain,
( ( ! [V_f: $i,V_A: $i,T_b: $i] :
( ! [T_a: $i] :
( ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[752]) ).
thf(1083,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_A: $i,V_B: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[754]) ).
thf(1084,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_A: $i] :
( ! [V_B: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[755]) ).
thf(1085,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Obot @ T_a )
| ! [V_x: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[756]) ).
thf(1086,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[757]) ).
thf(1087,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[758]) ).
thf(1088,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ! [V_g: $i] :
( ( c_lessequals @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_g @ V_x ) @ T_b )
| ! [T_a: $i] :
~ ( c_lessequals @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[759]) ).
thf(1089,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
| ! [V_x: $i] :
~ ( c_Natural_Oevaln @ V_c @ V_s @ V_x @ V_t ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[760]) ).
thf(1090,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
| ! [V_n: $i] :
~ ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[761]) ).
thf(1091,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_a: $i] :
( ! [T_b: $i] : ( hBOOL @ ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[765]) ).
thf(1092,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_b: $i] :
( ! [T_a: $i] : ( hBOOL @ ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[766]) ).
thf(1093,plain,
( ( ! [V_x: $i,V_A: $i,T_b: $i] :
( ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_b ) )
| ! [V_f: $i,T_a: $i] : ( hBOOL @ ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[767]) ).
thf(1094,plain,
( ( ! [V_x: $i,V_A: $i,T_aa: $i] :
( ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_aa ) )
| ! [V_f: $i,T_a: $i] : ( hBOOL @ ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_aa @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[768]) ).
thf(1095,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ! [V_n: $i] :
~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[769]) ).
thf(1096,plain,
( ( ! [V_com1: $i,V_com2: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[772]) ).
thf(1097,plain,
( ( ! [V_fun_H: $i,V_com_H: $i,V_fun: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[773]) ).
thf(1098,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ V_b ) )
| ! [V_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[774]) ).
thf(1099,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ V_b ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_b ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[775]) ).
thf(1100,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_combined,[status(esa)],[776]) ).
thf(1101,plain,
( ( ! [V_c: $i] :
( ( c_Com_OWT @ V_c )
| ! [V_Y: $i,V_a: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ V_Y @ V_a @ V_c ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[777]) ).
thf(1102,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[779]) ).
thf(1103,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[780]) ).
thf(1104,plain,
( ( ! [V_c: $i] :
( ( c_Com_OWT @ V_c )
| ! [V_b: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[782]) ).
thf(1105,plain,
( ( ! [V_fun: $i,V_com: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) )
| ( V_com = V_com_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[784]) ).
thf(1106,plain,
( ( ! [V_fun: $i,V_com: $i,V_fun_H: $i] :
( ! [V_com_H: $i] :
( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) )
| ( V_fun = V_fun_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[785]) ).
thf(1107,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[786]) ).
thf(1108,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[787]) ).
thf(1109,plain,
( ( ! [V_less__eq: $i,V_x: $i,V_Sup: $i,V_A: $i,T_a: $i,V_Inf: $i,V_less: $i,V_inf: $i,V_sup: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_x ) @ ( hAPP @ V_Sup @ V_A ) ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ! [V_bot: $i,V_top: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[789]) ).
thf(1110,plain,
( ( ! [V_less__eq: $i,V_Inf: $i,V_A: $i,V_x: $i,T_a: $i,V_Sup: $i,V_less: $i,V_inf: $i,V_sup: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ ( hAPP @ V_Inf @ V_A ) ) @ V_x ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ! [V_bot: $i,V_top: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[790]) ).
thf(1111,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[792]) ).
thf(1112,plain,
( ( ! [T_b: $i] :
( ~ ( class_HOL_Ominus @ T_b )
| ! [V_A: $i,V_B: $i] :
( ( 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(extcnf_combined,[status(esa)],[795]) ).
thf(1113,plain,
( ( ! [V_b: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $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 ) )
| ! [V_a: $i] :
( ~ ( hBOOL @ ( c_in @ V_b @ ( hAPP @ V_B @ V_a ) @ T_b ) )
| ~ ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[799]) ).
thf(1114,plain,
( ( ! [V_b: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $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 ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( c_in @ V_b @ ( hAPP @ V_B @ V_x ) @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[800]) ).
thf(1115,plain,
( ( ! [V_fun_H: $i,V_com_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[801]) ).
thf(1116,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) )
| ! [V_x: $i] :
( ( ( hAPP @ V_B @ V_x )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[804]) ).
thf(1117,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[805]) ).
thf(1118,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) )
| ! [V_A: $i] :
( ( 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(extcnf_combined,[status(esa)],[806]) ).
thf(1119,plain,
( ( ! [V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ! [V_A: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[811]) ).
thf(1120,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_c: $i,V_d: $i] : ( c_lessequals @ ( 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 ) )
| ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[812]) ).
thf(1121,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Suc @ V_nat )
!= ( c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[813]) ).
thf(1122,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[814]) ).
thf(1123,plain,
( ( ! [V_a: $i,T_a: $i,V_a_H: $i] :
( ( ( c_Option_Ooption_OSome @ V_a @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[817]) ).
thf(1124,plain,
( ( ! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i,V_fun: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H )
!= ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[818]) ).
thf(1125,plain,
( ( ! [V_xa: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_xa @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[819]) ).
thf(1126,plain,
( ( ! [V_a_H: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_a_H @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[820]) ).
thf(1127,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_c @ V_a @ T_a )
| ! [V_b: $i] :
( ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ! [V_d: $i] :
~ ( c_lessequals @ ( 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(extcnf_combined,[status(esa)],[821]) ).
thf(1128,plain,
( ( ! [T_a: $i,V_b: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_b @ V_d @ T_a )
| ! [V_a: $i] :
( ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ! [V_c: $i] :
~ ( c_lessequals @ ( 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(extcnf_combined,[status(esa)],[822]) ).
thf(1129,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_c: $i,V_d: $i] :
( ( c_lessequals @ ( 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 ) )
| ~ ( c_lessequals @ V_b @ V_d @ T_a )
| ~ ( c_lessequals @ V_c @ V_a @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[823]) ).
thf(1130,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ! [V_x: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[824]) ).
thf(1131,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ! [V_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_a @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[825]) ).
thf(1132,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ! [V_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[826]) ).
thf(1133,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ! [V_x: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[827]) ).
thf(1134,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ! [V_x: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[828]) ).
thf(1135,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i] :
( ! [V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) )
| ( V_fun = V_fun_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[829]) ).
thf(1136,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i] :
( ! [V_com2_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) )
| ( V_com1 = V_com1_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[830]) ).
thf(1137,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) )
| ( V_com2 = V_com2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[831]) ).
thf(1138,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(extcnf_combined,[status(esa)],[832]) ).
thf(1139,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[833]) ).
thf(1140,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ ( hAPP @ V_A @ V_x ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_I: $i,T_b: $i] :
( ~ ( hBOOL @ ( c_in @ V_x @ V_I @ T_b ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_I @ V_A @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[836]) ).
thf(1141,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i] :
( ~ ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) )
| ! [V_A: $i] :
~ ( hBOOL @ ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[837]) ).
thf(1142,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[838]) ).
thf(1143,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) )
| ! [V_B: $i] :
~ ( hBOOL @ ( c_in @ V_c @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[839]) ).
thf(1144,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[840]) ).
thf(1145,plain,
( ( ! [V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ! [V_x: $i] :
( ( ( hAPP @ V_B @ V_x )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_b ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[841]) ).
thf(1146,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[843]) ).
thf(1147,plain,
( ( ! [V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[844]) ).
thf(1148,plain,
( ( ! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ! [V_a: $i,V_A: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[845]) ).
thf(1149,plain,
( ( ! [V_com1: $i,V_com2: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[846]) ).
thf(1150,plain,
( ( ! [V_com1: $i,V_com2: $i,V_com1_H: $i] :
( ! [V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com1 = V_com1_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[847]) ).
thf(1151,plain,
( ( ! [V_com1: $i,V_com2: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) )
| ( V_com2 = V_com2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[848]) ).
thf(1152,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[850]) ).
thf(1153,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[851]) ).
thf(1154,plain,
( ( ! [V_fun_H: $i,V_com_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[853]) ).
thf(1155,plain,
( ( ! [V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_combined,[status(esa)],[854]) ).
thf(1156,plain,
( ( ! [V_vname: $i,V_pname: $i,V_fun: $i,V_vname_H: $i] :
( ! [V_pname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OCall @ V_vname @ V_pname @ V_fun )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) )
| ( V_vname = V_vname_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[855]) ).
thf(1157,plain,
( ( ! [V_vname: $i,V_pname: $i,V_fun: $i,V_vname_H: $i,V_pname_H: $i] :
( ! [V_fun_H: $i] :
( ( c_Com_Ocom_OCall @ V_vname @ V_pname @ V_fun )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) )
| ( V_pname = V_pname_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[856]) ).
thf(1158,plain,
( ( ! [V_vname: $i,V_pname: $i,V_fun: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( ( c_Com_Ocom_OCall @ V_vname @ V_pname @ V_fun )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) )
| ( V_fun = V_fun_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[857]) ).
thf(1159,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[859]) ).
thf(1160,plain,
( ( ! [V_B: $i,V_a: $i,V_A: $i,T_a: $i] :
( ! [T_b: $i] : ( c_lessequals @ ( hAPP @ V_B @ V_a ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[861]) ).
thf(1161,plain,
( ( ! [T_b: $i,V_M: $i,V_i: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_b )
| ! [V_A: $i,T_a: $i] :
( ( c_lessequals @ ( hAPP @ V_M @ V_i ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_M @ T_a @ T_b ) @ T_b )
| ~ ( hBOOL @ ( c_in @ V_i @ V_A @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[862]) ).
thf(1162,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[863]) ).
thf(1163,plain,
( ( ! [V_b: $i,V_c: $i,V_s: $i] :
( ! [V_n: $i] : ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s @ V_n @ V_s )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[865]) ).
thf(1164,plain,
( ( ! [V_f: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ V_f @ V_x ) @ V_B @ T_a ) )
| ! [V_A: $i,T_b: $i] :
( ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_b ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[869]) ).
thf(1165,plain,
( ( ! [V_c: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_b @ T_a ) @ V_A @ T_a @ T_b )
= ( c_Set_Oinsert @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) )
| ! [V_x: $i] :
~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[870]) ).
thf(1166,plain,
( ( ! [T_b: $i] :
( ~ ( class_Lattices_Olattice @ T_b )
| ! [V_f: $i,V_g: $i] :
( ( 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(extcnf_combined,[status(esa)],[871]) ).
thf(1167,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[873]) ).
thf(1168,plain,
( ( ! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[874]) ).
thf(1169,plain,
( ( ! [V_b: $i,V_s: $i,V_c1: $i,V_n: $i] :
( ~ ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ! [V_t: $i] :
( ( c_Natural_Oevaln @ V_c1 @ V_s @ V_n @ V_t )
| ! [V_c2: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[877]) ).
thf(1170,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(extcnf_combined,[status(esa)],[879]) ).
thf(1171,plain,
( ( ! [V_S: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_S @ V_x ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( c_in @ V_x @ V_S @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[880]) ).
thf(1172,plain,
( ( ! [V_b: $i,V_c: $i,V_s0: $i,V_n: $i,V_s2: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s0 @ V_n @ V_s2 )
| ! [V_s1: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s1 @ V_n @ V_s2 )
| ~ ( c_Natural_Oevaln @ V_c @ V_s0 @ V_n @ V_s1 )
| ~ ( hBOOL @ ( hAPP @ V_b @ V_s0 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[887]) ).
thf(1173,plain,
( ( ! [T_a: $i,V_y: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[888]) ).
thf(1174,plain,
( ( ! [T_a: $i,V_a_H: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[889]) ).
thf(1175,plain,
( ( ! [V_b: $i,V_c: $i,V_s0: $i,V_s2: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s0 @ V_s2 )
| ! [V_s1: $i] :
( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s1 @ V_s2 )
| ~ ( c_Natural_Oevalc @ V_c @ V_s0 @ V_s1 )
| ~ ( hBOOL @ ( hAPP @ V_b @ V_s0 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[890]) ).
thf(1176,plain,
( ( ! [T_a: $i,V_xa: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ! [V_y: $i] :
( ! [V_x: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_xa @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a ) )
| ( V_xa = V_y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[891]) ).
thf(1177,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ! [V_x_H: $i,V_y_H: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( V_x_H = V_y_H ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[892]) ).
thf(1178,plain,
( ( ! [V_c0: $i,V_c1: $i,V_s0: $i,V_n: $i,V_s2: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_n @ V_s2 )
| ! [V_s1: $i] :
( ~ ( c_Natural_Oevaln @ V_c1 @ V_s1 @ V_n @ V_s2 )
| ~ ( c_Natural_Oevaln @ V_c0 @ V_s0 @ V_n @ V_s1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[893]) ).
thf(1179,plain,
( ( ! [V_b: $i,V_s: $i,V_c1: $i] :
( ~ ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ! [V_t: $i] :
( ( c_Natural_Oevalc @ V_c1 @ V_s @ V_t )
| ! [V_c2: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) @ V_s @ V_t ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[896]) ).
thf(1180,plain,
( ( ! [V_c0: $i,V_c1: $i,V_s0: $i,V_s2: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_s2 )
| ! [V_s1: $i] :
( ~ ( c_Natural_Oevalc @ V_c1 @ V_s1 @ V_s2 )
| ~ ( c_Natural_Oevalc @ V_c0 @ V_s0 @ V_s1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[898]) ).
thf(1181,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $i] :
( ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[901]) ).
thf(1182,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $i] :
( ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[903]) ).
thf(1183,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_a: $i] :
( ! [T_b: $i] :
( ( c_Set_Oinsert @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
= ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[905]) ).
thf(1184,plain,
( ( ! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H )
!= ( c_Com_Ocom_OWhile @ V_fun @ V_com ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[906]) ).
thf(1185,plain,
( ( ! [T_b: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_b )
| ! [V_M: $i,T_a: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ ( c_COMBK @ V_M @ T_b @ T_a ) @ T_a @ T_b )
= V_M )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[907]) ).
thf(1186,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ! [V_A: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[909]) ).
thf(1187,plain,
( ( ! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[910]) ).
thf(1188,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( c_in @ V_a @ ( c_Collect @ V_P @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[913]) ).
thf(1189,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(extcnf_combined,[status(esa)],[914]) ).
thf(1190,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[916]) ).
thf(1191,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[917]) ).
thf(1192,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x = V_y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[918]) ).
thf(1193,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[920]) ).
thf(1194,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[923]) ).
thf(1195,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_x: $i] : ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[924]) ).
thf(1196,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[925]) ).
thf(1197,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_z: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[926]) ).
thf(1198,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_x: $i] : ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[927]) ).
thf(1199,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[928]) ).
thf(1200,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[929]) ).
thf(1201,plain,
( ( ! [V_P: $i] :
( ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ V_P ) )
| ! [V_X: $i,V_a: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCall @ V_X @ V_P @ V_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[934]) ).
thf(1202,plain,
( ( ! [V_X: $i,V_pn: $i] :
( ! [V_a: $i] : ( c_Com_OWT @ ( c_Com_Ocom_OCall @ V_X @ V_pn @ V_a ) )
| ~ ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[935]) ).
thf(1203,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[936]) ).
thf(1204,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[937]) ).
thf(1205,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[938]) ).
thf(1206,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[939]) ).
thf(1207,plain,
( ( c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ v_P ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) ) @ v_Q ) @ ( 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)],[941]) ).
thf(1208,plain,
( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ v_P ) @ ( hAPP @ c_Com_Ocom_OBODY @ v_pn ) ) @ v_Q ) @ v_G @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ v_P ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) ) @ v_Q ) @ ( 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)],[940]) ).
thf(1209,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1206]) ).
thf(1210,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1205]) ).
thf(1211,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1204]) ).
thf(1212,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1203]) ).
thf(1213,plain,
( ( ! [V_X: $i,V_pn: $i] :
( ! [V_a: $i] : ( c_Com_OWT @ ( c_Com_Ocom_OCall @ V_X @ V_pn @ V_a ) )
| ~ ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) ) )
= $true ),
inference(copy,[status(thm)],[1202]) ).
thf(1214,plain,
( ( ! [V_P: $i] :
( ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ V_P ) )
| ! [V_X: $i,V_a: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCall @ V_X @ V_P @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1201]) ).
thf(1215,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[933]) ).
thf(1216,plain,
( ( ! [V_B: $i,V_A: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[932]) ).
thf(1217,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[931]) ).
thf(1218,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[930]) ).
thf(1219,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_b: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1200]) ).
thf(1220,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1199]) ).
thf(1221,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_x: $i] : ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1198]) ).
thf(1222,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_z: $i,V_x: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_z @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1197]) ).
thf(1223,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_y: $i,V_z: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1196]) ).
thf(1224,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_y: $i,V_x: $i] : ( c_lessequals @ V_y @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1195]) ).
thf(1225,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] : ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1194]) ).
thf(1226,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)],[922]) ).
thf(1227,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ ( c_HOL_Ominus__class_Ominus @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[921]) ).
thf(1228,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(copy,[status(thm)],[1193]) ).
thf(1229,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[919]) ).
thf(1230,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_x = V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[1192]) ).
thf(1231,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1191]) ).
thf(1232,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a = V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1190]) ).
thf(1233,plain,
( ( ! [V_c: $i,T_a: $i,T_b: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_a @ T_b ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[915]) ).
thf(1234,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)],[1189]) ).
thf(1235,plain,
( ( ! [V_P: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_a ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( c_in @ V_a @ ( c_Collect @ V_P @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1188]) ).
thf(1236,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)],[912]) ).
thf(1237,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)],[911]) ).
thf(1238,plain,
( ( ! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(copy,[status(thm)],[1187]) ).
thf(1239,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ! [V_A: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1186]) ).
thf(1240,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)],[908]) ).
thf(1241,plain,
( ( ! [T_b: $i,V_A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_b )
| ! [V_M: $i,T_a: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ ( c_COMBK @ V_M @ T_b @ T_a ) @ T_a @ T_b )
= V_M )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1185]) ).
thf(1242,plain,
( ( ! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H )
!= ( c_Com_Ocom_OWhile @ V_fun @ V_com ) ) )
= $true ),
inference(copy,[status(thm)],[1184]) ).
thf(1243,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_a: $i] :
( ! [T_b: $i] :
( ( c_Set_Oinsert @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b )
= ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1183]) ).
thf(1244,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[904]) ).
thf(1245,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $i] :
( ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1182]) ).
thf(1246,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[902]) ).
thf(1247,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $i] :
( ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1181]) ).
thf(1248,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)],[900]) ).
thf(1249,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)],[899]) ).
thf(1250,plain,
( ( ! [V_c0: $i,V_c1: $i,V_s0: $i,V_s2: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_s2 )
| ! [V_s1: $i] :
( ~ ( c_Natural_Oevalc @ V_c1 @ V_s1 @ V_s2 )
| ~ ( c_Natural_Oevalc @ V_c0 @ V_s0 @ V_s1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1180]) ).
thf(1251,plain,
( ( ! [V_f: $i,V_A: $i,T_b: $i,T_a: $i,V_B: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Set_Oimage @ V_f @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[897]) ).
thf(1252,plain,
( ( ! [V_b: $i,V_s: $i,V_c1: $i] :
( ~ ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ! [V_t: $i] :
( ( c_Natural_Oevalc @ V_c1 @ V_s @ V_t )
| ! [V_c2: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) @ V_s @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[1179]) ).
thf(1253,plain,
( ( ! [V_b: $i,V_c0: $i,V_c1: $i,V_s: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c0 @ V_c1 ) @ V_s @ V_s1 )
| ~ ( c_Natural_Oevalc @ V_c0 @ V_s @ V_s1 )
| ~ ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[895]) ).
thf(1254,plain,
( ( c_Com_OWT @ c_Com_Ocom_OSKIP )
= $true ),
inference(copy,[status(thm)],[894]) ).
thf(1255,plain,
( ( ! [V_c0: $i,V_c1: $i,V_s0: $i,V_n: $i,V_s2: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) @ V_s0 @ V_n @ V_s2 )
| ! [V_s1: $i] :
( ~ ( c_Natural_Oevaln @ V_c1 @ V_s1 @ V_n @ V_s2 )
| ~ ( c_Natural_Oevaln @ V_c0 @ V_s0 @ V_n @ V_s1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1178]) ).
thf(1256,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ! [V_x_H: $i,V_y_H: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( V_x_H = V_y_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[1177]) ).
thf(1257,plain,
( ( ! [T_a: $i,V_xa: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ! [V_y: $i] :
( ! [V_x: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_xa @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a ) )
| ( V_xa = V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[1176]) ).
thf(1258,plain,
( ( ! [V_b: $i,V_c: $i,V_s0: $i,V_s2: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s0 @ V_s2 )
| ! [V_s1: $i] :
( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s1 @ V_s2 )
| ~ ( c_Natural_Oevalc @ V_c @ V_s0 @ V_s1 )
| ~ ( hBOOL @ ( hAPP @ V_b @ V_s0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1175]) ).
thf(1259,plain,
( ( ! [T_a: $i,V_a_H: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1174]) ).
thf(1260,plain,
( ( ! [T_a: $i,V_y: $i] :
( ( c_Option_Ooption_ONone @ T_a )
!= ( c_Option_Ooption_OSome @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1173]) ).
thf(1261,plain,
( ( ! [V_b: $i,V_c: $i,V_s0: $i,V_n: $i,V_s2: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s0 @ V_n @ V_s2 )
| ! [V_s1: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s1 @ V_n @ V_s2 )
| ~ ( c_Natural_Oevaln @ V_c @ V_s0 @ V_n @ V_s1 )
| ~ ( hBOOL @ ( hAPP @ V_b @ V_s0 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1172]) ).
thf(1262,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)],[886]) ).
thf(1263,plain,
( ( ! [V_P: $i,V_Q: $i,T_b: $i,T_c: $i,T_a: $i,V_R: $i] :
( ( hAPP @ ( c_COMBS @ V_P @ V_Q @ T_b @ T_c @ T_a ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ ( hAPP @ V_Q @ V_R ) ) ) )
= $true ),
inference(copy,[status(thm)],[885]) ).
thf(1264,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)],[884]) ).
thf(1265,plain,
( ( ! [T_a: $i,V_P: $i] :
( ( hAPP @ ( c_COMBI @ T_a ) @ V_P )
= V_P ) )
= $true ),
inference(copy,[status(thm)],[883]) ).
thf(1266,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)],[882]) ).
thf(1267,plain,
( ( ! [V_P: $i,V_Q: $i,T_b: $i,T_a: $i,T_c: $i,V_R: $i] :
( ( hAPP @ ( c_COMBB @ V_P @ V_Q @ T_b @ T_a @ T_c ) @ V_R )
= ( hAPP @ V_P @ ( hAPP @ V_Q @ V_R ) ) ) )
= $true ),
inference(copy,[status(thm)],[881]) ).
thf(1268,plain,
( ( ! [V_S: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_S @ V_x ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( c_in @ V_x @ V_S @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1171]) ).
thf(1269,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)],[1170]) ).
thf(1270,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)],[878]) ).
thf(1271,plain,
( ( ! [V_b: $i,V_s: $i,V_c1: $i,V_n: $i] :
( ~ ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ! [V_t: $i] :
( ( c_Natural_Oevaln @ V_c1 @ V_s @ V_n @ V_t )
| ! [V_c2: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[1169]) ).
thf(1272,plain,
( ( ! [V_b: $i,V_c0: $i,V_c1: $i,V_s: $i,V_n: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ V_b @ V_c0 @ V_c1 ) @ V_s @ V_n @ V_s1 )
| ~ ( c_Natural_Oevaln @ V_c0 @ V_s @ V_n @ V_s1 )
| ~ ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[876]) ).
thf(1273,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_f4: $i,V_f5: $i,V_f6: $i,V_f7: $i,V_f8: $i,V_vname: $i,V_pname: $i,V_fun: $i,T_a: $i] :
( ( c_Com_Ocom_Ocom__case @ V_f1 @ V_f2 @ V_f3 @ V_f4 @ V_f5 @ V_f6 @ V_f7 @ V_f8 @ ( c_Com_Ocom_OCall @ V_vname @ V_pname @ V_fun ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ V_f8 @ V_vname ) @ V_pname ) @ V_fun ) ) )
= $true ),
inference(copy,[status(thm)],[875]) ).
thf(1274,plain,
( ( ! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(copy,[status(thm)],[1168]) ).
thf(1275,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1167]) ).
thf(1276,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)],[872]) ).
thf(1277,plain,
( ( ! [T_b: $i] :
( ~ ( class_Lattices_Olattice @ T_b )
| ! [V_f: $i,V_g: $i] :
( ( 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)],[1166]) ).
thf(1278,plain,
( ( ! [V_c: $i,T_b: $i,T_a: $i,V_A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_b @ T_a ) @ V_A @ T_a @ T_b )
= ( c_Set_Oinsert @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b ) )
| ! [V_x: $i] :
~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1165]) ).
thf(1279,plain,
( ( ! [V_f: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ V_f @ V_x ) @ V_B @ T_a ) )
| ! [V_A: $i,T_b: $i] :
( ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_b ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1164]) ).
thf(1280,plain,
( ( ! [V_A: $i,V_x: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[868]) ).
thf(1281,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[867]) ).
thf(1282,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[866]) ).
thf(1283,plain,
( ( ! [V_b: $i,V_c: $i,V_s: $i] :
( ! [V_n: $i] : ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s @ V_n @ V_s )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[1163]) ).
thf(1284,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)],[864]) ).
thf(1285,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) ) )
= $true ),
inference(copy,[status(thm)],[1162]) ).
thf(1286,plain,
( ( ! [T_b: $i,V_M: $i,V_i: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_b )
| ! [V_A: $i,T_a: $i] :
( ( c_lessequals @ ( hAPP @ V_M @ V_i ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_M @ T_a @ T_b ) @ T_b )
| ~ ( hBOOL @ ( c_in @ V_i @ V_A @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1161]) ).
thf(1287,plain,
( ( ! [V_B: $i,V_a: $i,V_A: $i,T_a: $i] :
( ! [T_b: $i] : ( c_lessequals @ ( hAPP @ V_B @ V_a ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1160]) ).
thf(1288,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)],[860]) ).
thf(1289,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(copy,[status(thm)],[1159]) ).
thf(1290,plain,
( ( ! [T_a: $i,V_Y: $i] :
( ( c_Set_Oimage @ ( c_COMBI @ T_a ) @ V_Y @ T_a @ T_a )
= V_Y ) )
= $true ),
inference(copy,[status(thm)],[858]) ).
thf(1291,plain,
( ( ! [V_vname: $i,V_pname: $i,V_fun: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( ( c_Com_Ocom_OCall @ V_vname @ V_pname @ V_fun )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) )
| ( V_fun = V_fun_H ) ) )
= $true ),
inference(copy,[status(thm)],[1158]) ).
thf(1292,plain,
( ( ! [V_vname: $i,V_pname: $i,V_fun: $i,V_vname_H: $i,V_pname_H: $i] :
( ! [V_fun_H: $i] :
( ( c_Com_Ocom_OCall @ V_vname @ V_pname @ V_fun )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) )
| ( V_pname = V_pname_H ) ) )
= $true ),
inference(copy,[status(thm)],[1157]) ).
thf(1293,plain,
( ( ! [V_vname: $i,V_pname: $i,V_fun: $i,V_vname_H: $i] :
( ! [V_pname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OCall @ V_vname @ V_pname @ V_fun )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) )
| ( V_vname = V_vname_H ) ) )
= $true ),
inference(copy,[status(thm)],[1156]) ).
thf(1294,plain,
( ( ! [V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(copy,[status(thm)],[1155]) ).
thf(1295,plain,
( ( ! [V_fun_H: $i,V_com_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(copy,[status(thm)],[1154]) ).
thf(1296,plain,
( ( ! [V_b: $i,V_c: $i,V_s: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s @ V_s )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[852]) ).
thf(1297,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[1153]) ).
thf(1298,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[1152]) ).
thf(1299,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( c_Collect @ V_P @ T_a )
= V_P ) )
= $true ),
inference(copy,[status(thm)],[849]) ).
thf(1300,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)],[1151]) ).
thf(1301,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)],[1150]) ).
thf(1302,plain,
( ( ! [V_com1: $i,V_com2: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(copy,[status(thm)],[1149]) ).
thf(1303,plain,
( ( ! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ! [V_a: $i,V_A: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1148]) ).
thf(1304,plain,
( ( ! [V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(copy,[status(thm)],[1147]) ).
thf(1305,plain,
( ( ! [V_com1_H: $i,V_com2_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(copy,[status(thm)],[1146]) ).
thf(1306,plain,
( ( ! [V_n: $i,V_t: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ V_t @ T_a )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ V_n ) @ V_t @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[842]) ).
thf(1307,plain,
( ( ! [V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ! [V_x: $i] :
( ( ( hAPP @ V_B @ V_x )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1145]) ).
thf(1308,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(copy,[status(thm)],[1144]) ).
thf(1309,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) )
| ! [V_B: $i] :
~ ( 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)],[1143]) ).
thf(1310,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(copy,[status(thm)],[1142]) ).
thf(1311,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i] :
( ~ ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) )
| ! [V_A: $i] :
~ ( 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)],[1141]) ).
thf(1312,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ ( hAPP @ V_A @ V_x ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_I: $i,T_b: $i] :
( ~ ( hBOOL @ ( c_in @ V_x @ V_I @ T_b ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_I @ V_A @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1140]) ).
thf(1313,plain,
( ( ! [V_c: $i,T_b: $i,T_c: $i,V_f: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ ( c_COMBK @ V_c @ T_b @ T_c ) @ V_f @ T_c @ T_b @ t_a ) @ v_x )
= V_c ) )
= $true ),
inference(copy,[status(thm)],[835]) ).
thf(1314,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)],[834]) ).
thf(1315,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(copy,[status(thm)],[1139]) ).
thf(1316,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)],[1138]) ).
thf(1317,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) )
| ( V_com2 = V_com2_H ) ) )
= $true ),
inference(copy,[status(thm)],[1137]) ).
thf(1318,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i,V_com1_H: $i] :
( ! [V_com2_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) )
| ( V_com1 = V_com1_H ) ) )
= $true ),
inference(copy,[status(thm)],[1136]) ).
thf(1319,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_fun_H: $i] :
( ! [V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H ) )
| ( V_fun = V_fun_H ) ) )
= $true ),
inference(copy,[status(thm)],[1135]) ).
thf(1320,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ! [V_x: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1134]) ).
thf(1321,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ! [V_x: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1133]) ).
thf(1322,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ! [V_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1132]) ).
thf(1323,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ! [V_a: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_a @ V_a @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1131]) ).
thf(1324,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ! [V_x: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1130]) ).
thf(1325,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_c: $i,V_d: $i] :
( ( c_lessequals @ ( 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 ) )
| ~ ( c_lessequals @ V_b @ V_d @ T_a )
| ~ ( c_lessequals @ V_c @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1129]) ).
thf(1326,plain,
( ( ! [T_a: $i,V_b: $i,V_d: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_b @ V_d @ T_a )
| ! [V_a: $i] :
( ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ! [V_c: $i] :
~ ( c_lessequals @ ( 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)],[1128]) ).
thf(1327,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_c @ V_a @ T_a )
| ! [V_b: $i] :
( ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ! [V_d: $i] :
~ ( c_lessequals @ ( 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)],[1127]) ).
thf(1328,plain,
( ( ! [V_a_H: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_a_H @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1126]) ).
thf(1329,plain,
( ( ! [V_xa: $i,T_a: $i] :
( ( c_Option_Ooption_OSome @ V_xa @ T_a )
!= ( c_Option_Ooption_ONone @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1125]) ).
thf(1330,plain,
( ( ! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i,V_fun: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H )
!= ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 ) ) )
= $true ),
inference(copy,[status(thm)],[1124]) ).
thf(1331,plain,
( ( ! [V_a: $i,T_a: $i,V_a_H: $i] :
( ( ( c_Option_Ooption_OSome @ V_a @ T_a )
!= ( c_Option_Ooption_OSome @ V_a_H @ T_a ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(copy,[status(thm)],[1123]) ).
thf(1332,plain,
( ( ! [V_f: $i,V_g: $i,T_b: $i,T_a: $i,T_c: $i,V_x: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[816]) ).
thf(1333,plain,
( ( ! [V_a: $i,V_b: $i,V_v: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a ) @ V_v ) ) )
= $true ),
inference(copy,[status(thm)],[815]) ).
thf(1334,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[1122]) ).
thf(1335,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Suc @ V_nat )
!= ( c_Suc @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[1121]) ).
thf(1336,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_c: $i,V_d: $i] : ( c_lessequals @ ( 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 ) )
| ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1120]) ).
thf(1337,plain,
( ( ! [V_B: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_B @ V_x ) )
| ! [V_A: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1119]) ).
thf(1338,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)],[810]) ).
thf(1339,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)],[809]) ).
thf(1340,plain,
( ( ! [V_b: $i,V_c0: $i,V_c1: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ V_b @ V_c0 @ V_c1 ) )
| ~ ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ V_c0 ) ) )
= $true ),
inference(copy,[status(thm)],[808]) ).
thf(1341,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_f4: $i,V_f5: $i,V_f6: $i,V_f7: $i,V_f8: $i,T_a: $i] :
( ( c_Com_Ocom_Ocom__case @ V_f1 @ V_f2 @ V_f3 @ V_f4 @ V_f5 @ V_f6 @ V_f7 @ V_f8 @ c_Com_Ocom_OSKIP @ T_a )
= V_f1 ) )
= $true ),
inference(copy,[status(thm)],[807]) ).
thf(1342,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) )
| ! [V_A: $i] :
( ( 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)],[1118]) ).
thf(1343,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(copy,[status(thm)],[1117]) ).
thf(1344,plain,
( ( ! [T_a: $i,V_A: $i,V_B: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_b @ ( tc_fun @ T_a @ tc_bool ) ) )
| ! [V_x: $i] :
( ( ( hAPP @ V_B @ V_x )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1116]) ).
thf(1345,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)],[803]) ).
thf(1346,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)],[802]) ).
thf(1347,plain,
( ( ! [V_fun_H: $i,V_com_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(copy,[status(thm)],[1115]) ).
thf(1348,plain,
( ( ! [V_b: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $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 ) )
| ! [V_x: $i] :
( ~ ( 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)],[1114]) ).
thf(1349,plain,
( ( ! [V_b: $i,V_A: $i,V_B: $i,T_a: $i,T_b: $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 ) )
| ! [V_a: $i] :
( ~ ( 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)],[1113]) ).
thf(1350,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)],[798]) ).
thf(1351,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)],[797]) ).
thf(1352,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)],[796]) ).
thf(1353,plain,
( ( ! [T_b: $i] :
( ~ ( class_HOL_Ominus @ T_b )
| ! [V_A: $i,V_B: $i] :
( ( 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)],[1112]) ).
thf(1354,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)],[794]) ).
thf(1355,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_f4: $i,V_f5: $i,V_f6: $i,V_f7: $i,V_f8: $i,V_com1: $i,V_com2: $i,T_a: $i] :
( ( c_Com_Ocom_Ocom__case @ V_f1 @ V_f2 @ V_f3 @ V_f4 @ V_f5 @ V_f6 @ V_f7 @ V_f8 @ ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) @ T_a )
= ( hAPP @ ( hAPP @ V_f4 @ V_com1 ) @ V_com2 ) ) )
= $true ),
inference(copy,[status(thm)],[793]) ).
thf(1356,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OSemi @ V_com1_H @ V_com2_H ) ) )
= $true ),
inference(copy,[status(thm)],[1111]) ).
thf(1357,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)],[791]) ).
thf(1358,plain,
( ( ! [V_less__eq: $i,V_Inf: $i,V_A: $i,V_x: $i,T_a: $i,V_Sup: $i,V_less: $i,V_inf: $i,V_sup: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ ( hAPP @ V_Inf @ V_A ) ) @ V_x ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ! [V_bot: $i,V_top: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1110]) ).
thf(1359,plain,
( ( ! [V_less__eq: $i,V_x: $i,V_Sup: $i,V_A: $i,T_a: $i,V_Inf: $i,V_less: $i,V_inf: $i,V_sup: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_less__eq @ V_x ) @ ( hAPP @ V_Sup @ V_A ) ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ! [V_bot: $i,V_top: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1109]) ).
thf(1360,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)],[788]) ).
thf(1361,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1108]) ).
thf(1362,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1107]) ).
thf(1363,plain,
( ( ! [V_fun: $i,V_com: $i,V_fun_H: $i] :
( ! [V_com_H: $i] :
( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) )
| ( V_fun = V_fun_H ) ) )
= $true ),
inference(copy,[status(thm)],[1106]) ).
thf(1364,plain,
( ( ! [V_fun: $i,V_com: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H ) )
| ( V_com = V_com_H ) ) )
= $true ),
inference(copy,[status(thm)],[1105]) ).
thf(1365,plain,
( ( ! [V_b: $i,V_c: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) )
| ~ ( c_Com_OWT @ V_c ) ) )
= $true ),
inference(copy,[status(thm)],[783]) ).
thf(1366,plain,
( ( ! [V_c: $i] :
( ( c_Com_OWT @ V_c )
| ! [V_b: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) ) )
= $true ),
inference(copy,[status(thm)],[1104]) ).
thf(1367,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)],[781]) ).
thf(1368,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1103]) ).
thf(1369,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Olattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1102]) ).
thf(1370,plain,
( ( ! [V_Y: $i,V_a: $i,V_c: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ V_Y @ V_a @ V_c ) )
| ~ ( c_Com_OWT @ V_c ) ) )
= $true ),
inference(copy,[status(thm)],[778]) ).
thf(1371,plain,
( ( ! [V_c: $i] :
( ( c_Com_OWT @ V_c )
| ! [V_Y: $i,V_a: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ V_Y @ V_a @ V_c ) ) ) )
= $true ),
inference(copy,[status(thm)],[1101]) ).
thf(1372,plain,
( ( ! [V_fun_H: $i,V_com1_H: $i,V_com2_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun_H @ V_com1_H @ V_com2_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(copy,[status(thm)],[1100]) ).
thf(1373,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ V_b ) )
| ! [V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_x ) @ V_b ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1099]) ).
thf(1374,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,T_b: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ V_A @ V_B @ T_a @ ( tc_fun @ T_b @ tc_bool ) ) @ V_b ) )
| ! [V_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_B @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1098]) ).
thf(1375,plain,
( ( ! [V_fun_H: $i,V_com_H: $i,V_fun: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 ) ) )
= $true ),
inference(copy,[status(thm)],[1097]) ).
thf(1376,plain,
( ( ! [V_com1: $i,V_com2: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) ) )
= $true ),
inference(copy,[status(thm)],[1096]) ).
thf(1377,plain,
( ( ! [V_n: $i,V_P: $i,V_s: $i,V_s1: $i] :
( ( V_n
= ( c_Suc @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ V_P @ V_n @ V_s @ V_s1 ) ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_n @ V_s1 ) ) )
= $true ),
inference(copy,[status(thm)],[771]) ).
thf(1378,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)],[770]) ).
thf(1379,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ! [V_n: $i] :
~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[1095]) ).
thf(1380,plain,
( ( ! [V_x: $i,V_A: $i,T_aa: $i] :
( ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_aa ) )
| ! [V_f: $i,T_a: $i] : ( hBOOL @ ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_aa @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1094]) ).
thf(1381,plain,
( ( ! [V_x: $i,V_A: $i,T_b: $i] :
( ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_b ) )
| ! [V_f: $i,T_a: $i] : ( hBOOL @ ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1093]) ).
thf(1382,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_b: $i] :
( ! [T_a: $i] : ( hBOOL @ ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1092]) ).
thf(1383,plain,
( ( ! [V_f: $i,V_x: $i,V_A: $i,T_a: $i] :
( ! [T_b: $i] : ( hBOOL @ ( c_in @ ( hAPP @ V_f @ V_x ) @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ T_b ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1091]) ).
thf(1384,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[764]) ).
thf(1385,plain,
( ( ! [V_A: $i,V_B: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[763]) ).
thf(1386,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( V_t = V_s )
| ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ V_s @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[762]) ).
thf(1387,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
| ! [V_n: $i] :
~ ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[1090]) ).
thf(1388,plain,
( ( ! [V_c: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c @ V_s @ V_t )
| ! [V_x: $i] :
~ ( c_Natural_Oevaln @ V_c @ V_s @ V_x @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[1089]) ).
thf(1389,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i] :
( ~ ( class_HOL_Oord @ T_b )
| ! [V_g: $i] :
( ( c_lessequals @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_g @ V_x ) @ T_b )
| ! [T_a: $i] :
~ ( c_lessequals @ V_f @ V_g @ ( tc_fun @ T_a @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1088]) ).
thf(1390,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1087]) ).
thf(1391,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_x: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ ( c_Orderings_Obot__class_Obot @ T_a ) @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1086]) ).
thf(1392,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Obot @ T_a )
| ! [V_x: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1085]) ).
thf(1393,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_A: $i] :
( ! [V_B: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1084]) ).
thf(1394,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Obounded__lattice @ T_a )
| ! [V_A: $i,V_B: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ T_a )
!= ( c_Orderings_Obot__class_Obot @ T_a ) )
| ( V_B
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1083]) ).
thf(1395,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)],[753]) ).
thf(1396,plain,
( ( ! [V_f: $i,V_A: $i,T_b: $i] :
( ! [T_a: $i] :
( ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1082]) ).
thf(1397,plain,
( ( ! [V_Inf: $i,T_a: $i,V_top: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_inf: $i] :
( ( ( hAPP @ V_Inf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_top )
| ! [V_sup: $i,V_bot: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1081]) ).
thf(1398,plain,
( ( ! [V_Sup: $i,T_a: $i,V_bot: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i] :
( ( ( hAPP @ V_Sup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
= V_bot )
| ! [V_sup: $i,V_top: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1080]) ).
thf(1399,plain,
( ( ! [T_a: $i,V_P: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Collect @ V_P @ T_a ) )
| ! [V_x: $i] :
~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1079]) ).
thf(1400,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)],[748]) ).
thf(1401,plain,
( ( ! [V_P: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [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)],[1078]) ).
thf(1402,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)],[746]) ).
thf(1403,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)],[745]) ).
thf(1404,plain,
( ( ! [T_a: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[744]) ).
thf(1405,plain,
( ( ! [V_A: $i,T_a: $i] :
( ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[743]) ).
thf(1406,plain,
( ( ! [V_P: $i] :
( ! [T_a: $i] :
( ( c_Collect @ V_P @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ! [V_x: $i] :
~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1077]) ).
thf(1407,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)],[741]) ).
thf(1408,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)],[740]) ).
thf(1409,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)],[739]) ).
thf(1410,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)],[738]) ).
thf(1411,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)],[737]) ).
thf(1412,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)],[736]) ).
thf(1413,plain,
( ( ! [T_a: $i,V_A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[735]) ).
thf(1414,plain,
( ( ! [T_a: $i,V_f: $i,V_A: $i,T_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1076]) ).
thf(1415,plain,
( ( ! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[733]) ).
thf(1416,plain,
( ( ! [V_P: $i,V_x: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [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)],[1075]) ).
thf(1417,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)],[1074]) ).
thf(1418,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)],[1073]) ).
thf(1419,plain,
( ( ! [T_a: $i,V_f: $i,T_b: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_Set_Oimage @ V_f @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[729]) ).
thf(1420,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)],[728]) ).
thf(1421,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)],[727]) ).
thf(1422,plain,
( ( ! [V_c: $i,T_a: $i,T_b: $i,V_A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ V_c @ T_a @ T_b ) @ V_A @ T_b @ T_a )
= ( c_Set_Oinsert @ V_c @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_b @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[726]) ).
thf(1423,plain,
( ( ! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1072]) ).
thf(1424,plain,
( ( ! [V_A: $i,V_x: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[724]) ).
thf(1425,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)],[723]) ).
thf(1426,plain,
( ( ! [V_a: $i,V_C: $i,T_a: $i,V_D: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ V_a @ V_C @ T_a ) @ ( c_Set_Oinsert @ V_a @ V_D @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[722]) ).
thf(1427,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)],[721]) ).
thf(1428,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)],[720]) ).
thf(1429,plain,
( ( ! [V_f: $i,V_a: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Set_Oinsert @ V_a @ V_B @ T_b ) @ T_b @ T_a )
= ( c_Set_Oinsert @ ( hAPP @ V_f @ V_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[719]) ).
thf(1430,plain,
( ( ! [V_Inf: $i,V_a: $i,V_A: $i,T_a: $i,V_inf: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_sup: $i] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) )
= ( hAPP @ ( hAPP @ V_inf @ V_a ) @ ( hAPP @ V_Inf @ V_A ) ) )
| ! [V_bot: $i,V_top: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1071]) ).
thf(1431,plain,
( ( ! [V_Sup: $i,V_a: $i,V_A: $i,T_a: $i,V_sup: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ V_A @ T_a ) )
= ( hAPP @ ( hAPP @ V_sup @ V_a ) @ ( hAPP @ V_Sup @ V_A ) ) )
| ! [V_bot: $i,V_top: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1070]) ).
thf(1432,plain,
( ( ! [V_a: $i,V_A: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_a @ V_A @ T_a ) )
| ! [V_b: $i] :
( ( 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)],[1069]) ).
thf(1433,plain,
( ( ! [V_B: $i,V_a: $i,T_a: $i] : ( c_lessequals @ V_B @ ( c_Set_Oinsert @ V_a @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[715]) ).
thf(1434,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)],[714]) ).
thf(1435,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)],[713]) ).
thf(1436,plain,
( ( ! [V_A: $i,V_b: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_b @ V_B @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[712]) ).
thf(1437,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_x: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1068]) ).
thf(1438,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)],[710]) ).
thf(1439,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)],[709]) ).
thf(1440,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)],[708]) ).
thf(1441,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 ) )
| ( V_A = V_B )
| ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1067]) ).
thf(1442,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)],[706]) ).
thf(1443,plain,
( ( ! [V_G: $i,T_a: $i,V_P: $i,V_Q: $i,V_Procs: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ V_Q @ tc_Com_Opname @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ V_Procs @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_G @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ V_Q @ tc_Com_Opname @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ V_Procs @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ V_Q @ tc_Com_Opname @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ V_Procs @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[705]) ).
thf(1444,plain,
( ( ! [V_pname_H: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(copy,[status(thm)],[1066]) ).
thf(1445,plain,
( ( ! [V_fun: $i,V_com: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(copy,[status(thm)],[1065]) ).
thf(1446,plain,
( ( ! [V_pname_H: $i,V_fun: $i,V_com1: $i,V_com2: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 ) ) )
= $true ),
inference(copy,[status(thm)],[1064]) ).
thf(1447,plain,
( ( ! [V_fun: $i,V_com1: $i,V_com2: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 )
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(copy,[status(thm)],[1063]) ).
thf(1448,plain,
( ( ! [V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) ) )
= $true ),
inference(copy,[status(thm)],[1062]) ).
thf(1449,plain,
( ( ! [V_c: $i,V_s: $i,V_n: $i,V_s_H: $i] :
( ( c_Natural_Oevaln @ V_c @ V_s @ ( c_Suc @ V_n ) @ V_s_H )
| ~ ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_s_H ) ) )
= $true ),
inference(copy,[status(thm)],[699]) ).
thf(1450,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_D @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[698]) ).
thf(1451,plain,
( ( ! [V_c2: $i,V_s: $i,V_n: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c2 @ V_s @ V_n @ V_t )
| ! [V_b: $i] :
( ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ! [V_c1: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[1061]) ).
thf(1452,plain,
( ( ! [V_b: $i,V_c0: $i,V_c1: $i,V_s: $i,V_n: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ V_b @ V_c0 @ V_c1 ) @ V_s @ V_n @ V_s1 )
| ~ ( c_Natural_Oevaln @ V_c1 @ V_s @ V_n @ V_s1 )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[696]) ).
thf(1453,plain,
( ( ! [V_fun: $i,V_com: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OWhile @ V_fun @ V_com )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) ) )
= $true ),
inference(copy,[status(thm)],[1060]) ).
thf(1454,plain,
( ( ! [V_s: $i] : ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ V_s @ V_s ) )
= $true ),
inference(copy,[status(thm)],[694]) ).
thf(1455,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( V_A = V_B )
| ! [T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1059]) ).
thf(1456,plain,
( ( ! [V_u: $i,V_t: $i] :
( ( V_u = V_t )
| ! [V_c: $i,V_s: $i] :
( ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_u )
| ~ ( c_Natural_Oevalc @ V_c @ V_s @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[1058]) ).
thf(1457,plain,
( ( ! [V_A: $i,V_B: $i] :
( ( V_A = V_B )
| ! [T_a: $i] :
( ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1057]) ).
thf(1458,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1056]) ).
thf(1459,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1055]) ).
thf(1460,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1054]) ).
thf(1461,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1053]) ).
thf(1462,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1052]) ).
thf(1463,plain,
( ( ! [V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(copy,[status(thm)],[1051]) ).
thf(1464,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1050]) ).
thf(1465,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1049]) ).
thf(1466,plain,
( ( ! [T_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i,V_y: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1048]) ).
thf(1467,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_B )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[681]) ).
thf(1468,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_B @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[680]) ).
thf(1469,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
!= V_B )
| ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1047]) ).
thf(1470,plain,
( ( ! [V_s: $i,V_n: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ V_s @ V_n @ V_s ) )
= $true ),
inference(copy,[status(thm)],[678]) ).
thf(1471,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1046]) ).
thf(1472,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1045]) ).
thf(1473,plain,
( ( ! [V_Q: $i,V_Z: $i,V_s_H: $i,V_c: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_Q @ V_Z ) @ V_s_H ) )
| ! [V_n: $i] :
( ~ ( c_Natural_Oevaln @ V_c @ V_s @ V_n @ V_s_H )
| ! [V_P: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_Z ) @ V_s ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ t_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1044]) ).
thf(1474,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)],[674]) ).
thf(1475,plain,
( ( ! [V_c2: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c2 @ V_s @ V_t )
| ! [V_b: $i] :
( ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ! [V_c1: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) @ V_s @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[1043]) ).
thf(1476,plain,
( ( ! [V_b: $i,V_c0: $i,V_c1: $i,V_s: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c0 @ V_c1 ) @ V_s @ V_s1 )
| ~ ( c_Natural_Oevalc @ V_c1 @ V_s @ V_s1 )
| ( hBOOL @ ( hAPP @ V_b @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[672]) ).
thf(1477,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)],[671]) ).
thf(1478,plain,
( ( ! [V_c2: $i] :
( ( c_Com_OWT @ V_c2 )
| ! [V_c1: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1042]) ).
thf(1479,plain,
( ( ! [V_c1: $i] :
( ( c_Com_OWT @ V_c1 )
| ! [V_c2: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1041]) ).
thf(1480,plain,
( ( ! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ! [V_A: $i,V_x: $i] :
( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ V_A @ T_a ) @ V_x @ T_a )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1040]) ).
thf(1481,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) )
| ( c_lessequals @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1039]) ).
thf(1482,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a ) )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1038]) ).
thf(1483,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_f4: $i,V_f5: $i,V_f6: $i,V_f7: $i,V_f8: $i,V_loc: $i,V_fun: $i,V_com: $i,T_a: $i] :
( ( c_Com_Ocom_Ocom__case @ V_f1 @ V_f2 @ V_f3 @ V_f4 @ V_f5 @ V_f6 @ V_f7 @ V_f8 @ ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ V_f3 @ V_loc ) @ V_fun ) @ V_com ) ) )
= $true ),
inference(copy,[status(thm)],[665]) ).
thf(1484,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_f4: $i,V_f5: $i,V_f6: $i,V_f7: $i,V_f8: $i,V_fun: $i,V_com: $i,T_a: $i] :
( ( c_Com_Ocom_Ocom__case @ V_f1 @ V_f2 @ V_f3 @ V_f4 @ V_f5 @ V_f6 @ V_f7 @ V_f8 @ ( c_Com_Ocom_OWhile @ V_fun @ V_com ) @ T_a )
= ( hAPP @ ( hAPP @ V_f6 @ V_fun ) @ V_com ) ) )
= $true ),
inference(copy,[status(thm)],[664]) ).
thf(1485,plain,
( ( ! [V_A: $i,V_B: $i,T_a: $i,V_C: $i,V_D: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_C @ V_D @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_B @ V_D @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[663]) ).
thf(1486,plain,
( ( ! [V_f: $i,V_g: $i,V_h: $i,T_d: $i,T_c: $i,T_a: $i,T_b: $i] :
( ( c_Fun_Ocomp @ V_f @ ( c_Fun_Ocomp @ V_g @ V_h @ T_d @ T_c @ T_a ) @ T_c @ T_b @ T_a )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ V_f @ V_g @ T_c @ T_b @ T_d ) @ V_h @ T_d @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[662]) ).
thf(1487,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)],[1037]) ).
thf(1488,plain,
( ( ! [V_f: $i,V_g: $i,T_c: $i,T_b: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_c @ T_b @ t_a ) @ v_x )
= ( hAPP @ V_f @ ( hAPP @ V_g @ v_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[660]) ).
thf(1489,plain,
( ( ! [V_x: $i,V_A: $i,T_a: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ V_x @ V_A @ T_a ) @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[659]) ).
thf(1490,plain,
( ( ! [V_f: $i,V_g: $i,V_A: $i,T_c: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Set_Oimage @ V_g @ V_A @ T_c @ T_b ) @ T_b @ T_a )
= ( c_Set_Oimage @ ( c_COMBB @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_A @ T_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[658]) ).
thf(1491,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_loc_H: $i,V_fun_H: $i,V_com_H: $i] :
( ( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) )
| ( V_com = V_com_H ) ) )
= $true ),
inference(copy,[status(thm)],[1036]) ).
thf(1492,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_loc_H: $i,V_fun_H: $i] :
( ! [V_com_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) )
| ( V_fun = V_fun_H ) ) )
= $true ),
inference(copy,[status(thm)],[1035]) ).
thf(1493,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_loc_H: $i] :
( ! [V_fun_H: $i,V_com_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OLocal @ V_loc_H @ V_fun_H @ V_com_H ) )
| ( V_loc = V_loc_H ) ) )
= $true ),
inference(copy,[status(thm)],[1034]) ).
thf(1494,plain,
( ( ! [V_c0: $i,V_c1: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ V_c0 @ V_c1 ) )
| ~ ( c_Com_OWT @ V_c1 )
| ~ ( c_Com_OWT @ V_c0 ) ) )
= $true ),
inference(copy,[status(thm)],[654]) ).
thf(1495,plain,
( ( ! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) ) )
= $true ),
inference(copy,[status(thm)],[1033]) ).
thf(1496,plain,
( ( ! [V_f: $i,V_g: $i,T_c: $i,T_a: $i,T_b: $i,V_r: $i] :
( ( c_Set_Oimage @ ( c_Fun_Ocomp @ V_f @ V_g @ T_c @ T_a @ T_b ) @ V_r @ T_b @ T_a )
= ( c_Set_Oimage @ V_f @ ( c_Set_Oimage @ V_g @ V_r @ T_b @ T_c ) @ T_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[652]) ).
thf(1497,plain,
( ( ! [V_fun_H: $i,V_com_H: $i,V_com1: $i,V_com2: $i] :
( ( c_Com_Ocom_OWhile @ V_fun_H @ V_com_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(copy,[status(thm)],[1032]) ).
thf(1498,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)],[650]) ).
thf(1499,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)],[649]) ).
thf(1500,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)],[648]) ).
thf(1501,plain,
( ( ! [V_b: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ! [V_t: $i] :
( ( V_t = V_s )
| ! [V_c: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[1031]) ).
thf(1502,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(copy,[status(thm)],[1030]) ).
thf(1503,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1029]) ).
thf(1504,plain,
( ( ! [T_a: $i,V_y: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_y @ V_z @ T_a )
| ! [V_x: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1028]) ).
thf(1505,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1027]) ).
thf(1506,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1026]) ).
thf(1507,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_a: $i] :
( ! [V_b: $i] : ( c_lessequals @ V_x @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1025]) ).
thf(1508,plain,
( ( ! [T_a: $i,V_b: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_lessequals @ V_b @ V_x @ T_a )
| ! [V_a: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1024]) ).
thf(1509,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ T_a )
| ! [V_x: $i] :
( ( c_lessequals @ V_a @ V_x @ T_a )
| ! [V_b: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1023]) ).
thf(1510,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1022]) ).
thf(1511,plain,
( ( ! [V_B: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_A: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) @ V_C @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1021]) ).
thf(1512,plain,
( ( ! [T_a: $i,V_z: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] :
( ( c_lessequals @ V_z @ V_x @ T_a )
| ! [V_y: $i] :
( ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1020]) ).
thf(1513,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_z: $i] :
( ( c_lessequals @ V_x @ V_z @ T_a )
| ! [V_y: $i] :
( ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1019]) ).
thf(1514,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1018]) ).
thf(1515,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_c @ V_B @ T_a ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( c_in @ V_c @ V_A @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1017]) ).
thf(1516,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_lessequals @ V_x @ V_x @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[632]) ).
thf(1517,plain,
( ( ! [V_x: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_x @ V_B @ T_a ) )
| ! [V_A: $i] :
( ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1016]) ).
thf(1518,plain,
( ( ! [V_t: $i,V_B: $i,T_a: $i] :
( ( hBOOL @ ( c_in @ V_t @ V_B @ T_a ) )
| ! [V_A: $i] :
( ~ ( hBOOL @ ( c_in @ V_t @ V_A @ T_a ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1015]) ).
thf(1519,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_lessequals @ V_A @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) )
= $true ),
inference(copy,[status(thm)],[629]) ).
thf(1520,plain,
( ( ! [V_A: $i,V_C: $i,T_a: $i] :
( ( c_lessequals @ V_A @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ! [V_B: $i] :
( ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1014]) ).
thf(1521,plain,
( ( ! [V_Q: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ! [V_P: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ! [T_a: $i] :
~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1013]) ).
thf(1522,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1012]) ).
thf(1523,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1011]) ).
thf(1524,plain,
( ( ! [V_Q: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_Q @ V_x ) )
| ! [V_P: $i] :
( ! [T_a: $i] :
~ ( c_lessequals @ V_P @ V_Q @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1010]) ).
thf(1525,plain,
( ( ! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(copy,[status(thm)],[1009]) ).
thf(1526,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ( c_lessequals @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1008]) ).
thf(1527,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_a: $i,V_b: $i] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ V_a @ V_b @ T_a )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1007]) ).
thf(1528,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_f4: $i,V_f5: $i,V_f6: $i,V_f7: $i,V_f8: $i,V_fun: $i,V_com1: $i,V_com2: $i,T_a: $i] :
( ( c_Com_Ocom_Ocom__case @ V_f1 @ V_f2 @ V_f3 @ V_f4 @ V_f5 @ V_f6 @ V_f7 @ V_f8 @ ( c_Com_Ocom_OCond @ V_fun @ V_com1 @ V_com2 ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ V_f5 @ V_fun ) @ V_com1 ) @ V_com2 ) ) )
= $true ),
inference(copy,[status(thm)],[620]) ).
thf(1529,plain,
( ( ! [V_a: $i,V_b: $i,T_c: $i,T_b: $i,T_a: $i,V_c: $i,V_d: $i] :
( ! [T_d: $i] :
( ( c_Fun_Ocomp @ V_a @ V_b @ T_c @ T_b @ T_a )
!= ( c_Fun_Ocomp @ V_c @ V_d @ T_d @ T_b @ T_a ) )
| ! [V_v: $i] :
( ( hAPP @ V_a @ ( hAPP @ V_b @ V_v ) )
= ( hAPP @ V_c @ ( hAPP @ V_d @ V_v ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1006]) ).
thf(1530,plain,
( ( ! [V_f: $i,V_g: $i,V_x: $i,V_f_H: $i,V_g_H: $i,V_x_H: $i,T_b: $i,T_a: $i,T_c: $i] :
( ( ( hAPP @ V_f @ ( hAPP @ V_g @ V_x ) )
!= ( hAPP @ V_f_H @ ( hAPP @ V_g_H @ V_x_H ) ) )
| ! [T_d: $i,T_e: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ V_f @ V_g @ T_b @ T_a @ T_c ) @ V_x )
= ( hAPP @ ( c_Fun_Ocomp @ V_f_H @ V_g_H @ T_d @ T_a @ T_e ) @ V_x_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[1005]) ).
thf(1531,plain,
( ( ! [V_b: $i,V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ V_b @ V_s ) )
| ( V_t = V_s )
| ! [V_c: $i,V_n: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) @ V_s @ V_n @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[1004]) ).
thf(1532,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)],[616]) ).
thf(1533,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)],[615]) ).
thf(1534,plain,
( ( ! [V_B: $i,V_C: $i,V_A: $i,T_a: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_B @ ( c_HOL_Ominus__class_Ominus @ V_C @ V_A @ ( tc_fun @ T_a @ tc_bool ) ) @ ( tc_fun @ T_a @ tc_bool ) )
= V_A )
| ~ ( c_lessequals @ V_B @ V_C @ ( tc_fun @ T_a @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[614]) ).
thf(1535,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ! [V_x_H: $i,V_y_H: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y_H @ V_x_H @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1003]) ).
thf(1536,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ! [V_x_H: $i,V_y_H: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_y_H @ V_x_H @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1002]) ).
thf(1537,plain,
( ( ! [V_f: $i,V_A: $i,T_a: $i,T_b: $i,V_B: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_A @ T_a @ T_b ) @ ( c_Set_Oimage @ V_f @ V_B @ T_a @ T_b ) @ ( tc_fun @ T_b @ tc_bool ) )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[611]) ).
thf(1538,plain,
( ( ! [V_x: $i,V_A: $i,T_b: $i] :
( ~ ( c_lessequals @ V_x @ V_A @ ( tc_fun @ T_b @ tc_bool ) )
| ! [V_f: $i,T_a: $i] : ( c_lessequals @ ( c_Set_Oimage @ V_f @ V_x @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1001]) ).
thf(1539,plain,
( ( ! [V_c2: $i,V_s: $i,V_n: $i,V_t: $i] :
( ( c_Natural_Oevaln @ V_c2 @ V_s @ V_n @ V_t )
| ! [V_c1: $i] :
( ( c_Natural_Oevaln @ V_c1 @ V_s @ V_n @ V_t )
| ! [V_b: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) @ V_s @ V_n @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[1000]) ).
thf(1540,plain,
( ( ! [V_f: $i,V_A: $i,V_B: $i,T_b: $i,T_a: $i] :
( ( c_Set_Oimage @ V_f @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_A @ V_B @ ( tc_fun @ T_b @ tc_bool ) ) @ T_b @ T_a )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ V_f @ V_A @ T_b @ T_a ) @ ( c_Set_Oimage @ V_f @ V_B @ T_b @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[608]) ).
thf(1541,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) ) )
= $true ),
inference(copy,[status(thm)],[999]) ).
thf(1542,plain,
( ( ! [V_c2: $i,V_s: $i,V_t: $i] :
( ( c_Natural_Oevalc @ V_c2 @ V_s @ V_t )
| ! [V_c1: $i] :
( ( c_Natural_Oevalc @ V_c1 @ V_s @ V_t )
| ! [V_b: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) @ V_s @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[998]) ).
thf(1543,plain,
( ( ! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ! [V_x: $i,V_A: $i] :
( ( c_lessequals @ V_x @ ( c_Complete__Lattice_OSup__class_OSup @ V_A @ T_a ) @ T_a )
| ~ ( hBOOL @ ( c_in @ V_x @ V_A @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[997]) ).
thf(1544,plain,
( ( ! [V_c2: $i] :
( ( c_Com_OWT @ V_c2 )
| ! [V_b: $i,V_c1: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[996]) ).
thf(1545,plain,
( ( ! [V_c1: $i] :
( ( c_Com_OWT @ V_c1 )
| ! [V_b: $i,V_c2: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ V_b @ V_c1 @ V_c2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[995]) ).
thf(1546,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)],[994]) ).
thf(1547,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_y: $i,V_x: $i] :
( ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[993]) ).
thf(1548,plain,
( ( ! [V_pname_H: $i,V_loc: $i,V_fun: $i,V_com: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com ) ) )
= $true ),
inference(copy,[status(thm)],[992]) ).
thf(1549,plain,
( ( ! [V_pname_H: $i,V_fun: $i,V_com: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OWhile @ V_fun @ V_com ) ) )
= $true ),
inference(copy,[status(thm)],[991]) ).
thf(1550,plain,
( ( ! [V_vname_H: $i,V_pname_H: $i,V_fun_H: $i,V_pname: $i] :
( ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H )
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname ) ) )
= $true ),
inference(copy,[status(thm)],[990]) ).
thf(1551,plain,
( ( ! [V_pname_H: $i,V_com1: $i,V_com2: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H )
!= ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 ) ) )
= $true ),
inference(copy,[status(thm)],[989]) ).
thf(1552,plain,
( ( ! [V_com1: $i,V_com2: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OSemi @ V_com1 @ V_com2 )
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(copy,[status(thm)],[988]) ).
thf(1553,plain,
( ( ! [V_loc: $i,V_fun: $i,V_com: $i,V_pname_H: $i] :
( ( c_Com_Ocom_OLocal @ V_loc @ V_fun @ V_com )
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(copy,[status(thm)],[987]) ).
thf(1554,plain,
( ( ! [V_pname: $i,V_vname_H: $i,V_pname_H: $i,V_fun_H: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ V_pname )
!= ( c_Com_Ocom_OCall @ V_vname_H @ V_pname_H @ V_fun_H ) ) )
= $true ),
inference(copy,[status(thm)],[986]) ).
thf(1555,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_f4: $i,V_f5: $i,V_f6: $i,V_f7: $i,V_f8: $i,V_pname: $i,T_a: $i] :
( ( c_Com_Ocom_Ocom__case @ V_f1 @ V_f2 @ V_f3 @ V_f4 @ V_f5 @ V_f6 @ V_f7 @ V_f8 @ ( hAPP @ c_Com_Ocom_OBODY @ V_pname ) @ T_a )
= ( hAPP @ V_f7 @ V_pname ) ) )
= $true ),
inference(copy,[status(thm)],[593]) ).
thf(1556,plain,
( ( ! [V_pname_H: $i] :
( c_Com_Ocom_OSKIP
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H ) ) )
= $true ),
inference(copy,[status(thm)],[985]) ).
thf(1557,plain,
( ( ! [T_a: $i,V_P: $i,V_pn: $i,V_Q: $i] : ( c_Hoare__Mirabelle_Otriple__valid @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) @ V_Q ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[591]) ).
thf(1558,plain,
( ( ! [V_P: $i,V_f1: $i,V_xa: $i,V_xb: $i,V_xc: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ V_f1 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ V_xa ) @ V_xb ) @ V_xc ) @ t_b @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ ( hAPP @ V_f1 @ V_xa ) @ V_xb ) @ V_xc ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[590]) ).
thf(1559,plain,
( ( ! [V_P: $i,V_f1: $i,V_fun1: $i,V_com: $i,V_fun2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ V_f1 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ V_fun1 ) @ V_com ) @ V_fun2 ) @ t_b @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ ( hAPP @ V_f1 @ V_fun1 ) @ V_com ) @ V_fun2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[589]) ).
thf(1560,plain,
( ( ! [V_f1: $i,T_b: $i,V_fun1: $i,V_com: $i,V_fun2: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ V_f1 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b ) @ V_fun1 ) @ V_com ) @ V_fun2 ) @ T_b @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ V_f1 @ V_fun1 ) @ V_com ) @ V_fun2 ) ) )
= $true ),
inference(copy,[status(thm)],[588]) ).
thf(1561,plain,
( ( ! [V_f1: $i,T_b: $i,V_fun1: $i,V_com: $i,V_fun2: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ V_f1 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_b ) @ V_fun1 ) @ V_com ) @ V_fun2 ) @ T_b @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ V_f1 @ V_fun1 ) @ V_com ) @ V_fun2 ) ) )
= $true ),
inference(copy,[status(thm)],[587]) ).
thf(1562,plain,
( ( ! [V_G: $i,V_ts: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ! [V_ts_H: $i] :
( ~ ( c_lessequals @ V_ts @ V_ts_H @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts_H @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[984]) ).
thf(1563,plain,
( ( ! [V_G: $i,V_ts: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ! [V_G_H: $i] :
( ~ ( c_lessequals @ V_G_H @ V_G @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G_H @ V_ts @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[983]) ).
thf(1564,plain,
( ( ! [V_G: $i,V_ts: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ~ ( c_lessequals @ V_ts @ V_G @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[584]) ).
thf(1565,plain,
( ( ( hAPP @ ( c_COMBI @ t_a ) @ v_P )
= v_P )
= $true ),
inference(copy,[status(thm)],[583]) ).
thf(1566,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ ( 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 ) ) @ ( 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)],[582]) ).
thf(1567,plain,
( ( ! [V_G: $i,T_a: $i,V_P: $i,V_pn: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ ( hAPP @ V_P @ V_pn ) ) @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) @ ( hAPP @ V_Q @ V_pn ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ! [V_Procs: $i] :
( ~ ( hBOOL @ ( c_in @ V_pn @ V_Procs @ tc_Com_Opname ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ V_G @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ V_Q @ tc_Com_Opname @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ V_Procs @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) ) @ V_Q @ tc_Com_Opname @ ( tc_fun @ T_a @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ V_Procs @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[982]) ).
thf(1568,plain,
( ( ! [V_pn: $i] :
( ( ( hAPP @ c_Com_Obody @ V_pn )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) )
| ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) ) )
= $true ),
inference(copy,[status(thm)],[981]) ).
thf(1569,plain,
( ( ( hAPP @ ( c_COMBB @ v_P @ v_Q @ t_a @ t_b @ t_c ) @ v_R )
= ( hAPP @ v_P @ ( hAPP @ v_Q @ v_R ) ) )
= $true ),
inference(copy,[status(thm)],[579]) ).
thf(1570,plain,
( ( ( hAPP @ ( c_COMBS @ v_P @ v_Q @ t_a @ t_b @ t_c ) @ v_R )
= ( hAPP @ ( hAPP @ v_P @ v_R ) @ ( hAPP @ v_Q @ v_R ) ) )
= $true ),
inference(copy,[status(thm)],[578]) ).
thf(1571,plain,
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ v_P @ t_a @ t_b @ t_c ) @ v_Q ) @ v_R )
= ( hAPP @ ( hAPP @ v_P @ v_R ) @ v_Q ) )
= $true ),
inference(copy,[status(thm)],[577]) ).
thf(1572,plain,
( ( ! [T_a: $i,V_x: $i] :
( ( hAPP @ ( c_Option_Othe @ T_a ) @ ( c_Option_Ooption_OSome @ V_x @ T_a ) )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[576]) ).
thf(1573,plain,
( ( ! [V_G: $i,T_a: $i,V_P: $i,V_b: $i,V_c: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( c_Com_Ocom_OWhile @ V_b @ V_c ) ) @ ( c_Hoare__Mirabelle_Opeek__and @ V_P @ ( c_Fun_Ocomp @ c_Not @ V_b @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ T_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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ ( c_Hoare__Mirabelle_Opeek__and @ V_P @ V_b @ T_a ) ) @ V_c ) @ V_P ) @ ( 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)],[575]) ).
thf(1574,plain,
( ( ! [V_G: $i,T_a: $i,V_P: $i,V_b: $i,V_c: $i,V_d: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( c_Com_Ocom_OCond @ V_b @ V_c @ V_d ) ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ ( c_Hoare__Mirabelle_Opeek__and @ V_P @ ( c_Fun_Ocomp @ c_Not @ V_b @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ T_a ) ) @ V_d ) @ V_Q ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ ( c_Hoare__Mirabelle_Opeek__and @ V_P @ V_b @ T_a ) ) @ V_c ) @ V_Q ) @ ( 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)],[574]) ).
thf(1575,plain,
( ( ! [V_P: $i,V_s: $i,V_n: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_P ) ) @ V_s @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ V_P @ V_n @ V_s @ V_s1 ) @ V_s1 )
| ~ ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_n @ V_s1 ) ) )
= $true ),
inference(copy,[status(thm)],[573]) ).
thf(1576,plain,
( ( ! [V_pn: $i,V_s0: $i,V_n: $i,V_s1: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) @ V_s0 @ ( c_Suc @ V_n ) @ V_s1 )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_pn ) ) @ V_s0 @ V_n @ V_s1 ) ) )
= $true ),
inference(copy,[status(thm)],[572]) ).
thf(1577,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)],[571]) ).
thf(1578,plain,
( ( ! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a )
= ( c_Orderings_Obot__class_Obot @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[570]) ).
thf(1579,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)],[569]) ).
thf(1580,plain,
( ( ! [V_A: $i,V_x: $i,T_a: $i] :
( ( V_A
= ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
| ( V_A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) )
| ~ ( c_lessequals @ V_A @ ( c_Set_Oinsert @ V_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ ( tc_fun @ T_a @ tc_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[568]) ).
thf(1581,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)],[567]) ).
thf(1582,plain,
( ( ! [V_Inf: $i,V_a: $i,T_a: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= V_a )
| ! [V_bot: $i,V_top: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[980]) ).
thf(1583,plain,
( ( ! [V_Sup: $i,V_a: $i,T_a: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i,V_sup: $i] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) )
= V_a )
| ! [V_bot: $i,V_top: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[979]) ).
thf(1584,plain,
( ( ! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ! [V_a: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ V_a @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[978]) ).
thf(1585,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)],[563]) ).
thf(1586,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)],[562]) ).
thf(1587,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)],[561]) ).
thf(1588,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_a: $i] :
( ( 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)],[977]) ).
thf(1589,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)],[559]) ).
thf(1590,plain,
( ( ! [V_Inf: $i,V_a: $i,V_b: $i,T_a: $i,V_inf: $i,V_Sup: $i,V_less__eq: $i,V_less: $i,V_sup: $i] :
( ( ( hAPP @ V_Inf @ ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
= ( hAPP @ ( hAPP @ V_inf @ V_a ) @ V_b ) )
| ! [V_bot: $i,V_top: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[976]) ).
thf(1591,plain,
( ( ! [V_Sup: $i,V_a: $i,V_b: $i,T_a: $i,V_sup: $i,V_Inf: $i,V_less__eq: $i,V_less: $i,V_inf: $i] :
( ( ( hAPP @ V_Sup @ ( c_Set_Oinsert @ V_a @ ( c_Set_Oinsert @ V_b @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) @ T_a ) )
= ( hAPP @ ( hAPP @ V_sup @ V_a ) @ V_b ) )
| ! [V_bot: $i,V_top: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ V_Inf @ V_Sup @ V_less__eq @ V_less @ V_inf @ V_sup @ V_bot @ V_top @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[975]) ).
thf(1592,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)],[556]) ).
thf(1593,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)],[555]) ).
thf(1594,plain,
( ( ! [V_a: $i,V_b: $i] :
( ( V_a = V_b )
| ! [V_f: $i,T_a: $i] :
~ ( 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)],[974]) ).
thf(1595,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)],[553]) ).
thf(1596,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)],[552]) ).
thf(1597,plain,
( ( ! [V_b: $i,V_a: $i] :
( ( V_b = V_a )
| ! [T_a: $i] :
~ ( 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)],[973]) ).
thf(1598,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)],[550]) ).
thf(1599,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ! [V_a: $i] :
( ( 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)],[972]) ).
thf(1600,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)],[548]) ).
thf(1601,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_a: $i] :
( ( 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)],[971]) ).
thf(1602,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)],[970]) ).
thf(1603,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)],[545]) ).
thf(1604,plain,
( ( ! [T_a: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ T_a )
| ! [V_a: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( 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)],[969]) ).
thf(1605,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_xa: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [V_Z_H: $i,V_x: $i] :
( ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_x ) @ V_c ) @ V_xa ) @ ( 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)],[968]) ).
thf(1606,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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [V_Z_H: $i,V_P_H: $i] :
( ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P_H ) @ V_c ) @ V_Q_H ) @ ( 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)],[967]) ).
thf(1607,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i,V_xa: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [V_Z_H: $i,V_x: $i] :
( ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_x ) @ V_c ) @ V_xa ) @ ( 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)],[966]) ).
thf(1608,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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)],[540]) ).
thf(1609,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [V_x: $i,V_xa: $i] :
( ~ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_x ) @ V_c ) @ V_xa ) @ ( 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)],[965]) ).
thf(1610,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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)],[538]) ).
thf(1611,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [V_Q_H: $i] :
( ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q_H ) @ ( 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)],[964]) ).
thf(1612,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [V_P_H: $i,V_Q_H: $i] :
( ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P_H ) @ V_c ) @ V_Q_H ) @ ( 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)],[963]) ).
thf(1613,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [V_P_H: $i] :
( ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P_H ) @ V_c ) @ V_Q ) @ ( 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)],[962]) ).
thf(1614,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [V_x: $i,V_xa: $i] :
( ~ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_x ) @ V_c ) @ V_xa ) @ ( 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)],[961]) ).
thf(1615,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [V_P_H: $i] :
( ~ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P_H ) @ V_c ) @ V_Q ) @ ( 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)],[960]) ).
thf(1616,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [V_P_H: $i,V_Q_H: $i] :
( ~ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P_H ) @ V_c ) @ V_Q_H ) @ ( 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)],[959]) ).
thf(1617,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [V_Q_H: $i] :
( ~ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q_H ) @ ( 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)],[958]) ).
thf(1618,plain,
( ( ! [V_G: $i,V_P: $i,V_c: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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)],[530]) ).
thf(1619,plain,
( ( ( hAPP @ ( c_COMBK @ v_P @ t_a @ t_b ) @ v_Q )
= v_P )
= $true ),
inference(copy,[status(thm)],[529]) ).
thf(1620,plain,
( ( ! [V_n: $i,T_a: $i,V_P: $i,V_pn: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ V_n ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) @ V_Q ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_pn ) ) ) @ V_Q ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[528]) ).
thf(1621,plain,
( ( ! [V_n: $i,T_a: $i,V_P: $i,V_pn: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ V_n @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_pn ) ) ) @ V_Q ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ V_n ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) @ V_Q ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[527]) ).
thf(1622,plain,
( ( ! [V_pn: $i,V_s0: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) @ V_s0 @ V_s1 )
| ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_pn ) ) @ V_s0 @ V_s1 ) ) )
= $true ),
inference(copy,[status(thm)],[526]) ).
thf(1623,plain,
( ( ! [V_P: $i,V_s: $i,V_s1: $i] :
( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_P ) ) @ V_s @ V_s1 )
| ~ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ V_P ) @ V_s @ V_s1 ) ) )
= $true ),
inference(copy,[status(thm)],[525]) ).
thf(1624,plain,
( ( ! [V_G: $i,T_a: $i,V_P: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ c_Com_Ocom_OSKIP ) @ V_P ) @ ( 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(1625,plain,
( ( ! [V_G: $i,T_a: $i,V_P: $i,V_c: $i,V_d: $i,V_R: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( c_Com_Ocom_OSemi @ V_c @ V_d ) ) @ V_R ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ! [V_Q: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_Q ) @ V_d ) @ V_R ) @ ( 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 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ V_c ) @ V_Q ) @ ( 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)],[957]) ).
thf(1626,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)],[522]) ).
thf(1627,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)],[521]) ).
thf(1628,plain,
( ( ! [V_G: $i,V_ts: $i,T_a: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_ts @ T_a )
| ! [V_G_H: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ V_G_H @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G_H @ V_ts @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[956]) ).
thf(1629,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)],[955]) ).
thf(1630,plain,
( ( ! [T_a: $i,V_fun1: $i,V_com: $i,V_fun2: $i,V_fun1_H: $i,V_com_H: $i,V_fun2_H: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1 ) @ V_com ) @ V_fun2 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1_H ) @ V_com_H ) @ V_fun2_H ) )
| ( V_fun2 = V_fun2_H ) ) )
= $true ),
inference(copy,[status(thm)],[954]) ).
thf(1631,plain,
( ( ! [T_a: $i,V_fun1: $i,V_com: $i,V_fun2: $i,V_fun1_H: $i,V_com_H: $i] :
( ! [V_fun2_H: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1 ) @ V_com ) @ V_fun2 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1_H ) @ V_com_H ) @ V_fun2_H ) )
| ( V_com = V_com_H ) ) )
= $true ),
inference(copy,[status(thm)],[953]) ).
thf(1632,plain,
( ( ! [T_a: $i,V_fun1: $i,V_com: $i,V_fun2: $i,V_fun1_H: $i] :
( ! [V_com_H: $i,V_fun2_H: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1 ) @ V_com ) @ V_fun2 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_fun1_H ) @ V_com_H ) @ V_fun2_H ) )
| ( V_fun1 = V_fun1_H ) ) )
= $true ),
inference(copy,[status(thm)],[952]) ).
thf(1633,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)],[951]) ).
thf(1634,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)],[950]) ).
thf(1635,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)],[949]) ).
thf(1636,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)],[948]) ).
thf(1637,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)],[511]) ).
thf(1638,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)],[510]) ).
thf(1639,plain,
( ( ! [V_G: $i,T_a: $i,V_P: $i,V_pn: $i,V_Q: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ V_G @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) @ V_Q ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ T_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( hAPP @ c_Com_Ocom_OBODY @ V_pn ) ) @ V_Q ) @ V_G @ ( tc_Hoare__Mirabelle_Otriple @ T_a ) ) @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ T_a ) @ V_P ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ V_pn ) ) ) @ V_Q ) @ ( 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)],[509]) ).
thf(1640,plain,
( ( ! [V_A: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ! [V_y: $i] :
( ( V_y = V_x )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ V_y @ V_A @ T_a ) @ V_x ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[947]) ).
thf(1641,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)],[507]) ).
thf(1642,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)],[946]) ).
thf(1643,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)],[505]) ).
thf(1644,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)],[504]) ).
thf(1645,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)],[945]) ).
thf(1646,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)],[502]) ).
thf(1647,plain,
( ( ! [V_pname: $i,V_pname_H: $i] :
( ( ( hAPP @ c_Com_Ocom_OBODY @ V_pname )
!= ( hAPP @ c_Com_Ocom_OBODY @ V_pname_H ) )
| ( V_pname = V_pname_H ) ) )
= $true ),
inference(copy,[status(thm)],[944]) ).
thf(1648,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)],[500]) ).
thf(1649,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)],[499]) ).
thf(1650,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)],[498]) ).
thf(1651,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)],[497]) ).
thf(1652,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)],[496]) ).
thf(1653,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)],[495]) ).
thf(1654,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)],[494]) ).
thf(1655,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)],[493]) ).
thf(1656,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)],[492]) ).
thf(1657,plain,
( ( class_Lattices_Oupper__semilattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[491]) ).
thf(1658,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[490]) ).
thf(1659,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[489]) ).
thf(1660,plain,
( ( class_Lattices_Olattice @ tc_nat )
= $true ),
inference(copy,[status(thm)],[488]) ).
thf(1661,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[487]) ).
thf(1662,plain,
( ( class_Orderings_Obot @ tc_nat )
= $true ),
inference(copy,[status(thm)],[486]) ).
thf(1663,plain,
( ( class_HOL_Ominus @ tc_nat )
= $true ),
inference(copy,[status(thm)],[485]) ).
thf(1664,plain,
( ( class_HOL_Oord @ tc_nat )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(1665,plain,
( ( class_Complete__Lattice_Ocomplete__lattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(1666,plain,
( ( class_Lattices_Oupper__semilattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[482]) ).
thf(1667,plain,
( ( class_Lattices_Obounded__lattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(1668,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[480]) ).
thf(1669,plain,
( ( class_Lattices_Olattice @ tc_bool )
= $true ),
inference(copy,[status(thm)],[479]) ).
thf(1670,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[478]) ).
thf(1671,plain,
( ( class_Orderings_Obot @ tc_bool )
= $true ),
inference(copy,[status(thm)],[477]) ).
thf(1672,plain,
( ( class_HOL_Ominus @ tc_bool )
= $true ),
inference(copy,[status(thm)],[476]) ).
thf(1673,plain,
( ( class_HOL_Oord @ tc_bool )
= $true ),
inference(copy,[status(thm)],[475]) ).
thf(1674,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[474]) ).
thf(1675,plain,
( ( ! [V_X: $i,V_Y: $i] :
( ( V_X = V_Y )
| ! [T_a: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[943]) ).
thf(1676,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[942]) ).
thf(1677,plain,
( ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ v_P ) @ ( hAPP @ c_Com_Ocom_OBODY @ v_pn ) ) @ v_Q ) @ v_G @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ v_P ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) ) @ v_Q ) @ ( 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)],[1208]) ).
thf(1678,plain,
! [SV1: $i] :
( ( ! [SY1783: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV1 )
| ! [SY1784: $i,SY1785: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1783 @ SY1784 @ SV1 ) @ SY1785 @ SV1 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY1783 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1784 @ SY1785 @ SV1 ) @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1679,plain,
! [SV2: $i] :
( ( ! [SY1786: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV2 )
| ! [SY1787: $i,SY1788: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY1786 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1787 @ SY1788 @ SV2 ) @ SV2 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY1787 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1786 @ SY1788 @ SV2 ) @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1680,plain,
! [SV3: $i] :
( ( ! [SY1789: $i] :
( ~ ( class_Lattices_Olattice @ SV3 )
| ! [SY1790: $i,SY1791: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY1789 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1790 @ SY1791 @ SV3 ) @ SV3 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY1790 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1789 @ SY1791 @ SV3 ) @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1681,plain,
! [SV4: $i] :
( ( ! [SY1792: $i] :
( ~ ( class_Lattices_Olattice @ SV4 )
| ! [SY1793: $i,SY1794: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1792 @ SY1793 @ SV4 ) @ SY1794 @ SV4 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY1792 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1793 @ SY1794 @ SV4 ) @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1682,plain,
! [SV5: $i] :
( ( ! [SY1795: $i] :
( ! [SY1796: $i] : ( c_Com_OWT @ ( c_Com_Ocom_OCall @ SV5 @ SY1795 @ SY1796 ) )
| ~ ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ SY1795 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1683,plain,
! [SV6: $i] :
( ( ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ SV6 ) )
| ! [SY1797: $i,SY1798: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCall @ SY1797 @ SV6 @ SY1798 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1684,plain,
! [SV7: $i] :
( ( ! [SY1799: $i,SY1800: $i,SY1801: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV7 @ SY1799 @ ( tc_fun @ SY1800 @ tc_bool ) ) @ SY1801 @ ( tc_fun @ SY1800 @ tc_bool ) )
| ~ ( c_lessequals @ SY1799 @ SY1801 @ ( tc_fun @ SY1800 @ tc_bool ) )
| ~ ( c_lessequals @ SV7 @ SY1801 @ ( tc_fun @ SY1800 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1685,plain,
! [SV8: $i] :
( ( ! [SY1802: $i,SY1803: $i] : ( c_lessequals @ SV8 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1802 @ SV8 @ ( tc_fun @ SY1803 @ tc_bool ) ) @ ( tc_fun @ SY1803 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1216]) ).
thf(1686,plain,
! [SV9: $i] :
( ( ! [SY1804: $i,SY1805: $i] : ( c_lessequals @ SV9 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV9 @ SY1804 @ ( tc_fun @ SY1805 @ tc_bool ) ) @ ( tc_fun @ SY1805 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1687,plain,
! [SV10: $i] :
( ( ! [SY1806: $i,SY1807: $i,SY1808: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV10 @ SY1806 @ ( tc_fun @ SY1807 @ tc_bool ) ) @ SY1808 @ ( tc_fun @ SY1807 @ tc_bool ) )
| ~ ( c_lessequals @ SY1806 @ SY1808 @ ( tc_fun @ SY1807 @ tc_bool ) )
| ~ ( c_lessequals @ SV10 @ SY1808 @ ( tc_fun @ SY1807 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1688,plain,
! [SV11: $i] :
( ( ! [SY1809: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV11 )
| ! [SY1810: $i,SY1811: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1809 @ SY1810 @ SV11 ) @ SY1811 @ SV11 )
| ~ ( c_lessequals @ SY1810 @ SY1811 @ SV11 )
| ~ ( c_lessequals @ SY1809 @ SY1811 @ SV11 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1689,plain,
! [SV12: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV12 )
| ! [SY1812: $i,SY1813: $i] : ( c_lessequals @ SY1812 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1812 @ SY1813 @ SV12 ) @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1690,plain,
! [SV13: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV13 )
| ! [SY1814: $i,SY1815: $i] : ( c_lessequals @ SY1814 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1815 @ SY1814 @ SV13 ) @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1691,plain,
! [SV14: $i] :
( ( ! [SY1816: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV14 )
| ! [SY1817: $i,SY1818: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1816 @ SY1817 @ SV14 ) @ SY1818 @ SV14 )
| ~ ( c_lessequals @ SY1817 @ SY1818 @ SV14 )
| ~ ( c_lessequals @ SY1816 @ SY1818 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1692,plain,
! [SV15: $i] :
( ( ! [SY1819: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV15 )
| ! [SY1820: $i,SY1821: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1819 @ SY1820 @ SV15 ) @ SY1821 @ SV15 )
| ~ ( c_lessequals @ SY1820 @ SY1821 @ SV15 )
| ~ ( c_lessequals @ SY1819 @ SY1821 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1693,plain,
! [SV16: $i] :
( ( ~ ( class_Lattices_Olattice @ SV16 )
| ! [SY1822: $i,SY1823: $i] : ( c_lessequals @ SY1822 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1823 @ SY1822 @ SV16 ) @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1694,plain,
! [SV17: $i] :
( ( ~ ( class_Lattices_Olattice @ SV17 )
| ! [SY1824: $i,SY1825: $i] : ( c_lessequals @ SY1824 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1824 @ SY1825 @ SV17 ) @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1695,plain,
! [SV18: $i] :
( ( ! [SY1826: $i,SY1827: $i,SY1828: $i,SY1829: $i,SY1830: $i,SY1831: $i,SY1832: $i,SY1833: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV18 @ SY1826 @ ( c_COMBC @ SY1827 @ SY1828 @ SY1828 @ tc_bool ) @ ( c_COMBC @ SY1829 @ SY1828 @ SY1828 @ tc_bool ) @ SY1830 @ SY1831 @ SY1832 @ SY1833 @ SY1828 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SY1826 @ SV18 @ SY1827 @ SY1829 @ SY1831 @ SY1830 @ SY1833 @ SY1832 @ SY1828 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1696,plain,
! [SV19: $i] :
( ( ! [SY1834: $i,SY1835: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV19 @ ( c_HOL_Ominus__class_Ominus @ SY1834 @ SV19 @ ( tc_fun @ SY1835 @ tc_bool ) ) @ ( tc_fun @ SY1835 @ tc_bool ) )
= SY1834 )
| ~ ( c_lessequals @ SV19 @ SY1834 @ ( tc_fun @ SY1835 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1697,plain,
! [SV20: $i] :
( ( ! [SY1836: $i,SY1837: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCond @ SV20 @ SY1836 @ SY1837 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1698,plain,
! [SV21: $i] :
( ( ! [SY1838: $i,SY1839: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV21 @ SY1838 @ ( tc_fun @ SY1839 @ tc_bool ) ) @ SV21 @ ( tc_fun @ SY1839 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1699,plain,
! [SV22: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV22 )
| ~ ( class_Int_Onumber__ring @ SV22 )
| ! [SY1840: $i,SY1841: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SY1840 @ SY1841 @ SV22 )
!= ( c_HOL_Ozero__class_Ozero @ SV22 ) )
| ( SY1840 = SY1841 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1700,plain,
! [SV23: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV23 )
| ! [SY1842: $i,SY1843: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SY1842 @ SY1843 @ SV23 )
!= ( c_HOL_Ozero__class_Ozero @ SV23 ) )
| ( SY1842 = SY1843 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1701,plain,
! [SV24: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV24 )
| ! [SY1844: $i,SY1845: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SY1844 @ SY1845 @ SV24 )
!= ( c_HOL_Ozero__class_Ozero @ SV24 ) )
| ( SY1844 = SY1845 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1702,plain,
! [SV25: $i] :
( ( ! [SY1846: $i,SY1847: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ SV25 @ SY1846 @ SY1847 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1847 @ tc_bool ) ) @ SY1847 @ SY1846 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1846 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1703,plain,
! [SV26: $i] :
( ( ! [SY1848: $i] :
( ! [SY1849: $i] : ( hBOOL @ ( c_in @ SV26 @ ( c_Collect @ SY1848 @ SY1849 ) @ SY1849 ) )
| ~ ( hBOOL @ ( hAPP @ SY1848 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1704,plain,
! [SV27: $i] :
( ( ! [SY1850: $i] :
( ( hBOOL @ ( hAPP @ SV27 @ SY1850 ) )
| ! [SY1851: $i] :
~ ( hBOOL @ ( c_in @ SY1850 @ ( c_Collect @ SV27 @ SY1851 ) @ SY1851 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1705,plain,
! [SV28: $i] :
( ( ! [SY1852: $i,SY1853: $i,SY1854: $i] :
( ( hBOOL @ ( c_in @ SV28 @ ( c_HOL_Ominus__class_Ominus @ SY1852 @ SY1853 @ ( tc_fun @ SY1854 @ tc_bool ) ) @ SY1854 ) )
| ( hBOOL @ ( c_in @ SV28 @ SY1853 @ SY1854 ) )
| ~ ( hBOOL @ ( c_in @ SV28 @ SY1852 @ SY1854 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1706,plain,
! [SV29: $i] :
( ( ! [SY1855: $i,SY1856: $i,SY1857: $i] :
( ( hBOOL @ ( c_in @ SV29 @ ( c_HOL_Ominus__class_Ominus @ SY1855 @ SY1856 @ ( tc_fun @ SY1857 @ tc_bool ) ) @ SY1857 ) )
| ( hBOOL @ ( c_in @ SV29 @ SY1856 @ SY1857 ) )
| ~ ( hBOOL @ ( c_in @ SV29 @ SY1855 @ SY1857 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1707,plain,
! [SV30: $i] :
( ( ! [SY1858: $i,SY1859: $i,SY1860: $i,SY1861: $i,SY1862: $i] :
( ( c_Com_Ocom_OCall @ SV30 @ SY1858 @ SY1859 )
!= ( c_Com_Ocom_OLocal @ SY1860 @ SY1861 @ SY1862 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1708,plain,
! [SV31: $i] :
( ( ! [SY1863: $i,SY1864: $i] :
( ( hBOOL @ ( c_in @ SV31 @ SY1863 @ SY1864 ) )
| ! [SY1865: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SV31 @ SY1865 @ SY1864 ) @ SY1863 @ ( tc_fun @ SY1864 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1709,plain,
! [SV32: $i] :
( ( ! [SY1866: $i,SY1867: $i,SY1868: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV32 @ ( c_COMBK @ SY1866 @ ( tc_fun @ SY1867 @ tc_bool ) @ SY1868 ) @ SY1868 @ ( tc_fun @ SY1867 @ tc_bool ) )
= SY1866 )
| ( SV32
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1868 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1710,plain,
! [SV33: $i] :
( ( ! [SY1869: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV33 )
| ! [SY1870: $i,SY1871: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY1869 @ ( c_COMBK @ SY1870 @ SV33 @ SY1871 ) @ SY1871 @ SV33 )
= SY1870 )
| ( SY1869
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1871 @ tc_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1711,plain,
! [SV34: $i] :
( ( ! [SY1872: $i,SY1873: $i,SY1874: $i,SY1875: $i] :
( ( c_Com_Ocom_OCall @ SV34 @ SY1872 @ SY1873 )
!= ( c_Com_Ocom_OWhile @ SY1874 @ SY1875 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1712,plain,
! [SV35: $i] :
( ( ! [SY1876: $i,SY1877: $i,SY1878: $i] :
( ! [SY1879: $i] :
( ( c_Set_Oinsert @ ( hAPP @ SV35 @ SY1876 ) @ ( c_Set_Oimage @ SV35 @ SY1877 @ SY1878 @ SY1879 ) @ SY1879 )
= ( c_Set_Oimage @ SV35 @ SY1877 @ SY1878 @ SY1879 ) )
| ~ ( hBOOL @ ( c_in @ SY1876 @ SY1877 @ SY1878 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1713,plain,
! [SV36: $i] :
( ( ! [SY1880: $i,SY1881: $i,SY1882: $i] :
( ( c_lessequals @ SV36 @ ( c_Set_Oinsert @ SY1880 @ SY1881 @ SY1882 ) @ ( tc_fun @ SY1882 @ tc_bool ) )
| ~ ( c_lessequals @ SV36 @ SY1881 @ ( tc_fun @ SY1882 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SY1880 @ SV36 @ SY1882 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1714,plain,
! [SV37: $i] :
( ( ! [SY1883: $i,SY1884: $i] :
( ( c_lessequals @ SV37 @ SY1883 @ ( tc_fun @ SY1884 @ tc_bool ) )
| ! [SY1885: $i] :
( ( hBOOL @ ( c_in @ SY1885 @ SV37 @ SY1884 ) )
| ~ ( c_lessequals @ SV37 @ ( c_Set_Oinsert @ SY1885 @ SY1883 @ SY1884 ) @ ( tc_fun @ SY1884 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1715,plain,
! [SV38: $i] :
( ( ! [SY1886: $i,SY1887: $i,SY1888: $i] :
( ( c_lessequals @ SV38 @ ( c_Set_Oinsert @ SY1886 @ SY1887 @ SY1888 ) @ ( tc_fun @ SY1888 @ tc_bool ) )
| ~ ( c_lessequals @ SV38 @ SY1887 @ ( tc_fun @ SY1888 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SY1886 @ SV38 @ SY1888 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1716,plain,
! [SV39: $i] :
( ( ! [SY1889: $i,SY1890: $i] :
( ( c_lessequals @ SV39 @ SY1889 @ ( tc_fun @ SY1890 @ tc_bool ) )
| ! [SY1891: $i] :
( ~ ( c_lessequals @ SV39 @ ( c_Set_Oinsert @ SY1891 @ SY1889 @ SY1890 ) @ ( tc_fun @ SY1890 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SY1891 @ SV39 @ SY1890 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1717,plain,
! [SV40: $i] :
( ( ! [SY1892: $i,SY1893: $i,SY1894: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV40 @ SY1892 @ ( tc_fun @ SY1893 @ tc_bool ) ) @ SY1894 @ ( tc_fun @ SY1893 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV40 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1892 @ SY1894 @ ( tc_fun @ SY1893 @ tc_bool ) ) @ ( tc_fun @ SY1893 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1718,plain,
! [SV41: $i] :
( ( ! [SY1895: $i,SY1896: $i,SY1897: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV41 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1895 @ SY1896 @ ( tc_fun @ SY1897 @ tc_bool ) ) @ ( tc_fun @ SY1897 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY1895 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV41 @ SY1896 @ ( tc_fun @ SY1897 @ tc_bool ) ) @ ( tc_fun @ SY1897 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1719,plain,
! [SV42: $i] :
( ( ! [SY1898: $i,SY1899: $i,SY1900: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV42 @ SY1898 ) @ SY1899 @ SY1900 )
| ! [SY1901: $i] :
( ~ ( c_Natural_Oevalc @ SY1898 @ SY1901 @ SY1900 )
| ~ ( c_Natural_Oevalc @ SV42 @ SY1899 @ SY1901 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1720,plain,
! [SV43: $i] :
( ( ! [SY1902: $i,SY1903: $i,SY1904: $i,SY1905: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV43 @ SY1902 @ SY1903 @ SY1904 ) @ ( c_Set_Oimage @ SV43 @ SY1905 @ SY1903 @ SY1904 ) @ ( tc_fun @ SY1904 @ tc_bool ) ) @ ( c_Set_Oimage @ SV43 @ ( c_HOL_Ominus__class_Ominus @ SY1902 @ SY1905 @ ( tc_fun @ SY1903 @ tc_bool ) ) @ SY1903 @ SY1904 ) @ ( tc_fun @ SY1904 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1721,plain,
! [SV44: $i] :
( ( ! [SY1906: $i,SY1907: $i] :
( ~ ( hBOOL @ ( hAPP @ SV44 @ SY1906 ) )
| ! [SY1908: $i] :
( ( c_Natural_Oevalc @ SY1907 @ SY1906 @ SY1908 )
| ! [SY1909: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV44 @ SY1907 @ SY1909 ) @ SY1906 @ SY1908 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1722,plain,
! [SV45: $i] :
( ( ! [SY1910: $i,SY1911: $i,SY1912: $i,SY1913: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV45 @ SY1910 @ SY1911 ) @ SY1912 @ SY1913 )
| ~ ( c_Natural_Oevalc @ SY1910 @ SY1912 @ SY1913 )
| ~ ( hBOOL @ ( hAPP @ SV45 @ SY1912 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1723,plain,
! [SV46: $i] :
( ( ! [SY1914: $i,SY1915: $i,SY1916: $i,SY1917: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV46 @ SY1914 ) @ SY1915 @ SY1916 @ SY1917 )
| ! [SY1918: $i] :
( ~ ( c_Natural_Oevaln @ SY1914 @ SY1918 @ SY1916 @ SY1917 )
| ~ ( c_Natural_Oevaln @ SV46 @ SY1915 @ SY1916 @ SY1918 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1724,plain,
! [SV47: $i] :
( ( ! [SY1919: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV47 )
| ! [SY1920: $i,SY1921: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SY1919 @ SY1919 @ SV47 )
!= ( c_HOL_Ominus__class_Ominus @ SY1920 @ SY1921 @ SV47 ) )
| ( SY1920 = SY1921 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1725,plain,
! [SV48: $i] :
( ( ! [SY1922: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV48 )
| ! [SY1923: $i] :
( ! [SY1924: $i] :
( ( c_HOL_Ominus__class_Ominus @ SY1922 @ SY1923 @ SV48 )
!= ( c_HOL_Ominus__class_Ominus @ SY1924 @ SY1924 @ SV48 ) )
| ( SY1922 = SY1923 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1726,plain,
! [SV49: $i] :
( ( ! [SY1925: $i,SY1926: $i,SY1927: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV49 @ SY1925 ) @ SY1926 @ SY1927 )
| ! [SY1928: $i] :
( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV49 @ SY1925 ) @ SY1928 @ SY1927 )
| ~ ( c_Natural_Oevalc @ SY1925 @ SY1926 @ SY1928 )
| ~ ( hBOOL @ ( hAPP @ SV49 @ SY1926 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1727,plain,
! [SV50: $i] :
( ( ! [SY1929: $i] :
( ( c_Option_Ooption_ONone @ SV50 )
!= ( c_Option_Ooption_OSome @ SY1929 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1728,plain,
! [SV51: $i] :
( ( ! [SY1930: $i] :
( ( c_Option_Ooption_ONone @ SV51 )
!= ( c_Option_Ooption_OSome @ SY1930 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1729,plain,
! [SV52: $i] :
( ( ! [SY1931: $i,SY1932: $i,SY1933: $i,SY1934: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV52 @ SY1931 ) @ SY1932 @ SY1933 @ SY1934 )
| ! [SY1935: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV52 @ SY1931 ) @ SY1935 @ SY1933 @ SY1934 )
| ~ ( c_Natural_Oevaln @ SY1931 @ SY1932 @ SY1933 @ SY1935 )
| ~ ( hBOOL @ ( hAPP @ SV52 @ SY1932 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1730,plain,
! [SV53: $i] :
( ( ! [SY1936: $i,SY1937: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV53 @ SY1936 @ ( tc_fun @ SY1937 @ tc_bool ) ) @ SY1936 @ ( tc_fun @ SY1937 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV53 @ SY1936 @ ( tc_fun @ SY1937 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1731,plain,
! [SV54: $i] :
( ( ! [SY1938: $i,SY1939: $i,SY1940: $i,SY1941: $i,SY1942: $i] :
( ( hAPP @ ( c_COMBS @ SV54 @ SY1938 @ SY1939 @ SY1940 @ SY1941 ) @ SY1942 )
= ( hAPP @ ( hAPP @ SV54 @ SY1942 ) @ ( hAPP @ SY1938 @ SY1942 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1732,plain,
! [SV55: $i] :
( ( ! [SY1943: $i,SY1944: $i,SY1945: $i] :
( ( hAPP @ ( c_COMBK @ SV55 @ SY1943 @ SY1944 ) @ SY1945 )
= SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1733,plain,
! [SV56: $i] :
( ( ! [SY1946: $i] :
( ( hAPP @ ( c_COMBI @ SV56 ) @ SY1946 )
= SY1946 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1734,plain,
! [SV57: $i] :
( ( ! [SY1947: $i,SY1948: $i,SY1949: $i,SY1950: $i,SY1951: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV57 @ SY1947 @ SY1948 @ SY1949 ) @ SY1950 ) @ SY1951 )
= ( hAPP @ ( hAPP @ SV57 @ SY1951 ) @ SY1950 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1735,plain,
! [SV58: $i] :
( ( ! [SY1952: $i,SY1953: $i,SY1954: $i,SY1955: $i,SY1956: $i] :
( ( hAPP @ ( c_COMBB @ SV58 @ SY1952 @ SY1953 @ SY1954 @ SY1955 ) @ SY1956 )
= ( hAPP @ SV58 @ ( hAPP @ SY1952 @ SY1956 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1736,plain,
! [SV59: $i] :
( ( ! [SY1957: $i] :
( ( hBOOL @ ( hAPP @ SV59 @ SY1957 ) )
| ! [SY1958: $i] :
~ ( hBOOL @ ( c_in @ SY1957 @ SV59 @ SY1958 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1737,plain,
! [SV60: $i] :
( ( ! [SY1959: $i] :
( ! [SY1960: $i] : ( hBOOL @ ( c_in @ SV60 @ SY1959 @ SY1960 ) )
| ~ ( hBOOL @ ( hAPP @ SY1959 @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1738,plain,
! [SV61: $i] :
( ( ! [SY1961: $i,SY1962: $i,SY1963: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV61 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1961 @ tc_bool ) ) @ SY1962 @ SY1961 @ ( tc_fun @ SY1963 @ tc_bool ) ) @ ( tc_fun @ SY1963 @ tc_bool ) )
= SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1739,plain,
! [SV62: $i] :
( ( ! [SY1964: $i,SY1965: $i,SY1966: $i] :
( ~ ( hBOOL @ ( hAPP @ SV62 @ SY1964 ) )
| ! [SY1967: $i] :
( ( c_Natural_Oevaln @ SY1965 @ SY1964 @ SY1966 @ SY1967 )
| ! [SY1968: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV62 @ SY1965 @ SY1968 ) @ SY1964 @ SY1966 @ SY1967 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1740,plain,
! [SV63: $i] :
( ( ! [SY1969: $i,SY1970: $i,SY1971: $i,SY1972: $i,SY1973: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV63 @ SY1969 @ SY1970 ) @ SY1971 @ SY1972 @ SY1973 )
| ~ ( c_Natural_Oevaln @ SY1969 @ SY1971 @ SY1972 @ SY1973 )
| ~ ( hBOOL @ ( hAPP @ SV63 @ SY1971 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1741,plain,
! [SV64: $i] :
( ( ! [SY1974: $i,SY1975: $i,SY1976: $i,SY1977: $i,SY1978: $i,SY1979: $i,SY1980: $i,SY1981: $i,SY1982: $i,SY1983: $i,SY1984: $i] :
( ( c_Com_Ocom_Ocom__case @ SV64 @ SY1974 @ SY1975 @ SY1976 @ SY1977 @ SY1978 @ SY1979 @ SY1980 @ ( c_Com_Ocom_OCall @ SY1981 @ SY1982 @ SY1983 ) @ SY1984 )
= ( hAPP @ ( hAPP @ ( hAPP @ SY1980 @ SY1981 ) @ SY1982 ) @ SY1983 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1742,plain,
! [SV65: $i] :
( ( ! [SY1985: $i,SY1986: $i,SY1987: $i,SY1988: $i] :
( ( c_Com_Ocom_OCall @ SV65 @ SY1985 @ SY1986 )
!= ( c_Com_Ocom_OSemi @ SY1987 @ SY1988 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1743,plain,
! [SV66: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV66 )
| ! [SY1989: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY1989 @ SY1989 @ SV66 )
= SY1989 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1744,plain,
! [SV67: $i] :
( ( ! [SY1990: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV67 @ SV67 @ ( tc_fun @ SY1990 @ tc_bool ) )
= SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1745,plain,
! [SV68: $i] :
( ( ~ ( class_Lattices_Olattice @ SV68 )
| ! [SY1991: $i,SY1992: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1991 @ SY1992 @ ( tc_fun @ t_a @ SV68 ) ) @ v_x )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SY1991 @ v_x ) @ ( hAPP @ SY1992 @ v_x ) @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1746,plain,
! [SV69: $i] :
( ( ! [SY1993: $i,SY1994: $i,SY1995: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV69 @ SY1993 @ SY1994 ) @ SY1995 @ SY1994 @ SY1993 )
= ( c_Set_Oinsert @ SV69 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY1993 @ tc_bool ) ) @ SY1993 ) )
| ! [V_x: $i] :
~ ( hBOOL @ ( c_in @ V_x @ SY1995 @ SY1994 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1747,plain,
! [SV70: $i] :
( ( ! [SY1997: $i,SY1998: $i,SY1999: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ SV70 @ SY1997 ) @ SY1998 @ SY1999 ) )
| ! [SY2000: $i,SY2001: $i] :
( ~ ( hBOOL @ ( c_in @ SY1997 @ SY2000 @ SY2001 ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV70 @ SY2000 @ SY2001 @ SY1999 ) @ SY1998 @ ( tc_fun @ SY1999 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1748,plain,
! [SV71: $i] :
( ( ! [SY2002: $i,SY2003: $i,SY2004: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV71 @ ( c_Set_Oinsert @ SY2002 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2003 @ tc_bool ) ) @ SY2003 ) @ ( tc_fun @ SY2003 @ tc_bool ) ) @ SY2004 @ ( tc_fun @ SY2003 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SY2002 @ SV71 @ SY2003 ) )
| ~ ( c_lessequals @ SV71 @ ( c_Set_Oinsert @ SY2002 @ SY2004 @ SY2003 ) @ ( tc_fun @ SY2003 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1280]) ).
thf(1749,plain,
! [SV72: $i] :
( ( ! [SY2005: $i,SY2006: $i,SY2007: $i] :
( ( c_lessequals @ SV72 @ ( c_Set_Oinsert @ SY2005 @ SY2006 @ SY2007 ) @ ( tc_fun @ SY2007 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SY2005 @ SV72 @ SY2007 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV72 @ ( c_Set_Oinsert @ SY2005 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2007 @ tc_bool ) ) @ SY2007 ) @ ( tc_fun @ SY2007 @ tc_bool ) ) @ SY2006 @ ( tc_fun @ SY2007 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1750,plain,
! [SV73: $i] :
( ( ! [SY2008: $i,SY2009: $i,SY2010: $i] :
( ( c_lessequals @ SV73 @ ( c_Set_Oinsert @ SY2008 @ SY2009 @ SY2010 ) @ ( tc_fun @ SY2010 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SY2008 @ SV73 @ SY2010 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV73 @ ( c_Set_Oinsert @ SY2008 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2010 @ tc_bool ) ) @ SY2010 ) @ ( tc_fun @ SY2010 @ tc_bool ) ) @ SY2009 @ ( tc_fun @ SY2010 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1751,plain,
! [SV74: $i] :
( ( ! [SY2011: $i,SY2012: $i] :
( ! [SY2013: $i] : ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV74 @ SY2011 ) @ SY2012 @ SY2013 @ SY2012 )
| ( hBOOL @ ( hAPP @ SV74 @ SY2012 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1752,plain,
! [SV75: $i] :
( ( ! [SY2014: $i,SY2015: $i] :
( ( c_Finite__Set_Ofold1 @ SV75 @ SY2014 @ SY2015 )
= ( c_The @ ( c_Finite__Set_Ofold1Set @ SV75 @ SY2014 @ SY2015 ) @ SY2015 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1753,plain,
! [SV76: $i] :
( ( ! [SY2016: $i,SY2017: $i,SY2018: $i,SY2019: $i,SY2020: $i] :
( ( c_Com_Ocom_OCond @ SV76 @ SY2016 @ SY2017 )
!= ( c_Com_Ocom_OCall @ SY2018 @ SY2019 @ SY2020 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1754,plain,
! [SV77: $i] :
( ( ! [SY2021: $i,SY2022: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV77 )
| ! [SY2023: $i,SY2024: $i] :
( ( c_lessequals @ ( hAPP @ SY2021 @ SY2022 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2023 @ SY2021 @ SY2024 @ SV77 ) @ SV77 )
| ~ ( hBOOL @ ( c_in @ SY2022 @ SY2023 @ SY2024 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1755,plain,
! [SV78: $i] :
( ( ! [SY2025: $i,SY2026: $i,SY2027: $i] :
( ! [SY2028: $i] : ( c_lessequals @ ( hAPP @ SV78 @ SY2025 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2026 @ SV78 @ SY2027 @ ( tc_fun @ SY2028 @ tc_bool ) ) @ ( tc_fun @ SY2028 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SY2025 @ SY2026 @ SY2027 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1756,plain,
! [SV79: $i] :
( ( ! [SY2029: $i,SY2030: $i,SY2031: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV79 @ SY2029 @ SY2030 ) @ SY2031 @ ( tc_fun @ SY2030 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SY2029 @ SY2031 @ ( tc_fun @ SY2030 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SV79 @ SY2031 @ SY2030 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1757,plain,
! [SV80: $i] :
( ( ! [SY2032: $i,SY2033: $i,SY2034: $i,SY2035: $i,SY2036: $i] :
( ( c_Com_Ocom_OLocal @ SV80 @ SY2032 @ SY2033 )
!= ( c_Com_Ocom_OCond @ SY2034 @ SY2035 @ SY2036 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1758,plain,
! [SV81: $i] :
( ( ! [SY2037: $i] :
( ( c_Set_Oimage @ ( c_COMBI @ SV81 ) @ SY2037 @ SV81 @ SV81 )
= SY2037 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1759,plain,
! [SV82: $i] :
( ( ! [SY2038: $i,SY2039: $i,SY2040: $i,SY2041: $i,SY2042: $i] :
( ( ( c_Com_Ocom_OCall @ SV82 @ SY2038 @ SY2039 )
!= ( c_Com_Ocom_OCall @ SY2040 @ SY2041 @ SY2042 ) )
| ( SY2039 = SY2042 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1760,plain,
! [SV83: $i] :
( ( ! [SY2043: $i,SY2044: $i,SY2045: $i,SY2046: $i] :
( ! [SY2047: $i] :
( ( c_Com_Ocom_OCall @ SV83 @ SY2043 @ SY2044 )
!= ( c_Com_Ocom_OCall @ SY2045 @ SY2046 @ SY2047 ) )
| ( SY2043 = SY2046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1761,plain,
! [SV84: $i] :
( ( ! [SY2048: $i,SY2049: $i,SY2050: $i] :
( ! [SY2051: $i,SY2052: $i] :
( ( c_Com_Ocom_OCall @ SV84 @ SY2048 @ SY2049 )
!= ( c_Com_Ocom_OCall @ SY2050 @ SY2051 @ SY2052 ) )
| ( SV84 = SY2050 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1762,plain,
! [SV85: $i] :
( ( ! [SY2053: $i] :
( ( c_Com_Ocom_OWhile @ SV85 @ SY2053 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1763,plain,
! [SV86: $i] :
( ( ! [SY2054: $i,SY2055: $i,SY2056: $i,SY2057: $i] :
( ( c_Com_Ocom_OWhile @ SV86 @ SY2054 )
!= ( c_Com_Ocom_OLocal @ SY2055 @ SY2056 @ SY2057 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1764,plain,
! [SV87: $i] :
( ( ! [SY2058: $i,SY2059: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV87 @ SY2058 ) @ SY2059 @ SY2059 )
| ( hBOOL @ ( hAPP @ SV87 @ SY2059 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1765,plain,
! [SV88: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1766,plain,
! [SV89: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1298]) ).
thf(1767,plain,
! [SV90: $i] :
( ( ! [SY2060: $i] :
( ( c_Collect @ SV90 @ SY2060 )
= SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1768,plain,
! [SV91: $i] :
( ( ! [SY2061: $i,SY2062: $i,SY2063: $i] :
( ( ( c_Com_Ocom_OSemi @ SV91 @ SY2061 )
!= ( c_Com_Ocom_OSemi @ SY2062 @ SY2063 ) )
| ( SY2061 = SY2063 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1769,plain,
! [SV92: $i] :
( ( ! [SY2064: $i,SY2065: $i] :
( ! [SY2066: $i] :
( ( c_Com_Ocom_OSemi @ SV92 @ SY2064 )
!= ( c_Com_Ocom_OSemi @ SY2065 @ SY2066 ) )
| ( SV92 = SY2065 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1770,plain,
! [SV93: $i] :
( ( ! [SY2067: $i,SY2068: $i,SY2069: $i] :
( ( c_Com_Ocom_OSemi @ SV93 @ SY2067 )
!= ( c_Com_Ocom_OWhile @ SY2068 @ SY2069 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1771,plain,
! [SV94: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV94 )
| ! [SY2070: $i,SY2071: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SY2070 @ SY2071 @ SV94 ) @ SV94 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2070 @ ( c_Complete__Lattice_OSup__class_OSup @ SY2071 @ SV94 ) @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1772,plain,
! [SV95: $i] :
( ( ! [SY2072: $i,SY2073: $i,SY2074: $i,SY2075: $i] :
( ( c_Com_Ocom_OSemi @ SV95 @ SY2072 )
!= ( c_Com_Ocom_OCond @ SY2073 @ SY2074 @ SY2075 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1773,plain,
! [SV96: $i] :
( ( ! [SY2076: $i,SY2077: $i,SY2078: $i,SY2079: $i] :
( ( c_Com_Ocom_OSemi @ SV96 @ SY2076 )
!= ( c_Com_Ocom_OLocal @ SY2077 @ SY2078 @ SY2079 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1774,plain,
! [SV97: $i] :
( ( ! [SY2080: $i,SY2081: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ SV97 @ SY2080 @ SY2081 )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV97 ) @ SY2080 @ SY2081 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1775,plain,
! [SV98: $i] :
( ( ! [SY2082: $i,SY2083: $i,SY2084: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV98 @ SY2082 @ SY2083 @ ( tc_fun @ SY2084 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2084 @ tc_bool ) ) )
| ! [SY2085: $i] :
( ( ( hAPP @ SY2082 @ SY2085 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2084 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SY2085 @ SV98 @ SY2083 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1776,plain,
! [SV99: $i] :
( ( ! [SY2086: $i,SY2087: $i,SY2088: $i,SY2089: $i] :
( ( c_Com_Ocom_OCond @ SV99 @ SY2086 @ SY2087 )
!= ( c_Com_Ocom_OWhile @ SY2088 @ SY2089 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1777,plain,
! [SV100: $i] :
( ( ! [SY2090: $i,SY2091: $i] :
( ( hBOOL @ ( c_in @ SV100 @ SY2090 @ SY2091 ) )
| ! [SY2092: $i] :
~ ( hBOOL @ ( c_in @ SV100 @ ( c_HOL_Ominus__class_Ominus @ SY2090 @ SY2092 @ ( tc_fun @ SY2091 @ tc_bool ) ) @ SY2091 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1778,plain,
! [SV101: $i] :
( ( ! [SY2093: $i,SY2094: $i,SY2095: $i,SY2096: $i,SY2097: $i] :
( ( c_Com_Ocom_OCond @ SV101 @ SY2093 @ SY2094 )
!= ( c_Com_Ocom_OLocal @ SY2095 @ SY2096 @ SY2097 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1779,plain,
! [SV102: $i] :
( ( ! [SY2098: $i,SY2099: $i] :
( ~ ( hBOOL @ ( c_in @ SV102 @ SY2098 @ SY2099 ) )
| ! [SY2100: $i] :
~ ( hBOOL @ ( c_in @ SV102 @ ( c_HOL_Ominus__class_Ominus @ SY2100 @ SY2098 @ ( tc_fun @ SY2099 @ tc_bool ) ) @ SY2099 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1780,plain,
! [SV103: $i] :
( ( ! [SY2101: $i,SY2102: $i,SY2103: $i] :
( ( c_lessequals @ ( hAPP @ SV103 @ SY2101 ) @ SY2102 @ ( tc_fun @ SY2103 @ tc_bool ) )
| ! [SY2104: $i,SY2105: $i] :
( ~ ( hBOOL @ ( c_in @ SY2101 @ SY2104 @ SY2105 ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2104 @ SV103 @ SY2105 @ ( tc_fun @ SY2103 @ tc_bool ) ) @ SY2102 @ ( tc_fun @ SY2103 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1781,plain,
! [SV104: $i] :
( ( ! [SY2106: $i,SY2107: $i,SY2108: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ ( c_COMBK @ SV104 @ SY2106 @ SY2107 ) @ SY2108 @ SY2107 @ SY2106 @ t_a ) @ v_x )
= SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1782,plain,
! [SV105: $i] :
( ( ! [SY2109: $i] :
( ( c_The @ ( hAPP @ ( c_COMBC @ ( c_fequal @ SV105 ) @ SV105 @ SV105 @ tc_bool ) @ SY2109 ) @ SV105 )
= SY2109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1783,plain,
! [SV106: $i] :
( ( ! [SY2110: $i,SY2111: $i,SY2112: $i,SY2113: $i] :
( ( c_Com_Ocom_OCond @ SV106 @ SY2110 @ SY2111 )
!= ( c_Com_Ocom_OSemi @ SY2112 @ SY2113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1784,plain,
! [SV107: $i] :
( ( ! [SY2114: $i,SY2115: $i,SY2116: $i] :
( ! [SY2117: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV107 @ SY2114 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2115 @ SV107 @ SY2116 @ ( tc_fun @ SY2117 @ tc_bool ) ) @ ( tc_fun @ SY2117 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2115 @ SV107 @ SY2116 @ ( tc_fun @ SY2117 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SY2114 @ SY2115 @ SY2116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1785,plain,
! [SV108: $i] :
( ( ! [SY2118: $i,SY2119: $i,SY2120: $i,SY2121: $i,SY2122: $i] :
( ( ( c_Com_Ocom_OCond @ SV108 @ SY2118 @ SY2119 )
!= ( c_Com_Ocom_OCond @ SY2120 @ SY2121 @ SY2122 ) )
| ( SY2119 = SY2122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1786,plain,
! [SV109: $i] :
( ( ! [SY2123: $i,SY2124: $i,SY2125: $i,SY2126: $i] :
( ! [SY2127: $i] :
( ( c_Com_Ocom_OCond @ SV109 @ SY2123 @ SY2124 )
!= ( c_Com_Ocom_OCond @ SY2125 @ SY2126 @ SY2127 ) )
| ( SY2123 = SY2126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1787,plain,
! [SV110: $i] :
( ( ! [SY2128: $i,SY2129: $i,SY2130: $i] :
( ! [SY2131: $i,SY2132: $i] :
( ( c_Com_Ocom_OCond @ SV110 @ SY2128 @ SY2129 )
!= ( c_Com_Ocom_OCond @ SY2130 @ SY2131 @ SY2132 ) )
| ( SV110 = SY2130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1788,plain,
! [SV111: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV111 )
| ! [SY2133: $i] :
( ( c_HOL_Ominus__class_Ominus @ SY2133 @ SY2133 @ SV111 )
= ( c_HOL_Ozero__class_Ozero @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1789,plain,
! [SV112: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV112 )
| ! [SY2134: $i] :
( ( c_HOL_Ominus__class_Ominus @ SY2134 @ SY2134 @ SV112 )
= ( c_HOL_Ozero__class_Ozero @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1790,plain,
! [SV113: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV113 )
| ! [SY2135: $i] :
( ( c_HOL_Ominus__class_Ominus @ SY2135 @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV113 )
= SY2135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1791,plain,
! [SV114: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV114 )
| ! [SY2136: $i] :
( ( c_HOL_Ominus__class_Ominus @ SY2136 @ SY2136 @ SV114 )
= ( c_HOL_Ozero__class_Ozero @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1792,plain,
! [SV115: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV115 )
| ~ ( class_Int_Onumber__ring @ SV115 )
| ! [SY2137: $i] :
( ( c_HOL_Ominus__class_Ominus @ SY2137 @ SY2137 @ SV115 )
= ( c_HOL_Ozero__class_Ozero @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1793,plain,
! [SV116: $i] :
( ( ! [SY2138: $i,SY2139: $i] :
( ~ ( class_Orderings_Oorder @ SV116 )
| ! [SY2140: $i,SY2141: $i] :
( ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2138 @ SY2139 @ SV116 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2140 @ SY2141 @ SV116 ) @ ( tc_fun @ SV116 @ tc_bool ) )
| ~ ( c_lessequals @ SY2139 @ SY2141 @ SV116 )
| ~ ( c_lessequals @ SY2140 @ SY2138 @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1794,plain,
! [SV117: $i] :
( ( ! [SY2142: $i,SY2143: $i] :
( ~ ( class_Orderings_Oorder @ SV117 )
| ( c_lessequals @ SY2142 @ SY2143 @ SV117 )
| ! [SY2144: $i] :
( ~ ( c_lessequals @ SY2144 @ SY2142 @ SV117 )
| ! [SY2145: $i] :
~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2144 @ SY2142 @ SV117 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2145 @ SY2143 @ SV117 ) @ ( tc_fun @ SV117 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1795,plain,
! [SV118: $i] :
( ( ! [SY2146: $i,SY2147: $i] :
( ~ ( class_Orderings_Oorder @ SV118 )
| ( c_lessequals @ SY2146 @ SY2147 @ SV118 )
| ! [SY2148: $i] :
( ~ ( c_lessequals @ SY2147 @ SY2148 @ SV118 )
| ! [SY2149: $i] :
~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2147 @ SY2148 @ SV118 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2146 @ SY2149 @ SV118 ) @ ( tc_fun @ SV118 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1796,plain,
! [SV119: $i] :
( ( ! [SY2150: $i] :
( ( c_Option_Ooption_OSome @ SV119 @ SY2150 )
!= ( c_Option_Ooption_ONone @ SY2150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1797,plain,
! [SV120: $i] :
( ( ! [SY2151: $i] :
( ( c_Option_Ooption_OSome @ SV120 @ SY2151 )
!= ( c_Option_Ooption_ONone @ SY2151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1798,plain,
! [SV121: $i] :
( ( ! [SY2152: $i,SY2153: $i,SY2154: $i,SY2155: $i,SY2156: $i] :
( ( c_Com_Ocom_OCall @ SV121 @ SY2152 @ SY2153 )
!= ( c_Com_Ocom_OCond @ SY2154 @ SY2155 @ SY2156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1799,plain,
! [SV122: $i] :
( ( ! [SY2157: $i,SY2158: $i] :
( ( ( c_Option_Ooption_OSome @ SV122 @ SY2157 )
!= ( c_Option_Ooption_OSome @ SY2158 @ SY2157 ) )
| ( SV122 = SY2158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1800,plain,
! [SV123: $i] :
( ( ! [SY2159: $i,SY2160: $i,SY2161: $i,SY2162: $i,SY2163: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV123 @ SY2159 @ SY2160 @ SY2161 @ SY2162 ) @ SY2163 )
= ( hAPP @ SV123 @ ( hAPP @ SY2159 @ SY2163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1801,plain,
! [SV124: $i] :
( ( ! [SY2164: $i,SY2165: $i,SY2166: $i,SY2167: $i,SY2168: $i] :
( ( hAPP @ SV124 @ ( hAPP @ SY2164 @ SY2165 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV124 @ SY2164 @ SY2166 @ SY2167 @ SY2168 ) @ SY2165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1802,plain,
! [SV125: $i] :
( ( ! [SY2169: $i] :
( ( ( c_Suc @ SV125 )
!= ( c_Suc @ SY2169 ) )
| ( SV125 = SY2169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1803,plain,
! [SV126: $i] :
( ( ! [SY2170: $i] :
( ( ( c_Suc @ SV126 )
!= ( c_Suc @ SY2170 ) )
| ( SV126 = SY2170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1804,plain,
! [SV127: $i] :
( ( ! [SY2171: $i,SY2172: $i] :
( ~ ( class_Orderings_Oorder @ SV127 )
| ! [SY2173: $i,SY2174: $i] : ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2171 @ SY2172 @ SV127 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2173 @ SY2174 @ SV127 ) @ ( tc_fun @ SV127 @ tc_bool ) )
| ( c_lessequals @ SY2171 @ SY2172 @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1805,plain,
! [SV128: $i] :
( ( ! [SY2175: $i] :
( ( hBOOL @ ( hAPP @ SV128 @ SY2175 ) )
| ! [SY2176: $i] :
( ( hBOOL @ ( hAPP @ SY2176 @ SY2175 ) )
| ! [SY2177: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2176 @ SV128 @ ( tc_fun @ SY2177 @ tc_bool ) ) @ SY2175 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1806,plain,
! [SV129: $i] :
( ( ! [SY2178: $i,SY2179: $i,SY2180: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV129 @ SY2178 @ ( tc_fun @ SY2179 @ tc_bool ) ) @ SY2180 ) )
| ~ ( hBOOL @ ( hAPP @ SY2178 @ SY2180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1807,plain,
! [SV130: $i] :
( ( ! [SY2181: $i,SY2182: $i,SY2183: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV130 @ SY2181 @ ( tc_fun @ SY2182 @ tc_bool ) ) @ SY2183 ) )
| ~ ( hBOOL @ ( hAPP @ SV130 @ SY2183 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1808,plain,
! [SV131: $i] :
( ( ! [SY2184: $i,SY2185: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV131 @ SY2184 @ SY2185 ) )
| ~ ( c_Com_OWT @ SY2185 )
| ~ ( c_Com_OWT @ SY2184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1809,plain,
! [SV132: $i] :
( ( ! [SY2186: $i,SY2187: $i,SY2188: $i,SY2189: $i,SY2190: $i,SY2191: $i,SY2192: $i,SY2193: $i] :
( ( c_Com_Ocom_Ocom__case @ SV132 @ SY2186 @ SY2187 @ SY2188 @ SY2189 @ SY2190 @ SY2191 @ SY2192 @ c_Com_Ocom_OSKIP @ SY2193 )
= SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1810,plain,
! [SV133: $i] :
( ( ! [SY2194: $i,SY2195: $i] :
( ( hBOOL @ ( c_in @ SV133 @ SY2194 @ SY2195 ) )
| ! [SY2196: $i] :
( ( hBOOL @ ( c_in @ SV133 @ SY2196 @ SY2195 ) )
| ~ ( hBOOL @ ( c_in @ SV133 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2196 @ SY2194 @ ( tc_fun @ SY2195 @ tc_bool ) ) @ SY2195 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1811,plain,
! [SV134: $i] :
( ( ! [SY2197: $i,SY2198: $i,SY2199: $i,SY2200: $i] :
( ( c_Com_Ocom_OLocal @ SV134 @ SY2197 @ SY2198 )
!= ( c_Com_Ocom_OWhile @ SY2199 @ SY2200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1812,plain,
! [SV135: $i] :
( ( ! [SY2201: $i,SY2202: $i,SY2203: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV135 @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2201 @ SY2202 @ SY2203 @ ( tc_fun @ SV135 @ tc_bool ) ) )
| ! [SY2204: $i] :
( ( ( hAPP @ SY2202 @ SY2204 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV135 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SY2204 @ SY2201 @ SY2203 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1813,plain,
! [SV136: $i] :
( ( ! [SY2205: $i,SY2206: $i,SY2207: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV136 @ tc_bool ) ) @ SY2205 @ SV136 @ ( tc_fun @ SY2206 @ tc_bool ) ) @ SY2207 @ ( tc_fun @ SY2206 @ tc_bool ) )
= SY2207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1814,plain,
! [SV137: $i] :
( ( ! [SY2208: $i,SY2209: $i,SY2210: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV137 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2208 @ tc_bool ) ) @ SY2209 @ SY2208 @ ( tc_fun @ SY2210 @ tc_bool ) ) @ ( tc_fun @ SY2210 @ tc_bool ) )
= SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1815,plain,
! [SV138: $i] :
( ( ! [SY2211: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OWhile @ SV138 @ SY2211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(1816,plain,
! [SV139: $i] :
( ( ! [SY2212: $i,SY2213: $i,SY2214: $i,SY2215: $i] :
( ( hBOOL @ ( c_in @ SV139 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2212 @ SY2213 @ SY2214 @ ( tc_fun @ SY2215 @ tc_bool ) ) @ SY2215 ) )
| ! [SY2216: $i] :
( ~ ( hBOOL @ ( c_in @ SV139 @ ( hAPP @ SY2213 @ SY2216 ) @ SY2215 ) )
| ~ ( hBOOL @ ( c_in @ SY2216 @ SY2212 @ SY2214 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1348]) ).
thf(1817,plain,
! [SV140: $i] :
( ( ! [SY2217: $i,SY2218: $i,SY2219: $i,SY2220: $i] :
( ( hBOOL @ ( c_in @ SV140 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2217 @ SY2218 @ SY2219 @ ( tc_fun @ SY2220 @ tc_bool ) ) @ SY2220 ) )
| ! [SY2221: $i] :
( ~ ( hBOOL @ ( c_in @ SV140 @ ( hAPP @ SY2218 @ SY2221 ) @ SY2220 ) )
| ~ ( hBOOL @ ( c_in @ SY2221 @ SY2217 @ SY2219 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1818,plain,
! [SV141: $i] :
( ( ! [SY2222: $i,SY2223: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV141 @ SY2222 @ ( tc_fun @ SY2223 @ tc_bool ) ) @ SY2222 @ ( tc_fun @ SY2223 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV141 @ SY2222 @ ( tc_fun @ SY2223 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(1819,plain,
! [SV142: $i] :
( ( ! [SY2224: $i,SY2225: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV142 @ ( c_HOL_Ominus__class_Ominus @ SY2224 @ SV142 @ ( tc_fun @ SY2225 @ tc_bool ) ) @ ( tc_fun @ SY2225 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV142 @ SY2224 @ ( tc_fun @ SY2225 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1351]) ).
thf(1820,plain,
! [SV143: $i] :
( ( ! [SY2226: $i,SY2227: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV143 @ tc_bool ) ) @ ( c_COMBK @ SY2226 @ ( tc_fun @ SY2227 @ tc_bool ) @ SV143 ) @ SV143 @ ( tc_fun @ SY2227 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2227 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1352]) ).
thf(1821,plain,
! [SV144: $i] :
( ( ~ ( class_HOL_Ominus @ SV144 )
| ! [SY2228: $i,SY2229: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ SY2228 @ SY2229 @ ( tc_fun @ t_a @ SV144 ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ SY2228 @ v_x ) @ ( hAPP @ SY2229 @ v_x ) @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1353]) ).
thf(1822,plain,
! [SV145: $i] :
( ( ! [SY2230: $i,SY2231: $i,SY2232: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV145 @ SY2230 @ ( tc_fun @ SY2231 @ tc_bool ) ) @ SY2232 @ ( tc_fun @ SY2231 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV145 @ SY2232 @ ( tc_fun @ SY2231 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY2230 @ SY2232 @ ( tc_fun @ SY2231 @ tc_bool ) ) @ ( tc_fun @ SY2231 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1823,plain,
! [SV146: $i] :
( ( ! [SY2233: $i,SY2234: $i,SY2235: $i,SY2236: $i,SY2237: $i,SY2238: $i,SY2239: $i,SY2240: $i,SY2241: $i,SY2242: $i] :
( ( c_Com_Ocom_Ocom__case @ SV146 @ SY2233 @ SY2234 @ SY2235 @ SY2236 @ SY2237 @ SY2238 @ SY2239 @ ( c_Com_Ocom_OSemi @ SY2240 @ SY2241 ) @ SY2242 )
= ( hAPP @ ( hAPP @ SY2235 @ SY2240 ) @ SY2241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1824,plain,
! [SV147: $i] :
( ( ! [SY2243: $i,SY2244: $i,SY2245: $i,SY2246: $i] :
( ( c_Com_Ocom_OLocal @ SV147 @ SY2243 @ SY2244 )
!= ( c_Com_Ocom_OSemi @ SY2245 @ SY2246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(1825,plain,
! [SV148: $i] :
( ( ! [SY2247: $i,SY2248: $i] :
( ( c_Set_Oinsert @ SV148 @ SY2247 @ SY2248 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ SY2248 ) @ SY2248 @ SY2248 @ tc_bool ) @ SV148 ) @ SY2248 ) @ SY2247 @ ( tc_fun @ SY2248 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1826,plain,
! [SV149: $i] :
( ( ! [SY2249: $i,SY2250: $i,SY2251: $i,SY2252: $i,SY2253: $i,SY2254: $i,SY2255: $i,SY2256: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV149 @ ( hAPP @ SY2249 @ SY2250 ) ) @ SY2251 ) )
| ~ ( hBOOL @ ( c_in @ SY2251 @ SY2250 @ SY2252 ) )
| ! [SY2257: $i,SY2258: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY2249 @ SY2253 @ SV149 @ SY2254 @ SY2255 @ SY2256 @ SY2257 @ SY2258 @ SY2252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(1827,plain,
! [SV150: $i] :
( ( ! [SY2259: $i,SY2260: $i,SY2261: $i,SY2262: $i,SY2263: $i,SY2264: $i,SY2265: $i,SY2266: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV150 @ SY2259 ) @ ( hAPP @ SY2260 @ SY2261 ) ) )
| ~ ( hBOOL @ ( c_in @ SY2259 @ SY2261 @ SY2262 ) )
| ! [SY2267: $i,SY2268: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY2263 @ SY2260 @ SV150 @ SY2264 @ SY2265 @ SY2266 @ SY2267 @ SY2268 @ SY2262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(1828,plain,
! [SV151: $i] :
( ( ! [SY2269: $i,SY2270: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV151 @ SY2269 @ ( tc_fun @ SY2270 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2269 @ SV151 @ ( tc_fun @ SY2270 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(1829,plain,
! [SV152: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV152 )
| ! [SY2271: $i,SY2272: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2271 @ SY2272 @ SV152 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2272 @ SY2271 @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1830,plain,
! [SV153: $i] :
( ( ~ ( class_Lattices_Olattice @ SV153 )
| ! [SY2273: $i,SY2274: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2273 @ SY2274 @ SV153 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2274 @ SY2273 @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1362]) ).
thf(1831,plain,
! [SV154: $i] :
( ( ! [SY2275: $i,SY2276: $i] :
( ! [SY2277: $i] :
( ( c_Com_Ocom_OWhile @ SV154 @ SY2275 )
!= ( c_Com_Ocom_OWhile @ SY2276 @ SY2277 ) )
| ( SV154 = SY2276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1363]) ).
thf(1832,plain,
! [SV155: $i] :
( ( ! [SY2278: $i,SY2279: $i,SY2280: $i] :
( ( ( c_Com_Ocom_OWhile @ SV155 @ SY2278 )
!= ( c_Com_Ocom_OWhile @ SY2279 @ SY2280 ) )
| ( SY2278 = SY2280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1364]) ).
thf(1833,plain,
! [SV156: $i] :
( ( ! [SY2281: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ SV156 @ SY2281 ) )
| ~ ( c_Com_OWT @ SY2281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1365]) ).
thf(1834,plain,
! [SV157: $i] :
( ( ( c_Com_OWT @ SV157 )
| ! [SY2282: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ SY2282 @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1835,plain,
! [SV158: $i] :
( ( ! [SY2283: $i,SY2284: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV158 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV158 @ SY2283 @ ( tc_fun @ SY2284 @ tc_bool ) ) @ ( tc_fun @ SY2284 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV158 @ SY2283 @ ( tc_fun @ SY2284 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1367]) ).
thf(1836,plain,
! [SV159: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV159 )
| ! [SY2285: $i,SY2286: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2285 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2285 @ SY2286 @ SV159 ) @ SV159 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2285 @ SY2286 @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1368]) ).
thf(1837,plain,
! [SV160: $i] :
( ( ~ ( class_Lattices_Olattice @ SV160 )
| ! [SY2287: $i,SY2288: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2287 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2287 @ SY2288 @ SV160 ) @ SV160 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2287 @ SY2288 @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1838,plain,
! [SV161: $i] :
( ( ! [SY2289: $i,SY2290: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ SV161 @ SY2289 @ SY2290 ) )
| ~ ( c_Com_OWT @ SY2290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1839,plain,
! [SV162: $i] :
( ( ( c_Com_OWT @ SV162 )
| ! [SY2291: $i,SY2292: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ SY2291 @ SY2292 @ SV162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1840,plain,
! [SV163: $i] :
( ( ! [SY2293: $i,SY2294: $i] :
( ( c_Com_Ocom_OCond @ SV163 @ SY2293 @ SY2294 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(1841,plain,
! [SV164: $i] :
( ( ! [SY2295: $i,SY2296: $i,SY2297: $i,SY2298: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV164 @ SY2295 @ SY2296 @ ( tc_fun @ SY2297 @ tc_bool ) ) @ SY2298 ) )
| ! [SY2299: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2295 @ SY2299 ) @ SY2298 ) )
| ~ ( hBOOL @ ( c_in @ SY2299 @ SV164 @ SY2296 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1373]) ).
thf(1842,plain,
! [SV165: $i] :
( ( ! [SY2300: $i,SY2301: $i,SY2302: $i,SY2303: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV165 @ SY2300 @ SY2301 @ ( tc_fun @ SY2302 @ tc_bool ) ) @ SY2303 ) )
| ! [SY2304: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2300 @ SY2304 ) @ SY2303 ) )
| ~ ( hBOOL @ ( c_in @ SY2304 @ SV165 @ SY2301 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1843,plain,
! [SV166: $i] :
( ( ! [SY2305: $i,SY2306: $i,SY2307: $i,SY2308: $i] :
( ( c_Com_Ocom_OWhile @ SV166 @ SY2305 )
!= ( c_Com_Ocom_OCond @ SY2306 @ SY2307 @ SY2308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1844,plain,
! [SV167: $i] :
( ( ! [SY2309: $i,SY2310: $i,SY2311: $i,SY2312: $i] :
( ( c_Com_Ocom_OSemi @ SV167 @ SY2309 )
!= ( c_Com_Ocom_OCall @ SY2310 @ SY2311 @ SY2312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1845,plain,
! [SV168: $i] :
( ( ! [SY2313: $i,SY2314: $i,SY2315: $i] :
( ( SV168
= ( c_Suc @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ SY2313 @ SV168 @ SY2314 @ SY2315 ) ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ SY2313 ) @ SY2314 @ SV168 @ SY2315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1377]) ).
thf(1846,plain,
! [SV169: $i] :
( ( ! [SY2316: $i,SY2317: $i,SY2318: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV169 @ SY2316 @ SY2317 ) @ SY2318 @ ( tc_fun @ SY2317 @ tc_bool ) )
= ( c_Set_Oinsert @ SV169 @ ( c_HOL_Ominus__class_Ominus @ SY2316 @ SY2318 @ ( tc_fun @ SY2317 @ tc_bool ) ) @ SY2317 ) )
| ( hBOOL @ ( c_in @ SV169 @ SY2318 @ SY2317 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1378]) ).
thf(1847,plain,
! [SV170: $i] :
( ( ! [SY2319: $i] :
( ( SV170 = SY2319 )
| ! [SY2320: $i] :
~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SY2319 @ SY2320 @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(1848,plain,
! [SV171: $i] :
( ( ! [SY2321: $i,SY2322: $i] :
( ~ ( hBOOL @ ( c_in @ SV171 @ SY2321 @ SY2322 ) )
| ! [SY2323: $i,SY2324: $i] : ( hBOOL @ ( c_in @ ( hAPP @ SY2323 @ SV171 ) @ ( c_Set_Oimage @ SY2323 @ SY2321 @ SY2322 @ SY2324 ) @ SY2324 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1380]) ).
thf(1849,plain,
! [SV172: $i] :
( ( ! [SY2325: $i,SY2326: $i] :
( ~ ( hBOOL @ ( c_in @ SV172 @ SY2325 @ SY2326 ) )
| ! [SY2327: $i,SY2328: $i] : ( hBOOL @ ( c_in @ ( hAPP @ SY2327 @ SV172 ) @ ( c_Set_Oimage @ SY2327 @ SY2325 @ SY2326 @ SY2328 ) @ SY2328 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1381]) ).
thf(1850,plain,
! [SV173: $i] :
( ( ! [SY2329: $i,SY2330: $i,SY2331: $i] :
( ! [SY2332: $i] : ( hBOOL @ ( c_in @ ( hAPP @ SV173 @ SY2329 ) @ ( c_Set_Oimage @ SV173 @ SY2330 @ SY2331 @ SY2332 ) @ SY2332 ) )
| ~ ( hBOOL @ ( c_in @ SY2329 @ SY2330 @ SY2331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1382]) ).
thf(1851,plain,
! [SV174: $i] :
( ( ! [SY2333: $i,SY2334: $i,SY2335: $i] :
( ! [SY2336: $i] : ( hBOOL @ ( c_in @ ( hAPP @ SV174 @ SY2333 ) @ ( c_Set_Oimage @ SV174 @ SY2334 @ SY2335 @ SY2336 ) @ SY2336 ) )
| ~ ( hBOOL @ ( c_in @ SY2333 @ SY2334 @ SY2335 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1383]) ).
thf(1852,plain,
! [SV175: $i] :
( ( ! [SY2337: $i,SY2338: $i,SY2339: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV175 @ SY2337 @ ( tc_fun @ SY2338 @ tc_bool ) ) @ SY2339 @ ( tc_fun @ SY2338 @ tc_bool ) )
| ~ ( c_lessequals @ SV175 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2337 @ SY2339 @ ( tc_fun @ SY2338 @ tc_bool ) ) @ ( tc_fun @ SY2338 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1853,plain,
! [SV176: $i] :
( ( ! [SY2340: $i,SY2341: $i,SY2342: $i] :
( ( c_lessequals @ SV176 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2340 @ SY2341 @ ( tc_fun @ SY2342 @ tc_bool ) ) @ ( tc_fun @ SY2342 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV176 @ SY2340 @ ( tc_fun @ SY2342 @ tc_bool ) ) @ SY2341 @ ( tc_fun @ SY2342 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1854,plain,
! [SV177: $i] :
( ( ! [SY2343: $i] :
( ( SV177 = SY2343 )
| ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ SY2343 @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1855,plain,
! [SV178: $i] :
( ( ! [SY2344: $i,SY2345: $i] :
( ( c_Natural_Oevalc @ SV178 @ SY2344 @ SY2345 )
| ! [SY2346: $i] :
~ ( c_Natural_Oevaln @ SV178 @ SY2344 @ SY2346 @ SY2345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1387]) ).
thf(1856,plain,
! [SV179: $i] :
( ( ! [SY2347: $i,SY2348: $i] :
( ( c_Natural_Oevalc @ SV179 @ SY2347 @ SY2348 )
| ! [SY2349: $i] :
~ ( c_Natural_Oevaln @ SV179 @ SY2347 @ SY2349 @ SY2348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(1857,plain,
! [SV180: $i] :
( ( ! [SY2350: $i,SY2351: $i] :
( ~ ( class_HOL_Oord @ SV180 )
| ! [SY2352: $i] :
( ( c_lessequals @ ( hAPP @ SY2350 @ SY2351 ) @ ( hAPP @ SY2352 @ SY2351 ) @ SV180 )
| ! [SY2353: $i] :
~ ( c_lessequals @ SY2350 @ SY2352 @ ( tc_fun @ SY2353 @ SV180 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(1858,plain,
! [SV181: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV181 )
| ! [SY2354: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ SV181 ) @ SY2354 @ SV181 )
= SY2354 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1390]) ).
thf(1859,plain,
! [SV182: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV182 )
| ! [SY2355: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2355 @ ( c_Orderings_Obot__class_Obot @ SV182 ) @ SV182 )
= SY2355 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1391]) ).
thf(1860,plain,
! [SV183: $i] :
( ( ~ ( class_Orderings_Obot @ SV183 )
| ! [SY2356: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV183 ) @ SY2356 @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1392]) ).
thf(1861,plain,
! [SV184: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV184 )
| ! [SY2357: $i] :
( ! [SY2358: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2357 @ SY2358 @ SV184 )
!= ( c_Orderings_Obot__class_Obot @ SV184 ) )
| ( SY2357
= ( c_Orderings_Obot__class_Obot @ SV184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1862,plain,
! [SV185: $i] :
( ( ~ ( class_Lattices_Obounded__lattice @ SV185 )
| ! [SY2359: $i,SY2360: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2359 @ SY2360 @ SV185 )
!= ( c_Orderings_Obot__class_Obot @ SV185 ) )
| ( SY2360
= ( c_Orderings_Obot__class_Obot @ SV185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1863,plain,
! [SV186: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV186 @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV186 @ tc_bool ) ) @ ( tc_fun @ SV186 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV186 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1864,plain,
! [SV187: $i] :
( ( ! [SY2361: $i,SY2362: $i] :
( ! [SY2363: $i] :
( ( c_Set_Oimage @ SV187 @ SY2361 @ SY2362 @ SY2363 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2363 @ tc_bool ) ) )
| ( SY2361
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2362 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1396]) ).
thf(1865,plain,
! [SV188: $i] :
( ( ! [SY2364: $i,SY2365: $i,SY2366: $i,SY2367: $i,SY2368: $i,SY2369: $i] :
( ( ( hAPP @ SV188 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2364 @ tc_bool ) ) )
= SY2365 )
| ! [SY2370: $i,SY2371: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV188 @ SY2366 @ SY2367 @ SY2368 @ SY2369 @ SY2370 @ SY2371 @ SY2365 @ SY2364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(1866,plain,
! [SV189: $i] :
( ( ! [SY2372: $i,SY2373: $i,SY2374: $i,SY2375: $i,SY2376: $i,SY2377: $i] :
( ( ( hAPP @ SV189 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2372 @ tc_bool ) ) )
= SY2373 )
| ! [SY2378: $i,SY2379: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY2374 @ SV189 @ SY2375 @ SY2376 @ SY2377 @ SY2378 @ SY2373 @ SY2379 @ SY2372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1867,plain,
! [SV190: $i] :
( ( ! [SY2380: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV190 @ tc_bool ) )
!= ( c_Collect @ SY2380 @ SV190 ) )
| ! [V_x: $i] :
~ ( hBOOL @ ( hAPP @ SY2380 @ V_x ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(1868,plain,
! [SV191: $i] :
( ( ! [SY2382: $i] :
~ ( hBOOL @ ( c_in @ SV191 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2382 @ tc_bool ) ) @ SY2382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1400]) ).
thf(1869,plain,
! [SV192: $i] :
( ( ! [SY2383: $i] :
( ( hBOOL @ ( hAPP @ SV192 @ SY2383 ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( c_in @ SY2383 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(1870,plain,
! [SV193: $i] :
( ( ! [SY2385: $i] :
~ ( hBOOL @ ( c_in @ SV193 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2385 @ tc_bool ) ) @ SY2385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1402]) ).
thf(1871,plain,
! [SV194: $i] :
( ( ! [SY2386: $i] :
~ ( hBOOL @ ( c_in @ SV194 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2386 @ tc_bool ) ) @ SY2386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1403]) ).
thf(1872,plain,
! [SV195: $i] :
( ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV195 @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV195 @ tc_bool ) ) @ ( tc_fun @ SV195 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1873,plain,
! [SV196: $i] :
( ( ! [SY2387: $i] :
( ( SV196
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2387 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV196 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2387 @ tc_bool ) ) @ ( tc_fun @ SY2387 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1405]) ).
thf(1874,plain,
! [SV197: $i] :
( ( ! [SY2388: $i] :
( ( c_Collect @ SV197 @ SY2388 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2388 @ tc_bool ) ) )
| ! [SY2389: $i] :
~ ( hBOOL @ ( hAPP @ SV197 @ SY2389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1875,plain,
! [SV198: $i] :
( ( ! [SY2390: $i,SY2391: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV198 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2390 @ tc_bool ) ) @ SY2390 ) @ SY2391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(1876,plain,
! [SV199: $i] :
( ( ! [SY2392: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV199 @ tc_bool ) ) @ SY2392 @ ( tc_fun @ SV199 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV199 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1877,plain,
! [SV200: $i] :
( ( ! [SY2393: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2393 @ tc_bool ) ) @ ( tc_fun @ SY2393 @ tc_bool ) )
= SV200 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1409]) ).
thf(1878,plain,
! [SV201: $i] :
( ( ! [SY2394: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV201 @ tc_bool ) ) @ SY2394 @ ( tc_fun @ SV201 @ tc_bool ) )
= SY2394 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(1879,plain,
! [SV202: $i] :
( ( ! [SY2395: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV202 @ SV202 @ ( tc_fun @ SY2395 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2395 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(1880,plain,
! [SV203: $i] :
( ( ! [SY2396: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV203 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2396 @ tc_bool ) ) @ ( tc_fun @ SY2396 @ tc_bool ) )
= SV203 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(1881,plain,
! [SV204: $i] :
( ( ! [SY2397: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV204 @ tc_bool ) ) @ SY2397 @ ( tc_fun @ SV204 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(1882,plain,
! [SV205: $i] :
( ( ! [SY2398: $i,SY2399: $i,SY2400: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV205 @ tc_bool ) )
!= ( c_Set_Oimage @ SY2398 @ SY2399 @ SY2400 @ SV205 ) )
| ( SY2399
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2400 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1414]) ).
thf(1883,plain,
! [SV206: $i] :
( ( ! [SY2401: $i,SY2402: $i] :
( ( c_Set_Oimage @ SV206 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2401 @ tc_bool ) ) @ SY2401 @ SY2402 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2402 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(1884,plain,
! [SV207: $i] :
( ( ! [SY2403: $i] :
( ~ ( hBOOL @ ( hAPP @ SV207 @ SY2403 ) )
| ! [T_a: $i] :
~ ( hBOOL @ ( c_in @ SY2403 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ T_a @ tc_bool ) ) @ T_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1416]) ).
thf(1885,plain,
! [SV208: $i] :
( ( ! [SY2405: $i,SY2406: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV208 @ SY2405 @ ( tc_fun @ SY2406 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2406 @ tc_bool ) ) )
| ( SY2405
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2406 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(1886,plain,
! [SV209: $i] :
( ( ! [SY2407: $i,SY2408: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV209 @ SY2407 @ ( tc_fun @ SY2408 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2408 @ tc_bool ) ) )
| ( SV209
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2408 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1418]) ).
thf(1887,plain,
! [SV210: $i] :
( ( ! [SY2409: $i,SY2410: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV210 @ tc_bool ) )
= ( c_Set_Oimage @ SY2409 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2410 @ tc_bool ) ) @ SY2410 @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1888,plain,
! [SV211: $i] :
( ( ! [SY2411: $i] :
( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ SV211 ) @ SV211 @ SV211 @ tc_bool ) @ SY2411 ) @ SV211 )
= ( c_Set_Oinsert @ SY2411 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV211 @ tc_bool ) ) @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1889,plain,
! [SV212: $i] :
( ( ! [SY2412: $i,SY2413: $i] :
( ( ( c_Set_Oinsert @ SV212 @ ( c_HOL_Ominus__class_Ominus @ SY2412 @ ( c_Set_Oinsert @ SV212 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2413 @ tc_bool ) ) @ SY2413 ) @ ( tc_fun @ SY2413 @ tc_bool ) ) @ SY2413 )
= SY2412 )
| ~ ( hBOOL @ ( c_in @ SV212 @ SY2412 @ SY2413 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1890,plain,
! [SV213: $i] :
( ( ! [SY2414: $i,SY2415: $i,SY2416: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV213 @ SY2414 @ SY2415 ) @ SY2416 @ SY2415 @ SY2414 )
= ( c_Set_Oinsert @ SV213 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2414 @ tc_bool ) ) @ SY2414 ) )
| ( SY2416
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2415 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(1891,plain,
! [SV214: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV214 )
| ! [SY2417: $i,SY2418: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SY2417 @ ( c_Set_Oinsert @ SY2418 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV214 @ tc_bool ) ) @ SV214 ) @ SV214 ) @ SV214 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2417 @ SY2418 @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1892,plain,
! [SV215: $i] :
( ( ! [SY2419: $i,SY2420: $i,SY2421: $i] :
( ( c_lessequals @ SV215 @ ( c_Set_Oinsert @ SY2419 @ SY2420 @ SY2421 ) @ ( tc_fun @ SY2421 @ tc_bool ) )
| ~ ( c_lessequals @ SV215 @ SY2420 @ ( tc_fun @ SY2421 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV215 @ ( c_Set_Oinsert @ SY2419 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2421 @ tc_bool ) ) @ SY2421 ) @ ( tc_fun @ SY2421 @ tc_bool ) ) @ SY2420 @ ( tc_fun @ SY2421 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1893,plain,
! [SV216: $i] :
( ( ! [SY2422: $i,SY2423: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV216 @ SY2422 @ SY2423 ) @ ( c_Set_Oinsert @ SV216 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2423 @ tc_bool ) ) @ SY2423 ) @ ( tc_fun @ SY2423 @ tc_bool ) )
= SY2422 )
| ( hBOOL @ ( c_in @ SV216 @ SY2422 @ SY2423 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1894,plain,
! [SV217: $i] :
( ( ! [SY2424: $i,SY2425: $i,SY2426: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV217 @ SY2424 @ SY2425 ) @ ( c_Set_Oinsert @ SV217 @ SY2426 @ SY2425 ) @ ( tc_fun @ SY2425 @ tc_bool ) )
| ~ ( c_lessequals @ SY2424 @ SY2426 @ ( tc_fun @ SY2425 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1426]) ).
thf(1895,plain,
! [SV218: $i] :
( ( ! [SY2427: $i,SY2428: $i,SY2429: $i] :
( ( hBOOL @ ( c_in @ SV218 @ ( c_Set_Oinsert @ SY2427 @ SY2428 @ SY2429 ) @ SY2429 ) )
| ~ ( hBOOL @ ( c_in @ SV218 @ SY2428 @ SY2429 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1427]) ).
thf(1896,plain,
! [SV219: $i] :
( ( ! [SY2430: $i,SY2431: $i,SY2432: $i] :
( ( hBOOL @ ( c_in @ SV219 @ ( c_Set_Oinsert @ SY2430 @ SY2431 @ SY2432 ) @ SY2432 ) )
| ~ ( hBOOL @ ( c_in @ SV219 @ SY2431 @ SY2432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(1897,plain,
! [SV220: $i] :
( ( ! [SY2433: $i,SY2434: $i,SY2435: $i,SY2436: $i] :
( ( c_Set_Oimage @ SV220 @ ( c_Set_Oinsert @ SY2433 @ SY2434 @ SY2435 ) @ SY2435 @ SY2436 )
= ( c_Set_Oinsert @ ( hAPP @ SV220 @ SY2433 ) @ ( c_Set_Oimage @ SV220 @ SY2434 @ SY2435 @ SY2436 ) @ SY2436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1898,plain,
! [SV221: $i] :
( ( ! [SY2437: $i,SY2438: $i,SY2439: $i,SY2440: $i,SY2441: $i,SY2442: $i,SY2443: $i,SY2444: $i] :
( ( ( hAPP @ SV221 @ ( c_Set_Oinsert @ SY2437 @ SY2438 @ SY2439 ) )
= ( hAPP @ ( hAPP @ SY2440 @ SY2437 ) @ ( hAPP @ SV221 @ SY2438 ) ) )
| ! [SY2445: $i,SY2446: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV221 @ SY2441 @ SY2442 @ SY2443 @ SY2440 @ SY2444 @ SY2445 @ SY2446 @ SY2439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1899,plain,
! [SV222: $i] :
( ( ! [SY2447: $i,SY2448: $i,SY2449: $i,SY2450: $i,SY2451: $i,SY2452: $i,SY2453: $i,SY2454: $i] :
( ( ( hAPP @ SV222 @ ( c_Set_Oinsert @ SY2447 @ SY2448 @ SY2449 ) )
= ( hAPP @ ( hAPP @ SY2450 @ SY2447 ) @ ( hAPP @ SV222 @ SY2448 ) ) )
| ! [SY2455: $i,SY2456: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY2451 @ SV222 @ SY2452 @ SY2453 @ SY2454 @ SY2450 @ SY2455 @ SY2456 @ SY2449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1431]) ).
thf(1900,plain,
! [SV223: $i] :
( ( ! [SY2457: $i,SY2458: $i] :
( ( hBOOL @ ( c_in @ SV223 @ SY2457 @ SY2458 ) )
| ! [SY2459: $i] :
( ( SV223 = SY2459 )
| ~ ( hBOOL @ ( c_in @ SV223 @ ( c_Set_Oinsert @ SY2459 @ SY2457 @ SY2458 ) @ SY2458 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1901,plain,
! [SV224: $i] :
( ( ! [SY2460: $i,SY2461: $i] : ( c_lessequals @ SV224 @ ( c_Set_Oinsert @ SY2460 @ SV224 @ SY2461 ) @ ( tc_fun @ SY2461 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(1902,plain,
! [SV225: $i] :
( ( ! [SY2462: $i,SY2463: $i,SY2464: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV225 @ ( c_Set_Oinsert @ SY2462 @ SY2463 @ SY2464 ) @ ( tc_fun @ SY2464 @ tc_bool ) )
= ( c_Set_Oinsert @ SY2462 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV225 @ SY2463 @ ( tc_fun @ SY2464 @ tc_bool ) ) @ SY2464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1903,plain,
! [SV226: $i] :
( ( ! [SY2465: $i,SY2466: $i,SY2467: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV226 @ SY2465 @ SY2466 ) @ SY2467 @ ( tc_fun @ SY2466 @ tc_bool ) )
= ( c_Set_Oinsert @ SV226 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2465 @ SY2467 @ ( tc_fun @ SY2466 @ tc_bool ) ) @ SY2466 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(1904,plain,
! [SV227: $i] :
( ( ! [SY2468: $i,SY2469: $i,SY2470: $i] :
( ( c_lessequals @ SV227 @ ( c_Set_Oinsert @ SY2468 @ SY2469 @ SY2470 ) @ ( tc_fun @ SY2470 @ tc_bool ) )
| ~ ( c_lessequals @ SV227 @ SY2469 @ ( tc_fun @ SY2470 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1436]) ).
thf(1905,plain,
! [SV228: $i] :
( ( ! [SY2471: $i,SY2472: $i] :
( ( c_lessequals @ SV228 @ SY2471 @ ( tc_fun @ SY2472 @ tc_bool ) )
| ! [SY2473: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SY2473 @ SV228 @ SY2472 ) @ SY2471 @ ( tc_fun @ SY2472 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(1906,plain,
! [SV229: $i] :
( ( ! [SY2474: $i,SY2475: $i] : ( hBOOL @ ( c_in @ SV229 @ ( c_Set_Oinsert @ SV229 @ SY2474 @ SY2475 ) @ SY2475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1907,plain,
! [SV230: $i] :
( ( ! [SY2476: $i,SY2477: $i] : ( hBOOL @ ( c_in @ SV230 @ ( c_Set_Oinsert @ SV230 @ SY2476 @ SY2477 ) @ SY2477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(1908,plain,
! [SV231: $i] :
( ( ! [SY2478: $i,SY2479: $i] : ( hBOOL @ ( c_in @ SV231 @ ( c_Set_Oinsert @ SV231 @ SY2478 @ SY2479 ) @ SY2479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(1909,plain,
! [SV232: $i] :
( ( ! [SY2480: $i,SY2481: $i,SY2482: $i] :
( ( ( c_Set_Oinsert @ SV232 @ SY2480 @ SY2481 )
!= ( c_Set_Oinsert @ SV232 @ SY2482 @ SY2481 ) )
| ( hBOOL @ ( c_in @ SV232 @ SY2482 @ SY2481 ) )
| ( SY2480 = SY2482 )
| ( hBOOL @ ( c_in @ SV232 @ SY2480 @ SY2481 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1910,plain,
! [SV233: $i] :
( ( ! [SY2483: $i,SY2484: $i] :
( ( ( c_Set_Oinsert @ SV233 @ SY2483 @ SY2484 )
= SY2483 )
| ~ ( hBOOL @ ( c_in @ SV233 @ SY2483 @ SY2484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1911,plain,
! [SV234: $i] :
( ( ! [SY2485: $i,SY2486: $i,SY2487: $i,SY2488: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV234 @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2485 ) @ SY2486 @ ( tc_fun @ SY2485 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SY2485 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2485 ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SY2485 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2485 ) ) ) @ SY2487 @ tc_Com_Opname @ ( tc_fun @ SY2485 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2485 ) ) @ SY2488 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SY2485 ) ) @ SY2485 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV234 @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2485 ) @ SY2486 @ ( tc_fun @ SY2485 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SY2485 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2485 ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SY2485 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2485 ) ) ) @ SY2487 @ tc_Com_Opname @ ( tc_fun @ SY2485 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2485 ) ) @ SY2488 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SY2485 ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY2485 ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2485 ) @ SY2486 @ ( tc_fun @ SY2485 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SY2485 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2485 ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SY2485 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2485 ) ) ) @ SY2487 @ tc_Com_Opname @ ( tc_fun @ SY2485 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2485 ) ) @ SY2488 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SY2485 ) ) @ SY2485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(1912,plain,
! [SV235: $i] :
( ( ( hAPP @ c_Com_Ocom_OBODY @ SV235 )
!= c_Com_Ocom_OSKIP )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(1913,plain,
! [SV236: $i] :
( ( ! [SY2489: $i,SY2490: $i] :
( ( c_Com_Ocom_OWhile @ SV236 @ SY2489 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SY2490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(1914,plain,
! [SV237: $i] :
( ( ! [SY2491: $i,SY2492: $i,SY2493: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ SV237 )
!= ( c_Com_Ocom_OCond @ SY2491 @ SY2492 @ SY2493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1915,plain,
! [SV238: $i] :
( ( ! [SY2494: $i,SY2495: $i,SY2496: $i] :
( ( c_Com_Ocom_OCond @ SV238 @ SY2494 @ SY2495 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SY2496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1916,plain,
! [SV239: $i] :
( ( ! [SY2497: $i,SY2498: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OLocal @ SV239 @ SY2497 @ SY2498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(1917,plain,
! [SV240: $i] :
( ( ! [SY2499: $i,SY2500: $i,SY2501: $i] :
( ( c_Natural_Oevaln @ SV240 @ SY2499 @ ( c_Suc @ SY2500 ) @ SY2501 )
| ~ ( c_Natural_Oevaln @ SV240 @ SY2499 @ SY2500 @ SY2501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(1918,plain,
! [SV241: $i] :
( ( ! [SY2502: $i,SY2503: $i,SY2504: $i,SY2505: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV241 @ SY2502 @ ( tc_fun @ SY2503 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY2504 @ SY2505 @ ( tc_fun @ SY2503 @ tc_bool ) ) @ ( tc_fun @ SY2503 @ tc_bool ) )
| ~ ( c_lessequals @ SY2505 @ SY2502 @ ( tc_fun @ SY2503 @ tc_bool ) )
| ~ ( c_lessequals @ SV241 @ SY2504 @ ( tc_fun @ SY2503 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1919,plain,
! [SV242: $i] :
( ( ! [SY2506: $i,SY2507: $i,SY2508: $i] :
( ( c_Natural_Oevaln @ SV242 @ SY2506 @ SY2507 @ SY2508 )
| ! [SY2509: $i] :
( ( hBOOL @ ( hAPP @ SY2509 @ SY2506 ) )
| ! [SY2510: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SY2509 @ SY2510 @ SV242 ) @ SY2506 @ SY2507 @ SY2508 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1920,plain,
! [SV243: $i] :
( ( ! [SY2511: $i,SY2512: $i,SY2513: $i,SY2514: $i,SY2515: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV243 @ SY2511 @ SY2512 ) @ SY2513 @ SY2514 @ SY2515 )
| ~ ( c_Natural_Oevaln @ SY2512 @ SY2513 @ SY2514 @ SY2515 )
| ( hBOOL @ ( hAPP @ SV243 @ SY2513 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1921,plain,
! [SV244: $i] :
( ( ! [SY2516: $i,SY2517: $i,SY2518: $i,SY2519: $i] :
( ( c_Com_Ocom_OWhile @ SV244 @ SY2516 )
!= ( c_Com_Ocom_OCall @ SY2517 @ SY2518 @ SY2519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(1922,plain,
! [SV245: $i] :
( ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ SV245 @ SV245 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(1923,plain,
! [SV246: $i] :
( ( ! [SY2520: $i] :
( ( SV246 = SY2520 )
| ! [SY2521: $i] :
( ~ ( c_lessequals @ SY2520 @ SV246 @ ( tc_fun @ SY2521 @ tc_bool ) )
| ~ ( c_lessequals @ SV246 @ SY2520 @ ( tc_fun @ SY2521 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(1924,plain,
! [SV247: $i] :
( ( ! [SY2522: $i] :
( ( SV247 = SY2522 )
| ! [SY2523: $i,SY2524: $i] :
( ~ ( c_Natural_Oevalc @ SY2523 @ SY2524 @ SV247 )
| ~ ( c_Natural_Oevalc @ SY2523 @ SY2524 @ SY2522 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(1925,plain,
! [SV248: $i] :
( ( ! [SY2525: $i] :
( ( SV248 = SY2525 )
| ! [SY2526: $i] :
( ~ ( c_lessequals @ SY2525 @ SV248 @ ( tc_fun @ SY2526 @ tc_bool ) )
| ~ ( c_lessequals @ SV248 @ SY2525 @ ( tc_fun @ SY2526 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1926,plain,
! [SV249: $i] :
( ( ~ ( class_Orderings_Oorder @ SV249 )
| ! [SY2527: $i,SY2528: $i] :
( ( SY2527 = SY2528 )
| ~ ( c_lessequals @ SY2528 @ SY2527 @ SV249 )
| ~ ( c_lessequals @ SY2527 @ SY2528 @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(1927,plain,
! [SV250: $i] :
( ( ~ ( class_Orderings_Oorder @ SV250 )
| ! [SY2529: $i,SY2530: $i] :
( ( SY2529 = SY2530 )
| ~ ( c_lessequals @ SY2530 @ SY2529 @ SV250 )
| ~ ( c_lessequals @ SY2529 @ SY2530 @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1928,plain,
! [SV251: $i] :
( ( ~ ( class_Orderings_Oorder @ SV251 )
| ! [SY2531: $i,SY2532: $i] :
( ( SY2531 = SY2532 )
| ~ ( c_lessequals @ SY2531 @ SY2532 @ SV251 )
| ~ ( c_lessequals @ SY2532 @ SY2531 @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1929,plain,
! [SV252: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV252 )
| ! [SY2533: $i,SY2534: $i] :
( ( c_lessequals @ SY2533 @ SY2534 @ SV252 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SY2533 @ SY2534 @ SV252 ) @ ( c_HOL_Ozero__class_Ozero @ SV252 ) @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(1930,plain,
! [SV253: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV253 )
| ! [SY2535: $i,SY2536: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SY2535 @ SY2536 @ SV253 ) @ ( c_HOL_Ozero__class_Ozero @ SV253 ) @ SV253 )
| ~ ( c_lessequals @ SY2535 @ SY2536 @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(1931,plain,
! [SV254: $i] :
( ( ! [SY2537: $i,SY2538: $i] :
( ( c_Com_Ocom_OLocal @ SV254 @ SY2537 @ SY2538 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1932,plain,
! [SV255: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV255 )
| ! [SY2539: $i,SY2540: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2539 @ SY2540 @ SV255 )
= SY2539 )
| ~ ( c_lessequals @ SY2540 @ SY2539 @ SV255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(1933,plain,
! [SV256: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV256 )
| ! [SY2541: $i,SY2542: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2541 @ SY2542 @ SV256 )
!= SY2542 )
| ( c_lessequals @ SY2541 @ SY2542 @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1934,plain,
! [SV257: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV257 )
| ! [SY2543: $i,SY2544: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2543 @ SY2544 @ SV257 )
= SY2544 )
| ~ ( c_lessequals @ SY2543 @ SY2544 @ SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(1935,plain,
! [SV258: $i] :
( ( ! [SY2545: $i,SY2546: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV258 @ SY2545 @ ( tc_fun @ SY2546 @ tc_bool ) )
= SY2545 )
| ~ ( c_lessequals @ SV258 @ SY2545 @ ( tc_fun @ SY2546 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(1936,plain,
! [SV259: $i] :
( ( ! [SY2547: $i,SY2548: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV259 @ SY2547 @ ( tc_fun @ SY2548 @ tc_bool ) )
= SV259 )
| ~ ( c_lessequals @ SY2547 @ SV259 @ ( tc_fun @ SY2548 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1937,plain,
! [SV260: $i] :
( ( ! [SY2549: $i,SY2550: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV260 @ SY2549 @ ( tc_fun @ SY2550 @ tc_bool ) )
!= SY2549 )
| ( c_lessequals @ SV260 @ SY2549 @ ( tc_fun @ SY2550 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(1938,plain,
! [SV261: $i] :
( ( ! [SY2551: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV261 @ SY2551 @ SV261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(1939,plain,
! [SV262: $i] :
( ( ( c_Suc @ SV262 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1471]) ).
thf(1940,plain,
! [SV263: $i] :
( ( ( c_Suc @ SV263 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1472]) ).
thf(1941,plain,
! [SV264: $i] :
( ( ! [SY2552: $i,SY2553: $i,SY2554: $i,SY2555: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV264 @ SY2552 ) @ SY2553 ) )
| ! [SY2556: $i] :
( ~ ( c_Natural_Oevaln @ SY2554 @ SY2555 @ SY2556 @ SY2553 )
| ! [SY2557: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2557 @ SY2552 ) @ SY2555 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ SY2556 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY2557 ) @ SY2554 ) @ SV264 ) @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(1942,plain,
! [SV265: $i] :
( ( ! [SY2558: $i,SY2559: $i] :
( ( c_Natural_Oevalc @ SV265 @ SY2558 @ SY2559 )
| ! [SY2560: $i] :
( ( hBOOL @ ( hAPP @ SY2560 @ SY2558 ) )
| ! [SY2561: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY2560 @ SY2561 @ SV265 ) @ SY2558 @ SY2559 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1943,plain,
! [SV266: $i] :
( ( ! [SY2562: $i,SY2563: $i,SY2564: $i,SY2565: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV266 @ SY2562 @ SY2563 ) @ SY2564 @ SY2565 )
| ~ ( c_Natural_Oevalc @ SY2563 @ SY2564 @ SY2565 )
| ( hBOOL @ ( hAPP @ SV266 @ SY2564 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(1944,plain,
! [SV267: $i] :
( ( ! [SY2566: $i,SY2567: $i,SY2568: $i,SY2569: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ SV267 @ SY2566 @ SY2567 ) @ SY2568 @ SY2567 @ ( tc_fun @ SY2569 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SY2568 @ SV267 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2566 @ SY2568 @ SY2567 @ ( tc_fun @ SY2569 @ tc_bool ) ) @ ( tc_fun @ SY2569 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1945,plain,
! [SV268: $i] :
( ( ( c_Com_OWT @ SV268 )
| ! [SY2570: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SY2570 @ SV268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(1946,plain,
! [SV269: $i] :
( ( ( c_Com_OWT @ SV269 )
| ! [SY2571: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV269 @ SY2571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(1947,plain,
! [SV270: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV270 )
| ! [SY2572: $i,SY2573: $i] :
( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ SY2572 @ SV270 ) @ SY2573 @ SV270 )
| ~ ( hBOOL @ ( c_in @ SY2573 @ SY2572 @ SV270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(1948,plain,
! [SV271: $i] :
( ( ~ ( class_Orderings_Oorder @ SV271 )
| ! [SY2574: $i,SY2575: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV271 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2574 @ SY2575 @ SV271 ) )
| ( c_lessequals @ SY2574 @ SY2575 @ SV271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1481]) ).
thf(1949,plain,
! [SV272: $i] :
( ( ~ ( class_Orderings_Oorder @ SV272 )
| ! [SY2576: $i,SY2577: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV272 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2576 @ SY2577 @ SV272 ) )
| ~ ( c_lessequals @ SY2576 @ SY2577 @ SV272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(1950,plain,
! [SV273: $i] :
( ( ! [SY2578: $i,SY2579: $i,SY2580: $i,SY2581: $i,SY2582: $i,SY2583: $i,SY2584: $i,SY2585: $i,SY2586: $i,SY2587: $i,SY2588: $i] :
( ( c_Com_Ocom_Ocom__case @ SV273 @ SY2578 @ SY2579 @ SY2580 @ SY2581 @ SY2582 @ SY2583 @ SY2584 @ ( c_Com_Ocom_OLocal @ SY2585 @ SY2586 @ SY2587 ) @ SY2588 )
= ( hAPP @ ( hAPP @ ( hAPP @ SY2579 @ SY2585 ) @ SY2586 ) @ SY2587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1483]) ).
thf(1951,plain,
! [SV274: $i] :
( ( ! [SY2589: $i,SY2590: $i,SY2591: $i,SY2592: $i,SY2593: $i,SY2594: $i,SY2595: $i,SY2596: $i,SY2597: $i,SY2598: $i] :
( ( c_Com_Ocom_Ocom__case @ SV274 @ SY2589 @ SY2590 @ SY2591 @ SY2592 @ SY2593 @ SY2594 @ SY2595 @ ( c_Com_Ocom_OWhile @ SY2596 @ SY2597 ) @ SY2598 )
= ( hAPP @ ( hAPP @ SY2593 @ SY2596 ) @ SY2597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1952,plain,
! [SV275: $i] :
( ( ! [SY2599: $i,SY2600: $i,SY2601: $i,SY2602: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV275 @ SY2599 @ ( tc_fun @ SY2600 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2601 @ SY2602 @ ( tc_fun @ SY2600 @ tc_bool ) ) @ ( tc_fun @ SY2600 @ tc_bool ) )
| ~ ( c_lessequals @ SY2599 @ SY2602 @ ( tc_fun @ SY2600 @ tc_bool ) )
| ~ ( c_lessequals @ SV275 @ SY2601 @ ( tc_fun @ SY2600 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1485]) ).
thf(1953,plain,
! [SV276: $i] :
( ( ! [SY2603: $i,SY2604: $i,SY2605: $i,SY2606: $i,SY2607: $i,SY2608: $i] :
( ( c_Fun_Ocomp @ SV276 @ ( c_Fun_Ocomp @ SY2603 @ SY2604 @ SY2605 @ SY2606 @ SY2607 ) @ SY2606 @ SY2608 @ SY2607 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV276 @ SY2603 @ SY2606 @ SY2608 @ SY2605 ) @ SY2604 @ SY2605 @ SY2608 @ SY2607 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(1954,plain,
! [SV277: $i] :
( ( ! [SY2609: $i] :
( ( c_Com_Ocom_OSemi @ SV277 @ SY2609 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(1955,plain,
! [SV278: $i] :
( ( ! [SY2610: $i,SY2611: $i,SY2612: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV278 @ SY2610 @ SY2611 @ SY2612 @ t_a ) @ v_x )
= ( hAPP @ SV278 @ ( hAPP @ SY2610 @ v_x ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(1956,plain,
! [SV279: $i] :
( ( ! [SY2613: $i,SY2614: $i,SY2615: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV279 @ SY2613 @ SY2614 ) @ SY2615 @ ( tc_fun @ SY2614 @ tc_bool ) )
| ~ ( c_lessequals @ SY2613 @ SY2615 @ ( tc_fun @ SY2614 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV279 @ SY2615 @ SY2614 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(1957,plain,
! [SV280: $i] :
( ( ! [SY2616: $i,SY2617: $i,SY2618: $i,SY2619: $i,SY2620: $i] :
( ( c_Set_Oimage @ SV280 @ ( c_Set_Oimage @ SY2616 @ SY2617 @ SY2618 @ SY2619 ) @ SY2619 @ SY2620 )
= ( c_Set_Oimage @ ( c_COMBB @ SV280 @ SY2616 @ SY2619 @ SY2620 @ SY2618 ) @ SY2617 @ SY2618 @ SY2620 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1958,plain,
! [SV281: $i] :
( ( ! [SY2621: $i,SY2622: $i,SY2623: $i,SY2624: $i,SY2625: $i] :
( ( ( c_Com_Ocom_OLocal @ SV281 @ SY2621 @ SY2622 )
!= ( c_Com_Ocom_OLocal @ SY2623 @ SY2624 @ SY2625 ) )
| ( SY2622 = SY2625 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(1959,plain,
! [SV282: $i] :
( ( ! [SY2626: $i,SY2627: $i,SY2628: $i,SY2629: $i] :
( ! [SY2630: $i] :
( ( c_Com_Ocom_OLocal @ SV282 @ SY2626 @ SY2627 )
!= ( c_Com_Ocom_OLocal @ SY2628 @ SY2629 @ SY2630 ) )
| ( SY2626 = SY2629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(1960,plain,
! [SV283: $i] :
( ( ! [SY2631: $i,SY2632: $i,SY2633: $i] :
( ! [SY2634: $i,SY2635: $i] :
( ( c_Com_Ocom_OLocal @ SV283 @ SY2631 @ SY2632 )
!= ( c_Com_Ocom_OLocal @ SY2633 @ SY2634 @ SY2635 ) )
| ( SV283 = SY2633 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1961,plain,
! [SV284: $i] :
( ( ! [SY2636: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV284 @ SY2636 ) )
| ~ ( c_Com_OWT @ SY2636 )
| ~ ( c_Com_OWT @ SV284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1962,plain,
! [SV285: $i] :
( ( ! [SY2637: $i,SY2638: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCall @ SV285 @ SY2637 @ SY2638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(1963,plain,
! [SV286: $i] :
( ( ! [SY2639: $i,SY2640: $i,SY2641: $i,SY2642: $i,SY2643: $i] :
( ( c_Set_Oimage @ ( c_Fun_Ocomp @ SV286 @ SY2639 @ SY2640 @ SY2641 @ SY2642 ) @ SY2643 @ SY2642 @ SY2641 )
= ( c_Set_Oimage @ SV286 @ ( c_Set_Oimage @ SY2639 @ SY2643 @ SY2642 @ SY2640 ) @ SY2640 @ SY2641 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(1964,plain,
! [SV287: $i] :
( ( ! [SY2644: $i,SY2645: $i,SY2646: $i] :
( ( c_Com_Ocom_OWhile @ SV287 @ SY2644 )
!= ( c_Com_Ocom_OSemi @ SY2645 @ SY2646 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(1965,plain,
! [SV288: $i] :
( ( ! [SY2647: $i,SY2648: $i,SY2649: $i] :
( ( hBOOL @ ( c_in @ SV288 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2647 @ SY2648 @ ( tc_fun @ SY2649 @ tc_bool ) ) @ SY2649 ) )
| ~ ( hBOOL @ ( c_in @ SV288 @ SY2648 @ SY2649 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(1966,plain,
! [SV289: $i] :
( ( ! [SY2650: $i,SY2651: $i,SY2652: $i] :
( ( hBOOL @ ( c_in @ SV289 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2650 @ SY2651 @ ( tc_fun @ SY2652 @ tc_bool ) ) @ SY2652 ) )
| ~ ( hBOOL @ ( c_in @ SV289 @ SY2650 @ SY2652 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(1967,plain,
! [SV290: $i] :
( ( ! [SY2653: $i,SY2654: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV290 @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2653 @ tc_bool ) ) @ ( tc_fun @ SY2653 @ tc_bool ) @ SY2654 ) @ SY2654 @ ( tc_fun @ SY2653 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2653 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(1968,plain,
! [SV291: $i] :
( ( ! [SY2655: $i] :
( ( hBOOL @ ( hAPP @ SV291 @ SY2655 ) )
| ! [SY2656: $i] :
( ( SY2656 = SY2655 )
| ! [SY2657: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV291 @ SY2657 ) @ SY2655 @ SY2656 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1501]) ).
thf(1969,plain,
! [SV292: $i] :
( ( ( c_Suc @ SV292 )
!= SV292 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(1970,plain,
! [SV293: $i] :
( ( SV293
!= ( c_Suc @ SV293 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(1971,plain,
! [SV294: $i] :
( ( ! [SY2658: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV294 )
| ! [SY2659: $i] :
( ( c_lessequals @ SY2658 @ SY2659 @ SV294 )
| ! [SY2660: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2660 @ SY2658 @ SV294 ) @ SY2659 @ SV294 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(1972,plain,
! [SV295: $i] :
( ( ! [SY2661: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV295 )
| ! [SY2662: $i] :
( ( c_lessequals @ SY2661 @ SY2662 @ SV295 )
| ! [SY2663: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2661 @ SY2663 @ SV295 ) @ SY2662 @ SV295 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(1973,plain,
! [SV296: $i] :
( ( ! [SY2664: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV296 )
| ! [SY2665: $i,SY2666: $i] :
( ( c_lessequals @ SY2664 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2665 @ SY2666 @ SV296 ) @ SV296 )
| ~ ( c_lessequals @ SY2664 @ SY2666 @ SV296 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1974,plain,
! [SV297: $i] :
( ( ! [SY2667: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV297 )
| ! [SY2668: $i] :
( ! [SY2669: $i] : ( c_lessequals @ SY2667 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2668 @ SY2669 @ SV297 ) @ SV297 )
| ~ ( c_lessequals @ SY2667 @ SY2668 @ SV297 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(1975,plain,
! [SV298: $i] :
( ( ! [SY2670: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV298 )
| ! [SY2671: $i] :
( ( c_lessequals @ SY2670 @ SY2671 @ SV298 )
| ! [SY2672: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2672 @ SY2670 @ SV298 ) @ SY2671 @ SV298 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1976,plain,
! [SV299: $i] :
( ( ! [SY2673: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ SV299 )
| ! [SY2674: $i] :
( ( c_lessequals @ SY2673 @ SY2674 @ SV299 )
| ! [SY2675: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2673 @ SY2675 @ SV299 ) @ SY2674 @ SV299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(1977,plain,
! [SV300: $i] :
( ( ! [SY2676: $i,SY2677: $i] :
( ( c_lessequals @ SV300 @ SY2676 @ ( tc_fun @ SY2677 @ tc_bool ) )
| ! [SY2678: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV300 @ SY2678 @ ( tc_fun @ SY2677 @ tc_bool ) ) @ SY2676 @ ( tc_fun @ SY2677 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1978,plain,
! [SV301: $i] :
( ( ! [SY2679: $i,SY2680: $i] :
( ( c_lessequals @ SV301 @ SY2679 @ ( tc_fun @ SY2680 @ tc_bool ) )
| ! [SY2681: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2681 @ SV301 @ ( tc_fun @ SY2680 @ tc_bool ) ) @ SY2679 @ ( tc_fun @ SY2680 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(1979,plain,
! [SV302: $i] :
( ( ! [SY2682: $i] :
( ~ ( class_Orderings_Oorder @ SV302 )
| ! [SY2683: $i] :
( ( c_lessequals @ SY2682 @ SY2683 @ SV302 )
| ! [SY2684: $i] :
( ~ ( c_lessequals @ SY2682 @ SY2684 @ SV302 )
| ~ ( c_lessequals @ SY2684 @ SY2683 @ SV302 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(1980,plain,
! [SV303: $i] :
( ( ! [SY2685: $i] :
( ~ ( class_Orderings_Opreorder @ SV303 )
| ! [SY2686: $i] :
( ( c_lessequals @ SY2685 @ SY2686 @ SV303 )
| ! [SY2687: $i] :
( ~ ( c_lessequals @ SY2687 @ SY2686 @ SV303 )
| ~ ( c_lessequals @ SY2685 @ SY2687 @ SV303 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1981,plain,
! [SV304: $i] :
( ( ! [SY2688: $i,SY2689: $i] :
( ( hBOOL @ ( c_in @ SV304 @ SY2688 @ SY2689 ) )
| ! [SY2690: $i] :
( ~ ( hBOOL @ ( c_in @ SV304 @ SY2690 @ SY2689 ) )
| ~ ( c_lessequals @ SY2690 @ SY2688 @ ( tc_fun @ SY2689 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(1982,plain,
! [SV305: $i] :
( ( ! [SY2691: $i,SY2692: $i] :
( ( hBOOL @ ( c_in @ SV305 @ SY2691 @ SY2692 ) )
| ! [SY2693: $i] :
( ~ ( hBOOL @ ( c_in @ SV305 @ SY2693 @ SY2692 ) )
| ~ ( c_lessequals @ SY2693 @ SY2691 @ ( tc_fun @ SY2692 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(1983,plain,
! [SV306: $i] :
( ( ! [SY2694: $i] : ( c_lessequals @ SV306 @ SV306 @ ( tc_fun @ SY2694 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(1984,plain,
! [SV307: $i] :
( ( ! [SY2695: $i,SY2696: $i] :
( ( hBOOL @ ( c_in @ SV307 @ SY2695 @ SY2696 ) )
| ! [SY2697: $i] :
( ~ ( c_lessequals @ SY2697 @ SY2695 @ ( tc_fun @ SY2696 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV307 @ SY2697 @ SY2696 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(1985,plain,
! [SV308: $i] :
( ( ! [SY2698: $i,SY2699: $i] :
( ( hBOOL @ ( c_in @ SV308 @ SY2698 @ SY2699 ) )
| ! [SY2700: $i] :
( ~ ( hBOOL @ ( c_in @ SV308 @ SY2700 @ SY2699 ) )
| ~ ( c_lessequals @ SY2700 @ SY2698 @ ( tc_fun @ SY2699 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1986,plain,
! [SV309: $i] :
( ( ! [SY2701: $i] : ( c_lessequals @ SV309 @ SV309 @ ( tc_fun @ SY2701 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(1987,plain,
! [SV310: $i] :
( ( ! [SY2702: $i,SY2703: $i] :
( ( c_lessequals @ SV310 @ SY2702 @ ( tc_fun @ SY2703 @ tc_bool ) )
| ! [SY2704: $i] :
( ~ ( c_lessequals @ SY2704 @ SY2702 @ ( tc_fun @ SY2703 @ tc_bool ) )
| ~ ( c_lessequals @ SV310 @ SY2704 @ ( tc_fun @ SY2703 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1988,plain,
! [SV311: $i] :
( ( ! [SY2705: $i] :
( ( hBOOL @ ( hAPP @ SV311 @ SY2705 ) )
| ! [SY2706: $i] :
( ~ ( hBOOL @ ( hAPP @ SY2706 @ SY2705 ) )
| ! [SY2707: $i] :
~ ( c_lessequals @ SY2706 @ SV311 @ ( tc_fun @ SY2707 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(1989,plain,
! [SV312: $i] :
( ( ~ ( class_Orderings_Oorder @ SV312 )
| ! [SY2708: $i] : ( c_lessequals @ SY2708 @ SY2708 @ SV312 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1990,plain,
! [SV313: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV313 )
| ! [SY2709: $i] : ( c_lessequals @ SY2709 @ SY2709 @ SV313 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1991,plain,
! [SV314: $i] :
( ( ! [SY2710: $i] :
( ( hBOOL @ ( hAPP @ SV314 @ SY2710 ) )
| ! [SY2711: $i] :
( ! [SY2712: $i] :
~ ( c_lessequals @ SY2711 @ SV314 @ ( tc_fun @ SY2712 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SY2711 @ SY2710 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(1992,plain,
! [SV315: $i] :
( ( ! [SY2713: $i,SY2714: $i] :
( ( c_Com_Ocom_OCall @ SV315 @ SY2713 @ SY2714 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(1993,plain,
! [SV316: $i] :
( ( ~ ( class_Orderings_Oorder @ SV316 )
| ! [SY2715: $i,SY2716: $i] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2715 @ SY2716 @ SV316 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV316 @ tc_bool ) ) )
| ( c_lessequals @ SY2715 @ SY2716 @ SV316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1994,plain,
! [SV317: $i] :
( ( ~ ( class_Orderings_Oorder @ SV317 )
| ! [SY2717: $i,SY2718: $i] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2717 @ SY2718 @ SV317 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV317 @ tc_bool ) ) )
| ~ ( c_lessequals @ SY2717 @ SY2718 @ SV317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1995,plain,
! [SV318: $i] :
( ( ! [SY2719: $i,SY2720: $i,SY2721: $i,SY2722: $i,SY2723: $i,SY2724: $i,SY2725: $i,SY2726: $i,SY2727: $i,SY2728: $i,SY2729: $i] :
( ( c_Com_Ocom_Ocom__case @ SV318 @ SY2719 @ SY2720 @ SY2721 @ SY2722 @ SY2723 @ SY2724 @ SY2725 @ ( c_Com_Ocom_OCond @ SY2726 @ SY2727 @ SY2728 ) @ SY2729 )
= ( hAPP @ ( hAPP @ ( hAPP @ SY2722 @ SY2726 ) @ SY2727 ) @ SY2728 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1996,plain,
! [SV319: $i] :
( ( ! [SY2730: $i,SY2731: $i,SY2732: $i,SY2733: $i,SY2734: $i,SY2735: $i] :
( ! [SY2736: $i] :
( ( c_Fun_Ocomp @ SV319 @ SY2730 @ SY2731 @ SY2732 @ SY2733 )
!= ( c_Fun_Ocomp @ SY2734 @ SY2735 @ SY2736 @ SY2732 @ SY2733 ) )
| ! [SY2737: $i] :
( ( hAPP @ SV319 @ ( hAPP @ SY2730 @ SY2737 ) )
= ( hAPP @ SY2734 @ ( hAPP @ SY2735 @ SY2737 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1997,plain,
! [SV320: $i] :
( ( ! [SY2738: $i,SY2739: $i,SY2740: $i,SY2741: $i,SY2742: $i,SY2743: $i,SY2744: $i,SY2745: $i] :
( ( ( hAPP @ SV320 @ ( hAPP @ SY2738 @ SY2739 ) )
!= ( hAPP @ SY2740 @ ( hAPP @ SY2741 @ SY2742 ) ) )
| ! [SY2746: $i,SY2747: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV320 @ SY2738 @ SY2743 @ SY2744 @ SY2745 ) @ SY2739 )
= ( hAPP @ ( c_Fun_Ocomp @ SY2740 @ SY2741 @ SY2746 @ SY2744 @ SY2747 ) @ SY2742 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(1998,plain,
! [SV321: $i] :
( ( ! [SY2748: $i,SY2749: $i] :
( ( hBOOL @ ( hAPP @ SV321 @ SY2748 ) )
| ( SY2749 = SY2748 )
| ! [SY2750: $i,SY2751: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV321 @ SY2750 ) @ SY2748 @ SY2751 @ SY2749 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1999,plain,
! [SV322: $i] :
( ( ! [SY2752: $i,SY2753: $i,SY2754: $i,SY2755: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV322 @ SY2752 @ ( tc_fun @ SY2753 @ tc_bool ) ) @ SY2754 @ SY2753 @ ( tc_fun @ SY2755 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV322 @ SY2754 @ SY2753 @ ( tc_fun @ SY2755 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY2752 @ SY2754 @ SY2753 @ ( tc_fun @ SY2755 @ tc_bool ) ) @ ( tc_fun @ SY2755 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(2000,plain,
! [SV323: $i] :
( ( ! [SY2756: $i] :
( ( c_The @ ( hAPP @ ( c_fequal @ SV323 ) @ SY2756 ) @ SV323 )
= SY2756 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(2001,plain,
! [SV324: $i] :
( ( ! [SY2757: $i,SY2758: $i,SY2759: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV324 @ ( c_HOL_Ominus__class_Ominus @ SY2757 @ SY2758 @ ( tc_fun @ SY2759 @ tc_bool ) ) @ ( tc_fun @ SY2759 @ tc_bool ) )
= SY2758 )
| ~ ( c_lessequals @ SV324 @ SY2757 @ ( tc_fun @ SY2759 @ tc_bool ) )
| ~ ( c_lessequals @ SY2758 @ SV324 @ ( tc_fun @ SY2759 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(2002,plain,
! [SV325: $i] :
( ( ! [SY2760: $i,SY2761: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
| ! [SY2762: $i,SY2763: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SY2760 @ SY2761 @ SV325 )
!= ( c_HOL_Ominus__class_Ominus @ SY2762 @ SY2763 @ SV325 ) )
| ( c_lessequals @ SY2763 @ SY2762 @ SV325 )
| ~ ( c_lessequals @ SY2761 @ SY2760 @ SV325 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(2003,plain,
! [SV326: $i] :
( ( ! [SY2764: $i,SY2765: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV326 )
| ! [SY2766: $i,SY2767: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SY2764 @ SY2765 @ SV326 )
!= ( c_HOL_Ominus__class_Ominus @ SY2766 @ SY2767 @ SV326 ) )
| ( c_lessequals @ SY2765 @ SY2764 @ SV326 )
| ~ ( c_lessequals @ SY2767 @ SY2766 @ SV326 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(2004,plain,
! [SV327: $i] :
( ( ! [SY2768: $i,SY2769: $i,SY2770: $i,SY2771: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV327 @ SY2768 @ SY2769 @ SY2770 ) @ ( c_Set_Oimage @ SV327 @ SY2771 @ SY2769 @ SY2770 ) @ ( tc_fun @ SY2770 @ tc_bool ) )
| ~ ( c_lessequals @ SY2768 @ SY2771 @ ( tc_fun @ SY2769 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(2005,plain,
! [SV328: $i] :
( ( ! [SY2772: $i,SY2773: $i] :
( ~ ( c_lessequals @ SV328 @ SY2772 @ ( tc_fun @ SY2773 @ tc_bool ) )
| ! [SY2774: $i,SY2775: $i] : ( c_lessequals @ ( c_Set_Oimage @ SY2774 @ SV328 @ SY2773 @ SY2775 ) @ ( c_Set_Oimage @ SY2774 @ SY2772 @ SY2773 @ SY2775 ) @ ( tc_fun @ SY2775 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(2006,plain,
! [SV329: $i] :
( ( ! [SY2776: $i,SY2777: $i,SY2778: $i] :
( ( c_Natural_Oevaln @ SV329 @ SY2776 @ SY2777 @ SY2778 )
| ! [SY2779: $i] :
( ( c_Natural_Oevaln @ SY2779 @ SY2776 @ SY2777 @ SY2778 )
| ! [SY2780: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SY2780 @ SY2779 @ SV329 ) @ SY2776 @ SY2777 @ SY2778 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(2007,plain,
! [SV330: $i] :
( ( ! [SY2781: $i,SY2782: $i,SY2783: $i,SY2784: $i] :
( ( c_Set_Oimage @ SV330 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2781 @ SY2782 @ ( tc_fun @ SY2783 @ tc_bool ) ) @ SY2783 @ SY2784 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ SV330 @ SY2781 @ SY2783 @ SY2784 ) @ ( c_Set_Oimage @ SV330 @ SY2782 @ SY2783 @ SY2784 ) @ ( tc_fun @ SY2784 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(2008,plain,
! [SV331: $i] :
( ( ! [SY2785: $i,SY2786: $i,SY2787: $i,SY2788: $i,SY2789: $i] :
( ( c_Com_Ocom_OLocal @ SV331 @ SY2785 @ SY2786 )
!= ( c_Com_Ocom_OCall @ SY2787 @ SY2788 @ SY2789 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(2009,plain,
! [SV332: $i] :
( ( ! [SY2790: $i,SY2791: $i] :
( ( c_Natural_Oevalc @ SV332 @ SY2790 @ SY2791 )
| ! [SY2792: $i] :
( ( c_Natural_Oevalc @ SY2792 @ SY2790 @ SY2791 )
| ! [SY2793: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY2793 @ SY2792 @ SV332 ) @ SY2790 @ SY2791 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(2010,plain,
! [SV333: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV333 )
| ! [SY2794: $i,SY2795: $i] :
( ( c_lessequals @ SY2794 @ ( c_Complete__Lattice_OSup__class_OSup @ SY2795 @ SV333 ) @ SV333 )
| ~ ( hBOOL @ ( c_in @ SY2794 @ SY2795 @ SV333 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(2011,plain,
! [SV334: $i] :
( ( ( c_Com_OWT @ SV334 )
| ! [SY2796: $i,SY2797: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SY2796 @ SY2797 @ SV334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(2012,plain,
! [SV335: $i] :
( ( ( c_Com_OWT @ SV335 )
| ! [SY2798: $i,SY2799: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SY2798 @ SV335 @ SY2799 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(2013,plain,
! [SV336: $i] :
( ( ! [SY2800: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ SV336 @ SY2800 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(2014,plain,
! [SV337: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV337 )
| ! [SY2801: $i,SY2802: $i] :
( ( c_lessequals @ SY2801 @ SY2802 @ SV337 )
| ( c_lessequals @ SY2802 @ SY2801 @ SV337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(2015,plain,
! [SV338: $i] :
( ( ! [SY2803: $i,SY2804: $i,SY2805: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ SV338 )
!= ( c_Com_Ocom_OLocal @ SY2803 @ SY2804 @ SY2805 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(2016,plain,
! [SV339: $i] :
( ( ! [SY2806: $i,SY2807: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ SV339 )
!= ( c_Com_Ocom_OWhile @ SY2806 @ SY2807 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(2017,plain,
! [SV340: $i] :
( ( ! [SY2808: $i,SY2809: $i,SY2810: $i] :
( ( c_Com_Ocom_OCall @ SV340 @ SY2808 @ SY2809 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SY2810 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(2018,plain,
! [SV341: $i] :
( ( ! [SY2811: $i,SY2812: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ SV341 )
!= ( c_Com_Ocom_OSemi @ SY2811 @ SY2812 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(2019,plain,
! [SV342: $i] :
( ( ! [SY2813: $i,SY2814: $i] :
( ( c_Com_Ocom_OSemi @ SV342 @ SY2813 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SY2814 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(2020,plain,
! [SV343: $i] :
( ( ! [SY2815: $i,SY2816: $i,SY2817: $i] :
( ( c_Com_Ocom_OLocal @ SV343 @ SY2815 @ SY2816 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SY2817 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(2021,plain,
! [SV344: $i] :
( ( ! [SY2818: $i,SY2819: $i,SY2820: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ SV344 )
!= ( c_Com_Ocom_OCall @ SY2818 @ SY2819 @ SY2820 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1554]) ).
thf(2022,plain,
! [SV345: $i] :
( ( ! [SY2821: $i,SY2822: $i,SY2823: $i,SY2824: $i,SY2825: $i,SY2826: $i,SY2827: $i,SY2828: $i,SY2829: $i] :
( ( c_Com_Ocom_Ocom__case @ SV345 @ SY2821 @ SY2822 @ SY2823 @ SY2824 @ SY2825 @ SY2826 @ SY2827 @ ( hAPP @ c_Com_Ocom_OBODY @ SY2828 ) @ SY2829 )
= ( hAPP @ SY2826 @ SY2828 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(2023,plain,
! [SV346: $i] :
( ( c_Com_Ocom_OSKIP
!= ( hAPP @ c_Com_Ocom_OBODY @ SV346 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(2024,plain,
! [SV347: $i] :
( ( ! [SY2830: $i,SY2831: $i,SY2832: $i] : ( c_Hoare__Mirabelle_Otriple__valid @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV347 ) @ SY2830 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SY2831 ) ) @ SY2832 ) @ SV347 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(2025,plain,
! [SV348: $i] :
( ( ! [SY2833: $i,SY2834: $i,SY2835: $i,SY2836: $i] :
( ~ ( hBOOL @ ( hAPP @ SV348 @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SY2833 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ SY2834 ) @ SY2835 ) @ SY2836 ) @ t_b @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV348 @ ( hAPP @ ( hAPP @ ( hAPP @ SY2833 @ SY2834 ) @ SY2835 ) @ SY2836 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(2026,plain,
! [SV349: $i] :
( ( ! [SY2837: $i,SY2838: $i,SY2839: $i,SY2840: $i] :
( ~ ( hBOOL @ ( hAPP @ SV349 @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SY2837 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ SY2838 ) @ SY2839 ) @ SY2840 ) @ t_b @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV349 @ ( hAPP @ ( hAPP @ ( hAPP @ SY2837 @ SY2838 ) @ SY2839 ) @ SY2840 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(2027,plain,
! [SV350: $i] :
( ( ! [SY2841: $i,SY2842: $i,SY2843: $i,SY2844: $i,SY2845: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ SV350 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2841 ) @ SY2842 ) @ SY2843 ) @ SY2844 ) @ SY2841 @ SY2845 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV350 @ SY2842 ) @ SY2843 ) @ SY2844 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(2028,plain,
! [SV351: $i] :
( ( ! [SY2846: $i,SY2847: $i,SY2848: $i,SY2849: $i,SY2850: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SV351 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2846 ) @ SY2847 ) @ SY2848 ) @ SY2849 ) @ SY2846 @ SY2850 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV351 @ SY2847 ) @ SY2848 ) @ SY2849 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1561]) ).
thf(2029,plain,
! [SV352: $i] :
( ( ! [SY2851: $i,SY2852: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV352 @ SY2851 @ SY2852 )
| ! [SY2853: $i] :
( ~ ( c_lessequals @ SY2851 @ SY2853 @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY2852 ) @ tc_bool ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV352 @ SY2853 @ SY2852 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1562]) ).
thf(2030,plain,
! [SV353: $i] :
( ( ! [SY2854: $i,SY2855: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ SY2854 @ SY2855 )
| ! [SY2856: $i] :
( ~ ( c_lessequals @ SY2856 @ SV353 @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY2855 ) @ tc_bool ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY2856 @ SY2854 @ SY2855 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(2031,plain,
! [SV354: $i] :
( ( ! [SY2857: $i,SY2858: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV354 @ SY2857 @ SY2858 )
| ~ ( c_lessequals @ SY2857 @ SV354 @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY2858 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(2032,plain,
! [SV355: $i] :
( ( ! [SY2859: $i,SY2860: $i,SY2861: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV355 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY2859 ) @ SY2860 ) @ SY2861 ) @ ( 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 @ SV355 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ ( c_COMBK @ ( hAPP @ ( c_COMBC @ ( c_fequal @ tc_Com_Ostate ) @ tc_Com_Ostate @ tc_Com_Ostate @ tc_bool ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ SV355 @ SY2859 @ SY2861 @ SY2860 ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) ) @ SY2860 ) @ ( c_COMBK @ ( hAPP @ SY2861 @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ SV355 @ SY2859 @ SY2861 @ SY2860 ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_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)],[1566]) ).
thf(2033,plain,
! [SV356: $i] :
( ( ! [SY2862: $i,SY2863: $i,SY2864: $i,SY2865: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV356 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2862 ) @ ( hAPP @ SY2863 @ SY2864 ) ) @ ( hAPP @ c_Com_Ocom_OBODY @ SY2864 ) ) @ ( hAPP @ SY2865 @ SY2864 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY2862 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2862 ) ) @ SY2862 )
| ! [SY2866: $i] :
( ~ ( hBOOL @ ( c_in @ SY2864 @ SY2866 @ tc_Com_Opname ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV356 @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2862 ) @ SY2863 @ ( tc_fun @ SY2862 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SY2862 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2862 ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SY2862 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2862 ) ) ) @ SY2865 @ tc_Com_Opname @ ( tc_fun @ SY2862 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2862 ) ) @ SY2866 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SY2862 ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY2862 ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2862 ) @ SY2863 @ ( tc_fun @ SY2862 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SY2862 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2862 ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SY2862 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2862 ) ) ) @ SY2865 @ tc_Com_Opname @ ( tc_fun @ SY2862 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2862 ) ) @ SY2866 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SY2862 ) ) @ SY2862 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(2034,plain,
! [SV357: $i] :
( ( ( ( hAPP @ c_Com_Obody @ SV357 )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) )
| ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ SV357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(2035,plain,
! [SV358: $i] :
( ( ! [SY2867: $i] :
( ( hAPP @ ( c_Option_Othe @ SV358 ) @ ( c_Option_Ooption_OSome @ SY2867 @ SV358 ) )
= SY2867 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(2036,plain,
! [SV359: $i] :
( ( ! [SY2868: $i,SY2869: $i,SY2870: $i,SY2871: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV359 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2868 ) @ SY2869 ) @ ( c_Com_Ocom_OWhile @ SY2870 @ SY2871 ) ) @ ( c_Hoare__Mirabelle_Opeek__and @ SY2869 @ ( c_Fun_Ocomp @ c_Not @ SY2870 @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ SY2868 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY2868 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2868 ) ) @ SY2868 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV359 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2868 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SY2869 @ SY2870 @ SY2868 ) ) @ SY2871 ) @ SY2869 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY2868 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2868 ) ) @ SY2868 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(2037,plain,
! [SV360: $i] :
( ( ! [SY2872: $i,SY2873: $i,SY2874: $i,SY2875: $i,SY2876: $i,SY2877: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2872 ) @ SY2873 ) @ ( c_Com_Ocom_OCond @ SY2874 @ SY2875 @ SY2876 ) ) @ SY2877 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY2872 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2872 ) ) @ SY2872 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2872 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SY2873 @ ( c_Fun_Ocomp @ c_Not @ SY2874 @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ SY2872 ) ) @ SY2876 ) @ SY2877 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY2872 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2872 ) ) @ SY2872 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY2872 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SY2873 @ SY2874 @ SY2872 ) ) @ SY2875 ) @ SY2877 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY2872 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY2872 ) ) @ SY2872 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(2038,plain,
! [SV361: $i] :
( ( ! [SY2878: $i,SY2879: $i,SY2880: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV361 ) ) @ SY2878 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ SV361 @ SY2879 @ SY2878 @ SY2880 ) @ SY2880 )
| ~ ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ SV361 ) @ SY2878 @ SY2879 @ SY2880 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(2039,plain,
! [SV362: $i] :
( ( ! [SY2881: $i,SY2882: $i,SY2883: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ SV362 ) @ SY2881 @ ( c_Suc @ SY2882 ) @ SY2883 )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV362 ) ) @ SY2881 @ SY2882 @ SY2883 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(2040,plain,
! [SV363: $i] :
( ( ~ ( class_Orderings_Obot @ SV363 )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ SV363 ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ SV363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(2041,plain,
! [SV364: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV364 )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV364 @ tc_bool ) ) @ SV364 )
= ( c_Orderings_Obot__class_Obot @ SV364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(2042,plain,
! [SV365: $i] :
( ( ! [SY2884: $i] :
( ( c_Collect @ ( hAPP @ ( c_fequal @ SV365 ) @ SY2884 ) @ SV365 )
= ( c_Set_Oinsert @ SY2884 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV365 @ tc_bool ) ) @ SV365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(2043,plain,
! [SV366: $i] :
( ( ! [SY2885: $i,SY2886: $i] :
( ( SV366
= ( c_Set_Oinsert @ SY2885 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2886 @ tc_bool ) ) @ SY2886 ) )
| ( SV366
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2886 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV366 @ ( c_Set_Oinsert @ SY2885 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2886 @ tc_bool ) ) @ SY2886 ) @ ( tc_fun @ SY2886 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(2044,plain,
! [SV367: $i] :
( ( ! [SY2887: $i] : ( hBOOL @ ( c_in @ SV367 @ ( c_Set_Oinsert @ SV367 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2887 @ tc_bool ) ) @ SY2887 ) @ SY2887 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(2045,plain,
! [SV368: $i] :
( ( ! [SY2888: $i,SY2889: $i,SY2890: $i,SY2891: $i,SY2892: $i,SY2893: $i,SY2894: $i] :
( ( ( hAPP @ SV368 @ ( c_Set_Oinsert @ SY2888 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2889 @ tc_bool ) ) @ SY2889 ) )
= SY2888 )
| ! [SY2895: $i,SY2896: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV368 @ SY2890 @ SY2891 @ SY2892 @ SY2893 @ SY2894 @ SY2895 @ SY2896 @ SY2889 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(2046,plain,
! [SV369: $i] :
( ( ! [SY2897: $i,SY2898: $i,SY2899: $i,SY2900: $i,SY2901: $i,SY2902: $i,SY2903: $i] :
( ( ( hAPP @ SV369 @ ( c_Set_Oinsert @ SY2897 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2898 @ tc_bool ) ) @ SY2898 ) )
= SY2897 )
| ! [SY2904: $i,SY2905: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY2899 @ SV369 @ SY2900 @ SY2901 @ SY2902 @ SY2903 @ SY2904 @ SY2905 @ SY2898 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(2047,plain,
! [SV370: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV370 )
| ! [SY2906: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SY2906 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV370 @ tc_bool ) ) @ SV370 ) @ SV370 )
= SY2906 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(2048,plain,
! [SV371: $i] :
( ( ! [SY2907: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV371 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2907 @ tc_bool ) ) @ SY2907 ) @ ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ SV371 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2907 @ tc_bool ) ) @ SY2907 ) @ SY2907 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(2049,plain,
! [SV372: $i] :
( ( ! [SY2908: $i,SY2909: $i,SY2910: $i] :
( ( c_Set_Oinsert @ SV372 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2908 @ tc_bool ) ) @ SY2909 @ SY2908 @ ( tc_fun @ SY2910 @ tc_bool ) ) @ SY2910 )
= ( c_Set_Oinsert @ SV372 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2910 @ tc_bool ) ) @ SY2910 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(2050,plain,
! [SV373: $i] :
( ( ! [SY2911: $i,SY2912: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV373 @ ( c_Set_Oinsert @ SY2911 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2912 @ tc_bool ) ) @ SY2912 ) @ SY2912 ) @ SY2911 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(2051,plain,
! [SV374: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV374 )
| ! [SY2913: $i] :
( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ SY2913 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV374 @ tc_bool ) ) @ SV374 ) @ SV374 )
= SY2913 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1588]) ).
thf(2052,plain,
! [SV375: $i] :
( ( ! [SY2914: $i] :
( ( c_The @ ( c_Set_Oinsert @ SV375 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2914 @ tc_bool ) ) @ SY2914 ) @ SY2914 )
= SV375 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1589]) ).
thf(2053,plain,
! [SV376: $i] :
( ( ! [SY2915: $i,SY2916: $i,SY2917: $i,SY2918: $i,SY2919: $i,SY2920: $i,SY2921: $i,SY2922: $i] :
( ( ( hAPP @ SV376 @ ( c_Set_Oinsert @ SY2915 @ ( c_Set_Oinsert @ SY2916 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2917 @ tc_bool ) ) @ SY2917 ) @ SY2917 ) )
= ( hAPP @ ( hAPP @ SY2918 @ SY2915 ) @ SY2916 ) )
| ! [SY2923: $i,SY2924: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV376 @ SY2919 @ SY2920 @ SY2921 @ SY2918 @ SY2922 @ SY2923 @ SY2924 @ SY2917 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(2054,plain,
! [SV377: $i] :
( ( ! [SY2925: $i,SY2926: $i,SY2927: $i,SY2928: $i,SY2929: $i,SY2930: $i,SY2931: $i,SY2932: $i] :
( ( ( hAPP @ SV377 @ ( c_Set_Oinsert @ SY2925 @ ( c_Set_Oinsert @ SY2926 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2927 @ tc_bool ) ) @ SY2927 ) @ SY2927 ) )
= ( hAPP @ ( hAPP @ SY2928 @ SY2925 ) @ SY2926 ) )
| ! [SY2933: $i,SY2934: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY2929 @ SV377 @ SY2930 @ SY2931 @ SY2932 @ SY2928 @ SY2933 @ SY2934 @ SY2927 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(2055,plain,
! [SV378: $i] :
( ( ! [SY2935: $i,SY2936: $i,SY2937: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV378 @ ( c_Set_Oinsert @ SY2935 @ SY2936 @ SY2937 ) @ ( tc_fun @ SY2937 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV378 @ ( c_Set_Oinsert @ SY2935 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2937 @ tc_bool ) ) @ SY2937 ) @ ( tc_fun @ SY2937 @ tc_bool ) ) @ SY2936 @ ( tc_fun @ SY2937 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(2056,plain,
! [SV379: $i] :
( ( ! [SY2938: $i,SY2939: $i,SY2940: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV379 @ ( c_Set_Oinsert @ SY2938 @ SY2939 @ SY2940 ) @ ( tc_fun @ SY2940 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV379 @ SY2939 @ ( tc_fun @ SY2940 @ tc_bool ) ) @ ( c_Set_Oinsert @ SY2938 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2940 @ tc_bool ) ) @ SY2940 ) @ ( tc_fun @ SY2940 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(2057,plain,
! [SV380: $i] :
( ( ! [SY2941: $i] :
( ( SV380 = SY2941 )
| ! [SY2942: $i,SY2943: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SY2942 @ ( c_Set_Oinsert @ SV380 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2943 @ tc_bool ) ) @ SY2943 ) @ SY2943 ) @ SY2941 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(2058,plain,
! [SV381: $i] :
( ( ! [SY2944: $i] :
( ( c_Set_Ocontents @ ( c_Set_Oinsert @ SV381 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2944 @ tc_bool ) ) @ SY2944 ) @ SY2944 )
= SV381 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(2059,plain,
! [SV382: $i] :
( ( ! [SY2945: $i,SY2946: $i] :
( ( SV382
= ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ SY2945 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2946 @ tc_bool ) ) @ SY2946 ) @ SY2946 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY2945 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2946 @ tc_bool ) ) @ SY2946 ) @ SV382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(2060,plain,
! [SV383: $i] :
( ( ! [SY2947: $i] :
( ( SV383 = SY2947 )
| ! [SY2948: $i] :
~ ( hBOOL @ ( c_in @ SV383 @ ( c_Set_Oinsert @ SY2947 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2948 @ tc_bool ) ) @ SY2948 ) @ SY2948 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1597]) ).
thf(2061,plain,
! [SV384: $i] :
( ( ! [SY2949: $i,SY2950: $i] :
( ( c_Finite__Set_Ofold1 @ SV384 @ ( c_Set_Oinsert @ SY2949 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2950 @ tc_bool ) ) @ SY2950 ) @ SY2950 )
= SY2949 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(2062,plain,
! [SV385: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV385 )
| ! [SY2951: $i] :
( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ SY2951 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV385 @ tc_bool ) ) @ SV385 ) @ SV385 )
= SY2951 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1599]) ).
thf(2063,plain,
! [SV386: $i] :
( ( ! [SY2952: $i,SY2953: $i] :
( ( c_Set_Oinsert @ SV386 @ ( c_HOL_Ominus__class_Ominus @ SY2952 @ ( c_Set_Oinsert @ SV386 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2953 @ tc_bool ) ) @ SY2953 ) @ ( tc_fun @ SY2953 @ tc_bool ) ) @ SY2953 )
= ( c_Set_Oinsert @ SV386 @ SY2952 @ SY2953 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(2064,plain,
! [SV387: $i] :
( ( ~ ( class_Orderings_Oorder @ SV387 )
| ! [SY2954: $i] :
( ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2954 @ SY2954 @ SV387 )
= ( c_Set_Oinsert @ SY2954 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV387 @ tc_bool ) ) @ SV387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(2065,plain,
! [SV388: $i] :
( ( ! [SY2955: $i,SY2956: $i] :
( ( ( c_Set_Oinsert @ SV388 @ SY2955 @ SY2956 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2956 @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ SV388 @ SY2955 @ SY2956 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(2066,plain,
! [SV389: $i] :
( ( ! [SY2957: $i,SY2958: $i] :
( ( c_Set_Oinsert @ SV389 @ SY2957 @ SY2958 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV389 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2958 @ tc_bool ) ) @ SY2958 ) @ SY2957 @ ( tc_fun @ SY2958 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(2067,plain,
! [SV390: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV390 )
| ! [SY2959: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ SY2959 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV390 @ tc_bool ) ) @ SV390 ) @ SV390 )
= SY2959 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(2068,plain,
! [SV391: $i] :
( ( ! [SY2960: $i,SY2961: $i,SY2962: $i,SY2963: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV391 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY2960 ) @ SY2961 ) @ SY2962 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY2964: $i,SY2965: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SY2963 @ SY2964 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV391 @ SY2960 @ SY2962 @ SY2961 @ SY2965 @ SY2963 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2965 @ SY2964 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV391 @ SY2960 @ SY2962 @ SY2961 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV391 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY2965 ) @ SY2961 ) @ SY2963 ) @ ( 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)],[1605]) ).
thf(2069,plain,
! [SV392: $i] :
( ( ! [SY2966: $i,SY2967: $i,SY2968: $i,SY2969: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV392 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY2966 ) @ SY2967 ) @ SY2968 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY2970: $i,SY2971: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SY2969 @ SY2970 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SY2966 @ SY2971 @ SY2968 @ SY2969 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2971 @ SY2970 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SY2966 @ SY2971 @ SY2968 @ SY2969 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV392 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY2971 ) @ SY2967 ) @ SY2969 ) @ ( 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)],[1606]) ).
thf(2070,plain,
! [SV393: $i] :
( ( ! [SY2972: $i,SY2973: $i,SY2974: $i,SY2975: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV393 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY2972 ) @ SY2973 ) @ SY2974 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY2976: $i,SY2977: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SY2975 @ SY2976 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV393 @ SY2972 @ SY2974 @ SY2973 @ SY2977 @ SY2975 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2977 @ SY2976 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV393 @ SY2972 @ SY2974 @ SY2973 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV393 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY2977 ) @ SY2973 ) @ SY2975 ) @ ( 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)],[1607]) ).
thf(2071,plain,
! [SV394: $i] :
( ( ! [SY2978: $i,SY2979: $i,SY2980: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV394 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY2978 ) @ SY2979 ) @ SY2980 ) @ ( 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 @ SY2978 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV394 @ SY2978 @ SY2980 @ SY2979 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV394 @ SY2978 @ SY2980 @ SY2979 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(2072,plain,
! [SV395: $i] :
( ( ! [SY2981: $i,SY2982: $i,SY2983: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV395 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY2981 ) @ SY2982 ) @ SY2983 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY2984: $i,SY2985: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY2983 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV395 @ SY2981 @ SY2983 @ SY2982 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV395 @ SY2981 @ SY2983 @ SY2982 @ SY2984 @ SY2985 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV395 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY2984 ) @ SY2982 ) @ SY2985 ) @ ( 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)],[1609]) ).
thf(2073,plain,
! [SV396: $i] :
( ( ! [SY2986: $i,SY2987: $i,SY2988: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV396 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY2986 ) @ SY2987 ) @ SY2988 ) @ ( 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 @ SY2986 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV396 @ SY2986 @ SY2988 @ SY2987 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV396 @ SY2986 @ SY2988 @ SY2987 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(2074,plain,
! [SV397: $i] :
( ( ! [SY2989: $i,SY2990: $i,SY2991: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV397 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY2989 ) @ SY2990 ) @ SY2991 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY2992: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SY2992 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SY2991 @ SY2992 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SY2991 @ SY2992 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV397 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY2989 ) @ SY2990 ) @ SY2992 ) @ ( 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)],[1611]) ).
thf(2075,plain,
! [SV398: $i] :
( ( ! [SY2993: $i,SY2994: $i,SY2995: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV398 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY2993 ) @ SY2994 ) @ SY2995 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY2996: $i,SY2997: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SY2993 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SY2993 @ SY2996 @ SY2995 @ SY2997 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SY2993 @ SY2996 @ SY2995 @ SY2997 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV398 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY2996 ) @ SY2994 ) @ SY2997 ) @ ( 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)],[1612]) ).
thf(2076,plain,
! [SV399: $i] :
( ( ! [SY2998: $i,SY2999: $i,SY3000: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV399 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY2998 ) @ SY2999 ) @ SY3000 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY3001: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SY2998 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SY2998 @ SY3001 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SY2998 @ SY3001 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV399 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY3001 ) @ SY2999 ) @ SY3000 ) @ ( 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)],[1613]) ).
thf(2077,plain,
! [SV400: $i] :
( ( ! [SY3002: $i,SY3003: $i,SY3004: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV400 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY3002 ) @ SY3003 ) @ SY3004 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY3005: $i,SY3006: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3004 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV400 @ SY3002 @ SY3004 @ SY3003 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV400 @ SY3002 @ SY3004 @ SY3003 @ SY3005 @ SY3006 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV400 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY3005 ) @ SY3003 ) @ SY3006 ) @ ( 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)],[1614]) ).
thf(2078,plain,
! [SV401: $i] :
( ( ! [SY3007: $i,SY3008: $i,SY3009: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV401 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY3007 ) @ SY3008 ) @ SY3009 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY3010: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3010 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SY3007 @ SY3010 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SY3007 @ SY3010 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV401 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY3010 ) @ SY3008 ) @ SY3009 ) @ ( 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)],[1615]) ).
thf(2079,plain,
! [SV402: $i] :
( ( ! [SY3011: $i,SY3012: $i,SY3013: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV402 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY3011 ) @ SY3012 ) @ SY3013 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY3014: $i,SY3015: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3013 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SY3011 @ SY3014 @ SY3013 @ SY3015 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SY3011 @ SY3014 @ SY3013 @ SY3015 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV402 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY3014 ) @ SY3012 ) @ SY3015 ) @ ( 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)],[1616]) ).
thf(2080,plain,
! [SV403: $i] :
( ( ! [SY3016: $i,SY3017: $i,SY3018: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV403 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY3016 ) @ SY3017 ) @ SY3018 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY3019: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3018 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SY3018 @ SY3019 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SY3018 @ SY3019 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV403 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY3016 ) @ SY3017 ) @ SY3019 ) @ ( 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)],[1617]) ).
thf(2081,plain,
! [SV404: $i] :
( ( ! [SY3020: $i,SY3021: $i,SY3022: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV404 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY3020 ) @ SY3021 ) @ SY3022 ) @ ( 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 @ SY3020 @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ SV404 @ SY3020 @ SY3022 @ SY3021 ) ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ SV404 @ SY3020 @ SY3022 @ SY3021 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(2082,plain,
! [SV405: $i] :
( ( ! [SY3023: $i,SY3024: $i,SY3025: $i,SY3026: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV405 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3023 ) @ SY3024 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SY3025 ) ) @ SY3026 ) @ SY3023 )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ SV405 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3023 ) @ SY3024 ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY3025 ) ) ) @ SY3026 ) @ SY3023 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(2083,plain,
! [SV406: $i] :
( ( ! [SY3027: $i,SY3028: $i,SY3029: $i,SY3030: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ SV406 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3027 ) @ SY3028 ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY3029 ) ) ) @ SY3030 ) @ SY3027 )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV406 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3027 ) @ SY3028 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SY3029 ) ) @ SY3030 ) @ SY3027 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(2084,plain,
! [SV407: $i] :
( ( ! [SY3031: $i,SY3032: $i] :
( ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ SV407 ) @ SY3031 @ SY3032 )
| ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV407 ) ) @ SY3031 @ SY3032 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(2085,plain,
! [SV408: $i] :
( ( ! [SY3033: $i,SY3034: $i] :
( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV408 ) ) @ SY3033 @ SY3034 )
| ~ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ SV408 ) @ SY3033 @ SY3034 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(2086,plain,
! [SV409: $i] :
( ( ! [SY3035: $i,SY3036: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ SV409 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3035 ) @ SY3036 ) @ c_Com_Ocom_OSKIP ) @ SY3036 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3035 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3035 ) ) @ SY3035 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(2087,plain,
! [SV410: $i] :
( ( ! [SY3037: $i,SY3038: $i,SY3039: $i,SY3040: $i,SY3041: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3037 ) @ SY3038 ) @ ( c_Com_Ocom_OSemi @ SY3039 @ SY3040 ) ) @ SY3041 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3037 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3037 ) ) @ SY3037 )
| ! [SY3042: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3037 ) @ SY3042 ) @ SY3040 ) @ SY3041 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3037 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3037 ) ) @ SY3037 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3037 ) @ SY3038 ) @ SY3039 ) @ SY3042 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3037 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3037 ) ) @ SY3037 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(2088,plain,
! [SV411: $i] :
( ( ! [SY3043: $i,SY3044: $i,SY3045: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV411 @ ( c_Set_Oinsert @ SY3043 @ SY3044 @ ( tc_Hoare__Mirabelle_Otriple @ SY3045 ) ) @ SY3045 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV411 @ SY3044 @ SY3045 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV411 @ ( c_Set_Oinsert @ SY3043 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3045 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3045 ) ) @ SY3045 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(2089,plain,
! [SV412: $i] :
( ( ! [SY3046: $i,SY3047: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV412 @ SY3046 @ SY3047 ) @ SV412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1627]) ).
thf(2090,plain,
! [SV413: $i] :
( ( ! [SY3048: $i,SY3049: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV413 @ SY3048 @ SY3049 )
| ! [SY3050: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV413 @ SY3050 @ SY3049 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY3050 @ SY3048 @ SY3049 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(2091,plain,
! [SV414: $i] :
( ( ! [SY3051: $i,SY3052: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV414 @ tc_bool ) )
!= ( c_Set_Oinsert @ SY3051 @ SY3052 @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(2092,plain,
! [SV415: $i] :
( ( ! [SY3053: $i,SY3054: $i,SY3055: $i,SY3056: $i,SY3057: $i,SY3058: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV415 ) @ SY3053 ) @ SY3054 ) @ SY3055 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV415 ) @ SY3056 ) @ SY3057 ) @ SY3058 ) )
| ( SY3055 = SY3058 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(2093,plain,
! [SV416: $i] :
( ( ! [SY3059: $i,SY3060: $i,SY3061: $i,SY3062: $i,SY3063: $i] :
( ! [SY3064: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV416 ) @ SY3059 ) @ SY3060 ) @ SY3061 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV416 ) @ SY3062 ) @ SY3063 ) @ SY3064 ) )
| ( SY3060 = SY3063 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(2094,plain,
! [SV417: $i] :
( ( ! [SY3065: $i,SY3066: $i,SY3067: $i,SY3068: $i] :
( ! [SY3069: $i,SY3070: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV417 ) @ SY3065 ) @ SY3066 ) @ SY3067 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV417 ) @ SY3068 ) @ SY3069 ) @ SY3070 ) )
| ( SY3065 = SY3068 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(2095,plain,
! [SV418: $i] :
( ( ! [SY3071: $i,SY3072: $i,SY3073: $i,SY3074: $i] :
( ( ( c_Set_Oinsert @ SV418 @ ( c_Set_Oinsert @ SY3071 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3072 @ tc_bool ) ) @ SY3072 ) @ SY3072 )
!= ( c_Set_Oinsert @ SY3073 @ ( c_Set_Oinsert @ SY3074 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3072 @ tc_bool ) ) @ SY3072 ) @ SY3072 ) )
| ( SY3071 = SY3073 )
| ( SY3071 = SY3074 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(2096,plain,
! [SV419: $i] :
( ( ! [SY3075: $i,SY3076: $i,SY3077: $i,SY3078: $i] :
( ( ( c_Set_Oinsert @ SV419 @ ( c_Set_Oinsert @ SY3075 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3076 @ tc_bool ) ) @ SY3076 ) @ SY3076 )
!= ( c_Set_Oinsert @ SY3077 @ ( c_Set_Oinsert @ SY3078 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3076 @ tc_bool ) ) @ SY3076 ) @ SY3076 ) )
| ( SV419 = SY3078 )
| ( SY3075 = SY3078 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(2097,plain,
! [SV420: $i] :
( ( ! [SY3079: $i,SY3080: $i,SY3081: $i] :
( ! [SY3082: $i] :
( ( c_Set_Oinsert @ SV420 @ ( c_Set_Oinsert @ SY3079 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3080 @ tc_bool ) ) @ SY3080 ) @ SY3080 )
!= ( c_Set_Oinsert @ SY3081 @ ( c_Set_Oinsert @ SY3082 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3080 @ tc_bool ) ) @ SY3080 ) @ SY3080 ) )
| ( SY3079 = SY3081 )
| ( SV420 = SY3081 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(2098,plain,
! [SV421: $i] :
( ( ! [SY3083: $i,SY3084: $i,SY3085: $i,SY3086: $i] :
( ( ( c_Set_Oinsert @ SV421 @ ( c_Set_Oinsert @ SY3083 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3084 @ tc_bool ) ) @ SY3084 ) @ SY3084 )
!= ( c_Set_Oinsert @ SY3085 @ ( c_Set_Oinsert @ SY3086 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3084 @ tc_bool ) ) @ SY3084 ) @ SY3084 ) )
| ( SV421 = SY3086 )
| ( SV421 = SY3085 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(2099,plain,
! [SV422: $i] :
( ( ! [SY3087: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV422 @ tc_bool ) ) @ SY3087 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(2100,plain,
! [SV423: $i] :
( ( ! [SY3088: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ SV423 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3088 ) @ tc_bool ) ) @ SY3088 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(2101,plain,
! [SV424: $i] :
( ( ! [SY3089: $i,SY3090: $i,SY3091: $i,SY3092: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV424 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3089 ) @ SY3090 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SY3091 ) ) @ SY3092 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3089 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3089 ) ) @ SY3089 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3089 ) @ SY3090 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SY3091 ) ) @ SY3092 ) @ SV424 @ ( tc_Hoare__Mirabelle_Otriple @ SY3089 ) ) @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SY3089 ) @ SY3090 ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY3091 ) ) ) @ SY3092 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3089 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3089 ) ) @ SY3089 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(2102,plain,
! [SV425: $i] :
( ( ! [SY3093: $i] :
( ( hBOOL @ ( hAPP @ SV425 @ SY3093 ) )
| ! [SY3094: $i] :
( ( SY3094 = SY3093 )
| ! [SY3095: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3094 @ SV425 @ SY3095 ) @ SY3093 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1640]) ).
thf(2103,plain,
! [SV426: $i] :
( ( ! [SY3096: $i,SY3097: $i] :
( ( c_Set_Oinsert @ SV426 @ ( c_Set_Oinsert @ SV426 @ SY3096 @ SY3097 ) @ SY3097 )
= ( c_Set_Oinsert @ SV426 @ SY3096 @ SY3097 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1641]) ).
thf(2104,plain,
! [SV427: $i] :
( ( ! [SY3098: $i,SY3099: $i] :
( ( c_Set_Oinsert @ SV427 @ SY3098 @ SY3099 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3099 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1642]) ).
thf(2105,plain,
! [SV428: $i] :
( ( ! [SY3100: $i,SY3101: $i,SY3102: $i] :
( ( c_Set_Oinsert @ SV428 @ ( c_Set_Oinsert @ SY3100 @ SY3101 @ SY3102 ) @ SY3102 )
= ( c_Set_Oinsert @ SY3100 @ ( c_Set_Oinsert @ SV428 @ SY3101 @ SY3102 ) @ SY3102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(2106,plain,
! [SV429: $i] :
( ( ! [SY3103: $i,SY3104: $i] :
( ( c_Set_Oinsert @ SV429 @ ( c_Set_Oinsert @ SY3103 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3104 @ tc_bool ) ) @ SY3104 ) @ SY3104 )
= ( c_Set_Oinsert @ SY3103 @ ( c_Set_Oinsert @ SV429 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3104 @ tc_bool ) ) @ SY3104 ) @ SY3104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(2107,plain,
! [SV430: $i] :
( ( ! [SY3105: $i,SY3106: $i] :
( ( ( c_Set_Oinsert @ SV430 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3105 @ tc_bool ) ) @ SY3105 )
!= ( c_Set_Oinsert @ SY3106 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3105 @ tc_bool ) ) @ SY3105 ) )
| ( SV430 = SY3106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1645]) ).
thf(2108,plain,
! [SV431: $i] :
( ( ! [SY3107: $i,SY3108: $i,SY3109: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV431 @ SY3107 @ SY3108 ) @ SY3109 ) )
| ~ ( hBOOL @ ( hAPP @ SY3107 @ SY3109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(2109,plain,
! [SV432: $i] :
( ( ! [SY3110: $i] :
( ( ( hAPP @ c_Com_Ocom_OBODY @ SV432 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SY3110 ) )
| ( SV432 = SY3110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(2110,plain,
! [SV433: $i] :
( ( ! [SY3111: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV433 @ SY3111 ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ SY3111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(2111,plain,
! [SV434: $i] :
( ( ! [SY3112: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV434 @ SY3112 ) )
| ~ ( class_Lattices_Olattice @ SY3112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(2112,plain,
! [SV435: $i] :
( ( ! [SY3113: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV435 @ SY3113 ) )
| ~ ( class_Lattices_Obounded__lattice @ SY3113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(2113,plain,
! [SV436: $i] :
( ( ! [SY3114: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ SV436 @ SY3114 ) )
| ~ ( class_Orderings_Opreorder @ SY3114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(2114,plain,
! [SV437: $i] :
( ( ! [SY3115: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ SV437 @ SY3115 ) )
| ~ ( class_Lattices_Olattice @ SY3115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(2115,plain,
! [SV438: $i] :
( ( ! [SY3116: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ SV438 @ SY3116 ) )
| ~ ( class_Orderings_Oorder @ SY3116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(2116,plain,
! [SV439: $i] :
( ( ! [SY3117: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ SV439 @ SY3117 ) )
| ~ ( class_Orderings_Obot @ SY3117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(2117,plain,
! [SV440: $i] :
( ( ! [SY3118: $i] :
( ( class_HOL_Ominus @ ( tc_fun @ SV440 @ SY3118 ) )
| ~ ( class_HOL_Ominus @ SY3118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(2118,plain,
! [SV441: $i] :
( ( ! [SY3119: $i] :
( ( class_HOL_Oord @ ( tc_fun @ SV441 @ SY3119 ) )
| ~ ( class_HOL_Oord @ SY3119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(2119,plain,
! [SV442: $i] :
( ( ! [SY3120: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV442 ) @ SY3120 ) @ SY3120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(2120,plain,
! [SV443: $i] :
( ( ! [SY3121: $i] :
( ( SV443 = SY3121 )
| ! [SY3122: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY3122 ) @ SV443 ) @ SY3121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(2121,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[1676]) ).
thf(2122,plain,
! [SV444: $i,SV1: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV1 )
| ! [SY3123: $i,SY3124: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV444 @ SY3123 @ SV1 ) @ SY3124 @ SV1 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV444 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3123 @ SY3124 @ SV1 ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1678]) ).
thf(2123,plain,
! [SV445: $i,SV2: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV2 )
| ! [SY3125: $i,SY3126: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV445 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3125 @ SY3126 @ SV2 ) @ SV2 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3125 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV445 @ SY3126 @ SV2 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1679]) ).
thf(2124,plain,
! [SV446: $i,SV3: $i] :
( ( ~ ( class_Lattices_Olattice @ SV3 )
| ! [SY3127: $i,SY3128: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV446 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3127 @ SY3128 @ SV3 ) @ SV3 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3127 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV446 @ SY3128 @ SV3 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(2125,plain,
! [SV447: $i,SV4: $i] :
( ( ~ ( class_Lattices_Olattice @ SV4 )
| ! [SY3129: $i,SY3130: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV447 @ SY3129 @ SV4 ) @ SY3130 @ SV4 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV447 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3129 @ SY3130 @ SV4 ) @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(2126,plain,
! [SV448: $i,SV5: $i] :
( ( ! [SY3131: $i] : ( c_Com_OWT @ ( c_Com_Ocom_OCall @ SV5 @ SV448 @ SY3131 ) )
| ~ ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ SV448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(2127,plain,
! [SV6: $i] :
( ( ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ SV6 ) )
= $true )
| ( ( ! [SY1797: $i,SY1798: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCall @ SY1797 @ SV6 @ SY1798 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1683]) ).
thf(2128,plain,
! [SV449: $i,SV7: $i] :
( ( ! [SY3132: $i,SY3133: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV7 @ SV449 @ ( tc_fun @ SY3132 @ tc_bool ) ) @ SY3133 @ ( tc_fun @ SY3132 @ tc_bool ) )
| ~ ( c_lessequals @ SV449 @ SY3133 @ ( tc_fun @ SY3132 @ tc_bool ) )
| ~ ( c_lessequals @ SV7 @ SY3133 @ ( tc_fun @ SY3132 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1684]) ).
thf(2129,plain,
! [SV450: $i,SV8: $i] :
( ( ! [SY3134: $i] : ( c_lessequals @ SV8 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV450 @ SV8 @ ( tc_fun @ SY3134 @ tc_bool ) ) @ ( tc_fun @ SY3134 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1685]) ).
thf(2130,plain,
! [SV451: $i,SV9: $i] :
( ( ! [SY3135: $i] : ( c_lessequals @ SV9 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV9 @ SV451 @ ( tc_fun @ SY3135 @ tc_bool ) ) @ ( tc_fun @ SY3135 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(2131,plain,
! [SV452: $i,SV10: $i] :
( ( ! [SY3136: $i,SY3137: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV10 @ SV452 @ ( tc_fun @ SY3136 @ tc_bool ) ) @ SY3137 @ ( tc_fun @ SY3136 @ tc_bool ) )
| ~ ( c_lessequals @ SV452 @ SY3137 @ ( tc_fun @ SY3136 @ tc_bool ) )
| ~ ( c_lessequals @ SV10 @ SY3137 @ ( tc_fun @ SY3136 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1687]) ).
thf(2132,plain,
! [SV453: $i,SV11: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV11 )
| ! [SY3138: $i,SY3139: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV453 @ SY3138 @ SV11 ) @ SY3139 @ SV11 )
| ~ ( c_lessequals @ SY3138 @ SY3139 @ SV11 )
| ~ ( c_lessequals @ SV453 @ SY3139 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1688]) ).
thf(2133,plain,
! [SV12: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV12 ) )
= $true )
| ( ( ! [SY1812: $i,SY1813: $i] : ( c_lessequals @ SY1812 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1812 @ SY1813 @ SV12 ) @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1689]) ).
thf(2134,plain,
! [SV13: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV13 ) )
= $true )
| ( ( ! [SY1814: $i,SY1815: $i] : ( c_lessequals @ SY1814 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1815 @ SY1814 @ SV13 ) @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1690]) ).
thf(2135,plain,
! [SV454: $i,SV14: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV14 )
| ! [SY3140: $i,SY3141: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV454 @ SY3140 @ SV14 ) @ SY3141 @ SV14 )
| ~ ( c_lessequals @ SY3140 @ SY3141 @ SV14 )
| ~ ( c_lessequals @ SV454 @ SY3141 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(2136,plain,
! [SV455: $i,SV15: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV15 )
| ! [SY3142: $i,SY3143: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV455 @ SY3142 @ SV15 ) @ SY3143 @ SV15 )
| ~ ( c_lessequals @ SY3142 @ SY3143 @ SV15 )
| ~ ( c_lessequals @ SV455 @ SY3143 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(2137,plain,
! [SV16: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV16 ) )
= $true )
| ( ( ! [SY1822: $i,SY1823: $i] : ( c_lessequals @ SY1822 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1823 @ SY1822 @ SV16 ) @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1693]) ).
thf(2138,plain,
! [SV17: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV17 ) )
= $true )
| ( ( ! [SY1824: $i,SY1825: $i] : ( c_lessequals @ SY1824 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1824 @ SY1825 @ SV17 ) @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1694]) ).
thf(2139,plain,
! [SV456: $i,SV18: $i] :
( ( ! [SY3144: $i,SY3145: $i,SY3146: $i,SY3147: $i,SY3148: $i,SY3149: $i,SY3150: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV18 @ SV456 @ ( c_COMBC @ SY3144 @ SY3145 @ SY3145 @ tc_bool ) @ ( c_COMBC @ SY3146 @ SY3145 @ SY3145 @ tc_bool ) @ SY3147 @ SY3148 @ SY3149 @ SY3150 @ SY3145 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV456 @ SV18 @ SY3144 @ SY3146 @ SY3148 @ SY3147 @ SY3150 @ SY3149 @ SY3145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(2140,plain,
! [SV457: $i,SV19: $i] :
( ( ! [SY3151: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV19 @ ( c_HOL_Ominus__class_Ominus @ SV457 @ SV19 @ ( tc_fun @ SY3151 @ tc_bool ) ) @ ( tc_fun @ SY3151 @ tc_bool ) )
= SV457 )
| ~ ( c_lessequals @ SV19 @ SV457 @ ( tc_fun @ SY3151 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(2141,plain,
! [SV458: $i,SV20: $i] :
( ( ! [SY3152: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCond @ SV20 @ SV458 @ SY3152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(2142,plain,
! [SV459: $i,SV21: $i] :
( ( ! [SY3153: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV21 @ SV459 @ ( tc_fun @ SY3153 @ tc_bool ) ) @ SV21 @ ( tc_fun @ SY3153 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1698]) ).
thf(2143,plain,
! [SV22: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV22 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV22 )
| ! [SY1840: $i,SY1841: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SY1840 @ SY1841 @ SV22 )
!= ( c_HOL_Ozero__class_Ozero @ SV22 ) )
| ( SY1840 = SY1841 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1699]) ).
thf(2144,plain,
! [SV23: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV23 ) )
= $true )
| ( ( ! [SY1842: $i,SY1843: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SY1842 @ SY1843 @ SV23 )
!= ( c_HOL_Ozero__class_Ozero @ SV23 ) )
| ( SY1842 = SY1843 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1700]) ).
thf(2145,plain,
! [SV24: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV24 ) )
= $true )
| ( ( ! [SY1844: $i,SY1845: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SY1844 @ SY1845 @ SV24 )
!= ( c_HOL_Ozero__class_Ozero @ SV24 ) )
| ( SY1844 = SY1845 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1701]) ).
thf(2146,plain,
! [SV460: $i,SV25: $i] :
( ( ! [SY3154: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ SV25 @ SV460 @ SY3154 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3154 @ tc_bool ) ) @ SY3154 @ SV460 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV460 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(2147,plain,
! [SV461: $i,SV26: $i] :
( ( ! [SY3155: $i] : ( hBOOL @ ( c_in @ SV26 @ ( c_Collect @ SV461 @ SY3155 ) @ SY3155 ) )
| ~ ( hBOOL @ ( hAPP @ SV461 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(2148,plain,
! [SV462: $i,SV27: $i] :
( ( ( hBOOL @ ( hAPP @ SV27 @ SV462 ) )
| ! [SY3156: $i] :
~ ( hBOOL @ ( c_in @ SV462 @ ( c_Collect @ SV27 @ SY3156 ) @ SY3156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1704]) ).
thf(2149,plain,
! [SV463: $i,SV28: $i] :
( ( ! [SY3157: $i,SY3158: $i] :
( ( hBOOL @ ( c_in @ SV28 @ ( c_HOL_Ominus__class_Ominus @ SV463 @ SY3157 @ ( tc_fun @ SY3158 @ tc_bool ) ) @ SY3158 ) )
| ( hBOOL @ ( c_in @ SV28 @ SY3157 @ SY3158 ) )
| ~ ( hBOOL @ ( c_in @ SV28 @ SV463 @ SY3158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1705]) ).
thf(2150,plain,
! [SV464: $i,SV29: $i] :
( ( ! [SY3159: $i,SY3160: $i] :
( ( hBOOL @ ( c_in @ SV29 @ ( c_HOL_Ominus__class_Ominus @ SV464 @ SY3159 @ ( tc_fun @ SY3160 @ tc_bool ) ) @ SY3160 ) )
| ( hBOOL @ ( c_in @ SV29 @ SY3159 @ SY3160 ) )
| ~ ( hBOOL @ ( c_in @ SV29 @ SV464 @ SY3160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1706]) ).
thf(2151,plain,
! [SV465: $i,SV30: $i] :
( ( ! [SY3161: $i,SY3162: $i,SY3163: $i,SY3164: $i] :
( ( c_Com_Ocom_OCall @ SV30 @ SV465 @ SY3161 )
!= ( c_Com_Ocom_OLocal @ SY3162 @ SY3163 @ SY3164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1707]) ).
thf(2152,plain,
! [SV466: $i,SV31: $i] :
( ( ! [SY3165: $i] :
( ( hBOOL @ ( c_in @ SV31 @ SV466 @ SY3165 ) )
| ! [SY3166: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SV31 @ SY3166 @ SY3165 ) @ SV466 @ ( tc_fun @ SY3165 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(2153,plain,
! [SV467: $i,SV32: $i] :
( ( ! [SY3167: $i,SY3168: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV32 @ ( c_COMBK @ SV467 @ ( tc_fun @ SY3167 @ tc_bool ) @ SY3168 ) @ SY3168 @ ( tc_fun @ SY3167 @ tc_bool ) )
= SV467 )
| ( SV32
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3168 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(2154,plain,
! [SV468: $i,SV33: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV33 )
| ! [SY3169: $i,SY3170: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV468 @ ( c_COMBK @ SY3169 @ SV33 @ SY3170 ) @ SY3170 @ SV33 )
= SY3169 )
| ( SV468
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3170 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(2155,plain,
! [SV469: $i,SV34: $i] :
( ( ! [SY3171: $i,SY3172: $i,SY3173: $i] :
( ( c_Com_Ocom_OCall @ SV34 @ SV469 @ SY3171 )
!= ( c_Com_Ocom_OWhile @ SY3172 @ SY3173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1711]) ).
thf(2156,plain,
! [SV470: $i,SV35: $i] :
( ( ! [SY3174: $i,SY3175: $i] :
( ! [SY3176: $i] :
( ( c_Set_Oinsert @ ( hAPP @ SV35 @ SV470 ) @ ( c_Set_Oimage @ SV35 @ SY3174 @ SY3175 @ SY3176 ) @ SY3176 )
= ( c_Set_Oimage @ SV35 @ SY3174 @ SY3175 @ SY3176 ) )
| ~ ( hBOOL @ ( c_in @ SV470 @ SY3174 @ SY3175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(2157,plain,
! [SV471: $i,SV36: $i] :
( ( ! [SY3177: $i,SY3178: $i] :
( ( c_lessequals @ SV36 @ ( c_Set_Oinsert @ SV471 @ SY3177 @ SY3178 ) @ ( tc_fun @ SY3178 @ tc_bool ) )
| ~ ( c_lessequals @ SV36 @ SY3177 @ ( tc_fun @ SY3178 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SV471 @ SV36 @ SY3178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1713]) ).
thf(2158,plain,
! [SV472: $i,SV37: $i] :
( ( ! [SY3179: $i] :
( ( c_lessequals @ SV37 @ SV472 @ ( tc_fun @ SY3179 @ tc_bool ) )
| ! [SY3180: $i] :
( ( hBOOL @ ( c_in @ SY3180 @ SV37 @ SY3179 ) )
| ~ ( c_lessequals @ SV37 @ ( c_Set_Oinsert @ SY3180 @ SV472 @ SY3179 ) @ ( tc_fun @ SY3179 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1714]) ).
thf(2159,plain,
! [SV473: $i,SV38: $i] :
( ( ! [SY3181: $i,SY3182: $i] :
( ( c_lessequals @ SV38 @ ( c_Set_Oinsert @ SV473 @ SY3181 @ SY3182 ) @ ( tc_fun @ SY3182 @ tc_bool ) )
| ~ ( c_lessequals @ SV38 @ SY3181 @ ( tc_fun @ SY3182 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SV473 @ SV38 @ SY3182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(2160,plain,
! [SV474: $i,SV39: $i] :
( ( ! [SY3183: $i] :
( ( c_lessequals @ SV39 @ SV474 @ ( tc_fun @ SY3183 @ tc_bool ) )
| ! [SY3184: $i] :
( ~ ( c_lessequals @ SV39 @ ( c_Set_Oinsert @ SY3184 @ SV474 @ SY3183 ) @ ( tc_fun @ SY3183 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SY3184 @ SV39 @ SY3183 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(2161,plain,
! [SV475: $i,SV40: $i] :
( ( ! [SY3185: $i,SY3186: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV40 @ SV475 @ ( tc_fun @ SY3185 @ tc_bool ) ) @ SY3186 @ ( tc_fun @ SY3185 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV40 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV475 @ SY3186 @ ( tc_fun @ SY3185 @ tc_bool ) ) @ ( tc_fun @ SY3185 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1717]) ).
thf(2162,plain,
! [SV476: $i,SV41: $i] :
( ( ! [SY3187: $i,SY3188: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV41 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV476 @ SY3187 @ ( tc_fun @ SY3188 @ tc_bool ) ) @ ( tc_fun @ SY3188 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV476 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV41 @ SY3187 @ ( tc_fun @ SY3188 @ tc_bool ) ) @ ( tc_fun @ SY3188 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1718]) ).
thf(2163,plain,
! [SV477: $i,SV42: $i] :
( ( ! [SY3189: $i,SY3190: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV42 @ SV477 ) @ SY3189 @ SY3190 )
| ! [SY3191: $i] :
( ~ ( c_Natural_Oevalc @ SV477 @ SY3191 @ SY3190 )
| ~ ( c_Natural_Oevalc @ SV42 @ SY3189 @ SY3191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1719]) ).
thf(2164,plain,
! [SV478: $i,SV43: $i] :
( ( ! [SY3192: $i,SY3193: $i,SY3194: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV43 @ SV478 @ SY3192 @ SY3193 ) @ ( c_Set_Oimage @ SV43 @ SY3194 @ SY3192 @ SY3193 ) @ ( tc_fun @ SY3193 @ tc_bool ) ) @ ( c_Set_Oimage @ SV43 @ ( c_HOL_Ominus__class_Ominus @ SV478 @ SY3194 @ ( tc_fun @ SY3192 @ tc_bool ) ) @ SY3192 @ SY3193 ) @ ( tc_fun @ SY3193 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1720]) ).
thf(2165,plain,
! [SV479: $i,SV44: $i] :
( ( ! [SY3195: $i] :
( ~ ( hBOOL @ ( hAPP @ SV44 @ SV479 ) )
| ! [SY3196: $i] :
( ( c_Natural_Oevalc @ SY3195 @ SV479 @ SY3196 )
| ! [SY3197: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV44 @ SY3195 @ SY3197 ) @ SV479 @ SY3196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(2166,plain,
! [SV480: $i,SV45: $i] :
( ( ! [SY3198: $i,SY3199: $i,SY3200: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV45 @ SV480 @ SY3198 ) @ SY3199 @ SY3200 )
| ~ ( c_Natural_Oevalc @ SV480 @ SY3199 @ SY3200 )
| ~ ( hBOOL @ ( hAPP @ SV45 @ SY3199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1722]) ).
thf(2167,plain,
! [SV481: $i,SV46: $i] :
( ( ! [SY3201: $i,SY3202: $i,SY3203: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV46 @ SV481 ) @ SY3201 @ SY3202 @ SY3203 )
| ! [SY3204: $i] :
( ~ ( c_Natural_Oevaln @ SV481 @ SY3204 @ SY3202 @ SY3203 )
| ~ ( c_Natural_Oevaln @ SV46 @ SY3201 @ SY3202 @ SY3204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1723]) ).
thf(2168,plain,
! [SV482: $i,SV47: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV47 )
| ! [SY3205: $i,SY3206: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV482 @ SV482 @ SV47 )
!= ( c_HOL_Ominus__class_Ominus @ SY3205 @ SY3206 @ SV47 ) )
| ( SY3205 = SY3206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(2169,plain,
! [SV483: $i,SV48: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV48 )
| ! [SY3207: $i] :
( ! [SY3208: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV483 @ SY3207 @ SV48 )
!= ( c_HOL_Ominus__class_Ominus @ SY3208 @ SY3208 @ SV48 ) )
| ( SV483 = SY3207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1725]) ).
thf(2170,plain,
! [SV484: $i,SV49: $i] :
( ( ! [SY3209: $i,SY3210: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV49 @ SV484 ) @ SY3209 @ SY3210 )
| ! [SY3211: $i] :
( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV49 @ SV484 ) @ SY3211 @ SY3210 )
| ~ ( c_Natural_Oevalc @ SV484 @ SY3209 @ SY3211 )
| ~ ( hBOOL @ ( hAPP @ SV49 @ SY3209 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(2171,plain,
! [SV485: $i,SV50: $i] :
( ( ( c_Option_Ooption_ONone @ SV50 )
!= ( c_Option_Ooption_OSome @ SV485 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1727]) ).
thf(2172,plain,
! [SV486: $i,SV51: $i] :
( ( ( c_Option_Ooption_ONone @ SV51 )
!= ( c_Option_Ooption_OSome @ SV486 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(2173,plain,
! [SV487: $i,SV52: $i] :
( ( ! [SY3212: $i,SY3213: $i,SY3214: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV52 @ SV487 ) @ SY3212 @ SY3213 @ SY3214 )
| ! [SY3215: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV52 @ SV487 ) @ SY3215 @ SY3213 @ SY3214 )
| ~ ( c_Natural_Oevaln @ SV487 @ SY3212 @ SY3213 @ SY3215 )
| ~ ( hBOOL @ ( hAPP @ SV52 @ SY3212 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1729]) ).
thf(2174,plain,
! [SV488: $i,SV53: $i] :
( ( ! [SY3216: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV53 @ SV488 @ ( tc_fun @ SY3216 @ tc_bool ) ) @ SV488 @ ( tc_fun @ SY3216 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV53 @ SV488 @ ( tc_fun @ SY3216 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1730]) ).
thf(2175,plain,
! [SV489: $i,SV54: $i] :
( ( ! [SY3217: $i,SY3218: $i,SY3219: $i,SY3220: $i] :
( ( hAPP @ ( c_COMBS @ SV54 @ SV489 @ SY3217 @ SY3218 @ SY3219 ) @ SY3220 )
= ( hAPP @ ( hAPP @ SV54 @ SY3220 ) @ ( hAPP @ SV489 @ SY3220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(2176,plain,
! [SV490: $i,SV55: $i] :
( ( ! [SY3221: $i,SY3222: $i] :
( ( hAPP @ ( c_COMBK @ SV55 @ SV490 @ SY3221 ) @ SY3222 )
= SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1732]) ).
thf(2177,plain,
! [SV491: $i,SV56: $i] :
( ( ( hAPP @ ( c_COMBI @ SV56 ) @ SV491 )
= SV491 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1733]) ).
thf(2178,plain,
! [SV492: $i,SV57: $i] :
( ( ! [SY3223: $i,SY3224: $i,SY3225: $i,SY3226: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV57 @ SV492 @ SY3223 @ SY3224 ) @ SY3225 ) @ SY3226 )
= ( hAPP @ ( hAPP @ SV57 @ SY3226 ) @ SY3225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1734]) ).
thf(2179,plain,
! [SV493: $i,SV58: $i] :
( ( ! [SY3227: $i,SY3228: $i,SY3229: $i,SY3230: $i] :
( ( hAPP @ ( c_COMBB @ SV58 @ SV493 @ SY3227 @ SY3228 @ SY3229 ) @ SY3230 )
= ( hAPP @ SV58 @ ( hAPP @ SV493 @ SY3230 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1735]) ).
thf(2180,plain,
! [SV494: $i,SV59: $i] :
( ( ( hBOOL @ ( hAPP @ SV59 @ SV494 ) )
| ! [SY3231: $i] :
~ ( hBOOL @ ( c_in @ SV494 @ SV59 @ SY3231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1736]) ).
thf(2181,plain,
! [SV495: $i,SV60: $i] :
( ( ! [SY3232: $i] : ( hBOOL @ ( c_in @ SV60 @ SV495 @ SY3232 ) )
| ~ ( hBOOL @ ( hAPP @ SV495 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(2182,plain,
! [SV496: $i,SV61: $i] :
( ( ! [SY3233: $i,SY3234: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV61 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV496 @ tc_bool ) ) @ SY3233 @ SV496 @ ( tc_fun @ SY3234 @ tc_bool ) ) @ ( tc_fun @ SY3234 @ tc_bool ) )
= SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(2183,plain,
! [SV497: $i,SV62: $i] :
( ( ! [SY3235: $i,SY3236: $i] :
( ~ ( hBOOL @ ( hAPP @ SV62 @ SV497 ) )
| ! [SY3237: $i] :
( ( c_Natural_Oevaln @ SY3235 @ SV497 @ SY3236 @ SY3237 )
| ! [SY3238: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV62 @ SY3235 @ SY3238 ) @ SV497 @ SY3236 @ SY3237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1739]) ).
thf(2184,plain,
! [SV498: $i,SV63: $i] :
( ( ! [SY3239: $i,SY3240: $i,SY3241: $i,SY3242: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV63 @ SV498 @ SY3239 ) @ SY3240 @ SY3241 @ SY3242 )
| ~ ( c_Natural_Oevaln @ SV498 @ SY3240 @ SY3241 @ SY3242 )
| ~ ( hBOOL @ ( hAPP @ SV63 @ SY3240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(2185,plain,
! [SV499: $i,SV64: $i] :
( ( ! [SY3243: $i,SY3244: $i,SY3245: $i,SY3246: $i,SY3247: $i,SY3248: $i,SY3249: $i,SY3250: $i,SY3251: $i,SY3252: $i] :
( ( c_Com_Ocom_Ocom__case @ SV64 @ SV499 @ SY3243 @ SY3244 @ SY3245 @ SY3246 @ SY3247 @ SY3248 @ ( c_Com_Ocom_OCall @ SY3249 @ SY3250 @ SY3251 ) @ SY3252 )
= ( hAPP @ ( hAPP @ ( hAPP @ SY3248 @ SY3249 ) @ SY3250 ) @ SY3251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(2186,plain,
! [SV500: $i,SV65: $i] :
( ( ! [SY3253: $i,SY3254: $i,SY3255: $i] :
( ( c_Com_Ocom_OCall @ SV65 @ SV500 @ SY3253 )
!= ( c_Com_Ocom_OSemi @ SY3254 @ SY3255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1742]) ).
thf(2187,plain,
! [SV66: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV66 ) )
= $true )
| ( ( ! [SY1989: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY1989 @ SY1989 @ SV66 )
= SY1989 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1743]) ).
thf(2188,plain,
! [SV501: $i,SV67: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV67 @ SV67 @ ( tc_fun @ SV501 @ tc_bool ) )
= SV67 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(2189,plain,
! [SV68: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV68 ) )
= $true )
| ( ( ! [SY1991: $i,SY1992: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1991 @ SY1992 @ ( tc_fun @ t_a @ SV68 ) ) @ v_x )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SY1991 @ v_x ) @ ( hAPP @ SY1992 @ v_x ) @ SV68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1745]) ).
thf(2190,plain,
! [SV502: $i,SV69: $i] :
( ( ! [SY3256: $i,SY3257: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV69 @ SV502 @ SY3256 ) @ SY3257 @ SY3256 @ SV502 )
= ( c_Set_Oinsert @ SV69 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV502 @ tc_bool ) ) @ SV502 ) )
| ! [V_x: $i] :
~ ( hBOOL @ ( c_in @ V_x @ SY3257 @ SY3256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(2191,plain,
! [SV503: $i,SV70: $i] :
( ( ! [SY3259: $i,SY3260: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ SV70 @ SV503 ) @ SY3259 @ SY3260 ) )
| ! [SY3261: $i,SY3262: $i] :
( ~ ( hBOOL @ ( c_in @ SV503 @ SY3261 @ SY3262 ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV70 @ SY3261 @ SY3262 @ SY3260 ) @ SY3259 @ ( tc_fun @ SY3260 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(2192,plain,
! [SV504: $i,SV71: $i] :
( ( ! [SY3263: $i,SY3264: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV71 @ ( c_Set_Oinsert @ SV504 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3263 @ tc_bool ) ) @ SY3263 ) @ ( tc_fun @ SY3263 @ tc_bool ) ) @ SY3264 @ ( tc_fun @ SY3263 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV504 @ SV71 @ SY3263 ) )
| ~ ( c_lessequals @ SV71 @ ( c_Set_Oinsert @ SV504 @ SY3264 @ SY3263 ) @ ( tc_fun @ SY3263 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1748]) ).
thf(2193,plain,
! [SV505: $i,SV72: $i] :
( ( ! [SY3265: $i,SY3266: $i] :
( ( c_lessequals @ SV72 @ ( c_Set_Oinsert @ SV505 @ SY3265 @ SY3266 ) @ ( tc_fun @ SY3266 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV505 @ SV72 @ SY3266 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV72 @ ( c_Set_Oinsert @ SV505 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3266 @ tc_bool ) ) @ SY3266 ) @ ( tc_fun @ SY3266 @ tc_bool ) ) @ SY3265 @ ( tc_fun @ SY3266 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1749]) ).
thf(2194,plain,
! [SV506: $i,SV73: $i] :
( ( ! [SY3267: $i,SY3268: $i] :
( ( c_lessequals @ SV73 @ ( c_Set_Oinsert @ SV506 @ SY3267 @ SY3268 ) @ ( tc_fun @ SY3268 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV506 @ SV73 @ SY3268 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV73 @ ( c_Set_Oinsert @ SV506 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3268 @ tc_bool ) ) @ SY3268 ) @ ( tc_fun @ SY3268 @ tc_bool ) ) @ SY3267 @ ( tc_fun @ SY3268 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(2195,plain,
! [SV507: $i,SV74: $i] :
( ( ! [SY3269: $i] :
( ! [SY3270: $i] : ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV74 @ SV507 ) @ SY3269 @ SY3270 @ SY3269 )
| ( hBOOL @ ( hAPP @ SV74 @ SY3269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(2196,plain,
! [SV508: $i,SV75: $i] :
( ( ! [SY3271: $i] :
( ( c_Finite__Set_Ofold1 @ SV75 @ SV508 @ SY3271 )
= ( c_The @ ( c_Finite__Set_Ofold1Set @ SV75 @ SV508 @ SY3271 ) @ SY3271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(2197,plain,
! [SV509: $i,SV76: $i] :
( ( ! [SY3272: $i,SY3273: $i,SY3274: $i,SY3275: $i] :
( ( c_Com_Ocom_OCond @ SV76 @ SV509 @ SY3272 )
!= ( c_Com_Ocom_OCall @ SY3273 @ SY3274 @ SY3275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(2198,plain,
! [SV510: $i,SV77: $i] :
( ( ! [SY3276: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV77 )
| ! [SY3277: $i,SY3278: $i] :
( ( c_lessequals @ ( hAPP @ SV510 @ SY3276 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3277 @ SV510 @ SY3278 @ SV77 ) @ SV77 )
| ~ ( hBOOL @ ( c_in @ SY3276 @ SY3277 @ SY3278 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(2199,plain,
! [SV511: $i,SV78: $i] :
( ( ! [SY3279: $i,SY3280: $i] :
( ! [SY3281: $i] : ( c_lessequals @ ( hAPP @ SV78 @ SV511 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3279 @ SV78 @ SY3280 @ ( tc_fun @ SY3281 @ tc_bool ) ) @ ( tc_fun @ SY3281 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV511 @ SY3279 @ SY3280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(2200,plain,
! [SV512: $i,SV79: $i] :
( ( ! [SY3282: $i,SY3283: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV79 @ SV512 @ SY3282 ) @ SY3283 @ ( tc_fun @ SY3282 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV512 @ SY3283 @ ( tc_fun @ SY3282 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SV79 @ SY3283 @ SY3282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1756]) ).
thf(2201,plain,
! [SV513: $i,SV80: $i] :
( ( ! [SY3284: $i,SY3285: $i,SY3286: $i,SY3287: $i] :
( ( c_Com_Ocom_OLocal @ SV80 @ SV513 @ SY3284 )
!= ( c_Com_Ocom_OCond @ SY3285 @ SY3286 @ SY3287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(2202,plain,
! [SV514: $i,SV81: $i] :
( ( ( c_Set_Oimage @ ( c_COMBI @ SV81 ) @ SV514 @ SV81 @ SV81 )
= SV514 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(2203,plain,
! [SV515: $i,SV82: $i] :
( ( ! [SY3288: $i,SY3289: $i,SY3290: $i,SY3291: $i] :
( ( ( c_Com_Ocom_OCall @ SV82 @ SV515 @ SY3288 )
!= ( c_Com_Ocom_OCall @ SY3289 @ SY3290 @ SY3291 ) )
| ( SY3288 = SY3291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(2204,plain,
! [SV516: $i,SV83: $i] :
( ( ! [SY3292: $i,SY3293: $i,SY3294: $i] :
( ! [SY3295: $i] :
( ( c_Com_Ocom_OCall @ SV83 @ SV516 @ SY3292 )
!= ( c_Com_Ocom_OCall @ SY3293 @ SY3294 @ SY3295 ) )
| ( SV516 = SY3294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1760]) ).
thf(2205,plain,
! [SV517: $i,SV84: $i] :
( ( ! [SY3296: $i,SY3297: $i] :
( ! [SY3298: $i,SY3299: $i] :
( ( c_Com_Ocom_OCall @ SV84 @ SV517 @ SY3296 )
!= ( c_Com_Ocom_OCall @ SY3297 @ SY3298 @ SY3299 ) )
| ( SV84 = SY3297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(2206,plain,
! [SV518: $i,SV85: $i] :
( ( ( c_Com_Ocom_OWhile @ SV85 @ SV518 )
!= c_Com_Ocom_OSKIP )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(2207,plain,
! [SV519: $i,SV86: $i] :
( ( ! [SY3300: $i,SY3301: $i,SY3302: $i] :
( ( c_Com_Ocom_OWhile @ SV86 @ SV519 )
!= ( c_Com_Ocom_OLocal @ SY3300 @ SY3301 @ SY3302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(2208,plain,
! [SV520: $i,SV87: $i] :
( ( ! [SY3303: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV87 @ SV520 ) @ SY3303 @ SY3303 )
| ( hBOOL @ ( hAPP @ SV87 @ SY3303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(2209,plain,
! [SV88: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
= ( c_Suc @ SV88 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1765]) ).
thf(2210,plain,
! [SV89: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
= ( c_Suc @ SV89 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1766]) ).
thf(2211,plain,
! [SV521: $i,SV90: $i] :
( ( ( c_Collect @ SV90 @ SV521 )
= SV90 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1767]) ).
thf(2212,plain,
! [SV522: $i,SV91: $i] :
( ( ! [SY3304: $i,SY3305: $i] :
( ( ( c_Com_Ocom_OSemi @ SV91 @ SV522 )
!= ( c_Com_Ocom_OSemi @ SY3304 @ SY3305 ) )
| ( SV522 = SY3305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(2213,plain,
! [SV523: $i,SV92: $i] :
( ( ! [SY3306: $i] :
( ! [SY3307: $i] :
( ( c_Com_Ocom_OSemi @ SV92 @ SV523 )
!= ( c_Com_Ocom_OSemi @ SY3306 @ SY3307 ) )
| ( SV92 = SY3306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(2214,plain,
! [SV524: $i,SV93: $i] :
( ( ! [SY3308: $i,SY3309: $i] :
( ( c_Com_Ocom_OSemi @ SV93 @ SV524 )
!= ( c_Com_Ocom_OWhile @ SY3308 @ SY3309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(2215,plain,
! [SV94: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV94 ) )
= $true )
| ( ( ! [SY2070: $i,SY2071: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SY2070 @ SY2071 @ SV94 ) @ SV94 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2070 @ ( c_Complete__Lattice_OSup__class_OSup @ SY2071 @ SV94 ) @ SV94 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1771]) ).
thf(2216,plain,
! [SV525: $i,SV95: $i] :
( ( ! [SY3310: $i,SY3311: $i,SY3312: $i] :
( ( c_Com_Ocom_OSemi @ SV95 @ SV525 )
!= ( c_Com_Ocom_OCond @ SY3310 @ SY3311 @ SY3312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(2217,plain,
! [SV526: $i,SV96: $i] :
( ( ! [SY3313: $i,SY3314: $i,SY3315: $i] :
( ( c_Com_Ocom_OSemi @ SV96 @ SV526 )
!= ( c_Com_Ocom_OLocal @ SY3313 @ SY3314 @ SY3315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(2218,plain,
! [SV527: $i,SV97: $i] :
( ( ! [SY3316: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ SV97 @ SV527 @ SY3316 )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV97 ) @ SV527 @ SY3316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(2219,plain,
! [SV528: $i,SV98: $i] :
( ( ! [SY3317: $i,SY3318: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV98 @ SV528 @ SY3317 @ ( tc_fun @ SY3318 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3318 @ tc_bool ) ) )
| ! [SY3319: $i] :
( ( ( hAPP @ SV528 @ SY3319 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3318 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SY3319 @ SV98 @ SY3317 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(2220,plain,
! [SV529: $i,SV99: $i] :
( ( ! [SY3320: $i,SY3321: $i,SY3322: $i] :
( ( c_Com_Ocom_OCond @ SV99 @ SV529 @ SY3320 )
!= ( c_Com_Ocom_OWhile @ SY3321 @ SY3322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(2221,plain,
! [SV530: $i,SV100: $i] :
( ( ! [SY3323: $i] :
( ( hBOOL @ ( c_in @ SV100 @ SV530 @ SY3323 ) )
| ! [SY3324: $i] :
~ ( hBOOL @ ( c_in @ SV100 @ ( c_HOL_Ominus__class_Ominus @ SV530 @ SY3324 @ ( tc_fun @ SY3323 @ tc_bool ) ) @ SY3323 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1777]) ).
thf(2222,plain,
! [SV531: $i,SV101: $i] :
( ( ! [SY3325: $i,SY3326: $i,SY3327: $i,SY3328: $i] :
( ( c_Com_Ocom_OCond @ SV101 @ SV531 @ SY3325 )
!= ( c_Com_Ocom_OLocal @ SY3326 @ SY3327 @ SY3328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(2223,plain,
! [SV532: $i,SV102: $i] :
( ( ! [SY3329: $i] :
( ~ ( hBOOL @ ( c_in @ SV102 @ SV532 @ SY3329 ) )
| ! [SY3330: $i] :
~ ( hBOOL @ ( c_in @ SV102 @ ( c_HOL_Ominus__class_Ominus @ SY3330 @ SV532 @ ( tc_fun @ SY3329 @ tc_bool ) ) @ SY3329 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(2224,plain,
! [SV533: $i,SV103: $i] :
( ( ! [SY3331: $i,SY3332: $i] :
( ( c_lessequals @ ( hAPP @ SV103 @ SV533 ) @ SY3331 @ ( tc_fun @ SY3332 @ tc_bool ) )
| ! [SY3333: $i,SY3334: $i] :
( ~ ( hBOOL @ ( c_in @ SV533 @ SY3333 @ SY3334 ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3333 @ SV103 @ SY3334 @ ( tc_fun @ SY3332 @ tc_bool ) ) @ SY3331 @ ( tc_fun @ SY3332 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(2225,plain,
! [SV534: $i,SV104: $i] :
( ( ! [SY3335: $i,SY3336: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ ( c_COMBK @ SV104 @ SV534 @ SY3335 ) @ SY3336 @ SY3335 @ SV534 @ t_a ) @ v_x )
= SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1781]) ).
thf(2226,plain,
! [SV535: $i,SV105: $i] :
( ( ( c_The @ ( hAPP @ ( c_COMBC @ ( c_fequal @ SV105 ) @ SV105 @ SV105 @ tc_bool ) @ SV535 ) @ SV105 )
= SV535 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(2227,plain,
! [SV536: $i,SV106: $i] :
( ( ! [SY3337: $i,SY3338: $i,SY3339: $i] :
( ( c_Com_Ocom_OCond @ SV106 @ SV536 @ SY3337 )
!= ( c_Com_Ocom_OSemi @ SY3338 @ SY3339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(2228,plain,
! [SV537: $i,SV107: $i] :
( ( ! [SY3340: $i,SY3341: $i] :
( ! [SY3342: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV107 @ SV537 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3340 @ SV107 @ SY3341 @ ( tc_fun @ SY3342 @ tc_bool ) ) @ ( tc_fun @ SY3342 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY3340 @ SV107 @ SY3341 @ ( tc_fun @ SY3342 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SV537 @ SY3340 @ SY3341 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(2229,plain,
! [SV538: $i,SV108: $i] :
( ( ! [SY3343: $i,SY3344: $i,SY3345: $i,SY3346: $i] :
( ( ( c_Com_Ocom_OCond @ SV108 @ SV538 @ SY3343 )
!= ( c_Com_Ocom_OCond @ SY3344 @ SY3345 @ SY3346 ) )
| ( SY3343 = SY3346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(2230,plain,
! [SV539: $i,SV109: $i] :
( ( ! [SY3347: $i,SY3348: $i,SY3349: $i] :
( ! [SY3350: $i] :
( ( c_Com_Ocom_OCond @ SV109 @ SV539 @ SY3347 )
!= ( c_Com_Ocom_OCond @ SY3348 @ SY3349 @ SY3350 ) )
| ( SV539 = SY3349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(2231,plain,
! [SV540: $i,SV110: $i] :
( ( ! [SY3351: $i,SY3352: $i] :
( ! [SY3353: $i,SY3354: $i] :
( ( c_Com_Ocom_OCond @ SV110 @ SV540 @ SY3351 )
!= ( c_Com_Ocom_OCond @ SY3352 @ SY3353 @ SY3354 ) )
| ( SV110 = SY3352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(2232,plain,
! [SV111: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV111 ) )
= $true )
| ( ( ! [SY2133: $i] :
( ( c_HOL_Ominus__class_Ominus @ SY2133 @ SY2133 @ SV111 )
= ( c_HOL_Ozero__class_Ozero @ SV111 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1788]) ).
thf(2233,plain,
! [SV112: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV112 ) )
= $true )
| ( ( ! [SY2134: $i] :
( ( c_HOL_Ominus__class_Ominus @ SY2134 @ SY2134 @ SV112 )
= ( c_HOL_Ozero__class_Ozero @ SV112 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1789]) ).
thf(2234,plain,
! [SV113: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV113 ) )
= $true )
| ( ( ! [SY2135: $i] :
( ( c_HOL_Ominus__class_Ominus @ SY2135 @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV113 )
= SY2135 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1790]) ).
thf(2235,plain,
! [SV114: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV114 ) )
= $true )
| ( ( ! [SY2136: $i] :
( ( c_HOL_Ominus__class_Ominus @ SY2136 @ SY2136 @ SV114 )
= ( c_HOL_Ozero__class_Ozero @ SV114 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1791]) ).
thf(2236,plain,
! [SV115: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV115 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV115 )
| ! [SY2137: $i] :
( ( c_HOL_Ominus__class_Ominus @ SY2137 @ SY2137 @ SV115 )
= ( c_HOL_Ozero__class_Ozero @ SV115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1792]) ).
thf(2237,plain,
! [SV541: $i,SV116: $i] :
( ( ! [SY3355: $i] :
( ~ ( class_Orderings_Oorder @ SV116 )
| ! [SY3356: $i,SY3357: $i] :
( ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV541 @ SY3355 @ SV116 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3356 @ SY3357 @ SV116 ) @ ( tc_fun @ SV116 @ tc_bool ) )
| ~ ( c_lessequals @ SY3355 @ SY3357 @ SV116 )
| ~ ( c_lessequals @ SY3356 @ SV541 @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(2238,plain,
! [SV542: $i,SV117: $i] :
( ( ! [SY3358: $i] :
( ~ ( class_Orderings_Oorder @ SV117 )
| ( c_lessequals @ SV542 @ SY3358 @ SV117 )
| ! [SY3359: $i] :
( ~ ( c_lessequals @ SY3359 @ SV542 @ SV117 )
| ! [SY3360: $i] :
~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3359 @ SV542 @ SV117 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3360 @ SY3358 @ SV117 ) @ ( tc_fun @ SV117 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(2239,plain,
! [SV543: $i,SV118: $i] :
( ( ! [SY3361: $i] :
( ~ ( class_Orderings_Oorder @ SV118 )
| ( c_lessequals @ SV543 @ SY3361 @ SV118 )
| ! [SY3362: $i] :
( ~ ( c_lessequals @ SY3361 @ SY3362 @ SV118 )
| ! [SY3363: $i] :
~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3361 @ SY3362 @ SV118 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV543 @ SY3363 @ SV118 ) @ ( tc_fun @ SV118 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(2240,plain,
! [SV544: $i,SV119: $i] :
( ( ( c_Option_Ooption_OSome @ SV119 @ SV544 )
!= ( c_Option_Ooption_ONone @ SV544 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(2241,plain,
! [SV545: $i,SV120: $i] :
( ( ( c_Option_Ooption_OSome @ SV120 @ SV545 )
!= ( c_Option_Ooption_ONone @ SV545 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(2242,plain,
! [SV546: $i,SV121: $i] :
( ( ! [SY3364: $i,SY3365: $i,SY3366: $i,SY3367: $i] :
( ( c_Com_Ocom_OCall @ SV121 @ SV546 @ SY3364 )
!= ( c_Com_Ocom_OCond @ SY3365 @ SY3366 @ SY3367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(2243,plain,
! [SV547: $i,SV122: $i] :
( ( ! [SY3368: $i] :
( ( ( c_Option_Ooption_OSome @ SV122 @ SV547 )
!= ( c_Option_Ooption_OSome @ SY3368 @ SV547 ) )
| ( SV122 = SY3368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(2244,plain,
! [SV548: $i,SV123: $i] :
( ( ! [SY3369: $i,SY3370: $i,SY3371: $i,SY3372: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV123 @ SV548 @ SY3369 @ SY3370 @ SY3371 ) @ SY3372 )
= ( hAPP @ SV123 @ ( hAPP @ SV548 @ SY3372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1800]) ).
thf(2245,plain,
! [SV549: $i,SV124: $i] :
( ( ! [SY3373: $i,SY3374: $i,SY3375: $i,SY3376: $i] :
( ( hAPP @ SV124 @ ( hAPP @ SV549 @ SY3373 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV124 @ SV549 @ SY3374 @ SY3375 @ SY3376 ) @ SY3373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(2246,plain,
! [SV550: $i,SV125: $i] :
( ( ( ( c_Suc @ SV125 )
!= ( c_Suc @ SV550 ) )
| ( SV125 = SV550 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2247,plain,
! [SV551: $i,SV126: $i] :
( ( ( ( c_Suc @ SV126 )
!= ( c_Suc @ SV551 ) )
| ( SV126 = SV551 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1803]) ).
thf(2248,plain,
! [SV552: $i,SV127: $i] :
( ( ! [SY3377: $i] :
( ~ ( class_Orderings_Oorder @ SV127 )
| ! [SY3378: $i,SY3379: $i] : ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV552 @ SY3377 @ SV127 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY3378 @ SY3379 @ SV127 ) @ ( tc_fun @ SV127 @ tc_bool ) )
| ( c_lessequals @ SV552 @ SY3377 @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(2249,plain,
! [SV553: $i,SV128: $i] :
( ( ( hBOOL @ ( hAPP @ SV128 @ SV553 ) )
| ! [SY3380: $i] :
( ( hBOOL @ ( hAPP @ SY3380 @ SV553 ) )
| ! [SY3381: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3380 @ SV128 @ ( tc_fun @ SY3381 @ tc_bool ) ) @ SV553 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(2250,plain,
! [SV554: $i,SV129: $i] :
( ( ! [SY3382: $i,SY3383: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV129 @ SV554 @ ( tc_fun @ SY3382 @ tc_bool ) ) @ SY3383 ) )
| ~ ( hBOOL @ ( hAPP @ SV554 @ SY3383 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1806]) ).
thf(2251,plain,
! [SV555: $i,SV130: $i] :
( ( ! [SY3384: $i,SY3385: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV130 @ SV555 @ ( tc_fun @ SY3384 @ tc_bool ) ) @ SY3385 ) )
| ~ ( hBOOL @ ( hAPP @ SV130 @ SY3385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1807]) ).
thf(2252,plain,
! [SV556: $i,SV131: $i] :
( ( ! [SY3386: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV131 @ SV556 @ SY3386 ) )
| ~ ( c_Com_OWT @ SY3386 )
| ~ ( c_Com_OWT @ SV556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(2253,plain,
! [SV557: $i,SV132: $i] :
( ( ! [SY3387: $i,SY3388: $i,SY3389: $i,SY3390: $i,SY3391: $i,SY3392: $i,SY3393: $i] :
( ( c_Com_Ocom_Ocom__case @ SV132 @ SV557 @ SY3387 @ SY3388 @ SY3389 @ SY3390 @ SY3391 @ SY3392 @ c_Com_Ocom_OSKIP @ SY3393 )
= SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(2254,plain,
! [SV558: $i,SV133: $i] :
( ( ! [SY3394: $i] :
( ( hBOOL @ ( c_in @ SV133 @ SV558 @ SY3394 ) )
| ! [SY3395: $i] :
( ( hBOOL @ ( c_in @ SV133 @ SY3395 @ SY3394 ) )
| ~ ( hBOOL @ ( c_in @ SV133 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3395 @ SV558 @ ( tc_fun @ SY3394 @ tc_bool ) ) @ SY3394 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2255,plain,
! [SV559: $i,SV134: $i] :
( ( ! [SY3396: $i,SY3397: $i,SY3398: $i] :
( ( c_Com_Ocom_OLocal @ SV134 @ SV559 @ SY3396 )
!= ( c_Com_Ocom_OWhile @ SY3397 @ SY3398 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(2256,plain,
! [SV560: $i,SV135: $i] :
( ( ! [SY3399: $i,SY3400: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV135 @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV560 @ SY3399 @ SY3400 @ ( tc_fun @ SV135 @ tc_bool ) ) )
| ! [SY3401: $i] :
( ( ( hAPP @ SY3399 @ SY3401 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV135 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SY3401 @ SV560 @ SY3400 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(2257,plain,
! [SV561: $i,SV136: $i] :
( ( ! [SY3402: $i,SY3403: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV136 @ tc_bool ) ) @ SV561 @ SV136 @ ( tc_fun @ SY3402 @ tc_bool ) ) @ SY3403 @ ( tc_fun @ SY3402 @ tc_bool ) )
= SY3403 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(2258,plain,
! [SV562: $i,SV137: $i] :
( ( ! [SY3404: $i,SY3405: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV137 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV562 @ tc_bool ) ) @ SY3404 @ SV562 @ ( tc_fun @ SY3405 @ tc_bool ) ) @ ( tc_fun @ SY3405 @ tc_bool ) )
= SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1814]) ).
thf(2259,plain,
! [SV563: $i,SV138: $i] :
( ( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OWhile @ SV138 @ SV563 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1815]) ).
thf(2260,plain,
! [SV564: $i,SV139: $i] :
( ( ! [SY3406: $i,SY3407: $i,SY3408: $i] :
( ( hBOOL @ ( c_in @ SV139 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV564 @ SY3406 @ SY3407 @ ( tc_fun @ SY3408 @ tc_bool ) ) @ SY3408 ) )
| ! [SY3409: $i] :
( ~ ( hBOOL @ ( c_in @ SV139 @ ( hAPP @ SY3406 @ SY3409 ) @ SY3408 ) )
| ~ ( hBOOL @ ( c_in @ SY3409 @ SV564 @ SY3407 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1816]) ).
thf(2261,plain,
! [SV565: $i,SV140: $i] :
( ( ! [SY3410: $i,SY3411: $i,SY3412: $i] :
( ( hBOOL @ ( c_in @ SV140 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV565 @ SY3410 @ SY3411 @ ( tc_fun @ SY3412 @ tc_bool ) ) @ SY3412 ) )
| ! [SY3413: $i] :
( ~ ( hBOOL @ ( c_in @ SV140 @ ( hAPP @ SY3410 @ SY3413 ) @ SY3412 ) )
| ~ ( hBOOL @ ( c_in @ SY3413 @ SV565 @ SY3411 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1817]) ).
thf(2262,plain,
! [SV566: $i,SV141: $i] :
( ( ! [SY3414: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV141 @ SV566 @ ( tc_fun @ SY3414 @ tc_bool ) ) @ SV566 @ ( tc_fun @ SY3414 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV141 @ SV566 @ ( tc_fun @ SY3414 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1818]) ).
thf(2263,plain,
! [SV567: $i,SV142: $i] :
( ( ! [SY3415: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV142 @ ( c_HOL_Ominus__class_Ominus @ SV567 @ SV142 @ ( tc_fun @ SY3415 @ tc_bool ) ) @ ( tc_fun @ SY3415 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV142 @ SV567 @ ( tc_fun @ SY3415 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(2264,plain,
! [SV568: $i,SV143: $i] :
( ( ! [SY3416: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV143 @ tc_bool ) ) @ ( c_COMBK @ SV568 @ ( tc_fun @ SY3416 @ tc_bool ) @ SV143 ) @ SV143 @ ( tc_fun @ SY3416 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3416 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1820]) ).
thf(2265,plain,
! [SV144: $i] :
( ( ( ~ ( class_HOL_Ominus @ SV144 ) )
= $true )
| ( ( ! [SY2228: $i,SY2229: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ SY2228 @ SY2229 @ ( tc_fun @ t_a @ SV144 ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ SY2228 @ v_x ) @ ( hAPP @ SY2229 @ v_x ) @ SV144 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1821]) ).
thf(2266,plain,
! [SV569: $i,SV145: $i] :
( ( ! [SY3417: $i,SY3418: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV145 @ SV569 @ ( tc_fun @ SY3417 @ tc_bool ) ) @ SY3418 @ ( tc_fun @ SY3417 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV145 @ SY3418 @ ( tc_fun @ SY3417 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV569 @ SY3418 @ ( tc_fun @ SY3417 @ tc_bool ) ) @ ( tc_fun @ SY3417 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1822]) ).
thf(2267,plain,
! [SV570: $i,SV146: $i] :
( ( ! [SY3419: $i,SY3420: $i,SY3421: $i,SY3422: $i,SY3423: $i,SY3424: $i,SY3425: $i,SY3426: $i,SY3427: $i] :
( ( c_Com_Ocom_Ocom__case @ SV146 @ SV570 @ SY3419 @ SY3420 @ SY3421 @ SY3422 @ SY3423 @ SY3424 @ ( c_Com_Ocom_OSemi @ SY3425 @ SY3426 ) @ SY3427 )
= ( hAPP @ ( hAPP @ SY3420 @ SY3425 ) @ SY3426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1823]) ).
thf(2268,plain,
! [SV571: $i,SV147: $i] :
( ( ! [SY3428: $i,SY3429: $i,SY3430: $i] :
( ( c_Com_Ocom_OLocal @ SV147 @ SV571 @ SY3428 )
!= ( c_Com_Ocom_OSemi @ SY3429 @ SY3430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(2269,plain,
! [SV572: $i,SV148: $i] :
( ( ! [SY3431: $i] :
( ( c_Set_Oinsert @ SV148 @ SV572 @ SY3431 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ SY3431 ) @ SY3431 @ SY3431 @ tc_bool ) @ SV148 ) @ SY3431 ) @ SV572 @ ( tc_fun @ SY3431 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(2270,plain,
! [SV573: $i,SV149: $i] :
( ( ! [SY3432: $i,SY3433: $i,SY3434: $i,SY3435: $i,SY3436: $i,SY3437: $i,SY3438: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV149 @ ( hAPP @ SV573 @ SY3432 ) ) @ SY3433 ) )
| ~ ( hBOOL @ ( c_in @ SY3433 @ SY3432 @ SY3434 ) )
| ! [SY3439: $i,SY3440: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV573 @ SY3435 @ SV149 @ SY3436 @ SY3437 @ SY3438 @ SY3439 @ SY3440 @ SY3434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2271,plain,
! [SV574: $i,SV150: $i] :
( ( ! [SY3441: $i,SY3442: $i,SY3443: $i,SY3444: $i,SY3445: $i,SY3446: $i,SY3447: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV150 @ SV574 ) @ ( hAPP @ SY3441 @ SY3442 ) ) )
| ~ ( hBOOL @ ( c_in @ SV574 @ SY3442 @ SY3443 ) )
| ! [SY2267: $i,SY2268: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3444 @ SY3441 @ SV150 @ SY3445 @ SY3446 @ SY3447 @ SY2267 @ SY2268 @ SY3443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(2272,plain,
! [SV575: $i,SV151: $i] :
( ( ! [SY3450: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV151 @ SV575 @ ( tc_fun @ SY3450 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV575 @ SV151 @ ( tc_fun @ SY3450 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(2273,plain,
! [SV152: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV152 ) )
= $true )
| ( ( ! [SY2271: $i,SY2272: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2271 @ SY2272 @ SV152 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2272 @ SY2271 @ SV152 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1829]) ).
thf(2274,plain,
! [SV153: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV153 ) )
= $true )
| ( ( ! [SY2273: $i,SY2274: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2273 @ SY2274 @ SV153 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2274 @ SY2273 @ SV153 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1830]) ).
thf(2275,plain,
! [SV576: $i,SV154: $i] :
( ( ! [SY3451: $i] :
( ! [SY3452: $i] :
( ( c_Com_Ocom_OWhile @ SV154 @ SV576 )
!= ( c_Com_Ocom_OWhile @ SY3451 @ SY3452 ) )
| ( SV154 = SY3451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(2276,plain,
! [SV577: $i,SV155: $i] :
( ( ! [SY3453: $i,SY3454: $i] :
( ( ( c_Com_Ocom_OWhile @ SV155 @ SV577 )
!= ( c_Com_Ocom_OWhile @ SY3453 @ SY3454 ) )
| ( SV577 = SY3454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(2277,plain,
! [SV578: $i,SV156: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ SV156 @ SV578 ) )
| ~ ( c_Com_OWT @ SV578 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1833]) ).
thf(2278,plain,
! [SV157: $i] :
( ( ( c_Com_OWT @ SV157 )
= $true )
| ( ( ! [SY2282: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ SY2282 @ SV157 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1834]) ).
thf(2279,plain,
! [SV579: $i,SV158: $i] :
( ( ! [SY3455: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV158 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV158 @ SV579 @ ( tc_fun @ SY3455 @ tc_bool ) ) @ ( tc_fun @ SY3455 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV158 @ SV579 @ ( tc_fun @ SY3455 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(2280,plain,
! [SV159: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV159 ) )
= $true )
| ( ( ! [SY2285: $i,SY2286: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2285 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2285 @ SY2286 @ SV159 ) @ SV159 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2285 @ SY2286 @ SV159 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1836]) ).
thf(2281,plain,
! [SV160: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV160 ) )
= $true )
| ( ( ! [SY2287: $i,SY2288: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2287 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2287 @ SY2288 @ SV160 ) @ SV160 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2287 @ SY2288 @ SV160 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1837]) ).
thf(2282,plain,
! [SV580: $i,SV161: $i] :
( ( ! [SY3456: $i] :
( ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ SV161 @ SV580 @ SY3456 ) )
| ~ ( c_Com_OWT @ SY3456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(2283,plain,
! [SV162: $i] :
( ( ( c_Com_OWT @ SV162 )
= $true )
| ( ( ! [SY2291: $i,SY2292: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ SY2291 @ SY2292 @ SV162 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1839]) ).
thf(2284,plain,
! [SV581: $i,SV163: $i] :
( ( ! [SY3457: $i] :
( ( c_Com_Ocom_OCond @ SV163 @ SV581 @ SY3457 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(2285,plain,
! [SV582: $i,SV164: $i] :
( ( ! [SY3458: $i,SY3459: $i,SY3460: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV164 @ SV582 @ SY3458 @ ( tc_fun @ SY3459 @ tc_bool ) ) @ SY3460 ) )
| ! [SY3461: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV582 @ SY3461 ) @ SY3460 ) )
| ~ ( hBOOL @ ( c_in @ SY3461 @ SV164 @ SY3458 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(2286,plain,
! [SV583: $i,SV165: $i] :
( ( ! [SY3462: $i,SY3463: $i,SY3464: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV165 @ SV583 @ SY3462 @ ( tc_fun @ SY3463 @ tc_bool ) ) @ SY3464 ) )
| ! [SY3465: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV583 @ SY3465 ) @ SY3464 ) )
| ~ ( hBOOL @ ( c_in @ SY3465 @ SV165 @ SY3462 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(2287,plain,
! [SV584: $i,SV166: $i] :
( ( ! [SY3466: $i,SY3467: $i,SY3468: $i] :
( ( c_Com_Ocom_OWhile @ SV166 @ SV584 )
!= ( c_Com_Ocom_OCond @ SY3466 @ SY3467 @ SY3468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1843]) ).
thf(2288,plain,
! [SV585: $i,SV167: $i] :
( ( ! [SY3469: $i,SY3470: $i,SY3471: $i] :
( ( c_Com_Ocom_OSemi @ SV167 @ SV585 )
!= ( c_Com_Ocom_OCall @ SY3469 @ SY3470 @ SY3471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(2289,plain,
! [SV586: $i,SV168: $i] :
( ( ! [SY3472: $i,SY3473: $i] :
( ( SV168
= ( c_Suc @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ SV586 @ SV168 @ SY3472 @ SY3473 ) ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ SV586 ) @ SY3472 @ SV168 @ SY3473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(2290,plain,
! [SV587: $i,SV169: $i] :
( ( ! [SY3474: $i,SY3475: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV169 @ SV587 @ SY3474 ) @ SY3475 @ ( tc_fun @ SY3474 @ tc_bool ) )
= ( c_Set_Oinsert @ SV169 @ ( c_HOL_Ominus__class_Ominus @ SV587 @ SY3475 @ ( tc_fun @ SY3474 @ tc_bool ) ) @ SY3474 ) )
| ( hBOOL @ ( c_in @ SV169 @ SY3475 @ SY3474 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(2291,plain,
! [SV588: $i,SV170: $i] :
( ( ( SV170 = SV588 )
| ! [SY3476: $i] :
~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV588 @ SY3476 @ SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(2292,plain,
! [SV589: $i,SV171: $i] :
( ( ! [SY3477: $i] :
( ~ ( hBOOL @ ( c_in @ SV171 @ SV589 @ SY3477 ) )
| ! [SY3478: $i,SY3479: $i] : ( hBOOL @ ( c_in @ ( hAPP @ SY3478 @ SV171 ) @ ( c_Set_Oimage @ SY3478 @ SV589 @ SY3477 @ SY3479 ) @ SY3479 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(2293,plain,
! [SV590: $i,SV172: $i] :
( ( ! [SY3480: $i] :
( ~ ( hBOOL @ ( c_in @ SV172 @ SV590 @ SY3480 ) )
| ! [SY3481: $i,SY3482: $i] : ( hBOOL @ ( c_in @ ( hAPP @ SY3481 @ SV172 ) @ ( c_Set_Oimage @ SY3481 @ SV590 @ SY3480 @ SY3482 ) @ SY3482 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(2294,plain,
! [SV591: $i,SV173: $i] :
( ( ! [SY3483: $i,SY3484: $i] :
( ! [SY3485: $i] : ( hBOOL @ ( c_in @ ( hAPP @ SV173 @ SV591 ) @ ( c_Set_Oimage @ SV173 @ SY3483 @ SY3484 @ SY3485 ) @ SY3485 ) )
| ~ ( hBOOL @ ( c_in @ SV591 @ SY3483 @ SY3484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(2295,plain,
! [SV592: $i,SV174: $i] :
( ( ! [SY3486: $i,SY3487: $i] :
( ! [SY3488: $i] : ( hBOOL @ ( c_in @ ( hAPP @ SV174 @ SV592 ) @ ( c_Set_Oimage @ SV174 @ SY3486 @ SY3487 @ SY3488 ) @ SY3488 ) )
| ~ ( hBOOL @ ( c_in @ SV592 @ SY3486 @ SY3487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(2296,plain,
! [SV593: $i,SV175: $i] :
( ( ! [SY3489: $i,SY3490: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV175 @ SV593 @ ( tc_fun @ SY3489 @ tc_bool ) ) @ SY3490 @ ( tc_fun @ SY3489 @ tc_bool ) )
| ~ ( c_lessequals @ SV175 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV593 @ SY3490 @ ( tc_fun @ SY3489 @ tc_bool ) ) @ ( tc_fun @ SY3489 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(2297,plain,
! [SV594: $i,SV176: $i] :
( ( ! [SY3491: $i,SY3492: $i] :
( ( c_lessequals @ SV176 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV594 @ SY3491 @ ( tc_fun @ SY3492 @ tc_bool ) ) @ ( tc_fun @ SY3492 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV176 @ SV594 @ ( tc_fun @ SY3492 @ tc_bool ) ) @ SY3491 @ ( tc_fun @ SY3492 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(2298,plain,
! [SV595: $i,SV177: $i] :
( ( ( SV177 = SV595 )
| ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ SV595 @ SV177 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2299,plain,
! [SV596: $i,SV178: $i] :
( ( ! [SY3493: $i] :
( ( c_Natural_Oevalc @ SV178 @ SV596 @ SY3493 )
| ! [SY3494: $i] :
~ ( c_Natural_Oevaln @ SV178 @ SV596 @ SY3494 @ SY3493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(2300,plain,
! [SV597: $i,SV179: $i] :
( ( ! [SY3495: $i] :
( ( c_Natural_Oevalc @ SV179 @ SV597 @ SY3495 )
| ! [SY3496: $i] :
~ ( c_Natural_Oevaln @ SV179 @ SV597 @ SY3496 @ SY3495 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2301,plain,
! [SV598: $i,SV180: $i] :
( ( ! [SY3497: $i] :
( ~ ( class_HOL_Oord @ SV180 )
| ! [SY3498: $i] :
( ( c_lessequals @ ( hAPP @ SV598 @ SY3497 ) @ ( hAPP @ SY3498 @ SY3497 ) @ SV180 )
| ! [SY3499: $i] :
~ ( c_lessequals @ SV598 @ SY3498 @ ( tc_fun @ SY3499 @ SV180 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(2302,plain,
! [SV181: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV181 ) )
= $true )
| ( ( ! [SY2354: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ SV181 ) @ SY2354 @ SV181 )
= SY2354 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1858]) ).
thf(2303,plain,
! [SV182: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV182 ) )
= $true )
| ( ( ! [SY2355: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2355 @ ( c_Orderings_Obot__class_Obot @ SV182 ) @ SV182 )
= SY2355 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1859]) ).
thf(2304,plain,
! [SV183: $i] :
( ( ( ~ ( class_Orderings_Obot @ SV183 ) )
= $true )
| ( ( ! [SY2356: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV183 ) @ SY2356 @ SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1860]) ).
thf(2305,plain,
! [SV184: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV184 ) )
= $true )
| ( ( ! [SY2357: $i] :
( ! [SY2358: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2357 @ SY2358 @ SV184 )
!= ( c_Orderings_Obot__class_Obot @ SV184 ) )
| ( SY2357
= ( c_Orderings_Obot__class_Obot @ SV184 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1861]) ).
thf(2306,plain,
! [SV185: $i] :
( ( ( ~ ( class_Lattices_Obounded__lattice @ SV185 ) )
= $true )
| ( ( ! [SY2359: $i,SY2360: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2359 @ SY2360 @ SV185 )
!= ( c_Orderings_Obot__class_Obot @ SV185 ) )
| ( SY2360
= ( c_Orderings_Obot__class_Obot @ SV185 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1862]) ).
thf(2307,plain,
! [SV599: $i,SV187: $i] :
( ( ! [SY3500: $i] :
( ! [SY3501: $i] :
( ( c_Set_Oimage @ SV187 @ SV599 @ SY3500 @ SY3501 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3501 @ tc_bool ) ) )
| ( SV599
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3500 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2308,plain,
! [SV600: $i,SV188: $i] :
( ( ! [SY3502: $i,SY3503: $i,SY3504: $i,SY3505: $i,SY3506: $i] :
( ( ( hAPP @ SV188 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_bool ) ) )
= SY3502 )
| ! [SY3507: $i,SY3508: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV188 @ SY3503 @ SY3504 @ SY3505 @ SY3506 @ SY3507 @ SY3508 @ SY3502 @ SV600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1865]) ).
thf(2309,plain,
! [SV601: $i,SV189: $i] :
( ( ! [SY3509: $i,SY3510: $i,SY3511: $i,SY3512: $i,SY3513: $i] :
( ( ( hAPP @ SV189 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV601 @ tc_bool ) ) )
= SY3509 )
| ! [SY3514: $i,SY3515: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3510 @ SV189 @ SY3511 @ SY3512 @ SY3513 @ SY3514 @ SY3509 @ SY3515 @ SV601 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(2310,plain,
! [SV602: $i,SV190: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV190 @ tc_bool ) )
!= ( c_Collect @ SV602 @ SV190 ) )
| ! [SY3516: $i] :
~ ( hBOOL @ ( hAPP @ SV602 @ SY3516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1867]) ).
thf(2311,plain,
! [SV603: $i,SV191: $i] :
( ( ~ ( hBOOL @ ( c_in @ SV191 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV603 @ tc_bool ) ) @ SV603 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(2312,plain,
! [SV604: $i,SV192: $i] :
( ( ( hBOOL @ ( hAPP @ SV192 @ SV604 ) )
| ! [SY3517: $i] :
~ ( hBOOL @ ( c_in @ SV604 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3517 @ tc_bool ) ) @ SY3517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1869]) ).
thf(2313,plain,
! [SV605: $i,SV193: $i] :
( ( ~ ( hBOOL @ ( c_in @ SV193 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV605 @ tc_bool ) ) @ SV605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1870]) ).
thf(2314,plain,
! [SV606: $i,SV194: $i] :
( ( ~ ( hBOOL @ ( c_in @ SV194 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV606 @ tc_bool ) ) @ SV606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(2315,plain,
! [SV607: $i,SV196: $i] :
( ( ( SV196
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV607 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV196 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV607 @ tc_bool ) ) @ ( tc_fun @ SV607 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(2316,plain,
! [SV197: $i] :
( ( ( ! [SY2388: $i] :
( ( c_Collect @ SV197 @ SY2388 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY2388 @ tc_bool ) ) ) )
= $true )
| ( ( ! [SY2389: $i] :
~ ( hBOOL @ ( hAPP @ SV197 @ SY2389 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1874]) ).
thf(2317,plain,
! [SV608: $i,SV198: $i] :
( ( ! [SY3518: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV198 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV608 @ tc_bool ) ) @ SV608 ) @ SY3518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(2318,plain,
! [SV609: $i,SV199: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV199 @ tc_bool ) ) @ SV609 @ ( tc_fun @ SV199 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV199 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1876]) ).
thf(2319,plain,
! [SV610: $i,SV200: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV200 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV610 @ tc_bool ) ) @ ( tc_fun @ SV610 @ tc_bool ) )
= SV200 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(2320,plain,
! [SV611: $i,SV201: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV201 @ tc_bool ) ) @ SV611 @ ( tc_fun @ SV201 @ tc_bool ) )
= SV611 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(2321,plain,
! [SV612: $i,SV202: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV202 @ SV202 @ ( tc_fun @ SV612 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV612 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(2322,plain,
! [SV613: $i,SV203: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV203 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV613 @ tc_bool ) ) @ ( tc_fun @ SV613 @ tc_bool ) )
= SV203 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(2323,plain,
! [SV614: $i,SV204: $i] :
( ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV204 @ tc_bool ) ) @ SV614 @ ( tc_fun @ SV204 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2324,plain,
! [SV615: $i,SV205: $i] :
( ( ! [SY3519: $i,SY3520: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV205 @ tc_bool ) )
!= ( c_Set_Oimage @ SV615 @ SY3519 @ SY3520 @ SV205 ) )
| ( SY3519
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3520 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2325,plain,
! [SV616: $i,SV206: $i] :
( ( ! [SY3521: $i] :
( ( c_Set_Oimage @ SV206 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV616 @ tc_bool ) ) @ SV616 @ SY3521 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3521 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2326,plain,
! [SV617: $i,SV207: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV207 @ SV617 ) )
| ! [SY3522: $i] :
~ ( hBOOL @ ( c_in @ SV617 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3522 @ tc_bool ) ) @ SY3522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2327,plain,
! [SV618: $i,SV208: $i] :
( ( ! [SY3523: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV208 @ SV618 @ ( tc_fun @ SY3523 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3523 @ tc_bool ) ) )
| ( SV618
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3523 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2328,plain,
! [SV619: $i,SV209: $i] :
( ( ! [SY3524: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV209 @ SV619 @ ( tc_fun @ SY3524 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3524 @ tc_bool ) ) )
| ( SV209
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3524 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2329,plain,
! [SV620: $i,SV210: $i] :
( ( ! [SY3525: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV210 @ tc_bool ) )
= ( c_Set_Oimage @ SV620 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3525 @ tc_bool ) ) @ SY3525 @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(2330,plain,
! [SV621: $i,SV211: $i] :
( ( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ SV211 ) @ SV211 @ SV211 @ tc_bool ) @ SV621 ) @ SV211 )
= ( c_Set_Oinsert @ SV621 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV211 @ tc_bool ) ) @ SV211 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(2331,plain,
! [SV622: $i,SV212: $i] :
( ( ! [SY3526: $i] :
( ( ( c_Set_Oinsert @ SV212 @ ( c_HOL_Ominus__class_Ominus @ SV622 @ ( c_Set_Oinsert @ SV212 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3526 @ tc_bool ) ) @ SY3526 ) @ ( tc_fun @ SY3526 @ tc_bool ) ) @ SY3526 )
= SV622 )
| ~ ( hBOOL @ ( c_in @ SV212 @ SV622 @ SY3526 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2332,plain,
! [SV623: $i,SV213: $i] :
( ( ! [SY3527: $i,SY3528: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV213 @ SV623 @ SY3527 ) @ SY3528 @ SY3527 @ SV623 )
= ( c_Set_Oinsert @ SV213 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV623 @ tc_bool ) ) @ SV623 ) )
| ( SY3528
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3527 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1890]) ).
thf(2333,plain,
! [SV214: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV214 ) )
= $true )
| ( ( ! [SY2417: $i,SY2418: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SY2417 @ ( c_Set_Oinsert @ SY2418 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV214 @ tc_bool ) ) @ SV214 ) @ SV214 ) @ SV214 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2417 @ SY2418 @ SV214 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1891]) ).
thf(2334,plain,
! [SV624: $i,SV215: $i] :
( ( ! [SY3529: $i,SY3530: $i] :
( ( c_lessequals @ SV215 @ ( c_Set_Oinsert @ SV624 @ SY3529 @ SY3530 ) @ ( tc_fun @ SY3530 @ tc_bool ) )
| ~ ( c_lessequals @ SV215 @ SY3529 @ ( tc_fun @ SY3530 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV215 @ ( c_Set_Oinsert @ SV624 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3530 @ tc_bool ) ) @ SY3530 ) @ ( tc_fun @ SY3530 @ tc_bool ) ) @ SY3529 @ ( tc_fun @ SY3530 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(2335,plain,
! [SV625: $i,SV216: $i] :
( ( ! [SY3531: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV216 @ SV625 @ SY3531 ) @ ( c_Set_Oinsert @ SV216 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3531 @ tc_bool ) ) @ SY3531 ) @ ( tc_fun @ SY3531 @ tc_bool ) )
= SV625 )
| ( hBOOL @ ( c_in @ SV216 @ SV625 @ SY3531 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2336,plain,
! [SV626: $i,SV217: $i] :
( ( ! [SY3532: $i,SY3533: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV217 @ SV626 @ SY3532 ) @ ( c_Set_Oinsert @ SV217 @ SY3533 @ SY3532 ) @ ( tc_fun @ SY3532 @ tc_bool ) )
| ~ ( c_lessequals @ SV626 @ SY3533 @ ( tc_fun @ SY3532 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2337,plain,
! [SV627: $i,SV218: $i] :
( ( ! [SY3534: $i,SY3535: $i] :
( ( hBOOL @ ( c_in @ SV218 @ ( c_Set_Oinsert @ SV627 @ SY3534 @ SY3535 ) @ SY3535 ) )
| ~ ( hBOOL @ ( c_in @ SV218 @ SY3534 @ SY3535 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2338,plain,
! [SV628: $i,SV219: $i] :
( ( ! [SY3536: $i,SY3537: $i] :
( ( hBOOL @ ( c_in @ SV219 @ ( c_Set_Oinsert @ SV628 @ SY3536 @ SY3537 ) @ SY3537 ) )
| ~ ( hBOOL @ ( c_in @ SV219 @ SY3536 @ SY3537 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2339,plain,
! [SV629: $i,SV220: $i] :
( ( ! [SY3538: $i,SY3539: $i,SY3540: $i] :
( ( c_Set_Oimage @ SV220 @ ( c_Set_Oinsert @ SV629 @ SY3538 @ SY3539 ) @ SY3539 @ SY3540 )
= ( c_Set_Oinsert @ ( hAPP @ SV220 @ SV629 ) @ ( c_Set_Oimage @ SV220 @ SY3538 @ SY3539 @ SY3540 ) @ SY3540 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1897]) ).
thf(2340,plain,
! [SV630: $i,SV221: $i] :
( ( ! [SY3541: $i,SY3542: $i,SY3543: $i,SY3544: $i,SY3545: $i,SY3546: $i,SY3547: $i] :
( ( ( hAPP @ SV221 @ ( c_Set_Oinsert @ SV630 @ SY3541 @ SY3542 ) )
= ( hAPP @ ( hAPP @ SY3543 @ SV630 ) @ ( hAPP @ SV221 @ SY3541 ) ) )
| ! [SY2445: $i,SY2446: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV221 @ SY3544 @ SY3545 @ SY3546 @ SY3543 @ SY3547 @ SY2445 @ SY2446 @ SY3542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2341,plain,
! [SV631: $i,SV222: $i] :
( ( ! [SY3550: $i,SY3551: $i,SY3552: $i,SY3553: $i,SY3554: $i,SY3555: $i,SY3556: $i] :
( ( ( hAPP @ SV222 @ ( c_Set_Oinsert @ SV631 @ SY3550 @ SY3551 ) )
= ( hAPP @ ( hAPP @ SY3552 @ SV631 ) @ ( hAPP @ SV222 @ SY3550 ) ) )
| ! [SY2455: $i,SY2456: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3553 @ SV222 @ SY3554 @ SY3555 @ SY3556 @ SY3552 @ SY2455 @ SY2456 @ SY3551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1899]) ).
thf(2342,plain,
! [SV632: $i,SV223: $i] :
( ( ! [SY3559: $i] :
( ( hBOOL @ ( c_in @ SV223 @ SV632 @ SY3559 ) )
| ! [SY3560: $i] :
( ( SV223 = SY3560 )
| ~ ( hBOOL @ ( c_in @ SV223 @ ( c_Set_Oinsert @ SY3560 @ SV632 @ SY3559 ) @ SY3559 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(2343,plain,
! [SV633: $i,SV224: $i] :
( ( ! [SY3561: $i] : ( c_lessequals @ SV224 @ ( c_Set_Oinsert @ SV633 @ SV224 @ SY3561 ) @ ( tc_fun @ SY3561 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(2344,plain,
! [SV634: $i,SV225: $i] :
( ( ! [SY3562: $i,SY3563: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV225 @ ( c_Set_Oinsert @ SV634 @ SY3562 @ SY3563 ) @ ( tc_fun @ SY3563 @ tc_bool ) )
= ( c_Set_Oinsert @ SV634 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV225 @ SY3562 @ ( tc_fun @ SY3563 @ tc_bool ) ) @ SY3563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2345,plain,
! [SV635: $i,SV226: $i] :
( ( ! [SY3564: $i,SY3565: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV226 @ SV635 @ SY3564 ) @ SY3565 @ ( tc_fun @ SY3564 @ tc_bool ) )
= ( c_Set_Oinsert @ SV226 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV635 @ SY3565 @ ( tc_fun @ SY3564 @ tc_bool ) ) @ SY3564 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(2346,plain,
! [SV636: $i,SV227: $i] :
( ( ! [SY3566: $i,SY3567: $i] :
( ( c_lessequals @ SV227 @ ( c_Set_Oinsert @ SV636 @ SY3566 @ SY3567 ) @ ( tc_fun @ SY3567 @ tc_bool ) )
| ~ ( c_lessequals @ SV227 @ SY3566 @ ( tc_fun @ SY3567 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(2347,plain,
! [SV637: $i,SV228: $i] :
( ( ! [SY3568: $i] :
( ( c_lessequals @ SV228 @ SV637 @ ( tc_fun @ SY3568 @ tc_bool ) )
| ! [SY3569: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SY3569 @ SV228 @ SY3568 ) @ SV637 @ ( tc_fun @ SY3568 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2348,plain,
! [SV638: $i,SV229: $i] :
( ( ! [SY3570: $i] : ( hBOOL @ ( c_in @ SV229 @ ( c_Set_Oinsert @ SV229 @ SV638 @ SY3570 ) @ SY3570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2349,plain,
! [SV639: $i,SV230: $i] :
( ( ! [SY3571: $i] : ( hBOOL @ ( c_in @ SV230 @ ( c_Set_Oinsert @ SV230 @ SV639 @ SY3571 ) @ SY3571 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(2350,plain,
! [SV640: $i,SV231: $i] :
( ( ! [SY3572: $i] : ( hBOOL @ ( c_in @ SV231 @ ( c_Set_Oinsert @ SV231 @ SV640 @ SY3572 ) @ SY3572 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2351,plain,
! [SV641: $i,SV232: $i] :
( ( ! [SY3573: $i,SY3574: $i] :
( ( ( c_Set_Oinsert @ SV232 @ SV641 @ SY3573 )
!= ( c_Set_Oinsert @ SV232 @ SY3574 @ SY3573 ) )
| ( hBOOL @ ( c_in @ SV232 @ SY3574 @ SY3573 ) )
| ( SV641 = SY3574 )
| ( hBOOL @ ( c_in @ SV232 @ SV641 @ SY3573 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(2352,plain,
! [SV642: $i,SV233: $i] :
( ( ! [SY3575: $i] :
( ( ( c_Set_Oinsert @ SV233 @ SV642 @ SY3575 )
= SV642 )
| ~ ( hBOOL @ ( c_in @ SV233 @ SV642 @ SY3575 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(2353,plain,
! [SV643: $i,SV234: $i] :
( ( ! [SY3576: $i,SY3577: $i,SY3578: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV234 @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV643 ) @ SY3576 @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ SY3577 @ tc_Com_Opname @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SY3578 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SV643 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV234 @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV643 ) @ SY3576 @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ SY3577 @ tc_Com_Opname @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SY3578 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV643 ) @ SY3576 @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ SY3577 @ tc_Com_Opname @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SY3578 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SV643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(2354,plain,
! [SV235: $i] :
( ( ( hAPP @ c_Com_Ocom_OBODY @ SV235 )
= c_Com_Ocom_OSKIP )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1912]) ).
thf(2355,plain,
! [SV644: $i,SV236: $i] :
( ( ! [SY3579: $i] :
( ( c_Com_Ocom_OWhile @ SV236 @ SV644 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SY3579 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2356,plain,
! [SV645: $i,SV237: $i] :
( ( ! [SY3580: $i,SY3581: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ SV237 )
!= ( c_Com_Ocom_OCond @ SV645 @ SY3580 @ SY3581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(2357,plain,
! [SV646: $i,SV238: $i] :
( ( ! [SY3582: $i,SY3583: $i] :
( ( c_Com_Ocom_OCond @ SV238 @ SV646 @ SY3582 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SY3583 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2358,plain,
! [SV647: $i,SV239: $i] :
( ( ! [SY3584: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OLocal @ SV239 @ SV647 @ SY3584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2359,plain,
! [SV648: $i,SV240: $i] :
( ( ! [SY3585: $i,SY3586: $i] :
( ( c_Natural_Oevaln @ SV240 @ SV648 @ ( c_Suc @ SY3585 ) @ SY3586 )
| ~ ( c_Natural_Oevaln @ SV240 @ SV648 @ SY3585 @ SY3586 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2360,plain,
! [SV649: $i,SV241: $i] :
( ( ! [SY3587: $i,SY3588: $i,SY3589: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV241 @ SV649 @ ( tc_fun @ SY3587 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY3588 @ SY3589 @ ( tc_fun @ SY3587 @ tc_bool ) ) @ ( tc_fun @ SY3587 @ tc_bool ) )
| ~ ( c_lessequals @ SY3589 @ SV649 @ ( tc_fun @ SY3587 @ tc_bool ) )
| ~ ( c_lessequals @ SV241 @ SY3588 @ ( tc_fun @ SY3587 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2361,plain,
! [SV650: $i,SV242: $i] :
( ( ! [SY3590: $i,SY3591: $i] :
( ( c_Natural_Oevaln @ SV242 @ SV650 @ SY3590 @ SY3591 )
| ! [SY3592: $i] :
( ( hBOOL @ ( hAPP @ SY3592 @ SV650 ) )
| ! [SY3593: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SY3592 @ SY3593 @ SV242 ) @ SV650 @ SY3590 @ SY3591 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2362,plain,
! [SV651: $i,SV243: $i] :
( ( ! [SY3594: $i,SY3595: $i,SY3596: $i,SY3597: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV243 @ SV651 @ SY3594 ) @ SY3595 @ SY3596 @ SY3597 )
| ~ ( c_Natural_Oevaln @ SY3594 @ SY3595 @ SY3596 @ SY3597 )
| ( hBOOL @ ( hAPP @ SV243 @ SY3595 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(2363,plain,
! [SV652: $i,SV244: $i] :
( ( ! [SY3598: $i,SY3599: $i,SY3600: $i] :
( ( c_Com_Ocom_OWhile @ SV244 @ SV652 )
!= ( c_Com_Ocom_OCall @ SY3598 @ SY3599 @ SY3600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2364,plain,
! [SV653: $i,SV246: $i] :
( ( ( SV246 = SV653 )
| ! [SY3601: $i] :
( ~ ( c_lessequals @ SV653 @ SV246 @ ( tc_fun @ SY3601 @ tc_bool ) )
| ~ ( c_lessequals @ SV246 @ SV653 @ ( tc_fun @ SY3601 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2365,plain,
! [SV654: $i,SV247: $i] :
( ( ( SV247 = SV654 )
| ! [SY3602: $i,SY3603: $i] :
( ~ ( c_Natural_Oevalc @ SY3602 @ SY3603 @ SV247 )
| ~ ( c_Natural_Oevalc @ SY3602 @ SY3603 @ SV654 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2366,plain,
! [SV655: $i,SV248: $i] :
( ( ( SV248 = SV655 )
| ! [SY3604: $i] :
( ~ ( c_lessequals @ SV655 @ SV248 @ ( tc_fun @ SY3604 @ tc_bool ) )
| ~ ( c_lessequals @ SV248 @ SV655 @ ( tc_fun @ SY3604 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1925]) ).
thf(2367,plain,
! [SV249: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV249 ) )
= $true )
| ( ( ! [SY2527: $i,SY2528: $i] :
( ( SY2527 = SY2528 )
| ~ ( c_lessequals @ SY2528 @ SY2527 @ SV249 )
| ~ ( c_lessequals @ SY2527 @ SY2528 @ SV249 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1926]) ).
thf(2368,plain,
! [SV250: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV250 ) )
= $true )
| ( ( ! [SY2529: $i,SY2530: $i] :
( ( SY2529 = SY2530 )
| ~ ( c_lessequals @ SY2530 @ SY2529 @ SV250 )
| ~ ( c_lessequals @ SY2529 @ SY2530 @ SV250 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1927]) ).
thf(2369,plain,
! [SV251: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV251 ) )
= $true )
| ( ( ! [SY2531: $i,SY2532: $i] :
( ( SY2531 = SY2532 )
| ~ ( c_lessequals @ SY2531 @ SY2532 @ SV251 )
| ~ ( c_lessequals @ SY2532 @ SY2531 @ SV251 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1928]) ).
thf(2370,plain,
! [SV252: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV252 ) )
= $true )
| ( ( ! [SY2533: $i,SY2534: $i] :
( ( c_lessequals @ SY2533 @ SY2534 @ SV252 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SY2533 @ SY2534 @ SV252 ) @ ( c_HOL_Ozero__class_Ozero @ SV252 ) @ SV252 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1929]) ).
thf(2371,plain,
! [SV253: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV253 ) )
= $true )
| ( ( ! [SY2535: $i,SY2536: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SY2535 @ SY2536 @ SV253 ) @ ( c_HOL_Ozero__class_Ozero @ SV253 ) @ SV253 )
| ~ ( c_lessequals @ SY2535 @ SY2536 @ SV253 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1930]) ).
thf(2372,plain,
! [SV656: $i,SV254: $i] :
( ( ! [SY3605: $i] :
( ( c_Com_Ocom_OLocal @ SV254 @ SV656 @ SY3605 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2373,plain,
! [SV255: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV255 ) )
= $true )
| ( ( ! [SY2539: $i,SY2540: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2539 @ SY2540 @ SV255 )
= SY2539 )
| ~ ( c_lessequals @ SY2540 @ SY2539 @ SV255 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1932]) ).
thf(2374,plain,
! [SV256: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV256 ) )
= $true )
| ( ( ! [SY2541: $i,SY2542: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2541 @ SY2542 @ SV256 )
!= SY2542 )
| ( c_lessequals @ SY2541 @ SY2542 @ SV256 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1933]) ).
thf(2375,plain,
! [SV257: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV257 ) )
= $true )
| ( ( ! [SY2543: $i,SY2544: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2543 @ SY2544 @ SV257 )
= SY2544 )
| ~ ( c_lessequals @ SY2543 @ SY2544 @ SV257 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1934]) ).
thf(2376,plain,
! [SV657: $i,SV258: $i] :
( ( ! [SY3606: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV258 @ SV657 @ ( tc_fun @ SY3606 @ tc_bool ) )
= SV657 )
| ~ ( c_lessequals @ SV258 @ SV657 @ ( tc_fun @ SY3606 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2377,plain,
! [SV658: $i,SV259: $i] :
( ( ! [SY3607: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV259 @ SV658 @ ( tc_fun @ SY3607 @ tc_bool ) )
= SV259 )
| ~ ( c_lessequals @ SV658 @ SV259 @ ( tc_fun @ SY3607 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2378,plain,
! [SV659: $i,SV260: $i] :
( ( ! [SY3608: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV260 @ SV659 @ ( tc_fun @ SY3608 @ tc_bool ) )
!= SV659 )
| ( c_lessequals @ SV260 @ SV659 @ ( tc_fun @ SY3608 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2379,plain,
! [SV660: $i,SV261: $i] :
( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV261 @ SV660 @ SV261 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2380,plain,
! [SV262: $i] :
( ( ( c_Suc @ SV262 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1939]) ).
thf(2381,plain,
! [SV263: $i] :
( ( ( c_Suc @ SV263 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1940]) ).
thf(2382,plain,
! [SV661: $i,SV264: $i] :
( ( ! [SY3609: $i,SY3610: $i,SY3611: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV264 @ SV661 ) @ SY3609 ) )
| ! [SY3612: $i] :
( ~ ( c_Natural_Oevaln @ SY3610 @ SY3611 @ SY3612 @ SY3609 )
| ! [SY3613: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3613 @ SV661 ) @ SY3611 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ SY3612 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY3613 ) @ SY3610 ) @ SV264 ) @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(2383,plain,
! [SV662: $i,SV265: $i] :
( ( ! [SY3614: $i] :
( ( c_Natural_Oevalc @ SV265 @ SV662 @ SY3614 )
| ! [SY3615: $i] :
( ( hBOOL @ ( hAPP @ SY3615 @ SV662 ) )
| ! [SY3616: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY3615 @ SY3616 @ SV265 ) @ SV662 @ SY3614 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2384,plain,
! [SV663: $i,SV266: $i] :
( ( ! [SY3617: $i,SY3618: $i,SY3619: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV266 @ SV663 @ SY3617 ) @ SY3618 @ SY3619 )
| ~ ( c_Natural_Oevalc @ SY3617 @ SY3618 @ SY3619 )
| ( hBOOL @ ( hAPP @ SV266 @ SY3618 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2385,plain,
! [SV664: $i,SV267: $i] :
( ( ! [SY3620: $i,SY3621: $i,SY3622: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ SV267 @ SV664 @ SY3620 ) @ SY3621 @ SY3620 @ ( tc_fun @ SY3622 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SY3621 @ SV267 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV664 @ SY3621 @ SY3620 @ ( tc_fun @ SY3622 @ tc_bool ) ) @ ( tc_fun @ SY3622 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2386,plain,
! [SV268: $i] :
( ( ( c_Com_OWT @ SV268 )
= $true )
| ( ( ! [SY2570: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SY2570 @ SV268 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1945]) ).
thf(2387,plain,
! [SV269: $i] :
( ( ( c_Com_OWT @ SV269 )
= $true )
| ( ( ! [SY2571: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV269 @ SY2571 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1946]) ).
thf(2388,plain,
! [SV270: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV270 ) )
= $true )
| ( ( ! [SY2572: $i,SY2573: $i] :
( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ SY2572 @ SV270 ) @ SY2573 @ SV270 )
| ~ ( hBOOL @ ( c_in @ SY2573 @ SY2572 @ SV270 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1947]) ).
thf(2389,plain,
! [SV271: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV271 ) )
= $true )
| ( ( ! [SY2574: $i,SY2575: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV271 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2574 @ SY2575 @ SV271 ) )
| ( c_lessequals @ SY2574 @ SY2575 @ SV271 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1948]) ).
thf(2390,plain,
! [SV272: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV272 ) )
= $true )
| ( ( ! [SY2576: $i,SY2577: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV272 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2576 @ SY2577 @ SV272 ) )
| ~ ( c_lessequals @ SY2576 @ SY2577 @ SV272 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1949]) ).
thf(2391,plain,
! [SV665: $i,SV273: $i] :
( ( ! [SY3623: $i,SY3624: $i,SY3625: $i,SY3626: $i,SY3627: $i,SY3628: $i,SY3629: $i,SY3630: $i,SY3631: $i,SY3632: $i] :
( ( c_Com_Ocom_Ocom__case @ SV273 @ SV665 @ SY3623 @ SY3624 @ SY3625 @ SY3626 @ SY3627 @ SY3628 @ ( c_Com_Ocom_OLocal @ SY3629 @ SY3630 @ SY3631 ) @ SY3632 )
= ( hAPP @ ( hAPP @ ( hAPP @ SY3623 @ SY3629 ) @ SY3630 ) @ SY3631 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2392,plain,
! [SV666: $i,SV274: $i] :
( ( ! [SY3633: $i,SY3634: $i,SY3635: $i,SY3636: $i,SY3637: $i,SY3638: $i,SY3639: $i,SY3640: $i,SY3641: $i] :
( ( c_Com_Ocom_Ocom__case @ SV274 @ SV666 @ SY3633 @ SY3634 @ SY3635 @ SY3636 @ SY3637 @ SY3638 @ ( c_Com_Ocom_OWhile @ SY3639 @ SY3640 ) @ SY3641 )
= ( hAPP @ ( hAPP @ SY3636 @ SY3639 ) @ SY3640 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2393,plain,
! [SV667: $i,SV275: $i] :
( ( ! [SY3642: $i,SY3643: $i,SY3644: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV275 @ SV667 @ ( tc_fun @ SY3642 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3643 @ SY3644 @ ( tc_fun @ SY3642 @ tc_bool ) ) @ ( tc_fun @ SY3642 @ tc_bool ) )
| ~ ( c_lessequals @ SV667 @ SY3644 @ ( tc_fun @ SY3642 @ tc_bool ) )
| ~ ( c_lessequals @ SV275 @ SY3643 @ ( tc_fun @ SY3642 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2394,plain,
! [SV668: $i,SV276: $i] :
( ( ! [SY3645: $i,SY3646: $i,SY3647: $i,SY3648: $i,SY3649: $i] :
( ( c_Fun_Ocomp @ SV276 @ ( c_Fun_Ocomp @ SV668 @ SY3645 @ SY3646 @ SY3647 @ SY3648 ) @ SY3647 @ SY3649 @ SY3648 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV276 @ SV668 @ SY3647 @ SY3649 @ SY3646 ) @ SY3645 @ SY3646 @ SY3649 @ SY3648 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(2395,plain,
! [SV669: $i,SV277: $i] :
( ( ( c_Com_Ocom_OSemi @ SV277 @ SV669 )
!= c_Com_Ocom_OSKIP )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2396,plain,
! [SV670: $i,SV278: $i] :
( ( ! [SY3650: $i,SY3651: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV278 @ SV670 @ SY3650 @ SY3651 @ t_a ) @ v_x )
= ( hAPP @ SV278 @ ( hAPP @ SV670 @ v_x ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2397,plain,
! [SV671: $i,SV279: $i] :
( ( ! [SY3652: $i,SY3653: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV279 @ SV671 @ SY3652 ) @ SY3653 @ ( tc_fun @ SY3652 @ tc_bool ) )
| ~ ( c_lessequals @ SV671 @ SY3653 @ ( tc_fun @ SY3652 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV279 @ SY3653 @ SY3652 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2398,plain,
! [SV672: $i,SV280: $i] :
( ( ! [SY3654: $i,SY3655: $i,SY3656: $i,SY3657: $i] :
( ( c_Set_Oimage @ SV280 @ ( c_Set_Oimage @ SV672 @ SY3654 @ SY3655 @ SY3656 ) @ SY3656 @ SY3657 )
= ( c_Set_Oimage @ ( c_COMBB @ SV280 @ SV672 @ SY3656 @ SY3657 @ SY3655 ) @ SY3654 @ SY3655 @ SY3657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2399,plain,
! [SV673: $i,SV281: $i] :
( ( ! [SY3658: $i,SY3659: $i,SY3660: $i,SY3661: $i] :
( ( ( c_Com_Ocom_OLocal @ SV281 @ SV673 @ SY3658 )
!= ( c_Com_Ocom_OLocal @ SY3659 @ SY3660 @ SY3661 ) )
| ( SY3658 = SY3661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2400,plain,
! [SV674: $i,SV282: $i] :
( ( ! [SY3662: $i,SY3663: $i,SY3664: $i] :
( ! [SY3665: $i] :
( ( c_Com_Ocom_OLocal @ SV282 @ SV674 @ SY3662 )
!= ( c_Com_Ocom_OLocal @ SY3663 @ SY3664 @ SY3665 ) )
| ( SV674 = SY3664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2401,plain,
! [SV675: $i,SV283: $i] :
( ( ! [SY3666: $i,SY3667: $i] :
( ! [SY3668: $i,SY3669: $i] :
( ( c_Com_Ocom_OLocal @ SV283 @ SV675 @ SY3666 )
!= ( c_Com_Ocom_OLocal @ SY3667 @ SY3668 @ SY3669 ) )
| ( SV283 = SY3667 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2402,plain,
! [SV676: $i,SV284: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV284 @ SV676 ) )
| ~ ( c_Com_OWT @ SV676 )
| ~ ( c_Com_OWT @ SV284 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(2403,plain,
! [SV677: $i,SV285: $i] :
( ( ! [SY3670: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCall @ SV285 @ SV677 @ SY3670 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2404,plain,
! [SV678: $i,SV286: $i] :
( ( ! [SY3671: $i,SY3672: $i,SY3673: $i,SY3674: $i] :
( ( c_Set_Oimage @ ( c_Fun_Ocomp @ SV286 @ SV678 @ SY3671 @ SY3672 @ SY3673 ) @ SY3674 @ SY3673 @ SY3672 )
= ( c_Set_Oimage @ SV286 @ ( c_Set_Oimage @ SV678 @ SY3674 @ SY3673 @ SY3671 ) @ SY3671 @ SY3672 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2405,plain,
! [SV679: $i,SV287: $i] :
( ( ! [SY3675: $i,SY3676: $i] :
( ( c_Com_Ocom_OWhile @ SV287 @ SV679 )
!= ( c_Com_Ocom_OSemi @ SY3675 @ SY3676 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2406,plain,
! [SV680: $i,SV288: $i] :
( ( ! [SY3677: $i,SY3678: $i] :
( ( hBOOL @ ( c_in @ SV288 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV680 @ SY3677 @ ( tc_fun @ SY3678 @ tc_bool ) ) @ SY3678 ) )
| ~ ( hBOOL @ ( c_in @ SV288 @ SY3677 @ SY3678 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2407,plain,
! [SV681: $i,SV289: $i] :
( ( ! [SY3679: $i,SY3680: $i] :
( ( hBOOL @ ( c_in @ SV289 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV681 @ SY3679 @ ( tc_fun @ SY3680 @ tc_bool ) ) @ SY3680 ) )
| ~ ( hBOOL @ ( c_in @ SV289 @ SV681 @ SY3680 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(2408,plain,
! [SV682: $i,SV290: $i] :
( ( ! [SY3681: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV290 @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV682 @ tc_bool ) ) @ ( tc_fun @ SV682 @ tc_bool ) @ SY3681 ) @ SY3681 @ ( tc_fun @ SV682 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV682 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2409,plain,
! [SV683: $i,SV291: $i] :
( ( ( hBOOL @ ( hAPP @ SV291 @ SV683 ) )
| ! [SY3682: $i] :
( ( SY3682 = SV683 )
| ! [SY3683: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV291 @ SY3683 ) @ SV683 @ SY3682 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2410,plain,
! [SV292: $i] :
( ( ( c_Suc @ SV292 )
= SV292 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1969]) ).
thf(2411,plain,
! [SV293: $i] :
( ( SV293
= ( c_Suc @ SV293 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1970]) ).
thf(2412,plain,
! [SV684: $i,SV294: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV294 )
| ! [SY3684: $i] :
( ( c_lessequals @ SV684 @ SY3684 @ SV294 )
| ! [SY3685: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3685 @ SV684 @ SV294 ) @ SY3684 @ SV294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2413,plain,
! [SV685: $i,SV295: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV295 )
| ! [SY3686: $i] :
( ( c_lessequals @ SV685 @ SY3686 @ SV295 )
| ! [SY3687: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV685 @ SY3687 @ SV295 ) @ SY3686 @ SV295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2414,plain,
! [SV686: $i,SV296: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV296 )
| ! [SY3688: $i,SY3689: $i] :
( ( c_lessequals @ SV686 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3688 @ SY3689 @ SV296 ) @ SV296 )
| ~ ( c_lessequals @ SV686 @ SY3689 @ SV296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2415,plain,
! [SV687: $i,SV297: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV297 )
| ! [SY3690: $i] :
( ! [SY3691: $i] : ( c_lessequals @ SV687 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3690 @ SY3691 @ SV297 ) @ SV297 )
| ~ ( c_lessequals @ SV687 @ SY3690 @ SV297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2416,plain,
! [SV688: $i,SV298: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV298 )
| ! [SY3692: $i] :
( ( c_lessequals @ SV688 @ SY3692 @ SV298 )
| ! [SY3693: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3693 @ SV688 @ SV298 ) @ SY3692 @ SV298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2417,plain,
! [SV689: $i,SV299: $i] :
( ( ~ ( class_Lattices_Oupper__semilattice @ SV299 )
| ! [SY3694: $i] :
( ( c_lessequals @ SV689 @ SY3694 @ SV299 )
| ! [SY3695: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV689 @ SY3695 @ SV299 ) @ SY3694 @ SV299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2418,plain,
! [SV690: $i,SV300: $i] :
( ( ! [SY3696: $i] :
( ( c_lessequals @ SV300 @ SV690 @ ( tc_fun @ SY3696 @ tc_bool ) )
| ! [SY3697: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV300 @ SY3697 @ ( tc_fun @ SY3696 @ tc_bool ) ) @ SV690 @ ( tc_fun @ SY3696 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2419,plain,
! [SV691: $i,SV301: $i] :
( ( ! [SY3698: $i] :
( ( c_lessequals @ SV301 @ SV691 @ ( tc_fun @ SY3698 @ tc_bool ) )
| ! [SY3699: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3699 @ SV301 @ ( tc_fun @ SY3698 @ tc_bool ) ) @ SV691 @ ( tc_fun @ SY3698 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2420,plain,
! [SV692: $i,SV302: $i] :
( ( ~ ( class_Orderings_Oorder @ SV302 )
| ! [SY3700: $i] :
( ( c_lessequals @ SV692 @ SY3700 @ SV302 )
| ! [SY3701: $i] :
( ~ ( c_lessequals @ SV692 @ SY3701 @ SV302 )
| ~ ( c_lessequals @ SY3701 @ SY3700 @ SV302 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2421,plain,
! [SV693: $i,SV303: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV303 )
| ! [SY3702: $i] :
( ( c_lessequals @ SV693 @ SY3702 @ SV303 )
| ! [SY3703: $i] :
( ~ ( c_lessequals @ SY3703 @ SY3702 @ SV303 )
| ~ ( c_lessequals @ SV693 @ SY3703 @ SV303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2422,plain,
! [SV694: $i,SV304: $i] :
( ( ! [SY3704: $i] :
( ( hBOOL @ ( c_in @ SV304 @ SV694 @ SY3704 ) )
| ! [SY3705: $i] :
( ~ ( hBOOL @ ( c_in @ SV304 @ SY3705 @ SY3704 ) )
| ~ ( c_lessequals @ SY3705 @ SV694 @ ( tc_fun @ SY3704 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2423,plain,
! [SV695: $i,SV305: $i] :
( ( ! [SY3706: $i] :
( ( hBOOL @ ( c_in @ SV305 @ SV695 @ SY3706 ) )
| ! [SY3707: $i] :
( ~ ( hBOOL @ ( c_in @ SV305 @ SY3707 @ SY3706 ) )
| ~ ( c_lessequals @ SY3707 @ SV695 @ ( tc_fun @ SY3706 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2424,plain,
! [SV696: $i,SV306: $i] :
( ( c_lessequals @ SV306 @ SV306 @ ( tc_fun @ SV696 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2425,plain,
! [SV697: $i,SV307: $i] :
( ( ! [SY3708: $i] :
( ( hBOOL @ ( c_in @ SV307 @ SV697 @ SY3708 ) )
| ! [SY3709: $i] :
( ~ ( c_lessequals @ SY3709 @ SV697 @ ( tc_fun @ SY3708 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV307 @ SY3709 @ SY3708 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1984]) ).
thf(2426,plain,
! [SV698: $i,SV308: $i] :
( ( ! [SY3710: $i] :
( ( hBOOL @ ( c_in @ SV308 @ SV698 @ SY3710 ) )
| ! [SY3711: $i] :
( ~ ( hBOOL @ ( c_in @ SV308 @ SY3711 @ SY3710 ) )
| ~ ( c_lessequals @ SY3711 @ SV698 @ ( tc_fun @ SY3710 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(2427,plain,
! [SV699: $i,SV309: $i] :
( ( c_lessequals @ SV309 @ SV309 @ ( tc_fun @ SV699 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2428,plain,
! [SV700: $i,SV310: $i] :
( ( ! [SY3712: $i] :
( ( c_lessequals @ SV310 @ SV700 @ ( tc_fun @ SY3712 @ tc_bool ) )
| ! [SY3713: $i] :
( ~ ( c_lessequals @ SY3713 @ SV700 @ ( tc_fun @ SY3712 @ tc_bool ) )
| ~ ( c_lessequals @ SV310 @ SY3713 @ ( tc_fun @ SY3712 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2429,plain,
! [SV701: $i,SV311: $i] :
( ( ( hBOOL @ ( hAPP @ SV311 @ SV701 ) )
| ! [SY3714: $i] :
( ~ ( hBOOL @ ( hAPP @ SY3714 @ SV701 ) )
| ! [SY2707: $i] :
~ ( c_lessequals @ SY3714 @ SV311 @ ( tc_fun @ SY2707 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1988]) ).
thf(2430,plain,
! [SV312: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV312 ) )
= $true )
| ( ( ! [SY2708: $i] : ( c_lessequals @ SY2708 @ SY2708 @ SV312 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1989]) ).
thf(2431,plain,
! [SV313: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV313 ) )
= $true )
| ( ( ! [SY2709: $i] : ( c_lessequals @ SY2709 @ SY2709 @ SV313 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1990]) ).
thf(2432,plain,
! [SV702: $i,SV314: $i] :
( ( ( hBOOL @ ( hAPP @ SV314 @ SV702 ) )
| ! [SY3716: $i] :
( ! [SY2712: $i] :
~ ( c_lessequals @ SY3716 @ SV314 @ ( tc_fun @ SY2712 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SY3716 @ SV702 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2433,plain,
! [SV703: $i,SV315: $i] :
( ( ! [SY3718: $i] :
( ( c_Com_Ocom_OCall @ SV315 @ SV703 @ SY3718 )
!= c_Com_Ocom_OSKIP ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2434,plain,
! [SV316: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV316 ) )
= $true )
| ( ( ! [SY2715: $i,SY2716: $i] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2715 @ SY2716 @ SV316 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV316 @ tc_bool ) ) )
| ( c_lessequals @ SY2715 @ SY2716 @ SV316 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1993]) ).
thf(2435,plain,
! [SV317: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV317 ) )
= $true )
| ( ( ! [SY2717: $i,SY2718: $i] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2717 @ SY2718 @ SV317 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV317 @ tc_bool ) ) )
| ~ ( c_lessequals @ SY2717 @ SY2718 @ SV317 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1994]) ).
thf(2436,plain,
! [SV704: $i,SV318: $i] :
( ( ! [SY3719: $i,SY3720: $i,SY3721: $i,SY3722: $i,SY3723: $i,SY3724: $i,SY3725: $i,SY3726: $i,SY3727: $i,SY3728: $i] :
( ( c_Com_Ocom_Ocom__case @ SV318 @ SV704 @ SY3719 @ SY3720 @ SY3721 @ SY3722 @ SY3723 @ SY3724 @ ( c_Com_Ocom_OCond @ SY3725 @ SY3726 @ SY3727 ) @ SY3728 )
= ( hAPP @ ( hAPP @ ( hAPP @ SY3721 @ SY3725 ) @ SY3726 ) @ SY3727 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2437,plain,
! [SV705: $i,SV319: $i] :
( ( ! [SY3729: $i,SY3730: $i,SY3731: $i,SY3732: $i,SY3733: $i] :
( ! [SY3734: $i] :
( ( c_Fun_Ocomp @ SV319 @ SV705 @ SY3729 @ SY3730 @ SY3731 )
!= ( c_Fun_Ocomp @ SY3732 @ SY3733 @ SY3734 @ SY3730 @ SY3731 ) )
| ! [SY3735: $i] :
( ( hAPP @ SV319 @ ( hAPP @ SV705 @ SY3735 ) )
= ( hAPP @ SY3732 @ ( hAPP @ SY3733 @ SY3735 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2438,plain,
! [SV706: $i,SV320: $i] :
( ( ! [SY3736: $i,SY3737: $i,SY3738: $i,SY3739: $i,SY3740: $i,SY3741: $i,SY3742: $i] :
( ( ( hAPP @ SV320 @ ( hAPP @ SV706 @ SY3736 ) )
!= ( hAPP @ SY3737 @ ( hAPP @ SY3738 @ SY3739 ) ) )
| ! [SY3743: $i,SY3744: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV320 @ SV706 @ SY3740 @ SY3741 @ SY3742 ) @ SY3736 )
= ( hAPP @ ( c_Fun_Ocomp @ SY3737 @ SY3738 @ SY3743 @ SY3741 @ SY3744 ) @ SY3739 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2439,plain,
! [SV707: $i,SV321: $i] :
( ( ! [SY3745: $i] :
( ( hBOOL @ ( hAPP @ SV321 @ SV707 ) )
| ( SY3745 = SV707 )
| ! [SY3746: $i,SY3747: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV321 @ SY3746 ) @ SV707 @ SY3747 @ SY3745 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2440,plain,
! [SV708: $i,SV322: $i] :
( ( ! [SY3748: $i,SY3749: $i,SY3750: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV322 @ SV708 @ ( tc_fun @ SY3748 @ tc_bool ) ) @ SY3749 @ SY3748 @ ( tc_fun @ SY3750 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV322 @ SY3749 @ SY3748 @ ( tc_fun @ SY3750 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV708 @ SY3749 @ SY3748 @ ( tc_fun @ SY3750 @ tc_bool ) ) @ ( tc_fun @ SY3750 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2441,plain,
! [SV709: $i,SV323: $i] :
( ( ( c_The @ ( hAPP @ ( c_fequal @ SV323 ) @ SV709 ) @ SV323 )
= SV709 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2442,plain,
! [SV710: $i,SV324: $i] :
( ( ! [SY3751: $i,SY3752: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV324 @ ( c_HOL_Ominus__class_Ominus @ SV710 @ SY3751 @ ( tc_fun @ SY3752 @ tc_bool ) ) @ ( tc_fun @ SY3752 @ tc_bool ) )
= SY3751 )
| ~ ( c_lessequals @ SV324 @ SV710 @ ( tc_fun @ SY3752 @ tc_bool ) )
| ~ ( c_lessequals @ SY3751 @ SV324 @ ( tc_fun @ SY3752 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(2443,plain,
! [SV711: $i,SV325: $i] :
( ( ! [SY3753: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
| ! [SY3754: $i,SY3755: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV711 @ SY3753 @ SV325 )
!= ( c_HOL_Ominus__class_Ominus @ SY3754 @ SY3755 @ SV325 ) )
| ( c_lessequals @ SY3755 @ SY3754 @ SV325 )
| ~ ( c_lessequals @ SY3753 @ SV711 @ SV325 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2444,plain,
! [SV712: $i,SV326: $i] :
( ( ! [SY3756: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV326 )
| ! [SY3757: $i,SY3758: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV712 @ SY3756 @ SV326 )
!= ( c_HOL_Ominus__class_Ominus @ SY3757 @ SY3758 @ SV326 ) )
| ( c_lessequals @ SY3756 @ SV712 @ SV326 )
| ~ ( c_lessequals @ SY3758 @ SY3757 @ SV326 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2445,plain,
! [SV713: $i,SV327: $i] :
( ( ! [SY3759: $i,SY3760: $i,SY3761: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV327 @ SV713 @ SY3759 @ SY3760 ) @ ( c_Set_Oimage @ SV327 @ SY3761 @ SY3759 @ SY3760 ) @ ( tc_fun @ SY3760 @ tc_bool ) )
| ~ ( c_lessequals @ SV713 @ SY3761 @ ( tc_fun @ SY3759 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2446,plain,
! [SV714: $i,SV328: $i] :
( ( ! [SY3762: $i] :
( ~ ( c_lessequals @ SV328 @ SV714 @ ( tc_fun @ SY3762 @ tc_bool ) )
| ! [SY3763: $i,SY3764: $i] : ( c_lessequals @ ( c_Set_Oimage @ SY3763 @ SV328 @ SY3762 @ SY3764 ) @ ( c_Set_Oimage @ SY3763 @ SV714 @ SY3762 @ SY3764 ) @ ( tc_fun @ SY3764 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2447,plain,
! [SV715: $i,SV329: $i] :
( ( ! [SY3765: $i,SY3766: $i] :
( ( c_Natural_Oevaln @ SV329 @ SV715 @ SY3765 @ SY3766 )
| ! [SY3767: $i] :
( ( c_Natural_Oevaln @ SY3767 @ SV715 @ SY3765 @ SY3766 )
| ! [SY3768: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SY3768 @ SY3767 @ SV329 ) @ SV715 @ SY3765 @ SY3766 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2448,plain,
! [SV716: $i,SV330: $i] :
( ( ! [SY3769: $i,SY3770: $i,SY3771: $i] :
( ( c_Set_Oimage @ SV330 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV716 @ SY3769 @ ( tc_fun @ SY3770 @ tc_bool ) ) @ SY3770 @ SY3771 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ SV330 @ SV716 @ SY3770 @ SY3771 ) @ ( c_Set_Oimage @ SV330 @ SY3769 @ SY3770 @ SY3771 ) @ ( tc_fun @ SY3771 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2449,plain,
! [SV717: $i,SV331: $i] :
( ( ! [SY3772: $i,SY3773: $i,SY3774: $i,SY3775: $i] :
( ( c_Com_Ocom_OLocal @ SV331 @ SV717 @ SY3772 )
!= ( c_Com_Ocom_OCall @ SY3773 @ SY3774 @ SY3775 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2450,plain,
! [SV718: $i,SV332: $i] :
( ( ! [SY3776: $i] :
( ( c_Natural_Oevalc @ SV332 @ SV718 @ SY3776 )
| ! [SY3777: $i] :
( ( c_Natural_Oevalc @ SY3777 @ SV718 @ SY3776 )
| ! [SY3778: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY3778 @ SY3777 @ SV332 ) @ SV718 @ SY3776 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2009]) ).
thf(2451,plain,
! [SV333: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV333 ) )
= $true )
| ( ( ! [SY2794: $i,SY2795: $i] :
( ( c_lessequals @ SY2794 @ ( c_Complete__Lattice_OSup__class_OSup @ SY2795 @ SV333 ) @ SV333 )
| ~ ( hBOOL @ ( c_in @ SY2794 @ SY2795 @ SV333 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2010]) ).
thf(2452,plain,
! [SV334: $i] :
( ( ( c_Com_OWT @ SV334 )
= $true )
| ( ( ! [SY2796: $i,SY2797: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SY2796 @ SY2797 @ SV334 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2011]) ).
thf(2453,plain,
! [SV335: $i] :
( ( ( c_Com_OWT @ SV335 )
= $true )
| ( ( ! [SY2798: $i,SY2799: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SY2798 @ SV335 @ SY2799 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2012]) ).
thf(2454,plain,
! [SV719: $i,SV336: $i] :
( ( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ SV336 @ SV719 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2455,plain,
! [SV337: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV337 ) )
= $true )
| ( ( ! [SY2801: $i,SY2802: $i] :
( ( c_lessequals @ SY2801 @ SY2802 @ SV337 )
| ( c_lessequals @ SY2802 @ SY2801 @ SV337 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2014]) ).
thf(2456,plain,
! [SV720: $i,SV338: $i] :
( ( ! [SY3779: $i,SY3780: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ SV338 )
!= ( c_Com_Ocom_OLocal @ SV720 @ SY3779 @ SY3780 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2015]) ).
thf(2457,plain,
! [SV721: $i,SV339: $i] :
( ( ! [SY3781: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ SV339 )
!= ( c_Com_Ocom_OWhile @ SV721 @ SY3781 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(2458,plain,
! [SV722: $i,SV340: $i] :
( ( ! [SY3782: $i,SY3783: $i] :
( ( c_Com_Ocom_OCall @ SV340 @ SV722 @ SY3782 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SY3783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2017]) ).
thf(2459,plain,
! [SV723: $i,SV341: $i] :
( ( ! [SY3784: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ SV341 )
!= ( c_Com_Ocom_OSemi @ SV723 @ SY3784 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2018]) ).
thf(2460,plain,
! [SV724: $i,SV342: $i] :
( ( ! [SY3785: $i] :
( ( c_Com_Ocom_OSemi @ SV342 @ SV724 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SY3785 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2461,plain,
! [SV725: $i,SV343: $i] :
( ( ! [SY3786: $i,SY3787: $i] :
( ( c_Com_Ocom_OLocal @ SV343 @ SV725 @ SY3786 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SY3787 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2462,plain,
! [SV726: $i,SV344: $i] :
( ( ! [SY3788: $i,SY3789: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ SV344 )
!= ( c_Com_Ocom_OCall @ SV726 @ SY3788 @ SY3789 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2463,plain,
! [SV727: $i,SV345: $i] :
( ( ! [SY3790: $i,SY3791: $i,SY3792: $i,SY3793: $i,SY3794: $i,SY3795: $i,SY3796: $i,SY3797: $i] :
( ( c_Com_Ocom_Ocom__case @ SV345 @ SV727 @ SY3790 @ SY3791 @ SY3792 @ SY3793 @ SY3794 @ SY3795 @ ( hAPP @ c_Com_Ocom_OBODY @ SY3796 ) @ SY3797 )
= ( hAPP @ SY3794 @ SY3796 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2464,plain,
! [SV346: $i] :
( ( c_Com_Ocom_OSKIP
= ( hAPP @ c_Com_Ocom_OBODY @ SV346 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2023]) ).
thf(2465,plain,
! [SV728: $i,SV347: $i] :
( ( ! [SY3798: $i,SY3799: $i] : ( c_Hoare__Mirabelle_Otriple__valid @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV347 ) @ SV728 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SY3798 ) ) @ SY3799 ) @ SV347 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2466,plain,
! [SV729: $i,SV348: $i] :
( ( ! [SY3800: $i,SY3801: $i,SY3802: $i] :
( ~ ( hBOOL @ ( hAPP @ SV348 @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SV729 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ SY3800 ) @ SY3801 ) @ SY3802 ) @ t_b @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV348 @ ( hAPP @ ( hAPP @ ( hAPP @ SV729 @ SY3800 ) @ SY3801 ) @ SY3802 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2467,plain,
! [SV730: $i,SV349: $i] :
( ( ! [SY3803: $i,SY3804: $i,SY3805: $i] :
( ~ ( hBOOL @ ( hAPP @ SV349 @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SV730 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ SY3803 ) @ SY3804 ) @ SY3805 ) @ t_b @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV349 @ ( hAPP @ ( hAPP @ ( hAPP @ SV730 @ SY3803 ) @ SY3804 ) @ SY3805 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2468,plain,
! [SV731: $i,SV350: $i] :
( ( ! [SY3806: $i,SY3807: $i,SY3808: $i,SY3809: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ SV350 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV731 ) @ SY3806 ) @ SY3807 ) @ SY3808 ) @ SV731 @ SY3809 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV350 @ SY3806 ) @ SY3807 ) @ SY3808 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2469,plain,
! [SV732: $i,SV351: $i] :
( ( ! [SY3810: $i,SY3811: $i,SY3812: $i,SY3813: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SV351 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV732 ) @ SY3810 ) @ SY3811 ) @ SY3812 ) @ SV732 @ SY3813 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV351 @ SY3810 ) @ SY3811 ) @ SY3812 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2470,plain,
! [SV733: $i,SV352: $i] :
( ( ! [SY3814: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV352 @ SV733 @ SY3814 )
| ! [SY3815: $i] :
( ~ ( c_lessequals @ SV733 @ SY3815 @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3814 ) @ tc_bool ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV352 @ SY3815 @ SY3814 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2471,plain,
! [SV734: $i,SV353: $i] :
( ( ! [SY3816: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ SV734 @ SY3816 )
| ! [SY3817: $i] :
( ~ ( c_lessequals @ SY3817 @ SV353 @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3816 ) @ tc_bool ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY3817 @ SV734 @ SY3816 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2030]) ).
thf(2472,plain,
! [SV735: $i,SV354: $i] :
( ( ! [SY3818: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV354 @ SV735 @ SY3818 )
| ~ ( c_lessequals @ SV735 @ SV354 @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3818 ) @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(2473,plain,
! [SV736: $i,SV355: $i] :
( ( ! [SY3819: $i,SY3820: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV355 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV736 ) @ SY3819 ) @ SY3820 ) @ ( 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 @ SV355 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ ( c_COMBK @ ( hAPP @ ( c_COMBC @ ( c_fequal @ tc_Com_Ostate ) @ tc_Com_Ostate @ tc_Com_Ostate @ tc_bool ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ SV355 @ SV736 @ SY3820 @ SY3819 ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) ) @ SY3819 ) @ ( c_COMBK @ ( hAPP @ SY3820 @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ SV355 @ SV736 @ SY3820 @ SY3819 ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_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)],[2032]) ).
thf(2474,plain,
! [SV737: $i,SV356: $i] :
( ( ! [SY3821: $i,SY3822: $i,SY3823: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV356 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ ( hAPP @ SY3821 @ SY3822 ) ) @ ( hAPP @ c_Com_Ocom_OBODY @ SY3822 ) ) @ ( hAPP @ SY3823 @ SY3822 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV737 )
| ! [SY3824: $i] :
( ~ ( hBOOL @ ( c_in @ SY3822 @ SY3824 @ tc_Com_Opname ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV356 @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ SY3821 @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ SY3823 @ tc_Com_Opname @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SY3824 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ SY3821 @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ SY3823 @ tc_Com_Opname @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SY3824 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV737 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2475,plain,
! [SV357: $i] :
( ( ( ( hAPP @ c_Com_Obody @ SV357 )
= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) )
= $true )
| ( ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ SV357 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2034]) ).
thf(2476,plain,
! [SV738: $i,SV358: $i] :
( ( ( hAPP @ ( c_Option_Othe @ SV358 ) @ ( c_Option_Ooption_OSome @ SV738 @ SV358 ) )
= SV738 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2477,plain,
! [SV739: $i,SV359: $i] :
( ( ! [SY3825: $i,SY3826: $i,SY3827: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV359 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV739 ) @ SY3825 ) @ ( c_Com_Ocom_OWhile @ SY3826 @ SY3827 ) ) @ ( c_Hoare__Mirabelle_Opeek__and @ SY3825 @ ( c_Fun_Ocomp @ c_Not @ SY3826 @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ SV739 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV739 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV739 ) ) @ SV739 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV359 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV739 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SY3825 @ SY3826 @ SV739 ) ) @ SY3827 ) @ SY3825 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV739 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV739 ) ) @ SV739 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(2478,plain,
! [SV740: $i,SV360: $i] :
( ( ! [SY3828: $i,SY3829: $i,SY3830: $i,SY3831: $i,SY3832: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ SY3828 ) @ ( c_Com_Ocom_OCond @ SY3829 @ SY3830 @ SY3831 ) ) @ SY3832 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SY3828 @ ( c_Fun_Ocomp @ c_Not @ SY3829 @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ SV740 ) ) @ SY3831 ) @ SY3832 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SY3828 @ SY3829 @ SV740 ) ) @ SY3830 ) @ SY3832 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2479,plain,
! [SV741: $i,SV361: $i] :
( ( ! [SY3833: $i,SY3834: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV361 ) ) @ SV741 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ SV361 @ SY3833 @ SV741 @ SY3834 ) @ SY3834 )
| ~ ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ SV361 ) @ SV741 @ SY3833 @ SY3834 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2480,plain,
! [SV742: $i,SV362: $i] :
( ( ! [SY3835: $i,SY3836: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ SV362 ) @ SV742 @ ( c_Suc @ SY3835 ) @ SY3836 )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV362 ) ) @ SV742 @ SY3835 @ SY3836 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2481,plain,
! [SV363: $i] :
( ( ( ~ ( class_Orderings_Obot @ SV363 ) )
= $true )
| ( ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ SV363 ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ SV363 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2040]) ).
thf(2482,plain,
! [SV364: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV364 ) )
= $true )
| ( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV364 @ tc_bool ) ) @ SV364 )
= ( c_Orderings_Obot__class_Obot @ SV364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2041]) ).
thf(2483,plain,
! [SV743: $i,SV365: $i] :
( ( ( c_Collect @ ( hAPP @ ( c_fequal @ SV365 ) @ SV743 ) @ SV365 )
= ( c_Set_Oinsert @ SV743 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV365 @ tc_bool ) ) @ SV365 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2484,plain,
! [SV744: $i,SV366: $i] :
( ( ! [SY3837: $i] :
( ( SV366
= ( c_Set_Oinsert @ SV744 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3837 @ tc_bool ) ) @ SY3837 ) )
| ( SV366
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3837 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV366 @ ( c_Set_Oinsert @ SV744 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3837 @ tc_bool ) ) @ SY3837 ) @ ( tc_fun @ SY3837 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2485,plain,
! [SV745: $i,SV367: $i] :
( ( hBOOL @ ( c_in @ SV367 @ ( c_Set_Oinsert @ SV367 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV745 @ tc_bool ) ) @ SV745 ) @ SV745 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2486,plain,
! [SV746: $i,SV368: $i] :
( ( ! [SY3838: $i,SY3839: $i,SY3840: $i,SY3841: $i,SY3842: $i,SY3843: $i] :
( ( ( hAPP @ SV368 @ ( c_Set_Oinsert @ SV746 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3838 @ tc_bool ) ) @ SY3838 ) )
= SV746 )
| ! [SY2895: $i,SY2896: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV368 @ SY3839 @ SY3840 @ SY3841 @ SY3842 @ SY3843 @ SY2895 @ SY2896 @ SY3838 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2487,plain,
! [SV747: $i,SV369: $i] :
( ( ! [SY3846: $i,SY3847: $i,SY3848: $i,SY3849: $i,SY3850: $i,SY3851: $i] :
( ( ( hAPP @ SV369 @ ( c_Set_Oinsert @ SV747 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3846 @ tc_bool ) ) @ SY3846 ) )
= SV747 )
| ! [SY2904: $i,SY2905: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3847 @ SV369 @ SY3848 @ SY3849 @ SY3850 @ SY3851 @ SY2904 @ SY2905 @ SY3846 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2488,plain,
! [SV370: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV370 ) )
= $true )
| ( ( ! [SY2906: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SY2906 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV370 @ tc_bool ) ) @ SV370 ) @ SV370 )
= SY2906 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2047]) ).
thf(2489,plain,
! [SV748: $i,SV371: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV371 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV748 @ tc_bool ) ) @ SV748 ) @ ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ SV371 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV748 @ tc_bool ) ) @ SV748 ) @ SV748 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2490,plain,
! [SV749: $i,SV372: $i] :
( ( ! [SY3854: $i,SY3855: $i] :
( ( c_Set_Oinsert @ SV372 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SY3854 @ SV749 @ ( tc_fun @ SY3855 @ tc_bool ) ) @ SY3855 )
= ( c_Set_Oinsert @ SV372 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3855 @ tc_bool ) ) @ SY3855 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2049]) ).
thf(2491,plain,
! [SV750: $i,SV373: $i] :
( ( ! [SY3856: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV373 @ ( c_Set_Oinsert @ SV750 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3856 @ tc_bool ) ) @ SY3856 ) @ SY3856 ) @ SV750 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2492,plain,
! [SV374: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV374 ) )
= $true )
| ( ( ! [SY2913: $i] :
( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ SY2913 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV374 @ tc_bool ) ) @ SV374 ) @ SV374 )
= SY2913 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2051]) ).
thf(2493,plain,
! [SV751: $i,SV375: $i] :
( ( ( c_The @ ( c_Set_Oinsert @ SV375 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV751 @ tc_bool ) ) @ SV751 ) @ SV751 )
= SV375 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2494,plain,
! [SV752: $i,SV376: $i] :
( ( ! [SY3857: $i,SY3858: $i,SY3859: $i,SY3860: $i,SY3861: $i,SY3862: $i,SY3863: $i] :
( ( ( hAPP @ SV376 @ ( c_Set_Oinsert @ SV752 @ ( c_Set_Oinsert @ SY3857 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3858 @ tc_bool ) ) @ SY3858 ) @ SY3858 ) )
= ( hAPP @ ( hAPP @ SY3859 @ SV752 ) @ SY3857 ) )
| ! [SY2923: $i,SY2924: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV376 @ SY3860 @ SY3861 @ SY3862 @ SY3859 @ SY3863 @ SY2923 @ SY2924 @ SY3858 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2495,plain,
! [SV753: $i,SV377: $i] :
( ( ! [SY3866: $i,SY3867: $i,SY3868: $i,SY3869: $i,SY3870: $i,SY3871: $i,SY3872: $i] :
( ( ( hAPP @ SV377 @ ( c_Set_Oinsert @ SV753 @ ( c_Set_Oinsert @ SY3866 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3867 @ tc_bool ) ) @ SY3867 ) @ SY3867 ) )
= ( hAPP @ ( hAPP @ SY3868 @ SV753 ) @ SY3866 ) )
| ! [SY2933: $i,SY2934: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY3869 @ SV377 @ SY3870 @ SY3871 @ SY3872 @ SY3868 @ SY2933 @ SY2934 @ SY3867 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(2496,plain,
! [SV754: $i,SV378: $i] :
( ( ! [SY3875: $i,SY3876: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV378 @ ( c_Set_Oinsert @ SV754 @ SY3875 @ SY3876 ) @ ( tc_fun @ SY3876 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV378 @ ( c_Set_Oinsert @ SV754 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3876 @ tc_bool ) ) @ SY3876 ) @ ( tc_fun @ SY3876 @ tc_bool ) ) @ SY3875 @ ( tc_fun @ SY3876 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2055]) ).
thf(2497,plain,
! [SV755: $i,SV379: $i] :
( ( ! [SY3877: $i,SY3878: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV379 @ ( c_Set_Oinsert @ SV755 @ SY3877 @ SY3878 ) @ ( tc_fun @ SY3878 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV379 @ SY3877 @ ( tc_fun @ SY3878 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV755 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3878 @ tc_bool ) ) @ SY3878 ) @ ( tc_fun @ SY3878 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2056]) ).
thf(2498,plain,
! [SV756: $i,SV380: $i] :
( ( ( SV380 = SV756 )
| ! [SY3879: $i,SY3880: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SY3879 @ ( c_Set_Oinsert @ SV380 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3880 @ tc_bool ) ) @ SY3880 ) @ SY3880 ) @ SV756 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2057]) ).
thf(2499,plain,
! [SV757: $i,SV381: $i] :
( ( ( c_Set_Ocontents @ ( c_Set_Oinsert @ SV381 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV757 @ tc_bool ) ) @ SV757 ) @ SV757 )
= SV381 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2058]) ).
thf(2500,plain,
! [SV758: $i,SV382: $i] :
( ( ! [SY3881: $i] :
( ( SV382
= ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ SV758 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3881 @ tc_bool ) ) @ SY3881 ) @ SY3881 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV758 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3881 @ tc_bool ) ) @ SY3881 ) @ SV382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2501,plain,
! [SV759: $i,SV383: $i] :
( ( ( SV383 = SV759 )
| ! [SY3882: $i] :
~ ( hBOOL @ ( c_in @ SV383 @ ( c_Set_Oinsert @ SV759 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3882 @ tc_bool ) ) @ SY3882 ) @ SY3882 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2502,plain,
! [SV760: $i,SV384: $i] :
( ( ! [SY3883: $i] :
( ( c_Finite__Set_Ofold1 @ SV384 @ ( c_Set_Oinsert @ SV760 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3883 @ tc_bool ) ) @ SY3883 ) @ SY3883 )
= SV760 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2503,plain,
! [SV385: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV385 ) )
= $true )
| ( ( ! [SY2951: $i] :
( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ SY2951 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV385 @ tc_bool ) ) @ SV385 ) @ SV385 )
= SY2951 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2062]) ).
thf(2504,plain,
! [SV761: $i,SV386: $i] :
( ( ! [SY3884: $i] :
( ( c_Set_Oinsert @ SV386 @ ( c_HOL_Ominus__class_Ominus @ SV761 @ ( c_Set_Oinsert @ SV386 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3884 @ tc_bool ) ) @ SY3884 ) @ ( tc_fun @ SY3884 @ tc_bool ) ) @ SY3884 )
= ( c_Set_Oinsert @ SV386 @ SV761 @ SY3884 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2505,plain,
! [SV387: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV387 ) )
= $true )
| ( ( ! [SY2954: $i] :
( ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2954 @ SY2954 @ SV387 )
= ( c_Set_Oinsert @ SY2954 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV387 @ tc_bool ) ) @ SV387 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2064]) ).
thf(2506,plain,
! [SV762: $i,SV388: $i] :
( ( ! [SY3885: $i] :
( ( ( c_Set_Oinsert @ SV388 @ SV762 @ SY3885 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3885 @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ SV388 @ SV762 @ SY3885 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2507,plain,
! [SV763: $i,SV389: $i] :
( ( ! [SY3886: $i] :
( ( c_Set_Oinsert @ SV389 @ SV763 @ SY3886 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV389 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3886 @ tc_bool ) ) @ SY3886 ) @ SV763 @ ( tc_fun @ SY3886 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2508,plain,
! [SV390: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV390 ) )
= $true )
| ( ( ! [SY2959: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ SY2959 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV390 @ tc_bool ) ) @ SV390 ) @ SV390 )
= SY2959 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2067]) ).
thf(2509,plain,
! [SV764: $i,SV391: $i] :
( ( ! [SY3887: $i,SY3888: $i,SY3889: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV391 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV764 ) @ SY3887 ) @ SY3888 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY3890: $i,SY3891: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SY3889 @ SY3890 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV391 @ SV764 @ SY3888 @ SY3887 @ SY3891 @ SY3889 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3891 @ SY3890 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV391 @ SV764 @ SY3888 @ SY3887 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV391 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY3891 ) @ SY3887 ) @ SY3889 ) @ ( 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)],[2068]) ).
thf(2510,plain,
! [SV765: $i,SV392: $i] :
( ( ! [SY3892: $i,SY3893: $i,SY3894: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV392 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV765 ) @ SY3892 ) @ SY3893 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY3895: $i,SY3896: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SY3894 @ SY3895 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV765 @ SY3896 @ SY3893 @ SY3894 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3896 @ SY3895 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV765 @ SY3896 @ SY3893 @ SY3894 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV392 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY3896 ) @ SY3892 ) @ SY3894 ) @ ( 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)],[2069]) ).
thf(2511,plain,
! [SV766: $i,SV393: $i] :
( ( ! [SY3897: $i,SY3898: $i,SY3899: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV393 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV766 ) @ SY3897 ) @ SY3898 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY3900: $i,SY3901: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SY3899 @ SY3900 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV393 @ SV766 @ SY3898 @ SY3897 @ SY3901 @ SY3899 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3901 @ SY3900 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV393 @ SV766 @ SY3898 @ SY3897 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV393 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY3901 ) @ SY3897 ) @ SY3899 ) @ ( 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)],[2070]) ).
thf(2512,plain,
! [SV767: $i,SV394: $i] :
( ( ! [SY3902: $i,SY3903: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV394 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV767 ) @ SY3902 ) @ SY3903 ) @ ( 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 @ SV767 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV394 @ SV767 @ SY3903 @ SY3902 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV394 @ SV767 @ SY3903 @ SY3902 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2071]) ).
thf(2513,plain,
! [SV768: $i,SV395: $i] :
( ( ! [SY3904: $i,SY3905: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV395 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV768 ) @ SY3904 ) @ SY3905 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY3906: $i,SY3907: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3905 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV395 @ SV768 @ SY3905 @ SY3904 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV395 @ SV768 @ SY3905 @ SY3904 @ SY3906 @ SY3907 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV395 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY3906 ) @ SY3904 ) @ SY3907 ) @ ( 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)],[2072]) ).
thf(2514,plain,
! [SV769: $i,SV396: $i] :
( ( ! [SY3908: $i,SY3909: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV396 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV769 ) @ SY3908 ) @ SY3909 ) @ ( 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 @ SV769 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV396 @ SV769 @ SY3909 @ SY3908 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV396 @ SV769 @ SY3909 @ SY3908 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2515,plain,
! [SV770: $i,SV397: $i] :
( ( ! [SY3910: $i,SY3911: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV397 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV770 ) @ SY3910 ) @ SY3911 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY3912: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SY3912 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SY3911 @ SY3912 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SY3911 @ SY3912 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV397 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV770 ) @ SY3910 ) @ SY3912 ) @ ( 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)],[2074]) ).
thf(2516,plain,
! [SV771: $i,SV398: $i] :
( ( ! [SY3913: $i,SY3914: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV398 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV771 ) @ SY3913 ) @ SY3914 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY3915: $i,SY3916: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV771 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV771 @ SY3915 @ SY3914 @ SY3916 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV771 @ SY3915 @ SY3914 @ SY3916 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV398 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY3915 ) @ SY3913 ) @ SY3916 ) @ ( 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)],[2075]) ).
thf(2517,plain,
! [SV772: $i,SV399: $i] :
( ( ! [SY3917: $i,SY3918: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV399 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV772 ) @ SY3917 ) @ SY3918 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY3919: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV772 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV772 @ SY3919 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV772 @ SY3919 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV399 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY3919 ) @ SY3917 ) @ SY3918 ) @ ( 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)],[2076]) ).
thf(2518,plain,
! [SV773: $i,SV400: $i] :
( ( ! [SY3920: $i,SY3921: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV400 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV773 ) @ SY3920 ) @ SY3921 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY3922: $i,SY3923: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3921 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV400 @ SV773 @ SY3921 @ SY3920 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV400 @ SV773 @ SY3921 @ SY3920 @ SY3922 @ SY3923 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV400 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY3922 ) @ SY3920 ) @ SY3923 ) @ ( 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)],[2077]) ).
thf(2519,plain,
! [SV774: $i,SV401: $i] :
( ( ! [SY3924: $i,SY3925: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV401 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV774 ) @ SY3924 ) @ SY3925 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY3926: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3926 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV774 @ SY3926 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV774 @ SY3926 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV401 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY3926 ) @ SY3924 ) @ SY3925 ) @ ( 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)],[2078]) ).
thf(2520,plain,
! [SV775: $i,SV402: $i] :
( ( ! [SY3927: $i,SY3928: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV402 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV775 ) @ SY3927 ) @ SY3928 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY3929: $i,SY3930: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3928 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV775 @ SY3929 @ SY3928 @ SY3930 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV775 @ SY3929 @ SY3928 @ SY3930 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV402 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY3929 ) @ SY3927 ) @ SY3930 ) @ ( 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)],[2079]) ).
thf(2521,plain,
! [SV776: $i,SV403: $i] :
( ( ! [SY3931: $i,SY3932: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV403 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV776 ) @ SY3931 ) @ SY3932 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY3933: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3932 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SY3932 @ SY3933 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SY3932 @ SY3933 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV403 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV776 ) @ SY3931 ) @ SY3933 ) @ ( 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)],[2080]) ).
thf(2522,plain,
! [SV777: $i,SV404: $i] :
( ( ! [SY3934: $i,SY3935: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV404 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV777 ) @ SY3934 ) @ SY3935 ) @ ( 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 @ SV777 @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ SV404 @ SV777 @ SY3935 @ SY3934 ) ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ SV404 @ SV777 @ SY3935 @ SY3934 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2523,plain,
! [SV778: $i,SV405: $i] :
( ( ! [SY3936: $i,SY3937: $i,SY3938: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV405 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV778 ) @ SY3936 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SY3937 ) ) @ SY3938 ) @ SV778 )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ SV405 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV778 ) @ SY3936 ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY3937 ) ) ) @ SY3938 ) @ SV778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2524,plain,
! [SV779: $i,SV406: $i] :
( ( ! [SY3939: $i,SY3940: $i,SY3941: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ SV406 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV779 ) @ SY3939 ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY3940 ) ) ) @ SY3941 ) @ SV779 )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV406 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV779 ) @ SY3939 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SY3940 ) ) @ SY3941 ) @ SV779 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2525,plain,
! [SV780: $i,SV407: $i] :
( ( ! [SY3942: $i] :
( ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ SV407 ) @ SV780 @ SY3942 )
| ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV407 ) ) @ SV780 @ SY3942 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2526,plain,
! [SV781: $i,SV408: $i] :
( ( ! [SY3943: $i] :
( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV408 ) ) @ SV781 @ SY3943 )
| ~ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ SV408 ) @ SV781 @ SY3943 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(2527,plain,
! [SV782: $i,SV409: $i] :
( ( ! [SY3944: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ SV409 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV782 ) @ SY3944 ) @ c_Com_Ocom_OSKIP ) @ SY3944 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV782 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV782 ) ) @ SV782 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2528,plain,
! [SV783: $i,SV410: $i] :
( ( ! [SY3945: $i,SY3946: $i,SY3947: $i,SY3948: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SY3945 ) @ ( c_Com_Ocom_OSemi @ SY3946 @ SY3947 ) ) @ SY3948 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 )
| ! [SY3949: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SY3949 ) @ SY3947 ) @ SY3948 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SY3945 ) @ SY3946 ) @ SY3949 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2529,plain,
! [SV784: $i,SV411: $i] :
( ( ! [SY3950: $i,SY3951: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV411 @ ( c_Set_Oinsert @ SV784 @ SY3950 @ ( tc_Hoare__Mirabelle_Otriple @ SY3951 ) ) @ SY3951 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV411 @ SY3950 @ SY3951 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV411 @ ( c_Set_Oinsert @ SV784 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY3951 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY3951 ) ) @ SY3951 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2530,plain,
! [SV785: $i,SV412: $i] :
( ( ! [SY3952: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV412 @ SV785 @ SY3952 ) @ SV412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2531,plain,
! [SV786: $i,SV413: $i] :
( ( ! [SY3953: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV413 @ SV786 @ SY3953 )
| ! [SY3954: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV413 @ SY3954 @ SY3953 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY3954 @ SV786 @ SY3953 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(2532,plain,
! [SV787: $i,SV414: $i] :
( ( ! [SY3955: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV414 @ tc_bool ) )
!= ( c_Set_Oinsert @ SV787 @ SY3955 @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2091]) ).
thf(2533,plain,
! [SV788: $i,SV415: $i] :
( ( ! [SY3956: $i,SY3957: $i,SY3958: $i,SY3959: $i,SY3960: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV415 ) @ SV788 ) @ SY3956 ) @ SY3957 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV415 ) @ SY3958 ) @ SY3959 ) @ SY3960 ) )
| ( SY3957 = SY3960 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2092]) ).
thf(2534,plain,
! [SV789: $i,SV416: $i] :
( ( ! [SY3961: $i,SY3962: $i,SY3963: $i,SY3964: $i] :
( ! [SY3965: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV416 ) @ SV789 ) @ SY3961 ) @ SY3962 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV416 ) @ SY3963 ) @ SY3964 ) @ SY3965 ) )
| ( SY3961 = SY3964 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2093]) ).
thf(2535,plain,
! [SV790: $i,SV417: $i] :
( ( ! [SY3966: $i,SY3967: $i,SY3968: $i] :
( ! [SY3969: $i,SY3970: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV417 ) @ SV790 ) @ SY3966 ) @ SY3967 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV417 ) @ SY3968 ) @ SY3969 ) @ SY3970 ) )
| ( SV790 = SY3968 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2094]) ).
thf(2536,plain,
! [SV791: $i,SV418: $i] :
( ( ! [SY3971: $i,SY3972: $i,SY3973: $i] :
( ( ( c_Set_Oinsert @ SV418 @ ( c_Set_Oinsert @ SV791 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3971 @ tc_bool ) ) @ SY3971 ) @ SY3971 )
!= ( c_Set_Oinsert @ SY3972 @ ( c_Set_Oinsert @ SY3973 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3971 @ tc_bool ) ) @ SY3971 ) @ SY3971 ) )
| ( SV791 = SY3972 )
| ( SV791 = SY3973 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2095]) ).
thf(2537,plain,
! [SV792: $i,SV419: $i] :
( ( ! [SY3974: $i,SY3975: $i,SY3976: $i] :
( ( ( c_Set_Oinsert @ SV419 @ ( c_Set_Oinsert @ SV792 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3974 @ tc_bool ) ) @ SY3974 ) @ SY3974 )
!= ( c_Set_Oinsert @ SY3975 @ ( c_Set_Oinsert @ SY3976 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3974 @ tc_bool ) ) @ SY3974 ) @ SY3974 ) )
| ( SV419 = SY3976 )
| ( SV792 = SY3976 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2538,plain,
! [SV793: $i,SV420: $i] :
( ( ! [SY3977: $i,SY3978: $i] :
( ! [SY3979: $i] :
( ( c_Set_Oinsert @ SV420 @ ( c_Set_Oinsert @ SV793 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3977 @ tc_bool ) ) @ SY3977 ) @ SY3977 )
!= ( c_Set_Oinsert @ SY3978 @ ( c_Set_Oinsert @ SY3979 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3977 @ tc_bool ) ) @ SY3977 ) @ SY3977 ) )
| ( SV793 = SY3978 )
| ( SV420 = SY3978 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2539,plain,
! [SV794: $i,SV421: $i] :
( ( ! [SY3980: $i,SY3981: $i,SY3982: $i] :
( ( ( c_Set_Oinsert @ SV421 @ ( c_Set_Oinsert @ SV794 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3980 @ tc_bool ) ) @ SY3980 ) @ SY3980 )
!= ( c_Set_Oinsert @ SY3981 @ ( c_Set_Oinsert @ SY3982 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3980 @ tc_bool ) ) @ SY3980 ) @ SY3980 ) )
| ( SV421 = SY3982 )
| ( SV421 = SY3981 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2540,plain,
! [SV795: $i,SV422: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV422 @ tc_bool ) ) @ SV795 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2099]) ).
thf(2541,plain,
! [SV796: $i,SV423: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV423 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV796 ) @ tc_bool ) ) @ SV796 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2542,plain,
! [SV797: $i,SV424: $i] :
( ( ! [SY3983: $i,SY3984: $i,SY3985: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV424 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV797 ) @ SY3983 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SY3984 ) ) @ SY3985 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) ) @ SV797 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV797 ) @ SY3983 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SY3984 ) ) @ SY3985 ) @ SV424 @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) ) @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV797 ) @ SY3983 ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY3984 ) ) ) @ SY3985 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) ) @ SV797 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2543,plain,
! [SV798: $i,SV425: $i] :
( ( ( hBOOL @ ( hAPP @ SV425 @ SV798 ) )
| ! [SY3986: $i] :
( ( SY3986 = SV798 )
| ! [SY3987: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3986 @ SV425 @ SY3987 ) @ SV798 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2544,plain,
! [SV799: $i,SV426: $i] :
( ( ! [SY3988: $i] :
( ( c_Set_Oinsert @ SV426 @ ( c_Set_Oinsert @ SV426 @ SV799 @ SY3988 ) @ SY3988 )
= ( c_Set_Oinsert @ SV426 @ SV799 @ SY3988 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2103]) ).
thf(2545,plain,
! [SV800: $i,SV427: $i] :
( ( ! [SY3989: $i] :
( ( c_Set_Oinsert @ SV427 @ SV800 @ SY3989 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3989 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2104]) ).
thf(2546,plain,
! [SV801: $i,SV428: $i] :
( ( ! [SY3990: $i,SY3991: $i] :
( ( c_Set_Oinsert @ SV428 @ ( c_Set_Oinsert @ SV801 @ SY3990 @ SY3991 ) @ SY3991 )
= ( c_Set_Oinsert @ SV801 @ ( c_Set_Oinsert @ SV428 @ SY3990 @ SY3991 ) @ SY3991 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2105]) ).
thf(2547,plain,
! [SV802: $i,SV429: $i] :
( ( ! [SY3992: $i] :
( ( c_Set_Oinsert @ SV429 @ ( c_Set_Oinsert @ SV802 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3992 @ tc_bool ) ) @ SY3992 ) @ SY3992 )
= ( c_Set_Oinsert @ SV802 @ ( c_Set_Oinsert @ SV429 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3992 @ tc_bool ) ) @ SY3992 ) @ SY3992 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(2548,plain,
! [SV803: $i,SV430: $i] :
( ( ! [SY3993: $i] :
( ( ( c_Set_Oinsert @ SV430 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV803 @ tc_bool ) ) @ SV803 )
!= ( c_Set_Oinsert @ SY3993 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV803 @ tc_bool ) ) @ SV803 ) )
| ( SV430 = SY3993 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2107]) ).
thf(2549,plain,
! [SV804: $i,SV431: $i] :
( ( ! [SY3994: $i,SY3995: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV431 @ SV804 @ SY3994 ) @ SY3995 ) )
| ~ ( hBOOL @ ( hAPP @ SV804 @ SY3995 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2108]) ).
thf(2550,plain,
! [SV805: $i,SV432: $i] :
( ( ( ( hAPP @ c_Com_Ocom_OBODY @ SV432 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SV805 ) )
| ( SV432 = SV805 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2109]) ).
thf(2551,plain,
! [SV806: $i,SV433: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV433 @ SV806 ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV806 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2110]) ).
thf(2552,plain,
! [SV807: $i,SV434: $i] :
( ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV434 @ SV807 ) )
| ~ ( class_Lattices_Olattice @ SV807 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2111]) ).
thf(2553,plain,
! [SV808: $i,SV435: $i] :
( ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV435 @ SV808 ) )
| ~ ( class_Lattices_Obounded__lattice @ SV808 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2112]) ).
thf(2554,plain,
! [SV809: $i,SV436: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV436 @ SV809 ) )
| ~ ( class_Orderings_Opreorder @ SV809 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2555,plain,
! [SV810: $i,SV437: $i] :
( ( ( class_Lattices_Olattice @ ( tc_fun @ SV437 @ SV810 ) )
| ~ ( class_Lattices_Olattice @ SV810 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2114]) ).
thf(2556,plain,
! [SV811: $i,SV438: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV438 @ SV811 ) )
| ~ ( class_Orderings_Oorder @ SV811 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2115]) ).
thf(2557,plain,
! [SV812: $i,SV439: $i] :
( ( ( class_Orderings_Obot @ ( tc_fun @ SV439 @ SV812 ) )
| ~ ( class_Orderings_Obot @ SV812 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2116]) ).
thf(2558,plain,
! [SV813: $i,SV440: $i] :
( ( ( class_HOL_Ominus @ ( tc_fun @ SV440 @ SV813 ) )
| ~ ( class_HOL_Ominus @ SV813 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2559,plain,
! [SV814: $i,SV441: $i] :
( ( ( class_HOL_Oord @ ( tc_fun @ SV441 @ SV814 ) )
| ~ ( class_HOL_Oord @ SV814 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2118]) ).
thf(2560,plain,
! [SV815: $i,SV442: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV442 ) @ SV815 ) @ SV815 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2119]) ).
thf(2561,plain,
! [SV816: $i,SV443: $i] :
( ( ( SV443 = SV816 )
| ! [SY3996: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY3996 ) @ SV443 ) @ SV816 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2120]) ).
thf(2562,plain,
! [SV444: $i,SV1: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV1 ) )
= $true )
| ( ( ! [SY3123: $i,SY3124: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV444 @ SY3123 @ SV1 ) @ SY3124 @ SV1 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV444 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3123 @ SY3124 @ SV1 ) @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2122]) ).
thf(2563,plain,
! [SV445: $i,SV2: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV2 ) )
= $true )
| ( ( ! [SY3125: $i,SY3126: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV445 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3125 @ SY3126 @ SV2 ) @ SV2 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3125 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV445 @ SY3126 @ SV2 ) @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2123]) ).
thf(2564,plain,
! [SV446: $i,SV3: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV3 ) )
= $true )
| ( ( ! [SY3127: $i,SY3128: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV446 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3127 @ SY3128 @ SV3 ) @ SV3 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3127 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV446 @ SY3128 @ SV3 ) @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2124]) ).
thf(2565,plain,
! [SV447: $i,SV4: $i] :
( ( ( ~ ( class_Lattices_Olattice @ SV4 ) )
= $true )
| ( ( ! [SY3129: $i,SY3130: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV447 @ SY3129 @ SV4 ) @ SY3130 @ SV4 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV447 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3129 @ SY3130 @ SV4 ) @ SV4 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2125]) ).
thf(2566,plain,
! [SV448: $i,SV5: $i] :
( ( ( ! [SY3131: $i] : ( c_Com_OWT @ ( c_Com_Ocom_OCall @ SV5 @ SV448 @ SY3131 ) ) )
= $true )
| ( ( ~ ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ SV448 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2126]) ).
thf(2567,plain,
! [SV6: $i,SV817: $i] :
( ( ( ! [SY3997: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCall @ SV817 @ SV6 @ SY3997 ) ) )
= $true )
| ( ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ SV6 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2127]) ).
thf(2568,plain,
! [SV818: $i,SV449: $i,SV7: $i] :
( ( ! [SY3998: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV7 @ SV449 @ ( tc_fun @ SV818 @ tc_bool ) ) @ SY3998 @ ( tc_fun @ SV818 @ tc_bool ) )
| ~ ( c_lessequals @ SV449 @ SY3998 @ ( tc_fun @ SV818 @ tc_bool ) )
| ~ ( c_lessequals @ SV7 @ SY3998 @ ( tc_fun @ SV818 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(2569,plain,
! [SV819: $i,SV450: $i,SV8: $i] :
( ( c_lessequals @ SV8 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV450 @ SV8 @ ( tc_fun @ SV819 @ tc_bool ) ) @ ( tc_fun @ SV819 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2129]) ).
thf(2570,plain,
! [SV820: $i,SV451: $i,SV9: $i] :
( ( c_lessequals @ SV9 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV9 @ SV451 @ ( tc_fun @ SV820 @ tc_bool ) ) @ ( tc_fun @ SV820 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2130]) ).
thf(2571,plain,
! [SV821: $i,SV452: $i,SV10: $i] :
( ( ! [SY3999: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV10 @ SV452 @ ( tc_fun @ SV821 @ tc_bool ) ) @ SY3999 @ ( tc_fun @ SV821 @ tc_bool ) )
| ~ ( c_lessequals @ SV452 @ SY3999 @ ( tc_fun @ SV821 @ tc_bool ) )
| ~ ( c_lessequals @ SV10 @ SY3999 @ ( tc_fun @ SV821 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2131]) ).
thf(2572,plain,
! [SV453: $i,SV11: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV11 ) )
= $true )
| ( ( ! [SY3138: $i,SY3139: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV453 @ SY3138 @ SV11 ) @ SY3139 @ SV11 )
| ~ ( c_lessequals @ SY3138 @ SY3139 @ SV11 )
| ~ ( c_lessequals @ SV453 @ SY3139 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2132]) ).
thf(2573,plain,
! [SV12: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV12 )
= $false )
| ( ( ! [SY1812: $i,SY1813: $i] : ( c_lessequals @ SY1812 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1812 @ SY1813 @ SV12 ) @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2133]) ).
thf(2574,plain,
! [SV13: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV13 )
= $false )
| ( ( ! [SY1814: $i,SY1815: $i] : ( c_lessequals @ SY1814 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1815 @ SY1814 @ SV13 ) @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2134]) ).
thf(2575,plain,
! [SV454: $i,SV14: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV14 ) )
= $true )
| ( ( ! [SY3140: $i,SY3141: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV454 @ SY3140 @ SV14 ) @ SY3141 @ SV14 )
| ~ ( c_lessequals @ SY3140 @ SY3141 @ SV14 )
| ~ ( c_lessequals @ SV454 @ SY3141 @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2135]) ).
thf(2576,plain,
! [SV455: $i,SV15: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV15 ) )
= $true )
| ( ( ! [SY3142: $i,SY3143: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV455 @ SY3142 @ SV15 ) @ SY3143 @ SV15 )
| ~ ( c_lessequals @ SY3142 @ SY3143 @ SV15 )
| ~ ( c_lessequals @ SV455 @ SY3143 @ SV15 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2136]) ).
thf(2577,plain,
! [SV16: $i] :
( ( ( class_Lattices_Olattice @ SV16 )
= $false )
| ( ( ! [SY1822: $i,SY1823: $i] : ( c_lessequals @ SY1822 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1823 @ SY1822 @ SV16 ) @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2137]) ).
thf(2578,plain,
! [SV17: $i] :
( ( ( class_Lattices_Olattice @ SV17 )
= $false )
| ( ( ! [SY1824: $i,SY1825: $i] : ( c_lessequals @ SY1824 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1824 @ SY1825 @ SV17 ) @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2138]) ).
thf(2579,plain,
! [SV822: $i,SV456: $i,SV18: $i] :
( ( ! [SY4000: $i,SY4001: $i,SY4002: $i,SY4003: $i,SY4004: $i,SY4005: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV18 @ SV456 @ ( c_COMBC @ SV822 @ SY4000 @ SY4000 @ tc_bool ) @ ( c_COMBC @ SY4001 @ SY4000 @ SY4000 @ tc_bool ) @ SY4002 @ SY4003 @ SY4004 @ SY4005 @ SY4000 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV456 @ SV18 @ SV822 @ SY4001 @ SY4003 @ SY4002 @ SY4005 @ SY4004 @ SY4000 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2139]) ).
thf(2580,plain,
! [SV823: $i,SV457: $i,SV19: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV19 @ ( c_HOL_Ominus__class_Ominus @ SV457 @ SV19 @ ( tc_fun @ SV823 @ tc_bool ) ) @ ( tc_fun @ SV823 @ tc_bool ) )
= SV457 )
| ~ ( c_lessequals @ SV19 @ SV457 @ ( tc_fun @ SV823 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2140]) ).
thf(2581,plain,
! [SV824: $i,SV458: $i,SV20: $i] :
( ( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCond @ SV20 @ SV458 @ SV824 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2141]) ).
thf(2582,plain,
! [SV825: $i,SV459: $i,SV21: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV21 @ SV459 @ ( tc_fun @ SV825 @ tc_bool ) ) @ SV21 @ ( tc_fun @ SV825 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2142]) ).
thf(2583,plain,
! [SV22: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV22 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV22 )
| ! [SY1840: $i,SY1841: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SY1840 @ SY1841 @ SV22 )
!= ( c_HOL_Ozero__class_Ozero @ SV22 ) )
| ( SY1840 = SY1841 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2143]) ).
thf(2584,plain,
! [SV23: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV23 )
= $false )
| ( ( ! [SY1842: $i,SY1843: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SY1842 @ SY1843 @ SV23 )
!= ( c_HOL_Ozero__class_Ozero @ SV23 ) )
| ( SY1842 = SY1843 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2144]) ).
thf(2585,plain,
! [SV24: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV24 )
= $false )
| ( ( ! [SY1844: $i,SY1845: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SY1844 @ SY1845 @ SV24 )
!= ( c_HOL_Ozero__class_Ozero @ SV24 ) )
| ( SY1844 = SY1845 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2145]) ).
thf(2586,plain,
! [SV826: $i,SV460: $i,SV25: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV25 @ SV460 @ SV826 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV826 @ tc_bool ) ) @ SV826 @ SV460 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV460 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2146]) ).
thf(2587,plain,
! [SV461: $i,SV26: $i] :
( ( ( ! [SY3155: $i] : ( hBOOL @ ( c_in @ SV26 @ ( c_Collect @ SV461 @ SY3155 ) @ SY3155 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV461 @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2147]) ).
thf(2588,plain,
! [SV462: $i,SV27: $i] :
( ( ( hBOOL @ ( hAPP @ SV27 @ SV462 ) )
= $true )
| ( ( ! [SY3156: $i] :
~ ( hBOOL @ ( c_in @ SV462 @ ( c_Collect @ SV27 @ SY3156 ) @ SY3156 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2148]) ).
thf(2589,plain,
! [SV827: $i,SV463: $i,SV28: $i] :
( ( ! [SY4006: $i] :
( ( hBOOL @ ( c_in @ SV28 @ ( c_HOL_Ominus__class_Ominus @ SV463 @ SV827 @ ( tc_fun @ SY4006 @ tc_bool ) ) @ SY4006 ) )
| ( hBOOL @ ( c_in @ SV28 @ SV827 @ SY4006 ) )
| ~ ( hBOOL @ ( c_in @ SV28 @ SV463 @ SY4006 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2149]) ).
thf(2590,plain,
! [SV828: $i,SV464: $i,SV29: $i] :
( ( ! [SY4007: $i] :
( ( hBOOL @ ( c_in @ SV29 @ ( c_HOL_Ominus__class_Ominus @ SV464 @ SV828 @ ( tc_fun @ SY4007 @ tc_bool ) ) @ SY4007 ) )
| ( hBOOL @ ( c_in @ SV29 @ SV828 @ SY4007 ) )
| ~ ( hBOOL @ ( c_in @ SV29 @ SV464 @ SY4007 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2150]) ).
thf(2591,plain,
! [SV829: $i,SV465: $i,SV30: $i] :
( ( ! [SY4008: $i,SY4009: $i,SY4010: $i] :
( ( c_Com_Ocom_OCall @ SV30 @ SV465 @ SV829 )
!= ( c_Com_Ocom_OLocal @ SY4008 @ SY4009 @ SY4010 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2151]) ).
thf(2592,plain,
! [SV830: $i,SV466: $i,SV31: $i] :
( ( ( hBOOL @ ( c_in @ SV31 @ SV466 @ SV830 ) )
| ! [SY4011: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SV31 @ SY4011 @ SV830 ) @ SV466 @ ( tc_fun @ SV830 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2152]) ).
thf(2593,plain,
! [SV831: $i,SV467: $i,SV32: $i] :
( ( ! [SY4012: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV32 @ ( c_COMBK @ SV467 @ ( tc_fun @ SV831 @ tc_bool ) @ SY4012 ) @ SY4012 @ ( tc_fun @ SV831 @ tc_bool ) )
= SV467 )
| ( SV32
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4012 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2153]) ).
thf(2594,plain,
! [SV468: $i,SV33: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV33 ) )
= $true )
| ( ( ! [SY3169: $i,SY3170: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV468 @ ( c_COMBK @ SY3169 @ SV33 @ SY3170 ) @ SY3170 @ SV33 )
= SY3169 )
| ( SV468
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3170 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2154]) ).
thf(2595,plain,
! [SV832: $i,SV469: $i,SV34: $i] :
( ( ! [SY4013: $i,SY4014: $i] :
( ( c_Com_Ocom_OCall @ SV34 @ SV469 @ SV832 )
!= ( c_Com_Ocom_OWhile @ SY4013 @ SY4014 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2155]) ).
thf(2596,plain,
! [SV833: $i,SV470: $i,SV35: $i] :
( ( ! [SY4015: $i] :
( ! [SY4016: $i] :
( ( c_Set_Oinsert @ ( hAPP @ SV35 @ SV470 ) @ ( c_Set_Oimage @ SV35 @ SV833 @ SY4015 @ SY4016 ) @ SY4016 )
= ( c_Set_Oimage @ SV35 @ SV833 @ SY4015 @ SY4016 ) )
| ~ ( hBOOL @ ( c_in @ SV470 @ SV833 @ SY4015 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2156]) ).
thf(2597,plain,
! [SV834: $i,SV471: $i,SV36: $i] :
( ( ! [SY4017: $i] :
( ( c_lessequals @ SV36 @ ( c_Set_Oinsert @ SV471 @ SV834 @ SY4017 ) @ ( tc_fun @ SY4017 @ tc_bool ) )
| ~ ( c_lessequals @ SV36 @ SV834 @ ( tc_fun @ SY4017 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SV471 @ SV36 @ SY4017 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2157]) ).
thf(2598,plain,
! [SV835: $i,SV472: $i,SV37: $i] :
( ( ( c_lessequals @ SV37 @ SV472 @ ( tc_fun @ SV835 @ tc_bool ) )
| ! [SY4018: $i] :
( ( hBOOL @ ( c_in @ SY4018 @ SV37 @ SV835 ) )
| ~ ( c_lessequals @ SV37 @ ( c_Set_Oinsert @ SY4018 @ SV472 @ SV835 ) @ ( tc_fun @ SV835 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2158]) ).
thf(2599,plain,
! [SV836: $i,SV473: $i,SV38: $i] :
( ( ! [SY4019: $i] :
( ( c_lessequals @ SV38 @ ( c_Set_Oinsert @ SV473 @ SV836 @ SY4019 ) @ ( tc_fun @ SY4019 @ tc_bool ) )
| ~ ( c_lessequals @ SV38 @ SV836 @ ( tc_fun @ SY4019 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SV473 @ SV38 @ SY4019 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2159]) ).
thf(2600,plain,
! [SV837: $i,SV474: $i,SV39: $i] :
( ( ( c_lessequals @ SV39 @ SV474 @ ( tc_fun @ SV837 @ tc_bool ) )
| ! [SY4020: $i] :
( ~ ( c_lessequals @ SV39 @ ( c_Set_Oinsert @ SY4020 @ SV474 @ SV837 ) @ ( tc_fun @ SV837 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SY4020 @ SV39 @ SV837 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2160]) ).
thf(2601,plain,
! [SV838: $i,SV475: $i,SV40: $i] :
( ( ! [SY4021: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV40 @ SV475 @ ( tc_fun @ SV838 @ tc_bool ) ) @ SY4021 @ ( tc_fun @ SV838 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV40 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV475 @ SY4021 @ ( tc_fun @ SV838 @ tc_bool ) ) @ ( tc_fun @ SV838 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2161]) ).
thf(2602,plain,
! [SV839: $i,SV476: $i,SV41: $i] :
( ( ! [SY4022: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV41 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV476 @ SV839 @ ( tc_fun @ SY4022 @ tc_bool ) ) @ ( tc_fun @ SY4022 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV476 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV41 @ SV839 @ ( tc_fun @ SY4022 @ tc_bool ) ) @ ( tc_fun @ SY4022 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2162]) ).
thf(2603,plain,
! [SV840: $i,SV477: $i,SV42: $i] :
( ( ! [SY4023: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV42 @ SV477 ) @ SV840 @ SY4023 )
| ! [SY4024: $i] :
( ~ ( c_Natural_Oevalc @ SV477 @ SY4024 @ SY4023 )
| ~ ( c_Natural_Oevalc @ SV42 @ SV840 @ SY4024 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2163]) ).
thf(2604,plain,
! [SV841: $i,SV478: $i,SV43: $i] :
( ( ! [SY4025: $i,SY4026: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV43 @ SV478 @ SV841 @ SY4025 ) @ ( c_Set_Oimage @ SV43 @ SY4026 @ SV841 @ SY4025 ) @ ( tc_fun @ SY4025 @ tc_bool ) ) @ ( c_Set_Oimage @ SV43 @ ( c_HOL_Ominus__class_Ominus @ SV478 @ SY4026 @ ( tc_fun @ SV841 @ tc_bool ) ) @ SV841 @ SY4025 ) @ ( tc_fun @ SY4025 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2164]) ).
thf(2605,plain,
! [SV842: $i,SV479: $i,SV44: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV44 @ SV479 ) )
| ! [SY4027: $i] :
( ( c_Natural_Oevalc @ SV842 @ SV479 @ SY4027 )
| ! [SY4028: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV44 @ SV842 @ SY4028 ) @ SV479 @ SY4027 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2165]) ).
thf(2606,plain,
! [SV843: $i,SV480: $i,SV45: $i] :
( ( ! [SY4029: $i,SY4030: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV45 @ SV480 @ SV843 ) @ SY4029 @ SY4030 )
| ~ ( c_Natural_Oevalc @ SV480 @ SY4029 @ SY4030 )
| ~ ( hBOOL @ ( hAPP @ SV45 @ SY4029 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2166]) ).
thf(2607,plain,
! [SV844: $i,SV481: $i,SV46: $i] :
( ( ! [SY4031: $i,SY4032: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV46 @ SV481 ) @ SV844 @ SY4031 @ SY4032 )
| ! [SY4033: $i] :
( ~ ( c_Natural_Oevaln @ SV481 @ SY4033 @ SY4031 @ SY4032 )
| ~ ( c_Natural_Oevaln @ SV46 @ SV844 @ SY4031 @ SY4033 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2167]) ).
thf(2608,plain,
! [SV482: $i,SV47: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV47 ) )
= $true )
| ( ( ! [SY3205: $i,SY3206: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV482 @ SV482 @ SV47 )
!= ( c_HOL_Ominus__class_Ominus @ SY3205 @ SY3206 @ SV47 ) )
| ( SY3205 = SY3206 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2168]) ).
thf(2609,plain,
! [SV483: $i,SV48: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV48 ) )
= $true )
| ( ( ! [SY3207: $i] :
( ! [SY3208: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV483 @ SY3207 @ SV48 )
!= ( c_HOL_Ominus__class_Ominus @ SY3208 @ SY3208 @ SV48 ) )
| ( SV483 = SY3207 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2169]) ).
thf(2610,plain,
! [SV845: $i,SV484: $i,SV49: $i] :
( ( ! [SY4034: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV49 @ SV484 ) @ SV845 @ SY4034 )
| ! [SY4035: $i] :
( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV49 @ SV484 ) @ SY4035 @ SY4034 )
| ~ ( c_Natural_Oevalc @ SV484 @ SV845 @ SY4035 )
| ~ ( hBOOL @ ( hAPP @ SV49 @ SV845 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2170]) ).
thf(2611,plain,
! [SV485: $i,SV50: $i] :
( ( ( c_Option_Ooption_ONone @ SV50 )
= ( c_Option_Ooption_OSome @ SV485 @ SV50 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2171]) ).
thf(2612,plain,
! [SV486: $i,SV51: $i] :
( ( ( c_Option_Ooption_ONone @ SV51 )
= ( c_Option_Ooption_OSome @ SV486 @ SV51 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2172]) ).
thf(2613,plain,
! [SV846: $i,SV487: $i,SV52: $i] :
( ( ! [SY4036: $i,SY4037: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV52 @ SV487 ) @ SV846 @ SY4036 @ SY4037 )
| ! [SY4038: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV52 @ SV487 ) @ SY4038 @ SY4036 @ SY4037 )
| ~ ( c_Natural_Oevaln @ SV487 @ SV846 @ SY4036 @ SY4038 )
| ~ ( hBOOL @ ( hAPP @ SV52 @ SV846 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2173]) ).
thf(2614,plain,
! [SV847: $i,SV488: $i,SV53: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV53 @ SV488 @ ( tc_fun @ SV847 @ tc_bool ) ) @ SV488 @ ( tc_fun @ SV847 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV53 @ SV488 @ ( tc_fun @ SV847 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2174]) ).
thf(2615,plain,
! [SV848: $i,SV489: $i,SV54: $i] :
( ( ! [SY4039: $i,SY4040: $i,SY4041: $i] :
( ( hAPP @ ( c_COMBS @ SV54 @ SV489 @ SV848 @ SY4039 @ SY4040 ) @ SY4041 )
= ( hAPP @ ( hAPP @ SV54 @ SY4041 ) @ ( hAPP @ SV489 @ SY4041 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2175]) ).
thf(2616,plain,
! [SV849: $i,SV490: $i,SV55: $i] :
( ( ! [SY4042: $i] :
( ( hAPP @ ( c_COMBK @ SV55 @ SV490 @ SV849 ) @ SY4042 )
= SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2176]) ).
thf(2617,plain,
! [SV850: $i,SV492: $i,SV57: $i] :
( ( ! [SY4043: $i,SY4044: $i,SY4045: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV57 @ SV492 @ SV850 @ SY4043 ) @ SY4044 ) @ SY4045 )
= ( hAPP @ ( hAPP @ SV57 @ SY4045 ) @ SY4044 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2618,plain,
! [SV851: $i,SV493: $i,SV58: $i] :
( ( ! [SY4046: $i,SY4047: $i,SY4048: $i] :
( ( hAPP @ ( c_COMBB @ SV58 @ SV493 @ SV851 @ SY4046 @ SY4047 ) @ SY4048 )
= ( hAPP @ SV58 @ ( hAPP @ SV493 @ SY4048 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(2619,plain,
! [SV494: $i,SV59: $i] :
( ( ( hBOOL @ ( hAPP @ SV59 @ SV494 ) )
= $true )
| ( ( ! [SY3231: $i] :
~ ( hBOOL @ ( c_in @ SV494 @ SV59 @ SY3231 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2180]) ).
thf(2620,plain,
! [SV495: $i,SV60: $i] :
( ( ( ! [SY3232: $i] : ( hBOOL @ ( c_in @ SV60 @ SV495 @ SY3232 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV495 @ SV60 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2181]) ).
thf(2621,plain,
! [SV852: $i,SV496: $i,SV61: $i] :
( ( ! [SY4049: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV61 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV496 @ tc_bool ) ) @ SV852 @ SV496 @ ( tc_fun @ SY4049 @ tc_bool ) ) @ ( tc_fun @ SY4049 @ tc_bool ) )
= SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2182]) ).
thf(2622,plain,
! [SV853: $i,SV497: $i,SV62: $i] :
( ( ! [SY4050: $i] :
( ~ ( hBOOL @ ( hAPP @ SV62 @ SV497 ) )
| ! [SY4051: $i] :
( ( c_Natural_Oevaln @ SV853 @ SV497 @ SY4050 @ SY4051 )
| ! [SY4052: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV62 @ SV853 @ SY4052 ) @ SV497 @ SY4050 @ SY4051 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2183]) ).
thf(2623,plain,
! [SV854: $i,SV498: $i,SV63: $i] :
( ( ! [SY4053: $i,SY4054: $i,SY4055: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV63 @ SV498 @ SV854 ) @ SY4053 @ SY4054 @ SY4055 )
| ~ ( c_Natural_Oevaln @ SV498 @ SY4053 @ SY4054 @ SY4055 )
| ~ ( hBOOL @ ( hAPP @ SV63 @ SY4053 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2184]) ).
thf(2624,plain,
! [SV855: $i,SV499: $i,SV64: $i] :
( ( ! [SY4056: $i,SY4057: $i,SY4058: $i,SY4059: $i,SY4060: $i,SY4061: $i,SY4062: $i,SY4063: $i,SY4064: $i] :
( ( c_Com_Ocom_Ocom__case @ SV64 @ SV499 @ SV855 @ SY4056 @ SY4057 @ SY4058 @ SY4059 @ SY4060 @ ( c_Com_Ocom_OCall @ SY4061 @ SY4062 @ SY4063 ) @ SY4064 )
= ( hAPP @ ( hAPP @ ( hAPP @ SY4060 @ SY4061 ) @ SY4062 ) @ SY4063 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2185]) ).
thf(2625,plain,
! [SV856: $i,SV500: $i,SV65: $i] :
( ( ! [SY4065: $i,SY4066: $i] :
( ( c_Com_Ocom_OCall @ SV65 @ SV500 @ SV856 )
!= ( c_Com_Ocom_OSemi @ SY4065 @ SY4066 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2626,plain,
! [SV66: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV66 )
= $false )
| ( ( ! [SY1989: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY1989 @ SY1989 @ SV66 )
= SY1989 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2187]) ).
thf(2627,plain,
! [SV68: $i] :
( ( ( class_Lattices_Olattice @ SV68 )
= $false )
| ( ( ! [SY1991: $i,SY1992: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY1991 @ SY1992 @ ( tc_fun @ t_a @ SV68 ) ) @ v_x )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SY1991 @ v_x ) @ ( hAPP @ SY1992 @ v_x ) @ SV68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2189]) ).
thf(2628,plain,
! [SV857: $i,SV502: $i,SV69: $i] :
( ( ! [SY4067: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV69 @ SV502 @ SV857 ) @ SY4067 @ SV857 @ SV502 )
= ( c_Set_Oinsert @ SV69 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV502 @ tc_bool ) ) @ SV502 ) )
| ! [SY4068: $i] :
~ ( hBOOL @ ( c_in @ SY4068 @ SY4067 @ SV857 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2190]) ).
thf(2629,plain,
! [SV858: $i,SV503: $i,SV70: $i] :
( ( ! [SY4069: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ SV70 @ SV503 ) @ SV858 @ SY4069 ) )
| ! [SY4070: $i,SY4071: $i] :
( ~ ( hBOOL @ ( c_in @ SV503 @ SY4070 @ SY4071 ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV70 @ SY4070 @ SY4071 @ SY4069 ) @ SV858 @ ( tc_fun @ SY4069 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(2630,plain,
! [SV859: $i,SV504: $i,SV71: $i] :
( ( ! [SY4072: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV71 @ ( c_Set_Oinsert @ SV504 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV859 @ tc_bool ) ) @ SV859 ) @ ( tc_fun @ SV859 @ tc_bool ) ) @ SY4072 @ ( tc_fun @ SV859 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV504 @ SV71 @ SV859 ) )
| ~ ( c_lessequals @ SV71 @ ( c_Set_Oinsert @ SV504 @ SY4072 @ SV859 ) @ ( tc_fun @ SV859 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(2631,plain,
! [SV860: $i,SV505: $i,SV72: $i] :
( ( ! [SY4073: $i] :
( ( c_lessequals @ SV72 @ ( c_Set_Oinsert @ SV505 @ SV860 @ SY4073 ) @ ( tc_fun @ SY4073 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV505 @ SV72 @ SY4073 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV72 @ ( c_Set_Oinsert @ SV505 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4073 @ tc_bool ) ) @ SY4073 ) @ ( tc_fun @ SY4073 @ tc_bool ) ) @ SV860 @ ( tc_fun @ SY4073 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2193]) ).
thf(2632,plain,
! [SV861: $i,SV506: $i,SV73: $i] :
( ( ! [SY4074: $i] :
( ( c_lessequals @ SV73 @ ( c_Set_Oinsert @ SV506 @ SV861 @ SY4074 ) @ ( tc_fun @ SY4074 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV506 @ SV73 @ SY4074 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV73 @ ( c_Set_Oinsert @ SV506 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4074 @ tc_bool ) ) @ SY4074 ) @ ( tc_fun @ SY4074 @ tc_bool ) ) @ SV861 @ ( tc_fun @ SY4074 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(2633,plain,
! [SV862: $i,SV507: $i,SV74: $i] :
( ( ! [SY4075: $i] : ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV74 @ SV507 ) @ SV862 @ SY4075 @ SV862 )
| ( hBOOL @ ( hAPP @ SV74 @ SV862 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2195]) ).
thf(2634,plain,
! [SV863: $i,SV508: $i,SV75: $i] :
( ( ( c_Finite__Set_Ofold1 @ SV75 @ SV508 @ SV863 )
= ( c_The @ ( c_Finite__Set_Ofold1Set @ SV75 @ SV508 @ SV863 ) @ SV863 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2196]) ).
thf(2635,plain,
! [SV864: $i,SV509: $i,SV76: $i] :
( ( ! [SY4076: $i,SY4077: $i,SY4078: $i] :
( ( c_Com_Ocom_OCond @ SV76 @ SV509 @ SV864 )
!= ( c_Com_Ocom_OCall @ SY4076 @ SY4077 @ SY4078 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2636,plain,
! [SV865: $i,SV510: $i,SV77: $i] :
( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV77 )
| ! [SY4079: $i,SY4080: $i] :
( ( c_lessequals @ ( hAPP @ SV510 @ SV865 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY4079 @ SV510 @ SY4080 @ SV77 ) @ SV77 )
| ~ ( hBOOL @ ( c_in @ SV865 @ SY4079 @ SY4080 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2198]) ).
thf(2637,plain,
! [SV866: $i,SV511: $i,SV78: $i] :
( ( ! [SY4081: $i] :
( ! [SY4082: $i] : ( c_lessequals @ ( hAPP @ SV78 @ SV511 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV866 @ SV78 @ SY4081 @ ( tc_fun @ SY4082 @ tc_bool ) ) @ ( tc_fun @ SY4082 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV511 @ SV866 @ SY4081 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2199]) ).
thf(2638,plain,
! [SV867: $i,SV512: $i,SV79: $i] :
( ( ! [SY4083: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV79 @ SV512 @ SV867 ) @ SY4083 @ ( tc_fun @ SV867 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV512 @ SY4083 @ ( tc_fun @ SV867 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SV79 @ SY4083 @ SV867 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(2639,plain,
! [SV868: $i,SV513: $i,SV80: $i] :
( ( ! [SY4084: $i,SY4085: $i,SY4086: $i] :
( ( c_Com_Ocom_OLocal @ SV80 @ SV513 @ SV868 )
!= ( c_Com_Ocom_OCond @ SY4084 @ SY4085 @ SY4086 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2201]) ).
thf(2640,plain,
! [SV869: $i,SV515: $i,SV82: $i] :
( ( ! [SY4087: $i,SY4088: $i,SY4089: $i] :
( ( ( c_Com_Ocom_OCall @ SV82 @ SV515 @ SV869 )
!= ( c_Com_Ocom_OCall @ SY4087 @ SY4088 @ SY4089 ) )
| ( SV869 = SY4089 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2203]) ).
thf(2641,plain,
! [SV870: $i,SV516: $i,SV83: $i] :
( ( ! [SY4090: $i,SY4091: $i] :
( ! [SY4092: $i] :
( ( c_Com_Ocom_OCall @ SV83 @ SV516 @ SV870 )
!= ( c_Com_Ocom_OCall @ SY4090 @ SY4091 @ SY4092 ) )
| ( SV516 = SY4091 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2204]) ).
thf(2642,plain,
! [SV871: $i,SV517: $i,SV84: $i] :
( ( ! [SY4093: $i] :
( ! [SY4094: $i,SY4095: $i] :
( ( c_Com_Ocom_OCall @ SV84 @ SV517 @ SV871 )
!= ( c_Com_Ocom_OCall @ SY4093 @ SY4094 @ SY4095 ) )
| ( SV84 = SY4093 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2643,plain,
! [SV518: $i,SV85: $i] :
( ( ( c_Com_Ocom_OWhile @ SV85 @ SV518 )
= c_Com_Ocom_OSKIP )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2206]) ).
thf(2644,plain,
! [SV872: $i,SV519: $i,SV86: $i] :
( ( ! [SY4096: $i,SY4097: $i] :
( ( c_Com_Ocom_OWhile @ SV86 @ SV519 )
!= ( c_Com_Ocom_OLocal @ SV872 @ SY4096 @ SY4097 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(2645,plain,
! [SV873: $i,SV520: $i,SV87: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV87 @ SV520 ) @ SV873 @ SV873 )
| ( hBOOL @ ( hAPP @ SV87 @ SV873 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2208]) ).
thf(2646,plain,
! [SV874: $i,SV522: $i,SV91: $i] :
( ( ! [SY4098: $i] :
( ( ( c_Com_Ocom_OSemi @ SV91 @ SV522 )
!= ( c_Com_Ocom_OSemi @ SV874 @ SY4098 ) )
| ( SV522 = SY4098 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2212]) ).
thf(2647,plain,
! [SV875: $i,SV523: $i,SV92: $i] :
( ( ! [SY4099: $i] :
( ( c_Com_Ocom_OSemi @ SV92 @ SV523 )
!= ( c_Com_Ocom_OSemi @ SV875 @ SY4099 ) )
| ( SV92 = SV875 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2213]) ).
thf(2648,plain,
! [SV876: $i,SV524: $i,SV93: $i] :
( ( ! [SY4100: $i] :
( ( c_Com_Ocom_OSemi @ SV93 @ SV524 )
!= ( c_Com_Ocom_OWhile @ SV876 @ SY4100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2214]) ).
thf(2649,plain,
! [SV94: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV94 )
= $false )
| ( ( ! [SY2070: $i,SY2071: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SY2070 @ SY2071 @ SV94 ) @ SV94 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2070 @ ( c_Complete__Lattice_OSup__class_OSup @ SY2071 @ SV94 ) @ SV94 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2215]) ).
thf(2650,plain,
! [SV877: $i,SV525: $i,SV95: $i] :
( ( ! [SY4101: $i,SY4102: $i] :
( ( c_Com_Ocom_OSemi @ SV95 @ SV525 )
!= ( c_Com_Ocom_OCond @ SV877 @ SY4101 @ SY4102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2216]) ).
thf(2651,plain,
! [SV878: $i,SV526: $i,SV96: $i] :
( ( ! [SY4103: $i,SY4104: $i] :
( ( c_Com_Ocom_OSemi @ SV96 @ SV526 )
!= ( c_Com_Ocom_OLocal @ SV878 @ SY4103 @ SY4104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2217]) ).
thf(2652,plain,
! [SV879: $i,SV527: $i,SV97: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ SV97 @ SV527 @ SV879 )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV97 ) @ SV527 @ SV879 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(2653,plain,
! [SV880: $i,SV528: $i,SV98: $i] :
( ( ! [SY4105: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV98 @ SV528 @ SV880 @ ( tc_fun @ SY4105 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4105 @ tc_bool ) ) )
| ! [SY4106: $i] :
( ( ( hAPP @ SV528 @ SY4106 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4105 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SY4106 @ SV98 @ SV880 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2219]) ).
thf(2654,plain,
! [SV881: $i,SV529: $i,SV99: $i] :
( ( ! [SY4107: $i,SY4108: $i] :
( ( c_Com_Ocom_OCond @ SV99 @ SV529 @ SV881 )
!= ( c_Com_Ocom_OWhile @ SY4107 @ SY4108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2220]) ).
thf(2655,plain,
! [SV882: $i,SV530: $i,SV100: $i] :
( ( ( hBOOL @ ( c_in @ SV100 @ SV530 @ SV882 ) )
| ! [SY4109: $i] :
~ ( hBOOL @ ( c_in @ SV100 @ ( c_HOL_Ominus__class_Ominus @ SV530 @ SY4109 @ ( tc_fun @ SV882 @ tc_bool ) ) @ SV882 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2221]) ).
thf(2656,plain,
! [SV883: $i,SV531: $i,SV101: $i] :
( ( ! [SY4110: $i,SY4111: $i,SY4112: $i] :
( ( c_Com_Ocom_OCond @ SV101 @ SV531 @ SV883 )
!= ( c_Com_Ocom_OLocal @ SY4110 @ SY4111 @ SY4112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2222]) ).
thf(2657,plain,
! [SV884: $i,SV532: $i,SV102: $i] :
( ( ~ ( hBOOL @ ( c_in @ SV102 @ SV532 @ SV884 ) )
| ! [SY4113: $i] :
~ ( hBOOL @ ( c_in @ SV102 @ ( c_HOL_Ominus__class_Ominus @ SY4113 @ SV532 @ ( tc_fun @ SV884 @ tc_bool ) ) @ SV884 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2223]) ).
thf(2658,plain,
! [SV885: $i,SV533: $i,SV103: $i] :
( ( ! [SY4114: $i] :
( ( c_lessequals @ ( hAPP @ SV103 @ SV533 ) @ SV885 @ ( tc_fun @ SY4114 @ tc_bool ) )
| ! [SY4115: $i,SY4116: $i] :
( ~ ( hBOOL @ ( c_in @ SV533 @ SY4115 @ SY4116 ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY4115 @ SV103 @ SY4116 @ ( tc_fun @ SY4114 @ tc_bool ) ) @ SV885 @ ( tc_fun @ SY4114 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2224]) ).
thf(2659,plain,
! [SV886: $i,SV534: $i,SV104: $i] :
( ( ! [SY4117: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ ( c_COMBK @ SV104 @ SV534 @ SV886 ) @ SY4117 @ SV886 @ SV534 @ t_a ) @ v_x )
= SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(2660,plain,
! [SV887: $i,SV536: $i,SV106: $i] :
( ( ! [SY4118: $i,SY4119: $i] :
( ( c_Com_Ocom_OCond @ SV106 @ SV536 @ SV887 )
!= ( c_Com_Ocom_OSemi @ SY4118 @ SY4119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(2661,plain,
! [SV888: $i,SV537: $i,SV107: $i] :
( ( ! [SY4120: $i] :
( ! [SY4121: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV107 @ SV537 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV888 @ SV107 @ SY4120 @ ( tc_fun @ SY4121 @ tc_bool ) ) @ ( tc_fun @ SY4121 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV888 @ SV107 @ SY4120 @ ( tc_fun @ SY4121 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SV537 @ SV888 @ SY4120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2228]) ).
thf(2662,plain,
! [SV889: $i,SV538: $i,SV108: $i] :
( ( ! [SY4122: $i,SY4123: $i,SY4124: $i] :
( ( ( c_Com_Ocom_OCond @ SV108 @ SV538 @ SV889 )
!= ( c_Com_Ocom_OCond @ SY4122 @ SY4123 @ SY4124 ) )
| ( SV889 = SY4124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2229]) ).
thf(2663,plain,
! [SV890: $i,SV539: $i,SV109: $i] :
( ( ! [SY4125: $i,SY4126: $i] :
( ! [SY4127: $i] :
( ( c_Com_Ocom_OCond @ SV109 @ SV539 @ SV890 )
!= ( c_Com_Ocom_OCond @ SY4125 @ SY4126 @ SY4127 ) )
| ( SV539 = SY4126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2230]) ).
thf(2664,plain,
! [SV891: $i,SV540: $i,SV110: $i] :
( ( ! [SY4128: $i] :
( ! [SY4129: $i,SY4130: $i] :
( ( c_Com_Ocom_OCond @ SV110 @ SV540 @ SV891 )
!= ( c_Com_Ocom_OCond @ SY4128 @ SY4129 @ SY4130 ) )
| ( SV110 = SY4128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2231]) ).
thf(2665,plain,
! [SV111: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV111 )
= $false )
| ( ( ! [SY2133: $i] :
( ( c_HOL_Ominus__class_Ominus @ SY2133 @ SY2133 @ SV111 )
= ( c_HOL_Ozero__class_Ozero @ SV111 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2232]) ).
thf(2666,plain,
! [SV112: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV112 )
= $false )
| ( ( ! [SY2134: $i] :
( ( c_HOL_Ominus__class_Ominus @ SY2134 @ SY2134 @ SV112 )
= ( c_HOL_Ozero__class_Ozero @ SV112 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2233]) ).
thf(2667,plain,
! [SV113: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV113 )
= $false )
| ( ( ! [SY2135: $i] :
( ( c_HOL_Ominus__class_Ominus @ SY2135 @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV113 )
= SY2135 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2234]) ).
thf(2668,plain,
! [SV114: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV114 )
= $false )
| ( ( ! [SY2136: $i] :
( ( c_HOL_Ominus__class_Ominus @ SY2136 @ SY2136 @ SV114 )
= ( c_HOL_Ozero__class_Ozero @ SV114 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2235]) ).
thf(2669,plain,
! [SV115: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV115 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV115 )
| ! [SY2137: $i] :
( ( c_HOL_Ominus__class_Ominus @ SY2137 @ SY2137 @ SV115 )
= ( c_HOL_Ozero__class_Ozero @ SV115 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2236]) ).
thf(2670,plain,
! [SV892: $i,SV541: $i,SV116: $i] :
( ( ~ ( class_Orderings_Oorder @ SV116 )
| ! [SY4131: $i,SY4132: $i] :
( ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV541 @ SV892 @ SV116 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY4131 @ SY4132 @ SV116 ) @ ( tc_fun @ SV116 @ tc_bool ) )
| ~ ( c_lessequals @ SV892 @ SY4132 @ SV116 )
| ~ ( c_lessequals @ SY4131 @ SV541 @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2237]) ).
thf(2671,plain,
! [SV893: $i,SV542: $i,SV117: $i] :
( ( ~ ( class_Orderings_Oorder @ SV117 )
| ( c_lessequals @ SV542 @ SV893 @ SV117 )
| ! [SY4133: $i] :
( ~ ( c_lessequals @ SY4133 @ SV542 @ SV117 )
| ! [SY4134: $i] :
~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY4133 @ SV542 @ SV117 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY4134 @ SV893 @ SV117 ) @ ( tc_fun @ SV117 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2238]) ).
thf(2672,plain,
! [SV894: $i,SV543: $i,SV118: $i] :
( ( ~ ( class_Orderings_Oorder @ SV118 )
| ( c_lessequals @ SV543 @ SV894 @ SV118 )
| ! [SY4135: $i] :
( ~ ( c_lessequals @ SV894 @ SY4135 @ SV118 )
| ! [SY4136: $i] :
~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV894 @ SY4135 @ SV118 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV543 @ SY4136 @ SV118 ) @ ( tc_fun @ SV118 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2239]) ).
thf(2673,plain,
! [SV544: $i,SV119: $i] :
( ( ( c_Option_Ooption_OSome @ SV119 @ SV544 )
= ( c_Option_Ooption_ONone @ SV544 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2240]) ).
thf(2674,plain,
! [SV545: $i,SV120: $i] :
( ( ( c_Option_Ooption_OSome @ SV120 @ SV545 )
= ( c_Option_Ooption_ONone @ SV545 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2241]) ).
thf(2675,plain,
! [SV895: $i,SV546: $i,SV121: $i] :
( ( ! [SY4137: $i,SY4138: $i,SY4139: $i] :
( ( c_Com_Ocom_OCall @ SV121 @ SV546 @ SV895 )
!= ( c_Com_Ocom_OCond @ SY4137 @ SY4138 @ SY4139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2242]) ).
thf(2676,plain,
! [SV896: $i,SV547: $i,SV122: $i] :
( ( ( ( c_Option_Ooption_OSome @ SV122 @ SV547 )
!= ( c_Option_Ooption_OSome @ SV896 @ SV547 ) )
| ( SV122 = SV896 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(2677,plain,
! [SV897: $i,SV548: $i,SV123: $i] :
( ( ! [SY4140: $i,SY4141: $i,SY4142: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV123 @ SV548 @ SV897 @ SY4140 @ SY4141 ) @ SY4142 )
= ( hAPP @ SV123 @ ( hAPP @ SV548 @ SY4142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(2678,plain,
! [SV898: $i,SV549: $i,SV124: $i] :
( ( ! [SY4143: $i,SY4144: $i,SY4145: $i] :
( ( hAPP @ SV124 @ ( hAPP @ SV549 @ SV898 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV124 @ SV549 @ SY4143 @ SY4144 @ SY4145 ) @ SV898 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2245]) ).
thf(2679,plain,
! [SV550: $i,SV125: $i] :
( ( ( ( c_Suc @ SV125 )
!= ( c_Suc @ SV550 ) )
= $true )
| ( ( SV125 = SV550 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2246]) ).
thf(2680,plain,
! [SV551: $i,SV126: $i] :
( ( ( ( c_Suc @ SV126 )
!= ( c_Suc @ SV551 ) )
= $true )
| ( ( SV126 = SV551 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2247]) ).
thf(2681,plain,
! [SV899: $i,SV552: $i,SV127: $i] :
( ( ~ ( class_Orderings_Oorder @ SV127 )
| ! [SY4146: $i,SY4147: $i] : ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV552 @ SV899 @ SV127 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY4146 @ SY4147 @ SV127 ) @ ( tc_fun @ SV127 @ tc_bool ) )
| ( c_lessequals @ SV552 @ SV899 @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2248]) ).
thf(2682,plain,
! [SV553: $i,SV128: $i] :
( ( ( hBOOL @ ( hAPP @ SV128 @ SV553 ) )
= $true )
| ( ( ! [SY3380: $i] :
( ( hBOOL @ ( hAPP @ SY3380 @ SV553 ) )
| ! [SY3381: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3380 @ SV128 @ ( tc_fun @ SY3381 @ tc_bool ) ) @ SV553 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2249]) ).
thf(2683,plain,
! [SV900: $i,SV554: $i,SV129: $i] :
( ( ! [SY4148: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV129 @ SV554 @ ( tc_fun @ SV900 @ tc_bool ) ) @ SY4148 ) )
| ~ ( hBOOL @ ( hAPP @ SV554 @ SY4148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2250]) ).
thf(2684,plain,
! [SV901: $i,SV555: $i,SV130: $i] :
( ( ! [SY4149: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV130 @ SV555 @ ( tc_fun @ SV901 @ tc_bool ) ) @ SY4149 ) )
| ~ ( hBOOL @ ( hAPP @ SV130 @ SY4149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(2685,plain,
! [SV902: $i,SV556: $i,SV131: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV131 @ SV556 @ SV902 ) )
| ~ ( c_Com_OWT @ SV902 )
| ~ ( c_Com_OWT @ SV556 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2252]) ).
thf(2686,plain,
! [SV903: $i,SV557: $i,SV132: $i] :
( ( ! [SY4150: $i,SY4151: $i,SY4152: $i,SY4153: $i,SY4154: $i,SY4155: $i] :
( ( c_Com_Ocom_Ocom__case @ SV132 @ SV557 @ SV903 @ SY4150 @ SY4151 @ SY4152 @ SY4153 @ SY4154 @ c_Com_Ocom_OSKIP @ SY4155 )
= SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2253]) ).
thf(2687,plain,
! [SV904: $i,SV558: $i,SV133: $i] :
( ( ( hBOOL @ ( c_in @ SV133 @ SV558 @ SV904 ) )
| ! [SY4156: $i] :
( ( hBOOL @ ( c_in @ SV133 @ SY4156 @ SV904 ) )
| ~ ( hBOOL @ ( c_in @ SV133 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4156 @ SV558 @ ( tc_fun @ SV904 @ tc_bool ) ) @ SV904 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2254]) ).
thf(2688,plain,
! [SV905: $i,SV559: $i,SV134: $i] :
( ( ! [SY4157: $i,SY4158: $i] :
( ( c_Com_Ocom_OLocal @ SV134 @ SV559 @ SV905 )
!= ( c_Com_Ocom_OWhile @ SY4157 @ SY4158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2255]) ).
thf(2689,plain,
! [SV906: $i,SV560: $i,SV135: $i] :
( ( ! [SY4159: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV135 @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV560 @ SV906 @ SY4159 @ ( tc_fun @ SV135 @ tc_bool ) ) )
| ! [SY4160: $i] :
( ( ( hAPP @ SV906 @ SY4160 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV135 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SY4160 @ SV560 @ SY4159 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2256]) ).
thf(2690,plain,
! [SV907: $i,SV561: $i,SV136: $i] :
( ( ! [SY4161: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV136 @ tc_bool ) ) @ SV561 @ SV136 @ ( tc_fun @ SV907 @ tc_bool ) ) @ SY4161 @ ( tc_fun @ SV907 @ tc_bool ) )
= SY4161 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2257]) ).
thf(2691,plain,
! [SV908: $i,SV562: $i,SV137: $i] :
( ( ! [SY4162: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV137 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV562 @ tc_bool ) ) @ SV908 @ SV562 @ ( tc_fun @ SY4162 @ tc_bool ) ) @ ( tc_fun @ SY4162 @ tc_bool ) )
= SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(2692,plain,
! [SV563: $i,SV138: $i] :
( ( c_Com_Ocom_OSKIP
= ( c_Com_Ocom_OWhile @ SV138 @ SV563 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2259]) ).
thf(2693,plain,
! [SV909: $i,SV564: $i,SV139: $i] :
( ( ! [SY4163: $i,SY4164: $i] :
( ( hBOOL @ ( c_in @ SV139 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV564 @ SV909 @ SY4163 @ ( tc_fun @ SY4164 @ tc_bool ) ) @ SY4164 ) )
| ! [SY4165: $i] :
( ~ ( hBOOL @ ( c_in @ SV139 @ ( hAPP @ SV909 @ SY4165 ) @ SY4164 ) )
| ~ ( hBOOL @ ( c_in @ SY4165 @ SV564 @ SY4163 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2260]) ).
thf(2694,plain,
! [SV910: $i,SV565: $i,SV140: $i] :
( ( ! [SY4166: $i,SY4167: $i] :
( ( hBOOL @ ( c_in @ SV140 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV565 @ SV910 @ SY4166 @ ( tc_fun @ SY4167 @ tc_bool ) ) @ SY4167 ) )
| ! [SY4168: $i] :
( ~ ( hBOOL @ ( c_in @ SV140 @ ( hAPP @ SV910 @ SY4168 ) @ SY4167 ) )
| ~ ( hBOOL @ ( c_in @ SY4168 @ SV565 @ SY4166 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2261]) ).
thf(2695,plain,
! [SV911: $i,SV566: $i,SV141: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV141 @ SV566 @ ( tc_fun @ SV911 @ tc_bool ) ) @ SV566 @ ( tc_fun @ SV911 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV141 @ SV566 @ ( tc_fun @ SV911 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2262]) ).
thf(2696,plain,
! [SV912: $i,SV567: $i,SV142: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV142 @ ( c_HOL_Ominus__class_Ominus @ SV567 @ SV142 @ ( tc_fun @ SV912 @ tc_bool ) ) @ ( tc_fun @ SV912 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV142 @ SV567 @ ( tc_fun @ SV912 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2263]) ).
thf(2697,plain,
! [SV913: $i,SV568: $i,SV143: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV143 @ tc_bool ) ) @ ( c_COMBK @ SV568 @ ( tc_fun @ SV913 @ tc_bool ) @ SV143 ) @ SV143 @ ( tc_fun @ SV913 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV913 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2264]) ).
thf(2698,plain,
! [SV144: $i] :
( ( ( class_HOL_Ominus @ SV144 )
= $false )
| ( ( ! [SY2228: $i,SY2229: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ SY2228 @ SY2229 @ ( tc_fun @ t_a @ SV144 ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ SY2228 @ v_x ) @ ( hAPP @ SY2229 @ v_x ) @ SV144 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2265]) ).
thf(2699,plain,
! [SV914: $i,SV569: $i,SV145: $i] :
( ( ! [SY4169: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV145 @ SV569 @ ( tc_fun @ SV914 @ tc_bool ) ) @ SY4169 @ ( tc_fun @ SV914 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV145 @ SY4169 @ ( tc_fun @ SV914 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV569 @ SY4169 @ ( tc_fun @ SV914 @ tc_bool ) ) @ ( tc_fun @ SV914 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2266]) ).
thf(2700,plain,
! [SV915: $i,SV570: $i,SV146: $i] :
( ( ! [SY4170: $i,SY4171: $i,SY4172: $i,SY4173: $i,SY4174: $i,SY4175: $i,SY4176: $i,SY4177: $i] :
( ( c_Com_Ocom_Ocom__case @ SV146 @ SV570 @ SV915 @ SY4170 @ SY4171 @ SY4172 @ SY4173 @ SY4174 @ ( c_Com_Ocom_OSemi @ SY4175 @ SY4176 ) @ SY4177 )
= ( hAPP @ ( hAPP @ SY4170 @ SY4175 ) @ SY4176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2267]) ).
thf(2701,plain,
! [SV916: $i,SV571: $i,SV147: $i] :
( ( ! [SY4178: $i,SY4179: $i] :
( ( c_Com_Ocom_OLocal @ SV147 @ SV571 @ SV916 )
!= ( c_Com_Ocom_OSemi @ SY4178 @ SY4179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2268]) ).
thf(2702,plain,
! [SV917: $i,SV572: $i,SV148: $i] :
( ( ( c_Set_Oinsert @ SV148 @ SV572 @ SV917 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ SV917 ) @ SV917 @ SV917 @ tc_bool ) @ SV148 ) @ SV917 ) @ SV572 @ ( tc_fun @ SV917 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2269]) ).
thf(2703,plain,
! [SV918: $i,SV573: $i,SV149: $i] :
( ( ! [SY4180: $i,SY4181: $i,SY4182: $i,SY4183: $i,SY4184: $i,SY4185: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV149 @ ( hAPP @ SV573 @ SV918 ) ) @ SY4180 ) )
| ~ ( hBOOL @ ( c_in @ SY4180 @ SV918 @ SY4181 ) )
| ! [SY3439: $i,SY3440: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV573 @ SY4182 @ SV149 @ SY4183 @ SY4184 @ SY4185 @ SY3439 @ SY3440 @ SY4181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2270]) ).
thf(2704,plain,
! [SV919: $i,SV574: $i,SV150: $i] :
( ( ! [SY4188: $i,SY4189: $i,SY4190: $i,SY4191: $i,SY4192: $i,SY4193: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV150 @ SV574 ) @ ( hAPP @ SV919 @ SY4188 ) ) )
| ~ ( hBOOL @ ( c_in @ SV574 @ SY4188 @ SY4189 ) )
| ! [SY4194: $i,SY4195: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY4190 @ SV919 @ SV150 @ SY4191 @ SY4192 @ SY4193 @ SY4194 @ SY4195 @ SY4189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2271]) ).
thf(2705,plain,
! [SV920: $i,SV575: $i,SV151: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV151 @ SV575 @ ( tc_fun @ SV920 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV575 @ SV151 @ ( tc_fun @ SV920 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2272]) ).
thf(2706,plain,
! [SV152: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV152 )
= $false )
| ( ( ! [SY2271: $i,SY2272: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2271 @ SY2272 @ SV152 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2272 @ SY2271 @ SV152 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2273]) ).
thf(2707,plain,
! [SV153: $i] :
( ( ( class_Lattices_Olattice @ SV153 )
= $false )
| ( ( ! [SY2273: $i,SY2274: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2273 @ SY2274 @ SV153 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2274 @ SY2273 @ SV153 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2274]) ).
thf(2708,plain,
! [SV921: $i,SV576: $i,SV154: $i] :
( ( ! [SY4196: $i] :
( ( c_Com_Ocom_OWhile @ SV154 @ SV576 )
!= ( c_Com_Ocom_OWhile @ SV921 @ SY4196 ) )
| ( SV154 = SV921 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2275]) ).
thf(2709,plain,
! [SV922: $i,SV577: $i,SV155: $i] :
( ( ! [SY4197: $i] :
( ( ( c_Com_Ocom_OWhile @ SV155 @ SV577 )
!= ( c_Com_Ocom_OWhile @ SV922 @ SY4197 ) )
| ( SV577 = SY4197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2276]) ).
thf(2710,plain,
! [SV578: $i,SV156: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ SV156 @ SV578 ) )
= $true )
| ( ( ~ ( c_Com_OWT @ SV578 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2277]) ).
thf(2711,plain,
! [SV157: $i,SV923: $i] :
( ( ( ~ ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ SV923 @ SV157 ) ) )
= $true )
| ( ( c_Com_OWT @ SV157 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2278]) ).
thf(2712,plain,
! [SV924: $i,SV579: $i,SV158: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV158 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV158 @ SV579 @ ( tc_fun @ SV924 @ tc_bool ) ) @ ( tc_fun @ SV924 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV158 @ SV579 @ ( tc_fun @ SV924 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2279]) ).
thf(2713,plain,
! [SV159: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV159 )
= $false )
| ( ( ! [SY2285: $i,SY2286: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2285 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2285 @ SY2286 @ SV159 ) @ SV159 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2285 @ SY2286 @ SV159 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2280]) ).
thf(2714,plain,
! [SV160: $i] :
( ( ( class_Lattices_Olattice @ SV160 )
= $false )
| ( ( ! [SY2287: $i,SY2288: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2287 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY2287 @ SY2288 @ SV160 ) @ SV160 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2287 @ SY2288 @ SV160 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2281]) ).
thf(2715,plain,
! [SV925: $i,SV580: $i,SV161: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ SV161 @ SV580 @ SV925 ) )
| ~ ( c_Com_OWT @ SV925 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2282]) ).
thf(2716,plain,
! [SV162: $i,SV926: $i] :
( ( ( ! [SY4198: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ SV926 @ SY4198 @ SV162 ) ) )
= $true )
| ( ( c_Com_OWT @ SV162 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(2717,plain,
! [SV927: $i,SV581: $i,SV163: $i] :
( ( ( c_Com_Ocom_OCond @ SV163 @ SV581 @ SV927 )
!= c_Com_Ocom_OSKIP )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(2718,plain,
! [SV928: $i,SV582: $i,SV164: $i] :
( ( ! [SY4199: $i,SY4200: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV164 @ SV582 @ SV928 @ ( tc_fun @ SY4199 @ tc_bool ) ) @ SY4200 ) )
| ! [SY4201: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV582 @ SY4201 ) @ SY4200 ) )
| ~ ( hBOOL @ ( c_in @ SY4201 @ SV164 @ SV928 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2285]) ).
thf(2719,plain,
! [SV929: $i,SV583: $i,SV165: $i] :
( ( ! [SY4202: $i,SY4203: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV165 @ SV583 @ SV929 @ ( tc_fun @ SY4202 @ tc_bool ) ) @ SY4203 ) )
| ! [SY4204: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV583 @ SY4204 ) @ SY4203 ) )
| ~ ( hBOOL @ ( c_in @ SY4204 @ SV165 @ SV929 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2286]) ).
thf(2720,plain,
! [SV930: $i,SV584: $i,SV166: $i] :
( ( ! [SY4205: $i,SY4206: $i] :
( ( c_Com_Ocom_OWhile @ SV166 @ SV584 )
!= ( c_Com_Ocom_OCond @ SV930 @ SY4205 @ SY4206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2287]) ).
thf(2721,plain,
! [SV931: $i,SV585: $i,SV167: $i] :
( ( ! [SY4207: $i,SY4208: $i] :
( ( c_Com_Ocom_OSemi @ SV167 @ SV585 )
!= ( c_Com_Ocom_OCall @ SV931 @ SY4207 @ SY4208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2288]) ).
thf(2722,plain,
! [SV932: $i,SV586: $i,SV168: $i] :
( ( ! [SY4209: $i] :
( ( SV168
= ( c_Suc @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ SV586 @ SV168 @ SV932 @ SY4209 ) ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ SV586 ) @ SV932 @ SV168 @ SY4209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2289]) ).
thf(2723,plain,
! [SV933: $i,SV587: $i,SV169: $i] :
( ( ! [SY4210: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV169 @ SV587 @ SV933 ) @ SY4210 @ ( tc_fun @ SV933 @ tc_bool ) )
= ( c_Set_Oinsert @ SV169 @ ( c_HOL_Ominus__class_Ominus @ SV587 @ SY4210 @ ( tc_fun @ SV933 @ tc_bool ) ) @ SV933 ) )
| ( hBOOL @ ( c_in @ SV169 @ SY4210 @ SV933 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2290]) ).
thf(2724,plain,
! [SV588: $i,SV170: $i] :
( ( ( SV170 = SV588 )
= $true )
| ( ( ! [SY3476: $i] :
~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV588 @ SY3476 @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2291]) ).
thf(2725,plain,
! [SV934: $i,SV589: $i,SV171: $i] :
( ( ~ ( hBOOL @ ( c_in @ SV171 @ SV589 @ SV934 ) )
| ! [SY4211: $i,SY4212: $i] : ( hBOOL @ ( c_in @ ( hAPP @ SY4211 @ SV171 ) @ ( c_Set_Oimage @ SY4211 @ SV589 @ SV934 @ SY4212 ) @ SY4212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(2726,plain,
! [SV935: $i,SV590: $i,SV172: $i] :
( ( ~ ( hBOOL @ ( c_in @ SV172 @ SV590 @ SV935 ) )
| ! [SY4213: $i,SY4214: $i] : ( hBOOL @ ( c_in @ ( hAPP @ SY4213 @ SV172 ) @ ( c_Set_Oimage @ SY4213 @ SV590 @ SV935 @ SY4214 ) @ SY4214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2293]) ).
thf(2727,plain,
! [SV936: $i,SV591: $i,SV173: $i] :
( ( ! [SY4215: $i] :
( ! [SY4216: $i] : ( hBOOL @ ( c_in @ ( hAPP @ SV173 @ SV591 ) @ ( c_Set_Oimage @ SV173 @ SV936 @ SY4215 @ SY4216 ) @ SY4216 ) )
| ~ ( hBOOL @ ( c_in @ SV591 @ SV936 @ SY4215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2294]) ).
thf(2728,plain,
! [SV937: $i,SV592: $i,SV174: $i] :
( ( ! [SY4217: $i] :
( ! [SY4218: $i] : ( hBOOL @ ( c_in @ ( hAPP @ SV174 @ SV592 ) @ ( c_Set_Oimage @ SV174 @ SV937 @ SY4217 @ SY4218 ) @ SY4218 ) )
| ~ ( hBOOL @ ( c_in @ SV592 @ SV937 @ SY4217 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2295]) ).
thf(2729,plain,
! [SV938: $i,SV593: $i,SV175: $i] :
( ( ! [SY4219: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV175 @ SV593 @ ( tc_fun @ SV938 @ tc_bool ) ) @ SY4219 @ ( tc_fun @ SV938 @ tc_bool ) )
| ~ ( c_lessequals @ SV175 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV593 @ SY4219 @ ( tc_fun @ SV938 @ tc_bool ) ) @ ( tc_fun @ SV938 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2296]) ).
thf(2730,plain,
! [SV939: $i,SV594: $i,SV176: $i] :
( ( ! [SY4220: $i] :
( ( c_lessequals @ SV176 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV594 @ SV939 @ ( tc_fun @ SY4220 @ tc_bool ) ) @ ( tc_fun @ SY4220 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV176 @ SV594 @ ( tc_fun @ SY4220 @ tc_bool ) ) @ SV939 @ ( tc_fun @ SY4220 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2297]) ).
thf(2731,plain,
! [SV595: $i,SV177: $i] :
( ( ( SV177 = SV595 )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ SV595 @ SV177 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2298]) ).
thf(2732,plain,
! [SV940: $i,SV596: $i,SV178: $i] :
( ( ( c_Natural_Oevalc @ SV178 @ SV596 @ SV940 )
| ! [SY4221: $i] :
~ ( c_Natural_Oevaln @ SV178 @ SV596 @ SY4221 @ SV940 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2299]) ).
thf(2733,plain,
! [SV941: $i,SV597: $i,SV179: $i] :
( ( ( c_Natural_Oevalc @ SV179 @ SV597 @ SV941 )
| ! [SY4222: $i] :
~ ( c_Natural_Oevaln @ SV179 @ SV597 @ SY4222 @ SV941 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2300]) ).
thf(2734,plain,
! [SV942: $i,SV598: $i,SV180: $i] :
( ( ~ ( class_HOL_Oord @ SV180 )
| ! [SY4223: $i] :
( ( c_lessequals @ ( hAPP @ SV598 @ SV942 ) @ ( hAPP @ SY4223 @ SV942 ) @ SV180 )
| ! [SY3499: $i] :
~ ( c_lessequals @ SV598 @ SY4223 @ ( tc_fun @ SY3499 @ SV180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2301]) ).
thf(2735,plain,
! [SV181: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV181 )
= $false )
| ( ( ! [SY2354: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ SV181 ) @ SY2354 @ SV181 )
= SY2354 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2302]) ).
thf(2736,plain,
! [SV182: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV182 )
= $false )
| ( ( ! [SY2355: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2355 @ ( c_Orderings_Obot__class_Obot @ SV182 ) @ SV182 )
= SY2355 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2303]) ).
thf(2737,plain,
! [SV183: $i] :
( ( ( class_Orderings_Obot @ SV183 )
= $false )
| ( ( ! [SY2356: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV183 ) @ SY2356 @ SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2304]) ).
thf(2738,plain,
! [SV184: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV184 )
= $false )
| ( ( ! [SY2357: $i] :
( ! [SY2358: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2357 @ SY2358 @ SV184 )
!= ( c_Orderings_Obot__class_Obot @ SV184 ) )
| ( SY2357
= ( c_Orderings_Obot__class_Obot @ SV184 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2305]) ).
thf(2739,plain,
! [SV185: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV185 )
= $false )
| ( ( ! [SY2359: $i,SY2360: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2359 @ SY2360 @ SV185 )
!= ( c_Orderings_Obot__class_Obot @ SV185 ) )
| ( SY2360
= ( c_Orderings_Obot__class_Obot @ SV185 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2306]) ).
thf(2740,plain,
! [SV943: $i,SV599: $i,SV187: $i] :
( ( ! [SY4225: $i] :
( ( c_Set_Oimage @ SV187 @ SV599 @ SV943 @ SY4225 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4225 @ tc_bool ) ) )
| ( SV599
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV943 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2307]) ).
thf(2741,plain,
! [SV944: $i,SV600: $i,SV188: $i] :
( ( ! [SY4226: $i,SY4227: $i,SY4228: $i,SY4229: $i] :
( ( ( hAPP @ SV188 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_bool ) ) )
= SV944 )
| ! [SY4230: $i,SY4231: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV188 @ SY4226 @ SY4227 @ SY4228 @ SY4229 @ SY4230 @ SY4231 @ SV944 @ SV600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2308]) ).
thf(2742,plain,
! [SV945: $i,SV601: $i,SV189: $i] :
( ( ! [SY4232: $i,SY4233: $i,SY4234: $i,SY4235: $i] :
( ( ( hAPP @ SV189 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV601 @ tc_bool ) ) )
= SV945 )
| ! [SY4236: $i,SY4237: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY4232 @ SV189 @ SY4233 @ SY4234 @ SY4235 @ SY4236 @ SV945 @ SY4237 @ SV601 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2309]) ).
thf(2743,plain,
! [SV602: $i,SV190: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV190 @ tc_bool ) )
!= ( c_Collect @ SV602 @ SV190 ) )
= $true )
| ( ( ! [SY3516: $i] :
~ ( hBOOL @ ( hAPP @ SV602 @ SY3516 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2310]) ).
thf(2744,plain,
! [SV603: $i,SV191: $i] :
( ( hBOOL @ ( c_in @ SV191 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV603 @ tc_bool ) ) @ SV603 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2311]) ).
thf(2745,plain,
! [SV604: $i,SV192: $i] :
( ( ( hBOOL @ ( hAPP @ SV192 @ SV604 ) )
= $true )
| ( ( ! [SY3517: $i] :
~ ( hBOOL @ ( c_in @ SV604 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3517 @ tc_bool ) ) @ SY3517 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2312]) ).
thf(2746,plain,
! [SV605: $i,SV193: $i] :
( ( hBOOL @ ( c_in @ SV193 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV605 @ tc_bool ) ) @ SV605 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2313]) ).
thf(2747,plain,
! [SV606: $i,SV194: $i] :
( ( hBOOL @ ( c_in @ SV194 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV606 @ tc_bool ) ) @ SV606 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2314]) ).
thf(2748,plain,
! [SV607: $i,SV196: $i] :
( ( ( SV196
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV607 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV196 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV607 @ tc_bool ) ) @ ( tc_fun @ SV607 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2315]) ).
thf(2749,plain,
! [SV946: $i,SV197: $i] :
( ( ( ( c_Collect @ SV197 @ SV946 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV946 @ tc_bool ) ) )
= $true )
| ( ( ! [SY2389: $i] :
~ ( hBOOL @ ( hAPP @ SV197 @ SY2389 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2316]) ).
thf(2750,plain,
! [SV947: $i,SV608: $i,SV198: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV198 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV608 @ tc_bool ) ) @ SV608 ) @ SV947 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2317]) ).
thf(2751,plain,
! [SV948: $i,SV615: $i,SV205: $i] :
( ( ! [SY4238: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV205 @ tc_bool ) )
!= ( c_Set_Oimage @ SV615 @ SV948 @ SY4238 @ SV205 ) )
| ( SV948
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4238 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2324]) ).
thf(2752,plain,
! [SV949: $i,SV616: $i,SV206: $i] :
( ( ( c_Set_Oimage @ SV206 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV616 @ tc_bool ) ) @ SV616 @ SV949 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV949 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2325]) ).
thf(2753,plain,
! [SV617: $i,SV207: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV207 @ SV617 ) ) )
= $true )
| ( ( ! [SY3522: $i] :
~ ( hBOOL @ ( c_in @ SV617 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3522 @ tc_bool ) ) @ SY3522 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2326]) ).
thf(2754,plain,
! [SV950: $i,SV618: $i,SV208: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV208 @ SV618 @ ( tc_fun @ SV950 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV950 @ tc_bool ) ) )
| ( SV618
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV950 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2327]) ).
thf(2755,plain,
! [SV951: $i,SV619: $i,SV209: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV209 @ SV619 @ ( tc_fun @ SV951 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV951 @ tc_bool ) ) )
| ( SV209
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV951 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2328]) ).
thf(2756,plain,
! [SV952: $i,SV620: $i,SV210: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV210 @ tc_bool ) )
= ( c_Set_Oimage @ SV620 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV952 @ tc_bool ) ) @ SV952 @ SV210 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2329]) ).
thf(2757,plain,
! [SV953: $i,SV622: $i,SV212: $i] :
( ( ( ( c_Set_Oinsert @ SV212 @ ( c_HOL_Ominus__class_Ominus @ SV622 @ ( c_Set_Oinsert @ SV212 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV953 @ tc_bool ) ) @ SV953 ) @ ( tc_fun @ SV953 @ tc_bool ) ) @ SV953 )
= SV622 )
| ~ ( hBOOL @ ( c_in @ SV212 @ SV622 @ SV953 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2331]) ).
thf(2758,plain,
! [SV954: $i,SV623: $i,SV213: $i] :
( ( ! [SY4239: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ SV213 @ SV623 @ SV954 ) @ SY4239 @ SV954 @ SV623 )
= ( c_Set_Oinsert @ SV213 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV623 @ tc_bool ) ) @ SV623 ) )
| ( SY4239
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV954 @ tc_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2332]) ).
thf(2759,plain,
! [SV214: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV214 )
= $false )
| ( ( ! [SY2417: $i,SY2418: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SY2417 @ ( c_Set_Oinsert @ SY2418 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV214 @ tc_bool ) ) @ SV214 ) @ SV214 ) @ SV214 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY2417 @ SY2418 @ SV214 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2333]) ).
thf(2760,plain,
! [SV955: $i,SV624: $i,SV215: $i] :
( ( ! [SY4240: $i] :
( ( c_lessequals @ SV215 @ ( c_Set_Oinsert @ SV624 @ SV955 @ SY4240 ) @ ( tc_fun @ SY4240 @ tc_bool ) )
| ~ ( c_lessequals @ SV215 @ SV955 @ ( tc_fun @ SY4240 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV215 @ ( c_Set_Oinsert @ SV624 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4240 @ tc_bool ) ) @ SY4240 ) @ ( tc_fun @ SY4240 @ tc_bool ) ) @ SV955 @ ( tc_fun @ SY4240 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2334]) ).
thf(2761,plain,
! [SV956: $i,SV625: $i,SV216: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV216 @ SV625 @ SV956 ) @ ( c_Set_Oinsert @ SV216 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV956 @ tc_bool ) ) @ SV956 ) @ ( tc_fun @ SV956 @ tc_bool ) )
= SV625 )
| ( hBOOL @ ( c_in @ SV216 @ SV625 @ SV956 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2335]) ).
thf(2762,plain,
! [SV957: $i,SV626: $i,SV217: $i] :
( ( ! [SY4241: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV217 @ SV626 @ SV957 ) @ ( c_Set_Oinsert @ SV217 @ SY4241 @ SV957 ) @ ( tc_fun @ SV957 @ tc_bool ) )
| ~ ( c_lessequals @ SV626 @ SY4241 @ ( tc_fun @ SV957 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2336]) ).
thf(2763,plain,
! [SV958: $i,SV627: $i,SV218: $i] :
( ( ! [SY4242: $i] :
( ( hBOOL @ ( c_in @ SV218 @ ( c_Set_Oinsert @ SV627 @ SV958 @ SY4242 ) @ SY4242 ) )
| ~ ( hBOOL @ ( c_in @ SV218 @ SV958 @ SY4242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2337]) ).
thf(2764,plain,
! [SV959: $i,SV628: $i,SV219: $i] :
( ( ! [SY4243: $i] :
( ( hBOOL @ ( c_in @ SV219 @ ( c_Set_Oinsert @ SV628 @ SV959 @ SY4243 ) @ SY4243 ) )
| ~ ( hBOOL @ ( c_in @ SV219 @ SV959 @ SY4243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2338]) ).
thf(2765,plain,
! [SV960: $i,SV629: $i,SV220: $i] :
( ( ! [SY4244: $i,SY4245: $i] :
( ( c_Set_Oimage @ SV220 @ ( c_Set_Oinsert @ SV629 @ SV960 @ SY4244 ) @ SY4244 @ SY4245 )
= ( c_Set_Oinsert @ ( hAPP @ SV220 @ SV629 ) @ ( c_Set_Oimage @ SV220 @ SV960 @ SY4244 @ SY4245 ) @ SY4245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2339]) ).
thf(2766,plain,
! [SV961: $i,SV630: $i,SV221: $i] :
( ( ! [SY4246: $i,SY4247: $i,SY4248: $i,SY4249: $i,SY4250: $i,SY4251: $i] :
( ( ( hAPP @ SV221 @ ( c_Set_Oinsert @ SV630 @ SV961 @ SY4246 ) )
= ( hAPP @ ( hAPP @ SY4247 @ SV630 ) @ ( hAPP @ SV221 @ SV961 ) ) )
| ! [SY2445: $i,SY2446: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV221 @ SY4248 @ SY4249 @ SY4250 @ SY4247 @ SY4251 @ SY2445 @ SY2446 @ SY4246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2340]) ).
thf(2767,plain,
! [SV962: $i,SV631: $i,SV222: $i] :
( ( ! [SY4254: $i,SY4255: $i,SY4256: $i,SY4257: $i,SY4258: $i,SY4259: $i] :
( ( ( hAPP @ SV222 @ ( c_Set_Oinsert @ SV631 @ SV962 @ SY4254 ) )
= ( hAPP @ ( hAPP @ SY4255 @ SV631 ) @ ( hAPP @ SV222 @ SV962 ) ) )
| ! [SY2455: $i,SY2456: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY4256 @ SV222 @ SY4257 @ SY4258 @ SY4259 @ SY4255 @ SY2455 @ SY2456 @ SY4254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2341]) ).
thf(2768,plain,
! [SV963: $i,SV632: $i,SV223: $i] :
( ( ( hBOOL @ ( c_in @ SV223 @ SV632 @ SV963 ) )
| ! [SY4262: $i] :
( ( SV223 = SY4262 )
| ~ ( hBOOL @ ( c_in @ SV223 @ ( c_Set_Oinsert @ SY4262 @ SV632 @ SV963 ) @ SV963 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2342]) ).
thf(2769,plain,
! [SV964: $i,SV633: $i,SV224: $i] :
( ( c_lessequals @ SV224 @ ( c_Set_Oinsert @ SV633 @ SV224 @ SV964 ) @ ( tc_fun @ SV964 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(2770,plain,
! [SV965: $i,SV634: $i,SV225: $i] :
( ( ! [SY4263: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV225 @ ( c_Set_Oinsert @ SV634 @ SV965 @ SY4263 ) @ ( tc_fun @ SY4263 @ tc_bool ) )
= ( c_Set_Oinsert @ SV634 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV225 @ SV965 @ ( tc_fun @ SY4263 @ tc_bool ) ) @ SY4263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2344]) ).
thf(2771,plain,
! [SV966: $i,SV635: $i,SV226: $i] :
( ( ! [SY4264: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV226 @ SV635 @ SV966 ) @ SY4264 @ ( tc_fun @ SV966 @ tc_bool ) )
= ( c_Set_Oinsert @ SV226 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV635 @ SY4264 @ ( tc_fun @ SV966 @ tc_bool ) ) @ SV966 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2345]) ).
thf(2772,plain,
! [SV967: $i,SV636: $i,SV227: $i] :
( ( ! [SY4265: $i] :
( ( c_lessequals @ SV227 @ ( c_Set_Oinsert @ SV636 @ SV967 @ SY4265 ) @ ( tc_fun @ SY4265 @ tc_bool ) )
| ~ ( c_lessequals @ SV227 @ SV967 @ ( tc_fun @ SY4265 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2346]) ).
thf(2773,plain,
! [SV968: $i,SV637: $i,SV228: $i] :
( ( ( c_lessequals @ SV228 @ SV637 @ ( tc_fun @ SV968 @ tc_bool ) )
| ! [SY4266: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SY4266 @ SV228 @ SV968 ) @ SV637 @ ( tc_fun @ SV968 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2347]) ).
thf(2774,plain,
! [SV969: $i,SV638: $i,SV229: $i] :
( ( hBOOL @ ( c_in @ SV229 @ ( c_Set_Oinsert @ SV229 @ SV638 @ SV969 ) @ SV969 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2348]) ).
thf(2775,plain,
! [SV970: $i,SV639: $i,SV230: $i] :
( ( hBOOL @ ( c_in @ SV230 @ ( c_Set_Oinsert @ SV230 @ SV639 @ SV970 ) @ SV970 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2349]) ).
thf(2776,plain,
! [SV971: $i,SV640: $i,SV231: $i] :
( ( hBOOL @ ( c_in @ SV231 @ ( c_Set_Oinsert @ SV231 @ SV640 @ SV971 ) @ SV971 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2350]) ).
thf(2777,plain,
! [SV972: $i,SV641: $i,SV232: $i] :
( ( ! [SY4267: $i] :
( ( ( c_Set_Oinsert @ SV232 @ SV641 @ SV972 )
!= ( c_Set_Oinsert @ SV232 @ SY4267 @ SV972 ) )
| ( hBOOL @ ( c_in @ SV232 @ SY4267 @ SV972 ) )
| ( SV641 = SY4267 )
| ( hBOOL @ ( c_in @ SV232 @ SV641 @ SV972 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2351]) ).
thf(2778,plain,
! [SV973: $i,SV642: $i,SV233: $i] :
( ( ( ( c_Set_Oinsert @ SV233 @ SV642 @ SV973 )
= SV642 )
| ~ ( hBOOL @ ( c_in @ SV233 @ SV642 @ SV973 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2352]) ).
thf(2779,plain,
! [SV974: $i,SV643: $i,SV234: $i] :
( ( ! [SY4268: $i,SY4269: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV234 @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV643 ) @ SV974 @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ SY4268 @ tc_Com_Opname @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SY4269 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SV643 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV234 @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV643 ) @ SV974 @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ SY4268 @ tc_Com_Opname @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SY4269 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV643 ) @ SV974 @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ SY4268 @ tc_Com_Opname @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SY4269 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SV643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2353]) ).
thf(2780,plain,
! [SV975: $i,SV644: $i,SV236: $i] :
( ( ( c_Com_Ocom_OWhile @ SV236 @ SV644 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SV975 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2355]) ).
thf(2781,plain,
! [SV976: $i,SV645: $i,SV237: $i] :
( ( ! [SY4270: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ SV237 )
!= ( c_Com_Ocom_OCond @ SV645 @ SV976 @ SY4270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2356]) ).
thf(2782,plain,
! [SV977: $i,SV646: $i,SV238: $i] :
( ( ! [SY4271: $i] :
( ( c_Com_Ocom_OCond @ SV238 @ SV646 @ SV977 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SY4271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2357]) ).
thf(2783,plain,
! [SV978: $i,SV647: $i,SV239: $i] :
( ( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OLocal @ SV239 @ SV647 @ SV978 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2358]) ).
thf(2784,plain,
! [SV979: $i,SV648: $i,SV240: $i] :
( ( ! [SY4272: $i] :
( ( c_Natural_Oevaln @ SV240 @ SV648 @ ( c_Suc @ SV979 ) @ SY4272 )
| ~ ( c_Natural_Oevaln @ SV240 @ SV648 @ SV979 @ SY4272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2359]) ).
thf(2785,plain,
! [SV980: $i,SV649: $i,SV241: $i] :
( ( ! [SY4273: $i,SY4274: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV241 @ SV649 @ ( tc_fun @ SV980 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SY4273 @ SY4274 @ ( tc_fun @ SV980 @ tc_bool ) ) @ ( tc_fun @ SV980 @ tc_bool ) )
| ~ ( c_lessequals @ SY4274 @ SV649 @ ( tc_fun @ SV980 @ tc_bool ) )
| ~ ( c_lessequals @ SV241 @ SY4273 @ ( tc_fun @ SV980 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2360]) ).
thf(2786,plain,
! [SV981: $i,SV650: $i,SV242: $i] :
( ( ! [SY4275: $i] :
( ( c_Natural_Oevaln @ SV242 @ SV650 @ SV981 @ SY4275 )
| ! [SY4276: $i] :
( ( hBOOL @ ( hAPP @ SY4276 @ SV650 ) )
| ! [SY4277: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SY4276 @ SY4277 @ SV242 ) @ SV650 @ SV981 @ SY4275 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2361]) ).
thf(2787,plain,
! [SV982: $i,SV651: $i,SV243: $i] :
( ( ! [SY4278: $i,SY4279: $i,SY4280: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV243 @ SV651 @ SV982 ) @ SY4278 @ SY4279 @ SY4280 )
| ~ ( c_Natural_Oevaln @ SV982 @ SY4278 @ SY4279 @ SY4280 )
| ( hBOOL @ ( hAPP @ SV243 @ SY4278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2362]) ).
thf(2788,plain,
! [SV983: $i,SV652: $i,SV244: $i] :
( ( ! [SY4281: $i,SY4282: $i] :
( ( c_Com_Ocom_OWhile @ SV244 @ SV652 )
!= ( c_Com_Ocom_OCall @ SV983 @ SY4281 @ SY4282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2363]) ).
thf(2789,plain,
! [SV653: $i,SV246: $i] :
( ( ( SV246 = SV653 )
= $true )
| ( ( ! [SY3601: $i] :
( ~ ( c_lessequals @ SV653 @ SV246 @ ( tc_fun @ SY3601 @ tc_bool ) )
| ~ ( c_lessequals @ SV246 @ SV653 @ ( tc_fun @ SY3601 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2364]) ).
thf(2790,plain,
! [SV654: $i,SV247: $i] :
( ( ( SV247 = SV654 )
= $true )
| ( ( ! [SY3602: $i,SY3603: $i] :
( ~ ( c_Natural_Oevalc @ SY3602 @ SY3603 @ SV247 )
| ~ ( c_Natural_Oevalc @ SY3602 @ SY3603 @ SV654 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2365]) ).
thf(2791,plain,
! [SV655: $i,SV248: $i] :
( ( ( SV248 = SV655 )
= $true )
| ( ( ! [SY3604: $i] :
( ~ ( c_lessequals @ SV655 @ SV248 @ ( tc_fun @ SY3604 @ tc_bool ) )
| ~ ( c_lessequals @ SV248 @ SV655 @ ( tc_fun @ SY3604 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2366]) ).
thf(2792,plain,
! [SV249: $i] :
( ( ( class_Orderings_Oorder @ SV249 )
= $false )
| ( ( ! [SY2527: $i,SY2528: $i] :
( ( SY2527 = SY2528 )
| ~ ( c_lessequals @ SY2528 @ SY2527 @ SV249 )
| ~ ( c_lessequals @ SY2527 @ SY2528 @ SV249 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2367]) ).
thf(2793,plain,
! [SV250: $i] :
( ( ( class_Orderings_Oorder @ SV250 )
= $false )
| ( ( ! [SY2529: $i,SY2530: $i] :
( ( SY2529 = SY2530 )
| ~ ( c_lessequals @ SY2530 @ SY2529 @ SV250 )
| ~ ( c_lessequals @ SY2529 @ SY2530 @ SV250 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2368]) ).
thf(2794,plain,
! [SV251: $i] :
( ( ( class_Orderings_Oorder @ SV251 )
= $false )
| ( ( ! [SY2531: $i,SY2532: $i] :
( ( SY2531 = SY2532 )
| ~ ( c_lessequals @ SY2531 @ SY2532 @ SV251 )
| ~ ( c_lessequals @ SY2532 @ SY2531 @ SV251 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2369]) ).
thf(2795,plain,
! [SV252: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV252 )
= $false )
| ( ( ! [SY2533: $i,SY2534: $i] :
( ( c_lessequals @ SY2533 @ SY2534 @ SV252 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SY2533 @ SY2534 @ SV252 ) @ ( c_HOL_Ozero__class_Ozero @ SV252 ) @ SV252 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2370]) ).
thf(2796,plain,
! [SV253: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV253 )
= $false )
| ( ( ! [SY2535: $i,SY2536: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SY2535 @ SY2536 @ SV253 ) @ ( c_HOL_Ozero__class_Ozero @ SV253 ) @ SV253 )
| ~ ( c_lessequals @ SY2535 @ SY2536 @ SV253 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2371]) ).
thf(2797,plain,
! [SV984: $i,SV656: $i,SV254: $i] :
( ( ( c_Com_Ocom_OLocal @ SV254 @ SV656 @ SV984 )
!= c_Com_Ocom_OSKIP )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2372]) ).
thf(2798,plain,
! [SV255: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV255 )
= $false )
| ( ( ! [SY2539: $i,SY2540: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2539 @ SY2540 @ SV255 )
= SY2539 )
| ~ ( c_lessequals @ SY2540 @ SY2539 @ SV255 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2799,plain,
! [SV256: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV256 )
= $false )
| ( ( ! [SY2541: $i,SY2542: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2541 @ SY2542 @ SV256 )
!= SY2542 )
| ( c_lessequals @ SY2541 @ SY2542 @ SV256 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2374]) ).
thf(2800,plain,
! [SV257: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV257 )
= $false )
| ( ( ! [SY2543: $i,SY2544: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SY2543 @ SY2544 @ SV257 )
= SY2544 )
| ~ ( c_lessequals @ SY2543 @ SY2544 @ SV257 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2375]) ).
thf(2801,plain,
! [SV985: $i,SV657: $i,SV258: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV258 @ SV657 @ ( tc_fun @ SV985 @ tc_bool ) )
= SV657 )
| ~ ( c_lessequals @ SV258 @ SV657 @ ( tc_fun @ SV985 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2376]) ).
thf(2802,plain,
! [SV986: $i,SV658: $i,SV259: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV259 @ SV658 @ ( tc_fun @ SV986 @ tc_bool ) )
= SV259 )
| ~ ( c_lessequals @ SV658 @ SV259 @ ( tc_fun @ SV986 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2377]) ).
thf(2803,plain,
! [SV987: $i,SV659: $i,SV260: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV260 @ SV659 @ ( tc_fun @ SV987 @ tc_bool ) )
!= SV659 )
| ( c_lessequals @ SV260 @ SV659 @ ( tc_fun @ SV987 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2378]) ).
thf(2804,plain,
! [SV988: $i,SV661: $i,SV264: $i] :
( ( ! [SY4283: $i,SY4284: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV264 @ SV661 ) @ SV988 ) )
| ! [SY4285: $i] :
( ~ ( c_Natural_Oevaln @ SY4283 @ SY4284 @ SY4285 @ SV988 )
| ! [SY3613: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY3613 @ SV661 ) @ SY4284 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ SY4285 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY3613 ) @ SY4283 ) @ SV264 ) @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2382]) ).
thf(2805,plain,
! [SV989: $i,SV662: $i,SV265: $i] :
( ( ( c_Natural_Oevalc @ SV265 @ SV662 @ SV989 )
| ! [SY4287: $i] :
( ( hBOOL @ ( hAPP @ SY4287 @ SV662 ) )
| ! [SY4288: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY4287 @ SY4288 @ SV265 ) @ SV662 @ SV989 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2383]) ).
thf(2806,plain,
! [SV990: $i,SV663: $i,SV266: $i] :
( ( ! [SY4289: $i,SY4290: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV266 @ SV663 @ SV990 ) @ SY4289 @ SY4290 )
| ~ ( c_Natural_Oevalc @ SV990 @ SY4289 @ SY4290 )
| ( hBOOL @ ( hAPP @ SV266 @ SY4289 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2384]) ).
thf(2807,plain,
! [SV991: $i,SV664: $i,SV267: $i] :
( ( ! [SY4291: $i,SY4292: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ SV267 @ SV664 @ SV991 ) @ SY4291 @ SV991 @ ( tc_fun @ SY4292 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SY4291 @ SV267 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV664 @ SY4291 @ SV991 @ ( tc_fun @ SY4292 @ tc_bool ) ) @ ( tc_fun @ SY4292 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2385]) ).
thf(2808,plain,
! [SV268: $i,SV992: $i] :
( ( ( ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV992 @ SV268 ) ) )
= $true )
| ( ( c_Com_OWT @ SV268 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2386]) ).
thf(2809,plain,
! [SV993: $i,SV269: $i] :
( ( ( ~ ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV269 @ SV993 ) ) )
= $true )
| ( ( c_Com_OWT @ SV269 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2387]) ).
thf(2810,plain,
! [SV270: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV270 )
= $false )
| ( ( ! [SY2572: $i,SY2573: $i] :
( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ SY2572 @ SV270 ) @ SY2573 @ SV270 )
| ~ ( hBOOL @ ( c_in @ SY2573 @ SY2572 @ SV270 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2388]) ).
thf(2811,plain,
! [SV271: $i] :
( ( ( class_Orderings_Oorder @ SV271 )
= $false )
| ( ( ! [SY2574: $i,SY2575: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV271 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2574 @ SY2575 @ SV271 ) )
| ( c_lessequals @ SY2574 @ SY2575 @ SV271 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2389]) ).
thf(2812,plain,
! [SV272: $i] :
( ( ( class_Orderings_Oorder @ SV272 )
= $false )
| ( ( ! [SY2576: $i,SY2577: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV272 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2576 @ SY2577 @ SV272 ) )
| ~ ( c_lessequals @ SY2576 @ SY2577 @ SV272 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2390]) ).
thf(2813,plain,
! [SV994: $i,SV665: $i,SV273: $i] :
( ( ! [SY4293: $i,SY4294: $i,SY4295: $i,SY4296: $i,SY4297: $i,SY4298: $i,SY4299: $i,SY4300: $i,SY4301: $i] :
( ( c_Com_Ocom_Ocom__case @ SV273 @ SV665 @ SV994 @ SY4293 @ SY4294 @ SY4295 @ SY4296 @ SY4297 @ ( c_Com_Ocom_OLocal @ SY4298 @ SY4299 @ SY4300 ) @ SY4301 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV994 @ SY4298 ) @ SY4299 ) @ SY4300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2391]) ).
thf(2814,plain,
! [SV995: $i,SV666: $i,SV274: $i] :
( ( ! [SY4302: $i,SY4303: $i,SY4304: $i,SY4305: $i,SY4306: $i,SY4307: $i,SY4308: $i,SY4309: $i] :
( ( c_Com_Ocom_Ocom__case @ SV274 @ SV666 @ SV995 @ SY4302 @ SY4303 @ SY4304 @ SY4305 @ SY4306 @ ( c_Com_Ocom_OWhile @ SY4307 @ SY4308 ) @ SY4309 )
= ( hAPP @ ( hAPP @ SY4304 @ SY4307 ) @ SY4308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2392]) ).
thf(2815,plain,
! [SV996: $i,SV667: $i,SV275: $i] :
( ( ! [SY4310: $i,SY4311: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV275 @ SV667 @ ( tc_fun @ SV996 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4310 @ SY4311 @ ( tc_fun @ SV996 @ tc_bool ) ) @ ( tc_fun @ SV996 @ tc_bool ) )
| ~ ( c_lessequals @ SV667 @ SY4311 @ ( tc_fun @ SV996 @ tc_bool ) )
| ~ ( c_lessequals @ SV275 @ SY4310 @ ( tc_fun @ SV996 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2393]) ).
thf(2816,plain,
! [SV997: $i,SV668: $i,SV276: $i] :
( ( ! [SY4312: $i,SY4313: $i,SY4314: $i,SY4315: $i] :
( ( c_Fun_Ocomp @ SV276 @ ( c_Fun_Ocomp @ SV668 @ SV997 @ SY4312 @ SY4313 @ SY4314 ) @ SY4313 @ SY4315 @ SY4314 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV276 @ SV668 @ SY4313 @ SY4315 @ SY4312 ) @ SV997 @ SY4312 @ SY4315 @ SY4314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2394]) ).
thf(2817,plain,
! [SV669: $i,SV277: $i] :
( ( ( c_Com_Ocom_OSemi @ SV277 @ SV669 )
= c_Com_Ocom_OSKIP )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2395]) ).
thf(2818,plain,
! [SV998: $i,SV670: $i,SV278: $i] :
( ( ! [SY4316: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV278 @ SV670 @ SV998 @ SY4316 @ t_a ) @ v_x )
= ( hAPP @ SV278 @ ( hAPP @ SV670 @ v_x ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2396]) ).
thf(2819,plain,
! [SV999: $i,SV671: $i,SV279: $i] :
( ( ! [SY4317: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ SV279 @ SV671 @ SV999 ) @ SY4317 @ ( tc_fun @ SV999 @ tc_bool ) )
| ~ ( c_lessequals @ SV671 @ SY4317 @ ( tc_fun @ SV999 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV279 @ SY4317 @ SV999 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2397]) ).
thf(2820,plain,
! [SV1000: $i,SV672: $i,SV280: $i] :
( ( ! [SY4318: $i,SY4319: $i,SY4320: $i] :
( ( c_Set_Oimage @ SV280 @ ( c_Set_Oimage @ SV672 @ SV1000 @ SY4318 @ SY4319 ) @ SY4319 @ SY4320 )
= ( c_Set_Oimage @ ( c_COMBB @ SV280 @ SV672 @ SY4319 @ SY4320 @ SY4318 ) @ SV1000 @ SY4318 @ SY4320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2398]) ).
thf(2821,plain,
! [SV1001: $i,SV673: $i,SV281: $i] :
( ( ! [SY4321: $i,SY4322: $i,SY4323: $i] :
( ( ( c_Com_Ocom_OLocal @ SV281 @ SV673 @ SV1001 )
!= ( c_Com_Ocom_OLocal @ SY4321 @ SY4322 @ SY4323 ) )
| ( SV1001 = SY4323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2399]) ).
thf(2822,plain,
! [SV1002: $i,SV674: $i,SV282: $i] :
( ( ! [SY4324: $i,SY4325: $i] :
( ! [SY4326: $i] :
( ( c_Com_Ocom_OLocal @ SV282 @ SV674 @ SV1002 )
!= ( c_Com_Ocom_OLocal @ SY4324 @ SY4325 @ SY4326 ) )
| ( SV674 = SY4325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2400]) ).
thf(2823,plain,
! [SV1003: $i,SV675: $i,SV283: $i] :
( ( ! [SY4327: $i] :
( ! [SY4328: $i,SY4329: $i] :
( ( c_Com_Ocom_OLocal @ SV283 @ SV675 @ SV1003 )
!= ( c_Com_Ocom_OLocal @ SY4327 @ SY4328 @ SY4329 ) )
| ( SV283 = SY4327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2401]) ).
thf(2824,plain,
! [SV676: $i,SV284: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV284 @ SV676 ) )
= $true )
| ( ( ~ ( c_Com_OWT @ SV676 )
| ~ ( c_Com_OWT @ SV284 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2402]) ).
thf(2825,plain,
! [SV1004: $i,SV677: $i,SV285: $i] :
( ( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCall @ SV285 @ SV677 @ SV1004 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2403]) ).
thf(2826,plain,
! [SV1005: $i,SV678: $i,SV286: $i] :
( ( ! [SY4330: $i,SY4331: $i,SY4332: $i] :
( ( c_Set_Oimage @ ( c_Fun_Ocomp @ SV286 @ SV678 @ SV1005 @ SY4330 @ SY4331 ) @ SY4332 @ SY4331 @ SY4330 )
= ( c_Set_Oimage @ SV286 @ ( c_Set_Oimage @ SV678 @ SY4332 @ SY4331 @ SV1005 ) @ SV1005 @ SY4330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(2827,plain,
! [SV1006: $i,SV679: $i,SV287: $i] :
( ( ! [SY4333: $i] :
( ( c_Com_Ocom_OWhile @ SV287 @ SV679 )
!= ( c_Com_Ocom_OSemi @ SV1006 @ SY4333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2405]) ).
thf(2828,plain,
! [SV1007: $i,SV680: $i,SV288: $i] :
( ( ! [SY4334: $i] :
( ( hBOOL @ ( c_in @ SV288 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV680 @ SV1007 @ ( tc_fun @ SY4334 @ tc_bool ) ) @ SY4334 ) )
| ~ ( hBOOL @ ( c_in @ SV288 @ SV1007 @ SY4334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2406]) ).
thf(2829,plain,
! [SV1008: $i,SV681: $i,SV289: $i] :
( ( ! [SY4335: $i] :
( ( hBOOL @ ( c_in @ SV289 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV681 @ SV1008 @ ( tc_fun @ SY4335 @ tc_bool ) ) @ SY4335 ) )
| ~ ( hBOOL @ ( c_in @ SV289 @ SV681 @ SY4335 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2407]) ).
thf(2830,plain,
! [SV1009: $i,SV682: $i,SV290: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV290 @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV682 @ tc_bool ) ) @ ( tc_fun @ SV682 @ tc_bool ) @ SV1009 ) @ SV1009 @ ( tc_fun @ SV682 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV682 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2408]) ).
thf(2831,plain,
! [SV683: $i,SV291: $i] :
( ( ( hBOOL @ ( hAPP @ SV291 @ SV683 ) )
= $true )
| ( ( ! [SY3682: $i] :
( ( SY3682 = SV683 )
| ! [SY3683: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV291 @ SY3683 ) @ SV683 @ SY3682 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2409]) ).
thf(2832,plain,
! [SV684: $i,SV294: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV294 ) )
= $true )
| ( ( ! [SY3684: $i] :
( ( c_lessequals @ SV684 @ SY3684 @ SV294 )
| ! [SY3685: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3685 @ SV684 @ SV294 ) @ SY3684 @ SV294 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2412]) ).
thf(2833,plain,
! [SV685: $i,SV295: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV295 ) )
= $true )
| ( ( ! [SY3686: $i] :
( ( c_lessequals @ SV685 @ SY3686 @ SV295 )
| ! [SY3687: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV685 @ SY3687 @ SV295 ) @ SY3686 @ SV295 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2413]) ).
thf(2834,plain,
! [SV686: $i,SV296: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV296 ) )
= $true )
| ( ( ! [SY3688: $i,SY3689: $i] :
( ( c_lessequals @ SV686 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3688 @ SY3689 @ SV296 ) @ SV296 )
| ~ ( c_lessequals @ SV686 @ SY3689 @ SV296 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2414]) ).
thf(2835,plain,
! [SV687: $i,SV297: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV297 ) )
= $true )
| ( ( ! [SY3690: $i] :
( ! [SY3691: $i] : ( c_lessequals @ SV687 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3690 @ SY3691 @ SV297 ) @ SV297 )
| ~ ( c_lessequals @ SV687 @ SY3690 @ SV297 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2415]) ).
thf(2836,plain,
! [SV688: $i,SV298: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV298 ) )
= $true )
| ( ( ! [SY3692: $i] :
( ( c_lessequals @ SV688 @ SY3692 @ SV298 )
| ! [SY3693: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3693 @ SV688 @ SV298 ) @ SY3692 @ SV298 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2416]) ).
thf(2837,plain,
! [SV689: $i,SV299: $i] :
( ( ( ~ ( class_Lattices_Oupper__semilattice @ SV299 ) )
= $true )
| ( ( ! [SY3694: $i] :
( ( c_lessequals @ SV689 @ SY3694 @ SV299 )
| ! [SY3695: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV689 @ SY3695 @ SV299 ) @ SY3694 @ SV299 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2417]) ).
thf(2838,plain,
! [SV1010: $i,SV690: $i,SV300: $i] :
( ( ( c_lessequals @ SV300 @ SV690 @ ( tc_fun @ SV1010 @ tc_bool ) )
| ! [SY4336: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV300 @ SY4336 @ ( tc_fun @ SV1010 @ tc_bool ) ) @ SV690 @ ( tc_fun @ SV1010 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2418]) ).
thf(2839,plain,
! [SV1011: $i,SV691: $i,SV301: $i] :
( ( ( c_lessequals @ SV301 @ SV691 @ ( tc_fun @ SV1011 @ tc_bool ) )
| ! [SY4337: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4337 @ SV301 @ ( tc_fun @ SV1011 @ tc_bool ) ) @ SV691 @ ( tc_fun @ SV1011 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2419]) ).
thf(2840,plain,
! [SV692: $i,SV302: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV302 ) )
= $true )
| ( ( ! [SY3700: $i] :
( ( c_lessequals @ SV692 @ SY3700 @ SV302 )
| ! [SY3701: $i] :
( ~ ( c_lessequals @ SV692 @ SY3701 @ SV302 )
| ~ ( c_lessequals @ SY3701 @ SY3700 @ SV302 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2420]) ).
thf(2841,plain,
! [SV693: $i,SV303: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV303 ) )
= $true )
| ( ( ! [SY3702: $i] :
( ( c_lessequals @ SV693 @ SY3702 @ SV303 )
| ! [SY3703: $i] :
( ~ ( c_lessequals @ SY3703 @ SY3702 @ SV303 )
| ~ ( c_lessequals @ SV693 @ SY3703 @ SV303 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2421]) ).
thf(2842,plain,
! [SV1012: $i,SV694: $i,SV304: $i] :
( ( ( hBOOL @ ( c_in @ SV304 @ SV694 @ SV1012 ) )
| ! [SY4338: $i] :
( ~ ( hBOOL @ ( c_in @ SV304 @ SY4338 @ SV1012 ) )
| ~ ( c_lessequals @ SY4338 @ SV694 @ ( tc_fun @ SV1012 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2422]) ).
thf(2843,plain,
! [SV1013: $i,SV695: $i,SV305: $i] :
( ( ( hBOOL @ ( c_in @ SV305 @ SV695 @ SV1013 ) )
| ! [SY4339: $i] :
( ~ ( hBOOL @ ( c_in @ SV305 @ SY4339 @ SV1013 ) )
| ~ ( c_lessequals @ SY4339 @ SV695 @ ( tc_fun @ SV1013 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2423]) ).
thf(2844,plain,
! [SV1014: $i,SV697: $i,SV307: $i] :
( ( ( hBOOL @ ( c_in @ SV307 @ SV697 @ SV1014 ) )
| ! [SY4340: $i] :
( ~ ( c_lessequals @ SY4340 @ SV697 @ ( tc_fun @ SV1014 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV307 @ SY4340 @ SV1014 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2425]) ).
thf(2845,plain,
! [SV1015: $i,SV698: $i,SV308: $i] :
( ( ( hBOOL @ ( c_in @ SV308 @ SV698 @ SV1015 ) )
| ! [SY4341: $i] :
( ~ ( hBOOL @ ( c_in @ SV308 @ SY4341 @ SV1015 ) )
| ~ ( c_lessequals @ SY4341 @ SV698 @ ( tc_fun @ SV1015 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2426]) ).
thf(2846,plain,
! [SV1016: $i,SV700: $i,SV310: $i] :
( ( ( c_lessequals @ SV310 @ SV700 @ ( tc_fun @ SV1016 @ tc_bool ) )
| ! [SY4342: $i] :
( ~ ( c_lessequals @ SY4342 @ SV700 @ ( tc_fun @ SV1016 @ tc_bool ) )
| ~ ( c_lessequals @ SV310 @ SY4342 @ ( tc_fun @ SV1016 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2428]) ).
thf(2847,plain,
! [SV701: $i,SV311: $i] :
( ( ( hBOOL @ ( hAPP @ SV311 @ SV701 ) )
= $true )
| ( ( ! [SY3714: $i] :
( ~ ( hBOOL @ ( hAPP @ SY3714 @ SV701 ) )
| ! [SY2707: $i] :
~ ( c_lessequals @ SY3714 @ SV311 @ ( tc_fun @ SY2707 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2429]) ).
thf(2848,plain,
! [SV312: $i] :
( ( ( class_Orderings_Oorder @ SV312 )
= $false )
| ( ( ! [SY2708: $i] : ( c_lessequals @ SY2708 @ SY2708 @ SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2430]) ).
thf(2849,plain,
! [SV313: $i] :
( ( ( class_Orderings_Opreorder @ SV313 )
= $false )
| ( ( ! [SY2709: $i] : ( c_lessequals @ SY2709 @ SY2709 @ SV313 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2431]) ).
thf(2850,plain,
! [SV702: $i,SV314: $i] :
( ( ( hBOOL @ ( hAPP @ SV314 @ SV702 ) )
= $true )
| ( ( ! [SY3716: $i] :
( ! [SY2712: $i] :
~ ( c_lessequals @ SY3716 @ SV314 @ ( tc_fun @ SY2712 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SY3716 @ SV702 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2432]) ).
thf(2851,plain,
! [SV1017: $i,SV703: $i,SV315: $i] :
( ( ( c_Com_Ocom_OCall @ SV315 @ SV703 @ SV1017 )
!= c_Com_Ocom_OSKIP )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2433]) ).
thf(2852,plain,
! [SV316: $i] :
( ( ( class_Orderings_Oorder @ SV316 )
= $false )
| ( ( ! [SY2715: $i,SY2716: $i] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2715 @ SY2716 @ SV316 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV316 @ tc_bool ) ) )
| ( c_lessequals @ SY2715 @ SY2716 @ SV316 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2434]) ).
thf(2853,plain,
! [SV317: $i] :
( ( ( class_Orderings_Oorder @ SV317 )
= $false )
| ( ( ! [SY2717: $i,SY2718: $i] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2717 @ SY2718 @ SV317 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV317 @ tc_bool ) ) )
| ~ ( c_lessequals @ SY2717 @ SY2718 @ SV317 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2435]) ).
thf(2854,plain,
! [SV1018: $i,SV704: $i,SV318: $i] :
( ( ! [SY4343: $i,SY4344: $i,SY4345: $i,SY4346: $i,SY4347: $i,SY4348: $i,SY4349: $i,SY4350: $i,SY4351: $i] :
( ( c_Com_Ocom_Ocom__case @ SV318 @ SV704 @ SV1018 @ SY4343 @ SY4344 @ SY4345 @ SY4346 @ SY4347 @ ( c_Com_Ocom_OCond @ SY4348 @ SY4349 @ SY4350 ) @ SY4351 )
= ( hAPP @ ( hAPP @ ( hAPP @ SY4344 @ SY4348 ) @ SY4349 ) @ SY4350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2436]) ).
thf(2855,plain,
! [SV1019: $i,SV705: $i,SV319: $i] :
( ( ! [SY4352: $i,SY4353: $i,SY4354: $i,SY4355: $i] :
( ! [SY4356: $i] :
( ( c_Fun_Ocomp @ SV319 @ SV705 @ SV1019 @ SY4352 @ SY4353 )
!= ( c_Fun_Ocomp @ SY4354 @ SY4355 @ SY4356 @ SY4352 @ SY4353 ) )
| ! [SY3735: $i] :
( ( hAPP @ SV319 @ ( hAPP @ SV705 @ SY3735 ) )
= ( hAPP @ SY4354 @ ( hAPP @ SY4355 @ SY3735 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2437]) ).
thf(2856,plain,
! [SV1020: $i,SV706: $i,SV320: $i] :
( ( ! [SY4358: $i,SY4359: $i,SY4360: $i,SY4361: $i,SY4362: $i,SY4363: $i] :
( ( ( hAPP @ SV320 @ ( hAPP @ SV706 @ SV1020 ) )
!= ( hAPP @ SY4358 @ ( hAPP @ SY4359 @ SY4360 ) ) )
| ! [SY4364: $i,SY4365: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV320 @ SV706 @ SY4361 @ SY4362 @ SY4363 ) @ SV1020 )
= ( hAPP @ ( c_Fun_Ocomp @ SY4358 @ SY4359 @ SY4364 @ SY4362 @ SY4365 ) @ SY4360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2438]) ).
thf(2857,plain,
! [SV1021: $i,SV707: $i,SV321: $i] :
( ( ( hBOOL @ ( hAPP @ SV321 @ SV707 ) )
| ( SV1021 = SV707 )
| ! [SY4366: $i,SY4367: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV321 @ SY4366 ) @ SV707 @ SY4367 @ SV1021 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2439]) ).
thf(2858,plain,
! [SV1022: $i,SV708: $i,SV322: $i] :
( ( ! [SY4368: $i,SY4369: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV322 @ SV708 @ ( tc_fun @ SV1022 @ tc_bool ) ) @ SY4368 @ SV1022 @ ( tc_fun @ SY4369 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV322 @ SY4368 @ SV1022 @ ( tc_fun @ SY4369 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV708 @ SY4368 @ SV1022 @ ( tc_fun @ SY4369 @ tc_bool ) ) @ ( tc_fun @ SY4369 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2440]) ).
thf(2859,plain,
! [SV1023: $i,SV710: $i,SV324: $i] :
( ( ! [SY4370: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV324 @ ( c_HOL_Ominus__class_Ominus @ SV710 @ SV1023 @ ( tc_fun @ SY4370 @ tc_bool ) ) @ ( tc_fun @ SY4370 @ tc_bool ) )
= SV1023 )
| ~ ( c_lessequals @ SV324 @ SV710 @ ( tc_fun @ SY4370 @ tc_bool ) )
| ~ ( c_lessequals @ SV1023 @ SV324 @ ( tc_fun @ SY4370 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2442]) ).
thf(2860,plain,
! [SV1024: $i,SV711: $i,SV325: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
| ! [SY4371: $i,SY4372: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV711 @ SV1024 @ SV325 )
!= ( c_HOL_Ominus__class_Ominus @ SY4371 @ SY4372 @ SV325 ) )
| ( c_lessequals @ SY4372 @ SY4371 @ SV325 )
| ~ ( c_lessequals @ SV1024 @ SV711 @ SV325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2443]) ).
thf(2861,plain,
! [SV1025: $i,SV712: $i,SV326: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV326 )
| ! [SY4373: $i,SY4374: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV712 @ SV1025 @ SV326 )
!= ( c_HOL_Ominus__class_Ominus @ SY4373 @ SY4374 @ SV326 ) )
| ( c_lessequals @ SV1025 @ SV712 @ SV326 )
| ~ ( c_lessequals @ SY4374 @ SY4373 @ SV326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2444]) ).
thf(2862,plain,
! [SV1026: $i,SV713: $i,SV327: $i] :
( ( ! [SY4375: $i,SY4376: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV327 @ SV713 @ SV1026 @ SY4375 ) @ ( c_Set_Oimage @ SV327 @ SY4376 @ SV1026 @ SY4375 ) @ ( tc_fun @ SY4375 @ tc_bool ) )
| ~ ( c_lessequals @ SV713 @ SY4376 @ ( tc_fun @ SV1026 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2445]) ).
thf(2863,plain,
! [SV1027: $i,SV714: $i,SV328: $i] :
( ( ~ ( c_lessequals @ SV328 @ SV714 @ ( tc_fun @ SV1027 @ tc_bool ) )
| ! [SY4377: $i,SY4378: $i] : ( c_lessequals @ ( c_Set_Oimage @ SY4377 @ SV328 @ SV1027 @ SY4378 ) @ ( c_Set_Oimage @ SY4377 @ SV714 @ SV1027 @ SY4378 ) @ ( tc_fun @ SY4378 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2446]) ).
thf(2864,plain,
! [SV1028: $i,SV715: $i,SV329: $i] :
( ( ! [SY4379: $i] :
( ( c_Natural_Oevaln @ SV329 @ SV715 @ SV1028 @ SY4379 )
| ! [SY4380: $i] :
( ( c_Natural_Oevaln @ SY4380 @ SV715 @ SV1028 @ SY4379 )
| ! [SY4381: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SY4381 @ SY4380 @ SV329 ) @ SV715 @ SV1028 @ SY4379 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2447]) ).
thf(2865,plain,
! [SV1029: $i,SV716: $i,SV330: $i] :
( ( ! [SY4382: $i,SY4383: $i] :
( ( c_Set_Oimage @ SV330 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV716 @ SV1029 @ ( tc_fun @ SY4382 @ tc_bool ) ) @ SY4382 @ SY4383 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ SV330 @ SV716 @ SY4382 @ SY4383 ) @ ( c_Set_Oimage @ SV330 @ SV1029 @ SY4382 @ SY4383 ) @ ( tc_fun @ SY4383 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2448]) ).
thf(2866,plain,
! [SV1030: $i,SV717: $i,SV331: $i] :
( ( ! [SY4384: $i,SY4385: $i,SY4386: $i] :
( ( c_Com_Ocom_OLocal @ SV331 @ SV717 @ SV1030 )
!= ( c_Com_Ocom_OCall @ SY4384 @ SY4385 @ SY4386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2449]) ).
thf(2867,plain,
! [SV1031: $i,SV718: $i,SV332: $i] :
( ( ( c_Natural_Oevalc @ SV332 @ SV718 @ SV1031 )
| ! [SY4387: $i] :
( ( c_Natural_Oevalc @ SY4387 @ SV718 @ SV1031 )
| ! [SY4388: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY4388 @ SY4387 @ SV332 ) @ SV718 @ SV1031 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2450]) ).
thf(2868,plain,
! [SV333: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV333 )
= $false )
| ( ( ! [SY2794: $i,SY2795: $i] :
( ( c_lessequals @ SY2794 @ ( c_Complete__Lattice_OSup__class_OSup @ SY2795 @ SV333 ) @ SV333 )
| ~ ( hBOOL @ ( c_in @ SY2794 @ SY2795 @ SV333 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2451]) ).
thf(2869,plain,
! [SV334: $i,SV1032: $i] :
( ( ( ! [SY4389: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV1032 @ SY4389 @ SV334 ) ) )
= $true )
| ( ( c_Com_OWT @ SV334 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2452]) ).
thf(2870,plain,
! [SV335: $i,SV1033: $i] :
( ( ( ! [SY4390: $i] :
~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV1033 @ SV335 @ SY4390 ) ) )
= $true )
| ( ( c_Com_OWT @ SV335 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2453]) ).
thf(2871,plain,
! [SV719: $i,SV336: $i] :
( ( c_Com_Ocom_OSKIP
= ( c_Com_Ocom_OSemi @ SV336 @ SV719 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2454]) ).
thf(2872,plain,
! [SV337: $i] :
( ( ( class_Orderings_Olinorder @ SV337 )
= $false )
| ( ( ! [SY2801: $i,SY2802: $i] :
( ( c_lessequals @ SY2801 @ SY2802 @ SV337 )
| ( c_lessequals @ SY2802 @ SY2801 @ SV337 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2455]) ).
thf(2873,plain,
! [SV1034: $i,SV720: $i,SV338: $i] :
( ( ! [SY4391: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ SV338 )
!= ( c_Com_Ocom_OLocal @ SV720 @ SV1034 @ SY4391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2456]) ).
thf(2874,plain,
! [SV1035: $i,SV721: $i,SV339: $i] :
( ( ( hAPP @ c_Com_Ocom_OBODY @ SV339 )
!= ( c_Com_Ocom_OWhile @ SV721 @ SV1035 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2457]) ).
thf(2875,plain,
! [SV1036: $i,SV722: $i,SV340: $i] :
( ( ! [SY4392: $i] :
( ( c_Com_Ocom_OCall @ SV340 @ SV722 @ SV1036 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SY4392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2458]) ).
thf(2876,plain,
! [SV1037: $i,SV723: $i,SV341: $i] :
( ( ( hAPP @ c_Com_Ocom_OBODY @ SV341 )
!= ( c_Com_Ocom_OSemi @ SV723 @ SV1037 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2459]) ).
thf(2877,plain,
! [SV1038: $i,SV724: $i,SV342: $i] :
( ( ( c_Com_Ocom_OSemi @ SV342 @ SV724 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SV1038 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2460]) ).
thf(2878,plain,
! [SV1039: $i,SV725: $i,SV343: $i] :
( ( ! [SY4393: $i] :
( ( c_Com_Ocom_OLocal @ SV343 @ SV725 @ SV1039 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SY4393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2461]) ).
thf(2879,plain,
! [SV1040: $i,SV726: $i,SV344: $i] :
( ( ! [SY4394: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ SV344 )
!= ( c_Com_Ocom_OCall @ SV726 @ SV1040 @ SY4394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2462]) ).
thf(2880,plain,
! [SV1041: $i,SV727: $i,SV345: $i] :
( ( ! [SY4395: $i,SY4396: $i,SY4397: $i,SY4398: $i,SY4399: $i,SY4400: $i,SY4401: $i] :
( ( c_Com_Ocom_Ocom__case @ SV345 @ SV727 @ SV1041 @ SY4395 @ SY4396 @ SY4397 @ SY4398 @ SY4399 @ ( hAPP @ c_Com_Ocom_OBODY @ SY4400 ) @ SY4401 )
= ( hAPP @ SY4398 @ SY4400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2463]) ).
thf(2881,plain,
! [SV1042: $i,SV728: $i,SV347: $i] :
( ( ! [SY4402: $i] : ( c_Hoare__Mirabelle_Otriple__valid @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV347 ) @ SV728 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1042 ) ) @ SY4402 ) @ SV347 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2465]) ).
thf(2882,plain,
! [SV1043: $i,SV729: $i,SV348: $i] :
( ( ! [SY4403: $i,SY4404: $i] :
( ~ ( hBOOL @ ( hAPP @ SV348 @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SV729 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ SV1043 ) @ SY4403 ) @ SY4404 ) @ t_b @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV348 @ ( hAPP @ ( hAPP @ ( hAPP @ SV729 @ SV1043 ) @ SY4403 ) @ SY4404 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2466]) ).
thf(2883,plain,
! [SV1044: $i,SV730: $i,SV349: $i] :
( ( ! [SY4405: $i,SY4406: $i] :
( ~ ( hBOOL @ ( hAPP @ SV349 @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SV730 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ SV1044 ) @ SY4405 ) @ SY4406 ) @ t_b @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV349 @ ( hAPP @ ( hAPP @ ( hAPP @ SV730 @ SV1044 ) @ SY4405 ) @ SY4406 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2467]) ).
thf(2884,plain,
! [SV1045: $i,SV731: $i,SV350: $i] :
( ( ! [SY4407: $i,SY4408: $i,SY4409: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ SV350 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV731 ) @ SV1045 ) @ SY4407 ) @ SY4408 ) @ SV731 @ SY4409 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV350 @ SV1045 ) @ SY4407 ) @ SY4408 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2468]) ).
thf(2885,plain,
! [SV1046: $i,SV732: $i,SV351: $i] :
( ( ! [SY4410: $i,SY4411: $i,SY4412: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SV351 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV732 ) @ SV1046 ) @ SY4410 ) @ SY4411 ) @ SV732 @ SY4412 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV351 @ SV1046 ) @ SY4410 ) @ SY4411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2469]) ).
thf(2886,plain,
! [SV1047: $i,SV733: $i,SV352: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV352 @ SV733 @ SV1047 )
| ! [SY4413: $i] :
( ~ ( c_lessequals @ SV733 @ SY4413 @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1047 ) @ tc_bool ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV352 @ SY4413 @ SV1047 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2470]) ).
thf(2887,plain,
! [SV1048: $i,SV734: $i,SV353: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ SV734 @ SV1048 )
| ! [SY4414: $i] :
( ~ ( c_lessequals @ SY4414 @ SV353 @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1048 ) @ tc_bool ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY4414 @ SV734 @ SV1048 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2471]) ).
thf(2888,plain,
! [SV1049: $i,SV735: $i,SV354: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV354 @ SV735 @ SV1049 )
| ~ ( c_lessequals @ SV735 @ SV354 @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1049 ) @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2472]) ).
thf(2889,plain,
! [SV1050: $i,SV736: $i,SV355: $i] :
( ( ! [SY4415: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV355 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV736 ) @ SV1050 ) @ SY4415 ) @ ( 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 @ SV355 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ ( c_COMBK @ ( hAPP @ ( c_COMBC @ ( c_fequal @ tc_Com_Ostate ) @ tc_Com_Ostate @ tc_Com_Ostate @ tc_bool ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ SV355 @ SV736 @ SY4415 @ SV1050 ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) ) @ SV1050 ) @ ( c_COMBK @ ( hAPP @ SY4415 @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ SV355 @ SV736 @ SY4415 @ SV1050 ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_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)],[2473]) ).
thf(2890,plain,
! [SV1051: $i,SV737: $i,SV356: $i] :
( ( ! [SY4416: $i,SY4417: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV356 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ ( hAPP @ SV1051 @ SY4416 ) ) @ ( hAPP @ c_Com_Ocom_OBODY @ SY4416 ) ) @ ( hAPP @ SY4417 @ SY4416 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV737 )
| ! [SY4418: $i] :
( ~ ( hBOOL @ ( c_in @ SY4416 @ SY4418 @ tc_Com_Opname ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV356 @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ SV1051 @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ SY4417 @ tc_Com_Opname @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SY4418 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ SV1051 @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ SY4417 @ tc_Com_Opname @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SY4418 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV737 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2474]) ).
thf(2891,plain,
! [SV1052: $i,SV739: $i,SV359: $i] :
( ( ! [SY4419: $i,SY4420: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV359 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV739 ) @ SV1052 ) @ ( c_Com_Ocom_OWhile @ SY4419 @ SY4420 ) ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1052 @ ( c_Fun_Ocomp @ c_Not @ SY4419 @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ SV739 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV739 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV739 ) ) @ SV739 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV359 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV739 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1052 @ SY4419 @ SV739 ) ) @ SY4420 ) @ SV1052 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV739 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV739 ) ) @ SV739 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2477]) ).
thf(2892,plain,
! [SV1053: $i,SV740: $i,SV360: $i] :
( ( ! [SY4421: $i,SY4422: $i,SY4423: $i,SY4424: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ SV1053 ) @ ( c_Com_Ocom_OCond @ SY4421 @ SY4422 @ SY4423 ) ) @ SY4424 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1053 @ ( c_Fun_Ocomp @ c_Not @ SY4421 @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ SV740 ) ) @ SY4423 ) @ SY4424 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1053 @ SY4421 @ SV740 ) ) @ SY4422 ) @ SY4424 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2478]) ).
thf(2893,plain,
! [SV1054: $i,SV741: $i,SV361: $i] :
( ( ! [SY4425: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV361 ) ) @ SV741 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ SV361 @ SV1054 @ SV741 @ SY4425 ) @ SY4425 )
| ~ ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ SV361 ) @ SV741 @ SV1054 @ SY4425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2479]) ).
thf(2894,plain,
! [SV1055: $i,SV742: $i,SV362: $i] :
( ( ! [SY4426: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ SV362 ) @ SV742 @ ( c_Suc @ SV1055 ) @ SY4426 )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV362 ) ) @ SV742 @ SV1055 @ SY4426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2480]) ).
thf(2895,plain,
! [SV363: $i] :
( ( ( class_Orderings_Obot @ SV363 )
= $false )
| ( ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ SV363 ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ SV363 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2481]) ).
thf(2896,plain,
! [SV364: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV364 )
= $false )
| ( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV364 @ tc_bool ) ) @ SV364 )
= ( c_Orderings_Obot__class_Obot @ SV364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2482]) ).
thf(2897,plain,
! [SV1056: $i,SV744: $i,SV366: $i] :
( ( ( SV366
= ( c_Set_Oinsert @ SV744 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1056 @ tc_bool ) ) @ SV1056 ) )
| ( SV366
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1056 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV366 @ ( c_Set_Oinsert @ SV744 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1056 @ tc_bool ) ) @ SV1056 ) @ ( tc_fun @ SV1056 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2484]) ).
thf(2898,plain,
! [SV1057: $i,SV746: $i,SV368: $i] :
( ( ! [SY4427: $i,SY4428: $i,SY4429: $i,SY4430: $i,SY4431: $i] :
( ( ( hAPP @ SV368 @ ( c_Set_Oinsert @ SV746 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1057 @ tc_bool ) ) @ SV1057 ) )
= SV746 )
| ! [SY4432: $i,SY4433: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV368 @ SY4427 @ SY4428 @ SY4429 @ SY4430 @ SY4431 @ SY4432 @ SY4433 @ SV1057 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2486]) ).
thf(2899,plain,
! [SV1058: $i,SV747: $i,SV369: $i] :
( ( ! [SY4434: $i,SY4435: $i,SY4436: $i,SY4437: $i,SY4438: $i] :
( ( ( hAPP @ SV369 @ ( c_Set_Oinsert @ SV747 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1058 @ tc_bool ) ) @ SV1058 ) )
= SV747 )
| ! [SY4439: $i,SY4440: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY4434 @ SV369 @ SY4435 @ SY4436 @ SY4437 @ SY4438 @ SY4439 @ SY4440 @ SV1058 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2487]) ).
thf(2900,plain,
! [SV370: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV370 )
= $false )
| ( ( ! [SY2906: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SY2906 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV370 @ tc_bool ) ) @ SV370 ) @ SV370 )
= SY2906 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2488]) ).
thf(2901,plain,
! [SV1059: $i,SV749: $i,SV372: $i] :
( ( ! [SY4441: $i] :
( ( c_Set_Oinsert @ SV372 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV1059 @ SV749 @ ( tc_fun @ SY4441 @ tc_bool ) ) @ SY4441 )
= ( c_Set_Oinsert @ SV372 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4441 @ tc_bool ) ) @ SY4441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2490]) ).
thf(2902,plain,
! [SV1060: $i,SV750: $i,SV373: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV373 @ ( c_Set_Oinsert @ SV750 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1060 @ tc_bool ) ) @ SV1060 ) @ SV1060 ) @ SV750 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2491]) ).
thf(2903,plain,
! [SV374: $i] :
( ( ( class_Orderings_Olinorder @ SV374 )
= $false )
| ( ( ! [SY2913: $i] :
( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ SY2913 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV374 @ tc_bool ) ) @ SV374 ) @ SV374 )
= SY2913 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2492]) ).
thf(2904,plain,
! [SV1061: $i,SV752: $i,SV376: $i] :
( ( ! [SY4442: $i,SY4443: $i,SY4444: $i,SY4445: $i,SY4446: $i,SY4447: $i] :
( ( ( hAPP @ SV376 @ ( c_Set_Oinsert @ SV752 @ ( c_Set_Oinsert @ SV1061 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4442 @ tc_bool ) ) @ SY4442 ) @ SY4442 ) )
= ( hAPP @ ( hAPP @ SY4443 @ SV752 ) @ SV1061 ) )
| ! [SY2923: $i,SY2924: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV376 @ SY4444 @ SY4445 @ SY4446 @ SY4443 @ SY4447 @ SY2923 @ SY2924 @ SY4442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2494]) ).
thf(2905,plain,
! [SV1062: $i,SV753: $i,SV377: $i] :
( ( ! [SY4450: $i,SY4451: $i,SY4452: $i,SY4453: $i,SY4454: $i,SY4455: $i] :
( ( ( hAPP @ SV377 @ ( c_Set_Oinsert @ SV753 @ ( c_Set_Oinsert @ SV1062 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4450 @ tc_bool ) ) @ SY4450 ) @ SY4450 ) )
= ( hAPP @ ( hAPP @ SY4451 @ SV753 ) @ SV1062 ) )
| ! [SY2933: $i,SY2934: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY4452 @ SV377 @ SY4453 @ SY4454 @ SY4455 @ SY4451 @ SY2933 @ SY2934 @ SY4450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2495]) ).
thf(2906,plain,
! [SV1063: $i,SV754: $i,SV378: $i] :
( ( ! [SY4458: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV378 @ ( c_Set_Oinsert @ SV754 @ SV1063 @ SY4458 ) @ ( tc_fun @ SY4458 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV378 @ ( c_Set_Oinsert @ SV754 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4458 @ tc_bool ) ) @ SY4458 ) @ ( tc_fun @ SY4458 @ tc_bool ) ) @ SV1063 @ ( tc_fun @ SY4458 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2496]) ).
thf(2907,plain,
! [SV1064: $i,SV755: $i,SV379: $i] :
( ( ! [SY4459: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV379 @ ( c_Set_Oinsert @ SV755 @ SV1064 @ SY4459 ) @ ( tc_fun @ SY4459 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV379 @ SV1064 @ ( tc_fun @ SY4459 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV755 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4459 @ tc_bool ) ) @ SY4459 ) @ ( tc_fun @ SY4459 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2497]) ).
thf(2908,plain,
! [SV756: $i,SV380: $i] :
( ( ( SV380 = SV756 )
= $true )
| ( ( ! [SY3879: $i,SY3880: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SY3879 @ ( c_Set_Oinsert @ SV380 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3880 @ tc_bool ) ) @ SY3880 ) @ SY3880 ) @ SV756 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2498]) ).
thf(2909,plain,
! [SV1065: $i,SV758: $i,SV382: $i] :
( ( ( SV382
= ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ SV758 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1065 @ tc_bool ) ) @ SV1065 ) @ SV1065 ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV758 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1065 @ tc_bool ) ) @ SV1065 ) @ SV382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2500]) ).
thf(2910,plain,
! [SV759: $i,SV383: $i] :
( ( ( SV383 = SV759 )
= $true )
| ( ( ! [SY3882: $i] :
~ ( hBOOL @ ( c_in @ SV383 @ ( c_Set_Oinsert @ SV759 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3882 @ tc_bool ) ) @ SY3882 ) @ SY3882 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2501]) ).
thf(2911,plain,
! [SV1066: $i,SV760: $i,SV384: $i] :
( ( ( c_Finite__Set_Ofold1 @ SV384 @ ( c_Set_Oinsert @ SV760 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1066 @ tc_bool ) ) @ SV1066 ) @ SV1066 )
= SV760 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2502]) ).
thf(2912,plain,
! [SV385: $i] :
( ( ( class_Orderings_Olinorder @ SV385 )
= $false )
| ( ( ! [SY2951: $i] :
( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ SY2951 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV385 @ tc_bool ) ) @ SV385 ) @ SV385 )
= SY2951 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2503]) ).
thf(2913,plain,
! [SV1067: $i,SV761: $i,SV386: $i] :
( ( ( c_Set_Oinsert @ SV386 @ ( c_HOL_Ominus__class_Ominus @ SV761 @ ( c_Set_Oinsert @ SV386 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1067 @ tc_bool ) ) @ SV1067 ) @ ( tc_fun @ SV1067 @ tc_bool ) ) @ SV1067 )
= ( c_Set_Oinsert @ SV386 @ SV761 @ SV1067 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2504]) ).
thf(2914,plain,
! [SV387: $i] :
( ( ( class_Orderings_Oorder @ SV387 )
= $false )
| ( ( ! [SY2954: $i] :
( ( c_SetInterval_Oord__class_OatLeastAtMost @ SY2954 @ SY2954 @ SV387 )
= ( c_Set_Oinsert @ SY2954 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV387 @ tc_bool ) ) @ SV387 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2505]) ).
thf(2915,plain,
! [SV1068: $i,SV762: $i,SV388: $i] :
( ( ( ( c_Set_Oinsert @ SV388 @ SV762 @ SV1068 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1068 @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ SV388 @ SV762 @ SV1068 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2506]) ).
thf(2916,plain,
! [SV1069: $i,SV763: $i,SV389: $i] :
( ( ( c_Set_Oinsert @ SV389 @ SV763 @ SV1069 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV389 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1069 @ tc_bool ) ) @ SV1069 ) @ SV763 @ ( tc_fun @ SV1069 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2507]) ).
thf(2917,plain,
! [SV390: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV390 )
= $false )
| ( ( ! [SY2959: $i] :
( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ SY2959 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV390 @ tc_bool ) ) @ SV390 ) @ SV390 )
= SY2959 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2508]) ).
thf(2918,plain,
! [SV1070: $i,SV764: $i,SV391: $i] :
( ( ! [SY4460: $i,SY4461: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV391 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV764 ) @ SV1070 ) @ SY4460 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY4462: $i,SY4463: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SY4461 @ SY4462 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV391 @ SV764 @ SY4460 @ SV1070 @ SY4463 @ SY4461 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4463 @ SY4462 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV391 @ SV764 @ SY4460 @ SV1070 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV391 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4463 ) @ SV1070 ) @ SY4461 ) @ ( 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)],[2509]) ).
thf(2919,plain,
! [SV1071: $i,SV765: $i,SV392: $i] :
( ( ! [SY4464: $i,SY4465: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV392 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV765 ) @ SV1071 ) @ SY4464 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY4466: $i,SY4467: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SY4465 @ SY4466 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV765 @ SY4467 @ SY4464 @ SY4465 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4467 @ SY4466 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV765 @ SY4467 @ SY4464 @ SY4465 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV392 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4467 ) @ SV1071 ) @ SY4465 ) @ ( 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)],[2510]) ).
thf(2920,plain,
! [SV1072: $i,SV766: $i,SV393: $i] :
( ( ! [SY4468: $i,SY4469: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV393 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV766 ) @ SV1072 ) @ SY4468 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY4470: $i,SY4471: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SY4469 @ SY4470 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV393 @ SV766 @ SY4468 @ SV1072 @ SY4471 @ SY4469 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4471 @ SY4470 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV393 @ SV766 @ SY4468 @ SV1072 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV393 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4471 ) @ SV1072 ) @ SY4469 ) @ ( 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)],[2511]) ).
thf(2921,plain,
! [SV1073: $i,SV767: $i,SV394: $i] :
( ( ! [SY4472: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV394 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV767 ) @ SV1073 ) @ SY4472 ) @ ( 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 @ SV767 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV394 @ SV767 @ SY4472 @ SV1073 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV394 @ SV767 @ SY4472 @ SV1073 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2512]) ).
thf(2922,plain,
! [SV1074: $i,SV768: $i,SV395: $i] :
( ( ! [SY4473: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV395 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV768 ) @ SV1074 ) @ SY4473 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY4474: $i,SY4475: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4473 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV395 @ SV768 @ SY4473 @ SV1074 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV395 @ SV768 @ SY4473 @ SV1074 @ SY4474 @ SY4475 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV395 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4474 ) @ SV1074 ) @ SY4475 ) @ ( 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)],[2513]) ).
thf(2923,plain,
! [SV1075: $i,SV769: $i,SV396: $i] :
( ( ! [SY4476: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV396 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV769 ) @ SV1075 ) @ SY4476 ) @ ( 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 @ SV769 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV396 @ SV769 @ SY4476 @ SV1075 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV396 @ SV769 @ SY4476 @ SV1075 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2514]) ).
thf(2924,plain,
! [SV1076: $i,SV770: $i,SV397: $i] :
( ( ! [SY4477: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV397 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV770 ) @ SV1076 ) @ SY4477 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY4478: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SY4478 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SY4477 @ SY4478 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SY4477 @ SY4478 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV397 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV770 ) @ SV1076 ) @ SY4478 ) @ ( 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)],[2515]) ).
thf(2925,plain,
! [SV1077: $i,SV771: $i,SV398: $i] :
( ( ! [SY4479: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV398 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV771 ) @ SV1077 ) @ SY4479 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY4480: $i,SY4481: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV771 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV771 @ SY4480 @ SY4479 @ SY4481 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV771 @ SY4480 @ SY4479 @ SY4481 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV398 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4480 ) @ SV1077 ) @ SY4481 ) @ ( 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)],[2516]) ).
thf(2926,plain,
! [SV1078: $i,SV772: $i,SV399: $i] :
( ( ! [SY4482: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV399 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV772 ) @ SV1078 ) @ SY4482 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY4483: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV772 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV772 @ SY4483 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV772 @ SY4483 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV399 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4483 ) @ SV1078 ) @ SY4482 ) @ ( 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)],[2517]) ).
thf(2927,plain,
! [SV1079: $i,SV773: $i,SV400: $i] :
( ( ! [SY4484: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV400 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV773 ) @ SV1079 ) @ SY4484 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY4485: $i,SY4486: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4484 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV400 @ SV773 @ SY4484 @ SV1079 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV400 @ SV773 @ SY4484 @ SV1079 @ SY4485 @ SY4486 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV400 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4485 ) @ SV1079 ) @ SY4486 ) @ ( 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)],[2518]) ).
thf(2928,plain,
! [SV1080: $i,SV774: $i,SV401: $i] :
( ( ! [SY4487: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV401 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV774 ) @ SV1080 ) @ SY4487 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY4488: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4488 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV774 @ SY4488 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV774 @ SY4488 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV401 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4488 ) @ SV1080 ) @ SY4487 ) @ ( 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)],[2519]) ).
thf(2929,plain,
! [SV1081: $i,SV775: $i,SV402: $i] :
( ( ! [SY4489: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV402 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV775 ) @ SV1081 ) @ SY4489 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY4490: $i,SY4491: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4489 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV775 @ SY4490 @ SY4489 @ SY4491 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV775 @ SY4490 @ SY4489 @ SY4491 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV402 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4490 ) @ SV1081 ) @ SY4491 ) @ ( 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)],[2520]) ).
thf(2930,plain,
! [SV1082: $i,SV776: $i,SV403: $i] :
( ( ! [SY4492: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV403 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV776 ) @ SV1082 ) @ SY4492 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY4493: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4492 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SY4492 @ SY4493 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SY4492 @ SY4493 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV403 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV776 ) @ SV1082 ) @ SY4493 ) @ ( 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)],[2521]) ).
thf(2931,plain,
! [SV1083: $i,SV777: $i,SV404: $i] :
( ( ! [SY4494: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV404 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV777 ) @ SV1083 ) @ SY4494 ) @ ( 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 @ SV777 @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ SV404 @ SV777 @ SY4494 @ SV1083 ) ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ SV404 @ SV777 @ SY4494 @ SV1083 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2522]) ).
thf(2932,plain,
! [SV1084: $i,SV778: $i,SV405: $i] :
( ( ! [SY4495: $i,SY4496: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV405 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV778 ) @ SV1084 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SY4495 ) ) @ SY4496 ) @ SV778 )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ SV405 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV778 ) @ SV1084 ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY4495 ) ) ) @ SY4496 ) @ SV778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2523]) ).
thf(2933,plain,
! [SV1085: $i,SV779: $i,SV406: $i] :
( ( ! [SY4497: $i,SY4498: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ SV406 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV779 ) @ SV1085 ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY4497 ) ) ) @ SY4498 ) @ SV779 )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV406 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV779 ) @ SV1085 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SY4497 ) ) @ SY4498 ) @ SV779 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2524]) ).
thf(2934,plain,
! [SV1086: $i,SV780: $i,SV407: $i] :
( ( ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ SV407 ) @ SV780 @ SV1086 )
| ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV407 ) ) @ SV780 @ SV1086 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2525]) ).
thf(2935,plain,
! [SV1087: $i,SV781: $i,SV408: $i] :
( ( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV408 ) ) @ SV781 @ SV1087 )
| ~ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ SV408 ) @ SV781 @ SV1087 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2526]) ).
thf(2936,plain,
! [SV1088: $i,SV782: $i,SV409: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV409 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV782 ) @ SV1088 ) @ c_Com_Ocom_OSKIP ) @ SV1088 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV782 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV782 ) ) @ SV782 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2527]) ).
thf(2937,plain,
! [SV1089: $i,SV783: $i,SV410: $i] :
( ( ! [SY4499: $i,SY4500: $i,SY4501: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SV1089 ) @ ( c_Com_Ocom_OSemi @ SY4499 @ SY4500 ) ) @ SY4501 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 )
| ! [SY4502: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SY4502 ) @ SY4500 ) @ SY4501 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SV1089 ) @ SY4499 ) @ SY4502 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2528]) ).
thf(2938,plain,
! [SV1090: $i,SV784: $i,SV411: $i] :
( ( ! [SY4503: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV411 @ ( c_Set_Oinsert @ SV784 @ SV1090 @ ( tc_Hoare__Mirabelle_Otriple @ SY4503 ) ) @ SY4503 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV411 @ SV1090 @ SY4503 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV411 @ ( c_Set_Oinsert @ SV784 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SY4503 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SY4503 ) ) @ SY4503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2529]) ).
thf(2939,plain,
! [SV1091: $i,SV785: $i,SV412: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV412 @ SV785 @ SV1091 ) @ SV412 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2530]) ).
thf(2940,plain,
! [SV1092: $i,SV786: $i,SV413: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV413 @ SV786 @ SV1092 )
| ! [SY4504: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV413 @ SY4504 @ SV1092 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY4504 @ SV786 @ SV1092 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2531]) ).
thf(2941,plain,
! [SV1093: $i,SV787: $i,SV414: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV414 @ tc_bool ) )
!= ( c_Set_Oinsert @ SV787 @ SV1093 @ SV414 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2532]) ).
thf(2942,plain,
! [SV1094: $i,SV788: $i,SV415: $i] :
( ( ! [SY4505: $i,SY4506: $i,SY4507: $i,SY4508: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV415 ) @ SV788 ) @ SV1094 ) @ SY4505 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV415 ) @ SY4506 ) @ SY4507 ) @ SY4508 ) )
| ( SY4505 = SY4508 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2533]) ).
thf(2943,plain,
! [SV1095: $i,SV789: $i,SV416: $i] :
( ( ! [SY4509: $i,SY4510: $i,SY4511: $i] :
( ! [SY4512: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV416 ) @ SV789 ) @ SV1095 ) @ SY4509 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV416 ) @ SY4510 ) @ SY4511 ) @ SY4512 ) )
| ( SV1095 = SY4511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2534]) ).
thf(2944,plain,
! [SV1096: $i,SV790: $i,SV417: $i] :
( ( ! [SY4513: $i,SY4514: $i] :
( ! [SY4515: $i,SY4516: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV417 ) @ SV790 ) @ SV1096 ) @ SY4513 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV417 ) @ SY4514 ) @ SY4515 ) @ SY4516 ) )
| ( SV790 = SY4514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2535]) ).
thf(2945,plain,
! [SV1097: $i,SV791: $i,SV418: $i] :
( ( ! [SY4517: $i,SY4518: $i] :
( ( ( c_Set_Oinsert @ SV418 @ ( c_Set_Oinsert @ SV791 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1097 @ tc_bool ) ) @ SV1097 ) @ SV1097 )
!= ( c_Set_Oinsert @ SY4517 @ ( c_Set_Oinsert @ SY4518 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1097 @ tc_bool ) ) @ SV1097 ) @ SV1097 ) )
| ( SV791 = SY4517 )
| ( SV791 = SY4518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2536]) ).
thf(2946,plain,
! [SV1098: $i,SV792: $i,SV419: $i] :
( ( ! [SY4519: $i,SY4520: $i] :
( ( ( c_Set_Oinsert @ SV419 @ ( c_Set_Oinsert @ SV792 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1098 @ tc_bool ) ) @ SV1098 ) @ SV1098 )
!= ( c_Set_Oinsert @ SY4519 @ ( c_Set_Oinsert @ SY4520 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1098 @ tc_bool ) ) @ SV1098 ) @ SV1098 ) )
| ( SV419 = SY4520 )
| ( SV792 = SY4520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2537]) ).
thf(2947,plain,
! [SV1099: $i,SV793: $i,SV420: $i] :
( ( ! [SY4521: $i] :
( ! [SY4522: $i] :
( ( c_Set_Oinsert @ SV420 @ ( c_Set_Oinsert @ SV793 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1099 @ tc_bool ) ) @ SV1099 ) @ SV1099 )
!= ( c_Set_Oinsert @ SY4521 @ ( c_Set_Oinsert @ SY4522 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1099 @ tc_bool ) ) @ SV1099 ) @ SV1099 ) )
| ( SV793 = SY4521 )
| ( SV420 = SY4521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2538]) ).
thf(2948,plain,
! [SV1100: $i,SV794: $i,SV421: $i] :
( ( ! [SY4523: $i,SY4524: $i] :
( ( ( c_Set_Oinsert @ SV421 @ ( c_Set_Oinsert @ SV794 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1100 @ tc_bool ) ) @ SV1100 ) @ SV1100 )
!= ( c_Set_Oinsert @ SY4523 @ ( c_Set_Oinsert @ SY4524 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1100 @ tc_bool ) ) @ SV1100 ) @ SV1100 ) )
| ( SV421 = SY4524 )
| ( SV421 = SY4523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2539]) ).
thf(2949,plain,
! [SV795: $i,SV422: $i] :
( ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV422 @ tc_bool ) ) @ SV795 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2540]) ).
thf(2950,plain,
! [SV1101: $i,SV797: $i,SV424: $i] :
( ( ! [SY4525: $i,SY4526: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV424 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV797 ) @ SV1101 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SY4525 ) ) @ SY4526 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) ) @ SV797 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV797 ) @ SV1101 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SY4525 ) ) @ SY4526 ) @ SV424 @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) ) @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV797 ) @ SV1101 ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SY4525 ) ) ) @ SY4526 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) ) @ SV797 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2542]) ).
thf(2951,plain,
! [SV798: $i,SV425: $i] :
( ( ( hBOOL @ ( hAPP @ SV425 @ SV798 ) )
= $true )
| ( ( ! [SY3986: $i] :
( ( SY3986 = SV798 )
| ! [SY3987: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SY3986 @ SV425 @ SY3987 ) @ SV798 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2543]) ).
thf(2952,plain,
! [SV1102: $i,SV799: $i,SV426: $i] :
( ( ( c_Set_Oinsert @ SV426 @ ( c_Set_Oinsert @ SV426 @ SV799 @ SV1102 ) @ SV1102 )
= ( c_Set_Oinsert @ SV426 @ SV799 @ SV1102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2544]) ).
thf(2953,plain,
! [SV1103: $i,SV800: $i,SV427: $i] :
( ( ( c_Set_Oinsert @ SV427 @ SV800 @ SV1103 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1103 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2545]) ).
thf(2954,plain,
! [SV1104: $i,SV801: $i,SV428: $i] :
( ( ! [SY4527: $i] :
( ( c_Set_Oinsert @ SV428 @ ( c_Set_Oinsert @ SV801 @ SV1104 @ SY4527 ) @ SY4527 )
= ( c_Set_Oinsert @ SV801 @ ( c_Set_Oinsert @ SV428 @ SV1104 @ SY4527 ) @ SY4527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2546]) ).
thf(2955,plain,
! [SV1105: $i,SV802: $i,SV429: $i] :
( ( ( c_Set_Oinsert @ SV429 @ ( c_Set_Oinsert @ SV802 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1105 @ tc_bool ) ) @ SV1105 ) @ SV1105 )
= ( c_Set_Oinsert @ SV802 @ ( c_Set_Oinsert @ SV429 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1105 @ tc_bool ) ) @ SV1105 ) @ SV1105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2547]) ).
thf(2956,plain,
! [SV1106: $i,SV803: $i,SV430: $i] :
( ( ( ( c_Set_Oinsert @ SV430 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV803 @ tc_bool ) ) @ SV803 )
!= ( c_Set_Oinsert @ SV1106 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV803 @ tc_bool ) ) @ SV803 ) )
| ( SV430 = SV1106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2548]) ).
thf(2957,plain,
! [SV1107: $i,SV804: $i,SV431: $i] :
( ( ! [SY4528: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV431 @ SV804 @ SV1107 ) @ SY4528 ) )
| ~ ( hBOOL @ ( hAPP @ SV804 @ SY4528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2549]) ).
thf(2958,plain,
! [SV805: $i,SV432: $i] :
( ( ( ( hAPP @ c_Com_Ocom_OBODY @ SV432 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SV805 ) )
= $true )
| ( ( SV432 = SV805 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2550]) ).
thf(2959,plain,
! [SV806: $i,SV433: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV433 @ SV806 ) )
= $true )
| ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV806 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2551]) ).
thf(2960,plain,
! [SV807: $i,SV434: $i] :
( ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV434 @ SV807 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV807 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2552]) ).
thf(2961,plain,
! [SV808: $i,SV435: $i] :
( ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV435 @ SV808 ) )
= $true )
| ( ( ~ ( class_Lattices_Obounded__lattice @ SV808 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2553]) ).
thf(2962,plain,
! [SV809: $i,SV436: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV436 @ SV809 ) )
= $true )
| ( ( ~ ( class_Orderings_Opreorder @ SV809 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2554]) ).
thf(2963,plain,
! [SV810: $i,SV437: $i] :
( ( ( class_Lattices_Olattice @ ( tc_fun @ SV437 @ SV810 ) )
= $true )
| ( ( ~ ( class_Lattices_Olattice @ SV810 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2555]) ).
thf(2964,plain,
! [SV811: $i,SV438: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV438 @ SV811 ) )
= $true )
| ( ( ~ ( class_Orderings_Oorder @ SV811 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2556]) ).
thf(2965,plain,
! [SV812: $i,SV439: $i] :
( ( ( class_Orderings_Obot @ ( tc_fun @ SV439 @ SV812 ) )
= $true )
| ( ( ~ ( class_Orderings_Obot @ SV812 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2557]) ).
thf(2966,plain,
! [SV813: $i,SV440: $i] :
( ( ( class_HOL_Ominus @ ( tc_fun @ SV440 @ SV813 ) )
= $true )
| ( ( ~ ( class_HOL_Ominus @ SV813 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2558]) ).
thf(2967,plain,
! [SV814: $i,SV441: $i] :
( ( ( class_HOL_Oord @ ( tc_fun @ SV441 @ SV814 ) )
= $true )
| ( ( ~ ( class_HOL_Oord @ SV814 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2559]) ).
thf(2968,plain,
! [SV816: $i,SV443: $i] :
( ( ( SV443 = SV816 )
= $true )
| ( ( ! [SY3996: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY3996 ) @ SV443 ) @ SV816 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2561]) ).
thf(2969,plain,
! [SV444: $i,SV1: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV1 )
= $false )
| ( ( ! [SY3123: $i,SY3124: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV444 @ SY3123 @ SV1 ) @ SY3124 @ SV1 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV444 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3123 @ SY3124 @ SV1 ) @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2562]) ).
thf(2970,plain,
! [SV445: $i,SV2: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV2 )
= $false )
| ( ( ! [SY3125: $i,SY3126: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV445 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3125 @ SY3126 @ SV2 ) @ SV2 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3125 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV445 @ SY3126 @ SV2 ) @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2563]) ).
thf(2971,plain,
! [SV446: $i,SV3: $i] :
( ( ( class_Lattices_Olattice @ SV3 )
= $false )
| ( ( ! [SY3127: $i,SY3128: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV446 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3127 @ SY3128 @ SV3 ) @ SV3 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY3127 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV446 @ SY3128 @ SV3 ) @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2564]) ).
thf(2972,plain,
! [SV447: $i,SV4: $i] :
( ( ( class_Lattices_Olattice @ SV4 )
= $false )
| ( ( ! [SY3129: $i,SY3130: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV447 @ SY3129 @ SV4 ) @ SY3130 @ SV4 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV447 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3129 @ SY3130 @ SV4 ) @ SV4 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2565]) ).
thf(2973,plain,
! [SV1108: $i,SV448: $i,SV5: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OCall @ SV5 @ SV448 @ SV1108 ) )
= $true )
| ( ( ~ ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ SV448 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2566]) ).
thf(2974,plain,
! [SV1109: $i,SV6: $i,SV817: $i] :
( ( ( ~ ( c_Com_OWT @ ( c_Com_Ocom_OCall @ SV817 @ SV6 @ SV1109 ) ) )
= $true )
| ( ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ SV6 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2567]) ).
thf(2975,plain,
! [SV1110: $i,SV818: $i,SV449: $i,SV7: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV7 @ SV449 @ ( tc_fun @ SV818 @ tc_bool ) ) @ SV1110 @ ( tc_fun @ SV818 @ tc_bool ) )
| ~ ( c_lessequals @ SV449 @ SV1110 @ ( tc_fun @ SV818 @ tc_bool ) )
| ~ ( c_lessequals @ SV7 @ SV1110 @ ( tc_fun @ SV818 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2568]) ).
thf(2976,plain,
! [SV1111: $i,SV821: $i,SV452: $i,SV10: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV10 @ SV452 @ ( tc_fun @ SV821 @ tc_bool ) ) @ SV1111 @ ( tc_fun @ SV821 @ tc_bool ) )
| ~ ( c_lessequals @ SV452 @ SV1111 @ ( tc_fun @ SV821 @ tc_bool ) )
| ~ ( c_lessequals @ SV10 @ SV1111 @ ( tc_fun @ SV821 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2571]) ).
thf(2977,plain,
! [SV453: $i,SV11: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV11 )
= $false )
| ( ( ! [SY3138: $i,SY3139: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV453 @ SY3138 @ SV11 ) @ SY3139 @ SV11 )
| ~ ( c_lessequals @ SY3138 @ SY3139 @ SV11 )
| ~ ( c_lessequals @ SV453 @ SY3139 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2572]) ).
thf(2978,plain,
! [SV12: $i,SV1112: $i] :
( ( ( ! [SY4529: $i] : ( c_lessequals @ SV1112 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1112 @ SY4529 @ SV12 ) @ SV12 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(2979,plain,
! [SV13: $i,SV1113: $i] :
( ( ( ! [SY4530: $i] : ( c_lessequals @ SV1113 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4530 @ SV1113 @ SV13 ) @ SV13 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2574]) ).
thf(2980,plain,
! [SV454: $i,SV14: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV14 )
= $false )
| ( ( ! [SY3140: $i,SY3141: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV454 @ SY3140 @ SV14 ) @ SY3141 @ SV14 )
| ~ ( c_lessequals @ SY3140 @ SY3141 @ SV14 )
| ~ ( c_lessequals @ SV454 @ SY3141 @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2575]) ).
thf(2981,plain,
! [SV455: $i,SV15: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV15 )
= $false )
| ( ( ! [SY3142: $i,SY3143: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV455 @ SY3142 @ SV15 ) @ SY3143 @ SV15 )
| ~ ( c_lessequals @ SY3142 @ SY3143 @ SV15 )
| ~ ( c_lessequals @ SV455 @ SY3143 @ SV15 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2576]) ).
thf(2982,plain,
! [SV16: $i,SV1114: $i] :
( ( ( ! [SY4531: $i] : ( c_lessequals @ SV1114 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4531 @ SV1114 @ SV16 ) @ SV16 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2577]) ).
thf(2983,plain,
! [SV17: $i,SV1115: $i] :
( ( ( ! [SY4532: $i] : ( c_lessequals @ SV1115 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1115 @ SY4532 @ SV17 ) @ SV17 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2578]) ).
thf(2984,plain,
! [SV1116: $i,SV822: $i,SV456: $i,SV18: $i] :
( ( ! [SY4533: $i,SY4534: $i,SY4535: $i,SY4536: $i,SY4537: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV18 @ SV456 @ ( c_COMBC @ SV822 @ SV1116 @ SV1116 @ tc_bool ) @ ( c_COMBC @ SY4533 @ SV1116 @ SV1116 @ tc_bool ) @ SY4534 @ SY4535 @ SY4536 @ SY4537 @ SV1116 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV456 @ SV18 @ SV822 @ SY4533 @ SY4535 @ SY4534 @ SY4537 @ SY4536 @ SV1116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2579]) ).
thf(2985,plain,
! [SV823: $i,SV457: $i,SV19: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV19 @ ( c_HOL_Ominus__class_Ominus @ SV457 @ SV19 @ ( tc_fun @ SV823 @ tc_bool ) ) @ ( tc_fun @ SV823 @ tc_bool ) )
= SV457 )
= $true )
| ( ( ~ ( c_lessequals @ SV19 @ SV457 @ ( tc_fun @ SV823 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2580]) ).
thf(2986,plain,
! [SV824: $i,SV458: $i,SV20: $i] :
( ( c_Com_Ocom_OSKIP
= ( c_Com_Ocom_OCond @ SV20 @ SV458 @ SV824 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2581]) ).
thf(2987,plain,
! [SV22: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV22 ) )
= $true )
| ( ( ! [SY1840: $i,SY1841: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SY1840 @ SY1841 @ SV22 )
!= ( c_HOL_Ozero__class_Ozero @ SV22 ) )
| ( SY1840 = SY1841 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2583]) ).
thf(2988,plain,
! [SV23: $i,SV1117: $i] :
( ( ( ! [SY4538: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV1117 @ SY4538 @ SV23 )
!= ( c_HOL_Ozero__class_Ozero @ SV23 ) )
| ( SV1117 = SY4538 ) ) )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2584]) ).
thf(2989,plain,
! [SV24: $i,SV1118: $i] :
( ( ( ! [SY4539: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV1118 @ SY4539 @ SV24 )
!= ( c_HOL_Ozero__class_Ozero @ SV24 ) )
| ( SV1118 = SY4539 ) ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2585]) ).
thf(2990,plain,
! [SV1119: $i,SV461: $i,SV26: $i] :
( ( ( hBOOL @ ( c_in @ SV26 @ ( c_Collect @ SV461 @ SV1119 ) @ SV1119 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV461 @ SV26 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2587]) ).
thf(2991,plain,
! [SV1120: $i,SV27: $i,SV462: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV462 @ ( c_Collect @ SV27 @ SV1120 ) @ SV1120 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV27 @ SV462 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2588]) ).
thf(2992,plain,
! [SV1121: $i,SV827: $i,SV463: $i,SV28: $i] :
( ( ( hBOOL @ ( c_in @ SV28 @ ( c_HOL_Ominus__class_Ominus @ SV463 @ SV827 @ ( tc_fun @ SV1121 @ tc_bool ) ) @ SV1121 ) )
| ( hBOOL @ ( c_in @ SV28 @ SV827 @ SV1121 ) )
| ~ ( hBOOL @ ( c_in @ SV28 @ SV463 @ SV1121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2589]) ).
thf(2993,plain,
! [SV1122: $i,SV828: $i,SV464: $i,SV29: $i] :
( ( ( hBOOL @ ( c_in @ SV29 @ ( c_HOL_Ominus__class_Ominus @ SV464 @ SV828 @ ( tc_fun @ SV1122 @ tc_bool ) ) @ SV1122 ) )
| ( hBOOL @ ( c_in @ SV29 @ SV828 @ SV1122 ) )
| ~ ( hBOOL @ ( c_in @ SV29 @ SV464 @ SV1122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2590]) ).
thf(2994,plain,
! [SV1123: $i,SV829: $i,SV465: $i,SV30: $i] :
( ( ! [SY4540: $i,SY4541: $i] :
( ( c_Com_Ocom_OCall @ SV30 @ SV465 @ SV829 )
!= ( c_Com_Ocom_OLocal @ SV1123 @ SY4540 @ SY4541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2591]) ).
thf(2995,plain,
! [SV830: $i,SV466: $i,SV31: $i] :
( ( ( hBOOL @ ( c_in @ SV31 @ SV466 @ SV830 ) )
= $true )
| ( ( ! [SY4011: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SV31 @ SY4011 @ SV830 ) @ SV466 @ ( tc_fun @ SV830 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2592]) ).
thf(2996,plain,
! [SV1124: $i,SV831: $i,SV467: $i,SV32: $i] :
( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV32 @ ( c_COMBK @ SV467 @ ( tc_fun @ SV831 @ tc_bool ) @ SV1124 ) @ SV1124 @ ( tc_fun @ SV831 @ tc_bool ) )
= SV467 )
| ( SV32
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1124 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2593]) ).
thf(2997,plain,
! [SV468: $i,SV33: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV33 )
= $false )
| ( ( ! [SY3169: $i,SY3170: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV468 @ ( c_COMBK @ SY3169 @ SV33 @ SY3170 ) @ SY3170 @ SV33 )
= SY3169 )
| ( SV468
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3170 @ tc_bool ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2594]) ).
thf(2998,plain,
! [SV1125: $i,SV832: $i,SV469: $i,SV34: $i] :
( ( ! [SY4542: $i] :
( ( c_Com_Ocom_OCall @ SV34 @ SV469 @ SV832 )
!= ( c_Com_Ocom_OWhile @ SV1125 @ SY4542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2595]) ).
thf(2999,plain,
! [SV1126: $i,SV833: $i,SV470: $i,SV35: $i] :
( ( ! [SY4543: $i] :
( ( c_Set_Oinsert @ ( hAPP @ SV35 @ SV470 ) @ ( c_Set_Oimage @ SV35 @ SV833 @ SV1126 @ SY4543 ) @ SY4543 )
= ( c_Set_Oimage @ SV35 @ SV833 @ SV1126 @ SY4543 ) )
| ~ ( hBOOL @ ( c_in @ SV470 @ SV833 @ SV1126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2596]) ).
thf(3000,plain,
! [SV1127: $i,SV834: $i,SV471: $i,SV36: $i] :
( ( ( c_lessequals @ SV36 @ ( c_Set_Oinsert @ SV471 @ SV834 @ SV1127 ) @ ( tc_fun @ SV1127 @ tc_bool ) )
| ~ ( c_lessequals @ SV36 @ SV834 @ ( tc_fun @ SV1127 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SV471 @ SV36 @ SV1127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2597]) ).
thf(3001,plain,
! [SV835: $i,SV472: $i,SV37: $i] :
( ( ( c_lessequals @ SV37 @ SV472 @ ( tc_fun @ SV835 @ tc_bool ) )
= $true )
| ( ( ! [SY4018: $i] :
( ( hBOOL @ ( c_in @ SY4018 @ SV37 @ SV835 ) )
| ~ ( c_lessequals @ SV37 @ ( c_Set_Oinsert @ SY4018 @ SV472 @ SV835 ) @ ( tc_fun @ SV835 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2598]) ).
thf(3002,plain,
! [SV1128: $i,SV836: $i,SV473: $i,SV38: $i] :
( ( ( c_lessequals @ SV38 @ ( c_Set_Oinsert @ SV473 @ SV836 @ SV1128 ) @ ( tc_fun @ SV1128 @ tc_bool ) )
| ~ ( c_lessequals @ SV38 @ SV836 @ ( tc_fun @ SV1128 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SV473 @ SV38 @ SV1128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2599]) ).
thf(3003,plain,
! [SV837: $i,SV474: $i,SV39: $i] :
( ( ( c_lessequals @ SV39 @ SV474 @ ( tc_fun @ SV837 @ tc_bool ) )
= $true )
| ( ( ! [SY4020: $i] :
( ~ ( c_lessequals @ SV39 @ ( c_Set_Oinsert @ SY4020 @ SV474 @ SV837 ) @ ( tc_fun @ SV837 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SY4020 @ SV39 @ SV837 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2600]) ).
thf(3004,plain,
! [SV1129: $i,SV838: $i,SV475: $i,SV40: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV40 @ SV475 @ ( tc_fun @ SV838 @ tc_bool ) ) @ SV1129 @ ( tc_fun @ SV838 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV40 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV475 @ SV1129 @ ( tc_fun @ SV838 @ tc_bool ) ) @ ( tc_fun @ SV838 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2601]) ).
thf(3005,plain,
! [SV1130: $i,SV839: $i,SV476: $i,SV41: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV41 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV476 @ SV839 @ ( tc_fun @ SV1130 @ tc_bool ) ) @ ( tc_fun @ SV1130 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV476 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV41 @ SV839 @ ( tc_fun @ SV1130 @ tc_bool ) ) @ ( tc_fun @ SV1130 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2602]) ).
thf(3006,plain,
! [SV1131: $i,SV840: $i,SV477: $i,SV42: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV42 @ SV477 ) @ SV840 @ SV1131 )
| ! [SY4544: $i] :
( ~ ( c_Natural_Oevalc @ SV477 @ SY4544 @ SV1131 )
| ~ ( c_Natural_Oevalc @ SV42 @ SV840 @ SY4544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2603]) ).
thf(3007,plain,
! [SV1132: $i,SV841: $i,SV478: $i,SV43: $i] :
( ( ! [SY4545: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV43 @ SV478 @ SV841 @ SV1132 ) @ ( c_Set_Oimage @ SV43 @ SY4545 @ SV841 @ SV1132 ) @ ( tc_fun @ SV1132 @ tc_bool ) ) @ ( c_Set_Oimage @ SV43 @ ( c_HOL_Ominus__class_Ominus @ SV478 @ SY4545 @ ( tc_fun @ SV841 @ tc_bool ) ) @ SV841 @ SV1132 ) @ ( tc_fun @ SV1132 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2604]) ).
thf(3008,plain,
! [SV842: $i,SV479: $i,SV44: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV44 @ SV479 ) ) )
= $true )
| ( ( ! [SY4027: $i] :
( ( c_Natural_Oevalc @ SV842 @ SV479 @ SY4027 )
| ! [SY4028: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV44 @ SV842 @ SY4028 ) @ SV479 @ SY4027 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2605]) ).
thf(3009,plain,
! [SV1133: $i,SV843: $i,SV480: $i,SV45: $i] :
( ( ! [SY4546: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV45 @ SV480 @ SV843 ) @ SV1133 @ SY4546 )
| ~ ( c_Natural_Oevalc @ SV480 @ SV1133 @ SY4546 )
| ~ ( hBOOL @ ( hAPP @ SV45 @ SV1133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2606]) ).
thf(3010,plain,
! [SV1134: $i,SV844: $i,SV481: $i,SV46: $i] :
( ( ! [SY4547: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV46 @ SV481 ) @ SV844 @ SV1134 @ SY4547 )
| ! [SY4548: $i] :
( ~ ( c_Natural_Oevaln @ SV481 @ SY4548 @ SV1134 @ SY4547 )
| ~ ( c_Natural_Oevaln @ SV46 @ SV844 @ SV1134 @ SY4548 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2607]) ).
thf(3011,plain,
! [SV482: $i,SV47: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV47 )
= $false )
| ( ( ! [SY3205: $i,SY3206: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV482 @ SV482 @ SV47 )
!= ( c_HOL_Ominus__class_Ominus @ SY3205 @ SY3206 @ SV47 ) )
| ( SY3205 = SY3206 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2608]) ).
thf(3012,plain,
! [SV483: $i,SV48: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV48 )
= $false )
| ( ( ! [SY3207: $i] :
( ! [SY3208: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV483 @ SY3207 @ SV48 )
!= ( c_HOL_Ominus__class_Ominus @ SY3208 @ SY3208 @ SV48 ) )
| ( SV483 = SY3207 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2609]) ).
thf(3013,plain,
! [SV1135: $i,SV845: $i,SV484: $i,SV49: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV49 @ SV484 ) @ SV845 @ SV1135 )
| ! [SY4549: $i] :
( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV49 @ SV484 ) @ SY4549 @ SV1135 )
| ~ ( c_Natural_Oevalc @ SV484 @ SV845 @ SY4549 )
| ~ ( hBOOL @ ( hAPP @ SV49 @ SV845 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2610]) ).
thf(3014,plain,
! [SV1136: $i,SV846: $i,SV487: $i,SV52: $i] :
( ( ! [SY4550: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV52 @ SV487 ) @ SV846 @ SV1136 @ SY4550 )
| ! [SY4551: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV52 @ SV487 ) @ SY4551 @ SV1136 @ SY4550 )
| ~ ( c_Natural_Oevaln @ SV487 @ SV846 @ SV1136 @ SY4551 )
| ~ ( hBOOL @ ( hAPP @ SV52 @ SV846 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2613]) ).
thf(3015,plain,
! [SV1137: $i,SV848: $i,SV489: $i,SV54: $i] :
( ( ! [SY4552: $i,SY4553: $i] :
( ( hAPP @ ( c_COMBS @ SV54 @ SV489 @ SV848 @ SV1137 @ SY4552 ) @ SY4553 )
= ( hAPP @ ( hAPP @ SV54 @ SY4553 ) @ ( hAPP @ SV489 @ SY4553 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2615]) ).
thf(3016,plain,
! [SV1138: $i,SV849: $i,SV490: $i,SV55: $i] :
( ( ( hAPP @ ( c_COMBK @ SV55 @ SV490 @ SV849 ) @ SV1138 )
= SV55 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2616]) ).
thf(3017,plain,
! [SV1139: $i,SV850: $i,SV492: $i,SV57: $i] :
( ( ! [SY4554: $i,SY4555: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV57 @ SV492 @ SV850 @ SV1139 ) @ SY4554 ) @ SY4555 )
= ( hAPP @ ( hAPP @ SV57 @ SY4555 ) @ SY4554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2617]) ).
thf(3018,plain,
! [SV1140: $i,SV851: $i,SV493: $i,SV58: $i] :
( ( ! [SY4556: $i,SY4557: $i] :
( ( hAPP @ ( c_COMBB @ SV58 @ SV493 @ SV851 @ SV1140 @ SY4556 ) @ SY4557 )
= ( hAPP @ SV58 @ ( hAPP @ SV493 @ SY4557 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2618]) ).
thf(3019,plain,
! [SV1141: $i,SV59: $i,SV494: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV494 @ SV59 @ SV1141 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV59 @ SV494 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(3020,plain,
! [SV1142: $i,SV495: $i,SV60: $i] :
( ( ( hBOOL @ ( c_in @ SV60 @ SV495 @ SV1142 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV495 @ SV60 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2620]) ).
thf(3021,plain,
! [SV1143: $i,SV852: $i,SV496: $i,SV61: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV61 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV496 @ tc_bool ) ) @ SV852 @ SV496 @ ( tc_fun @ SV1143 @ tc_bool ) ) @ ( tc_fun @ SV1143 @ tc_bool ) )
= SV61 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2621]) ).
thf(3022,plain,
! [SV1144: $i,SV853: $i,SV497: $i,SV62: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV62 @ SV497 ) )
| ! [SY4558: $i] :
( ( c_Natural_Oevaln @ SV853 @ SV497 @ SV1144 @ SY4558 )
| ! [SY4559: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV62 @ SV853 @ SY4559 ) @ SV497 @ SV1144 @ SY4558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2622]) ).
thf(3023,plain,
! [SV1145: $i,SV854: $i,SV498: $i,SV63: $i] :
( ( ! [SY4560: $i,SY4561: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV63 @ SV498 @ SV854 ) @ SV1145 @ SY4560 @ SY4561 )
| ~ ( c_Natural_Oevaln @ SV498 @ SV1145 @ SY4560 @ SY4561 )
| ~ ( hBOOL @ ( hAPP @ SV63 @ SV1145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2623]) ).
thf(3024,plain,
! [SV1146: $i,SV855: $i,SV499: $i,SV64: $i] :
( ( ! [SY4562: $i,SY4563: $i,SY4564: $i,SY4565: $i,SY4566: $i,SY4567: $i,SY4568: $i,SY4569: $i] :
( ( c_Com_Ocom_Ocom__case @ SV64 @ SV499 @ SV855 @ SV1146 @ SY4562 @ SY4563 @ SY4564 @ SY4565 @ ( c_Com_Ocom_OCall @ SY4566 @ SY4567 @ SY4568 ) @ SY4569 )
= ( hAPP @ ( hAPP @ ( hAPP @ SY4565 @ SY4566 ) @ SY4567 ) @ SY4568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2624]) ).
thf(3025,plain,
! [SV1147: $i,SV856: $i,SV500: $i,SV65: $i] :
( ( ! [SY4570: $i] :
( ( c_Com_Ocom_OCall @ SV65 @ SV500 @ SV856 )
!= ( c_Com_Ocom_OSemi @ SV1147 @ SY4570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2625]) ).
thf(3026,plain,
! [SV66: $i,SV1148: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1148 @ SV1148 @ SV66 )
= SV1148 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2626]) ).
thf(3027,plain,
! [SV68: $i,SV1149: $i] :
( ( ( ! [SY4571: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1149 @ SY4571 @ ( tc_fun @ t_a @ SV68 ) ) @ v_x )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV1149 @ v_x ) @ ( hAPP @ SY4571 @ v_x ) @ SV68 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV68 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2627]) ).
thf(3028,plain,
! [SV1150: $i,SV857: $i,SV502: $i,SV69: $i] :
( ( ( ( c_Set_Oimage @ ( c_COMBK @ SV69 @ SV502 @ SV857 ) @ SV1150 @ SV857 @ SV502 )
= ( c_Set_Oinsert @ SV69 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV502 @ tc_bool ) ) @ SV502 ) )
| ! [SY4572: $i] :
~ ( hBOOL @ ( c_in @ SY4572 @ SV1150 @ SV857 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2628]) ).
thf(3029,plain,
! [SV1151: $i,SV858: $i,SV503: $i,SV70: $i] :
( ( ( hBOOL @ ( c_in @ ( hAPP @ SV70 @ SV503 ) @ SV858 @ SV1151 ) )
| ! [SY4573: $i,SY4574: $i] :
( ~ ( hBOOL @ ( c_in @ SV503 @ SY4573 @ SY4574 ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV70 @ SY4573 @ SY4574 @ SV1151 ) @ SV858 @ ( tc_fun @ SV1151 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2629]) ).
thf(3030,plain,
! [SV1152: $i,SV859: $i,SV504: $i,SV71: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV71 @ ( c_Set_Oinsert @ SV504 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV859 @ tc_bool ) ) @ SV859 ) @ ( tc_fun @ SV859 @ tc_bool ) ) @ SV1152 @ ( tc_fun @ SV859 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV504 @ SV71 @ SV859 ) )
| ~ ( c_lessequals @ SV71 @ ( c_Set_Oinsert @ SV504 @ SV1152 @ SV859 ) @ ( tc_fun @ SV859 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2630]) ).
thf(3031,plain,
! [SV1153: $i,SV860: $i,SV505: $i,SV72: $i] :
( ( ( c_lessequals @ SV72 @ ( c_Set_Oinsert @ SV505 @ SV860 @ SV1153 ) @ ( tc_fun @ SV1153 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV505 @ SV72 @ SV1153 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV72 @ ( c_Set_Oinsert @ SV505 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1153 @ tc_bool ) ) @ SV1153 ) @ ( tc_fun @ SV1153 @ tc_bool ) ) @ SV860 @ ( tc_fun @ SV1153 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2631]) ).
thf(3032,plain,
! [SV1154: $i,SV861: $i,SV506: $i,SV73: $i] :
( ( ( c_lessequals @ SV73 @ ( c_Set_Oinsert @ SV506 @ SV861 @ SV1154 ) @ ( tc_fun @ SV1154 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV506 @ SV73 @ SV1154 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV73 @ ( c_Set_Oinsert @ SV506 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1154 @ tc_bool ) ) @ SV1154 ) @ ( tc_fun @ SV1154 @ tc_bool ) ) @ SV861 @ ( tc_fun @ SV1154 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2632]) ).
thf(3033,plain,
! [SV862: $i,SV507: $i,SV74: $i] :
( ( ( ! [SY4075: $i] : ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV74 @ SV507 ) @ SV862 @ SY4075 @ SV862 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV74 @ SV862 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2633]) ).
thf(3034,plain,
! [SV1155: $i,SV864: $i,SV509: $i,SV76: $i] :
( ( ! [SY4575: $i,SY4576: $i] :
( ( c_Com_Ocom_OCond @ SV76 @ SV509 @ SV864 )
!= ( c_Com_Ocom_OCall @ SV1155 @ SY4575 @ SY4576 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2635]) ).
thf(3035,plain,
! [SV865: $i,SV510: $i,SV77: $i] :
( ( ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ SV77 ) )
= $true )
| ( ( ! [SY4079: $i,SY4080: $i] :
( ( c_lessequals @ ( hAPP @ SV510 @ SV865 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY4079 @ SV510 @ SY4080 @ SV77 ) @ SV77 )
| ~ ( hBOOL @ ( c_in @ SV865 @ SY4079 @ SY4080 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2636]) ).
thf(3036,plain,
! [SV1156: $i,SV866: $i,SV511: $i,SV78: $i] :
( ( ! [SY4577: $i] : ( c_lessequals @ ( hAPP @ SV78 @ SV511 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV866 @ SV78 @ SV1156 @ ( tc_fun @ SY4577 @ tc_bool ) ) @ ( tc_fun @ SY4577 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV511 @ SV866 @ SV1156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2637]) ).
thf(3037,plain,
! [SV1157: $i,SV867: $i,SV512: $i,SV79: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV79 @ SV512 @ SV867 ) @ SV1157 @ ( tc_fun @ SV867 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV512 @ SV1157 @ ( tc_fun @ SV867 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SV79 @ SV1157 @ SV867 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2638]) ).
thf(3038,plain,
! [SV1158: $i,SV868: $i,SV513: $i,SV80: $i] :
( ( ! [SY4578: $i,SY4579: $i] :
( ( c_Com_Ocom_OLocal @ SV80 @ SV513 @ SV868 )
!= ( c_Com_Ocom_OCond @ SV1158 @ SY4578 @ SY4579 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2639]) ).
thf(3039,plain,
! [SV1159: $i,SV869: $i,SV515: $i,SV82: $i] :
( ( ! [SY4580: $i,SY4581: $i] :
( ( ( c_Com_Ocom_OCall @ SV82 @ SV515 @ SV869 )
!= ( c_Com_Ocom_OCall @ SV1159 @ SY4580 @ SY4581 ) )
| ( SV869 = SY4581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2640]) ).
thf(3040,plain,
! [SV1160: $i,SV870: $i,SV516: $i,SV83: $i] :
( ( ! [SY4582: $i] :
( ! [SY4583: $i] :
( ( c_Com_Ocom_OCall @ SV83 @ SV516 @ SV870 )
!= ( c_Com_Ocom_OCall @ SV1160 @ SY4582 @ SY4583 ) )
| ( SV516 = SY4582 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2641]) ).
thf(3041,plain,
! [SV1161: $i,SV871: $i,SV517: $i,SV84: $i] :
( ( ! [SY4584: $i,SY4585: $i] :
( ( c_Com_Ocom_OCall @ SV84 @ SV517 @ SV871 )
!= ( c_Com_Ocom_OCall @ SV1161 @ SY4584 @ SY4585 ) )
| ( SV84 = SV1161 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2642]) ).
thf(3042,plain,
! [SV1162: $i,SV872: $i,SV519: $i,SV86: $i] :
( ( ! [SY4586: $i] :
( ( c_Com_Ocom_OWhile @ SV86 @ SV519 )
!= ( c_Com_Ocom_OLocal @ SV872 @ SV1162 @ SY4586 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2644]) ).
thf(3043,plain,
! [SV873: $i,SV520: $i,SV87: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV87 @ SV520 ) @ SV873 @ SV873 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV87 @ SV873 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2645]) ).
thf(3044,plain,
! [SV1163: $i,SV874: $i,SV522: $i,SV91: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV91 @ SV522 )
!= ( c_Com_Ocom_OSemi @ SV874 @ SV1163 ) )
| ( SV522 = SV1163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2646]) ).
thf(3045,plain,
! [SV875: $i,SV523: $i,SV92: $i] :
( ( ( ! [SY4099: $i] :
( ( c_Com_Ocom_OSemi @ SV92 @ SV523 )
!= ( c_Com_Ocom_OSemi @ SV875 @ SY4099 ) ) )
= $true )
| ( ( SV92 = SV875 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2647]) ).
thf(3046,plain,
! [SV1164: $i,SV876: $i,SV524: $i,SV93: $i] :
( ( ( c_Com_Ocom_OSemi @ SV93 @ SV524 )
!= ( c_Com_Ocom_OWhile @ SV876 @ SV1164 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2648]) ).
thf(3047,plain,
! [SV94: $i,SV1165: $i] :
( ( ( ! [SY4587: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SV1165 @ SY4587 @ SV94 ) @ SV94 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1165 @ ( c_Complete__Lattice_OSup__class_OSup @ SY4587 @ SV94 ) @ SV94 ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV94 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2649]) ).
thf(3048,plain,
! [SV1166: $i,SV877: $i,SV525: $i,SV95: $i] :
( ( ! [SY4588: $i] :
( ( c_Com_Ocom_OSemi @ SV95 @ SV525 )
!= ( c_Com_Ocom_OCond @ SV877 @ SV1166 @ SY4588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2650]) ).
thf(3049,plain,
! [SV1167: $i,SV878: $i,SV526: $i,SV96: $i] :
( ( ! [SY4589: $i] :
( ( c_Com_Ocom_OSemi @ SV96 @ SV526 )
!= ( c_Com_Ocom_OLocal @ SV878 @ SV1167 @ SY4589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2651]) ).
thf(3050,plain,
! [SV879: $i,SV527: $i,SV97: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ SV97 @ SV527 @ SV879 )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV97 ) @ SV527 @ SV879 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2652]) ).
thf(3051,plain,
! [SV1168: $i,SV880: $i,SV528: $i,SV98: $i] :
( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV98 @ SV528 @ SV880 @ ( tc_fun @ SV1168 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1168 @ tc_bool ) ) )
| ! [SY4590: $i] :
( ( ( hAPP @ SV528 @ SY4590 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1168 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SY4590 @ SV98 @ SV880 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2653]) ).
thf(3052,plain,
! [SV1169: $i,SV881: $i,SV529: $i,SV99: $i] :
( ( ! [SY4591: $i] :
( ( c_Com_Ocom_OCond @ SV99 @ SV529 @ SV881 )
!= ( c_Com_Ocom_OWhile @ SV1169 @ SY4591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2654]) ).
thf(3053,plain,
! [SV882: $i,SV530: $i,SV100: $i] :
( ( ( hBOOL @ ( c_in @ SV100 @ SV530 @ SV882 ) )
= $true )
| ( ( ! [SY4109: $i] :
~ ( hBOOL @ ( c_in @ SV100 @ ( c_HOL_Ominus__class_Ominus @ SV530 @ SY4109 @ ( tc_fun @ SV882 @ tc_bool ) ) @ SV882 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2655]) ).
thf(3054,plain,
! [SV1170: $i,SV883: $i,SV531: $i,SV101: $i] :
( ( ! [SY4592: $i,SY4593: $i] :
( ( c_Com_Ocom_OCond @ SV101 @ SV531 @ SV883 )
!= ( c_Com_Ocom_OLocal @ SV1170 @ SY4592 @ SY4593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2656]) ).
thf(3055,plain,
! [SV884: $i,SV532: $i,SV102: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV102 @ SV532 @ SV884 ) ) )
= $true )
| ( ( ! [SY4113: $i] :
~ ( hBOOL @ ( c_in @ SV102 @ ( c_HOL_Ominus__class_Ominus @ SY4113 @ SV532 @ ( tc_fun @ SV884 @ tc_bool ) ) @ SV884 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2657]) ).
thf(3056,plain,
! [SV1171: $i,SV885: $i,SV533: $i,SV103: $i] :
( ( ( c_lessequals @ ( hAPP @ SV103 @ SV533 ) @ SV885 @ ( tc_fun @ SV1171 @ tc_bool ) )
| ! [SY4594: $i,SY4595: $i] :
( ~ ( hBOOL @ ( c_in @ SV533 @ SY4594 @ SY4595 ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY4594 @ SV103 @ SY4595 @ ( tc_fun @ SV1171 @ tc_bool ) ) @ SV885 @ ( tc_fun @ SV1171 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2658]) ).
thf(3057,plain,
! [SV1172: $i,SV886: $i,SV534: $i,SV104: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ ( c_COMBK @ SV104 @ SV534 @ SV886 ) @ SV1172 @ SV886 @ SV534 @ t_a ) @ v_x )
= SV104 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2659]) ).
thf(3058,plain,
! [SV1173: $i,SV887: $i,SV536: $i,SV106: $i] :
( ( ! [SY4596: $i] :
( ( c_Com_Ocom_OCond @ SV106 @ SV536 @ SV887 )
!= ( c_Com_Ocom_OSemi @ SV1173 @ SY4596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2660]) ).
thf(3059,plain,
! [SV1174: $i,SV888: $i,SV537: $i,SV107: $i] :
( ( ! [SY4597: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV107 @ SV537 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV888 @ SV107 @ SV1174 @ ( tc_fun @ SY4597 @ tc_bool ) ) @ ( tc_fun @ SY4597 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV888 @ SV107 @ SV1174 @ ( tc_fun @ SY4597 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SV537 @ SV888 @ SV1174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2661]) ).
thf(3060,plain,
! [SV1175: $i,SV889: $i,SV538: $i,SV108: $i] :
( ( ! [SY4598: $i,SY4599: $i] :
( ( ( c_Com_Ocom_OCond @ SV108 @ SV538 @ SV889 )
!= ( c_Com_Ocom_OCond @ SV1175 @ SY4598 @ SY4599 ) )
| ( SV889 = SY4599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2662]) ).
thf(3061,plain,
! [SV1176: $i,SV890: $i,SV539: $i,SV109: $i] :
( ( ! [SY4600: $i] :
( ! [SY4601: $i] :
( ( c_Com_Ocom_OCond @ SV109 @ SV539 @ SV890 )
!= ( c_Com_Ocom_OCond @ SV1176 @ SY4600 @ SY4601 ) )
| ( SV539 = SY4600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2663]) ).
thf(3062,plain,
! [SV1177: $i,SV891: $i,SV540: $i,SV110: $i] :
( ( ! [SY4602: $i,SY4603: $i] :
( ( c_Com_Ocom_OCond @ SV110 @ SV540 @ SV891 )
!= ( c_Com_Ocom_OCond @ SV1177 @ SY4602 @ SY4603 ) )
| ( SV110 = SV1177 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2664]) ).
thf(3063,plain,
! [SV111: $i,SV1178: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1178 @ SV1178 @ SV111 )
= ( c_HOL_Ozero__class_Ozero @ SV111 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV111 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2665]) ).
thf(3064,plain,
! [SV112: $i,SV1179: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1179 @ SV1179 @ SV112 )
= ( c_HOL_Ozero__class_Ozero @ SV112 ) )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV112 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2666]) ).
thf(3065,plain,
! [SV113: $i,SV1180: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1180 @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV113 )
= SV1180 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2667]) ).
thf(3066,plain,
! [SV114: $i,SV1181: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1181 @ SV1181 @ SV114 )
= ( c_HOL_Ozero__class_Ozero @ SV114 ) )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV114 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2668]) ).
thf(3067,plain,
! [SV115: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV115 ) )
= $true )
| ( ( ! [SY2137: $i] :
( ( c_HOL_Ominus__class_Ominus @ SY2137 @ SY2137 @ SV115 )
= ( c_HOL_Ozero__class_Ozero @ SV115 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2669]) ).
thf(3068,plain,
! [SV892: $i,SV541: $i,SV116: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV116 ) )
= $true )
| ( ( ! [SY4131: $i,SY4132: $i] :
( ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV541 @ SV892 @ SV116 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY4131 @ SY4132 @ SV116 ) @ ( tc_fun @ SV116 @ tc_bool ) )
| ~ ( c_lessequals @ SV892 @ SY4132 @ SV116 )
| ~ ( c_lessequals @ SY4131 @ SV541 @ SV116 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2670]) ).
thf(3069,plain,
! [SV893: $i,SV542: $i,SV117: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV117 ) )
= $true )
| ( ( ( c_lessequals @ SV542 @ SV893 @ SV117 )
| ! [SY4133: $i] :
( ~ ( c_lessequals @ SY4133 @ SV542 @ SV117 )
| ! [SY4134: $i] :
~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY4133 @ SV542 @ SV117 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY4134 @ SV893 @ SV117 ) @ ( tc_fun @ SV117 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2671]) ).
thf(3070,plain,
! [SV894: $i,SV543: $i,SV118: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV118 ) )
= $true )
| ( ( ( c_lessequals @ SV543 @ SV894 @ SV118 )
| ! [SY4135: $i] :
( ~ ( c_lessequals @ SV894 @ SY4135 @ SV118 )
| ! [SY4136: $i] :
~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV894 @ SY4135 @ SV118 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV543 @ SY4136 @ SV118 ) @ ( tc_fun @ SV118 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2672]) ).
thf(3071,plain,
! [SV1182: $i,SV895: $i,SV546: $i,SV121: $i] :
( ( ! [SY4604: $i,SY4605: $i] :
( ( c_Com_Ocom_OCall @ SV121 @ SV546 @ SV895 )
!= ( c_Com_Ocom_OCond @ SV1182 @ SY4604 @ SY4605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2675]) ).
thf(3072,plain,
! [SV896: $i,SV547: $i,SV122: $i] :
( ( ( ( c_Option_Ooption_OSome @ SV122 @ SV547 )
!= ( c_Option_Ooption_OSome @ SV896 @ SV547 ) )
= $true )
| ( ( SV122 = SV896 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2676]) ).
thf(3073,plain,
! [SV1183: $i,SV897: $i,SV548: $i,SV123: $i] :
( ( ! [SY4606: $i,SY4607: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV123 @ SV548 @ SV897 @ SV1183 @ SY4606 ) @ SY4607 )
= ( hAPP @ SV123 @ ( hAPP @ SV548 @ SY4607 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2677]) ).
thf(3074,plain,
! [SV1184: $i,SV898: $i,SV549: $i,SV124: $i] :
( ( ! [SY4608: $i,SY4609: $i] :
( ( hAPP @ SV124 @ ( hAPP @ SV549 @ SV898 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV124 @ SV549 @ SV1184 @ SY4608 @ SY4609 ) @ SV898 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2678]) ).
thf(3075,plain,
! [SV550: $i,SV125: $i] :
( ( ( ( c_Suc @ SV125 )
= ( c_Suc @ SV550 ) )
= $false )
| ( ( SV125 = SV550 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2679]) ).
thf(3076,plain,
! [SV551: $i,SV126: $i] :
( ( ( ( c_Suc @ SV126 )
= ( c_Suc @ SV551 ) )
= $false )
| ( ( SV126 = SV551 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2680]) ).
thf(3077,plain,
! [SV899: $i,SV552: $i,SV127: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV127 ) )
= $true )
| ( ( ! [SY4146: $i,SY4147: $i] : ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV552 @ SV899 @ SV127 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY4146 @ SY4147 @ SV127 ) @ ( tc_fun @ SV127 @ tc_bool ) )
| ( c_lessequals @ SV552 @ SV899 @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2681]) ).
thf(3078,plain,
! [SV128: $i,SV553: $i,SV1185: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV1185 @ SV553 ) )
| ! [SY4610: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1185 @ SV128 @ ( tc_fun @ SY4610 @ tc_bool ) ) @ SV553 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV128 @ SV553 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2682]) ).
thf(3079,plain,
! [SV1186: $i,SV900: $i,SV554: $i,SV129: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV129 @ SV554 @ ( tc_fun @ SV900 @ tc_bool ) ) @ SV1186 ) )
| ~ ( hBOOL @ ( hAPP @ SV554 @ SV1186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2683]) ).
thf(3080,plain,
! [SV1187: $i,SV901: $i,SV555: $i,SV130: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV130 @ SV555 @ ( tc_fun @ SV901 @ tc_bool ) ) @ SV1187 ) )
| ~ ( hBOOL @ ( hAPP @ SV130 @ SV1187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2684]) ).
thf(3081,plain,
! [SV902: $i,SV556: $i,SV131: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV131 @ SV556 @ SV902 ) )
= $true )
| ( ( ~ ( c_Com_OWT @ SV902 )
| ~ ( c_Com_OWT @ SV556 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2685]) ).
thf(3082,plain,
! [SV1188: $i,SV903: $i,SV557: $i,SV132: $i] :
( ( ! [SY4611: $i,SY4612: $i,SY4613: $i,SY4614: $i,SY4615: $i] :
( ( c_Com_Ocom_Ocom__case @ SV132 @ SV557 @ SV903 @ SV1188 @ SY4611 @ SY4612 @ SY4613 @ SY4614 @ c_Com_Ocom_OSKIP @ SY4615 )
= SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2686]) ).
thf(3083,plain,
! [SV904: $i,SV558: $i,SV133: $i] :
( ( ( hBOOL @ ( c_in @ SV133 @ SV558 @ SV904 ) )
= $true )
| ( ( ! [SY4156: $i] :
( ( hBOOL @ ( c_in @ SV133 @ SY4156 @ SV904 ) )
| ~ ( hBOOL @ ( c_in @ SV133 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4156 @ SV558 @ ( tc_fun @ SV904 @ tc_bool ) ) @ SV904 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2687]) ).
thf(3084,plain,
! [SV1189: $i,SV905: $i,SV559: $i,SV134: $i] :
( ( ! [SY4616: $i] :
( ( c_Com_Ocom_OLocal @ SV134 @ SV559 @ SV905 )
!= ( c_Com_Ocom_OWhile @ SV1189 @ SY4616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2688]) ).
thf(3085,plain,
! [SV1190: $i,SV906: $i,SV560: $i,SV135: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV135 @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV560 @ SV906 @ SV1190 @ ( tc_fun @ SV135 @ tc_bool ) ) )
| ! [SY4617: $i] :
( ( ( hAPP @ SV906 @ SY4617 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV135 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SY4617 @ SV560 @ SV1190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2689]) ).
thf(3086,plain,
! [SV1191: $i,SV907: $i,SV561: $i,SV136: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV136 @ tc_bool ) ) @ SV561 @ SV136 @ ( tc_fun @ SV907 @ tc_bool ) ) @ SV1191 @ ( tc_fun @ SV907 @ tc_bool ) )
= SV1191 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2690]) ).
thf(3087,plain,
! [SV1192: $i,SV908: $i,SV562: $i,SV137: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV137 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV562 @ tc_bool ) ) @ SV908 @ SV562 @ ( tc_fun @ SV1192 @ tc_bool ) ) @ ( tc_fun @ SV1192 @ tc_bool ) )
= SV137 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2691]) ).
thf(3088,plain,
! [SV1193: $i,SV909: $i,SV564: $i,SV139: $i] :
( ( ! [SY4618: $i] :
( ( hBOOL @ ( c_in @ SV139 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV564 @ SV909 @ SV1193 @ ( tc_fun @ SY4618 @ tc_bool ) ) @ SY4618 ) )
| ! [SY4619: $i] :
( ~ ( hBOOL @ ( c_in @ SV139 @ ( hAPP @ SV909 @ SY4619 ) @ SY4618 ) )
| ~ ( hBOOL @ ( c_in @ SY4619 @ SV564 @ SV1193 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2693]) ).
thf(3089,plain,
! [SV1194: $i,SV910: $i,SV565: $i,SV140: $i] :
( ( ! [SY4620: $i] :
( ( hBOOL @ ( c_in @ SV140 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV565 @ SV910 @ SV1194 @ ( tc_fun @ SY4620 @ tc_bool ) ) @ SY4620 ) )
| ! [SY4621: $i] :
( ~ ( hBOOL @ ( c_in @ SV140 @ ( hAPP @ SV910 @ SY4621 ) @ SY4620 ) )
| ~ ( hBOOL @ ( c_in @ SY4621 @ SV565 @ SV1194 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2694]) ).
thf(3090,plain,
! [SV144: $i,SV1195: $i] :
( ( ( ! [SY4622: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ SV1195 @ SY4622 @ ( tc_fun @ t_a @ SV144 ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ SV1195 @ v_x ) @ ( hAPP @ SY4622 @ v_x ) @ SV144 ) ) )
= $true )
| ( ( class_HOL_Ominus @ SV144 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2698]) ).
thf(3091,plain,
! [SV1196: $i,SV914: $i,SV569: $i,SV145: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV145 @ SV569 @ ( tc_fun @ SV914 @ tc_bool ) ) @ SV1196 @ ( tc_fun @ SV914 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ SV145 @ SV1196 @ ( tc_fun @ SV914 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV569 @ SV1196 @ ( tc_fun @ SV914 @ tc_bool ) ) @ ( tc_fun @ SV914 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2699]) ).
thf(3092,plain,
! [SV1197: $i,SV915: $i,SV570: $i,SV146: $i] :
( ( ! [SY4623: $i,SY4624: $i,SY4625: $i,SY4626: $i,SY4627: $i,SY4628: $i,SY4629: $i] :
( ( c_Com_Ocom_Ocom__case @ SV146 @ SV570 @ SV915 @ SV1197 @ SY4623 @ SY4624 @ SY4625 @ SY4626 @ ( c_Com_Ocom_OSemi @ SY4627 @ SY4628 ) @ SY4629 )
= ( hAPP @ ( hAPP @ SV1197 @ SY4627 ) @ SY4628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2700]) ).
thf(3093,plain,
! [SV1198: $i,SV916: $i,SV571: $i,SV147: $i] :
( ( ! [SY4630: $i] :
( ( c_Com_Ocom_OLocal @ SV147 @ SV571 @ SV916 )
!= ( c_Com_Ocom_OSemi @ SV1198 @ SY4630 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2701]) ).
thf(3094,plain,
! [SV1199: $i,SV918: $i,SV573: $i,SV149: $i] :
( ( ! [SY4631: $i,SY4632: $i,SY4633: $i,SY4634: $i,SY4635: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV149 @ ( hAPP @ SV573 @ SV918 ) ) @ SV1199 ) )
| ~ ( hBOOL @ ( c_in @ SV1199 @ SV918 @ SY4631 ) )
| ! [SY3439: $i,SY3440: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV573 @ SY4632 @ SV149 @ SY4633 @ SY4634 @ SY4635 @ SY3439 @ SY3440 @ SY4631 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2703]) ).
thf(3095,plain,
! [SV1200: $i,SV919: $i,SV574: $i,SV150: $i] :
( ( ! [SY4638: $i,SY4639: $i,SY4640: $i,SY4641: $i,SY4642: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV150 @ SV574 ) @ ( hAPP @ SV919 @ SV1200 ) ) )
| ~ ( hBOOL @ ( c_in @ SV574 @ SV1200 @ SY4638 ) )
| ! [SY4194: $i,SY4195: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY4639 @ SV919 @ SV150 @ SY4640 @ SY4641 @ SY4642 @ SY4194 @ SY4195 @ SY4638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2704]) ).
thf(3096,plain,
! [SV152: $i,SV1201: $i] :
( ( ( ! [SY4645: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1201 @ SY4645 @ SV152 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY4645 @ SV1201 @ SV152 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV152 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2706]) ).
thf(3097,plain,
! [SV153: $i,SV1202: $i] :
( ( ( ! [SY4646: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1202 @ SY4646 @ SV153 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SY4646 @ SV1202 @ SV153 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV153 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2707]) ).
thf(3098,plain,
! [SV921: $i,SV576: $i,SV154: $i] :
( ( ( ! [SY4196: $i] :
( ( c_Com_Ocom_OWhile @ SV154 @ SV576 )
!= ( c_Com_Ocom_OWhile @ SV921 @ SY4196 ) ) )
= $true )
| ( ( SV154 = SV921 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2708]) ).
thf(3099,plain,
! [SV1203: $i,SV922: $i,SV577: $i,SV155: $i] :
( ( ( ( c_Com_Ocom_OWhile @ SV155 @ SV577 )
!= ( c_Com_Ocom_OWhile @ SV922 @ SV1203 ) )
| ( SV577 = SV1203 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2709]) ).
thf(3100,plain,
! [SV156: $i,SV578: $i] :
( ( ( c_Com_OWT @ SV578 )
= $false )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ SV156 @ SV578 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2710]) ).
thf(3101,plain,
! [SV157: $i,SV923: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OWhile @ SV923 @ SV157 ) )
= $false )
| ( ( c_Com_OWT @ SV157 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2711]) ).
thf(3102,plain,
! [SV159: $i,SV1204: $i] :
( ( ( ! [SY4647: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1204 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1204 @ SY4647 @ SV159 ) @ SV159 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1204 @ SY4647 @ SV159 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV159 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2713]) ).
thf(3103,plain,
! [SV160: $i,SV1205: $i] :
( ( ( ! [SY4648: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1205 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1205 @ SY4648 @ SV160 ) @ SV160 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1205 @ SY4648 @ SV160 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV160 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2714]) ).
thf(3104,plain,
! [SV925: $i,SV580: $i,SV161: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ SV161 @ SV580 @ SV925 ) )
= $true )
| ( ( ~ ( c_Com_OWT @ SV925 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2715]) ).
thf(3105,plain,
! [SV162: $i,SV1206: $i,SV926: $i] :
( ( ( ~ ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ SV926 @ SV1206 @ SV162 ) ) )
= $true )
| ( ( c_Com_OWT @ SV162 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2716]) ).
thf(3106,plain,
! [SV927: $i,SV581: $i,SV163: $i] :
( ( ( c_Com_Ocom_OCond @ SV163 @ SV581 @ SV927 )
= c_Com_Ocom_OSKIP )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2717]) ).
thf(3107,plain,
! [SV1207: $i,SV928: $i,SV582: $i,SV164: $i] :
( ( ! [SY4649: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV164 @ SV582 @ SV928 @ ( tc_fun @ SV1207 @ tc_bool ) ) @ SY4649 ) )
| ! [SY4201: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV582 @ SY4201 ) @ SY4649 ) )
| ~ ( hBOOL @ ( c_in @ SY4201 @ SV164 @ SV928 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2718]) ).
thf(3108,plain,
! [SV1208: $i,SV929: $i,SV583: $i,SV165: $i] :
( ( ! [SY4651: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV165 @ SV583 @ SV929 @ ( tc_fun @ SV1208 @ tc_bool ) ) @ SY4651 ) )
| ! [SY4204: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV583 @ SY4204 ) @ SY4651 ) )
| ~ ( hBOOL @ ( c_in @ SY4204 @ SV165 @ SV929 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2719]) ).
thf(3109,plain,
! [SV1209: $i,SV930: $i,SV584: $i,SV166: $i] :
( ( ! [SY4653: $i] :
( ( c_Com_Ocom_OWhile @ SV166 @ SV584 )
!= ( c_Com_Ocom_OCond @ SV930 @ SV1209 @ SY4653 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2720]) ).
thf(3110,plain,
! [SV1210: $i,SV931: $i,SV585: $i,SV167: $i] :
( ( ! [SY4654: $i] :
( ( c_Com_Ocom_OSemi @ SV167 @ SV585 )
!= ( c_Com_Ocom_OCall @ SV931 @ SV1210 @ SY4654 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2721]) ).
thf(3111,plain,
! [SV1211: $i,SV932: $i,SV586: $i,SV168: $i] :
( ( ( SV168
= ( c_Suc @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ SV586 @ SV168 @ SV932 @ SV1211 ) ) )
| ~ ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ SV586 ) @ SV932 @ SV168 @ SV1211 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2722]) ).
thf(3112,plain,
! [SV1212: $i,SV933: $i,SV587: $i,SV169: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV169 @ SV587 @ SV933 ) @ SV1212 @ ( tc_fun @ SV933 @ tc_bool ) )
= ( c_Set_Oinsert @ SV169 @ ( c_HOL_Ominus__class_Ominus @ SV587 @ SV1212 @ ( tc_fun @ SV933 @ tc_bool ) ) @ SV933 ) )
| ( hBOOL @ ( c_in @ SV169 @ SV1212 @ SV933 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2723]) ).
thf(3113,plain,
! [SV170: $i,SV1213: $i,SV588: $i] :
( ( ( ~ ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV588 @ SV1213 @ SV170 ) )
= $true )
| ( ( SV170 = SV588 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2724]) ).
thf(3114,plain,
! [SV934: $i,SV589: $i,SV171: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV171 @ SV589 @ SV934 ) ) )
= $true )
| ( ( ! [SY4211: $i,SY4212: $i] : ( hBOOL @ ( c_in @ ( hAPP @ SY4211 @ SV171 ) @ ( c_Set_Oimage @ SY4211 @ SV589 @ SV934 @ SY4212 ) @ SY4212 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2725]) ).
thf(3115,plain,
! [SV935: $i,SV590: $i,SV172: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV172 @ SV590 @ SV935 ) ) )
= $true )
| ( ( ! [SY4213: $i,SY4214: $i] : ( hBOOL @ ( c_in @ ( hAPP @ SY4213 @ SV172 ) @ ( c_Set_Oimage @ SY4213 @ SV590 @ SV935 @ SY4214 ) @ SY4214 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2726]) ).
thf(3116,plain,
! [SV1214: $i,SV936: $i,SV591: $i,SV173: $i] :
( ( ! [SY4655: $i] : ( hBOOL @ ( c_in @ ( hAPP @ SV173 @ SV591 ) @ ( c_Set_Oimage @ SV173 @ SV936 @ SV1214 @ SY4655 ) @ SY4655 ) )
| ~ ( hBOOL @ ( c_in @ SV591 @ SV936 @ SV1214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2727]) ).
thf(3117,plain,
! [SV1215: $i,SV937: $i,SV592: $i,SV174: $i] :
( ( ! [SY4656: $i] : ( hBOOL @ ( c_in @ ( hAPP @ SV174 @ SV592 ) @ ( c_Set_Oimage @ SV174 @ SV937 @ SV1215 @ SY4656 ) @ SY4656 ) )
| ~ ( hBOOL @ ( c_in @ SV592 @ SV937 @ SV1215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2728]) ).
thf(3118,plain,
! [SV1216: $i,SV938: $i,SV593: $i,SV175: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV175 @ SV593 @ ( tc_fun @ SV938 @ tc_bool ) ) @ SV1216 @ ( tc_fun @ SV938 @ tc_bool ) )
| ~ ( c_lessequals @ SV175 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV593 @ SV1216 @ ( tc_fun @ SV938 @ tc_bool ) ) @ ( tc_fun @ SV938 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2729]) ).
thf(3119,plain,
! [SV1217: $i,SV939: $i,SV594: $i,SV176: $i] :
( ( ( c_lessequals @ SV176 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV594 @ SV939 @ ( tc_fun @ SV1217 @ tc_bool ) ) @ ( tc_fun @ SV1217 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV176 @ SV594 @ ( tc_fun @ SV1217 @ tc_bool ) ) @ SV939 @ ( tc_fun @ SV1217 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2730]) ).
thf(3120,plain,
! [SV177: $i,SV595: $i] :
( ( ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ SV595 @ SV177 )
= $false )
| ( ( SV177 = SV595 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2731]) ).
thf(3121,plain,
! [SV940: $i,SV596: $i,SV178: $i] :
( ( ( c_Natural_Oevalc @ SV178 @ SV596 @ SV940 )
= $true )
| ( ( ! [SY4221: $i] :
~ ( c_Natural_Oevaln @ SV178 @ SV596 @ SY4221 @ SV940 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2732]) ).
thf(3122,plain,
! [SV941: $i,SV597: $i,SV179: $i] :
( ( ( c_Natural_Oevalc @ SV179 @ SV597 @ SV941 )
= $true )
| ( ( ! [SY4222: $i] :
~ ( c_Natural_Oevaln @ SV179 @ SV597 @ SY4222 @ SV941 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2733]) ).
thf(3123,plain,
! [SV942: $i,SV598: $i,SV180: $i] :
( ( ( ~ ( class_HOL_Oord @ SV180 ) )
= $true )
| ( ( ! [SY4223: $i] :
( ( c_lessequals @ ( hAPP @ SV598 @ SV942 ) @ ( hAPP @ SY4223 @ SV942 ) @ SV180 )
| ! [SY3499: $i] :
~ ( c_lessequals @ SV598 @ SY4223 @ ( tc_fun @ SY3499 @ SV180 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2734]) ).
thf(3124,plain,
! [SV1218: $i,SV181: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ SV181 ) @ SV1218 @ SV181 )
= SV1218 )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2735]) ).
thf(3125,plain,
! [SV182: $i,SV1219: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1219 @ ( c_Orderings_Obot__class_Obot @ SV182 ) @ SV182 )
= SV1219 )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV182 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2736]) ).
thf(3126,plain,
! [SV1220: $i,SV183: $i] :
( ( ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ SV183 ) @ SV1220 @ SV183 )
= $true )
| ( ( class_Orderings_Obot @ SV183 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2737]) ).
thf(3127,plain,
! [SV184: $i,SV1221: $i] :
( ( ( ! [SY4657: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1221 @ SY4657 @ SV184 )
!= ( c_Orderings_Obot__class_Obot @ SV184 ) )
| ( SV1221
= ( c_Orderings_Obot__class_Obot @ SV184 ) ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV184 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2738]) ).
thf(3128,plain,
! [SV185: $i,SV1222: $i] :
( ( ( ! [SY4658: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1222 @ SY4658 @ SV185 )
!= ( c_Orderings_Obot__class_Obot @ SV185 ) )
| ( SY4658
= ( c_Orderings_Obot__class_Obot @ SV185 ) ) ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV185 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2739]) ).
thf(3129,plain,
! [SV943: $i,SV599: $i,SV187: $i] :
( ( ( ! [SY4225: $i] :
( ( c_Set_Oimage @ SV187 @ SV599 @ SV943 @ SY4225 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4225 @ tc_bool ) ) ) )
= $true )
| ( ( SV599
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV943 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2740]) ).
thf(3130,plain,
! [SV1223: $i,SV944: $i,SV600: $i,SV188: $i] :
( ( ! [SY4659: $i,SY4660: $i,SY4661: $i] :
( ( ( hAPP @ SV188 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_bool ) ) )
= SV944 )
| ! [SY4662: $i,SY4663: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV188 @ SV1223 @ SY4659 @ SY4660 @ SY4661 @ SY4662 @ SY4663 @ SV944 @ SV600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2741]) ).
thf(3131,plain,
! [SV1224: $i,SV945: $i,SV601: $i,SV189: $i] :
( ( ! [SY4664: $i,SY4665: $i,SY4666: $i] :
( ( ( hAPP @ SV189 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV601 @ tc_bool ) ) )
= SV945 )
| ! [SY4667: $i,SY4668: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1224 @ SV189 @ SY4664 @ SY4665 @ SY4666 @ SY4667 @ SV945 @ SY4668 @ SV601 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2742]) ).
thf(3132,plain,
! [SV602: $i,SV190: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV190 @ tc_bool ) )
= ( c_Collect @ SV602 @ SV190 ) )
= $false )
| ( ( ! [SY3516: $i] :
~ ( hBOOL @ ( hAPP @ SV602 @ SY3516 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2743]) ).
thf(3133,plain,
! [SV192: $i,SV1225: $i,SV604: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV604 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1225 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV192 @ SV604 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2745]) ).
thf(3134,plain,
! [SV607: $i,SV196: $i] :
( ( ( c_lessequals @ SV196 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV607 @ tc_bool ) ) @ ( tc_fun @ SV607 @ tc_bool ) )
= $false )
| ( ( SV196
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV607 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2748]) ).
thf(3135,plain,
! [SV946: $i,SV197: $i] :
( ( ( ( c_Collect @ SV197 @ SV946 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV946 @ tc_bool ) ) )
= $false )
| ( ( ! [SY2389: $i] :
~ ( hBOOL @ ( hAPP @ SV197 @ SY2389 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2749]) ).
thf(3136,plain,
! [SV947: $i,SV608: $i,SV198: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV198 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV608 @ tc_bool ) ) @ SV608 ) @ SV947 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2750]) ).
thf(3137,plain,
! [SV1226: $i,SV948: $i,SV615: $i,SV205: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV205 @ tc_bool ) )
!= ( c_Set_Oimage @ SV615 @ SV948 @ SV1226 @ SV205 ) )
| ( SV948
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1226 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2751]) ).
thf(3138,plain,
! [SV617: $i,SV207: $i] :
( ( ( hBOOL @ ( hAPP @ SV207 @ SV617 ) )
= $false )
| ( ( ! [SY3522: $i] :
~ ( hBOOL @ ( c_in @ SV617 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY3522 @ tc_bool ) ) @ SY3522 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2753]) ).
thf(3139,plain,
! [SV950: $i,SV618: $i,SV208: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV208 @ SV618 @ ( tc_fun @ SV950 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV950 @ tc_bool ) ) )
= $true )
| ( ( SV618
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV950 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2754]) ).
thf(3140,plain,
! [SV951: $i,SV619: $i,SV209: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV209 @ SV619 @ ( tc_fun @ SV951 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV951 @ tc_bool ) ) )
= $true )
| ( ( SV209
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV951 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2755]) ).
thf(3141,plain,
! [SV953: $i,SV622: $i,SV212: $i] :
( ( ( ( c_Set_Oinsert @ SV212 @ ( c_HOL_Ominus__class_Ominus @ SV622 @ ( c_Set_Oinsert @ SV212 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV953 @ tc_bool ) ) @ SV953 ) @ ( tc_fun @ SV953 @ tc_bool ) ) @ SV953 )
= SV622 )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV212 @ SV622 @ SV953 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2757]) ).
thf(3142,plain,
! [SV1227: $i,SV954: $i,SV623: $i,SV213: $i] :
( ( ( ( c_Set_Oimage @ ( c_COMBK @ SV213 @ SV623 @ SV954 ) @ SV1227 @ SV954 @ SV623 )
= ( c_Set_Oinsert @ SV213 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV623 @ tc_bool ) ) @ SV623 ) )
| ( SV1227
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV954 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2758]) ).
thf(3143,plain,
! [SV214: $i,SV1228: $i] :
( ( ( ! [SY4669: $i] :
( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SV1228 @ ( c_Set_Oinsert @ SY4669 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV214 @ tc_bool ) ) @ SV214 ) @ SV214 ) @ SV214 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1228 @ SY4669 @ SV214 ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV214 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2759]) ).
thf(3144,plain,
! [SV1229: $i,SV955: $i,SV624: $i,SV215: $i] :
( ( ( c_lessequals @ SV215 @ ( c_Set_Oinsert @ SV624 @ SV955 @ SV1229 ) @ ( tc_fun @ SV1229 @ tc_bool ) )
| ~ ( c_lessequals @ SV215 @ SV955 @ ( tc_fun @ SV1229 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV215 @ ( c_Set_Oinsert @ SV624 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1229 @ tc_bool ) ) @ SV1229 ) @ ( tc_fun @ SV1229 @ tc_bool ) ) @ SV955 @ ( tc_fun @ SV1229 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2760]) ).
thf(3145,plain,
! [SV956: $i,SV625: $i,SV216: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV216 @ SV625 @ SV956 ) @ ( c_Set_Oinsert @ SV216 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV956 @ tc_bool ) ) @ SV956 ) @ ( tc_fun @ SV956 @ tc_bool ) )
= SV625 )
= $true )
| ( ( hBOOL @ ( c_in @ SV216 @ SV625 @ SV956 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2761]) ).
thf(3146,plain,
! [SV1230: $i,SV957: $i,SV626: $i,SV217: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV217 @ SV626 @ SV957 ) @ ( c_Set_Oinsert @ SV217 @ SV1230 @ SV957 ) @ ( tc_fun @ SV957 @ tc_bool ) )
| ~ ( c_lessequals @ SV626 @ SV1230 @ ( tc_fun @ SV957 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2762]) ).
thf(3147,plain,
! [SV1231: $i,SV958: $i,SV627: $i,SV218: $i] :
( ( ( hBOOL @ ( c_in @ SV218 @ ( c_Set_Oinsert @ SV627 @ SV958 @ SV1231 ) @ SV1231 ) )
| ~ ( hBOOL @ ( c_in @ SV218 @ SV958 @ SV1231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2763]) ).
thf(3148,plain,
! [SV1232: $i,SV959: $i,SV628: $i,SV219: $i] :
( ( ( hBOOL @ ( c_in @ SV219 @ ( c_Set_Oinsert @ SV628 @ SV959 @ SV1232 ) @ SV1232 ) )
| ~ ( hBOOL @ ( c_in @ SV219 @ SV959 @ SV1232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2764]) ).
thf(3149,plain,
! [SV1233: $i,SV960: $i,SV629: $i,SV220: $i] :
( ( ! [SY4670: $i] :
( ( c_Set_Oimage @ SV220 @ ( c_Set_Oinsert @ SV629 @ SV960 @ SV1233 ) @ SV1233 @ SY4670 )
= ( c_Set_Oinsert @ ( hAPP @ SV220 @ SV629 ) @ ( c_Set_Oimage @ SV220 @ SV960 @ SV1233 @ SY4670 ) @ SY4670 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2765]) ).
thf(3150,plain,
! [SV1234: $i,SV961: $i,SV630: $i,SV221: $i] :
( ( ! [SY4671: $i,SY4672: $i,SY4673: $i,SY4674: $i,SY4675: $i] :
( ( ( hAPP @ SV221 @ ( c_Set_Oinsert @ SV630 @ SV961 @ SV1234 ) )
= ( hAPP @ ( hAPP @ SY4671 @ SV630 ) @ ( hAPP @ SV221 @ SV961 ) ) )
| ! [SY4676: $i,SY4677: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV221 @ SY4672 @ SY4673 @ SY4674 @ SY4671 @ SY4675 @ SY4676 @ SY4677 @ SV1234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2766]) ).
thf(3151,plain,
! [SV1235: $i,SV962: $i,SV631: $i,SV222: $i] :
( ( ! [SY4678: $i,SY4679: $i,SY4680: $i,SY4681: $i,SY4682: $i] :
( ( ( hAPP @ SV222 @ ( c_Set_Oinsert @ SV631 @ SV962 @ SV1235 ) )
= ( hAPP @ ( hAPP @ SY4678 @ SV631 ) @ ( hAPP @ SV222 @ SV962 ) ) )
| ! [SY4683: $i,SY4684: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY4679 @ SV222 @ SY4680 @ SY4681 @ SY4682 @ SY4678 @ SY4683 @ SY4684 @ SV1235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2767]) ).
thf(3152,plain,
! [SV963: $i,SV632: $i,SV223: $i] :
( ( ( hBOOL @ ( c_in @ SV223 @ SV632 @ SV963 ) )
= $true )
| ( ( ! [SY4262: $i] :
( ( SV223 = SY4262 )
| ~ ( hBOOL @ ( c_in @ SV223 @ ( c_Set_Oinsert @ SY4262 @ SV632 @ SV963 ) @ SV963 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2768]) ).
thf(3153,plain,
! [SV1236: $i,SV965: $i,SV634: $i,SV225: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV225 @ ( c_Set_Oinsert @ SV634 @ SV965 @ SV1236 ) @ ( tc_fun @ SV1236 @ tc_bool ) )
= ( c_Set_Oinsert @ SV634 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV225 @ SV965 @ ( tc_fun @ SV1236 @ tc_bool ) ) @ SV1236 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2770]) ).
thf(3154,plain,
! [SV1237: $i,SV966: $i,SV635: $i,SV226: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ SV226 @ SV635 @ SV966 ) @ SV1237 @ ( tc_fun @ SV966 @ tc_bool ) )
= ( c_Set_Oinsert @ SV226 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV635 @ SV1237 @ ( tc_fun @ SV966 @ tc_bool ) ) @ SV966 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2771]) ).
thf(3155,plain,
! [SV1238: $i,SV967: $i,SV636: $i,SV227: $i] :
( ( ( c_lessequals @ SV227 @ ( c_Set_Oinsert @ SV636 @ SV967 @ SV1238 ) @ ( tc_fun @ SV1238 @ tc_bool ) )
| ~ ( c_lessequals @ SV227 @ SV967 @ ( tc_fun @ SV1238 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2772]) ).
thf(3156,plain,
! [SV968: $i,SV637: $i,SV228: $i] :
( ( ( c_lessequals @ SV228 @ SV637 @ ( tc_fun @ SV968 @ tc_bool ) )
= $true )
| ( ( ! [SY4266: $i] :
~ ( c_lessequals @ ( c_Set_Oinsert @ SY4266 @ SV228 @ SV968 ) @ SV637 @ ( tc_fun @ SV968 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2773]) ).
thf(3157,plain,
! [SV1239: $i,SV972: $i,SV641: $i,SV232: $i] :
( ( ( ( c_Set_Oinsert @ SV232 @ SV641 @ SV972 )
!= ( c_Set_Oinsert @ SV232 @ SV1239 @ SV972 ) )
| ( hBOOL @ ( c_in @ SV232 @ SV1239 @ SV972 ) )
| ( SV641 = SV1239 )
| ( hBOOL @ ( c_in @ SV232 @ SV641 @ SV972 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2777]) ).
thf(3158,plain,
! [SV973: $i,SV642: $i,SV233: $i] :
( ( ( ( c_Set_Oinsert @ SV233 @ SV642 @ SV973 )
= SV642 )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV233 @ SV642 @ SV973 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2778]) ).
thf(3159,plain,
! [SV1240: $i,SV974: $i,SV643: $i,SV234: $i] :
( ( ! [SY4685: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV234 @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV643 ) @ SV974 @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ SV1240 @ tc_Com_Opname @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SY4685 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SV643 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV234 @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV643 ) @ SV974 @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ SV1240 @ tc_Com_Opname @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SY4685 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV643 ) @ SV974 @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ SV1240 @ tc_Com_Opname @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SY4685 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SV643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2779]) ).
thf(3160,plain,
! [SV975: $i,SV644: $i,SV236: $i] :
( ( ( c_Com_Ocom_OWhile @ SV236 @ SV644 )
= ( hAPP @ c_Com_Ocom_OBODY @ SV975 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2780]) ).
thf(3161,plain,
! [SV1241: $i,SV976: $i,SV645: $i,SV237: $i] :
( ( ( hAPP @ c_Com_Ocom_OBODY @ SV237 )
!= ( c_Com_Ocom_OCond @ SV645 @ SV976 @ SV1241 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2781]) ).
thf(3162,plain,
! [SV1242: $i,SV977: $i,SV646: $i,SV238: $i] :
( ( ( c_Com_Ocom_OCond @ SV238 @ SV646 @ SV977 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SV1242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2782]) ).
thf(3163,plain,
! [SV978: $i,SV647: $i,SV239: $i] :
( ( c_Com_Ocom_OSKIP
= ( c_Com_Ocom_OLocal @ SV239 @ SV647 @ SV978 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2783]) ).
thf(3164,plain,
! [SV1243: $i,SV979: $i,SV648: $i,SV240: $i] :
( ( ( c_Natural_Oevaln @ SV240 @ SV648 @ ( c_Suc @ SV979 ) @ SV1243 )
| ~ ( c_Natural_Oevaln @ SV240 @ SV648 @ SV979 @ SV1243 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2784]) ).
thf(3165,plain,
! [SV1244: $i,SV980: $i,SV649: $i,SV241: $i] :
( ( ! [SY4686: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV241 @ SV649 @ ( tc_fun @ SV980 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1244 @ SY4686 @ ( tc_fun @ SV980 @ tc_bool ) ) @ ( tc_fun @ SV980 @ tc_bool ) )
| ~ ( c_lessequals @ SY4686 @ SV649 @ ( tc_fun @ SV980 @ tc_bool ) )
| ~ ( c_lessequals @ SV241 @ SV1244 @ ( tc_fun @ SV980 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2785]) ).
thf(3166,plain,
! [SV1245: $i,SV981: $i,SV650: $i,SV242: $i] :
( ( ( c_Natural_Oevaln @ SV242 @ SV650 @ SV981 @ SV1245 )
| ! [SY4687: $i] :
( ( hBOOL @ ( hAPP @ SY4687 @ SV650 ) )
| ! [SY4688: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SY4687 @ SY4688 @ SV242 ) @ SV650 @ SV981 @ SV1245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2786]) ).
thf(3167,plain,
! [SV1246: $i,SV982: $i,SV651: $i,SV243: $i] :
( ( ! [SY4689: $i,SY4690: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV243 @ SV651 @ SV982 ) @ SV1246 @ SY4689 @ SY4690 )
| ~ ( c_Natural_Oevaln @ SV982 @ SV1246 @ SY4689 @ SY4690 )
| ( hBOOL @ ( hAPP @ SV243 @ SV1246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2787]) ).
thf(3168,plain,
! [SV1247: $i,SV983: $i,SV652: $i,SV244: $i] :
( ( ! [SY4691: $i] :
( ( c_Com_Ocom_OWhile @ SV244 @ SV652 )
!= ( c_Com_Ocom_OCall @ SV983 @ SV1247 @ SY4691 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2788]) ).
thf(3169,plain,
! [SV1248: $i,SV246: $i,SV653: $i] :
( ( ( ~ ( c_lessequals @ SV653 @ SV246 @ ( tc_fun @ SV1248 @ tc_bool ) )
| ~ ( c_lessequals @ SV246 @ SV653 @ ( tc_fun @ SV1248 @ tc_bool ) ) )
= $true )
| ( ( SV246 = SV653 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2789]) ).
thf(3170,plain,
! [SV654: $i,SV247: $i,SV1249: $i] :
( ( ( ! [SY4692: $i] :
( ~ ( c_Natural_Oevalc @ SV1249 @ SY4692 @ SV247 )
| ~ ( c_Natural_Oevalc @ SV1249 @ SY4692 @ SV654 ) ) )
= $true )
| ( ( SV247 = SV654 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2790]) ).
thf(3171,plain,
! [SV1250: $i,SV248: $i,SV655: $i] :
( ( ( ~ ( c_lessequals @ SV655 @ SV248 @ ( tc_fun @ SV1250 @ tc_bool ) )
| ~ ( c_lessequals @ SV248 @ SV655 @ ( tc_fun @ SV1250 @ tc_bool ) ) )
= $true )
| ( ( SV248 = SV655 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2791]) ).
thf(3172,plain,
! [SV249: $i,SV1251: $i] :
( ( ( ! [SY4693: $i] :
( ( SV1251 = SY4693 )
| ~ ( c_lessequals @ SY4693 @ SV1251 @ SV249 )
| ~ ( c_lessequals @ SV1251 @ SY4693 @ SV249 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV249 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2792]) ).
thf(3173,plain,
! [SV250: $i,SV1252: $i] :
( ( ( ! [SY4694: $i] :
( ( SV1252 = SY4694 )
| ~ ( c_lessequals @ SY4694 @ SV1252 @ SV250 )
| ~ ( c_lessequals @ SV1252 @ SY4694 @ SV250 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV250 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2793]) ).
thf(3174,plain,
! [SV251: $i,SV1253: $i] :
( ( ( ! [SY4695: $i] :
( ( SV1253 = SY4695 )
| ~ ( c_lessequals @ SV1253 @ SY4695 @ SV251 )
| ~ ( c_lessequals @ SY4695 @ SV1253 @ SV251 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV251 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2794]) ).
thf(3175,plain,
! [SV252: $i,SV1254: $i] :
( ( ( ! [SY4696: $i] :
( ( c_lessequals @ SV1254 @ SY4696 @ SV252 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1254 @ SY4696 @ SV252 ) @ ( c_HOL_Ozero__class_Ozero @ SV252 ) @ SV252 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV252 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2795]) ).
thf(3176,plain,
! [SV253: $i,SV1255: $i] :
( ( ( ! [SY4697: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1255 @ SY4697 @ SV253 ) @ ( c_HOL_Ozero__class_Ozero @ SV253 ) @ SV253 )
| ~ ( c_lessequals @ SV1255 @ SY4697 @ SV253 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV253 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2796]) ).
thf(3177,plain,
! [SV984: $i,SV656: $i,SV254: $i] :
( ( ( c_Com_Ocom_OLocal @ SV254 @ SV656 @ SV984 )
= c_Com_Ocom_OSKIP )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2797]) ).
thf(3178,plain,
! [SV255: $i,SV1256: $i] :
( ( ( ! [SY4698: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1256 @ SY4698 @ SV255 )
= SV1256 )
| ~ ( c_lessequals @ SY4698 @ SV1256 @ SV255 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV255 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2798]) ).
thf(3179,plain,
! [SV256: $i,SV1257: $i] :
( ( ( ! [SY4699: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1257 @ SY4699 @ SV256 )
!= SY4699 )
| ( c_lessequals @ SV1257 @ SY4699 @ SV256 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV256 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2799]) ).
thf(3180,plain,
! [SV257: $i,SV1258: $i] :
( ( ( ! [SY4700: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1258 @ SY4700 @ SV257 )
= SY4700 )
| ~ ( c_lessequals @ SV1258 @ SY4700 @ SV257 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV257 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2800]) ).
thf(3181,plain,
! [SV985: $i,SV657: $i,SV258: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV258 @ SV657 @ ( tc_fun @ SV985 @ tc_bool ) )
= SV657 )
= $true )
| ( ( ~ ( c_lessequals @ SV258 @ SV657 @ ( tc_fun @ SV985 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2801]) ).
thf(3182,plain,
! [SV986: $i,SV658: $i,SV259: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV259 @ SV658 @ ( tc_fun @ SV986 @ tc_bool ) )
= SV259 )
= $true )
| ( ( ~ ( c_lessequals @ SV658 @ SV259 @ ( tc_fun @ SV986 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2802]) ).
thf(3183,plain,
! [SV987: $i,SV659: $i,SV260: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV260 @ SV659 @ ( tc_fun @ SV987 @ tc_bool ) )
!= SV659 )
= $true )
| ( ( c_lessequals @ SV260 @ SV659 @ ( tc_fun @ SV987 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2803]) ).
thf(3184,plain,
! [SV1259: $i,SV988: $i,SV661: $i,SV264: $i] :
( ( ! [SY4701: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV264 @ SV661 ) @ SV988 ) )
| ! [SY4702: $i] :
( ~ ( c_Natural_Oevaln @ SV1259 @ SY4701 @ SY4702 @ SV988 )
| ! [SY4703: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4703 @ SV661 ) @ SY4701 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ SY4702 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4703 ) @ SV1259 ) @ SV264 ) @ t_a ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2804]) ).
thf(3185,plain,
! [SV989: $i,SV662: $i,SV265: $i] :
( ( ( c_Natural_Oevalc @ SV265 @ SV662 @ SV989 )
= $true )
| ( ( ! [SY4287: $i] :
( ( hBOOL @ ( hAPP @ SY4287 @ SV662 ) )
| ! [SY4288: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY4287 @ SY4288 @ SV265 ) @ SV662 @ SV989 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2805]) ).
thf(3186,plain,
! [SV1260: $i,SV990: $i,SV663: $i,SV266: $i] :
( ( ! [SY4704: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV266 @ SV663 @ SV990 ) @ SV1260 @ SY4704 )
| ~ ( c_Natural_Oevalc @ SV990 @ SV1260 @ SY4704 )
| ( hBOOL @ ( hAPP @ SV266 @ SV1260 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2806]) ).
thf(3187,plain,
! [SV1261: $i,SV991: $i,SV664: $i,SV267: $i] :
( ( ! [SY4705: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ SV267 @ SV664 @ SV991 ) @ SV1261 @ SV991 @ ( tc_fun @ SY4705 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV1261 @ SV267 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV664 @ SV1261 @ SV991 @ ( tc_fun @ SY4705 @ tc_bool ) ) @ ( tc_fun @ SY4705 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2807]) ).
thf(3188,plain,
! [SV268: $i,SV992: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV992 @ SV268 ) )
= $false )
| ( ( c_Com_OWT @ SV268 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2808]) ).
thf(3189,plain,
! [SV993: $i,SV269: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV269 @ SV993 ) )
= $false )
| ( ( c_Com_OWT @ SV269 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2809]) ).
thf(3190,plain,
! [SV270: $i,SV1262: $i] :
( ( ( ! [SY4706: $i] :
( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ SV1262 @ SV270 ) @ SY4706 @ SV270 )
| ~ ( hBOOL @ ( c_in @ SY4706 @ SV1262 @ SV270 ) ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV270 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2810]) ).
thf(3191,plain,
! [SV1263: $i,SV271: $i] :
( ( ( ! [SY4707: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV271 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1263 @ SY4707 @ SV271 ) )
| ( c_lessequals @ SV1263 @ SY4707 @ SV271 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV271 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2811]) ).
thf(3192,plain,
! [SV1264: $i,SV272: $i] :
( ( ( ! [SY4708: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV272 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1264 @ SY4708 @ SV272 ) )
| ~ ( c_lessequals @ SV1264 @ SY4708 @ SV272 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2812]) ).
thf(3193,plain,
! [SV1265: $i,SV994: $i,SV665: $i,SV273: $i] :
( ( ! [SY4709: $i,SY4710: $i,SY4711: $i,SY4712: $i,SY4713: $i,SY4714: $i,SY4715: $i,SY4716: $i] :
( ( c_Com_Ocom_Ocom__case @ SV273 @ SV665 @ SV994 @ SV1265 @ SY4709 @ SY4710 @ SY4711 @ SY4712 @ ( c_Com_Ocom_OLocal @ SY4713 @ SY4714 @ SY4715 ) @ SY4716 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV994 @ SY4713 ) @ SY4714 ) @ SY4715 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2813]) ).
thf(3194,plain,
! [SV1266: $i,SV995: $i,SV666: $i,SV274: $i] :
( ( ! [SY4717: $i,SY4718: $i,SY4719: $i,SY4720: $i,SY4721: $i,SY4722: $i,SY4723: $i] :
( ( c_Com_Ocom_Ocom__case @ SV274 @ SV666 @ SV995 @ SV1266 @ SY4717 @ SY4718 @ SY4719 @ SY4720 @ ( c_Com_Ocom_OWhile @ SY4721 @ SY4722 ) @ SY4723 )
= ( hAPP @ ( hAPP @ SY4718 @ SY4721 ) @ SY4722 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2814]) ).
thf(3195,plain,
! [SV1267: $i,SV996: $i,SV667: $i,SV275: $i] :
( ( ! [SY4724: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV275 @ SV667 @ ( tc_fun @ SV996 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1267 @ SY4724 @ ( tc_fun @ SV996 @ tc_bool ) ) @ ( tc_fun @ SV996 @ tc_bool ) )
| ~ ( c_lessequals @ SV667 @ SY4724 @ ( tc_fun @ SV996 @ tc_bool ) )
| ~ ( c_lessequals @ SV275 @ SV1267 @ ( tc_fun @ SV996 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2815]) ).
thf(3196,plain,
! [SV1268: $i,SV997: $i,SV668: $i,SV276: $i] :
( ( ! [SY4725: $i,SY4726: $i,SY4727: $i] :
( ( c_Fun_Ocomp @ SV276 @ ( c_Fun_Ocomp @ SV668 @ SV997 @ SV1268 @ SY4725 @ SY4726 ) @ SY4725 @ SY4727 @ SY4726 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV276 @ SV668 @ SY4725 @ SY4727 @ SV1268 ) @ SV997 @ SV1268 @ SY4727 @ SY4726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2816]) ).
thf(3197,plain,
! [SV1269: $i,SV998: $i,SV670: $i,SV278: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SV278 @ SV670 @ SV998 @ SV1269 @ t_a ) @ v_x )
= ( hAPP @ SV278 @ ( hAPP @ SV670 @ v_x ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2818]) ).
thf(3198,plain,
! [SV1270: $i,SV999: $i,SV671: $i,SV279: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV279 @ SV671 @ SV999 ) @ SV1270 @ ( tc_fun @ SV999 @ tc_bool ) )
| ~ ( c_lessequals @ SV671 @ SV1270 @ ( tc_fun @ SV999 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV279 @ SV1270 @ SV999 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2819]) ).
thf(3199,plain,
! [SV1271: $i,SV1000: $i,SV672: $i,SV280: $i] :
( ( ! [SY4728: $i,SY4729: $i] :
( ( c_Set_Oimage @ SV280 @ ( c_Set_Oimage @ SV672 @ SV1000 @ SV1271 @ SY4728 ) @ SY4728 @ SY4729 )
= ( c_Set_Oimage @ ( c_COMBB @ SV280 @ SV672 @ SY4728 @ SY4729 @ SV1271 ) @ SV1000 @ SV1271 @ SY4729 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2820]) ).
thf(3200,plain,
! [SV1272: $i,SV1001: $i,SV673: $i,SV281: $i] :
( ( ! [SY4730: $i,SY4731: $i] :
( ( ( c_Com_Ocom_OLocal @ SV281 @ SV673 @ SV1001 )
!= ( c_Com_Ocom_OLocal @ SV1272 @ SY4730 @ SY4731 ) )
| ( SV1001 = SY4731 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2821]) ).
thf(3201,plain,
! [SV1273: $i,SV1002: $i,SV674: $i,SV282: $i] :
( ( ! [SY4732: $i] :
( ! [SY4733: $i] :
( ( c_Com_Ocom_OLocal @ SV282 @ SV674 @ SV1002 )
!= ( c_Com_Ocom_OLocal @ SV1273 @ SY4732 @ SY4733 ) )
| ( SV674 = SY4732 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2822]) ).
thf(3202,plain,
! [SV1274: $i,SV1003: $i,SV675: $i,SV283: $i] :
( ( ! [SY4734: $i,SY4735: $i] :
( ( c_Com_Ocom_OLocal @ SV283 @ SV675 @ SV1003 )
!= ( c_Com_Ocom_OLocal @ SV1274 @ SY4734 @ SY4735 ) )
| ( SV283 = SV1274 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2823]) ).
thf(3203,plain,
! [SV284: $i,SV676: $i] :
( ( ( ~ ( c_Com_OWT @ SV676 ) )
= $true )
| ( ( ~ ( c_Com_OWT @ SV284 ) )
= $true )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV284 @ SV676 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2824]) ).
thf(3204,plain,
! [SV1004: $i,SV677: $i,SV285: $i] :
( ( c_Com_Ocom_OSKIP
= ( c_Com_Ocom_OCall @ SV285 @ SV677 @ SV1004 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2825]) ).
thf(3205,plain,
! [SV1275: $i,SV1005: $i,SV678: $i,SV286: $i] :
( ( ! [SY4736: $i,SY4737: $i] :
( ( c_Set_Oimage @ ( c_Fun_Ocomp @ SV286 @ SV678 @ SV1005 @ SV1275 @ SY4736 ) @ SY4737 @ SY4736 @ SV1275 )
= ( c_Set_Oimage @ SV286 @ ( c_Set_Oimage @ SV678 @ SY4737 @ SY4736 @ SV1005 ) @ SV1005 @ SV1275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2826]) ).
thf(3206,plain,
! [SV1276: $i,SV1006: $i,SV679: $i,SV287: $i] :
( ( ( c_Com_Ocom_OWhile @ SV287 @ SV679 )
!= ( c_Com_Ocom_OSemi @ SV1006 @ SV1276 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2827]) ).
thf(3207,plain,
! [SV1277: $i,SV1007: $i,SV680: $i,SV288: $i] :
( ( ( hBOOL @ ( c_in @ SV288 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV680 @ SV1007 @ ( tc_fun @ SV1277 @ tc_bool ) ) @ SV1277 ) )
| ~ ( hBOOL @ ( c_in @ SV288 @ SV1007 @ SV1277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2828]) ).
thf(3208,plain,
! [SV1278: $i,SV1008: $i,SV681: $i,SV289: $i] :
( ( ( hBOOL @ ( c_in @ SV289 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV681 @ SV1008 @ ( tc_fun @ SV1278 @ tc_bool ) ) @ SV1278 ) )
| ~ ( hBOOL @ ( c_in @ SV289 @ SV681 @ SV1278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2829]) ).
thf(3209,plain,
! [SV291: $i,SV683: $i,SV1279: $i] :
( ( ( ( SV1279 = SV683 )
| ! [SY4738: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV291 @ SY4738 ) @ SV683 @ SV1279 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV291 @ SV683 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2831]) ).
thf(3210,plain,
! [SV684: $i,SV294: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV294 )
= $false )
| ( ( ! [SY3684: $i] :
( ( c_lessequals @ SV684 @ SY3684 @ SV294 )
| ! [SY3685: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3685 @ SV684 @ SV294 ) @ SY3684 @ SV294 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2832]) ).
thf(3211,plain,
! [SV685: $i,SV295: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV295 )
= $false )
| ( ( ! [SY3686: $i] :
( ( c_lessequals @ SV685 @ SY3686 @ SV295 )
| ! [SY3687: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV685 @ SY3687 @ SV295 ) @ SY3686 @ SV295 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2833]) ).
thf(3212,plain,
! [SV686: $i,SV296: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV296 )
= $false )
| ( ( ! [SY3688: $i,SY3689: $i] :
( ( c_lessequals @ SV686 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3688 @ SY3689 @ SV296 ) @ SV296 )
| ~ ( c_lessequals @ SV686 @ SY3689 @ SV296 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2834]) ).
thf(3213,plain,
! [SV687: $i,SV297: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV297 )
= $false )
| ( ( ! [SY3690: $i] :
( ! [SY3691: $i] : ( c_lessequals @ SV687 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3690 @ SY3691 @ SV297 ) @ SV297 )
| ~ ( c_lessequals @ SV687 @ SY3690 @ SV297 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2835]) ).
thf(3214,plain,
! [SV688: $i,SV298: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV298 )
= $false )
| ( ( ! [SY3692: $i] :
( ( c_lessequals @ SV688 @ SY3692 @ SV298 )
| ! [SY3693: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY3693 @ SV688 @ SV298 ) @ SY3692 @ SV298 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2836]) ).
thf(3215,plain,
! [SV689: $i,SV299: $i] :
( ( ( class_Lattices_Oupper__semilattice @ SV299 )
= $false )
| ( ( ! [SY3694: $i] :
( ( c_lessequals @ SV689 @ SY3694 @ SV299 )
| ! [SY3695: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV689 @ SY3695 @ SV299 ) @ SY3694 @ SV299 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2837]) ).
thf(3216,plain,
! [SV1010: $i,SV690: $i,SV300: $i] :
( ( ( c_lessequals @ SV300 @ SV690 @ ( tc_fun @ SV1010 @ tc_bool ) )
= $true )
| ( ( ! [SY4336: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV300 @ SY4336 @ ( tc_fun @ SV1010 @ tc_bool ) ) @ SV690 @ ( tc_fun @ SV1010 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2838]) ).
thf(3217,plain,
! [SV1011: $i,SV691: $i,SV301: $i] :
( ( ( c_lessequals @ SV301 @ SV691 @ ( tc_fun @ SV1011 @ tc_bool ) )
= $true )
| ( ( ! [SY4337: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4337 @ SV301 @ ( tc_fun @ SV1011 @ tc_bool ) ) @ SV691 @ ( tc_fun @ SV1011 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2839]) ).
thf(3218,plain,
! [SV692: $i,SV302: $i] :
( ( ( class_Orderings_Oorder @ SV302 )
= $false )
| ( ( ! [SY3700: $i] :
( ( c_lessequals @ SV692 @ SY3700 @ SV302 )
| ! [SY3701: $i] :
( ~ ( c_lessequals @ SV692 @ SY3701 @ SV302 )
| ~ ( c_lessequals @ SY3701 @ SY3700 @ SV302 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2840]) ).
thf(3219,plain,
! [SV693: $i,SV303: $i] :
( ( ( class_Orderings_Opreorder @ SV303 )
= $false )
| ( ( ! [SY3702: $i] :
( ( c_lessequals @ SV693 @ SY3702 @ SV303 )
| ! [SY3703: $i] :
( ~ ( c_lessequals @ SY3703 @ SY3702 @ SV303 )
| ~ ( c_lessequals @ SV693 @ SY3703 @ SV303 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2841]) ).
thf(3220,plain,
! [SV1012: $i,SV694: $i,SV304: $i] :
( ( ( hBOOL @ ( c_in @ SV304 @ SV694 @ SV1012 ) )
= $true )
| ( ( ! [SY4338: $i] :
( ~ ( hBOOL @ ( c_in @ SV304 @ SY4338 @ SV1012 ) )
| ~ ( c_lessequals @ SY4338 @ SV694 @ ( tc_fun @ SV1012 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2842]) ).
thf(3221,plain,
! [SV1013: $i,SV695: $i,SV305: $i] :
( ( ( hBOOL @ ( c_in @ SV305 @ SV695 @ SV1013 ) )
= $true )
| ( ( ! [SY4339: $i] :
( ~ ( hBOOL @ ( c_in @ SV305 @ SY4339 @ SV1013 ) )
| ~ ( c_lessequals @ SY4339 @ SV695 @ ( tc_fun @ SV1013 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2843]) ).
thf(3222,plain,
! [SV1014: $i,SV697: $i,SV307: $i] :
( ( ( hBOOL @ ( c_in @ SV307 @ SV697 @ SV1014 ) )
= $true )
| ( ( ! [SY4340: $i] :
( ~ ( c_lessequals @ SY4340 @ SV697 @ ( tc_fun @ SV1014 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV307 @ SY4340 @ SV1014 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2844]) ).
thf(3223,plain,
! [SV1015: $i,SV698: $i,SV308: $i] :
( ( ( hBOOL @ ( c_in @ SV308 @ SV698 @ SV1015 ) )
= $true )
| ( ( ! [SY4341: $i] :
( ~ ( hBOOL @ ( c_in @ SV308 @ SY4341 @ SV1015 ) )
| ~ ( c_lessequals @ SY4341 @ SV698 @ ( tc_fun @ SV1015 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2845]) ).
thf(3224,plain,
! [SV1016: $i,SV700: $i,SV310: $i] :
( ( ( c_lessequals @ SV310 @ SV700 @ ( tc_fun @ SV1016 @ tc_bool ) )
= $true )
| ( ( ! [SY4342: $i] :
( ~ ( c_lessequals @ SY4342 @ SV700 @ ( tc_fun @ SV1016 @ tc_bool ) )
| ~ ( c_lessequals @ SV310 @ SY4342 @ ( tc_fun @ SV1016 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2846]) ).
thf(3225,plain,
! [SV311: $i,SV701: $i,SV1280: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1280 @ SV701 ) )
| ! [SY4739: $i] :
~ ( c_lessequals @ SV1280 @ SV311 @ ( tc_fun @ SY4739 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV311 @ SV701 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2847]) ).
thf(3226,plain,
! [SV312: $i,SV1281: $i] :
( ( ( c_lessequals @ SV1281 @ SV1281 @ SV312 )
= $true )
| ( ( class_Orderings_Oorder @ SV312 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2848]) ).
thf(3227,plain,
! [SV313: $i,SV1282: $i] :
( ( ( c_lessequals @ SV1282 @ SV1282 @ SV313 )
= $true )
| ( ( class_Orderings_Opreorder @ SV313 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2849]) ).
thf(3228,plain,
! [SV702: $i,SV314: $i,SV1283: $i] :
( ( ( ! [SY4740: $i] :
~ ( c_lessequals @ SV1283 @ SV314 @ ( tc_fun @ SY4740 @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ SV1283 @ SV702 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV314 @ SV702 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2850]) ).
thf(3229,plain,
! [SV1017: $i,SV703: $i,SV315: $i] :
( ( ( c_Com_Ocom_OCall @ SV315 @ SV703 @ SV1017 )
= c_Com_Ocom_OSKIP )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2851]) ).
thf(3230,plain,
! [SV316: $i,SV1284: $i] :
( ( ( ! [SY4741: $i] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1284 @ SY4741 @ SV316 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV316 @ tc_bool ) ) )
| ( c_lessequals @ SV1284 @ SY4741 @ SV316 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV316 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2852]) ).
thf(3231,plain,
! [SV317: $i,SV1285: $i] :
( ( ( ! [SY4742: $i] :
( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1285 @ SY4742 @ SV317 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV317 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV1285 @ SY4742 @ SV317 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV317 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2853]) ).
thf(3232,plain,
! [SV1286: $i,SV1018: $i,SV704: $i,SV318: $i] :
( ( ! [SY4743: $i,SY4744: $i,SY4745: $i,SY4746: $i,SY4747: $i,SY4748: $i,SY4749: $i,SY4750: $i] :
( ( c_Com_Ocom_Ocom__case @ SV318 @ SV704 @ SV1018 @ SV1286 @ SY4743 @ SY4744 @ SY4745 @ SY4746 @ ( c_Com_Ocom_OCond @ SY4747 @ SY4748 @ SY4749 ) @ SY4750 )
= ( hAPP @ ( hAPP @ ( hAPP @ SY4743 @ SY4747 ) @ SY4748 ) @ SY4749 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2854]) ).
thf(3233,plain,
! [SV1287: $i,SV1019: $i,SV705: $i,SV319: $i] :
( ( ! [SY4751: $i,SY4752: $i,SY4753: $i] :
( ! [SY4754: $i] :
( ( c_Fun_Ocomp @ SV319 @ SV705 @ SV1019 @ SV1287 @ SY4751 )
!= ( c_Fun_Ocomp @ SY4752 @ SY4753 @ SY4754 @ SV1287 @ SY4751 ) )
| ! [SY3735: $i] :
( ( hAPP @ SV319 @ ( hAPP @ SV705 @ SY3735 ) )
= ( hAPP @ SY4752 @ ( hAPP @ SY4753 @ SY3735 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2855]) ).
thf(3234,plain,
! [SV1288: $i,SV1020: $i,SV706: $i,SV320: $i] :
( ( ! [SY4756: $i,SY4757: $i,SY4758: $i,SY4759: $i,SY4760: $i] :
( ( ( hAPP @ SV320 @ ( hAPP @ SV706 @ SV1020 ) )
!= ( hAPP @ SV1288 @ ( hAPP @ SY4756 @ SY4757 ) ) )
| ! [SY4761: $i,SY4762: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV320 @ SV706 @ SY4758 @ SY4759 @ SY4760 ) @ SV1020 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1288 @ SY4756 @ SY4761 @ SY4759 @ SY4762 ) @ SY4757 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2856]) ).
thf(3235,plain,
! [SV1021: $i,SV707: $i,SV321: $i] :
( ( ( hBOOL @ ( hAPP @ SV321 @ SV707 ) )
= $true )
| ( ( ( SV1021 = SV707 )
| ! [SY4366: $i,SY4367: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV321 @ SY4366 ) @ SV707 @ SY4367 @ SV1021 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2857]) ).
thf(3236,plain,
! [SV1289: $i,SV1022: $i,SV708: $i,SV322: $i] :
( ( ! [SY4763: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV322 @ SV708 @ ( tc_fun @ SV1022 @ tc_bool ) ) @ SV1289 @ SV1022 @ ( tc_fun @ SY4763 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV322 @ SV1289 @ SV1022 @ ( tc_fun @ SY4763 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV708 @ SV1289 @ SV1022 @ ( tc_fun @ SY4763 @ tc_bool ) ) @ ( tc_fun @ SY4763 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2858]) ).
thf(3237,plain,
! [SV1290: $i,SV1023: $i,SV710: $i,SV324: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV324 @ ( c_HOL_Ominus__class_Ominus @ SV710 @ SV1023 @ ( tc_fun @ SV1290 @ tc_bool ) ) @ ( tc_fun @ SV1290 @ tc_bool ) )
= SV1023 )
| ~ ( c_lessequals @ SV324 @ SV710 @ ( tc_fun @ SV1290 @ tc_bool ) )
| ~ ( c_lessequals @ SV1023 @ SV324 @ ( tc_fun @ SV1290 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2859]) ).
thf(3238,plain,
! [SV1024: $i,SV711: $i,SV325: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV325 ) )
= $true )
| ( ( ! [SY4371: $i,SY4372: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV711 @ SV1024 @ SV325 )
!= ( c_HOL_Ominus__class_Ominus @ SY4371 @ SY4372 @ SV325 ) )
| ( c_lessequals @ SY4372 @ SY4371 @ SV325 )
| ~ ( c_lessequals @ SV1024 @ SV711 @ SV325 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2860]) ).
thf(3239,plain,
! [SV1025: $i,SV712: $i,SV326: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV326 ) )
= $true )
| ( ( ! [SY4373: $i,SY4374: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV712 @ SV1025 @ SV326 )
!= ( c_HOL_Ominus__class_Ominus @ SY4373 @ SY4374 @ SV326 ) )
| ( c_lessequals @ SV1025 @ SV712 @ SV326 )
| ~ ( c_lessequals @ SY4374 @ SY4373 @ SV326 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2861]) ).
thf(3240,plain,
! [SV1291: $i,SV1026: $i,SV713: $i,SV327: $i] :
( ( ! [SY4764: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ SV327 @ SV713 @ SV1026 @ SV1291 ) @ ( c_Set_Oimage @ SV327 @ SY4764 @ SV1026 @ SV1291 ) @ ( tc_fun @ SV1291 @ tc_bool ) )
| ~ ( c_lessequals @ SV713 @ SY4764 @ ( tc_fun @ SV1026 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2862]) ).
thf(3241,plain,
! [SV1027: $i,SV714: $i,SV328: $i] :
( ( ( ~ ( c_lessequals @ SV328 @ SV714 @ ( tc_fun @ SV1027 @ tc_bool ) ) )
= $true )
| ( ( ! [SY4377: $i,SY4378: $i] : ( c_lessequals @ ( c_Set_Oimage @ SY4377 @ SV328 @ SV1027 @ SY4378 ) @ ( c_Set_Oimage @ SY4377 @ SV714 @ SV1027 @ SY4378 ) @ ( tc_fun @ SY4378 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2863]) ).
thf(3242,plain,
! [SV1292: $i,SV1028: $i,SV715: $i,SV329: $i] :
( ( ( c_Natural_Oevaln @ SV329 @ SV715 @ SV1028 @ SV1292 )
| ! [SY4765: $i] :
( ( c_Natural_Oevaln @ SY4765 @ SV715 @ SV1028 @ SV1292 )
| ! [SY4766: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SY4766 @ SY4765 @ SV329 ) @ SV715 @ SV1028 @ SV1292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2864]) ).
thf(3243,plain,
! [SV1293: $i,SV1029: $i,SV716: $i,SV330: $i] :
( ( ! [SY4767: $i] :
( ( c_Set_Oimage @ SV330 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV716 @ SV1029 @ ( tc_fun @ SV1293 @ tc_bool ) ) @ SV1293 @ SY4767 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ SV330 @ SV716 @ SV1293 @ SY4767 ) @ ( c_Set_Oimage @ SV330 @ SV1029 @ SV1293 @ SY4767 ) @ ( tc_fun @ SY4767 @ tc_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2865]) ).
thf(3244,plain,
! [SV1294: $i,SV1030: $i,SV717: $i,SV331: $i] :
( ( ! [SY4768: $i,SY4769: $i] :
( ( c_Com_Ocom_OLocal @ SV331 @ SV717 @ SV1030 )
!= ( c_Com_Ocom_OCall @ SV1294 @ SY4768 @ SY4769 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2866]) ).
thf(3245,plain,
! [SV1031: $i,SV718: $i,SV332: $i] :
( ( ( c_Natural_Oevalc @ SV332 @ SV718 @ SV1031 )
= $true )
| ( ( ! [SY4387: $i] :
( ( c_Natural_Oevalc @ SY4387 @ SV718 @ SV1031 )
| ! [SY4388: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY4388 @ SY4387 @ SV332 ) @ SV718 @ SV1031 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2867]) ).
thf(3246,plain,
! [SV333: $i,SV1295: $i] :
( ( ( ! [SY4770: $i] :
( ( c_lessequals @ SV1295 @ ( c_Complete__Lattice_OSup__class_OSup @ SY4770 @ SV333 ) @ SV333 )
| ~ ( hBOOL @ ( c_in @ SV1295 @ SY4770 @ SV333 ) ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV333 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2868]) ).
thf(3247,plain,
! [SV334: $i,SV1296: $i,SV1032: $i] :
( ( ( ~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV1032 @ SV1296 @ SV334 ) ) )
= $true )
| ( ( c_Com_OWT @ SV334 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2869]) ).
thf(3248,plain,
! [SV1297: $i,SV335: $i,SV1033: $i] :
( ( ( ~ ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV1033 @ SV335 @ SV1297 ) ) )
= $true )
| ( ( c_Com_OWT @ SV335 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2870]) ).
thf(3249,plain,
! [SV337: $i,SV1298: $i] :
( ( ( ! [SY4771: $i] :
( ( c_lessequals @ SV1298 @ SY4771 @ SV337 )
| ( c_lessequals @ SY4771 @ SV1298 @ SV337 ) ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV337 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2872]) ).
thf(3250,plain,
! [SV1299: $i,SV1034: $i,SV720: $i,SV338: $i] :
( ( ( hAPP @ c_Com_Ocom_OBODY @ SV338 )
!= ( c_Com_Ocom_OLocal @ SV720 @ SV1034 @ SV1299 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2873]) ).
thf(3251,plain,
! [SV1035: $i,SV721: $i,SV339: $i] :
( ( ( hAPP @ c_Com_Ocom_OBODY @ SV339 )
= ( c_Com_Ocom_OWhile @ SV721 @ SV1035 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2874]) ).
thf(3252,plain,
! [SV1300: $i,SV1036: $i,SV722: $i,SV340: $i] :
( ( ( c_Com_Ocom_OCall @ SV340 @ SV722 @ SV1036 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SV1300 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2875]) ).
thf(3253,plain,
! [SV1037: $i,SV723: $i,SV341: $i] :
( ( ( hAPP @ c_Com_Ocom_OBODY @ SV341 )
= ( c_Com_Ocom_OSemi @ SV723 @ SV1037 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2876]) ).
thf(3254,plain,
! [SV1038: $i,SV724: $i,SV342: $i] :
( ( ( c_Com_Ocom_OSemi @ SV342 @ SV724 )
= ( hAPP @ c_Com_Ocom_OBODY @ SV1038 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2877]) ).
thf(3255,plain,
! [SV1301: $i,SV1039: $i,SV725: $i,SV343: $i] :
( ( ( c_Com_Ocom_OLocal @ SV343 @ SV725 @ SV1039 )
!= ( hAPP @ c_Com_Ocom_OBODY @ SV1301 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2878]) ).
thf(3256,plain,
! [SV1302: $i,SV1040: $i,SV726: $i,SV344: $i] :
( ( ( hAPP @ c_Com_Ocom_OBODY @ SV344 )
!= ( c_Com_Ocom_OCall @ SV726 @ SV1040 @ SV1302 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2879]) ).
thf(3257,plain,
! [SV1303: $i,SV1041: $i,SV727: $i,SV345: $i] :
( ( ! [SY4772: $i,SY4773: $i,SY4774: $i,SY4775: $i,SY4776: $i,SY4777: $i] :
( ( c_Com_Ocom_Ocom__case @ SV345 @ SV727 @ SV1041 @ SV1303 @ SY4772 @ SY4773 @ SY4774 @ SY4775 @ ( hAPP @ c_Com_Ocom_OBODY @ SY4776 ) @ SY4777 )
= ( hAPP @ SY4774 @ SY4776 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2880]) ).
thf(3258,plain,
! [SV1304: $i,SV1042: $i,SV728: $i,SV347: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV347 ) @ SV728 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1042 ) ) @ SV1304 ) @ SV347 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2881]) ).
thf(3259,plain,
! [SV1305: $i,SV1043: $i,SV729: $i,SV348: $i] :
( ( ! [SY4778: $i] :
( ~ ( hBOOL @ ( hAPP @ SV348 @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SV729 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ SV1043 ) @ SV1305 ) @ SY4778 ) @ t_b @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV348 @ ( hAPP @ ( hAPP @ ( hAPP @ SV729 @ SV1043 ) @ SV1305 ) @ SY4778 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2882]) ).
thf(3260,plain,
! [SV1306: $i,SV1044: $i,SV730: $i,SV349: $i] :
( ( ! [SY4779: $i] :
( ~ ( hBOOL @ ( hAPP @ SV349 @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SV730 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ SV1044 ) @ SV1306 ) @ SY4779 ) @ t_b @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV349 @ ( hAPP @ ( hAPP @ ( hAPP @ SV730 @ SV1044 ) @ SV1306 ) @ SY4779 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2883]) ).
thf(3261,plain,
! [SV1307: $i,SV1045: $i,SV731: $i,SV350: $i] :
( ( ! [SY4780: $i,SY4781: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ SV350 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV731 ) @ SV1045 ) @ SV1307 ) @ SY4780 ) @ SV731 @ SY4781 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV350 @ SV1045 ) @ SV1307 ) @ SY4780 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2884]) ).
thf(3262,plain,
! [SV1308: $i,SV1046: $i,SV732: $i,SV351: $i] :
( ( ! [SY4782: $i,SY4783: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SV351 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV732 ) @ SV1046 ) @ SV1308 ) @ SY4782 ) @ SV732 @ SY4783 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV351 @ SV1046 ) @ SV1308 ) @ SY4782 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2885]) ).
thf(3263,plain,
! [SV1047: $i,SV733: $i,SV352: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV352 @ SV733 @ SV1047 )
= $true )
| ( ( ! [SY4413: $i] :
( ~ ( c_lessequals @ SV733 @ SY4413 @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1047 ) @ tc_bool ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV352 @ SY4413 @ SV1047 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2886]) ).
thf(3264,plain,
! [SV1048: $i,SV734: $i,SV353: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ SV734 @ SV1048 )
= $true )
| ( ( ! [SY4414: $i] :
( ~ ( c_lessequals @ SY4414 @ SV353 @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1048 ) @ tc_bool ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY4414 @ SV734 @ SV1048 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2887]) ).
thf(3265,plain,
! [SV1049: $i,SV735: $i,SV354: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV354 @ SV735 @ SV1049 )
= $true )
| ( ( ~ ( c_lessequals @ SV735 @ SV354 @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1049 ) @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2888]) ).
thf(3266,plain,
! [SV1309: $i,SV1050: $i,SV736: $i,SV355: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV355 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV736 ) @ SV1050 ) @ SV1309 ) @ ( 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 @ SV355 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ ( c_COMBK @ ( hAPP @ ( c_COMBC @ ( c_fequal @ tc_Com_Ostate ) @ tc_Com_Ostate @ tc_Com_Ostate @ tc_bool ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ SV355 @ SV736 @ SV1309 @ SV1050 ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) ) @ SV1050 ) @ ( c_COMBK @ ( hAPP @ SV1309 @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ SV355 @ SV736 @ SV1309 @ SV1050 ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_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)],[2889]) ).
thf(3267,plain,
! [SV1310: $i,SV1051: $i,SV737: $i,SV356: $i] :
( ( ! [SY4784: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV356 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ ( hAPP @ SV1051 @ SV1310 ) ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1310 ) ) @ ( hAPP @ SY4784 @ SV1310 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV737 )
| ! [SY4785: $i] :
( ~ ( hBOOL @ ( c_in @ SV1310 @ SY4785 @ tc_Com_Opname ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV356 @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ SV1051 @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ SY4784 @ tc_Com_Opname @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SY4785 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ SV1051 @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ SY4784 @ tc_Com_Opname @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SY4785 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV737 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2890]) ).
thf(3268,plain,
! [SV1311: $i,SV1052: $i,SV739: $i,SV359: $i] :
( ( ! [SY4786: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV359 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV739 ) @ SV1052 ) @ ( c_Com_Ocom_OWhile @ SV1311 @ SY4786 ) ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1052 @ ( c_Fun_Ocomp @ c_Not @ SV1311 @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ SV739 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV739 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV739 ) ) @ SV739 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV359 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV739 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1052 @ SV1311 @ SV739 ) ) @ SY4786 ) @ SV1052 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV739 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV739 ) ) @ SV739 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2891]) ).
thf(3269,plain,
! [SV1312: $i,SV1053: $i,SV740: $i,SV360: $i] :
( ( ! [SY4787: $i,SY4788: $i,SY4789: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ SV1053 ) @ ( c_Com_Ocom_OCond @ SV1312 @ SY4787 @ SY4788 ) ) @ SY4789 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1053 @ ( c_Fun_Ocomp @ c_Not @ SV1312 @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ SV740 ) ) @ SY4788 ) @ SY4789 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1053 @ SV1312 @ SV740 ) ) @ SY4787 ) @ SY4789 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2892]) ).
thf(3270,plain,
! [SV1313: $i,SV1054: $i,SV741: $i,SV361: $i] :
( ( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV361 ) ) @ SV741 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ SV361 @ SV1054 @ SV741 @ SV1313 ) @ SV1313 )
| ~ ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ SV361 ) @ SV741 @ SV1054 @ SV1313 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2893]) ).
thf(3271,plain,
! [SV1314: $i,SV1055: $i,SV742: $i,SV362: $i] :
( ( ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ SV362 ) @ SV742 @ ( c_Suc @ SV1055 ) @ SV1314 )
| ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV362 ) ) @ SV742 @ SV1055 @ SV1314 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2894]) ).
thf(3272,plain,
! [SV1056: $i,SV744: $i,SV366: $i] :
( ( ( SV366
= ( c_Set_Oinsert @ SV744 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1056 @ tc_bool ) ) @ SV1056 ) )
= $true )
| ( ( ( SV366
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1056 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV366 @ ( c_Set_Oinsert @ SV744 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1056 @ tc_bool ) ) @ SV1056 ) @ ( tc_fun @ SV1056 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2897]) ).
thf(3273,plain,
! [SV1315: $i,SV1057: $i,SV746: $i,SV368: $i] :
( ( ! [SY4790: $i,SY4791: $i,SY4792: $i,SY4793: $i] :
( ( ( hAPP @ SV368 @ ( c_Set_Oinsert @ SV746 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1057 @ tc_bool ) ) @ SV1057 ) )
= SV746 )
| ! [SY4794: $i,SY4795: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV368 @ SV1315 @ SY4790 @ SY4791 @ SY4792 @ SY4793 @ SY4794 @ SY4795 @ SV1057 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2898]) ).
thf(3274,plain,
! [SV1316: $i,SV1058: $i,SV747: $i,SV369: $i] :
( ( ! [SY4796: $i,SY4797: $i,SY4798: $i,SY4799: $i] :
( ( ( hAPP @ SV369 @ ( c_Set_Oinsert @ SV747 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1058 @ tc_bool ) ) @ SV1058 ) )
= SV747 )
| ! [SY4800: $i,SY4801: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1316 @ SV369 @ SY4796 @ SY4797 @ SY4798 @ SY4799 @ SY4800 @ SY4801 @ SV1058 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2899]) ).
thf(3275,plain,
! [SV370: $i,SV1317: $i] :
( ( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SV1317 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV370 @ tc_bool ) ) @ SV370 ) @ SV370 )
= SV1317 )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV370 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2900]) ).
thf(3276,plain,
! [SV1318: $i,SV1059: $i,SV749: $i,SV372: $i] :
( ( ( c_Set_Oinsert @ SV372 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV749 @ tc_bool ) ) @ SV1059 @ SV749 @ ( tc_fun @ SV1318 @ tc_bool ) ) @ SV1318 )
= ( c_Set_Oinsert @ SV372 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1318 @ tc_bool ) ) @ SV1318 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2901]) ).
thf(3277,plain,
! [SV374: $i,SV1319: $i] :
( ( ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ SV1319 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV374 @ tc_bool ) ) @ SV374 ) @ SV374 )
= SV1319 )
= $true )
| ( ( class_Orderings_Olinorder @ SV374 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2903]) ).
thf(3278,plain,
! [SV1320: $i,SV1061: $i,SV752: $i,SV376: $i] :
( ( ! [SY4802: $i,SY4803: $i,SY4804: $i,SY4805: $i,SY4806: $i] :
( ( ( hAPP @ SV376 @ ( c_Set_Oinsert @ SV752 @ ( c_Set_Oinsert @ SV1061 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1320 @ tc_bool ) ) @ SV1320 ) @ SV1320 ) )
= ( hAPP @ ( hAPP @ SY4802 @ SV752 ) @ SV1061 ) )
| ! [SY4807: $i,SY4808: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV376 @ SY4803 @ SY4804 @ SY4805 @ SY4802 @ SY4806 @ SY4807 @ SY4808 @ SV1320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2904]) ).
thf(3279,plain,
! [SV1321: $i,SV1062: $i,SV753: $i,SV377: $i] :
( ( ! [SY4809: $i,SY4810: $i,SY4811: $i,SY4812: $i,SY4813: $i] :
( ( ( hAPP @ SV377 @ ( c_Set_Oinsert @ SV753 @ ( c_Set_Oinsert @ SV1062 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1321 @ tc_bool ) ) @ SV1321 ) @ SV1321 ) )
= ( hAPP @ ( hAPP @ SY4809 @ SV753 ) @ SV1062 ) )
| ! [SY4814: $i,SY4815: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY4810 @ SV377 @ SY4811 @ SY4812 @ SY4813 @ SY4809 @ SY4814 @ SY4815 @ SV1321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2905]) ).
thf(3280,plain,
! [SV1322: $i,SV1063: $i,SV754: $i,SV378: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV378 @ ( c_Set_Oinsert @ SV754 @ SV1063 @ SV1322 ) @ ( tc_fun @ SV1322 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV378 @ ( c_Set_Oinsert @ SV754 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1322 @ tc_bool ) ) @ SV1322 ) @ ( tc_fun @ SV1322 @ tc_bool ) ) @ SV1063 @ ( tc_fun @ SV1322 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2906]) ).
thf(3281,plain,
! [SV1323: $i,SV1064: $i,SV755: $i,SV379: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV379 @ ( c_Set_Oinsert @ SV755 @ SV1064 @ SV1323 ) @ ( tc_fun @ SV1323 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV379 @ SV1064 @ ( tc_fun @ SV1323 @ tc_bool ) ) @ ( c_Set_Oinsert @ SV755 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1323 @ tc_bool ) ) @ SV1323 ) @ ( tc_fun @ SV1323 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2907]) ).
thf(3282,plain,
! [SV756: $i,SV380: $i,SV1324: $i] :
( ( ( ! [SY4816: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV1324 @ ( c_Set_Oinsert @ SV380 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4816 @ tc_bool ) ) @ SY4816 ) @ SY4816 ) @ SV756 ) ) )
= $true )
| ( ( SV380 = SV756 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2908]) ).
thf(3283,plain,
! [SV1065: $i,SV758: $i,SV382: $i] :
( ( ( SV382
= ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ SV758 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1065 @ tc_bool ) ) @ SV1065 ) @ SV1065 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV758 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1065 @ tc_bool ) ) @ SV1065 ) @ SV382 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2909]) ).
thf(3284,plain,
! [SV1325: $i,SV759: $i,SV383: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV383 @ ( c_Set_Oinsert @ SV759 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1325 @ tc_bool ) ) @ SV1325 ) @ SV1325 ) ) )
= $true )
| ( ( SV383 = SV759 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2910]) ).
thf(3285,plain,
! [SV385: $i,SV1326: $i] :
( ( ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ SV1326 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV385 @ tc_bool ) ) @ SV385 ) @ SV385 )
= SV1326 )
= $true )
| ( ( class_Orderings_Olinorder @ SV385 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2912]) ).
thf(3286,plain,
! [SV387: $i,SV1327: $i] :
( ( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1327 @ SV1327 @ SV387 )
= ( c_Set_Oinsert @ SV1327 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV387 @ tc_bool ) ) @ SV387 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV387 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2914]) ).
thf(3287,plain,
! [SV1068: $i,SV762: $i,SV388: $i] :
( ( ( ( c_Set_Oinsert @ SV388 @ SV762 @ SV1068 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1068 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV388 @ SV762 @ SV1068 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2915]) ).
thf(3288,plain,
! [SV390: $i,SV1328: $i] :
( ( ( ( c_Complete__Lattice_OInf__class_OInf @ ( c_Set_Oinsert @ SV1328 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV390 @ tc_bool ) ) @ SV390 ) @ SV390 )
= SV1328 )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV390 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2917]) ).
thf(3289,plain,
! [SV1329: $i,SV1070: $i,SV764: $i,SV391: $i] :
( ( ! [SY4817: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV391 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV764 ) @ SV1070 ) @ SV1329 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY4818: $i,SY4819: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SY4817 @ SY4818 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV391 @ SV764 @ SV1329 @ SV1070 @ SY4819 @ SY4817 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4819 @ SY4818 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV391 @ SV764 @ SV1329 @ SV1070 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV391 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4819 ) @ SV1070 ) @ SY4817 ) @ ( 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)],[2918]) ).
thf(3290,plain,
! [SV1330: $i,SV1071: $i,SV765: $i,SV392: $i] :
( ( ! [SY4820: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV392 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV765 ) @ SV1071 ) @ SV1330 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY4821: $i,SY4822: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SY4820 @ SY4821 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV765 @ SY4822 @ SV1330 @ SY4820 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4822 @ SY4821 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV765 @ SY4822 @ SV1330 @ SY4820 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV392 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4822 ) @ SV1071 ) @ SY4820 ) @ ( 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)],[2919]) ).
thf(3291,plain,
! [SV1331: $i,SV1072: $i,SV766: $i,SV393: $i] :
( ( ! [SY4823: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV393 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV766 ) @ SV1072 ) @ SV1331 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY4824: $i,SY4825: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SY4823 @ SY4824 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV393 @ SV766 @ SV1331 @ SV1072 @ SY4825 @ SY4823 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4825 @ SY4824 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV393 @ SV766 @ SV1331 @ SV1072 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV393 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4825 ) @ SV1072 ) @ SY4823 ) @ ( 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)],[2920]) ).
thf(3292,plain,
! [SV1332: $i,SV1073: $i,SV767: $i,SV394: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV394 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV767 ) @ SV1073 ) @ SV1332 ) @ ( 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 @ SV767 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV394 @ SV767 @ SV1332 @ SV1073 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV394 @ SV767 @ SV1332 @ SV1073 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2921]) ).
thf(3293,plain,
! [SV1333: $i,SV1074: $i,SV768: $i,SV395: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV395 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV768 ) @ SV1074 ) @ SV1333 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY4826: $i,SY4827: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1333 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV395 @ SV768 @ SV1333 @ SV1074 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV395 @ SV768 @ SV1333 @ SV1074 @ SY4826 @ SY4827 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV395 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4826 ) @ SV1074 ) @ SY4827 ) @ ( 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)],[2922]) ).
thf(3294,plain,
! [SV1334: $i,SV1075: $i,SV769: $i,SV396: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV396 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV769 ) @ SV1075 ) @ SV1334 ) @ ( 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 @ SV769 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV396 @ SV769 @ SV1334 @ SV1075 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV396 @ SV769 @ SV1334 @ SV1075 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2923]) ).
thf(3295,plain,
! [SV1335: $i,SV1076: $i,SV770: $i,SV397: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV397 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV770 ) @ SV1076 ) @ SV1335 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY4828: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SY4828 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SV1335 @ SY4828 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SV1335 @ SY4828 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV397 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV770 ) @ SV1076 ) @ SY4828 ) @ ( 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)],[2924]) ).
thf(3296,plain,
! [SV1336: $i,SV1077: $i,SV771: $i,SV398: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV398 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV771 ) @ SV1077 ) @ SV1336 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY4829: $i,SY4830: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV771 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV771 @ SY4829 @ SV1336 @ SY4830 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV771 @ SY4829 @ SV1336 @ SY4830 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV398 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4829 ) @ SV1077 ) @ SY4830 ) @ ( 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)],[2925]) ).
thf(3297,plain,
! [SV1337: $i,SV1078: $i,SV772: $i,SV399: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV399 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV772 ) @ SV1078 ) @ SV1337 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY4831: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV772 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV772 @ SY4831 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV772 @ SY4831 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV399 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4831 ) @ SV1078 ) @ SV1337 ) @ ( 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)],[2926]) ).
thf(3298,plain,
! [SV1338: $i,SV1079: $i,SV773: $i,SV400: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV400 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV773 ) @ SV1079 ) @ SV1338 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY4832: $i,SY4833: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1338 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV400 @ SV773 @ SV1338 @ SV1079 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV400 @ SV773 @ SV1338 @ SV1079 @ SY4832 @ SY4833 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV400 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4832 ) @ SV1079 ) @ SY4833 ) @ ( 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)],[2927]) ).
thf(3299,plain,
! [SV1339: $i,SV1080: $i,SV774: $i,SV401: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV401 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV774 ) @ SV1080 ) @ SV1339 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY4834: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4834 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV774 @ SY4834 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV774 @ SY4834 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV401 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4834 ) @ SV1080 ) @ SV1339 ) @ ( 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)],[2928]) ).
thf(3300,plain,
! [SV1340: $i,SV1081: $i,SV775: $i,SV402: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV402 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV775 ) @ SV1081 ) @ SV1340 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY4835: $i,SY4836: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1340 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV775 @ SY4835 @ SV1340 @ SY4836 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV775 @ SY4835 @ SV1340 @ SY4836 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV402 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4835 ) @ SV1081 ) @ SY4836 ) @ ( 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)],[2929]) ).
thf(3301,plain,
! [SV1341: $i,SV1082: $i,SV776: $i,SV403: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV403 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV776 ) @ SV1082 ) @ SV1341 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY4837: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1341 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SV1341 @ SY4837 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SV1341 @ SY4837 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV403 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV776 ) @ SV1082 ) @ SY4837 ) @ ( 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)],[2930]) ).
thf(3302,plain,
! [SV1342: $i,SV1083: $i,SV777: $i,SV404: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV404 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV777 ) @ SV1083 ) @ SV1342 ) @ ( 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 @ SV777 @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ SV404 @ SV777 @ SV1342 @ SV1083 ) ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ SV404 @ SV777 @ SV1342 @ SV1083 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2931]) ).
thf(3303,plain,
! [SV1343: $i,SV1084: $i,SV778: $i,SV405: $i] :
( ( ! [SY4838: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV405 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV778 ) @ SV1084 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1343 ) ) @ SY4838 ) @ SV778 )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ SV405 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV778 ) @ SV1084 ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV1343 ) ) ) @ SY4838 ) @ SV778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2932]) ).
thf(3304,plain,
! [SV1344: $i,SV1085: $i,SV779: $i,SV406: $i] :
( ( ! [SY4839: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ SV406 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV779 ) @ SV1085 ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV1344 ) ) ) @ SY4839 ) @ SV779 )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV406 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV779 ) @ SV1085 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1344 ) ) @ SY4839 ) @ SV779 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2933]) ).
thf(3305,plain,
! [SV1086: $i,SV780: $i,SV407: $i] :
( ( ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ SV407 ) @ SV780 @ SV1086 )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV407 ) ) @ SV780 @ SV1086 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2934]) ).
thf(3306,plain,
! [SV1087: $i,SV781: $i,SV408: $i] :
( ( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV408 ) ) @ SV781 @ SV1087 )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ SV408 ) @ SV781 @ SV1087 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2935]) ).
thf(3307,plain,
! [SV1345: $i,SV1089: $i,SV783: $i,SV410: $i] :
( ( ! [SY4840: $i,SY4841: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SV1089 ) @ ( c_Com_Ocom_OSemi @ SV1345 @ SY4840 ) ) @ SY4841 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 )
| ! [SY4842: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SY4842 ) @ SY4840 ) @ SY4841 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SV1089 ) @ SV1345 ) @ SY4842 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2937]) ).
thf(3308,plain,
! [SV1346: $i,SV1090: $i,SV784: $i,SV411: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV411 @ ( c_Set_Oinsert @ SV784 @ SV1090 @ ( tc_Hoare__Mirabelle_Otriple @ SV1346 ) ) @ SV1346 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV411 @ SV1090 @ SV1346 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV411 @ ( c_Set_Oinsert @ SV784 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1346 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1346 ) ) @ SV1346 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2938]) ).
thf(3309,plain,
! [SV1092: $i,SV786: $i,SV413: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV413 @ SV786 @ SV1092 )
= $true )
| ( ( ! [SY4504: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV413 @ SY4504 @ SV1092 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SY4504 @ SV786 @ SV1092 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2940]) ).
thf(3310,plain,
! [SV1093: $i,SV787: $i,SV414: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV414 @ tc_bool ) )
= ( c_Set_Oinsert @ SV787 @ SV1093 @ SV414 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2941]) ).
thf(3311,plain,
! [SV1347: $i,SV1094: $i,SV788: $i,SV415: $i] :
( ( ! [SY4843: $i,SY4844: $i,SY4845: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV415 ) @ SV788 ) @ SV1094 ) @ SV1347 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV415 ) @ SY4843 ) @ SY4844 ) @ SY4845 ) )
| ( SV1347 = SY4845 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2942]) ).
thf(3312,plain,
! [SV1348: $i,SV1095: $i,SV789: $i,SV416: $i] :
( ( ! [SY4846: $i,SY4847: $i] :
( ! [SY4848: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV416 ) @ SV789 ) @ SV1095 ) @ SV1348 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV416 ) @ SY4846 ) @ SY4847 ) @ SY4848 ) )
| ( SV1095 = SY4847 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2943]) ).
thf(3313,plain,
! [SV1349: $i,SV1096: $i,SV790: $i,SV417: $i] :
( ( ! [SY4849: $i] :
( ! [SY4850: $i,SY4851: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV417 ) @ SV790 ) @ SV1096 ) @ SV1349 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV417 ) @ SY4849 ) @ SY4850 ) @ SY4851 ) )
| ( SV790 = SY4849 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2944]) ).
thf(3314,plain,
! [SV1350: $i,SV1097: $i,SV791: $i,SV418: $i] :
( ( ! [SY4852: $i] :
( ( ( c_Set_Oinsert @ SV418 @ ( c_Set_Oinsert @ SV791 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1097 @ tc_bool ) ) @ SV1097 ) @ SV1097 )
!= ( c_Set_Oinsert @ SV1350 @ ( c_Set_Oinsert @ SY4852 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1097 @ tc_bool ) ) @ SV1097 ) @ SV1097 ) )
| ( SV791 = SV1350 )
| ( SV791 = SY4852 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2945]) ).
thf(3315,plain,
! [SV1351: $i,SV1098: $i,SV792: $i,SV419: $i] :
( ( ! [SY4853: $i] :
( ( ( c_Set_Oinsert @ SV419 @ ( c_Set_Oinsert @ SV792 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1098 @ tc_bool ) ) @ SV1098 ) @ SV1098 )
!= ( c_Set_Oinsert @ SV1351 @ ( c_Set_Oinsert @ SY4853 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1098 @ tc_bool ) ) @ SV1098 ) @ SV1098 ) )
| ( SV419 = SY4853 )
| ( SV792 = SY4853 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2946]) ).
thf(3316,plain,
! [SV1352: $i,SV1099: $i,SV793: $i,SV420: $i] :
( ( ! [SY4854: $i] :
( ( c_Set_Oinsert @ SV420 @ ( c_Set_Oinsert @ SV793 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1099 @ tc_bool ) ) @ SV1099 ) @ SV1099 )
!= ( c_Set_Oinsert @ SV1352 @ ( c_Set_Oinsert @ SY4854 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1099 @ tc_bool ) ) @ SV1099 ) @ SV1099 ) )
| ( SV793 = SV1352 )
| ( SV420 = SV1352 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2947]) ).
thf(3317,plain,
! [SV1353: $i,SV1100: $i,SV794: $i,SV421: $i] :
( ( ! [SY4855: $i] :
( ( ( c_Set_Oinsert @ SV421 @ ( c_Set_Oinsert @ SV794 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1100 @ tc_bool ) ) @ SV1100 ) @ SV1100 )
!= ( c_Set_Oinsert @ SV1353 @ ( c_Set_Oinsert @ SY4855 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1100 @ tc_bool ) ) @ SV1100 ) @ SV1100 ) )
| ( SV421 = SY4855 )
| ( SV421 = SV1353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2948]) ).
thf(3318,plain,
! [SV1354: $i,SV1101: $i,SV797: $i,SV424: $i] :
( ( ! [SY4856: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV424 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV797 ) @ SV1101 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1354 ) ) @ SY4856 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) ) @ SV797 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV797 ) @ SV1101 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1354 ) ) @ SY4856 ) @ SV424 @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) ) @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV797 ) @ SV1101 ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV1354 ) ) ) @ SY4856 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) ) @ SV797 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2950]) ).
thf(3319,plain,
! [SV425: $i,SV798: $i,SV1355: $i] :
( ( ( ( SV1355 = SV798 )
| ! [SY4857: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1355 @ SV425 @ SY4857 ) @ SV798 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV425 @ SV798 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2951]) ).
thf(3320,plain,
! [SV1103: $i,SV800: $i,SV427: $i] :
( ( ( c_Set_Oinsert @ SV427 @ SV800 @ SV1103 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1103 @ tc_bool ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2953]) ).
thf(3321,plain,
! [SV1356: $i,SV1104: $i,SV801: $i,SV428: $i] :
( ( ( c_Set_Oinsert @ SV428 @ ( c_Set_Oinsert @ SV801 @ SV1104 @ SV1356 ) @ SV1356 )
= ( c_Set_Oinsert @ SV801 @ ( c_Set_Oinsert @ SV428 @ SV1104 @ SV1356 ) @ SV1356 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2954]) ).
thf(3322,plain,
! [SV1106: $i,SV803: $i,SV430: $i] :
( ( ( ( c_Set_Oinsert @ SV430 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV803 @ tc_bool ) ) @ SV803 )
!= ( c_Set_Oinsert @ SV1106 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV803 @ tc_bool ) ) @ SV803 ) )
= $true )
| ( ( SV430 = SV1106 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2956]) ).
thf(3323,plain,
! [SV1357: $i,SV1107: $i,SV804: $i,SV431: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV431 @ SV804 @ SV1107 ) @ SV1357 ) )
| ~ ( hBOOL @ ( hAPP @ SV804 @ SV1357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2957]) ).
thf(3324,plain,
! [SV805: $i,SV432: $i] :
( ( ( ( hAPP @ c_Com_Ocom_OBODY @ SV432 )
= ( hAPP @ c_Com_Ocom_OBODY @ SV805 ) )
= $false )
| ( ( SV432 = SV805 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2958]) ).
thf(3325,plain,
! [SV433: $i,SV806: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV806 )
= $false )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ SV433 @ SV806 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2959]) ).
thf(3326,plain,
! [SV434: $i,SV807: $i] :
( ( ( class_Lattices_Olattice @ SV807 )
= $false )
| ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ SV434 @ SV807 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2960]) ).
thf(3327,plain,
! [SV435: $i,SV808: $i] :
( ( ( class_Lattices_Obounded__lattice @ SV808 )
= $false )
| ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ SV435 @ SV808 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2961]) ).
thf(3328,plain,
! [SV436: $i,SV809: $i] :
( ( ( class_Orderings_Opreorder @ SV809 )
= $false )
| ( ( class_Orderings_Opreorder @ ( tc_fun @ SV436 @ SV809 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2962]) ).
thf(3329,plain,
! [SV437: $i,SV810: $i] :
( ( ( class_Lattices_Olattice @ SV810 )
= $false )
| ( ( class_Lattices_Olattice @ ( tc_fun @ SV437 @ SV810 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2963]) ).
thf(3330,plain,
! [SV438: $i,SV811: $i] :
( ( ( class_Orderings_Oorder @ SV811 )
= $false )
| ( ( class_Orderings_Oorder @ ( tc_fun @ SV438 @ SV811 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2964]) ).
thf(3331,plain,
! [SV439: $i,SV812: $i] :
( ( ( class_Orderings_Obot @ SV812 )
= $false )
| ( ( class_Orderings_Obot @ ( tc_fun @ SV439 @ SV812 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2965]) ).
thf(3332,plain,
! [SV440: $i,SV813: $i] :
( ( ( class_HOL_Ominus @ SV813 )
= $false )
| ( ( class_HOL_Ominus @ ( tc_fun @ SV440 @ SV813 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2966]) ).
thf(3333,plain,
! [SV441: $i,SV814: $i] :
( ( ( class_HOL_Oord @ SV814 )
= $false )
| ( ( class_HOL_Oord @ ( tc_fun @ SV441 @ SV814 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2967]) ).
thf(3334,plain,
! [SV816: $i,SV443: $i,SV1358: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV1358 ) @ SV443 ) @ SV816 ) ) )
= $true )
| ( ( SV443 = SV816 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2968]) ).
thf(3335,plain,
! [SV1: $i,SV1359: $i,SV444: $i] :
( ( ( ! [SY4858: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV444 @ SV1359 @ SV1 ) @ SY4858 @ SV1 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV444 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1359 @ SY4858 @ SV1 ) @ SV1 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2969]) ).
thf(3336,plain,
! [SV2: $i,SV1360: $i,SV445: $i] :
( ( ( ! [SY4859: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV445 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1360 @ SY4859 @ SV2 ) @ SV2 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1360 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV445 @ SY4859 @ SV2 ) @ SV2 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2970]) ).
thf(3337,plain,
! [SV3: $i,SV1361: $i,SV446: $i] :
( ( ( ! [SY4860: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV446 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1361 @ SY4860 @ SV3 ) @ SV3 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1361 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV446 @ SY4860 @ SV3 ) @ SV3 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2971]) ).
thf(3338,plain,
! [SV4: $i,SV1362: $i,SV447: $i] :
( ( ( ! [SY4861: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV447 @ SV1362 @ SV4 ) @ SY4861 @ SV4 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV447 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1362 @ SY4861 @ SV4 ) @ SV4 ) ) )
= $true )
| ( ( class_Lattices_Olattice @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2972]) ).
thf(3339,plain,
! [SV1108: $i,SV5: $i,SV448: $i] :
( ( ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ SV448 ) )
= $false )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OCall @ SV5 @ SV448 @ SV1108 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2973]) ).
thf(3340,plain,
! [SV1109: $i,SV6: $i,SV817: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OCall @ SV817 @ SV6 @ SV1109 ) )
= $false )
| ( ( c_Com_OWT @ ( hAPP @ c_Com_Ocom_OBODY @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2974]) ).
thf(3341,plain,
! [SV1110: $i,SV818: $i,SV449: $i,SV7: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV7 @ SV449 @ ( tc_fun @ SV818 @ tc_bool ) ) @ SV1110 @ ( tc_fun @ SV818 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV449 @ SV1110 @ ( tc_fun @ SV818 @ tc_bool ) )
| ~ ( c_lessequals @ SV7 @ SV1110 @ ( tc_fun @ SV818 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2975]) ).
thf(3342,plain,
! [SV1111: $i,SV821: $i,SV452: $i,SV10: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV10 @ SV452 @ ( tc_fun @ SV821 @ tc_bool ) ) @ SV1111 @ ( tc_fun @ SV821 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV452 @ SV1111 @ ( tc_fun @ SV821 @ tc_bool ) )
| ~ ( c_lessequals @ SV10 @ SV1111 @ ( tc_fun @ SV821 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2976]) ).
thf(3343,plain,
! [SV11: $i,SV1363: $i,SV453: $i] :
( ( ( ! [SY4862: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV453 @ SV1363 @ SV11 ) @ SY4862 @ SV11 )
| ~ ( c_lessequals @ SV1363 @ SY4862 @ SV11 )
| ~ ( c_lessequals @ SV453 @ SY4862 @ SV11 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2977]) ).
thf(3344,plain,
! [SV12: $i,SV1364: $i,SV1112: $i] :
( ( ( c_lessequals @ SV1112 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1112 @ SV1364 @ SV12 ) @ SV12 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2978]) ).
thf(3345,plain,
! [SV13: $i,SV1365: $i,SV1113: $i] :
( ( ( c_lessequals @ SV1113 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1365 @ SV1113 @ SV13 ) @ SV13 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2979]) ).
thf(3346,plain,
! [SV14: $i,SV1366: $i,SV454: $i] :
( ( ( ! [SY4863: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV454 @ SV1366 @ SV14 ) @ SY4863 @ SV14 )
| ~ ( c_lessequals @ SV1366 @ SY4863 @ SV14 )
| ~ ( c_lessequals @ SV454 @ SY4863 @ SV14 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2980]) ).
thf(3347,plain,
! [SV15: $i,SV1367: $i,SV455: $i] :
( ( ( ! [SY4864: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV455 @ SV1367 @ SV15 ) @ SY4864 @ SV15 )
| ~ ( c_lessequals @ SV1367 @ SY4864 @ SV15 )
| ~ ( c_lessequals @ SV455 @ SY4864 @ SV15 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2981]) ).
thf(3348,plain,
! [SV16: $i,SV1368: $i,SV1114: $i] :
( ( ( c_lessequals @ SV1114 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1368 @ SV1114 @ SV16 ) @ SV16 )
= $true )
| ( ( class_Lattices_Olattice @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2982]) ).
thf(3349,plain,
! [SV17: $i,SV1369: $i,SV1115: $i] :
( ( ( c_lessequals @ SV1115 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1115 @ SV1369 @ SV17 ) @ SV17 )
= $true )
| ( ( class_Lattices_Olattice @ SV17 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2983]) ).
thf(3350,plain,
! [SV1370: $i,SV1116: $i,SV822: $i,SV456: $i,SV18: $i] :
( ( ! [SY4865: $i,SY4866: $i,SY4867: $i,SY4868: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV18 @ SV456 @ ( c_COMBC @ SV822 @ SV1116 @ SV1116 @ tc_bool ) @ ( c_COMBC @ SV1370 @ SV1116 @ SV1116 @ tc_bool ) @ SY4865 @ SY4866 @ SY4867 @ SY4868 @ SV1116 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV456 @ SV18 @ SV822 @ SV1370 @ SY4866 @ SY4865 @ SY4868 @ SY4867 @ SV1116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2984]) ).
thf(3351,plain,
! [SV823: $i,SV457: $i,SV19: $i] :
( ( ( c_lessequals @ SV19 @ SV457 @ ( tc_fun @ SV823 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV19 @ ( c_HOL_Ominus__class_Ominus @ SV457 @ SV19 @ ( tc_fun @ SV823 @ tc_bool ) ) @ ( tc_fun @ SV823 @ tc_bool ) )
= SV457 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2985]) ).
thf(3352,plain,
! [SV22: $i] :
( ( ( class_Int_Onumber__ring @ SV22 )
= $false )
| ( ( ! [SY1840: $i,SY1841: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SY1840 @ SY1841 @ SV22 )
!= ( c_HOL_Ozero__class_Ozero @ SV22 ) )
| ( SY1840 = SY1841 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2987]) ).
thf(3353,plain,
! [SV23: $i,SV1371: $i,SV1117: $i] :
( ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1117 @ SV1371 @ SV23 )
!= ( c_HOL_Ozero__class_Ozero @ SV23 ) )
| ( SV1117 = SV1371 ) )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2988]) ).
thf(3354,plain,
! [SV24: $i,SV1372: $i,SV1118: $i] :
( ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1118 @ SV1372 @ SV24 )
!= ( c_HOL_Ozero__class_Ozero @ SV24 ) )
| ( SV1118 = SV1372 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2989]) ).
thf(3355,plain,
! [SV1119: $i,SV26: $i,SV461: $i] :
( ( ( hBOOL @ ( hAPP @ SV461 @ SV26 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV26 @ ( c_Collect @ SV461 @ SV1119 ) @ SV1119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2990]) ).
thf(3356,plain,
! [SV1120: $i,SV27: $i,SV462: $i] :
( ( ( hBOOL @ ( c_in @ SV462 @ ( c_Collect @ SV27 @ SV1120 ) @ SV1120 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV27 @ SV462 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2991]) ).
thf(3357,plain,
! [SV1121: $i,SV827: $i,SV463: $i,SV28: $i] :
( ( ( hBOOL @ ( c_in @ SV28 @ ( c_HOL_Ominus__class_Ominus @ SV463 @ SV827 @ ( tc_fun @ SV1121 @ tc_bool ) ) @ SV1121 ) )
= $true )
| ( ( ( hBOOL @ ( c_in @ SV28 @ SV827 @ SV1121 ) )
| ~ ( hBOOL @ ( c_in @ SV28 @ SV463 @ SV1121 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2992]) ).
thf(3358,plain,
! [SV1122: $i,SV828: $i,SV464: $i,SV29: $i] :
( ( ( hBOOL @ ( c_in @ SV29 @ ( c_HOL_Ominus__class_Ominus @ SV464 @ SV828 @ ( tc_fun @ SV1122 @ tc_bool ) ) @ SV1122 ) )
= $true )
| ( ( ( hBOOL @ ( c_in @ SV29 @ SV828 @ SV1122 ) )
| ~ ( hBOOL @ ( c_in @ SV29 @ SV464 @ SV1122 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2993]) ).
thf(3359,plain,
! [SV1373: $i,SV1123: $i,SV829: $i,SV465: $i,SV30: $i] :
( ( ! [SY4869: $i] :
( ( c_Com_Ocom_OCall @ SV30 @ SV465 @ SV829 )
!= ( c_Com_Ocom_OLocal @ SV1123 @ SV1373 @ SY4869 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2994]) ).
thf(3360,plain,
! [SV466: $i,SV830: $i,SV1374: $i,SV31: $i] :
( ( ( ~ ( c_lessequals @ ( c_Set_Oinsert @ SV31 @ SV1374 @ SV830 ) @ SV466 @ ( tc_fun @ SV830 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV31 @ SV466 @ SV830 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2995]) ).
thf(3361,plain,
! [SV1124: $i,SV831: $i,SV467: $i,SV32: $i] :
( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV32 @ ( c_COMBK @ SV467 @ ( tc_fun @ SV831 @ tc_bool ) @ SV1124 ) @ SV1124 @ ( tc_fun @ SV831 @ tc_bool ) )
= SV467 )
= $true )
| ( ( SV32
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1124 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2996]) ).
thf(3362,plain,
! [SV33: $i,SV1375: $i,SV468: $i] :
( ( ( ! [SY4870: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV468 @ ( c_COMBK @ SV1375 @ SV33 @ SY4870 ) @ SY4870 @ SV33 )
= SV1375 )
| ( SV468
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SY4870 @ tc_bool ) ) ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2997]) ).
thf(3363,plain,
! [SV1376: $i,SV1125: $i,SV832: $i,SV469: $i,SV34: $i] :
( ( ( c_Com_Ocom_OCall @ SV34 @ SV469 @ SV832 )
!= ( c_Com_Ocom_OWhile @ SV1125 @ SV1376 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2998]) ).
thf(3364,plain,
! [SV1126: $i,SV833: $i,SV470: $i,SV35: $i] :
( ( ( ! [SY4543: $i] :
( ( c_Set_Oinsert @ ( hAPP @ SV35 @ SV470 ) @ ( c_Set_Oimage @ SV35 @ SV833 @ SV1126 @ SY4543 ) @ SY4543 )
= ( c_Set_Oimage @ SV35 @ SV833 @ SV1126 @ SY4543 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV470 @ SV833 @ SV1126 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2999]) ).
thf(3365,plain,
! [SV1127: $i,SV834: $i,SV471: $i,SV36: $i] :
( ( ( c_lessequals @ SV36 @ ( c_Set_Oinsert @ SV471 @ SV834 @ SV1127 ) @ ( tc_fun @ SV1127 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV36 @ SV834 @ ( tc_fun @ SV1127 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SV471 @ SV36 @ SV1127 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3000]) ).
thf(3366,plain,
! [SV472: $i,SV835: $i,SV37: $i,SV1377: $i] :
( ( ( ( hBOOL @ ( c_in @ SV1377 @ SV37 @ SV835 ) )
| ~ ( c_lessequals @ SV37 @ ( c_Set_Oinsert @ SV1377 @ SV472 @ SV835 ) @ ( tc_fun @ SV835 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV37 @ SV472 @ ( tc_fun @ SV835 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3001]) ).
thf(3367,plain,
! [SV1128: $i,SV836: $i,SV473: $i,SV38: $i] :
( ( ( c_lessequals @ SV38 @ ( c_Set_Oinsert @ SV473 @ SV836 @ SV1128 ) @ ( tc_fun @ SV1128 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV38 @ SV836 @ ( tc_fun @ SV1128 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SV473 @ SV38 @ SV1128 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3002]) ).
thf(3368,plain,
! [SV837: $i,SV474: $i,SV1378: $i,SV39: $i] :
( ( ( ~ ( c_lessequals @ SV39 @ ( c_Set_Oinsert @ SV1378 @ SV474 @ SV837 ) @ ( tc_fun @ SV837 @ tc_bool ) )
| ( hBOOL @ ( c_in @ SV1378 @ SV39 @ SV837 ) ) )
= $true )
| ( ( c_lessequals @ SV39 @ SV474 @ ( tc_fun @ SV837 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3003]) ).
thf(3369,plain,
! [SV1131: $i,SV840: $i,SV477: $i,SV42: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV42 @ SV477 ) @ SV840 @ SV1131 )
= $true )
| ( ( ! [SY4544: $i] :
( ~ ( c_Natural_Oevalc @ SV477 @ SY4544 @ SV1131 )
| ~ ( c_Natural_Oevalc @ SV42 @ SV840 @ SY4544 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3006]) ).
thf(3370,plain,
! [SV1379: $i,SV1132: $i,SV841: $i,SV478: $i,SV43: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ SV43 @ SV478 @ SV841 @ SV1132 ) @ ( c_Set_Oimage @ SV43 @ SV1379 @ SV841 @ SV1132 ) @ ( tc_fun @ SV1132 @ tc_bool ) ) @ ( c_Set_Oimage @ SV43 @ ( c_HOL_Ominus__class_Ominus @ SV478 @ SV1379 @ ( tc_fun @ SV841 @ tc_bool ) ) @ SV841 @ SV1132 ) @ ( tc_fun @ SV1132 @ tc_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3007]) ).
thf(3371,plain,
! [SV842: $i,SV479: $i,SV44: $i] :
( ( ( hBOOL @ ( hAPP @ SV44 @ SV479 ) )
= $false )
| ( ( ! [SY4027: $i] :
( ( c_Natural_Oevalc @ SV842 @ SV479 @ SY4027 )
| ! [SY4028: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV44 @ SV842 @ SY4028 ) @ SV479 @ SY4027 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3008]) ).
thf(3372,plain,
! [SV1380: $i,SV1133: $i,SV843: $i,SV480: $i,SV45: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV45 @ SV480 @ SV843 ) @ SV1133 @ SV1380 )
| ~ ( c_Natural_Oevalc @ SV480 @ SV1133 @ SV1380 )
| ~ ( hBOOL @ ( hAPP @ SV45 @ SV1133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3009]) ).
thf(3373,plain,
! [SV1381: $i,SV1134: $i,SV844: $i,SV481: $i,SV46: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV46 @ SV481 ) @ SV844 @ SV1134 @ SV1381 )
| ! [SY4871: $i] :
( ~ ( c_Natural_Oevaln @ SV481 @ SY4871 @ SV1134 @ SV1381 )
| ~ ( c_Natural_Oevaln @ SV46 @ SV844 @ SV1134 @ SY4871 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3010]) ).
thf(3374,plain,
! [SV1382: $i,SV47: $i,SV482: $i] :
( ( ( ! [SY4872: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV482 @ SV482 @ SV47 )
!= ( c_HOL_Ominus__class_Ominus @ SV1382 @ SY4872 @ SV47 ) )
| ( SV1382 = SY4872 ) ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3011]) ).
thf(3375,plain,
! [SV48: $i,SV1383: $i,SV483: $i] :
( ( ( ! [SY4873: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV483 @ SV1383 @ SV48 )
!= ( c_HOL_Ominus__class_Ominus @ SY4873 @ SY4873 @ SV48 ) )
| ( SV483 = SV1383 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3012]) ).
thf(3376,plain,
! [SV1135: $i,SV845: $i,SV484: $i,SV49: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV49 @ SV484 ) @ SV845 @ SV1135 )
= $true )
| ( ( ! [SY4549: $i] :
( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV49 @ SV484 ) @ SY4549 @ SV1135 )
| ~ ( c_Natural_Oevalc @ SV484 @ SV845 @ SY4549 )
| ~ ( hBOOL @ ( hAPP @ SV49 @ SV845 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3013]) ).
thf(3377,plain,
! [SV1384: $i,SV1136: $i,SV846: $i,SV487: $i,SV52: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV52 @ SV487 ) @ SV846 @ SV1136 @ SV1384 )
| ! [SY4874: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV52 @ SV487 ) @ SY4874 @ SV1136 @ SV1384 )
| ~ ( c_Natural_Oevaln @ SV487 @ SV846 @ SV1136 @ SY4874 )
| ~ ( hBOOL @ ( hAPP @ SV52 @ SV846 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3014]) ).
thf(3378,plain,
! [SV1385: $i,SV1137: $i,SV848: $i,SV489: $i,SV54: $i] :
( ( ! [SY4875: $i] :
( ( hAPP @ ( c_COMBS @ SV54 @ SV489 @ SV848 @ SV1137 @ SV1385 ) @ SY4875 )
= ( hAPP @ ( hAPP @ SV54 @ SY4875 ) @ ( hAPP @ SV489 @ SY4875 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3015]) ).
thf(3379,plain,
! [SV1386: $i,SV1139: $i,SV850: $i,SV492: $i,SV57: $i] :
( ( ! [SY4876: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ SV57 @ SV492 @ SV850 @ SV1139 ) @ SV1386 ) @ SY4876 )
= ( hAPP @ ( hAPP @ SV57 @ SY4876 ) @ SV1386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3017]) ).
thf(3380,plain,
! [SV1387: $i,SV1140: $i,SV851: $i,SV493: $i,SV58: $i] :
( ( ! [SY4877: $i] :
( ( hAPP @ ( c_COMBB @ SV58 @ SV493 @ SV851 @ SV1140 @ SV1387 ) @ SY4877 )
= ( hAPP @ SV58 @ ( hAPP @ SV493 @ SY4877 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3018]) ).
thf(3381,plain,
! [SV1141: $i,SV59: $i,SV494: $i] :
( ( ( hBOOL @ ( c_in @ SV494 @ SV59 @ SV1141 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV59 @ SV494 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3019]) ).
thf(3382,plain,
! [SV1142: $i,SV60: $i,SV495: $i] :
( ( ( hBOOL @ ( hAPP @ SV495 @ SV60 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV60 @ SV495 @ SV1142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3020]) ).
thf(3383,plain,
! [SV1144: $i,SV853: $i,SV497: $i,SV62: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV62 @ SV497 ) ) )
= $true )
| ( ( ! [SY4558: $i] :
( ( c_Natural_Oevaln @ SV853 @ SV497 @ SV1144 @ SY4558 )
| ! [SY4559: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV62 @ SV853 @ SY4559 ) @ SV497 @ SV1144 @ SY4558 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3022]) ).
thf(3384,plain,
! [SV1388: $i,SV1145: $i,SV854: $i,SV498: $i,SV63: $i] :
( ( ! [SY4878: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV63 @ SV498 @ SV854 ) @ SV1145 @ SV1388 @ SY4878 )
| ~ ( c_Natural_Oevaln @ SV498 @ SV1145 @ SV1388 @ SY4878 )
| ~ ( hBOOL @ ( hAPP @ SV63 @ SV1145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3023]) ).
thf(3385,plain,
! [SV1389: $i,SV1146: $i,SV855: $i,SV499: $i,SV64: $i] :
( ( ! [SY4879: $i,SY4880: $i,SY4881: $i,SY4882: $i,SY4883: $i,SY4884: $i,SY4885: $i] :
( ( c_Com_Ocom_Ocom__case @ SV64 @ SV499 @ SV855 @ SV1146 @ SV1389 @ SY4879 @ SY4880 @ SY4881 @ ( c_Com_Ocom_OCall @ SY4882 @ SY4883 @ SY4884 ) @ SY4885 )
= ( hAPP @ ( hAPP @ ( hAPP @ SY4881 @ SY4882 ) @ SY4883 ) @ SY4884 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3024]) ).
thf(3386,plain,
! [SV1390: $i,SV1147: $i,SV856: $i,SV500: $i,SV65: $i] :
( ( ( c_Com_Ocom_OCall @ SV65 @ SV500 @ SV856 )
!= ( c_Com_Ocom_OSemi @ SV1147 @ SV1390 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3025]) ).
thf(3387,plain,
! [SV68: $i,SV1391: $i,SV1149: $i] :
( ( ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1149 @ SV1391 @ ( tc_fun @ t_a @ SV68 ) ) @ v_x )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV1149 @ v_x ) @ ( hAPP @ SV1391 @ v_x ) @ SV68 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV68 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3027]) ).
thf(3388,plain,
! [SV1150: $i,SV857: $i,SV502: $i,SV69: $i] :
( ( ( ( c_Set_Oimage @ ( c_COMBK @ SV69 @ SV502 @ SV857 ) @ SV1150 @ SV857 @ SV502 )
= ( c_Set_Oinsert @ SV69 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV502 @ tc_bool ) ) @ SV502 ) )
= $true )
| ( ( ! [SY4572: $i] :
~ ( hBOOL @ ( c_in @ SY4572 @ SV1150 @ SV857 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3028]) ).
thf(3389,plain,
! [SV1151: $i,SV858: $i,SV503: $i,SV70: $i] :
( ( ( hBOOL @ ( c_in @ ( hAPP @ SV70 @ SV503 ) @ SV858 @ SV1151 ) )
= $true )
| ( ( ! [SY4573: $i,SY4574: $i] :
( ~ ( hBOOL @ ( c_in @ SV503 @ SY4573 @ SY4574 ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV70 @ SY4573 @ SY4574 @ SV1151 ) @ SV858 @ ( tc_fun @ SV1151 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3029]) ).
thf(3390,plain,
! [SV1152: $i,SV859: $i,SV504: $i,SV71: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV71 @ ( c_Set_Oinsert @ SV504 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV859 @ tc_bool ) ) @ SV859 ) @ ( tc_fun @ SV859 @ tc_bool ) ) @ SV1152 @ ( tc_fun @ SV859 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV504 @ SV71 @ SV859 ) )
| ~ ( c_lessequals @ SV71 @ ( c_Set_Oinsert @ SV504 @ SV1152 @ SV859 ) @ ( tc_fun @ SV859 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3030]) ).
thf(3391,plain,
! [SV1153: $i,SV860: $i,SV505: $i,SV72: $i] :
( ( ( c_lessequals @ SV72 @ ( c_Set_Oinsert @ SV505 @ SV860 @ SV1153 ) @ ( tc_fun @ SV1153 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV505 @ SV72 @ SV1153 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV72 @ ( c_Set_Oinsert @ SV505 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1153 @ tc_bool ) ) @ SV1153 ) @ ( tc_fun @ SV1153 @ tc_bool ) ) @ SV860 @ ( tc_fun @ SV1153 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3031]) ).
thf(3392,plain,
! [SV1154: $i,SV861: $i,SV506: $i,SV73: $i] :
( ( ( c_lessequals @ SV73 @ ( c_Set_Oinsert @ SV506 @ SV861 @ SV1154 ) @ ( tc_fun @ SV1154 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV506 @ SV73 @ SV1154 ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV73 @ ( c_Set_Oinsert @ SV506 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1154 @ tc_bool ) ) @ SV1154 ) @ ( tc_fun @ SV1154 @ tc_bool ) ) @ SV861 @ ( tc_fun @ SV1154 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3032]) ).
thf(3393,plain,
! [SV1392: $i,SV862: $i,SV507: $i,SV74: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV74 @ SV507 ) @ SV862 @ SV1392 @ SV862 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV74 @ SV862 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3033]) ).
thf(3394,plain,
! [SV1393: $i,SV1155: $i,SV864: $i,SV509: $i,SV76: $i] :
( ( ! [SY4886: $i] :
( ( c_Com_Ocom_OCond @ SV76 @ SV509 @ SV864 )
!= ( c_Com_Ocom_OCall @ SV1155 @ SV1393 @ SY4886 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3034]) ).
thf(3395,plain,
! [SV865: $i,SV510: $i,SV77: $i] :
( ( ( class_Complete__Lattice_Ocomplete__lattice @ SV77 )
= $false )
| ( ( ! [SY4079: $i,SY4080: $i] :
( ( c_lessequals @ ( hAPP @ SV510 @ SV865 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY4079 @ SV510 @ SY4080 @ SV77 ) @ SV77 )
| ~ ( hBOOL @ ( c_in @ SV865 @ SY4079 @ SY4080 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3035]) ).
thf(3396,plain,
! [SV1156: $i,SV866: $i,SV511: $i,SV78: $i] :
( ( ( ! [SY4577: $i] : ( c_lessequals @ ( hAPP @ SV78 @ SV511 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV866 @ SV78 @ SV1156 @ ( tc_fun @ SY4577 @ tc_bool ) ) @ ( tc_fun @ SY4577 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV511 @ SV866 @ SV1156 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3036]) ).
thf(3397,plain,
! [SV1157: $i,SV867: $i,SV512: $i,SV79: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV79 @ SV512 @ SV867 ) @ SV1157 @ ( tc_fun @ SV867 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV512 @ SV1157 @ ( tc_fun @ SV867 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV79 @ SV1157 @ SV867 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3037]) ).
thf(3398,plain,
! [SV1394: $i,SV1158: $i,SV868: $i,SV513: $i,SV80: $i] :
( ( ! [SY4887: $i] :
( ( c_Com_Ocom_OLocal @ SV80 @ SV513 @ SV868 )
!= ( c_Com_Ocom_OCond @ SV1158 @ SV1394 @ SY4887 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3038]) ).
thf(3399,plain,
! [SV1395: $i,SV1159: $i,SV869: $i,SV515: $i,SV82: $i] :
( ( ! [SY4888: $i] :
( ( ( c_Com_Ocom_OCall @ SV82 @ SV515 @ SV869 )
!= ( c_Com_Ocom_OCall @ SV1159 @ SV1395 @ SY4888 ) )
| ( SV869 = SY4888 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3039]) ).
thf(3400,plain,
! [SV1396: $i,SV1160: $i,SV870: $i,SV516: $i,SV83: $i] :
( ( ! [SY4889: $i] :
( ( c_Com_Ocom_OCall @ SV83 @ SV516 @ SV870 )
!= ( c_Com_Ocom_OCall @ SV1160 @ SV1396 @ SY4889 ) )
| ( SV516 = SV1396 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3040]) ).
thf(3401,plain,
! [SV1161: $i,SV871: $i,SV517: $i,SV84: $i] :
( ( ( ! [SY4584: $i,SY4585: $i] :
( ( c_Com_Ocom_OCall @ SV84 @ SV517 @ SV871 )
!= ( c_Com_Ocom_OCall @ SV1161 @ SY4584 @ SY4585 ) ) )
= $true )
| ( ( SV84 = SV1161 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3041]) ).
thf(3402,plain,
! [SV1397: $i,SV1162: $i,SV872: $i,SV519: $i,SV86: $i] :
( ( ( c_Com_Ocom_OWhile @ SV86 @ SV519 )
!= ( c_Com_Ocom_OLocal @ SV872 @ SV1162 @ SV1397 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3042]) ).
thf(3403,plain,
! [SV1163: $i,SV874: $i,SV522: $i,SV91: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV91 @ SV522 )
!= ( c_Com_Ocom_OSemi @ SV874 @ SV1163 ) )
= $true )
| ( ( SV522 = SV1163 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3044]) ).
thf(3404,plain,
! [SV1398: $i,SV875: $i,SV523: $i,SV92: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV92 @ SV523 )
!= ( c_Com_Ocom_OSemi @ SV875 @ SV1398 ) )
= $true )
| ( ( SV92 = SV875 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3045]) ).
thf(3405,plain,
! [SV1164: $i,SV876: $i,SV524: $i,SV93: $i] :
( ( ( c_Com_Ocom_OSemi @ SV93 @ SV524 )
= ( c_Com_Ocom_OWhile @ SV876 @ SV1164 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3046]) ).
thf(3406,plain,
! [SV94: $i,SV1399: $i,SV1165: $i] :
( ( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SV1165 @ SV1399 @ SV94 ) @ SV94 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1165 @ ( c_Complete__Lattice_OSup__class_OSup @ SV1399 @ SV94 ) @ SV94 ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV94 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3047]) ).
thf(3407,plain,
! [SV1400: $i,SV1166: $i,SV877: $i,SV525: $i,SV95: $i] :
( ( ( c_Com_Ocom_OSemi @ SV95 @ SV525 )
!= ( c_Com_Ocom_OCond @ SV877 @ SV1166 @ SV1400 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3048]) ).
thf(3408,plain,
! [SV1401: $i,SV1167: $i,SV878: $i,SV526: $i,SV96: $i] :
( ( ( c_Com_Ocom_OSemi @ SV96 @ SV526 )
!= ( c_Com_Ocom_OLocal @ SV878 @ SV1167 @ SV1401 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3049]) ).
thf(3409,plain,
! [SV879: $i,SV527: $i,SV97: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV97 ) @ SV527 @ SV879 )
= $false )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV97 @ SV527 @ SV879 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3050]) ).
thf(3410,plain,
! [SV1168: $i,SV880: $i,SV528: $i,SV98: $i] :
( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV98 @ SV528 @ SV880 @ ( tc_fun @ SV1168 @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1168 @ tc_bool ) ) )
= $true )
| ( ( ! [SY4590: $i] :
( ( ( hAPP @ SV528 @ SY4590 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1168 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SY4590 @ SV98 @ SV880 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3051]) ).
thf(3411,plain,
! [SV1402: $i,SV1169: $i,SV881: $i,SV529: $i,SV99: $i] :
( ( ( c_Com_Ocom_OCond @ SV99 @ SV529 @ SV881 )
!= ( c_Com_Ocom_OWhile @ SV1169 @ SV1402 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3052]) ).
thf(3412,plain,
! [SV882: $i,SV1403: $i,SV530: $i,SV100: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV100 @ ( c_HOL_Ominus__class_Ominus @ SV530 @ SV1403 @ ( tc_fun @ SV882 @ tc_bool ) ) @ SV882 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV100 @ SV530 @ SV882 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3053]) ).
thf(3413,plain,
! [SV1404: $i,SV1170: $i,SV883: $i,SV531: $i,SV101: $i] :
( ( ! [SY4890: $i] :
( ( c_Com_Ocom_OCond @ SV101 @ SV531 @ SV883 )
!= ( c_Com_Ocom_OLocal @ SV1170 @ SV1404 @ SY4890 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3054]) ).
thf(3414,plain,
! [SV884: $i,SV532: $i,SV102: $i] :
( ( ( hBOOL @ ( c_in @ SV102 @ SV532 @ SV884 ) )
= $false )
| ( ( ! [SY4113: $i] :
~ ( hBOOL @ ( c_in @ SV102 @ ( c_HOL_Ominus__class_Ominus @ SY4113 @ SV532 @ ( tc_fun @ SV884 @ tc_bool ) ) @ SV884 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3055]) ).
thf(3415,plain,
! [SV1171: $i,SV885: $i,SV533: $i,SV103: $i] :
( ( ( c_lessequals @ ( hAPP @ SV103 @ SV533 ) @ SV885 @ ( tc_fun @ SV1171 @ tc_bool ) )
= $true )
| ( ( ! [SY4594: $i,SY4595: $i] :
( ~ ( hBOOL @ ( c_in @ SV533 @ SY4594 @ SY4595 ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SY4594 @ SV103 @ SY4595 @ ( tc_fun @ SV1171 @ tc_bool ) ) @ SV885 @ ( tc_fun @ SV1171 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3056]) ).
thf(3416,plain,
! [SV1405: $i,SV1173: $i,SV887: $i,SV536: $i,SV106: $i] :
( ( ( c_Com_Ocom_OCond @ SV106 @ SV536 @ SV887 )
!= ( c_Com_Ocom_OSemi @ SV1173 @ SV1405 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3058]) ).
thf(3417,plain,
! [SV1174: $i,SV888: $i,SV537: $i,SV107: $i] :
( ( ( ! [SY4597: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV107 @ SV537 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV888 @ SV107 @ SV1174 @ ( tc_fun @ SY4597 @ tc_bool ) ) @ ( tc_fun @ SY4597 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV888 @ SV107 @ SV1174 @ ( tc_fun @ SY4597 @ tc_bool ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV537 @ SV888 @ SV1174 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3059]) ).
thf(3418,plain,
! [SV1406: $i,SV1175: $i,SV889: $i,SV538: $i,SV108: $i] :
( ( ! [SY4891: $i] :
( ( ( c_Com_Ocom_OCond @ SV108 @ SV538 @ SV889 )
!= ( c_Com_Ocom_OCond @ SV1175 @ SV1406 @ SY4891 ) )
| ( SV889 = SY4891 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3060]) ).
thf(3419,plain,
! [SV1407: $i,SV1176: $i,SV890: $i,SV539: $i,SV109: $i] :
( ( ! [SY4892: $i] :
( ( c_Com_Ocom_OCond @ SV109 @ SV539 @ SV890 )
!= ( c_Com_Ocom_OCond @ SV1176 @ SV1407 @ SY4892 ) )
| ( SV539 = SV1407 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3061]) ).
thf(3420,plain,
! [SV1177: $i,SV891: $i,SV540: $i,SV110: $i] :
( ( ( ! [SY4602: $i,SY4603: $i] :
( ( c_Com_Ocom_OCond @ SV110 @ SV540 @ SV891 )
!= ( c_Com_Ocom_OCond @ SV1177 @ SY4602 @ SY4603 ) ) )
= $true )
| ( ( SV110 = SV1177 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3062]) ).
thf(3421,plain,
! [SV115: $i] :
( ( ( class_Int_Onumber__ring @ SV115 )
= $false )
| ( ( ! [SY2137: $i] :
( ( c_HOL_Ominus__class_Ominus @ SY2137 @ SY2137 @ SV115 )
= ( c_HOL_Ozero__class_Ozero @ SV115 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3067]) ).
thf(3422,plain,
! [SV892: $i,SV541: $i,SV116: $i] :
( ( ( class_Orderings_Oorder @ SV116 )
= $false )
| ( ( ! [SY4131: $i,SY4132: $i] :
( ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV541 @ SV892 @ SV116 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY4131 @ SY4132 @ SV116 ) @ ( tc_fun @ SV116 @ tc_bool ) )
| ~ ( c_lessequals @ SV892 @ SY4132 @ SV116 )
| ~ ( c_lessequals @ SY4131 @ SV541 @ SV116 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3068]) ).
thf(3423,plain,
! [SV893: $i,SV542: $i,SV117: $i] :
( ( ( class_Orderings_Oorder @ SV117 )
= $false )
| ( ( ( c_lessequals @ SV542 @ SV893 @ SV117 )
| ! [SY4133: $i] :
( ~ ( c_lessequals @ SY4133 @ SV542 @ SV117 )
| ! [SY4134: $i] :
~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY4133 @ SV542 @ SV117 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY4134 @ SV893 @ SV117 ) @ ( tc_fun @ SV117 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3069]) ).
thf(3424,plain,
! [SV894: $i,SV543: $i,SV118: $i] :
( ( ( class_Orderings_Oorder @ SV118 )
= $false )
| ( ( ( c_lessequals @ SV543 @ SV894 @ SV118 )
| ! [SY4135: $i] :
( ~ ( c_lessequals @ SV894 @ SY4135 @ SV118 )
| ! [SY4136: $i] :
~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV894 @ SY4135 @ SV118 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV543 @ SY4136 @ SV118 ) @ ( tc_fun @ SV118 @ tc_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3070]) ).
thf(3425,plain,
! [SV1408: $i,SV1182: $i,SV895: $i,SV546: $i,SV121: $i] :
( ( ! [SY4893: $i] :
( ( c_Com_Ocom_OCall @ SV121 @ SV546 @ SV895 )
!= ( c_Com_Ocom_OCond @ SV1182 @ SV1408 @ SY4893 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3071]) ).
thf(3426,plain,
! [SV896: $i,SV547: $i,SV122: $i] :
( ( ( ( c_Option_Ooption_OSome @ SV122 @ SV547 )
= ( c_Option_Ooption_OSome @ SV896 @ SV547 ) )
= $false )
| ( ( SV122 = SV896 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3072]) ).
thf(3427,plain,
! [SV1409: $i,SV1183: $i,SV897: $i,SV548: $i,SV123: $i] :
( ( ! [SY4894: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV123 @ SV548 @ SV897 @ SV1183 @ SV1409 ) @ SY4894 )
= ( hAPP @ SV123 @ ( hAPP @ SV548 @ SY4894 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3073]) ).
thf(3428,plain,
! [SV1410: $i,SV1184: $i,SV898: $i,SV549: $i,SV124: $i] :
( ( ! [SY4895: $i] :
( ( hAPP @ SV124 @ ( hAPP @ SV549 @ SV898 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV124 @ SV549 @ SV1184 @ SV1410 @ SY4895 ) @ SV898 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3074]) ).
thf(3429,plain,
! [SV899: $i,SV552: $i,SV127: $i] :
( ( ( class_Orderings_Oorder @ SV127 )
= $false )
| ( ( ! [SY4146: $i,SY4147: $i] : ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV552 @ SV899 @ SV127 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY4146 @ SY4147 @ SV127 ) @ ( tc_fun @ SV127 @ tc_bool ) )
| ( c_lessequals @ SV552 @ SV899 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3077]) ).
thf(3430,plain,
! [SV128: $i,SV553: $i,SV1185: $i] :
( ( ( hBOOL @ ( hAPP @ SV1185 @ SV553 ) )
= $true )
| ( ( ! [SY4610: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1185 @ SV128 @ ( tc_fun @ SY4610 @ tc_bool ) ) @ SV553 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV128 @ SV553 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3078]) ).
thf(3431,plain,
! [SV1186: $i,SV900: $i,SV554: $i,SV129: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV129 @ SV554 @ ( tc_fun @ SV900 @ tc_bool ) ) @ SV1186 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV554 @ SV1186 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3079]) ).
thf(3432,plain,
! [SV1187: $i,SV901: $i,SV555: $i,SV130: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV130 @ SV555 @ ( tc_fun @ SV901 @ tc_bool ) ) @ SV1187 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV130 @ SV1187 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3080]) ).
thf(3433,plain,
! [SV131: $i,SV556: $i,SV902: $i] :
( ( ( ~ ( c_Com_OWT @ SV902 ) )
= $true )
| ( ( ~ ( c_Com_OWT @ SV556 ) )
= $true )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV131 @ SV556 @ SV902 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3081]) ).
thf(3434,plain,
! [SV1411: $i,SV1188: $i,SV903: $i,SV557: $i,SV132: $i] :
( ( ! [SY4896: $i,SY4897: $i,SY4898: $i,SY4899: $i] :
( ( c_Com_Ocom_Ocom__case @ SV132 @ SV557 @ SV903 @ SV1188 @ SV1411 @ SY4896 @ SY4897 @ SY4898 @ c_Com_Ocom_OSKIP @ SY4899 )
= SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3082]) ).
thf(3435,plain,
! [SV558: $i,SV904: $i,SV1412: $i,SV133: $i] :
( ( ( ( hBOOL @ ( c_in @ SV133 @ SV1412 @ SV904 ) )
| ~ ( hBOOL @ ( c_in @ SV133 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1412 @ SV558 @ ( tc_fun @ SV904 @ tc_bool ) ) @ SV904 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV133 @ SV558 @ SV904 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3083]) ).
thf(3436,plain,
! [SV1413: $i,SV1189: $i,SV905: $i,SV559: $i,SV134: $i] :
( ( ( c_Com_Ocom_OLocal @ SV134 @ SV559 @ SV905 )
!= ( c_Com_Ocom_OWhile @ SV1189 @ SV1413 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3084]) ).
thf(3437,plain,
! [SV1190: $i,SV906: $i,SV560: $i,SV135: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV135 @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV560 @ SV906 @ SV1190 @ ( tc_fun @ SV135 @ tc_bool ) ) )
= $true )
| ( ( ! [SY4617: $i] :
( ( ( hAPP @ SV906 @ SY4617 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV135 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SY4617 @ SV560 @ SV1190 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3085]) ).
thf(3438,plain,
! [SV1414: $i,SV1193: $i,SV909: $i,SV564: $i,SV139: $i] :
( ( ( hBOOL @ ( c_in @ SV139 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV564 @ SV909 @ SV1193 @ ( tc_fun @ SV1414 @ tc_bool ) ) @ SV1414 ) )
| ! [SY4900: $i] :
( ~ ( hBOOL @ ( c_in @ SV139 @ ( hAPP @ SV909 @ SY4900 ) @ SV1414 ) )
| ~ ( hBOOL @ ( c_in @ SY4900 @ SV564 @ SV1193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3088]) ).
thf(3439,plain,
! [SV1415: $i,SV1194: $i,SV910: $i,SV565: $i,SV140: $i] :
( ( ( hBOOL @ ( c_in @ SV140 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV565 @ SV910 @ SV1194 @ ( tc_fun @ SV1415 @ tc_bool ) ) @ SV1415 ) )
| ! [SY4901: $i] :
( ~ ( hBOOL @ ( c_in @ SV140 @ ( hAPP @ SV910 @ SY4901 ) @ SV1415 ) )
| ~ ( hBOOL @ ( c_in @ SY4901 @ SV565 @ SV1194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3089]) ).
thf(3440,plain,
! [SV144: $i,SV1416: $i,SV1195: $i] :
( ( ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ SV1195 @ SV1416 @ ( tc_fun @ t_a @ SV144 ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ SV1195 @ v_x ) @ ( hAPP @ SV1416 @ v_x ) @ SV144 ) )
= $true )
| ( ( class_HOL_Ominus @ SV144 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3090]) ).
thf(3441,plain,
! [SV1417: $i,SV1197: $i,SV915: $i,SV570: $i,SV146: $i] :
( ( ! [SY4902: $i,SY4903: $i,SY4904: $i,SY4905: $i,SY4906: $i,SY4907: $i] :
( ( c_Com_Ocom_Ocom__case @ SV146 @ SV570 @ SV915 @ SV1197 @ SV1417 @ SY4902 @ SY4903 @ SY4904 @ ( c_Com_Ocom_OSemi @ SY4905 @ SY4906 ) @ SY4907 )
= ( hAPP @ ( hAPP @ SV1197 @ SY4905 ) @ SY4906 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3092]) ).
thf(3442,plain,
! [SV1418: $i,SV1198: $i,SV916: $i,SV571: $i,SV147: $i] :
( ( ( c_Com_Ocom_OLocal @ SV147 @ SV571 @ SV916 )
!= ( c_Com_Ocom_OSemi @ SV1198 @ SV1418 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3093]) ).
thf(3443,plain,
! [SV1419: $i,SV1199: $i,SV918: $i,SV573: $i,SV149: $i] :
( ( ! [SY4908: $i,SY4909: $i,SY4910: $i,SY4911: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV149 @ ( hAPP @ SV573 @ SV918 ) ) @ SV1199 ) )
| ~ ( hBOOL @ ( c_in @ SV1199 @ SV918 @ SV1419 ) )
| ! [SY4912: $i,SY4913: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV573 @ SY4908 @ SV149 @ SY4909 @ SY4910 @ SY4911 @ SY4912 @ SY4913 @ SV1419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3094]) ).
thf(3444,plain,
! [SV1420: $i,SV1200: $i,SV919: $i,SV574: $i,SV150: $i] :
( ( ! [SY4914: $i,SY4915: $i,SY4916: $i,SY4917: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV150 @ SV574 ) @ ( hAPP @ SV919 @ SV1200 ) ) )
| ~ ( hBOOL @ ( c_in @ SV574 @ SV1200 @ SV1420 ) )
| ! [SY4918: $i,SY4919: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY4914 @ SV919 @ SV150 @ SY4915 @ SY4916 @ SY4917 @ SY4918 @ SY4919 @ SV1420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3095]) ).
thf(3445,plain,
! [SV152: $i,SV1421: $i,SV1201: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1201 @ SV1421 @ SV152 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1421 @ SV1201 @ SV152 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV152 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3096]) ).
thf(3446,plain,
! [SV153: $i,SV1422: $i,SV1202: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1202 @ SV1422 @ SV153 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1422 @ SV1202 @ SV153 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV153 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3097]) ).
thf(3447,plain,
! [SV1423: $i,SV921: $i,SV576: $i,SV154: $i] :
( ( ( ( c_Com_Ocom_OWhile @ SV154 @ SV576 )
!= ( c_Com_Ocom_OWhile @ SV921 @ SV1423 ) )
= $true )
| ( ( SV154 = SV921 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3098]) ).
thf(3448,plain,
! [SV1203: $i,SV922: $i,SV577: $i,SV155: $i] :
( ( ( ( c_Com_Ocom_OWhile @ SV155 @ SV577 )
!= ( c_Com_Ocom_OWhile @ SV922 @ SV1203 ) )
= $true )
| ( ( SV577 = SV1203 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3099]) ).
thf(3449,plain,
! [SV159: $i,SV1424: $i,SV1204: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1204 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1204 @ SV1424 @ SV159 ) @ SV159 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1204 @ SV1424 @ SV159 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV159 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3102]) ).
thf(3450,plain,
! [SV160: $i,SV1425: $i,SV1205: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1205 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1205 @ SV1425 @ SV160 ) @ SV160 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1205 @ SV1425 @ SV160 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV160 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3103]) ).
thf(3451,plain,
! [SV580: $i,SV161: $i,SV925: $i] :
( ( ( c_Com_OWT @ SV925 )
= $false )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ SV161 @ SV580 @ SV925 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3104]) ).
thf(3452,plain,
! [SV162: $i,SV1206: $i,SV926: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OLocal @ SV926 @ SV1206 @ SV162 ) )
= $false )
| ( ( c_Com_OWT @ SV162 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3105]) ).
thf(3453,plain,
! [SV1426: $i,SV1207: $i,SV928: $i,SV582: $i,SV164: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV164 @ SV582 @ SV928 @ ( tc_fun @ SV1207 @ tc_bool ) ) @ SV1426 ) )
| ! [SY4920: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV582 @ SY4920 ) @ SV1426 ) )
| ~ ( hBOOL @ ( c_in @ SY4920 @ SV164 @ SV928 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3107]) ).
thf(3454,plain,
! [SV1427: $i,SV1208: $i,SV929: $i,SV583: $i,SV165: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV165 @ SV583 @ SV929 @ ( tc_fun @ SV1208 @ tc_bool ) ) @ SV1427 ) )
| ! [SY4921: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV583 @ SY4921 ) @ SV1427 ) )
| ~ ( hBOOL @ ( c_in @ SY4921 @ SV165 @ SV929 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3108]) ).
thf(3455,plain,
! [SV1428: $i,SV1209: $i,SV930: $i,SV584: $i,SV166: $i] :
( ( ( c_Com_Ocom_OWhile @ SV166 @ SV584 )
!= ( c_Com_Ocom_OCond @ SV930 @ SV1209 @ SV1428 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3109]) ).
thf(3456,plain,
! [SV1429: $i,SV1210: $i,SV931: $i,SV585: $i,SV167: $i] :
( ( ( c_Com_Ocom_OSemi @ SV167 @ SV585 )
!= ( c_Com_Ocom_OCall @ SV931 @ SV1210 @ SV1429 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3110]) ).
thf(3457,plain,
! [SV1211: $i,SV932: $i,SV586: $i,SV168: $i] :
( ( ( SV168
= ( c_Suc @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ SV586 @ SV168 @ SV932 @ SV1211 ) ) )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ SV586 ) @ SV932 @ SV168 @ SV1211 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3111]) ).
thf(3458,plain,
! [SV1212: $i,SV933: $i,SV587: $i,SV169: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV169 @ SV587 @ SV933 ) @ SV1212 @ ( tc_fun @ SV933 @ tc_bool ) )
= ( c_Set_Oinsert @ SV169 @ ( c_HOL_Ominus__class_Ominus @ SV587 @ SV1212 @ ( tc_fun @ SV933 @ tc_bool ) ) @ SV933 ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV169 @ SV1212 @ SV933 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3112]) ).
thf(3459,plain,
! [SV170: $i,SV1213: $i,SV588: $i] :
( ( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ SV588 @ SV1213 @ SV170 )
= $false )
| ( ( SV170 = SV588 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3113]) ).
thf(3460,plain,
! [SV934: $i,SV589: $i,SV171: $i] :
( ( ( hBOOL @ ( c_in @ SV171 @ SV589 @ SV934 ) )
= $false )
| ( ( ! [SY4211: $i,SY4212: $i] : ( hBOOL @ ( c_in @ ( hAPP @ SY4211 @ SV171 ) @ ( c_Set_Oimage @ SY4211 @ SV589 @ SV934 @ SY4212 ) @ SY4212 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3114]) ).
thf(3461,plain,
! [SV935: $i,SV590: $i,SV172: $i] :
( ( ( hBOOL @ ( c_in @ SV172 @ SV590 @ SV935 ) )
= $false )
| ( ( ! [SY4213: $i,SY4214: $i] : ( hBOOL @ ( c_in @ ( hAPP @ SY4213 @ SV172 ) @ ( c_Set_Oimage @ SY4213 @ SV590 @ SV935 @ SY4214 ) @ SY4214 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3115]) ).
thf(3462,plain,
! [SV1214: $i,SV936: $i,SV591: $i,SV173: $i] :
( ( ( ! [SY4655: $i] : ( hBOOL @ ( c_in @ ( hAPP @ SV173 @ SV591 ) @ ( c_Set_Oimage @ SV173 @ SV936 @ SV1214 @ SY4655 ) @ SY4655 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV591 @ SV936 @ SV1214 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3116]) ).
thf(3463,plain,
! [SV1215: $i,SV937: $i,SV592: $i,SV174: $i] :
( ( ( ! [SY4656: $i] : ( hBOOL @ ( c_in @ ( hAPP @ SV174 @ SV592 ) @ ( c_Set_Oimage @ SV174 @ SV937 @ SV1215 @ SY4656 ) @ SY4656 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV592 @ SV937 @ SV1215 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3117]) ).
thf(3464,plain,
! [SV1216: $i,SV938: $i,SV593: $i,SV175: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV175 @ SV593 @ ( tc_fun @ SV938 @ tc_bool ) ) @ SV1216 @ ( tc_fun @ SV938 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV175 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV593 @ SV1216 @ ( tc_fun @ SV938 @ tc_bool ) ) @ ( tc_fun @ SV938 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3118]) ).
thf(3465,plain,
! [SV1217: $i,SV939: $i,SV594: $i,SV176: $i] :
( ( ( c_lessequals @ SV176 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV594 @ SV939 @ ( tc_fun @ SV1217 @ tc_bool ) ) @ ( tc_fun @ SV1217 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV176 @ SV594 @ ( tc_fun @ SV1217 @ tc_bool ) ) @ SV939 @ ( tc_fun @ SV1217 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3119]) ).
thf(3466,plain,
! [SV940: $i,SV1430: $i,SV596: $i,SV178: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV178 @ SV596 @ SV1430 @ SV940 ) )
= $true )
| ( ( c_Natural_Oevalc @ SV178 @ SV596 @ SV940 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3121]) ).
thf(3467,plain,
! [SV941: $i,SV1431: $i,SV597: $i,SV179: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV179 @ SV597 @ SV1431 @ SV941 ) )
= $true )
| ( ( c_Natural_Oevalc @ SV179 @ SV597 @ SV941 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3122]) ).
thf(3468,plain,
! [SV942: $i,SV598: $i,SV180: $i] :
( ( ( class_HOL_Oord @ SV180 )
= $false )
| ( ( ! [SY4223: $i] :
( ( c_lessequals @ ( hAPP @ SV598 @ SV942 ) @ ( hAPP @ SY4223 @ SV942 ) @ SV180 )
| ! [SY3499: $i] :
~ ( c_lessequals @ SV598 @ SY4223 @ ( tc_fun @ SY3499 @ SV180 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3123]) ).
thf(3469,plain,
! [SV184: $i,SV1221: $i] :
( ( ( ! [SY4657: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1221 @ SY4657 @ SV184 )
!= ( c_Orderings_Obot__class_Obot @ SV184 ) ) )
= $true )
| ( ( SV1221
= ( c_Orderings_Obot__class_Obot @ SV184 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3127]) ).
thf(3470,plain,
! [SV185: $i,SV1432: $i,SV1222: $i] :
( ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1222 @ SV1432 @ SV185 )
!= ( c_Orderings_Obot__class_Obot @ SV185 ) )
| ( SV1432
= ( c_Orderings_Obot__class_Obot @ SV185 ) ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV185 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3128]) ).
thf(3471,plain,
! [SV1433: $i,SV943: $i,SV599: $i,SV187: $i] :
( ( ( ( c_Set_Oimage @ SV187 @ SV599 @ SV943 @ SV1433 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1433 @ tc_bool ) ) )
= $true )
| ( ( SV599
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV943 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3129]) ).
thf(3472,plain,
! [SV1434: $i,SV1223: $i,SV944: $i,SV600: $i,SV188: $i] :
( ( ! [SY4922: $i,SY4923: $i] :
( ( ( hAPP @ SV188 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_bool ) ) )
= SV944 )
| ! [SY4924: $i,SY4925: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV188 @ SV1223 @ SV1434 @ SY4922 @ SY4923 @ SY4924 @ SY4925 @ SV944 @ SV600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3130]) ).
thf(3473,plain,
! [SV1435: $i,SV1224: $i,SV945: $i,SV601: $i,SV189: $i] :
( ( ! [SY4926: $i,SY4927: $i] :
( ( ( hAPP @ SV189 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV601 @ tc_bool ) ) )
= SV945 )
| ! [SY4928: $i,SY4929: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1224 @ SV189 @ SV1435 @ SY4926 @ SY4927 @ SY4928 @ SV945 @ SY4929 @ SV601 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3131]) ).
thf(3474,plain,
! [SV190: $i,SV1436: $i,SV602: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV602 @ SV1436 ) ) )
= $true )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV190 @ tc_bool ) )
= ( c_Collect @ SV602 @ SV190 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3132]) ).
thf(3475,plain,
! [SV192: $i,SV1225: $i,SV604: $i] :
( ( ( hBOOL @ ( c_in @ SV604 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1225 @ tc_bool ) ) @ SV1225 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV192 @ SV604 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3133]) ).
thf(3476,plain,
! [SV946: $i,SV1437: $i,SV197: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV197 @ SV1437 ) ) )
= $true )
| ( ( ( c_Collect @ SV197 @ SV946 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV946 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3135]) ).
thf(3477,plain,
! [SV1226: $i,SV948: $i,SV615: $i,SV205: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV205 @ tc_bool ) )
!= ( c_Set_Oimage @ SV615 @ SV948 @ SV1226 @ SV205 ) )
= $true )
| ( ( SV948
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1226 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3137]) ).
thf(3478,plain,
! [SV207: $i,SV1438: $i,SV617: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV617 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1438 @ tc_bool ) ) @ SV1438 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV207 @ SV617 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3138]) ).
thf(3479,plain,
! [SV950: $i,SV618: $i,SV208: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV208 @ SV618 @ ( tc_fun @ SV950 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV950 @ tc_bool ) ) )
= $false )
| ( ( SV618
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV950 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3139]) ).
thf(3480,plain,
! [SV951: $i,SV619: $i,SV209: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV209 @ SV619 @ ( tc_fun @ SV951 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV951 @ tc_bool ) ) )
= $false )
| ( ( SV209
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV951 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3140]) ).
thf(3481,plain,
! [SV953: $i,SV622: $i,SV212: $i] :
( ( ( hBOOL @ ( c_in @ SV212 @ SV622 @ SV953 ) )
= $false )
| ( ( ( c_Set_Oinsert @ SV212 @ ( c_HOL_Ominus__class_Ominus @ SV622 @ ( c_Set_Oinsert @ SV212 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV953 @ tc_bool ) ) @ SV953 ) @ ( tc_fun @ SV953 @ tc_bool ) ) @ SV953 )
= SV622 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3141]) ).
thf(3482,plain,
! [SV1227: $i,SV954: $i,SV623: $i,SV213: $i] :
( ( ( ( c_Set_Oimage @ ( c_COMBK @ SV213 @ SV623 @ SV954 ) @ SV1227 @ SV954 @ SV623 )
= ( c_Set_Oinsert @ SV213 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV623 @ tc_bool ) ) @ SV623 ) )
= $true )
| ( ( SV1227
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV954 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3142]) ).
thf(3483,plain,
! [SV214: $i,SV1439: $i,SV1228: $i] :
( ( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ SV1228 @ ( c_Set_Oinsert @ SV1439 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV214 @ tc_bool ) ) @ SV214 ) @ SV214 ) @ SV214 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1228 @ SV1439 @ SV214 ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV214 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3143]) ).
thf(3484,plain,
! [SV1229: $i,SV955: $i,SV624: $i,SV215: $i] :
( ( ( c_lessequals @ SV215 @ ( c_Set_Oinsert @ SV624 @ SV955 @ SV1229 ) @ ( tc_fun @ SV1229 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV215 @ SV955 @ ( tc_fun @ SV1229 @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV215 @ ( c_Set_Oinsert @ SV624 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1229 @ tc_bool ) ) @ SV1229 ) @ ( tc_fun @ SV1229 @ tc_bool ) ) @ SV955 @ ( tc_fun @ SV1229 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3144]) ).
thf(3485,plain,
! [SV1230: $i,SV957: $i,SV626: $i,SV217: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV217 @ SV626 @ SV957 ) @ ( c_Set_Oinsert @ SV217 @ SV1230 @ SV957 ) @ ( tc_fun @ SV957 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV626 @ SV1230 @ ( tc_fun @ SV957 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3146]) ).
thf(3486,plain,
! [SV1231: $i,SV958: $i,SV627: $i,SV218: $i] :
( ( ( hBOOL @ ( c_in @ SV218 @ ( c_Set_Oinsert @ SV627 @ SV958 @ SV1231 ) @ SV1231 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV218 @ SV958 @ SV1231 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3147]) ).
thf(3487,plain,
! [SV1232: $i,SV959: $i,SV628: $i,SV219: $i] :
( ( ( hBOOL @ ( c_in @ SV219 @ ( c_Set_Oinsert @ SV628 @ SV959 @ SV1232 ) @ SV1232 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV219 @ SV959 @ SV1232 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3148]) ).
thf(3488,plain,
! [SV1440: $i,SV1233: $i,SV960: $i,SV629: $i,SV220: $i] :
( ( ( c_Set_Oimage @ SV220 @ ( c_Set_Oinsert @ SV629 @ SV960 @ SV1233 ) @ SV1233 @ SV1440 )
= ( c_Set_Oinsert @ ( hAPP @ SV220 @ SV629 ) @ ( c_Set_Oimage @ SV220 @ SV960 @ SV1233 @ SV1440 ) @ SV1440 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3149]) ).
thf(3489,plain,
! [SV1441: $i,SV1234: $i,SV961: $i,SV630: $i,SV221: $i] :
( ( ! [SY4930: $i,SY4931: $i,SY4932: $i,SY4933: $i] :
( ( ( hAPP @ SV221 @ ( c_Set_Oinsert @ SV630 @ SV961 @ SV1234 ) )
= ( hAPP @ ( hAPP @ SV1441 @ SV630 ) @ ( hAPP @ SV221 @ SV961 ) ) )
| ! [SY4934: $i,SY4935: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV221 @ SY4930 @ SY4931 @ SY4932 @ SV1441 @ SY4933 @ SY4934 @ SY4935 @ SV1234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3150]) ).
thf(3490,plain,
! [SV1442: $i,SV1235: $i,SV962: $i,SV631: $i,SV222: $i] :
( ( ! [SY4936: $i,SY4937: $i,SY4938: $i,SY4939: $i] :
( ( ( hAPP @ SV222 @ ( c_Set_Oinsert @ SV631 @ SV962 @ SV1235 ) )
= ( hAPP @ ( hAPP @ SV1442 @ SV631 ) @ ( hAPP @ SV222 @ SV962 ) ) )
| ! [SY4940: $i,SY4941: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY4936 @ SV222 @ SY4937 @ SY4938 @ SY4939 @ SV1442 @ SY4940 @ SY4941 @ SV1235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3151]) ).
thf(3491,plain,
! [SV963: $i,SV632: $i,SV1443: $i,SV223: $i] :
( ( ( ( SV223 = SV1443 )
| ~ ( hBOOL @ ( c_in @ SV223 @ ( c_Set_Oinsert @ SV1443 @ SV632 @ SV963 ) @ SV963 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV223 @ SV632 @ SV963 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3152]) ).
thf(3492,plain,
! [SV1238: $i,SV967: $i,SV636: $i,SV227: $i] :
( ( ( c_lessequals @ SV227 @ ( c_Set_Oinsert @ SV636 @ SV967 @ SV1238 ) @ ( tc_fun @ SV1238 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV227 @ SV967 @ ( tc_fun @ SV1238 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3155]) ).
thf(3493,plain,
! [SV637: $i,SV968: $i,SV228: $i,SV1444: $i] :
( ( ( ~ ( c_lessequals @ ( c_Set_Oinsert @ SV1444 @ SV228 @ SV968 ) @ SV637 @ ( tc_fun @ SV968 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV228 @ SV637 @ ( tc_fun @ SV968 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3156]) ).
thf(3494,plain,
! [SV1239: $i,SV972: $i,SV641: $i,SV232: $i] :
( ( ( ( c_Set_Oinsert @ SV232 @ SV641 @ SV972 )
!= ( c_Set_Oinsert @ SV232 @ SV1239 @ SV972 ) )
= $true )
| ( ( ( hBOOL @ ( c_in @ SV232 @ SV1239 @ SV972 ) )
| ( SV641 = SV1239 )
| ( hBOOL @ ( c_in @ SV232 @ SV641 @ SV972 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3157]) ).
thf(3495,plain,
! [SV973: $i,SV642: $i,SV233: $i] :
( ( ( hBOOL @ ( c_in @ SV233 @ SV642 @ SV973 ) )
= $false )
| ( ( ( c_Set_Oinsert @ SV233 @ SV642 @ SV973 )
= SV642 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3158]) ).
thf(3496,plain,
! [SV1445: $i,SV1240: $i,SV974: $i,SV643: $i,SV234: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV234 @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV643 ) @ SV974 @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ SV1240 @ tc_Com_Opname @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SV1445 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SV643 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV234 @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV643 ) @ SV974 @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ SV1240 @ tc_Com_Opname @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SV1445 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV643 ) @ SV974 @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ SV1240 @ tc_Com_Opname @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SV1445 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SV643 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3159]) ).
thf(3497,plain,
! [SV1241: $i,SV976: $i,SV645: $i,SV237: $i] :
( ( ( hAPP @ c_Com_Ocom_OBODY @ SV237 )
= ( c_Com_Ocom_OCond @ SV645 @ SV976 @ SV1241 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3161]) ).
thf(3498,plain,
! [SV1242: $i,SV977: $i,SV646: $i,SV238: $i] :
( ( ( c_Com_Ocom_OCond @ SV238 @ SV646 @ SV977 )
= ( hAPP @ c_Com_Ocom_OBODY @ SV1242 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3162]) ).
thf(3499,plain,
! [SV1243: $i,SV979: $i,SV648: $i,SV240: $i] :
( ( ( c_Natural_Oevaln @ SV240 @ SV648 @ ( c_Suc @ SV979 ) @ SV1243 )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ SV240 @ SV648 @ SV979 @ SV1243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3164]) ).
thf(3500,plain,
! [SV1446: $i,SV1244: $i,SV980: $i,SV649: $i,SV241: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV241 @ SV649 @ ( tc_fun @ SV980 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1244 @ SV1446 @ ( tc_fun @ SV980 @ tc_bool ) ) @ ( tc_fun @ SV980 @ tc_bool ) )
| ~ ( c_lessequals @ SV1446 @ SV649 @ ( tc_fun @ SV980 @ tc_bool ) )
| ~ ( c_lessequals @ SV241 @ SV1244 @ ( tc_fun @ SV980 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3165]) ).
thf(3501,plain,
! [SV1245: $i,SV981: $i,SV650: $i,SV242: $i] :
( ( ( c_Natural_Oevaln @ SV242 @ SV650 @ SV981 @ SV1245 )
= $true )
| ( ( ! [SY4687: $i] :
( ( hBOOL @ ( hAPP @ SY4687 @ SV650 ) )
| ! [SY4688: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SY4687 @ SY4688 @ SV242 ) @ SV650 @ SV981 @ SV1245 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3166]) ).
thf(3502,plain,
! [SV1447: $i,SV1246: $i,SV982: $i,SV651: $i,SV243: $i] :
( ( ! [SY4942: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV243 @ SV651 @ SV982 ) @ SV1246 @ SV1447 @ SY4942 )
| ~ ( c_Natural_Oevaln @ SV982 @ SV1246 @ SV1447 @ SY4942 )
| ( hBOOL @ ( hAPP @ SV243 @ SV1246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3167]) ).
thf(3503,plain,
! [SV1448: $i,SV1247: $i,SV983: $i,SV652: $i,SV244: $i] :
( ( ( c_Com_Ocom_OWhile @ SV244 @ SV652 )
!= ( c_Com_Ocom_OCall @ SV983 @ SV1247 @ SV1448 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3168]) ).
thf(3504,plain,
! [SV1248: $i,SV246: $i,SV653: $i] :
( ( ( ~ ( c_lessequals @ SV653 @ SV246 @ ( tc_fun @ SV1248 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV246 @ SV653 @ ( tc_fun @ SV1248 @ tc_bool ) ) )
= $true )
| ( ( SV246 = SV653 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3169]) ).
thf(3505,plain,
! [SV654: $i,SV247: $i,SV1449: $i,SV1249: $i] :
( ( ( ~ ( c_Natural_Oevalc @ SV1249 @ SV1449 @ SV247 )
| ~ ( c_Natural_Oevalc @ SV1249 @ SV1449 @ SV654 ) )
= $true )
| ( ( SV247 = SV654 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3170]) ).
thf(3506,plain,
! [SV1250: $i,SV248: $i,SV655: $i] :
( ( ( ~ ( c_lessequals @ SV655 @ SV248 @ ( tc_fun @ SV1250 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV248 @ SV655 @ ( tc_fun @ SV1250 @ tc_bool ) ) )
= $true )
| ( ( SV248 = SV655 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3171]) ).
thf(3507,plain,
! [SV249: $i,SV1450: $i,SV1251: $i] :
( ( ( ( SV1251 = SV1450 )
| ~ ( c_lessequals @ SV1450 @ SV1251 @ SV249 )
| ~ ( c_lessequals @ SV1251 @ SV1450 @ SV249 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV249 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3172]) ).
thf(3508,plain,
! [SV250: $i,SV1451: $i,SV1252: $i] :
( ( ( ( SV1252 = SV1451 )
| ~ ( c_lessequals @ SV1451 @ SV1252 @ SV250 )
| ~ ( c_lessequals @ SV1252 @ SV1451 @ SV250 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV250 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3173]) ).
thf(3509,plain,
! [SV251: $i,SV1452: $i,SV1253: $i] :
( ( ( ( SV1253 = SV1452 )
| ~ ( c_lessequals @ SV1253 @ SV1452 @ SV251 )
| ~ ( c_lessequals @ SV1452 @ SV1253 @ SV251 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV251 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3174]) ).
thf(3510,plain,
! [SV252: $i,SV1453: $i,SV1254: $i] :
( ( ( ( c_lessequals @ SV1254 @ SV1453 @ SV252 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1254 @ SV1453 @ SV252 ) @ ( c_HOL_Ozero__class_Ozero @ SV252 ) @ SV252 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV252 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3175]) ).
thf(3511,plain,
! [SV253: $i,SV1454: $i,SV1255: $i] :
( ( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1255 @ SV1454 @ SV253 ) @ ( c_HOL_Ozero__class_Ozero @ SV253 ) @ SV253 )
| ~ ( c_lessequals @ SV1255 @ SV1454 @ SV253 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV253 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3176]) ).
thf(3512,plain,
! [SV255: $i,SV1455: $i,SV1256: $i] :
( ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1256 @ SV1455 @ SV255 )
= SV1256 )
| ~ ( c_lessequals @ SV1455 @ SV1256 @ SV255 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV255 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3178]) ).
thf(3513,plain,
! [SV256: $i,SV1456: $i,SV1257: $i] :
( ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1257 @ SV1456 @ SV256 )
!= SV1456 )
| ( c_lessequals @ SV1257 @ SV1456 @ SV256 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV256 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3179]) ).
thf(3514,plain,
! [SV257: $i,SV1457: $i,SV1258: $i] :
( ( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1258 @ SV1457 @ SV257 )
= SV1457 )
| ~ ( c_lessequals @ SV1258 @ SV1457 @ SV257 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV257 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3180]) ).
thf(3515,plain,
! [SV985: $i,SV657: $i,SV258: $i] :
( ( ( c_lessequals @ SV258 @ SV657 @ ( tc_fun @ SV985 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV258 @ SV657 @ ( tc_fun @ SV985 @ tc_bool ) )
= SV657 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3181]) ).
thf(3516,plain,
! [SV986: $i,SV259: $i,SV658: $i] :
( ( ( c_lessequals @ SV658 @ SV259 @ ( tc_fun @ SV986 @ tc_bool ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV259 @ SV658 @ ( tc_fun @ SV986 @ tc_bool ) )
= SV259 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3182]) ).
thf(3517,plain,
! [SV987: $i,SV659: $i,SV260: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV260 @ SV659 @ ( tc_fun @ SV987 @ tc_bool ) )
= SV659 )
= $false )
| ( ( c_lessequals @ SV260 @ SV659 @ ( tc_fun @ SV987 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3183]) ).
thf(3518,plain,
! [SV1458: $i,SV1259: $i,SV988: $i,SV661: $i,SV264: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV264 @ SV661 ) @ SV988 ) )
| ! [SY4943: $i] :
( ~ ( c_Natural_Oevaln @ SV1259 @ SV1458 @ SY4943 @ SV988 )
| ! [SY4944: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4944 @ SV661 ) @ SV1458 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ SY4943 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4944 ) @ SV1259 ) @ SV264 ) @ t_a ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3184]) ).
thf(3519,plain,
! [SV989: $i,SV265: $i,SV662: $i,SV1459: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV1459 @ SV662 ) )
| ! [SY4945: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV1459 @ SY4945 @ SV265 ) @ SV662 @ SV989 ) )
= $true )
| ( ( c_Natural_Oevalc @ SV265 @ SV662 @ SV989 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3185]) ).
thf(3520,plain,
! [SV1460: $i,SV1260: $i,SV990: $i,SV663: $i,SV266: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV266 @ SV663 @ SV990 ) @ SV1260 @ SV1460 )
| ~ ( c_Natural_Oevalc @ SV990 @ SV1260 @ SV1460 )
| ( hBOOL @ ( hAPP @ SV266 @ SV1260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3186]) ).
thf(3521,plain,
! [SV1461: $i,SV1261: $i,SV991: $i,SV664: $i,SV267: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ SV267 @ SV664 @ SV991 ) @ SV1261 @ SV991 @ ( tc_fun @ SV1461 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV1261 @ SV267 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV664 @ SV1261 @ SV991 @ ( tc_fun @ SV1461 @ tc_bool ) ) @ ( tc_fun @ SV1461 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3187]) ).
thf(3522,plain,
! [SV1462: $i,SV270: $i,SV1262: $i] :
( ( ( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ SV1262 @ SV270 ) @ SV1462 @ SV270 )
| ~ ( hBOOL @ ( c_in @ SV1462 @ SV1262 @ SV270 ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV270 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3190]) ).
thf(3523,plain,
! [SV1463: $i,SV1263: $i,SV271: $i] :
( ( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV271 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1263 @ SV1463 @ SV271 ) )
| ( c_lessequals @ SV1263 @ SV1463 @ SV271 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV271 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3191]) ).
thf(3524,plain,
! [SV1464: $i,SV1264: $i,SV272: $i] :
( ( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV272 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1264 @ SV1464 @ SV272 ) )
| ~ ( c_lessequals @ SV1264 @ SV1464 @ SV272 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV272 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3192]) ).
thf(3525,plain,
! [SV1465: $i,SV1265: $i,SV994: $i,SV665: $i,SV273: $i] :
( ( ! [SY4946: $i,SY4947: $i,SY4948: $i,SY4949: $i,SY4950: $i,SY4951: $i,SY4952: $i] :
( ( c_Com_Ocom_Ocom__case @ SV273 @ SV665 @ SV994 @ SV1265 @ SV1465 @ SY4946 @ SY4947 @ SY4948 @ ( c_Com_Ocom_OLocal @ SY4949 @ SY4950 @ SY4951 ) @ SY4952 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV994 @ SY4949 ) @ SY4950 ) @ SY4951 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3193]) ).
thf(3526,plain,
! [SV1466: $i,SV1266: $i,SV995: $i,SV666: $i,SV274: $i] :
( ( ! [SY4953: $i,SY4954: $i,SY4955: $i,SY4956: $i,SY4957: $i,SY4958: $i] :
( ( c_Com_Ocom_Ocom__case @ SV274 @ SV666 @ SV995 @ SV1266 @ SV1466 @ SY4953 @ SY4954 @ SY4955 @ ( c_Com_Ocom_OWhile @ SY4956 @ SY4957 ) @ SY4958 )
= ( hAPP @ ( hAPP @ SY4953 @ SY4956 ) @ SY4957 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3194]) ).
thf(3527,plain,
! [SV1467: $i,SV1267: $i,SV996: $i,SV667: $i,SV275: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV275 @ SV667 @ ( tc_fun @ SV996 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1267 @ SV1467 @ ( tc_fun @ SV996 @ tc_bool ) ) @ ( tc_fun @ SV996 @ tc_bool ) )
| ~ ( c_lessequals @ SV667 @ SV1467 @ ( tc_fun @ SV996 @ tc_bool ) )
| ~ ( c_lessequals @ SV275 @ SV1267 @ ( tc_fun @ SV996 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3195]) ).
thf(3528,plain,
! [SV1468: $i,SV1268: $i,SV997: $i,SV668: $i,SV276: $i] :
( ( ! [SY4959: $i,SY4960: $i] :
( ( c_Fun_Ocomp @ SV276 @ ( c_Fun_Ocomp @ SV668 @ SV997 @ SV1268 @ SV1468 @ SY4959 ) @ SV1468 @ SY4960 @ SY4959 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV276 @ SV668 @ SV1468 @ SY4960 @ SV1268 ) @ SV997 @ SV1268 @ SY4960 @ SY4959 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3196]) ).
thf(3529,plain,
! [SV1270: $i,SV999: $i,SV671: $i,SV279: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV279 @ SV671 @ SV999 ) @ SV1270 @ ( tc_fun @ SV999 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV671 @ SV1270 @ ( tc_fun @ SV999 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV279 @ SV1270 @ SV999 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3198]) ).
thf(3530,plain,
! [SV1469: $i,SV1271: $i,SV1000: $i,SV672: $i,SV280: $i] :
( ( ! [SY4961: $i] :
( ( c_Set_Oimage @ SV280 @ ( c_Set_Oimage @ SV672 @ SV1000 @ SV1271 @ SV1469 ) @ SV1469 @ SY4961 )
= ( c_Set_Oimage @ ( c_COMBB @ SV280 @ SV672 @ SV1469 @ SY4961 @ SV1271 ) @ SV1000 @ SV1271 @ SY4961 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3199]) ).
thf(3531,plain,
! [SV1470: $i,SV1272: $i,SV1001: $i,SV673: $i,SV281: $i] :
( ( ! [SY4962: $i] :
( ( ( c_Com_Ocom_OLocal @ SV281 @ SV673 @ SV1001 )
!= ( c_Com_Ocom_OLocal @ SV1272 @ SV1470 @ SY4962 ) )
| ( SV1001 = SY4962 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3200]) ).
thf(3532,plain,
! [SV1471: $i,SV1273: $i,SV1002: $i,SV674: $i,SV282: $i] :
( ( ! [SY4963: $i] :
( ( c_Com_Ocom_OLocal @ SV282 @ SV674 @ SV1002 )
!= ( c_Com_Ocom_OLocal @ SV1273 @ SV1471 @ SY4963 ) )
| ( SV674 = SV1471 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3201]) ).
thf(3533,plain,
! [SV1274: $i,SV1003: $i,SV675: $i,SV283: $i] :
( ( ( ! [SY4734: $i,SY4735: $i] :
( ( c_Com_Ocom_OLocal @ SV283 @ SV675 @ SV1003 )
!= ( c_Com_Ocom_OLocal @ SV1274 @ SY4734 @ SY4735 ) ) )
= $true )
| ( ( SV283 = SV1274 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3202]) ).
thf(3534,plain,
! [SV284: $i,SV676: $i] :
( ( ( c_Com_OWT @ SV676 )
= $false )
| ( ( ~ ( c_Com_OWT @ SV284 ) )
= $true )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV284 @ SV676 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3203]) ).
thf(3535,plain,
! [SV1472: $i,SV1275: $i,SV1005: $i,SV678: $i,SV286: $i] :
( ( ! [SY4964: $i] :
( ( c_Set_Oimage @ ( c_Fun_Ocomp @ SV286 @ SV678 @ SV1005 @ SV1275 @ SV1472 ) @ SY4964 @ SV1472 @ SV1275 )
= ( c_Set_Oimage @ SV286 @ ( c_Set_Oimage @ SV678 @ SY4964 @ SV1472 @ SV1005 ) @ SV1005 @ SV1275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3205]) ).
thf(3536,plain,
! [SV1276: $i,SV1006: $i,SV679: $i,SV287: $i] :
( ( ( c_Com_Ocom_OWhile @ SV287 @ SV679 )
= ( c_Com_Ocom_OSemi @ SV1006 @ SV1276 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3206]) ).
thf(3537,plain,
! [SV1277: $i,SV1007: $i,SV680: $i,SV288: $i] :
( ( ( hBOOL @ ( c_in @ SV288 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV680 @ SV1007 @ ( tc_fun @ SV1277 @ tc_bool ) ) @ SV1277 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV288 @ SV1007 @ SV1277 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3207]) ).
thf(3538,plain,
! [SV1278: $i,SV1008: $i,SV681: $i,SV289: $i] :
( ( ( hBOOL @ ( c_in @ SV289 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV681 @ SV1008 @ ( tc_fun @ SV1278 @ tc_bool ) ) @ SV1278 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV289 @ SV681 @ SV1278 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3208]) ).
thf(3539,plain,
! [SV291: $i,SV683: $i,SV1279: $i] :
( ( ( SV1279 = SV683 )
= $true )
| ( ( ! [SY4738: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV291 @ SY4738 ) @ SV683 @ SV1279 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV291 @ SV683 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3209]) ).
thf(3540,plain,
! [SV294: $i,SV1473: $i,SV684: $i] :
( ( ( ( c_lessequals @ SV684 @ SV1473 @ SV294 )
| ! [SY4965: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4965 @ SV684 @ SV294 ) @ SV1473 @ SV294 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV294 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3210]) ).
thf(3541,plain,
! [SV295: $i,SV1474: $i,SV685: $i] :
( ( ( ( c_lessequals @ SV685 @ SV1474 @ SV295 )
| ! [SY4966: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV685 @ SY4966 @ SV295 ) @ SV1474 @ SV295 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV295 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3211]) ).
thf(3542,plain,
! [SV296: $i,SV1475: $i,SV686: $i] :
( ( ( ! [SY4967: $i] :
( ( c_lessequals @ SV686 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1475 @ SY4967 @ SV296 ) @ SV296 )
| ~ ( c_lessequals @ SV686 @ SY4967 @ SV296 ) ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV296 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3212]) ).
thf(3543,plain,
! [SV297: $i,SV1476: $i,SV687: $i] :
( ( ( ! [SY4968: $i] : ( c_lessequals @ SV687 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1476 @ SY4968 @ SV297 ) @ SV297 )
| ~ ( c_lessequals @ SV687 @ SV1476 @ SV297 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV297 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3213]) ).
thf(3544,plain,
! [SV298: $i,SV1477: $i,SV688: $i] :
( ( ( ( c_lessequals @ SV688 @ SV1477 @ SV298 )
| ! [SY4969: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4969 @ SV688 @ SV298 ) @ SV1477 @ SV298 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV298 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3214]) ).
thf(3545,plain,
! [SV299: $i,SV1478: $i,SV689: $i] :
( ( ( ( c_lessequals @ SV689 @ SV1478 @ SV299 )
| ! [SY4970: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV689 @ SY4970 @ SV299 ) @ SV1478 @ SV299 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV299 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3215]) ).
thf(3546,plain,
! [SV690: $i,SV1010: $i,SV1479: $i,SV300: $i] :
( ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV300 @ SV1479 @ ( tc_fun @ SV1010 @ tc_bool ) ) @ SV690 @ ( tc_fun @ SV1010 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV300 @ SV690 @ ( tc_fun @ SV1010 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3216]) ).
thf(3547,plain,
! [SV691: $i,SV1011: $i,SV301: $i,SV1480: $i] :
( ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1480 @ SV301 @ ( tc_fun @ SV1011 @ tc_bool ) ) @ SV691 @ ( tc_fun @ SV1011 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV301 @ SV691 @ ( tc_fun @ SV1011 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3217]) ).
thf(3548,plain,
! [SV302: $i,SV1481: $i,SV692: $i] :
( ( ( ( c_lessequals @ SV692 @ SV1481 @ SV302 )
| ! [SY4971: $i] :
( ~ ( c_lessequals @ SV692 @ SY4971 @ SV302 )
| ~ ( c_lessequals @ SY4971 @ SV1481 @ SV302 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV302 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3218]) ).
thf(3549,plain,
! [SV303: $i,SV1482: $i,SV693: $i] :
( ( ( ( c_lessequals @ SV693 @ SV1482 @ SV303 )
| ! [SY4972: $i] :
( ~ ( c_lessequals @ SY4972 @ SV1482 @ SV303 )
| ~ ( c_lessequals @ SV693 @ SY4972 @ SV303 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV303 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3219]) ).
thf(3550,plain,
! [SV694: $i,SV1012: $i,SV1483: $i,SV304: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV304 @ SV1483 @ SV1012 ) )
| ~ ( c_lessequals @ SV1483 @ SV694 @ ( tc_fun @ SV1012 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV304 @ SV694 @ SV1012 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3220]) ).
thf(3551,plain,
! [SV695: $i,SV1013: $i,SV1484: $i,SV305: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV305 @ SV1484 @ SV1013 ) )
| ~ ( c_lessequals @ SV1484 @ SV695 @ ( tc_fun @ SV1013 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV305 @ SV695 @ SV1013 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3221]) ).
thf(3552,plain,
! [SV307: $i,SV1014: $i,SV697: $i,SV1485: $i] :
( ( ( ~ ( c_lessequals @ SV1485 @ SV697 @ ( tc_fun @ SV1014 @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ SV307 @ SV1485 @ SV1014 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV307 @ SV697 @ SV1014 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3222]) ).
thf(3553,plain,
! [SV698: $i,SV1015: $i,SV1486: $i,SV308: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV308 @ SV1486 @ SV1015 ) )
| ~ ( c_lessequals @ SV1486 @ SV698 @ ( tc_fun @ SV1015 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV308 @ SV698 @ SV1015 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3223]) ).
thf(3554,plain,
! [SV310: $i,SV1016: $i,SV700: $i,SV1487: $i] :
( ( ( ~ ( c_lessequals @ SV1487 @ SV700 @ ( tc_fun @ SV1016 @ tc_bool ) )
| ~ ( c_lessequals @ SV310 @ SV1487 @ ( tc_fun @ SV1016 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV310 @ SV700 @ ( tc_fun @ SV1016 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3224]) ).
thf(3555,plain,
! [SV311: $i,SV701: $i,SV1280: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV1280 @ SV701 ) ) )
= $true )
| ( ( ! [SY4739: $i] :
~ ( c_lessequals @ SV1280 @ SV311 @ ( tc_fun @ SY4739 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV311 @ SV701 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3225]) ).
thf(3556,plain,
! [SV702: $i,SV314: $i,SV1283: $i] :
( ( ( ! [SY4740: $i] :
~ ( c_lessequals @ SV1283 @ SV314 @ ( tc_fun @ SY4740 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1283 @ SV702 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV314 @ SV702 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3228]) ).
thf(3557,plain,
! [SV316: $i,SV1488: $i,SV1284: $i] :
( ( ( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1284 @ SV1488 @ SV316 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV316 @ tc_bool ) ) )
| ( c_lessequals @ SV1284 @ SV1488 @ SV316 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV316 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3230]) ).
thf(3558,plain,
! [SV317: $i,SV1489: $i,SV1285: $i] :
( ( ( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1285 @ SV1489 @ SV317 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV317 @ tc_bool ) ) )
| ~ ( c_lessequals @ SV1285 @ SV1489 @ SV317 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV317 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3231]) ).
thf(3559,plain,
! [SV1490: $i,SV1286: $i,SV1018: $i,SV704: $i,SV318: $i] :
( ( ! [SY4973: $i,SY4974: $i,SY4975: $i,SY4976: $i,SY4977: $i,SY4978: $i,SY4979: $i] :
( ( c_Com_Ocom_Ocom__case @ SV318 @ SV704 @ SV1018 @ SV1286 @ SV1490 @ SY4973 @ SY4974 @ SY4975 @ ( c_Com_Ocom_OCond @ SY4976 @ SY4977 @ SY4978 ) @ SY4979 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV1490 @ SY4976 ) @ SY4977 ) @ SY4978 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3232]) ).
thf(3560,plain,
! [SV1491: $i,SV1287: $i,SV1019: $i,SV705: $i,SV319: $i] :
( ( ! [SY4980: $i,SY4981: $i] :
( ! [SY4982: $i] :
( ( c_Fun_Ocomp @ SV319 @ SV705 @ SV1019 @ SV1287 @ SV1491 )
!= ( c_Fun_Ocomp @ SY4980 @ SY4981 @ SY4982 @ SV1287 @ SV1491 ) )
| ! [SY3735: $i] :
( ( hAPP @ SV319 @ ( hAPP @ SV705 @ SY3735 ) )
= ( hAPP @ SY4980 @ ( hAPP @ SY4981 @ SY3735 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3233]) ).
thf(3561,plain,
! [SV1492: $i,SV1288: $i,SV1020: $i,SV706: $i,SV320: $i] :
( ( ! [SY4984: $i,SY4985: $i,SY4986: $i,SY4987: $i] :
( ( ( hAPP @ SV320 @ ( hAPP @ SV706 @ SV1020 ) )
!= ( hAPP @ SV1288 @ ( hAPP @ SV1492 @ SY4984 ) ) )
| ! [SY4988: $i,SY4989: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV320 @ SV706 @ SY4985 @ SY4986 @ SY4987 ) @ SV1020 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1288 @ SV1492 @ SY4988 @ SY4986 @ SY4989 ) @ SY4984 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3234]) ).
thf(3562,plain,
! [SV321: $i,SV707: $i,SV1021: $i] :
( ( ( SV1021 = SV707 )
= $true )
| ( ( ! [SY4366: $i,SY4367: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV321 @ SY4366 ) @ SV707 @ SY4367 @ SV1021 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV321 @ SV707 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3235]) ).
thf(3563,plain,
! [SV1493: $i,SV1289: $i,SV1022: $i,SV708: $i,SV322: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV322 @ SV708 @ ( tc_fun @ SV1022 @ tc_bool ) ) @ SV1289 @ SV1022 @ ( tc_fun @ SV1493 @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV322 @ SV1289 @ SV1022 @ ( tc_fun @ SV1493 @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV708 @ SV1289 @ SV1022 @ ( tc_fun @ SV1493 @ tc_bool ) ) @ ( tc_fun @ SV1493 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3236]) ).
thf(3564,plain,
! [SV1290: $i,SV1023: $i,SV710: $i,SV324: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV324 @ ( c_HOL_Ominus__class_Ominus @ SV710 @ SV1023 @ ( tc_fun @ SV1290 @ tc_bool ) ) @ ( tc_fun @ SV1290 @ tc_bool ) )
= SV1023 )
= $true )
| ( ( ~ ( c_lessequals @ SV324 @ SV710 @ ( tc_fun @ SV1290 @ tc_bool ) )
| ~ ( c_lessequals @ SV1023 @ SV324 @ ( tc_fun @ SV1290 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3237]) ).
thf(3565,plain,
! [SV1024: $i,SV711: $i,SV325: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
= $false )
| ( ( ! [SY4371: $i,SY4372: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV711 @ SV1024 @ SV325 )
!= ( c_HOL_Ominus__class_Ominus @ SY4371 @ SY4372 @ SV325 ) )
| ( c_lessequals @ SY4372 @ SY4371 @ SV325 )
| ~ ( c_lessequals @ SV1024 @ SV711 @ SV325 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3238]) ).
thf(3566,plain,
! [SV1025: $i,SV712: $i,SV326: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV326 )
= $false )
| ( ( ! [SY4373: $i,SY4374: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV712 @ SV1025 @ SV326 )
!= ( c_HOL_Ominus__class_Ominus @ SY4373 @ SY4374 @ SV326 ) )
| ( c_lessequals @ SV1025 @ SV712 @ SV326 )
| ~ ( c_lessequals @ SY4374 @ SY4373 @ SV326 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3239]) ).
thf(3567,plain,
! [SV1494: $i,SV1291: $i,SV1026: $i,SV713: $i,SV327: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV327 @ SV713 @ SV1026 @ SV1291 ) @ ( c_Set_Oimage @ SV327 @ SV1494 @ SV1026 @ SV1291 ) @ ( tc_fun @ SV1291 @ tc_bool ) )
| ~ ( c_lessequals @ SV713 @ SV1494 @ ( tc_fun @ SV1026 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3240]) ).
thf(3568,plain,
! [SV1027: $i,SV714: $i,SV328: $i] :
( ( ( c_lessequals @ SV328 @ SV714 @ ( tc_fun @ SV1027 @ tc_bool ) )
= $false )
| ( ( ! [SY4377: $i,SY4378: $i] : ( c_lessequals @ ( c_Set_Oimage @ SY4377 @ SV328 @ SV1027 @ SY4378 ) @ ( c_Set_Oimage @ SY4377 @ SV714 @ SV1027 @ SY4378 ) @ ( tc_fun @ SY4378 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3241]) ).
thf(3569,plain,
! [SV1292: $i,SV1028: $i,SV715: $i,SV329: $i] :
( ( ( c_Natural_Oevaln @ SV329 @ SV715 @ SV1028 @ SV1292 )
= $true )
| ( ( ! [SY4765: $i] :
( ( c_Natural_Oevaln @ SY4765 @ SV715 @ SV1028 @ SV1292 )
| ! [SY4766: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SY4766 @ SY4765 @ SV329 ) @ SV715 @ SV1028 @ SV1292 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3242]) ).
thf(3570,plain,
! [SV1495: $i,SV1293: $i,SV1029: $i,SV716: $i,SV330: $i] :
( ( ( c_Set_Oimage @ SV330 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV716 @ SV1029 @ ( tc_fun @ SV1293 @ tc_bool ) ) @ SV1293 @ SV1495 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ SV330 @ SV716 @ SV1293 @ SV1495 ) @ ( c_Set_Oimage @ SV330 @ SV1029 @ SV1293 @ SV1495 ) @ ( tc_fun @ SV1495 @ tc_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3243]) ).
thf(3571,plain,
! [SV1496: $i,SV1294: $i,SV1030: $i,SV717: $i,SV331: $i] :
( ( ! [SY4990: $i] :
( ( c_Com_Ocom_OLocal @ SV331 @ SV717 @ SV1030 )
!= ( c_Com_Ocom_OCall @ SV1294 @ SV1496 @ SY4990 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3244]) ).
thf(3572,plain,
! [SV332: $i,SV1031: $i,SV718: $i,SV1497: $i] :
( ( ( ( c_Natural_Oevalc @ SV1497 @ SV718 @ SV1031 )
| ! [SY4991: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY4991 @ SV1497 @ SV332 ) @ SV718 @ SV1031 ) )
= $true )
| ( ( c_Natural_Oevalc @ SV332 @ SV718 @ SV1031 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3245]) ).
thf(3573,plain,
! [SV333: $i,SV1498: $i,SV1295: $i] :
( ( ( ( c_lessequals @ SV1295 @ ( c_Complete__Lattice_OSup__class_OSup @ SV1498 @ SV333 ) @ SV333 )
| ~ ( hBOOL @ ( c_in @ SV1295 @ SV1498 @ SV333 ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV333 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3246]) ).
thf(3574,plain,
! [SV334: $i,SV1296: $i,SV1032: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV1032 @ SV1296 @ SV334 ) )
= $false )
| ( ( c_Com_OWT @ SV334 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3247]) ).
thf(3575,plain,
! [SV1297: $i,SV335: $i,SV1033: $i] :
( ( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV1033 @ SV335 @ SV1297 ) )
= $false )
| ( ( c_Com_OWT @ SV335 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3248]) ).
thf(3576,plain,
! [SV337: $i,SV1499: $i,SV1298: $i] :
( ( ( ( c_lessequals @ SV1298 @ SV1499 @ SV337 )
| ( c_lessequals @ SV1499 @ SV1298 @ SV337 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV337 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3249]) ).
thf(3577,plain,
! [SV1299: $i,SV1034: $i,SV720: $i,SV338: $i] :
( ( ( hAPP @ c_Com_Ocom_OBODY @ SV338 )
= ( c_Com_Ocom_OLocal @ SV720 @ SV1034 @ SV1299 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3250]) ).
thf(3578,plain,
! [SV1300: $i,SV1036: $i,SV722: $i,SV340: $i] :
( ( ( c_Com_Ocom_OCall @ SV340 @ SV722 @ SV1036 )
= ( hAPP @ c_Com_Ocom_OBODY @ SV1300 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3252]) ).
thf(3579,plain,
! [SV1301: $i,SV1039: $i,SV725: $i,SV343: $i] :
( ( ( c_Com_Ocom_OLocal @ SV343 @ SV725 @ SV1039 )
= ( hAPP @ c_Com_Ocom_OBODY @ SV1301 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3255]) ).
thf(3580,plain,
! [SV1302: $i,SV1040: $i,SV726: $i,SV344: $i] :
( ( ( hAPP @ c_Com_Ocom_OBODY @ SV344 )
= ( c_Com_Ocom_OCall @ SV726 @ SV1040 @ SV1302 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3256]) ).
thf(3581,plain,
! [SV1500: $i,SV1303: $i,SV1041: $i,SV727: $i,SV345: $i] :
( ( ! [SY4992: $i,SY4993: $i,SY4994: $i,SY4995: $i,SY4996: $i] :
( ( c_Com_Ocom_Ocom__case @ SV345 @ SV727 @ SV1041 @ SV1303 @ SV1500 @ SY4992 @ SY4993 @ SY4994 @ ( hAPP @ c_Com_Ocom_OBODY @ SY4995 ) @ SY4996 )
= ( hAPP @ SY4993 @ SY4995 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3257]) ).
thf(3582,plain,
! [SV1501: $i,SV1305: $i,SV1043: $i,SV729: $i,SV348: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV348 @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SV729 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ SV1043 ) @ SV1305 ) @ SV1501 ) @ t_b @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV348 @ ( hAPP @ ( hAPP @ ( hAPP @ SV729 @ SV1043 ) @ SV1305 ) @ SV1501 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3259]) ).
thf(3583,plain,
! [SV1502: $i,SV1306: $i,SV1044: $i,SV730: $i,SV349: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV349 @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SV730 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ SV1044 ) @ SV1306 ) @ SV1502 ) @ t_b @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV349 @ ( hAPP @ ( hAPP @ ( hAPP @ SV730 @ SV1044 ) @ SV1306 ) @ SV1502 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3260]) ).
thf(3584,plain,
! [SV1503: $i,SV1307: $i,SV1045: $i,SV731: $i,SV350: $i] :
( ( ! [SY4997: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ SV350 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV731 ) @ SV1045 ) @ SV1307 ) @ SV1503 ) @ SV731 @ SY4997 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV350 @ SV1045 ) @ SV1307 ) @ SV1503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3261]) ).
thf(3585,plain,
! [SV1504: $i,SV1308: $i,SV1046: $i,SV732: $i,SV351: $i] :
( ( ! [SY4998: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SV351 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV732 ) @ SV1046 ) @ SV1308 ) @ SV1504 ) @ SV732 @ SY4998 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV351 @ SV1046 ) @ SV1308 ) @ SV1504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3262]) ).
thf(3586,plain,
! [SV352: $i,SV1047: $i,SV1505: $i,SV733: $i] :
( ( ( ~ ( c_lessequals @ SV733 @ SV1505 @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1047 ) @ tc_bool ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV352 @ SV1505 @ SV1047 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV352 @ SV733 @ SV1047 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3263]) ).
thf(3587,plain,
! [SV734: $i,SV1048: $i,SV353: $i,SV1506: $i] :
( ( ( ~ ( c_lessequals @ SV1506 @ SV353 @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1048 ) @ tc_bool ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV1506 @ SV734 @ SV1048 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ SV734 @ SV1048 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3264]) ).
thf(3588,plain,
! [SV1049: $i,SV354: $i,SV735: $i] :
( ( ( c_lessequals @ SV735 @ SV354 @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1049 ) @ tc_bool ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV354 @ SV735 @ SV1049 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3265]) ).
thf(3589,plain,
! [SV1309: $i,SV1050: $i,SV736: $i,SV355: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV355 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV736 ) @ SV1050 ) @ SV1309 ) @ ( 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 @ SV355 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ ( c_COMBK @ ( hAPP @ ( c_COMBC @ ( c_fequal @ tc_Com_Ostate ) @ tc_Com_Ostate @ tc_Com_Ostate @ tc_bool ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ SV355 @ SV736 @ SV1309 @ SV1050 ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) ) @ SV1050 ) @ ( c_COMBK @ ( hAPP @ SV1309 @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ SV355 @ SV736 @ SV1309 @ SV1050 ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_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)],[3266]) ).
thf(3590,plain,
! [SV1507: $i,SV1310: $i,SV1051: $i,SV737: $i,SV356: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV356 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ ( hAPP @ SV1051 @ SV1310 ) ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1310 ) ) @ ( hAPP @ SV1507 @ SV1310 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV737 )
| ! [SY4999: $i] :
( ~ ( hBOOL @ ( c_in @ SV1310 @ SY4999 @ tc_Com_Opname ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV356 @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ SV1051 @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ SV1507 @ tc_Com_Opname @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SY4999 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ SV1051 @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ SV1507 @ tc_Com_Opname @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SY4999 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV737 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3267]) ).
thf(3591,plain,
! [SV1508: $i,SV1311: $i,SV1052: $i,SV739: $i,SV359: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV359 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV739 ) @ SV1052 ) @ ( c_Com_Ocom_OWhile @ SV1311 @ SV1508 ) ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1052 @ ( c_Fun_Ocomp @ c_Not @ SV1311 @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ SV739 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV739 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV739 ) ) @ SV739 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV359 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV739 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1052 @ SV1311 @ SV739 ) ) @ SV1508 ) @ SV1052 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV739 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV739 ) ) @ SV739 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3268]) ).
thf(3592,plain,
! [SV1509: $i,SV1312: $i,SV1053: $i,SV740: $i,SV360: $i] :
( ( ! [SY5000: $i,SY5001: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ SV1053 ) @ ( c_Com_Ocom_OCond @ SV1312 @ SV1509 @ SY5000 ) ) @ SY5001 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1053 @ ( c_Fun_Ocomp @ c_Not @ SV1312 @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ SV740 ) ) @ SY5000 ) @ SY5001 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1053 @ SV1312 @ SV740 ) ) @ SV1509 ) @ SY5001 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3269]) ).
thf(3593,plain,
! [SV1313: $i,SV1054: $i,SV741: $i,SV361: $i] :
( ( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV361 ) ) @ SV741 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ SV361 @ SV1054 @ SV741 @ SV1313 ) @ SV1313 )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ SV361 ) @ SV741 @ SV1054 @ SV1313 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3270]) ).
thf(3594,plain,
! [SV1314: $i,SV1055: $i,SV742: $i,SV362: $i] :
( ( ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ SV362 ) @ SV742 @ ( c_Suc @ SV1055 ) @ SV1314 )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV362 ) ) @ SV742 @ SV1055 @ SV1314 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3271]) ).
thf(3595,plain,
! [SV744: $i,SV1056: $i,SV366: $i] :
( ( ( SV366
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1056 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV366 @ ( c_Set_Oinsert @ SV744 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1056 @ tc_bool ) ) @ SV1056 ) @ ( tc_fun @ SV1056 @ tc_bool ) ) )
= $true )
| ( ( SV366
= ( c_Set_Oinsert @ SV744 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1056 @ tc_bool ) ) @ SV1056 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3272]) ).
thf(3596,plain,
! [SV1510: $i,SV1315: $i,SV1057: $i,SV746: $i,SV368: $i] :
( ( ! [SY5002: $i,SY5003: $i,SY5004: $i] :
( ( ( hAPP @ SV368 @ ( c_Set_Oinsert @ SV746 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1057 @ tc_bool ) ) @ SV1057 ) )
= SV746 )
| ! [SY5005: $i,SY5006: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV368 @ SV1315 @ SV1510 @ SY5002 @ SY5003 @ SY5004 @ SY5005 @ SY5006 @ SV1057 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3273]) ).
thf(3597,plain,
! [SV1511: $i,SV1316: $i,SV1058: $i,SV747: $i,SV369: $i] :
( ( ! [SY5007: $i,SY5008: $i,SY5009: $i] :
( ( ( hAPP @ SV369 @ ( c_Set_Oinsert @ SV747 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1058 @ tc_bool ) ) @ SV1058 ) )
= SV747 )
| ! [SY5010: $i,SY5011: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1316 @ SV369 @ SV1511 @ SY5007 @ SY5008 @ SY5009 @ SY5010 @ SY5011 @ SV1058 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3274]) ).
thf(3598,plain,
! [SV1512: $i,SV1320: $i,SV1061: $i,SV752: $i,SV376: $i] :
( ( ! [SY5012: $i,SY5013: $i,SY5014: $i,SY5015: $i] :
( ( ( hAPP @ SV376 @ ( c_Set_Oinsert @ SV752 @ ( c_Set_Oinsert @ SV1061 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1320 @ tc_bool ) ) @ SV1320 ) @ SV1320 ) )
= ( hAPP @ ( hAPP @ SV1512 @ SV752 ) @ SV1061 ) )
| ! [SY5016: $i,SY5017: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV376 @ SY5012 @ SY5013 @ SY5014 @ SV1512 @ SY5015 @ SY5016 @ SY5017 @ SV1320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3278]) ).
thf(3599,plain,
! [SV1513: $i,SV1321: $i,SV1062: $i,SV753: $i,SV377: $i] :
( ( ! [SY5018: $i,SY5019: $i,SY5020: $i,SY5021: $i] :
( ( ( hAPP @ SV377 @ ( c_Set_Oinsert @ SV753 @ ( c_Set_Oinsert @ SV1062 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1321 @ tc_bool ) ) @ SV1321 ) @ SV1321 ) )
= ( hAPP @ ( hAPP @ SV1513 @ SV753 ) @ SV1062 ) )
| ! [SY5022: $i,SY5023: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SY5018 @ SV377 @ SY5019 @ SY5020 @ SY5021 @ SV1513 @ SY5022 @ SY5023 @ SV1321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3279]) ).
thf(3600,plain,
! [SV756: $i,SV1514: $i,SV380: $i,SV1324: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV1324 @ ( c_Set_Oinsert @ SV380 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1514 @ tc_bool ) ) @ SV1514 ) @ SV1514 ) @ SV756 ) ) )
= $true )
| ( ( SV380 = SV756 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3282]) ).
thf(3601,plain,
! [SV382: $i,SV1065: $i,SV758: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV758 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1065 @ tc_bool ) ) @ SV1065 ) @ SV382 ) )
= $false )
| ( ( SV382
= ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ SV758 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1065 @ tc_bool ) ) @ SV1065 ) @ SV1065 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3283]) ).
thf(3602,plain,
! [SV1325: $i,SV759: $i,SV383: $i] :
( ( ( hBOOL @ ( c_in @ SV383 @ ( c_Set_Oinsert @ SV759 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1325 @ tc_bool ) ) @ SV1325 ) @ SV1325 ) )
= $false )
| ( ( SV383 = SV759 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3284]) ).
thf(3603,plain,
! [SV1068: $i,SV762: $i,SV388: $i] :
( ( ( ( c_Set_Oinsert @ SV388 @ SV762 @ SV1068 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1068 @ tc_bool ) ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV388 @ SV762 @ SV1068 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3287]) ).
thf(3604,plain,
! [SV1515: $i,SV1329: $i,SV1070: $i,SV764: $i,SV391: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV391 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV764 ) @ SV1070 ) @ SV1329 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY5024: $i,SY5025: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV1515 @ SY5024 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV391 @ SV764 @ SV1329 @ SV1070 @ SY5025 @ SV1515 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY5025 @ SY5024 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV391 @ SV764 @ SV1329 @ SV1070 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV391 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY5025 ) @ SV1070 ) @ SV1515 ) @ ( 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)],[3289]) ).
thf(3605,plain,
! [SV1516: $i,SV1330: $i,SV1071: $i,SV765: $i,SV392: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV392 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV765 ) @ SV1071 ) @ SV1330 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY5026: $i,SY5027: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV1516 @ SY5026 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV765 @ SY5027 @ SV1330 @ SV1516 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY5027 @ SY5026 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV765 @ SY5027 @ SV1330 @ SV1516 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV392 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY5027 ) @ SV1071 ) @ SV1516 ) @ ( 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)],[3290]) ).
thf(3606,plain,
! [SV1517: $i,SV1331: $i,SV1072: $i,SV766: $i,SV393: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV393 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV766 ) @ SV1072 ) @ SV1331 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ! [SY5028: $i,SY5029: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV1517 @ SY5028 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV393 @ SV766 @ SV1331 @ SV1072 @ SY5029 @ SV1517 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY5029 @ SY5028 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV393 @ SV766 @ SV1331 @ SV1072 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV393 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY5029 ) @ SV1072 ) @ SV1517 ) @ ( 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(3607,plain,
! [SV1332: $i,SV1073: $i,SV767: $i,SV394: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV394 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV767 ) @ SV1073 ) @ SV1332 ) @ ( 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 @ SV767 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV394 @ SV767 @ SV1332 @ SV1073 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV394 @ SV767 @ SV1332 @ SV1073 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3292]) ).
thf(3608,plain,
! [SV1333: $i,SV1074: $i,SV768: $i,SV395: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV395 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV768 ) @ SV1074 ) @ SV1333 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
= $true )
| ( ( ! [SY4826: $i,SY4827: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1333 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV395 @ SV768 @ SV1333 @ SV1074 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV395 @ SV768 @ SV1333 @ SV1074 @ SY4826 @ SY4827 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV395 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4826 ) @ SV1074 ) @ SY4827 ) @ ( 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)],[3293]) ).
thf(3609,plain,
! [SV1334: $i,SV1075: $i,SV769: $i,SV396: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV396 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV769 ) @ SV1075 ) @ SV1334 ) @ ( 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 @ SV769 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV396 @ SV769 @ SV1334 @ SV1075 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV396 @ SV769 @ SV1334 @ SV1075 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3294]) ).
thf(3610,plain,
! [SV1335: $i,SV1076: $i,SV770: $i,SV397: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV397 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV770 ) @ SV1076 ) @ SV1335 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
= $true )
| ( ( ! [SY4828: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SY4828 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SV1335 @ SY4828 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SV1335 @ SY4828 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV397 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV770 ) @ SV1076 ) @ SY4828 ) @ ( 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)],[3295]) ).
thf(3611,plain,
! [SV1336: $i,SV1077: $i,SV771: $i,SV398: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV398 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV771 ) @ SV1077 ) @ SV1336 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
= $true )
| ( ( ! [SY4829: $i,SY4830: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV771 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV771 @ SY4829 @ SV1336 @ SY4830 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV771 @ SY4829 @ SV1336 @ SY4830 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV398 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4829 ) @ SV1077 ) @ SY4830 ) @ ( 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(3612,plain,
! [SV1337: $i,SV1078: $i,SV772: $i,SV399: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV399 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV772 ) @ SV1078 ) @ SV1337 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
= $true )
| ( ( ! [SY4831: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV772 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV772 @ SY4831 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV772 @ SY4831 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV399 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4831 ) @ SV1078 ) @ SV1337 ) @ ( 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)],[3297]) ).
thf(3613,plain,
! [SV1338: $i,SV1079: $i,SV773: $i,SV400: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV400 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV773 ) @ SV1079 ) @ SV1338 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
= $true )
| ( ( ! [SY4832: $i,SY4833: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1338 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV400 @ SV773 @ SV1338 @ SV1079 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV400 @ SV773 @ SV1338 @ SV1079 @ SY4832 @ SY4833 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV400 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4832 ) @ SV1079 ) @ SY4833 ) @ ( 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)],[3298]) ).
thf(3614,plain,
! [SV1339: $i,SV1080: $i,SV774: $i,SV401: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV401 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV774 ) @ SV1080 ) @ SV1339 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
= $true )
| ( ( ! [SY4834: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4834 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV774 @ SY4834 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV774 @ SY4834 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV401 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4834 ) @ SV1080 ) @ SV1339 ) @ ( 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)],[3299]) ).
thf(3615,plain,
! [SV1340: $i,SV1081: $i,SV775: $i,SV402: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV402 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV775 ) @ SV1081 ) @ SV1340 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
= $true )
| ( ( ! [SY4835: $i,SY4836: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1340 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV775 @ SY4835 @ SV1340 @ SY4836 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV775 @ SY4835 @ SV1340 @ SY4836 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV402 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4835 ) @ SV1081 ) @ SY4836 ) @ ( 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)],[3300]) ).
thf(3616,plain,
! [SV1341: $i,SV1082: $i,SV776: $i,SV403: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV403 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV776 ) @ SV1082 ) @ SV1341 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
= $true )
| ( ( ! [SY4837: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1341 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SV1341 @ SY4837 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SV1341 @ SY4837 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV403 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV776 ) @ SV1082 ) @ SY4837 ) @ ( 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)],[3301]) ).
thf(3617,plain,
! [SV1342: $i,SV1083: $i,SV777: $i,SV404: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV404 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV777 ) @ SV1083 ) @ SV1342 ) @ ( 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 @ SV777 @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ SV404 @ SV777 @ SV1342 @ SV1083 ) ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ SV404 @ SV777 @ SV1342 @ SV1083 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3302]) ).
thf(3618,plain,
! [SV1518: $i,SV1343: $i,SV1084: $i,SV778: $i,SV405: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV405 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV778 ) @ SV1084 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1343 ) ) @ SV1518 ) @ SV778 )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ SV405 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV778 ) @ SV1084 ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV1343 ) ) ) @ SV1518 ) @ SV778 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3303]) ).
thf(3619,plain,
! [SV1519: $i,SV1344: $i,SV1085: $i,SV779: $i,SV406: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ SV406 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV779 ) @ SV1085 ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV1344 ) ) ) @ SV1519 ) @ SV779 )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV406 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV779 ) @ SV1085 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1344 ) ) @ SV1519 ) @ SV779 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3304]) ).
thf(3620,plain,
! [SV1086: $i,SV780: $i,SV407: $i] :
( ( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV407 ) ) @ SV780 @ SV1086 )
= $false )
| ( ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ SV407 ) @ SV780 @ SV1086 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3305]) ).
thf(3621,plain,
! [SV1087: $i,SV781: $i,SV408: $i] :
( ( ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ SV408 ) @ SV781 @ SV1087 )
= $false )
| ( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV408 ) ) @ SV781 @ SV1087 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3306]) ).
thf(3622,plain,
! [SV1520: $i,SV1345: $i,SV1089: $i,SV783: $i,SV410: $i] :
( ( ! [SY5030: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SV1089 ) @ ( c_Com_Ocom_OSemi @ SV1345 @ SV1520 ) ) @ SY5030 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 )
| ! [SY5031: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SY5031 ) @ SV1520 ) @ SY5030 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SV1089 ) @ SV1345 ) @ SY5031 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3307]) ).
thf(3623,plain,
! [SV1346: $i,SV1090: $i,SV784: $i,SV411: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV411 @ ( c_Set_Oinsert @ SV784 @ SV1090 @ ( tc_Hoare__Mirabelle_Otriple @ SV1346 ) ) @ SV1346 )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV411 @ SV1090 @ SV1346 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV411 @ ( c_Set_Oinsert @ SV784 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1346 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1346 ) ) @ SV1346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3308]) ).
thf(3624,plain,
! [SV786: $i,SV1092: $i,SV1521: $i,SV413: $i] :
( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV413 @ SV1521 @ SV1092 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV1521 @ SV786 @ SV1092 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV413 @ SV786 @ SV1092 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3309]) ).
thf(3625,plain,
! [SV1522: $i,SV1347: $i,SV1094: $i,SV788: $i,SV415: $i] :
( ( ! [SY5032: $i,SY5033: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV415 ) @ SV788 ) @ SV1094 ) @ SV1347 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV415 ) @ SV1522 ) @ SY5032 ) @ SY5033 ) )
| ( SV1347 = SY5033 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3311]) ).
thf(3626,plain,
! [SV1523: $i,SV1348: $i,SV1095: $i,SV789: $i,SV416: $i] :
( ( ! [SY5034: $i] :
( ! [SY5035: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV416 ) @ SV789 ) @ SV1095 ) @ SV1348 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV416 ) @ SV1523 ) @ SY5034 ) @ SY5035 ) )
| ( SV1095 = SY5034 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3312]) ).
thf(3627,plain,
! [SV1524: $i,SV1349: $i,SV1096: $i,SV790: $i,SV417: $i] :
( ( ! [SY5036: $i,SY5037: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV417 ) @ SV790 ) @ SV1096 ) @ SV1349 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV417 ) @ SV1524 ) @ SY5036 ) @ SY5037 ) )
| ( SV790 = SV1524 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3313]) ).
thf(3628,plain,
! [SV1525: $i,SV1350: $i,SV1097: $i,SV791: $i,SV418: $i] :
( ( ( ( c_Set_Oinsert @ SV418 @ ( c_Set_Oinsert @ SV791 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1097 @ tc_bool ) ) @ SV1097 ) @ SV1097 )
!= ( c_Set_Oinsert @ SV1350 @ ( c_Set_Oinsert @ SV1525 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1097 @ tc_bool ) ) @ SV1097 ) @ SV1097 ) )
| ( SV791 = SV1350 )
| ( SV791 = SV1525 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3314]) ).
thf(3629,plain,
! [SV1526: $i,SV1351: $i,SV1098: $i,SV792: $i,SV419: $i] :
( ( ( ( c_Set_Oinsert @ SV419 @ ( c_Set_Oinsert @ SV792 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1098 @ tc_bool ) ) @ SV1098 ) @ SV1098 )
!= ( c_Set_Oinsert @ SV1351 @ ( c_Set_Oinsert @ SV1526 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1098 @ tc_bool ) ) @ SV1098 ) @ SV1098 ) )
| ( SV419 = SV1526 )
| ( SV792 = SV1526 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3315]) ).
thf(3630,plain,
! [SV1352: $i,SV1099: $i,SV793: $i,SV420: $i] :
( ( ( ! [SY4854: $i] :
( ( c_Set_Oinsert @ SV420 @ ( c_Set_Oinsert @ SV793 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1099 @ tc_bool ) ) @ SV1099 ) @ SV1099 )
!= ( c_Set_Oinsert @ SV1352 @ ( c_Set_Oinsert @ SY4854 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1099 @ tc_bool ) ) @ SV1099 ) @ SV1099 ) ) )
= $true )
| ( ( ( SV793 = SV1352 )
| ( SV420 = SV1352 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3316]) ).
thf(3631,plain,
! [SV1527: $i,SV1353: $i,SV1100: $i,SV794: $i,SV421: $i] :
( ( ( ( c_Set_Oinsert @ SV421 @ ( c_Set_Oinsert @ SV794 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1100 @ tc_bool ) ) @ SV1100 ) @ SV1100 )
!= ( c_Set_Oinsert @ SV1353 @ ( c_Set_Oinsert @ SV1527 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1100 @ tc_bool ) ) @ SV1100 ) @ SV1100 ) )
| ( SV421 = SV1527 )
| ( SV421 = SV1353 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3317]) ).
thf(3632,plain,
! [SV1528: $i,SV1354: $i,SV1101: $i,SV797: $i,SV424: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV424 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV797 ) @ SV1101 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1354 ) ) @ SV1528 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) ) @ SV797 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV797 ) @ SV1101 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1354 ) ) @ SV1528 ) @ SV424 @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) ) @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV797 ) @ SV1101 ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV1354 ) ) ) @ SV1528 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) ) @ SV797 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3318]) ).
thf(3633,plain,
! [SV425: $i,SV798: $i,SV1355: $i] :
( ( ( SV1355 = SV798 )
= $true )
| ( ( ! [SY4857: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1355 @ SV425 @ SY4857 ) @ SV798 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV425 @ SV798 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3319]) ).
thf(3634,plain,
! [SV1106: $i,SV803: $i,SV430: $i] :
( ( ( ( c_Set_Oinsert @ SV430 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV803 @ tc_bool ) ) @ SV803 )
= ( c_Set_Oinsert @ SV1106 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV803 @ tc_bool ) ) @ SV803 ) )
= $false )
| ( ( SV430 = SV1106 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3322]) ).
thf(3635,plain,
! [SV1357: $i,SV1107: $i,SV804: $i,SV431: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV431 @ SV804 @ SV1107 ) @ SV1357 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV804 @ SV1357 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3323]) ).
thf(3636,plain,
! [SV816: $i,SV443: $i,SV1358: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV1358 ) @ SV443 ) @ SV816 ) )
= $false )
| ( ( SV443 = SV816 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3334]) ).
thf(3637,plain,
! [SV1529: $i,SV1: $i,SV1359: $i,SV444: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV444 @ SV1359 @ SV1 ) @ SV1529 @ SV1 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV444 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1359 @ SV1529 @ SV1 ) @ SV1 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3335]) ).
thf(3638,plain,
! [SV2: $i,SV1530: $i,SV1360: $i,SV445: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV445 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1360 @ SV1530 @ SV2 ) @ SV2 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1360 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV445 @ SV1530 @ SV2 ) @ SV2 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3336]) ).
thf(3639,plain,
! [SV3: $i,SV1531: $i,SV1361: $i,SV446: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV446 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1361 @ SV1531 @ SV3 ) @ SV3 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV1361 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV446 @ SV1531 @ SV3 ) @ SV3 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3337]) ).
thf(3640,plain,
! [SV1532: $i,SV4: $i,SV1362: $i,SV447: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV447 @ SV1362 @ SV4 ) @ SV1532 @ SV4 )
= ( c_Lattices_Oupper__semilattice__class_Osup @ SV447 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1362 @ SV1532 @ SV4 ) @ SV4 ) )
= $true )
| ( ( class_Lattices_Olattice @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3338]) ).
thf(3641,plain,
! [SV7: $i,SV818: $i,SV1110: $i,SV449: $i] :
( ( ( ~ ( c_lessequals @ SV449 @ SV1110 @ ( tc_fun @ SV818 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV7 @ SV1110 @ ( tc_fun @ SV818 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV7 @ SV449 @ ( tc_fun @ SV818 @ tc_bool ) ) @ SV1110 @ ( tc_fun @ SV818 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3341]) ).
thf(3642,plain,
! [SV10: $i,SV821: $i,SV1111: $i,SV452: $i] :
( ( ( ~ ( c_lessequals @ SV452 @ SV1111 @ ( tc_fun @ SV821 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV10 @ SV1111 @ ( tc_fun @ SV821 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV10 @ SV452 @ ( tc_fun @ SV821 @ tc_bool ) ) @ SV1111 @ ( tc_fun @ SV821 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3342]) ).
thf(3643,plain,
! [SV1533: $i,SV11: $i,SV1363: $i,SV453: $i] :
( ( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV453 @ SV1363 @ SV11 ) @ SV1533 @ SV11 )
| ~ ( c_lessequals @ SV1363 @ SV1533 @ SV11 )
| ~ ( c_lessequals @ SV453 @ SV1533 @ SV11 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3343]) ).
thf(3644,plain,
! [SV1534: $i,SV14: $i,SV1366: $i,SV454: $i] :
( ( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV454 @ SV1366 @ SV14 ) @ SV1534 @ SV14 )
| ~ ( c_lessequals @ SV1366 @ SV1534 @ SV14 )
| ~ ( c_lessequals @ SV454 @ SV1534 @ SV14 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3346]) ).
thf(3645,plain,
! [SV1535: $i,SV15: $i,SV1367: $i,SV455: $i] :
( ( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV455 @ SV1367 @ SV15 ) @ SV1535 @ SV15 )
| ~ ( c_lessequals @ SV1367 @ SV1535 @ SV15 )
| ~ ( c_lessequals @ SV455 @ SV1535 @ SV15 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3347]) ).
thf(3646,plain,
! [SV1536: $i,SV1370: $i,SV1116: $i,SV822: $i,SV456: $i,SV18: $i] :
( ( ! [SY5038: $i,SY5039: $i,SY5040: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV18 @ SV456 @ ( c_COMBC @ SV822 @ SV1116 @ SV1116 @ tc_bool ) @ ( c_COMBC @ SV1370 @ SV1116 @ SV1116 @ tc_bool ) @ SV1536 @ SY5038 @ SY5039 @ SY5040 @ SV1116 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV456 @ SV18 @ SV822 @ SV1370 @ SY5038 @ SV1536 @ SY5040 @ SY5039 @ SV1116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3350]) ).
thf(3647,plain,
! [SV22: $i,SV1537: $i] :
( ( ( ! [SY5041: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV1537 @ SY5041 @ SV22 )
!= ( c_HOL_Ozero__class_Ozero @ SV22 ) )
| ( SV1537 = SY5041 ) ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV22 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3352]) ).
thf(3648,plain,
! [SV23: $i,SV1371: $i,SV1117: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1117 @ SV1371 @ SV23 )
!= ( c_HOL_Ozero__class_Ozero @ SV23 ) )
= $true )
| ( ( SV1117 = SV1371 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3353]) ).
thf(3649,plain,
! [SV24: $i,SV1372: $i,SV1118: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1118 @ SV1372 @ SV24 )
!= ( c_HOL_Ozero__class_Ozero @ SV24 ) )
= $true )
| ( ( SV1118 = SV1372 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3354]) ).
thf(3650,plain,
! [SV463: $i,SV1121: $i,SV827: $i,SV28: $i] :
( ( ( hBOOL @ ( c_in @ SV28 @ SV827 @ SV1121 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV28 @ SV463 @ SV1121 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV28 @ ( c_HOL_Ominus__class_Ominus @ SV463 @ SV827 @ ( tc_fun @ SV1121 @ tc_bool ) ) @ SV1121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3357]) ).
thf(3651,plain,
! [SV464: $i,SV1122: $i,SV828: $i,SV29: $i] :
( ( ( hBOOL @ ( c_in @ SV29 @ SV828 @ SV1122 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV29 @ SV464 @ SV1122 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV29 @ ( c_HOL_Ominus__class_Ominus @ SV464 @ SV828 @ ( tc_fun @ SV1122 @ tc_bool ) ) @ SV1122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3358]) ).
thf(3652,plain,
! [SV1538: $i,SV1373: $i,SV1123: $i,SV829: $i,SV465: $i,SV30: $i] :
( ( ( c_Com_Ocom_OCall @ SV30 @ SV465 @ SV829 )
!= ( c_Com_Ocom_OLocal @ SV1123 @ SV1373 @ SV1538 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3359]) ).
thf(3653,plain,
! [SV466: $i,SV830: $i,SV1374: $i,SV31: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV31 @ SV1374 @ SV830 ) @ SV466 @ ( tc_fun @ SV830 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV31 @ SV466 @ SV830 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3360]) ).
thf(3654,plain,
! [SV1539: $i,SV33: $i,SV1375: $i,SV468: $i] :
( ( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV468 @ ( c_COMBK @ SV1375 @ SV33 @ SV1539 ) @ SV1539 @ SV33 )
= SV1375 )
| ( SV468
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1539 @ tc_bool ) ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV33 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3362]) ).
thf(3655,plain,
! [SV1376: $i,SV1125: $i,SV832: $i,SV469: $i,SV34: $i] :
( ( ( c_Com_Ocom_OCall @ SV34 @ SV469 @ SV832 )
= ( c_Com_Ocom_OWhile @ SV1125 @ SV1376 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3363]) ).
thf(3656,plain,
! [SV1540: $i,SV1126: $i,SV833: $i,SV470: $i,SV35: $i] :
( ( ( ( c_Set_Oinsert @ ( hAPP @ SV35 @ SV470 ) @ ( c_Set_Oimage @ SV35 @ SV833 @ SV1126 @ SV1540 ) @ SV1540 )
= ( c_Set_Oimage @ SV35 @ SV833 @ SV1126 @ SV1540 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV470 @ SV833 @ SV1126 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3364]) ).
thf(3657,plain,
! [SV471: $i,SV1127: $i,SV834: $i,SV36: $i] :
( ( ( ~ ( c_lessequals @ SV36 @ SV834 @ ( tc_fun @ SV1127 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV471 @ SV36 @ SV1127 ) )
= $true )
| ( ( c_lessequals @ SV36 @ ( c_Set_Oinsert @ SV471 @ SV834 @ SV1127 ) @ ( tc_fun @ SV1127 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3365]) ).
thf(3658,plain,
! [SV472: $i,SV835: $i,SV37: $i,SV1377: $i] :
( ( ( hBOOL @ ( c_in @ SV1377 @ SV37 @ SV835 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV37 @ ( c_Set_Oinsert @ SV1377 @ SV472 @ SV835 ) @ ( tc_fun @ SV835 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV37 @ SV472 @ ( tc_fun @ SV835 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3366]) ).
thf(3659,plain,
! [SV473: $i,SV1128: $i,SV836: $i,SV38: $i] :
( ( ( ~ ( c_lessequals @ SV38 @ SV836 @ ( tc_fun @ SV1128 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV473 @ SV38 @ SV1128 ) )
= $true )
| ( ( c_lessequals @ SV38 @ ( c_Set_Oinsert @ SV473 @ SV836 @ SV1128 ) @ ( tc_fun @ SV1128 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3367]) ).
thf(3660,plain,
! [SV837: $i,SV474: $i,SV1378: $i,SV39: $i] :
( ( ( ~ ( c_lessequals @ SV39 @ ( c_Set_Oinsert @ SV1378 @ SV474 @ SV837 ) @ ( tc_fun @ SV837 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV1378 @ SV39 @ SV837 ) )
= $true )
| ( ( c_lessequals @ SV39 @ SV474 @ ( tc_fun @ SV837 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3368]) ).
thf(3661,plain,
! [SV840: $i,SV42: $i,SV1131: $i,SV1541: $i,SV477: $i] :
( ( ( ~ ( c_Natural_Oevalc @ SV477 @ SV1541 @ SV1131 )
| ~ ( c_Natural_Oevalc @ SV42 @ SV840 @ SV1541 ) )
= $true )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV42 @ SV477 ) @ SV840 @ SV1131 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3369]) ).
thf(3662,plain,
! [SV44: $i,SV1542: $i,SV479: $i,SV842: $i] :
( ( ( ( c_Natural_Oevalc @ SV842 @ SV479 @ SV1542 )
| ! [SY5042: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV44 @ SV842 @ SY5042 ) @ SV479 @ SV1542 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV44 @ SV479 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3371]) ).
thf(3663,plain,
! [SV1380: $i,SV1133: $i,SV843: $i,SV480: $i,SV45: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV45 @ SV480 @ SV843 ) @ SV1133 @ SV1380 )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ SV480 @ SV1133 @ SV1380 )
| ~ ( hBOOL @ ( hAPP @ SV45 @ SV1133 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3372]) ).
thf(3664,plain,
! [SV1381: $i,SV1134: $i,SV844: $i,SV481: $i,SV46: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV46 @ SV481 ) @ SV844 @ SV1134 @ SV1381 )
= $true )
| ( ( ! [SY4871: $i] :
( ~ ( c_Natural_Oevaln @ SV481 @ SY4871 @ SV1134 @ SV1381 )
| ~ ( c_Natural_Oevaln @ SV46 @ SV844 @ SV1134 @ SY4871 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3373]) ).
thf(3665,plain,
! [SV1543: $i,SV1382: $i,SV47: $i,SV482: $i] :
( ( ( ( ( c_HOL_Ominus__class_Ominus @ SV482 @ SV482 @ SV47 )
!= ( c_HOL_Ominus__class_Ominus @ SV1382 @ SV1543 @ SV47 ) )
| ( SV1382 = SV1543 ) )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3374]) ).
thf(3666,plain,
! [SV48: $i,SV1383: $i,SV483: $i] :
( ( ( ! [SY4873: $i] :
( ( c_HOL_Ominus__class_Ominus @ SV483 @ SV1383 @ SV48 )
!= ( c_HOL_Ominus__class_Ominus @ SY4873 @ SY4873 @ SV48 ) ) )
= $true )
| ( ( SV483 = SV1383 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3375]) ).
thf(3667,plain,
! [SV845: $i,SV1135: $i,SV1544: $i,SV484: $i,SV49: $i] :
( ( ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV49 @ SV484 ) @ SV1544 @ SV1135 )
| ~ ( c_Natural_Oevalc @ SV484 @ SV845 @ SV1544 )
| ~ ( hBOOL @ ( hAPP @ SV49 @ SV845 ) ) )
= $true )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV49 @ SV484 ) @ SV845 @ SV1135 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3376]) ).
thf(3668,plain,
! [SV1384: $i,SV1136: $i,SV846: $i,SV487: $i,SV52: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV52 @ SV487 ) @ SV846 @ SV1136 @ SV1384 )
= $true )
| ( ( ! [SY4874: $i] :
( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV52 @ SV487 ) @ SY4874 @ SV1136 @ SV1384 )
| ~ ( c_Natural_Oevaln @ SV487 @ SV846 @ SV1136 @ SY4874 )
| ~ ( hBOOL @ ( hAPP @ SV52 @ SV846 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3377]) ).
thf(3669,plain,
! [SV1545: $i,SV1385: $i,SV1137: $i,SV848: $i,SV489: $i,SV54: $i] :
( ( ( hAPP @ ( c_COMBS @ SV54 @ SV489 @ SV848 @ SV1137 @ SV1385 ) @ SV1545 )
= ( hAPP @ ( hAPP @ SV54 @ SV1545 ) @ ( hAPP @ SV489 @ SV1545 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3378]) ).
thf(3670,plain,
! [SV1546: $i,SV1386: $i,SV1139: $i,SV850: $i,SV492: $i,SV57: $i] :
( ( ( hAPP @ ( hAPP @ ( c_COMBC @ SV57 @ SV492 @ SV850 @ SV1139 ) @ SV1386 ) @ SV1546 )
= ( hAPP @ ( hAPP @ SV57 @ SV1546 ) @ SV1386 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3379]) ).
thf(3671,plain,
! [SV1547: $i,SV1387: $i,SV1140: $i,SV851: $i,SV493: $i,SV58: $i] :
( ( ( hAPP @ ( c_COMBB @ SV58 @ SV493 @ SV851 @ SV1140 @ SV1387 ) @ SV1547 )
= ( hAPP @ SV58 @ ( hAPP @ SV493 @ SV1547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3380]) ).
thf(3672,plain,
! [SV1144: $i,SV853: $i,SV497: $i,SV62: $i] :
( ( ( hBOOL @ ( hAPP @ SV62 @ SV497 ) )
= $false )
| ( ( ! [SY4558: $i] :
( ( c_Natural_Oevaln @ SV853 @ SV497 @ SV1144 @ SY4558 )
| ! [SY4559: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV62 @ SV853 @ SY4559 ) @ SV497 @ SV1144 @ SY4558 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3383]) ).
thf(3673,plain,
! [SV1548: $i,SV1388: $i,SV1145: $i,SV854: $i,SV498: $i,SV63: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV63 @ SV498 @ SV854 ) @ SV1145 @ SV1388 @ SV1548 )
| ~ ( c_Natural_Oevaln @ SV498 @ SV1145 @ SV1388 @ SV1548 )
| ~ ( hBOOL @ ( hAPP @ SV63 @ SV1145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3384]) ).
thf(3674,plain,
! [SV1549: $i,SV1389: $i,SV1146: $i,SV855: $i,SV499: $i,SV64: $i] :
( ( ! [SY5043: $i,SY5044: $i,SY5045: $i,SY5046: $i,SY5047: $i,SY5048: $i] :
( ( c_Com_Ocom_Ocom__case @ SV64 @ SV499 @ SV855 @ SV1146 @ SV1389 @ SV1549 @ SY5043 @ SY5044 @ ( c_Com_Ocom_OCall @ SY5045 @ SY5046 @ SY5047 ) @ SY5048 )
= ( hAPP @ ( hAPP @ ( hAPP @ SY5044 @ SY5045 ) @ SY5046 ) @ SY5047 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3385]) ).
thf(3675,plain,
! [SV1390: $i,SV1147: $i,SV856: $i,SV500: $i,SV65: $i] :
( ( ( c_Com_Ocom_OCall @ SV65 @ SV500 @ SV856 )
= ( c_Com_Ocom_OSemi @ SV1147 @ SV1390 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3386]) ).
thf(3676,plain,
! [SV502: $i,SV69: $i,SV857: $i,SV1150: $i,SV1550: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV1550 @ SV1150 @ SV857 ) ) )
= $true )
| ( ( ( c_Set_Oimage @ ( c_COMBK @ SV69 @ SV502 @ SV857 ) @ SV1150 @ SV857 @ SV502 )
= ( c_Set_Oinsert @ SV69 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV502 @ tc_bool ) ) @ SV502 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3388]) ).
thf(3677,plain,
! [SV858: $i,SV1151: $i,SV70: $i,SV1551: $i,SV503: $i] :
( ( ( ! [SY5049: $i] :
( ~ ( hBOOL @ ( c_in @ SV503 @ SV1551 @ SY5049 ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV70 @ SV1551 @ SY5049 @ SV1151 ) @ SV858 @ ( tc_fun @ SV1151 @ tc_bool ) ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ ( hAPP @ SV70 @ SV503 ) @ SV858 @ SV1151 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3389]) ).
thf(3678,plain,
! [SV1152: $i,SV859: $i,SV71: $i,SV504: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV504 @ SV71 @ SV859 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV71 @ ( c_Set_Oinsert @ SV504 @ SV1152 @ SV859 ) @ ( tc_fun @ SV859 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV71 @ ( c_Set_Oinsert @ SV504 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV859 @ tc_bool ) ) @ SV859 ) @ ( tc_fun @ SV859 @ tc_bool ) ) @ SV1152 @ ( tc_fun @ SV859 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3390]) ).
thf(3679,plain,
! [SV860: $i,SV1153: $i,SV72: $i,SV505: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV505 @ SV72 @ SV1153 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV72 @ ( c_Set_Oinsert @ SV505 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1153 @ tc_bool ) ) @ SV1153 ) @ ( tc_fun @ SV1153 @ tc_bool ) ) @ SV860 @ ( tc_fun @ SV1153 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV72 @ ( c_Set_Oinsert @ SV505 @ SV860 @ SV1153 ) @ ( tc_fun @ SV1153 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3391]) ).
thf(3680,plain,
! [SV861: $i,SV1154: $i,SV73: $i,SV506: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV506 @ SV73 @ SV1154 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV73 @ ( c_Set_Oinsert @ SV506 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1154 @ tc_bool ) ) @ SV1154 ) @ ( tc_fun @ SV1154 @ tc_bool ) ) @ SV861 @ ( tc_fun @ SV1154 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV73 @ ( c_Set_Oinsert @ SV506 @ SV861 @ SV1154 ) @ ( tc_fun @ SV1154 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3392]) ).
thf(3681,plain,
! [SV1552: $i,SV1393: $i,SV1155: $i,SV864: $i,SV509: $i,SV76: $i] :
( ( ( c_Com_Ocom_OCond @ SV76 @ SV509 @ SV864 )
!= ( c_Com_Ocom_OCall @ SV1155 @ SV1393 @ SV1552 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3394]) ).
thf(3682,plain,
! [SV77: $i,SV1553: $i,SV865: $i,SV510: $i] :
( ( ( ! [SY5050: $i] :
( ( c_lessequals @ ( hAPP @ SV510 @ SV865 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1553 @ SV510 @ SY5050 @ SV77 ) @ SV77 )
| ~ ( hBOOL @ ( c_in @ SV865 @ SV1553 @ SY5050 ) ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3395]) ).
thf(3683,plain,
! [SV1554: $i,SV1156: $i,SV866: $i,SV511: $i,SV78: $i] :
( ( ( c_lessequals @ ( hAPP @ SV78 @ SV511 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV866 @ SV78 @ SV1156 @ ( tc_fun @ SV1554 @ tc_bool ) ) @ ( tc_fun @ SV1554 @ tc_bool ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV511 @ SV866 @ SV1156 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3396]) ).
thf(3684,plain,
! [SV512: $i,SV867: $i,SV1157: $i,SV79: $i] :
( ( ( hBOOL @ ( c_in @ SV79 @ SV1157 @ SV867 ) )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ SV79 @ SV512 @ SV867 ) @ SV1157 @ ( tc_fun @ SV867 @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ SV512 @ SV1157 @ ( tc_fun @ SV867 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3397]) ).
thf(3685,plain,
! [SV1555: $i,SV1394: $i,SV1158: $i,SV868: $i,SV513: $i,SV80: $i] :
( ( ( c_Com_Ocom_OLocal @ SV80 @ SV513 @ SV868 )
!= ( c_Com_Ocom_OCond @ SV1158 @ SV1394 @ SV1555 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3398]) ).
thf(3686,plain,
! [SV1556: $i,SV1395: $i,SV1159: $i,SV869: $i,SV515: $i,SV82: $i] :
( ( ( ( c_Com_Ocom_OCall @ SV82 @ SV515 @ SV869 )
!= ( c_Com_Ocom_OCall @ SV1159 @ SV1395 @ SV1556 ) )
| ( SV869 = SV1556 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3399]) ).
thf(3687,plain,
! [SV1396: $i,SV1160: $i,SV870: $i,SV516: $i,SV83: $i] :
( ( ( ! [SY4889: $i] :
( ( c_Com_Ocom_OCall @ SV83 @ SV516 @ SV870 )
!= ( c_Com_Ocom_OCall @ SV1160 @ SV1396 @ SY4889 ) ) )
= $true )
| ( ( SV516 = SV1396 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3400]) ).
thf(3688,plain,
! [SV1557: $i,SV1161: $i,SV871: $i,SV517: $i,SV84: $i] :
( ( ( ! [SY5051: $i] :
( ( c_Com_Ocom_OCall @ SV84 @ SV517 @ SV871 )
!= ( c_Com_Ocom_OCall @ SV1161 @ SV1557 @ SY5051 ) ) )
= $true )
| ( ( SV84 = SV1161 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3401]) ).
thf(3689,plain,
! [SV1397: $i,SV1162: $i,SV872: $i,SV519: $i,SV86: $i] :
( ( ( c_Com_Ocom_OWhile @ SV86 @ SV519 )
= ( c_Com_Ocom_OLocal @ SV872 @ SV1162 @ SV1397 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3402]) ).
thf(3690,plain,
! [SV1163: $i,SV874: $i,SV522: $i,SV91: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV91 @ SV522 )
= ( c_Com_Ocom_OSemi @ SV874 @ SV1163 ) )
= $false )
| ( ( SV522 = SV1163 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3403]) ).
thf(3691,plain,
! [SV1398: $i,SV875: $i,SV523: $i,SV92: $i] :
( ( ( ( c_Com_Ocom_OSemi @ SV92 @ SV523 )
= ( c_Com_Ocom_OSemi @ SV875 @ SV1398 ) )
= $false )
| ( ( SV92 = SV875 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3404]) ).
thf(3692,plain,
! [SV1400: $i,SV1166: $i,SV877: $i,SV525: $i,SV95: $i] :
( ( ( c_Com_Ocom_OSemi @ SV95 @ SV525 )
= ( c_Com_Ocom_OCond @ SV877 @ SV1166 @ SV1400 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3407]) ).
thf(3693,plain,
! [SV1401: $i,SV1167: $i,SV878: $i,SV526: $i,SV96: $i] :
( ( ( c_Com_Ocom_OSemi @ SV96 @ SV526 )
= ( c_Com_Ocom_OLocal @ SV878 @ SV1167 @ SV1401 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3408]) ).
thf(3694,plain,
! [SV1168: $i,SV880: $i,SV528: $i,SV98: $i] :
( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV98 @ SV528 @ SV880 @ ( tc_fun @ SV1168 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1168 @ tc_bool ) ) )
= $false )
| ( ( ! [SY4590: $i] :
( ( ( hAPP @ SV528 @ SY4590 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1168 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SY4590 @ SV98 @ SV880 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3410]) ).
thf(3695,plain,
! [SV1402: $i,SV1169: $i,SV881: $i,SV529: $i,SV99: $i] :
( ( ( c_Com_Ocom_OCond @ SV99 @ SV529 @ SV881 )
= ( c_Com_Ocom_OWhile @ SV1169 @ SV1402 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3411]) ).
thf(3696,plain,
! [SV882: $i,SV1403: $i,SV530: $i,SV100: $i] :
( ( ( hBOOL @ ( c_in @ SV100 @ ( c_HOL_Ominus__class_Ominus @ SV530 @ SV1403 @ ( tc_fun @ SV882 @ tc_bool ) ) @ SV882 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV100 @ SV530 @ SV882 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3412]) ).
thf(3697,plain,
! [SV1558: $i,SV1404: $i,SV1170: $i,SV883: $i,SV531: $i,SV101: $i] :
( ( ( c_Com_Ocom_OCond @ SV101 @ SV531 @ SV883 )
!= ( c_Com_Ocom_OLocal @ SV1170 @ SV1404 @ SV1558 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3413]) ).
thf(3698,plain,
! [SV884: $i,SV532: $i,SV1559: $i,SV102: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV102 @ ( c_HOL_Ominus__class_Ominus @ SV1559 @ SV532 @ ( tc_fun @ SV884 @ tc_bool ) ) @ SV884 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV102 @ SV532 @ SV884 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3414]) ).
thf(3699,plain,
! [SV885: $i,SV1171: $i,SV103: $i,SV1560: $i,SV533: $i] :
( ( ( ! [SY5052: $i] :
( ~ ( hBOOL @ ( c_in @ SV533 @ SV1560 @ SY5052 ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1560 @ SV103 @ SY5052 @ ( tc_fun @ SV1171 @ tc_bool ) ) @ SV885 @ ( tc_fun @ SV1171 @ tc_bool ) ) ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ SV103 @ SV533 ) @ SV885 @ ( tc_fun @ SV1171 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3415]) ).
thf(3700,plain,
! [SV1405: $i,SV1173: $i,SV887: $i,SV536: $i,SV106: $i] :
( ( ( c_Com_Ocom_OCond @ SV106 @ SV536 @ SV887 )
= ( c_Com_Ocom_OSemi @ SV1173 @ SV1405 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3416]) ).
thf(3701,plain,
! [SV1561: $i,SV1174: $i,SV888: $i,SV537: $i,SV107: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV107 @ SV537 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV888 @ SV107 @ SV1174 @ ( tc_fun @ SV1561 @ tc_bool ) ) @ ( tc_fun @ SV1561 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV888 @ SV107 @ SV1174 @ ( tc_fun @ SV1561 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV537 @ SV888 @ SV1174 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3417]) ).
thf(3702,plain,
! [SV1562: $i,SV1406: $i,SV1175: $i,SV889: $i,SV538: $i,SV108: $i] :
( ( ( ( c_Com_Ocom_OCond @ SV108 @ SV538 @ SV889 )
!= ( c_Com_Ocom_OCond @ SV1175 @ SV1406 @ SV1562 ) )
| ( SV889 = SV1562 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3418]) ).
thf(3703,plain,
! [SV1407: $i,SV1176: $i,SV890: $i,SV539: $i,SV109: $i] :
( ( ( ! [SY4892: $i] :
( ( c_Com_Ocom_OCond @ SV109 @ SV539 @ SV890 )
!= ( c_Com_Ocom_OCond @ SV1176 @ SV1407 @ SY4892 ) ) )
= $true )
| ( ( SV539 = SV1407 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3419]) ).
thf(3704,plain,
! [SV1563: $i,SV1177: $i,SV891: $i,SV540: $i,SV110: $i] :
( ( ( ! [SY5053: $i] :
( ( c_Com_Ocom_OCond @ SV110 @ SV540 @ SV891 )
!= ( c_Com_Ocom_OCond @ SV1177 @ SV1563 @ SY5053 ) ) )
= $true )
| ( ( SV110 = SV1177 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3420]) ).
thf(3705,plain,
! [SV115: $i,SV1564: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1564 @ SV1564 @ SV115 )
= ( c_HOL_Ozero__class_Ozero @ SV115 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV115 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV115 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3421]) ).
thf(3706,plain,
! [SV1565: $i,SV116: $i,SV892: $i,SV541: $i] :
( ( ( ! [SY5054: $i] :
( ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV541 @ SV892 @ SV116 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1565 @ SY5054 @ SV116 ) @ ( tc_fun @ SV116 @ tc_bool ) )
| ~ ( c_lessequals @ SV892 @ SY5054 @ SV116 )
| ~ ( c_lessequals @ SV1565 @ SV541 @ SV116 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV116 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3422]) ).
thf(3707,plain,
! [SV117: $i,SV893: $i,SV542: $i] :
( ( ( c_lessequals @ SV542 @ SV893 @ SV117 )
= $true )
| ( ( ! [SY4133: $i] :
( ~ ( c_lessequals @ SY4133 @ SV542 @ SV117 )
| ! [SY4134: $i] :
~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY4133 @ SV542 @ SV117 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY4134 @ SV893 @ SV117 ) @ ( tc_fun @ SV117 @ tc_bool ) ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3423]) ).
thf(3708,plain,
! [SV118: $i,SV894: $i,SV543: $i] :
( ( ( c_lessequals @ SV543 @ SV894 @ SV118 )
= $true )
| ( ( ! [SY4135: $i] :
( ~ ( c_lessequals @ SV894 @ SY4135 @ SV118 )
| ! [SY4136: $i] :
~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV894 @ SY4135 @ SV118 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV543 @ SY4136 @ SV118 ) @ ( tc_fun @ SV118 @ tc_bool ) ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3424]) ).
thf(3709,plain,
! [SV1566: $i,SV1408: $i,SV1182: $i,SV895: $i,SV546: $i,SV121: $i] :
( ( ( c_Com_Ocom_OCall @ SV121 @ SV546 @ SV895 )
!= ( c_Com_Ocom_OCond @ SV1182 @ SV1408 @ SV1566 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3425]) ).
thf(3710,plain,
! [SV1567: $i,SV1409: $i,SV1183: $i,SV897: $i,SV548: $i,SV123: $i] :
( ( ( hAPP @ ( c_Fun_Ocomp @ SV123 @ SV548 @ SV897 @ SV1183 @ SV1409 ) @ SV1567 )
= ( hAPP @ SV123 @ ( hAPP @ SV548 @ SV1567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3427]) ).
thf(3711,plain,
! [SV1568: $i,SV1410: $i,SV1184: $i,SV898: $i,SV549: $i,SV124: $i] :
( ( ( hAPP @ SV124 @ ( hAPP @ SV549 @ SV898 ) )
= ( hAPP @ ( c_Fun_Ocomp @ SV124 @ SV549 @ SV1184 @ SV1410 @ SV1568 ) @ SV898 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3428]) ).
thf(3712,plain,
! [SV127: $i,SV899: $i,SV552: $i] :
( ( ( ! [SY4146: $i,SY4147: $i] : ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV552 @ SV899 @ SV127 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY4146 @ SY4147 @ SV127 ) @ ( tc_fun @ SV127 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV552 @ SV899 @ SV127 )
= $true )
| ( ( class_Orderings_Oorder @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3429]) ).
thf(3713,plain,
! [SV553: $i,SV1569: $i,SV128: $i,SV1185: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1185 @ SV128 @ ( tc_fun @ SV1569 @ tc_bool ) ) @ SV553 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1185 @ SV553 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV128 @ SV553 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3430]) ).
thf(3714,plain,
! [SV900: $i,SV129: $i,SV1186: $i,SV554: $i] :
( ( ( hBOOL @ ( hAPP @ SV554 @ SV1186 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV129 @ SV554 @ ( tc_fun @ SV900 @ tc_bool ) ) @ SV1186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3431]) ).
thf(3715,plain,
! [SV901: $i,SV555: $i,SV1187: $i,SV130: $i] :
( ( ( hBOOL @ ( hAPP @ SV130 @ SV1187 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV130 @ SV555 @ ( tc_fun @ SV901 @ tc_bool ) ) @ SV1187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3432]) ).
thf(3716,plain,
! [SV131: $i,SV556: $i,SV902: $i] :
( ( ( c_Com_OWT @ SV902 )
= $false )
| ( ( ~ ( c_Com_OWT @ SV556 ) )
= $true )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV131 @ SV556 @ SV902 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3433]) ).
thf(3717,plain,
! [SV1570: $i,SV1411: $i,SV1188: $i,SV903: $i,SV557: $i,SV132: $i] :
( ( ! [SY5055: $i,SY5056: $i,SY5057: $i] :
( ( c_Com_Ocom_Ocom__case @ SV132 @ SV557 @ SV903 @ SV1188 @ SV1411 @ SV1570 @ SY5055 @ SY5056 @ c_Com_Ocom_OSKIP @ SY5057 )
= SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3434]) ).
thf(3718,plain,
! [SV558: $i,SV904: $i,SV1412: $i,SV133: $i] :
( ( ( hBOOL @ ( c_in @ SV133 @ SV1412 @ SV904 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV133 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1412 @ SV558 @ ( tc_fun @ SV904 @ tc_bool ) ) @ SV904 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV133 @ SV558 @ SV904 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3435]) ).
thf(3719,plain,
! [SV1413: $i,SV1189: $i,SV905: $i,SV559: $i,SV134: $i] :
( ( ( c_Com_Ocom_OLocal @ SV134 @ SV559 @ SV905 )
= ( c_Com_Ocom_OWhile @ SV1189 @ SV1413 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3436]) ).
thf(3720,plain,
! [SV1190: $i,SV906: $i,SV560: $i,SV135: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV135 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV560 @ SV906 @ SV1190 @ ( tc_fun @ SV135 @ tc_bool ) ) )
= $false )
| ( ( ! [SY4617: $i] :
( ( ( hAPP @ SV906 @ SY4617 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV135 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SY4617 @ SV560 @ SV1190 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3437]) ).
thf(3721,plain,
! [SV1414: $i,SV1193: $i,SV909: $i,SV564: $i,SV139: $i] :
( ( ( hBOOL @ ( c_in @ SV139 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV564 @ SV909 @ SV1193 @ ( tc_fun @ SV1414 @ tc_bool ) ) @ SV1414 ) )
= $true )
| ( ( ! [SY4900: $i] :
( ~ ( hBOOL @ ( c_in @ SV139 @ ( hAPP @ SV909 @ SY4900 ) @ SV1414 ) )
| ~ ( hBOOL @ ( c_in @ SY4900 @ SV564 @ SV1193 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3438]) ).
thf(3722,plain,
! [SV1415: $i,SV1194: $i,SV910: $i,SV565: $i,SV140: $i] :
( ( ( hBOOL @ ( c_in @ SV140 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV565 @ SV910 @ SV1194 @ ( tc_fun @ SV1415 @ tc_bool ) ) @ SV1415 ) )
= $true )
| ( ( ! [SY4901: $i] :
( ~ ( hBOOL @ ( c_in @ SV140 @ ( hAPP @ SV910 @ SY4901 ) @ SV1415 ) )
| ~ ( hBOOL @ ( c_in @ SY4901 @ SV565 @ SV1194 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3439]) ).
thf(3723,plain,
! [SV1571: $i,SV1417: $i,SV1197: $i,SV915: $i,SV570: $i,SV146: $i] :
( ( ! [SY5058: $i,SY5059: $i,SY5060: $i,SY5061: $i,SY5062: $i] :
( ( c_Com_Ocom_Ocom__case @ SV146 @ SV570 @ SV915 @ SV1197 @ SV1417 @ SV1571 @ SY5058 @ SY5059 @ ( c_Com_Ocom_OSemi @ SY5060 @ SY5061 ) @ SY5062 )
= ( hAPP @ ( hAPP @ SV1197 @ SY5060 ) @ SY5061 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3441]) ).
thf(3724,plain,
! [SV1418: $i,SV1198: $i,SV916: $i,SV571: $i,SV147: $i] :
( ( ( c_Com_Ocom_OLocal @ SV147 @ SV571 @ SV916 )
= ( c_Com_Ocom_OSemi @ SV1198 @ SV1418 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3442]) ).
thf(3725,plain,
! [SV1572: $i,SV1419: $i,SV1199: $i,SV918: $i,SV573: $i,SV149: $i] :
( ( ! [SY5063: $i,SY5064: $i,SY5065: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV149 @ ( hAPP @ SV573 @ SV918 ) ) @ SV1199 ) )
| ~ ( hBOOL @ ( c_in @ SV1199 @ SV918 @ SV1419 ) )
| ! [SY5066: $i,SY5067: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV573 @ SV1572 @ SV149 @ SY5063 @ SY5064 @ SY5065 @ SY5066 @ SY5067 @ SV1419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3443]) ).
thf(3726,plain,
! [SV1573: $i,SV1420: $i,SV1200: $i,SV919: $i,SV574: $i,SV150: $i] :
( ( ! [SY5068: $i,SY5069: $i,SY5070: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV150 @ SV574 ) @ ( hAPP @ SV919 @ SV1200 ) ) )
| ~ ( hBOOL @ ( c_in @ SV574 @ SV1200 @ SV1420 ) )
| ! [SY5071: $i,SY5072: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1573 @ SV919 @ SV150 @ SY5068 @ SY5069 @ SY5070 @ SY5071 @ SY5072 @ SV1420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3444]) ).
thf(3727,plain,
! [SV1423: $i,SV921: $i,SV576: $i,SV154: $i] :
( ( ( ( c_Com_Ocom_OWhile @ SV154 @ SV576 )
= ( c_Com_Ocom_OWhile @ SV921 @ SV1423 ) )
= $false )
| ( ( SV154 = SV921 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3447]) ).
thf(3728,plain,
! [SV1203: $i,SV922: $i,SV577: $i,SV155: $i] :
( ( ( ( c_Com_Ocom_OWhile @ SV155 @ SV577 )
= ( c_Com_Ocom_OWhile @ SV922 @ SV1203 ) )
= $false )
| ( ( SV577 = SV1203 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3448]) ).
thf(3729,plain,
! [SV1426: $i,SV1207: $i,SV928: $i,SV582: $i,SV164: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV164 @ SV582 @ SV928 @ ( tc_fun @ SV1207 @ tc_bool ) ) @ SV1426 ) )
= $true )
| ( ( ! [SY4920: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV582 @ SY4920 ) @ SV1426 ) )
| ~ ( hBOOL @ ( c_in @ SY4920 @ SV164 @ SV928 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3453]) ).
thf(3730,plain,
! [SV1427: $i,SV1208: $i,SV929: $i,SV583: $i,SV165: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV165 @ SV583 @ SV929 @ ( tc_fun @ SV1208 @ tc_bool ) ) @ SV1427 ) )
= $true )
| ( ( ! [SY4921: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV583 @ SY4921 ) @ SV1427 ) )
| ~ ( hBOOL @ ( c_in @ SY4921 @ SV165 @ SV929 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3454]) ).
thf(3731,plain,
! [SV1428: $i,SV1209: $i,SV930: $i,SV584: $i,SV166: $i] :
( ( ( c_Com_Ocom_OWhile @ SV166 @ SV584 )
= ( c_Com_Ocom_OCond @ SV930 @ SV1209 @ SV1428 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3455]) ).
thf(3732,plain,
! [SV1429: $i,SV1210: $i,SV931: $i,SV585: $i,SV167: $i] :
( ( ( c_Com_Ocom_OSemi @ SV167 @ SV585 )
= ( c_Com_Ocom_OCall @ SV931 @ SV1210 @ SV1429 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3456]) ).
thf(3733,plain,
! [SV1211: $i,SV168: $i,SV932: $i,SV586: $i] :
( ( ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ SV586 ) @ SV932 @ SV168 @ SV1211 )
= $false )
| ( ( SV168
= ( c_Suc @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ SV586 @ SV168 @ SV932 @ SV1211 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3457]) ).
thf(3734,plain,
! [SV934: $i,SV589: $i,SV171: $i,SV1574: $i] :
( ( ( ! [SY5073: $i] : ( hBOOL @ ( c_in @ ( hAPP @ SV1574 @ SV171 ) @ ( c_Set_Oimage @ SV1574 @ SV589 @ SV934 @ SY5073 ) @ SY5073 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV171 @ SV589 @ SV934 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3460]) ).
thf(3735,plain,
! [SV935: $i,SV590: $i,SV172: $i,SV1575: $i] :
( ( ( ! [SY5074: $i] : ( hBOOL @ ( c_in @ ( hAPP @ SV1575 @ SV172 ) @ ( c_Set_Oimage @ SV1575 @ SV590 @ SV935 @ SY5074 ) @ SY5074 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV172 @ SV590 @ SV935 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3461]) ).
thf(3736,plain,
! [SV1576: $i,SV1214: $i,SV936: $i,SV591: $i,SV173: $i] :
( ( ( hBOOL @ ( c_in @ ( hAPP @ SV173 @ SV591 ) @ ( c_Set_Oimage @ SV173 @ SV936 @ SV1214 @ SV1576 ) @ SV1576 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV591 @ SV936 @ SV1214 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3462]) ).
thf(3737,plain,
! [SV1577: $i,SV1215: $i,SV937: $i,SV592: $i,SV174: $i] :
( ( ( hBOOL @ ( c_in @ ( hAPP @ SV174 @ SV592 ) @ ( c_Set_Oimage @ SV174 @ SV937 @ SV1215 @ SV1577 ) @ SV1577 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV592 @ SV937 @ SV1215 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3463]) ).
thf(3738,plain,
! [SV938: $i,SV1216: $i,SV593: $i,SV175: $i] :
( ( ( c_lessequals @ SV175 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV593 @ SV1216 @ ( tc_fun @ SV938 @ tc_bool ) ) @ ( tc_fun @ SV938 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV175 @ SV593 @ ( tc_fun @ SV938 @ tc_bool ) ) @ SV1216 @ ( tc_fun @ SV938 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3464]) ).
thf(3739,plain,
! [SV939: $i,SV1217: $i,SV594: $i,SV176: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV176 @ SV594 @ ( tc_fun @ SV1217 @ tc_bool ) ) @ SV939 @ ( tc_fun @ SV1217 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV176 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV594 @ SV939 @ ( tc_fun @ SV1217 @ tc_bool ) ) @ ( tc_fun @ SV1217 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3465]) ).
thf(3740,plain,
! [SV940: $i,SV1430: $i,SV596: $i,SV178: $i] :
( ( ( c_Natural_Oevaln @ SV178 @ SV596 @ SV1430 @ SV940 )
= $false )
| ( ( c_Natural_Oevalc @ SV178 @ SV596 @ SV940 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3466]) ).
thf(3741,plain,
! [SV941: $i,SV1431: $i,SV597: $i,SV179: $i] :
( ( ( c_Natural_Oevaln @ SV179 @ SV597 @ SV1431 @ SV941 )
= $false )
| ( ( c_Natural_Oevalc @ SV179 @ SV597 @ SV941 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3467]) ).
thf(3742,plain,
! [SV180: $i,SV1578: $i,SV942: $i,SV598: $i] :
( ( ( ( c_lessequals @ ( hAPP @ SV598 @ SV942 ) @ ( hAPP @ SV1578 @ SV942 ) @ SV180 )
| ! [SY5075: $i] :
~ ( c_lessequals @ SV598 @ SV1578 @ ( tc_fun @ SY5075 @ SV180 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV180 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3468]) ).
thf(3743,plain,
! [SV184: $i,SV1579: $i,SV1221: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1221 @ SV1579 @ SV184 )
!= ( c_Orderings_Obot__class_Obot @ SV184 ) )
= $true )
| ( ( SV1221
= ( c_Orderings_Obot__class_Obot @ SV184 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV184 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3469]) ).
thf(3744,plain,
! [SV185: $i,SV1432: $i,SV1222: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1222 @ SV1432 @ SV185 )
!= ( c_Orderings_Obot__class_Obot @ SV185 ) )
= $true )
| ( ( SV1432
= ( c_Orderings_Obot__class_Obot @ SV185 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3470]) ).
thf(3745,plain,
! [SV1433: $i,SV943: $i,SV599: $i,SV187: $i] :
( ( ( ( c_Set_Oimage @ SV187 @ SV599 @ SV943 @ SV1433 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1433 @ tc_bool ) ) )
= $false )
| ( ( SV599
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV943 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3471]) ).
thf(3746,plain,
! [SV1580: $i,SV1434: $i,SV1223: $i,SV944: $i,SV600: $i,SV188: $i] :
( ( ! [SY5076: $i] :
( ( ( hAPP @ SV188 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_bool ) ) )
= SV944 )
| ! [SY5077: $i,SY5078: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV188 @ SV1223 @ SV1434 @ SV1580 @ SY5076 @ SY5077 @ SY5078 @ SV944 @ SV600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3472]) ).
thf(3747,plain,
! [SV1581: $i,SV1435: $i,SV1224: $i,SV945: $i,SV601: $i,SV189: $i] :
( ( ! [SY5079: $i] :
( ( ( hAPP @ SV189 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV601 @ tc_bool ) ) )
= SV945 )
| ! [SY5080: $i,SY5081: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1224 @ SV189 @ SV1435 @ SV1581 @ SY5079 @ SY5080 @ SV945 @ SY5081 @ SV601 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3473]) ).
thf(3748,plain,
! [SV190: $i,SV1436: $i,SV602: $i] :
( ( ( hBOOL @ ( hAPP @ SV602 @ SV1436 ) )
= $false )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV190 @ tc_bool ) )
= ( c_Collect @ SV602 @ SV190 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3474]) ).
thf(3749,plain,
! [SV946: $i,SV1437: $i,SV197: $i] :
( ( ( hBOOL @ ( hAPP @ SV197 @ SV1437 ) )
= $false )
| ( ( ( c_Collect @ SV197 @ SV946 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV946 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3476]) ).
thf(3750,plain,
! [SV1226: $i,SV948: $i,SV615: $i,SV205: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV205 @ tc_bool ) )
= ( c_Set_Oimage @ SV615 @ SV948 @ SV1226 @ SV205 ) )
= $false )
| ( ( SV948
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1226 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3477]) ).
thf(3751,plain,
! [SV207: $i,SV1438: $i,SV617: $i] :
( ( ( hBOOL @ ( c_in @ SV617 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1438 @ tc_bool ) ) @ SV1438 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV207 @ SV617 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3478]) ).
thf(3752,plain,
! [SV624: $i,SV1229: $i,SV955: $i,SV215: $i] :
( ( ( ~ ( c_lessequals @ SV215 @ SV955 @ ( tc_fun @ SV1229 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV215 @ ( c_Set_Oinsert @ SV624 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1229 @ tc_bool ) ) @ SV1229 ) @ ( tc_fun @ SV1229 @ tc_bool ) ) @ SV955 @ ( tc_fun @ SV1229 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV215 @ ( c_Set_Oinsert @ SV624 @ SV955 @ SV1229 ) @ ( tc_fun @ SV1229 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3484]) ).
thf(3753,plain,
! [SV217: $i,SV957: $i,SV1230: $i,SV626: $i] :
( ( ( c_lessequals @ SV626 @ SV1230 @ ( tc_fun @ SV957 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Set_Oinsert @ SV217 @ SV626 @ SV957 ) @ ( c_Set_Oinsert @ SV217 @ SV1230 @ SV957 ) @ ( tc_fun @ SV957 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3485]) ).
thf(3754,plain,
! [SV627: $i,SV1231: $i,SV958: $i,SV218: $i] :
( ( ( hBOOL @ ( c_in @ SV218 @ SV958 @ SV1231 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV218 @ ( c_Set_Oinsert @ SV627 @ SV958 @ SV1231 ) @ SV1231 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3486]) ).
thf(3755,plain,
! [SV628: $i,SV1232: $i,SV959: $i,SV219: $i] :
( ( ( hBOOL @ ( c_in @ SV219 @ SV959 @ SV1232 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV219 @ ( c_Set_Oinsert @ SV628 @ SV959 @ SV1232 ) @ SV1232 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3487]) ).
thf(3756,plain,
! [SV1582: $i,SV1441: $i,SV1234: $i,SV961: $i,SV630: $i,SV221: $i] :
( ( ! [SY5082: $i,SY5083: $i,SY5084: $i] :
( ( ( hAPP @ SV221 @ ( c_Set_Oinsert @ SV630 @ SV961 @ SV1234 ) )
= ( hAPP @ ( hAPP @ SV1441 @ SV630 ) @ ( hAPP @ SV221 @ SV961 ) ) )
| ! [SY5085: $i,SY5086: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV221 @ SV1582 @ SY5082 @ SY5083 @ SV1441 @ SY5084 @ SY5085 @ SY5086 @ SV1234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3489]) ).
thf(3757,plain,
! [SV1583: $i,SV1442: $i,SV1235: $i,SV962: $i,SV631: $i,SV222: $i] :
( ( ! [SY5087: $i,SY5088: $i,SY5089: $i] :
( ( ( hAPP @ SV222 @ ( c_Set_Oinsert @ SV631 @ SV962 @ SV1235 ) )
= ( hAPP @ ( hAPP @ SV1442 @ SV631 ) @ ( hAPP @ SV222 @ SV962 ) ) )
| ! [SY5090: $i,SY5091: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1583 @ SV222 @ SY5087 @ SY5088 @ SY5089 @ SV1442 @ SY5090 @ SY5091 @ SV1235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3490]) ).
thf(3758,plain,
! [SV963: $i,SV632: $i,SV1443: $i,SV223: $i] :
( ( ( SV223 = SV1443 )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV223 @ ( c_Set_Oinsert @ SV1443 @ SV632 @ SV963 ) @ SV963 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV223 @ SV632 @ SV963 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3491]) ).
thf(3759,plain,
! [SV636: $i,SV1238: $i,SV967: $i,SV227: $i] :
( ( ( c_lessequals @ SV227 @ SV967 @ ( tc_fun @ SV1238 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV227 @ ( c_Set_Oinsert @ SV636 @ SV967 @ SV1238 ) @ ( tc_fun @ SV1238 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3492]) ).
thf(3760,plain,
! [SV637: $i,SV968: $i,SV228: $i,SV1444: $i] :
( ( ( c_lessequals @ ( c_Set_Oinsert @ SV1444 @ SV228 @ SV968 ) @ SV637 @ ( tc_fun @ SV968 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV228 @ SV637 @ ( tc_fun @ SV968 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3493]) ).
thf(3761,plain,
! [SV1239: $i,SV972: $i,SV641: $i,SV232: $i] :
( ( ( ( c_Set_Oinsert @ SV232 @ SV641 @ SV972 )
= ( c_Set_Oinsert @ SV232 @ SV1239 @ SV972 ) )
= $false )
| ( ( ( hBOOL @ ( c_in @ SV232 @ SV1239 @ SV972 ) )
| ( SV641 = SV1239 )
| ( hBOOL @ ( c_in @ SV232 @ SV641 @ SV972 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3494]) ).
thf(3762,plain,
! [SV1445: $i,SV1240: $i,SV974: $i,SV643: $i,SV234: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV234 @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV643 ) @ SV974 @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ SV1240 @ tc_Com_Opname @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SV1445 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SV643 )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV234 @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV643 ) @ SV974 @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ SV1240 @ tc_Com_Opname @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SV1445 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV643 ) @ SV974 @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ SV1240 @ tc_Com_Opname @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SV1445 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SV643 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3496]) ).
thf(3763,plain,
! [SV1243: $i,SV979: $i,SV648: $i,SV240: $i] :
( ( ( c_Natural_Oevaln @ SV240 @ SV648 @ SV979 @ SV1243 )
= $false )
| ( ( c_Natural_Oevaln @ SV240 @ SV648 @ ( c_Suc @ SV979 ) @ SV1243 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3499]) ).
thf(3764,plain,
! [SV1446: $i,SV1244: $i,SV980: $i,SV649: $i,SV241: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV241 @ SV649 @ ( tc_fun @ SV980 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1244 @ SV1446 @ ( tc_fun @ SV980 @ tc_bool ) ) @ ( tc_fun @ SV980 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1446 @ SV649 @ ( tc_fun @ SV980 @ tc_bool ) )
| ~ ( c_lessequals @ SV241 @ SV1244 @ ( tc_fun @ SV980 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3500]) ).
thf(3765,plain,
! [SV1245: $i,SV981: $i,SV242: $i,SV650: $i,SV1584: $i] :
( ( ( ( hBOOL @ ( hAPP @ SV1584 @ SV650 ) )
| ! [SY5092: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV1584 @ SY5092 @ SV242 ) @ SV650 @ SV981 @ SV1245 ) )
= $true )
| ( ( c_Natural_Oevaln @ SV242 @ SV650 @ SV981 @ SV1245 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3501]) ).
thf(3766,plain,
! [SV1585: $i,SV1447: $i,SV1246: $i,SV982: $i,SV651: $i,SV243: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV243 @ SV651 @ SV982 ) @ SV1246 @ SV1447 @ SV1585 )
| ~ ( c_Natural_Oevaln @ SV982 @ SV1246 @ SV1447 @ SV1585 )
| ( hBOOL @ ( hAPP @ SV243 @ SV1246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3502]) ).
thf(3767,plain,
! [SV1448: $i,SV1247: $i,SV983: $i,SV652: $i,SV244: $i] :
( ( ( c_Com_Ocom_OWhile @ SV244 @ SV652 )
= ( c_Com_Ocom_OCall @ SV983 @ SV1247 @ SV1448 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3503]) ).
thf(3768,plain,
! [SV1248: $i,SV246: $i,SV653: $i] :
( ( ( c_lessequals @ SV653 @ SV246 @ ( tc_fun @ SV1248 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV246 @ SV653 @ ( tc_fun @ SV1248 @ tc_bool ) ) )
= $true )
| ( ( SV246 = SV653 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3504]) ).
thf(3769,plain,
! [SV654: $i,SV247: $i,SV1449: $i,SV1249: $i] :
( ( ( ~ ( c_Natural_Oevalc @ SV1249 @ SV1449 @ SV247 ) )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ SV1249 @ SV1449 @ SV654 ) )
= $true )
| ( ( SV247 = SV654 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3505]) ).
thf(3770,plain,
! [SV1250: $i,SV248: $i,SV655: $i] :
( ( ( c_lessequals @ SV655 @ SV248 @ ( tc_fun @ SV1250 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV248 @ SV655 @ ( tc_fun @ SV1250 @ tc_bool ) ) )
= $true )
| ( ( SV248 = SV655 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3506]) ).
thf(3771,plain,
! [SV249: $i,SV1450: $i,SV1251: $i] :
( ( ( SV1251 = SV1450 )
= $true )
| ( ( ~ ( c_lessequals @ SV1450 @ SV1251 @ SV249 )
| ~ ( c_lessequals @ SV1251 @ SV1450 @ SV249 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV249 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3507]) ).
thf(3772,plain,
! [SV250: $i,SV1451: $i,SV1252: $i] :
( ( ( SV1252 = SV1451 )
= $true )
| ( ( ~ ( c_lessequals @ SV1451 @ SV1252 @ SV250 )
| ~ ( c_lessequals @ SV1252 @ SV1451 @ SV250 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV250 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3508]) ).
thf(3773,plain,
! [SV251: $i,SV1452: $i,SV1253: $i] :
( ( ( SV1253 = SV1452 )
= $true )
| ( ( ~ ( c_lessequals @ SV1253 @ SV1452 @ SV251 )
| ~ ( c_lessequals @ SV1452 @ SV1253 @ SV251 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV251 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3509]) ).
thf(3774,plain,
! [SV252: $i,SV1453: $i,SV1254: $i] :
( ( ( c_lessequals @ SV1254 @ SV1453 @ SV252 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1254 @ SV1453 @ SV252 ) @ ( c_HOL_Ozero__class_Ozero @ SV252 ) @ SV252 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3510]) ).
thf(3775,plain,
! [SV253: $i,SV1454: $i,SV1255: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1255 @ SV1454 @ SV253 ) @ ( c_HOL_Ozero__class_Ozero @ SV253 ) @ SV253 )
= $true )
| ( ( ~ ( c_lessequals @ SV1255 @ SV1454 @ SV253 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV253 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3511]) ).
thf(3776,plain,
! [SV255: $i,SV1455: $i,SV1256: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1256 @ SV1455 @ SV255 )
= SV1256 )
= $true )
| ( ( ~ ( c_lessequals @ SV1455 @ SV1256 @ SV255 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV255 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3512]) ).
thf(3777,plain,
! [SV256: $i,SV1456: $i,SV1257: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1257 @ SV1456 @ SV256 )
!= SV1456 )
= $true )
| ( ( c_lessequals @ SV1257 @ SV1456 @ SV256 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV256 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3513]) ).
thf(3778,plain,
! [SV257: $i,SV1457: $i,SV1258: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1258 @ SV1457 @ SV257 )
= SV1457 )
= $true )
| ( ( ~ ( c_lessequals @ SV1258 @ SV1457 @ SV257 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV257 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3514]) ).
thf(3779,plain,
! [SV1458: $i,SV1259: $i,SV988: $i,SV661: $i,SV264: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV264 @ SV661 ) @ SV988 ) )
= $true )
| ( ( ! [SY4943: $i] :
( ~ ( c_Natural_Oevaln @ SV1259 @ SV1458 @ SY4943 @ SV988 )
| ! [SY4944: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY4944 @ SV661 ) @ SV1458 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ SY4943 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY4944 ) @ SV1259 ) @ SV264 ) @ t_a ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3518]) ).
thf(3780,plain,
! [SV989: $i,SV265: $i,SV662: $i,SV1459: $i] :
( ( ( hBOOL @ ( hAPP @ SV1459 @ SV662 ) )
= $true )
| ( ( ! [SY4945: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV1459 @ SY4945 @ SV265 ) @ SV662 @ SV989 ) )
= $true )
| ( ( c_Natural_Oevalc @ SV265 @ SV662 @ SV989 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3519]) ).
thf(3781,plain,
! [SV1460: $i,SV1260: $i,SV990: $i,SV663: $i,SV266: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV266 @ SV663 @ SV990 ) @ SV1260 @ SV1460 )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ SV990 @ SV1260 @ SV1460 )
| ( hBOOL @ ( hAPP @ SV266 @ SV1260 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3520]) ).
thf(3782,plain,
! [SV1462: $i,SV270: $i,SV1262: $i] :
( ( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ SV1262 @ SV270 ) @ SV1462 @ SV270 )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1462 @ SV1262 @ SV270 ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV270 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3522]) ).
thf(3783,plain,
! [SV1463: $i,SV1263: $i,SV271: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV271 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1263 @ SV1463 @ SV271 ) )
= $true )
| ( ( c_lessequals @ SV1263 @ SV1463 @ SV271 )
= $true )
| ( ( class_Orderings_Oorder @ SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3523]) ).
thf(3784,plain,
! [SV1464: $i,SV1264: $i,SV272: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV272 @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1264 @ SV1464 @ SV272 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1264 @ SV1464 @ SV272 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3524]) ).
thf(3785,plain,
! [SV1586: $i,SV1465: $i,SV1265: $i,SV994: $i,SV665: $i,SV273: $i] :
( ( ! [SY5093: $i,SY5094: $i,SY5095: $i,SY5096: $i,SY5097: $i,SY5098: $i] :
( ( c_Com_Ocom_Ocom__case @ SV273 @ SV665 @ SV994 @ SV1265 @ SV1465 @ SV1586 @ SY5093 @ SY5094 @ ( c_Com_Ocom_OLocal @ SY5095 @ SY5096 @ SY5097 ) @ SY5098 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV994 @ SY5095 ) @ SY5096 ) @ SY5097 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3525]) ).
thf(3786,plain,
! [SV1587: $i,SV1466: $i,SV1266: $i,SV995: $i,SV666: $i,SV274: $i] :
( ( ! [SY5099: $i,SY5100: $i,SY5101: $i,SY5102: $i,SY5103: $i] :
( ( c_Com_Ocom_Ocom__case @ SV274 @ SV666 @ SV995 @ SV1266 @ SV1466 @ SV1587 @ SY5099 @ SY5100 @ ( c_Com_Ocom_OWhile @ SY5101 @ SY5102 ) @ SY5103 )
= ( hAPP @ ( hAPP @ SV1587 @ SY5101 ) @ SY5102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3526]) ).
thf(3787,plain,
! [SV1467: $i,SV1267: $i,SV996: $i,SV667: $i,SV275: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV275 @ SV667 @ ( tc_fun @ SV996 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1267 @ SV1467 @ ( tc_fun @ SV996 @ tc_bool ) ) @ ( tc_fun @ SV996 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV667 @ SV1467 @ ( tc_fun @ SV996 @ tc_bool ) )
| ~ ( c_lessequals @ SV275 @ SV1267 @ ( tc_fun @ SV996 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3527]) ).
thf(3788,plain,
! [SV1588: $i,SV1468: $i,SV1268: $i,SV997: $i,SV668: $i,SV276: $i] :
( ( ! [SY5104: $i] :
( ( c_Fun_Ocomp @ SV276 @ ( c_Fun_Ocomp @ SV668 @ SV997 @ SV1268 @ SV1468 @ SV1588 ) @ SV1468 @ SY5104 @ SV1588 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV276 @ SV668 @ SV1468 @ SY5104 @ SV1268 ) @ SV997 @ SV1268 @ SY5104 @ SV1588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3528]) ).
thf(3789,plain,
! [SV279: $i,SV999: $i,SV1270: $i,SV671: $i] :
( ( ( ~ ( c_lessequals @ SV671 @ SV1270 @ ( tc_fun @ SV999 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV279 @ SV1270 @ SV999 ) ) )
= $true )
| ( ( c_lessequals @ ( c_Set_Oinsert @ SV279 @ SV671 @ SV999 ) @ SV1270 @ ( tc_fun @ SV999 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3529]) ).
thf(3790,plain,
! [SV1589: $i,SV1469: $i,SV1271: $i,SV1000: $i,SV672: $i,SV280: $i] :
( ( ( c_Set_Oimage @ SV280 @ ( c_Set_Oimage @ SV672 @ SV1000 @ SV1271 @ SV1469 ) @ SV1469 @ SV1589 )
= ( c_Set_Oimage @ ( c_COMBB @ SV280 @ SV672 @ SV1469 @ SV1589 @ SV1271 ) @ SV1000 @ SV1271 @ SV1589 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3530]) ).
thf(3791,plain,
! [SV1590: $i,SV1470: $i,SV1272: $i,SV1001: $i,SV673: $i,SV281: $i] :
( ( ( ( c_Com_Ocom_OLocal @ SV281 @ SV673 @ SV1001 )
!= ( c_Com_Ocom_OLocal @ SV1272 @ SV1470 @ SV1590 ) )
| ( SV1001 = SV1590 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3531]) ).
thf(3792,plain,
! [SV1471: $i,SV1273: $i,SV1002: $i,SV674: $i,SV282: $i] :
( ( ( ! [SY4963: $i] :
( ( c_Com_Ocom_OLocal @ SV282 @ SV674 @ SV1002 )
!= ( c_Com_Ocom_OLocal @ SV1273 @ SV1471 @ SY4963 ) ) )
= $true )
| ( ( SV674 = SV1471 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3532]) ).
thf(3793,plain,
! [SV1591: $i,SV1274: $i,SV1003: $i,SV675: $i,SV283: $i] :
( ( ( ! [SY5105: $i] :
( ( c_Com_Ocom_OLocal @ SV283 @ SV675 @ SV1003 )
!= ( c_Com_Ocom_OLocal @ SV1274 @ SV1591 @ SY5105 ) ) )
= $true )
| ( ( SV283 = SV1274 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3533]) ).
thf(3794,plain,
! [SV676: $i,SV284: $i] :
( ( ( c_Com_OWT @ SV284 )
= $false )
| ( ( c_Com_OWT @ SV676 )
= $false )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OSemi @ SV284 @ SV676 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3534]) ).
thf(3795,plain,
! [SV1592: $i,SV1472: $i,SV1275: $i,SV1005: $i,SV678: $i,SV286: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ocomp @ SV286 @ SV678 @ SV1005 @ SV1275 @ SV1472 ) @ SV1592 @ SV1472 @ SV1275 )
= ( c_Set_Oimage @ SV286 @ ( c_Set_Oimage @ SV678 @ SV1592 @ SV1472 @ SV1005 ) @ SV1005 @ SV1275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3535]) ).
thf(3796,plain,
! [SV680: $i,SV1277: $i,SV1007: $i,SV288: $i] :
( ( ( hBOOL @ ( c_in @ SV288 @ SV1007 @ SV1277 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV288 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV680 @ SV1007 @ ( tc_fun @ SV1277 @ tc_bool ) ) @ SV1277 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3537]) ).
thf(3797,plain,
! [SV1008: $i,SV1278: $i,SV681: $i,SV289: $i] :
( ( ( hBOOL @ ( c_in @ SV289 @ SV681 @ SV1278 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV289 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV681 @ SV1008 @ ( tc_fun @ SV1278 @ tc_bool ) ) @ SV1278 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3538]) ).
thf(3798,plain,
! [SV1279: $i,SV683: $i,SV1593: $i,SV291: $i] :
( ( ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV291 @ SV1593 ) @ SV683 @ SV1279 ) )
= $true )
| ( ( SV1279 = SV683 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV291 @ SV683 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3539]) ).
thf(3799,plain,
! [SV294: $i,SV1473: $i,SV684: $i] :
( ( ( c_lessequals @ SV684 @ SV1473 @ SV294 )
= $true )
| ( ( ! [SY4965: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4965 @ SV684 @ SV294 ) @ SV1473 @ SV294 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV294 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3540]) ).
thf(3800,plain,
! [SV295: $i,SV1474: $i,SV685: $i] :
( ( ( c_lessequals @ SV685 @ SV1474 @ SV295 )
= $true )
| ( ( ! [SY4966: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV685 @ SY4966 @ SV295 ) @ SV1474 @ SV295 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV295 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3541]) ).
thf(3801,plain,
! [SV296: $i,SV1594: $i,SV1475: $i,SV686: $i] :
( ( ( ( c_lessequals @ SV686 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1475 @ SV1594 @ SV296 ) @ SV296 )
| ~ ( c_lessequals @ SV686 @ SV1594 @ SV296 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV296 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3542]) ).
thf(3802,plain,
! [SV297: $i,SV1476: $i,SV687: $i] :
( ( ( ! [SY4968: $i] : ( c_lessequals @ SV687 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1476 @ SY4968 @ SV297 ) @ SV297 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV687 @ SV1476 @ SV297 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV297 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3543]) ).
thf(3803,plain,
! [SV298: $i,SV1477: $i,SV688: $i] :
( ( ( c_lessequals @ SV688 @ SV1477 @ SV298 )
= $true )
| ( ( ! [SY4969: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SY4969 @ SV688 @ SV298 ) @ SV1477 @ SV298 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV298 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3544]) ).
thf(3804,plain,
! [SV299: $i,SV1478: $i,SV689: $i] :
( ( ( c_lessequals @ SV689 @ SV1478 @ SV299 )
= $true )
| ( ( ! [SY4970: $i] :
~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV689 @ SY4970 @ SV299 ) @ SV1478 @ SV299 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV299 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3545]) ).
thf(3805,plain,
! [SV690: $i,SV1010: $i,SV1479: $i,SV300: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV300 @ SV1479 @ ( tc_fun @ SV1010 @ tc_bool ) ) @ SV690 @ ( tc_fun @ SV1010 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV300 @ SV690 @ ( tc_fun @ SV1010 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3546]) ).
thf(3806,plain,
! [SV691: $i,SV1011: $i,SV301: $i,SV1480: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1480 @ SV301 @ ( tc_fun @ SV1011 @ tc_bool ) ) @ SV691 @ ( tc_fun @ SV1011 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV301 @ SV691 @ ( tc_fun @ SV1011 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3547]) ).
thf(3807,plain,
! [SV302: $i,SV1481: $i,SV692: $i] :
( ( ( c_lessequals @ SV692 @ SV1481 @ SV302 )
= $true )
| ( ( ! [SY4971: $i] :
( ~ ( c_lessequals @ SV692 @ SY4971 @ SV302 )
| ~ ( c_lessequals @ SY4971 @ SV1481 @ SV302 ) ) )
= $true )
| ( ( class_Orderings_Oorder @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3548]) ).
thf(3808,plain,
! [SV303: $i,SV1482: $i,SV693: $i] :
( ( ( c_lessequals @ SV693 @ SV1482 @ SV303 )
= $true )
| ( ( ! [SY4972: $i] :
( ~ ( c_lessequals @ SY4972 @ SV1482 @ SV303 )
| ~ ( c_lessequals @ SV693 @ SY4972 @ SV303 ) ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV303 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3549]) ).
thf(3809,plain,
! [SV694: $i,SV1012: $i,SV1483: $i,SV304: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV304 @ SV1483 @ SV1012 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1483 @ SV694 @ ( tc_fun @ SV1012 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV304 @ SV694 @ SV1012 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3550]) ).
thf(3810,plain,
! [SV695: $i,SV1013: $i,SV1484: $i,SV305: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV305 @ SV1484 @ SV1013 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1484 @ SV695 @ ( tc_fun @ SV1013 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV305 @ SV695 @ SV1013 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3551]) ).
thf(3811,plain,
! [SV307: $i,SV1014: $i,SV697: $i,SV1485: $i] :
( ( ( ~ ( c_lessequals @ SV1485 @ SV697 @ ( tc_fun @ SV1014 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV307 @ SV1485 @ SV1014 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV307 @ SV697 @ SV1014 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3552]) ).
thf(3812,plain,
! [SV698: $i,SV1015: $i,SV1486: $i,SV308: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV308 @ SV1486 @ SV1015 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1486 @ SV698 @ ( tc_fun @ SV1015 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV308 @ SV698 @ SV1015 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3553]) ).
thf(3813,plain,
! [SV310: $i,SV1016: $i,SV700: $i,SV1487: $i] :
( ( ( ~ ( c_lessequals @ SV1487 @ SV700 @ ( tc_fun @ SV1016 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV310 @ SV1487 @ ( tc_fun @ SV1016 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV310 @ SV700 @ ( tc_fun @ SV1016 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3554]) ).
thf(3814,plain,
! [SV311: $i,SV701: $i,SV1280: $i] :
( ( ( hBOOL @ ( hAPP @ SV1280 @ SV701 ) )
= $false )
| ( ( ! [SY4739: $i] :
~ ( c_lessequals @ SV1280 @ SV311 @ ( tc_fun @ SY4739 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV311 @ SV701 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3555]) ).
thf(3815,plain,
! [SV702: $i,SV1595: $i,SV314: $i,SV1283: $i] :
( ( ( ~ ( c_lessequals @ SV1283 @ SV314 @ ( tc_fun @ SV1595 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1283 @ SV702 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV314 @ SV702 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3556]) ).
thf(3816,plain,
! [SV316: $i,SV1488: $i,SV1284: $i] :
( ( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1284 @ SV1488 @ SV316 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV316 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV1284 @ SV1488 @ SV316 )
= $true )
| ( ( class_Orderings_Oorder @ SV316 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3557]) ).
thf(3817,plain,
! [SV317: $i,SV1489: $i,SV1285: $i] :
( ( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1285 @ SV1489 @ SV317 )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV317 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1285 @ SV1489 @ SV317 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV317 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3558]) ).
thf(3818,plain,
! [SV1596: $i,SV1490: $i,SV1286: $i,SV1018: $i,SV704: $i,SV318: $i] :
( ( ! [SY5106: $i,SY5107: $i,SY5108: $i,SY5109: $i,SY5110: $i,SY5111: $i] :
( ( c_Com_Ocom_Ocom__case @ SV318 @ SV704 @ SV1018 @ SV1286 @ SV1490 @ SV1596 @ SY5106 @ SY5107 @ ( c_Com_Ocom_OCond @ SY5108 @ SY5109 @ SY5110 ) @ SY5111 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV1490 @ SY5108 ) @ SY5109 ) @ SY5110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3559]) ).
thf(3819,plain,
! [SV1597: $i,SV1491: $i,SV1287: $i,SV1019: $i,SV705: $i,SV319: $i] :
( ( ! [SY5112: $i] :
( ! [SY5113: $i] :
( ( c_Fun_Ocomp @ SV319 @ SV705 @ SV1019 @ SV1287 @ SV1491 )
!= ( c_Fun_Ocomp @ SV1597 @ SY5112 @ SY5113 @ SV1287 @ SV1491 ) )
| ! [SY5114: $i] :
( ( hAPP @ SV319 @ ( hAPP @ SV705 @ SY5114 ) )
= ( hAPP @ SV1597 @ ( hAPP @ SY5112 @ SY5114 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3560]) ).
thf(3820,plain,
! [SV1598: $i,SV1492: $i,SV1288: $i,SV1020: $i,SV706: $i,SV320: $i] :
( ( ! [SY5115: $i,SY5116: $i,SY5117: $i] :
( ( ( hAPP @ SV320 @ ( hAPP @ SV706 @ SV1020 ) )
!= ( hAPP @ SV1288 @ ( hAPP @ SV1492 @ SV1598 ) ) )
| ! [SY5118: $i,SY5119: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV320 @ SV706 @ SY5115 @ SY5116 @ SY5117 ) @ SV1020 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1288 @ SV1492 @ SY5118 @ SY5116 @ SY5119 ) @ SV1598 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3561]) ).
thf(3821,plain,
! [SV1021: $i,SV707: $i,SV1599: $i,SV321: $i] :
( ( ( ! [SY5120: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV321 @ SV1599 ) @ SV707 @ SY5120 @ SV1021 ) )
= $true )
| ( ( SV1021 = SV707 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV321 @ SV707 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3562]) ).
thf(3822,plain,
! [SV1023: $i,SV1290: $i,SV710: $i,SV324: $i] :
( ( ( ~ ( c_lessequals @ SV324 @ SV710 @ ( tc_fun @ SV1290 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1023 @ SV324 @ ( tc_fun @ SV1290 @ tc_bool ) ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV324 @ ( c_HOL_Ominus__class_Ominus @ SV710 @ SV1023 @ ( tc_fun @ SV1290 @ tc_bool ) ) @ ( tc_fun @ SV1290 @ tc_bool ) )
= SV1023 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3564]) ).
thf(3823,plain,
! [SV1600: $i,SV325: $i,SV1024: $i,SV711: $i] :
( ( ( ! [SY5121: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV711 @ SV1024 @ SV325 )
!= ( c_HOL_Ominus__class_Ominus @ SV1600 @ SY5121 @ SV325 ) )
| ( c_lessequals @ SY5121 @ SV1600 @ SV325 )
| ~ ( c_lessequals @ SV1024 @ SV711 @ SV325 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3565]) ).
thf(3824,plain,
! [SV1601: $i,SV326: $i,SV1025: $i,SV712: $i] :
( ( ( ! [SY5122: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV712 @ SV1025 @ SV326 )
!= ( c_HOL_Ominus__class_Ominus @ SV1601 @ SY5122 @ SV326 ) )
| ( c_lessequals @ SV1025 @ SV712 @ SV326 )
| ~ ( c_lessequals @ SY5122 @ SV1601 @ SV326 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV326 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3566]) ).
thf(3825,plain,
! [SV1494: $i,SV1291: $i,SV1026: $i,SV713: $i,SV327: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV327 @ SV713 @ SV1026 @ SV1291 ) @ ( c_Set_Oimage @ SV327 @ SV1494 @ SV1026 @ SV1291 ) @ ( tc_fun @ SV1291 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV713 @ SV1494 @ ( tc_fun @ SV1026 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3567]) ).
thf(3826,plain,
! [SV714: $i,SV1027: $i,SV328: $i,SV1602: $i] :
( ( ( ! [SY5123: $i] : ( c_lessequals @ ( c_Set_Oimage @ SV1602 @ SV328 @ SV1027 @ SY5123 ) @ ( c_Set_Oimage @ SV1602 @ SV714 @ SV1027 @ SY5123 ) @ ( tc_fun @ SY5123 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV328 @ SV714 @ ( tc_fun @ SV1027 @ tc_bool ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3568]) ).
thf(3827,plain,
! [SV329: $i,SV1292: $i,SV1028: $i,SV715: $i,SV1603: $i] :
( ( ( ( c_Natural_Oevaln @ SV1603 @ SV715 @ SV1028 @ SV1292 )
| ! [SY5124: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SY5124 @ SV1603 @ SV329 ) @ SV715 @ SV1028 @ SV1292 ) )
= $true )
| ( ( c_Natural_Oevaln @ SV329 @ SV715 @ SV1028 @ SV1292 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3569]) ).
thf(3828,plain,
! [SV1604: $i,SV1496: $i,SV1294: $i,SV1030: $i,SV717: $i,SV331: $i] :
( ( ( c_Com_Ocom_OLocal @ SV331 @ SV717 @ SV1030 )
!= ( c_Com_Ocom_OCall @ SV1294 @ SV1496 @ SV1604 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3571]) ).
thf(3829,plain,
! [SV332: $i,SV1031: $i,SV718: $i,SV1497: $i] :
( ( ( c_Natural_Oevalc @ SV1497 @ SV718 @ SV1031 )
= $true )
| ( ( ! [SY4991: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SY4991 @ SV1497 @ SV332 ) @ SV718 @ SV1031 ) )
= $true )
| ( ( c_Natural_Oevalc @ SV332 @ SV718 @ SV1031 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3572]) ).
thf(3830,plain,
! [SV333: $i,SV1498: $i,SV1295: $i] :
( ( ( c_lessequals @ SV1295 @ ( c_Complete__Lattice_OSup__class_OSup @ SV1498 @ SV333 ) @ SV333 )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1295 @ SV1498 @ SV333 ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV333 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3573]) ).
thf(3831,plain,
! [SV337: $i,SV1499: $i,SV1298: $i] :
( ( ( c_lessequals @ SV1298 @ SV1499 @ SV337 )
= $true )
| ( ( c_lessequals @ SV1499 @ SV1298 @ SV337 )
= $true )
| ( ( class_Orderings_Olinorder @ SV337 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3576]) ).
thf(3832,plain,
! [SV1605: $i,SV1500: $i,SV1303: $i,SV1041: $i,SV727: $i,SV345: $i] :
( ( ! [SY5125: $i,SY5126: $i,SY5127: $i,SY5128: $i] :
( ( c_Com_Ocom_Ocom__case @ SV345 @ SV727 @ SV1041 @ SV1303 @ SV1500 @ SV1605 @ SY5125 @ SY5126 @ ( hAPP @ c_Com_Ocom_OBODY @ SY5127 ) @ SY5128 )
= ( hAPP @ SY5125 @ SY5127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3581]) ).
thf(3833,plain,
! [SV1501: $i,SV1305: $i,SV1043: $i,SV729: $i,SV348: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV348 @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SV729 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ SV1043 ) @ SV1305 ) @ SV1501 ) @ t_b @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV348 @ ( hAPP @ ( hAPP @ ( hAPP @ SV729 @ SV1043 ) @ SV1305 ) @ SV1501 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3582]) ).
thf(3834,plain,
! [SV1502: $i,SV1306: $i,SV1044: $i,SV730: $i,SV349: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV349 @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SV730 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ SV1044 ) @ SV1306 ) @ SV1502 ) @ t_b @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV349 @ ( hAPP @ ( hAPP @ ( hAPP @ SV730 @ SV1044 ) @ SV1306 ) @ SV1502 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3583]) ).
thf(3835,plain,
! [SV1606: $i,SV1503: $i,SV1307: $i,SV1045: $i,SV731: $i,SV350: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ SV350 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV731 ) @ SV1045 ) @ SV1307 ) @ SV1503 ) @ SV731 @ SV1606 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV350 @ SV1045 ) @ SV1307 ) @ SV1503 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3584]) ).
thf(3836,plain,
! [SV1607: $i,SV1504: $i,SV1308: $i,SV1046: $i,SV732: $i,SV351: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SV351 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV732 ) @ SV1046 ) @ SV1308 ) @ SV1504 ) @ SV732 @ SV1607 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV351 @ SV1046 ) @ SV1308 ) @ SV1504 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3585]) ).
thf(3837,plain,
! [SV352: $i,SV1047: $i,SV1505: $i,SV733: $i] :
( ( ( ~ ( c_lessequals @ SV733 @ SV1505 @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1047 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV352 @ SV1505 @ SV1047 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV352 @ SV733 @ SV1047 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3586]) ).
thf(3838,plain,
! [SV734: $i,SV1048: $i,SV353: $i,SV1506: $i] :
( ( ( ~ ( c_lessequals @ SV1506 @ SV353 @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1048 ) @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV1506 @ SV734 @ SV1048 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ SV734 @ SV1048 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3587]) ).
thf(3839,plain,
! [SV1050: $i,SV1309: $i,SV736: $i,SV355: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV355 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ ( c_COMBK @ ( hAPP @ ( c_COMBC @ ( c_fequal @ tc_Com_Ostate ) @ tc_Com_Ostate @ tc_Com_Ostate @ tc_bool ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ SV355 @ SV736 @ SV1309 @ SV1050 ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) ) @ SV1050 ) @ ( c_COMBK @ ( hAPP @ SV1309 @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ SV355 @ SV736 @ SV1309 @ SV1050 ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_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 @ SV355 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV736 ) @ SV1050 ) @ SV1309 ) @ ( 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)],[3589]) ).
thf(3840,plain,
! [SV1507: $i,SV1310: $i,SV1051: $i,SV737: $i,SV356: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV356 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ ( hAPP @ SV1051 @ SV1310 ) ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1310 ) ) @ ( hAPP @ SV1507 @ SV1310 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV737 )
= $true )
| ( ( ! [SY4999: $i] :
( ~ ( hBOOL @ ( c_in @ SV1310 @ SY4999 @ tc_Com_Opname ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV356 @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ SV1051 @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ SV1507 @ tc_Com_Opname @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SY4999 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ SV1051 @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ SV1507 @ tc_Com_Opname @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SY4999 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV737 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3590]) ).
thf(3841,plain,
! [SV1508: $i,SV1311: $i,SV1052: $i,SV739: $i,SV359: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV359 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV739 ) @ SV1052 ) @ ( c_Com_Ocom_OWhile @ SV1311 @ SV1508 ) ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1052 @ ( c_Fun_Ocomp @ c_Not @ SV1311 @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ SV739 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV739 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV739 ) ) @ SV739 )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV359 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV739 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1052 @ SV1311 @ SV739 ) ) @ SV1508 ) @ SV1052 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV739 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV739 ) ) @ SV739 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3591]) ).
thf(3842,plain,
! [SV1608: $i,SV1509: $i,SV1312: $i,SV1053: $i,SV740: $i,SV360: $i] :
( ( ! [SY5129: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ SV1053 ) @ ( c_Com_Ocom_OCond @ SV1312 @ SV1509 @ SV1608 ) ) @ SY5129 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1053 @ ( c_Fun_Ocomp @ c_Not @ SV1312 @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ SV740 ) ) @ SV1608 ) @ SY5129 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1053 @ SV1312 @ SV740 ) ) @ SV1509 ) @ SY5129 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3592]) ).
thf(3843,plain,
! [SV1313: $i,SV1054: $i,SV741: $i,SV361: $i] :
( ( ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ SV361 ) @ SV741 @ SV1054 @ SV1313 )
= $false )
| ( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV361 ) ) @ SV741 @ ( c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 @ SV361 @ SV1054 @ SV741 @ SV1313 ) @ SV1313 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3593]) ).
thf(3844,plain,
! [SV1314: $i,SV1055: $i,SV742: $i,SV362: $i] :
( ( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV362 ) ) @ SV742 @ SV1055 @ SV1314 )
= $false )
| ( ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ SV362 ) @ SV742 @ ( c_Suc @ SV1055 ) @ SV1314 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3594]) ).
thf(3845,plain,
! [SV1056: $i,SV744: $i,SV366: $i] :
( ( ( c_lessequals @ SV366 @ ( c_Set_Oinsert @ SV744 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1056 @ tc_bool ) ) @ SV1056 ) @ ( tc_fun @ SV1056 @ tc_bool ) )
= $false )
| ( ( SV366
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1056 @ tc_bool ) ) )
= $true )
| ( ( SV366
= ( c_Set_Oinsert @ SV744 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1056 @ tc_bool ) ) @ SV1056 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3595]) ).
thf(3846,plain,
! [SV1609: $i,SV1510: $i,SV1315: $i,SV1057: $i,SV746: $i,SV368: $i] :
( ( ! [SY5130: $i,SY5131: $i] :
( ( ( hAPP @ SV368 @ ( c_Set_Oinsert @ SV746 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1057 @ tc_bool ) ) @ SV1057 ) )
= SV746 )
| ! [SY5132: $i,SY5133: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV368 @ SV1315 @ SV1510 @ SV1609 @ SY5130 @ SY5131 @ SY5132 @ SY5133 @ SV1057 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3596]) ).
thf(3847,plain,
! [SV1610: $i,SV1511: $i,SV1316: $i,SV1058: $i,SV747: $i,SV369: $i] :
( ( ! [SY5134: $i,SY5135: $i] :
( ( ( hAPP @ SV369 @ ( c_Set_Oinsert @ SV747 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1058 @ tc_bool ) ) @ SV1058 ) )
= SV747 )
| ! [SY5136: $i,SY5137: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1316 @ SV369 @ SV1511 @ SV1610 @ SY5134 @ SY5135 @ SY5136 @ SY5137 @ SV1058 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3597]) ).
thf(3848,plain,
! [SV1611: $i,SV1512: $i,SV1320: $i,SV1061: $i,SV752: $i,SV376: $i] :
( ( ! [SY5138: $i,SY5139: $i,SY5140: $i] :
( ( ( hAPP @ SV376 @ ( c_Set_Oinsert @ SV752 @ ( c_Set_Oinsert @ SV1061 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1320 @ tc_bool ) ) @ SV1320 ) @ SV1320 ) )
= ( hAPP @ ( hAPP @ SV1512 @ SV752 ) @ SV1061 ) )
| ! [SY5141: $i,SY5142: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV376 @ SV1611 @ SY5138 @ SY5139 @ SV1512 @ SY5140 @ SY5141 @ SY5142 @ SV1320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3598]) ).
thf(3849,plain,
! [SV1612: $i,SV1513: $i,SV1321: $i,SV1062: $i,SV753: $i,SV377: $i] :
( ( ! [SY5143: $i,SY5144: $i,SY5145: $i] :
( ( ( hAPP @ SV377 @ ( c_Set_Oinsert @ SV753 @ ( c_Set_Oinsert @ SV1062 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1321 @ tc_bool ) ) @ SV1321 ) @ SV1321 ) )
= ( hAPP @ ( hAPP @ SV1513 @ SV753 ) @ SV1062 ) )
| ! [SY5146: $i,SY5147: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1612 @ SV377 @ SY5143 @ SY5144 @ SY5145 @ SV1513 @ SY5146 @ SY5147 @ SV1321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3599]) ).
thf(3850,plain,
! [SV756: $i,SV1514: $i,SV380: $i,SV1324: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ SV1324 @ ( c_Set_Oinsert @ SV380 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1514 @ tc_bool ) ) @ SV1514 ) @ SV1514 ) @ SV756 ) )
= $false )
| ( ( SV380 = SV756 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3600]) ).
thf(3851,plain,
! [SV1515: $i,SV1329: $i,SV1070: $i,SV764: $i,SV391: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV391 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV764 ) @ SV1070 ) @ SV1329 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
= $true )
| ( ( ! [SY5024: $i,SY5025: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV1515 @ SY5024 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV391 @ SV764 @ SV1329 @ SV1070 @ SY5025 @ SV1515 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY5025 @ SY5024 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV391 @ SV764 @ SV1329 @ SV1070 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV391 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY5025 ) @ SV1070 ) @ SV1515 ) @ ( 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)],[3604]) ).
thf(3852,plain,
! [SV1516: $i,SV1330: $i,SV1071: $i,SV765: $i,SV392: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV392 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV765 ) @ SV1071 ) @ SV1330 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
= $true )
| ( ( ! [SY5026: $i,SY5027: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV1516 @ SY5026 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV765 @ SY5027 @ SV1330 @ SV1516 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY5027 @ SY5026 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV765 @ SY5027 @ SV1330 @ SV1516 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV392 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY5027 ) @ SV1071 ) @ SV1516 ) @ ( 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)],[3605]) ).
thf(3853,plain,
! [SV1517: $i,SV1331: $i,SV1072: $i,SV766: $i,SV393: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV393 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV766 ) @ SV1072 ) @ SV1331 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
= $true )
| ( ( ! [SY5028: $i,SY5029: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV1517 @ SY5028 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV393 @ SV766 @ SV1331 @ SV1072 @ SY5029 @ SV1517 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY5029 @ SY5028 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV393 @ SV766 @ SV1331 @ SV1072 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV393 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY5029 ) @ SV1072 ) @ SV1517 ) @ ( 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)],[3606]) ).
thf(3854,plain,
! [SV1613: $i,SV1074: $i,SV768: $i,SV395: $i,SV1333: $i] :
( ( ( ! [SY5148: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1333 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV395 @ SV768 @ SV1333 @ SV1074 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV395 @ SV768 @ SV1333 @ SV1074 @ SV1613 @ SY5148 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV395 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1613 ) @ SV1074 ) @ SY5148 ) @ ( 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 @ SV395 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV768 ) @ SV1074 ) @ SV1333 ) @ ( 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)],[3608]) ).
thf(3855,plain,
! [SV1076: $i,SV770: $i,SV397: $i,SV1335: $i,SV1614: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1614 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SV1335 @ SV1614 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SV1335 @ SV1614 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV397 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV770 ) @ SV1076 ) @ SV1614 ) @ ( 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 @ SV397 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV770 ) @ SV1076 ) @ SV1335 ) @ ( 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)],[3610]) ).
thf(3856,plain,
! [SV1077: $i,SV398: $i,SV1336: $i,SV1615: $i,SV771: $i] :
( ( ( ! [SY5149: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV771 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV771 @ SV1615 @ SV1336 @ SY5149 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV771 @ SV1615 @ SV1336 @ SY5149 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV398 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1615 ) @ SV1077 ) @ SY5149 ) @ ( 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 @ SV398 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV771 ) @ SV1077 ) @ SV1336 ) @ ( 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)],[3611]) ).
thf(3857,plain,
! [SV1337: $i,SV1078: $i,SV399: $i,SV1616: $i,SV772: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV772 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV772 @ SV1616 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV772 @ SV1616 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV399 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1616 ) @ SV1078 ) @ SV1337 ) @ ( 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 @ SV399 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV772 ) @ SV1078 ) @ SV1337 ) @ ( 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)],[3612]) ).
thf(3858,plain,
! [SV1617: $i,SV1079: $i,SV773: $i,SV400: $i,SV1338: $i] :
( ( ( ! [SY5150: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1338 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV400 @ SV773 @ SV1338 @ SV1079 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV400 @ SV773 @ SV1338 @ SV1079 @ SV1617 @ SY5150 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV400 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1617 ) @ SV1079 ) @ SY5150 ) @ ( 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 @ SV400 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV773 ) @ SV1079 ) @ SV1338 ) @ ( 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)],[3613]) ).
thf(3859,plain,
! [SV1339: $i,SV1080: $i,SV401: $i,SV774: $i,SV1618: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1618 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV774 @ SV1618 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV774 @ SV1618 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV401 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1618 ) @ SV1080 ) @ SV1339 ) @ ( 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 @ SV401 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV774 ) @ SV1080 ) @ SV1339 ) @ ( 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)],[3614]) ).
thf(3860,plain,
! [SV1081: $i,SV402: $i,SV1619: $i,SV775: $i,SV1340: $i] :
( ( ( ! [SY5151: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1340 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV775 @ SV1619 @ SV1340 @ SY5151 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV775 @ SV1619 @ SV1340 @ SY5151 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV402 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1619 ) @ SV1081 ) @ SY5151 ) @ ( 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 @ SV402 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV775 ) @ SV1081 ) @ SV1340 ) @ ( 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)],[3615]) ).
thf(3861,plain,
! [SV1082: $i,SV776: $i,SV403: $i,SV1620: $i,SV1341: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1341 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SV1341 @ SV1620 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SV1341 @ SV1620 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV403 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV776 ) @ SV1082 ) @ SV1620 ) @ ( 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 @ SV403 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV776 ) @ SV1082 ) @ SV1341 ) @ ( 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)],[3616]) ).
thf(3862,plain,
! [SV1518: $i,SV1343: $i,SV1084: $i,SV778: $i,SV405: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV405 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV778 ) @ SV1084 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1343 ) ) @ SV1518 ) @ SV778 )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Otriple__valid @ SV405 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV778 ) @ SV1084 ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV1343 ) ) ) @ SV1518 ) @ SV778 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3618]) ).
thf(3863,plain,
! [SV1519: $i,SV1344: $i,SV1085: $i,SV779: $i,SV406: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ SV406 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV779 ) @ SV1085 ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV1344 ) ) ) @ SV1519 ) @ SV779 )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV406 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV779 ) @ SV1085 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1344 ) ) @ SV1519 ) @ SV779 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3619]) ).
thf(3864,plain,
! [SV1621: $i,SV1520: $i,SV1345: $i,SV1089: $i,SV783: $i,SV410: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SV1089 ) @ ( c_Com_Ocom_OSemi @ SV1345 @ SV1520 ) ) @ SV1621 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 )
| ! [SY5152: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SY5152 ) @ SV1520 ) @ SV1621 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SV1089 ) @ SV1345 ) @ SY5152 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3622]) ).
thf(3865,plain,
! [SV784: $i,SV1346: $i,SV1090: $i,SV411: $i] :
( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV411 @ SV1090 @ SV1346 ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV411 @ ( c_Set_Oinsert @ SV784 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1346 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1346 ) ) @ SV1346 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV411 @ ( c_Set_Oinsert @ SV784 @ SV1090 @ ( tc_Hoare__Mirabelle_Otriple @ SV1346 ) ) @ SV1346 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3623]) ).
thf(3866,plain,
! [SV786: $i,SV1092: $i,SV1521: $i,SV413: $i] :
( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV413 @ SV1521 @ SV1092 ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV1521 @ SV786 @ SV1092 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV413 @ SV786 @ SV1092 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3624]) ).
thf(3867,plain,
! [SV1622: $i,SV1522: $i,SV1347: $i,SV1094: $i,SV788: $i,SV415: $i] :
( ( ! [SY5153: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV415 ) @ SV788 ) @ SV1094 ) @ SV1347 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV415 ) @ SV1522 ) @ SV1622 ) @ SY5153 ) )
| ( SV1347 = SY5153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3625]) ).
thf(3868,plain,
! [SV1623: $i,SV1523: $i,SV1348: $i,SV1095: $i,SV789: $i,SV416: $i] :
( ( ! [SY5154: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV416 ) @ SV789 ) @ SV1095 ) @ SV1348 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV416 ) @ SV1523 ) @ SV1623 ) @ SY5154 ) )
| ( SV1095 = SV1623 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3626]) ).
thf(3869,plain,
! [SV1524: $i,SV1349: $i,SV1096: $i,SV790: $i,SV417: $i] :
( ( ( ! [SY5036: $i,SY5037: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV417 ) @ SV790 ) @ SV1096 ) @ SV1349 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV417 ) @ SV1524 ) @ SY5036 ) @ SY5037 ) ) )
= $true )
| ( ( SV790 = SV1524 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3627]) ).
thf(3870,plain,
! [SV1525: $i,SV1350: $i,SV1097: $i,SV791: $i,SV418: $i] :
( ( ( ( c_Set_Oinsert @ SV418 @ ( c_Set_Oinsert @ SV791 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1097 @ tc_bool ) ) @ SV1097 ) @ SV1097 )
!= ( c_Set_Oinsert @ SV1350 @ ( c_Set_Oinsert @ SV1525 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1097 @ tc_bool ) ) @ SV1097 ) @ SV1097 ) )
= $true )
| ( ( ( SV791 = SV1350 )
| ( SV791 = SV1525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3628]) ).
thf(3871,plain,
! [SV1526: $i,SV1351: $i,SV1098: $i,SV792: $i,SV419: $i] :
( ( ( ( c_Set_Oinsert @ SV419 @ ( c_Set_Oinsert @ SV792 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1098 @ tc_bool ) ) @ SV1098 ) @ SV1098 )
!= ( c_Set_Oinsert @ SV1351 @ ( c_Set_Oinsert @ SV1526 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1098 @ tc_bool ) ) @ SV1098 ) @ SV1098 ) )
= $true )
| ( ( ( SV419 = SV1526 )
| ( SV792 = SV1526 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3629]) ).
thf(3872,plain,
! [SV1624: $i,SV1352: $i,SV1099: $i,SV793: $i,SV420: $i] :
( ( ( ( c_Set_Oinsert @ SV420 @ ( c_Set_Oinsert @ SV793 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1099 @ tc_bool ) ) @ SV1099 ) @ SV1099 )
!= ( c_Set_Oinsert @ SV1352 @ ( c_Set_Oinsert @ SV1624 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1099 @ tc_bool ) ) @ SV1099 ) @ SV1099 ) )
= $true )
| ( ( ( SV793 = SV1352 )
| ( SV420 = SV1352 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3630]) ).
thf(3873,plain,
! [SV1527: $i,SV1353: $i,SV1100: $i,SV794: $i,SV421: $i] :
( ( ( ( c_Set_Oinsert @ SV421 @ ( c_Set_Oinsert @ SV794 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1100 @ tc_bool ) ) @ SV1100 ) @ SV1100 )
!= ( c_Set_Oinsert @ SV1353 @ ( c_Set_Oinsert @ SV1527 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1100 @ tc_bool ) ) @ SV1100 ) @ SV1100 ) )
= $true )
| ( ( ( SV421 = SV1527 )
| ( SV421 = SV1353 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3631]) ).
thf(3874,plain,
! [SV1528: $i,SV1354: $i,SV1101: $i,SV797: $i,SV424: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV424 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV797 ) @ SV1101 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1354 ) ) @ SV1528 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) ) @ SV797 )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV797 ) @ SV1101 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1354 ) ) @ SV1528 ) @ SV424 @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) ) @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV797 ) @ SV1101 ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV1354 ) ) ) @ SV1528 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) ) @ SV797 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3632]) ).
thf(3875,plain,
! [SV798: $i,SV1625: $i,SV425: $i,SV1355: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1355 @ SV425 @ SV1625 ) @ SV798 ) ) )
= $true )
| ( ( SV1355 = SV798 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV425 @ SV798 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3633]) ).
thf(3876,plain,
! [SV1107: $i,SV431: $i,SV1357: $i,SV804: $i] :
( ( ( hBOOL @ ( hAPP @ SV804 @ SV1357 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV431 @ SV804 @ SV1107 ) @ SV1357 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3635]) ).
thf(3877,plain,
! [SV7: $i,SV818: $i,SV1110: $i,SV449: $i] :
( ( ( c_lessequals @ SV449 @ SV1110 @ ( tc_fun @ SV818 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV7 @ SV1110 @ ( tc_fun @ SV818 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV7 @ SV449 @ ( tc_fun @ SV818 @ tc_bool ) ) @ SV1110 @ ( tc_fun @ SV818 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3641]) ).
thf(3878,plain,
! [SV10: $i,SV821: $i,SV1111: $i,SV452: $i] :
( ( ( c_lessequals @ SV452 @ SV1111 @ ( tc_fun @ SV821 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV10 @ SV1111 @ ( tc_fun @ SV821 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV10 @ SV452 @ ( tc_fun @ SV821 @ tc_bool ) ) @ SV1111 @ ( tc_fun @ SV821 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3642]) ).
thf(3879,plain,
! [SV1533: $i,SV11: $i,SV1363: $i,SV453: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV453 @ SV1363 @ SV11 ) @ SV1533 @ SV11 )
= $true )
| ( ( ~ ( c_lessequals @ SV1363 @ SV1533 @ SV11 )
| ~ ( c_lessequals @ SV453 @ SV1533 @ SV11 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3643]) ).
thf(3880,plain,
! [SV1534: $i,SV14: $i,SV1366: $i,SV454: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV454 @ SV1366 @ SV14 ) @ SV1534 @ SV14 )
= $true )
| ( ( ~ ( c_lessequals @ SV1366 @ SV1534 @ SV14 )
| ~ ( c_lessequals @ SV454 @ SV1534 @ SV14 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3644]) ).
thf(3881,plain,
! [SV1535: $i,SV15: $i,SV1367: $i,SV455: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV455 @ SV1367 @ SV15 ) @ SV1535 @ SV15 )
= $true )
| ( ( ~ ( c_lessequals @ SV1367 @ SV1535 @ SV15 )
| ~ ( c_lessequals @ SV455 @ SV1535 @ SV15 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3645]) ).
thf(3882,plain,
! [SV1626: $i,SV1536: $i,SV1370: $i,SV1116: $i,SV822: $i,SV456: $i,SV18: $i] :
( ( ! [SY5155: $i,SY5156: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV18 @ SV456 @ ( c_COMBC @ SV822 @ SV1116 @ SV1116 @ tc_bool ) @ ( c_COMBC @ SV1370 @ SV1116 @ SV1116 @ tc_bool ) @ SV1536 @ SV1626 @ SY5155 @ SY5156 @ SV1116 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV456 @ SV18 @ SV822 @ SV1370 @ SV1626 @ SV1536 @ SY5156 @ SY5155 @ SV1116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3646]) ).
thf(3883,plain,
! [SV22: $i,SV1627: $i,SV1537: $i] :
( ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1537 @ SV1627 @ SV22 )
!= ( c_HOL_Ozero__class_Ozero @ SV22 ) )
| ( SV1537 = SV1627 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV22 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3647]) ).
thf(3884,plain,
! [SV23: $i,SV1371: $i,SV1117: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1117 @ SV1371 @ SV23 )
= ( c_HOL_Ozero__class_Ozero @ SV23 ) )
= $false )
| ( ( SV1117 = SV1371 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3648]) ).
thf(3885,plain,
! [SV24: $i,SV1372: $i,SV1118: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1118 @ SV1372 @ SV24 )
= ( c_HOL_Ozero__class_Ozero @ SV24 ) )
= $false )
| ( ( SV1118 = SV1372 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3649]) ).
thf(3886,plain,
! [SV827: $i,SV1121: $i,SV463: $i,SV28: $i] :
( ( ( hBOOL @ ( c_in @ SV28 @ SV463 @ SV1121 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV28 @ SV827 @ SV1121 ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV28 @ ( c_HOL_Ominus__class_Ominus @ SV463 @ SV827 @ ( tc_fun @ SV1121 @ tc_bool ) ) @ SV1121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3650]) ).
thf(3887,plain,
! [SV828: $i,SV1122: $i,SV464: $i,SV29: $i] :
( ( ( hBOOL @ ( c_in @ SV29 @ SV464 @ SV1122 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV29 @ SV828 @ SV1122 ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV29 @ ( c_HOL_Ominus__class_Ominus @ SV464 @ SV828 @ ( tc_fun @ SV1122 @ tc_bool ) ) @ SV1122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3651]) ).
thf(3888,plain,
! [SV1538: $i,SV1373: $i,SV1123: $i,SV829: $i,SV465: $i,SV30: $i] :
( ( ( c_Com_Ocom_OCall @ SV30 @ SV465 @ SV829 )
= ( c_Com_Ocom_OLocal @ SV1123 @ SV1373 @ SV1538 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3652]) ).
thf(3889,plain,
! [SV1539: $i,SV33: $i,SV1375: $i,SV468: $i] :
( ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV468 @ ( c_COMBK @ SV1375 @ SV33 @ SV1539 ) @ SV1539 @ SV33 )
= SV1375 )
= $true )
| ( ( SV468
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1539 @ tc_bool ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3654]) ).
thf(3890,plain,
! [SV1540: $i,SV35: $i,SV1126: $i,SV833: $i,SV470: $i] :
( ( ( hBOOL @ ( c_in @ SV470 @ SV833 @ SV1126 ) )
= $false )
| ( ( ( c_Set_Oinsert @ ( hAPP @ SV35 @ SV470 ) @ ( c_Set_Oimage @ SV35 @ SV833 @ SV1126 @ SV1540 ) @ SV1540 )
= ( c_Set_Oimage @ SV35 @ SV833 @ SV1126 @ SV1540 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3656]) ).
thf(3891,plain,
! [SV471: $i,SV1127: $i,SV834: $i,SV36: $i] :
( ( ( c_lessequals @ SV36 @ SV834 @ ( tc_fun @ SV1127 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV471 @ SV36 @ SV1127 ) )
= $true )
| ( ( c_lessequals @ SV36 @ ( c_Set_Oinsert @ SV471 @ SV834 @ SV1127 ) @ ( tc_fun @ SV1127 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3657]) ).
thf(3892,plain,
! [SV835: $i,SV472: $i,SV1377: $i,SV37: $i] :
( ( ( c_lessequals @ SV37 @ ( c_Set_Oinsert @ SV1377 @ SV472 @ SV835 ) @ ( tc_fun @ SV835 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV1377 @ SV37 @ SV835 ) )
= $true )
| ( ( c_lessequals @ SV37 @ SV472 @ ( tc_fun @ SV835 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3658]) ).
thf(3893,plain,
! [SV473: $i,SV1128: $i,SV836: $i,SV38: $i] :
( ( ( c_lessequals @ SV38 @ SV836 @ ( tc_fun @ SV1128 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV473 @ SV38 @ SV1128 ) )
= $true )
| ( ( c_lessequals @ SV38 @ ( c_Set_Oinsert @ SV473 @ SV836 @ SV1128 ) @ ( tc_fun @ SV1128 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3659]) ).
thf(3894,plain,
! [SV837: $i,SV474: $i,SV1378: $i,SV39: $i] :
( ( ( c_lessequals @ SV39 @ ( c_Set_Oinsert @ SV1378 @ SV474 @ SV837 ) @ ( tc_fun @ SV837 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV1378 @ SV39 @ SV837 ) )
= $true )
| ( ( c_lessequals @ SV39 @ SV474 @ ( tc_fun @ SV837 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3660]) ).
thf(3895,plain,
! [SV840: $i,SV42: $i,SV1131: $i,SV1541: $i,SV477: $i] :
( ( ( ~ ( c_Natural_Oevalc @ SV477 @ SV1541 @ SV1131 ) )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ SV42 @ SV840 @ SV1541 ) )
= $true )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV42 @ SV477 ) @ SV840 @ SV1131 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3661]) ).
thf(3896,plain,
! [SV44: $i,SV1542: $i,SV479: $i,SV842: $i] :
( ( ( c_Natural_Oevalc @ SV842 @ SV479 @ SV1542 )
= $true )
| ( ( ! [SY5042: $i] :
~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV44 @ SV842 @ SY5042 ) @ SV479 @ SV1542 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV44 @ SV479 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3662]) ).
thf(3897,plain,
! [SV843: $i,SV45: $i,SV1380: $i,SV1133: $i,SV480: $i] :
( ( ( ~ ( c_Natural_Oevalc @ SV480 @ SV1133 @ SV1380 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV45 @ SV1133 ) ) )
= $true )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV45 @ SV480 @ SV843 ) @ SV1133 @ SV1380 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3663]) ).
thf(3898,plain,
! [SV844: $i,SV46: $i,SV1381: $i,SV1134: $i,SV1628: $i,SV481: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV481 @ SV1628 @ SV1134 @ SV1381 )
| ~ ( c_Natural_Oevaln @ SV46 @ SV844 @ SV1134 @ SV1628 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV46 @ SV481 ) @ SV844 @ SV1134 @ SV1381 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3664]) ).
thf(3899,plain,
! [SV1543: $i,SV1382: $i,SV47: $i,SV482: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV482 @ SV482 @ SV47 )
!= ( c_HOL_Ominus__class_Ominus @ SV1382 @ SV1543 @ SV47 ) )
= $true )
| ( ( SV1382 = SV1543 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3665]) ).
thf(3900,plain,
! [SV1629: $i,SV48: $i,SV1383: $i,SV483: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV483 @ SV1383 @ SV48 )
!= ( c_HOL_Ominus__class_Ominus @ SV1629 @ SV1629 @ SV48 ) )
= $true )
| ( ( SV483 = SV1383 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3666]) ).
thf(3901,plain,
! [SV845: $i,SV1135: $i,SV1544: $i,SV484: $i,SV49: $i] :
( ( ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV49 @ SV484 ) @ SV1544 @ SV1135 ) )
= $true )
| ( ( ~ ( c_Natural_Oevalc @ SV484 @ SV845 @ SV1544 )
| ~ ( hBOOL @ ( hAPP @ SV49 @ SV845 ) ) )
= $true )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV49 @ SV484 ) @ SV845 @ SV1135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3667]) ).
thf(3902,plain,
! [SV846: $i,SV1384: $i,SV1136: $i,SV1630: $i,SV487: $i,SV52: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV52 @ SV487 ) @ SV1630 @ SV1136 @ SV1384 )
| ~ ( c_Natural_Oevaln @ SV487 @ SV846 @ SV1136 @ SV1630 )
| ~ ( hBOOL @ ( hAPP @ SV52 @ SV846 ) ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV52 @ SV487 ) @ SV846 @ SV1136 @ SV1384 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3668]) ).
thf(3903,plain,
! [SV62: $i,SV1631: $i,SV1144: $i,SV497: $i,SV853: $i] :
( ( ( ( c_Natural_Oevaln @ SV853 @ SV497 @ SV1144 @ SV1631 )
| ! [SY5157: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV62 @ SV853 @ SY5157 ) @ SV497 @ SV1144 @ SV1631 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV62 @ SV497 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3672]) ).
thf(3904,plain,
! [SV1548: $i,SV1388: $i,SV1145: $i,SV854: $i,SV498: $i,SV63: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV63 @ SV498 @ SV854 ) @ SV1145 @ SV1388 @ SV1548 )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ SV498 @ SV1145 @ SV1388 @ SV1548 )
| ~ ( hBOOL @ ( hAPP @ SV63 @ SV1145 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3673]) ).
thf(3905,plain,
! [SV1632: $i,SV1549: $i,SV1389: $i,SV1146: $i,SV855: $i,SV499: $i,SV64: $i] :
( ( ! [SY5158: $i,SY5159: $i,SY5160: $i,SY5161: $i,SY5162: $i] :
( ( c_Com_Ocom_Ocom__case @ SV64 @ SV499 @ SV855 @ SV1146 @ SV1389 @ SV1549 @ SV1632 @ SY5158 @ ( c_Com_Ocom_OCall @ SY5159 @ SY5160 @ SY5161 ) @ SY5162 )
= ( hAPP @ ( hAPP @ ( hAPP @ SY5158 @ SY5159 ) @ SY5160 ) @ SY5161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3674]) ).
thf(3906,plain,
! [SV502: $i,SV69: $i,SV857: $i,SV1150: $i,SV1550: $i] :
( ( ( hBOOL @ ( c_in @ SV1550 @ SV1150 @ SV857 ) )
= $false )
| ( ( ( c_Set_Oimage @ ( c_COMBK @ SV69 @ SV502 @ SV857 ) @ SV1150 @ SV857 @ SV502 )
= ( c_Set_Oinsert @ SV69 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV502 @ tc_bool ) ) @ SV502 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3676]) ).
thf(3907,plain,
! [SV858: $i,SV1151: $i,SV70: $i,SV1633: $i,SV1551: $i,SV503: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV503 @ SV1551 @ SV1633 ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ SV70 @ SV1551 @ SV1633 @ SV1151 ) @ SV858 @ ( tc_fun @ SV1151 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ ( hAPP @ SV70 @ SV503 ) @ SV858 @ SV1151 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3677]) ).
thf(3908,plain,
! [SV1152: $i,SV859: $i,SV71: $i,SV504: $i] :
( ( ( hBOOL @ ( c_in @ SV504 @ SV71 @ SV859 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV71 @ ( c_Set_Oinsert @ SV504 @ SV1152 @ SV859 ) @ ( tc_fun @ SV859 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV71 @ ( c_Set_Oinsert @ SV504 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV859 @ tc_bool ) ) @ SV859 ) @ ( tc_fun @ SV859 @ tc_bool ) ) @ SV1152 @ ( tc_fun @ SV859 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3678]) ).
thf(3909,plain,
! [SV860: $i,SV1153: $i,SV72: $i,SV505: $i] :
( ( ( hBOOL @ ( c_in @ SV505 @ SV72 @ SV1153 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV72 @ ( c_Set_Oinsert @ SV505 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1153 @ tc_bool ) ) @ SV1153 ) @ ( tc_fun @ SV1153 @ tc_bool ) ) @ SV860 @ ( tc_fun @ SV1153 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV72 @ ( c_Set_Oinsert @ SV505 @ SV860 @ SV1153 ) @ ( tc_fun @ SV1153 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3679]) ).
thf(3910,plain,
! [SV861: $i,SV1154: $i,SV73: $i,SV506: $i] :
( ( ( hBOOL @ ( c_in @ SV506 @ SV73 @ SV1154 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV73 @ ( c_Set_Oinsert @ SV506 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1154 @ tc_bool ) ) @ SV1154 ) @ ( tc_fun @ SV1154 @ tc_bool ) ) @ SV861 @ ( tc_fun @ SV1154 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV73 @ ( c_Set_Oinsert @ SV506 @ SV861 @ SV1154 ) @ ( tc_fun @ SV1154 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3680]) ).
thf(3911,plain,
! [SV1552: $i,SV1393: $i,SV1155: $i,SV864: $i,SV509: $i,SV76: $i] :
( ( ( c_Com_Ocom_OCond @ SV76 @ SV509 @ SV864 )
= ( c_Com_Ocom_OCall @ SV1155 @ SV1393 @ SV1552 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3681]) ).
thf(3912,plain,
! [SV77: $i,SV1634: $i,SV1553: $i,SV865: $i,SV510: $i] :
( ( ( ( c_lessequals @ ( hAPP @ SV510 @ SV865 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1553 @ SV510 @ SV1634 @ SV77 ) @ SV77 )
| ~ ( hBOOL @ ( c_in @ SV865 @ SV1553 @ SV1634 ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV77 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3682]) ).
thf(3913,plain,
! [SV1554: $i,SV78: $i,SV1156: $i,SV866: $i,SV511: $i] :
( ( ( hBOOL @ ( c_in @ SV511 @ SV866 @ SV1156 ) )
= $false )
| ( ( c_lessequals @ ( hAPP @ SV78 @ SV511 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV866 @ SV78 @ SV1156 @ ( tc_fun @ SV1554 @ tc_bool ) ) @ ( tc_fun @ SV1554 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3683]) ).
thf(3914,plain,
! [SV1555: $i,SV1394: $i,SV1158: $i,SV868: $i,SV513: $i,SV80: $i] :
( ( ( c_Com_Ocom_OLocal @ SV80 @ SV513 @ SV868 )
= ( c_Com_Ocom_OCond @ SV1158 @ SV1394 @ SV1555 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3685]) ).
thf(3915,plain,
! [SV1556: $i,SV1395: $i,SV1159: $i,SV869: $i,SV515: $i,SV82: $i] :
( ( ( ( c_Com_Ocom_OCall @ SV82 @ SV515 @ SV869 )
!= ( c_Com_Ocom_OCall @ SV1159 @ SV1395 @ SV1556 ) )
= $true )
| ( ( SV869 = SV1556 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3686]) ).
thf(3916,plain,
! [SV1635: $i,SV1396: $i,SV1160: $i,SV870: $i,SV516: $i,SV83: $i] :
( ( ( ( c_Com_Ocom_OCall @ SV83 @ SV516 @ SV870 )
!= ( c_Com_Ocom_OCall @ SV1160 @ SV1396 @ SV1635 ) )
= $true )
| ( ( SV516 = SV1396 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3687]) ).
thf(3917,plain,
! [SV1636: $i,SV1557: $i,SV1161: $i,SV871: $i,SV517: $i,SV84: $i] :
( ( ( ( c_Com_Ocom_OCall @ SV84 @ SV517 @ SV871 )
!= ( c_Com_Ocom_OCall @ SV1161 @ SV1557 @ SV1636 ) )
= $true )
| ( ( SV84 = SV1161 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3688]) ).
thf(3918,plain,
! [SV880: $i,SV98: $i,SV1168: $i,SV1637: $i,SV528: $i] :
( ( ( ( ( hAPP @ SV528 @ SV1637 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1168 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SV1637 @ SV98 @ SV880 ) ) )
= $true )
| ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV98 @ SV528 @ SV880 @ ( tc_fun @ SV1168 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1168 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3694]) ).
thf(3919,plain,
! [SV1558: $i,SV1404: $i,SV1170: $i,SV883: $i,SV531: $i,SV101: $i] :
( ( ( c_Com_Ocom_OCond @ SV101 @ SV531 @ SV883 )
= ( c_Com_Ocom_OLocal @ SV1170 @ SV1404 @ SV1558 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3697]) ).
thf(3920,plain,
! [SV884: $i,SV532: $i,SV1559: $i,SV102: $i] :
( ( ( hBOOL @ ( c_in @ SV102 @ ( c_HOL_Ominus__class_Ominus @ SV1559 @ SV532 @ ( tc_fun @ SV884 @ tc_bool ) ) @ SV884 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV102 @ SV532 @ SV884 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3698]) ).
thf(3921,plain,
! [SV885: $i,SV1171: $i,SV103: $i,SV1638: $i,SV1560: $i,SV533: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV533 @ SV1560 @ SV1638 ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1560 @ SV103 @ SV1638 @ ( tc_fun @ SV1171 @ tc_bool ) ) @ SV885 @ ( tc_fun @ SV1171 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ SV103 @ SV533 ) @ SV885 @ ( tc_fun @ SV1171 @ tc_bool ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3699]) ).
thf(3922,plain,
! [SV1561: $i,SV107: $i,SV1174: $i,SV888: $i,SV537: $i] :
( ( ( hBOOL @ ( c_in @ SV537 @ SV888 @ SV1174 ) )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ SV107 @ SV537 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV888 @ SV107 @ SV1174 @ ( tc_fun @ SV1561 @ tc_bool ) ) @ ( tc_fun @ SV1561 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV888 @ SV107 @ SV1174 @ ( tc_fun @ SV1561 @ tc_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3701]) ).
thf(3923,plain,
! [SV1562: $i,SV1406: $i,SV1175: $i,SV889: $i,SV538: $i,SV108: $i] :
( ( ( ( c_Com_Ocom_OCond @ SV108 @ SV538 @ SV889 )
!= ( c_Com_Ocom_OCond @ SV1175 @ SV1406 @ SV1562 ) )
= $true )
| ( ( SV889 = SV1562 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3702]) ).
thf(3924,plain,
! [SV1639: $i,SV1407: $i,SV1176: $i,SV890: $i,SV539: $i,SV109: $i] :
( ( ( ( c_Com_Ocom_OCond @ SV109 @ SV539 @ SV890 )
!= ( c_Com_Ocom_OCond @ SV1176 @ SV1407 @ SV1639 ) )
= $true )
| ( ( SV539 = SV1407 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3703]) ).
thf(3925,plain,
! [SV1640: $i,SV1563: $i,SV1177: $i,SV891: $i,SV540: $i,SV110: $i] :
( ( ( ( c_Com_Ocom_OCond @ SV110 @ SV540 @ SV891 )
!= ( c_Com_Ocom_OCond @ SV1177 @ SV1563 @ SV1640 ) )
= $true )
| ( ( SV110 = SV1177 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3704]) ).
thf(3926,plain,
! [SV1641: $i,SV1565: $i,SV116: $i,SV892: $i,SV541: $i] :
( ( ( ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV541 @ SV892 @ SV116 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1565 @ SV1641 @ SV116 ) @ ( tc_fun @ SV116 @ tc_bool ) )
| ~ ( c_lessequals @ SV892 @ SV1641 @ SV116 )
| ~ ( c_lessequals @ SV1565 @ SV541 @ SV116 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV116 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3706]) ).
thf(3927,plain,
! [SV893: $i,SV117: $i,SV542: $i,SV1642: $i] :
( ( ( ~ ( c_lessequals @ SV1642 @ SV542 @ SV117 )
| ! [SY5163: $i] :
~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1642 @ SV542 @ SV117 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY5163 @ SV893 @ SV117 ) @ ( tc_fun @ SV117 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV542 @ SV893 @ SV117 )
= $true )
| ( ( class_Orderings_Oorder @ SV117 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3707]) ).
thf(3928,plain,
! [SV543: $i,SV118: $i,SV1643: $i,SV894: $i] :
( ( ( ~ ( c_lessequals @ SV894 @ SV1643 @ SV118 )
| ! [SY5164: $i] :
~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV894 @ SV1643 @ SV118 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV543 @ SY5164 @ SV118 ) @ ( tc_fun @ SV118 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV543 @ SV894 @ SV118 )
= $true )
| ( ( class_Orderings_Oorder @ SV118 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3708]) ).
thf(3929,plain,
! [SV1566: $i,SV1408: $i,SV1182: $i,SV895: $i,SV546: $i,SV121: $i] :
( ( ( c_Com_Ocom_OCall @ SV121 @ SV546 @ SV895 )
= ( c_Com_Ocom_OCond @ SV1182 @ SV1408 @ SV1566 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3709]) ).
thf(3930,plain,
! [SV1644: $i,SV127: $i,SV899: $i,SV552: $i] :
( ( ( ! [SY5165: $i] : ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV552 @ SV899 @ SV127 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1644 @ SY5165 @ SV127 ) @ ( tc_fun @ SV127 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV552 @ SV899 @ SV127 )
= $true )
| ( ( class_Orderings_Oorder @ SV127 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3712]) ).
thf(3931,plain,
! [SV553: $i,SV1569: $i,SV128: $i,SV1185: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1185 @ SV128 @ ( tc_fun @ SV1569 @ tc_bool ) ) @ SV553 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1185 @ SV553 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV128 @ SV553 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3713]) ).
thf(3932,plain,
! [SV131: $i,SV902: $i,SV556: $i] :
( ( ( c_Com_OWT @ SV556 )
= $false )
| ( ( c_Com_OWT @ SV902 )
= $false )
| ( ( c_Com_OWT @ ( c_Com_Ocom_OCond @ SV131 @ SV556 @ SV902 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3716]) ).
thf(3933,plain,
! [SV1645: $i,SV1570: $i,SV1411: $i,SV1188: $i,SV903: $i,SV557: $i,SV132: $i] :
( ( ! [SY5166: $i,SY5167: $i] :
( ( c_Com_Ocom_Ocom__case @ SV132 @ SV557 @ SV903 @ SV1188 @ SV1411 @ SV1570 @ SV1645 @ SY5166 @ c_Com_Ocom_OSKIP @ SY5167 )
= SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3717]) ).
thf(3934,plain,
! [SV904: $i,SV558: $i,SV1412: $i,SV133: $i] :
( ( ( hBOOL @ ( c_in @ SV133 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1412 @ SV558 @ ( tc_fun @ SV904 @ tc_bool ) ) @ SV904 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV133 @ SV1412 @ SV904 ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV133 @ SV558 @ SV904 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3718]) ).
thf(3935,plain,
! [SV1190: $i,SV560: $i,SV135: $i,SV1646: $i,SV906: $i] :
( ( ( ( ( hAPP @ SV906 @ SV1646 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV135 @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ SV1646 @ SV560 @ SV1190 ) ) )
= $true )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV135 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV560 @ SV906 @ SV1190 @ ( tc_fun @ SV135 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3720]) ).
thf(3936,plain,
! [SV1193: $i,SV564: $i,SV1414: $i,SV1647: $i,SV909: $i,SV139: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV139 @ ( hAPP @ SV909 @ SV1647 ) @ SV1414 ) )
| ~ ( hBOOL @ ( c_in @ SV1647 @ SV564 @ SV1193 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV139 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV564 @ SV909 @ SV1193 @ ( tc_fun @ SV1414 @ tc_bool ) ) @ SV1414 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3721]) ).
thf(3937,plain,
! [SV1194: $i,SV565: $i,SV1415: $i,SV1648: $i,SV910: $i,SV140: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV140 @ ( hAPP @ SV910 @ SV1648 ) @ SV1415 ) )
| ~ ( hBOOL @ ( c_in @ SV1648 @ SV565 @ SV1194 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV140 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV565 @ SV910 @ SV1194 @ ( tc_fun @ SV1415 @ tc_bool ) ) @ SV1415 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3722]) ).
thf(3938,plain,
! [SV1649: $i,SV1571: $i,SV1417: $i,SV1197: $i,SV915: $i,SV570: $i,SV146: $i] :
( ( ! [SY5168: $i,SY5169: $i,SY5170: $i,SY5171: $i] :
( ( c_Com_Ocom_Ocom__case @ SV146 @ SV570 @ SV915 @ SV1197 @ SV1417 @ SV1571 @ SV1649 @ SY5168 @ ( c_Com_Ocom_OSemi @ SY5169 @ SY5170 ) @ SY5171 )
= ( hAPP @ ( hAPP @ SV1197 @ SY5169 ) @ SY5170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3723]) ).
thf(3939,plain,
! [SV1650: $i,SV1572: $i,SV1419: $i,SV1199: $i,SV918: $i,SV573: $i,SV149: $i] :
( ( ! [SY5172: $i,SY5173: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV149 @ ( hAPP @ SV573 @ SV918 ) ) @ SV1199 ) )
| ~ ( hBOOL @ ( c_in @ SV1199 @ SV918 @ SV1419 ) )
| ! [SY5174: $i,SY5175: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV573 @ SV1572 @ SV149 @ SV1650 @ SY5172 @ SY5173 @ SY5174 @ SY5175 @ SV1419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3725]) ).
thf(3940,plain,
! [SV1651: $i,SV1573: $i,SV1420: $i,SV1200: $i,SV919: $i,SV574: $i,SV150: $i] :
( ( ! [SY5176: $i,SY5177: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV150 @ SV574 ) @ ( hAPP @ SV919 @ SV1200 ) ) )
| ~ ( hBOOL @ ( c_in @ SV574 @ SV1200 @ SV1420 ) )
| ! [SY5178: $i,SY5179: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1573 @ SV919 @ SV150 @ SV1651 @ SY5176 @ SY5177 @ SY5178 @ SY5179 @ SV1420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3726]) ).
thf(3941,plain,
! [SV1207: $i,SV928: $i,SV164: $i,SV1426: $i,SV1652: $i,SV582: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV582 @ SV1652 ) @ SV1426 ) )
| ~ ( hBOOL @ ( c_in @ SV1652 @ SV164 @ SV928 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV164 @ SV582 @ SV928 @ ( tc_fun @ SV1207 @ tc_bool ) ) @ SV1426 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3729]) ).
thf(3942,plain,
! [SV1208: $i,SV929: $i,SV165: $i,SV1427: $i,SV1653: $i,SV583: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV583 @ SV1653 ) @ SV1427 ) )
| ~ ( hBOOL @ ( c_in @ SV1653 @ SV165 @ SV929 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV165 @ SV583 @ SV929 @ ( tc_fun @ SV1208 @ tc_bool ) ) @ SV1427 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3730]) ).
thf(3943,plain,
! [SV1654: $i,SV934: $i,SV589: $i,SV171: $i,SV1574: $i] :
( ( ( hBOOL @ ( c_in @ ( hAPP @ SV1574 @ SV171 ) @ ( c_Set_Oimage @ SV1574 @ SV589 @ SV934 @ SV1654 ) @ SV1654 ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV171 @ SV589 @ SV934 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3734]) ).
thf(3944,plain,
! [SV1655: $i,SV935: $i,SV590: $i,SV172: $i,SV1575: $i] :
( ( ( hBOOL @ ( c_in @ ( hAPP @ SV1575 @ SV172 ) @ ( c_Set_Oimage @ SV1575 @ SV590 @ SV935 @ SV1655 ) @ SV1655 ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV172 @ SV590 @ SV935 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3735]) ).
thf(3945,plain,
! [SV1576: $i,SV173: $i,SV1214: $i,SV936: $i,SV591: $i] :
( ( ( hBOOL @ ( c_in @ SV591 @ SV936 @ SV1214 ) )
= $false )
| ( ( hBOOL @ ( c_in @ ( hAPP @ SV173 @ SV591 ) @ ( c_Set_Oimage @ SV173 @ SV936 @ SV1214 @ SV1576 ) @ SV1576 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3736]) ).
thf(3946,plain,
! [SV1577: $i,SV174: $i,SV1215: $i,SV937: $i,SV592: $i] :
( ( ( hBOOL @ ( c_in @ SV592 @ SV937 @ SV1215 ) )
= $false )
| ( ( hBOOL @ ( c_in @ ( hAPP @ SV174 @ SV592 ) @ ( c_Set_Oimage @ SV174 @ SV937 @ SV1215 @ SV1577 ) @ SV1577 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3737]) ).
thf(3947,plain,
! [SV180: $i,SV1578: $i,SV942: $i,SV598: $i] :
( ( ( c_lessequals @ ( hAPP @ SV598 @ SV942 ) @ ( hAPP @ SV1578 @ SV942 ) @ SV180 )
= $true )
| ( ( ! [SY5075: $i] :
~ ( c_lessequals @ SV598 @ SV1578 @ ( tc_fun @ SY5075 @ SV180 ) ) )
= $true )
| ( ( class_HOL_Oord @ SV180 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3742]) ).
thf(3948,plain,
! [SV184: $i,SV1579: $i,SV1221: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1221 @ SV1579 @ SV184 )
= ( c_Orderings_Obot__class_Obot @ SV184 ) )
= $false )
| ( ( SV1221
= ( c_Orderings_Obot__class_Obot @ SV184 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3743]) ).
thf(3949,plain,
! [SV185: $i,SV1432: $i,SV1222: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1222 @ SV1432 @ SV185 )
= ( c_Orderings_Obot__class_Obot @ SV185 ) )
= $false )
| ( ( SV1432
= ( c_Orderings_Obot__class_Obot @ SV185 ) )
= $true )
| ( ( class_Lattices_Obounded__lattice @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3744]) ).
thf(3950,plain,
! [SV1656: $i,SV1580: $i,SV1434: $i,SV1223: $i,SV944: $i,SV600: $i,SV188: $i] :
( ( ( ( hAPP @ SV188 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_bool ) ) )
= SV944 )
| ! [SY5180: $i,SY5181: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV188 @ SV1223 @ SV1434 @ SV1580 @ SV1656 @ SY5180 @ SY5181 @ SV944 @ SV600 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3746]) ).
thf(3951,plain,
! [SV1657: $i,SV1581: $i,SV1435: $i,SV1224: $i,SV945: $i,SV601: $i,SV189: $i] :
( ( ( ( hAPP @ SV189 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV601 @ tc_bool ) ) )
= SV945 )
| ! [SY5182: $i,SY5183: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1224 @ SV189 @ SV1435 @ SV1581 @ SV1657 @ SY5182 @ SV945 @ SY5183 @ SV601 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3747]) ).
thf(3952,plain,
! [SV624: $i,SV1229: $i,SV955: $i,SV215: $i] :
( ( ( c_lessequals @ SV215 @ SV955 @ ( tc_fun @ SV1229 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV215 @ ( c_Set_Oinsert @ SV624 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1229 @ tc_bool ) ) @ SV1229 ) @ ( tc_fun @ SV1229 @ tc_bool ) ) @ SV955 @ ( tc_fun @ SV1229 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV215 @ ( c_Set_Oinsert @ SV624 @ SV955 @ SV1229 ) @ ( tc_fun @ SV1229 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3752]) ).
thf(3953,plain,
! [SV1658: $i,SV1582: $i,SV1441: $i,SV1234: $i,SV961: $i,SV630: $i,SV221: $i] :
( ( ! [SY5184: $i,SY5185: $i] :
( ( ( hAPP @ SV221 @ ( c_Set_Oinsert @ SV630 @ SV961 @ SV1234 ) )
= ( hAPP @ ( hAPP @ SV1441 @ SV630 ) @ ( hAPP @ SV221 @ SV961 ) ) )
| ! [SY5186: $i,SY5187: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV221 @ SV1582 @ SV1658 @ SY5184 @ SV1441 @ SY5185 @ SY5186 @ SY5187 @ SV1234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3756]) ).
thf(3954,plain,
! [SV1659: $i,SV1583: $i,SV1442: $i,SV1235: $i,SV962: $i,SV631: $i,SV222: $i] :
( ( ! [SY5188: $i,SY5189: $i] :
( ( ( hAPP @ SV222 @ ( c_Set_Oinsert @ SV631 @ SV962 @ SV1235 ) )
= ( hAPP @ ( hAPP @ SV1442 @ SV631 ) @ ( hAPP @ SV222 @ SV962 ) ) )
| ! [SY5190: $i,SY5191: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1583 @ SV222 @ SV1659 @ SY5188 @ SY5189 @ SV1442 @ SY5190 @ SY5191 @ SV1235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3757]) ).
thf(3955,plain,
! [SV963: $i,SV632: $i,SV1443: $i,SV223: $i] :
( ( ( hBOOL @ ( c_in @ SV223 @ ( c_Set_Oinsert @ SV1443 @ SV632 @ SV963 ) @ SV963 ) )
= $false )
| ( ( SV223 = SV1443 )
= $true )
| ( ( hBOOL @ ( c_in @ SV223 @ SV632 @ SV963 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3758]) ).
thf(3956,plain,
! [SV641: $i,SV972: $i,SV1239: $i,SV232: $i] :
( ( ( hBOOL @ ( c_in @ SV232 @ SV1239 @ SV972 ) )
= $true )
| ( ( ( SV641 = SV1239 )
| ( hBOOL @ ( c_in @ SV232 @ SV641 @ SV972 ) ) )
= $true )
| ( ( ( c_Set_Oinsert @ SV232 @ SV641 @ SV972 )
= ( c_Set_Oinsert @ SV232 @ SV1239 @ SV972 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3761]) ).
thf(3957,plain,
! [SV1445: $i,SV1240: $i,SV974: $i,SV643: $i,SV234: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV234 @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV643 ) @ SV974 @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ SV1240 @ tc_Com_Opname @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SV1445 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV643 ) @ SV974 @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ SV1240 @ tc_Com_Opname @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SV1445 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SV643 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV234 @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV643 ) @ SV974 @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) ) @ SV1240 @ tc_Com_Opname @ ( tc_fun @ SV643 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SV1445 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV643 ) ) @ SV643 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3762]) ).
thf(3958,plain,
! [SV1244: $i,SV241: $i,SV980: $i,SV649: $i,SV1446: $i] :
( ( ( ~ ( c_lessequals @ SV1446 @ SV649 @ ( tc_fun @ SV980 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV241 @ SV1244 @ ( tc_fun @ SV980 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV241 @ SV649 @ ( tc_fun @ SV980 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1244 @ SV1446 @ ( tc_fun @ SV980 @ tc_bool ) ) @ ( tc_fun @ SV980 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3764]) ).
thf(3959,plain,
! [SV1245: $i,SV981: $i,SV242: $i,SV650: $i,SV1584: $i] :
( ( ( hBOOL @ ( hAPP @ SV1584 @ SV650 ) )
= $true )
| ( ( ! [SY5092: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV1584 @ SY5092 @ SV242 ) @ SV650 @ SV981 @ SV1245 ) )
= $true )
| ( ( c_Natural_Oevaln @ SV242 @ SV650 @ SV981 @ SV1245 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3765]) ).
thf(3960,plain,
! [SV1585: $i,SV1447: $i,SV1246: $i,SV982: $i,SV651: $i,SV243: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV243 @ SV651 @ SV982 ) @ SV1246 @ SV1447 @ SV1585 )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ SV982 @ SV1246 @ SV1447 @ SV1585 )
| ( hBOOL @ ( hAPP @ SV243 @ SV1246 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3766]) ).
thf(3961,plain,
! [SV1248: $i,SV653: $i,SV246: $i] :
( ( ( c_lessequals @ SV246 @ SV653 @ ( tc_fun @ SV1248 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV653 @ SV246 @ ( tc_fun @ SV1248 @ tc_bool ) )
= $false )
| ( ( SV246 = SV653 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3768]) ).
thf(3962,plain,
! [SV654: $i,SV247: $i,SV1449: $i,SV1249: $i] :
( ( ( c_Natural_Oevalc @ SV1249 @ SV1449 @ SV247 )
= $false )
| ( ( ~ ( c_Natural_Oevalc @ SV1249 @ SV1449 @ SV654 ) )
= $true )
| ( ( SV247 = SV654 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3769]) ).
thf(3963,plain,
! [SV1250: $i,SV655: $i,SV248: $i] :
( ( ( c_lessequals @ SV248 @ SV655 @ ( tc_fun @ SV1250 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV655 @ SV248 @ ( tc_fun @ SV1250 @ tc_bool ) )
= $false )
| ( ( SV248 = SV655 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3770]) ).
thf(3964,plain,
! [SV249: $i,SV1251: $i,SV1450: $i] :
( ( ( ~ ( c_lessequals @ SV1450 @ SV1251 @ SV249 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1251 @ SV1450 @ SV249 ) )
= $true )
| ( ( SV1251 = SV1450 )
= $true )
| ( ( class_Orderings_Oorder @ SV249 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3771]) ).
thf(3965,plain,
! [SV250: $i,SV1252: $i,SV1451: $i] :
( ( ( ~ ( c_lessequals @ SV1451 @ SV1252 @ SV250 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1252 @ SV1451 @ SV250 ) )
= $true )
| ( ( SV1252 = SV1451 )
= $true )
| ( ( class_Orderings_Oorder @ SV250 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3772]) ).
thf(3966,plain,
! [SV251: $i,SV1452: $i,SV1253: $i] :
( ( ( ~ ( c_lessequals @ SV1253 @ SV1452 @ SV251 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1452 @ SV1253 @ SV251 ) )
= $true )
| ( ( SV1253 = SV1452 )
= $true )
| ( ( class_Orderings_Oorder @ SV251 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3773]) ).
thf(3967,plain,
! [SV252: $i,SV1453: $i,SV1254: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1254 @ SV1453 @ SV252 ) @ ( c_HOL_Ozero__class_Ozero @ SV252 ) @ SV252 )
= $false )
| ( ( c_lessequals @ SV1254 @ SV1453 @ SV252 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3774]) ).
thf(3968,plain,
! [SV253: $i,SV1454: $i,SV1255: $i] :
( ( ( c_lessequals @ SV1255 @ SV1454 @ SV253 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV1255 @ SV1454 @ SV253 ) @ ( c_HOL_Ozero__class_Ozero @ SV253 ) @ SV253 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV253 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3775]) ).
thf(3969,plain,
! [SV255: $i,SV1256: $i,SV1455: $i] :
( ( ( c_lessequals @ SV1455 @ SV1256 @ SV255 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1256 @ SV1455 @ SV255 )
= SV1256 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV255 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3776]) ).
thf(3970,plain,
! [SV256: $i,SV1456: $i,SV1257: $i] :
( ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1257 @ SV1456 @ SV256 )
= SV1456 )
= $false )
| ( ( c_lessequals @ SV1257 @ SV1456 @ SV256 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV256 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3777]) ).
thf(3971,plain,
! [SV257: $i,SV1457: $i,SV1258: $i] :
( ( ( c_lessequals @ SV1258 @ SV1457 @ SV257 )
= $false )
| ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ SV1258 @ SV1457 @ SV257 )
= SV1457 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV257 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3778]) ).
thf(3972,plain,
! [SV264: $i,SV661: $i,SV988: $i,SV1660: $i,SV1458: $i,SV1259: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV1259 @ SV1458 @ SV1660 @ SV988 )
| ! [SY5192: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY5192 @ SV661 ) @ SV1458 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ SV1660 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY5192 ) @ SV1259 ) @ SV264 ) @ t_a ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV264 @ SV661 ) @ SV988 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3779]) ).
thf(3973,plain,
! [SV989: $i,SV662: $i,SV265: $i,SV1661: $i,SV1459: $i] :
( ( ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV1459 @ SV1661 @ SV265 ) @ SV662 @ SV989 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1459 @ SV662 ) )
= $true )
| ( ( c_Natural_Oevalc @ SV265 @ SV662 @ SV989 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3780]) ).
thf(3974,plain,
! [SV663: $i,SV266: $i,SV1460: $i,SV1260: $i,SV990: $i] :
( ( ( ~ ( c_Natural_Oevalc @ SV990 @ SV1260 @ SV1460 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV266 @ SV1260 ) )
= $true )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV266 @ SV663 @ SV990 ) @ SV1260 @ SV1460 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3781]) ).
thf(3975,plain,
! [SV270: $i,SV1262: $i,SV1462: $i] :
( ( ( hBOOL @ ( c_in @ SV1462 @ SV1262 @ SV270 ) )
= $false )
| ( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ SV1262 @ SV270 ) @ SV1462 @ SV270 )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV270 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3782]) ).
thf(3976,plain,
! [SV1464: $i,SV1264: $i,SV272: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV272 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1264 @ SV1464 @ SV272 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1264 @ SV1464 @ SV272 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3784]) ).
thf(3977,plain,
! [SV1662: $i,SV1586: $i,SV1465: $i,SV1265: $i,SV994: $i,SV665: $i,SV273: $i] :
( ( ! [SY5193: $i,SY5194: $i,SY5195: $i,SY5196: $i,SY5197: $i] :
( ( c_Com_Ocom_Ocom__case @ SV273 @ SV665 @ SV994 @ SV1265 @ SV1465 @ SV1586 @ SV1662 @ SY5193 @ ( c_Com_Ocom_OLocal @ SY5194 @ SY5195 @ SY5196 ) @ SY5197 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV994 @ SY5194 ) @ SY5195 ) @ SY5196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3785]) ).
thf(3978,plain,
! [SV1663: $i,SV1587: $i,SV1466: $i,SV1266: $i,SV995: $i,SV666: $i,SV274: $i] :
( ( ! [SY5198: $i,SY5199: $i,SY5200: $i,SY5201: $i] :
( ( c_Com_Ocom_Ocom__case @ SV274 @ SV666 @ SV995 @ SV1266 @ SV1466 @ SV1587 @ SV1663 @ SY5198 @ ( c_Com_Ocom_OWhile @ SY5199 @ SY5200 ) @ SY5201 )
= ( hAPP @ ( hAPP @ SV1587 @ SY5199 ) @ SY5200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3786]) ).
thf(3979,plain,
! [SV1267: $i,SV275: $i,SV996: $i,SV1467: $i,SV667: $i] :
( ( ( ~ ( c_lessequals @ SV667 @ SV1467 @ ( tc_fun @ SV996 @ tc_bool ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV275 @ SV1267 @ ( tc_fun @ SV996 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV275 @ SV667 @ ( tc_fun @ SV996 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1267 @ SV1467 @ ( tc_fun @ SV996 @ tc_bool ) ) @ ( tc_fun @ SV996 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3787]) ).
thf(3980,plain,
! [SV1664: $i,SV1588: $i,SV1468: $i,SV1268: $i,SV997: $i,SV668: $i,SV276: $i] :
( ( ( c_Fun_Ocomp @ SV276 @ ( c_Fun_Ocomp @ SV668 @ SV997 @ SV1268 @ SV1468 @ SV1588 ) @ SV1468 @ SV1664 @ SV1588 )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ SV276 @ SV668 @ SV1468 @ SV1664 @ SV1268 ) @ SV997 @ SV1268 @ SV1664 @ SV1588 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3788]) ).
thf(3981,plain,
! [SV279: $i,SV999: $i,SV1270: $i,SV671: $i] :
( ( ( c_lessequals @ SV671 @ SV1270 @ ( tc_fun @ SV999 @ tc_bool ) )
= $false )
| ( ( ~ ( hBOOL @ ( c_in @ SV279 @ SV1270 @ SV999 ) ) )
= $true )
| ( ( c_lessequals @ ( c_Set_Oinsert @ SV279 @ SV671 @ SV999 ) @ SV1270 @ ( tc_fun @ SV999 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3789]) ).
thf(3982,plain,
! [SV1590: $i,SV1470: $i,SV1272: $i,SV1001: $i,SV673: $i,SV281: $i] :
( ( ( ( c_Com_Ocom_OLocal @ SV281 @ SV673 @ SV1001 )
!= ( c_Com_Ocom_OLocal @ SV1272 @ SV1470 @ SV1590 ) )
= $true )
| ( ( SV1001 = SV1590 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3791]) ).
thf(3983,plain,
! [SV1665: $i,SV1471: $i,SV1273: $i,SV1002: $i,SV674: $i,SV282: $i] :
( ( ( ( c_Com_Ocom_OLocal @ SV282 @ SV674 @ SV1002 )
!= ( c_Com_Ocom_OLocal @ SV1273 @ SV1471 @ SV1665 ) )
= $true )
| ( ( SV674 = SV1471 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3792]) ).
thf(3984,plain,
! [SV1666: $i,SV1591: $i,SV1274: $i,SV1003: $i,SV675: $i,SV283: $i] :
( ( ( ( c_Com_Ocom_OLocal @ SV283 @ SV675 @ SV1003 )
!= ( c_Com_Ocom_OLocal @ SV1274 @ SV1591 @ SV1666 ) )
= $true )
| ( ( SV283 = SV1274 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3793]) ).
thf(3985,plain,
! [SV1279: $i,SV683: $i,SV1593: $i,SV291: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV291 @ SV1593 ) @ SV683 @ SV1279 )
= $false )
| ( ( SV1279 = SV683 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV291 @ SV683 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3798]) ).
thf(3986,plain,
! [SV1473: $i,SV294: $i,SV684: $i,SV1667: $i] :
( ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1667 @ SV684 @ SV294 ) @ SV1473 @ SV294 ) )
= $true )
| ( ( c_lessequals @ SV684 @ SV1473 @ SV294 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV294 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3799]) ).
thf(3987,plain,
! [SV1474: $i,SV295: $i,SV1668: $i,SV685: $i] :
( ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV685 @ SV1668 @ SV295 ) @ SV1474 @ SV295 ) )
= $true )
| ( ( c_lessequals @ SV685 @ SV1474 @ SV295 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV295 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3800]) ).
thf(3988,plain,
! [SV296: $i,SV1594: $i,SV1475: $i,SV686: $i] :
( ( ( c_lessequals @ SV686 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1475 @ SV1594 @ SV296 ) @ SV296 )
= $true )
| ( ( ~ ( c_lessequals @ SV686 @ SV1594 @ SV296 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV296 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3801]) ).
thf(3989,plain,
! [SV297: $i,SV1669: $i,SV1476: $i,SV687: $i] :
( ( ( c_lessequals @ SV687 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1476 @ SV1669 @ SV297 ) @ SV297 )
= $true )
| ( ( ~ ( c_lessequals @ SV687 @ SV1476 @ SV297 ) )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV297 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3802]) ).
thf(3990,plain,
! [SV1477: $i,SV298: $i,SV688: $i,SV1670: $i] :
( ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1670 @ SV688 @ SV298 ) @ SV1477 @ SV298 ) )
= $true )
| ( ( c_lessequals @ SV688 @ SV1477 @ SV298 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV298 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3803]) ).
thf(3991,plain,
! [SV1478: $i,SV299: $i,SV1671: $i,SV689: $i] :
( ( ( ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV689 @ SV1671 @ SV299 ) @ SV1478 @ SV299 ) )
= $true )
| ( ( c_lessequals @ SV689 @ SV1478 @ SV299 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV299 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3804]) ).
thf(3992,plain,
! [SV1481: $i,SV302: $i,SV1672: $i,SV692: $i] :
( ( ( ~ ( c_lessequals @ SV692 @ SV1672 @ SV302 )
| ~ ( c_lessequals @ SV1672 @ SV1481 @ SV302 ) )
= $true )
| ( ( c_lessequals @ SV692 @ SV1481 @ SV302 )
= $true )
| ( ( class_Orderings_Oorder @ SV302 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3807]) ).
thf(3993,plain,
! [SV693: $i,SV303: $i,SV1482: $i,SV1673: $i] :
( ( ( ~ ( c_lessequals @ SV1673 @ SV1482 @ SV303 )
| ~ ( c_lessequals @ SV693 @ SV1673 @ SV303 ) )
= $true )
| ( ( c_lessequals @ SV693 @ SV1482 @ SV303 )
= $true )
| ( ( class_Orderings_Opreorder @ SV303 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3808]) ).
thf(3994,plain,
! [SV694: $i,SV1012: $i,SV1483: $i,SV304: $i] :
( ( ( hBOOL @ ( c_in @ SV304 @ SV1483 @ SV1012 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1483 @ SV694 @ ( tc_fun @ SV1012 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV304 @ SV694 @ SV1012 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3809]) ).
thf(3995,plain,
! [SV695: $i,SV1013: $i,SV1484: $i,SV305: $i] :
( ( ( hBOOL @ ( c_in @ SV305 @ SV1484 @ SV1013 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1484 @ SV695 @ ( tc_fun @ SV1013 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV305 @ SV695 @ SV1013 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3810]) ).
thf(3996,plain,
! [SV307: $i,SV1014: $i,SV697: $i,SV1485: $i] :
( ( ( c_lessequals @ SV1485 @ SV697 @ ( tc_fun @ SV1014 @ tc_bool ) )
= $false )
| ( ( ~ ( hBOOL @ ( c_in @ SV307 @ SV1485 @ SV1014 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV307 @ SV697 @ SV1014 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3811]) ).
thf(3997,plain,
! [SV698: $i,SV1015: $i,SV1486: $i,SV308: $i] :
( ( ( hBOOL @ ( c_in @ SV308 @ SV1486 @ SV1015 ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1486 @ SV698 @ ( tc_fun @ SV1015 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV308 @ SV698 @ SV1015 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3812]) ).
thf(3998,plain,
! [SV310: $i,SV1016: $i,SV700: $i,SV1487: $i] :
( ( ( c_lessequals @ SV1487 @ SV700 @ ( tc_fun @ SV1016 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV310 @ SV1487 @ ( tc_fun @ SV1016 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV310 @ SV700 @ ( tc_fun @ SV1016 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3813]) ).
thf(3999,plain,
! [SV701: $i,SV1674: $i,SV311: $i,SV1280: $i] :
( ( ( ~ ( c_lessequals @ SV1280 @ SV311 @ ( tc_fun @ SV1674 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1280 @ SV701 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV311 @ SV701 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3814]) ).
thf(4000,plain,
! [SV702: $i,SV1595: $i,SV314: $i,SV1283: $i] :
( ( ( c_lessequals @ SV1283 @ SV314 @ ( tc_fun @ SV1595 @ tc_bool ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV1283 @ SV702 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV314 @ SV702 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3815]) ).
thf(4001,plain,
! [SV317: $i,SV1489: $i,SV1285: $i] :
( ( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1285 @ SV1489 @ SV317 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV317 @ tc_bool ) ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1285 @ SV1489 @ SV317 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV317 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3817]) ).
thf(4002,plain,
! [SV1675: $i,SV1596: $i,SV1490: $i,SV1286: $i,SV1018: $i,SV704: $i,SV318: $i] :
( ( ! [SY5202: $i,SY5203: $i,SY5204: $i,SY5205: $i,SY5206: $i] :
( ( c_Com_Ocom_Ocom__case @ SV318 @ SV704 @ SV1018 @ SV1286 @ SV1490 @ SV1596 @ SV1675 @ SY5202 @ ( c_Com_Ocom_OCond @ SY5203 @ SY5204 @ SY5205 ) @ SY5206 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV1490 @ SY5203 ) @ SY5204 ) @ SY5205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3818]) ).
thf(4003,plain,
! [SV1676: $i,SV1597: $i,SV1491: $i,SV1287: $i,SV1019: $i,SV705: $i,SV319: $i] :
( ( ! [SY5207: $i] :
( ( c_Fun_Ocomp @ SV319 @ SV705 @ SV1019 @ SV1287 @ SV1491 )
!= ( c_Fun_Ocomp @ SV1597 @ SV1676 @ SY5207 @ SV1287 @ SV1491 ) )
| ! [SY5208: $i] :
( ( hAPP @ SV319 @ ( hAPP @ SV705 @ SY5208 ) )
= ( hAPP @ SV1597 @ ( hAPP @ SV1676 @ SY5208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3819]) ).
thf(4004,plain,
! [SV1677: $i,SV1598: $i,SV1492: $i,SV1288: $i,SV1020: $i,SV706: $i,SV320: $i] :
( ( ! [SY5209: $i,SY5210: $i] :
( ( ( hAPP @ SV320 @ ( hAPP @ SV706 @ SV1020 ) )
!= ( hAPP @ SV1288 @ ( hAPP @ SV1492 @ SV1598 ) ) )
| ! [SY5211: $i,SY5212: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV320 @ SV706 @ SV1677 @ SY5209 @ SY5210 ) @ SV1020 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1288 @ SV1492 @ SY5211 @ SY5209 @ SY5212 ) @ SV1598 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3820]) ).
thf(4005,plain,
! [SV1021: $i,SV1678: $i,SV707: $i,SV1599: $i,SV321: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV321 @ SV1599 ) @ SV707 @ SV1678 @ SV1021 ) )
= $true )
| ( ( SV1021 = SV707 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV321 @ SV707 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3821]) ).
thf(4006,plain,
! [SV1023: $i,SV1290: $i,SV710: $i,SV324: $i] :
( ( ( c_lessequals @ SV324 @ SV710 @ ( tc_fun @ SV1290 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1023 @ SV324 @ ( tc_fun @ SV1290 @ tc_bool ) ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV324 @ ( c_HOL_Ominus__class_Ominus @ SV710 @ SV1023 @ ( tc_fun @ SV1290 @ tc_bool ) ) @ ( tc_fun @ SV1290 @ tc_bool ) )
= SV1023 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3822]) ).
thf(4007,plain,
! [SV1679: $i,SV1600: $i,SV325: $i,SV1024: $i,SV711: $i] :
( ( ( ( ( c_HOL_Ominus__class_Ominus @ SV711 @ SV1024 @ SV325 )
!= ( c_HOL_Ominus__class_Ominus @ SV1600 @ SV1679 @ SV325 ) )
| ( c_lessequals @ SV1679 @ SV1600 @ SV325 )
| ~ ( c_lessequals @ SV1024 @ SV711 @ SV325 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3823]) ).
thf(4008,plain,
! [SV1680: $i,SV1601: $i,SV326: $i,SV1025: $i,SV712: $i] :
( ( ( ( ( c_HOL_Ominus__class_Ominus @ SV712 @ SV1025 @ SV326 )
!= ( c_HOL_Ominus__class_Ominus @ SV1601 @ SV1680 @ SV326 ) )
| ( c_lessequals @ SV1025 @ SV712 @ SV326 )
| ~ ( c_lessequals @ SV1680 @ SV1601 @ SV326 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV326 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3824]) ).
thf(4009,plain,
! [SV1291: $i,SV327: $i,SV1026: $i,SV1494: $i,SV713: $i] :
( ( ( c_lessequals @ SV713 @ SV1494 @ ( tc_fun @ SV1026 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Set_Oimage @ SV327 @ SV713 @ SV1026 @ SV1291 ) @ ( c_Set_Oimage @ SV327 @ SV1494 @ SV1026 @ SV1291 ) @ ( tc_fun @ SV1291 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3825]) ).
thf(4010,plain,
! [SV714: $i,SV1681: $i,SV1027: $i,SV328: $i,SV1602: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV1602 @ SV328 @ SV1027 @ SV1681 ) @ ( c_Set_Oimage @ SV1602 @ SV714 @ SV1027 @ SV1681 ) @ ( tc_fun @ SV1681 @ tc_bool ) )
= $true )
| ( ( c_lessequals @ SV328 @ SV714 @ ( tc_fun @ SV1027 @ tc_bool ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3826]) ).
thf(4011,plain,
! [SV329: $i,SV1292: $i,SV1028: $i,SV715: $i,SV1603: $i] :
( ( ( c_Natural_Oevaln @ SV1603 @ SV715 @ SV1028 @ SV1292 )
= $true )
| ( ( ! [SY5124: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SY5124 @ SV1603 @ SV329 ) @ SV715 @ SV1028 @ SV1292 ) )
= $true )
| ( ( c_Natural_Oevaln @ SV329 @ SV715 @ SV1028 @ SV1292 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3827]) ).
thf(4012,plain,
! [SV1604: $i,SV1496: $i,SV1294: $i,SV1030: $i,SV717: $i,SV331: $i] :
( ( ( c_Com_Ocom_OLocal @ SV331 @ SV717 @ SV1030 )
= ( c_Com_Ocom_OCall @ SV1294 @ SV1496 @ SV1604 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3828]) ).
thf(4013,plain,
! [SV1031: $i,SV718: $i,SV332: $i,SV1497: $i,SV1682: $i] :
( ( ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV1682 @ SV1497 @ SV332 ) @ SV718 @ SV1031 ) )
= $true )
| ( ( c_Natural_Oevalc @ SV1497 @ SV718 @ SV1031 )
= $true )
| ( ( c_Natural_Oevalc @ SV332 @ SV718 @ SV1031 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3829]) ).
thf(4014,plain,
! [SV333: $i,SV1498: $i,SV1295: $i] :
( ( ( hBOOL @ ( c_in @ SV1295 @ SV1498 @ SV333 ) )
= $false )
| ( ( c_lessequals @ SV1295 @ ( c_Complete__Lattice_OSup__class_OSup @ SV1498 @ SV333 ) @ SV333 )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV333 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3830]) ).
thf(4015,plain,
! [SV1683: $i,SV1605: $i,SV1500: $i,SV1303: $i,SV1041: $i,SV727: $i,SV345: $i] :
( ( ! [SY5213: $i,SY5214: $i,SY5215: $i] :
( ( c_Com_Ocom_Ocom__case @ SV345 @ SV727 @ SV1041 @ SV1303 @ SV1500 @ SV1605 @ SV1683 @ SY5213 @ ( hAPP @ c_Com_Ocom_OBODY @ SY5214 ) @ SY5215 )
= ( hAPP @ SV1683 @ SY5214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3832]) ).
thf(4016,plain,
! [SV1501: $i,SV1305: $i,SV1043: $i,SV729: $i,SV348: $i] :
( ( ( hBOOL @ ( hAPP @ SV348 @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SV729 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ SV1043 ) @ SV1305 ) @ SV1501 ) @ t_b @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV348 @ ( hAPP @ ( hAPP @ ( hAPP @ SV729 @ SV1043 ) @ SV1305 ) @ SV1501 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3833]) ).
thf(4017,plain,
! [SV1502: $i,SV1306: $i,SV1044: $i,SV730: $i,SV349: $i] :
( ( ( hBOOL @ ( hAPP @ SV349 @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ SV730 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_b ) @ SV1044 ) @ SV1306 ) @ SV1502 ) @ t_b @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV349 @ ( hAPP @ ( hAPP @ ( hAPP @ SV730 @ SV1044 ) @ SV1306 ) @ SV1502 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3834]) ).
thf(4018,plain,
! [SV352: $i,SV1047: $i,SV1505: $i,SV733: $i] :
( ( ( c_lessequals @ SV733 @ SV1505 @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1047 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV352 @ SV1505 @ SV1047 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV352 @ SV733 @ SV1047 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3837]) ).
thf(4019,plain,
! [SV734: $i,SV1048: $i,SV353: $i,SV1506: $i] :
( ( ( c_lessequals @ SV1506 @ SV353 @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1048 ) @ tc_bool ) )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV1506 @ SV734 @ SV1048 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ SV734 @ SV1048 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3838]) ).
thf(4020,plain,
! [SV1507: $i,SV1051: $i,SV737: $i,SV356: $i,SV1684: $i,SV1310: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV1310 @ SV1684 @ tc_Com_Opname ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV356 @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ SV1051 @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ SV1507 @ tc_Com_Opname @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV1684 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ SV1051 @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ SV1507 @ tc_Com_Opname @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV1684 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV737 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV356 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ ( hAPP @ SV1051 @ SV1310 ) ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1310 ) ) @ ( hAPP @ SV1507 @ SV1310 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV737 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3840]) ).
thf(4021,plain,
! [SV1508: $i,SV1311: $i,SV1052: $i,SV739: $i,SV359: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV359 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV739 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1052 @ SV1311 @ SV739 ) ) @ SV1508 ) @ SV1052 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV739 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV739 ) ) @ SV739 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV359 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV739 ) @ SV1052 ) @ ( c_Com_Ocom_OWhile @ SV1311 @ SV1508 ) ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1052 @ ( c_Fun_Ocomp @ c_Not @ SV1311 @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ SV739 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV739 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV739 ) ) @ SV739 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3841]) ).
thf(4022,plain,
! [SV1685: $i,SV1608: $i,SV1509: $i,SV1312: $i,SV1053: $i,SV740: $i,SV360: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ SV1053 ) @ ( c_Com_Ocom_OCond @ SV1312 @ SV1509 @ SV1608 ) ) @ SV1685 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1053 @ ( c_Fun_Ocomp @ c_Not @ SV1312 @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ SV740 ) ) @ SV1608 ) @ SV1685 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1053 @ SV1312 @ SV740 ) ) @ SV1509 ) @ SV1685 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3842]) ).
thf(4023,plain,
! [SV1686: $i,SV1609: $i,SV1510: $i,SV1315: $i,SV1057: $i,SV746: $i,SV368: $i] :
( ( ! [SY5216: $i] :
( ( ( hAPP @ SV368 @ ( c_Set_Oinsert @ SV746 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1057 @ tc_bool ) ) @ SV1057 ) )
= SV746 )
| ! [SY5217: $i,SY5218: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV368 @ SV1315 @ SV1510 @ SV1609 @ SV1686 @ SY5216 @ SY5217 @ SY5218 @ SV1057 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3846]) ).
thf(4024,plain,
! [SV1687: $i,SV1610: $i,SV1511: $i,SV1316: $i,SV1058: $i,SV747: $i,SV369: $i] :
( ( ! [SY5219: $i] :
( ( ( hAPP @ SV369 @ ( c_Set_Oinsert @ SV747 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1058 @ tc_bool ) ) @ SV1058 ) )
= SV747 )
| ! [SY5220: $i,SY5221: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1316 @ SV369 @ SV1511 @ SV1610 @ SV1687 @ SY5219 @ SY5220 @ SY5221 @ SV1058 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3847]) ).
thf(4025,plain,
! [SV1688: $i,SV1611: $i,SV1512: $i,SV1320: $i,SV1061: $i,SV752: $i,SV376: $i] :
( ( ! [SY5222: $i,SY5223: $i] :
( ( ( hAPP @ SV376 @ ( c_Set_Oinsert @ SV752 @ ( c_Set_Oinsert @ SV1061 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1320 @ tc_bool ) ) @ SV1320 ) @ SV1320 ) )
= ( hAPP @ ( hAPP @ SV1512 @ SV752 ) @ SV1061 ) )
| ! [SY5224: $i,SY5225: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV376 @ SV1611 @ SV1688 @ SY5222 @ SV1512 @ SY5223 @ SY5224 @ SY5225 @ SV1320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3848]) ).
thf(4026,plain,
! [SV1689: $i,SV1612: $i,SV1513: $i,SV1321: $i,SV1062: $i,SV753: $i,SV377: $i] :
( ( ! [SY5226: $i,SY5227: $i] :
( ( ( hAPP @ SV377 @ ( c_Set_Oinsert @ SV753 @ ( c_Set_Oinsert @ SV1062 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1321 @ tc_bool ) ) @ SV1321 ) @ SV1321 ) )
= ( hAPP @ ( hAPP @ SV1513 @ SV753 ) @ SV1062 ) )
| ! [SY5228: $i,SY5229: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1612 @ SV377 @ SV1689 @ SY5226 @ SY5227 @ SV1513 @ SY5228 @ SY5229 @ SV1321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3849]) ).
thf(4027,plain,
! [SV1070: $i,SV1329: $i,SV764: $i,SV391: $i,SV1690: $i,SV1515: $i] :
( ( ( ! [SY5230: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV1515 @ SV1690 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV391 @ SV764 @ SV1329 @ SV1070 @ SY5230 @ SV1515 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY5230 @ SV1690 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV391 @ SV764 @ SV1329 @ SV1070 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV391 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY5230 ) @ SV1070 ) @ SV1515 ) @ ( 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 @ SV391 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV764 ) @ SV1070 ) @ SV1329 ) @ ( 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)],[3851]) ).
thf(4028,plain,
! [SV1071: $i,SV392: $i,SV1330: $i,SV765: $i,SV1691: $i,SV1516: $i] :
( ( ( ! [SY5231: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV1516 @ SV1691 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV765 @ SY5231 @ SV1330 @ SV1516 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY5231 @ SV1691 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV765 @ SY5231 @ SV1330 @ SV1516 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV392 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY5231 ) @ SV1071 ) @ SV1516 ) @ ( 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 @ SV392 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV765 ) @ SV1071 ) @ SV1330 ) @ ( 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)],[3852]) ).
thf(4029,plain,
! [SV1072: $i,SV1331: $i,SV766: $i,SV393: $i,SV1692: $i,SV1517: $i] :
( ( ( ! [SY5232: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV1517 @ SV1692 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV393 @ SV766 @ SV1331 @ SV1072 @ SY5232 @ SV1517 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY5232 @ SV1692 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV393 @ SV766 @ SV1331 @ SV1072 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV393 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY5232 ) @ SV1072 ) @ SV1517 ) @ ( 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 @ SV393 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV766 ) @ SV1072 ) @ SV1331 ) @ ( 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)],[3853]) ).
thf(4030,plain,
! [SV1693: $i,SV1613: $i,SV1074: $i,SV768: $i,SV395: $i,SV1333: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1333 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV395 @ SV768 @ SV1333 @ SV1074 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV395 @ SV768 @ SV1333 @ SV1074 @ SV1613 @ SV1693 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV395 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1613 ) @ SV1074 ) @ SV1693 ) @ ( 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 @ SV395 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV768 ) @ SV1074 ) @ SV1333 ) @ ( 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)],[3854]) ).
thf(4031,plain,
! [SV1076: $i,SV770: $i,SV397: $i,SV1335: $i,SV1614: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1614 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SV1335 @ SV1614 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SV1335 @ SV1614 ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV397 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV770 ) @ SV1076 ) @ SV1614 ) @ ( 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 @ SV397 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV770 ) @ SV1076 ) @ SV1335 ) @ ( 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)],[3855]) ).
thf(4032,plain,
! [SV1077: $i,SV398: $i,SV1694: $i,SV1336: $i,SV1615: $i,SV771: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV771 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV771 @ SV1615 @ SV1336 @ SV1694 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV771 @ SV1615 @ SV1336 @ SV1694 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV398 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1615 ) @ SV1077 ) @ SV1694 ) @ ( 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 @ SV398 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV771 ) @ SV1077 ) @ SV1336 ) @ ( 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)],[3856]) ).
thf(4033,plain,
! [SV1337: $i,SV1078: $i,SV399: $i,SV1616: $i,SV772: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV772 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV772 @ SV1616 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV772 @ SV1616 ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV399 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1616 ) @ SV1078 ) @ SV1337 ) @ ( 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 @ SV399 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV772 ) @ SV1078 ) @ SV1337 ) @ ( 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)],[3857]) ).
thf(4034,plain,
! [SV1695: $i,SV1617: $i,SV1079: $i,SV773: $i,SV400: $i,SV1338: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1338 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV400 @ SV773 @ SV1338 @ SV1079 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV400 @ SV773 @ SV1338 @ SV1079 @ SV1617 @ SV1695 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV400 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1617 ) @ SV1079 ) @ SV1695 ) @ ( 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 @ SV400 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV773 ) @ SV1079 ) @ SV1338 ) @ ( 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)],[3858]) ).
thf(4035,plain,
! [SV1339: $i,SV1080: $i,SV401: $i,SV774: $i,SV1618: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1618 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV774 @ SV1618 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV774 @ SV1618 ) ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV401 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1618 ) @ SV1080 ) @ SV1339 ) @ ( 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 @ SV401 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV774 ) @ SV1080 ) @ SV1339 ) @ ( 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)],[3859]) ).
thf(4036,plain,
! [SV1081: $i,SV402: $i,SV1696: $i,SV1619: $i,SV775: $i,SV1340: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1340 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV775 @ SV1619 @ SV1340 @ SV1696 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV775 @ SV1619 @ SV1340 @ SV1696 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV402 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1619 ) @ SV1081 ) @ SV1696 ) @ ( 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 @ SV402 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV775 ) @ SV1081 ) @ SV1340 ) @ ( 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)],[3860]) ).
thf(4037,plain,
! [SV1082: $i,SV776: $i,SV403: $i,SV1620: $i,SV1341: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1341 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SV1341 @ SV1620 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SV1341 @ SV1620 ) ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV403 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV776 ) @ SV1082 ) @ SV1620 ) @ ( 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 @ SV403 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV776 ) @ SV1082 ) @ SV1341 ) @ ( 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)],[3861]) ).
thf(4038,plain,
! [SV1518: $i,SV1343: $i,SV1084: $i,SV778: $i,SV405: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ SV405 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV778 ) @ SV1084 ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV1343 ) ) ) @ SV1518 ) @ SV778 )
= $false )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV405 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV778 ) @ SV1084 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1343 ) ) @ SV1518 ) @ SV778 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3862]) ).
thf(4039,plain,
! [SV1519: $i,SV1344: $i,SV1085: $i,SV779: $i,SV406: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ ( c_Suc @ SV406 ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV779 ) @ SV1085 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1344 ) ) @ SV1519 ) @ SV779 )
= $false )
| ( ( c_Hoare__Mirabelle_Otriple__valid @ SV406 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV779 ) @ SV1085 ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV1344 ) ) ) @ SV1519 ) @ SV779 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3863]) ).
thf(4040,plain,
! [SV1621: $i,SV1520: $i,SV1345: $i,SV1089: $i,SV783: $i,SV410: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SV1089 ) @ ( c_Com_Ocom_OSemi @ SV1345 @ SV1520 ) ) @ SV1621 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 )
= $true )
| ( ( ! [SY5152: $i] :
( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SY5152 ) @ SV1520 ) @ SV1621 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SV1089 ) @ SV1345 ) @ SY5152 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3864]) ).
thf(4041,plain,
! [SV784: $i,SV1346: $i,SV1090: $i,SV411: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV411 @ SV1090 @ SV1346 )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV411 @ ( c_Set_Oinsert @ SV784 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1346 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1346 ) ) @ SV1346 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV411 @ ( c_Set_Oinsert @ SV784 @ SV1090 @ ( tc_Hoare__Mirabelle_Otriple @ SV1346 ) ) @ SV1346 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3865]) ).
thf(4042,plain,
! [SV786: $i,SV1092: $i,SV1521: $i,SV413: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV413 @ SV1521 @ SV1092 )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV1521 @ SV786 @ SV1092 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV413 @ SV786 @ SV1092 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3866]) ).
thf(4043,plain,
! [SV1697: $i,SV1622: $i,SV1522: $i,SV1347: $i,SV1094: $i,SV788: $i,SV415: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV415 ) @ SV788 ) @ SV1094 ) @ SV1347 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV415 ) @ SV1522 ) @ SV1622 ) @ SV1697 ) )
| ( SV1347 = SV1697 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3867]) ).
thf(4044,plain,
! [SV1623: $i,SV1523: $i,SV1348: $i,SV1095: $i,SV789: $i,SV416: $i] :
( ( ( ! [SY5154: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV416 ) @ SV789 ) @ SV1095 ) @ SV1348 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV416 ) @ SV1523 ) @ SV1623 ) @ SY5154 ) ) )
= $true )
| ( ( SV1095 = SV1623 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3868]) ).
thf(4045,plain,
! [SV1698: $i,SV1524: $i,SV1349: $i,SV1096: $i,SV790: $i,SV417: $i] :
( ( ( ! [SY5233: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV417 ) @ SV790 ) @ SV1096 ) @ SV1349 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV417 ) @ SV1524 ) @ SV1698 ) @ SY5233 ) ) )
= $true )
| ( ( SV790 = SV1524 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3869]) ).
thf(4046,plain,
! [SV1525: $i,SV1350: $i,SV1097: $i,SV791: $i,SV418: $i] :
( ( ( ( c_Set_Oinsert @ SV418 @ ( c_Set_Oinsert @ SV791 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1097 @ tc_bool ) ) @ SV1097 ) @ SV1097 )
= ( c_Set_Oinsert @ SV1350 @ ( c_Set_Oinsert @ SV1525 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1097 @ tc_bool ) ) @ SV1097 ) @ SV1097 ) )
= $false )
| ( ( ( SV791 = SV1350 )
| ( SV791 = SV1525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3870]) ).
thf(4047,plain,
! [SV1526: $i,SV1351: $i,SV1098: $i,SV792: $i,SV419: $i] :
( ( ( ( c_Set_Oinsert @ SV419 @ ( c_Set_Oinsert @ SV792 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1098 @ tc_bool ) ) @ SV1098 ) @ SV1098 )
= ( c_Set_Oinsert @ SV1351 @ ( c_Set_Oinsert @ SV1526 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1098 @ tc_bool ) ) @ SV1098 ) @ SV1098 ) )
= $false )
| ( ( ( SV419 = SV1526 )
| ( SV792 = SV1526 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3871]) ).
thf(4048,plain,
! [SV1624: $i,SV1352: $i,SV1099: $i,SV793: $i,SV420: $i] :
( ( ( ( c_Set_Oinsert @ SV420 @ ( c_Set_Oinsert @ SV793 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1099 @ tc_bool ) ) @ SV1099 ) @ SV1099 )
= ( c_Set_Oinsert @ SV1352 @ ( c_Set_Oinsert @ SV1624 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1099 @ tc_bool ) ) @ SV1099 ) @ SV1099 ) )
= $false )
| ( ( ( SV793 = SV1352 )
| ( SV420 = SV1352 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3872]) ).
thf(4049,plain,
! [SV1527: $i,SV1353: $i,SV1100: $i,SV794: $i,SV421: $i] :
( ( ( ( c_Set_Oinsert @ SV421 @ ( c_Set_Oinsert @ SV794 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1100 @ tc_bool ) ) @ SV1100 ) @ SV1100 )
= ( c_Set_Oinsert @ SV1353 @ ( c_Set_Oinsert @ SV1527 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1100 @ tc_bool ) ) @ SV1100 ) @ SV1100 ) )
= $false )
| ( ( ( SV421 = SV1527 )
| ( SV421 = SV1353 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3873]) ).
thf(4050,plain,
! [SV424: $i,SV1528: $i,SV1354: $i,SV1101: $i,SV797: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV797 ) @ SV1101 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1354 ) ) @ SV1528 ) @ SV424 @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) ) @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV797 ) @ SV1101 ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ SV1354 ) ) ) @ SV1528 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) ) @ SV797 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV424 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV797 ) @ SV1101 ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1354 ) ) @ SV1528 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV797 ) ) @ SV797 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3874]) ).
thf(4051,plain,
! [SV798: $i,SV1625: $i,SV425: $i,SV1355: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ SV1355 @ SV425 @ SV1625 ) @ SV798 ) )
= $false )
| ( ( SV1355 = SV798 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV425 @ SV798 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3875]) ).
thf(4052,plain,
! [SV449: $i,SV818: $i,SV1110: $i,SV7: $i] :
( ( ( c_lessequals @ SV7 @ SV1110 @ ( tc_fun @ SV818 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV449 @ SV1110 @ ( tc_fun @ SV818 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV7 @ SV449 @ ( tc_fun @ SV818 @ tc_bool ) ) @ SV1110 @ ( tc_fun @ SV818 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3877]) ).
thf(4053,plain,
! [SV452: $i,SV821: $i,SV1111: $i,SV10: $i] :
( ( ( c_lessequals @ SV10 @ SV1111 @ ( tc_fun @ SV821 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV452 @ SV1111 @ ( tc_fun @ SV821 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV10 @ SV452 @ ( tc_fun @ SV821 @ tc_bool ) ) @ SV1111 @ ( tc_fun @ SV821 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3878]) ).
thf(4054,plain,
! [SV453: $i,SV11: $i,SV1533: $i,SV1363: $i] :
( ( ( ~ ( c_lessequals @ SV1363 @ SV1533 @ SV11 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV453 @ SV1533 @ SV11 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV453 @ SV1363 @ SV11 ) @ SV1533 @ SV11 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3879]) ).
thf(4055,plain,
! [SV454: $i,SV14: $i,SV1534: $i,SV1366: $i] :
( ( ( ~ ( c_lessequals @ SV1366 @ SV1534 @ SV14 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV454 @ SV1534 @ SV14 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV454 @ SV1366 @ SV14 ) @ SV1534 @ SV14 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3880]) ).
thf(4056,plain,
! [SV455: $i,SV15: $i,SV1535: $i,SV1367: $i] :
( ( ( ~ ( c_lessequals @ SV1367 @ SV1535 @ SV15 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV455 @ SV1535 @ SV15 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV455 @ SV1367 @ SV15 ) @ SV1535 @ SV15 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3881]) ).
thf(4057,plain,
! [SV1699: $i,SV1626: $i,SV1536: $i,SV1370: $i,SV1116: $i,SV822: $i,SV456: $i,SV18: $i] :
( ( ! [SY5234: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ SV18 @ SV456 @ ( c_COMBC @ SV822 @ SV1116 @ SV1116 @ tc_bool ) @ ( c_COMBC @ SV1370 @ SV1116 @ SV1116 @ tc_bool ) @ SV1536 @ SV1626 @ SV1699 @ SY5234 @ SV1116 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV456 @ SV18 @ SV822 @ SV1370 @ SV1626 @ SV1536 @ SY5234 @ SV1699 @ SV1116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3882]) ).
thf(4058,plain,
! [SV22: $i,SV1627: $i,SV1537: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1537 @ SV1627 @ SV22 )
!= ( c_HOL_Ozero__class_Ozero @ SV22 ) )
= $true )
| ( ( SV1537 = SV1627 )
= $true )
| ( ( class_Int_Onumber__ring @ SV22 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3883]) ).
thf(4059,plain,
! [SV840: $i,SV42: $i,SV1131: $i,SV1541: $i,SV477: $i] :
( ( ( c_Natural_Oevalc @ SV477 @ SV1541 @ SV1131 )
= $false )
| ( ( ~ ( c_Natural_Oevalc @ SV42 @ SV840 @ SV1541 ) )
= $true )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV42 @ SV477 ) @ SV840 @ SV1131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3895]) ).
thf(4060,plain,
! [SV1542: $i,SV479: $i,SV1700: $i,SV842: $i,SV44: $i] :
( ( ( ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV44 @ SV842 @ SV1700 ) @ SV479 @ SV1542 ) )
= $true )
| ( ( c_Natural_Oevalc @ SV842 @ SV479 @ SV1542 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV44 @ SV479 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3896]) ).
thf(4061,plain,
! [SV843: $i,SV45: $i,SV1380: $i,SV1133: $i,SV480: $i] :
( ( ( c_Natural_Oevalc @ SV480 @ SV1133 @ SV1380 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV45 @ SV1133 ) ) )
= $true )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV45 @ SV480 @ SV843 ) @ SV1133 @ SV1380 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3897]) ).
thf(4062,plain,
! [SV844: $i,SV46: $i,SV1381: $i,SV1134: $i,SV1628: $i,SV481: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV481 @ SV1628 @ SV1134 @ SV1381 ) )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ SV46 @ SV844 @ SV1134 @ SV1628 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV46 @ SV481 ) @ SV844 @ SV1134 @ SV1381 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3898]) ).
thf(4063,plain,
! [SV1543: $i,SV1382: $i,SV47: $i,SV482: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV482 @ SV482 @ SV47 )
= ( c_HOL_Ominus__class_Ominus @ SV1382 @ SV1543 @ SV47 ) )
= $false )
| ( ( SV1382 = SV1543 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3899]) ).
thf(4064,plain,
! [SV1629: $i,SV48: $i,SV1383: $i,SV483: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV483 @ SV1383 @ SV48 )
= ( c_HOL_Ominus__class_Ominus @ SV1629 @ SV1629 @ SV48 ) )
= $false )
| ( ( SV483 = SV1383 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3900]) ).
thf(4065,plain,
! [SV845: $i,SV1135: $i,SV1544: $i,SV484: $i,SV49: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV49 @ SV484 ) @ SV1544 @ SV1135 )
= $false )
| ( ( ~ ( c_Natural_Oevalc @ SV484 @ SV845 @ SV1544 )
| ~ ( hBOOL @ ( hAPP @ SV49 @ SV845 ) ) )
= $true )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV49 @ SV484 ) @ SV845 @ SV1135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3901]) ).
thf(4066,plain,
! [SV846: $i,SV1384: $i,SV1136: $i,SV1630: $i,SV487: $i,SV52: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV52 @ SV487 ) @ SV1630 @ SV1136 @ SV1384 ) )
= $true )
| ( ( ~ ( c_Natural_Oevaln @ SV487 @ SV846 @ SV1136 @ SV1630 )
| ~ ( hBOOL @ ( hAPP @ SV52 @ SV846 ) ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV52 @ SV487 ) @ SV846 @ SV1136 @ SV1384 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3902]) ).
thf(4067,plain,
! [SV62: $i,SV1631: $i,SV1144: $i,SV497: $i,SV853: $i] :
( ( ( c_Natural_Oevaln @ SV853 @ SV497 @ SV1144 @ SV1631 )
= $true )
| ( ( ! [SY5157: $i] :
~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV62 @ SV853 @ SY5157 ) @ SV497 @ SV1144 @ SV1631 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV62 @ SV497 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3903]) ).
thf(4068,plain,
! [SV854: $i,SV63: $i,SV1548: $i,SV1388: $i,SV1145: $i,SV498: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV498 @ SV1145 @ SV1388 @ SV1548 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV63 @ SV1145 ) ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV63 @ SV498 @ SV854 ) @ SV1145 @ SV1388 @ SV1548 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3904]) ).
thf(4069,plain,
! [SV1701: $i,SV1632: $i,SV1549: $i,SV1389: $i,SV1146: $i,SV855: $i,SV499: $i,SV64: $i] :
( ( ! [SY5235: $i,SY5236: $i,SY5237: $i,SY5238: $i] :
( ( c_Com_Ocom_Ocom__case @ SV64 @ SV499 @ SV855 @ SV1146 @ SV1389 @ SV1549 @ SV1632 @ SV1701 @ ( c_Com_Ocom_OCall @ SY5235 @ SY5236 @ SY5237 ) @ SY5238 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV1701 @ SY5235 ) @ SY5236 ) @ SY5237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3905]) ).
thf(4070,plain,
! [SV858: $i,SV1151: $i,SV70: $i,SV1633: $i,SV1551: $i,SV503: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV503 @ SV1551 @ SV1633 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Set_Oimage @ SV70 @ SV1551 @ SV1633 @ SV1151 ) @ SV858 @ ( tc_fun @ SV1151 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ ( hAPP @ SV70 @ SV503 ) @ SV858 @ SV1151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3907]) ).
thf(4071,plain,
! [SV859: $i,SV1152: $i,SV504: $i,SV71: $i] :
( ( ( c_lessequals @ SV71 @ ( c_Set_Oinsert @ SV504 @ SV1152 @ SV859 ) @ ( tc_fun @ SV859 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV504 @ SV71 @ SV859 ) )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV71 @ ( c_Set_Oinsert @ SV504 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV859 @ tc_bool ) ) @ SV859 ) @ ( tc_fun @ SV859 @ tc_bool ) ) @ SV1152 @ ( tc_fun @ SV859 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3908]) ).
thf(4072,plain,
! [SV860: $i,SV1153: $i,SV505: $i,SV72: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV72 @ ( c_Set_Oinsert @ SV505 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1153 @ tc_bool ) ) @ SV1153 ) @ ( tc_fun @ SV1153 @ tc_bool ) ) @ SV860 @ ( tc_fun @ SV1153 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV505 @ SV72 @ SV1153 ) )
= $false )
| ( ( c_lessequals @ SV72 @ ( c_Set_Oinsert @ SV505 @ SV860 @ SV1153 ) @ ( tc_fun @ SV1153 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3909]) ).
thf(4073,plain,
! [SV861: $i,SV1154: $i,SV506: $i,SV73: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV73 @ ( c_Set_Oinsert @ SV506 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1154 @ tc_bool ) ) @ SV1154 ) @ ( tc_fun @ SV1154 @ tc_bool ) ) @ SV861 @ ( tc_fun @ SV1154 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV506 @ SV73 @ SV1154 ) )
= $false )
| ( ( c_lessequals @ SV73 @ ( c_Set_Oinsert @ SV506 @ SV861 @ SV1154 ) @ ( tc_fun @ SV1154 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3910]) ).
thf(4074,plain,
! [SV77: $i,SV1634: $i,SV1553: $i,SV865: $i,SV510: $i] :
( ( ( c_lessequals @ ( hAPP @ SV510 @ SV865 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1553 @ SV510 @ SV1634 @ SV77 ) @ SV77 )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV865 @ SV1553 @ SV1634 ) ) )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3912]) ).
thf(4075,plain,
! [SV1556: $i,SV1395: $i,SV1159: $i,SV869: $i,SV515: $i,SV82: $i] :
( ( ( ( c_Com_Ocom_OCall @ SV82 @ SV515 @ SV869 )
= ( c_Com_Ocom_OCall @ SV1159 @ SV1395 @ SV1556 ) )
= $false )
| ( ( SV869 = SV1556 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3915]) ).
thf(4076,plain,
! [SV1635: $i,SV1396: $i,SV1160: $i,SV870: $i,SV516: $i,SV83: $i] :
( ( ( ( c_Com_Ocom_OCall @ SV83 @ SV516 @ SV870 )
= ( c_Com_Ocom_OCall @ SV1160 @ SV1396 @ SV1635 ) )
= $false )
| ( ( SV516 = SV1396 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3916]) ).
thf(4077,plain,
! [SV1636: $i,SV1557: $i,SV1161: $i,SV871: $i,SV517: $i,SV84: $i] :
( ( ( ( c_Com_Ocom_OCall @ SV84 @ SV517 @ SV871 )
= ( c_Com_Ocom_OCall @ SV1161 @ SV1557 @ SV1636 ) )
= $false )
| ( ( SV84 = SV1161 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3917]) ).
thf(4078,plain,
! [SV880: $i,SV98: $i,SV1168: $i,SV1637: $i,SV528: $i] :
( ( ( ( hAPP @ SV528 @ SV1637 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1168 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1637 @ SV98 @ SV880 ) ) )
= $true )
| ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV98 @ SV528 @ SV880 @ ( tc_fun @ SV1168 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1168 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3918]) ).
thf(4079,plain,
! [SV885: $i,SV1171: $i,SV103: $i,SV1638: $i,SV1560: $i,SV533: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV533 @ SV1560 @ SV1638 ) ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1560 @ SV103 @ SV1638 @ ( tc_fun @ SV1171 @ tc_bool ) ) @ SV885 @ ( tc_fun @ SV1171 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ SV103 @ SV533 ) @ SV885 @ ( tc_fun @ SV1171 @ tc_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3921]) ).
thf(4080,plain,
! [SV1562: $i,SV1406: $i,SV1175: $i,SV889: $i,SV538: $i,SV108: $i] :
( ( ( ( c_Com_Ocom_OCond @ SV108 @ SV538 @ SV889 )
= ( c_Com_Ocom_OCond @ SV1175 @ SV1406 @ SV1562 ) )
= $false )
| ( ( SV889 = SV1562 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3923]) ).
thf(4081,plain,
! [SV1639: $i,SV1407: $i,SV1176: $i,SV890: $i,SV539: $i,SV109: $i] :
( ( ( ( c_Com_Ocom_OCond @ SV109 @ SV539 @ SV890 )
= ( c_Com_Ocom_OCond @ SV1176 @ SV1407 @ SV1639 ) )
= $false )
| ( ( SV539 = SV1407 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3924]) ).
thf(4082,plain,
! [SV1640: $i,SV1563: $i,SV1177: $i,SV891: $i,SV540: $i,SV110: $i] :
( ( ( ( c_Com_Ocom_OCond @ SV110 @ SV540 @ SV891 )
= ( c_Com_Ocom_OCond @ SV1177 @ SV1563 @ SV1640 ) )
= $false )
| ( ( SV110 = SV1177 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3925]) ).
thf(4083,plain,
! [SV1641: $i,SV1565: $i,SV116: $i,SV892: $i,SV541: $i] :
( ( ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV541 @ SV892 @ SV116 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1565 @ SV1641 @ SV116 ) @ ( tc_fun @ SV116 @ tc_bool ) )
= $true )
| ( ( ~ ( c_lessequals @ SV892 @ SV1641 @ SV116 )
| ~ ( c_lessequals @ SV1565 @ SV541 @ SV116 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3926]) ).
thf(4084,plain,
! [SV893: $i,SV117: $i,SV542: $i,SV1642: $i] :
( ( ( ~ ( c_lessequals @ SV1642 @ SV542 @ SV117 ) )
= $true )
| ( ( ! [SY5163: $i] :
~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1642 @ SV542 @ SV117 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY5163 @ SV893 @ SV117 ) @ ( tc_fun @ SV117 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV542 @ SV893 @ SV117 )
= $true )
| ( ( class_Orderings_Oorder @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3927]) ).
thf(4085,plain,
! [SV543: $i,SV118: $i,SV1643: $i,SV894: $i] :
( ( ( ~ ( c_lessequals @ SV894 @ SV1643 @ SV118 ) )
= $true )
| ( ( ! [SY5164: $i] :
~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV894 @ SV1643 @ SV118 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV543 @ SY5164 @ SV118 ) @ ( tc_fun @ SV118 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV543 @ SV894 @ SV118 )
= $true )
| ( ( class_Orderings_Oorder @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3928]) ).
thf(4086,plain,
! [SV1702: $i,SV1644: $i,SV127: $i,SV899: $i,SV552: $i] :
( ( ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV552 @ SV899 @ SV127 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1644 @ SV1702 @ SV127 ) @ ( tc_fun @ SV127 @ tc_bool ) )
= $true )
| ( ( c_lessequals @ SV552 @ SV899 @ SV127 )
= $true )
| ( ( class_Orderings_Oorder @ SV127 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3930]) ).
thf(4087,plain,
! [SV1703: $i,SV1645: $i,SV1570: $i,SV1411: $i,SV1188: $i,SV903: $i,SV557: $i,SV132: $i] :
( ( ! [SY5239: $i] :
( ( c_Com_Ocom_Ocom__case @ SV132 @ SV557 @ SV903 @ SV1188 @ SV1411 @ SV1570 @ SV1645 @ SV1703 @ c_Com_Ocom_OSKIP @ SY5239 )
= SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3933]) ).
thf(4088,plain,
! [SV1190: $i,SV560: $i,SV135: $i,SV1646: $i,SV906: $i] :
( ( ( ( hAPP @ SV906 @ SV1646 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV135 @ tc_bool ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1646 @ SV560 @ SV1190 ) ) )
= $true )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV135 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV560 @ SV906 @ SV1190 @ ( tc_fun @ SV135 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3935]) ).
thf(4089,plain,
! [SV1193: $i,SV564: $i,SV1414: $i,SV1647: $i,SV909: $i,SV139: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV139 @ ( hAPP @ SV909 @ SV1647 ) @ SV1414 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1647 @ SV564 @ SV1193 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV139 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV564 @ SV909 @ SV1193 @ ( tc_fun @ SV1414 @ tc_bool ) ) @ SV1414 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3936]) ).
thf(4090,plain,
! [SV1194: $i,SV565: $i,SV1415: $i,SV1648: $i,SV910: $i,SV140: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV140 @ ( hAPP @ SV910 @ SV1648 ) @ SV1415 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1648 @ SV565 @ SV1194 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV140 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV565 @ SV910 @ SV1194 @ ( tc_fun @ SV1415 @ tc_bool ) ) @ SV1415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3937]) ).
thf(4091,plain,
! [SV1704: $i,SV1649: $i,SV1571: $i,SV1417: $i,SV1197: $i,SV915: $i,SV570: $i,SV146: $i] :
( ( ! [SY5240: $i,SY5241: $i,SY5242: $i] :
( ( c_Com_Ocom_Ocom__case @ SV146 @ SV570 @ SV915 @ SV1197 @ SV1417 @ SV1571 @ SV1649 @ SV1704 @ ( c_Com_Ocom_OSemi @ SY5240 @ SY5241 ) @ SY5242 )
= ( hAPP @ ( hAPP @ SV1197 @ SY5240 ) @ SY5241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3938]) ).
thf(4092,plain,
! [SV1705: $i,SV1650: $i,SV1572: $i,SV1419: $i,SV1199: $i,SV918: $i,SV573: $i,SV149: $i] :
( ( ! [SY5243: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV149 @ ( hAPP @ SV573 @ SV918 ) ) @ SV1199 ) )
| ~ ( hBOOL @ ( c_in @ SV1199 @ SV918 @ SV1419 ) )
| ! [SY5244: $i,SY5245: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV573 @ SV1572 @ SV149 @ SV1650 @ SV1705 @ SY5243 @ SY5244 @ SY5245 @ SV1419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3939]) ).
thf(4093,plain,
! [SV1706: $i,SV1651: $i,SV1573: $i,SV1420: $i,SV1200: $i,SV919: $i,SV574: $i,SV150: $i] :
( ( ! [SY5246: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV150 @ SV574 ) @ ( hAPP @ SV919 @ SV1200 ) ) )
| ~ ( hBOOL @ ( c_in @ SV574 @ SV1200 @ SV1420 ) )
| ! [SY5247: $i,SY5248: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1573 @ SV919 @ SV150 @ SV1651 @ SV1706 @ SY5246 @ SY5247 @ SY5248 @ SV1420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3940]) ).
thf(4094,plain,
! [SV1207: $i,SV928: $i,SV164: $i,SV1426: $i,SV1652: $i,SV582: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV582 @ SV1652 ) @ SV1426 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1652 @ SV164 @ SV928 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV164 @ SV582 @ SV928 @ ( tc_fun @ SV1207 @ tc_bool ) ) @ SV1426 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3941]) ).
thf(4095,plain,
! [SV1208: $i,SV929: $i,SV165: $i,SV1427: $i,SV1653: $i,SV583: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV583 @ SV1653 ) @ SV1427 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1653 @ SV165 @ SV929 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV165 @ SV583 @ SV929 @ ( tc_fun @ SV1208 @ tc_bool ) ) @ SV1427 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3942]) ).
thf(4096,plain,
! [SV942: $i,SV180: $i,SV1707: $i,SV1578: $i,SV598: $i] :
( ( ( ~ ( c_lessequals @ SV598 @ SV1578 @ ( tc_fun @ SV1707 @ SV180 ) ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ SV598 @ SV942 ) @ ( hAPP @ SV1578 @ SV942 ) @ SV180 )
= $true )
| ( ( class_HOL_Oord @ SV180 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3947]) ).
thf(4097,plain,
! [SV1656: $i,SV1580: $i,SV1434: $i,SV1223: $i,SV944: $i,SV600: $i,SV188: $i] :
( ( ( ( hAPP @ SV188 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_bool ) ) )
= SV944 )
= $true )
| ( ( ! [SY5180: $i,SY5181: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV188 @ SV1223 @ SV1434 @ SV1580 @ SV1656 @ SY5180 @ SY5181 @ SV944 @ SV600 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3950]) ).
thf(4098,plain,
! [SV1657: $i,SV1581: $i,SV1435: $i,SV1224: $i,SV945: $i,SV601: $i,SV189: $i] :
( ( ( ( hAPP @ SV189 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV601 @ tc_bool ) ) )
= SV945 )
= $true )
| ( ( ! [SY5182: $i,SY5183: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1224 @ SV189 @ SV1435 @ SV1581 @ SV1657 @ SY5182 @ SV945 @ SY5183 @ SV601 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3951]) ).
thf(4099,plain,
! [SV955: $i,SV1229: $i,SV624: $i,SV215: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV215 @ ( c_Set_Oinsert @ SV624 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1229 @ tc_bool ) ) @ SV1229 ) @ ( tc_fun @ SV1229 @ tc_bool ) ) @ SV955 @ ( tc_fun @ SV1229 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV215 @ SV955 @ ( tc_fun @ SV1229 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV215 @ ( c_Set_Oinsert @ SV624 @ SV955 @ SV1229 ) @ ( tc_fun @ SV1229 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3952]) ).
thf(4100,plain,
! [SV1708: $i,SV1658: $i,SV1582: $i,SV1441: $i,SV1234: $i,SV961: $i,SV630: $i,SV221: $i] :
( ( ! [SY5249: $i] :
( ( ( hAPP @ SV221 @ ( c_Set_Oinsert @ SV630 @ SV961 @ SV1234 ) )
= ( hAPP @ ( hAPP @ SV1441 @ SV630 ) @ ( hAPP @ SV221 @ SV961 ) ) )
| ! [SY5250: $i,SY5251: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV221 @ SV1582 @ SV1658 @ SV1708 @ SV1441 @ SY5249 @ SY5250 @ SY5251 @ SV1234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3953]) ).
thf(4101,plain,
! [SV1709: $i,SV1659: $i,SV1583: $i,SV1442: $i,SV1235: $i,SV962: $i,SV631: $i,SV222: $i] :
( ( ! [SY5252: $i] :
( ( ( hAPP @ SV222 @ ( c_Set_Oinsert @ SV631 @ SV962 @ SV1235 ) )
= ( hAPP @ ( hAPP @ SV1442 @ SV631 ) @ ( hAPP @ SV222 @ SV962 ) ) )
| ! [SY5253: $i,SY5254: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1583 @ SV222 @ SV1659 @ SV1709 @ SY5252 @ SV1442 @ SY5253 @ SY5254 @ SV1235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3954]) ).
thf(4102,plain,
! [SV972: $i,SV232: $i,SV1239: $i,SV641: $i] :
( ( ( SV641 = SV1239 )
= $true )
| ( ( hBOOL @ ( c_in @ SV232 @ SV641 @ SV972 ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV232 @ SV1239 @ SV972 ) )
= $true )
| ( ( ( c_Set_Oinsert @ SV232 @ SV641 @ SV972 )
= ( c_Set_Oinsert @ SV232 @ SV1239 @ SV972 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3956]) ).
thf(4103,plain,
! [SV1244: $i,SV241: $i,SV980: $i,SV649: $i,SV1446: $i] :
( ( ( c_lessequals @ SV1446 @ SV649 @ ( tc_fun @ SV980 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV241 @ SV1244 @ ( tc_fun @ SV980 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV241 @ SV649 @ ( tc_fun @ SV980 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1244 @ SV1446 @ ( tc_fun @ SV980 @ tc_bool ) ) @ ( tc_fun @ SV980 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3958]) ).
thf(4104,plain,
! [SV1245: $i,SV981: $i,SV650: $i,SV242: $i,SV1710: $i,SV1584: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV1584 @ SV1710 @ SV242 ) @ SV650 @ SV981 @ SV1245 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV1584 @ SV650 ) )
= $true )
| ( ( c_Natural_Oevaln @ SV242 @ SV650 @ SV981 @ SV1245 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3959]) ).
thf(4105,plain,
! [SV651: $i,SV243: $i,SV1585: $i,SV1447: $i,SV1246: $i,SV982: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV982 @ SV1246 @ SV1447 @ SV1585 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV243 @ SV1246 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV243 @ SV651 @ SV982 ) @ SV1246 @ SV1447 @ SV1585 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3960]) ).
thf(4106,plain,
! [SV247: $i,SV654: $i,SV1449: $i,SV1249: $i] :
( ( ( c_Natural_Oevalc @ SV1249 @ SV1449 @ SV654 )
= $false )
| ( ( c_Natural_Oevalc @ SV1249 @ SV1449 @ SV247 )
= $false )
| ( ( SV247 = SV654 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3962]) ).
thf(4107,plain,
! [SV249: $i,SV1251: $i,SV1450: $i] :
( ( ( c_lessequals @ SV1450 @ SV1251 @ SV249 )
= $false )
| ( ( ~ ( c_lessequals @ SV1251 @ SV1450 @ SV249 ) )
= $true )
| ( ( SV1251 = SV1450 )
= $true )
| ( ( class_Orderings_Oorder @ SV249 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3964]) ).
thf(4108,plain,
! [SV250: $i,SV1252: $i,SV1451: $i] :
( ( ( c_lessequals @ SV1451 @ SV1252 @ SV250 )
= $false )
| ( ( ~ ( c_lessequals @ SV1252 @ SV1451 @ SV250 ) )
= $true )
| ( ( SV1252 = SV1451 )
= $true )
| ( ( class_Orderings_Oorder @ SV250 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3965]) ).
thf(4109,plain,
! [SV251: $i,SV1452: $i,SV1253: $i] :
( ( ( c_lessequals @ SV1253 @ SV1452 @ SV251 )
= $false )
| ( ( ~ ( c_lessequals @ SV1452 @ SV1253 @ SV251 ) )
= $true )
| ( ( SV1253 = SV1452 )
= $true )
| ( ( class_Orderings_Oorder @ SV251 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3966]) ).
thf(4110,plain,
! [SV264: $i,SV661: $i,SV988: $i,SV1660: $i,SV1458: $i,SV1259: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV1259 @ SV1458 @ SV1660 @ SV988 ) )
= $true )
| ( ( ! [SY5192: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY5192 @ SV661 ) @ SV1458 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ SV1660 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY5192 ) @ SV1259 ) @ SV264 ) @ t_a ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV264 @ SV661 ) @ SV988 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3972]) ).
thf(4111,plain,
! [SV989: $i,SV662: $i,SV265: $i,SV1661: $i,SV1459: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV1459 @ SV1661 @ SV265 ) @ SV662 @ SV989 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1459 @ SV662 ) )
= $true )
| ( ( c_Natural_Oevalc @ SV265 @ SV662 @ SV989 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3973]) ).
thf(4112,plain,
! [SV663: $i,SV266: $i,SV1460: $i,SV1260: $i,SV990: $i] :
( ( ( c_Natural_Oevalc @ SV990 @ SV1260 @ SV1460 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV266 @ SV1260 ) )
= $true )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV266 @ SV663 @ SV990 ) @ SV1260 @ SV1460 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3974]) ).
thf(4113,plain,
! [SV272: $i,SV1464: $i,SV1264: $i] :
( ( ( c_lessequals @ SV1264 @ SV1464 @ SV272 )
= $false )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV272 @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1264 @ SV1464 @ SV272 ) )
= $false )
| ( ( class_Orderings_Oorder @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3976]) ).
thf(4114,plain,
! [SV1711: $i,SV1662: $i,SV1586: $i,SV1465: $i,SV1265: $i,SV994: $i,SV665: $i,SV273: $i] :
( ( ! [SY5255: $i,SY5256: $i,SY5257: $i,SY5258: $i] :
( ( c_Com_Ocom_Ocom__case @ SV273 @ SV665 @ SV994 @ SV1265 @ SV1465 @ SV1586 @ SV1662 @ SV1711 @ ( c_Com_Ocom_OLocal @ SY5255 @ SY5256 @ SY5257 ) @ SY5258 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV994 @ SY5255 ) @ SY5256 ) @ SY5257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3977]) ).
thf(4115,plain,
! [SV1712: $i,SV1663: $i,SV1587: $i,SV1466: $i,SV1266: $i,SV995: $i,SV666: $i,SV274: $i] :
( ( ! [SY5259: $i,SY5260: $i,SY5261: $i] :
( ( c_Com_Ocom_Ocom__case @ SV274 @ SV666 @ SV995 @ SV1266 @ SV1466 @ SV1587 @ SV1663 @ SV1712 @ ( c_Com_Ocom_OWhile @ SY5259 @ SY5260 ) @ SY5261 )
= ( hAPP @ ( hAPP @ SV1587 @ SY5259 ) @ SY5260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3978]) ).
thf(4116,plain,
! [SV1267: $i,SV275: $i,SV996: $i,SV1467: $i,SV667: $i] :
( ( ( c_lessequals @ SV667 @ SV1467 @ ( tc_fun @ SV996 @ tc_bool ) )
= $false )
| ( ( ~ ( c_lessequals @ SV275 @ SV1267 @ ( tc_fun @ SV996 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV275 @ SV667 @ ( tc_fun @ SV996 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1267 @ SV1467 @ ( tc_fun @ SV996 @ tc_bool ) ) @ ( tc_fun @ SV996 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3979]) ).
thf(4117,plain,
! [SV671: $i,SV999: $i,SV1270: $i,SV279: $i] :
( ( ( hBOOL @ ( c_in @ SV279 @ SV1270 @ SV999 ) )
= $false )
| ( ( c_lessequals @ SV671 @ SV1270 @ ( tc_fun @ SV999 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Set_Oinsert @ SV279 @ SV671 @ SV999 ) @ SV1270 @ ( tc_fun @ SV999 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3981]) ).
thf(4118,plain,
! [SV1590: $i,SV1470: $i,SV1272: $i,SV1001: $i,SV673: $i,SV281: $i] :
( ( ( ( c_Com_Ocom_OLocal @ SV281 @ SV673 @ SV1001 )
= ( c_Com_Ocom_OLocal @ SV1272 @ SV1470 @ SV1590 ) )
= $false )
| ( ( SV1001 = SV1590 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3982]) ).
thf(4119,plain,
! [SV1665: $i,SV1471: $i,SV1273: $i,SV1002: $i,SV674: $i,SV282: $i] :
( ( ( ( c_Com_Ocom_OLocal @ SV282 @ SV674 @ SV1002 )
= ( c_Com_Ocom_OLocal @ SV1273 @ SV1471 @ SV1665 ) )
= $false )
| ( ( SV674 = SV1471 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3983]) ).
thf(4120,plain,
! [SV1666: $i,SV1591: $i,SV1274: $i,SV1003: $i,SV675: $i,SV283: $i] :
( ( ( ( c_Com_Ocom_OLocal @ SV283 @ SV675 @ SV1003 )
= ( c_Com_Ocom_OLocal @ SV1274 @ SV1591 @ SV1666 ) )
= $false )
| ( ( SV283 = SV1274 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3984]) ).
thf(4121,plain,
! [SV1473: $i,SV294: $i,SV684: $i,SV1667: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1667 @ SV684 @ SV294 ) @ SV1473 @ SV294 )
= $false )
| ( ( c_lessequals @ SV684 @ SV1473 @ SV294 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3986]) ).
thf(4122,plain,
! [SV1474: $i,SV295: $i,SV1668: $i,SV685: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV685 @ SV1668 @ SV295 ) @ SV1474 @ SV295 )
= $false )
| ( ( c_lessequals @ SV685 @ SV1474 @ SV295 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV295 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3987]) ).
thf(4123,plain,
! [SV1475: $i,SV296: $i,SV1594: $i,SV686: $i] :
( ( ( c_lessequals @ SV686 @ SV1594 @ SV296 )
= $false )
| ( ( c_lessequals @ SV686 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1475 @ SV1594 @ SV296 ) @ SV296 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV296 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3988]) ).
thf(4124,plain,
! [SV1669: $i,SV297: $i,SV1476: $i,SV687: $i] :
( ( ( c_lessequals @ SV687 @ SV1476 @ SV297 )
= $false )
| ( ( c_lessequals @ SV687 @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1476 @ SV1669 @ SV297 ) @ SV297 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV297 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3989]) ).
thf(4125,plain,
! [SV1477: $i,SV298: $i,SV688: $i,SV1670: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1670 @ SV688 @ SV298 ) @ SV1477 @ SV298 )
= $false )
| ( ( c_lessequals @ SV688 @ SV1477 @ SV298 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV298 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3990]) ).
thf(4126,plain,
! [SV1478: $i,SV299: $i,SV1671: $i,SV689: $i] :
( ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV689 @ SV1671 @ SV299 ) @ SV1478 @ SV299 )
= $false )
| ( ( c_lessequals @ SV689 @ SV1478 @ SV299 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV299 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3991]) ).
thf(4127,plain,
! [SV1481: $i,SV302: $i,SV1672: $i,SV692: $i] :
( ( ( ~ ( c_lessequals @ SV692 @ SV1672 @ SV302 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1672 @ SV1481 @ SV302 ) )
= $true )
| ( ( c_lessequals @ SV692 @ SV1481 @ SV302 )
= $true )
| ( ( class_Orderings_Oorder @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3992]) ).
thf(4128,plain,
! [SV693: $i,SV303: $i,SV1482: $i,SV1673: $i] :
( ( ( ~ ( c_lessequals @ SV1673 @ SV1482 @ SV303 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV693 @ SV1673 @ SV303 ) )
= $true )
| ( ( c_lessequals @ SV693 @ SV1482 @ SV303 )
= $true )
| ( ( class_Orderings_Opreorder @ SV303 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3993]) ).
thf(4129,plain,
! [SV304: $i,SV1012: $i,SV694: $i,SV1483: $i] :
( ( ( c_lessequals @ SV1483 @ SV694 @ ( tc_fun @ SV1012 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV304 @ SV1483 @ SV1012 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV304 @ SV694 @ SV1012 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3994]) ).
thf(4130,plain,
! [SV305: $i,SV1013: $i,SV695: $i,SV1484: $i] :
( ( ( c_lessequals @ SV1484 @ SV695 @ ( tc_fun @ SV1013 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV305 @ SV1484 @ SV1013 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV305 @ SV695 @ SV1013 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3995]) ).
thf(4131,plain,
! [SV697: $i,SV1014: $i,SV1485: $i,SV307: $i] :
( ( ( hBOOL @ ( c_in @ SV307 @ SV1485 @ SV1014 ) )
= $false )
| ( ( c_lessequals @ SV1485 @ SV697 @ ( tc_fun @ SV1014 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV307 @ SV697 @ SV1014 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3996]) ).
thf(4132,plain,
! [SV308: $i,SV1015: $i,SV698: $i,SV1486: $i] :
( ( ( c_lessequals @ SV1486 @ SV698 @ ( tc_fun @ SV1015 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV308 @ SV1486 @ SV1015 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV308 @ SV698 @ SV1015 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3997]) ).
thf(4133,plain,
! [SV700: $i,SV1016: $i,SV1487: $i,SV310: $i] :
( ( ( c_lessequals @ SV310 @ SV1487 @ ( tc_fun @ SV1016 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV1487 @ SV700 @ ( tc_fun @ SV1016 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV310 @ SV700 @ ( tc_fun @ SV1016 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3998]) ).
thf(4134,plain,
! [SV701: $i,SV1674: $i,SV311: $i,SV1280: $i] :
( ( ( c_lessequals @ SV1280 @ SV311 @ ( tc_fun @ SV1674 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1280 @ SV701 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV311 @ SV701 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3999]) ).
thf(4135,plain,
! [SV1595: $i,SV314: $i,SV702: $i,SV1283: $i] :
( ( ( hBOOL @ ( hAPP @ SV1283 @ SV702 ) )
= $false )
| ( ( c_lessequals @ SV1283 @ SV314 @ ( tc_fun @ SV1595 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV314 @ SV702 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4000]) ).
thf(4136,plain,
! [SV317: $i,SV1489: $i,SV1285: $i] :
( ( ( c_lessequals @ SV1285 @ SV1489 @ SV317 )
= $false )
| ( ( ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1285 @ SV1489 @ SV317 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV317 @ tc_bool ) ) )
= $false )
| ( ( class_Orderings_Oorder @ SV317 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4001]) ).
thf(4137,plain,
! [SV1713: $i,SV1675: $i,SV1596: $i,SV1490: $i,SV1286: $i,SV1018: $i,SV704: $i,SV318: $i] :
( ( ! [SY5262: $i,SY5263: $i,SY5264: $i,SY5265: $i] :
( ( c_Com_Ocom_Ocom__case @ SV318 @ SV704 @ SV1018 @ SV1286 @ SV1490 @ SV1596 @ SV1675 @ SV1713 @ ( c_Com_Ocom_OCond @ SY5262 @ SY5263 @ SY5264 ) @ SY5265 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV1490 @ SY5262 ) @ SY5263 ) @ SY5264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4002]) ).
thf(4138,plain,
! [SV1676: $i,SV1597: $i,SV1491: $i,SV1287: $i,SV1019: $i,SV705: $i,SV319: $i] :
( ( ( ! [SY5207: $i] :
( ( c_Fun_Ocomp @ SV319 @ SV705 @ SV1019 @ SV1287 @ SV1491 )
!= ( c_Fun_Ocomp @ SV1597 @ SV1676 @ SY5207 @ SV1287 @ SV1491 ) ) )
= $true )
| ( ( ! [SY5208: $i] :
( ( hAPP @ SV319 @ ( hAPP @ SV705 @ SY5208 ) )
= ( hAPP @ SV1597 @ ( hAPP @ SV1676 @ SY5208 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4003]) ).
thf(4139,plain,
! [SV1714: $i,SV1677: $i,SV1598: $i,SV1492: $i,SV1288: $i,SV1020: $i,SV706: $i,SV320: $i] :
( ( ! [SY5266: $i] :
( ( ( hAPP @ SV320 @ ( hAPP @ SV706 @ SV1020 ) )
!= ( hAPP @ SV1288 @ ( hAPP @ SV1492 @ SV1598 ) ) )
| ! [SY5267: $i,SY5268: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV320 @ SV706 @ SV1677 @ SV1714 @ SY5266 ) @ SV1020 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1288 @ SV1492 @ SY5267 @ SV1714 @ SY5268 ) @ SV1598 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4004]) ).
thf(4140,plain,
! [SV1021: $i,SV1678: $i,SV707: $i,SV1599: $i,SV321: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV321 @ SV1599 ) @ SV707 @ SV1678 @ SV1021 )
= $false )
| ( ( SV1021 = SV707 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV321 @ SV707 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4005]) ).
thf(4141,plain,
! [SV710: $i,SV1290: $i,SV324: $i,SV1023: $i] :
( ( ( c_lessequals @ SV1023 @ SV324 @ ( tc_fun @ SV1290 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV324 @ SV710 @ ( tc_fun @ SV1290 @ tc_bool ) )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV324 @ ( c_HOL_Ominus__class_Ominus @ SV710 @ SV1023 @ ( tc_fun @ SV1290 @ tc_bool ) ) @ ( tc_fun @ SV1290 @ tc_bool ) )
= SV1023 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4006]) ).
thf(4142,plain,
! [SV1679: $i,SV1600: $i,SV325: $i,SV1024: $i,SV711: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV711 @ SV1024 @ SV325 )
!= ( c_HOL_Ominus__class_Ominus @ SV1600 @ SV1679 @ SV325 ) )
= $true )
| ( ( ( c_lessequals @ SV1679 @ SV1600 @ SV325 )
| ~ ( c_lessequals @ SV1024 @ SV711 @ SV325 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4007]) ).
thf(4143,plain,
! [SV1680: $i,SV1601: $i,SV326: $i,SV1025: $i,SV712: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV712 @ SV1025 @ SV326 )
!= ( c_HOL_Ominus__class_Ominus @ SV1601 @ SV1680 @ SV326 ) )
= $true )
| ( ( ( c_lessequals @ SV1025 @ SV712 @ SV326 )
| ~ ( c_lessequals @ SV1680 @ SV1601 @ SV326 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV326 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4008]) ).
thf(4144,plain,
! [SV1292: $i,SV1028: $i,SV715: $i,SV329: $i,SV1603: $i,SV1715: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV1715 @ SV1603 @ SV329 ) @ SV715 @ SV1028 @ SV1292 ) )
= $true )
| ( ( c_Natural_Oevaln @ SV1603 @ SV715 @ SV1028 @ SV1292 )
= $true )
| ( ( c_Natural_Oevaln @ SV329 @ SV715 @ SV1028 @ SV1292 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4011]) ).
thf(4145,plain,
! [SV1031: $i,SV718: $i,SV332: $i,SV1497: $i,SV1682: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV1682 @ SV1497 @ SV332 ) @ SV718 @ SV1031 )
= $false )
| ( ( c_Natural_Oevalc @ SV1497 @ SV718 @ SV1031 )
= $true )
| ( ( c_Natural_Oevalc @ SV332 @ SV718 @ SV1031 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4013]) ).
thf(4146,plain,
! [SV1716: $i,SV1683: $i,SV1605: $i,SV1500: $i,SV1303: $i,SV1041: $i,SV727: $i,SV345: $i] :
( ( ! [SY5269: $i,SY5270: $i] :
( ( c_Com_Ocom_Ocom__case @ SV345 @ SV727 @ SV1041 @ SV1303 @ SV1500 @ SV1605 @ SV1683 @ SV1716 @ ( hAPP @ c_Com_Ocom_OBODY @ SY5269 ) @ SY5270 )
= ( hAPP @ SV1683 @ SY5269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4015]) ).
thf(4147,plain,
! [SV733: $i,SV1047: $i,SV1505: $i,SV352: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV352 @ SV1505 @ SV1047 )
= $false )
| ( ( c_lessequals @ SV733 @ SV1505 @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1047 ) @ tc_bool ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV352 @ SV733 @ SV1047 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4018]) ).
thf(4148,plain,
! [SV353: $i,SV1048: $i,SV734: $i,SV1506: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV1506 @ SV734 @ SV1048 )
= $false )
| ( ( c_lessequals @ SV1506 @ SV353 @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1048 ) @ tc_bool ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV353 @ SV734 @ SV1048 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4019]) ).
thf(4149,plain,
! [SV1507: $i,SV1051: $i,SV737: $i,SV356: $i,SV1684: $i,SV1310: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV1310 @ SV1684 @ tc_Com_Opname ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV356 @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ SV1051 @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ SV1507 @ tc_Com_Opname @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV1684 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ SV1051 @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ SV1507 @ tc_Com_Opname @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV1684 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV737 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV356 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ ( hAPP @ SV1051 @ SV1310 ) ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1310 ) ) @ ( hAPP @ SV1507 @ SV1310 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV737 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4020]) ).
thf(4150,plain,
! [SV1685: $i,SV1608: $i,SV1509: $i,SV1312: $i,SV1053: $i,SV740: $i,SV360: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ SV1053 ) @ ( c_Com_Ocom_OCond @ SV1312 @ SV1509 @ SV1608 ) ) @ SV1685 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1053 @ ( c_Fun_Ocomp @ c_Not @ SV1312 @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ SV740 ) ) @ SV1608 ) @ SV1685 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1053 @ SV1312 @ SV740 ) ) @ SV1509 ) @ SV1685 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4022]) ).
thf(4151,plain,
! [SV1717: $i,SV1686: $i,SV1609: $i,SV1510: $i,SV1315: $i,SV1057: $i,SV746: $i,SV368: $i] :
( ( ( ( hAPP @ SV368 @ ( c_Set_Oinsert @ SV746 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1057 @ tc_bool ) ) @ SV1057 ) )
= SV746 )
| ! [SY5271: $i,SY5272: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV368 @ SV1315 @ SV1510 @ SV1609 @ SV1686 @ SV1717 @ SY5271 @ SY5272 @ SV1057 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4023]) ).
thf(4152,plain,
! [SV1718: $i,SV1687: $i,SV1610: $i,SV1511: $i,SV1316: $i,SV1058: $i,SV747: $i,SV369: $i] :
( ( ( ( hAPP @ SV369 @ ( c_Set_Oinsert @ SV747 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1058 @ tc_bool ) ) @ SV1058 ) )
= SV747 )
| ! [SY5273: $i,SY5274: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1316 @ SV369 @ SV1511 @ SV1610 @ SV1687 @ SV1718 @ SY5273 @ SY5274 @ SV1058 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4024]) ).
thf(4153,plain,
! [SV1719: $i,SV1688: $i,SV1611: $i,SV1512: $i,SV1320: $i,SV1061: $i,SV752: $i,SV376: $i] :
( ( ! [SY5275: $i] :
( ( ( hAPP @ SV376 @ ( c_Set_Oinsert @ SV752 @ ( c_Set_Oinsert @ SV1061 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1320 @ tc_bool ) ) @ SV1320 ) @ SV1320 ) )
= ( hAPP @ ( hAPP @ SV1512 @ SV752 ) @ SV1061 ) )
| ! [SY5276: $i,SY5277: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV376 @ SV1611 @ SV1688 @ SV1719 @ SV1512 @ SY5275 @ SY5276 @ SY5277 @ SV1320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4025]) ).
thf(4154,plain,
! [SV1720: $i,SV1689: $i,SV1612: $i,SV1513: $i,SV1321: $i,SV1062: $i,SV753: $i,SV377: $i] :
( ( ! [SY5278: $i] :
( ( ( hAPP @ SV377 @ ( c_Set_Oinsert @ SV753 @ ( c_Set_Oinsert @ SV1062 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1321 @ tc_bool ) ) @ SV1321 ) @ SV1321 ) )
= ( hAPP @ ( hAPP @ SV1513 @ SV753 ) @ SV1062 ) )
| ! [SY5279: $i,SY5280: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1612 @ SV377 @ SV1689 @ SV1720 @ SY5278 @ SV1513 @ SY5279 @ SY5280 @ SV1321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4026]) ).
thf(4155,plain,
! [SV1721: $i,SV1070: $i,SV1329: $i,SV764: $i,SV391: $i,SV1690: $i,SV1515: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1515 @ SV1690 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV391 @ SV764 @ SV1329 @ SV1070 @ SV1721 @ SV1515 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1721 @ SV1690 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV391 @ SV764 @ SV1329 @ SV1070 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV391 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1721 ) @ SV1070 ) @ SV1515 ) @ ( 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 @ SV391 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV764 ) @ SV1070 ) @ SV1329 ) @ ( 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)],[4027]) ).
thf(4156,plain,
! [SV1071: $i,SV392: $i,SV1330: $i,SV1722: $i,SV765: $i,SV1691: $i,SV1516: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1516 @ SV1691 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV765 @ SV1722 @ SV1330 @ SV1516 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1722 @ SV1691 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV765 @ SV1722 @ SV1330 @ SV1516 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV392 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1722 ) @ SV1071 ) @ SV1516 ) @ ( 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 @ SV392 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV765 ) @ SV1071 ) @ SV1330 ) @ ( 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)],[4028]) ).
thf(4157,plain,
! [SV1723: $i,SV1072: $i,SV1331: $i,SV766: $i,SV393: $i,SV1692: $i,SV1517: $i] :
( ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1517 @ SV1692 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV393 @ SV766 @ SV1331 @ SV1072 @ SV1723 @ SV1517 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1723 @ SV1692 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV393 @ SV766 @ SV1331 @ SV1072 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV393 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1723 ) @ SV1072 ) @ SV1517 ) @ ( 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 @ SV393 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV766 ) @ SV1072 ) @ SV1331 ) @ ( 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)],[4029]) ).
thf(4158,plain,
! [SV1693: $i,SV1613: $i,SV1074: $i,SV768: $i,SV395: $i,SV1333: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1333 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV395 @ SV768 @ SV1333 @ SV1074 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV395 @ SV768 @ SV1333 @ SV1074 @ SV1613 @ SV1693 ) ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV395 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1613 ) @ SV1074 ) @ SV1693 ) @ ( 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 @ SV395 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV768 ) @ SV1074 ) @ SV1333 ) @ ( 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)],[4030]) ).
thf(4159,plain,
! [SV1335: $i,SV1614: $i,SV1076: $i,SV770: $i,SV397: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV397 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV770 ) @ SV1076 ) @ SV1614 ) @ ( 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 @ SV1614 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SV1335 @ SV1614 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SV1335 @ SV1614 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV397 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV770 ) @ SV1076 ) @ SV1335 ) @ ( 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)],[4031]) ).
thf(4160,plain,
! [SV1077: $i,SV398: $i,SV1694: $i,SV1336: $i,SV1615: $i,SV771: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV771 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV771 @ SV1615 @ SV1336 @ SV1694 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV771 @ SV1615 @ SV1336 @ SV1694 ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV398 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1615 ) @ SV1077 ) @ SV1694 ) @ ( 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 @ SV398 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV771 ) @ SV1077 ) @ SV1336 ) @ ( 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)],[4032]) ).
thf(4161,plain,
! [SV772: $i,SV1337: $i,SV1078: $i,SV1616: $i,SV399: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV399 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1616 ) @ SV1078 ) @ SV1337 ) @ ( 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 @ SV772 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV772 @ SV1616 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV772 @ SV1616 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV399 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV772 ) @ SV1078 ) @ SV1337 ) @ ( 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)],[4033]) ).
thf(4162,plain,
! [SV1695: $i,SV1617: $i,SV1079: $i,SV773: $i,SV400: $i,SV1338: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1338 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV400 @ SV773 @ SV1338 @ SV1079 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV400 @ SV773 @ SV1338 @ SV1079 @ SV1617 @ SV1695 ) ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV400 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1617 ) @ SV1079 ) @ SV1695 ) @ ( 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 @ SV400 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV773 ) @ SV1079 ) @ SV1338 ) @ ( 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)],[4034]) ).
thf(4163,plain,
! [SV1339: $i,SV1080: $i,SV401: $i,SV774: $i,SV1618: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1618 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV774 @ SV1618 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV774 @ SV1618 ) ) )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV401 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1618 ) @ SV1080 ) @ SV1339 ) @ ( 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 @ SV401 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV774 ) @ SV1080 ) @ SV1339 ) @ ( 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)],[4035]) ).
thf(4164,plain,
! [SV1081: $i,SV402: $i,SV1696: $i,SV1619: $i,SV775: $i,SV1340: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1340 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV775 @ SV1619 @ SV1340 @ SV1696 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV775 @ SV1619 @ SV1340 @ SV1696 ) ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV402 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1619 ) @ SV1081 ) @ SV1696 ) @ ( 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 @ SV402 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV775 ) @ SV1081 ) @ SV1340 ) @ ( 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)],[4036]) ).
thf(4165,plain,
! [SV1082: $i,SV776: $i,SV403: $i,SV1620: $i,SV1341: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1341 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SV1341 @ SV1620 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SV1341 @ SV1620 ) ) )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV403 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV776 ) @ SV1082 ) @ SV1620 ) @ ( 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 @ SV403 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV776 ) @ SV1082 ) @ SV1341 ) @ ( 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)],[4037]) ).
thf(4166,plain,
! [SV1345: $i,SV1089: $i,SV1621: $i,SV1520: $i,SV1724: $i,SV783: $i,SV410: $i] :
( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SV1724 ) @ SV1520 ) @ SV1621 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SV1089 ) @ SV1345 ) @ SV1724 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SV1089 ) @ ( c_Com_Ocom_OSemi @ SV1345 @ SV1520 ) ) @ SV1621 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4040]) ).
thf(4167,plain,
! [SV1090: $i,SV1346: $i,SV784: $i,SV411: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV411 @ ( c_Set_Oinsert @ SV784 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV1346 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV1346 ) ) @ SV1346 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV411 @ SV1090 @ SV1346 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV411 @ ( c_Set_Oinsert @ SV784 @ SV1090 @ ( tc_Hoare__Mirabelle_Otriple @ SV1346 ) ) @ SV1346 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4041]) ).
thf(4168,plain,
! [SV413: $i,SV1092: $i,SV786: $i,SV1521: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV1521 @ SV786 @ SV1092 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV413 @ SV1521 @ SV1092 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV413 @ SV786 @ SV1092 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4042]) ).
thf(4169,plain,
! [SV1697: $i,SV1622: $i,SV1522: $i,SV1347: $i,SV1094: $i,SV788: $i,SV415: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV415 ) @ SV788 ) @ SV1094 ) @ SV1347 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV415 ) @ SV1522 ) @ SV1622 ) @ SV1697 ) )
= $true )
| ( ( SV1347 = SV1697 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4043]) ).
thf(4170,plain,
! [SV1725: $i,SV1623: $i,SV1523: $i,SV1348: $i,SV1095: $i,SV789: $i,SV416: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV416 ) @ SV789 ) @ SV1095 ) @ SV1348 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV416 ) @ SV1523 ) @ SV1623 ) @ SV1725 ) )
= $true )
| ( ( SV1095 = SV1623 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4044]) ).
thf(4171,plain,
! [SV1726: $i,SV1698: $i,SV1524: $i,SV1349: $i,SV1096: $i,SV790: $i,SV417: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV417 ) @ SV790 ) @ SV1096 ) @ SV1349 )
!= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV417 ) @ SV1524 ) @ SV1698 ) @ SV1726 ) )
= $true )
| ( ( SV790 = SV1524 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4045]) ).
thf(4172,plain,
! [SV1097: $i,SV418: $i,SV1525: $i,SV1350: $i,SV791: $i] :
( ( ( SV791 = SV1350 )
= $true )
| ( ( SV791 = SV1525 )
= $true )
| ( ( ( c_Set_Oinsert @ SV418 @ ( c_Set_Oinsert @ SV791 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1097 @ tc_bool ) ) @ SV1097 ) @ SV1097 )
= ( c_Set_Oinsert @ SV1350 @ ( c_Set_Oinsert @ SV1525 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1097 @ tc_bool ) ) @ SV1097 ) @ SV1097 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4046]) ).
thf(4173,plain,
! [SV1351: $i,SV1098: $i,SV792: $i,SV1526: $i,SV419: $i] :
( ( ( SV419 = SV1526 )
= $true )
| ( ( SV792 = SV1526 )
= $true )
| ( ( ( c_Set_Oinsert @ SV419 @ ( c_Set_Oinsert @ SV792 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1098 @ tc_bool ) ) @ SV1098 ) @ SV1098 )
= ( c_Set_Oinsert @ SV1351 @ ( c_Set_Oinsert @ SV1526 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1098 @ tc_bool ) ) @ SV1098 ) @ SV1098 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4047]) ).
thf(4174,plain,
! [SV1624: $i,SV1099: $i,SV420: $i,SV1352: $i,SV793: $i] :
( ( ( SV793 = SV1352 )
= $true )
| ( ( SV420 = SV1352 )
= $true )
| ( ( ( c_Set_Oinsert @ SV420 @ ( c_Set_Oinsert @ SV793 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1099 @ tc_bool ) ) @ SV1099 ) @ SV1099 )
= ( c_Set_Oinsert @ SV1352 @ ( c_Set_Oinsert @ SV1624 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1099 @ tc_bool ) ) @ SV1099 ) @ SV1099 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4048]) ).
thf(4175,plain,
! [SV1100: $i,SV794: $i,SV1353: $i,SV1527: $i,SV421: $i] :
( ( ( SV421 = SV1527 )
= $true )
| ( ( SV421 = SV1353 )
= $true )
| ( ( ( c_Set_Oinsert @ SV421 @ ( c_Set_Oinsert @ SV794 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1100 @ tc_bool ) ) @ SV1100 ) @ SV1100 )
= ( c_Set_Oinsert @ SV1353 @ ( c_Set_Oinsert @ SV1527 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1100 @ tc_bool ) ) @ SV1100 ) @ SV1100 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4049]) ).
thf(4176,plain,
! [SV453: $i,SV11: $i,SV1533: $i,SV1363: $i] :
( ( ( c_lessequals @ SV1363 @ SV1533 @ SV11 )
= $false )
| ( ( ~ ( c_lessequals @ SV453 @ SV1533 @ SV11 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV453 @ SV1363 @ SV11 ) @ SV1533 @ SV11 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4054]) ).
thf(4177,plain,
! [SV454: $i,SV14: $i,SV1534: $i,SV1366: $i] :
( ( ( c_lessequals @ SV1366 @ SV1534 @ SV14 )
= $false )
| ( ( ~ ( c_lessequals @ SV454 @ SV1534 @ SV14 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV454 @ SV1366 @ SV14 ) @ SV1534 @ SV14 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4055]) ).
thf(4178,plain,
! [SV455: $i,SV15: $i,SV1535: $i,SV1367: $i] :
( ( ( c_lessequals @ SV1367 @ SV1535 @ SV15 )
= $false )
| ( ( ~ ( c_lessequals @ SV455 @ SV1535 @ SV15 ) )
= $true )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV455 @ SV1367 @ SV15 ) @ SV1535 @ SV15 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4056]) ).
thf(4179,plain,
! [SV1727: $i,SV1699: $i,SV1626: $i,SV1536: $i,SV1370: $i,SV1116: $i,SV822: $i,SV456: $i,SV18: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV18 @ SV456 @ ( c_COMBC @ SV822 @ SV1116 @ SV1116 @ tc_bool ) @ ( c_COMBC @ SV1370 @ SV1116 @ SV1116 @ tc_bool ) @ SV1536 @ SV1626 @ SV1699 @ SV1727 @ SV1116 )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV456 @ SV18 @ SV822 @ SV1370 @ SV1626 @ SV1536 @ SV1727 @ SV1699 @ SV1116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4057]) ).
thf(4180,plain,
! [SV22: $i,SV1627: $i,SV1537: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1537 @ SV1627 @ SV22 )
= ( c_HOL_Ozero__class_Ozero @ SV22 ) )
= $false )
| ( ( SV1537 = SV1627 )
= $true )
| ( ( class_Int_Onumber__ring @ SV22 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4058]) ).
thf(4181,plain,
! [SV1131: $i,SV477: $i,SV1541: $i,SV840: $i,SV42: $i] :
( ( ( c_Natural_Oevalc @ SV42 @ SV840 @ SV1541 )
= $false )
| ( ( c_Natural_Oevalc @ SV477 @ SV1541 @ SV1131 )
= $false )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ SV42 @ SV477 ) @ SV840 @ SV1131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4059]) ).
thf(4182,plain,
! [SV1542: $i,SV479: $i,SV1700: $i,SV842: $i,SV44: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV44 @ SV842 @ SV1700 ) @ SV479 @ SV1542 )
= $false )
| ( ( c_Natural_Oevalc @ SV842 @ SV479 @ SV1542 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV44 @ SV479 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4060]) ).
thf(4183,plain,
! [SV843: $i,SV1380: $i,SV480: $i,SV1133: $i,SV45: $i] :
( ( ( hBOOL @ ( hAPP @ SV45 @ SV1133 ) )
= $false )
| ( ( c_Natural_Oevalc @ SV480 @ SV1133 @ SV1380 )
= $false )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ SV45 @ SV480 @ SV843 ) @ SV1133 @ SV1380 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4061]) ).
thf(4184,plain,
! [SV844: $i,SV46: $i,SV1381: $i,SV1134: $i,SV1628: $i,SV481: $i] :
( ( ( c_Natural_Oevaln @ SV481 @ SV1628 @ SV1134 @ SV1381 )
= $false )
| ( ( ~ ( c_Natural_Oevaln @ SV46 @ SV844 @ SV1134 @ SV1628 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV46 @ SV481 ) @ SV844 @ SV1134 @ SV1381 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4062]) ).
thf(4185,plain,
! [SV1135: $i,SV49: $i,SV1544: $i,SV845: $i,SV484: $i] :
( ( ( ~ ( c_Natural_Oevalc @ SV484 @ SV845 @ SV1544 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV49 @ SV845 ) ) )
= $true )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV49 @ SV484 ) @ SV1544 @ SV1135 )
= $false )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV49 @ SV484 ) @ SV845 @ SV1135 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4065]) ).
thf(4186,plain,
! [SV846: $i,SV1384: $i,SV1136: $i,SV1630: $i,SV487: $i,SV52: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV52 @ SV487 ) @ SV1630 @ SV1136 @ SV1384 )
= $false )
| ( ( ~ ( c_Natural_Oevaln @ SV487 @ SV846 @ SV1136 @ SV1630 )
| ~ ( hBOOL @ ( hAPP @ SV52 @ SV846 ) ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV52 @ SV487 ) @ SV846 @ SV1136 @ SV1384 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4066]) ).
thf(4187,plain,
! [SV1631: $i,SV1144: $i,SV497: $i,SV1728: $i,SV853: $i,SV62: $i] :
( ( ( ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV62 @ SV853 @ SV1728 ) @ SV497 @ SV1144 @ SV1631 ) )
= $true )
| ( ( c_Natural_Oevaln @ SV853 @ SV497 @ SV1144 @ SV1631 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV62 @ SV497 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4067]) ).
thf(4188,plain,
! [SV854: $i,SV63: $i,SV1548: $i,SV1388: $i,SV1145: $i,SV498: $i] :
( ( ( c_Natural_Oevaln @ SV498 @ SV1145 @ SV1388 @ SV1548 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV63 @ SV1145 ) ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV63 @ SV498 @ SV854 ) @ SV1145 @ SV1388 @ SV1548 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4068]) ).
thf(4189,plain,
! [SV1729: $i,SV1701: $i,SV1632: $i,SV1549: $i,SV1389: $i,SV1146: $i,SV855: $i,SV499: $i,SV64: $i] :
( ( ! [SY5281: $i,SY5282: $i,SY5283: $i] :
( ( c_Com_Ocom_Ocom__case @ SV64 @ SV499 @ SV855 @ SV1146 @ SV1389 @ SV1549 @ SV1632 @ SV1701 @ ( c_Com_Ocom_OCall @ SV1729 @ SY5281 @ SY5282 ) @ SY5283 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV1701 @ SV1729 ) @ SY5281 ) @ SY5282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4069]) ).
thf(4190,plain,
! [SV858: $i,SV1151: $i,SV70: $i,SV1633: $i,SV1551: $i,SV503: $i] :
( ( ( hBOOL @ ( c_in @ SV503 @ SV1551 @ SV1633 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Set_Oimage @ SV70 @ SV1551 @ SV1633 @ SV1151 ) @ SV858 @ ( tc_fun @ SV1151 @ tc_bool ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ ( hAPP @ SV70 @ SV503 ) @ SV858 @ SV1151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4070]) ).
thf(4191,plain,
! [SV77: $i,SV510: $i,SV1634: $i,SV1553: $i,SV865: $i] :
( ( ( hBOOL @ ( c_in @ SV865 @ SV1553 @ SV1634 ) )
= $false )
| ( ( c_lessequals @ ( hAPP @ SV510 @ SV865 ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1553 @ SV510 @ SV1634 @ SV77 ) @ SV77 )
= $true )
| ( ( class_Complete__Lattice_Ocomplete__lattice @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4074]) ).
thf(4192,plain,
! [SV1168: $i,SV528: $i,SV880: $i,SV98: $i,SV1637: $i] :
( ( ( hBOOL @ ( c_in @ SV1637 @ SV98 @ SV880 ) )
= $false )
| ( ( ( hAPP @ SV528 @ SV1637 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1168 @ tc_bool ) ) )
= $true )
| ( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV98 @ SV528 @ SV880 @ ( tc_fun @ SV1168 @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1168 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4078]) ).
thf(4193,plain,
! [SV885: $i,SV1171: $i,SV103: $i,SV1638: $i,SV1560: $i,SV533: $i] :
( ( ( hBOOL @ ( c_in @ SV533 @ SV1560 @ SV1638 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1560 @ SV103 @ SV1638 @ ( tc_fun @ SV1171 @ tc_bool ) ) @ SV885 @ ( tc_fun @ SV1171 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ SV103 @ SV533 ) @ SV885 @ ( tc_fun @ SV1171 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4079]) ).
thf(4194,plain,
! [SV541: $i,SV1565: $i,SV116: $i,SV1641: $i,SV892: $i] :
( ( ( ~ ( c_lessequals @ SV892 @ SV1641 @ SV116 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1565 @ SV541 @ SV116 ) )
= $true )
| ( ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV541 @ SV892 @ SV116 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1565 @ SV1641 @ SV116 ) @ ( tc_fun @ SV116 @ tc_bool ) )
= $true )
| ( ( class_Orderings_Oorder @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4083]) ).
thf(4195,plain,
! [SV893: $i,SV117: $i,SV542: $i,SV1642: $i] :
( ( ( c_lessequals @ SV1642 @ SV542 @ SV117 )
= $false )
| ( ( ! [SY5163: $i] :
~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1642 @ SV542 @ SV117 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SY5163 @ SV893 @ SV117 ) @ ( tc_fun @ SV117 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV542 @ SV893 @ SV117 )
= $true )
| ( ( class_Orderings_Oorder @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4084]) ).
thf(4196,plain,
! [SV543: $i,SV118: $i,SV1643: $i,SV894: $i] :
( ( ( c_lessequals @ SV894 @ SV1643 @ SV118 )
= $false )
| ( ( ! [SY5164: $i] :
~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV894 @ SV1643 @ SV118 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV543 @ SY5164 @ SV118 ) @ ( tc_fun @ SV118 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV543 @ SV894 @ SV118 )
= $true )
| ( ( class_Orderings_Oorder @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4085]) ).
thf(4197,plain,
! [SV1730: $i,SV1703: $i,SV1645: $i,SV1570: $i,SV1411: $i,SV1188: $i,SV903: $i,SV557: $i,SV132: $i] :
( ( ( c_Com_Ocom_Ocom__case @ SV132 @ SV557 @ SV903 @ SV1188 @ SV1411 @ SV1570 @ SV1645 @ SV1703 @ c_Com_Ocom_OSKIP @ SV1730 )
= SV132 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4087]) ).
thf(4198,plain,
! [SV135: $i,SV906: $i,SV1190: $i,SV560: $i,SV1646: $i] :
( ( ( hBOOL @ ( c_in @ SV1646 @ SV560 @ SV1190 ) )
= $false )
| ( ( ( hAPP @ SV906 @ SV1646 )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV135 @ tc_bool ) ) )
= $true )
| ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV135 @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV560 @ SV906 @ SV1190 @ ( tc_fun @ SV135 @ tc_bool ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4088]) ).
thf(4199,plain,
! [SV1193: $i,SV564: $i,SV1414: $i,SV1647: $i,SV909: $i,SV139: $i] :
( ( ( hBOOL @ ( c_in @ SV139 @ ( hAPP @ SV909 @ SV1647 ) @ SV1414 ) )
= $false )
| ( ( ~ ( hBOOL @ ( c_in @ SV1647 @ SV564 @ SV1193 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV139 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV564 @ SV909 @ SV1193 @ ( tc_fun @ SV1414 @ tc_bool ) ) @ SV1414 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4089]) ).
thf(4200,plain,
! [SV1194: $i,SV565: $i,SV1415: $i,SV1648: $i,SV910: $i,SV140: $i] :
( ( ( hBOOL @ ( c_in @ SV140 @ ( hAPP @ SV910 @ SV1648 ) @ SV1415 ) )
= $false )
| ( ( ~ ( hBOOL @ ( c_in @ SV1648 @ SV565 @ SV1194 ) ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV140 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV565 @ SV910 @ SV1194 @ ( tc_fun @ SV1415 @ tc_bool ) ) @ SV1415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4090]) ).
thf(4201,plain,
! [SV1731: $i,SV1704: $i,SV1649: $i,SV1571: $i,SV1417: $i,SV1197: $i,SV915: $i,SV570: $i,SV146: $i] :
( ( ! [SY5284: $i,SY5285: $i] :
( ( c_Com_Ocom_Ocom__case @ SV146 @ SV570 @ SV915 @ SV1197 @ SV1417 @ SV1571 @ SV1649 @ SV1704 @ ( c_Com_Ocom_OSemi @ SV1731 @ SY5284 ) @ SY5285 )
= ( hAPP @ ( hAPP @ SV1197 @ SV1731 ) @ SY5284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4091]) ).
thf(4202,plain,
! [SV1732: $i,SV1705: $i,SV1650: $i,SV1572: $i,SV1419: $i,SV1199: $i,SV918: $i,SV573: $i,SV149: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV149 @ ( hAPP @ SV573 @ SV918 ) ) @ SV1199 ) )
| ~ ( hBOOL @ ( c_in @ SV1199 @ SV918 @ SV1419 ) )
| ! [SY5286: $i,SY5287: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV573 @ SV1572 @ SV149 @ SV1650 @ SV1705 @ SV1732 @ SY5286 @ SY5287 @ SV1419 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4092]) ).
thf(4203,plain,
! [SV1733: $i,SV1706: $i,SV1651: $i,SV1573: $i,SV1420: $i,SV1200: $i,SV919: $i,SV574: $i,SV150: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV150 @ SV574 ) @ ( hAPP @ SV919 @ SV1200 ) ) )
| ~ ( hBOOL @ ( c_in @ SV574 @ SV1200 @ SV1420 ) )
| ! [SY5288: $i,SY5289: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1573 @ SV919 @ SV150 @ SV1651 @ SV1706 @ SV1733 @ SY5288 @ SY5289 @ SV1420 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4093]) ).
thf(4204,plain,
! [SV1207: $i,SV928: $i,SV164: $i,SV1426: $i,SV1652: $i,SV582: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV582 @ SV1652 ) @ SV1426 ) )
= $false )
| ( ( ~ ( hBOOL @ ( c_in @ SV1652 @ SV164 @ SV928 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV164 @ SV582 @ SV928 @ ( tc_fun @ SV1207 @ tc_bool ) ) @ SV1426 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4094]) ).
thf(4205,plain,
! [SV1208: $i,SV929: $i,SV165: $i,SV1427: $i,SV1653: $i,SV583: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV583 @ SV1653 ) @ SV1427 ) )
= $false )
| ( ( ~ ( hBOOL @ ( c_in @ SV1653 @ SV165 @ SV929 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV165 @ SV583 @ SV929 @ ( tc_fun @ SV1208 @ tc_bool ) ) @ SV1427 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4095]) ).
thf(4206,plain,
! [SV942: $i,SV180: $i,SV1707: $i,SV1578: $i,SV598: $i] :
( ( ( c_lessequals @ SV598 @ SV1578 @ ( tc_fun @ SV1707 @ SV180 ) )
= $false )
| ( ( c_lessequals @ ( hAPP @ SV598 @ SV942 ) @ ( hAPP @ SV1578 @ SV942 ) @ SV180 )
= $true )
| ( ( class_HOL_Oord @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4096]) ).
thf(4207,plain,
! [SV600: $i,SV944: $i,SV1734: $i,SV1656: $i,SV1580: $i,SV1434: $i,SV1223: $i,SV188: $i] :
( ( ( ! [SY5290: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV188 @ SV1223 @ SV1434 @ SV1580 @ SV1656 @ SV1734 @ SY5290 @ SV944 @ SV600 ) )
= $true )
| ( ( ( hAPP @ SV188 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_bool ) ) )
= SV944 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4097]) ).
thf(4208,plain,
! [SV601: $i,SV945: $i,SV1735: $i,SV1657: $i,SV1581: $i,SV1435: $i,SV189: $i,SV1224: $i] :
( ( ( ! [SY5291: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1224 @ SV189 @ SV1435 @ SV1581 @ SV1657 @ SV1735 @ SV945 @ SY5291 @ SV601 ) )
= $true )
| ( ( ( hAPP @ SV189 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV601 @ tc_bool ) ) )
= SV945 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4098]) ).
thf(4209,plain,
! [SV1736: $i,SV1708: $i,SV1658: $i,SV1582: $i,SV1441: $i,SV1234: $i,SV961: $i,SV630: $i,SV221: $i] :
( ( ( ( hAPP @ SV221 @ ( c_Set_Oinsert @ SV630 @ SV961 @ SV1234 ) )
= ( hAPP @ ( hAPP @ SV1441 @ SV630 ) @ ( hAPP @ SV221 @ SV961 ) ) )
| ! [SY5292: $i,SY5293: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV221 @ SV1582 @ SV1658 @ SV1708 @ SV1441 @ SV1736 @ SY5292 @ SY5293 @ SV1234 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4100]) ).
thf(4210,plain,
! [SV1737: $i,SV1709: $i,SV1659: $i,SV1583: $i,SV1442: $i,SV1235: $i,SV962: $i,SV631: $i,SV222: $i] :
( ( ( ( hAPP @ SV222 @ ( c_Set_Oinsert @ SV631 @ SV962 @ SV1235 ) )
= ( hAPP @ ( hAPP @ SV1442 @ SV631 ) @ ( hAPP @ SV222 @ SV962 ) ) )
| ! [SY5294: $i,SY5295: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1583 @ SV222 @ SV1659 @ SV1709 @ SV1737 @ SV1442 @ SY5294 @ SY5295 @ SV1235 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4101]) ).
thf(4211,plain,
! [SV649: $i,SV1446: $i,SV980: $i,SV1244: $i,SV241: $i] :
( ( ( c_lessequals @ SV241 @ SV1244 @ ( tc_fun @ SV980 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV1446 @ SV649 @ ( tc_fun @ SV980 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV241 @ SV649 @ ( tc_fun @ SV980 @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ SV1244 @ SV1446 @ ( tc_fun @ SV980 @ tc_bool ) ) @ ( tc_fun @ SV980 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4103]) ).
thf(4212,plain,
! [SV1245: $i,SV981: $i,SV650: $i,SV242: $i,SV1710: $i,SV1584: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV1584 @ SV1710 @ SV242 ) @ SV650 @ SV981 @ SV1245 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV1584 @ SV650 ) )
= $true )
| ( ( c_Natural_Oevaln @ SV242 @ SV650 @ SV981 @ SV1245 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4104]) ).
thf(4213,plain,
! [SV651: $i,SV243: $i,SV1585: $i,SV1447: $i,SV1246: $i,SV982: $i] :
( ( ( c_Natural_Oevaln @ SV982 @ SV1246 @ SV1447 @ SV1585 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV243 @ SV1246 ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV243 @ SV651 @ SV982 ) @ SV1246 @ SV1447 @ SV1585 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4105]) ).
thf(4214,plain,
! [SV249: $i,SV1450: $i,SV1251: $i] :
( ( ( c_lessequals @ SV1251 @ SV1450 @ SV249 )
= $false )
| ( ( c_lessequals @ SV1450 @ SV1251 @ SV249 )
= $false )
| ( ( SV1251 = SV1450 )
= $true )
| ( ( class_Orderings_Oorder @ SV249 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4107]) ).
thf(4215,plain,
! [SV250: $i,SV1451: $i,SV1252: $i] :
( ( ( c_lessequals @ SV1252 @ SV1451 @ SV250 )
= $false )
| ( ( c_lessequals @ SV1451 @ SV1252 @ SV250 )
= $false )
| ( ( SV1252 = SV1451 )
= $true )
| ( ( class_Orderings_Oorder @ SV250 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4108]) ).
thf(4216,plain,
! [SV251: $i,SV1253: $i,SV1452: $i] :
( ( ( c_lessequals @ SV1452 @ SV1253 @ SV251 )
= $false )
| ( ( c_lessequals @ SV1253 @ SV1452 @ SV251 )
= $false )
| ( ( SV1253 = SV1452 )
= $true )
| ( ( class_Orderings_Oorder @ SV251 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4109]) ).
thf(4217,plain,
! [SV264: $i,SV661: $i,SV988: $i,SV1660: $i,SV1458: $i,SV1259: $i] :
( ( ( c_Natural_Oevaln @ SV1259 @ SV1458 @ SV1660 @ SV988 )
= $false )
| ( ( ! [SY5192: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SY5192 @ SV661 ) @ SV1458 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ SV1660 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SY5192 ) @ SV1259 ) @ SV264 ) @ t_a ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV264 @ SV661 ) @ SV988 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4110]) ).
thf(4218,plain,
! [SV1738: $i,SV1711: $i,SV1662: $i,SV1586: $i,SV1465: $i,SV1265: $i,SV994: $i,SV665: $i,SV273: $i] :
( ( ! [SY5296: $i,SY5297: $i,SY5298: $i] :
( ( c_Com_Ocom_Ocom__case @ SV273 @ SV665 @ SV994 @ SV1265 @ SV1465 @ SV1586 @ SV1662 @ SV1711 @ ( c_Com_Ocom_OLocal @ SV1738 @ SY5296 @ SY5297 ) @ SY5298 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV994 @ SV1738 ) @ SY5296 ) @ SY5297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4114]) ).
thf(4219,plain,
! [SV1739: $i,SV1712: $i,SV1663: $i,SV1587: $i,SV1466: $i,SV1266: $i,SV995: $i,SV666: $i,SV274: $i] :
( ( ! [SY5299: $i,SY5300: $i] :
( ( c_Com_Ocom_Ocom__case @ SV274 @ SV666 @ SV995 @ SV1266 @ SV1466 @ SV1587 @ SV1663 @ SV1712 @ ( c_Com_Ocom_OWhile @ SV1739 @ SY5299 ) @ SY5300 )
= ( hAPP @ ( hAPP @ SV1587 @ SV1739 ) @ SY5299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4115]) ).
thf(4220,plain,
! [SV1467: $i,SV667: $i,SV996: $i,SV1267: $i,SV275: $i] :
( ( ( c_lessequals @ SV275 @ SV1267 @ ( tc_fun @ SV996 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV667 @ SV1467 @ ( tc_fun @ SV996 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV275 @ SV667 @ ( tc_fun @ SV996 @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV1267 @ SV1467 @ ( tc_fun @ SV996 @ tc_bool ) ) @ ( tc_fun @ SV996 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4116]) ).
thf(4221,plain,
! [SV1481: $i,SV302: $i,SV1672: $i,SV692: $i] :
( ( ( c_lessequals @ SV692 @ SV1672 @ SV302 )
= $false )
| ( ( ~ ( c_lessequals @ SV1672 @ SV1481 @ SV302 ) )
= $true )
| ( ( c_lessequals @ SV692 @ SV1481 @ SV302 )
= $true )
| ( ( class_Orderings_Oorder @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4127]) ).
thf(4222,plain,
! [SV693: $i,SV303: $i,SV1482: $i,SV1673: $i] :
( ( ( c_lessequals @ SV1673 @ SV1482 @ SV303 )
= $false )
| ( ( ~ ( c_lessequals @ SV693 @ SV1673 @ SV303 ) )
= $true )
| ( ( c_lessequals @ SV693 @ SV1482 @ SV303 )
= $true )
| ( ( class_Orderings_Opreorder @ SV303 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4128]) ).
thf(4223,plain,
! [SV1740: $i,SV1713: $i,SV1675: $i,SV1596: $i,SV1490: $i,SV1286: $i,SV1018: $i,SV704: $i,SV318: $i] :
( ( ! [SY5301: $i,SY5302: $i,SY5303: $i] :
( ( c_Com_Ocom_Ocom__case @ SV318 @ SV704 @ SV1018 @ SV1286 @ SV1490 @ SV1596 @ SV1675 @ SV1713 @ ( c_Com_Ocom_OCond @ SV1740 @ SY5301 @ SY5302 ) @ SY5303 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV1490 @ SV1740 ) @ SY5301 ) @ SY5302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4137]) ).
thf(4224,plain,
! [SV1741: $i,SV1676: $i,SV1597: $i,SV1491: $i,SV1287: $i,SV1019: $i,SV705: $i,SV319: $i] :
( ( ( ( c_Fun_Ocomp @ SV319 @ SV705 @ SV1019 @ SV1287 @ SV1491 )
!= ( c_Fun_Ocomp @ SV1597 @ SV1676 @ SV1741 @ SV1287 @ SV1491 ) )
= $true )
| ( ( ! [SY5208: $i] :
( ( hAPP @ SV319 @ ( hAPP @ SV705 @ SY5208 ) )
= ( hAPP @ SV1597 @ ( hAPP @ SV1676 @ SY5208 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4138]) ).
thf(4225,plain,
! [SV1742: $i,SV1714: $i,SV1677: $i,SV1598: $i,SV1492: $i,SV1288: $i,SV1020: $i,SV706: $i,SV320: $i] :
( ( ( ( hAPP @ SV320 @ ( hAPP @ SV706 @ SV1020 ) )
!= ( hAPP @ SV1288 @ ( hAPP @ SV1492 @ SV1598 ) ) )
| ! [SY5304: $i,SY5305: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV320 @ SV706 @ SV1677 @ SV1714 @ SV1742 ) @ SV1020 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1288 @ SV1492 @ SY5304 @ SV1714 @ SY5305 ) @ SV1598 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4139]) ).
thf(4226,plain,
! [SV1679: $i,SV1600: $i,SV325: $i,SV1024: $i,SV711: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV711 @ SV1024 @ SV325 )
= ( c_HOL_Ominus__class_Ominus @ SV1600 @ SV1679 @ SV325 ) )
= $false )
| ( ( ( c_lessequals @ SV1679 @ SV1600 @ SV325 )
| ~ ( c_lessequals @ SV1024 @ SV711 @ SV325 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4142]) ).
thf(4227,plain,
! [SV1680: $i,SV1601: $i,SV326: $i,SV1025: $i,SV712: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV712 @ SV1025 @ SV326 )
= ( c_HOL_Ominus__class_Ominus @ SV1601 @ SV1680 @ SV326 ) )
= $false )
| ( ( ( c_lessequals @ SV1025 @ SV712 @ SV326 )
| ~ ( c_lessequals @ SV1680 @ SV1601 @ SV326 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV326 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4143]) ).
thf(4228,plain,
! [SV1292: $i,SV1028: $i,SV715: $i,SV329: $i,SV1603: $i,SV1715: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV1715 @ SV1603 @ SV329 ) @ SV715 @ SV1028 @ SV1292 )
= $false )
| ( ( c_Natural_Oevaln @ SV1603 @ SV715 @ SV1028 @ SV1292 )
= $true )
| ( ( c_Natural_Oevaln @ SV329 @ SV715 @ SV1028 @ SV1292 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4144]) ).
thf(4229,plain,
! [SV1743: $i,SV1716: $i,SV1683: $i,SV1605: $i,SV1500: $i,SV1303: $i,SV1041: $i,SV727: $i,SV345: $i] :
( ( ! [SY5306: $i] :
( ( c_Com_Ocom_Ocom__case @ SV345 @ SV727 @ SV1041 @ SV1303 @ SV1500 @ SV1605 @ SV1683 @ SV1716 @ ( hAPP @ c_Com_Ocom_OBODY @ SV1743 ) @ SY5306 )
= ( hAPP @ SV1683 @ SV1743 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4146]) ).
thf(4230,plain,
! [SV1507: $i,SV1051: $i,SV737: $i,SV356: $i,SV1684: $i,SV1310: $i] :
( ( ( hBOOL @ ( c_in @ SV1310 @ SV1684 @ tc_Com_Opname ) )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV356 @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ SV1051 @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ SV1507 @ tc_Com_Opname @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV1684 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ SV1051 @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ SV1507 @ tc_Com_Opname @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV1684 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV737 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV356 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ ( hAPP @ SV1051 @ SV1310 ) ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1310 ) ) @ ( hAPP @ SV1507 @ SV1310 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV737 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4149]) ).
thf(4231,plain,
! [SV1509: $i,SV1685: $i,SV1608: $i,SV1312: $i,SV1053: $i,SV740: $i,SV360: $i] :
( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1053 @ ( c_Fun_Ocomp @ c_Not @ SV1312 @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ SV740 ) ) @ SV1608 ) @ SV1685 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1053 @ SV1312 @ SV740 ) ) @ SV1509 ) @ SV1685 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ SV1053 ) @ ( c_Com_Ocom_OCond @ SV1312 @ SV1509 @ SV1608 ) ) @ SV1685 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4150]) ).
thf(4232,plain,
! [SV1717: $i,SV1686: $i,SV1609: $i,SV1510: $i,SV1315: $i,SV1057: $i,SV746: $i,SV368: $i] :
( ( ( ( hAPP @ SV368 @ ( c_Set_Oinsert @ SV746 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1057 @ tc_bool ) ) @ SV1057 ) )
= SV746 )
= $true )
| ( ( ! [SY5271: $i,SY5272: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV368 @ SV1315 @ SV1510 @ SV1609 @ SV1686 @ SV1717 @ SY5271 @ SY5272 @ SV1057 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4151]) ).
thf(4233,plain,
! [SV1718: $i,SV1687: $i,SV1610: $i,SV1511: $i,SV1316: $i,SV1058: $i,SV747: $i,SV369: $i] :
( ( ( ( hAPP @ SV369 @ ( c_Set_Oinsert @ SV747 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1058 @ tc_bool ) ) @ SV1058 ) )
= SV747 )
= $true )
| ( ( ! [SY5273: $i,SY5274: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1316 @ SV369 @ SV1511 @ SV1610 @ SV1687 @ SV1718 @ SY5273 @ SY5274 @ SV1058 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4152]) ).
thf(4234,plain,
! [SV1744: $i,SV1719: $i,SV1688: $i,SV1611: $i,SV1512: $i,SV1320: $i,SV1061: $i,SV752: $i,SV376: $i] :
( ( ( ( hAPP @ SV376 @ ( c_Set_Oinsert @ SV752 @ ( c_Set_Oinsert @ SV1061 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1320 @ tc_bool ) ) @ SV1320 ) @ SV1320 ) )
= ( hAPP @ ( hAPP @ SV1512 @ SV752 ) @ SV1061 ) )
| ! [SY5307: $i,SY5308: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV376 @ SV1611 @ SV1688 @ SV1719 @ SV1512 @ SV1744 @ SY5307 @ SY5308 @ SV1320 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4153]) ).
thf(4235,plain,
! [SV1745: $i,SV1720: $i,SV1689: $i,SV1612: $i,SV1513: $i,SV1321: $i,SV1062: $i,SV753: $i,SV377: $i] :
( ( ( ( hAPP @ SV377 @ ( c_Set_Oinsert @ SV753 @ ( c_Set_Oinsert @ SV1062 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1321 @ tc_bool ) ) @ SV1321 ) @ SV1321 ) )
= ( hAPP @ ( hAPP @ SV1513 @ SV753 ) @ SV1062 ) )
| ! [SY5309: $i,SY5310: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1612 @ SV377 @ SV1689 @ SV1720 @ SV1745 @ SV1513 @ SY5309 @ SY5310 @ SV1321 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4154]) ).
thf(4236,plain,
! [SV1721: $i,SV1070: $i,SV1329: $i,SV764: $i,SV391: $i,SV1690: $i,SV1515: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1515 @ SV1690 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV391 @ SV764 @ SV1329 @ SV1070 @ SV1721 @ SV1515 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1721 @ SV1690 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV391 @ SV764 @ SV1329 @ SV1070 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV391 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1721 ) @ SV1070 ) @ SV1515 ) @ ( 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 @ SV391 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV764 ) @ SV1070 ) @ SV1329 ) @ ( 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)],[4155]) ).
thf(4237,plain,
! [SV1071: $i,SV392: $i,SV1330: $i,SV1722: $i,SV765: $i,SV1691: $i,SV1516: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1516 @ SV1691 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV765 @ SV1722 @ SV1330 @ SV1516 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1722 @ SV1691 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV765 @ SV1722 @ SV1330 @ SV1516 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV392 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1722 ) @ SV1071 ) @ SV1516 ) @ ( 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 @ SV392 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV765 ) @ SV1071 ) @ SV1330 ) @ ( 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)],[4156]) ).
thf(4238,plain,
! [SV1723: $i,SV1072: $i,SV1331: $i,SV766: $i,SV393: $i,SV1692: $i,SV1517: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1517 @ SV1692 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV393 @ SV766 @ SV1331 @ SV1072 @ SV1723 @ SV1517 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1723 @ SV1692 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV393 @ SV766 @ SV1331 @ SV1072 ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV393 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1723 ) @ SV1072 ) @ SV1517 ) @ ( 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 @ SV393 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV766 ) @ SV1072 ) @ SV1331 ) @ ( 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)],[4157]) ).
thf(4239,plain,
! [SV1693: $i,SV1613: $i,SV1074: $i,SV768: $i,SV395: $i,SV1333: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1333 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV395 @ SV768 @ SV1333 @ SV1074 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV395 @ SV768 @ SV1333 @ SV1074 @ SV1613 @ SV1693 ) ) )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV395 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1613 ) @ SV1074 ) @ SV1693 ) @ ( 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 @ SV395 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV768 ) @ SV1074 ) @ SV1333 ) @ ( 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)],[4158]) ).
thf(4240,plain,
! [SV1336: $i,SV771: $i,SV1694: $i,SV1077: $i,SV1615: $i,SV398: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV398 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1615 ) @ SV1077 ) @ SV1694 ) @ ( 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 @ SV771 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV771 @ SV1615 @ SV1336 @ SV1694 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV771 @ SV1615 @ SV1336 @ SV1694 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV398 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV771 ) @ SV1077 ) @ SV1336 ) @ ( 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)],[4160]) ).
thf(4241,plain,
! [SV1695: $i,SV1617: $i,SV1079: $i,SV773: $i,SV400: $i,SV1338: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1338 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV400 @ SV773 @ SV1338 @ SV1079 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV400 @ SV773 @ SV1338 @ SV1079 @ SV1617 @ SV1695 ) ) )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV400 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1617 ) @ SV1079 ) @ SV1695 ) @ ( 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 @ SV400 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV773 ) @ SV1079 ) @ SV1338 ) @ ( 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)],[4162]) ).
thf(4242,plain,
! [SV774: $i,SV1339: $i,SV1080: $i,SV1618: $i,SV401: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV401 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1618 ) @ SV1080 ) @ SV1339 ) @ ( 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 @ SV1618 @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ SV774 @ SV1618 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ SV774 @ SV1618 ) ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV401 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV774 ) @ SV1080 ) @ SV1339 ) @ ( 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)],[4163]) ).
thf(4243,plain,
! [SV1081: $i,SV402: $i,SV1696: $i,SV1619: $i,SV775: $i,SV1340: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1340 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV775 @ SV1619 @ SV1340 @ SV1696 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV775 @ SV1619 @ SV1340 @ SV1696 ) ) )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV402 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1619 ) @ SV1081 ) @ SV1696 ) @ ( 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 @ SV402 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV775 ) @ SV1081 ) @ SV1340 ) @ ( 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)],[4164]) ).
thf(4244,plain,
! [SV1341: $i,SV1620: $i,SV1082: $i,SV776: $i,SV403: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV403 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV776 ) @ SV1082 ) @ SV1620 ) @ ( 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 @ SV1341 @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ SV1341 @ SV1620 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ SV1341 @ SV1620 ) ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV403 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV776 ) @ SV1082 ) @ SV1341 ) @ ( 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)],[4165]) ).
thf(4245,plain,
! [SV1345: $i,SV1089: $i,SV1621: $i,SV1520: $i,SV1724: $i,SV783: $i,SV410: $i] :
( ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SV1724 ) @ SV1520 ) @ SV1621 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SV1089 ) @ SV1345 ) @ SV1724 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SV1089 ) @ ( c_Com_Ocom_OSemi @ SV1345 @ SV1520 ) ) @ SV1621 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4166]) ).
thf(4246,plain,
! [SV1697: $i,SV1622: $i,SV1522: $i,SV1347: $i,SV1094: $i,SV788: $i,SV415: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV415 ) @ SV788 ) @ SV1094 ) @ SV1347 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV415 ) @ SV1522 ) @ SV1622 ) @ SV1697 ) )
= $false )
| ( ( SV1347 = SV1697 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4169]) ).
thf(4247,plain,
! [SV1725: $i,SV1623: $i,SV1523: $i,SV1348: $i,SV1095: $i,SV789: $i,SV416: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV416 ) @ SV789 ) @ SV1095 ) @ SV1348 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV416 ) @ SV1523 ) @ SV1623 ) @ SV1725 ) )
= $false )
| ( ( SV1095 = SV1623 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4170]) ).
thf(4248,plain,
! [SV1726: $i,SV1698: $i,SV1524: $i,SV1349: $i,SV1096: $i,SV790: $i,SV417: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV417 ) @ SV790 ) @ SV1096 ) @ SV1349 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV417 ) @ SV1524 ) @ SV1698 ) @ SV1726 ) )
= $false )
| ( ( SV790 = SV1524 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4171]) ).
thf(4249,plain,
! [SV1363: $i,SV11: $i,SV1533: $i,SV453: $i] :
( ( ( c_lessequals @ SV453 @ SV1533 @ SV11 )
= $false )
| ( ( c_lessequals @ SV1363 @ SV1533 @ SV11 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV453 @ SV1363 @ SV11 ) @ SV1533 @ SV11 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4176]) ).
thf(4250,plain,
! [SV1366: $i,SV14: $i,SV1534: $i,SV454: $i] :
( ( ( c_lessequals @ SV454 @ SV1534 @ SV14 )
= $false )
| ( ( c_lessequals @ SV1366 @ SV1534 @ SV14 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV454 @ SV1366 @ SV14 ) @ SV1534 @ SV14 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4177]) ).
thf(4251,plain,
! [SV1367: $i,SV15: $i,SV1535: $i,SV455: $i] :
( ( ( c_lessequals @ SV455 @ SV1535 @ SV15 )
= $false )
| ( ( c_lessequals @ SV1367 @ SV1535 @ SV15 )
= $false )
| ( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV455 @ SV1367 @ SV15 ) @ SV1535 @ SV15 )
= $true )
| ( ( class_Lattices_Oupper__semilattice @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4178]) ).
thf(4252,plain,
! [SV1727: $i,SV1699: $i,SV1626: $i,SV1536: $i,SV1370: $i,SV1116: $i,SV822: $i,SV456: $i,SV18: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV18 @ SV456 @ ( c_COMBC @ SV822 @ SV1116 @ SV1116 @ tc_bool ) @ ( c_COMBC @ SV1370 @ SV1116 @ SV1116 @ tc_bool ) @ SV1536 @ SV1626 @ SV1699 @ SV1727 @ SV1116 )
= $true )
| ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV456 @ SV18 @ SV822 @ SV1370 @ SV1626 @ SV1536 @ SV1727 @ SV1699 @ SV1116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4179]) ).
thf(4253,plain,
! [SV1381: $i,SV481: $i,SV1628: $i,SV1134: $i,SV844: $i,SV46: $i] :
( ( ( c_Natural_Oevaln @ SV46 @ SV844 @ SV1134 @ SV1628 )
= $false )
| ( ( c_Natural_Oevaln @ SV481 @ SV1628 @ SV1134 @ SV1381 )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ SV46 @ SV481 ) @ SV844 @ SV1134 @ SV1381 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4184]) ).
thf(4254,plain,
! [SV1135: $i,SV49: $i,SV1544: $i,SV845: $i,SV484: $i] :
( ( ( c_Natural_Oevalc @ SV484 @ SV845 @ SV1544 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV49 @ SV845 ) ) )
= $true )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV49 @ SV484 ) @ SV1544 @ SV1135 )
= $false )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV49 @ SV484 ) @ SV845 @ SV1135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4185]) ).
thf(4255,plain,
! [SV1384: $i,SV52: $i,SV1630: $i,SV1136: $i,SV846: $i,SV487: $i] :
( ( ( ~ ( c_Natural_Oevaln @ SV487 @ SV846 @ SV1136 @ SV1630 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV52 @ SV846 ) ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV52 @ SV487 ) @ SV1630 @ SV1136 @ SV1384 )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV52 @ SV487 ) @ SV846 @ SV1136 @ SV1384 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4186]) ).
thf(4256,plain,
! [SV1631: $i,SV1144: $i,SV497: $i,SV1728: $i,SV853: $i,SV62: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV62 @ SV853 @ SV1728 ) @ SV497 @ SV1144 @ SV1631 )
= $false )
| ( ( c_Natural_Oevaln @ SV853 @ SV497 @ SV1144 @ SV1631 )
= $true )
| ( ( hBOOL @ ( hAPP @ SV62 @ SV497 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4187]) ).
thf(4257,plain,
! [SV854: $i,SV1548: $i,SV1388: $i,SV498: $i,SV1145: $i,SV63: $i] :
( ( ( hBOOL @ ( hAPP @ SV63 @ SV1145 ) )
= $false )
| ( ( c_Natural_Oevaln @ SV498 @ SV1145 @ SV1388 @ SV1548 )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ SV63 @ SV498 @ SV854 ) @ SV1145 @ SV1388 @ SV1548 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4188]) ).
thf(4258,plain,
! [SV1746: $i,SV1729: $i,SV1701: $i,SV1632: $i,SV1549: $i,SV1389: $i,SV1146: $i,SV855: $i,SV499: $i,SV64: $i] :
( ( ! [SY5311: $i,SY5312: $i] :
( ( c_Com_Ocom_Ocom__case @ SV64 @ SV499 @ SV855 @ SV1146 @ SV1389 @ SV1549 @ SV1632 @ SV1701 @ ( c_Com_Ocom_OCall @ SV1729 @ SV1746 @ SY5311 ) @ SY5312 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV1701 @ SV1729 ) @ SV1746 ) @ SY5311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4189]) ).
thf(4259,plain,
! [SV503: $i,SV858: $i,SV1151: $i,SV1633: $i,SV1551: $i,SV70: $i] :
( ( ( c_lessequals @ ( c_Set_Oimage @ SV70 @ SV1551 @ SV1633 @ SV1151 ) @ SV858 @ ( tc_fun @ SV1151 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV503 @ SV1551 @ SV1633 ) )
= $false )
| ( ( hBOOL @ ( c_in @ ( hAPP @ SV70 @ SV503 ) @ SV858 @ SV1151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4190]) ).
thf(4260,plain,
! [SV533: $i,SV885: $i,SV1171: $i,SV1638: $i,SV103: $i,SV1560: $i] :
( ( ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV1560 @ SV103 @ SV1638 @ ( tc_fun @ SV1171 @ tc_bool ) ) @ SV885 @ ( tc_fun @ SV1171 @ tc_bool ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV533 @ SV1560 @ SV1638 ) )
= $false )
| ( ( c_lessequals @ ( hAPP @ SV103 @ SV533 ) @ SV885 @ ( tc_fun @ SV1171 @ tc_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4193]) ).
thf(4261,plain,
! [SV541: $i,SV1565: $i,SV116: $i,SV1641: $i,SV892: $i] :
( ( ( c_lessequals @ SV892 @ SV1641 @ SV116 )
= $false )
| ( ( ~ ( c_lessequals @ SV1565 @ SV541 @ SV116 ) )
= $true )
| ( ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV541 @ SV892 @ SV116 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1565 @ SV1641 @ SV116 ) @ ( tc_fun @ SV116 @ tc_bool ) )
= $true )
| ( ( class_Orderings_Oorder @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4194]) ).
thf(4262,plain,
! [SV893: $i,SV1747: $i,SV117: $i,SV542: $i,SV1642: $i] :
( ( ( ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1642 @ SV542 @ SV117 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1747 @ SV893 @ SV117 ) @ ( tc_fun @ SV117 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV1642 @ SV542 @ SV117 )
= $false )
| ( ( c_lessequals @ SV542 @ SV893 @ SV117 )
= $true )
| ( ( class_Orderings_Oorder @ SV117 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4195]) ).
thf(4263,plain,
! [SV1748: $i,SV543: $i,SV118: $i,SV1643: $i,SV894: $i] :
( ( ( ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV894 @ SV1643 @ SV118 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV543 @ SV1748 @ SV118 ) @ ( tc_fun @ SV118 @ tc_bool ) ) )
= $true )
| ( ( c_lessequals @ SV894 @ SV1643 @ SV118 )
= $false )
| ( ( c_lessequals @ SV543 @ SV894 @ SV118 )
= $true )
| ( ( class_Orderings_Oorder @ SV118 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4196]) ).
thf(4264,plain,
! [SV1414: $i,SV909: $i,SV139: $i,SV1193: $i,SV564: $i,SV1647: $i] :
( ( ( hBOOL @ ( c_in @ SV1647 @ SV564 @ SV1193 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV139 @ ( hAPP @ SV909 @ SV1647 ) @ SV1414 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV139 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV564 @ SV909 @ SV1193 @ ( tc_fun @ SV1414 @ tc_bool ) ) @ SV1414 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4199]) ).
thf(4265,plain,
! [SV1415: $i,SV910: $i,SV140: $i,SV1194: $i,SV565: $i,SV1648: $i] :
( ( ( hBOOL @ ( c_in @ SV1648 @ SV565 @ SV1194 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV140 @ ( hAPP @ SV910 @ SV1648 ) @ SV1415 ) )
= $false )
| ( ( hBOOL @ ( c_in @ SV140 @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV565 @ SV910 @ SV1194 @ ( tc_fun @ SV1415 @ tc_bool ) ) @ SV1415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4200]) ).
thf(4266,plain,
! [SV1749: $i,SV1731: $i,SV1704: $i,SV1649: $i,SV1571: $i,SV1417: $i,SV1197: $i,SV915: $i,SV570: $i,SV146: $i] :
( ( ! [SY5313: $i] :
( ( c_Com_Ocom_Ocom__case @ SV146 @ SV570 @ SV915 @ SV1197 @ SV1417 @ SV1571 @ SV1649 @ SV1704 @ ( c_Com_Ocom_OSemi @ SV1731 @ SV1749 ) @ SY5313 )
= ( hAPP @ ( hAPP @ SV1197 @ SV1731 ) @ SV1749 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4201]) ).
thf(4267,plain,
! [SV1732: $i,SV1705: $i,SV1650: $i,SV1572: $i,SV1419: $i,SV1199: $i,SV918: $i,SV573: $i,SV149: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV149 @ ( hAPP @ SV573 @ SV918 ) ) @ SV1199 ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV1199 @ SV918 @ SV1419 ) )
| ! [SY5286: $i,SY5287: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV573 @ SV1572 @ SV149 @ SV1650 @ SV1705 @ SV1732 @ SY5286 @ SY5287 @ SV1419 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4202]) ).
thf(4268,plain,
! [SV1733: $i,SV1706: $i,SV1651: $i,SV1573: $i,SV1420: $i,SV1200: $i,SV919: $i,SV574: $i,SV150: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV150 @ SV574 ) @ ( hAPP @ SV919 @ SV1200 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( c_in @ SV574 @ SV1200 @ SV1420 ) )
| ! [SY5288: $i,SY5289: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1573 @ SV919 @ SV150 @ SV1651 @ SV1706 @ SV1733 @ SY5288 @ SY5289 @ SV1420 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4203]) ).
thf(4269,plain,
! [SV1207: $i,SV1426: $i,SV582: $i,SV928: $i,SV164: $i,SV1652: $i] :
( ( ( hBOOL @ ( c_in @ SV1652 @ SV164 @ SV928 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV582 @ SV1652 ) @ SV1426 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV164 @ SV582 @ SV928 @ ( tc_fun @ SV1207 @ tc_bool ) ) @ SV1426 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4204]) ).
thf(4270,plain,
! [SV1208: $i,SV1427: $i,SV583: $i,SV929: $i,SV165: $i,SV1653: $i] :
( ( ( hBOOL @ ( c_in @ SV1653 @ SV165 @ SV929 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV583 @ SV1653 ) @ SV1427 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ SV165 @ SV583 @ SV929 @ ( tc_fun @ SV1208 @ tc_bool ) ) @ SV1427 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4205]) ).
thf(4271,plain,
! [SV600: $i,SV944: $i,SV1750: $i,SV1734: $i,SV1656: $i,SV1580: $i,SV1434: $i,SV1223: $i,SV188: $i] :
( ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV188 @ SV1223 @ SV1434 @ SV1580 @ SV1656 @ SV1734 @ SV1750 @ SV944 @ SV600 ) )
= $true )
| ( ( ( hAPP @ SV188 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_bool ) ) )
= SV944 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4207]) ).
thf(4272,plain,
! [SV601: $i,SV1751: $i,SV945: $i,SV1735: $i,SV1657: $i,SV1581: $i,SV1435: $i,SV189: $i,SV1224: $i] :
( ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1224 @ SV189 @ SV1435 @ SV1581 @ SV1657 @ SV1735 @ SV945 @ SV1751 @ SV601 ) )
= $true )
| ( ( ( hAPP @ SV189 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV601 @ tc_bool ) ) )
= SV945 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4208]) ).
thf(4273,plain,
! [SV1736: $i,SV1708: $i,SV1658: $i,SV1582: $i,SV1441: $i,SV1234: $i,SV961: $i,SV630: $i,SV221: $i] :
( ( ( ( hAPP @ SV221 @ ( c_Set_Oinsert @ SV630 @ SV961 @ SV1234 ) )
= ( hAPP @ ( hAPP @ SV1441 @ SV630 ) @ ( hAPP @ SV221 @ SV961 ) ) )
= $true )
| ( ( ! [SY5292: $i,SY5293: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV221 @ SV1582 @ SV1658 @ SV1708 @ SV1441 @ SV1736 @ SY5292 @ SY5293 @ SV1234 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4209]) ).
thf(4274,plain,
! [SV1737: $i,SV1709: $i,SV1659: $i,SV1583: $i,SV1442: $i,SV1235: $i,SV962: $i,SV631: $i,SV222: $i] :
( ( ( ( hAPP @ SV222 @ ( c_Set_Oinsert @ SV631 @ SV962 @ SV1235 ) )
= ( hAPP @ ( hAPP @ SV1442 @ SV631 ) @ ( hAPP @ SV222 @ SV962 ) ) )
= $true )
| ( ( ! [SY5294: $i,SY5295: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1583 @ SV222 @ SV1659 @ SV1709 @ SV1737 @ SV1442 @ SY5294 @ SY5295 @ SV1235 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4210]) ).
thf(4275,plain,
! [SV988: $i,SV264: $i,SV1259: $i,SV1660: $i,SV1458: $i,SV661: $i,SV1752: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1752 @ SV661 ) @ SV1458 ) )
| ~ ( c_Hoare__Mirabelle_Otriple__valid @ SV1660 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1752 ) @ SV1259 ) @ SV264 ) @ t_a ) )
= $true )
| ( ( c_Natural_Oevaln @ SV1259 @ SV1458 @ SV1660 @ SV988 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV264 @ SV661 ) @ SV988 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4217]) ).
thf(4276,plain,
! [SV1753: $i,SV1738: $i,SV1711: $i,SV1662: $i,SV1586: $i,SV1465: $i,SV1265: $i,SV994: $i,SV665: $i,SV273: $i] :
( ( ! [SY5314: $i,SY5315: $i] :
( ( c_Com_Ocom_Ocom__case @ SV273 @ SV665 @ SV994 @ SV1265 @ SV1465 @ SV1586 @ SV1662 @ SV1711 @ ( c_Com_Ocom_OLocal @ SV1738 @ SV1753 @ SY5314 ) @ SY5315 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV994 @ SV1738 ) @ SV1753 ) @ SY5314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4218]) ).
thf(4277,plain,
! [SV1754: $i,SV1739: $i,SV1712: $i,SV1663: $i,SV1587: $i,SV1466: $i,SV1266: $i,SV995: $i,SV666: $i,SV274: $i] :
( ( ! [SY5316: $i] :
( ( c_Com_Ocom_Ocom__case @ SV274 @ SV666 @ SV995 @ SV1266 @ SV1466 @ SV1587 @ SV1663 @ SV1712 @ ( c_Com_Ocom_OWhile @ SV1739 @ SV1754 ) @ SY5316 )
= ( hAPP @ ( hAPP @ SV1587 @ SV1739 ) @ SV1754 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4219]) ).
thf(4278,plain,
! [SV692: $i,SV302: $i,SV1481: $i,SV1672: $i] :
( ( ( c_lessequals @ SV1672 @ SV1481 @ SV302 )
= $false )
| ( ( c_lessequals @ SV692 @ SV1672 @ SV302 )
= $false )
| ( ( c_lessequals @ SV692 @ SV1481 @ SV302 )
= $true )
| ( ( class_Orderings_Oorder @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4221]) ).
thf(4279,plain,
! [SV1482: $i,SV303: $i,SV1673: $i,SV693: $i] :
( ( ( c_lessequals @ SV693 @ SV1673 @ SV303 )
= $false )
| ( ( c_lessequals @ SV1673 @ SV1482 @ SV303 )
= $false )
| ( ( c_lessequals @ SV693 @ SV1482 @ SV303 )
= $true )
| ( ( class_Orderings_Opreorder @ SV303 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4222]) ).
thf(4280,plain,
! [SV1755: $i,SV1740: $i,SV1713: $i,SV1675: $i,SV1596: $i,SV1490: $i,SV1286: $i,SV1018: $i,SV704: $i,SV318: $i] :
( ( ! [SY5317: $i,SY5318: $i] :
( ( c_Com_Ocom_Ocom__case @ SV318 @ SV704 @ SV1018 @ SV1286 @ SV1490 @ SV1596 @ SV1675 @ SV1713 @ ( c_Com_Ocom_OCond @ SV1740 @ SV1755 @ SY5317 ) @ SY5318 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV1490 @ SV1740 ) @ SV1755 ) @ SY5317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4223]) ).
thf(4281,plain,
! [SV1741: $i,SV1676: $i,SV1597: $i,SV1491: $i,SV1287: $i,SV1019: $i,SV705: $i,SV319: $i] :
( ( ( ( c_Fun_Ocomp @ SV319 @ SV705 @ SV1019 @ SV1287 @ SV1491 )
= ( c_Fun_Ocomp @ SV1597 @ SV1676 @ SV1741 @ SV1287 @ SV1491 ) )
= $false )
| ( ( ! [SY5208: $i] :
( ( hAPP @ SV319 @ ( hAPP @ SV705 @ SY5208 ) )
= ( hAPP @ SV1597 @ ( hAPP @ SV1676 @ SY5208 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4224]) ).
thf(4282,plain,
! [SV1742: $i,SV1714: $i,SV1677: $i,SV1598: $i,SV1492: $i,SV1288: $i,SV1020: $i,SV706: $i,SV320: $i] :
( ( ( ( hAPP @ SV320 @ ( hAPP @ SV706 @ SV1020 ) )
!= ( hAPP @ SV1288 @ ( hAPP @ SV1492 @ SV1598 ) ) )
= $true )
| ( ( ! [SY5304: $i,SY5305: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV320 @ SV706 @ SV1677 @ SV1714 @ SV1742 ) @ SV1020 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1288 @ SV1492 @ SY5304 @ SV1714 @ SY5305 ) @ SV1598 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4225]) ).
thf(4283,plain,
! [SV711: $i,SV1024: $i,SV325: $i,SV1600: $i,SV1679: $i] :
( ( ( c_lessequals @ SV1679 @ SV1600 @ SV325 )
= $true )
| ( ( ~ ( c_lessequals @ SV1024 @ SV711 @ SV325 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV711 @ SV1024 @ SV325 )
= ( c_HOL_Ominus__class_Ominus @ SV1600 @ SV1679 @ SV325 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4226]) ).
thf(4284,plain,
! [SV1601: $i,SV1680: $i,SV326: $i,SV712: $i,SV1025: $i] :
( ( ( c_lessequals @ SV1025 @ SV712 @ SV326 )
= $true )
| ( ( ~ ( c_lessequals @ SV1680 @ SV1601 @ SV326 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV712 @ SV1025 @ SV326 )
= ( c_HOL_Ominus__class_Ominus @ SV1601 @ SV1680 @ SV326 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV326 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4227]) ).
thf(4285,plain,
! [SV1756: $i,SV1743: $i,SV1716: $i,SV1683: $i,SV1605: $i,SV1500: $i,SV1303: $i,SV1041: $i,SV727: $i,SV345: $i] :
( ( ( c_Com_Ocom_Ocom__case @ SV345 @ SV727 @ SV1041 @ SV1303 @ SV1500 @ SV1605 @ SV1683 @ SV1716 @ ( hAPP @ c_Com_Ocom_OBODY @ SV1743 ) @ SV1756 )
= ( hAPP @ SV1683 @ SV1743 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4229]) ).
thf(4286,plain,
! [SV1310: $i,SV1684: $i,SV1507: $i,SV1051: $i,SV737: $i,SV356: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ ( c_Lattices_Oupper__semilattice__class_Osup @ SV356 @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ SV1051 @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ tc_Com_Opname ) @ c_Com_Ocom_OBODY @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ SV1507 @ tc_Com_Opname @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV1684 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) @ tc_bool ) ) @ ( c_Set_Oimage @ ( c_COMBS @ ( c_COMBS @ ( c_COMBB @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ SV1051 @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_fun @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ tc_Com_Opname ) @ ( c_COMBB @ ( c_Option_Othe @ tc_Com_Ocom ) @ c_Com_Obody @ ( tc_Option_Ooption @ tc_Com_Ocom ) @ tc_Com_Ocom @ tc_Com_Opname ) @ tc_Com_Opname @ tc_Com_Ocom @ ( tc_fun @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) ) @ SV1507 @ tc_Com_Opname @ ( tc_fun @ SV737 @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV1684 @ tc_Com_Opname @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV737 )
= $false )
| ( ( hBOOL @ ( c_in @ SV1310 @ SV1684 @ tc_Com_Opname ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV356 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV737 ) @ ( hAPP @ SV1051 @ SV1310 ) ) @ ( hAPP @ c_Com_Ocom_OBODY @ SV1310 ) ) @ ( hAPP @ SV1507 @ SV1310 ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV737 ) ) @ SV737 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4230]) ).
thf(4287,plain,
! [SV1509: $i,SV1685: $i,SV1608: $i,SV1312: $i,SV1053: $i,SV740: $i,SV360: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1053 @ ( c_Fun_Ocomp @ c_Not @ SV1312 @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ SV740 ) ) @ SV1608 ) @ SV1685 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1053 @ SV1312 @ SV740 ) ) @ SV1509 ) @ SV1685 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ SV1053 ) @ ( c_Com_Ocom_OCond @ SV1312 @ SV1509 @ SV1608 ) ) @ SV1685 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4231]) ).
thf(4288,plain,
! [SV746: $i,SV1057: $i,SV1757: $i,SV1717: $i,SV1686: $i,SV1609: $i,SV1510: $i,SV1315: $i,SV368: $i] :
( ( ( ! [SY5319: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV368 @ SV1315 @ SV1510 @ SV1609 @ SV1686 @ SV1717 @ SV1757 @ SY5319 @ SV1057 ) )
= $true )
| ( ( ( hAPP @ SV368 @ ( c_Set_Oinsert @ SV746 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1057 @ tc_bool ) ) @ SV1057 ) )
= SV746 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4232]) ).
thf(4289,plain,
! [SV747: $i,SV1058: $i,SV1758: $i,SV1718: $i,SV1687: $i,SV1610: $i,SV1511: $i,SV369: $i,SV1316: $i] :
( ( ( ! [SY5320: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1316 @ SV369 @ SV1511 @ SV1610 @ SV1687 @ SV1718 @ SV1758 @ SY5320 @ SV1058 ) )
= $true )
| ( ( ( hAPP @ SV369 @ ( c_Set_Oinsert @ SV747 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1058 @ tc_bool ) ) @ SV1058 ) )
= SV747 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4233]) ).
thf(4290,plain,
! [SV1744: $i,SV1719: $i,SV1688: $i,SV1611: $i,SV1512: $i,SV1320: $i,SV1061: $i,SV752: $i,SV376: $i] :
( ( ( ( hAPP @ SV376 @ ( c_Set_Oinsert @ SV752 @ ( c_Set_Oinsert @ SV1061 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1320 @ tc_bool ) ) @ SV1320 ) @ SV1320 ) )
= ( hAPP @ ( hAPP @ SV1512 @ SV752 ) @ SV1061 ) )
= $true )
| ( ( ! [SY5307: $i,SY5308: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV376 @ SV1611 @ SV1688 @ SV1719 @ SV1512 @ SV1744 @ SY5307 @ SY5308 @ SV1320 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4234]) ).
thf(4291,plain,
! [SV1745: $i,SV1720: $i,SV1689: $i,SV1612: $i,SV1513: $i,SV1321: $i,SV1062: $i,SV753: $i,SV377: $i] :
( ( ( ( hAPP @ SV377 @ ( c_Set_Oinsert @ SV753 @ ( c_Set_Oinsert @ SV1062 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1321 @ tc_bool ) ) @ SV1321 ) @ SV1321 ) )
= ( hAPP @ ( hAPP @ SV1513 @ SV753 ) @ SV1062 ) )
= $true )
| ( ( ! [SY5309: $i,SY5310: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1612 @ SV377 @ SV1689 @ SV1720 @ SV1745 @ SV1513 @ SY5309 @ SY5310 @ SV1321 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4235]) ).
thf(4292,plain,
! [SV1515: $i,SV1070: $i,SV1329: $i,SV764: $i,SV391: $i,SV1690: $i,SV1721: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1721 @ SV1690 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV391 @ SV764 @ SV1329 @ SV1070 ) ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV391 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1721 ) @ SV1070 ) @ SV1515 ) @ ( 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 @ SV1515 @ SV1690 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV391 @ SV764 @ SV1329 @ SV1070 @ SV1721 @ SV1515 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV391 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV764 ) @ SV1070 ) @ SV1329 ) @ ( 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)],[4236]) ).
thf(4293,plain,
! [SV1071: $i,SV392: $i,SV1516: $i,SV1330: $i,SV765: $i,SV1691: $i,SV1722: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1722 @ SV1691 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV765 @ SV1722 @ SV1330 @ SV1516 ) ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV392 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1722 ) @ SV1071 ) @ SV1516 ) @ ( 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 @ SV1516 @ SV1691 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV765 @ SV1722 @ SV1330 @ SV1516 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV392 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV765 ) @ SV1071 ) @ SV1330 ) @ ( 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)],[4237]) ).
thf(4294,plain,
! [SV1517: $i,SV1072: $i,SV1331: $i,SV766: $i,SV393: $i,SV1692: $i,SV1723: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1723 @ SV1692 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV393 @ SV766 @ SV1331 @ SV1072 ) ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV393 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1723 ) @ SV1072 ) @ SV1517 ) @ ( 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 @ SV1517 @ SV1692 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV393 @ SV766 @ SV1331 @ SV1072 @ SV1723 @ SV1517 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV393 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV766 ) @ SV1072 ) @ SV1331 ) @ ( 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)],[4238]) ).
thf(4295,plain,
! [SV768: $i,SV1333: $i,SV1693: $i,SV1074: $i,SV1613: $i,SV395: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV395 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1613 ) @ SV1074 ) @ SV1693 ) @ ( 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 @ SV1333 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ SV395 @ SV768 @ SV1333 @ SV1074 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV395 @ SV768 @ SV1333 @ SV1074 @ SV1613 @ SV1693 ) ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV395 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV768 ) @ SV1074 ) @ SV1333 ) @ ( 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)],[4239]) ).
thf(4296,plain,
! [SV773: $i,SV1338: $i,SV1695: $i,SV1079: $i,SV1617: $i,SV400: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV400 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1617 ) @ SV1079 ) @ SV1695 ) @ ( 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 @ SV1338 @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ SV400 @ SV773 @ SV1338 @ SV1079 ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV400 @ SV773 @ SV1338 @ SV1079 @ SV1617 @ SV1695 ) ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV400 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV773 ) @ SV1079 ) @ SV1338 ) @ ( 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)],[4241]) ).
thf(4297,plain,
! [SV775: $i,SV1340: $i,SV1696: $i,SV1081: $i,SV1619: $i,SV402: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV402 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1619 ) @ SV1081 ) @ SV1696 ) @ ( 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 @ SV1340 @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ SV775 @ SV1619 @ SV1340 @ SV1696 ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV775 @ SV1619 @ SV1340 @ SV1696 ) ) )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV402 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV775 ) @ SV1081 ) @ SV1340 ) @ ( 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)],[4243]) ).
thf(4298,plain,
! [SV1345: $i,SV1089: $i,SV1621: $i,SV1520: $i,SV1724: $i,SV783: $i,SV410: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SV1724 ) @ SV1520 ) @ SV1621 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SV1089 ) @ SV1345 ) @ SV1724 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SV1089 ) @ ( c_Com_Ocom_OSemi @ SV1345 @ SV1520 ) ) @ SV1621 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4245]) ).
thf(4299,plain,
! [SV1116: $i,SV1699: $i,SV1727: $i,SV1536: $i,SV1626: $i,SV1370: $i,SV822: $i,SV18: $i,SV456: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV456 @ SV18 @ SV822 @ SV1370 @ SV1626 @ SV1536 @ SV1727 @ SV1699 @ SV1116 )
= $false )
| ( ( c_Complete__Lattice_Ocomplete__lattice @ SV18 @ SV456 @ ( c_COMBC @ SV822 @ SV1116 @ SV1116 @ tc_bool ) @ ( c_COMBC @ SV1370 @ SV1116 @ SV1116 @ tc_bool ) @ SV1536 @ SV1626 @ SV1699 @ SV1727 @ SV1116 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4252]) ).
thf(4300,plain,
! [SV1135: $i,SV1544: $i,SV484: $i,SV845: $i,SV49: $i] :
( ( ( hBOOL @ ( hAPP @ SV49 @ SV845 ) )
= $false )
| ( ( c_Natural_Oevalc @ SV484 @ SV845 @ SV1544 )
= $false )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV49 @ SV484 ) @ SV1544 @ SV1135 )
= $false )
| ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ SV49 @ SV484 ) @ SV845 @ SV1135 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4254]) ).
thf(4301,plain,
! [SV1384: $i,SV52: $i,SV1630: $i,SV1136: $i,SV846: $i,SV487: $i] :
( ( ( c_Natural_Oevaln @ SV487 @ SV846 @ SV1136 @ SV1630 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV52 @ SV846 ) ) )
= $true )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV52 @ SV487 ) @ SV1630 @ SV1136 @ SV1384 )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV52 @ SV487 ) @ SV846 @ SV1136 @ SV1384 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4255]) ).
thf(4302,plain,
! [SV1759: $i,SV1746: $i,SV1729: $i,SV1701: $i,SV1632: $i,SV1549: $i,SV1389: $i,SV1146: $i,SV855: $i,SV499: $i,SV64: $i] :
( ( ! [SY5321: $i] :
( ( c_Com_Ocom_Ocom__case @ SV64 @ SV499 @ SV855 @ SV1146 @ SV1389 @ SV1549 @ SV1632 @ SV1701 @ ( c_Com_Ocom_OCall @ SV1729 @ SV1746 @ SV1759 ) @ SY5321 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV1701 @ SV1729 ) @ SV1746 ) @ SV1759 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4258]) ).
thf(4303,plain,
! [SV1641: $i,SV892: $i,SV116: $i,SV541: $i,SV1565: $i] :
( ( ( c_lessequals @ SV1565 @ SV541 @ SV116 )
= $false )
| ( ( c_lessequals @ SV892 @ SV1641 @ SV116 )
= $false )
| ( ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV541 @ SV892 @ SV116 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1565 @ SV1641 @ SV116 ) @ ( tc_fun @ SV116 @ tc_bool ) )
= $true )
| ( ( class_Orderings_Oorder @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4261]) ).
thf(4304,plain,
! [SV893: $i,SV1747: $i,SV117: $i,SV542: $i,SV1642: $i] :
( ( ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1642 @ SV542 @ SV117 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV1747 @ SV893 @ SV117 ) @ ( tc_fun @ SV117 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV1642 @ SV542 @ SV117 )
= $false )
| ( ( c_lessequals @ SV542 @ SV893 @ SV117 )
= $true )
| ( ( class_Orderings_Oorder @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4262]) ).
thf(4305,plain,
! [SV1748: $i,SV543: $i,SV118: $i,SV1643: $i,SV894: $i] :
( ( ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV894 @ SV1643 @ SV118 ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ SV543 @ SV1748 @ SV118 ) @ ( tc_fun @ SV118 @ tc_bool ) )
= $false )
| ( ( c_lessequals @ SV894 @ SV1643 @ SV118 )
= $false )
| ( ( c_lessequals @ SV543 @ SV894 @ SV118 )
= $true )
| ( ( class_Orderings_Oorder @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4263]) ).
thf(4306,plain,
! [SV1760: $i,SV1749: $i,SV1731: $i,SV1704: $i,SV1649: $i,SV1571: $i,SV1417: $i,SV1197: $i,SV915: $i,SV570: $i,SV146: $i] :
( ( ( c_Com_Ocom_Ocom__case @ SV146 @ SV570 @ SV915 @ SV1197 @ SV1417 @ SV1571 @ SV1649 @ SV1704 @ ( c_Com_Ocom_OSemi @ SV1731 @ SV1749 ) @ SV1760 )
= ( hAPP @ ( hAPP @ SV1197 @ SV1731 ) @ SV1749 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4266]) ).
thf(4307,plain,
! [SV1732: $i,SV1705: $i,SV1650: $i,SV149: $i,SV1572: $i,SV573: $i,SV1419: $i,SV918: $i,SV1199: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV1199 @ SV918 @ SV1419 ) ) )
= $true )
| ( ( ! [SY5286: $i,SY5287: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV573 @ SV1572 @ SV149 @ SV1650 @ SV1705 @ SV1732 @ SY5286 @ SY5287 @ SV1419 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV149 @ ( hAPP @ SV573 @ SV918 ) ) @ SV1199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4267]) ).
thf(4308,plain,
! [SV1733: $i,SV1706: $i,SV1651: $i,SV150: $i,SV919: $i,SV1573: $i,SV1420: $i,SV1200: $i,SV574: $i] :
( ( ( ~ ( hBOOL @ ( c_in @ SV574 @ SV1200 @ SV1420 ) ) )
= $true )
| ( ( ! [SY5288: $i,SY5289: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1573 @ SV919 @ SV150 @ SV1651 @ SV1706 @ SV1733 @ SY5288 @ SY5289 @ SV1420 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV150 @ SV574 ) @ ( hAPP @ SV919 @ SV1200 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4268]) ).
thf(4309,plain,
! [SV600: $i,SV944: $i,SV1750: $i,SV1734: $i,SV1656: $i,SV1580: $i,SV1434: $i,SV1223: $i,SV188: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV188 @ SV1223 @ SV1434 @ SV1580 @ SV1656 @ SV1734 @ SV1750 @ SV944 @ SV600 )
= $false )
| ( ( ( hAPP @ SV188 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV600 @ tc_bool ) ) )
= SV944 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4271]) ).
thf(4310,plain,
! [SV601: $i,SV1751: $i,SV945: $i,SV1735: $i,SV1657: $i,SV1581: $i,SV1435: $i,SV189: $i,SV1224: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV1224 @ SV189 @ SV1435 @ SV1581 @ SV1657 @ SV1735 @ SV945 @ SV1751 @ SV601 )
= $false )
| ( ( ( hAPP @ SV189 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV601 @ tc_bool ) ) )
= SV945 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4272]) ).
thf(4311,plain,
! [SV961: $i,SV630: $i,SV1234: $i,SV1761: $i,SV1736: $i,SV1441: $i,SV1708: $i,SV1658: $i,SV1582: $i,SV221: $i] :
( ( ( ! [SY5322: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV221 @ SV1582 @ SV1658 @ SV1708 @ SV1441 @ SV1736 @ SV1761 @ SY5322 @ SV1234 ) )
= $true )
| ( ( ( hAPP @ SV221 @ ( c_Set_Oinsert @ SV630 @ SV961 @ SV1234 ) )
= ( hAPP @ ( hAPP @ SV1441 @ SV630 ) @ ( hAPP @ SV221 @ SV961 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4273]) ).
thf(4312,plain,
! [SV962: $i,SV631: $i,SV1235: $i,SV1762: $i,SV1442: $i,SV1737: $i,SV1709: $i,SV1659: $i,SV222: $i,SV1583: $i] :
( ( ( ! [SY5323: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1583 @ SV222 @ SV1659 @ SV1709 @ SV1737 @ SV1442 @ SV1762 @ SY5323 @ SV1235 ) )
= $true )
| ( ( ( hAPP @ SV222 @ ( c_Set_Oinsert @ SV631 @ SV962 @ SV1235 ) )
= ( hAPP @ ( hAPP @ SV1442 @ SV631 ) @ ( hAPP @ SV222 @ SV962 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4274]) ).
thf(4313,plain,
! [SV988: $i,SV264: $i,SV1259: $i,SV1660: $i,SV1458: $i,SV661: $i,SV1752: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV1752 @ SV661 ) @ SV1458 ) ) )
= $true )
| ( ( ~ ( c_Hoare__Mirabelle_Otriple__valid @ SV1660 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1752 ) @ SV1259 ) @ SV264 ) @ t_a ) )
= $true )
| ( ( c_Natural_Oevaln @ SV1259 @ SV1458 @ SV1660 @ SV988 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV264 @ SV661 ) @ SV988 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4275]) ).
thf(4314,plain,
! [SV1763: $i,SV1753: $i,SV1738: $i,SV1711: $i,SV1662: $i,SV1586: $i,SV1465: $i,SV1265: $i,SV994: $i,SV665: $i,SV273: $i] :
( ( ! [SY5324: $i] :
( ( c_Com_Ocom_Ocom__case @ SV273 @ SV665 @ SV994 @ SV1265 @ SV1465 @ SV1586 @ SV1662 @ SV1711 @ ( c_Com_Ocom_OLocal @ SV1738 @ SV1753 @ SV1763 ) @ SY5324 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV994 @ SV1738 ) @ SV1753 ) @ SV1763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4276]) ).
thf(4315,plain,
! [SV1764: $i,SV1754: $i,SV1739: $i,SV1712: $i,SV1663: $i,SV1587: $i,SV1466: $i,SV1266: $i,SV995: $i,SV666: $i,SV274: $i] :
( ( ( c_Com_Ocom_Ocom__case @ SV274 @ SV666 @ SV995 @ SV1266 @ SV1466 @ SV1587 @ SV1663 @ SV1712 @ ( c_Com_Ocom_OWhile @ SV1739 @ SV1754 ) @ SV1764 )
= ( hAPP @ ( hAPP @ SV1587 @ SV1739 ) @ SV1754 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4277]) ).
thf(4316,plain,
! [SV1765: $i,SV1755: $i,SV1740: $i,SV1713: $i,SV1675: $i,SV1596: $i,SV1490: $i,SV1286: $i,SV1018: $i,SV704: $i,SV318: $i] :
( ( ! [SY5325: $i] :
( ( c_Com_Ocom_Ocom__case @ SV318 @ SV704 @ SV1018 @ SV1286 @ SV1490 @ SV1596 @ SV1675 @ SV1713 @ ( c_Com_Ocom_OCond @ SV1740 @ SV1755 @ SV1765 ) @ SY5325 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV1490 @ SV1740 ) @ SV1755 ) @ SV1765 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4280]) ).
thf(4317,plain,
! [SV1741: $i,SV1491: $i,SV1287: $i,SV1019: $i,SV1676: $i,SV1597: $i,SV1766: $i,SV705: $i,SV319: $i] :
( ( ( ( hAPP @ SV319 @ ( hAPP @ SV705 @ SV1766 ) )
= ( hAPP @ SV1597 @ ( hAPP @ SV1676 @ SV1766 ) ) )
= $true )
| ( ( ( c_Fun_Ocomp @ SV319 @ SV705 @ SV1019 @ SV1287 @ SV1491 )
= ( c_Fun_Ocomp @ SV1597 @ SV1676 @ SV1741 @ SV1287 @ SV1491 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4281]) ).
thf(4318,plain,
! [SV1742: $i,SV1714: $i,SV1677: $i,SV1598: $i,SV1492: $i,SV1288: $i,SV1020: $i,SV706: $i,SV320: $i] :
( ( ( ( hAPP @ SV320 @ ( hAPP @ SV706 @ SV1020 ) )
= ( hAPP @ SV1288 @ ( hAPP @ SV1492 @ SV1598 ) ) )
= $false )
| ( ( ! [SY5304: $i,SY5305: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV320 @ SV706 @ SV1677 @ SV1714 @ SV1742 ) @ SV1020 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1288 @ SV1492 @ SY5304 @ SV1714 @ SY5305 ) @ SV1598 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4282]) ).
thf(4319,plain,
! [SV1600: $i,SV1679: $i,SV325: $i,SV711: $i,SV1024: $i] :
( ( ( c_lessequals @ SV1024 @ SV711 @ SV325 )
= $false )
| ( ( c_lessequals @ SV1679 @ SV1600 @ SV325 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV711 @ SV1024 @ SV325 )
= ( c_HOL_Ominus__class_Ominus @ SV1600 @ SV1679 @ SV325 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV325 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4283]) ).
thf(4320,plain,
! [SV712: $i,SV1025: $i,SV326: $i,SV1601: $i,SV1680: $i] :
( ( ( c_lessequals @ SV1680 @ SV1601 @ SV326 )
= $false )
| ( ( c_lessequals @ SV1025 @ SV712 @ SV326 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV712 @ SV1025 @ SV326 )
= ( c_HOL_Ominus__class_Ominus @ SV1601 @ SV1680 @ SV326 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV326 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4284]) ).
thf(4321,plain,
! [SV1608: $i,SV1685: $i,SV1509: $i,SV1312: $i,SV1053: $i,SV740: $i,SV360: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1053 @ SV1312 @ SV740 ) ) @ SV1509 ) @ SV1685 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ ( c_Hoare__Mirabelle_Opeek__and @ SV1053 @ ( c_Fun_Ocomp @ c_Not @ SV1312 @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ SV740 ) ) @ SV1608 ) @ SV1685 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV360 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV740 ) @ SV1053 ) @ ( c_Com_Ocom_OCond @ SV1312 @ SV1509 @ SV1608 ) ) @ SV1685 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV740 ) ) @ SV740 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4287]) ).
thf(4322,plain,
! [SV746: $i,SV1057: $i,SV1767: $i,SV1757: $i,SV1717: $i,SV1686: $i,SV1609: $i,SV1510: $i,SV1315: $i,SV368: $i] :
( ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV368 @ SV1315 @ SV1510 @ SV1609 @ SV1686 @ SV1717 @ SV1757 @ SV1767 @ SV1057 ) )
= $true )
| ( ( ( hAPP @ SV368 @ ( c_Set_Oinsert @ SV746 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1057 @ tc_bool ) ) @ SV1057 ) )
= SV746 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4288]) ).
thf(4323,plain,
! [SV747: $i,SV1058: $i,SV1768: $i,SV1758: $i,SV1718: $i,SV1687: $i,SV1610: $i,SV1511: $i,SV369: $i,SV1316: $i] :
( ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1316 @ SV369 @ SV1511 @ SV1610 @ SV1687 @ SV1718 @ SV1758 @ SV1768 @ SV1058 ) )
= $true )
| ( ( ( hAPP @ SV369 @ ( c_Set_Oinsert @ SV747 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1058 @ tc_bool ) ) @ SV1058 ) )
= SV747 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4289]) ).
thf(4324,plain,
! [SV1061: $i,SV752: $i,SV1320: $i,SV1769: $i,SV1744: $i,SV1512: $i,SV1719: $i,SV1688: $i,SV1611: $i,SV376: $i] :
( ( ( ! [SY5326: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV376 @ SV1611 @ SV1688 @ SV1719 @ SV1512 @ SV1744 @ SV1769 @ SY5326 @ SV1320 ) )
= $true )
| ( ( ( hAPP @ SV376 @ ( c_Set_Oinsert @ SV752 @ ( c_Set_Oinsert @ SV1061 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1320 @ tc_bool ) ) @ SV1320 ) @ SV1320 ) )
= ( hAPP @ ( hAPP @ SV1512 @ SV752 ) @ SV1061 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4290]) ).
thf(4325,plain,
! [SV1062: $i,SV753: $i,SV1321: $i,SV1770: $i,SV1513: $i,SV1745: $i,SV1720: $i,SV1689: $i,SV377: $i,SV1612: $i] :
( ( ( ! [SY5327: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1612 @ SV377 @ SV1689 @ SV1720 @ SV1745 @ SV1513 @ SV1770 @ SY5327 @ SV1321 ) )
= $true )
| ( ( ( hAPP @ SV377 @ ( c_Set_Oinsert @ SV753 @ ( c_Set_Oinsert @ SV1062 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1321 @ tc_bool ) ) @ SV1321 ) @ SV1321 ) )
= ( hAPP @ ( hAPP @ SV1513 @ SV753 ) @ SV1062 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4291]) ).
thf(4326,plain,
! [SV1515: $i,SV1070: $i,SV1329: $i,SV764: $i,SV391: $i,SV1690: $i,SV1721: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1721 @ SV1690 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV391 @ SV764 @ SV1329 @ SV1070 ) ) )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV391 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1721 ) @ SV1070 ) @ SV1515 ) @ ( 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 @ SV1515 @ SV1690 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV391 @ SV764 @ SV1329 @ SV1070 @ SV1721 @ SV1515 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV391 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV764 ) @ SV1070 ) @ SV1329 ) @ ( 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)],[4292]) ).
thf(4327,plain,
! [SV1071: $i,SV392: $i,SV1516: $i,SV1330: $i,SV765: $i,SV1691: $i,SV1722: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1722 @ SV1691 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV765 @ SV1722 @ SV1330 @ SV1516 ) ) )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV392 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1722 ) @ SV1071 ) @ SV1516 ) @ ( 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 @ SV1516 @ SV1691 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV765 @ SV1722 @ SV1330 @ SV1516 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV392 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV765 ) @ SV1071 ) @ SV1330 ) @ ( 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)],[4293]) ).
thf(4328,plain,
! [SV1517: $i,SV1072: $i,SV1331: $i,SV766: $i,SV393: $i,SV1692: $i,SV1723: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1723 @ SV1692 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV393 @ SV766 @ SV1331 @ SV1072 ) ) )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ SV393 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1723 ) @ SV1072 ) @ SV1517 ) @ ( 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 @ SV1517 @ SV1692 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV393 @ SV766 @ SV1331 @ SV1072 @ SV1723 @ SV1517 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV393 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV766 ) @ SV1072 ) @ SV1331 ) @ ( 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)],[4294]) ).
thf(4329,plain,
! [SV1621: $i,SV1520: $i,SV1724: $i,SV1345: $i,SV1089: $i,SV783: $i,SV410: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SV1089 ) @ SV1345 ) @ SV1724 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SV1724 ) @ SV1520 ) @ SV1621 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 )
= $false )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV410 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ SV783 ) @ SV1089 ) @ ( c_Com_Ocom_OSemi @ SV1345 @ SV1520 ) ) @ SV1621 ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ SV783 ) ) @ SV783 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4298]) ).
thf(4330,plain,
! [SV1384: $i,SV1630: $i,SV1136: $i,SV487: $i,SV846: $i,SV52: $i] :
( ( ( hBOOL @ ( hAPP @ SV52 @ SV846 ) )
= $false )
| ( ( c_Natural_Oevaln @ SV487 @ SV846 @ SV1136 @ SV1630 )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV52 @ SV487 ) @ SV1630 @ SV1136 @ SV1384 )
= $false )
| ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ SV52 @ SV487 ) @ SV846 @ SV1136 @ SV1384 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4301]) ).
thf(4331,plain,
! [SV1771: $i,SV1759: $i,SV1746: $i,SV1729: $i,SV1701: $i,SV1632: $i,SV1549: $i,SV1389: $i,SV1146: $i,SV855: $i,SV499: $i,SV64: $i] :
( ( ( c_Com_Ocom_Ocom__case @ SV64 @ SV499 @ SV855 @ SV1146 @ SV1389 @ SV1549 @ SV1632 @ SV1701 @ ( c_Com_Ocom_OCall @ SV1729 @ SV1746 @ SV1759 ) @ SV1771 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV1701 @ SV1729 ) @ SV1746 ) @ SV1759 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4302]) ).
thf(4332,plain,
! [SV1732: $i,SV1705: $i,SV1650: $i,SV149: $i,SV1572: $i,SV573: $i,SV1419: $i,SV918: $i,SV1199: $i] :
( ( ( hBOOL @ ( c_in @ SV1199 @ SV918 @ SV1419 ) )
= $false )
| ( ( ! [SY5286: $i,SY5287: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV573 @ SV1572 @ SV149 @ SV1650 @ SV1705 @ SV1732 @ SY5286 @ SY5287 @ SV1419 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV149 @ ( hAPP @ SV573 @ SV918 ) ) @ SV1199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4307]) ).
thf(4333,plain,
! [SV1733: $i,SV1706: $i,SV1651: $i,SV150: $i,SV919: $i,SV1573: $i,SV1420: $i,SV1200: $i,SV574: $i] :
( ( ( hBOOL @ ( c_in @ SV574 @ SV1200 @ SV1420 ) )
= $false )
| ( ( ! [SY5288: $i,SY5289: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1573 @ SV919 @ SV150 @ SV1651 @ SV1706 @ SV1733 @ SY5288 @ SY5289 @ SV1420 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV150 @ SV574 ) @ ( hAPP @ SV919 @ SV1200 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4308]) ).
thf(4334,plain,
! [SV961: $i,SV630: $i,SV1234: $i,SV1772: $i,SV1761: $i,SV1736: $i,SV1441: $i,SV1708: $i,SV1658: $i,SV1582: $i,SV221: $i] :
( ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV221 @ SV1582 @ SV1658 @ SV1708 @ SV1441 @ SV1736 @ SV1761 @ SV1772 @ SV1234 ) )
= $true )
| ( ( ( hAPP @ SV221 @ ( c_Set_Oinsert @ SV630 @ SV961 @ SV1234 ) )
= ( hAPP @ ( hAPP @ SV1441 @ SV630 ) @ ( hAPP @ SV221 @ SV961 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4311]) ).
thf(4335,plain,
! [SV962: $i,SV631: $i,SV1235: $i,SV1773: $i,SV1762: $i,SV1442: $i,SV1737: $i,SV1709: $i,SV1659: $i,SV222: $i,SV1583: $i] :
( ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1583 @ SV222 @ SV1659 @ SV1709 @ SV1737 @ SV1442 @ SV1762 @ SV1773 @ SV1235 ) )
= $true )
| ( ( ( hAPP @ SV222 @ ( c_Set_Oinsert @ SV631 @ SV962 @ SV1235 ) )
= ( hAPP @ ( hAPP @ SV1442 @ SV631 ) @ ( hAPP @ SV222 @ SV962 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4312]) ).
thf(4336,plain,
! [SV988: $i,SV264: $i,SV1259: $i,SV1660: $i,SV1458: $i,SV661: $i,SV1752: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1752 @ SV661 ) @ SV1458 ) )
= $false )
| ( ( ~ ( c_Hoare__Mirabelle_Otriple__valid @ SV1660 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1752 ) @ SV1259 ) @ SV264 ) @ t_a ) )
= $true )
| ( ( c_Natural_Oevaln @ SV1259 @ SV1458 @ SV1660 @ SV988 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV264 @ SV661 ) @ SV988 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4313]) ).
thf(4337,plain,
! [SV1774: $i,SV1763: $i,SV1753: $i,SV1738: $i,SV1711: $i,SV1662: $i,SV1586: $i,SV1465: $i,SV1265: $i,SV994: $i,SV665: $i,SV273: $i] :
( ( ( c_Com_Ocom_Ocom__case @ SV273 @ SV665 @ SV994 @ SV1265 @ SV1465 @ SV1586 @ SV1662 @ SV1711 @ ( c_Com_Ocom_OLocal @ SV1738 @ SV1753 @ SV1763 ) @ SV1774 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV994 @ SV1738 ) @ SV1753 ) @ SV1763 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4314]) ).
thf(4338,plain,
! [SV1775: $i,SV1765: $i,SV1755: $i,SV1740: $i,SV1713: $i,SV1675: $i,SV1596: $i,SV1490: $i,SV1286: $i,SV1018: $i,SV704: $i,SV318: $i] :
( ( ( c_Com_Ocom_Ocom__case @ SV318 @ SV704 @ SV1018 @ SV1286 @ SV1490 @ SV1596 @ SV1675 @ SV1713 @ ( c_Com_Ocom_OCond @ SV1740 @ SV1755 @ SV1765 ) @ SV1775 )
= ( hAPP @ ( hAPP @ ( hAPP @ SV1490 @ SV1740 ) @ SV1755 ) @ SV1765 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4316]) ).
thf(4339,plain,
! [SV1598: $i,SV1776: $i,SV1492: $i,SV1288: $i,SV1020: $i,SV1742: $i,SV1714: $i,SV1677: $i,SV706: $i,SV320: $i] :
( ( ( ! [SY5328: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ SV320 @ SV706 @ SV1677 @ SV1714 @ SV1742 ) @ SV1020 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1288 @ SV1492 @ SV1776 @ SV1714 @ SY5328 ) @ SV1598 ) ) )
= $true )
| ( ( ( hAPP @ SV320 @ ( hAPP @ SV706 @ SV1020 ) )
= ( hAPP @ SV1288 @ ( hAPP @ SV1492 @ SV1598 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4318]) ).
thf(4340,plain,
! [SV746: $i,SV1057: $i,SV1767: $i,SV1757: $i,SV1717: $i,SV1686: $i,SV1609: $i,SV1510: $i,SV1315: $i,SV368: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV368 @ SV1315 @ SV1510 @ SV1609 @ SV1686 @ SV1717 @ SV1757 @ SV1767 @ SV1057 )
= $false )
| ( ( ( hAPP @ SV368 @ ( c_Set_Oinsert @ SV746 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1057 @ tc_bool ) ) @ SV1057 ) )
= SV746 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4322]) ).
thf(4341,plain,
! [SV747: $i,SV1058: $i,SV1768: $i,SV1758: $i,SV1718: $i,SV1687: $i,SV1610: $i,SV1511: $i,SV369: $i,SV1316: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV1316 @ SV369 @ SV1511 @ SV1610 @ SV1687 @ SV1718 @ SV1758 @ SV1768 @ SV1058 )
= $false )
| ( ( ( hAPP @ SV369 @ ( c_Set_Oinsert @ SV747 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1058 @ tc_bool ) ) @ SV1058 ) )
= SV747 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4323]) ).
thf(4342,plain,
! [SV1061: $i,SV752: $i,SV1320: $i,SV1777: $i,SV1769: $i,SV1744: $i,SV1512: $i,SV1719: $i,SV1688: $i,SV1611: $i,SV376: $i] :
( ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV376 @ SV1611 @ SV1688 @ SV1719 @ SV1512 @ SV1744 @ SV1769 @ SV1777 @ SV1320 ) )
= $true )
| ( ( ( hAPP @ SV376 @ ( c_Set_Oinsert @ SV752 @ ( c_Set_Oinsert @ SV1061 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1320 @ tc_bool ) ) @ SV1320 ) @ SV1320 ) )
= ( hAPP @ ( hAPP @ SV1512 @ SV752 ) @ SV1061 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4324]) ).
thf(4343,plain,
! [SV1062: $i,SV753: $i,SV1321: $i,SV1778: $i,SV1770: $i,SV1513: $i,SV1745: $i,SV1720: $i,SV1689: $i,SV377: $i,SV1612: $i] :
( ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1612 @ SV377 @ SV1689 @ SV1720 @ SV1745 @ SV1513 @ SV1770 @ SV1778 @ SV1321 ) )
= $true )
| ( ( ( hAPP @ SV377 @ ( c_Set_Oinsert @ SV753 @ ( c_Set_Oinsert @ SV1062 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1321 @ tc_bool ) ) @ SV1321 ) @ SV1321 ) )
= ( hAPP @ ( hAPP @ SV1513 @ SV753 ) @ SV1062 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4325]) ).
thf(4344,plain,
! [SV1329: $i,SV764: $i,SV1690: $i,SV1515: $i,SV1070: $i,SV1721: $i,SV391: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV391 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1721 ) @ SV1070 ) @ SV1515 ) @ ( 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 @ SV1721 @ SV1690 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ SV391 @ SV764 @ SV1329 @ SV1070 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1515 @ SV1690 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ SV391 @ SV764 @ SV1329 @ SV1070 @ SV1721 @ SV1515 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV391 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV764 ) @ SV1070 ) @ SV1329 ) @ ( 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)],[4326]) ).
thf(4345,plain,
! [SV1330: $i,SV765: $i,SV1691: $i,SV1516: $i,SV1071: $i,SV1722: $i,SV392: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV392 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1722 ) @ SV1071 ) @ SV1516 ) @ ( 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 @ SV1722 @ SV1691 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ SV765 @ SV1722 @ SV1330 @ SV1516 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1516 @ SV1691 ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ SV765 @ SV1722 @ SV1330 @ SV1516 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV392 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV765 ) @ SV1071 ) @ SV1330 ) @ ( 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)],[4327]) ).
thf(4346,plain,
! [SV1331: $i,SV766: $i,SV1692: $i,SV1517: $i,SV1072: $i,SV1723: $i,SV393: $i] :
( ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV393 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1723 ) @ SV1072 ) @ SV1517 ) @ ( 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 @ SV1723 @ SV1692 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ SV393 @ SV766 @ SV1331 @ SV1072 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1517 @ SV1692 ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ SV393 @ SV766 @ SV1331 @ SV1072 @ SV1723 @ SV1517 ) ) )
= $true )
| ( ( c_Hoare__Mirabelle_Ohoare__derivs @ SV393 @ ( c_Set_Oinsert @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV766 ) @ SV1072 ) @ SV1331 ) @ ( 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)],[4328]) ).
thf(4347,plain,
! [SV918: $i,SV1199: $i,SV1419: $i,SV1779: $i,SV1732: $i,SV1705: $i,SV1650: $i,SV149: $i,SV1572: $i,SV573: $i] :
( ( ( ! [SY5329: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV573 @ SV1572 @ SV149 @ SV1650 @ SV1705 @ SV1732 @ SV1779 @ SY5329 @ SV1419 ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV1199 @ SV918 @ SV1419 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV149 @ ( hAPP @ SV573 @ SV918 ) ) @ SV1199 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4332]) ).
thf(4348,plain,
! [SV1200: $i,SV574: $i,SV1420: $i,SV1780: $i,SV1733: $i,SV1706: $i,SV1651: $i,SV150: $i,SV919: $i,SV1573: $i] :
( ( ( ! [SY5330: $i] :
~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1573 @ SV919 @ SV150 @ SV1651 @ SV1706 @ SV1733 @ SV1780 @ SY5330 @ SV1420 ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV574 @ SV1200 @ SV1420 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV150 @ SV574 ) @ ( hAPP @ SV919 @ SV1200 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4333]) ).
thf(4349,plain,
! [SV961: $i,SV630: $i,SV1234: $i,SV1772: $i,SV1761: $i,SV1736: $i,SV1441: $i,SV1708: $i,SV1658: $i,SV1582: $i,SV221: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV221 @ SV1582 @ SV1658 @ SV1708 @ SV1441 @ SV1736 @ SV1761 @ SV1772 @ SV1234 )
= $false )
| ( ( ( hAPP @ SV221 @ ( c_Set_Oinsert @ SV630 @ SV961 @ SV1234 ) )
= ( hAPP @ ( hAPP @ SV1441 @ SV630 ) @ ( hAPP @ SV221 @ SV961 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4334]) ).
thf(4350,plain,
! [SV962: $i,SV631: $i,SV1235: $i,SV1773: $i,SV1762: $i,SV1442: $i,SV1737: $i,SV1709: $i,SV1659: $i,SV222: $i,SV1583: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV1583 @ SV222 @ SV1659 @ SV1709 @ SV1737 @ SV1442 @ SV1762 @ SV1773 @ SV1235 )
= $false )
| ( ( ( hAPP @ SV222 @ ( c_Set_Oinsert @ SV631 @ SV962 @ SV1235 ) )
= ( hAPP @ ( hAPP @ SV1442 @ SV631 ) @ ( hAPP @ SV222 @ SV962 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4335]) ).
thf(4351,plain,
! [SV988: $i,SV1458: $i,SV661: $i,SV264: $i,SV1259: $i,SV1752: $i,SV1660: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ SV1660 @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ t_a ) @ SV1752 ) @ SV1259 ) @ SV264 ) @ t_a )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1752 @ SV661 ) @ SV1458 ) )
= $false )
| ( ( c_Natural_Oevaln @ SV1259 @ SV1458 @ SV1660 @ SV988 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV264 @ SV661 ) @ SV988 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4336]) ).
thf(4352,plain,
! [SV1598: $i,SV1781: $i,SV1776: $i,SV1492: $i,SV1288: $i,SV1020: $i,SV1742: $i,SV1714: $i,SV1677: $i,SV706: $i,SV320: $i] :
( ( ( ( hAPP @ ( c_Fun_Ocomp @ SV320 @ SV706 @ SV1677 @ SV1714 @ SV1742 ) @ SV1020 )
= ( hAPP @ ( c_Fun_Ocomp @ SV1288 @ SV1492 @ SV1776 @ SV1714 @ SV1781 ) @ SV1598 ) )
= $true )
| ( ( ( hAPP @ SV320 @ ( hAPP @ SV706 @ SV1020 ) )
= ( hAPP @ SV1288 @ ( hAPP @ SV1492 @ SV1598 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4339]) ).
thf(4353,plain,
! [SV1061: $i,SV752: $i,SV1320: $i,SV1777: $i,SV1769: $i,SV1744: $i,SV1512: $i,SV1719: $i,SV1688: $i,SV1611: $i,SV376: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV376 @ SV1611 @ SV1688 @ SV1719 @ SV1512 @ SV1744 @ SV1769 @ SV1777 @ SV1320 )
= $false )
| ( ( ( hAPP @ SV376 @ ( c_Set_Oinsert @ SV752 @ ( c_Set_Oinsert @ SV1061 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1320 @ tc_bool ) ) @ SV1320 ) @ SV1320 ) )
= ( hAPP @ ( hAPP @ SV1512 @ SV752 ) @ SV1061 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4342]) ).
thf(4354,plain,
! [SV1062: $i,SV753: $i,SV1321: $i,SV1778: $i,SV1770: $i,SV1513: $i,SV1745: $i,SV1720: $i,SV1689: $i,SV377: $i,SV1612: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV1612 @ SV377 @ SV1689 @ SV1720 @ SV1745 @ SV1513 @ SV1770 @ SV1778 @ SV1321 )
= $false )
| ( ( ( hAPP @ SV377 @ ( c_Set_Oinsert @ SV753 @ ( c_Set_Oinsert @ SV1062 @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ SV1321 @ tc_bool ) ) @ SV1321 ) @ SV1321 ) )
= ( hAPP @ ( hAPP @ SV1513 @ SV753 ) @ SV1062 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4343]) ).
thf(4355,plain,
! [SV918: $i,SV1199: $i,SV1419: $i,SV1782: $i,SV1779: $i,SV1732: $i,SV1705: $i,SV1650: $i,SV149: $i,SV1572: $i,SV573: $i] :
( ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV573 @ SV1572 @ SV149 @ SV1650 @ SV1705 @ SV1732 @ SV1779 @ SV1782 @ SV1419 ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV1199 @ SV918 @ SV1419 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV149 @ ( hAPP @ SV573 @ SV918 ) ) @ SV1199 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4347]) ).
thf(4356,plain,
! [SV1200: $i,SV574: $i,SV1420: $i,SV1783: $i,SV1780: $i,SV1733: $i,SV1706: $i,SV1651: $i,SV150: $i,SV919: $i,SV1573: $i] :
( ( ( ~ ( c_Complete__Lattice_Ocomplete__lattice @ SV1573 @ SV919 @ SV150 @ SV1651 @ SV1706 @ SV1733 @ SV1780 @ SV1783 @ SV1420 ) )
= $true )
| ( ( hBOOL @ ( c_in @ SV574 @ SV1200 @ SV1420 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV150 @ SV574 ) @ ( hAPP @ SV919 @ SV1200 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4348]) ).
thf(4357,plain,
! [SV918: $i,SV1199: $i,SV1419: $i,SV1782: $i,SV1779: $i,SV1732: $i,SV1705: $i,SV1650: $i,SV149: $i,SV1572: $i,SV573: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV573 @ SV1572 @ SV149 @ SV1650 @ SV1705 @ SV1732 @ SV1779 @ SV1782 @ SV1419 )
= $false )
| ( ( hBOOL @ ( c_in @ SV1199 @ SV918 @ SV1419 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV149 @ ( hAPP @ SV573 @ SV918 ) ) @ SV1199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4355]) ).
thf(4358,plain,
! [SV1200: $i,SV574: $i,SV1420: $i,SV1783: $i,SV1780: $i,SV1733: $i,SV1706: $i,SV1651: $i,SV150: $i,SV919: $i,SV1573: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice @ SV1573 @ SV919 @ SV150 @ SV1651 @ SV1706 @ SV1733 @ SV1780 @ SV1783 @ SV1420 )
= $false )
| ( ( hBOOL @ ( c_in @ SV574 @ SV1200 @ SV1420 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV150 @ SV574 ) @ ( hAPP @ SV919 @ SV1200 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4356]) ).
thf(4359,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1207,4358,4357,4354,4353,4352,4351,4350,4349,4346,4345,4344,4341,4340,4338,4337,4331,4330,4329,4321,4320,4319,4317,4315,4310,4309,4306,4305,4304,4303,4300,4299,4297,4296,4295,4286,4285,4279,4278,4270,4269,4265,4264,4260,4259,4257,4256,4253,4251,4250,4249,4248,4247,4246,4244,4242,4240,4228,4220,4216,4215,4214,4213,4212,4211,4206,4198,4197,4192,4191,4183,4182,4181,4180,4175,4174,4173,4172,4168,4167,4161,4159,4148,4147,4145,4141,4140,4136,4135,4134,4133,4132,4131,4130,4129,4126,4125,4124,4123,4122,4121,4120,4119,4118,4117,4113,4112,4111,4106,4102,4099,4086,4082,4081,4080,4077,4076,4075,4073,4072,4071,4064,4063,4053,4052,4051,4050,4039,4038,4021,4017,4016,4014,4012,4010,4009,3985,3980,3975,3971,3970,3969,3968,3967,3963,3961,3957,3955,3949,3948,3946,3945,3944,3943,3934,3932,3931,3929,3922,3920,3919,3914,3913,3911,3906,3894,3893,3892,3891,3890,3889,3888,3887,3886,3885,3884,3876,3850,3845,3844,3843,3839,3836,3835,3831,3816,3806,3805,3797,3796,3795,3794,3790,3783,3767,3763,3760,3759,3755,3754,3753,3751,3750,3749,3748,3745,3741,3740,3739,3738,3733,3732,3731,3728,3727,3724,3719,3715,3714,3711,3710,3705,3700,3696,3695,3693,3692,3691,3690,3689,3684,3675,3671,3670,3669,3655,3653,3640,3639,3638,3637,3636,3634,3621,3620,3617,3609,3607,3603,3602,3601,3588,3580,3579,3578,3577,3575,3574,3570,3563,3536,3521,3517,3516,3515,3498,3497,3495,3488,3483,3482,3481,3480,3479,3475,3459,3458,3452,3451,3450,3449,3446,3445,3440,3426,3409,3406,3405,3393,3387,3382,3381,3370,3361,3356,3355,3351,3349,3348,3345,3344,3340,3339,3333,3332,3331,3330,3329,3328,3327,3326,3325,3324,3321,3320,3310,3288,3286,3285,3281,3280,3277,3276,3275,3258,3254,3253,3251,3229,3227,3226,3204,3197,3189,3188,3177,3163,3160,3154,3153,3145,3136,3134,3126,3125,3124,3120,3106,3101,3100,3091,3087,3086,3076,3075,3066,3065,3064,3063,3057,3043,3026,3021,3016,3005,3004,2986,2955,2952,2949,2939,2936,2916,2913,2911,2902,2896,2895,2871,2830,2817,2776,2775,2774,2769,2756,2752,2747,2746,2744,2712,2705,2702,2697,2696,2695,2692,2674,2673,2643,2634,2614,2612,2611,2586,2582,2570,2569,2560,2541,2499,2493,2489,2485,2483,2476,2475,2464,2441,2427,2424,2411,2410,2381,2380,2379,2354,2330,2323,2322,2321,2320,2319,2318,2226,2211,2210,2209,2202,2188,2177,2121,1922,1872,1863,1677,1673,1672,1671,1670,1669,1668,1667,1666,1665,1664,1663,1662,1661,1660,1659,1658,1657,1619,1571,1570,1569,1565,1474,1254]) ).
thf(4360,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[4359]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV840-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.19 % Computer : n017.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 16:41:31 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 195.52/32.95 ...
% 195.52/32.95
% 195.52/32.95 No.of.Axioms: 469
% 195.52/32.95
% 195.52/32.95 Length.of.Defs: 0
% 195.52/32.95
% 195.52/32.95 Contains.Choice.Funs: false
% 195.52/32.95 .....................................................................................................................................................................................................
% 195.52/32.95
% 195.52/32.95 ********************************
% 195.52/32.95 * All subproblems solved! *
% 195.52/32.95 ********************************
% 195.52/32.95 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:469,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:297,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:4359,loop_count:0,foatp_calls:1,translation:fof_full)
% 195.52/32.95
% 195.52/32.95 %**** Beginning of derivation protocol ****
% 195.52/32.95 % SZS output start CNFRefutation
% See solution above
% 195.52/32.98
% 195.52/32.98 %**** End of derivation protocol ****
% 195.52/32.98 %**** no. of clauses in derivation: 4360 ****
% 195.52/32.98 %**** clause counter: 4359 ****
% 195.52/32.98
% 195.52/32.98 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:469,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:297,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:4359,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------