%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL848-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 10:30:54 AM UTC 2026
% Result : Unsatisfiable 216.65s 36.32s
% Output : CNFRefutation 216.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 724
% Syntax : Number of formulae : 5914 (3872 unt; 0 typ; 0 def)
% Number of atoms : 30198 (12317 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 84610 (6690 ~;8776 |; 0 &;69144 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 100 ( 97 usr; 14 con; 0-5 aty)
% Number of variables : 18928 ( 0 ^;18928 !; 0 ?;18928 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_COMBC,type,
c_COMBC: $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_Oone__class_Oone,type,
c_HOL_Oone__class_Oone: $i > $i ).
thf(tp_c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(tp_c_HOL_Oplus__class_Oplus,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
thf(tp_c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(tp_c_InductTermi_OIT,type,
c_InductTermi_OIT: $i ).
thf(tp_c_Int_Onumber__class_Onumber__of,type,
c_Int_Onumber__class_Onumber__of: $i > $i > $i ).
thf(tp_c_Lambda_Obeta,type,
c_Lambda_Obeta: $i ).
thf(tp_c_Lambda_OdB_OAbs,type,
c_Lambda_OdB_OAbs: $i > $i ).
thf(tp_c_Lambda_OdB_OApp,type,
c_Lambda_OdB_OApp: $i ).
thf(tp_c_Lambda_OdB_OVar,type,
c_Lambda_OdB_OVar: $i > $i ).
thf(tp_c_Lambda_OdB_OdB__case,type,
c_Lambda_OdB_OdB__case: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Lambda_OdB_OdB__size,type,
c_Lambda_OdB_OdB__size: $i > $i ).
thf(tp_c_Lambda_Olift,type,
c_Lambda_Olift: $i ).
thf(tp_c_Lambda_Osubst,type,
c_Lambda_Osubst: $i ).
thf(tp_c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1,type,
c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1,type,
c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1: $i > $i > $i > $i ).
thf(tp_c_ListOrder_Ostep1,type,
c_ListOrder_Ostep1: $i > $i > $i > $i > $o ).
thf(tp_c_List_Oappend,type,
c_List_Oappend: $i > $i > $i > $i ).
thf(tp_c_List_Obutlast,type,
c_List_Obutlast: $i > $i > $i ).
thf(tp_c_List_Odrop,type,
c_List_Odrop: $i > $i > $i > $i ).
thf(tp_c_List_Ofoldl,type,
c_List_Ofoldl: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Ohd,type,
c_List_Ohd: $i > $i > $i ).
thf(tp_c_List_Olast,type,
c_List_Olast: $i > $i > $i ).
thf(tp_c_List_Olength__unique,type,
c_List_Olength__unique: $i > $i > $i ).
thf(tp_c_List_Olinorder__class_Oinsort__key,type,
c_List_Olinorder__class_Oinsort__key: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Olinorder__class_Osorted,type,
c_List_Olinorder__class_Osorted: $i > $i > $o ).
thf(tp_c_List_Olist_OCons,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(tp_c_List_Olist_ONil,type,
c_List_Olist_ONil: $i > $i ).
thf(tp_c_List_Olist_Olist__size,type,
c_List_Olist_Olist__size: $i > $i > $i > $i ).
thf(tp_c_List_Olist__update,type,
c_List_Olist__update: $i > $i > $i > $i > $i ).
thf(tp_c_List_Olistsp,type,
c_List_Olistsp: $i > $i > $i > $o ).
thf(tp_c_List_Olistsum,type,
c_List_Olistsum: $i > $i > $i ).
thf(tp_c_List_Omap,type,
c_List_Omap: $i > $i > $i > $i > $i ).
thf(tp_c_List_Onth,type,
c_List_Onth: $i > $i > $i > $i ).
thf(tp_c_List_Oreplicate,type,
c_List_Oreplicate: $i > $i > $i > $i ).
thf(tp_c_List_Orev,type,
c_List_Orev: $i > $i > $i ).
thf(tp_c_List_Oset,type,
c_List_Oset: $i > $i > $i ).
thf(tp_c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1,type,
c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_List_Osplice,type,
c_List_Osplice: $i > $i > $i > $i ).
thf(tp_c_List_Osublist,type,
c_List_Osublist: $i > $i > $i > $i ).
thf(tp_c_List_Otake,type,
c_List_Otake: $i > $i > $i > $i ).
thf(tp_c_List_OtakeWhile,type,
c_List_OtakeWhile: $i > $i > $i > $i ).
thf(tp_c_Nat_Osemiring__1__class_Oof__nat,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).
thf(tp_c_Nat_Osize__class_Osize,type,
c_Nat_Osize__class_Osize: $i > $i > $i ).
thf(tp_c_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(tp_c_Suc,type,
c_Suc: $i > $i ).
thf(tp_c_Type_Otyping,type,
c_Type_Otyping: $i > $i > $i > $o ).
thf(tp_c_fequal,type,
c_fequal: $i > $i > $i > $o ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_class_Int_Onumber,type,
class_Int_Onumber: $i > $o ).
thf(tp_class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
thf(tp_class_Int_Oring__char__0,type,
class_Int_Oring__char__0: $i > $o ).
thf(tp_class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(tp_class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Oab__semigroup__add,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Ocancel__ab__semigroup__add,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Ocancel__semigroup__add,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Ocomm__monoid__add,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
thf(tp_class_OrderedGroup_Ogroup__add,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Olordered__ab__group__add,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Omonoid__add,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
thf(tp_class_OrderedGroup_Omonoid__mult,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__ab__semigroup__add,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__cancel__ab__semigroup__add,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
thf(tp_class_OrderedGroup_Opordered__comm__monoid__add,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
thf(tp_class_OrderedGroup_Osemigroup__add,type,
class_OrderedGroup_Osemigroup__add: $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_Power_Opower,type,
class_Power_Opower: $i > $o ).
thf(tp_class_Ring__and__Field_Ocomm__semiring__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
thf(tp_class_Ring__and__Field_Oidom,type,
class_Ring__and__Field_Oidom: $i > $o ).
thf(tp_class_Ring__and__Field_Omult__zero,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
thf(tp_class_Ring__and__Field_Ono__zero__divisors,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
thf(tp_class_Ring__and__Field_Oring__1,type,
class_Ring__and__Field_Oring__1: $i > $o ).
thf(tp_class_Ring__and__Field_Oring__1__no__zero__divisors,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
thf(tp_class_Ring__and__Field_Osemiring__0,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(tp_class_Ring__and__Field_Osemiring__1,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(tp_class_Ring__and__Field_Ozero__neq__one,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
thf(tp_hAPP,type,
hAPP: $i > $i > $i ).
thf(tp_hBOOL,type,
hBOOL: $i > $o ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_tc_Int_Oint,type,
tc_Int_Oint: $i ).
thf(tp_tc_Lambda_OdB,type,
tc_Lambda_OdB: $i ).
thf(tp_tc_List_Olist,type,
tc_List_Olist: $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_s____,type,
v_s____: $i ).
thf(tp_v_ta____,type,
v_ta____: $i ).
thf(1,axiom,
! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( c_fequal @ V_X @ V_Y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(2,axiom,
! [V_x: $i,T_a: $i] : ( c_fequal @ V_x @ V_x @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(3,axiom,
class_Int_Onumber @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).
thf(4,axiom,
class_Power_Opower @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Power_Opower) ).
thf(5,axiom,
class_Int_Onumber__ring @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).
thf(6,axiom,
class_Int_Oring__char__0 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).
thf(7,axiom,
class_Orderings_Oorder @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).
thf(8,axiom,
class_Orderings_Olinorder @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).
thf(9,axiom,
class_Orderings_Opreorder @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).
thf(10,axiom,
class_Nat_Osemiring__char__0 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Nat_Osemiring__char__0) ).
thf(11,axiom,
class_Ring__and__Field_Oidom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).
thf(12,axiom,
class_Ring__and__Field_Oring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1) ).
thf(13,axiom,
class_OrderedGroup_Ogroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).
thf(14,axiom,
class_OrderedGroup_Omonoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__add) ).
thf(15,axiom,
class_OrderedGroup_Omonoid__mult @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).
thf(16,axiom,
class_Ring__and__Field_Omult__zero @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).
thf(17,axiom,
class_OrderedGroup_Oab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).
thf(18,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__0) ).
thf(19,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring__1) ).
thf(20,axiom,
class_OrderedGroup_Osemigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Osemigroup__add) ).
thf(21,axiom,
class_Ring__and__Field_Oordered__idom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).
thf(22,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).
thf(23,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).
thf(24,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) ).
thf(25,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).
thf(26,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).
thf(27,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).
thf(28,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) ).
thf(29,axiom,
class_OrderedGroup_Olordered__ab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).
thf(30,axiom,
class_OrderedGroup_Opordered__ab__group__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).
thf(31,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(32,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) ).
thf(33,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(34,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) ).
thf(35,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(36,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_Int_Oint,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(37,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(38,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(39,axiom,
class_Int_Onumber @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).
thf(40,axiom,
class_Power_Opower @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(41,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(42,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(43,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(44,axiom,
class_Nat_Osemiring__char__0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(45,axiom,
class_OrderedGroup_Omonoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(46,axiom,
class_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(47,axiom,
class_Ring__and__Field_Omult__zero @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(48,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(49,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(50,axiom,
class_OrderedGroup_Osemigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
thf(51,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
thf(52,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(53,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(54,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(55,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(56,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
thf(57,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(58,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(59,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(60,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(61,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(62,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(63,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(64,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(65,axiom,
c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Olist_OCons @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ v_ta____ ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(66,axiom,
! [V_dB1_H: $i,V_dB2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
thf(67,axiom,
! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ ( c_Lambda_OdB_OVar @ V_i ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
thf(68,axiom,
! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).
thf(69,axiom,
! [V_xs: $i,V_x: $i,T_a: $i] :
( V_xs
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(70,axiom,
! [V_x: $i,V_t: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_t @ T_a )
!= V_t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(71,axiom,
! [V_r: $i,V_ts: $i,V_s: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).
thf(72,axiom,
! [V_a_H: $i,V_list_H: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(73,axiom,
! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xa @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(74,axiom,
! [V_f: $i,V_a: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( hAPP @ ( hAPP @ V_f @ V_a ) @ V_x ) @ V_xs @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
thf(75,axiom,
! [V_m: $i] :
( ( c_Lambda_OdB_OVar @ V_m )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_2) ).
thf(76,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ta____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App_I4_J_0) ).
thf(77,axiom,
! [V_s: $i,V_t: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_k ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_k ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
thf(78,axiom,
! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__IT_0) ).
thf(79,axiom,
! [V_f: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b )
= V_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
thf(80,axiom,
! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__IT_0) ).
thf(81,axiom,
! [V_nat: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
thf(82,axiom,
! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ V_m )
= V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
thf(83,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB2 = V_dB2_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
thf(84,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB1 = V_dB1_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
thf(85,axiom,
! [T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(86,axiom,
! [V_r: $i,V_s: $i,V_t: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_0) ).
thf(87,axiom,
! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_a = V_a_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(88,axiom,
! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_list = V_list_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(89,axiom,
! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).
thf(90,axiom,
! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).
thf(91,axiom,
! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OVar @ V_nat_H ) )
| ( V_nat = V_nat_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
thf(92,axiom,
! [V_r: $i,V_s: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_4) ).
thf(93,axiom,
! [V_r: $i,V_s: $i,V_xa: $i] :
( ( V_r
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ V_xa @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ ( c_List_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_5) ).
thf(94,axiom,
! [V_t: $i,V_ts: $i,V_u: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_u )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Oappend @ V_ts @ ( c_List_Olist_OCons @ V_u @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_app__last_0) ).
thf(95,axiom,
! [V_x: $i,V_s: $i,V_t: $i] :
( ( ( c_List_Oappend @ V_x @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_x @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Oappend @ V_x @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_3) ).
thf(96,axiom,
! [V_n: $i,V_rs: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ V_rs @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
thf(97,axiom,
! [V_r: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ V_r ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_2) ).
thf(98,axiom,
! [V_s: $i,V_ss: $i,V_r: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ V_r ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).
thf(99,axiom,
! [V_r: $i,V_s: $i,V_t: $i,V_ts: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ V_r @ V_s @ V_t @ V_ts ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_2) ).
thf(100,axiom,
! [V_r: $i] :
( ( c_Lambda_OdB_OAbs @ V_r )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_2) ).
thf(101,axiom,
! [V_r: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_1) ).
thf(102,axiom,
! [V_s: $i,V_t: $i,V_n: $i,V_ss: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
thf(103,axiom,
! [V_n: $i,V_ts: $i,V_r: $i,V_ss: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
thf(104,axiom,
! [V_T: $i,V_U: $i,V_e: $i,V_i: $i,V_ts: $i] :
( ( V_T = V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).
thf(105,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__Cons_H_0) ).
thf(106,axiom,
! [V_r: $i,V_s: $i,V_t: $i,V_ts: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ V_r @ V_s @ V_t @ V_ts ) @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_1) ).
thf(107,axiom,
! [V_i: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
thf(108,axiom,
! [V_r: $i,V_i: $i,V_j: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_r ) @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_j ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
thf(109,axiom,
! [V_r: $i,V_s: $i,V_ss: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) ) @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_s ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_r ) @ V_s ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Beta_0) ).
thf(110,axiom,
! [V_r: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ V_r )
= V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).
thf(111,axiom,
! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
thf(112,axiom,
! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).
thf(113,axiom,
! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).
thf(114,axiom,
! [V_s: $i,V_ss: $i,V_r: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ V_r ) )
| ( V_s
= ( c_Lambda_OdB_OAbs @ V_r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
thf(115,axiom,
! [V_nat: $i] :
( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OVar @ V_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osize_I1_J_0) ).
thf(116,axiom,
! [V_nat: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OVar @ V_nat ) @ tc_Lambda_OdB )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osize_I4_J_0) ).
thf(117,axiom,
! [T_a: $i,V_x: $i,V_zs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_zs @ T_a @ T_a ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x @ V_zs @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).
thf(118,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I2_J_0) ).
thf(119,axiom,
! [V_x: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_1) ).
thf(120,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
thf(121,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Osimps_1) ).
thf(122,axiom,
! [V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_1) ).
thf(123,axiom,
! [V_x: $i,T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__rev__conv_0) ).
thf(124,axiom,
! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_OtakeWhile @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_1) ).
thf(125,axiom,
! [V_xs: $i,T_a: $i,V_x: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__singleton__conv_0) ).
thf(126,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice_Osimps_I2_J_0) ).
thf(127,axiom,
! [V_x: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_0) ).
thf(128,axiom,
! [V_x: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= V_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last_Osimps_0) ).
thf(129,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I2_J_1) ).
thf(130,axiom,
! [T_b: $i,V_f: $i,V_x: $i,T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_b )
| ( ( c_List_Olinorder__class_Oinsort__key @ V_f @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a @ T_b )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insort__key_Osimps_I1_J_0) ).
thf(131,axiom,
! [T_a: $i,V_x: $i,V_xs: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).
thf(132,axiom,
! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
( ( ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
!= ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs = V_ys ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
thf(133,axiom,
! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
( ( ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
!= ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
thf(134,axiom,
! [V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__empty_1) ).
thf(135,axiom,
! [T_a: $i] :
( ( c_List_Olength__unique @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__unique_Osimps_I1_J_0) ).
thf(136,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__eq__Nil_0) ).
thf(137,axiom,
! [T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_1) ).
thf(138,axiom,
! [T_a: $i,V_x: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__replicate_1) ).
thf(139,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_xs @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__0_0) ).
thf(140,axiom,
! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Oreplicate @ V_n @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__empty_0) ).
thf(141,axiom,
! [T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__replicate_0) ).
thf(142,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__0__conv_0) ).
thf(143,axiom,
! [V_f: $i,T_a: $i] :
( ( c_List_Olist_Olist__size @ V_f @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Olist__size__simp_I1_J_0) ).
thf(144,axiom,
! [V_fa: $i,T_a: $i] :
( ( c_List_Olist_Olist__size @ V_fa @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list_Osize_I1_J_0) ).
thf(145,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_y @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__code_I2_J_0) ).
thf(146,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Cons_H_0) ).
thf(147,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= V_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__Cons_H_0) ).
thf(148,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_Osimps_I1_J_0) ).
thf(149,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
thf(150,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
thf(151,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_1) ).
thf(152,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
thf(153,axiom,
! [V_t: $i,V_ts: $i,V_i: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_i )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ V_i @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__map_0) ).
thf(154,axiom,
! [V_v: $i,V_n: $i,V_rs: $i] :
( ( V_v
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).
thf(155,axiom,
! [V_x: $i,T_a: $i,V_A: $i] :
( ( ( c_List_Osublist @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ V_A @ T_a )
= ( c_List_Olist_ONil @ T_a ) )
| ( c_in @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sublist__singleton_1) ).
thf(156,axiom,
! [V_v: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__Cons__number__of_0) ).
thf(157,axiom,
! [V_x: $i,T_a: $i,V_A: $i] :
( ( ( c_List_Osublist @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ V_A @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
| ~ ( c_in @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sublist__singleton_0) ).
thf(158,axiom,
! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_r ) @ V_i ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
thf(159,axiom,
! [V_t: $i,V_k: $i,V_s: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_k ) ) @ V_s ) @ V_k )
= V_t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lift_0) ).
thf(160,axiom,
! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lambda_0) ).
thf(161,axiom,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_s____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_App_I2_J_0) ).
thf(162,axiom,
! [V_ts: $i] :
( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ V_ts @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lifts__IT_0) ).
thf(163,axiom,
! [V_env: $i,V_x: $i] : ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OVar @ V_x ) @ ( hAPP @ V_env @ V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
thf(164,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_nat: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I10_J_0) ).
thf(165,axiom,
! [V_e: $i,V_i: $i,V_T: $i] :
( ( ( hAPP @ V_e @ V_i )
= V_T )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OVar @ V_i ) @ V_T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
thf(166,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(167,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(168,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(169,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(170,axiom,
! [V_xs: $i,V_x: $i,V_ts: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_x @ V_ts @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_x @ T_a ) @ V_ts @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
thf(171,axiom,
! [V_zs: $i,V_x: $i,T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ V_zs @ V_x @ T_a ) @ V_ys @ T_a )
= ( c_List_Oappend @ V_zs @ ( c_List_Oappend @ V_x @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).
thf(172,axiom,
! [V_xs: $i,V_xs1: $i,V_us: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_xs1 @ V_us @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_xs1 @ T_a ) @ V_us @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
thf(173,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_zs @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_ys @ V_zs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__assoc_0) ).
thf(174,axiom,
! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i @ V_y @ T_a )
= ( c_List_Olist__update @ V_xs @ V_i @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__overwrite_0) ).
thf(175,axiom,
! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_j: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_j @ T_a )
= ( c_List_Onth @ V_xs @ V_j @ T_a ) )
| ( V_i = V_j )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__list__update_1) ).
thf(176,axiom,
! [T_a: $i,V_xs: $i,V_ys: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_List_Olistsum @ V_xs @ T_a ) ) @ ( c_List_Olistsum @ V_ys @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum__append_0) ).
thf(177,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Obutlast @ V_ys @ T_a ) @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__append_1) ).
thf(178,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__rev_0) ).
thf(179,axiom,
! [V_n: $i,V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Odrop @ V_n @ V_xs @ T_b ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__map_0) ).
thf(180,axiom,
! [V_n: $i,V_x: $i,T_a: $i,V_xs: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).
thf(181,axiom,
! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_i_H: $i,V_x_H: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i_H @ V_x_H @ T_a )
= ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i_H @ V_x_H @ T_a ) @ V_i @ V_x @ T_a ) )
| ( V_i = V_i_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__swap_0) ).
thf(182,axiom,
! [T_a: $i,V_ys: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ V_ys @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_1) ).
thf(183,axiom,
! [T_a: $i,V_xs: $i,V_ys: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ V_xs @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_0) ).
thf(184,axiom,
! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_t ) @ V_t_H ) )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
thf(185,axiom,
! [V_ys_092_060_094isub_0621: $i,T_a: $i,V_xs_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
!= V_ys_092_060_094isub_0622 )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a )
!= V_ys_092_060_094isub_0621 )
| ( V_xs_092_060_094isub_0621
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) )
| ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_6) ).
thf(186,axiom,
! [V_n: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_Odrop @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( ( c_List_Onth @ V_xs @ V_n @ T_a )
= V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__via__drop_0) ).
thf(187,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(188,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(189,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(190,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(191,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(192,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(193,axiom,
! [V_xs: $i,V_x: $i,V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ T_a ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_y @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__length_0) ).
thf(194,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_xa ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f3 @ V_xa ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit__asm_2) ).
thf(195,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_dB: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_dB ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f3 @ V_dB ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit_2) ).
thf(196,axiom,
! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_j ) ) @ V_u ) @ V_i )
= ( c_Lambda_OdB_OVar @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__lt_0) ).
thf(197,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(198,axiom,
! [V_xs: $i,V_i: $i,T_a: $i] :
( ( c_List_Olist__update @ V_xs @ V_i @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__id_0) ).
thf(199,axiom,
! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( tc_List_Olist @ T_a ) )
= V_n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__replicate_0) ).
thf(200,axiom,
! [V_A: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_2) ).
thf(201,axiom,
! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Olistsum @ V_xs @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum__rev_0) ).
thf(202,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__append_0) ).
thf(203,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
thf(204,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
thf(205,axiom,
! [V_xs: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Orev @ V_ys @ T_a ) )
| ( V_xs = V_ys ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__rev__conv_0) ).
thf(206,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
thf(207,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
thf(208,axiom,
! [V_f: $i,V_xs: $i,T_a: $i,T_b: $i,V_n: $i] :
( ( ( c_List_Onth @ ( c_List_Omap @ V_f @ V_xs @ T_a @ T_b ) @ V_n @ T_b )
= ( hAPP @ V_f @ ( c_List_Onth @ V_xs @ V_n @ T_a ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__map_0) ).
thf(209,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(210,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(211,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(212,axiom,
! [V_n: $i,V_x: $i,T_a: $i,V_k: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).
thf(213,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(214,axiom,
! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(215,axiom,
! [V_P: $i,V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_n ) @ V_m ) )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
thf(216,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(217,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(218,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(219,axiom,
! [V_f: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ T_b @ T_a )
= ( c_List_Oappend @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ ( c_List_Omap @ V_f @ V_ys @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__append_0) ).
thf(220,axiom,
! [T_a: $i,V_x: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Olistsum @ V_xs @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_Osimps_I2_J_0) ).
thf(221,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(222,axiom,
! [V_s: $i,V_t: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_s ) @ V_t ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta_0) ).
thf(223,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Olast @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__append_1) ).
thf(224,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(225,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(226,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(227,axiom,
! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(228,axiom,
! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(229,axiom,
! [V_P: $i,V_xs: $i,V_x: $i,V_l: $i,T_a: $i] :
( ( ( c_List_OtakeWhile @ V_P @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ V_l @ T_a ) @ T_a ) @ T_a )
= ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__tail_0) ).
thf(230,axiom,
! [V_n: $i,V_x: $i,T_a: $i,V_i: $i] :
( ( ( c_List_Onth @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ V_i @ T_a )
= V_x )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__replicate_0) ).
thf(231,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_i: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_i @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__append1_0) ).
thf(232,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_n @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__append_0) ).
thf(233,axiom,
! [V_xs: $i,T_a: $i,V_zs: $i] :
( ( V_xs
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_zs @ T_a ) )
| ( ( c_List_Oappend @ V_xs @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_zs @ T_a ) @ T_a )
= V_zs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_2) ).
thf(234,axiom,
! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
!= ( c_List_Omap @ V_f @ V_ys @ T_b @ T_a ) )
| ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_b ) )
= ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__imp__length__eq_0) ).
thf(235,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a )
= ( c_List_Otake @ V_n @ V_xs @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__butlast_0) ).
thf(236,axiom,
! [V_dB: $i,V_dB_H: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_dB )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) )
| ( V_dB = V_dB_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
thf(237,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__drop_0) ).
thf(238,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
thf(239,axiom,
! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i @ T_a )
= V_x )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__list__update__eq_0) ).
thf(240,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_xa: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_x @ V_xa @ T_a ) @ V_x @ T_a )
= V_xa ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__list__update_0) ).
thf(241,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(242,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(243,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(244,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(245,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
thf(246,axiom,
! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__replicate_0) ).
thf(247,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(248,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(249,axiom,
! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(250,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i] :
( ( ( c_List_Onth @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ T_a )
= ( c_List_Onth @ V_xs @ V_n @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__append_0) ).
thf(251,axiom,
! [V_f: $i,V_n: $i,V_x: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Oreplicate @ V_n @ V_x @ T_b ) @ T_b @ T_a )
= ( c_List_Oreplicate @ V_n @ ( hAPP @ V_f @ V_x ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__replicate_0) ).
thf(252,axiom,
! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__map_0) ).
thf(253,axiom,
! [V_xs: $i,T_a: $i,V_ys: $i] :
( V_xs
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_0) ).
thf(254,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Oappend @ ( c_List_Obutlast @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= V_xs )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__butlast__last__id_0) ).
thf(255,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__rev__ident_0) ).
thf(256,axiom,
! [V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_ys @ T_a ) @ T_a )
= V_ys ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_1) ).
thf(257,axiom,
! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__swap_0) ).
thf(258,axiom,
! [V_P: $i,V_xs: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Onth @ V_xs @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ T_a ) ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__length__takeWhile_0) ).
thf(259,axiom,
! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_OtakeWhile @ V_P @ V_xs @ T_a )
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__eq__take_0) ).
thf(260,axiom,
! [V_xs: $i,V_x: $i,V_ys: $i,T_a: $i] :
( ( c_List_Onth @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ T_a ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ T_a )
= V_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__append__length_0) ).
thf(261,axiom,
! [T_a: $i,V_n: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__take_0) ).
thf(262,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Oappend @ V_xs @ V_zs @ T_a ) )
| ( V_ys = V_zs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
thf(263,axiom,
! [V_ys: $i,V_xs: $i,T_a: $i,V_zs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_xs @ T_a )
!= ( c_List_Oappend @ V_zs @ V_xs @ T_a ) )
| ( V_ys = V_zs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
thf(264,axiom,
! [V_m: $i,V_x: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_List_Oreplicate @ V_m @ V_x @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_y @ T_a ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).
thf(265,axiom,
! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Orev @ V_xs @ T_b ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__map_0) ).
thf(266,axiom,
! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
thf(267,axiom,
! [V_i: $i,V_t: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
thf(268,axiom,
! [V_k: $i,V_u: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_k ) ) @ V_u ) @ V_k )
= V_u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__eq_0) ).
thf(269,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_nat: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit_0) ).
thf(270,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_xd: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_xd ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_xd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit__asm_0) ).
thf(271,axiom,
! [V_dB_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
thf(272,axiom,
! [V_f: $i,V_a: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( c_List_Ofoldl @ V_f @ V_a @ V_xs @ T_a @ T_b ) @ V_ys @ T_a @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__append_0) ).
thf(273,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_zs: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ T_a )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) @ V_zs @ T_a @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y @ V_zs @ T_a @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).
thf(274,axiom,
! [V_s: $i,V_u: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_u ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appL_0) ).
thf(275,axiom,
! [V_u: $i,V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_s ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_appR_0) ).
thf(276,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB1: $i,V_dB2: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ T_a )
= ( hAPP @ ( hAPP @ V_f2 @ V_dB1 ) @ V_dB2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I11_J_0) ).
thf(277,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_dB1: $i,V_dB2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_dB1 ) @ V_dB2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit_1) ).
thf(278,axiom,
! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_xb: $i,V_xc: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_xb ) @ V_xc ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_xb ) @ V_xc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osplit__asm_1) ).
thf(279,axiom,
! [V_dB_H: $i,V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
thf(280,axiom,
! [V_dB1: $i,V_dB2: $i,V_dB_H: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
thf(281,axiom,
! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) @ V_s ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_k ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_u ) @ V_s ) @ V_k ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__App_0) ).
thf(282,axiom,
! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ V_xs @ T_a )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_xs @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsum_0) ).
thf(283,axiom,
! [V_xs: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_k @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__nonempty_0) ).
thf(284,axiom,
! [T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_1) ).
thf(285,axiom,
! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).
thf(286,axiom,
! [T_a: $i,V_f: $i,T_b: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).
thf(287,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__is__Nil__conv_0) ).
thf(288,axiom,
! [T_a: $i,V_i: $i,V_v: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_i @ V_v @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update_Osimps_I1_J_0) ).
thf(289,axiom,
! [T_a: $i,V_i: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_i @ V_y @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__code_I1_J_0) ).
thf(290,axiom,
! [T_a: $i,V_k: $i,V_x: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_k @ V_x @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__nonempty_1) ).
thf(291,axiom,
! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I1_J_0) ).
thf(292,axiom,
! [T_a: $i,V_A: $i] :
( ( c_List_Osublist @ ( c_List_Olist_ONil @ T_a ) @ V_A @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sublist__nil_0) ).
thf(293,axiom,
! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_1) ).
thf(294,axiom,
! [V_A: $i,T_a: $i] : ( c_List_Olistsp @ V_A @ ( c_List_Olist_ONil @ T_a ) @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
thf(295,axiom,
! [V_n: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__eq__Nil_2) ).
thf(296,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
thf(297,axiom,
! [V_x: $i,T_a: $i] :
( V_x
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
thf(298,axiom,
! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
thf(299,axiom,
! [T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a )
= V_ys ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Nil_0) ).
thf(300,axiom,
! [V_ys: $i,T_a: $i] :
( V_ys
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
thf(301,axiom,
! [T_a: $i,V_f: $i,V_xs: $i,T_b: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__map__conv_0) ).
thf(302,axiom,
! [V_n: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Nil_0) ).
thf(303,axiom,
! [T_a: $i,V_xs: $i,V_ys: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
thf(304,axiom,
! [T_a: $i,V_xs: $i,V_ys: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
thf(305,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
thf(306,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
thf(307,axiom,
! [T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_0) ).
thf(308,axiom,
! [T_a: $i,V_ys: $i] :
( ( c_List_Osplice @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a )
= V_ys ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice_Osimps_I1_J_0) ).
thf(309,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Osplice @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice__Nil2_0) ).
thf(310,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= V_xs )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
thf(311,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( V_xs
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
thf(312,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= V_ys )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
thf(313,axiom,
! [V_ys: $i,V_xs: $i,T_a: $i] :
( ( V_ys
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
thf(314,axiom,
! [V_P: $i,T_a: $i] :
( ( c_List_OtakeWhile @ V_P @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I1_J_0) ).
thf(315,axiom,
! [T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast_Osimps_I1_J_0) ).
thf(316,axiom,
! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nil__is__rev__conv_1) ).
thf(317,axiom,
! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).
thf(318,axiom,
! [T_a: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).
thf(319,axiom,
! [V_i: $i,V_x: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_i @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oreplicate @ V_i @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).
thf(320,axiom,
! [V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_1) ).
thf(321,axiom,
! [V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__eq__Cons__iff_0) ).
thf(322,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev_Osimps_I2_J_0) ).
thf(323,axiom,
! [V_xs: $i,V_x: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__snoc_0) ).
thf(324,axiom,
! [V_xs: $i,V_x: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= V_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__snoc_0) ).
thf(325,axiom,
! [T_a: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__greater__0__conv_0) ).
thf(326,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__greater__0__conv_1) ).
thf(327,axiom,
! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_OtakeWhile @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile_Osimps_I2_J_0) ).
thf(328,axiom,
! [T_a: $i,V_xs: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ V_xs @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__Cons_0) ).
thf(329,axiom,
! [V_x: $i,V_xs1: $i,V_zs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xs1 @ V_zs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xs1 @ T_a ) @ V_zs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
thf(330,axiom,
! [V_x: $i,V_xa: $i,V_zs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xa @ V_zs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ V_zs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
thf(331,axiom,
! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_x ) @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).
thf(332,axiom,
! [V_f: $i,V_xa: $i,V_xb: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_xa ) @ ( c_List_Omap @ V_f @ V_xb @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_xa @ V_xb @ T_b ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__eq__map__conv_3) ).
thf(333,axiom,
! [V_f: $i,V_x: $i,V_xa: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_x ) @ ( c_List_Omap @ V_f @ V_xa @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__Cons__conv_3) ).
thf(334,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ V_ys @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__Cons_0) ).
thf(335,axiom,
! [V_x: $i,V_xa: $i,T_a: $i,V_zs: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ V_zs @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xa @ V_zs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
thf(336,axiom,
! [T_a: $i,V_y: $i,V_zs: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_y @ V_zs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ V_zs @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_1) ).
thf(337,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ ( c_List_Osplice @ V_xs @ V_ys @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splice__Cons__Cons_0) ).
thf(338,axiom,
! [V_v: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Cons__number__of_0) ).
thf(339,axiom,
! [V_v: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Onth @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat ) @ T_a )
= V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__Cons__number__of_0) ).
thf(340,axiom,
! [V_m: $i,V_x: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_List_Oreplicate @ V_m @ V_x @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_y @ T_a ) )
| ( V_x = V_y )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_1) ).
thf(341,axiom,
! [V_x: $i,T_a: $i,V_y: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__eq__replicate_2) ).
thf(342,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_xs @ T_a )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__0_0) ).
thf(343,axiom,
! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(344,axiom,
! [V_m: $i] :
~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(345,axiom,
! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(346,axiom,
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(347,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(348,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(349,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(350,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(351,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(352,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(353,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(354,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_x )
= V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(355,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(356,axiom,
! [T_a: $i,V_x: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(357,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(358,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
thf(359,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
thf(360,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(361,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(362,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__append_0) ).
thf(363,axiom,
! [V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs_0) ).
thf(364,axiom,
! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a )
!= V_xs )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( ( c_List_Onth @ V_xs @ V_i @ T_a )
= V_x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__same__conv_0) ).
thf(365,axiom,
! [V_f: $i,V_xs: $i,V_k: $i,V_y: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist__update @ V_xs @ V_k @ V_y @ T_b ) @ T_b @ T_a )
= ( c_List_Olist__update @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ V_k @ ( hAPP @ V_f @ V_y ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__update_0) ).
thf(366,axiom,
! [T_a: $i,V_a: $i,V_N: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_N @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).
thf(367,axiom,
! [V_xs: $i,T_a: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__pos__if__in__set_0) ).
thf(368,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) )
| ( V_a = V_b )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).
thf(369,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__power_0) ).
thf(370,axiom,
! [V_xa: $i,V_xs: $i,T_a: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_xa @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( c_in @ ( c_List_Onth @ V_xs @ V_xa @ T_a ) @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__conv__nth_2) ).
thf(371,axiom,
! [V_xs: $i,V_n: $i,T_a: $i] :
( ( c_in @ ( c_List_Onth @ V_xs @ V_n @ T_a ) @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__mem_0) ).
thf(372,axiom,
! [V_x: $i,V_xs: $i,V_n: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Olist__update @ V_xs @ V_n @ V_x @ T_a ) @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__update__memI_0) ).
thf(373,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i] :
( ( ( c_List_Onth @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ T_a )
= ( c_List_Onth @ V_ys @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__append_1) ).
thf(374,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ V_x @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist__update @ V_ys @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) @ V_x @ T_a ) @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__append_1) ).
thf(375,axiom,
! [V_P: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( ( c_List_OtakeWhile @ V_P @ V_xs @ T_a )
= ( c_List_Otake @ V_n @ V_xs @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ V_P @ V_n @ V_xs @ T_a ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__eq__take__P__nth_0) ).
thf(376,axiom,
! [V_P: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( ( c_List_OtakeWhile @ V_P @ V_xs @ T_a )
= ( c_List_Otake @ V_n @ V_xs @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ V_P @ V_n @ V_xs @ T_a ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__eq__take__P__nth_2) ).
thf(377,axiom,
! [V_ys_092_060_094isub_0621: $i,T_a: $i,V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i] :
( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a )
!= V_ys_092_060_094isub_0621 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a ) @ V_xs_092_060_094isub_0622 @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_4) ).
thf(378,axiom,
! [V_xs_092_060_094isub_0621: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( V_xs_092_060_094isub_0621
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) )
| ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_5) ).
thf(379,axiom,
! [V_P: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( ( c_List_OtakeWhile @ V_P @ V_xs @ T_a )
= ( c_List_Otake @ V_n @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Onth @ V_xs @ V_n @ T_a ) ) )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ V_P @ V_n @ V_xs @ T_a ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__eq__take__P__nth_1) ).
thf(380,axiom,
! [V_i: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_i @ tc_nat ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__take_0) ).
thf(381,axiom,
! [V_i: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Odrop @ V_i @ V_xs @ T_a ) @ T_a )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_i @ tc_nat ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__drop_0) ).
thf(382,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
thf(383,axiom,
! [V_xs: $i,V_i: $i,T_a: $i] :
( ( ( c_List_Olist_OCons @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ ( c_List_Odrop @ ( c_Suc @ V_i ) @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_i @ V_xs @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__drop_H_0) ).
thf(384,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Onth @ V_xs @ V_n @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__drop__conv__nth_0) ).
thf(385,axiom,
! [V_P: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( ( c_List_OtakeWhile @ V_P @ V_xs @ T_a )
= ( c_List_Otake @ V_n @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Onth @ V_xs @ V_n @ T_a ) ) )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ V_P @ V_n @ V_xs @ T_a ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__eq__take__P__nth_3) ).
thf(386,axiom,
! [V_P: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( ( c_List_OtakeWhile @ V_P @ V_xs @ T_a )
= ( c_List_Otake @ V_n @ V_xs @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Onth @ V_xs @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ V_P @ V_n @ V_xs @ T_a ) @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__eq__take__P__nth_4) ).
thf(387,axiom,
! [V_rs: $i,V_n: $i,V_v: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_head__Var__reduction_0) ).
thf(388,axiom,
! [V_t: $i,V_ts: $i,V_u: $i,V_i: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_u ) @ V_i )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ V_u @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ V_i @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__map_0) ).
thf(389,axiom,
! [V_i: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ ( c_Suc @ V_i ) @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__Suc__conv__app__nth_0) ).
thf(390,axiom,
! [V_xs: $i,V_i: $i,T_a: $i] :
( ( V_xs
= ( c_List_Oappend @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ ( c_List_Odrop @ ( c_Suc @ V_i ) @ V_xs @ T_a ) @ T_a ) @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__take__nth__drop_0) ).
thf(391,axiom,
! [V_xs: $i,V_i: $i,V_a: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_i @ V_a @ T_a )
= ( c_List_Oappend @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_a @ ( c_List_Odrop @ ( c_Suc @ V_i ) @ V_xs @ T_a ) @ T_a ) @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_upd__conv__take__nth__drop_0) ).
thf(392,axiom,
! [V_i: $i,V_xs: $i,T_a: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( ( c_List_Olist__update @ V_xs @ V_i @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ T_a )
= V_xs ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__same__conv_1) ).
thf(393,axiom,
! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_r ) @ V_t ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_s ) @ V_t ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
thf(394,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_dB ) @ T_a )
= ( hAPP @ V_f3 @ V_dB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dB_Osimps_I12_J_0) ).
thf(395,axiom,
! [V_A: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).
thf(396,axiom,
! [V_A: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Olistsp @ V_A @ V_xs @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__in__listsp__conv_0) ).
thf(397,axiom,
! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_s ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_2) ).
thf(398,axiom,
! [T_a: $i,V_n: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__drop_0) ).
thf(399,axiom,
! [V_n: $i,V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Otake @ V_n @ V_xs @ T_b ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__map_0) ).
thf(400,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(401,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(402,axiom,
! [V_n: $i,V_xs: $i,T_a: $i,V_i: $i] :
( ( ( c_List_Onth @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ V_i @ T_a )
= ( c_List_Onth @ V_xs @ V_i @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__take_0) ).
thf(403,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) ) @ V_z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(404,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(405,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(406,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(407,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(408,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_d ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(409,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(410,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_d ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(411,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(412,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_u: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_u ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z )
= V_u ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(413,axiom,
! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_j: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_j @ T_a )
= ( c_List_Onth @ V_xs @ V_j @ T_a ) )
| ( V_i = V_j ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__list__update__neq_0) ).
thf(414,axiom,
! [V_x: $i,V_S: $i,T_a: $i] :
( ( c_in @ V_x @ V_S @ T_a )
| ~ ( hBOOL @ ( hAPP @ V_S @ V_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(415,axiom,
! [V_S: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_S @ V_x ) )
| ~ ( c_in @ V_x @ V_S @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(416,axiom,
! [V_P: $i,V_Q: $i,T_b: $i,T_c: $i,T_a: $i,V_R: $i] :
( ( hAPP @ ( c_COMBC @ V_P @ V_Q @ T_b @ T_c @ T_a ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(417,axiom,
! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) ) @ V_s ) @ V_x )
= V_s ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subst__Var_1) ).
thf(418,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Int_Oring__char__0 @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_Int_Onumber__class_Onumber__of @ V_x @ T_a )
!= ( c_Int_Onumber__class_Onumber__of @ V_y @ T_a ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__number__of_0) ).
thf(419,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a )
= ( c_List_Obutlast @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__butlast_0) ).
thf(420,axiom,
! [V_P: $i,V_xs: $i,T_a: $i,V_j: $i] :
( ( ( c_List_Onth @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ V_j @ T_a )
= ( c_List_Onth @ V_xs @ V_j @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__nth_0) ).
thf(421,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(422,axiom,
! [V_ys: $i,V_xs: $i,T_a: $i] :
( V_ys
= ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__conv__conj_1) ).
thf(423,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(424,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(425,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(426,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) )
| ( V_b = V_c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(427,axiom,
! [T_a: $i,V_P: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__takeWhile_0) ).
thf(428,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= V_xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__take__drop__id_0) ).
thf(429,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_n @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__drop_0) ).
thf(430,axiom,
! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= V_x )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__replicate_0) ).
thf(431,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(432,axiom,
! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
thf(433,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Obutlast @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_butlast__append_0) ).
thf(434,axiom,
! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__list__update_0) ).
thf(435,axiom,
! [T_a: $i,V_f: $i,V_xs: $i,T_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ V_f @ ( c_List_Olinorder__class_Oinsort__key @ V_f @ V_x @ V_xs @ T_b @ T_a ) @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__insort__key_0) ).
thf(436,axiom,
! [T_a: $i,V_f: $i,V_x: $i,V_xs: $i,T_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ V_f @ ( c_List_Olinorder__class_Oinsort__key @ V_f @ V_x @ V_xs @ T_b @ T_a ) @ T_b @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__insort__key_1) ).
thf(437,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Oappend @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Otake @ ( c_Suc @ V_n ) @ V_xs @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__hd__drop_0) ).
thf(438,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Olength__unique @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olength__unique @ V_xs @ T_a ) )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__unique_Osimps_I2_J_0) ).
thf(439,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Ohd @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__rev_0) ).
thf(440,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__rev_0) ).
thf(441,axiom,
! [V_P: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( ( c_List_OtakeWhile @ V_P @ V_xs @ T_a )
= ( c_List_Otake @ V_n @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Onth @ V_xs @ V_n @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Onth @ V_xs @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ V_P @ V_n @ V_xs @ T_a ) @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__eq__take__P__nth_5) ).
thf(442,axiom,
! [V_y: $i,V_f: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ ( c_List_Olist_Olist__size @ V_f @ V_xs @ T_a ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ ( hAPP @ V_f @ V_x ) @ tc_nat )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__size__estimation_0) ).
thf(443,axiom,
! [V_as: $i,T_a: $i] :
( ( c_in @ ( c_List_Olast @ V_as @ T_a ) @ ( c_List_Oset @ V_as @ T_a ) @ T_a )
| ( V_as
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_last__in__set_0) ).
thf(444,axiom,
! [V_x: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__butlast__appendI_0) ).
thf(445,axiom,
! [V_x: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Obutlast @ V_ys @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__butlast__appendI_1) ).
thf(446,axiom,
! [V_n: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__append_0) ).
thf(447,axiom,
! [V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
!= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a ) @ V_xs_092_060_094isub_0622 @ T_a )
= V_ys_092_060_094isub_0622 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_3) ).
thf(448,axiom,
! [V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
!= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ( V_xs_092_060_094isub_0622
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_1) ).
thf(449,axiom,
! [V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
!= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ( V_xs_092_060_094isub_0621
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_0) ).
thf(450,axiom,
! [V_n: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__append_0) ).
thf(451,axiom,
! [V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
!= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a )
= V_ys_092_060_094isub_0621 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__eq__append__conv__if_2) ).
thf(452,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Odrop @ V_n @ V_xs @ T_a )
= ( c_List_Olist_ONil @ T_a ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__all_0) ).
thf(453,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Odrop @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__eq__Nil_0) ).
thf(454,axiom,
! [V_r: $i,V_rs: $i,V_ss: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ V_ss @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_apps__preserves__betas_0) ).
thf(455,axiom,
! [V_P: $i,V_xs: $i,V_ys: $i,T_a: $i,V_x: $i] :
( ( ( c_List_OtakeWhile @ V_P @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__append1_0) ).
thf(456,axiom,
! [V_xs: $i,T_a: $i] :
( ( ( c_List_Ohd @ V_xs @ T_a )
= ( c_List_Onth @ V_xs @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__conv__nth_0) ).
thf(457,axiom,
! [V_ys: $i,V_xs: $i,V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( V_ys = V_xs )
| ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_0) ).
thf(458,axiom,
! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_1) ).
thf(459,axiom,
! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ( V_y = V_x )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_3) ).
thf(460,axiom,
! [V_ys: $i,V_xs: $i,V_y: $i,V_x: $i,V_r: $i,T_a: $i] :
( ( V_ys = V_xs )
| ( V_y = V_x )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_2) ).
thf(461,axiom,
! [T_a: $i,V_b: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).
thf(462,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).
thf(463,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_N: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_N @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).
thf(464,axiom,
! [T_a: $i,V_m: $i,V_n: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).
thf(465,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__left_0) ).
thf(466,axiom,
! [V_x: $i,V_xa: $i,V_xb: $i,T_a: $i] : ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_x @ V_xb @ T_a ) @ T_a ) @ T_a ) @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__conv__decomp_1) ).
thf(467,axiom,
! [V_x: $i,V_xa: $i,V_xb: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_x @ V_xb @ T_a ) @ T_a ) @ T_a ) @ T_a )
| ( c_in @ V_x @ ( c_List_Oset @ V_xb @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__conv__decomp__last_2) ).
thf(468,axiom,
! [V_x: $i,V_xa: $i,V_xb: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_x @ V_xb @ T_a ) @ T_a ) @ T_a ) @ T_a )
| ( c_in @ V_x @ ( c_List_Oset @ V_xa @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__conv__decomp__first_2) ).
thf(469,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
thf(470,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) ) @ ( c_HOL_Oone__class_Oone @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
thf(471,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
thf(472,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
thf(473,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
thf(474,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
thf(475,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
thf(476,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
thf(477,axiom,
! [T_a: $i,V_xs: $i,V_j: $i,V_i: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_List_Onth @ V_xs @ V_j @ T_a ) @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__rev__nth__mono_0) ).
thf(478,axiom,
! [V_r: $i,T_a: $i,V_xs: $i] :
~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_ONil @ T_a ) @ V_xs @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).
thf(479,axiom,
! [V_r: $i,V_xs: $i,T_a: $i] :
~ ( c_ListOrder_Ostep1 @ V_r @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).
thf(480,axiom,
! [V_x: $i,V_y: $i,V_r: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( V_x = V_y )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_0) ).
thf(481,axiom,
! [V_x: $i,V_y: $i,V_xs: $i,V_ys: $i,V_r: $i,T_a: $i] :
( ( V_x = V_y )
| ( V_xs = V_ys )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_2) ).
thf(482,axiom,
! [V_r: $i,V_y: $i,V_xa: $i,V_x: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_xa ) )
| ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_xa @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_4) ).
thf(483,axiom,
! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( V_xs = V_ys )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_3) ).
thf(484,axiom,
! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_1) ).
thf(485,axiom,
! [V_r: $i,V_x: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Cons__step1__Cons_5) ).
thf(486,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd_Osimps_0) ).
thf(487,axiom,
! [V_n: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le0_0) ).
thf(488,axiom,
! [V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
thf(489,axiom,
! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(490,axiom,
! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(491,axiom,
! [V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_m @ V_m @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
thf(492,axiom,
! [V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= V_m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
thf(493,axiom,
! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
thf(494,axiom,
! [V_n: $i,V_m: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
thf(495,axiom,
! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(496,axiom,
! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(497,axiom,
c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_1) ).
thf(498,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/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
thf(499,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/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
thf(500,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/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
thf(501,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(502,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/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
thf(503,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/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
thf(504,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/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
thf(505,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/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).
thf(506,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/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
thf(507,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Oone__class_Oone @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(508,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(509,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(510,axiom,
! [V_x: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_x ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(511,axiom,
! [T_a: $i,V_b: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing__iff_1) ).
thf(512,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing__iff_0) ).
thf(513,axiom,
! [T_a: $i,V_m: $i,V_n: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__imp__le__exp_0) ).
thf(514,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ V_b @ T_a )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
thf(515,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_in @ ( c_List_Ohd @ V_xs @ T_a ) @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__in__set_0) ).
thf(516,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a )
!= ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) )
| ( V_a = V_b )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__base_0) ).
thf(517,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(518,axiom,
! [V_m: $i,V_n: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(519,axiom,
! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(520,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m
= ( c_Suc @ V_n ) )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucE_0) ).
thf(521,axiom,
! [V_n: $i,V_i: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_i @ tc_nat ) @ tc_nat )
= V_i )
| ~ ( c_lessequals @ V_i @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
thf(522,axiom,
! [V_n: $i] : ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_n ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).
thf(523,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) @ ( c_Suc @ V_k ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).
thf(524,axiom,
! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
thf(525,axiom,
! [V_m: $i,V_n: $i] :
( ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
thf(526,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
| ( ( c_Suc @ V_m )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(527,axiom,
! [V_a: $i,V_c: $i,V_b: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_c @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_c @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_c @ V_a @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).
thf(528,axiom,
! [V_i: $i,V_j: $i,V_k: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_k @ tc_nat ) @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__commute_0) ).
thf(529,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).
thf(530,axiom,
! [V_m: $i,V_n: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
thf(531,axiom,
! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ V_m ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).
thf(532,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).
thf(533,axiom,
! [T_a: $i,V_x: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( V_x_H = V_y_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(534,axiom,
! [T_a: $i,V_xa: $i,V_y: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_xa @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a ) )
| ( V_xa = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(535,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).
thf(536,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__diff__iff_1) ).
thf(537,axiom,
! [T_b: $i,V_f: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_b )
| ( ( c_Nat_Osize__class_Osize @ ( c_List_Olinorder__class_Oinsort__key @ V_f @ V_x @ V_xs @ T_a @ T_b ) @ ( tc_List_Olist @ T_a ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__insert_0) ).
thf(538,axiom,
! [T_b: $i,V_f: $i,V_x: $i,V_y: $i,V_ys: $i,T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_b )
| ( ( c_List_Olinorder__class_Oinsort__key @ V_f @ V_x @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a @ T_b )
= ( c_List_Olist_OCons @ V_y @ ( c_List_Olinorder__class_Oinsort__key @ V_f @ V_x @ V_ys @ T_a @ T_b ) @ T_a ) )
| ( c_lessequals @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_f @ V_y ) @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insort__key_Osimps_I2_J_1) ).
thf(539,axiom,
! [T_b: $i,V_f: $i,V_x: $i,V_y: $i,V_ys: $i,T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_b )
| ( ( c_List_Olinorder__class_Oinsort__key @ V_f @ V_x @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a @ T_b )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_f @ V_y ) @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insort__key_Osimps_I2_J_0) ).
thf(540,axiom,
! [V_i: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( c_List_Odrop @ V_i @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ V_k @ V_i @ tc_nat ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__replicate_0) ).
thf(541,axiom,
! [V_x: $i,V_xs: $i,V_I: $i,T_a: $i] :
( ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Osublist @ V_xs @ V_I @ T_a ) @ T_a ) @ T_a )
| ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_notin__set__sublistI_0) ).
thf(542,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_I: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Osublist @ V_xs @ V_I @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__sublistD_0) ).
thf(543,axiom,
! [V_n: $i,V_m: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Otake @ V_m @ V_xs @ T_a ) @ T_a )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__take_0) ).
thf(544,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__butlastD_0) ).
thf(545,axiom,
! [V_P: $i,V_xs: $i,T_a: $i] : ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__takeWhile__le_0) ).
thf(546,axiom,
! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a )
= V_xs )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__beyond_0) ).
thf(547,axiom,
! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ V_n ) @ V_x @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_replicate__Suc_0) ).
thf(548,axiom,
! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= V_x )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__replicate_0) ).
thf(549,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_i: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Suc @ V_i ) @ V_y @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist__update @ V_xs @ V_i @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__update__code_I3_J_0) ).
thf(550,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__drop_0) ).
thf(551,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_zs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ V_zs @ T_a ) @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_y @ V_zs @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_2) ).
thf(552,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_zs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ V_zs @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted_Osimps_I3_J_0) ).
thf(553,axiom,
! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ V_xs @ T_a )
= V_xs )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__all_0) ).
thf(554,axiom,
! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_Suc @ V_n ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_n @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_drop__Suc__Cons_0) ).
thf(555,axiom,
! [T_a: $i,V_xs: $i,V_i: $i,V_j: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ ( c_List_Onth @ V_xs @ V_j @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__nth__mono_0) ).
thf(556,axiom,
! [T_a: $i,V_xs: $i,V_i: $i,V_j: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ ( c_List_Onth @ V_xs @ V_j @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__equals__nth__mono_0) ).
thf(557,axiom,
! [V_xs: $i,T_a: $i,V_n: $i] :
( ( ( c_List_Onth @ ( c_List_Orev @ V_xs @ T_a ) @ V_n @ T_a )
= ( c_List_Onth @ V_xs @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ ( c_Suc @ V_n ) @ tc_nat ) @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__nth_0) ).
thf(558,axiom,
! [V_x: $i,V_y: $i,V_n: $i,T_a: $i] :
( ( V_x = V_y )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Oreplicate @ V_n @ V_y @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__replicateD_0) ).
thf(559,axiom,
! [V_A: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__listsp__conv__set_0) ).
thf(560,axiom,
! [V_P: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ( ( c_List_OtakeWhile @ V_P @ V_xs @ T_a )
!= V_xs )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_takeWhile__eq__all__conv_0) ).
thf(561,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_P: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__takeWhileD_0) ).
thf(562,axiom,
! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__takeWhileD_1) ).
thf(563,axiom,
! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_Suc @ V_n ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_take__Suc__Cons_0) ).
thf(564,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Suc @ V_n ) @ T_a )
= ( c_List_Onth @ V_xs @ V_n @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nth__Cons__Suc_0) ).
thf(565,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__dropD_0) ).
thf(566,axiom,
! [V_x: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__set__takeD_0) ).
thf(567,axiom,
! [T_a: $i,V_ys: $i] :
( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a ) @ T_a )
= ( c_List_Ohd @ V_ys @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__append_0) ).
thf(568,axiom,
! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Ohd @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hd__append_1) ).
thf(569,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
thf(570,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0_0) ).
thf(571,axiom,
! [V_x: $i,V_ys: $i,T_a: $i] :
~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_a ) ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_impossible__Cons_0) ).
thf(572,axiom,
! [V_xa: $i,T_a: $i,V_x: $i] :
( ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xa @ ( tc_List_Olist @ T_a ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( tc_List_Olist @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__length__conv_2) ).
thf(573,axiom,
! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xa @ ( tc_List_Olist @ T_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__Suc__conv_2) ).
thf(574,axiom,
! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i,V_g: $i,V_x: $i] :
( ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
!= ( c_List_Omap @ V_g @ V_xs @ T_b @ T_a ) )
| ( ( hAPP @ V_f @ V_x )
= ( hAPP @ V_g @ V_x ) )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_b ) @ T_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__eq__conv_0) ).
thf(575,axiom,
! [T_a: $i,V_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a )
!= ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
thf(576,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Suc @ V_n ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
thf(577,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
thf(578,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono_0) ).
thf(579,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less_0) ).
thf(580,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
thf(581,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
thf(582,axiom,
! [V_P: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ tc_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__diff__split_0) ).
thf(583,axiom,
c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
thf(584,axiom,
! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
thf(585,axiom,
! [V_n: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_n ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
thf(586,axiom,
! [V_x: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_x ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
thf(587,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).
thf(588,axiom,
! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).
thf(589,axiom,
! [V_y: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ( c_in @ V_y @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ( V_y = V_x )
| ~ ( c_in @ V_y @ ( c_List_Oset @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__ConsD_0) ).
thf(590,axiom,
! [T_a: $i,V_v: $i,V_w: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( class_Int_Onumber @ T_a )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ V_v @ T_a ) @ ( c_Int_Onumber__class_Onumber__of @ V_w @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ V_w @ T_a ) @ ( c_Int_Onumber__class_Onumber__of @ V_v @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_1) ).
thf(591,axiom,
! [T_a: $i,V_w: $i,V_v: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( class_Int_Onumber @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ V_w @ T_a ) @ ( c_Int_Onumber__class_Onumber__of @ V_v @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ V_v @ T_a ) @ ( c_Int_Onumber__class_Onumber__of @ V_w @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_0) ).
thf(592,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__one_0) ).
thf(593,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
thf(594,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
thf(595,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
thf(596,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
thf(597,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
thf(598,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
thf(599,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
thf(600,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_lessequals @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
thf(601,axiom,
! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_lessequals @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).
thf(602,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
thf(603,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
thf(604,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
thf(605,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
thf(606,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
thf(607,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
thf(608,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
thf(609,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
thf(610,axiom,
! [V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Olength__unique @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_Suc @ ( c_List_Olength__unique @ V_xs @ T_a ) ) )
| ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_length__unique_Osimps_I2_J_1) ).
thf(611,axiom,
! [T_a: $i,V_x: $i,V_xa: $i,V_ys: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_xa @ T_a )
| ~ ( c_in @ V_xa @ ( c_List_Oset @ V_ys @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__append_2) ).
thf(612,axiom,
! [T_a: $i,V_x: $i,V_xa: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_xa @ T_a )
| ~ ( c_in @ V_xa @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sorted__Cons_1) ).
thf(613,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).
thf(614,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(615,axiom,
! [V_n: $i,V_m: $i] :
( ( c_lessequals @ V_n @ V_m @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(616,axiom,
! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
thf(617,axiom,
! [V_n: $i,V_m: $i] :
( ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
thf(618,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(619,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(620,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(621,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(622,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(623,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(624,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).
thf(625,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
thf(626,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
thf(627,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(628,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(629,axiom,
! [V_n: $i,V_i: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Suc @ V_i ) @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
thf(630,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(631,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(632,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_y_H @ V_x_H @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(633,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y_H @ V_x_H @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(634,axiom,
! [V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__pred_0) ).
thf(635,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(636,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(637,axiom,
! [V_m: $i,V_l: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_l @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_l @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
thf(638,axiom,
! [V_l: $i,V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_n @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
thf(639,axiom,
! [T_a: $i,V_a: $i,V_n: $i,V_N: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_n @ V_N @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__increasing_0) ).
thf(640,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(641,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(642,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(643,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(644,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(645,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(646,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(647,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(648,axiom,
! [T_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__one_0) ).
thf(649,axiom,
! [V_m: $i,V_n: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ ( c_Suc @ V_m ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
thf(650,axiom,
! [V_x: $i] :
( ~ ( c_lessequals @ V_x @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).
thf(651,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
thf(652,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
thf(653,axiom,
! [V_y: $i,V_f: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_y @ ( c_List_Olist_Olist__size @ V_f @ V_xs @ T_a ) @ tc_nat )
| ~ ( c_lessequals @ V_y @ ( hAPP @ V_f @ V_x ) @ tc_nat )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_list__size__estimation_H_0) ).
thf(654,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).
thf(655,axiom,
! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ~ ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ V_x @ T_a ) @ ( c_List_Oappend @ V_xs @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__step1I_0) ).
thf(656,axiom,
! [V_r: $i,V_x: $i,V_vs: $i,T_a: $i,V_us: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_x @ V_vs @ T_a ) @ ( c_List_Oappend @ V_x @ V_us @ T_a ) @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ V_vs @ V_us @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_append__step1I_1) ).
thf(657,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) ) @ V_b )
= V_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
thf(658,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__le__iff_1) ).
thf(659,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__le__iff_0) ).
thf(660,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).
thf(661,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).
thf(662,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__power_0) ).
thf(663,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leI_0) ).
thf(664,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).
thf(665,axiom,
! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).
thf(666,axiom,
! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
thf(667,axiom,
! [T_a: $i,V_a: $i,V_N: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_n @ V_N @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__decreasing_0) ).
thf(668,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).
thf(669,axiom,
! [V_l: $i,V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_n @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_l @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
thf(670,axiom,
! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(671,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/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(672,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
thf(673,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(674,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(675,axiom,
! [V_n: $i,V_m: $i] :
( ( V_n = V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(676,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
thf(677,axiom,
! [V_j: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_n @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
thf(678,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(679,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
thf(680,axiom,
! [V_xs: $i,T_a: $i] :
( ( c_List_Oset @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Oset @ V_xs @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev_0) ).
thf(681,axiom,
! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(682,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(683,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(684,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(685,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/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
thf(686,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/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
thf(687,axiom,
! [V_x: $i,V_y: $i] :
( ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
thf(688,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
thf(689,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(690,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(691,axiom,
! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__gt1_0) ).
thf(692,axiom,
! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(693,axiom,
! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(694,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_i ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(695,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
thf(696,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
thf(697,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
thf(698,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
thf(699,axiom,
! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
thf(700,axiom,
! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
thf(701,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).
thf(702,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
thf(703,axiom,
! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucI_0) ).
thf(704,axiom,
! [V_n: $i] :
~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_n @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
thf(705,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).
thf(706,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__diff__iff_1) ).
thf(707,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__diff_0) ).
thf(708,axiom,
! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(709,axiom,
! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(710,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(711,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(712,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(713,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(714,axiom,
! [V_n: $i] : ( c_lessequals @ V_n @ V_n @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(715,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ V_i @ V_k @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_k @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(716,axiom,
! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(717,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(718,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(719,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(720,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(721,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_d: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
thf(722,axiom,
! [V_n: $i,V_m: $i] :
( ( V_n = V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
thf(723,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(724,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[723]) ).
thf(725,negated_conjecture,
~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Olist_OCons @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ v_ta____ ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(726,plain,
$false = $false,
inference(unfold_def,[status(thm)],[724]) ).
thf(727,plain,
( ( ! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( c_fequal @ V_X @ V_Y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(728,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_fequal @ V_x @ V_x @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(729,plain,
( ( class_Int_Onumber @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(730,plain,
( ( class_Power_Opower @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(731,plain,
( ( class_Int_Onumber__ring @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(732,plain,
( ( class_Int_Oring__char__0 @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(733,plain,
( ( class_Orderings_Oorder @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(734,plain,
( ( class_Orderings_Olinorder @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(735,plain,
( ( class_Orderings_Opreorder @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(736,plain,
( ( class_Nat_Osemiring__char__0 @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(737,plain,
( ( class_Ring__and__Field_Oidom @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(738,plain,
( ( class_Ring__and__Field_Oring__1 @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(739,plain,
( ( class_OrderedGroup_Ogroup__add @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(740,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(741,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(742,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(743,plain,
( ( class_OrderedGroup_Oab__group__add @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(744,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(745,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(746,plain,
( ( class_OrderedGroup_Osemigroup__add @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(747,plain,
( ( class_Ring__and__Field_Oordered__idom @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(748,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(749,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(750,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(751,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(752,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(753,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(754,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(755,plain,
( ( class_OrderedGroup_Olordered__ab__group__add @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(756,plain,
( ( class_OrderedGroup_Opordered__ab__group__add @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(757,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(758,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(759,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(760,plain,
( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(761,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(762,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_Int_Oint )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(763,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(764,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(765,plain,
( ( class_Int_Onumber @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(766,plain,
( ( class_Power_Opower @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(767,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(768,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(769,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(770,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(771,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(772,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(773,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(774,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(775,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(776,plain,
( ( class_OrderedGroup_Osemigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(777,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(778,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(779,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(780,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(781,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(782,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(783,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(784,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(785,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(786,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(787,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(788,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(789,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)],[63]) ).
thf(790,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)],[64]) ).
thf(791,plain,
( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Olist_OCons @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ v_ta____ ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(792,plain,
( ( ! [V_dB1_H: $i,V_dB2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(793,plain,
( ( ! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ ( c_Lambda_OdB_OVar @ V_i ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(794,plain,
( ( ! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(795,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( V_xs
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(796,plain,
( ( ! [V_x: $i,V_t: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_t @ T_a )
!= V_t ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(797,plain,
( ( ! [V_r: $i,V_ts: $i,V_s: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(798,plain,
( ( ! [V_a_H: $i,V_list_H: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(799,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xa @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(800,plain,
( ( ! [V_f: $i,V_a: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( hAPP @ ( hAPP @ V_f @ V_a ) @ V_x ) @ V_xs @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(801,plain,
( ( ! [V_m: $i] :
( ( c_Lambda_OdB_OVar @ V_m )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(802,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ta____ ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(803,plain,
( ( ! [V_s: $i,V_t: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_k ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(804,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(805,plain,
( ( ! [V_f: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b )
= V_a ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(806,plain,
( ( ! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(807,plain,
( ( ! [V_nat: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(808,plain,
( ( ! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ V_m )
= V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(809,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB2 = V_dB2_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(810,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB1 = V_dB1_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(811,plain,
( ( ! [T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(812,plain,
( ( ! [V_r: $i,V_s: $i,V_t: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(813,plain,
( ( ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(814,plain,
( ( ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_list = V_list_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(815,plain,
( ( ! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(816,plain,
( ( ! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(817,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OVar @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(818,plain,
( ( ! [V_r: $i,V_s: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(819,plain,
( ( ! [V_r: $i,V_s: $i,V_xa: $i] :
( ( V_r
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ V_xa @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ ( c_List_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(820,plain,
( ( ! [V_t: $i,V_ts: $i,V_u: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_u )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Oappend @ V_ts @ ( c_List_Olist_OCons @ V_u @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(821,plain,
( ( ! [V_x: $i,V_s: $i,V_t: $i] :
( ( ( c_List_Oappend @ V_x @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_x @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Oappend @ V_x @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(822,plain,
( ( ! [V_n: $i,V_rs: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ V_rs @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(823,plain,
( ( ! [V_r: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ V_r ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(824,plain,
( ( ! [V_s: $i,V_ss: $i,V_r: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ V_r ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(825,plain,
( ( ! [V_r: $i,V_s: $i,V_t: $i,V_ts: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ V_r @ V_s @ V_t @ V_ts ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(826,plain,
( ( ! [V_r: $i] :
( ( c_Lambda_OdB_OAbs @ V_r )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(827,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(828,plain,
( ( ! [V_s: $i,V_t: $i,V_n: $i,V_ss: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(829,plain,
( ( ! [V_n: $i,V_ts: $i,V_r: $i,V_ss: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(830,plain,
( ( ! [V_T: $i,V_U: $i,V_e: $i,V_i: $i,V_ts: $i] :
( ( V_T = V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(831,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(832,plain,
( ( ! [V_r: $i,V_s: $i,V_t: $i,V_ts: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ V_r @ V_s @ V_t @ V_ts ) @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(833,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(834,plain,
( ( ! [V_r: $i,V_i: $i,V_j: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_r ) @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_j ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(835,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) ) @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_s ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_r ) @ V_s ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(836,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ V_r )
= V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[110]) ).
thf(837,plain,
( ( ! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(838,plain,
( ( ! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(839,plain,
( ( ! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(840,plain,
( ( ! [V_s: $i,V_ss: $i,V_r: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ V_r ) )
| ( V_s
= ( c_Lambda_OdB_OAbs @ V_r ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(841,plain,
( ( ! [V_nat: $i] :
( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OVar @ V_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(842,plain,
( ( ! [V_nat: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OVar @ V_nat ) @ tc_Lambda_OdB )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[116]) ).
thf(843,plain,
( ( ! [T_a: $i,V_x: $i,V_zs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_zs @ T_a @ T_a ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x @ V_zs @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(844,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(845,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[119]) ).
thf(846,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(847,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(848,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(849,plain,
( ( ! [V_x: $i,T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(850,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_OtakeWhile @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(851,plain,
( ( ! [V_xs: $i,T_a: $i,V_x: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[125]) ).
thf(852,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(853,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(854,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[128]) ).
thf(855,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(856,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i,T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_b )
| ( ( c_List_Olinorder__class_Oinsort__key @ V_f @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a @ T_b )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[130]) ).
thf(857,plain,
( ( ! [T_a: $i,V_x: $i,V_xs: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(858,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
( ( ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
!= ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs = V_ys ) ) )
= $true ),
inference(unfold_def,[status(thm)],[132]) ).
thf(859,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
( ( ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
!= ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(860,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(861,plain,
( ( ! [T_a: $i] :
( ( c_List_Olength__unique @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(862,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(863,plain,
( ( ! [T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(864,plain,
( ( ! [T_a: $i,V_x: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[138]) ).
thf(865,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_xs @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[139]) ).
thf(866,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Oreplicate @ V_n @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(867,plain,
( ( ! [T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(868,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[142]) ).
thf(869,plain,
( ( ! [V_f: $i,T_a: $i] :
( ( c_List_Olist_Olist__size @ V_f @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(870,plain,
( ( ! [V_fa: $i,T_a: $i] :
( ( c_List_Olist_Olist__size @ V_fa @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[144]) ).
thf(871,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_y @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[145]) ).
thf(872,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(873,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(874,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(875,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(876,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(877,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[151]) ).
thf(878,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(879,plain,
( ( ! [V_t: $i,V_ts: $i,V_i: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_i )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ V_i @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(880,plain,
( ( ! [V_v: $i,V_n: $i,V_rs: $i] :
( ( V_v
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(881,plain,
( ( ! [V_x: $i,T_a: $i,V_A: $i] :
( ( ( c_List_Osublist @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ V_A @ T_a )
= ( c_List_Olist_ONil @ T_a ) )
| ( c_in @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_A @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(882,plain,
( ( ! [V_v: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(883,plain,
( ( ! [V_x: $i,T_a: $i,V_A: $i] :
( ( ( c_List_Osublist @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ V_A @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
| ~ ( c_in @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_A @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(884,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_r ) @ V_i ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(885,plain,
( ( ! [V_t: $i,V_k: $i,V_s: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_k ) ) @ V_s ) @ V_k )
= V_t ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(886,plain,
( ( ! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(887,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_s____ ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(888,plain,
( ( ! [V_ts: $i] :
( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ V_ts @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(889,plain,
( ( ! [V_env: $i,V_x: $i] : ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OVar @ V_x ) @ ( hAPP @ V_env @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(890,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_nat: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[164]) ).
thf(891,plain,
( ( ! [V_e: $i,V_i: $i,V_T: $i] :
( ( ( hAPP @ V_e @ V_i )
= V_T )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OVar @ V_i ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[165]) ).
thf(892,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[166]) ).
thf(893,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[167]) ).
thf(894,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[168]) ).
thf(895,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[169]) ).
thf(896,plain,
( ( ! [V_xs: $i,V_x: $i,V_ts: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_x @ V_ts @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_x @ T_a ) @ V_ts @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(897,plain,
( ( ! [V_zs: $i,V_x: $i,T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ V_zs @ V_x @ T_a ) @ V_ys @ T_a )
= ( c_List_Oappend @ V_zs @ ( c_List_Oappend @ V_x @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(898,plain,
( ( ! [V_xs: $i,V_xs1: $i,V_us: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_xs1 @ V_us @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_xs1 @ T_a ) @ V_us @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(899,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_zs @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_ys @ V_zs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(900,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i @ V_y @ T_a )
= ( c_List_Olist__update @ V_xs @ V_i @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[174]) ).
thf(901,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_j: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_j @ T_a )
= ( c_List_Onth @ V_xs @ V_j @ T_a ) )
| ( V_i = V_j )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(902,plain,
( ( ! [T_a: $i,V_xs: $i,V_ys: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_List_Olistsum @ V_xs @ T_a ) ) @ ( c_List_Olistsum @ V_ys @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(903,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Obutlast @ V_ys @ T_a ) @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[177]) ).
thf(904,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(905,plain,
( ( ! [V_n: $i,V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Odrop @ V_n @ V_xs @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(906,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i,V_xs: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(907,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_i_H: $i,V_x_H: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i_H @ V_x_H @ T_a )
= ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i_H @ V_x_H @ T_a ) @ V_i @ V_x @ T_a ) )
| ( V_i = V_i_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[181]) ).
thf(908,plain,
( ( ! [T_a: $i,V_ys: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ V_ys @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[182]) ).
thf(909,plain,
( ( ! [T_a: $i,V_xs: $i,V_ys: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ V_xs @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[183]) ).
thf(910,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_t ) @ V_t_H ) )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[184]) ).
thf(911,plain,
( ( ! [V_ys_092_060_094isub_0621: $i,T_a: $i,V_xs_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
!= V_ys_092_060_094isub_0622 )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a )
!= V_ys_092_060_094isub_0621 )
| ( V_xs_092_060_094isub_0621
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) )
| ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(912,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_Odrop @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( ( c_List_Onth @ V_xs @ V_n @ T_a )
= V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(913,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(914,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(915,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[189]) ).
thf(916,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(917,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[191]) ).
thf(918,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(919,plain,
( ( ! [V_xs: $i,V_x: $i,V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ T_a ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_y @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[193]) ).
thf(920,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_xa ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f3 @ V_xa ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(921,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_dB: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_dB ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f3 @ V_dB ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[195]) ).
thf(922,plain,
( ( ! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_j ) ) @ V_u ) @ V_i )
= ( c_Lambda_OdB_OVar @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[196]) ).
thf(923,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[197]) ).
thf(924,plain,
( ( ! [V_xs: $i,V_i: $i,T_a: $i] :
( ( c_List_Olist__update @ V_xs @ V_i @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[198]) ).
thf(925,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( tc_List_Olist @ T_a ) )
= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[199]) ).
thf(926,plain,
( ( ! [V_A: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[200]) ).
thf(927,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Olistsum @ V_xs @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[201]) ).
thf(928,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(929,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[203]) ).
thf(930,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(931,plain,
( ( ! [V_xs: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Orev @ V_ys @ T_a ) )
| ( V_xs = V_ys ) ) )
= $true ),
inference(unfold_def,[status(thm)],[205]) ).
thf(932,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[206]) ).
thf(933,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(934,plain,
( ( ! [V_f: $i,V_xs: $i,T_a: $i,T_b: $i,V_n: $i] :
( ( ( c_List_Onth @ ( c_List_Omap @ V_f @ V_xs @ T_a @ T_b ) @ V_n @ T_b )
= ( hAPP @ V_f @ ( c_List_Onth @ V_xs @ V_n @ T_a ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[208]) ).
thf(935,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[209]) ).
thf(936,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(937,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(938,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i,V_k: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[212]) ).
thf(939,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[213]) ).
thf(940,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[214]) ).
thf(941,plain,
( ( ! [V_P: $i,V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_n ) @ V_m ) )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(942,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(943,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(944,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(945,plain,
( ( ! [V_f: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ T_b @ T_a )
= ( c_List_Oappend @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ ( c_List_Omap @ V_f @ V_ys @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(946,plain,
( ( ! [T_a: $i,V_x: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Olistsum @ V_xs @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220]) ).
thf(947,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(948,plain,
( ( ! [V_s: $i,V_t: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_s ) @ V_t ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(949,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Olast @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(950,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(951,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(952,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(953,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[227]) ).
thf(954,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[228]) ).
thf(955,plain,
( ( ! [V_P: $i,V_xs: $i,V_x: $i,V_l: $i,T_a: $i] :
( ( ( c_List_OtakeWhile @ V_P @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ V_l @ T_a ) @ T_a ) @ T_a )
= ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229]) ).
thf(956,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i,V_i: $i] :
( ( ( c_List_Onth @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ V_i @ T_a )
= V_x )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230]) ).
thf(957,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_i: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_i @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231]) ).
thf(958,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_n @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(959,plain,
( ( ! [V_xs: $i,T_a: $i,V_zs: $i] :
( ( V_xs
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_zs @ T_a ) )
| ( ( c_List_Oappend @ V_xs @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_zs @ T_a ) @ T_a )
= V_zs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(960,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
!= ( c_List_Omap @ V_f @ V_ys @ T_b @ T_a ) )
| ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_b ) )
= ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_b ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(961,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a )
= ( c_List_Otake @ V_n @ V_xs @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(962,plain,
( ( ! [V_dB: $i,V_dB_H: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_dB )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) )
| ( V_dB = V_dB_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(963,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237]) ).
thf(964,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(965,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i @ T_a )
= V_x )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(966,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_xa: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_x @ V_xa @ T_a ) @ V_x @ T_a )
= V_xa ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(967,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(968,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(969,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(970,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(971,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(972,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(973,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(974,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(975,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(976,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i] :
( ( ( c_List_Onth @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ T_a )
= ( c_List_Onth @ V_xs @ V_n @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(977,plain,
( ( ! [V_f: $i,V_n: $i,V_x: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Oreplicate @ V_n @ V_x @ T_b ) @ T_b @ T_a )
= ( c_List_Oreplicate @ V_n @ ( hAPP @ V_f @ V_x ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(978,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(979,plain,
( ( ! [V_xs: $i,T_a: $i,V_ys: $i] :
( V_xs
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(980,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Oappend @ ( c_List_Obutlast @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= V_xs )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(981,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(982,plain,
( ( ! [V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_ys @ T_a ) @ T_a )
= V_ys ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(983,plain,
( ( ! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(984,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Onth @ V_xs @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ T_a ) ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(985,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_OtakeWhile @ V_P @ V_xs @ T_a )
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(986,plain,
( ( ! [V_xs: $i,V_x: $i,V_ys: $i,T_a: $i] :
( ( c_List_Onth @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ T_a ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ T_a )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(987,plain,
( ( ! [T_a: $i,V_n: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(988,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Oappend @ V_xs @ V_zs @ T_a ) )
| ( V_ys = V_zs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(989,plain,
( ( ! [V_ys: $i,V_xs: $i,T_a: $i,V_zs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_xs @ T_a )
!= ( c_List_Oappend @ V_zs @ V_xs @ T_a ) )
| ( V_ys = V_zs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(990,plain,
( ( ! [V_m: $i,V_x: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_List_Oreplicate @ V_m @ V_x @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_y @ T_a ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(991,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Orev @ V_xs @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(992,plain,
( ( ! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266]) ).
thf(993,plain,
( ( ! [V_i: $i,V_t: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_t ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(994,plain,
( ( ! [V_k: $i,V_u: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_k ) ) @ V_u ) @ V_k )
= V_u ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(995,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_nat: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[269]) ).
thf(996,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_xd: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_xd ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_xd ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270]) ).
thf(997,plain,
( ( ! [V_dB_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(998,plain,
( ( ! [V_f: $i,V_a: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( c_List_Ofoldl @ V_f @ V_a @ V_xs @ T_a @ T_b ) @ V_ys @ T_a @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272]) ).
thf(999,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_zs: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ T_a )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) @ V_zs @ T_a @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y @ V_zs @ T_a @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(1000,plain,
( ( ! [V_s: $i,V_u: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_u ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(1001,plain,
( ( ! [V_u: $i,V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_s ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275]) ).
thf(1002,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB1: $i,V_dB2: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ T_a )
= ( hAPP @ ( hAPP @ V_f2 @ V_dB1 ) @ V_dB2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276]) ).
thf(1003,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_dB1: $i,V_dB2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_dB1 ) @ V_dB2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277]) ).
thf(1004,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_xb: $i,V_xc: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_xb ) @ V_xc ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_xb ) @ V_xc ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278]) ).
thf(1005,plain,
( ( ! [V_dB_H: $i,V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279]) ).
thf(1006,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB_H: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(1007,plain,
( ( ! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) @ V_s ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_k ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_u ) @ V_s ) @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281]) ).
thf(1008,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ V_xs @ T_a )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_xs @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(1009,plain,
( ( ! [V_xs: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_k @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283]) ).
thf(1010,plain,
( ( ! [T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(1011,plain,
( ( ! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285]) ).
thf(1012,plain,
( ( ! [T_a: $i,V_f: $i,T_b: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286]) ).
thf(1013,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(1014,plain,
( ( ! [T_a: $i,V_i: $i,V_v: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_i @ V_v @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(1015,plain,
( ( ! [T_a: $i,V_i: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_i @ V_y @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(1016,plain,
( ( ! [T_a: $i,V_k: $i,V_x: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_k @ V_x @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(1017,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(1018,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( c_List_Osublist @ ( c_List_Olist_ONil @ T_a ) @ V_A @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(1019,plain,
( ( ! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(1020,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_List_Olistsp @ V_A @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(1021,plain,
( ( ! [V_n: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(1022,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(1023,plain,
( ( ! [V_x: $i,T_a: $i] :
( V_x
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(1024,plain,
( ( ! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(1025,plain,
( ( ! [T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a )
= V_ys ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(1026,plain,
( ( ! [V_ys: $i,T_a: $i] :
( V_ys
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(1027,plain,
( ( ! [T_a: $i,V_f: $i,V_xs: $i,T_b: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(1028,plain,
( ( ! [V_n: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(1029,plain,
( ( ! [T_a: $i,V_xs: $i,V_ys: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(1030,plain,
( ( ! [T_a: $i,V_xs: $i,V_ys: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(1031,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(1032,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(1033,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(1034,plain,
( ( ! [T_a: $i,V_ys: $i] :
( ( c_List_Osplice @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a )
= V_ys ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(1035,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Osplice @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(1036,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= V_xs )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(1037,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( V_xs
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(1038,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= V_ys )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(1039,plain,
( ( ! [V_ys: $i,V_xs: $i,T_a: $i] :
( ( V_ys
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(1040,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( c_List_OtakeWhile @ V_P @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(1041,plain,
( ( ! [T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(1042,plain,
( ( ! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(1043,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(1044,plain,
( ( ! [T_a: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(1045,plain,
( ( ! [V_i: $i,V_x: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_i @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oreplicate @ V_i @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(1046,plain,
( ( ! [V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(1047,plain,
( ( ! [V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321]) ).
thf(1048,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(1049,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(1050,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[324]) ).
thf(1051,plain,
( ( ! [T_a: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[325]) ).
thf(1052,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326]) ).
thf(1053,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_OtakeWhile @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327]) ).
thf(1054,plain,
( ( ! [T_a: $i,V_xs: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ V_xs @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328]) ).
thf(1055,plain,
( ( ! [V_x: $i,V_xs1: $i,V_zs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xs1 @ V_zs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xs1 @ T_a ) @ V_zs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(1056,plain,
( ( ! [V_x: $i,V_xa: $i,V_zs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xa @ V_zs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ V_zs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330]) ).
thf(1057,plain,
( ( ! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_x ) @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331]) ).
thf(1058,plain,
( ( ! [V_f: $i,V_xa: $i,V_xb: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_xa ) @ ( c_List_Omap @ V_f @ V_xb @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_xa @ V_xb @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332]) ).
thf(1059,plain,
( ( ! [V_f: $i,V_x: $i,V_xa: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_x ) @ ( c_List_Omap @ V_f @ V_xa @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333]) ).
thf(1060,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ V_ys @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(1061,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i,V_zs: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ V_zs @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xa @ V_zs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(1062,plain,
( ( ! [T_a: $i,V_y: $i,V_zs: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_y @ V_zs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ V_zs @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(1063,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ ( c_List_Osplice @ V_xs @ V_ys @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(1064,plain,
( ( ! [V_v: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(1065,plain,
( ( ! [V_v: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Onth @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat ) @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339]) ).
thf(1066,plain,
( ( ! [V_m: $i,V_x: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_List_Oreplicate @ V_m @ V_x @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_y @ T_a ) )
| ( V_x = V_y )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340]) ).
thf(1067,plain,
( ( ! [V_x: $i,T_a: $i,V_y: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341]) ).
thf(1068,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_xs @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(1069,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[343]) ).
thf(1070,plain,
( ( ! [V_m: $i] :
~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(1071,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(1072,plain,
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[346]) ).
thf(1073,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347]) ).
thf(1074,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(1075,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(1076,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(1077,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(1078,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(1079,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353]) ).
thf(1080,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_x )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(1081,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355]) ).
thf(1082,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356]) ).
thf(1083,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357]) ).
thf(1084,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358]) ).
thf(1085,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359]) ).
thf(1086,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(1087,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(1088,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362]) ).
thf(1089,plain,
( ( ! [V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(1090,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a )
!= V_xs )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( ( c_List_Onth @ V_xs @ V_i @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(1091,plain,
( ( ! [V_f: $i,V_xs: $i,V_k: $i,V_y: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist__update @ V_xs @ V_k @ V_y @ T_b ) @ T_b @ T_a )
= ( c_List_Olist__update @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ V_k @ ( hAPP @ V_f @ V_y ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365]) ).
thf(1092,plain,
( ( ! [T_a: $i,V_a: $i,V_N: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_N @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(1093,plain,
( ( ! [V_xs: $i,T_a: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(1094,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) )
| ( V_a = V_b )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(1095,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369]) ).
thf(1096,plain,
( ( ! [V_xa: $i,V_xs: $i,T_a: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_xa @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( c_in @ ( c_List_Onth @ V_xs @ V_xa @ T_a ) @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370]) ).
thf(1097,plain,
( ( ! [V_xs: $i,V_n: $i,T_a: $i] :
( ( c_in @ ( c_List_Onth @ V_xs @ V_n @ T_a ) @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371]) ).
thf(1098,plain,
( ( ! [V_x: $i,V_xs: $i,V_n: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Olist__update @ V_xs @ V_n @ V_x @ T_a ) @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372]) ).
thf(1099,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i] :
( ( ( c_List_Onth @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ T_a )
= ( c_List_Onth @ V_ys @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373]) ).
thf(1100,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ V_x @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist__update @ V_ys @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) @ V_x @ T_a ) @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374]) ).
thf(1101,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( ( c_List_OtakeWhile @ V_P @ V_xs @ T_a )
= ( c_List_Otake @ V_n @ V_xs @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ V_P @ V_n @ V_xs @ T_a ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375]) ).
thf(1102,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( ( c_List_OtakeWhile @ V_P @ V_xs @ T_a )
= ( c_List_Otake @ V_n @ V_xs @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ V_P @ V_n @ V_xs @ T_a ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376]) ).
thf(1103,plain,
( ( ! [V_ys_092_060_094isub_0621: $i,T_a: $i,V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i] :
( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a )
!= V_ys_092_060_094isub_0621 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a ) @ V_xs_092_060_094isub_0622 @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377]) ).
thf(1104,plain,
( ( ! [V_xs_092_060_094isub_0621: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( V_xs_092_060_094isub_0621
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) )
| ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(1105,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( ( c_List_OtakeWhile @ V_P @ V_xs @ T_a )
= ( c_List_Otake @ V_n @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Onth @ V_xs @ V_n @ T_a ) ) )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ V_P @ V_n @ V_xs @ T_a ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379]) ).
thf(1106,plain,
( ( ! [V_i: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_i @ tc_nat ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380]) ).
thf(1107,plain,
( ( ! [V_i: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Odrop @ V_i @ V_xs @ T_a ) @ T_a )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_i @ tc_nat ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381]) ).
thf(1108,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382]) ).
thf(1109,plain,
( ( ! [V_xs: $i,V_i: $i,T_a: $i] :
( ( ( c_List_Olist_OCons @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ ( c_List_Odrop @ ( c_Suc @ V_i ) @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_i @ V_xs @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383]) ).
thf(1110,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Onth @ V_xs @ V_n @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384]) ).
thf(1111,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( ( c_List_OtakeWhile @ V_P @ V_xs @ T_a )
= ( c_List_Otake @ V_n @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Onth @ V_xs @ V_n @ T_a ) ) )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ V_P @ V_n @ V_xs @ T_a ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385]) ).
thf(1112,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( ( c_List_OtakeWhile @ V_P @ V_xs @ T_a )
= ( c_List_Otake @ V_n @ V_xs @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Onth @ V_xs @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ V_P @ V_n @ V_xs @ T_a ) @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386]) ).
thf(1113,plain,
( ( ! [V_rs: $i,V_n: $i,V_v: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387]) ).
thf(1114,plain,
( ( ! [V_t: $i,V_ts: $i,V_u: $i,V_i: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_u ) @ V_i )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ V_u @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ V_i @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388]) ).
thf(1115,plain,
( ( ! [V_i: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ ( c_Suc @ V_i ) @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389]) ).
thf(1116,plain,
( ( ! [V_xs: $i,V_i: $i,T_a: $i] :
( ( V_xs
= ( c_List_Oappend @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ ( c_List_Odrop @ ( c_Suc @ V_i ) @ V_xs @ T_a ) @ T_a ) @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390]) ).
thf(1117,plain,
( ( ! [V_xs: $i,V_i: $i,V_a: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_i @ V_a @ T_a )
= ( c_List_Oappend @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_a @ ( c_List_Odrop @ ( c_Suc @ V_i ) @ V_xs @ T_a ) @ T_a ) @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391]) ).
thf(1118,plain,
( ( ! [V_i: $i,V_xs: $i,T_a: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( ( c_List_Olist__update @ V_xs @ V_i @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ T_a )
= V_xs ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392]) ).
thf(1119,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_r ) @ V_t ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_s ) @ V_t ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393]) ).
thf(1120,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_dB ) @ T_a )
= ( hAPP @ V_f3 @ V_dB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(1121,plain,
( ( ! [V_A: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(1122,plain,
( ( ! [V_A: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Olistsp @ V_A @ V_xs @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(1123,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_s ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(1124,plain,
( ( ! [T_a: $i,V_n: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(1125,plain,
( ( ! [V_n: $i,V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Otake @ V_n @ V_xs @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[399]) ).
thf(1126,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[400]) ).
thf(1127,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401]) ).
thf(1128,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i,V_i: $i] :
( ( ( c_List_Onth @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ V_i @ T_a )
= ( c_List_Onth @ V_xs @ V_i @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402]) ).
thf(1129,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) ) @ V_z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(1130,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(1131,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405]) ).
thf(1132,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406]) ).
thf(1133,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407]) ).
thf(1134,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_d ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[408]) ).
thf(1135,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(1136,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_d ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410]) ).
thf(1137,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(1138,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_u: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_u ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z )
= V_u ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412]) ).
thf(1139,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_j: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_j @ T_a )
= ( c_List_Onth @ V_xs @ V_j @ T_a ) )
| ( V_i = V_j ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413]) ).
thf(1140,plain,
( ( ! [V_x: $i,V_S: $i,T_a: $i] :
( ( c_in @ V_x @ V_S @ T_a )
| ~ ( hBOOL @ ( hAPP @ V_S @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414]) ).
thf(1141,plain,
( ( ! [V_S: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_S @ V_x ) )
| ~ ( c_in @ V_x @ V_S @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[415]) ).
thf(1142,plain,
( ( ! [V_P: $i,V_Q: $i,T_b: $i,T_c: $i,T_a: $i,V_R: $i] :
( ( hAPP @ ( c_COMBC @ V_P @ V_Q @ T_b @ T_c @ T_a ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416]) ).
thf(1143,plain,
( ( ! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) ) @ V_s ) @ V_x )
= V_s ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417]) ).
thf(1144,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Int_Oring__char__0 @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_Int_Onumber__class_Onumber__of @ V_x @ T_a )
!= ( c_Int_Onumber__class_Onumber__of @ V_y @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418]) ).
thf(1145,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a )
= ( c_List_Obutlast @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[419]) ).
thf(1146,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_j: $i] :
( ( ( c_List_Onth @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ V_j @ T_a )
= ( c_List_Onth @ V_xs @ V_j @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420]) ).
thf(1147,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421]) ).
thf(1148,plain,
( ( ! [V_ys: $i,V_xs: $i,T_a: $i] :
( V_ys
= ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[422]) ).
thf(1149,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423]) ).
thf(1150,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424]) ).
thf(1151,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[425]) ).
thf(1152,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) )
| ( V_b = V_c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[426]) ).
thf(1153,plain,
( ( ! [T_a: $i,V_P: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[427]) ).
thf(1154,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(unfold_def,[status(thm)],[428]) ).
thf(1155,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_n @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[429]) ).
thf(1156,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= V_x )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[430]) ).
thf(1157,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(1158,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[432]) ).
thf(1159,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Obutlast @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[433]) ).
thf(1160,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434]) ).
thf(1161,plain,
( ( ! [T_a: $i,V_f: $i,V_xs: $i,T_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ V_f @ ( c_List_Olinorder__class_Oinsort__key @ V_f @ V_x @ V_xs @ T_b @ T_a ) @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435]) ).
thf(1162,plain,
( ( ! [T_a: $i,V_f: $i,V_x: $i,V_xs: $i,T_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ V_f @ ( c_List_Olinorder__class_Oinsort__key @ V_f @ V_x @ V_xs @ T_b @ T_a ) @ T_b @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[436]) ).
thf(1163,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Oappend @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Otake @ ( c_Suc @ V_n ) @ V_xs @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(1164,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Olength__unique @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olength__unique @ V_xs @ T_a ) )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[438]) ).
thf(1165,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Ohd @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439]) ).
thf(1166,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(1167,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( ( c_List_OtakeWhile @ V_P @ V_xs @ T_a )
= ( c_List_Otake @ V_n @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Onth @ V_xs @ V_n @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Onth @ V_xs @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ V_P @ V_n @ V_xs @ T_a ) @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441]) ).
thf(1168,plain,
( ( ! [V_y: $i,V_f: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ ( c_List_Olist_Olist__size @ V_f @ V_xs @ T_a ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ ( hAPP @ V_f @ V_x ) @ tc_nat )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[442]) ).
thf(1169,plain,
( ( ! [V_as: $i,T_a: $i] :
( ( c_in @ ( c_List_Olast @ V_as @ T_a ) @ ( c_List_Oset @ V_as @ T_a ) @ T_a )
| ( V_as
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(1170,plain,
( ( ! [V_x: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(1171,plain,
( ( ! [V_x: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Obutlast @ V_ys @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445]) ).
thf(1172,plain,
( ( ! [V_n: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(1173,plain,
( ( ! [V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
!= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a ) @ V_xs_092_060_094isub_0622 @ T_a )
= V_ys_092_060_094isub_0622 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(1174,plain,
( ( ! [V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
!= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ( V_xs_092_060_094isub_0622
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(1175,plain,
( ( ! [V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
!= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ( V_xs_092_060_094isub_0621
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449]) ).
thf(1176,plain,
( ( ! [V_n: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450]) ).
thf(1177,plain,
( ( ! [V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
!= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a )
= V_ys_092_060_094isub_0621 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451]) ).
thf(1178,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Odrop @ V_n @ V_xs @ T_a )
= ( c_List_Olist_ONil @ T_a ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452]) ).
thf(1179,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Odrop @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453]) ).
thf(1180,plain,
( ( ! [V_r: $i,V_rs: $i,V_ss: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ V_ss @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454]) ).
thf(1181,plain,
( ( ! [V_P: $i,V_xs: $i,V_ys: $i,T_a: $i,V_x: $i] :
( ( ( c_List_OtakeWhile @ V_P @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455]) ).
thf(1182,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Ohd @ V_xs @ T_a )
= ( c_List_Onth @ V_xs @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456]) ).
thf(1183,plain,
( ( ! [V_ys: $i,V_xs: $i,V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( V_ys = V_xs )
| ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457]) ).
thf(1184,plain,
( ( ! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(1185,plain,
( ( ! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ( V_y = V_x )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[459]) ).
thf(1186,plain,
( ( ! [V_ys: $i,V_xs: $i,V_y: $i,V_x: $i,V_r: $i,T_a: $i] :
( ( V_ys = V_xs )
| ( V_y = V_x )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(1187,plain,
( ( ! [T_a: $i,V_b: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461]) ).
thf(1188,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[462]) ).
thf(1189,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_N: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_N @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(1190,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(1191,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(1192,plain,
( ( ! [V_x: $i,V_xa: $i,V_xb: $i,T_a: $i] : ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_x @ V_xb @ T_a ) @ T_a ) @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[466]) ).
thf(1193,plain,
( ( ! [V_x: $i,V_xa: $i,V_xb: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_x @ V_xb @ T_a ) @ T_a ) @ T_a ) @ T_a )
| ( c_in @ V_x @ ( c_List_Oset @ V_xb @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467]) ).
thf(1194,plain,
( ( ! [V_x: $i,V_xa: $i,V_xb: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_x @ V_xb @ T_a ) @ T_a ) @ T_a ) @ T_a )
| ( c_in @ V_x @ ( c_List_Oset @ V_xa @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(1195,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(1196,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) ) @ ( c_HOL_Oone__class_Oone @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(1197,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(1198,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(1199,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(1200,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474]) ).
thf(1201,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(1202,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[476]) ).
thf(1203,plain,
( ( ! [T_a: $i,V_xs: $i,V_j: $i,V_i: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_List_Onth @ V_xs @ V_j @ T_a ) @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[477]) ).
thf(1204,plain,
( ( ! [V_r: $i,T_a: $i,V_xs: $i] :
~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_ONil @ T_a ) @ V_xs @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[478]) ).
thf(1205,plain,
( ( ! [V_r: $i,V_xs: $i,T_a: $i] :
~ ( c_ListOrder_Ostep1 @ V_r @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
= $true ),
inference(unfold_def,[status(thm)],[479]) ).
thf(1206,plain,
( ( ! [V_x: $i,V_y: $i,V_r: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( V_x = V_y )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[480]) ).
thf(1207,plain,
( ( ! [V_x: $i,V_y: $i,V_xs: $i,V_ys: $i,V_r: $i,T_a: $i] :
( ( V_x = V_y )
| ( V_xs = V_ys )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[481]) ).
thf(1208,plain,
( ( ! [V_r: $i,V_y: $i,V_xa: $i,V_x: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_xa ) )
| ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_xa @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[482]) ).
thf(1209,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( V_xs = V_ys )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[483]) ).
thf(1210,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[484]) ).
thf(1211,plain,
( ( ! [V_r: $i,V_x: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485]) ).
thf(1212,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(unfold_def,[status(thm)],[486]) ).
thf(1213,plain,
( ( ! [V_n: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[487]) ).
thf(1214,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[488]) ).
thf(1215,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[489]) ).
thf(1216,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[490]) ).
thf(1217,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_m @ V_m @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491]) ).
thf(1218,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= V_m ) )
= $true ),
inference(unfold_def,[status(thm)],[492]) ).
thf(1219,plain,
( ( ! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493]) ).
thf(1220,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494]) ).
thf(1221,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(1222,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496]) ).
thf(1223,plain,
( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[497]) ).
thf(1224,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)],[498]) ).
thf(1225,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)],[499]) ).
thf(1226,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)],[500]) ).
thf(1227,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[501]) ).
thf(1228,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)],[502]) ).
thf(1229,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)],[503]) ).
thf(1230,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)],[504]) ).
thf(1231,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)],[505]) ).
thf(1232,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)],[506]) ).
thf(1233,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Oone__class_Oone @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[507]) ).
thf(1234,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[508]) ).
thf(1235,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[509]) ).
thf(1236,plain,
( ( ! [V_x: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_x ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[510]) ).
thf(1237,plain,
( ( ! [T_a: $i,V_b: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[511]) ).
thf(1238,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512]) ).
thf(1239,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[513]) ).
thf(1240,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ V_b @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514]) ).
thf(1241,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_in @ ( c_List_Ohd @ V_xs @ T_a ) @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[515]) ).
thf(1242,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a )
!= ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) )
| ( V_a = V_b )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[516]) ).
thf(1243,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[517]) ).
thf(1244,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[518]) ).
thf(1245,plain,
( ( ! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[519]) ).
thf(1246,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m
= ( c_Suc @ V_n ) )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[520]) ).
thf(1247,plain,
( ( ! [V_n: $i,V_i: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_i @ tc_nat ) @ tc_nat )
= V_i )
| ~ ( c_lessequals @ V_i @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[521]) ).
thf(1248,plain,
( ( ! [V_n: $i] : ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[522]) ).
thf(1249,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) @ ( c_Suc @ V_k ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[523]) ).
thf(1250,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[524]) ).
thf(1251,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[525]) ).
thf(1252,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
| ( ( c_Suc @ V_m )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526]) ).
thf(1253,plain,
( ( ! [V_a: $i,V_c: $i,V_b: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_c @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_c @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_c @ V_a @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[527]) ).
thf(1254,plain,
( ( ! [V_i: $i,V_j: $i,V_k: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_k @ tc_nat ) @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[528]) ).
thf(1255,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[529]) ).
thf(1256,plain,
( ( ! [V_m: $i,V_n: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[530]) ).
thf(1257,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ V_m ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[531]) ).
thf(1258,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[532]) ).
thf(1259,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)],[533]) ).
thf(1260,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)],[534]) ).
thf(1261,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[535]) ).
thf(1262,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[536]) ).
thf(1263,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_b )
| ( ( c_Nat_Osize__class_Osize @ ( c_List_Olinorder__class_Oinsort__key @ V_f @ V_x @ V_xs @ T_a @ T_b ) @ ( tc_List_Olist @ T_a ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[537]) ).
thf(1264,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i,V_y: $i,V_ys: $i,T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_b )
| ( ( c_List_Olinorder__class_Oinsort__key @ V_f @ V_x @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a @ T_b )
= ( c_List_Olist_OCons @ V_y @ ( c_List_Olinorder__class_Oinsort__key @ V_f @ V_x @ V_ys @ T_a @ T_b ) @ T_a ) )
| ( c_lessequals @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_f @ V_y ) @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[538]) ).
thf(1265,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i,V_y: $i,V_ys: $i,T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_b )
| ( ( c_List_Olinorder__class_Oinsort__key @ V_f @ V_x @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a @ T_b )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_f @ V_y ) @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539]) ).
thf(1266,plain,
( ( ! [V_i: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( c_List_Odrop @ V_i @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ V_k @ V_i @ tc_nat ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[540]) ).
thf(1267,plain,
( ( ! [V_x: $i,V_xs: $i,V_I: $i,T_a: $i] :
( ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Osublist @ V_xs @ V_I @ T_a ) @ T_a ) @ T_a )
| ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[541]) ).
thf(1268,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_I: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Osublist @ V_xs @ V_I @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542]) ).
thf(1269,plain,
( ( ! [V_n: $i,V_m: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Otake @ V_m @ V_xs @ T_a ) @ T_a )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[543]) ).
thf(1270,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[544]) ).
thf(1271,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] : ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[545]) ).
thf(1272,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a )
= V_xs )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[546]) ).
thf(1273,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ V_n ) @ V_x @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[547]) ).
thf(1274,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= V_x )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[548]) ).
thf(1275,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_i: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Suc @ V_i ) @ V_y @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist__update @ V_xs @ V_i @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[549]) ).
thf(1276,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[550]) ).
thf(1277,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_zs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ V_zs @ T_a ) @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_y @ V_zs @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[551]) ).
thf(1278,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_zs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ V_zs @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[552]) ).
thf(1279,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ V_xs @ T_a )
= V_xs )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[553]) ).
thf(1280,plain,
( ( ! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_Suc @ V_n ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_n @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[554]) ).
thf(1281,plain,
( ( ! [T_a: $i,V_xs: $i,V_i: $i,V_j: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ ( c_List_Onth @ V_xs @ V_j @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[555]) ).
thf(1282,plain,
( ( ! [T_a: $i,V_xs: $i,V_i: $i,V_j: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ ( c_List_Onth @ V_xs @ V_j @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[556]) ).
thf(1283,plain,
( ( ! [V_xs: $i,T_a: $i,V_n: $i] :
( ( ( c_List_Onth @ ( c_List_Orev @ V_xs @ T_a ) @ V_n @ T_a )
= ( c_List_Onth @ V_xs @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ ( c_Suc @ V_n ) @ tc_nat ) @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[557]) ).
thf(1284,plain,
( ( ! [V_x: $i,V_y: $i,V_n: $i,T_a: $i] :
( ( V_x = V_y )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Oreplicate @ V_n @ V_y @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[558]) ).
thf(1285,plain,
( ( ! [V_A: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[559]) ).
thf(1286,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ( ( c_List_OtakeWhile @ V_P @ V_xs @ T_a )
!= V_xs )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[560]) ).
thf(1287,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_P: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[561]) ).
thf(1288,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[562]) ).
thf(1289,plain,
( ( ! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_Suc @ V_n ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[563]) ).
thf(1290,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Suc @ V_n ) @ T_a )
= ( c_List_Onth @ V_xs @ V_n @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[564]) ).
thf(1291,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[565]) ).
thf(1292,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[566]) ).
thf(1293,plain,
( ( ! [T_a: $i,V_ys: $i] :
( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a ) @ T_a )
= ( c_List_Ohd @ V_ys @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[567]) ).
thf(1294,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Ohd @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[568]) ).
thf(1295,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[569]) ).
thf(1296,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[570]) ).
thf(1297,plain,
( ( ! [V_x: $i,V_ys: $i,T_a: $i] :
~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[571]) ).
thf(1298,plain,
( ( ! [V_xa: $i,T_a: $i,V_x: $i] :
( ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xa @ ( tc_List_Olist @ T_a ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[572]) ).
thf(1299,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xa @ ( tc_List_Olist @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[573]) ).
thf(1300,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i,V_g: $i,V_x: $i] :
( ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
!= ( c_List_Omap @ V_g @ V_xs @ T_b @ T_a ) )
| ( ( hAPP @ V_f @ V_x )
= ( hAPP @ V_g @ V_x ) )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_b ) @ T_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[574]) ).
thf(1301,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a )
!= ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[575]) ).
thf(1302,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Suc @ V_n ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[576]) ).
thf(1303,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[577]) ).
thf(1304,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[578]) ).
thf(1305,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[579]) ).
thf(1306,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[580]) ).
thf(1307,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[581]) ).
thf(1308,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[582]) ).
thf(1309,plain,
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[583]) ).
thf(1310,plain,
( ( ! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[584]) ).
thf(1311,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[585]) ).
thf(1312,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[586]) ).
thf(1313,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[587]) ).
thf(1314,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[588]) ).
thf(1315,plain,
( ( ! [V_y: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ( c_in @ V_y @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ( V_y = V_x )
| ~ ( c_in @ V_y @ ( c_List_Oset @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[589]) ).
thf(1316,plain,
( ( ! [T_a: $i,V_v: $i,V_w: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( class_Int_Onumber @ T_a )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ V_v @ T_a ) @ ( c_Int_Onumber__class_Onumber__of @ V_w @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ V_w @ T_a ) @ ( c_Int_Onumber__class_Onumber__of @ V_v @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[590]) ).
thf(1317,plain,
( ( ! [T_a: $i,V_w: $i,V_v: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( class_Int_Onumber @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ V_w @ T_a ) @ ( c_Int_Onumber__class_Onumber__of @ V_v @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ V_v @ T_a ) @ ( c_Int_Onumber__class_Onumber__of @ V_w @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[591]) ).
thf(1318,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[592]) ).
thf(1319,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[593]) ).
thf(1320,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[594]) ).
thf(1321,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[595]) ).
thf(1322,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[596]) ).
thf(1323,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[597]) ).
thf(1324,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[598]) ).
thf(1325,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[599]) ).
thf(1326,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_lessequals @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[600]) ).
thf(1327,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_lessequals @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[601]) ).
thf(1328,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[602]) ).
thf(1329,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[603]) ).
thf(1330,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[604]) ).
thf(1331,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[605]) ).
thf(1332,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[606]) ).
thf(1333,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[607]) ).
thf(1334,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[608]) ).
thf(1335,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[609]) ).
thf(1336,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Olength__unique @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_Suc @ ( c_List_Olength__unique @ V_xs @ T_a ) ) )
| ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[610]) ).
thf(1337,plain,
( ( ! [T_a: $i,V_x: $i,V_xa: $i,V_ys: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_xa @ T_a )
| ~ ( c_in @ V_xa @ ( c_List_Oset @ V_ys @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[611]) ).
thf(1338,plain,
( ( ! [T_a: $i,V_x: $i,V_xa: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_xa @ T_a )
| ~ ( c_in @ V_xa @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[612]) ).
thf(1339,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[613]) ).
thf(1340,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)],[614]) ).
thf(1341,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ V_n @ V_m @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[615]) ).
thf(1342,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[616]) ).
thf(1343,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[617]) ).
thf(1344,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[618]) ).
thf(1345,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[619]) ).
thf(1346,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[620]) ).
thf(1347,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[621]) ).
thf(1348,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[622]) ).
thf(1349,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[623]) ).
thf(1350,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[624]) ).
thf(1351,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[625]) ).
thf(1352,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[626]) ).
thf(1353,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ( V_a = V_b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[627]) ).
thf(1354,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[628]) ).
thf(1355,plain,
( ( ! [V_n: $i,V_i: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Suc @ V_i ) @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[629]) ).
thf(1356,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[630]) ).
thf(1357,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[631]) ).
thf(1358,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)],[632]) ).
thf(1359,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)],[633]) ).
thf(1360,plain,
( ( ! [V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[634]) ).
thf(1361,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[635]) ).
thf(1362,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[636]) ).
thf(1363,plain,
( ( ! [V_m: $i,V_l: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_l @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_l @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[637]) ).
thf(1364,plain,
( ( ! [V_l: $i,V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_n @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[638]) ).
thf(1365,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_N: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_n @ V_N @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[639]) ).
thf(1366,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[640]) ).
thf(1367,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[641]) ).
thf(1368,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[642]) ).
thf(1369,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[643]) ).
thf(1370,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[644]) ).
thf(1371,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[645]) ).
thf(1372,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[646]) ).
thf(1373,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[647]) ).
thf(1374,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[648]) ).
thf(1375,plain,
( ( ! [V_m: $i,V_n: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ ( c_Suc @ V_m ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[649]) ).
thf(1376,plain,
( ( ! [V_x: $i] :
( ~ ( c_lessequals @ V_x @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[650]) ).
thf(1377,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[651]) ).
thf(1378,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[652]) ).
thf(1379,plain,
( ( ! [V_y: $i,V_f: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_y @ ( c_List_Olist_Olist__size @ V_f @ V_xs @ T_a ) @ tc_nat )
| ~ ( c_lessequals @ V_y @ ( hAPP @ V_f @ V_x ) @ tc_nat )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[653]) ).
thf(1380,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[654]) ).
thf(1381,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ~ ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ V_x @ T_a ) @ ( c_List_Oappend @ V_xs @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[655]) ).
thf(1382,plain,
( ( ! [V_r: $i,V_x: $i,V_vs: $i,T_a: $i,V_us: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_x @ V_vs @ T_a ) @ ( c_List_Oappend @ V_x @ V_us @ T_a ) @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ V_vs @ V_us @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[656]) ).
thf(1383,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) ) @ V_b )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[657]) ).
thf(1384,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[658]) ).
thf(1385,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[659]) ).
thf(1386,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[660]) ).
thf(1387,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[661]) ).
thf(1388,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[662]) ).
thf(1389,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[663]) ).
thf(1390,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[664]) ).
thf(1391,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[665]) ).
thf(1392,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[666]) ).
thf(1393,plain,
( ( ! [T_a: $i,V_a: $i,V_N: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_n @ V_N @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[667]) ).
thf(1394,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[668]) ).
thf(1395,plain,
( ( ! [V_l: $i,V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_n @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_l @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[669]) ).
thf(1396,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)],[670]) ).
thf(1397,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)],[671]) ).
thf(1398,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[672]) ).
thf(1399,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[673]) ).
thf(1400,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[674]) ).
thf(1401,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( V_n = V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[675]) ).
thf(1402,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[676]) ).
thf(1403,plain,
( ( ! [V_j: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_n @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[677]) ).
thf(1404,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[678]) ).
thf(1405,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[679]) ).
thf(1406,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Oset @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Oset @ V_xs @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[680]) ).
thf(1407,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[681]) ).
thf(1408,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)],[682]) ).
thf(1409,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)],[683]) ).
thf(1410,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)],[684]) ).
thf(1411,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)],[685]) ).
thf(1412,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)],[686]) ).
thf(1413,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[687]) ).
thf(1414,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[688]) ).
thf(1415,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[689]) ).
thf(1416,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[690]) ).
thf(1417,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[691]) ).
thf(1418,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[692]) ).
thf(1419,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[693]) ).
thf(1420,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_i ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[694]) ).
thf(1421,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[695]) ).
thf(1422,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[696]) ).
thf(1423,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[697]) ).
thf(1424,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[698]) ).
thf(1425,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[699]) ).
thf(1426,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[700]) ).
thf(1427,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[701]) ).
thf(1428,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[702]) ).
thf(1429,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[703]) ).
thf(1430,plain,
( ( ! [V_n: $i] :
~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[704]) ).
thf(1431,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[705]) ).
thf(1432,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[706]) ).
thf(1433,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[707]) ).
thf(1434,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[708]) ).
thf(1435,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[709]) ).
thf(1436,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)],[710]) ).
thf(1437,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[711]) ).
thf(1438,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[712]) ).
thf(1439,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)],[713]) ).
thf(1440,plain,
( ( ! [V_n: $i] : ( c_lessequals @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[714]) ).
thf(1441,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ V_i @ V_k @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_k @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[715]) ).
thf(1442,plain,
( ( ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[716]) ).
thf(1443,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)],[717]) ).
thf(1444,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)],[718]) ).
thf(1445,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[719]) ).
thf(1446,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[720]) ).
thf(1447,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_d: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[721]) ).
thf(1448,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( V_n = V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[722]) ).
thf(1449,plain,
( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Olist_OCons @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ v_ta____ ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[725]) ).
thf(1450,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[726]) ).
thf(1451,plain,
( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Olist_OCons @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ v_ta____ ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(copy,[status(thm)],[1449]) ).
thf(1452,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( V_n = V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1448]) ).
thf(1453,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_d: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1447]) ).
thf(1454,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1446]) ).
thf(1455,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1445]) ).
thf(1456,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1444]) ).
thf(1457,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1443]) ).
thf(1458,plain,
( ( ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1442]) ).
thf(1459,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_lessequals @ V_i @ V_k @ tc_nat )
| ~ ( c_lessequals @ V_j @ V_k @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1441]) ).
thf(1460,plain,
( ( ! [V_n: $i] : ( c_lessequals @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1440]) ).
thf(1461,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1439]) ).
thf(1462,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1438]) ).
thf(1463,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1437]) ).
thf(1464,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1436]) ).
thf(1465,plain,
( ( ! [V_n: $i] :
( V_n
!= ( c_Suc @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1435]) ).
thf(1466,plain,
( ( ! [V_n: $i] :
( ( c_Suc @ V_n )
!= V_n ) )
= $true ),
inference(copy,[status(thm)],[1434]) ).
thf(1467,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ T_a )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1433]) ).
thf(1468,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1432]) ).
thf(1469,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1431]) ).
thf(1470,plain,
( ( ! [V_n: $i] :
~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1430]) ).
thf(1471,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1429]) ).
thf(1472,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1428]) ).
thf(1473,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1427]) ).
thf(1474,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1426]) ).
thf(1475,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1425]) ).
thf(1476,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1424]) ).
thf(1477,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1423]) ).
thf(1478,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1422]) ).
thf(1479,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1421]) ).
thf(1480,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_i ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1420]) ).
thf(1481,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1419]) ).
thf(1482,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1418]) ).
thf(1483,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1417]) ).
thf(1484,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1416]) ).
thf(1485,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1415]) ).
thf(1486,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1414]) ).
thf(1487,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1413]) ).
thf(1488,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(copy,[status(thm)],[1412]) ).
thf(1489,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(copy,[status(thm)],[1411]) ).
thf(1490,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1410]) ).
thf(1491,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1409]) ).
thf(1492,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1408]) ).
thf(1493,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1407]) ).
thf(1494,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Oset @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Oset @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1406]) ).
thf(1495,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1405]) ).
thf(1496,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1404]) ).
thf(1497,plain,
( ( ! [V_j: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_j @ V_n @ tc_nat ) @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1403]) ).
thf(1498,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1402]) ).
thf(1499,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( V_n = V_m )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1401]) ).
thf(1500,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1400]) ).
thf(1501,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1399]) ).
thf(1502,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1398]) ).
thf(1503,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)],[1397]) ).
thf(1504,plain,
( ( ! [V_x: $i,V_y: $i] :
( ( ( c_Suc @ V_x )
!= ( c_Suc @ V_y ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[1396]) ).
thf(1505,plain,
( ( ! [V_l: $i,V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_n @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_l @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1395]) ).
thf(1506,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) ) )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1394]) ).
thf(1507,plain,
( ( ! [T_a: $i,V_a: $i,V_N: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_n @ V_N @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1393]) ).
thf(1508,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1392]) ).
thf(1509,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1391]) ).
thf(1510,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1390]) ).
thf(1511,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1389]) ).
thf(1512,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1388]) ).
thf(1513,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1387]) ).
thf(1514,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1386]) ).
thf(1515,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1385]) ).
thf(1516,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1384]) ).
thf(1517,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) ) @ V_b )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1383]) ).
thf(1518,plain,
( ( ! [V_r: $i,V_x: $i,V_vs: $i,T_a: $i,V_us: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_x @ V_vs @ T_a ) @ ( c_List_Oappend @ V_x @ V_us @ T_a ) @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ V_vs @ V_us @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1382]) ).
thf(1519,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ~ ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ V_x @ T_a ) @ ( c_List_Oappend @ V_xs @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1381]) ).
thf(1520,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1380]) ).
thf(1521,plain,
( ( ! [V_y: $i,V_f: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ( c_lessequals @ V_y @ ( c_List_Olist_Olist__size @ V_f @ V_xs @ T_a ) @ tc_nat )
| ~ ( c_lessequals @ V_y @ ( hAPP @ V_f @ V_x ) @ tc_nat )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1379]) ).
thf(1522,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1378]) ).
thf(1523,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1377]) ).
thf(1524,plain,
( ( ! [V_x: $i] :
( ~ ( c_lessequals @ V_x @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1376]) ).
thf(1525,plain,
( ( ! [V_m: $i,V_n: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ ( c_Suc @ V_m ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1375]) ).
thf(1526,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_n @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1374]) ).
thf(1527,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1373]) ).
thf(1528,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1372]) ).
thf(1529,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1371]) ).
thf(1530,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1370]) ).
thf(1531,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1369]) ).
thf(1532,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1368]) ).
thf(1533,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1367]) ).
thf(1534,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1366]) ).
thf(1535,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_N: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_n @ V_N @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1365]) ).
thf(1536,plain,
( ( ! [V_l: $i,V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_n @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_l @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1364]) ).
thf(1537,plain,
( ( ! [V_m: $i,V_l: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_l @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_l @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1363]) ).
thf(1538,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1362]) ).
thf(1539,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1361]) ).
thf(1540,plain,
( ( ! [V_n: $i] :
( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1360]) ).
thf(1541,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y_H @ V_x_H @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1359]) ).
thf(1542,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_y_H @ V_x_H @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1358]) ).
thf(1543,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1357]) ).
thf(1544,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x_H @ V_y_H @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1356]) ).
thf(1545,plain,
( ( ! [V_n: $i,V_i: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Suc @ V_i ) @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1355]) ).
thf(1546,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1354]) ).
thf(1547,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[1353]) ).
thf(1548,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1352]) ).
thf(1549,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1351]) ).
thf(1550,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1350]) ).
thf(1551,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1349]) ).
thf(1552,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1348]) ).
thf(1553,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1347]) ).
thf(1554,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ( V_a = V_b ) ) )
= $true ),
inference(copy,[status(thm)],[1346]) ).
thf(1555,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1345]) ).
thf(1556,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1344]) ).
thf(1557,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ V_n @ V_m @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1343]) ).
thf(1558,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_m ) @ tc_nat )
| ~ ( c_lessequals @ V_n @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1342]) ).
thf(1559,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ V_n @ V_m @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1341]) ).
thf(1560,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1340]) ).
thf(1561,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1339]) ).
thf(1562,plain,
( ( ! [T_a: $i,V_x: $i,V_xa: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_xa @ T_a )
| ~ ( c_in @ V_xa @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1338]) ).
thf(1563,plain,
( ( ! [T_a: $i,V_x: $i,V_xa: $i,V_ys: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_xa @ T_a )
| ~ ( c_in @ V_xa @ ( c_List_Oset @ V_ys @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1337]) ).
thf(1564,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Olength__unique @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_Suc @ ( c_List_Olength__unique @ V_xs @ T_a ) ) )
| ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1336]) ).
thf(1565,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1335]) ).
thf(1566,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1334]) ).
thf(1567,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1333]) ).
thf(1568,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1332]) ).
thf(1569,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1331]) ).
thf(1570,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1330]) ).
thf(1571,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1329]) ).
thf(1572,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1328]) ).
thf(1573,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_lessequals @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1327]) ).
thf(1574,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_lessequals @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_c @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1326]) ).
thf(1575,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ( V_y
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1325]) ).
thf(1576,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_y @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_x @ T_a )
| ( V_x
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1324]) ).
thf(1577,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1323]) ).
thf(1578,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1322]) ).
thf(1579,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1321]) ).
thf(1580,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_lessequals @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1320]) ).
thf(1581,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1319]) ).
thf(1582,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1318]) ).
thf(1583,plain,
( ( ! [T_a: $i,V_w: $i,V_v: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( class_Int_Onumber @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ V_w @ T_a ) @ ( c_Int_Onumber__class_Onumber__of @ V_v @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ V_v @ T_a ) @ ( c_Int_Onumber__class_Onumber__of @ V_w @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1317]) ).
thf(1584,plain,
( ( ! [T_a: $i,V_v: $i,V_w: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( class_Int_Onumber @ T_a )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ V_v @ T_a ) @ ( c_Int_Onumber__class_Onumber__of @ V_w @ T_a ) @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ V_w @ T_a ) @ ( c_Int_Onumber__class_Onumber__of @ V_v @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1316]) ).
thf(1585,plain,
( ( ! [V_y: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ( c_in @ V_y @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ( V_y = V_x )
| ~ ( c_in @ V_y @ ( c_List_Oset @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1315]) ).
thf(1586,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1314]) ).
thf(1587,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1313]) ).
thf(1588,plain,
( ( ! [V_x: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_x ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1312]) ).
thf(1589,plain,
( ( ! [V_n: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1311]) ).
thf(1590,plain,
( ( ! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1310]) ).
thf(1591,plain,
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= $true ),
inference(copy,[status(thm)],[1309]) ).
thf(1592,plain,
( ( ! [V_P: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1308]) ).
thf(1593,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1307]) ).
thf(1594,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1306]) ).
thf(1595,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1305]) ).
thf(1596,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1304]) ).
thf(1597,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1303]) ).
thf(1598,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Suc @ V_n ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1302]) ).
thf(1599,plain,
( ( ! [T_a: $i,V_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a )
!= ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1301]) ).
thf(1600,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i,V_g: $i,V_x: $i] :
( ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
!= ( c_List_Omap @ V_g @ V_xs @ T_b @ T_a ) )
| ( ( hAPP @ V_f @ V_x )
= ( hAPP @ V_g @ V_x ) )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_b ) @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1300]) ).
thf(1601,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xa @ ( tc_List_Olist @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1299]) ).
thf(1602,plain,
( ( ! [V_xa: $i,T_a: $i,V_x: $i] :
( ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xa @ ( tc_List_Olist @ T_a ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1298]) ).
thf(1603,plain,
( ( ! [V_x: $i,V_ys: $i,T_a: $i] :
~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1297]) ).
thf(1604,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1296]) ).
thf(1605,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_x @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1295]) ).
thf(1606,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Ohd @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1294]) ).
thf(1607,plain,
( ( ! [T_a: $i,V_ys: $i] :
( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a ) @ T_a )
= ( c_List_Ohd @ V_ys @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1293]) ).
thf(1608,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1292]) ).
thf(1609,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1291]) ).
thf(1610,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Suc @ V_n ) @ T_a )
= ( c_List_Onth @ V_xs @ V_n @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1290]) ).
thf(1611,plain,
( ( ! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_Suc @ V_n ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1289]) ).
thf(1612,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1288]) ).
thf(1613,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_P: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1287]) ).
thf(1614,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ( ( c_List_OtakeWhile @ V_P @ V_xs @ T_a )
!= V_xs )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1286]) ).
thf(1615,plain,
( ( ! [V_A: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_A @ V_x ) )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1285]) ).
thf(1616,plain,
( ( ! [V_x: $i,V_y: $i,V_n: $i,T_a: $i] :
( ( V_x = V_y )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Oreplicate @ V_n @ V_y @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1284]) ).
thf(1617,plain,
( ( ! [V_xs: $i,T_a: $i,V_n: $i] :
( ( ( c_List_Onth @ ( c_List_Orev @ V_xs @ T_a ) @ V_n @ T_a )
= ( c_List_Onth @ V_xs @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ ( c_Suc @ V_n ) @ tc_nat ) @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1283]) ).
thf(1618,plain,
( ( ! [T_a: $i,V_xs: $i,V_i: $i,V_j: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ ( c_List_Onth @ V_xs @ V_j @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1282]) ).
thf(1619,plain,
( ( ! [T_a: $i,V_xs: $i,V_i: $i,V_j: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ ( c_List_Onth @ V_xs @ V_j @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1281]) ).
thf(1620,plain,
( ( ! [V_n: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_Suc @ V_n ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_n @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1280]) ).
thf(1621,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ V_xs @ T_a )
= V_xs )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1279]) ).
thf(1622,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_zs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ V_zs @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1278]) ).
thf(1623,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_zs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ V_zs @ T_a ) @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_y @ V_zs @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1277]) ).
thf(1624,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1276]) ).
thf(1625,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_i: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Suc @ V_i ) @ V_y @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist__update @ V_xs @ V_i @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1275]) ).
thf(1626,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= V_x )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1274]) ).
thf(1627,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ V_n ) @ V_x @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1273]) ).
thf(1628,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a )
= V_xs )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1272]) ).
thf(1629,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] : ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1271]) ).
thf(1630,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1270]) ).
thf(1631,plain,
( ( ! [V_n: $i,V_m: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Otake @ V_m @ V_xs @ T_a ) @ T_a )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1269]) ).
thf(1632,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_I: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Osublist @ V_xs @ V_I @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1268]) ).
thf(1633,plain,
( ( ! [V_x: $i,V_xs: $i,V_I: $i,T_a: $i] :
( ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Osublist @ V_xs @ V_I @ T_a ) @ T_a ) @ T_a )
| ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1267]) ).
thf(1634,plain,
( ( ! [V_i: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( c_List_Odrop @ V_i @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ V_k @ V_i @ tc_nat ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1266]) ).
thf(1635,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i,V_y: $i,V_ys: $i,T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_b )
| ( ( c_List_Olinorder__class_Oinsort__key @ V_f @ V_x @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a @ T_b )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a ) )
| ~ ( c_lessequals @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_f @ V_y ) @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1265]) ).
thf(1636,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i,V_y: $i,V_ys: $i,T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_b )
| ( ( c_List_Olinorder__class_Oinsort__key @ V_f @ V_x @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a @ T_b )
= ( c_List_Olist_OCons @ V_y @ ( c_List_Olinorder__class_Oinsort__key @ V_f @ V_x @ V_ys @ T_a @ T_b ) @ T_a ) )
| ( c_lessequals @ ( hAPP @ V_f @ V_x ) @ ( hAPP @ V_f @ V_y ) @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[1264]) ).
thf(1637,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_b )
| ( ( c_Nat_Osize__class_Osize @ ( c_List_Olinorder__class_Oinsort__key @ V_f @ V_x @ V_xs @ T_a @ T_b ) @ ( tc_List_Olist @ T_a ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1263]) ).
thf(1638,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1262]) ).
thf(1639,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1261]) ).
thf(1640,plain,
( ( ! [T_a: $i,V_xa: $i,V_y: $i,V_x: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_xa @ V_y @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a ) )
| ( V_xa = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[1260]) ).
thf(1641,plain,
( ( ! [T_a: $i,V_x: $i,V_x_H: $i,V_y_H: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a )
!= ( c_HOL_Ominus__class_Ominus @ V_x_H @ V_y_H @ T_a ) )
| ( V_x_H = V_y_H ) ) )
= $true ),
inference(copy,[status(thm)],[1259]) ).
thf(1642,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1258]) ).
thf(1643,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ V_m ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1257]) ).
thf(1644,plain,
( ( ! [V_m: $i,V_n: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_m @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1256]) ).
thf(1645,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_k @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_k @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) )
| ~ ( c_lessequals @ V_k @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_k @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1255]) ).
thf(1646,plain,
( ( ! [V_i: $i,V_j: $i,V_k: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_j @ tc_nat ) @ V_k @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_i @ V_k @ tc_nat ) @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1254]) ).
thf(1647,plain,
( ( ! [V_a: $i,V_c: $i,V_b: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ V_a @ V_c @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ V_b @ V_c @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ V_c @ V_a @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1253]) ).
thf(1648,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ V_n @ tc_nat )
| ( ( c_Suc @ V_m )
= V_n )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1252]) ).
thf(1649,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1251]) ).
thf(1650,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_lessequals @ ( c_Suc @ V_n ) @ V_m @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1250]) ).
thf(1651,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ V_m ) @ V_n @ tc_nat ) @ ( c_Suc @ V_k ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1249]) ).
thf(1652,plain,
( ( ! [V_n: $i] : ( c_lessequals @ ( c_Suc @ V_n ) @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1248]) ).
thf(1653,plain,
( ( ! [V_n: $i,V_i: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_HOL_Ominus__class_Ominus @ V_n @ V_i @ tc_nat ) @ tc_nat )
= V_i )
| ~ ( c_lessequals @ V_i @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1247]) ).
thf(1654,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( V_m
= ( c_Suc @ V_n ) )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1246]) ).
thf(1655,plain,
( ( ! [V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Suc @ V_x ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1245]) ).
thf(1656,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1244]) ).
thf(1657,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ ( c_Suc @ V_m ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1243]) ).
thf(1658,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_Suc @ V_n ) @ T_a )
!= ( c_Power_Opower__class_Opower @ V_b @ ( c_Suc @ V_n ) @ T_a ) )
| ( V_a = V_b )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1242]) ).
thf(1659,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_in @ ( c_List_Ohd @ V_xs @ T_a ) @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1241]) ).
thf(1660,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ T_a )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ V_b @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1240]) ).
thf(1661,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_m @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1239]) ).
thf(1662,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1238]) ).
thf(1663,plain,
( ( ! [T_a: $i,V_b: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1237]) ).
thf(1664,plain,
( ( ! [V_x: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_x ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1236]) ).
thf(1665,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1235]) ).
thf(1666,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ V_m ) @ ( c_Suc @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1234]) ).
thf(1667,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Oone__class_Oone @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1233]) ).
thf(1668,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(copy,[status(thm)],[1232]) ).
thf(1669,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(copy,[status(thm)],[1231]) ).
thf(1670,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(copy,[status(thm)],[1230]) ).
thf(1671,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(copy,[status(thm)],[1229]) ).
thf(1672,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(copy,[status(thm)],[1228]) ).
thf(1673,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ( ( c_HOL_Ozero__class_Ozero @ T_a )
!= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1227]) ).
thf(1674,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(copy,[status(thm)],[1226]) ).
thf(1675,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(copy,[status(thm)],[1225]) ).
thf(1676,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(copy,[status(thm)],[1224]) ).
thf(1677,plain,
( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $true ),
inference(copy,[status(thm)],[1223]) ).
thf(1678,plain,
( ( ! [V_m: $i] :
( ( c_Suc @ V_m )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1222]) ).
thf(1679,plain,
( ( ! [V_nat_H: $i] :
( ( c_Suc @ V_nat_H )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1221]) ).
thf(1680,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ V_n @ V_m @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ V_m @ V_n @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[1220]) ).
thf(1681,plain,
( ( ! [V_n: $i] :
( ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1219]) ).
thf(1682,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= V_m ) )
= $true ),
inference(copy,[status(thm)],[1218]) ).
thf(1683,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ominus__class_Ominus @ V_m @ V_m @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1217]) ).
thf(1684,plain,
( ( ! [V_m: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[1216]) ).
thf(1685,plain,
( ( ! [V_nat_H: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[1215]) ).
thf(1686,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1214]) ).
thf(1687,plain,
( ( ! [V_n: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1213]) ).
thf(1688,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[1212]) ).
thf(1689,plain,
( ( ! [V_r: $i,V_x: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1211]) ).
thf(1690,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1210]) ).
thf(1691,plain,
( ( ! [V_r: $i,V_ys: $i,V_xs: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ( V_xs = V_ys )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1209]) ).
thf(1692,plain,
( ( ! [V_r: $i,V_y: $i,V_xa: $i,V_x: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_xa ) )
| ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_xa @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1208]) ).
thf(1693,plain,
( ( ! [V_x: $i,V_y: $i,V_xs: $i,V_ys: $i,V_r: $i,T_a: $i] :
( ( V_x = V_y )
| ( V_xs = V_ys )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1207]) ).
thf(1694,plain,
( ( ! [V_x: $i,V_y: $i,V_r: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( V_x = V_y )
| ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1206]) ).
thf(1695,plain,
( ( ! [V_r: $i,V_xs: $i,T_a: $i] :
~ ( c_ListOrder_Ostep1 @ V_r @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1205]) ).
thf(1696,plain,
( ( ! [V_r: $i,T_a: $i,V_xs: $i] :
~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Olist_ONil @ T_a ) @ V_xs @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1204]) ).
thf(1697,plain,
( ( ! [T_a: $i,V_xs: $i,V_j: $i,V_i: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_List_Onth @ V_xs @ V_j @ T_a ) @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ~ ( c_lessequals @ V_i @ V_j @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1203]) ).
thf(1698,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1202]) ).
thf(1699,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1201]) ).
thf(1700,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_lessequals @ V_b @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1200]) ).
thf(1701,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_c @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1199]) ).
thf(1702,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1198]) ).
thf(1703,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1197]) ).
thf(1704,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Oone__class_Oone @ T_a ) ) @ ( c_HOL_Oone__class_Oone @ T_a ) ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1196]) ).
thf(1705,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1195]) ).
thf(1706,plain,
( ( ! [V_x: $i,V_xa: $i,V_xb: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_x @ V_xb @ T_a ) @ T_a ) @ T_a ) @ T_a )
| ( c_in @ V_x @ ( c_List_Oset @ V_xa @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1194]) ).
thf(1707,plain,
( ( ! [V_x: $i,V_xa: $i,V_xb: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_x @ V_xb @ T_a ) @ T_a ) @ T_a ) @ T_a )
| ( c_in @ V_x @ ( c_List_Oset @ V_xb @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1193]) ).
thf(1708,plain,
( ( ! [V_x: $i,V_xa: $i,V_xb: $i,T_a: $i] : ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_x @ V_xb @ T_a ) @ T_a ) @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1192]) ).
thf(1709,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1191]) ).
thf(1710,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_m @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1190]) ).
thf(1711,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_N: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_N @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1189]) ).
thf(1712,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1188]) ).
thf(1713,plain,
( ( ! [T_a: $i,V_b: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_b @ V_x @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1187]) ).
thf(1714,plain,
( ( ! [V_ys: $i,V_xs: $i,V_y: $i,V_x: $i,V_r: $i,T_a: $i] :
( ( V_ys = V_xs )
| ( V_y = V_x )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1186]) ).
thf(1715,plain,
( ( ! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ( V_y = V_x )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1185]) ).
thf(1716,plain,
( ( ! [V_r: $i,V_y: $i,V_x: $i,V_ys: $i,V_xs: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_x ) )
| ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1184]) ).
thf(1717,plain,
( ( ! [V_ys: $i,V_xs: $i,V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( V_ys = V_xs )
| ( c_ListOrder_Ostep1 @ V_r @ V_ys @ V_xs @ T_a )
| ~ ( c_ListOrder_Ostep1 @ V_r @ ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1183]) ).
thf(1718,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Ohd @ V_xs @ T_a )
= ( c_List_Onth @ V_xs @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1182]) ).
thf(1719,plain,
( ( ! [V_P: $i,V_xs: $i,V_ys: $i,T_a: $i,V_x: $i] :
( ( ( c_List_OtakeWhile @ V_P @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1181]) ).
thf(1720,plain,
( ( ! [V_r: $i,V_rs: $i,V_ss: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ V_ss @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[1180]) ).
thf(1721,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Odrop @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1179]) ).
thf(1722,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Odrop @ V_n @ V_xs @ T_a )
= ( c_List_Olist_ONil @ T_a ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1178]) ).
thf(1723,plain,
( ( ! [V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
!= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a )
= V_ys_092_060_094isub_0621 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1177]) ).
thf(1724,plain,
( ( ! [V_n: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1176]) ).
thf(1725,plain,
( ( ! [V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
!= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ( V_xs_092_060_094isub_0621
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1175]) ).
thf(1726,plain,
( ( ! [V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
!= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ( V_xs_092_060_094isub_0622
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1174]) ).
thf(1727,plain,
( ( ! [V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
!= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a ) @ V_xs_092_060_094isub_0622 @ T_a )
= V_ys_092_060_094isub_0622 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1173]) ).
thf(1728,plain,
( ( ! [V_n: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1172]) ).
thf(1729,plain,
( ( ! [V_x: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Obutlast @ V_ys @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1171]) ).
thf(1730,plain,
( ( ! [V_x: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) @ T_a ) @ T_a )
| ~ ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1170]) ).
thf(1731,plain,
( ( ! [V_as: $i,T_a: $i] :
( ( c_in @ ( c_List_Olast @ V_as @ T_a ) @ ( c_List_Oset @ V_as @ T_a ) @ T_a )
| ( V_as
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1169]) ).
thf(1732,plain,
( ( ! [V_y: $i,V_f: $i,V_xs: $i,T_a: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ ( c_List_Olist_Olist__size @ V_f @ V_xs @ T_a ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ ( hAPP @ V_f @ V_x ) @ tc_nat )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1168]) ).
thf(1733,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( ( c_List_OtakeWhile @ V_P @ V_xs @ T_a )
= ( c_List_Otake @ V_n @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Onth @ V_xs @ V_n @ T_a ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Onth @ V_xs @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ V_P @ V_n @ V_xs @ T_a ) @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1167]) ).
thf(1734,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1166]) ).
thf(1735,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Ohd @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1165]) ).
thf(1736,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Olength__unique @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olength__unique @ V_xs @ T_a ) )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1164]) ).
thf(1737,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Oappend @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Otake @ ( c_Suc @ V_n ) @ V_xs @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1163]) ).
thf(1738,plain,
( ( ! [T_a: $i,V_f: $i,V_x: $i,V_xs: $i,T_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ V_f @ ( c_List_Olinorder__class_Oinsort__key @ V_f @ V_x @ V_xs @ T_b @ T_a ) @ T_b @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1162]) ).
thf(1739,plain,
( ( ! [T_a: $i,V_f: $i,V_xs: $i,T_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ V_f @ ( c_List_Olinorder__class_Oinsort__key @ V_f @ V_x @ V_xs @ T_b @ T_a ) @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1161]) ).
thf(1740,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1160]) ).
thf(1741,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Obutlast @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1159]) ).
thf(1742,plain,
( ( ! [T_a: $i,V_m: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1158]) ).
thf(1743,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1157]) ).
thf(1744,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= V_x )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1156]) ).
thf(1745,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_n @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1155]) ).
thf(1746,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[1154]) ).
thf(1747,plain,
( ( ! [T_a: $i,V_P: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1153]) ).
thf(1748,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) )
| ( V_b = V_c ) ) )
= $true ),
inference(copy,[status(thm)],[1152]) ).
thf(1749,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ) )
= $true ),
inference(copy,[status(thm)],[1151]) ).
thf(1750,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) )
| ( V_b = V_c ) ) )
= $true ),
inference(copy,[status(thm)],[1150]) ).
thf(1751,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ) )
= $true ),
inference(copy,[status(thm)],[1149]) ).
thf(1752,plain,
( ( ! [V_ys: $i,V_xs: $i,T_a: $i] :
( V_ys
= ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1148]) ).
thf(1753,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1147]) ).
thf(1754,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_j: $i] :
( ( ( c_List_Onth @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ V_j @ T_a )
= ( c_List_Onth @ V_xs @ V_j @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1146]) ).
thf(1755,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a )
= ( c_List_Obutlast @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1145]) ).
thf(1756,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Int_Oring__char__0 @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( ( c_Int_Onumber__class_Onumber__of @ V_x @ T_a )
!= ( c_Int_Onumber__class_Onumber__of @ V_y @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[1144]) ).
thf(1757,plain,
( ( ! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_x ) ) @ V_s ) @ V_x )
= V_s ) ) )
= $true ),
inference(copy,[status(thm)],[1143]) ).
thf(1758,plain,
( ( ! [V_P: $i,V_Q: $i,T_b: $i,T_c: $i,T_a: $i,V_R: $i] :
( ( hAPP @ ( c_COMBC @ V_P @ V_Q @ T_b @ T_c @ T_a ) @ V_R )
= ( hAPP @ ( hAPP @ V_P @ V_R ) @ V_Q ) ) )
= $true ),
inference(copy,[status(thm)],[1142]) ).
thf(1759,plain,
( ( ! [V_S: $i,V_x: $i,T_a: $i] :
( ( hBOOL @ ( hAPP @ V_S @ V_x ) )
| ~ ( c_in @ V_x @ V_S @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1141]) ).
thf(1760,plain,
( ( ! [V_x: $i,V_S: $i,T_a: $i] :
( ( c_in @ V_x @ V_S @ T_a )
| ~ ( hBOOL @ ( hAPP @ V_S @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1140]) ).
thf(1761,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_j: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_j @ T_a )
= ( c_List_Onth @ V_xs @ V_j @ T_a ) )
| ( V_i = V_j ) ) )
= $true ),
inference(copy,[status(thm)],[1139]) ).
thf(1762,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i,V_u: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_u ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z )
= V_u ) ) )
= $true ),
inference(copy,[status(thm)],[1138]) ).
thf(1763,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1137]) ).
thf(1764,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_d ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1136]) ).
thf(1765,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1135]) ).
thf(1766,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_d: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) @ V_d ) ) ) )
= $true ),
inference(copy,[status(thm)],[1134]) ).
thf(1767,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1133]) ).
thf(1768,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1132]) ).
thf(1769,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1131]) ).
thf(1770,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1130]) ).
thf(1771,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) ) @ V_z ) ) ) )
= $true ),
inference(copy,[status(thm)],[1129]) ).
thf(1772,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i,V_i: $i] :
( ( ( c_List_Onth @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ V_i @ T_a )
= ( c_List_Onth @ V_xs @ V_i @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1128]) ).
thf(1773,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1127]) ).
thf(1774,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1126]) ).
thf(1775,plain,
( ( ! [V_n: $i,V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Otake @ V_n @ V_xs @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1125]) ).
thf(1776,plain,
( ( ! [T_a: $i,V_n: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1124]) ).
thf(1777,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_s ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ( V_i = V_k )
| ( c_HOL_Oord__class_Oless @ V_k @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1123]) ).
thf(1778,plain,
( ( ! [V_A: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Olistsp @ V_A @ V_xs @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1122]) ).
thf(1779,plain,
( ( ! [V_A: $i,V_ys: $i,T_a: $i,V_xs: $i] :
( ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1121]) ).
thf(1780,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_dB ) @ T_a )
= ( hAPP @ V_f3 @ V_dB ) ) )
= $true ),
inference(copy,[status(thm)],[1120]) ).
thf(1781,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_r ) @ V_t ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_s ) @ V_t ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[1119]) ).
thf(1782,plain,
( ( ! [V_i: $i,V_xs: $i,T_a: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( ( c_List_Olist__update @ V_xs @ V_i @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ T_a )
= V_xs ) ) )
= $true ),
inference(copy,[status(thm)],[1118]) ).
thf(1783,plain,
( ( ! [V_xs: $i,V_i: $i,V_a: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_i @ V_a @ T_a )
= ( c_List_Oappend @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_a @ ( c_List_Odrop @ ( c_Suc @ V_i ) @ V_xs @ T_a ) @ T_a ) @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1117]) ).
thf(1784,plain,
( ( ! [V_xs: $i,V_i: $i,T_a: $i] :
( ( V_xs
= ( c_List_Oappend @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ ( c_List_Odrop @ ( c_Suc @ V_i ) @ V_xs @ T_a ) @ T_a ) @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1116]) ).
thf(1785,plain,
( ( ! [V_i: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ ( c_Suc @ V_i ) @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1115]) ).
thf(1786,plain,
( ( ! [V_t: $i,V_ts: $i,V_u: $i,V_i: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_u ) @ V_i )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ V_u @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ V_i @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[1114]) ).
thf(1787,plain,
( ( ! [V_rs: $i,V_n: $i,V_v: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ V_rs @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ) )
= $true ),
inference(copy,[status(thm)],[1113]) ).
thf(1788,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( ( c_List_OtakeWhile @ V_P @ V_xs @ T_a )
= ( c_List_Otake @ V_n @ V_xs @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Onth @ V_xs @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ V_P @ V_n @ V_xs @ T_a ) @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1112]) ).
thf(1789,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( ( c_List_OtakeWhile @ V_P @ V_xs @ T_a )
= ( c_List_Otake @ V_n @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Onth @ V_xs @ V_n @ T_a ) ) )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ V_P @ V_n @ V_xs @ T_a ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1111]) ).
thf(1790,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Ohd @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Onth @ V_xs @ V_n @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1110]) ).
thf(1791,plain,
( ( ! [V_xs: $i,V_i: $i,T_a: $i] :
( ( ( c_List_Olist_OCons @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ ( c_List_Odrop @ ( c_Suc @ V_i ) @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ V_i @ V_xs @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1109]) ).
thf(1792,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1108]) ).
thf(1793,plain,
( ( ! [V_i: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Odrop @ V_i @ V_xs @ T_a ) @ T_a )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_i @ tc_nat ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1107]) ).
thf(1794,plain,
( ( ! [V_i: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Otake @ V_i @ V_xs @ T_a ) @ T_a )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_i @ tc_nat ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1106]) ).
thf(1795,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( ( c_List_OtakeWhile @ V_P @ V_xs @ T_a )
= ( c_List_Otake @ V_n @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_List_Onth @ V_xs @ V_n @ T_a ) ) )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ V_P @ V_n @ V_xs @ T_a ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1105]) ).
thf(1796,plain,
( ( ! [V_xs_092_060_094isub_0621: $i,T_a: $i,V_ys_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( V_xs_092_060_094isub_0621
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) )
| ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1104]) ).
thf(1797,plain,
( ( ! [V_ys_092_060_094isub_0621: $i,T_a: $i,V_xs_092_060_094isub_0621: $i,V_xs_092_060_094isub_0622: $i] :
( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a )
!= V_ys_092_060_094isub_0621 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ V_xs_092_060_094isub_0622 @ T_a )
= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a ) @ V_xs_092_060_094isub_0622 @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1103]) ).
thf(1798,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( ( c_List_OtakeWhile @ V_P @ V_xs @ T_a )
= ( c_List_Otake @ V_n @ V_xs @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ V_P @ V_n @ V_xs @ T_a ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1102]) ).
thf(1799,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i,V_n: $i] :
( ( ( c_List_OtakeWhile @ V_P @ V_xs @ T_a )
= ( c_List_Otake @ V_n @ V_xs @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ V_P @ V_n @ V_xs @ T_a ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1101]) ).
thf(1800,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ V_x @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist__update @ V_ys @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) @ V_x @ T_a ) @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1100]) ).
thf(1801,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i] :
( ( ( c_List_Onth @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ T_a )
= ( c_List_Onth @ V_ys @ ( c_HOL_Ominus__class_Ominus @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) @ T_a ) )
| ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1099]) ).
thf(1802,plain,
( ( ! [V_x: $i,V_xs: $i,V_n: $i,T_a: $i] :
( ( c_in @ V_x @ ( c_List_Oset @ ( c_List_Olist__update @ V_xs @ V_n @ V_x @ T_a ) @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1098]) ).
thf(1803,plain,
( ( ! [V_xs: $i,V_n: $i,T_a: $i] :
( ( c_in @ ( c_List_Onth @ V_xs @ V_n @ T_a ) @ ( c_List_Oset @ V_xs @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1097]) ).
thf(1804,plain,
( ( ! [V_xa: $i,V_xs: $i,T_a: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_xa @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( c_in @ ( c_List_Onth @ V_xs @ V_xa @ T_a ) @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1096]) ).
thf(1805,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1095]) ).
thf(1806,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i,V_b: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_Power_Opower__class_Opower @ V_b @ V_n @ T_a ) )
| ( V_a = V_b )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1094]) ).
thf(1807,plain,
( ( ! [V_xs: $i,T_a: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ~ ( c_in @ V_x @ ( c_List_Oset @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1093]) ).
thf(1808,plain,
( ( ! [T_a: $i,V_a: $i,V_N: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ V_a @ V_N @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ V_N @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1092]) ).
thf(1809,plain,
( ( ! [V_f: $i,V_xs: $i,V_k: $i,V_y: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist__update @ V_xs @ V_k @ V_y @ T_b ) @ T_b @ T_a )
= ( c_List_Olist__update @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ V_k @ ( hAPP @ V_f @ V_y ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1091]) ).
thf(1810,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a )
!= V_xs )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( ( c_List_Onth @ V_xs @ V_i @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1090]) ).
thf(1811,plain,
( ( ! [V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[1089]) ).
thf(1812,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1088]) ).
thf(1813,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1087]) ).
thf(1814,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1086]) ).
thf(1815,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1085]) ).
thf(1816,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1084]) ).
thf(1817,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1083]) ).
thf(1818,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1082]) ).
thf(1819,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1081]) ).
thf(1820,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_x )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1080]) ).
thf(1821,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1079]) ).
thf(1822,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oidom @ T_a )
| ~ ( class_Int_Onumber__ring @ T_a )
| ( V_x
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1078]) ).
thf(1823,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1077]) ).
thf(1824,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1076]) ).
thf(1825,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1075]) ).
thf(1826,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1074]) ).
thf(1827,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) ) @ V_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1073]) ).
thf(1828,plain,
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1072]) ).
thf(1829,plain,
( ( ! [V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1071]) ).
thf(1830,plain,
( ( ! [V_m: $i] :
~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1070]) ).
thf(1831,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1069]) ).
thf(1832,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_xs @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[1068]) ).
thf(1833,plain,
( ( ! [V_x: $i,T_a: $i,V_y: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1067]) ).
thf(1834,plain,
( ( ! [V_m: $i,V_x: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_List_Oreplicate @ V_m @ V_x @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_y @ T_a ) )
| ( V_x = V_y )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[1066]) ).
thf(1835,plain,
( ( ! [V_v: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Onth @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat ) @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1065]) ).
thf(1836,plain,
( ( ! [V_v: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1064]) ).
thf(1837,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ ( c_List_Osplice @ V_xs @ V_ys @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1063]) ).
thf(1838,plain,
( ( ! [T_a: $i,V_y: $i,V_zs: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_y @ V_zs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_OCons @ V_y @ V_zs @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1062]) ).
thf(1839,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i,V_zs: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ V_zs @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xa @ V_zs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1061]) ).
thf(1840,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ V_ys @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1060]) ).
thf(1841,plain,
( ( ! [V_f: $i,V_x: $i,V_xa: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_x ) @ ( c_List_Omap @ V_f @ V_xa @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1059]) ).
thf(1842,plain,
( ( ! [V_f: $i,V_xa: $i,V_xb: $i,T_b: $i,T_a: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_xa ) @ ( c_List_Omap @ V_f @ V_xb @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_xa @ V_xb @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1058]) ).
thf(1843,plain,
( ( ! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_OCons @ ( hAPP @ V_f @ V_x ) @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1057]) ).
thf(1844,plain,
( ( ! [V_x: $i,V_xa: $i,V_zs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xa @ V_zs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xa @ T_a ) @ V_zs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1056]) ).
thf(1845,plain,
( ( ! [V_x: $i,V_xs1: $i,V_zs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ V_xs1 @ V_zs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ V_x @ V_xs1 @ T_a ) @ V_zs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1055]) ).
thf(1846,plain,
( ( ! [T_a: $i,V_xs: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ V_xs @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1054]) ).
thf(1847,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_OtakeWhile @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ T_a ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[1053]) ).
thf(1848,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1052]) ).
thf(1849,plain,
( ( ! [T_a: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[1051]) ).
thf(1850,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[1050]) ).
thf(1851,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[1049]) ).
thf(1852,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Orev @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1048]) ).
thf(1853,plain,
( ( ! [V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1047]) ).
thf(1854,plain,
( ( ! [V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ V_ys @ T_a ) @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1046]) ).
thf(1855,plain,
( ( ! [V_i: $i,V_x: $i,T_a: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_i @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oreplicate @ V_i @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1045]) ).
thf(1856,plain,
( ( ! [T_a: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1044]) ).
thf(1857,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1043]) ).
thf(1858,plain,
( ( ! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1042]) ).
thf(1859,plain,
( ( ! [T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1041]) ).
thf(1860,plain,
( ( ! [V_P: $i,T_a: $i] :
( ( c_List_OtakeWhile @ V_P @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1040]) ).
thf(1861,plain,
( ( ! [V_ys: $i,V_xs: $i,T_a: $i] :
( ( V_ys
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1039]) ).
thf(1862,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= V_ys )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1038]) ).
thf(1863,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( V_xs
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1037]) ).
thf(1864,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= V_xs )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1036]) ).
thf(1865,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Osplice @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[1035]) ).
thf(1866,plain,
( ( ! [T_a: $i,V_ys: $i] :
( ( c_List_Osplice @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a )
= V_ys ) )
= $true ),
inference(copy,[status(thm)],[1034]) ).
thf(1867,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1033]) ).
thf(1868,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1032]) ).
thf(1869,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1031]) ).
thf(1870,plain,
( ( ! [T_a: $i,V_xs: $i,V_ys: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1030]) ).
thf(1871,plain,
( ( ! [T_a: $i,V_xs: $i,V_ys: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oappend @ V_xs @ V_ys @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1029]) ).
thf(1872,plain,
( ( ! [V_n: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1028]) ).
thf(1873,plain,
( ( ! [T_a: $i,V_f: $i,V_xs: $i,T_b: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[1027]) ).
thf(1874,plain,
( ( ! [V_ys: $i,T_a: $i] :
( V_ys
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1026]) ).
thf(1875,plain,
( ( ! [T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_ys @ T_a )
= V_ys ) )
= $true ),
inference(copy,[status(thm)],[1025]) ).
thf(1876,plain,
( ( ! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1024]) ).
thf(1877,plain,
( ( ! [V_x: $i,T_a: $i] :
( V_x
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1023]) ).
thf(1878,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[1022]) ).
thf(1879,plain,
( ( ! [V_n: $i,T_a: $i] :
( ( c_List_Otake @ V_n @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1021]) ).
thf(1880,plain,
( ( ! [V_A: $i,T_a: $i] : ( c_List_Olistsp @ V_A @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
= $true ),
inference(copy,[status(thm)],[1020]) ).
thf(1881,plain,
( ( ! [V_f: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1019]) ).
thf(1882,plain,
( ( ! [T_a: $i,V_A: $i] :
( ( c_List_Osublist @ ( c_List_Olist_ONil @ T_a ) @ V_A @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1018]) ).
thf(1883,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1017]) ).
thf(1884,plain,
( ( ! [T_a: $i,V_k: $i,V_x: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_k @ V_x @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1016]) ).
thf(1885,plain,
( ( ! [T_a: $i,V_i: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_i @ V_y @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1015]) ).
thf(1886,plain,
( ( ! [T_a: $i,V_i: $i,V_v: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ T_a ) @ V_i @ V_v @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1014]) ).
thf(1887,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1013]) ).
thf(1888,plain,
( ( ! [T_a: $i,V_f: $i,T_b: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Olist_ONil @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1012]) ).
thf(1889,plain,
( ( ! [T_a: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1011]) ).
thf(1890,plain,
( ( ! [T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1010]) ).
thf(1891,plain,
( ( ! [V_xs: $i,V_k: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Olist__update @ V_xs @ V_k @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1009]) ).
thf(1892,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ V_xs @ T_a )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_xs @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1008]) ).
thf(1893,plain,
( ( ! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) @ V_s ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_k ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_u ) @ V_s ) @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[1007]) ).
thf(1894,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB_H: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(copy,[status(thm)],[1006]) ).
thf(1895,plain,
( ( ! [V_dB_H: $i,V_dB1: $i,V_dB2: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) ) )
= $true ),
inference(copy,[status(thm)],[1005]) ).
thf(1896,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_xb: $i,V_xc: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_xb ) @ V_xc ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_xb ) @ V_xc ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1004]) ).
thf(1897,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_dB1: $i,V_dB2: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ ( hAPP @ V_f2 @ V_dB1 ) @ V_dB2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1003]) ).
thf(1898,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB1: $i,V_dB2: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ T_a )
= ( hAPP @ ( hAPP @ V_f2 @ V_dB1 ) @ V_dB2 ) ) )
= $true ),
inference(copy,[status(thm)],[1002]) ).
thf(1899,plain,
( ( ! [V_u: $i,V_s: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_s ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_u ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[1001]) ).
thf(1900,plain,
( ( ! [V_s: $i,V_u: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_u ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_s ) @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[1000]) ).
thf(1901,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_zs: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ T_a )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y ) @ V_zs @ T_a @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y @ V_zs @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[999]) ).
thf(1902,plain,
( ( ! [V_f: $i,V_a: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( c_List_Ofoldl @ V_f @ V_a @ V_xs @ T_a @ T_b ) @ V_ys @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[998]) ).
thf(1903,plain,
( ( ! [V_dB_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(copy,[status(thm)],[997]) ).
thf(1904,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_xd: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_xd ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_xd ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[996]) ).
thf(1905,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_nat: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_nat ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f1 @ V_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[995]) ).
thf(1906,plain,
( ( ! [V_k: $i,V_u: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_k ) ) @ V_u ) @ V_k )
= V_u ) )
= $true ),
inference(copy,[status(thm)],[994]) ).
thf(1907,plain,
( ( ! [V_i: $i,V_t: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_t ) ) )
= $true ),
inference(copy,[status(thm)],[993]) ).
thf(1908,plain,
( ( ! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ) )
= $true ),
inference(copy,[status(thm)],[992]) ).
thf(1909,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Orev @ V_xs @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[991]) ).
thf(1910,plain,
( ( ! [V_m: $i,V_x: $i,T_a: $i,V_n: $i,V_y: $i] :
( ( ( c_List_Oreplicate @ V_m @ V_x @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_y @ T_a ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[990]) ).
thf(1911,plain,
( ( ! [V_ys: $i,V_xs: $i,T_a: $i,V_zs: $i] :
( ( ( c_List_Oappend @ V_ys @ V_xs @ T_a )
!= ( c_List_Oappend @ V_zs @ V_xs @ T_a ) )
| ( V_ys = V_zs ) ) )
= $true ),
inference(copy,[status(thm)],[989]) ).
thf(1912,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
( ( ( c_List_Oappend @ V_xs @ V_ys @ T_a )
!= ( c_List_Oappend @ V_xs @ V_zs @ T_a ) )
| ( V_ys = V_zs ) ) )
= $true ),
inference(copy,[status(thm)],[988]) ).
thf(1913,plain,
( ( ! [T_a: $i,V_n: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ V_n @ V_xs @ T_a ) @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[987]) ).
thf(1914,plain,
( ( ! [V_xs: $i,V_x: $i,V_ys: $i,T_a: $i] :
( ( c_List_Onth @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ T_a ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ T_a )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[986]) ).
thf(1915,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ( c_List_OtakeWhile @ V_P @ V_xs @ T_a )
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[985]) ).
thf(1916,plain,
( ( ! [V_P: $i,V_xs: $i,T_a: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Onth @ V_xs @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ T_a ) ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[984]) ).
thf(1917,plain,
( ( ! [V_xs: $i,T_a: $i] :
( V_xs
= ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[983]) ).
thf(1918,plain,
( ( ! [V_ys: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_ys @ T_a ) @ T_a )
= V_ys ) )
= $true ),
inference(copy,[status(thm)],[982]) ).
thf(1919,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[981]) ).
thf(1920,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_List_Oappend @ ( c_List_Obutlast @ V_xs @ T_a ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= V_xs )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[980]) ).
thf(1921,plain,
( ( ! [V_xs: $i,T_a: $i,V_ys: $i] :
( V_xs
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[979]) ).
thf(1922,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[978]) ).
thf(1923,plain,
( ( ! [V_f: $i,V_n: $i,V_x: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Oreplicate @ V_n @ V_x @ T_b ) @ T_b @ T_a )
= ( c_List_Oreplicate @ V_n @ ( hAPP @ V_f @ V_x ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[977]) ).
thf(1924,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i] :
( ( ( c_List_Onth @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ T_a )
= ( c_List_Onth @ V_xs @ V_n @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[976]) ).
thf(1925,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[975]) ).
thf(1926,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[974]) ).
thf(1927,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[973]) ).
thf(1928,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a )
= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[972]) ).
thf(1929,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[971]) ).
thf(1930,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[970]) ).
thf(1931,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[969]) ).
thf(1932,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[968]) ).
thf(1933,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[967]) ).
thf(1934,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_xa: $i] :
( ~ ( c_HOL_Oord__class_Oless @ V_x @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat )
| ( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_x @ V_xa @ T_a ) @ V_x @ T_a )
= V_xa ) ) )
= $true ),
inference(copy,[status(thm)],[966]) ).
thf(1935,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i @ T_a )
= V_x )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[965]) ).
thf(1936,plain,
( ( ! [T_a: $i,V_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Power_Opower__class_Opower @ V_a @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[964]) ).
thf(1937,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Odrop @ V_n @ V_xs @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[963]) ).
thf(1938,plain,
( ( ! [V_dB: $i,V_dB_H: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_dB )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) )
| ( V_dB = V_dB_H ) ) )
= $true ),
inference(copy,[status(thm)],[962]) ).
thf(1939,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a )
= ( c_List_Otake @ V_n @ V_xs @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[961]) ).
thf(1940,plain,
( ( ! [V_f: $i,V_xs: $i,T_b: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a )
!= ( c_List_Omap @ V_f @ V_ys @ T_b @ T_a ) )
| ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_b ) )
= ( c_Nat_Osize__class_Osize @ V_ys @ ( tc_List_Olist @ T_b ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[960]) ).
thf(1941,plain,
( ( ! [V_xs: $i,T_a: $i,V_zs: $i] :
( ( V_xs
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_zs @ T_a ) )
| ( ( c_List_Oappend @ V_xs @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_zs @ T_a ) @ T_a )
= V_zs ) ) )
= $true ),
inference(copy,[status(thm)],[959]) ).
thf(1942,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_n @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_n @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[958]) ).
thf(1943,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_i: $i,V_x: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_i @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_ys @ T_a ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[957]) ).
thf(1944,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i,V_i: $i] :
( ( ( c_List_Onth @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ V_i @ T_a )
= V_x )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[956]) ).
thf(1945,plain,
( ( ! [V_P: $i,V_xs: $i,V_x: $i,V_l: $i,T_a: $i] :
( ( ( c_List_OtakeWhile @ V_P @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ V_l @ T_a ) @ T_a ) @ T_a )
= ( c_List_OtakeWhile @ V_P @ V_xs @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[955]) ).
thf(1946,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[954]) ).
thf(1947,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[953]) ).
thf(1948,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[952]) ).
thf(1949,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[951]) ).
thf(1950,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[950]) ).
thf(1951,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Olast @ V_ys @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[949]) ).
thf(1952,plain,
( ( ! [V_s: $i,V_t: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_s ) @ V_t ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[948]) ).
thf(1953,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[947]) ).
thf(1954,plain,
( ( ! [T_a: $i,V_x: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Olistsum @ V_xs @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[946]) ).
thf(1955,plain,
( ( ! [V_f: $i,V_xs: $i,V_ys: $i,T_b: $i,T_a: $i] :
( ( c_List_Omap @ V_f @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ T_b @ T_a )
= ( c_List_Oappend @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ ( c_List_Omap @ V_f @ V_ys @ T_b @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[945]) ).
thf(1956,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[944]) ).
thf(1957,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[943]) ).
thf(1958,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[942]) ).
thf(1959,plain,
( ( ! [V_P: $i,V_n: $i,V_m: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_P @ V_n ) @ V_m ) )
| ( c_HOL_Oord__class_Oless @ V_n @ V_m @ tc_nat )
| ( V_m = V_n )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[941]) ).
thf(1960,plain,
( ( ! [V_y: $i,V_x: $i] :
( ( c_HOL_Oord__class_Oless @ V_y @ V_x @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[940]) ).
thf(1961,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[939]) ).
thf(1962,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i,V_k: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oreplicate @ V_k @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[938]) ).
thf(1963,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[937]) ).
thf(1964,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[936]) ).
thf(1965,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i,V_d: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_d ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_c @ V_d @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[935]) ).
thf(1966,plain,
( ( ! [V_f: $i,V_xs: $i,T_a: $i,T_b: $i,V_n: $i] :
( ( ( c_List_Onth @ ( c_List_Omap @ V_f @ V_xs @ T_a @ T_b ) @ V_n @ T_b )
= ( hAPP @ V_f @ ( c_List_Onth @ V_xs @ V_n @ T_a ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[934]) ).
thf(1967,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[933]) ).
thf(1968,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[932]) ).
thf(1969,plain,
( ( ! [V_xs: $i,T_a: $i,V_ys: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Orev @ V_ys @ T_a ) )
| ( V_xs = V_ys ) ) )
= $true ),
inference(copy,[status(thm)],[931]) ).
thf(1970,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[930]) ).
thf(1971,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[929]) ).
thf(1972,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[928]) ).
thf(1973,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Orev @ V_xs @ T_a ) @ T_a )
= ( c_List_Olistsum @ V_xs @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[927]) ).
thf(1974,plain,
( ( ! [V_A: $i,V_xs: $i,V_ys: $i,T_a: $i] :
( ( c_List_Olistsp @ V_A @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_ys @ T_a )
| ~ ( c_List_Olistsp @ V_A @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[926]) ).
thf(1975,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( tc_List_Olist @ T_a ) )
= V_n ) )
= $true ),
inference(copy,[status(thm)],[925]) ).
thf(1976,plain,
( ( ! [V_xs: $i,V_i: $i,T_a: $i] :
( ( c_List_Olist__update @ V_xs @ V_i @ ( c_List_Onth @ V_xs @ V_i @ T_a ) @ T_a )
= V_xs ) )
= $true ),
inference(copy,[status(thm)],[924]) ).
thf(1977,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i,V_c: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_c @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[923]) ).
thf(1978,plain,
( ( ! [V_j: $i,V_u: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ V_j ) ) @ V_u ) @ V_i )
= ( c_Lambda_OdB_OVar @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[922]) ).
thf(1979,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_dB: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_dB ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f3 @ V_dB ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[921]) ).
thf(1980,plain,
( ( ! [V_P: $i,V_f1: $i,V_f2: $i,V_f3: $i,V_xa: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_xa ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ V_P @ ( hAPP @ V_f3 @ V_xa ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[920]) ).
thf(1981,plain,
( ( ! [V_xs: $i,V_x: $i,V_ys: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ V_ys @ T_a ) @ T_a ) @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ V_y @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[919]) ).
thf(1982,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[918]) ).
thf(1983,plain,
( ( ! [T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[917]) ).
thf(1984,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ V_c ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_b ) @ V_c ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[916]) ).
thf(1985,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[915]) ).
thf(1986,plain,
( ( ! [T_a: $i,V_c: $i,V_a: $i,V_b: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[914]) ).
thf(1987,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_c: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_a ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_c ) @ V_b ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[913]) ).
thf(1988,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i,V_y: $i,V_ys: $i] :
( ( ( c_List_Odrop @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_y @ V_ys @ T_a ) )
| ( ( c_List_Onth @ V_xs @ V_n @ T_a )
= V_y ) ) )
= $true ),
inference(copy,[status(thm)],[912]) ).
thf(1989,plain,
( ( ! [V_ys_092_060_094isub_0621: $i,T_a: $i,V_xs_092_060_094isub_0621: $i,V_ys_092_060_094isub_0622: $i] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
!= V_ys_092_060_094isub_0622 )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_ys_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_xs_092_060_094isub_0621 @ T_a )
!= V_ys_092_060_094isub_0621 )
| ( V_xs_092_060_094isub_0621
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) )
| ( ( c_List_Oappend @ V_xs_092_060_094isub_0621 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ V_xs_092_060_094isub_0621 @ ( tc_List_Olist @ T_a ) ) @ V_ys_092_060_094isub_0621 @ T_a ) @ V_ys_092_060_094isub_0622 @ T_a ) @ T_a )
= ( c_List_Oappend @ V_ys_092_060_094isub_0621 @ V_ys_092_060_094isub_0622 @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[911]) ).
thf(1990,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_t ) @ V_t_H ) )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[910]) ).
thf(1991,plain,
( ( ! [T_a: $i,V_xs: $i,V_ys: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ V_xs @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[909]) ).
thf(1992,plain,
( ( ! [T_a: $i,V_ys: $i,V_xs: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ V_ys @ T_a )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[908]) ).
thf(1993,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_i_H: $i,V_x_H: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i_H @ V_x_H @ T_a )
= ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i_H @ V_x_H @ T_a ) @ V_i @ V_x @ T_a ) )
| ( V_i = V_i_H ) ) )
= $true ),
inference(copy,[status(thm)],[907]) ).
thf(1994,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i,V_xs: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[906]) ).
thf(1995,plain,
( ( ! [V_n: $i,V_f: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Odrop @ V_n @ ( c_List_Omap @ V_f @ V_xs @ T_b @ T_a ) @ T_a )
= ( c_List_Omap @ V_f @ ( c_List_Odrop @ V_n @ V_xs @ T_b ) @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[905]) ).
thf(1996,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ V_xs @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[904]) ).
thf(1997,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Obutlast @ V_ys @ T_a ) @ T_a ) )
| ( V_ys
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[903]) ).
thf(1998,plain,
( ( ! [T_a: $i,V_xs: $i,V_ys: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_List_Olistsum @ V_xs @ T_a ) ) @ ( c_List_Olistsum @ V_ys @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[902]) ).
thf(1999,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_j: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_j @ T_a )
= ( c_List_Onth @ V_xs @ V_j @ T_a ) )
| ( V_i = V_j )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[901]) ).
thf(2000,plain,
( ( ! [V_xs: $i,V_i: $i,V_x: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ V_xs @ V_i @ V_x @ T_a ) @ V_i @ V_y @ T_a )
= ( c_List_Olist__update @ V_xs @ V_i @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[900]) ).
thf(2001,plain,
( ( ! [V_xs: $i,V_ys: $i,T_a: $i,V_zs: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_ys @ T_a ) @ V_zs @ T_a )
= ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_ys @ V_zs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[899]) ).
thf(2002,plain,
( ( ! [V_xs: $i,V_xs1: $i,V_us: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_xs1 @ V_us @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_xs1 @ T_a ) @ V_us @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[898]) ).
thf(2003,plain,
( ( ! [V_zs: $i,V_x: $i,T_a: $i,V_ys: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ V_zs @ V_x @ T_a ) @ V_ys @ T_a )
= ( c_List_Oappend @ V_zs @ ( c_List_Oappend @ V_x @ V_ys @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[897]) ).
thf(2004,plain,
( ( ! [V_xs: $i,V_x: $i,V_ts: $i,T_a: $i] :
( ( c_List_Oappend @ V_xs @ ( c_List_Oappend @ V_x @ V_ts @ T_a ) @ T_a )
= ( c_List_Oappend @ ( c_List_Oappend @ V_xs @ V_x @ T_a ) @ V_ts @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[896]) ).
thf(2005,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[895]) ).
thf(2006,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[894]) ).
thf(2007,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[893]) ).
thf(2008,plain,
( ( ! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[892]) ).
thf(2009,plain,
( ( ! [V_e: $i,V_i: $i,V_T: $i] :
( ( ( hAPP @ V_e @ V_i )
= V_T )
| ~ ( c_Type_Otyping @ V_e @ ( c_Lambda_OdB_OVar @ V_i ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[891]) ).
thf(2010,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_nat: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__case @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ) )
= $true ),
inference(copy,[status(thm)],[890]) ).
thf(2011,plain,
( ( ! [V_env: $i,V_x: $i] : ( c_Type_Otyping @ V_env @ ( c_Lambda_OdB_OVar @ V_x ) @ ( hAPP @ V_env @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[889]) ).
thf(2012,plain,
( ( ! [V_ts: $i] :
( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ V_ts @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[888]) ).
thf(2013,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_s____ ) )
= $true ),
inference(copy,[status(thm)],[887]) ).
thf(2014,plain,
( ( ! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ V_r ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) ) ) )
= $true ),
inference(copy,[status(thm)],[886]) ).
thf(2015,plain,
( ( ! [V_t: $i,V_k: $i,V_s: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_k ) ) @ V_s ) @ V_k )
= V_t ) )
= $true ),
inference(copy,[status(thm)],[885]) ).
thf(2016,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_r ) @ V_i ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[884]) ).
thf(2017,plain,
( ( ! [V_x: $i,T_a: $i,V_A: $i] :
( ( ( c_List_Osublist @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ V_A @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
| ~ ( c_in @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_A @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[883]) ).
thf(2018,plain,
( ( ! [V_v: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ V_v @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[882]) ).
thf(2019,plain,
( ( ! [V_x: $i,T_a: $i,V_A: $i] :
( ( ( c_List_Osublist @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ V_A @ T_a )
= ( c_List_Olist_ONil @ T_a ) )
| ( c_in @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_A @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[881]) ).
thf(2020,plain,
( ( ! [V_v: $i,V_n: $i,V_rs: $i] :
( ( V_v
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ V_n @ V_rs @ V_v ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_v ) ) ) )
= $true ),
inference(copy,[status(thm)],[880]) ).
thf(2021,plain,
( ( ! [V_t: $i,V_ts: $i,V_i: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_i )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ V_i @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[879]) ).
thf(2022,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[878]) ).
thf(2023,plain,
( ( ! [T_a: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_n @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[877]) ).
thf(2024,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ T_a )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ T_a )
| ~ ( class_Ring__and__Field_Omult__zero @ T_a )
| ~ ( class_Power_Opower @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
!= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[876]) ).
thf(2025,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[875]) ).
thf(2026,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[874]) ).
thf(2027,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ T_a )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[873]) ).
thf(2028,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[872]) ).
thf(2029,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i,V_y: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_y @ T_a )
= ( c_List_Olist_OCons @ V_y @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[871]) ).
thf(2030,plain,
( ( ! [V_fa: $i,T_a: $i] :
( ( c_List_Olist_Olist__size @ V_fa @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[870]) ).
thf(2031,plain,
( ( ! [V_f: $i,T_a: $i] :
( ( c_List_Olist_Olist__size @ V_f @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[869]) ).
thf(2032,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( ( c_Nat_Osize__class_Osize @ V_xs @ ( tc_List_Olist @ T_a ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[868]) ).
thf(2033,plain,
( ( ! [T_a: $i,V_n: $i,V_x: $i] :
( ( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Oreplicate @ V_n @ V_x @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[867]) ).
thf(2034,plain,
( ( ! [V_n: $i,V_x: $i,T_a: $i] :
( ( ( c_List_Oreplicate @ V_n @ V_x @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[866]) ).
thf(2035,plain,
( ( ! [V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_xs @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[865]) ).
thf(2036,plain,
( ( ! [T_a: $i,V_x: $i] :
( ( c_List_Olist_ONil @ T_a )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[864]) ).
thf(2037,plain,
( ( ! [T_a: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ T_a ) @ ( tc_List_Olist @ T_a ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[863]) ).
thf(2038,plain,
( ( ! [V_n: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Otake @ V_n @ V_xs @ T_a )
!= ( c_List_Olist_ONil @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[862]) ).
thf(2039,plain,
( ( ! [T_a: $i] :
( ( c_List_Olength__unique @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[861]) ).
thf(2040,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_x @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[860]) ).
thf(2041,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
( ( ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
!= ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_x = V_y ) ) )
= $true ),
inference(copy,[status(thm)],[859]) ).
thf(2042,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i,V_ys: $i,V_y: $i] :
( ( ( c_List_Oappend @ V_xs @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
!= ( c_List_Oappend @ V_ys @ ( c_List_Olist_OCons @ V_y @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) )
| ( V_xs = V_ys ) ) )
= $true ),
inference(copy,[status(thm)],[858]) ).
thf(2043,plain,
( ( ! [T_a: $i,V_x: $i,V_xs: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[857]) ).
thf(2044,plain,
( ( ! [T_b: $i,V_f: $i,V_x: $i,T_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_b )
| ( ( c_List_Olinorder__class_Oinsort__key @ V_f @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a @ T_b )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[856]) ).
thf(2045,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Obutlast @ V_xs @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[855]) ).
thf(2046,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Olast @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= V_x ) )
= $true ),
inference(copy,[status(thm)],[854]) ).
thf(2047,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[853]) ).
thf(2048,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[852]) ).
thf(2049,plain,
( ( ! [V_xs: $i,T_a: $i,V_x: $i] :
( ( ( c_List_Orev @ V_xs @ T_a )
!= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[851]) ).
thf(2050,plain,
( ( ! [V_P: $i,V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_OtakeWhile @ V_P @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) )
| ( hBOOL @ ( hAPP @ V_P @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[850]) ).
thf(2051,plain,
( ( ! [V_x: $i,T_a: $i,V_xs: $i] :
( ( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
!= ( c_List_Orev @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[849]) ).
thf(2052,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a )
= ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[848]) ).
thf(2053,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olast @ V_xs @ T_a ) )
| ( V_xs
= ( c_List_Olist_ONil @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[847]) ).
thf(2054,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xs @ T_a )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ T_a ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[846]) ).
thf(2055,plain,
( ( ! [V_x: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a )
= ( c_List_Orev @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[845]) ).
thf(2056,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ V_x @ ( c_List_Olist_ONil @ T_a ) @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[844]) ).
thf(2057,plain,
( ( ! [T_a: $i,V_x: $i,V_zs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_zs @ T_a @ T_a ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x @ V_zs @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[843]) ).
thf(2058,plain,
( ( ! [V_nat: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OVar @ V_nat ) @ tc_Lambda_OdB )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[842]) ).
thf(2059,plain,
( ( ! [V_nat: $i] :
( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OVar @ V_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[841]) ).
thf(2060,plain,
( ( ! [V_s: $i,V_ss: $i,V_r: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ V_r ) )
| ( V_s
= ( c_Lambda_OdB_OAbs @ V_r ) ) ) )
= $true ),
inference(copy,[status(thm)],[840]) ).
thf(2061,plain,
( ( ! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ) )
= $true ),
inference(copy,[status(thm)],[839]) ).
thf(2062,plain,
( ( ! [V_r: $i,V_rs: $i,V_s: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ) )
= $true ),
inference(copy,[status(thm)],[838]) ).
thf(2063,plain,
( ( ! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[837]) ).
thf(2064,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ V_r )
= V_s ) ) )
= $true ),
inference(copy,[status(thm)],[836]) ).
thf(2065,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) ) @ V_s ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_s ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_r ) @ V_s ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[835]) ).
thf(2066,plain,
( ( ! [V_r: $i,V_i: $i,V_j: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_r ) @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_j ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) ) ) )
= $true ),
inference(copy,[status(thm)],[834]) ).
thf(2067,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_k )
= ( c_Lambda_OdB_OVar @ V_i ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[833]) ).
thf(2068,plain,
( ( ! [V_r: $i,V_s: $i,V_t: $i,V_ts: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ V_r @ V_s @ V_t @ V_ts ) @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(copy,[status(thm)],[832]) ).
thf(2069,plain,
( ( ! [V_x: $i,V_xs: $i,T_a: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) @ T_a )
= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[831]) ).
thf(2070,plain,
( ( ! [V_T: $i,V_U: $i,V_e: $i,V_i: $i,V_ts: $i] :
( ( V_T = V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_U )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[830]) ).
thf(2071,plain,
( ( ! [V_n: $i,V_ts: $i,V_r: $i,V_ss: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[829]) ).
thf(2072,plain,
( ( ! [V_s: $i,V_t: $i,V_n: $i,V_ss: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_t )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[828]) ).
thf(2073,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OAbs @ V_r )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(copy,[status(thm)],[827]) ).
thf(2074,plain,
( ( ! [V_r: $i] :
( ( c_Lambda_OdB_OAbs @ V_r )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[826]) ).
thf(2075,plain,
( ( ! [V_r: $i,V_s: $i,V_t: $i,V_ts: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ V_r @ V_s @ V_t @ V_ts ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ts
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(copy,[status(thm)],[825]) ).
thf(2076,plain,
( ( ! [V_s: $i,V_ss: $i,V_r: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ V_r ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(copy,[status(thm)],[824]) ).
thf(2077,plain,
( ( ! [V_r: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ V_r ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ V_r ) ) )
= $true ),
inference(copy,[status(thm)],[823]) ).
thf(2078,plain,
( ( ! [V_n: $i,V_rs: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ V_rs @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[822]) ).
thf(2079,plain,
( ( ! [V_x: $i,V_s: $i,V_t: $i] :
( ( ( c_List_Oappend @ V_x @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_x @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Oappend @ V_x @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(copy,[status(thm)],[821]) ).
thf(2080,plain,
( ( ! [V_t: $i,V_ts: $i,V_u: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ V_u )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Oappend @ V_ts @ ( c_List_Olist_OCons @ V_u @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[820]) ).
thf(2081,plain,
( ( ! [V_r: $i,V_s: $i,V_xa: $i] :
( ( V_r
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ V_xa @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ ( c_List_Oappend @ V_xa @ ( c_List_Olist_OCons @ V_s @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(copy,[status(thm)],[819]) ).
thf(2082,plain,
( ( ! [V_r: $i,V_s: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[818]) ).
thf(2083,plain,
( ( ! [V_nat: $i,V_nat_H: $i] :
( ( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OVar @ V_nat_H ) )
| ( V_nat = V_nat_H ) ) )
= $true ),
inference(copy,[status(thm)],[817]) ).
thf(2084,plain,
( ( ! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[816]) ).
thf(2085,plain,
( ( ! [V_m: $i,V_rs: $i,V_n: $i,V_ss: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ V_rs @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_n ) @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_rs = V_ss ) ) )
= $true ),
inference(copy,[status(thm)],[815]) ).
thf(2086,plain,
( ( ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_list = V_list_H ) ) )
= $true ),
inference(copy,[status(thm)],[814]) ).
thf(2087,plain,
( ( ! [V_a: $i,V_list: $i,T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( ( c_List_Olist_OCons @ V_a @ V_list @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) )
| ( V_a = V_a_H ) ) )
= $true ),
inference(copy,[status(thm)],[813]) ).
thf(2088,plain,
( ( ! [V_r: $i,V_s: $i,V_t: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_t @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_r ) @ V_s )
= V_t ) ) )
= $true ),
inference(copy,[status(thm)],[812]) ).
thf(2089,plain,
( ( ! [T_a: $i,V_a_H: $i,V_list_H: $i] :
( ( c_List_Olist_ONil @ T_a )
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[811]) ).
thf(2090,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB1 = V_dB1_H ) ) )
= $true ),
inference(copy,[status(thm)],[810]) ).
thf(2091,plain,
( ( ! [V_dB1: $i,V_dB2: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) )
| ( V_dB2 = V_dB2_H ) ) )
= $true ),
inference(copy,[status(thm)],[809]) ).
thf(2092,plain,
( ( ! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ V_m )
= V_s ) ) )
= $true ),
inference(copy,[status(thm)],[808]) ).
thf(2093,plain,
( ( ! [V_nat: $i,V_dB1_H: $i,V_dB2_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H ) ) )
= $true ),
inference(copy,[status(thm)],[807]) ).
thf(2094,plain,
( ( ! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[806]) ).
thf(2095,plain,
( ( ! [V_f: $i,V_a: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_ONil @ T_b ) @ T_a @ T_b )
= V_a ) )
= $true ),
inference(copy,[status(thm)],[805]) ).
thf(2096,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[804]) ).
thf(2097,plain,
( ( ! [V_s: $i,V_t: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_k ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[803]) ).
thf(2098,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_ta____ ) )
= $true ),
inference(copy,[status(thm)],[802]) ).
thf(2099,plain,
( ( ! [V_m: $i] :
( ( c_Lambda_OdB_OVar @ V_m )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_m ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[801]) ).
thf(2100,plain,
( ( ! [V_f: $i,V_a: $i,V_x: $i,V_xs: $i,T_b: $i,T_a: $i] :
( ( c_List_Ofoldl @ V_f @ V_a @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ T_a @ T_b )
= ( c_List_Ofoldl @ V_f @ ( hAPP @ ( hAPP @ V_f @ V_a ) @ V_x ) @ V_xs @ T_a @ T_b ) ) )
= $true ),
inference(copy,[status(thm)],[800]) ).
thf(2101,plain,
( ( ! [V_x: $i,V_xa: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_xa @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[799]) ).
thf(2102,plain,
( ( ! [V_a_H: $i,V_list_H: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a )
!= ( c_List_Olist_ONil @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[798]) ).
thf(2103,plain,
( ( ! [V_r: $i,V_ts: $i,V_s: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_r @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_r = V_s ) ) )
= $true ),
inference(copy,[status(thm)],[797]) ).
thf(2104,plain,
( ( ! [V_x: $i,V_t: $i,T_a: $i] :
( ( c_List_Olist_OCons @ V_x @ V_t @ T_a )
!= V_t ) )
= $true ),
inference(copy,[status(thm)],[796]) ).
thf(2105,plain,
( ( ! [V_xs: $i,V_x: $i,T_a: $i] :
( V_xs
!= ( c_List_Olist_OCons @ V_x @ V_xs @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[795]) ).
thf(2106,plain,
( ( ! [V_m: $i,V_s: $i,V_ss: $i] :
( ( ( c_Lambda_OdB_OVar @ V_m )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ V_s @ V_ss @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_ss
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(copy,[status(thm)],[794]) ).
thf(2107,plain,
( ( ! [V_t: $i,V_i: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ ( c_Lambda_OdB_OVar @ V_i ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[793]) ).
thf(2108,plain,
( ( ! [V_dB1_H: $i,V_dB2_H: $i,V_nat: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1_H ) @ V_dB2_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ) )
= $true ),
inference(copy,[status(thm)],[792]) ).
thf(2109,plain,
( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Olist_OCons @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ v_ta____ ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $true ),
inference(copy,[status(thm)],[791]) ).
thf(2110,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)],[790]) ).
thf(2111,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)],[789]) ).
thf(2112,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[788]) ).
thf(2113,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(copy,[status(thm)],[787]) ).
thf(2114,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[786]) ).
thf(2115,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[785]) ).
thf(2116,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[784]) ).
thf(2117,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[783]) ).
thf(2118,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_nat )
= $true ),
inference(copy,[status(thm)],[782]) ).
thf(2119,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(copy,[status(thm)],[781]) ).
thf(2120,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[780]) ).
thf(2121,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[779]) ).
thf(2122,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[778]) ).
thf(2123,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_nat )
= $true ),
inference(copy,[status(thm)],[777]) ).
thf(2124,plain,
( ( class_OrderedGroup_Osemigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[776]) ).
thf(2125,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[775]) ).
thf(2126,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[774]) ).
thf(2127,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_nat )
= $true ),
inference(copy,[status(thm)],[773]) ).
thf(2128,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_nat )
= $true ),
inference(copy,[status(thm)],[772]) ).
thf(2129,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[771]) ).
thf(2130,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[770]) ).
thf(2131,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[769]) ).
thf(2132,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[768]) ).
thf(2133,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[767]) ).
thf(2134,plain,
( ( class_Power_Opower @ tc_nat )
= $true ),
inference(copy,[status(thm)],[766]) ).
thf(2135,plain,
( ( class_Int_Onumber @ tc_nat )
= $true ),
inference(copy,[status(thm)],[765]) ).
thf(2136,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[764]) ).
thf(2137,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[763]) ).
thf(2138,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[762]) ).
thf(2139,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[761]) ).
thf(2140,plain,
( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[760]) ).
thf(2141,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[759]) ).
thf(2142,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[758]) ).
thf(2143,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[757]) ).
thf(2144,plain,
( ( class_OrderedGroup_Opordered__ab__group__add @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[756]) ).
thf(2145,plain,
( ( class_OrderedGroup_Olordered__ab__group__add @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[755]) ).
thf(2146,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[754]) ).
thf(2147,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[753]) ).
thf(2148,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[752]) ).
thf(2149,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[751]) ).
thf(2150,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[750]) ).
thf(2151,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[749]) ).
thf(2152,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[748]) ).
thf(2153,plain,
( ( class_Ring__and__Field_Oordered__idom @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[747]) ).
thf(2154,plain,
( ( class_OrderedGroup_Osemigroup__add @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[746]) ).
thf(2155,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[745]) ).
thf(2156,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[744]) ).
thf(2157,plain,
( ( class_OrderedGroup_Oab__group__add @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[743]) ).
thf(2158,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[742]) ).
thf(2159,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[741]) ).
thf(2160,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[740]) ).
thf(2161,plain,
( ( class_OrderedGroup_Ogroup__add @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[739]) ).
thf(2162,plain,
( ( class_Ring__and__Field_Oring__1 @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[738]) ).
thf(2163,plain,
( ( class_Ring__and__Field_Oidom @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[737]) ).
thf(2164,plain,
( ( class_Nat_Osemiring__char__0 @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[736]) ).
thf(2165,plain,
( ( class_Orderings_Opreorder @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[735]) ).
thf(2166,plain,
( ( class_Orderings_Olinorder @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[734]) ).
thf(2167,plain,
( ( class_Orderings_Oorder @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[733]) ).
thf(2168,plain,
( ( class_Int_Oring__char__0 @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[732]) ).
thf(2169,plain,
( ( class_Int_Onumber__ring @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[731]) ).
thf(2170,plain,
( ( class_Power_Opower @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[730]) ).
thf(2171,plain,
( ( class_Int_Onumber @ tc_Int_Oint )
= $true ),
inference(copy,[status(thm)],[729]) ).
thf(2172,plain,
( ( ! [V_x: $i,T_a: $i] : ( c_fequal @ V_x @ V_x @ T_a ) )
= $true ),
inference(copy,[status(thm)],[728]) ).
thf(2173,plain,
( ( ! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( c_fequal @ V_X @ V_Y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[727]) ).
thf(2174,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[1450]) ).
thf(2175,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1938]) ).
thf(2176,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oreplicate @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oreplicate @ SX3 @ SX4 @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1910]) ).
thf(2177,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0
!= ( c_List_Oappend @ SX1 @ SX0 @ SX2 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1861]) ).
thf(2178,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX2 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX3 ) @ SX2 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1748]) ).
thf(2179,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2101]) ).
thf(2180,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Odrop @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SX1 @ ( tc_List_Olist @ SX2 ) ) @ SX0 @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1721]) ).
thf(2181,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OVar @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2083]) ).
thf(2182,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX1 @ SX2 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SX0 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2092]) ).
thf(2183,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OVar @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1903]) ).
thf(2184,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0
!= ( c_List_Oappend @ SX0 @ SX1 @ SX2 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1863]) ).
thf(2185,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oappend @ SX0 @ ( c_List_Olist_OCons @ SX1 @ ( c_List_Olist_ONil @ SX2 ) @ SX2 ) @ SX2 )
!= ( c_List_Oappend @ SX3 @ ( c_List_Olist_OCons @ SX4 @ ( c_List_Olist_ONil @ SX2 ) @ SX2 ) @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2042]) ).
thf(2186,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX2 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2088]) ).
thf(2187,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX2 @ SX3 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX3
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( c_List_Olist_OCons @ SX1 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SX3
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2068]) ).
thf(2188,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SX0 ) @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SX2 ) @ SX3 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2061]) ).
thf(2189,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ SX2 @ SX0 )
!= ( c_Power_Opower__class_Opower @ SX3 @ SX2 @ SX0 ) )
| ( SX1 = SX3 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SX2 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX3 @ SX0 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1806]) ).
thf(2190,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Olist_OCons @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2089]) ).
thf(2191,plain,
( ( ! [SX0: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1684]) ).
thf(2192,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ SX0 )
!= ( c_Suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1503]) ).
thf(2193,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oappend @ SX0 @ SX3 @ SX2 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1912]) ).
thf(2194,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX3 @ SX3 @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1640]) ).
thf(2195,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) ) @ SX2 @ SX1 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SX2 @ ( tc_List_Olist @ SX1 ) ) @ SX0 @ SX1 ) @ SX3 @ SX1 ) @ SX1 )
!= SX3 )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) ) @ SX2 @ SX1 )
!= SX0 )
| ( SX2
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SX2 @ ( tc_List_Olist @ SX1 ) ) @ SX0 @ SX1 ) )
| ( ( c_List_Oappend @ SX2 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SX2 @ ( tc_List_Olist @ SX1 ) ) @ SX0 @ SX1 ) @ SX3 @ SX1 ) @ SX1 )
= ( c_List_Oappend @ SX0 @ SX3 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1989]) ).
thf(2196,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Suc @ SX0 )
!= ( c_Suc @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1504]) ).
thf(2197,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1676]) ).
thf(2198,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Oappend @ SX1 @ SX2 @ SX0 ) )
| ( SX2
= ( c_List_Olist_ONil @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1870]) ).
thf(2199,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SX0 ) @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SX2 ) @ SX3 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2085]) ).
thf(2200,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX1 @ SX2 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX2
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2106]) ).
thf(2201,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Lambda_OdB_OVar @ SX0 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX1 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2093]) ).
thf(2202,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2102]) ).
thf(2203,plain,
( ( ! [SX0: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SX0 )
| ( ( c_HOL_Oone__class_Oone @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1667]) ).
thf(2204,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SX0 ) @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SX2 ) @ SX3 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2084]) ).
thf(2205,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX2 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX3 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1750]) ).
thf(2206,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
!= ( c_Lambda_OdB_OVar @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2108]) ).
thf(2207,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oappend @ SX3 @ SX1 @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1911]) ).
thf(2208,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oappend @ SX0 @ ( c_List_Olist_OCons @ SX1 @ ( c_List_Olist_ONil @ SX2 ) @ SX2 ) @ SX2 )
!= ( c_List_Oappend @ SX3 @ ( c_List_Olist_OCons @ SX4 @ ( c_List_Olist_ONil @ SX2 ) @ SX2 ) @ SX2 ) )
| ( SX1 = SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2041]) ).
thf(2209,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oappend @ SX3 @ SX4 @ SX2 ) )
| ( SX1
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX2 ) ) @ SX3 @ SX2 ) @ SX4 @ SX2 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX2 ) ) @ ( c_Nat_Osize__class_Osize @ SX3 @ ( tc_List_Olist @ SX2 ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1726]) ).
thf(2210,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Olist_OCons @ SX0 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 )
!= ( c_List_Orev @ SX2 @ SX1 ) )
| ( SX2
= ( c_List_Olist_OCons @ SX0 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2051]) ).
thf(2211,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Orev @ SX0 @ SX1 )
!= ( c_List_Olist_OCons @ SX2 @ SX3 @ SX1 ) )
| ( SX0
= ( c_List_Oappend @ ( c_List_Orev @ SX3 @ SX1 ) @ ( c_List_Olist_OCons @ SX2 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1853]) ).
thf(2212,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SX0 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SX0 )
| ~ ( class_Ring__and__Field_Omult__zero @ SX0 )
| ~ ( class_Power_Opower @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1815]) ).
thf(2213,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX3 @ SX4 @ SX0 ) )
| ( c_HOL_Oord__class_Oless @ SX3 @ SX4 @ SX0 )
| ~ ( c_HOL_Oord__class_Oless @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1543]) ).
thf(2214,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1678]) ).
thf(2215,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ SX0 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Onth @ ( c_List_Olist_OCons @ SX1 @ SX2 @ SX3 ) @ ( c_Int_Onumber__class_Onumber__of @ SX0 @ tc_nat ) @ SX3 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1835]) ).
thf(2216,plain,
( ( ! [SX0: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SX0 )
| ( ( c_HOL_Ozero__class_Ozero @ SX0 )
!= ( c_HOL_Oone__class_Oone @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1673]) ).
thf(2217,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) )
| ( SX1 = SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2086]) ).
thf(2218,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) )
| ( SX0
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1869]) ).
thf(2219,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1816]) ).
thf(2220,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_OtakeWhile @ SX0 @ SX1 @ SX2 )
!= SX1 )
| ( hBOOL @ ( hAPP @ SX0 @ SX3 ) )
| ~ ( c_in @ SX3 @ ( c_List_Oset @ SX1 @ SX2 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1614]) ).
thf(2221,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX1 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1895]) ).
thf(2222,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX1 @ SX2 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SX0 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2064]) ).
thf(2223,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Omap @ SX1 @ SX2 @ SX3 @ SX0 ) )
| ( SX2
= ( c_List_Olist_ONil @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1873]) ).
thf(2224,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Oappend @ SX1 @ SX2 @ SX0 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1871]) ).
thf(2225,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Orev @ SX1 @ SX0 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1867]) ).
thf(2226,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Otake @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX2 ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2038]) ).
thf(2227,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX1 @ SX2 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX2
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2073]) ).
thf(2228,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_List_Orev @ SX0 @ SX1 )
!= ( c_List_Olist_ONil @ SX1 ) )
| ( SX0
= ( c_List_Olist_ONil @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1887]) ).
thf(2229,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX3 @ SX4 @ SX0 ) )
| ( c_HOL_Oord__class_Oless @ SX1 @ SX2 @ SX0 )
| ~ ( c_HOL_Oord__class_Oless @ SX3 @ SX4 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1544]) ).
thf(2230,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX0 @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SX2 ) )
| ( SX0
= ( c_Lambda_OdB_OAbs @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2060]) ).
thf(2231,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oappend @ SX3 @ SX4 @ SX2 ) )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SX3 @ ( tc_List_Olist @ SX2 ) ) @ SX0 @ SX2 )
= SX3 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX2 ) ) @ ( c_Nat_Osize__class_Osize @ SX3 @ ( tc_List_Olist @ SX2 ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1723]) ).
thf(2232,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[2104]) ).
thf(2233,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) ) @ SX2 @ SX1 ) )
| ( ( c_List_Oappend @ SX0 @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) ) @ SX2 @ SX1 ) @ SX1 )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1941]) ).
thf(2234,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ SX0 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ SX0 @ tc_nat ) @ ( c_List_Olist_OCons @ SX1 @ SX2 @ SX3 ) @ SX3 )
= ( c_List_Olist_OCons @ SX1 @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1836]) ).
thf(2235,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Orev @ SX0 @ SX1 )
!= ( c_List_Orev @ SX2 @ SX1 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1969]) ).
thf(2236,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX0 @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SX2 ) )
| ( SX1
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2076]) ).
thf(2237,plain,
( ( ! [SX0: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1685]) ).
thf(2238,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( SX0
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) ) @ SX2 @ SX1 ) )
| ( ( c_List_Oappend @ SX0 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) ) @ SX2 @ SX1 ) @ SX3 @ SX1 ) @ SX1 )
= ( c_List_Oappend @ SX2 @ SX3 @ SX1 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) ) @ ( c_Nat_Osize__class_Osize @ SX2 @ ( tc_List_Olist @ SX1 ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1796]) ).
thf(2239,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Olist_ONil @ SX0 )
!= ( c_List_Oreplicate @ SX1 @ SX2 @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2033]) ).
thf(2240,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= SX1 )
| ( SX0
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1862]) ).
thf(2241,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ SX0 @ SX1 @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1514]) ).
thf(2242,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i,SX5: $i] :
( ( ( c_List_Omap @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( c_List_Omap @ SX4 @ SX1 @ SX2 @ SX3 ) )
| ( ( hAPP @ SX0 @ SX5 )
= ( hAPP @ SX4 @ SX5 ) )
| ~ ( c_in @ SX5 @ ( c_List_Oset @ SX1 @ SX2 ) @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1600]) ).
thf(2243,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX2 ) @ SX3 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2090]) ).
thf(2244,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX2 ) @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2091]) ).
thf(2245,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1868]) ).
thf(2246,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SX0 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SX1 @ SX0 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SX2 @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1929]) ).
thf(2247,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1675]) ).
thf(2248,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Odrop @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) )
| ( ( c_List_Onth @ SX1 @ SX0 @ SX2 )
= SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1988]) ).
thf(2249,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oappend @ SX3 @ SX4 @ SX2 ) )
| ( SX0
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX2 ) ) @ SX3 @ SX2 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX2 ) ) @ ( c_Nat_Osize__class_Osize @ SX3 @ ( tc_List_Olist @ SX2 ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1725]) ).
thf(2250,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( SX1
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX2 ) )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1818]) ).
thf(2251,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SX0 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SX0 )
| ~ ( class_Ring__and__Field_Omult__zero @ SX0 )
| ~ ( class_Power_Opower @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2024]) ).
thf(2252,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX2 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX2 @ SX0 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX1 @ SX0 )
| ( SX2
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1575]) ).
thf(2253,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ SX2 @ SX0 )
!= ( c_Power_Opower__class_Opower @ SX1 @ SX3 @ SX0 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SX0 ) @ SX1 @ SX0 )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1599]) ).
thf(2254,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Oreplicate @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_ONil @ SX2 ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2034]) ).
thf(2255,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( SX0
!= ( c_List_Olist_OCons @ SX1 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2105]) ).
thf(2256,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX3 @ SX4 @ SX0 ) )
| ( c_lessequals @ SX2 @ SX1 @ SX0 )
| ~ ( c_lessequals @ SX4 @ SX3 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1542]) ).
thf(2257,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oreplicate @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oreplicate @ SX3 @ SX4 @ SX2 ) )
| ( SX1 = SX4 )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1834]) ).
thf(2258,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX1 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX2 @ SX3 @ SX0 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1641]) ).
thf(2259,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1674]) ).
thf(2260,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SX0 )
| ( ( c_Power_Opower__class_Opower @ SX1 @ ( c_Suc @ SX2 ) @ SX0 )
!= ( c_Power_Opower__class_Opower @ SX3 @ ( c_Suc @ SX2 ) @ SX0 ) )
| ( SX1 = SX3 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX3 @ SX0 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1658]) ).
thf(2261,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SX0 )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX2 @ SX0 )
!= ( c_HOL_Ominus__class_Ominus @ SX3 @ SX4 @ SX0 ) )
| ( c_lessequals @ SX4 @ SX3 @ SX0 )
| ~ ( c_lessequals @ SX2 @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1541]) ).
thf(2262,plain,
( ( ! [SX0: $i] :
( SX0
!= ( c_Suc @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1465]) ).
thf(2263,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX0
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 ) @ SX2 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 ) @ ( c_List_Oappend @ SX2 @ ( c_List_Olist_OCons @ SX1 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2081]) ).
thf(2264,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Olist__update @ SX0 @ SX1 @ SX2 @ SX3 )
!= SX0 )
| ~ ( c_HOL_Oord__class_Oless @ SX1 @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX3 ) ) @ tc_nat )
| ( ( c_List_Onth @ SX0 @ SX1 @ SX3 )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1810]) ).
thf(2265,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= ( c_List_Oappend @ SX3 @ SX4 @ SX2 ) )
| ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SX3 @ ( tc_List_Olist @ SX2 ) ) @ SX0 @ SX2 ) @ SX1 @ SX2 )
= SX4 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX2 ) ) @ ( c_Nat_Osize__class_Osize @ SX3 @ ( tc_List_Olist @ SX2 ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1727]) ).
thf(2266,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= ( c_List_Olist_OCons @ SX3 @ SX4 @ SX2 ) )
| ( SX0 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2087]) ).
thf(2267,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX0 @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX2 @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2103]) ).
thf(2268,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( ( c_List_Omap @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( c_List_Omap @ SX0 @ SX4 @ SX2 @ SX3 ) )
| ( ( c_Nat_Osize__class_Osize @ SX1 @ ( tc_List_Olist @ SX2 ) )
= ( c_Nat_Osize__class_Osize @ SX4 @ ( tc_List_Olist @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1940]) ).
thf(2269,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX1 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1817]) ).
thf(2270,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1679]) ).
thf(2271,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Orev @ SX0 @ SX1 )
!= ( c_List_Olist_OCons @ SX2 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 ) )
| ( SX0
= ( c_List_Olist_OCons @ SX2 @ ( c_List_Olist_ONil @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2049]) ).
thf(2272,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX2 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX3 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1751]) ).
thf(2273,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX2 @ SX3 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX0
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SX2 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SX0 @ SX1 @ SX2 @ SX3 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX3
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2075]) ).
thf(2274,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Int_Oring__char__0 @ SX0 )
| ~ ( class_Int_Onumber__ring @ SX0 )
| ( ( c_Int_Onumber__class_Onumber__of @ SX1 @ SX0 )
!= ( c_Int_Onumber__class_Onumber__of @ SX2 @ SX0 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1756]) ).
thf(2275,plain,
( ( ! [SX0: $i] :
( ( c_Suc @ SX0 )
!= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[1466]) ).
thf(2276,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Olist__update @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( c_List_Olist_ONil @ SX3 ) )
| ( SX0
= ( c_List_Olist_ONil @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1891]) ).
thf(2277,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1908]) ).
thf(2278,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SX0 ) @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SX2 ) @ SX3 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2062]) ).
thf(2279,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) ) @ SX2 @ SX1 )
!= SX0 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SX2 @ ( tc_List_Olist @ SX1 ) ) @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) ) @ tc_nat )
| ( ( c_List_Oappend @ SX2 @ SX3 @ SX1 )
= ( c_List_Oappend @ SX0 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) ) @ SX2 @ SX1 ) @ SX3 @ SX1 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1797]) ).
thf(2280,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ SX0 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ SX0 @ tc_nat ) @ ( c_List_Olist_OCons @ SX1 @ SX2 @ SX3 ) @ SX3 )
= ( c_List_Olist_ONil @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2018]) ).
thf(2281,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ SX2 @ SX1 @ tc_nat ) )
| ~ ( c_lessequals @ SX1 @ SX2 @ tc_nat )
| ~ ( c_lessequals @ SX1 @ SX0 @ tc_nat )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1642]) ).
thf(2282,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX2 )
!= ( c_HOL_Ozero__class_Ozero @ SX0 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX2 @ SX0 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SX0 ) @ SX1 @ SX0 )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1576]) ).
thf(2283,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX2 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX3 ) )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1749]) ).
thf(2284,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SX0 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX2 ) @ SX3 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX2 ) @ SX4 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SX0 ) @ SX1 ) @ SX3 )
= SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1762]) ).
thf(2285,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SX0 ) @ SX1 )
!= ( c_Lambda_OdB_OAbs @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1894]) ).
thf(2286,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SX0 ) ) @ SX1 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SX2 ) @ SX3 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2072]) ).
thf(2287,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( c_List_Omap @ SX0 @ SX1 @ SX2 @ SX3 )
!= ( c_List_Olist_ONil @ SX3 ) )
| ( SX1
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1857]) ).
thf(2288,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_List_Oappend @ SX0 @ SX1 @ SX2 )
!= SX0 )
| ( SX1
= ( c_List_Olist_ONil @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1864]) ).
thf(2289,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SX0 @ SX1 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ SX1 @ SX0 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1680]) ).
thf(2290,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Nat_Osize__class_Osize @ SX0 @ ( tc_List_Olist @ SX1 ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX0
= ( c_List_Olist_ONil @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2032]) ).
thf(2291,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SX0 ) @ SX1 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SX2 ) @ SX3 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2071]) ).
thf(2292,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Olist_OCons @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ v_ta____ ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(2293,plain,
! [SV1: $i] :
( ( ! [SY2027: $i] :
( ( SV1 = SY2027 )
| ~ ( c_HOL_Oord__class_Oless @ SV1 @ ( c_Suc @ SY2027 ) @ tc_nat )
| ~ ( c_lessequals @ SY2027 @ SV1 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(2294,plain,
! [SV2: $i] :
( ( ! [SY2028: $i,SY2029: $i,SY2030: $i,SY2031: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV2 )
| ( c_lessequals @ SY2028 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SY2029 ) @ SY2030 ) @ SV2 )
| ~ ( c_lessequals @ SY2031 @ SY2030 @ SV2 )
| ~ ( c_lessequals @ SY2028 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SY2029 ) @ SY2031 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(2295,plain,
! [SV3: $i] :
( ( ! [SY2032: $i,SY2033: $i,SY2034: $i] :
( ~ ( class_Orderings_Opreorder @ SV3 )
| ( c_HOL_Oord__class_Oless @ SY2032 @ SY2033 @ SV3 )
| ~ ( c_lessequals @ SY2034 @ SY2033 @ SV3 )
| ~ ( c_HOL_Oord__class_Oless @ SY2032 @ SY2034 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(2296,plain,
! [SV4: $i] :
( ( ! [SY2035: $i,SY2036: $i,SY2037: $i] :
( ~ ( class_Orderings_Opreorder @ SV4 )
| ( c_HOL_Oord__class_Oless @ SY2035 @ SY2036 @ SV4 )
| ~ ( c_HOL_Oord__class_Oless @ SY2037 @ SY2036 @ SV4 )
| ~ ( c_lessequals @ SY2035 @ SY2037 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(2297,plain,
! [SV5: $i] :
( ( ! [SY2038: $i] :
( ~ ( class_Orderings_Opreorder @ SV5 )
| ( c_lessequals @ SY2038 @ SY2038 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(2298,plain,
! [SV6: $i] :
( ( ! [SY2039: $i] :
( ~ ( class_Orderings_Oorder @ SV6 )
| ( c_lessequals @ SY2039 @ SY2039 @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(2299,plain,
! [SV7: $i] :
( ( c_lessequals @ SV7 @ SV7 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(2300,plain,
! [SV8: $i] :
( ( ! [SY2040: $i,SY2041: $i] :
( ( c_lessequals @ SV8 @ SY2040 @ tc_nat )
| ~ ( c_lessequals @ SY2041 @ SY2040 @ tc_nat )
| ~ ( c_lessequals @ SV8 @ SY2041 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(2301,plain,
! [SV9: $i] :
( ( c_lessequals @ SV9 @ SV9 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(2302,plain,
! [SV10: $i] :
( ( ! [SY2042: $i,SY2043: $i,SY2044: $i] :
( ~ ( class_Orderings_Opreorder @ SV10 )
| ( c_lessequals @ SY2042 @ SY2043 @ SV10 )
| ~ ( c_lessequals @ SY2044 @ SY2043 @ SV10 )
| ~ ( c_lessequals @ SY2042 @ SY2044 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(2303,plain,
! [SV11: $i] :
( ( ! [SY2045: $i,SY2046: $i,SY2047: $i] :
( ~ ( class_Orderings_Oorder @ SV11 )
| ( c_HOL_Oord__class_Oless @ SY2045 @ SY2046 @ SV11 )
| ~ ( c_HOL_Oord__class_Oless @ SY2045 @ SY2047 @ SV11 )
| ~ ( c_lessequals @ SY2047 @ SY2046 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(2304,plain,
! [SV12: $i] :
( ( ! [SY2048: $i,SY2049: $i,SY2050: $i] :
( ~ ( class_Orderings_Oorder @ SV12 )
| ( c_HOL_Oord__class_Oless @ SY2048 @ SY2049 @ SV12 )
| ~ ( c_lessequals @ SY2048 @ SY2050 @ SV12 )
| ~ ( c_HOL_Oord__class_Oless @ SY2050 @ SY2049 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(2305,plain,
! [SV13: $i] :
( ( ! [SY2051: $i,SY2052: $i,SY2053: $i] :
( ~ ( class_Orderings_Oorder @ SV13 )
| ( c_lessequals @ SY2051 @ SY2052 @ SV13 )
| ~ ( c_lessequals @ SY2051 @ SY2053 @ SV13 )
| ~ ( c_lessequals @ SY2053 @ SY2052 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(2306,plain,
! [SV14: $i] :
( ( ! [SY2054: $i,SY2055: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ SV14 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SY2054 @ SY2055 @ tc_nat ) @ SV14 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2054 @ SV14 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2055 @ SV14 ) @ SV14 ) )
| ~ ( c_lessequals @ SY2055 @ SY2054 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(2307,plain,
! [SV15: $i] :
( ( ! [SY2056: $i,SY2057: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV15 @ SY2056 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY2057 @ SY2056 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV15 @ SY2057 @ tc_nat )
| ~ ( c_lessequals @ SY2056 @ SY2057 @ tc_nat )
| ~ ( c_lessequals @ SY2056 @ SV15 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(2308,plain,
! [SV16: $i] :
( ( ! [SY2058: $i,SY2059: $i] :
( ( c_HOL_Oord__class_Oless @ SV16 @ SY2058 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV16 @ SY2059 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY2058 @ SY2059 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2059 @ SY2058 @ tc_nat )
| ~ ( c_lessequals @ SY2059 @ SV16 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(2309,plain,
! [SV17: $i] :
( ( ~ ( c_lessequals @ ( c_Suc @ SV17 ) @ SV17 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(2310,plain,
! [SV18: $i] :
( ( ! [SY2060: $i] :
( ( c_lessequals @ SV18 @ ( c_Suc @ SY2060 ) @ tc_nat )
| ~ ( c_lessequals @ SV18 @ SY2060 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1471]) ).
thf(2311,plain,
! [SV19: $i] :
( ( ! [SY2061: $i] :
( ( c_lessequals @ SV19 @ SY2061 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV19 ) @ SY2061 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1472]) ).
thf(2312,plain,
! [SV20: $i] :
( ( ! [SY2062: $i,SY2063: $i,SY2064: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV20 )
| ( c_lessequals @ SY2062 @ SY2063 @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SY2063 @ SV20 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY2062 @ ( c_Suc @ SY2064 ) @ SV20 ) @ ( c_Power_Opower__class_Opower @ SY2063 @ ( c_Suc @ SY2064 ) @ SV20 ) @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(2313,plain,
! [SV21: $i] :
( ( ! [SY2065: $i,SY2066: $i,SY2067: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV21 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SY2065 ) @ SY2066 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SY2065 ) @ SY2067 ) @ SV21 )
| ~ ( c_lessequals @ SY2066 @ SY2067 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(2314,plain,
! [SV22: $i] :
( ( ! [SY2068: $i,SY2069: $i,SY2070: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV22 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SY2068 ) @ SY2069 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SY2070 ) @ SY2069 ) @ SV22 )
| ~ ( c_lessequals @ SY2068 @ SY2070 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(2315,plain,
! [SV23: $i] :
( ( ! [SY2071: $i,SY2072: $i,SY2073: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV23 )
| ( c_lessequals @ SY2071 @ SY2072 @ SV23 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV23 ) @ SY2073 ) @ SY2071 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV23 ) @ SY2073 ) @ SY2072 ) @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(2316,plain,
! [SV24: $i] :
( ( ! [SY2074: $i,SY2075: $i,SY2076: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV24 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ SY2074 ) @ SY2075 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ SY2074 ) @ SY2076 ) @ SV24 )
| ~ ( c_lessequals @ SY2075 @ SY2076 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(2317,plain,
! [SV25: $i] :
( ( ! [SY2077: $i,SY2078: $i,SY2079: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV25 )
| ( c_lessequals @ SY2077 @ SY2078 @ SV25 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SY2077 ) @ SY2079 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SY2078 ) @ SY2079 ) @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(2318,plain,
! [SV26: $i] :
( ( ! [SY2080: $i,SY2081: $i,SY2082: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV26 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV26 ) @ SY2080 ) @ SY2081 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV26 ) @ SY2082 ) @ SY2081 ) @ SV26 )
| ~ ( c_lessequals @ SY2080 @ SY2082 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(2319,plain,
! [SV27: $i] :
( ( ! [SY2083: $i,SY2084: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV27 ) @ SY2083 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2084 @ SY2083 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV27 @ SY2084 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(2320,plain,
! [SV28: $i] :
( ( c_HOL_Oord__class_Oless @ SV28 @ ( c_Suc @ SV28 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1481]) ).
thf(2321,plain,
! [SV29: $i] :
( ( c_HOL_Oord__class_Oless @ SV29 @ ( c_Suc @ SV29 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(2322,plain,
! [SV30: $i] :
( ( ! [SY2085: $i,SY2086: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV30 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV30 ) @ ( c_Power_Opower__class_Opower @ SY2085 @ ( c_Suc @ SY2086 ) @ SV30 ) @ SV30 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SY2085 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1483]) ).
thf(2323,plain,
! [SV31: $i] :
( ( ! [SY2087: $i,SY2088: $i] :
( ~ ( class_Orderings_Opreorder @ SV31 )
| ( c_lessequals @ SY2087 @ SY2088 @ SV31 )
| ~ ( c_HOL_Oord__class_Oless @ SY2087 @ SY2088 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(2324,plain,
! [SV32: $i] :
( ( ! [SY2089: $i,SY2090: $i] :
( ~ ( class_Orderings_Oorder @ SV32 )
| ( c_lessequals @ SY2089 @ SY2090 @ SV32 )
| ~ ( c_HOL_Oord__class_Oless @ SY2089 @ SY2090 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1485]) ).
thf(2325,plain,
! [SV33: $i] :
( ( ! [SY2091: $i] :
( ( c_lessequals @ SV33 @ SY2091 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV33 @ SY2091 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(2326,plain,
! [SV34: $i] :
( ( ! [SY2092: $i] :
( ( c_lessequals @ SV34 @ SY2092 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV34 @ SY2092 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(2327,plain,
! [SV35: $i] :
( ( ! [SY2093: $i,SY2094: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV35 )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SY2093 @ SY2094 @ SV35 ) @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ SV35 )
| ~ ( c_lessequals @ SY2093 @ SY2094 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(2328,plain,
! [SV36: $i] :
( ( ! [SY2095: $i,SY2096: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV36 )
| ( c_lessequals @ SY2095 @ SY2096 @ SV36 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SY2095 @ SY2096 @ SV36 ) @ ( c_HOL_Ozero__class_Ozero @ SV36 ) @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(2329,plain,
! [SV37: $i] :
( ( ! [SY2097: $i,SY2098: $i] :
( ~ ( class_Orderings_Oorder @ SV37 )
| ( SY2097 = SY2098 )
| ~ ( c_lessequals @ SY2097 @ SY2098 @ SV37 )
| ~ ( c_lessequals @ SY2098 @ SY2097 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(2330,plain,
! [SV38: $i] :
( ( ! [SY2099: $i,SY2100: $i] :
( ~ ( class_Orderings_Oorder @ SV38 )
| ( SY2099 = SY2100 )
| ~ ( c_lessequals @ SY2100 @ SY2099 @ SV38 )
| ~ ( c_lessequals @ SY2099 @ SY2100 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(2331,plain,
! [SV39: $i] :
( ( ! [SY2101: $i,SY2102: $i] :
( ~ ( class_Orderings_Oorder @ SV39 )
| ( SY2101 = SY2102 )
| ~ ( c_lessequals @ SY2102 @ SY2101 @ SV39 )
| ~ ( c_lessequals @ SY2101 @ SY2102 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(2332,plain,
! [SV40: $i] :
( ( ! [SY2103: $i] :
( ( SV40 = SY2103 )
| ~ ( c_lessequals @ SY2103 @ SV40 @ tc_nat )
| ~ ( c_lessequals @ SV40 @ SY2103 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(2333,plain,
! [SV41: $i] :
( ( ! [SY2104: $i] :
( ( c_List_Oset @ ( c_List_Orev @ SV41 @ SY2104 ) @ SY2104 )
= ( c_List_Oset @ SV41 @ SY2104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(2334,plain,
! [SV42: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV42 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV42 ) @ ( c_HOL_Ozero__class_Ozero @ SV42 ) @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(2335,plain,
! [SV43: $i] :
( ( ! [SY2105: $i,SY2106: $i] :
( ~ ( class_Orderings_Opreorder @ SV43 )
| ( c_HOL_Oord__class_Oless @ SY2105 @ SY2106 @ SV43 )
| ( c_lessequals @ SY2106 @ SY2105 @ SV43 )
| ~ ( c_lessequals @ SY2105 @ SY2106 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(2336,plain,
! [SV44: $i] :
( ( ! [SY2107: $i,SY2108: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV44 @ SY2107 @ tc_nat ) @ SY2108 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV44 @ SY2108 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(2337,plain,
! [SV45: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV45 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV45 ) @ ( c_HOL_Oone__class_Oone @ SV45 ) @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(2338,plain,
! [SV46: $i] :
( ( ! [SY2109: $i] :
( ( SV46 = SY2109 )
| ~ ( c_HOL_Oord__class_Oless @ SV46 @ ( c_Suc @ SY2109 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV46 @ SY2109 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(2339,plain,
! [SV47: $i] :
( ( ! [SY2110: $i] :
( ( SV47 = SY2110 )
| ~ ( c_HOL_Oord__class_Oless @ SY2110 @ ( c_Suc @ SV47 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY2110 @ SV47 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(2340,plain,
! [SV48: $i] :
( ( ! [SY2111: $i] :
( ( SV48 = SY2111 )
| ( c_HOL_Oord__class_Oless @ SV48 @ SY2111 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV48 @ ( c_Suc @ SY2111 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1501]) ).
thf(2341,plain,
! [SV49: $i] :
( ( ! [SY2112: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV49 ) @ ( c_Suc @ SY2112 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV49 @ SY2112 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(2342,plain,
! [SV50: $i] :
( ( ! [SY2113: $i,SY2114: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV50 @ SY2113 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV50 @ SY2114 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2114 @ SV50 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2114 @ SY2113 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(2343,plain,
! [SV51: $i] :
( ( ! [SY2115: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV51 ) @ SY2115 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV51 @ SY2115 @ tc_nat ) ) )
| ~ ( c_lessequals @ SY2115 @ SV51 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(2344,plain,
! [SV52: $i] :
( ( ! [SY2116: $i,SY2117: $i,SY2118: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV52 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY2116 @ SY2117 @ SV52 ) @ ( c_Power_Opower__class_Opower @ SY2116 @ SY2118 @ SV52 ) @ SV52 )
| ~ ( c_lessequals @ SY2116 @ ( c_HOL_Oone__class_Oone @ SV52 ) @ SV52 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SY2116 @ SV52 )
| ~ ( c_lessequals @ SY2118 @ SY2117 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1507]) ).
thf(2345,plain,
! [SV53: $i] :
( ( ! [SY2119: $i] :
( ( c_HOL_Oord__class_Oless @ SV53 @ SY2119 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV53 ) @ SY2119 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(2346,plain,
! [SV54: $i] :
( ( ! [SY2120: $i] :
( ( c_lessequals @ ( c_Suc @ SV54 ) @ SY2120 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV54 @ SY2120 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(2347,plain,
! [SV55: $i] :
( ( ! [SY2121: $i] :
( ( c_HOL_Oord__class_Oless @ SV55 @ SY2121 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV55 ) @ SY2121 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(2348,plain,
! [SV56: $i] :
( ( ! [SY2122: $i] :
( ( c_lessequals @ ( c_Suc @ SV56 ) @ SY2122 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV56 @ SY2122 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(2349,plain,
! [SV57: $i] :
( ( ! [SY2123: $i,SY2124: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV57 )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV57 ) @ ( c_Power_Opower__class_Opower @ SY2123 @ SY2124 @ SV57 ) @ SV57 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV57 ) @ SY2123 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(2350,plain,
! [SV58: $i] :
( ( ! [SY2125: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV58 @ SY2125 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ SV58 @ SY2125 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(2351,plain,
! [SV59: $i] :
( ( ! [SY2126: $i,SY2127: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV59 )
| ( c_lessequals @ SY2126 @ SY2127 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2126 @ SV59 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2127 @ SV59 ) @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(2352,plain,
! [SV60: $i] :
( ( ! [SY2128: $i,SY2129: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV60 )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2128 @ SV60 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2129 @ SV60 ) @ SV60 )
| ~ ( c_lessequals @ SY2128 @ SY2129 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(2353,plain,
! [SV61: $i] :
( ( ! [SY2130: $i,SY2131: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV61 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ ( c_HOL_Ominus__class_Ominus @ SY2130 @ SY2131 @ SV61 ) ) @ SY2131 )
= SY2130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(2354,plain,
! [SV62: $i] :
( ( ! [SY2132: $i,SY2133: $i,SY2134: $i,SY2135: $i] :
( ( c_ListOrder_Ostep1 @ SV62 @ ( c_List_Oappend @ SY2132 @ SY2133 @ SY2134 ) @ ( c_List_Oappend @ SY2132 @ SY2135 @ SY2134 ) @ SY2134 )
| ~ ( c_ListOrder_Ostep1 @ SV62 @ SY2133 @ SY2135 @ SY2134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(2355,plain,
! [SV63: $i] :
( ( ! [SY2136: $i,SY2137: $i,SY2138: $i,SY2139: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV63 @ SY2136 @ SY2137 @ SY2138 )
| ( c_ListOrder_Ostep1 @ SV63 @ ( c_List_Oappend @ SY2136 @ SY2139 @ SY2138 ) @ ( c_List_Oappend @ SY2137 @ SY2139 @ SY2138 ) @ SY2138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(2356,plain,
! [SV64: $i] :
( ( ! [SY2140: $i,SY2141: $i,SY2142: $i,SY2143: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV64 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SY2140 ) @ SY2141 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SY2142 ) @ SY2143 ) @ SV64 )
| ~ ( c_lessequals @ SY2141 @ SY2143 @ SV64 )
| ~ ( c_lessequals @ SY2140 @ SY2142 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(2357,plain,
! [SV65: $i] :
( ( ! [SY2144: $i,SY2145: $i,SY2146: $i,SY2147: $i] :
( ( c_lessequals @ SV65 @ ( c_List_Olist_Olist__size @ SY2144 @ SY2145 @ SY2146 ) @ tc_nat )
| ~ ( c_lessequals @ SV65 @ ( hAPP @ SY2144 @ SY2147 ) @ tc_nat )
| ~ ( c_in @ SY2147 @ ( c_List_Oset @ SY2145 @ SY2146 ) @ SY2146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(2358,plain,
! [SV66: $i] :
( ( ! [SY2148: $i] :
( ( c_HOL_Oord__class_Oless @ SV66 @ ( c_Suc @ SY2148 ) @ tc_nat )
| ~ ( c_lessequals @ SV66 @ SY2148 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(2359,plain,
! [SV67: $i] :
( ( ! [SY2149: $i] :
( ( c_lessequals @ SV67 @ SY2149 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV67 @ ( c_Suc @ SY2149 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(2360,plain,
! [SV68: $i] :
( ( ~ ( c_lessequals @ SV68 @ SV68 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV68 @ ( c_Suc @ SV68 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(2361,plain,
! [SV69: $i] :
( ( ! [SY2150: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV69 @ SY2150 @ tc_nat ) @ ( c_Suc @ SV69 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(2362,plain,
! [SV70: $i] :
( ( ! [SY2151: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV70 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV70 ) @ SY2151 @ SV70 )
= ( c_HOL_Oone__class_Oone @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(2363,plain,
! [SV71: $i] :
( ( ! [SY2152: $i,SY2153: $i] :
( ~ ( class_Orderings_Olinorder @ SV71 )
| ( c_HOL_Oord__class_Oless @ SY2152 @ SY2153 @ SV71 )
| ( c_lessequals @ SY2153 @ SY2152 @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(2364,plain,
! [SV72: $i] :
( ( ! [SY2154: $i] :
( ~ ( class_Orderings_Olinorder @ SV72 )
| ~ ( c_lessequals @ SY2154 @ SY2154 @ SV72 )
| ~ ( c_HOL_Oord__class_Oless @ SY2154 @ SY2154 @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(2365,plain,
! [SV73: $i] :
( ( ! [SY2155: $i] :
( ~ ( class_Orderings_Olinorder @ SV73 )
| ( c_HOL_Oord__class_Oless @ SY2155 @ SY2155 @ SV73 )
| ( c_lessequals @ SY2155 @ SY2155 @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(2366,plain,
! [SV74: $i] :
( ( ! [SY2156: $i,SY2157: $i] :
( ~ ( class_Orderings_Olinorder @ SV74 )
| ~ ( c_HOL_Oord__class_Oless @ SY2156 @ SY2157 @ SV74 )
| ~ ( c_lessequals @ SY2157 @ SY2156 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(2367,plain,
! [SV75: $i] :
( ( ! [SY2158: $i,SY2159: $i] :
( ~ ( class_Orderings_Olinorder @ SV75 )
| ( c_lessequals @ SY2158 @ SY2159 @ SV75 )
| ( c_HOL_Oord__class_Oless @ SY2159 @ SY2158 @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(2368,plain,
! [SV76: $i] :
( ( ! [SY2160: $i,SY2161: $i] :
( ~ ( class_Orderings_Olinorder @ SV76 )
| ~ ( c_lessequals @ SY2160 @ SY2161 @ SV76 )
| ~ ( c_HOL_Oord__class_Oless @ SY2161 @ SY2160 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(2369,plain,
! [SV77: $i] :
( ( ! [SY2162: $i,SY2163: $i] :
( ~ ( class_Orderings_Olinorder @ SV77 )
| ( c_HOL_Oord__class_Oless @ SY2162 @ SY2163 @ SV77 )
| ( c_lessequals @ SY2163 @ SY2162 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(2370,plain,
! [SV78: $i] :
( ( ! [SY2164: $i,SY2165: $i] :
( ~ ( class_Orderings_Opreorder @ SV78 )
| ~ ( c_lessequals @ SY2164 @ SY2165 @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ SY2165 @ SY2164 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(2371,plain,
! [SV79: $i] :
( ( ! [SY2166: $i,SY2167: $i,SY2168: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV79 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY2166 @ SY2167 @ SV79 ) @ ( c_Power_Opower__class_Opower @ SY2166 @ SY2168 @ SV79 ) @ SV79 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV79 ) @ SY2166 @ SV79 )
| ~ ( c_lessequals @ SY2167 @ SY2168 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1535]) ).
thf(2372,plain,
! [SV80: $i] :
( ( ! [SY2169: $i,SY2170: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV80 @ SY2169 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV80 @ SY2170 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2170 @ SY2169 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(2373,plain,
! [SV81: $i] :
( ( ! [SY2171: $i,SY2172: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV81 @ SY2171 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY2172 @ SY2171 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV81 @ SY2172 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(2374,plain,
! [SV82: $i] :
( ( ! [SY2173: $i] :
( ( c_HOL_Oord__class_Oless @ SV82 @ SY2173 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV82 ) @ SY2173 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(2375,plain,
! [SV83: $i] :
( ( ! [SY2174: $i] :
( ( c_HOL_Oord__class_Oless @ SV83 @ ( c_Suc @ SY2174 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV83 @ SY2174 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(2376,plain,
! [SV84: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV84 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= SV84 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV84 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(2377,plain,
! [SV85: $i] :
( ( ! [SY2175: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV85 @ ( c_Suc @ SY2175 ) @ tc_nat ) @ SV85 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV85 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(2378,plain,
! [SV86: $i] :
( ( ! [SY2176: $i,SY2177: $i] :
( ~ ( class_Orderings_Oorder @ SV86 )
| ( c_HOL_Oord__class_Oless @ SY2176 @ SY2177 @ SV86 )
| ( SY2177 = SY2176 )
| ~ ( c_lessequals @ SY2176 @ SY2177 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(2379,plain,
! [SV87: $i] :
( ( ! [SY2178: $i,SY2179: $i] :
( ~ ( class_Orderings_Oorder @ SV87 )
| ( c_HOL_Oord__class_Oless @ SY2178 @ SY2179 @ SV87 )
| ~ ( c_lessequals @ SY2178 @ SY2179 @ SV87 )
| ( SY2179 = SY2178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(2380,plain,
! [SV88: $i] :
( ( ! [SY2180: $i] :
( ( c_HOL_Oord__class_Oless @ SV88 @ SY2180 @ tc_nat )
| ( SV88 = SY2180 )
| ~ ( c_lessequals @ SV88 @ SY2180 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(2381,plain,
! [SV89: $i] :
( ( ! [SY2181: $i] :
( ( SV89 = SY2181 )
| ( c_HOL_Oord__class_Oless @ SV89 @ SY2181 @ tc_nat )
| ~ ( c_lessequals @ SV89 @ SY2181 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(2382,plain,
! [SV90: $i] :
( ( ! [SY2182: $i] :
( ( c_HOL_Oord__class_Oless @ SV90 @ SY2182 @ tc_nat )
| ( SV90 = SY2182 )
| ~ ( c_lessequals @ SV90 @ SY2182 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(2383,plain,
! [SV91: $i] :
( ( ! [SY2183: $i,SY2184: $i] :
( ~ ( class_Orderings_Oorder @ SV91 )
| ( SY2183 = SY2184 )
| ( c_HOL_Oord__class_Oless @ SY2183 @ SY2184 @ SV91 )
| ~ ( c_lessequals @ SY2183 @ SY2184 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(2384,plain,
! [SV92: $i] :
( ( ! [SY2185: $i,SY2186: $i] :
( ~ ( class_Orderings_Oorder @ SV92 )
| ( c_HOL_Oord__class_Oless @ SY2185 @ SY2186 @ SV92 )
| ( SY2185 = SY2186 )
| ~ ( c_lessequals @ SY2185 @ SY2186 @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(2385,plain,
! [SV93: $i] :
( ( ! [SY2187: $i,SY2188: $i] :
( ~ ( class_Orderings_Oorder @ SV93 )
| ( c_HOL_Oord__class_Oless @ SY2187 @ SY2188 @ SV93 )
| ( SY2187 = SY2188 )
| ~ ( c_lessequals @ SY2187 @ SY2188 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(2386,plain,
! [SV94: $i] :
( ( ! [SY2189: $i,SY2190: $i] :
( ~ ( class_Orderings_Oorder @ SV94 )
| ( c_HOL_Oord__class_Oless @ SY2189 @ SY2190 @ SV94 )
| ~ ( c_lessequals @ SY2189 @ SY2190 @ SV94 )
| ( SY2189 = SY2190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1554]) ).
thf(2387,plain,
! [SV95: $i] :
( ( ! [SY2191: $i,SY2192: $i] :
( ~ ( class_Orderings_Olinorder @ SV95 )
| ( SY2191 = SY2192 )
| ~ ( c_lessequals @ SY2191 @ SY2192 @ SV95 )
| ( c_HOL_Oord__class_Oless @ SY2191 @ SY2192 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(2388,plain,
! [SV96: $i] :
( ( ! [SY2193: $i,SY2194: $i] :
( ~ ( class_Orderings_Olinorder @ SV96 )
| ( SY2193 = SY2194 )
| ( c_HOL_Oord__class_Oless @ SY2193 @ SY2194 @ SV96 )
| ~ ( c_lessequals @ SY2193 @ SY2194 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(2389,plain,
! [SV97: $i] :
( ( ! [SY2195: $i] :
( ( c_lessequals @ SV97 @ SY2195 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV97 ) @ ( c_Suc @ SY2195 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(2390,plain,
! [SV98: $i] :
( ( ! [SY2196: $i] :
( ( c_lessequals @ ( c_Suc @ SV98 ) @ ( c_Suc @ SY2196 ) @ tc_nat )
| ~ ( c_lessequals @ SV98 @ SY2196 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(2391,plain,
! [SV99: $i] :
( ( ! [SY2197: $i] :
( ( c_lessequals @ SV99 @ SY2197 @ tc_nat )
| ( c_lessequals @ SY2197 @ SV99 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(2392,plain,
! [SV100: $i] :
( ( ! [SY2198: $i,SY2199: $i] :
( ~ ( class_Orderings_Olinorder @ SV100 )
| ( c_lessequals @ SY2198 @ SY2199 @ SV100 )
| ( c_lessequals @ SY2199 @ SY2198 @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(2393,plain,
! [SV101: $i] :
( ( ! [SY2200: $i,SY2201: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV101 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2200 @ ( c_Suc @ SY2201 ) @ SV101 ) @ ( c_HOL_Oone__class_Oone @ SV101 ) @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ SY2200 @ ( c_HOL_Oone__class_Oone @ SV101 ) @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ SY2200 @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1561]) ).
thf(2394,plain,
! [SV102: $i] :
( ( ! [SY2202: $i,SY2203: $i,SY2204: $i] :
( ~ ( class_Orderings_Olinorder @ SV102 )
| ( c_lessequals @ SY2202 @ SY2203 @ SV102 )
| ~ ( c_in @ SY2203 @ ( c_List_Oset @ SY2204 @ SV102 ) @ SV102 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY2202 @ SY2204 @ SV102 ) @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1562]) ).
thf(2395,plain,
! [SV103: $i] :
( ( ! [SY2205: $i,SY2206: $i,SY2207: $i,SY2208: $i] :
( ~ ( class_Orderings_Olinorder @ SV103 )
| ( c_lessequals @ SY2205 @ SY2206 @ SV103 )
| ~ ( c_in @ SY2206 @ ( c_List_Oset @ SY2207 @ SV103 ) @ SV103 )
| ~ ( c_in @ SY2205 @ ( c_List_Oset @ SY2208 @ SV103 ) @ SV103 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SY2208 @ SY2207 @ SV103 ) @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(2396,plain,
! [SV104: $i] :
( ( ! [SY2209: $i,SY2210: $i] :
( ( ( c_List_Olength__unique @ ( c_List_Olist_OCons @ SV104 @ SY2209 @ SY2210 ) @ SY2210 )
= ( c_Suc @ ( c_List_Olength__unique @ SY2209 @ SY2210 ) ) )
| ( c_in @ SV104 @ ( c_List_Oset @ SY2209 @ SY2210 ) @ SY2210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(2397,plain,
! [SV105: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV105 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV105 ) @ ( c_HOL_Ozero__class_Ozero @ SV105 ) @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(2398,plain,
! [SV106: $i] :
( ( ! [SY2211: $i,SY2212: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV106 )
| ( c_HOL_Oord__class_Oless @ SY2211 @ SY2212 @ SV106 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SY2211 @ SY2212 @ SV106 ) @ ( c_HOL_Ozero__class_Ozero @ SV106 ) @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(2399,plain,
! [SV107: $i] :
( ( ! [SY2213: $i,SY2214: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV107 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SY2213 @ SY2214 @ SV107 ) @ ( c_HOL_Ozero__class_Ozero @ SV107 ) @ SV107 )
| ~ ( c_HOL_Oord__class_Oless @ SY2213 @ SY2214 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(2400,plain,
! [SV108: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV108 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV108 ) @ ( c_HOL_Oone__class_Oone @ SV108 ) @ SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(2401,plain,
! [SV109: $i] :
( ( ! [SY2215: $i,SY2216: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV109 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ SY2215 ) @ SY2216 ) @ SV109 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SY2216 @ SV109 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SY2215 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1569]) ).
thf(2402,plain,
! [SV110: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV110 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV110 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV110 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) )
= ( c_HOL_Ozero__class_Ozero @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(2403,plain,
! [SV111: $i] :
( ( ! [SY2217: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV111 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV111 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SY2217 ) @ SY2217 ) @ SV111 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV111 ) @ SY2217 @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(2404,plain,
! [SV112: $i] :
( ( ! [SY2218: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV112 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV112 ) @ SY2218 @ SV112 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV112 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SY2218 ) @ SY2218 ) @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1572]) ).
thf(2405,plain,
! [SV113: $i] :
( ( ! [SY2219: $i,SY2220: $i,SY2221: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV113 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV113 )
| ( c_lessequals @ SY2219 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SY2220 ) @ SY2221 ) @ SV113 )
| ~ ( c_lessequals @ SY2219 @ SY2221 @ SV113 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SY2220 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(2406,plain,
! [SV114: $i] :
( ( ! [SY2222: $i,SY2223: $i,SY2224: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV114 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV114 )
| ( c_lessequals @ SY2222 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SY2223 ) @ SY2224 ) @ SV114 )
| ~ ( c_lessequals @ SY2222 @ SY2223 @ SV114 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SY2224 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(2407,plain,
! [SV115: $i] :
( ( ! [SY2225: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV115 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SY2225 ) @ SY2225 ) @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 )
| ~ ( c_lessequals @ SY2225 @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(2408,plain,
! [SV116: $i] :
( ( ! [SY2226: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV116 )
| ( c_lessequals @ SY2226 @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SY2226 ) @ SY2226 ) @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(2409,plain,
! [SV117: $i] :
( ( ! [SY2227: $i,SY2228: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV117 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SY2227 ) @ SY2228 ) @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
| ~ ( c_lessequals @ SY2228 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
| ~ ( c_lessequals @ SY2227 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(2410,plain,
! [SV118: $i] :
( ( ! [SY2229: $i,SY2230: $i,SY2231: $i,SY2232: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV118 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SY2229 ) @ SY2230 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SY2231 ) @ SY2232 ) @ SV118 )
| ~ ( c_lessequals @ SY2230 @ SY2232 @ SV118 )
| ~ ( c_HOL_Oord__class_Oless @ SY2229 @ SY2231 @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(2411,plain,
! [SV119: $i] :
( ( ! [SY2233: $i,SY2234: $i,SY2235: $i,SY2236: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV119 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV119 ) @ SY2233 ) @ SY2234 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV119 ) @ SY2235 ) @ SY2236 ) @ SV119 )
| ~ ( c_HOL_Oord__class_Oless @ SY2234 @ SY2236 @ SV119 )
| ~ ( c_lessequals @ SY2233 @ SY2235 @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(2412,plain,
! [SV120: $i] :
( ( ! [SY2237: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV120 )
| ( c_HOL_Oord__class_Oless @ SY2237 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV120 ) @ SY2237 ) @ ( c_HOL_Oone__class_Oone @ SV120 ) ) @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(2413,plain,
! [SV121: $i] :
( ( ! [SY2238: $i,SY2239: $i] :
( ~ ( class_Orderings_Olinorder @ SV121 )
| ~ ( class_Int_Onumber @ SV121 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ SY2238 @ SV121 ) @ ( c_Int_Onumber__class_Onumber__of @ SY2239 @ SV121 ) @ SV121 )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ SY2239 @ SV121 ) @ ( c_Int_Onumber__class_Onumber__of @ SY2238 @ SV121 ) @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(2414,plain,
! [SV122: $i] :
( ( ! [SY2240: $i,SY2241: $i] :
( ~ ( class_Orderings_Olinorder @ SV122 )
| ~ ( class_Int_Onumber @ SV122 )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ SY2240 @ SV122 ) @ ( c_Int_Onumber__class_Onumber__of @ SY2241 @ SV122 ) @ SV122 )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ SY2241 @ SV122 ) @ ( c_Int_Onumber__class_Onumber__of @ SY2240 @ SV122 ) @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(2415,plain,
! [SV123: $i] :
( ( ! [SY2242: $i,SY2243: $i,SY2244: $i] :
( ( c_in @ SV123 @ ( c_List_Oset @ SY2242 @ SY2243 ) @ SY2243 )
| ( SV123 = SY2244 )
| ~ ( c_in @ SV123 @ ( c_List_Oset @ ( c_List_Olist_OCons @ SY2244 @ SY2242 @ SY2243 ) @ SY2243 ) @ SY2243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(2416,plain,
! [SV124: $i] :
( ( ! [SY2245: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV124 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2245 @ SV124 ) @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(2417,plain,
! [SV125: $i] :
( ( ! [SY2246: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV125 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV125 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2246 @ SV125 ) @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(2418,plain,
! [SV126: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ SV126 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1588]) ).
thf(2419,plain,
! [SV127: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ SV127 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1589]) ).
thf(2420,plain,
! [SV128: $i] :
( ( ( SV128
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ SV128 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(2421,plain,
! [SV129: $i] :
( ( ! [SY2247: $i,SY2248: $i] :
( ( hBOOL @ ( hAPP @ SV129 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2247 @ SY2248 @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV129 @ ( c_HOL_Ominus__class_Ominus @ SY2247 @ SY2248 @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(2422,plain,
! [SV130: $i] :
( ( ! [SY2249: $i] :
( ( c_HOL_Oord__class_Oless @ SV130 @ SY2249 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY2249 @ SV130 @ tc_nat ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(2423,plain,
! [SV131: $i] :
( ( ! [SY2250: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV131 @ SY2250 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2250 @ SV131 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(2424,plain,
! [SV132: $i] :
( ( ! [SY2251: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV132 @ SY2251 @ tc_nat ) @ SV132 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV132 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2251 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1595]) ).
thf(2425,plain,
! [SV133: $i] :
( ( ! [SY2252: $i,SY2253: $i,SY2254: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV133 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY2252 @ SY2253 @ SV133 ) @ ( c_Power_Opower__class_Opower @ SY2254 @ SY2253 @ SV133 ) @ SV133 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV133 ) @ SY2252 @ SV133 )
| ~ ( c_lessequals @ SY2252 @ SY2254 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(2426,plain,
! [SV134: $i] :
( ( ! [SY2255: $i,SY2256: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV134 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV134 ) @ ( c_Power_Opower__class_Opower @ SY2255 @ SY2256 @ SV134 ) @ SV134 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV134 ) @ SY2255 @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1597]) ).
thf(2427,plain,
! [SV135: $i] :
( ( ! [SY2257: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ SV135 )
| ~ ( class_Power_Opower @ SV135 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_Suc @ SY2257 ) @ SV135 )
= ( c_HOL_Ozero__class_Ozero @ SV135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(2428,plain,
! [SV136: $i] :
( ( ! [SY2258: $i,SY2259: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV136 @ SY2258 @ SY2259 ) @ ( tc_List_Olist @ SY2259 ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ SY2258 @ ( tc_List_Olist @ SY2259 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(2429,plain,
! [SV137: $i] :
( ( ! [SY2260: $i,SY2261: $i] :
( ( c_Suc @ ( c_Nat_Osize__class_Osize @ SV137 @ ( tc_List_Olist @ SY2260 ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SY2261 @ SV137 @ SY2260 ) @ ( tc_List_Olist @ SY2260 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(2430,plain,
! [SV138: $i] :
( ( ! [SY2262: $i,SY2263: $i] :
~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV138 @ SY2262 @ SY2263 ) @ ( tc_List_Olist @ SY2263 ) ) @ ( c_Nat_Osize__class_Osize @ SY2262 @ ( tc_List_Olist @ SY2263 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(2431,plain,
! [SV139: $i] :
( ( ! [SY2264: $i] :
( ~ ( class_Power_Opower @ SV139 )
| ( ( c_Power_Opower__class_Opower @ SY2264 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV139 )
= ( c_HOL_Oone__class_Oone @ SV139 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1604]) ).
thf(2432,plain,
! [SV140: $i] :
( ( ! [SY2265: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV140 )
| ( ( c_Power_Opower__class_Opower @ SY2265 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV140 )
= ( c_HOL_Oone__class_Oone @ SV140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(2433,plain,
! [SV141: $i] :
( ( ! [SY2266: $i,SY2267: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ SV141 @ SY2266 @ SY2267 ) @ SY2267 )
= ( c_List_Ohd @ SV141 @ SY2267 ) )
| ( SV141
= ( c_List_Olist_ONil @ SY2267 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1606]) ).
thf(2434,plain,
! [SV142: $i] :
( ( ! [SY2268: $i] :
( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ SV142 ) @ SY2268 @ SV142 ) @ SV142 )
= ( c_List_Ohd @ SY2268 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1607]) ).
thf(2435,plain,
! [SV143: $i] :
( ( ! [SY2269: $i,SY2270: $i,SY2271: $i] :
( ( c_in @ SV143 @ ( c_List_Oset @ SY2269 @ SY2270 ) @ SY2270 )
| ~ ( c_in @ SV143 @ ( c_List_Oset @ ( c_List_Otake @ SY2271 @ SY2269 @ SY2270 ) @ SY2270 ) @ SY2270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(2436,plain,
! [SV144: $i] :
( ( ! [SY2272: $i,SY2273: $i,SY2274: $i] :
( ( c_in @ SV144 @ ( c_List_Oset @ SY2272 @ SY2273 ) @ SY2273 )
| ~ ( c_in @ SV144 @ ( c_List_Oset @ ( c_List_Odrop @ SY2274 @ SY2272 @ SY2273 ) @ SY2273 ) @ SY2273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(2437,plain,
! [SV145: $i] :
( ( ! [SY2275: $i,SY2276: $i,SY2277: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ SV145 @ SY2275 @ SY2276 ) @ ( c_Suc @ SY2277 ) @ SY2276 )
= ( c_List_Onth @ SY2275 @ SY2277 @ SY2276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(2438,plain,
! [SV146: $i] :
( ( ! [SY2278: $i,SY2279: $i,SY2280: $i] :
( ( c_List_Otake @ ( c_Suc @ SV146 ) @ ( c_List_Olist_OCons @ SY2278 @ SY2279 @ SY2280 ) @ SY2280 )
= ( c_List_Olist_OCons @ SY2278 @ ( c_List_Otake @ SV146 @ SY2279 @ SY2280 ) @ SY2280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(2439,plain,
! [SV147: $i] :
( ( ! [SY2281: $i,SY2282: $i,SY2283: $i] :
( ( hBOOL @ ( hAPP @ SV147 @ SY2281 ) )
| ~ ( c_in @ SY2281 @ ( c_List_Oset @ ( c_List_OtakeWhile @ SV147 @ SY2282 @ SY2283 ) @ SY2283 ) @ SY2283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(2440,plain,
! [SV148: $i] :
( ( ! [SY2284: $i,SY2285: $i,SY2286: $i] :
( ( c_in @ SV148 @ ( c_List_Oset @ SY2284 @ SY2285 ) @ SY2285 )
| ~ ( c_in @ SV148 @ ( c_List_Oset @ ( c_List_OtakeWhile @ SY2286 @ SY2284 @ SY2285 ) @ SY2285 ) @ SY2285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1613]) ).
thf(2441,plain,
! [SV149: $i] :
( ( ! [SY2287: $i,SY2288: $i,SY2289: $i] :
( ( hBOOL @ ( hAPP @ SV149 @ SY2287 ) )
| ~ ( c_in @ SY2287 @ ( c_List_Oset @ SY2288 @ SY2289 ) @ SY2289 )
| ~ ( c_List_Olistsp @ SV149 @ SY2288 @ SY2289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(2442,plain,
! [SV150: $i] :
( ( ! [SY2290: $i,SY2291: $i,SY2292: $i] :
( ( SV150 = SY2290 )
| ~ ( c_in @ SV150 @ ( c_List_Oset @ ( c_List_Oreplicate @ SY2291 @ SY2290 @ SY2292 ) @ SY2292 ) @ SY2292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(2443,plain,
! [SV151: $i] :
( ( ! [SY2293: $i,SY2294: $i] :
( ( ( c_List_Onth @ ( c_List_Orev @ SV151 @ SY2293 ) @ SY2294 @ SY2293 )
= ( c_List_Onth @ SV151 @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SV151 @ ( tc_List_Olist @ SY2293 ) ) @ ( c_Suc @ SY2294 ) @ tc_nat ) @ SY2293 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2294 @ ( c_Nat_Osize__class_Osize @ SV151 @ ( tc_List_Olist @ SY2293 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1617]) ).
thf(2444,plain,
! [SV152: $i] :
( ( ! [SY2295: $i,SY2296: $i,SY2297: $i] :
( ~ ( class_Orderings_Olinorder @ SV152 )
| ( c_lessequals @ ( c_List_Onth @ SY2295 @ SY2296 @ SV152 ) @ ( c_List_Onth @ SY2295 @ SY2297 @ SV152 ) @ SV152 )
| ~ ( c_lessequals @ SY2296 @ SY2297 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2297 @ ( c_Nat_Osize__class_Osize @ SY2295 @ ( tc_List_Olist @ SV152 ) ) @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ SY2295 @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(2445,plain,
! [SV153: $i] :
( ( ! [SY2298: $i,SY2299: $i,SY2300: $i] :
( ~ ( class_Orderings_Olinorder @ SV153 )
| ( c_lessequals @ ( c_List_Onth @ SY2298 @ SY2299 @ SV153 ) @ ( c_List_Onth @ SY2298 @ SY2300 @ SV153 ) @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SY2300 @ ( c_Nat_Osize__class_Osize @ SY2298 @ ( tc_List_Olist @ SV153 ) ) @ tc_nat )
| ~ ( c_lessequals @ SY2299 @ SY2300 @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ SY2298 @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1619]) ).
thf(2446,plain,
! [SV154: $i] :
( ( ! [SY2301: $i,SY2302: $i,SY2303: $i] :
( ( c_List_Odrop @ ( c_Suc @ SV154 ) @ ( c_List_Olist_OCons @ SY2301 @ SY2302 @ SY2303 ) @ SY2303 )
= ( c_List_Odrop @ SV154 @ SY2302 @ SY2303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(2447,plain,
! [SV155: $i] :
( ( ! [SY2304: $i,SY2305: $i] :
( ( ( c_List_Otake @ SV155 @ SY2304 @ SY2305 )
= SY2304 )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SY2304 @ ( tc_List_Olist @ SY2305 ) ) @ SV155 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(2448,plain,
! [SV156: $i] :
( ( ! [SY2306: $i,SY2307: $i,SY2308: $i] :
( ~ ( class_Orderings_Olinorder @ SV156 )
| ( c_lessequals @ SY2306 @ SY2307 @ SV156 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY2306 @ ( c_List_Olist_OCons @ SY2307 @ SY2308 @ SV156 ) @ SV156 ) @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(2449,plain,
! [SV157: $i] :
( ( ! [SY2309: $i,SY2310: $i,SY2311: $i] :
( ~ ( class_Orderings_Olinorder @ SV157 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY2309 @ ( c_List_Olist_OCons @ SY2310 @ SY2311 @ SV157 ) @ SV157 ) @ SV157 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY2310 @ SY2311 @ SV157 ) @ SV157 )
| ~ ( c_lessequals @ SY2309 @ SY2310 @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(2450,plain,
! [SV158: $i] :
( ( ! [SY2312: $i,SY2313: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Odrop @ SV158 @ SY2312 @ SY2313 ) @ ( tc_List_Olist @ SY2313 ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SY2312 @ ( tc_List_Olist @ SY2313 ) ) @ SV158 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(2451,plain,
! [SV159: $i] :
( ( ! [SY2314: $i,SY2315: $i,SY2316: $i,SY2317: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV159 @ SY2314 @ SY2315 ) @ ( c_Suc @ SY2316 ) @ SY2317 @ SY2315 )
= ( c_List_Olist_OCons @ SV159 @ ( c_List_Olist__update @ SY2314 @ SY2316 @ SY2317 @ SY2315 ) @ SY2315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(2452,plain,
! [SV160: $i] :
( ( ! [SY2318: $i,SY2319: $i] :
( ( ( c_List_Ohd @ ( c_List_Oreplicate @ SV160 @ SY2318 @ SY2319 ) @ SY2319 )
= SY2318 )
| ( SV160
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(2453,plain,
! [SV161: $i] :
( ( ! [SY2320: $i,SY2321: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ SV161 ) @ SY2320 @ SY2321 )
= ( c_List_Olist_OCons @ SY2320 @ ( c_List_Oreplicate @ SV161 @ SY2320 @ SY2321 ) @ SY2321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1627]) ).
thf(2454,plain,
! [SV162: $i] :
( ( ! [SY2322: $i,SY2323: $i,SY2324: $i] :
( ( ( c_List_Olist__update @ SV162 @ SY2322 @ SY2323 @ SY2324 )
= SV162 )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV162 @ ( tc_List_Olist @ SY2324 ) ) @ SY2322 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1628]) ).
thf(2455,plain,
! [SV163: $i] :
( ( ! [SY2325: $i,SY2326: $i] : ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ SV163 @ SY2325 @ SY2326 ) @ ( tc_List_Olist @ SY2326 ) ) @ ( c_Nat_Osize__class_Osize @ SY2325 @ ( tc_List_Olist @ SY2326 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1629]) ).
thf(2456,plain,
! [SV164: $i] :
( ( ! [SY2327: $i,SY2328: $i] :
( ( c_in @ SV164 @ ( c_List_Oset @ SY2327 @ SY2328 ) @ SY2328 )
| ~ ( c_in @ SV164 @ ( c_List_Oset @ ( c_List_Obutlast @ SY2327 @ SY2328 ) @ SY2328 ) @ SY2328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1630]) ).
thf(2457,plain,
! [SV165: $i] :
( ( ! [SY2329: $i,SY2330: $i,SY2331: $i] :
( ( c_List_Odrop @ SV165 @ ( c_List_Otake @ SY2329 @ SY2330 @ SY2331 ) @ SY2331 )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ SY2329 @ SV165 @ tc_nat ) @ ( c_List_Odrop @ SV165 @ SY2330 @ SY2331 ) @ SY2331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(2458,plain,
! [SV166: $i] :
( ( ! [SY2332: $i,SY2333: $i,SY2334: $i] :
( ( c_in @ SV166 @ ( c_List_Oset @ SY2332 @ SY2333 ) @ SY2333 )
| ~ ( c_in @ SV166 @ ( c_List_Oset @ ( c_List_Osublist @ SY2332 @ SY2334 @ SY2333 ) @ SY2333 ) @ SY2333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(2459,plain,
! [SV167: $i] :
( ( ! [SY2335: $i,SY2336: $i,SY2337: $i] :
( ~ ( c_in @ SV167 @ ( c_List_Oset @ ( c_List_Osublist @ SY2335 @ SY2336 @ SY2337 ) @ SY2337 ) @ SY2337 )
| ( c_in @ SV167 @ ( c_List_Oset @ SY2335 @ SY2337 ) @ SY2337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(2460,plain,
! [SV168: $i] :
( ( ! [SY2338: $i,SY2339: $i,SY2340: $i] :
( ( c_List_Odrop @ SV168 @ ( c_List_Oreplicate @ SY2338 @ SY2339 @ SY2340 ) @ SY2340 )
= ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ SY2338 @ SV168 @ tc_nat ) @ SY2339 @ SY2340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(2461,plain,
! [SV169: $i] :
( ( ! [SY2341: $i,SY2342: $i,SY2343: $i,SY2344: $i,SY2345: $i] :
( ~ ( class_Orderings_Olinorder @ SV169 )
| ( ( c_List_Olinorder__class_Oinsort__key @ SY2341 @ SY2342 @ ( c_List_Olist_OCons @ SY2343 @ SY2344 @ SY2345 ) @ SY2345 @ SV169 )
= ( c_List_Olist_OCons @ SY2342 @ ( c_List_Olist_OCons @ SY2343 @ SY2344 @ SY2345 ) @ SY2345 ) )
| ~ ( c_lessequals @ ( hAPP @ SY2341 @ SY2342 ) @ ( hAPP @ SY2341 @ SY2343 ) @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1635]) ).
thf(2462,plain,
! [SV170: $i] :
( ( ! [SY2346: $i,SY2347: $i,SY2348: $i,SY2349: $i,SY2350: $i] :
( ~ ( class_Orderings_Olinorder @ SV170 )
| ( ( c_List_Olinorder__class_Oinsort__key @ SY2346 @ SY2347 @ ( c_List_Olist_OCons @ SY2348 @ SY2349 @ SY2350 ) @ SY2350 @ SV170 )
= ( c_List_Olist_OCons @ SY2348 @ ( c_List_Olinorder__class_Oinsort__key @ SY2346 @ SY2347 @ SY2349 @ SY2350 @ SV170 ) @ SY2350 ) )
| ( c_lessequals @ ( hAPP @ SY2346 @ SY2347 ) @ ( hAPP @ SY2346 @ SY2348 ) @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(2463,plain,
! [SV171: $i] :
( ( ! [SY2351: $i,SY2352: $i,SY2353: $i,SY2354: $i] :
( ~ ( class_Orderings_Olinorder @ SV171 )
| ( ( c_Nat_Osize__class_Osize @ ( c_List_Olinorder__class_Oinsort__key @ SY2351 @ SY2352 @ SY2353 @ SY2354 @ SV171 ) @ ( tc_List_Olist @ SY2354 ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ SY2353 @ ( tc_List_Olist @ SY2354 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(2464,plain,
! [SV172: $i] :
( ( ! [SY2355: $i,SY2356: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV172 @ SY2355 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY2356 @ SY2355 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV172 @ SY2356 @ tc_nat )
| ~ ( c_lessequals @ SY2355 @ SY2356 @ tc_nat )
| ~ ( c_lessequals @ SY2355 @ SV172 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(2465,plain,
! [SV173: $i] :
( ( ! [SY2357: $i,SY2358: $i] :
( ( c_lessequals @ SV173 @ SY2357 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV173 @ SY2358 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY2357 @ SY2358 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2358 @ SY2357 @ tc_nat )
| ~ ( c_lessequals @ SY2358 @ SV173 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(2466,plain,
! [SV174: $i] :
( ( ! [SY2359: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV174 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ SY2359 ) @ SV174 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV174 ) @ ( c_HOL_Oone__class_Oone @ SV174 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2359 @ SV174 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(2467,plain,
! [SV175: $i] :
( ( ! [SY2360: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV175 @ SY2360 @ tc_nat ) @ SV175 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(2468,plain,
! [SV176: $i] :
( ( ! [SY2361: $i,SY2362: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV176 @ SY2361 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY2362 @ SY2361 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV176 @ SY2362 @ tc_nat ) )
| ~ ( c_lessequals @ SY2361 @ SY2362 @ tc_nat )
| ~ ( c_lessequals @ SY2361 @ SV176 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1645]) ).
thf(2469,plain,
! [SV177: $i] :
( ( ! [SY2363: $i,SY2364: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV177 @ SY2363 @ tc_nat ) @ SY2364 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV177 @ SY2364 @ tc_nat ) @ SY2363 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1646]) ).
thf(2470,plain,
! [SV178: $i] :
( ( ! [SY2365: $i,SY2366: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV178 @ SY2365 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY2366 @ SY2365 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY2365 @ SV178 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV178 @ SY2366 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1647]) ).
thf(2471,plain,
! [SV179: $i] :
( ( ! [SY2367: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV179 ) @ SY2367 @ tc_nat )
| ( ( c_Suc @ SV179 )
= SY2367 )
| ~ ( c_HOL_Oord__class_Oless @ SV179 @ SY2367 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1648]) ).
thf(2472,plain,
! [SV180: $i] :
( ( ! [SY2368: $i] :
( ~ ( c_lessequals @ SV180 @ SY2368 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SY2368 ) @ SV180 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(2473,plain,
! [SV181: $i] :
( ( ! [SY2369: $i] :
( ( c_lessequals @ ( c_Suc @ SV181 ) @ SY2369 @ tc_nat )
| ( c_lessequals @ SY2369 @ SV181 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(2474,plain,
! [SV182: $i] :
( ( ! [SY2370: $i,SY2371: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV182 ) @ SY2370 @ tc_nat ) @ ( c_Suc @ SY2371 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV182 @ SY2370 @ tc_nat ) @ SY2371 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(2475,plain,
! [SV183: $i] :
( ( c_lessequals @ ( c_Suc @ SV183 ) @ ( c_Suc @ SV183 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(2476,plain,
! [SV184: $i] :
( ( ! [SY2372: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV184 @ ( c_HOL_Ominus__class_Ominus @ SV184 @ SY2372 @ tc_nat ) @ tc_nat )
= SY2372 )
| ~ ( c_lessequals @ SY2372 @ SV184 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(2477,plain,
! [SV185: $i] :
( ( ! [SY2373: $i] :
( ( SV185
= ( c_Suc @ SY2373 ) )
| ( c_lessequals @ SV185 @ SY2373 @ tc_nat )
| ~ ( c_lessequals @ SV185 @ ( c_Suc @ SY2373 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(2478,plain,
! [SV186: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV186 @ SV186 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV186 @ ( c_Suc @ SV186 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(2479,plain,
! [SV187: $i] :
( ( ! [SY2374: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV187 @ SY2374 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2374 @ ( c_Suc @ SV187 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(2480,plain,
! [SV188: $i] :
( ( ! [SY2375: $i] :
( ( c_HOL_Oord__class_Oless @ SV188 @ ( c_Suc @ SY2375 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY2375 @ SV188 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1657]) ).
thf(2481,plain,
! [SV189: $i] :
( ( ! [SY2376: $i] :
( ( c_in @ ( c_List_Ohd @ SV189 @ SY2376 ) @ ( c_List_Oset @ SV189 @ SY2376 ) @ SY2376 )
| ( SV189
= ( c_List_Olist_ONil @ SY2376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1659]) ).
thf(2482,plain,
! [SV190: $i] :
( ( ! [SY2377: $i,SY2378: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV190 )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV190 ) @ SY2377 ) @ SY2378 ) @ SY2378 @ SV190 )
= SY2377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(2483,plain,
! [SV191: $i] :
( ( ! [SY2379: $i,SY2380: $i,SY2381: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV191 )
| ( c_lessequals @ SY2379 @ SY2380 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY2381 @ SY2379 @ SV191 ) @ ( c_Power_Opower__class_Opower @ SY2381 @ SY2380 @ SV191 ) @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV191 ) @ SY2381 @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(2484,plain,
! [SV192: $i] :
( ( ! [SY2382: $i,SY2383: $i,SY2384: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV192 )
| ( c_lessequals @ SY2382 @ SY2383 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY2384 @ SY2382 @ SV192 ) @ ( c_Power_Opower__class_Opower @ SY2384 @ SY2383 @ SV192 ) @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV192 ) @ SY2384 @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1662]) ).
thf(2485,plain,
! [SV193: $i] :
( ( ! [SY2385: $i,SY2386: $i,SY2387: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV193 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY2385 @ SY2386 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SY2385 @ SY2387 @ SV193 ) @ SV193 )
| ~ ( c_lessequals @ SY2386 @ SY2387 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV193 ) @ SY2385 @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1663]) ).
thf(2486,plain,
! [SV194: $i] :
( ( ! [SY2388: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV194 ) @ ( c_Suc @ SY2388 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV194 @ SY2388 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1664]) ).
thf(2487,plain,
! [SV195: $i] :
( ( ! [SY2389: $i] :
( ( c_HOL_Oord__class_Oless @ SV195 @ SY2389 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV195 ) @ ( c_Suc @ SY2389 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(2488,plain,
! [SV196: $i] :
( ( ! [SY2390: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV196 ) @ ( c_Suc @ SY2390 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV196 @ SY2390 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(2489,plain,
! [SV197: $i] :
( ( ! [SY2391: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV197 )
| ~ ( class_Int_Onumber__ring @ SV197 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2391 @ SY2391 @ SV197 )
= ( c_HOL_Ozero__class_Ozero @ SV197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(2490,plain,
! [SV198: $i] :
( ( ! [SY2392: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV198 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2392 @ SY2392 @ SV198 )
= ( c_HOL_Ozero__class_Ozero @ SV198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(2491,plain,
! [SV199: $i] :
( ( ! [SY2393: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV199 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2393 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
= SY2393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(2492,plain,
! [SV200: $i] :
( ( ! [SY2394: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV200 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2394 @ SY2394 @ SV200 )
= ( c_HOL_Ozero__class_Ozero @ SV200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1671]) ).
thf(2493,plain,
! [SV201: $i] :
( ( ! [SY2395: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV201 )
| ( ( c_HOL_Ominus__class_Ominus @ SY2395 @ SY2395 @ SV201 )
= ( c_HOL_Ozero__class_Ozero @ SV201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(2494,plain,
! [SV202: $i] :
( ( ( SV202
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ SV202 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(2495,plain,
! [SV203: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV203 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= SV203 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(2496,plain,
! [SV204: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV204 @ SV204 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(2497,plain,
! [SV205: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV205 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(2498,plain,
! [SV206: $i] :
( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV206 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1687]) ).
thf(2499,plain,
! [SV207: $i] :
( ( ! [SY2396: $i,SY2397: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ SV207 @ SY2396 @ SY2397 ) @ SY2397 )
= SV207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1688]) ).
thf(2500,plain,
! [SV208: $i] :
( ( ! [SY2398: $i,SY2399: $i,SY2400: $i,SY2401: $i] :
( ( c_ListOrder_Ostep1 @ SV208 @ ( c_List_Olist_OCons @ SY2398 @ SY2399 @ SY2400 ) @ ( c_List_Olist_OCons @ SY2398 @ SY2401 @ SY2400 ) @ SY2400 )
| ~ ( c_ListOrder_Ostep1 @ SV208 @ SY2399 @ SY2401 @ SY2400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(2501,plain,
! [SV209: $i] :
( ( ! [SY2402: $i,SY2403: $i,SY2404: $i,SY2405: $i,SY2406: $i] :
( ( c_ListOrder_Ostep1 @ SV209 @ SY2402 @ SY2403 @ SY2404 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV209 @ SY2405 ) @ SY2406 ) )
| ~ ( c_ListOrder_Ostep1 @ SV209 @ ( c_List_Olist_OCons @ SY2405 @ SY2402 @ SY2404 ) @ ( c_List_Olist_OCons @ SY2406 @ SY2403 @ SY2404 ) @ SY2404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1690]) ).
thf(2502,plain,
! [SV210: $i] :
( ( ! [SY2407: $i,SY2408: $i,SY2409: $i,SY2410: $i,SY2411: $i] :
( ( c_ListOrder_Ostep1 @ SV210 @ SY2407 @ SY2408 @ SY2409 )
| ( SY2408 = SY2407 )
| ~ ( c_ListOrder_Ostep1 @ SV210 @ ( c_List_Olist_OCons @ SY2410 @ SY2407 @ SY2409 ) @ ( c_List_Olist_OCons @ SY2411 @ SY2408 @ SY2409 ) @ SY2409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(2503,plain,
! [SV211: $i] :
( ( ! [SY2412: $i,SY2413: $i,SY2414: $i,SY2415: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV211 @ SY2412 ) @ SY2413 ) )
| ( c_ListOrder_Ostep1 @ SV211 @ ( c_List_Olist_OCons @ SY2412 @ SY2414 @ SY2415 ) @ ( c_List_Olist_OCons @ SY2413 @ SY2414 @ SY2415 ) @ SY2415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(2504,plain,
! [SV212: $i] :
( ( ! [SY2416: $i,SY2417: $i,SY2418: $i,SY2419: $i,SY2420: $i] :
( ( SV212 = SY2416 )
| ( SY2417 = SY2418 )
| ~ ( c_ListOrder_Ostep1 @ SY2419 @ ( c_List_Olist_OCons @ SY2416 @ SY2418 @ SY2420 ) @ ( c_List_Olist_OCons @ SV212 @ SY2417 @ SY2420 ) @ SY2420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(2505,plain,
! [SV213: $i] :
( ( ! [SY2421: $i,SY2422: $i,SY2423: $i,SY2424: $i,SY2425: $i] :
( ( SV213 = SY2421 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2422 @ SY2421 ) @ SV213 ) )
| ~ ( c_ListOrder_Ostep1 @ SY2422 @ ( c_List_Olist_OCons @ SY2421 @ SY2423 @ SY2424 ) @ ( c_List_Olist_OCons @ SV213 @ SY2425 @ SY2424 ) @ SY2424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1694]) ).
thf(2506,plain,
! [SV214: $i] :
( ( ! [SY2426: $i,SY2427: $i] :
~ ( c_ListOrder_Ostep1 @ SV214 @ SY2426 @ ( c_List_Olist_ONil @ SY2427 ) @ SY2427 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(2507,plain,
! [SV215: $i] :
( ( ! [SY2428: $i,SY2429: $i] :
~ ( c_ListOrder_Ostep1 @ SV215 @ ( c_List_Olist_ONil @ SY2428 ) @ SY2429 @ SY2428 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(2508,plain,
! [SV216: $i] :
( ( ! [SY2430: $i,SY2431: $i,SY2432: $i] :
( ~ ( class_Orderings_Olinorder @ SV216 )
| ( c_lessequals @ ( c_List_Onth @ SY2430 @ SY2431 @ SV216 ) @ ( c_List_Onth @ SY2430 @ SY2432 @ SV216 ) @ SV216 )
| ~ ( c_HOL_Oord__class_Oless @ SY2431 @ ( c_Nat_Osize__class_Osize @ SY2430 @ ( tc_List_Olist @ SV216 ) ) @ tc_nat )
| ~ ( c_lessequals @ SY2432 @ SY2431 @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Orev @ SY2430 @ SV216 ) @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(2509,plain,
! [SV217: $i] :
( ( ! [SY2433: $i,SY2434: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV217 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV217 ) @ SY2433 ) @ SY2434 ) @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 )
| ~ ( c_lessequals @ SY2434 @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 )
| ~ ( c_HOL_Oord__class_Oless @ SY2433 @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1698]) ).
thf(2510,plain,
! [SV218: $i] :
( ( ! [SY2435: $i,SY2436: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV218 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV218 ) @ SY2435 ) @ SY2436 ) @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
| ~ ( c_HOL_Oord__class_Oless @ SY2436 @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
| ~ ( c_lessequals @ SY2435 @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(2511,plain,
! [SV219: $i] :
( ( ! [SY2437: $i,SY2438: $i,SY2439: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV219 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV219 )
| ( c_HOL_Oord__class_Oless @ SY2437 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV219 ) @ SY2438 ) @ SY2439 ) @ SV219 )
| ~ ( c_lessequals @ SY2437 @ SY2439 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SY2438 @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1700]) ).
thf(2512,plain,
! [SV220: $i] :
( ( ! [SY2440: $i,SY2441: $i,SY2442: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV220 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV220 )
| ( c_HOL_Oord__class_Oless @ SY2440 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV220 ) @ SY2441 ) @ SY2442 ) @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ SY2440 @ SY2442 @ SV220 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SY2441 @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1701]) ).
thf(2513,plain,
! [SV221: $i] :
( ( ! [SY2443: $i,SY2444: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV221 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SY2443 ) @ SY2444 ) @ SV221 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ SY2444 @ SV221 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ SY2443 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(2514,plain,
! [SV222: $i] :
( ( ! [SY2445: $i,SY2446: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV222 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SY2445 ) @ SY2446 ) @ SV222 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ SY2446 @ SV222 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ SY2445 @ SV222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(2515,plain,
! [SV223: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV223 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV223 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV223 ) @ ( c_HOL_Oone__class_Oone @ SV223 ) ) @ ( c_HOL_Oone__class_Oone @ SV223 ) ) @ SV223 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1704]) ).
thf(2516,plain,
! [SV224: $i] :
( ( ! [SY2447: $i,SY2448: $i,SY2449: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV224 )
| ( c_HOL_Oord__class_Oless @ SY2447 @ SY2448 @ SV224 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV224 ) @ SY2448 @ SV224 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2447 @ SY2449 @ SV224 ) @ ( c_Power_Opower__class_Opower @ SY2448 @ SY2449 @ SV224 ) @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1705]) ).
thf(2517,plain,
! [SV225: $i] :
( ( ! [SY2450: $i,SY2451: $i,SY2452: $i] :
( ( c_in @ SV225 @ ( c_List_Oset @ ( c_List_Oappend @ SY2450 @ ( c_List_Olist_OCons @ SV225 @ SY2451 @ SY2452 ) @ SY2452 ) @ SY2452 ) @ SY2452 )
| ( c_in @ SV225 @ ( c_List_Oset @ SY2450 @ SY2452 ) @ SY2452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1706]) ).
thf(2518,plain,
! [SV226: $i] :
( ( ! [SY2453: $i,SY2454: $i,SY2455: $i] :
( ( c_in @ SV226 @ ( c_List_Oset @ ( c_List_Oappend @ SY2453 @ ( c_List_Olist_OCons @ SV226 @ SY2454 @ SY2455 ) @ SY2455 ) @ SY2455 ) @ SY2455 )
| ( c_in @ SV226 @ ( c_List_Oset @ SY2454 @ SY2455 ) @ SY2455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1707]) ).
thf(2519,plain,
! [SV227: $i] :
( ( ! [SY2456: $i,SY2457: $i,SY2458: $i] : ( c_in @ SV227 @ ( c_List_Oset @ ( c_List_Oappend @ SY2456 @ ( c_List_Olist_OCons @ SV227 @ SY2457 @ SY2458 ) @ SY2458 ) @ SY2458 ) @ SY2458 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(2520,plain,
! [SV228: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV228 )
| ~ ( class_Power_Opower @ SV228 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV228 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV228 )
= ( c_HOL_Oone__class_Oone @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(2521,plain,
! [SV229: $i] :
( ( ! [SY2459: $i,SY2460: $i,SY2461: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV229 )
| ( c_HOL_Oord__class_Oless @ SY2459 @ SY2460 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2461 @ SY2459 @ SV229 ) @ ( c_Power_Opower__class_Opower @ SY2461 @ SY2460 @ SV229 ) @ SV229 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV229 ) @ SY2461 @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(2522,plain,
! [SV230: $i] :
( ( ! [SY2462: $i,SY2463: $i,SY2464: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV230 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2462 @ SY2463 @ SV230 ) @ ( c_Power_Opower__class_Opower @ SY2462 @ SY2464 @ SV230 ) @ SV230 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV230 ) @ SY2462 @ SV230 )
| ~ ( c_HOL_Oord__class_Oless @ SY2463 @ SY2464 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1711]) ).
thf(2523,plain,
! [SV231: $i] :
( ( ! [SY2465: $i,SY2466: $i,SY2467: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV231 )
| ( c_HOL_Oord__class_Oless @ SY2465 @ SY2466 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2467 @ SY2465 @ SV231 ) @ ( c_Power_Opower__class_Opower @ SY2467 @ SY2466 @ SV231 ) @ SV231 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV231 ) @ SY2467 @ SV231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(2524,plain,
! [SV232: $i] :
( ( ! [SY2468: $i,SY2469: $i,SY2470: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV232 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2468 @ SY2469 @ SV232 ) @ ( c_Power_Opower__class_Opower @ SY2468 @ SY2470 @ SV232 ) @ SV232 )
| ~ ( c_HOL_Oord__class_Oless @ SY2469 @ SY2470 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV232 ) @ SY2468 @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1713]) ).
thf(2525,plain,
! [SV233: $i] :
( ( ! [SY2471: $i,SY2472: $i,SY2473: $i,SY2474: $i,SY2475: $i] :
( ( SV233 = SY2471 )
| ( SY2472 = SY2473 )
| ~ ( c_ListOrder_Ostep1 @ SY2474 @ ( c_List_Oappend @ SV233 @ ( c_List_Olist_OCons @ SY2472 @ ( c_List_Olist_ONil @ SY2475 ) @ SY2475 ) @ SY2475 ) @ ( c_List_Oappend @ SY2471 @ ( c_List_Olist_OCons @ SY2473 @ ( c_List_Olist_ONil @ SY2475 ) @ SY2475 ) @ SY2475 ) @ SY2475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1714]) ).
thf(2526,plain,
! [SV234: $i] :
( ( ! [SY2476: $i,SY2477: $i,SY2478: $i,SY2479: $i,SY2480: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV234 @ SY2476 ) @ SY2477 ) )
| ( SY2476 = SY2477 )
| ~ ( c_ListOrder_Ostep1 @ SV234 @ ( c_List_Oappend @ SY2478 @ ( c_List_Olist_OCons @ SY2476 @ ( c_List_Olist_ONil @ SY2479 ) @ SY2479 ) @ SY2479 ) @ ( c_List_Oappend @ SY2480 @ ( c_List_Olist_OCons @ SY2477 @ ( c_List_Olist_ONil @ SY2479 ) @ SY2479 ) @ SY2479 ) @ SY2479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(2527,plain,
! [SV235: $i] :
( ( ! [SY2481: $i,SY2482: $i,SY2483: $i,SY2484: $i,SY2485: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SY2481 ) @ SY2482 ) )
| ( c_ListOrder_Ostep1 @ SV235 @ SY2483 @ SY2484 @ SY2485 )
| ~ ( c_ListOrder_Ostep1 @ SV235 @ ( c_List_Oappend @ SY2483 @ ( c_List_Olist_OCons @ SY2481 @ ( c_List_Olist_ONil @ SY2485 ) @ SY2485 ) @ SY2485 ) @ ( c_List_Oappend @ SY2484 @ ( c_List_Olist_OCons @ SY2482 @ ( c_List_Olist_ONil @ SY2485 ) @ SY2485 ) @ SY2485 ) @ SY2485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(2528,plain,
! [SV236: $i] :
( ( ! [SY2486: $i,SY2487: $i,SY2488: $i,SY2489: $i,SY2490: $i] :
( ( SV236 = SY2486 )
| ( c_ListOrder_Ostep1 @ SY2487 @ SV236 @ SY2486 @ SY2488 )
| ~ ( c_ListOrder_Ostep1 @ SY2487 @ ( c_List_Oappend @ SV236 @ ( c_List_Olist_OCons @ SY2489 @ ( c_List_Olist_ONil @ SY2488 ) @ SY2488 ) @ SY2488 ) @ ( c_List_Oappend @ SY2486 @ ( c_List_Olist_OCons @ SY2490 @ ( c_List_Olist_ONil @ SY2488 ) @ SY2488 ) @ SY2488 ) @ SY2488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1717]) ).
thf(2529,plain,
! [SV237: $i] :
( ( ! [SY2491: $i] :
( ( ( c_List_Ohd @ SV237 @ SY2491 )
= ( c_List_Onth @ SV237 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2491 ) )
| ( SV237
= ( c_List_Olist_ONil @ SY2491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1718]) ).
thf(2530,plain,
! [SV238: $i] :
( ( ! [SY2492: $i,SY2493: $i,SY2494: $i,SY2495: $i] :
( ( ( c_List_OtakeWhile @ SV238 @ ( c_List_Oappend @ SY2492 @ SY2493 @ SY2494 ) @ SY2494 )
= ( c_List_OtakeWhile @ SV238 @ SY2492 @ SY2494 ) )
| ( hBOOL @ ( hAPP @ SV238 @ SY2495 ) )
| ~ ( c_in @ SY2495 @ ( c_List_Oset @ SY2492 @ SY2494 ) @ SY2494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1719]) ).
thf(2531,plain,
! [SV239: $i] :
( ( ! [SY2496: $i,SY2497: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV239 @ SY2496 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV239 @ SY2497 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SY2496 @ SY2497 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1720]) ).
thf(2532,plain,
! [SV240: $i] :
( ( ! [SY2498: $i,SY2499: $i] :
( ( ( c_List_Odrop @ SV240 @ SY2498 @ SY2499 )
= ( c_List_Olist_ONil @ SY2499 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SY2498 @ ( tc_List_Olist @ SY2499 ) ) @ SV240 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1722]) ).
thf(2533,plain,
! [SV241: $i] :
( ( ! [SY2500: $i,SY2501: $i,SY2502: $i] :
( ( c_List_Otake @ SV241 @ ( c_List_Oappend @ SY2500 @ SY2501 @ SY2502 ) @ SY2502 )
= ( c_List_Oappend @ ( c_List_Otake @ SV241 @ SY2500 @ SY2502 ) @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ SV241 @ ( c_Nat_Osize__class_Osize @ SY2500 @ ( tc_List_Olist @ SY2502 ) ) @ tc_nat ) @ SY2501 @ SY2502 ) @ SY2502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(2534,plain,
! [SV242: $i] :
( ( ! [SY2503: $i,SY2504: $i,SY2505: $i] :
( ( c_List_Odrop @ SV242 @ ( c_List_Oappend @ SY2503 @ SY2504 @ SY2505 ) @ SY2505 )
= ( c_List_Oappend @ ( c_List_Odrop @ SV242 @ SY2503 @ SY2505 ) @ ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ SV242 @ ( c_Nat_Osize__class_Osize @ SY2503 @ ( tc_List_Olist @ SY2505 ) ) @ tc_nat ) @ SY2504 @ SY2505 ) @ SY2505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(2535,plain,
! [SV243: $i] :
( ( ! [SY2506: $i,SY2507: $i,SY2508: $i] :
( ( c_in @ SV243 @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ SY2506 @ SY2507 @ SY2508 ) @ SY2508 ) @ SY2508 ) @ SY2508 )
| ~ ( c_in @ SV243 @ ( c_List_Oset @ ( c_List_Obutlast @ SY2507 @ SY2508 ) @ SY2508 ) @ SY2508 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1729]) ).
thf(2536,plain,
! [SV244: $i] :
( ( ! [SY2509: $i,SY2510: $i,SY2511: $i] :
( ( c_in @ SV244 @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ SY2509 @ SY2510 @ SY2511 ) @ SY2511 ) @ SY2511 ) @ SY2511 )
| ~ ( c_in @ SV244 @ ( c_List_Oset @ ( c_List_Obutlast @ SY2509 @ SY2511 ) @ SY2511 ) @ SY2511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1730]) ).
thf(2537,plain,
! [SV245: $i] :
( ( ! [SY2512: $i] :
( ( c_in @ ( c_List_Olast @ SV245 @ SY2512 ) @ ( c_List_Oset @ SV245 @ SY2512 ) @ SY2512 )
| ( SV245
= ( c_List_Olist_ONil @ SY2512 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(2538,plain,
! [SV246: $i] :
( ( ! [SY2513: $i,SY2514: $i,SY2515: $i,SY2516: $i] :
( ( c_HOL_Oord__class_Oless @ SV246 @ ( c_List_Olist_Olist__size @ SY2513 @ SY2514 @ SY2515 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV246 @ ( hAPP @ SY2513 @ SY2516 ) @ tc_nat )
| ~ ( c_in @ SY2516 @ ( c_List_Oset @ SY2514 @ SY2515 ) @ SY2515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1732]) ).
thf(2539,plain,
! [SV247: $i] :
( ( ! [SY2517: $i,SY2518: $i,SY2519: $i] :
( ( ( c_List_OtakeWhile @ SV247 @ SY2517 @ SY2518 )
= ( c_List_Otake @ SY2519 @ SY2517 @ SY2518 ) )
| ( hBOOL @ ( hAPP @ SV247 @ ( c_List_Onth @ SY2517 @ SY2519 @ SY2518 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV247 @ ( c_List_Onth @ SY2517 @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV247 @ SY2519 @ SY2517 @ SY2518 ) @ SY2518 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1733]) ).
thf(2540,plain,
! [SV248: $i] :
( ( ! [SY2520: $i] :
( ( ( c_List_Ohd @ ( c_List_Orev @ SV248 @ SY2520 ) @ SY2520 )
= ( c_List_Olast @ SV248 @ SY2520 ) )
| ( SV248
= ( c_List_Olist_ONil @ SY2520 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1734]) ).
thf(2541,plain,
! [SV249: $i] :
( ( ! [SY2521: $i] :
( ( ( c_List_Olast @ ( c_List_Orev @ SV249 @ SY2521 ) @ SY2521 )
= ( c_List_Ohd @ SV249 @ SY2521 ) )
| ( SV249
= ( c_List_Olist_ONil @ SY2521 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1735]) ).
thf(2542,plain,
! [SV250: $i] :
( ( ! [SY2522: $i,SY2523: $i] :
( ( ( c_List_Olength__unique @ ( c_List_Olist_OCons @ SV250 @ SY2522 @ SY2523 ) @ SY2523 )
= ( c_List_Olength__unique @ SY2522 @ SY2523 ) )
| ~ ( c_in @ SV250 @ ( c_List_Oset @ SY2522 @ SY2523 ) @ SY2523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1736]) ).
thf(2543,plain,
! [SV251: $i] :
( ( ! [SY2524: $i,SY2525: $i] :
( ( ( c_List_Oappend @ ( c_List_Otake @ SV251 @ SY2524 @ SY2525 ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ ( c_List_Odrop @ SV251 @ SY2524 @ SY2525 ) @ SY2525 ) @ ( c_List_Olist_ONil @ SY2525 ) @ SY2525 ) @ SY2525 )
= ( c_List_Otake @ ( c_Suc @ SV251 ) @ SY2524 @ SY2525 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV251 @ ( c_Nat_Osize__class_Osize @ SY2524 @ ( tc_List_Olist @ SY2525 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(2544,plain,
! [SV252: $i] :
( ( ! [SY2526: $i,SY2527: $i,SY2528: $i,SY2529: $i] :
( ~ ( class_Orderings_Olinorder @ SV252 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SY2526 @ ( c_List_Olinorder__class_Oinsort__key @ SY2526 @ SY2527 @ SY2528 @ SY2529 @ SV252 ) @ SY2529 @ SV252 ) @ SV252 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SY2526 @ SY2528 @ SY2529 @ SV252 ) @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(2545,plain,
! [SV253: $i] :
( ( ! [SY2530: $i,SY2531: $i,SY2532: $i,SY2533: $i] :
( ~ ( class_Orderings_Olinorder @ SV253 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SY2530 @ SY2531 @ SY2532 @ SV253 ) @ SV253 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SY2530 @ ( c_List_Olinorder__class_Oinsort__key @ SY2530 @ SY2533 @ SY2531 @ SY2532 @ SV253 ) @ SY2532 @ SV253 ) @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1739]) ).
thf(2546,plain,
! [SV254: $i] :
( ( ! [SY2534: $i,SY2535: $i,SY2536: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ SV254 @ SY2534 @ SY2535 @ SY2536 ) @ ( tc_List_Olist @ SY2536 ) )
= ( c_Nat_Osize__class_Osize @ SV254 @ ( tc_List_Olist @ SY2536 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(2547,plain,
! [SV255: $i] :
( ( ! [SY2537: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ SV255 @ ( c_List_Olist_ONil @ SY2537 ) @ SY2537 ) @ SY2537 )
= ( c_List_Obutlast @ SV255 @ SY2537 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(2548,plain,
! [SV256: $i] :
( ( ! [SY2538: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV256 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2538 @ SV256 ) @ ( c_HOL_Ozero__class_Ozero @ SV256 ) @ SV256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1742]) ).
thf(2549,plain,
! [SV257: $i] :
( ( ! [SY2539: $i,SY2540: $i,SY2541: $i,SY2542: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV257 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SY2539 ) @ SY2540 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SY2541 ) @ SY2542 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SY2539 ) @ SY2541 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SY2540 ) @ SY2542 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1743]) ).
thf(2550,plain,
! [SV258: $i] :
( ( ! [SY2543: $i,SY2544: $i] :
( ( ( c_List_Olast @ ( c_List_Oreplicate @ SV258 @ SY2543 @ SY2544 ) @ SY2544 )
= SY2543 )
| ( SV258
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(2551,plain,
! [SV259: $i] :
( ( ! [SY2545: $i,SY2546: $i] :
( ( c_List_Obutlast @ ( c_List_Odrop @ SV259 @ SY2545 @ SY2546 ) @ SY2546 )
= ( c_List_Odrop @ SV259 @ ( c_List_Obutlast @ SY2545 @ SY2546 ) @ SY2546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(2552,plain,
! [SV260: $i] :
( ( ! [SY2547: $i,SY2548: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ SV260 @ SY2547 @ SY2548 ) @ ( c_List_Odrop @ SV260 @ SY2547 @ SY2548 ) @ SY2548 )
= SY2547 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(2553,plain,
! [SV261: $i] :
( ( ! [SY2549: $i,SY2550: $i] :
( ~ ( class_Orderings_Olinorder @ SV261 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_OtakeWhile @ SY2549 @ SY2550 @ SV261 ) @ SV261 )
| ~ ( c_List_Olinorder__class_Osorted @ SY2550 @ SV261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(2554,plain,
! [SV262: $i] :
( ( ! [SY2551: $i,SY2552: $i] :
( SV262
= ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SY2551 @ ( tc_List_Olist @ SY2552 ) ) @ ( c_List_Oappend @ SY2551 @ SV262 @ SY2552 ) @ SY2552 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(2555,plain,
! [SV263: $i] :
( ( ! [SY2553: $i,SY2554: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV263 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV263 ) @ SY2553 ) @ SY2554 ) @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ SY2554 @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ SY2553 @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1753]) ).
thf(2556,plain,
! [SV264: $i] :
( ( ! [SY2555: $i,SY2556: $i,SY2557: $i] :
( ( ( c_List_Onth @ ( c_List_OtakeWhile @ SV264 @ SY2555 @ SY2556 ) @ SY2557 @ SY2556 )
= ( c_List_Onth @ SY2555 @ SY2557 @ SY2556 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2557 @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ SV264 @ SY2555 @ SY2556 ) @ ( tc_List_Olist @ SY2556 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(2557,plain,
! [SV265: $i] :
( ( ! [SY2558: $i,SY2559: $i] :
( ( c_List_Odrop @ SV265 @ ( c_List_Obutlast @ SY2558 @ SY2559 ) @ SY2559 )
= ( c_List_Obutlast @ ( c_List_Odrop @ SV265 @ SY2558 @ SY2559 ) @ SY2559 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(2558,plain,
! [SV266: $i] :
( ( ! [SY2560: $i] :
( ( c_HOL_Oord__class_Oless @ SV266 @ SV266 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV266 ) ) @ SY2560 ) @ SV266 )
= SY2560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(2559,plain,
! [SV267: $i] :
( ( ! [SY2561: $i,SY2562: $i,SY2563: $i,SY2564: $i,SY2565: $i] :
( ( hAPP @ ( c_COMBC @ SV267 @ SY2561 @ SY2562 @ SY2563 @ SY2564 ) @ SY2565 )
= ( hAPP @ ( hAPP @ SV267 @ SY2565 ) @ SY2561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(2560,plain,
! [SV268: $i] :
( ( ! [SY2566: $i,SY2567: $i] :
( ( hBOOL @ ( hAPP @ SV268 @ SY2566 ) )
| ~ ( c_in @ SY2566 @ SV268 @ SY2567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(2561,plain,
! [SV269: $i] :
( ( ! [SY2568: $i,SY2569: $i] :
( ( c_in @ SV269 @ SY2568 @ SY2569 )
| ~ ( hBOOL @ ( hAPP @ SY2568 @ SV269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1760]) ).
thf(2562,plain,
! [SV270: $i] :
( ( ! [SY2570: $i,SY2571: $i,SY2572: $i,SY2573: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ SV270 @ SY2570 @ SY2571 @ SY2572 ) @ SY2573 @ SY2572 )
= ( c_List_Onth @ SV270 @ SY2573 @ SY2572 ) )
| ( SY2570 = SY2573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(2563,plain,
! [SV271: $i] :
( ( ! [SY2574: $i,SY2575: $i,SY2576: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV271 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ SY2574 ) @ SY2575 ) ) @ SY2576 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ SY2574 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ SY2575 ) @ SY2576 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(2564,plain,
! [SV272: $i] :
( ( ! [SY2577: $i,SY2578: $i,SY2579: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV272 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SY2577 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SY2578 ) @ SY2579 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SY2578 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SY2577 ) @ SY2579 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(2565,plain,
! [SV273: $i] :
( ( ! [SY2580: $i,SY2581: $i,SY2582: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV273 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ SY2580 ) @ SY2581 ) ) @ SY2582 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ SY2580 ) @ SY2582 ) ) @ SY2581 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1765]) ).
thf(2566,plain,
! [SV274: $i] :
( ( ! [SY2583: $i,SY2584: $i,SY2585: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV274 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ SY2583 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ SY2584 ) @ SY2585 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ SY2583 ) @ SY2584 ) ) @ SY2585 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(2567,plain,
! [SV275: $i] :
( ( ! [SY2586: $i,SY2587: $i,SY2588: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV275 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ SY2586 ) @ SY2587 ) ) @ SY2588 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ SY2586 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ SY2587 ) @ SY2588 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1767]) ).
thf(2568,plain,
! [SV276: $i] :
( ( ! [SY2589: $i,SY2590: $i,SY2591: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV276 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ SY2589 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ SY2590 ) @ SY2591 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ SY2590 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ SY2589 ) @ SY2591 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(2569,plain,
! [SV277: $i] :
( ( ! [SY2592: $i,SY2593: $i,SY2594: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV277 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ SY2592 ) @ SY2593 ) ) @ SY2594 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ SY2592 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ SY2593 ) @ SY2594 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(2570,plain,
! [SV278: $i] :
( ( ! [SY2595: $i,SY2596: $i,SY2597: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV278 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV278 ) @ SY2595 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV278 ) @ SY2596 ) @ SY2597 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV278 ) @ SY2596 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV278 ) @ SY2595 ) @ SY2597 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(2571,plain,
! [SV279: $i] :
( ( ! [SY2598: $i,SY2599: $i,SY2600: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV279 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV279 ) @ SY2598 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV279 ) @ SY2599 ) @ SY2600 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV279 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV279 ) @ SY2598 ) @ SY2599 ) ) @ SY2600 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1771]) ).
thf(2572,plain,
! [SV280: $i] :
( ( ! [SY2601: $i,SY2602: $i,SY2603: $i] :
( ( ( c_List_Onth @ ( c_List_Otake @ SV280 @ SY2601 @ SY2602 ) @ SY2603 @ SY2602 )
= ( c_List_Onth @ SY2601 @ SY2603 @ SY2602 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2603 @ SV280 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(2573,plain,
! [SV281: $i] :
( ( ! [SY2604: $i,SY2605: $i,SY2606: $i] :
( ~ ( class_Orderings_Oorder @ SV281 )
| ( c_HOL_Oord__class_Oless @ SY2604 @ SY2605 @ SV281 )
| ~ ( c_HOL_Oord__class_Oless @ SY2604 @ SY2606 @ SV281 )
| ~ ( c_HOL_Oord__class_Oless @ SY2606 @ SY2605 @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(2574,plain,
! [SV282: $i] :
( ( ! [SY2607: $i,SY2608: $i,SY2609: $i] :
( ~ ( class_Orderings_Opreorder @ SV282 )
| ( c_HOL_Oord__class_Oless @ SY2607 @ SY2608 @ SV282 )
| ~ ( c_HOL_Oord__class_Oless @ SY2609 @ SY2608 @ SV282 )
| ~ ( c_HOL_Oord__class_Oless @ SY2607 @ SY2609 @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(2575,plain,
! [SV283: $i] :
( ( ! [SY2610: $i,SY2611: $i,SY2612: $i,SY2613: $i] :
( ( c_List_Otake @ SV283 @ ( c_List_Omap @ SY2610 @ SY2611 @ SY2612 @ SY2613 ) @ SY2613 )
= ( c_List_Omap @ SY2610 @ ( c_List_Otake @ SV283 @ SY2611 @ SY2612 ) @ SY2612 @ SY2613 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(2576,plain,
! [SV284: $i] :
( ( ! [SY2614: $i,SY2615: $i] :
( ~ ( class_Orderings_Olinorder @ SV284 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ SY2614 @ SY2615 @ SV284 ) @ SV284 )
| ~ ( c_List_Olinorder__class_Osorted @ SY2615 @ SV284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(2577,plain,
! [SV285: $i] :
( ( ! [SY2616: $i,SY2617: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV285 ) ) @ SY2616 ) @ SY2617 )
= ( c_Lambda_OdB_OVar @ SV285 ) )
| ( SV285 = SY2617 )
| ( c_HOL_Oord__class_Oless @ SY2617 @ SV285 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1777]) ).
thf(2578,plain,
! [SV286: $i] :
( ( ! [SY2618: $i,SY2619: $i,SY2620: $i] :
( ( c_List_Olistsp @ SV286 @ SY2618 @ SY2619 )
| ~ ( c_List_Olistsp @ SV286 @ ( c_List_Oappend @ SY2618 @ SY2620 @ SY2619 ) @ SY2619 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(2579,plain,
! [SV287: $i] :
( ( ! [SY2621: $i,SY2622: $i,SY2623: $i] :
( ( c_List_Olistsp @ SV287 @ SY2621 @ SY2622 )
| ~ ( c_List_Olistsp @ SV287 @ ( c_List_Oappend @ SY2623 @ SY2621 @ SY2622 ) @ SY2622 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(2580,plain,
! [SV288: $i] :
( ( ! [SY2624: $i,SY2625: $i,SY2626: $i,SY2627: $i] :
( ( c_Lambda_OdB_OdB__case @ SV288 @ SY2624 @ SY2625 @ ( c_Lambda_OdB_OAbs @ SY2626 ) @ SY2627 )
= ( hAPP @ SY2625 @ SY2626 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(2581,plain,
! [SV289: $i] :
( ( ! [SY2628: $i,SY2629: $i,SY2630: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV289 ) @ SY2628 ) @ SY2629 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY2630 ) @ SY2628 ) @ SY2629 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV289 ) @ SY2630 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1781]) ).
thf(2582,plain,
! [SV290: $i] :
( ( ! [SY2631: $i,SY2632: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV290 @ ( c_Nat_Osize__class_Osize @ SY2631 @ ( tc_List_Olist @ SY2632 ) ) @ tc_nat )
| ( ( c_List_Olist__update @ SY2631 @ SV290 @ ( c_List_Onth @ SY2631 @ SV290 @ SY2632 ) @ SY2632 )
= SY2631 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(2583,plain,
! [SV291: $i] :
( ( ! [SY2633: $i,SY2634: $i,SY2635: $i] :
( ( ( c_List_Olist__update @ SV291 @ SY2633 @ SY2634 @ SY2635 )
= ( c_List_Oappend @ ( c_List_Otake @ SY2633 @ SV291 @ SY2635 ) @ ( c_List_Olist_OCons @ SY2634 @ ( c_List_Odrop @ ( c_Suc @ SY2633 ) @ SV291 @ SY2635 ) @ SY2635 ) @ SY2635 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2633 @ ( c_Nat_Osize__class_Osize @ SV291 @ ( tc_List_Olist @ SY2635 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(2584,plain,
! [SV292: $i] :
( ( ! [SY2636: $i,SY2637: $i] :
( ( SV292
= ( c_List_Oappend @ ( c_List_Otake @ SY2636 @ SV292 @ SY2637 ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ SV292 @ SY2636 @ SY2637 ) @ ( c_List_Odrop @ ( c_Suc @ SY2636 ) @ SV292 @ SY2637 ) @ SY2637 ) @ SY2637 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2636 @ ( c_Nat_Osize__class_Osize @ SV292 @ ( tc_List_Olist @ SY2637 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(2585,plain,
! [SV293: $i] :
( ( ! [SY2638: $i,SY2639: $i] :
( ( ( c_List_Otake @ ( c_Suc @ SV293 ) @ SY2638 @ SY2639 )
= ( c_List_Oappend @ ( c_List_Otake @ SV293 @ SY2638 @ SY2639 ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ SY2638 @ SV293 @ SY2639 ) @ ( c_List_Olist_ONil @ SY2639 ) @ SY2639 ) @ SY2639 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV293 @ ( c_Nat_Osize__class_Osize @ SY2638 @ ( tc_List_Olist @ SY2639 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(2586,plain,
! [SV294: $i] :
( ( ! [SY2640: $i,SY2641: $i,SY2642: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV294 @ SY2640 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY2641 ) @ SY2642 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV294 ) @ SY2641 ) @ SY2642 ) @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SY2641 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SY2642 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY2640 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(2587,plain,
! [SV295: $i] :
( ( ! [SY2643: $i,SY2644: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV295 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SY2643 @ SV295 @ SY2644 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2643 ) @ SV295 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY2644 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(2588,plain,
! [SV296: $i] :
( ( ! [SY2645: $i,SY2646: $i,SY2647: $i] :
( ( ( c_List_OtakeWhile @ SV296 @ SY2645 @ SY2646 )
= ( c_List_Otake @ SY2647 @ SY2645 @ SY2646 ) )
| ( c_HOL_Oord__class_Oless @ SY2647 @ ( c_Nat_Osize__class_Osize @ SY2645 @ ( tc_List_Olist @ SY2646 ) ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV296 @ ( c_List_Onth @ SY2645 @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV296 @ SY2647 @ SY2645 @ SY2646 ) @ SY2646 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1788]) ).
thf(2589,plain,
! [SV297: $i] :
( ( ! [SY2648: $i,SY2649: $i,SY2650: $i] :
( ( ( c_List_OtakeWhile @ SV297 @ SY2648 @ SY2649 )
= ( c_List_Otake @ SY2650 @ SY2648 @ SY2649 ) )
| ( hBOOL @ ( hAPP @ SV297 @ ( c_List_Onth @ SY2648 @ SY2650 @ SY2649 ) ) )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV297 @ SY2650 @ SY2648 @ SY2649 ) @ ( c_Nat_Osize__class_Osize @ SY2648 @ ( tc_List_Olist @ SY2649 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(2590,plain,
! [SV298: $i] :
( ( ! [SY2651: $i,SY2652: $i] :
( ( ( c_List_Ohd @ ( c_List_Odrop @ SV298 @ SY2651 @ SY2652 ) @ SY2652 )
= ( c_List_Onth @ SY2651 @ SV298 @ SY2652 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV298 @ ( c_Nat_Osize__class_Osize @ SY2651 @ ( tc_List_Olist @ SY2652 ) ) @ tc_nat )
| ( SY2651
= ( c_List_Olist_ONil @ SY2652 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1790]) ).
thf(2591,plain,
! [SV299: $i] :
( ( ! [SY2653: $i,SY2654: $i] :
( ( ( c_List_Olist_OCons @ ( c_List_Onth @ SV299 @ SY2653 @ SY2654 ) @ ( c_List_Odrop @ ( c_Suc @ SY2653 ) @ SV299 @ SY2654 ) @ SY2654 )
= ( c_List_Odrop @ SY2653 @ SV299 @ SY2654 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2653 @ ( c_Nat_Osize__class_Osize @ SV299 @ ( tc_List_Olist @ SY2654 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1791]) ).
thf(2592,plain,
! [SV300: $i] :
( ( ! [SY2655: $i,SY2656: $i,SY2657: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV300 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2655 @ SY2656 @ SV300 ) @ ( c_Power_Opower__class_Opower @ SY2657 @ SY2656 @ SV300 ) @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2656 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SY2655 @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ SY2655 @ SY2657 @ SV300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(2593,plain,
! [SV301: $i] :
( ( ! [SY2658: $i,SY2659: $i] :
( ( c_List_Orev @ ( c_List_Odrop @ SV301 @ SY2658 @ SY2659 ) @ SY2659 )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SY2658 @ ( tc_List_Olist @ SY2659 ) ) @ SV301 @ tc_nat ) @ ( c_List_Orev @ SY2658 @ SY2659 ) @ SY2659 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(2594,plain,
! [SV302: $i] :
( ( ! [SY2660: $i,SY2661: $i] :
( ( c_List_Orev @ ( c_List_Otake @ SV302 @ SY2660 @ SY2661 ) @ SY2661 )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SY2660 @ ( tc_List_Olist @ SY2661 ) ) @ SV302 @ tc_nat ) @ ( c_List_Orev @ SY2660 @ SY2661 ) @ SY2661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(2595,plain,
! [SV303: $i] :
( ( ! [SY2662: $i,SY2663: $i,SY2664: $i] :
( ( ( c_List_OtakeWhile @ SV303 @ SY2662 @ SY2663 )
= ( c_List_Otake @ SY2664 @ SY2662 @ SY2663 ) )
| ( hBOOL @ ( hAPP @ SV303 @ ( c_List_Onth @ SY2662 @ SY2664 @ SY2663 ) ) )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV303 @ SY2664 @ SY2662 @ SY2663 ) @ SY2664 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(2596,plain,
! [SV304: $i] :
( ( ! [SY2665: $i,SY2666: $i,SY2667: $i] :
( ( ( c_List_OtakeWhile @ SV304 @ SY2665 @ SY2666 )
= ( c_List_Otake @ SY2667 @ SY2665 @ SY2666 ) )
| ( c_HOL_Oord__class_Oless @ SY2667 @ ( c_Nat_Osize__class_Osize @ SY2665 @ ( tc_List_Olist @ SY2666 ) ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV304 @ SY2667 @ SY2665 @ SY2666 ) @ ( c_Nat_Osize__class_Osize @ SY2665 @ ( tc_List_Olist @ SY2666 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(2597,plain,
! [SV305: $i] :
( ( ! [SY2668: $i,SY2669: $i,SY2670: $i] :
( ( ( c_List_OtakeWhile @ SV305 @ SY2668 @ SY2669 )
= ( c_List_Otake @ SY2670 @ SY2668 @ SY2669 ) )
| ( c_HOL_Oord__class_Oless @ SY2670 @ ( c_Nat_Osize__class_Osize @ SY2668 @ ( tc_List_Olist @ SY2669 ) ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV305 @ SY2670 @ SY2668 @ SY2669 ) @ SY2670 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(2598,plain,
! [SV306: $i] :
( ( ! [SY2671: $i,SY2672: $i,SY2673: $i,SY2674: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV306 @ SY2671 @ SY2672 ) @ SY2673 @ SY2674 @ SY2672 )
= ( c_List_Oappend @ SV306 @ ( c_List_Olist__update @ SY2671 @ ( c_HOL_Ominus__class_Ominus @ SY2673 @ ( c_Nat_Osize__class_Osize @ SV306 @ ( tc_List_Olist @ SY2672 ) ) @ tc_nat ) @ SY2674 @ SY2672 ) @ SY2672 ) )
| ( c_HOL_Oord__class_Oless @ SY2673 @ ( c_Nat_Osize__class_Osize @ SV306 @ ( tc_List_Olist @ SY2672 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1800]) ).
thf(2599,plain,
! [SV307: $i] :
( ( ! [SY2675: $i,SY2676: $i,SY2677: $i] :
( ( ( c_List_Onth @ ( c_List_Oappend @ SV307 @ SY2675 @ SY2676 ) @ SY2677 @ SY2676 )
= ( c_List_Onth @ SY2675 @ ( c_HOL_Ominus__class_Ominus @ SY2677 @ ( c_Nat_Osize__class_Osize @ SV307 @ ( tc_List_Olist @ SY2676 ) ) @ tc_nat ) @ SY2676 ) )
| ( c_HOL_Oord__class_Oless @ SY2677 @ ( c_Nat_Osize__class_Osize @ SV307 @ ( tc_List_Olist @ SY2676 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(2600,plain,
! [SV308: $i] :
( ( ! [SY2678: $i,SY2679: $i,SY2680: $i] :
( ( c_in @ SV308 @ ( c_List_Oset @ ( c_List_Olist__update @ SY2678 @ SY2679 @ SV308 @ SY2680 ) @ SY2680 ) @ SY2680 )
| ~ ( c_HOL_Oord__class_Oless @ SY2679 @ ( c_Nat_Osize__class_Osize @ SY2678 @ ( tc_List_Olist @ SY2680 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2601,plain,
! [SV309: $i] :
( ( ! [SY2681: $i,SY2682: $i] :
( ( c_in @ ( c_List_Onth @ SV309 @ SY2681 @ SY2682 ) @ ( c_List_Oset @ SV309 @ SY2682 ) @ SY2682 )
| ~ ( c_HOL_Oord__class_Oless @ SY2681 @ ( c_Nat_Osize__class_Osize @ SV309 @ ( tc_List_Olist @ SY2682 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1803]) ).
thf(2602,plain,
! [SV310: $i] :
( ( ! [SY2683: $i,SY2684: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV310 @ ( c_Nat_Osize__class_Osize @ SY2683 @ ( tc_List_Olist @ SY2684 ) ) @ tc_nat )
| ( c_in @ ( c_List_Onth @ SY2683 @ SV310 @ SY2684 ) @ ( c_List_Oset @ SY2683 @ SY2684 ) @ SY2684 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(2603,plain,
! [SV311: $i] :
( ( ! [SY2685: $i,SY2686: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV311 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV311 ) @ ( c_Power_Opower__class_Opower @ SY2685 @ SY2686 @ SV311 ) @ SV311 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2686 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV311 ) @ SY2685 @ SV311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(2604,plain,
! [SV312: $i] :
( ( ! [SY2687: $i,SY2688: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV312 @ ( tc_List_Olist @ SY2687 ) ) @ tc_nat )
| ~ ( c_in @ SY2688 @ ( c_List_Oset @ SV312 @ SY2687 ) @ SY2687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1807]) ).
thf(2605,plain,
! [SV313: $i] :
( ( ! [SY2689: $i,SY2690: $i,SY2691: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV313 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2689 @ SY2690 @ SV313 ) @ ( c_Power_Opower__class_Opower @ SY2689 @ SY2691 @ SV313 ) @ SV313 )
| ~ ( c_HOL_Oord__class_Oless @ SY2689 @ ( c_HOL_Oone__class_Oone @ SV313 ) @ SV313 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV313 ) @ SY2689 @ SV313 )
| ~ ( c_HOL_Oord__class_Oless @ SY2691 @ SY2690 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(2606,plain,
! [SV314: $i] :
( ( ! [SY2692: $i,SY2693: $i,SY2694: $i,SY2695: $i,SY2696: $i] :
( ( c_List_Omap @ SV314 @ ( c_List_Olist__update @ SY2692 @ SY2693 @ SY2694 @ SY2695 ) @ SY2695 @ SY2696 )
= ( c_List_Olist__update @ ( c_List_Omap @ SV314 @ SY2692 @ SY2695 @ SY2696 ) @ SY2693 @ ( hAPP @ SV314 @ SY2694 ) @ SY2696 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(2607,plain,
! [SV315: $i] :
( ( ! [SY2697: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV315 ) ) @ ( c_Lambda_OdB_OAbs @ SY2697 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV315 ) @ SY2697 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(2608,plain,
! [SV316: $i] :
( ( ! [SY2698: $i,SY2699: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ SV316 @ SY2698 @ SY2699 ) @ SY2699 )
= ( c_List_Oappend @ ( c_List_Orev @ SY2698 @ SY2699 ) @ ( c_List_Orev @ SV316 @ SY2699 ) @ SY2699 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(2609,plain,
! [SV317: $i] :
( ( ! [SY2700: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV317 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ SY2700 @ SV317 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV317 ) @ SY2700 ) @ SY2700 ) @ SV317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(2610,plain,
! [SV318: $i] :
( ( ! [SY2701: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV318 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV318 ) @ SY2701 ) @ SY2701 ) @ SV318 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ SY2701 @ SV318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1814]) ).
thf(2611,plain,
! [SV319: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV319 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV319 ) @ ( c_HOL_Ozero__class_Ozero @ SV319 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV319 ) )
= ( c_HOL_Ozero__class_Ozero @ SV319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(2612,plain,
! [SV320: $i] :
( ( ! [SY2702: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV320 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ ( c_HOL_Ozero__class_Ozero @ SV320 ) ) @ SY2702 )
= SY2702 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1820]) ).
thf(2613,plain,
! [SV321: $i] :
( ( ! [SY2703: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV321 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV321 ) @ ( c_HOL_Ozero__class_Ozero @ SV321 ) ) @ SY2703 )
= SY2703 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1821]) ).
thf(2614,plain,
! [SV322: $i] :
( ( ! [SY2704: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV322 )
| ~ ( class_Int_Onumber__ring @ SV322 )
| ( SY2704
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV322 ) @ SY2704 ) @ ( c_HOL_Ozero__class_Ozero @ SV322 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1822]) ).
thf(2615,plain,
! [SV323: $i] :
( ( ! [SY2705: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV323 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV323 ) @ SY2705 ) @ ( c_HOL_Ozero__class_Ozero @ SV323 ) )
= SY2705 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1823]) ).
thf(2616,plain,
! [SV324: $i] :
( ( ! [SY2706: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV324 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV324 ) @ ( c_HOL_Ozero__class_Ozero @ SV324 ) ) @ SY2706 )
= SY2706 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(2617,plain,
! [SV325: $i] :
( ( ! [SY2707: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV325 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV325 ) @ SY2707 ) @ ( c_HOL_Ozero__class_Ozero @ SV325 ) )
= SY2707 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(2618,plain,
! [SV326: $i] :
( ( ! [SY2708: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV326 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV326 ) @ SY2708 ) @ ( c_HOL_Ozero__class_Ozero @ SV326 ) )
= SY2708 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2619,plain,
! [SV327: $i] :
( ( ! [SY2709: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV327 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ ( c_HOL_Ozero__class_Ozero @ SV327 ) ) @ SY2709 )
= SY2709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(2620,plain,
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1828]) ).
thf(2621,plain,
! [SV328: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV328 @ tc_nat )
| ( SV328
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(2622,plain,
! [SV329: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV329 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(2623,plain,
! [SV330: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV330 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(2624,plain,
! [SV331: $i] :
( ( ! [SY2710: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV331 @ SY2710 )
= SV331 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(2625,plain,
! [SV332: $i] :
( ( ! [SY2711: $i,SY2712: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV332 @ SY2711 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2712 @ SY2711 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1833]) ).
thf(2626,plain,
! [SV333: $i] :
( ( ! [SY2713: $i,SY2714: $i,SY2715: $i,SY2716: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV333 @ SY2713 @ SY2714 ) @ ( c_List_Olist_OCons @ SY2715 @ SY2716 @ SY2714 ) @ SY2714 )
= ( c_List_Olist_OCons @ SV333 @ ( c_List_Olist_OCons @ SY2715 @ ( c_List_Osplice @ SY2713 @ SY2716 @ SY2714 ) @ SY2714 ) @ SY2714 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(2627,plain,
! [SV334: $i] :
( ( ! [SY2717: $i,SY2718: $i,SY2719: $i] :
( ~ ( class_Orderings_Olinorder @ SV334 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY2717 @ SY2718 @ SV334 ) @ SV334 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY2719 @ ( c_List_Olist_OCons @ SY2717 @ SY2718 @ SV334 ) @ SV334 ) @ SV334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(2628,plain,
! [SV335: $i] :
( ( ! [SY2720: $i,SY2721: $i,SY2722: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV335 @ SY2720 @ SY2721 ) @ SY2722 @ SY2721 )
= ( c_List_Olist_OCons @ SV335 @ ( c_List_Oappend @ SY2720 @ SY2722 @ SY2721 ) @ SY2721 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(2629,plain,
! [SV336: $i] :
( ( ! [SY2723: $i,SY2724: $i,SY2725: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV336 @ SY2723 @ SY2724 ) @ SY2725 @ SY2724 )
= ( c_List_Olist_OCons @ SV336 @ ( c_List_Oappend @ SY2723 @ SY2725 @ SY2724 ) @ SY2724 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(2630,plain,
! [SV337: $i] :
( ( ! [SY2726: $i,SY2727: $i,SY2728: $i,SY2729: $i] :
( ( c_List_Omap @ SV337 @ ( c_List_Olist_OCons @ SY2726 @ SY2727 @ SY2728 ) @ SY2728 @ SY2729 )
= ( c_List_Olist_OCons @ ( hAPP @ SV337 @ SY2726 ) @ ( c_List_Omap @ SV337 @ SY2727 @ SY2728 @ SY2729 ) @ SY2729 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(2631,plain,
! [SV338: $i] :
( ( ! [SY2730: $i,SY2731: $i,SY2732: $i,SY2733: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ SV338 @ SY2730 ) @ ( c_List_Omap @ SV338 @ SY2731 @ SY2732 @ SY2733 ) @ SY2733 )
= ( c_List_Omap @ SV338 @ ( c_List_Olist_OCons @ SY2730 @ SY2731 @ SY2732 ) @ SY2732 @ SY2733 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(2632,plain,
! [SV339: $i] :
( ( ! [SY2734: $i,SY2735: $i,SY2736: $i,SY2737: $i] :
( ( c_List_Omap @ SV339 @ ( c_List_Olist_OCons @ SY2734 @ SY2735 @ SY2736 ) @ SY2736 @ SY2737 )
= ( c_List_Olist_OCons @ ( hAPP @ SV339 @ SY2734 ) @ ( c_List_Omap @ SV339 @ SY2735 @ SY2736 @ SY2737 ) @ SY2737 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1843]) ).
thf(2633,plain,
! [SV340: $i] :
( ( ! [SY2738: $i,SY2739: $i,SY2740: $i] :
( ( c_List_Olist_OCons @ SV340 @ ( c_List_Oappend @ SY2738 @ SY2739 @ SY2740 ) @ SY2740 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV340 @ SY2738 @ SY2740 ) @ SY2739 @ SY2740 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1844]) ).
thf(2634,plain,
! [SV341: $i] :
( ( ! [SY2741: $i,SY2742: $i,SY2743: $i] :
( ( c_List_Olist_OCons @ SV341 @ ( c_List_Oappend @ SY2741 @ SY2742 @ SY2743 ) @ SY2743 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV341 @ SY2741 @ SY2743 ) @ SY2742 @ SY2743 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(2635,plain,
! [SV342: $i] :
( ( ! [SY2744: $i,SY2745: $i] :
( ~ ( class_Orderings_Olinorder @ SV342 )
| ( c_List_Olinorder__class_Osorted @ SY2744 @ SV342 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY2745 @ SY2744 @ SV342 ) @ SV342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(2636,plain,
! [SV343: $i] :
( ( ! [SY2746: $i,SY2747: $i,SY2748: $i] :
( ( ( c_List_OtakeWhile @ SV343 @ ( c_List_Olist_OCons @ SY2746 @ SY2747 @ SY2748 ) @ SY2748 )
= ( c_List_Olist_OCons @ SY2746 @ ( c_List_OtakeWhile @ SV343 @ SY2747 @ SY2748 ) @ SY2748 ) )
| ~ ( hBOOL @ ( hAPP @ SV343 @ SY2746 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(2637,plain,
! [SV344: $i] :
( ( ! [SY2749: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV344 @ ( tc_List_Olist @ SY2749 ) ) @ tc_nat )
| ( SV344
= ( c_List_Olist_ONil @ SY2749 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(2638,plain,
! [SV345: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ SV345 ) @ ( tc_List_Olist @ SV345 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(2639,plain,
! [SV346: $i] :
( ( ! [SY2750: $i,SY2751: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ SV346 @ ( c_List_Olist_OCons @ SY2750 @ ( c_List_Olist_ONil @ SY2751 ) @ SY2751 ) @ SY2751 ) @ SY2751 )
= SY2750 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(2640,plain,
! [SV347: $i] :
( ( ! [SY2752: $i,SY2753: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ SV347 @ ( c_List_Olist_OCons @ SY2752 @ ( c_List_Olist_ONil @ SY2753 ) @ SY2753 ) @ SY2753 ) @ SY2753 )
= SV347 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(2641,plain,
! [SV348: $i] :
( ( ! [SY2754: $i,SY2755: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ SV348 @ SY2754 @ SY2755 ) @ SY2755 )
= ( c_List_Oappend @ ( c_List_Orev @ SY2754 @ SY2755 ) @ ( c_List_Olist_OCons @ SV348 @ ( c_List_Olist_ONil @ SY2755 ) @ SY2755 ) @ SY2755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(2642,plain,
! [SV349: $i] :
( ( ! [SY2756: $i,SY2757: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ SV349 @ SY2756 ) @ ( c_List_Olist_OCons @ SY2757 @ ( c_List_Olist_ONil @ SY2756 ) @ SY2756 ) @ SY2756 ) @ SY2756 )
= ( c_List_Olist_OCons @ SY2757 @ SV349 @ SY2756 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2643,plain,
! [SV350: $i] :
( ( ! [SY2758: $i,SY2759: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV350 @ SY2758 @ SY2759 ) @ ( c_List_Olist_OCons @ SY2758 @ ( c_List_Olist_ONil @ SY2759 ) @ SY2759 ) @ SY2759 )
= ( c_List_Olist_OCons @ SY2758 @ ( c_List_Oreplicate @ SV350 @ SY2758 @ SY2759 ) @ SY2759 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(2644,plain,
! [SV351: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV351 ) @ ( c_List_Olist_ONil @ SV351 ) @ SV351 )
= ( c_List_Olist_ONil @ SV351 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2645,plain,
! [SV352: $i] :
( ( ( c_List_Olist_ONil @ SV352 )
= ( c_List_Orev @ ( c_List_Olist_ONil @ SV352 ) @ SV352 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1858]) ).
thf(2646,plain,
! [SV353: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_ONil @ SV353 ) @ SV353 )
= ( c_List_Olist_ONil @ SV353 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(2647,plain,
! [SV354: $i] :
( ( ! [SY2760: $i] :
( ( c_List_OtakeWhile @ SV354 @ ( c_List_Olist_ONil @ SY2760 ) @ SY2760 )
= ( c_List_Olist_ONil @ SY2760 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(2648,plain,
! [SV355: $i] :
( ( ! [SY2761: $i] :
( ( c_List_Osplice @ SV355 @ ( c_List_Olist_ONil @ SY2761 ) @ SY2761 )
= SV355 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1865]) ).
thf(2649,plain,
! [SV356: $i] :
( ( ! [SY2762: $i] :
( ( c_List_Osplice @ ( c_List_Olist_ONil @ SV356 ) @ SY2762 @ SV356 )
= SY2762 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(2650,plain,
! [SV357: $i] :
( ( ! [SY2763: $i] :
( ( c_List_Odrop @ SV357 @ ( c_List_Olist_ONil @ SY2763 ) @ SY2763 )
= ( c_List_Olist_ONil @ SY2763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1872]) ).
thf(2651,plain,
! [SV358: $i] :
( ( ! [SY2764: $i] :
( SV358
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY2764 ) @ SV358 @ SY2764 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(2652,plain,
! [SV359: $i] :
( ( ! [SY2765: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV359 ) @ SY2765 @ SV359 )
= SY2765 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(2653,plain,
! [SV360: $i] :
( ( ! [SY2766: $i] :
( SV360
= ( c_List_Oappend @ SV360 @ ( c_List_Olist_ONil @ SY2766 ) @ SY2766 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1876]) ).
thf(2654,plain,
! [SV361: $i] :
( ( ! [SY2767: $i] :
( SV361
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY2767 ) @ SV361 @ SY2767 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(2655,plain,
! [SV362: $i] :
( ( ! [SY2768: $i] :
( ( c_List_Oappend @ SV362 @ ( c_List_Olist_ONil @ SY2768 ) @ SY2768 )
= SV362 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(2656,plain,
! [SV363: $i] :
( ( ! [SY2769: $i] :
( ( c_List_Otake @ SV363 @ ( c_List_Olist_ONil @ SY2769 ) @ SY2769 )
= ( c_List_Olist_ONil @ SY2769 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(2657,plain,
! [SV364: $i] :
( ( ! [SY2770: $i] : ( c_List_Olistsp @ SV364 @ ( c_List_Olist_ONil @ SY2770 ) @ SY2770 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(2658,plain,
! [SV365: $i] :
( ( ! [SY2771: $i,SY2772: $i] :
( ( c_List_Omap @ SV365 @ ( c_List_Olist_ONil @ SY2771 ) @ SY2771 @ SY2772 )
= ( c_List_Olist_ONil @ SY2772 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2659,plain,
! [SV366: $i] :
( ( ! [SY2773: $i] :
( ( c_List_Osublist @ ( c_List_Olist_ONil @ SV366 ) @ SY2773 @ SV366 )
= ( c_List_Olist_ONil @ SV366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2660,plain,
! [SV367: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV367 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ SV367 ) @ SV367 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2661,plain,
! [SV368: $i] :
( ( ! [SY2774: $i,SY2775: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV368 ) @ SY2774 @ SY2775 @ SV368 )
= ( c_List_Olist_ONil @ SV368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2662,plain,
! [SV369: $i] :
( ( ! [SY2776: $i,SY2777: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV369 ) @ SY2776 @ SY2777 @ SV369 )
= ( c_List_Olist_ONil @ SV369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2663,plain,
! [SV370: $i] :
( ( ! [SY2778: $i,SY2779: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV370 ) @ SY2778 @ SY2779 @ SV370 )
= ( c_List_Olist_ONil @ SV370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2664,plain,
! [SV371: $i] :
( ( ! [SY2780: $i,SY2781: $i] :
( ( c_List_Olist_ONil @ SV371 )
= ( c_List_Omap @ SY2780 @ ( c_List_Olist_ONil @ SY2781 ) @ SY2781 @ SV371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(2665,plain,
! [SV372: $i] :
( ( ( c_List_Olist_ONil @ SV372 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV372 ) @ ( c_List_Olist_ONil @ SV372 ) @ SV372 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2666,plain,
! [SV373: $i] :
( ( ( c_List_Orev @ ( c_List_Olist_ONil @ SV373 ) @ SV373 )
= ( c_List_Olist_ONil @ SV373 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1890]) ).
thf(2667,plain,
! [SV374: $i] :
( ( ! [SY2782: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV374 )
| ( ( c_List_Olistsum @ SY2782 @ SV374 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV374 ) @ ( c_HOL_Ozero__class_Ozero @ SV374 ) @ SY2782 @ SV374 @ SV374 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(2668,plain,
! [SV375: $i] :
( ( ! [SY2783: $i,SY2784: $i,SY2785: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV375 ) @ SY2783 ) ) @ SY2784 ) @ SY2785 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV375 ) @ SY2784 ) @ SY2785 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY2783 ) @ SY2784 ) @ SY2785 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2669,plain,
! [SV376: $i] :
( ( ! [SY2786: $i,SY2787: $i,SY2788: $i,SY2789: $i,SY2790: $i] :
( ~ ( hBOOL @ ( hAPP @ SV376 @ ( c_Lambda_OdB_OdB__case @ SY2786 @ SY2787 @ SY2788 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2789 ) @ SY2790 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SY2787 @ SY2789 ) @ SY2790 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2670,plain,
! [SV377: $i] :
( ( ! [SY2791: $i,SY2792: $i,SY2793: $i,SY2794: $i,SY2795: $i] :
( ~ ( hBOOL @ ( hAPP @ SV377 @ ( c_Lambda_OdB_OdB__case @ SY2791 @ SY2792 @ SY2793 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2794 ) @ SY2795 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV377 @ ( hAPP @ ( hAPP @ SY2792 @ SY2794 ) @ SY2795 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1897]) ).
thf(2671,plain,
! [SV378: $i] :
( ( ! [SY2796: $i,SY2797: $i,SY2798: $i,SY2799: $i,SY2800: $i] :
( ( c_Lambda_OdB_OdB__case @ SV378 @ SY2796 @ SY2797 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2798 ) @ SY2799 ) @ SY2800 )
= ( hAPP @ ( hAPP @ SY2796 @ SY2798 ) @ SY2799 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2672,plain,
! [SV379: $i] :
( ( ! [SY2801: $i,SY2802: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV379 ) @ SY2801 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV379 ) @ SY2802 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY2801 ) @ SY2802 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1899]) ).
thf(2673,plain,
! [SV380: $i] :
( ( ! [SY2803: $i,SY2804: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV380 ) @ SY2803 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2804 ) @ SY2803 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV380 ) @ SY2804 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(2674,plain,
! [SV381: $i] :
( ( ! [SY2805: $i,SY2806: $i,SY2807: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV381 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SY2805 ) @ SY2806 ) @ SY2807 @ SV381 @ SV381 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SY2805 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SY2806 @ SY2807 @ SV381 @ SV381 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(2675,plain,
! [SV382: $i] :
( ( ! [SY2808: $i,SY2809: $i,SY2810: $i,SY2811: $i,SY2812: $i] :
( ( c_List_Ofoldl @ SV382 @ SY2808 @ ( c_List_Oappend @ SY2809 @ SY2810 @ SY2811 ) @ SY2812 @ SY2811 )
= ( c_List_Ofoldl @ SV382 @ ( c_List_Ofoldl @ SV382 @ SY2808 @ SY2809 @ SY2812 @ SY2811 ) @ SY2810 @ SY2812 @ SY2811 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2676,plain,
! [SV383: $i] :
( ( ! [SY2813: $i,SY2814: $i,SY2815: $i,SY2816: $i] :
( ~ ( hBOOL @ ( hAPP @ SV383 @ ( c_Lambda_OdB_OdB__case @ SY2813 @ SY2814 @ SY2815 @ ( c_Lambda_OdB_OVar @ SY2816 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV383 @ ( hAPP @ SY2813 @ SY2816 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(2677,plain,
! [SV384: $i] :
( ( ! [SY2817: $i,SY2818: $i,SY2819: $i,SY2820: $i] :
( ~ ( hBOOL @ ( hAPP @ SV384 @ ( c_Lambda_OdB_OdB__case @ SY2817 @ SY2818 @ SY2819 @ ( c_Lambda_OdB_OVar @ SY2820 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV384 @ ( hAPP @ SY2817 @ SY2820 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2678,plain,
! [SV385: $i] :
( ( ! [SY2821: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV385 ) ) @ SY2821 ) @ SV385 )
= SY2821 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2679,plain,
! [SV386: $i] :
( ( ! [SY2822: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV386 ) ) @ SY2822 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(2680,plain,
! [SV387: $i] :
( ( ! [SY2823: $i,SY2824: $i,SY2825: $i] :
( ( c_List_Orev @ ( c_List_Omap @ SV387 @ SY2823 @ SY2824 @ SY2825 ) @ SY2825 )
= ( c_List_Omap @ SV387 @ ( c_List_Orev @ SY2823 @ SY2824 ) @ SY2824 @ SY2825 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(2681,plain,
! [SV388: $i] :
( ( ! [SY2826: $i,SY2827: $i] :
( ~ ( class_Orderings_Olinorder @ SV388 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ SY2826 @ SY2827 @ SV388 ) @ SV388 )
| ~ ( c_List_Olinorder__class_Osorted @ SY2827 @ SV388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2682,plain,
! [SV389: $i] :
( ( ! [SY2828: $i,SY2829: $i,SY2830: $i] :
( ( c_List_Onth @ ( c_List_Oappend @ SV389 @ ( c_List_Olist_OCons @ SY2828 @ SY2829 @ SY2830 ) @ SY2830 ) @ ( c_Nat_Osize__class_Osize @ SV389 @ ( tc_List_Olist @ SY2830 ) ) @ SY2830 )
= SY2828 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(2683,plain,
! [SV390: $i] :
( ( ! [SY2831: $i,SY2832: $i] :
( ( c_List_OtakeWhile @ SV390 @ SY2831 @ SY2832 )
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ SV390 @ SY2831 @ SY2832 ) @ ( tc_List_Olist @ SY2832 ) ) @ SY2831 @ SY2832 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2684,plain,
! [SV391: $i] :
( ( ! [SY2833: $i,SY2834: $i] :
( ~ ( hBOOL @ ( hAPP @ SV391 @ ( c_List_Onth @ SY2833 @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ SV391 @ SY2833 @ SY2834 ) @ ( tc_List_Olist @ SY2834 ) ) @ SY2834 ) ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ SV391 @ SY2833 @ SY2834 ) @ ( tc_List_Olist @ SY2834 ) ) @ ( c_Nat_Osize__class_Osize @ SY2833 @ ( tc_List_Olist @ SY2834 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2685,plain,
! [SV392: $i] :
( ( ! [SY2835: $i] :
( SV392
= ( c_List_Orev @ ( c_List_Orev @ SV392 @ SY2835 ) @ SY2835 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2686,plain,
! [SV393: $i] :
( ( ! [SY2836: $i] :
( ( c_List_Orev @ ( c_List_Orev @ SV393 @ SY2836 ) @ SY2836 )
= SV393 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2687,plain,
! [SV394: $i] :
( ( ! [SY2837: $i] :
( ( c_List_Orev @ ( c_List_Orev @ SV394 @ SY2837 ) @ SY2837 )
= SV394 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2688,plain,
! [SV395: $i] :
( ( ! [SY2838: $i] :
( ( ( c_List_Oappend @ ( c_List_Obutlast @ SV395 @ SY2838 ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ SV395 @ SY2838 ) @ ( c_List_Olist_ONil @ SY2838 ) @ SY2838 ) @ SY2838 )
= SV395 )
| ( SV395
= ( c_List_Olist_ONil @ SY2838 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(2689,plain,
! [SV396: $i] :
( ( ! [SY2839: $i,SY2840: $i] :
( SV396
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV396 @ ( tc_List_Olist @ SY2839 ) ) @ ( c_List_Oappend @ SV396 @ SY2840 @ SY2839 ) @ SY2839 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2690,plain,
! [SV397: $i] :
( ( ! [SY2841: $i,SY2842: $i,SY2843: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ SV397 @ SY2841 @ SY2842 @ SY2843 ) @ ( tc_List_Olist @ SY2843 ) )
= ( c_Nat_Osize__class_Osize @ SY2841 @ ( tc_List_Olist @ SY2842 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2691,plain,
! [SV398: $i] :
( ( ! [SY2844: $i,SY2845: $i,SY2846: $i,SY2847: $i] :
( ( c_List_Omap @ SV398 @ ( c_List_Oreplicate @ SY2844 @ SY2845 @ SY2846 ) @ SY2846 @ SY2847 )
= ( c_List_Oreplicate @ SY2844 @ ( hAPP @ SV398 @ SY2845 ) @ SY2847 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2692,plain,
! [SV399: $i] :
( ( ! [SY2848: $i,SY2849: $i,SY2850: $i] :
( ( ( c_List_Onth @ ( c_List_Oappend @ SV399 @ SY2848 @ SY2849 ) @ SY2850 @ SY2849 )
= ( c_List_Onth @ SV399 @ SY2850 @ SY2849 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2850 @ ( c_Nat_Osize__class_Osize @ SV399 @ ( tc_List_Olist @ SY2849 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2693,plain,
! [SV400: $i] :
( ( ! [SY2851: $i,SY2852: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV400 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV400 ) @ SY2851 ) @ SY2852 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV400 ) @ SY2852 ) @ SY2851 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1925]) ).
thf(2694,plain,
! [SV401: $i] :
( ( ! [SY2853: $i,SY2854: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV401 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV401 ) @ SY2853 ) @ SY2854 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV401 ) @ SY2854 ) @ SY2853 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1926]) ).
thf(2695,plain,
! [SV402: $i] :
( ( ! [SY2855: $i,SY2856: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV402 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV402 ) @ SY2855 ) @ SY2856 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV402 ) @ SY2856 ) @ SY2855 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2696,plain,
! [SV403: $i] :
( ( ! [SY2857: $i,SY2858: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ SV403 @ SY2857 @ SY2858 ) @ SY2858 )
= ( c_List_Oreplicate @ SV403 @ SY2857 @ SY2858 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2697,plain,
! [SV404: $i] :
( ( ! [SY2859: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV404 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV404 ) @ SY2859 ) @ SY2859 ) @ ( c_HOL_Ozero__class_Ozero @ SV404 ) @ SV404 )
| ~ ( c_HOL_Oord__class_Oless @ SY2859 @ ( c_HOL_Ozero__class_Ozero @ SV404 ) @ SV404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2698,plain,
! [SV405: $i] :
( ( ! [SY2860: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV405 )
| ( c_HOL_Oord__class_Oless @ SY2860 @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SV405 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV405 ) @ SY2860 ) @ SY2860 ) @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SV405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2699,plain,
! [SV406: $i] :
( ( ! [SY2861: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV406 )
| ( c_HOL_Oord__class_Oless @ SY2861 @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV406 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV406 ) @ SY2861 ) @ SY2861 ) @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2700,plain,
! [SV407: $i] :
( ( ! [SY2862: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV407 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV407 ) @ SY2862 ) @ SY2862 ) @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 )
| ~ ( c_HOL_Oord__class_Oless @ SY2862 @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2701,plain,
! [SV408: $i] :
( ( ! [SY2863: $i,SY2864: $i,SY2865: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV408 @ ( c_Nat_Osize__class_Osize @ SY2863 @ ( tc_List_Olist @ SY2864 ) ) @ tc_nat )
| ( ( c_List_Onth @ ( c_List_Olist__update @ SY2863 @ SV408 @ SY2865 @ SY2864 ) @ SV408 @ SY2864 )
= SY2865 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2702,plain,
! [SV409: $i] :
( ( ! [SY2866: $i,SY2867: $i,SY2868: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ SV409 @ SY2866 @ SY2867 @ SY2868 ) @ SY2866 @ SY2868 )
= SY2867 )
| ~ ( c_HOL_Oord__class_Oless @ SY2866 @ ( c_Nat_Osize__class_Osize @ SV409 @ ( tc_List_Olist @ SY2868 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2703,plain,
! [SV410: $i] :
( ( ! [SY2869: $i,SY2870: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV410 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV410 ) @ ( c_Power_Opower__class_Opower @ SY2869 @ SY2870 @ SV410 ) @ SV410 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV410 ) @ SY2869 @ SV410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2704,plain,
! [SV411: $i] :
( ( ! [SY2871: $i,SY2872: $i] :
( ( ( c_List_Olast @ ( c_List_Odrop @ SV411 @ SY2871 @ SY2872 ) @ SY2872 )
= ( c_List_Olast @ SY2871 @ SY2872 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV411 @ ( c_Nat_Osize__class_Osize @ SY2871 @ ( tc_List_Olist @ SY2872 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2705,plain,
! [SV412: $i] :
( ( ! [SY2873: $i,SY2874: $i] :
( ( ( c_List_Otake @ SV412 @ ( c_List_Obutlast @ SY2873 @ SY2874 ) @ SY2874 )
= ( c_List_Otake @ SV412 @ SY2873 @ SY2874 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV412 @ ( c_Nat_Osize__class_Osize @ SY2873 @ ( tc_List_Olist @ SY2874 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2706,plain,
! [SV413: $i] :
( ( ! [SY2875: $i,SY2876: $i,SY2877: $i,SY2878: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV413 @ SY2875 @ SY2876 ) @ SY2877 @ SY2878 @ SY2876 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV413 @ SY2877 @ SY2878 @ SY2876 ) @ SY2875 @ SY2876 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2877 @ ( c_Nat_Osize__class_Osize @ SV413 @ ( tc_List_Olist @ SY2876 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2707,plain,
! [SV414: $i] :
( ( ! [SY2879: $i,SY2880: $i,SY2881: $i,SY2882: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV414 @ SY2879 @ SY2880 ) @ SY2881 @ SY2882 @ SY2880 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV414 @ SY2881 @ SY2882 @ SY2880 ) @ SY2879 @ SY2880 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2881 @ ( c_Nat_Osize__class_Osize @ SV414 @ ( tc_List_Olist @ SY2880 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2708,plain,
! [SV415: $i] :
( ( ! [SY2883: $i,SY2884: $i,SY2885: $i] :
( ( ( c_List_Onth @ ( c_List_Oreplicate @ SV415 @ SY2883 @ SY2884 ) @ SY2885 @ SY2884 )
= SY2883 )
| ~ ( c_HOL_Oord__class_Oless @ SY2885 @ SV415 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2709,plain,
! [SV416: $i] :
( ( ! [SY2886: $i,SY2887: $i,SY2888: $i,SY2889: $i] :
( ( ( c_List_OtakeWhile @ SV416 @ ( c_List_Oappend @ SY2886 @ ( c_List_Olist_OCons @ SY2887 @ SY2888 @ SY2889 ) @ SY2889 ) @ SY2889 )
= ( c_List_OtakeWhile @ SV416 @ SY2886 @ SY2889 ) )
| ( hBOOL @ ( hAPP @ SV416 @ SY2887 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2710,plain,
! [SV417: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV417 @ SV417 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2711,plain,
! [SV418: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV418 @ SV418 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2712,plain,
! [SV419: $i] :
( ( ! [SY2890: $i] :
( ~ ( class_Orderings_Oorder @ SV419 )
| ~ ( c_HOL_Oord__class_Oless @ SY2890 @ SY2890 @ SV419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2713,plain,
! [SV420: $i] :
( ( ! [SY2891: $i] :
( ~ ( class_Orderings_Olinorder @ SV420 )
| ~ ( c_HOL_Oord__class_Oless @ SY2891 @ SY2891 @ SV420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2714,plain,
! [SV421: $i] :
( ( ! [SY2892: $i] :
( ~ ( class_Orderings_Opreorder @ SV421 )
| ~ ( c_HOL_Oord__class_Oless @ SY2892 @ SY2892 @ SV421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2715,plain,
! [SV422: $i] :
( ( ! [SY2893: $i,SY2894: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ SV422 @ SY2893 @ SY2894 ) @ SY2894 )
= ( c_List_Olast @ SY2893 @ SY2894 ) )
| ( SY2893
= ( c_List_Olist_ONil @ SY2894 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2716,plain,
! [SV423: $i] :
( ( ! [SY2895: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV423 ) ) @ SY2895 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV423 ) @ SY2895 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2717,plain,
! [SV424: $i] :
( ( ! [SY2896: $i,SY2897: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV424 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SY2896 ) @ SY2897 ) @ SV424 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SY2897 @ SV424 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SY2896 @ SV424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(2718,plain,
! [SV425: $i] :
( ( ! [SY2898: $i,SY2899: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV425 )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SY2898 @ SY2899 @ SV425 ) @ SV425 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV425 ) @ SY2898 ) @ ( c_List_Olistsum @ SY2899 @ SV425 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2719,plain,
! [SV426: $i] :
( ( ! [SY2900: $i,SY2901: $i,SY2902: $i,SY2903: $i] :
( ( c_List_Omap @ SV426 @ ( c_List_Oappend @ SY2900 @ SY2901 @ SY2902 ) @ SY2902 @ SY2903 )
= ( c_List_Oappend @ ( c_List_Omap @ SV426 @ SY2900 @ SY2902 @ SY2903 ) @ ( c_List_Omap @ SV426 @ SY2901 @ SY2902 @ SY2903 ) @ SY2903 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2720,plain,
! [SV427: $i] :
( ( ! [SY2904: $i,SY2905: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV427 )
| ( c_HOL_Oord__class_Oless @ SY2904 @ SY2905 @ SV427 )
| ( c_HOL_Oord__class_Oless @ SY2905 @ SY2904 @ SV427 )
| ( SY2905 = SY2904 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2721,plain,
! [SV428: $i] :
( ( ! [SY2906: $i,SY2907: $i] :
( ~ ( class_Orderings_Olinorder @ SV428 )
| ( SY2906 = SY2907 )
| ( c_HOL_Oord__class_Oless @ SY2907 @ SY2906 @ SV428 )
| ( c_HOL_Oord__class_Oless @ SY2906 @ SY2907 @ SV428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2722,plain,
! [SV429: $i] :
( ( ! [SY2908: $i] :
( ( c_HOL_Oord__class_Oless @ SV429 @ SY2908 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY2908 @ SV429 @ tc_nat )
| ( SY2908 = SV429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2723,plain,
! [SV430: $i] :
( ( ! [SY2909: $i,SY2910: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV430 @ SY2909 ) @ SY2910 ) )
| ( c_HOL_Oord__class_Oless @ SY2909 @ SY2910 @ tc_nat )
| ( SY2910 = SY2909 )
| ( c_HOL_Oord__class_Oless @ SY2910 @ SY2909 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2724,plain,
! [SV431: $i] :
( ( ! [SY2911: $i] :
( ( c_HOL_Oord__class_Oless @ SV431 @ SY2911 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY2911 @ SV431 @ tc_nat )
| ( SY2911 = SV431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2725,plain,
! [SV432: $i] :
( ( ! [SY2912: $i,SY2913: $i] :
( ~ ( class_Orderings_Olinorder @ SV432 )
| ( c_HOL_Oord__class_Oless @ SY2912 @ SY2913 @ SV432 )
| ( c_HOL_Oord__class_Oless @ SY2913 @ SY2912 @ SV432 )
| ( SY2913 = SY2912 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(2726,plain,
! [SV433: $i] :
( ( ! [SY2914: $i,SY2915: $i,SY2916: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV433 @ SY2914 @ SY2915 ) @ ( c_List_Oreplicate @ SY2916 @ SY2914 @ SY2915 ) @ SY2915 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SY2916 @ SY2914 @ SY2915 ) @ ( c_List_Oreplicate @ SV433 @ SY2914 @ SY2915 ) @ SY2915 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2727,plain,
! [SV434: $i] :
( ( ! [SY2917: $i,SY2918: $i] :
( ~ ( class_Orderings_Olinorder @ SV434 )
| ( c_HOL_Oord__class_Oless @ SY2917 @ SY2918 @ SV434 )
| ( SY2918 = SY2917 )
| ( c_HOL_Oord__class_Oless @ SY2918 @ SY2917 @ SV434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2728,plain,
! [SV435: $i] :
( ( ! [SY2919: $i,SY2920: $i] :
( ~ ( class_Orderings_Olinorder @ SV435 )
| ( SY2919 = SY2920 )
| ( c_HOL_Oord__class_Oless @ SY2919 @ SY2920 @ SV435 )
| ( c_HOL_Oord__class_Oless @ SY2920 @ SY2919 @ SV435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2729,plain,
! [SV436: $i] :
( ( ! [SY2921: $i,SY2922: $i,SY2923: $i,SY2924: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV436 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV436 ) @ SY2921 ) @ SY2922 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV436 ) @ SY2923 ) @ SY2924 ) @ SV436 )
| ~ ( c_HOL_Oord__class_Oless @ SY2922 @ SY2924 @ SV436 )
| ~ ( c_HOL_Oord__class_Oless @ SY2921 @ SY2923 @ SV436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2730,plain,
! [SV437: $i] :
( ( ! [SY2925: $i,SY2926: $i,SY2927: $i,SY2928: $i] :
( ( ( c_List_Onth @ ( c_List_Omap @ SV437 @ SY2925 @ SY2926 @ SY2927 ) @ SY2928 @ SY2927 )
= ( hAPP @ SV437 @ ( c_List_Onth @ SY2925 @ SY2928 @ SY2926 ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2928 @ ( c_Nat_Osize__class_Osize @ SY2925 @ ( tc_List_Olist @ SY2926 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(2731,plain,
! [SV438: $i] :
( ( ! [SY2929: $i,SY2930: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV438 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2929 @ SV438 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2930 @ SV438 ) @ SV438 )
| ~ ( c_HOL_Oord__class_Oless @ SY2929 @ SY2930 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2732,plain,
! [SV439: $i] :
( ( ! [SY2931: $i,SY2932: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV439 )
| ( c_HOL_Oord__class_Oless @ SY2931 @ SY2932 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2931 @ SV439 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2932 @ SV439 ) @ SV439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2733,plain,
! [SV440: $i] :
( ( ! [SY2933: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV440 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV440 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2933 @ SV440 ) @ SV440 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2933 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2734,plain,
! [SV441: $i] :
( ( ! [SY2934: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV441 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2934 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV441 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2934 @ SV441 ) @ SV441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2735,plain,
! [SV442: $i] :
( ( ! [SY2935: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ SV442 @ ( c_List_Olist_ONil @ SY2935 ) @ SY2935 ) @ SY2935 )
= ( c_List_Olast @ SV442 @ SY2935 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2736,plain,
! [SV443: $i] :
( ( ! [SY2936: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV443 )
| ( ( c_List_Olistsum @ ( c_List_Orev @ SY2936 @ SV443 ) @ SV443 )
= ( c_List_Olistsum @ SY2936 @ SV443 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2737,plain,
! [SV444: $i] :
( ( ! [SY2937: $i,SY2938: $i,SY2939: $i] :
( ( c_List_Olistsp @ SV444 @ ( c_List_Oappend @ SY2937 @ SY2938 @ SY2939 ) @ SY2939 )
| ~ ( c_List_Olistsp @ SV444 @ SY2938 @ SY2939 )
| ~ ( c_List_Olistsp @ SV444 @ SY2937 @ SY2939 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2738,plain,
! [SV445: $i] :
( ( ! [SY2940: $i,SY2941: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ SV445 @ SY2940 @ SY2941 ) @ ( tc_List_Olist @ SY2941 ) )
= SV445 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2739,plain,
! [SV446: $i] :
( ( ! [SY2942: $i,SY2943: $i] :
( ( c_List_Olist__update @ SV446 @ SY2942 @ ( c_List_Onth @ SV446 @ SY2942 @ SY2943 ) @ SY2943 )
= SV446 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2740,plain,
! [SV447: $i] :
( ( ! [SY2944: $i,SY2945: $i,SY2946: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV447 )
| ( c_HOL_Oord__class_Oless @ SY2944 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV447 ) @ SY2945 ) @ SY2946 ) @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ SY2944 @ SY2946 @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SY2945 @ SV447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2741,plain,
! [SV448: $i] :
( ( ! [SY2947: $i,SY2948: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV448 ) ) @ SY2947 ) @ SY2948 )
= ( c_Lambda_OdB_OVar @ SV448 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV448 @ SY2948 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2742,plain,
! [SV449: $i] :
( ( ! [SY2949: $i,SY2950: $i,SY2951: $i,SY2952: $i] :
( ~ ( hBOOL @ ( hAPP @ SV449 @ ( c_Lambda_OdB_OdB__case @ SY2949 @ SY2950 @ SY2951 @ ( c_Lambda_OdB_OAbs @ SY2952 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV449 @ ( hAPP @ SY2951 @ SY2952 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2743,plain,
! [SV450: $i] :
( ( ! [SY2953: $i,SY2954: $i,SY2955: $i,SY2956: $i] :
( ~ ( hBOOL @ ( hAPP @ SV450 @ ( c_Lambda_OdB_OdB__case @ SY2953 @ SY2954 @ SY2955 @ ( c_Lambda_OdB_OAbs @ SY2956 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV450 @ ( hAPP @ SY2955 @ SY2956 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2744,plain,
! [SV451: $i] :
( ( ! [SY2957: $i,SY2958: $i,SY2959: $i,SY2960: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV451 @ ( c_List_Olist_OCons @ SY2957 @ SY2958 @ SY2959 ) @ SY2959 ) @ ( c_Nat_Osize__class_Osize @ SV451 @ ( tc_List_Olist @ SY2959 ) ) @ SY2960 @ SY2959 )
= ( c_List_Oappend @ SV451 @ ( c_List_Olist_OCons @ SY2960 @ SY2958 @ SY2959 ) @ SY2959 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2745,plain,
! [SV452: $i] :
( ( ! [SY2961: $i,SY2962: $i,SY2963: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV452 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV452 ) @ SY2961 ) @ SY2962 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV452 ) @ SY2963 ) @ SY2962 ) @ SV452 )
| ~ ( c_HOL_Oord__class_Oless @ SY2961 @ SY2963 @ SV452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2746,plain,
! [SV453: $i] :
( ( ! [SY2964: $i,SY2965: $i,SY2966: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV453 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV453 ) @ SY2964 ) @ SY2965 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV453 ) @ SY2966 ) @ SY2965 ) @ SV453 )
| ~ ( c_HOL_Oord__class_Oless @ SY2964 @ SY2966 @ SV453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2747,plain,
! [SV454: $i] :
( ( ! [SY2967: $i,SY2968: $i,SY2969: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV454 )
| ( c_HOL_Oord__class_Oless @ SY2967 @ SY2968 @ SV454 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV454 ) @ SY2967 ) @ SY2969 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV454 ) @ SY2968 ) @ SY2969 ) @ SV454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1984]) ).
thf(2748,plain,
! [SV455: $i] :
( ( ! [SY2970: $i,SY2971: $i,SY2972: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV455 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV455 ) @ SY2970 ) @ SY2971 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV455 ) @ SY2970 ) @ SY2972 ) @ SV455 )
| ~ ( c_HOL_Oord__class_Oless @ SY2971 @ SY2972 @ SV455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(2749,plain,
! [SV456: $i] :
( ( ! [SY2973: $i,SY2974: $i,SY2975: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV456 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV456 ) @ SY2973 ) @ SY2974 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV456 ) @ SY2973 ) @ SY2975 ) @ SV456 )
| ~ ( c_HOL_Oord__class_Oless @ SY2974 @ SY2975 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2750,plain,
! [SV457: $i] :
( ( ! [SY2976: $i,SY2977: $i,SY2978: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV457 )
| ( c_HOL_Oord__class_Oless @ SY2976 @ SY2977 @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SY2978 ) @ SY2976 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SY2978 ) @ SY2977 ) @ SV457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2751,plain,
! [SV458: $i] :
( ( ! [SY2979: $i,SY2980: $i,SY2981: $i] :
( ( c_Type_Otyping @ SV458 @ SY2979 @ SY2980 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY2981 ) @ SY2979 ) )
| ~ ( c_Type_Otyping @ SV458 @ SY2981 @ SY2980 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1990]) ).
thf(2752,plain,
! [SV459: $i] :
( ( ! [SY2982: $i,SY2983: $i] :
( ~ ( class_Orderings_Olinorder @ SV459 )
| ( c_List_Olinorder__class_Osorted @ SY2982 @ SV459 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SY2982 @ SY2983 @ SV459 ) @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2753,plain,
! [SV460: $i] :
( ( ! [SY2984: $i,SY2985: $i] :
( ~ ( class_Orderings_Olinorder @ SV460 )
| ( c_List_Olinorder__class_Osorted @ SY2984 @ SV460 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SY2985 @ SY2984 @ SV460 ) @ SV460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2754,plain,
! [SV461: $i] :
( ( ! [SY2986: $i,SY2987: $i,SY2988: $i,SY2989: $i,SY2990: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV461 @ SY2986 @ SY2987 @ SY2988 ) @ SY2989 @ SY2990 @ SY2988 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV461 @ SY2989 @ SY2990 @ SY2988 ) @ SY2986 @ SY2987 @ SY2988 ) )
| ( SY2986 = SY2989 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2755,plain,
! [SV462: $i] :
( ( ! [SY2991: $i,SY2992: $i,SY2993: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV462 @ SY2991 @ SY2992 ) @ ( c_List_Olist_OCons @ SY2991 @ SY2993 @ SY2992 ) @ SY2992 )
= ( c_List_Olist_OCons @ SY2991 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV462 @ SY2991 @ SY2992 ) @ SY2993 @ SY2992 ) @ SY2992 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1994]) ).
thf(2756,plain,
! [SV463: $i] :
( ( ! [SY2994: $i,SY2995: $i,SY2996: $i,SY2997: $i] :
( ( c_List_Odrop @ SV463 @ ( c_List_Omap @ SY2994 @ SY2995 @ SY2996 @ SY2997 ) @ SY2997 )
= ( c_List_Omap @ SY2994 @ ( c_List_Odrop @ SV463 @ SY2995 @ SY2996 ) @ SY2996 @ SY2997 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2757,plain,
! [SV464: $i] :
( ( ! [SY2998: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ SV464 @ SY2998 ) @ ( tc_List_Olist @ SY2998 ) )
= ( c_Nat_Osize__class_Osize @ SV464 @ ( tc_List_Olist @ SY2998 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2758,plain,
! [SV465: $i] :
( ( ! [SY2999: $i,SY3000: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV465 @ SY2999 @ SY3000 ) @ SY3000 )
= ( c_List_Oappend @ SV465 @ ( c_List_Obutlast @ SY2999 @ SY3000 ) @ SY3000 ) )
| ( SY2999
= ( c_List_Olist_ONil @ SY3000 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2759,plain,
! [SV466: $i] :
( ( ! [SY3001: $i,SY3002: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV466 )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ SY3001 @ SY3002 @ SV466 ) @ SV466 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV466 ) @ ( c_List_Olistsum @ SY3001 @ SV466 ) ) @ ( c_List_Olistsum @ SY3002 @ SV466 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2760,plain,
! [SV467: $i] :
( ( ! [SY3003: $i,SY3004: $i,SY3005: $i,SY3006: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ SV467 @ SY3003 @ SY3004 @ SY3005 ) @ SY3006 @ SY3005 )
= ( c_List_Onth @ SV467 @ SY3006 @ SY3005 ) )
| ( SY3003 = SY3006 )
| ~ ( c_HOL_Oord__class_Oless @ SY3003 @ ( c_Nat_Osize__class_Osize @ SV467 @ ( tc_List_Olist @ SY3005 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2761,plain,
! [SV468: $i] :
( ( ! [SY3007: $i,SY3008: $i,SY3009: $i,SY3010: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV468 @ SY3007 @ SY3008 @ SY3009 ) @ SY3007 @ SY3010 @ SY3009 )
= ( c_List_Olist__update @ SV468 @ SY3007 @ SY3010 @ SY3009 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2762,plain,
! [SV469: $i] :
( ( ! [SY3011: $i,SY3012: $i,SY3013: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV469 @ SY3011 @ SY3012 ) @ SY3013 @ SY3012 )
= ( c_List_Oappend @ SV469 @ ( c_List_Oappend @ SY3011 @ SY3013 @ SY3012 ) @ SY3012 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(2763,plain,
! [SV470: $i] :
( ( ! [SY3014: $i,SY3015: $i,SY3016: $i] :
( ( c_List_Oappend @ SV470 @ ( c_List_Oappend @ SY3014 @ SY3015 @ SY3016 ) @ SY3016 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV470 @ SY3014 @ SY3016 ) @ SY3015 @ SY3016 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2764,plain,
! [SV471: $i] :
( ( ! [SY3017: $i,SY3018: $i,SY3019: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV471 @ SY3017 @ SY3018 ) @ SY3019 @ SY3018 )
= ( c_List_Oappend @ SV471 @ ( c_List_Oappend @ SY3017 @ SY3019 @ SY3018 ) @ SY3018 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2765,plain,
! [SV472: $i] :
( ( ! [SY3020: $i,SY3021: $i,SY3022: $i] :
( ( c_List_Oappend @ SV472 @ ( c_List_Oappend @ SY3020 @ SY3021 @ SY3022 ) @ SY3022 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV472 @ SY3020 @ SY3022 ) @ SY3021 @ SY3022 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2766,plain,
! [SV473: $i] :
( ( ! [SY3023: $i,SY3024: $i] :
( ~ ( class_Orderings_Oorder @ SV473 )
| ~ ( c_HOL_Oord__class_Oless @ SY3023 @ SY3024 @ SV473 )
| ~ ( c_HOL_Oord__class_Oless @ SY3024 @ SY3023 @ SV473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2767,plain,
! [SV474: $i] :
( ( ! [SY3025: $i,SY3026: $i] :
( ~ ( class_Orderings_Olinorder @ SV474 )
| ~ ( c_HOL_Oord__class_Oless @ SY3025 @ SY3026 @ SV474 )
| ~ ( c_HOL_Oord__class_Oless @ SY3026 @ SY3025 @ SV474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2768,plain,
! [SV475: $i] :
( ( ! [SY3027: $i,SY3028: $i] :
( ~ ( class_Orderings_Opreorder @ SV475 )
| ~ ( c_HOL_Oord__class_Oless @ SY3027 @ SY3028 @ SV475 )
| ~ ( c_HOL_Oord__class_Oless @ SY3028 @ SY3027 @ SV475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2769,plain,
! [SV476: $i] :
( ( ! [SY3029: $i,SY3030: $i] :
( ~ ( class_Orderings_Opreorder @ SV476 )
| ~ ( c_HOL_Oord__class_Oless @ SY3029 @ SY3030 @ SV476 )
| ~ ( c_HOL_Oord__class_Oless @ SY3030 @ SY3029 @ SV476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2770,plain,
! [SV477: $i] :
( ( ! [SY3031: $i,SY3032: $i] :
( ( ( hAPP @ SV477 @ SY3031 )
= SY3032 )
| ~ ( c_Type_Otyping @ SV477 @ ( c_Lambda_OdB_OVar @ SY3031 ) @ SY3032 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2009]) ).
thf(2771,plain,
! [SV478: $i] :
( ( ! [SY3033: $i,SY3034: $i,SY3035: $i,SY3036: $i] :
( ( c_Lambda_OdB_OdB__case @ SV478 @ SY3033 @ SY3034 @ ( c_Lambda_OdB_OVar @ SY3035 ) @ SY3036 )
= ( hAPP @ SV478 @ SY3035 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2010]) ).
thf(2772,plain,
! [SV479: $i] :
( ( ! [SY3037: $i] : ( c_Type_Otyping @ SV479 @ ( c_Lambda_OdB_OVar @ SY3037 ) @ ( hAPP @ SV479 @ SY3037 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2011]) ).
thf(2773,plain,
! [SV480: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV480 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV480 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2774,plain,
! [SV481: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV481 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2775,plain,
! [SV482: $i] :
( ( ! [SY3038: $i,SY3039: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV482 ) @ SY3038 ) ) @ SY3039 ) @ SY3038 )
= SV482 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2015]) ).
thf(2776,plain,
! [SV483: $i] :
( ( ! [SY3040: $i,SY3041: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV483 ) @ SY3040 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY3041 ) @ SY3040 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV483 ) @ SY3041 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(2777,plain,
! [SV484: $i] :
( ( ! [SY3042: $i,SY3043: $i] :
( ( ( c_List_Osublist @ ( c_List_Olist_OCons @ SV484 @ ( c_List_Olist_ONil @ SY3042 ) @ SY3042 ) @ SY3043 @ SY3042 )
= ( c_List_Olist_OCons @ SV484 @ ( c_List_Olist_ONil @ SY3042 ) @ SY3042 ) )
| ~ ( c_in @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3043 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2017]) ).
thf(2778,plain,
! [SV485: $i] :
( ( ! [SY3044: $i,SY3045: $i] :
( ( ( c_List_Osublist @ ( c_List_Olist_OCons @ SV485 @ ( c_List_Olist_ONil @ SY3044 ) @ SY3044 ) @ SY3045 @ SY3044 )
= ( c_List_Olist_ONil @ SY3044 ) )
| ( c_in @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3045 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2779,plain,
! [SV486: $i] :
( ( ! [SY3046: $i,SY3047: $i] :
( ( SV486
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY3046 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SY3046 @ SY3047 @ SV486 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY3046 ) @ SY3047 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV486 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2020]) ).
thf(2780,plain,
! [SV487: $i] :
( ( ! [SY3048: $i,SY3049: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV487 @ SY3048 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY3049 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV487 ) @ SY3049 ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ SY3049 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY3048 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2781,plain,
! [SV488: $i] :
( ( ! [SY3050: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV488 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV488 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV488 )
| ~ ( class_Power_Opower @ SV488 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV488 ) @ SY3050 @ SV488 )
= ( c_HOL_Ozero__class_Ozero @ SV488 ) )
| ( SY3050
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2782,plain,
! [SV489: $i] :
( ( ! [SY3051: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ SV489 )
| ~ ( class_Power_Opower @ SV489 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SY3051 @ SV489 )
= ( c_HOL_Ozero__class_Ozero @ SV489 ) )
| ( SY3051
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2783,plain,
! [SV490: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV490 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV490 )
= ( c_HOL_Ozero__class_Ozero @ SV490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2784,plain,
! [SV491: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV491 )
| ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ SV491 ) @ SV491 )
= ( c_HOL_Ozero__class_Ozero @ SV491 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2785,plain,
! [SV492: $i] :
( ( ! [SY3052: $i,SY3053: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ SV492 @ SY3052 @ SY3053 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3053 )
= SV492 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2786,plain,
! [SV493: $i] :
( ( ! [SY3054: $i,SY3055: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ SV493 @ SY3054 @ SY3055 ) @ SY3055 )
= ( c_List_Olist_OCons @ SV493 @ SY3054 @ SY3055 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2787,plain,
! [SV494: $i] :
( ( ! [SY3056: $i,SY3057: $i,SY3058: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV494 @ SY3056 @ SY3057 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3058 @ SY3057 )
= ( c_List_Olist_OCons @ SY3058 @ SY3056 @ SY3057 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2788,plain,
! [SV495: $i] :
( ( ! [SY3059: $i] :
( ( c_List_Olist_Olist__size @ SV495 @ ( c_List_Olist_ONil @ SY3059 ) @ SY3059 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2030]) ).
thf(2789,plain,
! [SV496: $i] :
( ( ! [SY3060: $i] :
( ( c_List_Olist_Olist__size @ SV496 @ ( c_List_Olist_ONil @ SY3060 ) @ SY3060 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(2790,plain,
! [SV497: $i] :
( ( ! [SY3061: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV497 @ SY3061 )
= ( c_List_Olist_ONil @ SY3061 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2791,plain,
! [SV498: $i] :
( ( ! [SY3062: $i] :
( ( c_List_Olist_ONil @ SV498 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3062 @ SV498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(2792,plain,
! [SV499: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ SV499 ) @ ( tc_List_Olist @ SV499 ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2793,plain,
! [SV500: $i] :
( ( ( c_List_Olength__unique @ ( c_List_Olist_ONil @ SV500 ) @ SV500 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2794,plain,
! [SV501: $i] :
( ( ! [SY3063: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV501 @ SY3063 )
= ( c_List_Olist_ONil @ SY3063 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2795,plain,
! [SV502: $i] :
( ( ! [SY3064: $i,SY3065: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV502 ) @ ( c_List_Olist_OCons @ SY3064 @ SY3065 @ SV502 ) @ SV502 )
= ( c_List_Olist_OCons @ SY3064 @ SY3065 @ SV502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2796,plain,
! [SV503: $i] :
( ( ! [SY3066: $i,SY3067: $i,SY3068: $i] :
( ~ ( class_Orderings_Olinorder @ SV503 )
| ( ( c_List_Olinorder__class_Oinsort__key @ SY3066 @ SY3067 @ ( c_List_Olist_ONil @ SY3068 ) @ SY3068 @ SV503 )
= ( c_List_Olist_OCons @ SY3067 @ ( c_List_Olist_ONil @ SY3068 ) @ SY3068 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2797,plain,
! [SV504: $i] :
( ( ! [SY3069: $i,SY3070: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV504 @ SY3069 @ SY3070 ) @ SY3070 )
= ( c_List_Olist_OCons @ SV504 @ ( c_List_Obutlast @ SY3069 @ SY3070 ) @ SY3070 ) )
| ( SY3069
= ( c_List_Olist_ONil @ SY3070 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2798,plain,
! [SV505: $i] :
( ( ! [SY3071: $i] :
( ( c_List_Olast @ ( c_List_Olist_OCons @ SV505 @ ( c_List_Olist_ONil @ SY3071 ) @ SY3071 ) @ SY3071 )
= SV505 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2799,plain,
! [SV506: $i] :
( ( ! [SY3072: $i] :
( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV506 @ ( c_List_Olist_ONil @ SY3072 ) @ SY3072 ) @ SY3072 )
= ( c_List_Olist_ONil @ SY3072 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2800,plain,
! [SV507: $i] :
( ( ! [SY3073: $i,SY3074: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV507 @ SY3073 @ SY3074 ) @ ( c_List_Olist_ONil @ SY3074 ) @ SY3074 )
= ( c_List_Olist_OCons @ SV507 @ SY3073 @ SY3074 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2801,plain,
! [SV508: $i] :
( ( ! [SY3075: $i,SY3076: $i,SY3077: $i] :
( ( ( c_List_OtakeWhile @ SV508 @ ( c_List_Olist_OCons @ SY3075 @ SY3076 @ SY3077 ) @ SY3077 )
= ( c_List_Olist_ONil @ SY3077 ) )
| ( hBOOL @ ( hAPP @ SV508 @ SY3075 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2802,plain,
! [SV509: $i] :
( ( ! [SY3078: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ SV509 @ ( c_List_Olist_ONil @ SY3078 ) @ SY3078 ) @ SY3078 )
= ( c_List_Olist_OCons @ SV509 @ ( c_List_Olist_ONil @ SY3078 ) @ SY3078 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2803,plain,
! [SV510: $i] :
( ( ! [SY3079: $i,SY3080: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV510 @ SY3079 @ SY3080 ) @ SY3080 )
= ( c_List_Olast @ SY3079 @ SY3080 ) )
| ( SY3079
= ( c_List_Olist_ONil @ SY3080 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2804,plain,
! [SV511: $i] :
( ( ! [SY3081: $i,SY3082: $i] :
( ( c_List_Olist_OCons @ SV511 @ SY3081 @ SY3082 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY3082 ) @ ( c_List_Olist_OCons @ SV511 @ SY3081 @ SY3082 ) @ SY3082 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(2805,plain,
! [SV512: $i] :
( ( ! [SY3083: $i] :
( ( c_List_Olist_OCons @ SV512 @ ( c_List_Olist_ONil @ SY3083 ) @ SY3083 )
= ( c_List_Orev @ ( c_List_Olist_OCons @ SV512 @ ( c_List_Olist_ONil @ SY3083 ) @ SY3083 ) @ SY3083 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2055]) ).
thf(2806,plain,
! [SV513: $i] :
( ( ! [SY3084: $i] :
( ~ ( class_Orderings_Olinorder @ SV513 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY3084 @ ( c_List_Olist_ONil @ SV513 ) @ SV513 ) @ SV513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2056]) ).
thf(2807,plain,
! [SV514: $i] :
( ( ! [SY3085: $i,SY3086: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV514 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SY3085 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ ( c_HOL_Ozero__class_Ozero @ SV514 ) @ SY3086 @ SV514 @ SV514 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SY3085 @ SY3086 @ SV514 @ SV514 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2057]) ).
thf(2808,plain,
! [SV515: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OVar @ SV515 ) @ tc_Lambda_OdB )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2058]) ).
thf(2809,plain,
! [SV516: $i] :
( ( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OVar @ SV516 ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2810,plain,
! [SV517: $i] :
( ( ! [SY3087: $i,SY3088: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV517 @ SY3087 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3088 @ SY3087 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV517 ) @ SY3088 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2811,plain,
! [SV518: $i] :
( ( ! [SY3089: $i,SY3090: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV518 ) ) @ SY3089 ) @ SY3090 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY3089 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV518 ) @ SY3089 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY3090 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2812,plain,
! [SV519: $i] :
( ( ! [SY3091: $i,SY3092: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV519 ) @ ( c_Lambda_OdB_OVar @ SY3091 ) ) @ SY3092 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV519 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2813,plain,
! [SV520: $i] :
( ( ! [SY3093: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV520 ) ) @ SY3093 )
= ( c_Lambda_OdB_OVar @ SV520 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV520 @ SY3093 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2814,plain,
! [SV521: $i] :
( ( ! [SY3094: $i,SY3095: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ SV521 @ SY3094 @ SY3095 ) @ SY3095 )
= ( c_List_Olist_ONil @ SY3095 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2815,plain,
! [SV522: $i] :
( ( ! [SY3096: $i,SY3097: $i,SY3098: $i,SY3099: $i] :
( ( SV522 = SY3096 )
| ~ ( c_Type_Otyping @ SY3097 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY3098 ) @ SY3099 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY3096 )
| ~ ( c_Type_Otyping @ SY3097 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY3098 ) @ SY3099 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(2816,plain,
! [SV523: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV523 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV523 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2817,plain,
! [SV524: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV524 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV524 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2818,plain,
! [SV525: $i] :
( ( ! [SY3100: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV525 ) @ SY3100 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SY3100 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2819,plain,
! [SV526: $i] :
( ( ! [SY3101: $i,SY3102: $i] :
( ( ( c_List_Oappend @ SV526 @ ( c_List_Olist_OCons @ SY3101 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3102 @ SV526 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY3101 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3102 @ ( c_List_Oappend @ SV526 @ ( c_List_Olist_OCons @ SY3101 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2079]) ).
thf(2820,plain,
! [SV527: $i] :
( ( ! [SY3103: $i,SY3104: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV527 @ SY3103 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY3104 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV527 @ ( c_List_Oappend @ SY3103 @ ( c_List_Olist_OCons @ SY3104 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(2821,plain,
! [SV528: $i] :
( ( ! [SY3105: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV528 ) @ SY3105 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV528 ) @ SY3105 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2822,plain,
! [SV529: $i] :
( ( ! [SY3106: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV529 ) @ SY3106 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV529 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2094]) ).
thf(2823,plain,
! [SV530: $i] :
( ( ! [SY3107: $i,SY3108: $i,SY3109: $i] :
( ( c_List_Ofoldl @ SV530 @ SY3107 @ ( c_List_Olist_ONil @ SY3108 ) @ SY3109 @ SY3108 )
= SY3107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2095]) ).
thf(2824,plain,
! [SV531: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ SV531 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2825,plain,
! [SV532: $i] :
( ( ! [SY3110: $i,SY3111: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV532 ) @ SY3110 ) ) @ SY3111 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV532 ) @ SY3111 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY3110 ) @ SY3111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2826,plain,
! [SV533: $i] :
( ( ( c_Lambda_OdB_OVar @ SV533 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV533 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2099]) ).
thf(2827,plain,
! [SV534: $i] :
( ( ! [SY3112: $i,SY3113: $i,SY3114: $i,SY3115: $i,SY3116: $i] :
( ( c_List_Ofoldl @ SV534 @ SY3112 @ ( c_List_Olist_OCons @ SY3113 @ SY3114 @ SY3115 ) @ SY3116 @ SY3115 )
= ( c_List_Ofoldl @ SV534 @ ( hAPP @ ( hAPP @ SV534 @ SY3112 ) @ SY3113 ) @ SY3114 @ SY3116 @ SY3115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2828,plain,
! [SV535: $i] :
( ( ! [SY3117: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV535 ) @ ( c_Lambda_OdB_OVar @ SY3117 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV535 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2107]) ).
thf(2829,plain,
! [SV536: $i] :
( ( ! [SY3118: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ SV536 @ SY3118 ) )
| ~ ( class_Orderings_Opreorder @ SY3118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2110]) ).
thf(2830,plain,
! [SV537: $i] :
( ( ! [SY3119: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ SV537 @ SY3119 ) )
| ~ ( class_Orderings_Oorder @ SY3119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2111]) ).
thf(2831,plain,
! [SV538: $i] :
( ( ! [SY3120: $i] : ( c_fequal @ SV538 @ SV538 @ SY3120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2172]) ).
thf(2832,plain,
! [SV539: $i] :
( ( ! [SY3121: $i,SY3122: $i] :
( ( SV539 = SY3121 )
| ~ ( c_fequal @ SV539 @ SY3121 @ SY3122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2173]) ).
thf(2833,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[2174]) ).
thf(2834,plain,
! [SV540: $i] :
( ( ! [SY3123: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV540 )
!= ( c_Lambda_OdB_OAbs @ SY3123 ) )
| ( SV540 = SY3123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2175]) ).
thf(2835,plain,
! [SV541: $i] :
( ( ! [SY3124: $i,SY3125: $i,SY3126: $i,SY3127: $i] :
( ( ( c_List_Oreplicate @ SV541 @ SY3124 @ SY3125 )
!= ( c_List_Oreplicate @ SY3126 @ SY3127 @ SY3125 ) )
| ( SV541 = SY3126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2176]) ).
thf(2836,plain,
! [SV542: $i] :
( ( ! [SY3128: $i,SY3129: $i] :
( ( SV542
!= ( c_List_Oappend @ SY3128 @ SV542 @ SY3129 ) )
| ( SY3128
= ( c_List_Olist_ONil @ SY3129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2177]) ).
thf(2837,plain,
! [SV543: $i] :
( ( ! [SY3130: $i,SY3131: $i,SY3132: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV543 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV543 ) @ SY3130 ) @ SY3131 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV543 ) @ SY3132 ) @ SY3131 ) )
| ( SY3130 = SY3132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2838,plain,
! [SV544: $i] :
( ( ! [SY3133: $i,SY3134: $i] :
( ( c_List_Olist_OCons @ SV544 @ SY3133 @ SY3134 )
!= ( c_List_Olist_ONil @ SY3134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(2839,plain,
! [SV545: $i] :
( ( ! [SY3135: $i,SY3136: $i] :
( ( ( c_List_Odrop @ SV545 @ SY3135 @ SY3136 )
!= ( c_List_Olist_ONil @ SY3136 ) )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SY3135 @ ( tc_List_Olist @ SY3136 ) ) @ SV545 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2180]) ).
thf(2840,plain,
! [SV546: $i] :
( ( ! [SY3137: $i] :
( ( ( c_Lambda_OdB_OVar @ SV546 )
!= ( c_Lambda_OdB_OVar @ SY3137 ) )
| ( SV546 = SY3137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2181]) ).
thf(2841,plain,
! [SV547: $i] :
( ( ! [SY3138: $i,SY3139: $i] :
( ( ( c_Lambda_OdB_OVar @ SV547 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3138 @ SY3139 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV547 )
= SY3138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2182]) ).
thf(2842,plain,
! [SV548: $i] :
( ( ! [SY3140: $i] :
( ( c_Lambda_OdB_OAbs @ SV548 )
!= ( c_Lambda_OdB_OVar @ SY3140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2183]) ).
thf(2843,plain,
! [SV549: $i] :
( ( ! [SY3141: $i,SY3142: $i] :
( ( SV549
!= ( c_List_Oappend @ SV549 @ SY3141 @ SY3142 ) )
| ( SY3141
= ( c_List_Olist_ONil @ SY3142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2184]) ).
thf(2844,plain,
! [SV550: $i] :
( ( ! [SY3143: $i,SY3144: $i,SY3145: $i,SY3146: $i] :
( ( ( c_List_Oappend @ SV550 @ ( c_List_Olist_OCons @ SY3143 @ ( c_List_Olist_ONil @ SY3144 ) @ SY3144 ) @ SY3144 )
!= ( c_List_Oappend @ SY3145 @ ( c_List_Olist_OCons @ SY3146 @ ( c_List_Olist_ONil @ SY3144 ) @ SY3144 ) @ SY3144 ) )
| ( SV550 = SY3145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2185]) ).
thf(2845,plain,
! [SV551: $i] :
( ( ! [SY3147: $i,SY3148: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV551 ) @ SY3147 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3148 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV551 ) @ SY3147 )
= SY3148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2846,plain,
! [SV552: $i] :
( ( ! [SY3149: $i,SY3150: $i,SY3151: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV552 ) @ SY3149 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3150 @ SY3151 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY3151
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV552 @ SY3149 @ SY3150 @ SY3151 ) @ ( c_List_Olist_OCons @ SY3149 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SY3151
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2187]) ).
thf(2847,plain,
! [SV553: $i] :
( ( ! [SY3152: $i,SY3153: $i,SY3154: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV553 ) @ SY3152 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY3153 ) @ SY3154 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV553 = SY3153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2188]) ).
thf(2848,plain,
! [SV554: $i] :
( ( ! [SY3155: $i,SY3156: $i,SY3157: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV554 )
| ( ( c_Power_Opower__class_Opower @ SY3155 @ SY3156 @ SV554 )
!= ( c_Power_Opower__class_Opower @ SY3157 @ SY3156 @ SV554 ) )
| ( SY3155 = SY3157 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3156 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SY3157 @ SV554 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SY3155 @ SV554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(2849,plain,
! [SV555: $i] :
( ( ! [SY3158: $i,SY3159: $i] :
( ( c_List_Olist_ONil @ SV555 )
!= ( c_List_Olist_OCons @ SY3158 @ SY3159 @ SV555 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2190]) ).
thf(2850,plain,
! [SV556: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SV556 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(2851,plain,
! [SV557: $i] :
( ( ! [SY3160: $i] :
( ( ( c_Suc @ SV557 )
!= ( c_Suc @ SY3160 ) )
| ( SV557 = SY3160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(2852,plain,
! [SV558: $i] :
( ( ! [SY3161: $i,SY3162: $i,SY3163: $i] :
( ( ( c_List_Oappend @ SV558 @ SY3161 @ SY3162 )
!= ( c_List_Oappend @ SV558 @ SY3163 @ SY3162 ) )
| ( SY3161 = SY3163 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2193]) ).
thf(2853,plain,
! [SV559: $i] :
( ( ! [SY3164: $i,SY3165: $i,SY3166: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV559 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3164 @ SY3165 @ SV559 )
!= ( c_HOL_Ominus__class_Ominus @ SY3166 @ SY3166 @ SV559 ) )
| ( SY3164 = SY3165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(2854,plain,
! [SV560: $i] :
( ( ! [SY3167: $i,SY3168: $i,SY3169: $i] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV560 @ ( tc_List_Olist @ SY3167 ) ) @ SY3168 @ SY3167 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SY3168 @ ( tc_List_Olist @ SY3167 ) ) @ SV560 @ SY3167 ) @ SY3169 @ SY3167 ) @ SY3167 )
!= SY3169 )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV560 @ ( tc_List_Olist @ SY3167 ) ) @ SY3168 @ SY3167 )
!= SV560 )
| ( SY3168
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SY3168 @ ( tc_List_Olist @ SY3167 ) ) @ SV560 @ SY3167 ) )
| ( ( c_List_Oappend @ SY3168 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SY3168 @ ( tc_List_Olist @ SY3167 ) ) @ SV560 @ SY3167 ) @ SY3169 @ SY3167 ) @ SY3167 )
= ( c_List_Oappend @ SV560 @ SY3169 @ SY3167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2195]) ).
thf(2855,plain,
! [SV561: $i] :
( ( ! [SY3170: $i] :
( ( ( c_Suc @ SV561 )
!= ( c_Suc @ SY3170 ) )
| ( SV561 = SY3170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2196]) ).
thf(2856,plain,
! [SV562: $i] :
( ( ! [SY3171: $i,SY3172: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV562 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3171 @ SY3172 @ SV562 )
!= ( c_HOL_Ozero__class_Ozero @ SV562 ) )
| ( SY3171 = SY3172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2857,plain,
! [SV563: $i] :
( ( ! [SY3173: $i,SY3174: $i] :
( ( ( c_List_Olist_ONil @ SV563 )
!= ( c_List_Oappend @ SY3173 @ SY3174 @ SV563 ) )
| ( SY3174
= ( c_List_Olist_ONil @ SV563 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2198]) ).
thf(2858,plain,
! [SV564: $i] :
( ( ! [SY3175: $i,SY3176: $i,SY3177: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV564 ) @ SY3175 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY3176 ) @ SY3177 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY3175 = SY3177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2199]) ).
thf(2859,plain,
! [SV565: $i] :
( ( ! [SY3178: $i,SY3179: $i] :
( ( ( c_Lambda_OdB_OVar @ SV565 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3178 @ SY3179 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY3179
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(2860,plain,
! [SV566: $i] :
( ( ! [SY3180: $i,SY3181: $i] :
( ( c_Lambda_OdB_OVar @ SV566 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3180 ) @ SY3181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2201]) ).
thf(2861,plain,
! [SV567: $i] :
( ( ! [SY3182: $i,SY3183: $i] :
( ( c_List_Olist_OCons @ SV567 @ SY3182 @ SY3183 )
!= ( c_List_Olist_ONil @ SY3183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2202]) ).
thf(2862,plain,
! [SV568: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV568 )
| ( ( c_HOL_Oone__class_Oone @ SV568 )
!= ( c_HOL_Ozero__class_Ozero @ SV568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2203]) ).
thf(2863,plain,
! [SV569: $i] :
( ( ! [SY3184: $i,SY3185: $i,SY3186: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV569 ) @ SY3184 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY3185 ) @ SY3186 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV569 = SY3185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2204]) ).
thf(2864,plain,
! [SV570: $i] :
( ( ! [SY3187: $i,SY3188: $i,SY3189: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV570 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV570 ) @ SY3187 ) @ SY3188 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV570 ) @ SY3187 ) @ SY3189 ) )
| ( SY3188 = SY3189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2865,plain,
! [SV571: $i] :
( ( ! [SY3190: $i,SY3191: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV571 ) @ SY3190 )
!= ( c_Lambda_OdB_OVar @ SY3191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2206]) ).
thf(2866,plain,
! [SV572: $i] :
( ( ! [SY3192: $i,SY3193: $i,SY3194: $i] :
( ( ( c_List_Oappend @ SV572 @ SY3192 @ SY3193 )
!= ( c_List_Oappend @ SY3194 @ SY3192 @ SY3193 ) )
| ( SV572 = SY3194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(2867,plain,
! [SV573: $i] :
( ( ! [SY3195: $i,SY3196: $i,SY3197: $i,SY3198: $i] :
( ( ( c_List_Oappend @ SV573 @ ( c_List_Olist_OCons @ SY3195 @ ( c_List_Olist_ONil @ SY3196 ) @ SY3196 ) @ SY3196 )
!= ( c_List_Oappend @ SY3197 @ ( c_List_Olist_OCons @ SY3198 @ ( c_List_Olist_ONil @ SY3196 ) @ SY3196 ) @ SY3196 ) )
| ( SY3195 = SY3198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2208]) ).
thf(2868,plain,
! [SV574: $i] :
( ( ! [SY3199: $i,SY3200: $i,SY3201: $i,SY3202: $i] :
( ( ( c_List_Oappend @ SV574 @ SY3199 @ SY3200 )
!= ( c_List_Oappend @ SY3201 @ SY3202 @ SY3200 ) )
| ( SY3199
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV574 @ ( tc_List_Olist @ SY3200 ) ) @ SY3201 @ SY3200 ) @ SY3202 @ SY3200 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV574 @ ( tc_List_Olist @ SY3200 ) ) @ ( c_Nat_Osize__class_Osize @ SY3201 @ ( tc_List_Olist @ SY3200 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2209]) ).
thf(2869,plain,
! [SV575: $i] :
( ( ! [SY3203: $i,SY3204: $i] :
( ( ( c_List_Olist_OCons @ SV575 @ ( c_List_Olist_ONil @ SY3203 ) @ SY3203 )
!= ( c_List_Orev @ SY3204 @ SY3203 ) )
| ( SY3204
= ( c_List_Olist_OCons @ SV575 @ ( c_List_Olist_ONil @ SY3203 ) @ SY3203 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2210]) ).
thf(2870,plain,
! [SV576: $i] :
( ( ! [SY3205: $i,SY3206: $i,SY3207: $i] :
( ( ( c_List_Orev @ SV576 @ SY3205 )
!= ( c_List_Olist_OCons @ SY3206 @ SY3207 @ SY3205 ) )
| ( SV576
= ( c_List_Oappend @ ( c_List_Orev @ SY3207 @ SY3205 ) @ ( c_List_Olist_OCons @ SY3206 @ ( c_List_Olist_ONil @ SY3205 ) @ SY3205 ) @ SY3205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2211]) ).
thf(2871,plain,
! [SV577: $i] :
( ( ! [SY3208: $i,SY3209: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV577 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV577 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV577 )
| ~ ( class_Power_Opower @ SV577 )
| ( ( c_Power_Opower__class_Opower @ SY3208 @ SY3209 @ SV577 )
!= ( c_HOL_Ozero__class_Ozero @ SV577 ) )
| ( SY3208
= ( c_HOL_Ozero__class_Ozero @ SV577 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2212]) ).
thf(2872,plain,
! [SV578: $i] :
( ( ! [SY3210: $i,SY3211: $i,SY3212: $i,SY3213: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV578 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3210 @ SY3211 @ SV578 )
!= ( c_HOL_Ominus__class_Ominus @ SY3212 @ SY3213 @ SV578 ) )
| ( c_HOL_Oord__class_Oless @ SY3212 @ SY3213 @ SV578 )
| ~ ( c_HOL_Oord__class_Oless @ SY3210 @ SY3211 @ SV578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2213]) ).
thf(2873,plain,
! [SV579: $i] :
( ( ( c_Suc @ SV579 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2214]) ).
thf(2874,plain,
! [SV580: $i] :
( ( ! [SY3214: $i,SY3215: $i,SY3216: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ SV580 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Onth @ ( c_List_Olist_OCons @ SY3214 @ SY3215 @ SY3216 ) @ ( c_Int_Onumber__class_Onumber__of @ SV580 @ tc_nat ) @ SY3216 )
= SY3214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2215]) ).
thf(2875,plain,
! [SV581: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV581 )
| ( ( c_HOL_Ozero__class_Ozero @ SV581 )
!= ( c_HOL_Oone__class_Oone @ SV581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2216]) ).
thf(2876,plain,
! [SV582: $i] :
( ( ! [SY3217: $i,SY3218: $i,SY3219: $i,SY3220: $i] :
( ( ( c_List_Olist_OCons @ SV582 @ SY3217 @ SY3218 )
!= ( c_List_Olist_OCons @ SY3219 @ SY3220 @ SY3218 ) )
| ( SY3217 = SY3220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2217]) ).
thf(2877,plain,
! [SV583: $i] :
( ( ! [SY3221: $i,SY3222: $i] :
( ( ( c_List_Oappend @ SV583 @ SY3221 @ SY3222 )
!= ( c_List_Olist_ONil @ SY3222 ) )
| ( SV583
= ( c_List_Olist_ONil @ SY3222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(2878,plain,
! [SV584: $i] :
( ( ! [SY3223: $i,SY3224: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV584 )
| ( ( c_Power_Opower__class_Opower @ SY3223 @ SY3224 @ SV584 )
!= ( c_HOL_Ozero__class_Ozero @ SV584 ) )
| ( SY3223
= ( c_HOL_Ozero__class_Ozero @ SV584 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2219]) ).
thf(2879,plain,
! [SV585: $i] :
( ( ! [SY3225: $i,SY3226: $i,SY3227: $i] :
( ( ( c_List_OtakeWhile @ SV585 @ SY3225 @ SY3226 )
!= SY3225 )
| ( hBOOL @ ( hAPP @ SV585 @ SY3227 ) )
| ~ ( c_in @ SY3227 @ ( c_List_Oset @ SY3225 @ SY3226 ) @ SY3226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2220]) ).
thf(2880,plain,
! [SV586: $i] :
( ( ! [SY3228: $i,SY3229: $i] :
( ( c_Lambda_OdB_OAbs @ SV586 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3228 ) @ SY3229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2221]) ).
thf(2881,plain,
! [SV587: $i] :
( ( ! [SY3230: $i,SY3231: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV587 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3230 @ SY3231 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV587 )
= SY3230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2222]) ).
thf(2882,plain,
! [SV588: $i] :
( ( ! [SY3232: $i,SY3233: $i,SY3234: $i] :
( ( ( c_List_Olist_ONil @ SV588 )
!= ( c_List_Omap @ SY3232 @ SY3233 @ SY3234 @ SV588 ) )
| ( SY3233
= ( c_List_Olist_ONil @ SY3234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2223]) ).
thf(2883,plain,
! [SV589: $i] :
( ( ! [SY3235: $i,SY3236: $i] :
( ( ( c_List_Olist_ONil @ SV589 )
!= ( c_List_Oappend @ SY3235 @ SY3236 @ SV589 ) )
| ( SY3235
= ( c_List_Olist_ONil @ SV589 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2224]) ).
thf(2884,plain,
! [SV590: $i] :
( ( ! [SY3237: $i] :
( ( ( c_List_Olist_ONil @ SV590 )
!= ( c_List_Orev @ SY3237 @ SV590 ) )
| ( SY3237
= ( c_List_Olist_ONil @ SV590 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(2885,plain,
! [SV591: $i] :
( ( ! [SY3238: $i,SY3239: $i] :
( ( ( c_List_Otake @ SV591 @ SY3238 @ SY3239 )
!= ( c_List_Olist_ONil @ SY3239 ) )
| ( SY3238
= ( c_List_Olist_ONil @ SY3239 ) )
| ( SV591
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2226]) ).
thf(2886,plain,
! [SV592: $i] :
( ( ! [SY3240: $i,SY3241: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV592 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3240 @ SY3241 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY3241
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(2887,plain,
! [SV593: $i] :
( ( ! [SY3242: $i] :
( ( ( c_List_Orev @ SV593 @ SY3242 )
!= ( c_List_Olist_ONil @ SY3242 ) )
| ( SV593
= ( c_List_Olist_ONil @ SY3242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2228]) ).
thf(2888,plain,
! [SV594: $i] :
( ( ! [SY3243: $i,SY3244: $i,SY3245: $i,SY3246: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV594 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3243 @ SY3244 @ SV594 )
!= ( c_HOL_Ominus__class_Ominus @ SY3245 @ SY3246 @ SV594 ) )
| ( c_HOL_Oord__class_Oless @ SY3243 @ SY3244 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SY3245 @ SY3246 @ SV594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2229]) ).
thf(2889,plain,
! [SV595: $i] :
( ( ! [SY3247: $i,SY3248: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV595 @ SY3247 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY3248 ) )
| ( SV595
= ( c_Lambda_OdB_OAbs @ SY3248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2230]) ).
thf(2890,plain,
! [SV596: $i] :
( ( ! [SY3249: $i,SY3250: $i,SY3251: $i,SY3252: $i] :
( ( ( c_List_Oappend @ SV596 @ SY3249 @ SY3250 )
!= ( c_List_Oappend @ SY3251 @ SY3252 @ SY3250 ) )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SY3251 @ ( tc_List_Olist @ SY3250 ) ) @ SV596 @ SY3250 )
= SY3251 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV596 @ ( tc_List_Olist @ SY3250 ) ) @ ( c_Nat_Osize__class_Osize @ SY3251 @ ( tc_List_Olist @ SY3250 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2231]) ).
thf(2891,plain,
! [SV597: $i] :
( ( ! [SY3253: $i,SY3254: $i] :
( ( c_List_Olist_OCons @ SV597 @ SY3253 @ SY3254 )
!= SY3253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(2892,plain,
! [SV598: $i] :
( ( ! [SY3255: $i,SY3256: $i] :
( ( SV598
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV598 @ ( tc_List_Olist @ SY3255 ) ) @ SY3256 @ SY3255 ) )
| ( ( c_List_Oappend @ SV598 @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV598 @ ( tc_List_Olist @ SY3255 ) ) @ SY3256 @ SY3255 ) @ SY3255 )
= SY3256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2233]) ).
thf(2893,plain,
! [SV599: $i] :
( ( ! [SY3257: $i,SY3258: $i,SY3259: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ SV599 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ SV599 @ tc_nat ) @ ( c_List_Olist_OCons @ SY3257 @ SY3258 @ SY3259 ) @ SY3259 )
= ( c_List_Olist_OCons @ SY3257 @ SY3258 @ SY3259 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2234]) ).
thf(2894,plain,
! [SV600: $i] :
( ( ! [SY3260: $i,SY3261: $i] :
( ( ( c_List_Orev @ SV600 @ SY3260 )
!= ( c_List_Orev @ SY3261 @ SY3260 ) )
| ( SV600 = SY3261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2235]) ).
thf(2895,plain,
! [SV601: $i] :
( ( ! [SY3262: $i,SY3263: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV601 @ SY3262 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY3263 ) )
| ( SY3262
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(2896,plain,
! [SV602: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ SV602 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2237]) ).
thf(2897,plain,
! [SV603: $i] :
( ( ! [SY3264: $i,SY3265: $i,SY3266: $i] :
( ( SV603
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV603 @ ( tc_List_Olist @ SY3264 ) ) @ SY3265 @ SY3264 ) )
| ( ( c_List_Oappend @ SV603 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV603 @ ( tc_List_Olist @ SY3264 ) ) @ SY3265 @ SY3264 ) @ SY3266 @ SY3264 ) @ SY3264 )
= ( c_List_Oappend @ SY3265 @ SY3266 @ SY3264 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV603 @ ( tc_List_Olist @ SY3264 ) ) @ ( c_Nat_Osize__class_Osize @ SY3265 @ ( tc_List_Olist @ SY3264 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2238]) ).
thf(2898,plain,
! [SV604: $i] :
( ( ! [SY3267: $i,SY3268: $i] :
( ( ( c_List_Olist_ONil @ SV604 )
!= ( c_List_Oreplicate @ SY3267 @ SY3268 @ SV604 ) )
| ( SY3267
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2239]) ).
thf(2899,plain,
! [SV605: $i] :
( ( ! [SY3269: $i,SY3270: $i] :
( ( ( c_List_Oappend @ SV605 @ SY3269 @ SY3270 )
!= SY3269 )
| ( SV605
= ( c_List_Olist_ONil @ SY3270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2240]) ).
thf(2900,plain,
! [SV606: $i] :
( ( ! [SY3271: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV606 @ SY3271 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ SV606 @ SY3271 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2241]) ).
thf(2901,plain,
! [SV607: $i] :
( ( ! [SY3272: $i,SY3273: $i,SY3274: $i,SY3275: $i,SY3276: $i] :
( ( ( c_List_Omap @ SV607 @ SY3272 @ SY3273 @ SY3274 )
!= ( c_List_Omap @ SY3275 @ SY3272 @ SY3273 @ SY3274 ) )
| ( ( hAPP @ SV607 @ SY3276 )
= ( hAPP @ SY3275 @ SY3276 ) )
| ~ ( c_in @ SY3276 @ ( c_List_Oset @ SY3272 @ SY3273 ) @ SY3273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2242]) ).
thf(2902,plain,
! [SV608: $i] :
( ( ! [SY3277: $i,SY3278: $i,SY3279: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV608 ) @ SY3277 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3278 ) @ SY3279 ) )
| ( SV608 = SY3278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(2903,plain,
! [SV609: $i] :
( ( ! [SY3280: $i,SY3281: $i,SY3282: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV609 ) @ SY3280 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3281 ) @ SY3282 ) )
| ( SY3280 = SY3282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(2904,plain,
! [SV610: $i] :
( ( ! [SY3283: $i,SY3284: $i] :
( ( ( c_List_Oappend @ SV610 @ SY3283 @ SY3284 )
!= ( c_List_Olist_ONil @ SY3284 ) )
| ( SY3283
= ( c_List_Olist_ONil @ SY3284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2245]) ).
thf(2905,plain,
! [SV611: $i] :
( ( ! [SY3285: $i,SY3286: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV611 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SY3285 @ SV611 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY3286 @ SV611 ) )
| ( SY3285 = SY3286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2246]) ).
thf(2906,plain,
! [SV612: $i] :
( ( ! [SY3287: $i,SY3288: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV612 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3287 @ SY3288 @ SV612 )
!= ( c_HOL_Ozero__class_Ozero @ SV612 ) )
| ( SY3287 = SY3288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2247]) ).
thf(2907,plain,
! [SV613: $i] :
( ( ! [SY3289: $i,SY3290: $i,SY3291: $i,SY3292: $i] :
( ( ( c_List_Odrop @ SV613 @ SY3289 @ SY3290 )
!= ( c_List_Olist_OCons @ SY3291 @ SY3292 @ SY3290 ) )
| ( ( c_List_Onth @ SY3289 @ SV613 @ SY3290 )
= SY3291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2248]) ).
thf(2908,plain,
! [SV614: $i] :
( ( ! [SY3293: $i,SY3294: $i,SY3295: $i,SY3296: $i] :
( ( ( c_List_Oappend @ SV614 @ SY3293 @ SY3294 )
!= ( c_List_Oappend @ SY3295 @ SY3296 @ SY3294 ) )
| ( SV614
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV614 @ ( tc_List_Olist @ SY3294 ) ) @ SY3295 @ SY3294 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV614 @ ( tc_List_Olist @ SY3294 ) ) @ ( c_Nat_Osize__class_Osize @ SY3295 @ ( tc_List_Olist @ SY3294 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2249]) ).
thf(2909,plain,
! [SV615: $i] :
( ( ! [SY3297: $i,SY3298: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV615 )
| ~ ( class_Int_Onumber__ring @ SV615 )
| ( SY3297
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV615 ) @ SY3297 ) @ SY3298 ) )
| ( SY3298
= ( c_HOL_Ozero__class_Ozero @ SV615 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2250]) ).
thf(2910,plain,
! [SV616: $i] :
( ( ! [SY3299: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV616 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV616 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV616 )
| ~ ( class_Power_Opower @ SV616 )
| ( ( c_Power_Opower__class_Opower @ SY3299 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV616 )
!= ( c_HOL_Ozero__class_Ozero @ SV616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(2911,plain,
! [SV617: $i] :
( ( ! [SY3300: $i,SY3301: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV617 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV617 ) @ SY3300 ) @ SY3301 )
!= ( c_HOL_Ozero__class_Ozero @ SV617 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV617 ) @ SY3301 @ SV617 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV617 ) @ SY3300 @ SV617 )
| ( SY3301
= ( c_HOL_Ozero__class_Ozero @ SV617 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2252]) ).
thf(2912,plain,
! [SV618: $i] :
( ( ! [SY3302: $i,SY3303: $i,SY3304: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV618 )
| ( ( c_Power_Opower__class_Opower @ SY3302 @ SY3303 @ SV618 )
!= ( c_Power_Opower__class_Opower @ SY3302 @ SY3304 @ SV618 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV618 ) @ SY3302 @ SV618 )
| ( SY3303 = SY3304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2253]) ).
thf(2913,plain,
! [SV619: $i] :
( ( ! [SY3305: $i,SY3306: $i] :
( ( ( c_List_Oreplicate @ SV619 @ SY3305 @ SY3306 )
!= ( c_List_Olist_ONil @ SY3306 ) )
| ( SV619
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2254]) ).
thf(2914,plain,
! [SV620: $i] :
( ( ! [SY3307: $i,SY3308: $i] :
( SV620
!= ( c_List_Olist_OCons @ SY3307 @ SV620 @ SY3308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2255]) ).
thf(2915,plain,
! [SV621: $i] :
( ( ! [SY3309: $i,SY3310: $i,SY3311: $i,SY3312: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV621 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3309 @ SY3310 @ SV621 )
!= ( c_HOL_Ominus__class_Ominus @ SY3311 @ SY3312 @ SV621 ) )
| ( c_lessequals @ SY3310 @ SY3309 @ SV621 )
| ~ ( c_lessequals @ SY3312 @ SY3311 @ SV621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2256]) ).
thf(2916,plain,
! [SV622: $i] :
( ( ! [SY3313: $i,SY3314: $i,SY3315: $i,SY3316: $i] :
( ( ( c_List_Oreplicate @ SV622 @ SY3313 @ SY3314 )
!= ( c_List_Oreplicate @ SY3315 @ SY3316 @ SY3314 ) )
| ( SY3313 = SY3316 )
| ( SV622
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2257]) ).
thf(2917,plain,
! [SV623: $i] :
( ( ! [SY3317: $i,SY3318: $i,SY3319: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV623 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3317 @ SY3317 @ SV623 )
!= ( c_HOL_Ominus__class_Ominus @ SY3318 @ SY3319 @ SV623 ) )
| ( SY3318 = SY3319 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(2918,plain,
! [SV624: $i] :
( ( ! [SY3320: $i,SY3321: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV624 )
| ~ ( class_Int_Onumber__ring @ SV624 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3320 @ SY3321 @ SV624 )
!= ( c_HOL_Ozero__class_Ozero @ SV624 ) )
| ( SY3320 = SY3321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2259]) ).
thf(2919,plain,
! [SV625: $i] :
( ( ! [SY3322: $i,SY3323: $i,SY3324: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV625 )
| ( ( c_Power_Opower__class_Opower @ SY3322 @ ( c_Suc @ SY3323 ) @ SV625 )
!= ( c_Power_Opower__class_Opower @ SY3324 @ ( c_Suc @ SY3323 ) @ SV625 ) )
| ( SY3322 = SY3324 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV625 ) @ SY3324 @ SV625 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV625 ) @ SY3322 @ SV625 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2260]) ).
thf(2920,plain,
! [SV626: $i] :
( ( ! [SY3325: $i,SY3326: $i,SY3327: $i,SY3328: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV626 )
| ( ( c_HOL_Ominus__class_Ominus @ SY3325 @ SY3326 @ SV626 )
!= ( c_HOL_Ominus__class_Ominus @ SY3327 @ SY3328 @ SV626 ) )
| ( c_lessequals @ SY3328 @ SY3327 @ SV626 )
| ~ ( c_lessequals @ SY3326 @ SY3325 @ SV626 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2261]) ).
thf(2921,plain,
! [SV627: $i] :
( ( SV627
!= ( c_Suc @ SV627 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2262]) ).
thf(2922,plain,
! [SV628: $i] :
( ( ! [SY3329: $i,SY3330: $i] :
( ( SV628
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV628 ) @ SY3329 ) @ SY3330 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV628 ) @ SY3329 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV628 ) @ SY3329 ) @ ( c_List_Oappend @ SY3330 @ ( c_List_Olist_OCons @ SY3329 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2263]) ).
thf(2923,plain,
! [SV629: $i] :
( ( ! [SY3331: $i,SY3332: $i,SY3333: $i] :
( ( ( c_List_Olist__update @ SV629 @ SY3331 @ SY3332 @ SY3333 )
!= SV629 )
| ~ ( c_HOL_Oord__class_Oless @ SY3331 @ ( c_Nat_Osize__class_Osize @ SV629 @ ( tc_List_Olist @ SY3333 ) ) @ tc_nat )
| ( ( c_List_Onth @ SV629 @ SY3331 @ SY3333 )
= SY3332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2264]) ).
thf(2924,plain,
! [SV630: $i] :
( ( ! [SY3334: $i,SY3335: $i,SY3336: $i,SY3337: $i] :
( ( ( c_List_Oappend @ SV630 @ SY3334 @ SY3335 )
!= ( c_List_Oappend @ SY3336 @ SY3337 @ SY3335 ) )
| ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SY3336 @ ( tc_List_Olist @ SY3335 ) ) @ SV630 @ SY3335 ) @ SY3334 @ SY3335 )
= SY3337 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV630 @ ( tc_List_Olist @ SY3335 ) ) @ ( c_Nat_Osize__class_Osize @ SY3336 @ ( tc_List_Olist @ SY3335 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2265]) ).
thf(2925,plain,
! [SV631: $i] :
( ( ! [SY3338: $i,SY3339: $i,SY3340: $i,SY3341: $i] :
( ( ( c_List_Olist_OCons @ SV631 @ SY3338 @ SY3339 )
!= ( c_List_Olist_OCons @ SY3340 @ SY3341 @ SY3339 ) )
| ( SV631 = SY3340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2266]) ).
thf(2926,plain,
! [SV632: $i] :
( ( ! [SY3342: $i,SY3343: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV632 @ SY3342 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3343 @ SY3342 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV632 = SY3343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2267]) ).
thf(2927,plain,
! [SV633: $i] :
( ( ! [SY3344: $i,SY3345: $i,SY3346: $i,SY3347: $i] :
( ( ( c_List_Omap @ SV633 @ SY3344 @ SY3345 @ SY3346 )
!= ( c_List_Omap @ SV633 @ SY3347 @ SY3345 @ SY3346 ) )
| ( ( c_Nat_Osize__class_Osize @ SY3344 @ ( tc_List_Olist @ SY3345 ) )
= ( c_Nat_Osize__class_Osize @ SY3347 @ ( tc_List_Olist @ SY3345 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2268]) ).
thf(2928,plain,
! [SV634: $i] :
( ( ! [SY3348: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV634 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV634 ) @ SY3348 ) @ SY3348 )
!= ( c_HOL_Ozero__class_Ozero @ SV634 ) )
| ( SY3348
= ( c_HOL_Ozero__class_Ozero @ SV634 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2269]) ).
thf(2929,plain,
! [SV635: $i] :
( ( ( c_Suc @ SV635 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2270]) ).
thf(2930,plain,
! [SV636: $i] :
( ( ! [SY3349: $i,SY3350: $i] :
( ( ( c_List_Orev @ SV636 @ SY3349 )
!= ( c_List_Olist_OCons @ SY3350 @ ( c_List_Olist_ONil @ SY3349 ) @ SY3349 ) )
| ( SV636
= ( c_List_Olist_OCons @ SY3350 @ ( c_List_Olist_ONil @ SY3349 ) @ SY3349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2271]) ).
thf(2931,plain,
! [SV637: $i] :
( ( ! [SY3351: $i,SY3352: $i,SY3353: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV637 )
| ~ ( class_Int_Onumber__ring @ SV637 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SY3351 ) @ SY3352 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SY3351 ) @ SY3353 ) )
| ( SY3352 = SY3353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2272]) ).
thf(2932,plain,
! [SV638: $i] :
( ( ! [SY3354: $i,SY3355: $i,SY3356: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV638 ) @ SY3354 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3355 @ SY3356 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV638
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3355 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV638 @ SY3354 @ SY3355 @ SY3356 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY3356
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2273]) ).
thf(2933,plain,
! [SV639: $i] :
( ( ! [SY3357: $i,SY3358: $i] :
( ~ ( class_Int_Oring__char__0 @ SV639 )
| ~ ( class_Int_Onumber__ring @ SV639 )
| ( ( c_Int_Onumber__class_Onumber__of @ SY3357 @ SV639 )
!= ( c_Int_Onumber__class_Onumber__of @ SY3358 @ SV639 ) )
| ( SY3357 = SY3358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2274]) ).
thf(2934,plain,
! [SV640: $i] :
( ( ( c_Suc @ SV640 )
!= SV640 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2275]) ).
thf(2935,plain,
! [SV641: $i] :
( ( ! [SY3359: $i,SY3360: $i,SY3361: $i] :
( ( ( c_List_Olist__update @ SV641 @ SY3359 @ SY3360 @ SY3361 )
!= ( c_List_Olist_ONil @ SY3361 ) )
| ( SV641
= ( c_List_Olist_ONil @ SY3361 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2276]) ).
thf(2936,plain,
! [SV642: $i] :
( ( ! [SY3362: $i] :
( ( c_Lambda_OdB_OVar @ SV642 )
!= ( c_Lambda_OdB_OAbs @ SY3362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2277]) ).
thf(2937,plain,
! [SV643: $i] :
( ( ! [SY3363: $i,SY3364: $i,SY3365: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV643 ) @ SY3363 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY3364 ) @ SY3365 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY3363 = SY3365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2278]) ).
thf(2938,plain,
! [SV644: $i] :
( ( ! [SY3366: $i,SY3367: $i,SY3368: $i] :
( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV644 @ ( tc_List_Olist @ SY3366 ) ) @ SY3367 @ SY3366 )
!= SV644 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SY3367 @ ( tc_List_Olist @ SY3366 ) ) @ ( c_Nat_Osize__class_Osize @ SV644 @ ( tc_List_Olist @ SY3366 ) ) @ tc_nat )
| ( ( c_List_Oappend @ SY3367 @ SY3368 @ SY3366 )
= ( c_List_Oappend @ SV644 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV644 @ ( tc_List_Olist @ SY3366 ) ) @ SY3367 @ SY3366 ) @ SY3368 @ SY3366 ) @ SY3366 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2279]) ).
thf(2939,plain,
! [SV645: $i] :
( ( ! [SY3369: $i,SY3370: $i,SY3371: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ SV645 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ SV645 @ tc_nat ) @ ( c_List_Olist_OCons @ SY3369 @ SY3370 @ SY3371 ) @ SY3371 )
= ( c_List_Olist_ONil @ SY3371 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2280]) ).
thf(2940,plain,
! [SV646: $i] :
( ( ! [SY3372: $i,SY3373: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV646 @ SY3372 @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ SY3373 @ SY3372 @ tc_nat ) )
| ~ ( c_lessequals @ SY3372 @ SY3373 @ tc_nat )
| ~ ( c_lessequals @ SY3372 @ SV646 @ tc_nat )
| ( SV646 = SY3373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2281]) ).
thf(2941,plain,
! [SV647: $i] :
( ( ! [SY3374: $i,SY3375: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV647 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV647 ) @ SY3374 ) @ SY3375 )
!= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV647 ) @ SY3375 @ SV647 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV647 ) @ SY3374 @ SV647 )
| ( SY3374
= ( c_HOL_Ozero__class_Ozero @ SV647 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2282]) ).
thf(2942,plain,
! [SV648: $i] :
( ( ! [SY3376: $i,SY3377: $i,SY3378: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV648 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV648 ) @ SY3376 ) @ SY3377 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV648 ) @ SY3376 ) @ SY3378 ) )
| ( SY3377 = SY3378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(2943,plain,
! [SV649: $i] :
( ( ! [SY3379: $i,SY3380: $i,SY3381: $i,SY3382: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV649 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SY3379 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SY3380 ) @ SY3381 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SY3380 ) @ SY3382 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SY3379 ) @ SY3381 )
= SY3382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(2944,plain,
! [SV650: $i] :
( ( ! [SY3383: $i,SY3384: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV650 ) @ SY3383 )
!= ( c_Lambda_OdB_OAbs @ SY3384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2285]) ).
thf(2945,plain,
! [SV651: $i] :
( ( ! [SY3385: $i,SY3386: $i,SY3387: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV651 ) ) @ SY3385 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY3386 ) @ SY3387 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2286]) ).
thf(2946,plain,
! [SV652: $i] :
( ( ! [SY3388: $i,SY3389: $i,SY3390: $i] :
( ( ( c_List_Omap @ SV652 @ SY3388 @ SY3389 @ SY3390 )
!= ( c_List_Olist_ONil @ SY3390 ) )
| ( SY3388
= ( c_List_Olist_ONil @ SY3389 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2287]) ).
thf(2947,plain,
! [SV653: $i] :
( ( ! [SY3391: $i,SY3392: $i] :
( ( ( c_List_Oappend @ SV653 @ SY3391 @ SY3392 )
!= SV653 )
| ( SY3391
= ( c_List_Olist_ONil @ SY3392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2288]) ).
thf(2948,plain,
! [SV654: $i] :
( ( ! [SY3393: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV654 @ SY3393 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ SY3393 @ SV654 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY3393 = SV654 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2289]) ).
thf(2949,plain,
! [SV655: $i] :
( ( ! [SY3394: $i] :
( ( ( c_Nat_Osize__class_Osize @ SV655 @ ( tc_List_Olist @ SY3394 ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV655
= ( c_List_Olist_ONil @ SY3394 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2290]) ).
thf(2950,plain,
! [SV656: $i] :
( ( ! [SY3395: $i,SY3396: $i,SY3397: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV656 ) @ SY3395 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY3396 ) @ SY3397 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2291]) ).
thf(2951,plain,
! [SV657: $i,SV1: $i] :
( ( ( SV1 = SV657 )
| ~ ( c_HOL_Oord__class_Oless @ SV1 @ ( c_Suc @ SV657 ) @ tc_nat )
| ~ ( c_lessequals @ SV657 @ SV1 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2293]) ).
thf(2952,plain,
! [SV658: $i,SV2: $i] :
( ( ! [SY3398: $i,SY3399: $i,SY3400: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV2 )
| ( c_lessequals @ SV658 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SY3398 ) @ SY3399 ) @ SV2 )
| ~ ( c_lessequals @ SY3400 @ SY3399 @ SV2 )
| ~ ( c_lessequals @ SV658 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SY3398 ) @ SY3400 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2294]) ).
thf(2953,plain,
! [SV659: $i,SV3: $i] :
( ( ! [SY3401: $i,SY3402: $i] :
( ~ ( class_Orderings_Opreorder @ SV3 )
| ( c_HOL_Oord__class_Oless @ SV659 @ SY3401 @ SV3 )
| ~ ( c_lessequals @ SY3402 @ SY3401 @ SV3 )
| ~ ( c_HOL_Oord__class_Oless @ SV659 @ SY3402 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2295]) ).
thf(2954,plain,
! [SV660: $i,SV4: $i] :
( ( ! [SY3403: $i,SY3404: $i] :
( ~ ( class_Orderings_Opreorder @ SV4 )
| ( c_HOL_Oord__class_Oless @ SV660 @ SY3403 @ SV4 )
| ~ ( c_HOL_Oord__class_Oless @ SY3404 @ SY3403 @ SV4 )
| ~ ( c_lessequals @ SV660 @ SY3404 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2296]) ).
thf(2955,plain,
! [SV661: $i,SV5: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV5 )
| ( c_lessequals @ SV661 @ SV661 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2297]) ).
thf(2956,plain,
! [SV662: $i,SV6: $i] :
( ( ~ ( class_Orderings_Oorder @ SV6 )
| ( c_lessequals @ SV662 @ SV662 @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2298]) ).
thf(2957,plain,
! [SV663: $i,SV8: $i] :
( ( ! [SY3405: $i] :
( ( c_lessequals @ SV8 @ SV663 @ tc_nat )
| ~ ( c_lessequals @ SY3405 @ SV663 @ tc_nat )
| ~ ( c_lessequals @ SV8 @ SY3405 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2300]) ).
thf(2958,plain,
! [SV664: $i,SV10: $i] :
( ( ! [SY3406: $i,SY3407: $i] :
( ~ ( class_Orderings_Opreorder @ SV10 )
| ( c_lessequals @ SV664 @ SY3406 @ SV10 )
| ~ ( c_lessequals @ SY3407 @ SY3406 @ SV10 )
| ~ ( c_lessequals @ SV664 @ SY3407 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2302]) ).
thf(2959,plain,
! [SV665: $i,SV11: $i] :
( ( ! [SY3408: $i,SY3409: $i] :
( ~ ( class_Orderings_Oorder @ SV11 )
| ( c_HOL_Oord__class_Oless @ SV665 @ SY3408 @ SV11 )
| ~ ( c_HOL_Oord__class_Oless @ SV665 @ SY3409 @ SV11 )
| ~ ( c_lessequals @ SY3409 @ SY3408 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(2960,plain,
! [SV666: $i,SV12: $i] :
( ( ! [SY3410: $i,SY3411: $i] :
( ~ ( class_Orderings_Oorder @ SV12 )
| ( c_HOL_Oord__class_Oless @ SV666 @ SY3410 @ SV12 )
| ~ ( c_lessequals @ SV666 @ SY3411 @ SV12 )
| ~ ( c_HOL_Oord__class_Oless @ SY3411 @ SY3410 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2304]) ).
thf(2961,plain,
! [SV667: $i,SV13: $i] :
( ( ! [SY3412: $i,SY3413: $i] :
( ~ ( class_Orderings_Oorder @ SV13 )
| ( c_lessequals @ SV667 @ SY3412 @ SV13 )
| ~ ( c_lessequals @ SV667 @ SY3413 @ SV13 )
| ~ ( c_lessequals @ SY3413 @ SY3412 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2305]) ).
thf(2962,plain,
! [SV668: $i,SV14: $i] :
( ( ! [SY3414: $i] :
( ~ ( class_Ring__and__Field_Oring__1 @ SV14 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV668 @ SY3414 @ tc_nat ) @ SV14 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV668 @ SV14 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3414 @ SV14 ) @ SV14 ) )
| ~ ( c_lessequals @ SY3414 @ SV668 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2306]) ).
thf(2963,plain,
! [SV669: $i,SV15: $i] :
( ( ! [SY3415: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV15 @ SV669 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3415 @ SV669 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV15 @ SY3415 @ tc_nat )
| ~ ( c_lessequals @ SV669 @ SY3415 @ tc_nat )
| ~ ( c_lessequals @ SV669 @ SV15 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2307]) ).
thf(2964,plain,
! [SV670: $i,SV16: $i] :
( ( ! [SY3416: $i] :
( ( c_HOL_Oord__class_Oless @ SV16 @ SV670 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV16 @ SY3416 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV670 @ SY3416 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3416 @ SV670 @ tc_nat )
| ~ ( c_lessequals @ SY3416 @ SV16 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2308]) ).
thf(2965,plain,
! [SV17: $i] :
( ( c_lessequals @ ( c_Suc @ SV17 ) @ SV17 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2309]) ).
thf(2966,plain,
! [SV671: $i,SV18: $i] :
( ( ( c_lessequals @ SV18 @ ( c_Suc @ SV671 ) @ tc_nat )
| ~ ( c_lessequals @ SV18 @ SV671 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2310]) ).
thf(2967,plain,
! [SV672: $i,SV19: $i] :
( ( ( c_lessequals @ SV19 @ SV672 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV19 ) @ SV672 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2311]) ).
thf(2968,plain,
! [SV673: $i,SV20: $i] :
( ( ! [SY3417: $i,SY3418: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV20 )
| ( c_lessequals @ SV673 @ SY3417 @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SY3417 @ SV20 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV673 @ ( c_Suc @ SY3418 ) @ SV20 ) @ ( c_Power_Opower__class_Opower @ SY3417 @ ( c_Suc @ SY3418 ) @ SV20 ) @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2312]) ).
thf(2969,plain,
! [SV674: $i,SV21: $i] :
( ( ! [SY3419: $i,SY3420: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV21 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SV674 ) @ SY3419 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SV674 ) @ SY3420 ) @ SV21 )
| ~ ( c_lessequals @ SY3419 @ SY3420 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2313]) ).
thf(2970,plain,
! [SV675: $i,SV22: $i] :
( ( ! [SY3421: $i,SY3422: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV22 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV675 ) @ SY3421 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SY3422 ) @ SY3421 ) @ SV22 )
| ~ ( c_lessequals @ SV675 @ SY3422 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2314]) ).
thf(2971,plain,
! [SV676: $i,SV23: $i] :
( ( ! [SY3423: $i,SY3424: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV23 )
| ( c_lessequals @ SV676 @ SY3423 @ SV23 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV23 ) @ SY3424 ) @ SV676 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV23 ) @ SY3424 ) @ SY3423 ) @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2315]) ).
thf(2972,plain,
! [SV677: $i,SV24: $i] :
( ( ! [SY3425: $i,SY3426: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV24 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ SV677 ) @ SY3425 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ SV677 ) @ SY3426 ) @ SV24 )
| ~ ( c_lessequals @ SY3425 @ SY3426 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2316]) ).
thf(2973,plain,
! [SV678: $i,SV25: $i] :
( ( ! [SY3427: $i,SY3428: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV25 )
| ( c_lessequals @ SV678 @ SY3427 @ SV25 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SV678 ) @ SY3428 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SY3427 ) @ SY3428 ) @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2317]) ).
thf(2974,plain,
! [SV679: $i,SV26: $i] :
( ( ! [SY3429: $i,SY3430: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV26 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV26 ) @ SV679 ) @ SY3429 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV26 ) @ SY3430 ) @ SY3429 ) @ SV26 )
| ~ ( c_lessequals @ SV679 @ SY3430 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2318]) ).
thf(2975,plain,
! [SV680: $i,SV27: $i] :
( ( ! [SY3431: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV27 ) @ SV680 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY3431 @ SV680 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV27 @ SY3431 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2319]) ).
thf(2976,plain,
! [SV681: $i,SV30: $i] :
( ( ! [SY3432: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV30 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV30 ) @ ( c_Power_Opower__class_Opower @ SV681 @ ( c_Suc @ SY3432 ) @ SV30 ) @ SV30 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SV681 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2322]) ).
thf(2977,plain,
! [SV682: $i,SV31: $i] :
( ( ! [SY3433: $i] :
( ~ ( class_Orderings_Opreorder @ SV31 )
| ( c_lessequals @ SV682 @ SY3433 @ SV31 )
| ~ ( c_HOL_Oord__class_Oless @ SV682 @ SY3433 @ SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2323]) ).
thf(2978,plain,
! [SV683: $i,SV32: $i] :
( ( ! [SY3434: $i] :
( ~ ( class_Orderings_Oorder @ SV32 )
| ( c_lessequals @ SV683 @ SY3434 @ SV32 )
| ~ ( c_HOL_Oord__class_Oless @ SV683 @ SY3434 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2324]) ).
thf(2979,plain,
! [SV684: $i,SV33: $i] :
( ( ( c_lessequals @ SV33 @ SV684 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV33 @ SV684 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2325]) ).
thf(2980,plain,
! [SV685: $i,SV34: $i] :
( ( ( c_lessequals @ SV34 @ SV685 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV34 @ SV685 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2326]) ).
thf(2981,plain,
! [SV686: $i,SV35: $i] :
( ( ! [SY3435: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV35 )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV686 @ SY3435 @ SV35 ) @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ SV35 )
| ~ ( c_lessequals @ SV686 @ SY3435 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2327]) ).
thf(2982,plain,
! [SV687: $i,SV36: $i] :
( ( ! [SY3436: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV36 )
| ( c_lessequals @ SV687 @ SY3436 @ SV36 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV687 @ SY3436 @ SV36 ) @ ( c_HOL_Ozero__class_Ozero @ SV36 ) @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2328]) ).
thf(2983,plain,
! [SV688: $i,SV37: $i] :
( ( ! [SY3437: $i] :
( ~ ( class_Orderings_Oorder @ SV37 )
| ( SV688 = SY3437 )
| ~ ( c_lessequals @ SV688 @ SY3437 @ SV37 )
| ~ ( c_lessequals @ SY3437 @ SV688 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2329]) ).
thf(2984,plain,
! [SV689: $i,SV38: $i] :
( ( ! [SY3438: $i] :
( ~ ( class_Orderings_Oorder @ SV38 )
| ( SV689 = SY3438 )
| ~ ( c_lessequals @ SY3438 @ SV689 @ SV38 )
| ~ ( c_lessequals @ SV689 @ SY3438 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2330]) ).
thf(2985,plain,
! [SV690: $i,SV39: $i] :
( ( ! [SY3439: $i] :
( ~ ( class_Orderings_Oorder @ SV39 )
| ( SV690 = SY3439 )
| ~ ( c_lessequals @ SY3439 @ SV690 @ SV39 )
| ~ ( c_lessequals @ SV690 @ SY3439 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2331]) ).
thf(2986,plain,
! [SV691: $i,SV40: $i] :
( ( ( SV40 = SV691 )
| ~ ( c_lessequals @ SV691 @ SV40 @ tc_nat )
| ~ ( c_lessequals @ SV40 @ SV691 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2332]) ).
thf(2987,plain,
! [SV692: $i,SV41: $i] :
( ( ( c_List_Oset @ ( c_List_Orev @ SV41 @ SV692 ) @ SV692 )
= ( c_List_Oset @ SV41 @ SV692 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2333]) ).
thf(2988,plain,
! [SV42: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV42 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV42 ) @ ( c_HOL_Ozero__class_Ozero @ SV42 ) @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2334]) ).
thf(2989,plain,
! [SV693: $i,SV43: $i] :
( ( ! [SY3440: $i] :
( ~ ( class_Orderings_Opreorder @ SV43 )
| ( c_HOL_Oord__class_Oless @ SV693 @ SY3440 @ SV43 )
| ( c_lessequals @ SY3440 @ SV693 @ SV43 )
| ~ ( c_lessequals @ SV693 @ SY3440 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2335]) ).
thf(2990,plain,
! [SV694: $i,SV44: $i] :
( ( ! [SY3441: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV44 @ SV694 @ tc_nat ) @ SY3441 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV44 @ SY3441 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2336]) ).
thf(2991,plain,
! [SV45: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV45 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV45 ) @ ( c_HOL_Oone__class_Oone @ SV45 ) @ SV45 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2337]) ).
thf(2992,plain,
! [SV695: $i,SV46: $i] :
( ( ( SV46 = SV695 )
| ~ ( c_HOL_Oord__class_Oless @ SV46 @ ( c_Suc @ SV695 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV46 @ SV695 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2338]) ).
thf(2993,plain,
! [SV696: $i,SV47: $i] :
( ( ( SV47 = SV696 )
| ~ ( c_HOL_Oord__class_Oless @ SV696 @ ( c_Suc @ SV47 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV696 @ SV47 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2339]) ).
thf(2994,plain,
! [SV697: $i,SV48: $i] :
( ( ( SV48 = SV697 )
| ( c_HOL_Oord__class_Oless @ SV48 @ SV697 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV48 @ ( c_Suc @ SV697 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2340]) ).
thf(2995,plain,
! [SV698: $i,SV49: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV49 ) @ ( c_Suc @ SV698 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV49 @ SV698 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2341]) ).
thf(2996,plain,
! [SV699: $i,SV50: $i] :
( ( ! [SY3442: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV50 @ SV699 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV50 @ SY3442 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY3442 @ SV50 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY3442 @ SV699 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2342]) ).
thf(2997,plain,
! [SV700: $i,SV51: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV51 ) @ SV700 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV51 @ SV700 @ tc_nat ) ) )
| ~ ( c_lessequals @ SV700 @ SV51 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(2998,plain,
! [SV701: $i,SV52: $i] :
( ( ! [SY3443: $i,SY3444: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV52 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV701 @ SY3443 @ SV52 ) @ ( c_Power_Opower__class_Opower @ SV701 @ SY3444 @ SV52 ) @ SV52 )
| ~ ( c_lessequals @ SV701 @ ( c_HOL_Oone__class_Oone @ SV52 ) @ SV52 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV701 @ SV52 )
| ~ ( c_lessequals @ SY3444 @ SY3443 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2344]) ).
thf(2999,plain,
! [SV702: $i,SV53: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV53 @ SV702 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV53 ) @ SV702 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2345]) ).
thf(3000,plain,
! [SV703: $i,SV54: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV54 ) @ SV703 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV54 @ SV703 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2346]) ).
thf(3001,plain,
! [SV704: $i,SV55: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV55 @ SV704 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV55 ) @ SV704 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2347]) ).
thf(3002,plain,
! [SV705: $i,SV56: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV56 ) @ SV705 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV56 @ SV705 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2348]) ).
thf(3003,plain,
! [SV706: $i,SV57: $i] :
( ( ! [SY3445: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV57 )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV57 ) @ ( c_Power_Opower__class_Opower @ SV706 @ SY3445 @ SV57 ) @ SV57 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV57 ) @ SV706 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2349]) ).
thf(3004,plain,
! [SV707: $i,SV58: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV58 @ SV707 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ SV58 @ SV707 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2350]) ).
thf(3005,plain,
! [SV708: $i,SV59: $i] :
( ( ! [SY3446: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV59 )
| ( c_lessequals @ SV708 @ SY3446 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV708 @ SV59 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3446 @ SV59 ) @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2351]) ).
thf(3006,plain,
! [SV709: $i,SV60: $i] :
( ( ! [SY3447: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV60 )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV709 @ SV60 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3447 @ SV60 ) @ SV60 )
| ~ ( c_lessequals @ SV709 @ SY3447 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2352]) ).
thf(3007,plain,
! [SV710: $i,SV61: $i] :
( ( ! [SY3448: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV61 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ ( c_HOL_Ominus__class_Ominus @ SV710 @ SY3448 @ SV61 ) ) @ SY3448 )
= SV710 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2353]) ).
thf(3008,plain,
! [SV711: $i,SV62: $i] :
( ( ! [SY3449: $i,SY3450: $i,SY3451: $i] :
( ( c_ListOrder_Ostep1 @ SV62 @ ( c_List_Oappend @ SV711 @ SY3449 @ SY3450 ) @ ( c_List_Oappend @ SV711 @ SY3451 @ SY3450 ) @ SY3450 )
| ~ ( c_ListOrder_Ostep1 @ SV62 @ SY3449 @ SY3451 @ SY3450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2354]) ).
thf(3009,plain,
! [SV712: $i,SV63: $i] :
( ( ! [SY3452: $i,SY3453: $i,SY3454: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV63 @ SV712 @ SY3452 @ SY3453 )
| ( c_ListOrder_Ostep1 @ SV63 @ ( c_List_Oappend @ SV712 @ SY3454 @ SY3453 ) @ ( c_List_Oappend @ SY3452 @ SY3454 @ SY3453 ) @ SY3453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2355]) ).
thf(3010,plain,
! [SV713: $i,SV64: $i] :
( ( ! [SY3455: $i,SY3456: $i,SY3457: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV64 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV713 ) @ SY3455 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SY3456 ) @ SY3457 ) @ SV64 )
| ~ ( c_lessequals @ SY3455 @ SY3457 @ SV64 )
| ~ ( c_lessequals @ SV713 @ SY3456 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2356]) ).
thf(3011,plain,
! [SV714: $i,SV65: $i] :
( ( ! [SY3458: $i,SY3459: $i,SY3460: $i] :
( ( c_lessequals @ SV65 @ ( c_List_Olist_Olist__size @ SV714 @ SY3458 @ SY3459 ) @ tc_nat )
| ~ ( c_lessequals @ SV65 @ ( hAPP @ SV714 @ SY3460 ) @ tc_nat )
| ~ ( c_in @ SY3460 @ ( c_List_Oset @ SY3458 @ SY3459 ) @ SY3459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2357]) ).
thf(3012,plain,
! [SV715: $i,SV66: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV66 @ ( c_Suc @ SV715 ) @ tc_nat )
| ~ ( c_lessequals @ SV66 @ SV715 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2358]) ).
thf(3013,plain,
! [SV716: $i,SV67: $i] :
( ( ( c_lessequals @ SV67 @ SV716 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV67 @ ( c_Suc @ SV716 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2359]) ).
thf(3014,plain,
! [SV68: $i] :
( ( ( ~ ( c_lessequals @ SV68 @ SV68 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV68 @ ( c_Suc @ SV68 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2360]) ).
thf(3015,plain,
! [SV717: $i,SV69: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV69 @ SV717 @ tc_nat ) @ ( c_Suc @ SV69 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2361]) ).
thf(3016,plain,
! [SV718: $i,SV70: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV70 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV70 ) @ SV718 @ SV70 )
= ( c_HOL_Oone__class_Oone @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2362]) ).
thf(3017,plain,
! [SV719: $i,SV71: $i] :
( ( ! [SY3461: $i] :
( ~ ( class_Orderings_Olinorder @ SV71 )
| ( c_HOL_Oord__class_Oless @ SV719 @ SY3461 @ SV71 )
| ( c_lessequals @ SY3461 @ SV719 @ SV71 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2363]) ).
thf(3018,plain,
! [SV720: $i,SV72: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV72 )
| ~ ( c_lessequals @ SV720 @ SV720 @ SV72 )
| ~ ( c_HOL_Oord__class_Oless @ SV720 @ SV720 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2364]) ).
thf(3019,plain,
! [SV721: $i,SV73: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV73 )
| ( c_HOL_Oord__class_Oless @ SV721 @ SV721 @ SV73 )
| ( c_lessequals @ SV721 @ SV721 @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2365]) ).
thf(3020,plain,
! [SV722: $i,SV74: $i] :
( ( ! [SY3462: $i] :
( ~ ( class_Orderings_Olinorder @ SV74 )
| ~ ( c_HOL_Oord__class_Oless @ SV722 @ SY3462 @ SV74 )
| ~ ( c_lessequals @ SY3462 @ SV722 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2366]) ).
thf(3021,plain,
! [SV723: $i,SV75: $i] :
( ( ! [SY3463: $i] :
( ~ ( class_Orderings_Olinorder @ SV75 )
| ( c_lessequals @ SV723 @ SY3463 @ SV75 )
| ( c_HOL_Oord__class_Oless @ SY3463 @ SV723 @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2367]) ).
thf(3022,plain,
! [SV724: $i,SV76: $i] :
( ( ! [SY3464: $i] :
( ~ ( class_Orderings_Olinorder @ SV76 )
| ~ ( c_lessequals @ SV724 @ SY3464 @ SV76 )
| ~ ( c_HOL_Oord__class_Oless @ SY3464 @ SV724 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2368]) ).
thf(3023,plain,
! [SV725: $i,SV77: $i] :
( ( ! [SY3465: $i] :
( ~ ( class_Orderings_Olinorder @ SV77 )
| ( c_HOL_Oord__class_Oless @ SV725 @ SY3465 @ SV77 )
| ( c_lessequals @ SY3465 @ SV725 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2369]) ).
thf(3024,plain,
! [SV726: $i,SV78: $i] :
( ( ! [SY3466: $i] :
( ~ ( class_Orderings_Opreorder @ SV78 )
| ~ ( c_lessequals @ SV726 @ SY3466 @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ SY3466 @ SV726 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2370]) ).
thf(3025,plain,
! [SV727: $i,SV79: $i] :
( ( ! [SY3467: $i,SY3468: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV79 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV727 @ SY3467 @ SV79 ) @ ( c_Power_Opower__class_Opower @ SV727 @ SY3468 @ SV79 ) @ SV79 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV79 ) @ SV727 @ SV79 )
| ~ ( c_lessequals @ SY3467 @ SY3468 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2371]) ).
thf(3026,plain,
! [SV728: $i,SV80: $i] :
( ( ! [SY3469: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV80 @ SV728 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV80 @ SY3469 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3469 @ SV728 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2372]) ).
thf(3027,plain,
! [SV729: $i,SV81: $i] :
( ( ! [SY3470: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV81 @ SV729 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3470 @ SV729 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV81 @ SY3470 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2373]) ).
thf(3028,plain,
! [SV730: $i,SV82: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV82 @ SV730 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV82 ) @ SV730 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2374]) ).
thf(3029,plain,
! [SV731: $i,SV83: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV83 @ ( c_Suc @ SV731 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV83 @ SV731 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2375]) ).
thf(3030,plain,
! [SV84: $i] :
( ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV84 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= SV84 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV84 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2376]) ).
thf(3031,plain,
! [SV732: $i,SV85: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV85 @ ( c_Suc @ SV732 ) @ tc_nat ) @ SV85 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV85 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2377]) ).
thf(3032,plain,
! [SV733: $i,SV86: $i] :
( ( ! [SY3471: $i] :
( ~ ( class_Orderings_Oorder @ SV86 )
| ( c_HOL_Oord__class_Oless @ SV733 @ SY3471 @ SV86 )
| ( SY3471 = SV733 )
| ~ ( c_lessequals @ SV733 @ SY3471 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2378]) ).
thf(3033,plain,
! [SV734: $i,SV87: $i] :
( ( ! [SY3472: $i] :
( ~ ( class_Orderings_Oorder @ SV87 )
| ( c_HOL_Oord__class_Oless @ SV734 @ SY3472 @ SV87 )
| ~ ( c_lessequals @ SV734 @ SY3472 @ SV87 )
| ( SY3472 = SV734 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2379]) ).
thf(3034,plain,
! [SV735: $i,SV88: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV88 @ SV735 @ tc_nat )
| ( SV88 = SV735 )
| ~ ( c_lessequals @ SV88 @ SV735 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2380]) ).
thf(3035,plain,
! [SV736: $i,SV89: $i] :
( ( ( SV89 = SV736 )
| ( c_HOL_Oord__class_Oless @ SV89 @ SV736 @ tc_nat )
| ~ ( c_lessequals @ SV89 @ SV736 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2381]) ).
thf(3036,plain,
! [SV737: $i,SV90: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV90 @ SV737 @ tc_nat )
| ( SV90 = SV737 )
| ~ ( c_lessequals @ SV90 @ SV737 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2382]) ).
thf(3037,plain,
! [SV738: $i,SV91: $i] :
( ( ! [SY3473: $i] :
( ~ ( class_Orderings_Oorder @ SV91 )
| ( SV738 = SY3473 )
| ( c_HOL_Oord__class_Oless @ SV738 @ SY3473 @ SV91 )
| ~ ( c_lessequals @ SV738 @ SY3473 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2383]) ).
thf(3038,plain,
! [SV739: $i,SV92: $i] :
( ( ! [SY3474: $i] :
( ~ ( class_Orderings_Oorder @ SV92 )
| ( c_HOL_Oord__class_Oless @ SV739 @ SY3474 @ SV92 )
| ( SV739 = SY3474 )
| ~ ( c_lessequals @ SV739 @ SY3474 @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2384]) ).
thf(3039,plain,
! [SV740: $i,SV93: $i] :
( ( ! [SY3475: $i] :
( ~ ( class_Orderings_Oorder @ SV93 )
| ( c_HOL_Oord__class_Oless @ SV740 @ SY3475 @ SV93 )
| ( SV740 = SY3475 )
| ~ ( c_lessequals @ SV740 @ SY3475 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2385]) ).
thf(3040,plain,
! [SV741: $i,SV94: $i] :
( ( ! [SY3476: $i] :
( ~ ( class_Orderings_Oorder @ SV94 )
| ( c_HOL_Oord__class_Oless @ SV741 @ SY3476 @ SV94 )
| ~ ( c_lessequals @ SV741 @ SY3476 @ SV94 )
| ( SV741 = SY3476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2386]) ).
thf(3041,plain,
! [SV742: $i,SV95: $i] :
( ( ! [SY3477: $i] :
( ~ ( class_Orderings_Olinorder @ SV95 )
| ( SV742 = SY3477 )
| ~ ( c_lessequals @ SV742 @ SY3477 @ SV95 )
| ( c_HOL_Oord__class_Oless @ SV742 @ SY3477 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2387]) ).
thf(3042,plain,
! [SV743: $i,SV96: $i] :
( ( ! [SY3478: $i] :
( ~ ( class_Orderings_Olinorder @ SV96 )
| ( SV743 = SY3478 )
| ( c_HOL_Oord__class_Oless @ SV743 @ SY3478 @ SV96 )
| ~ ( c_lessequals @ SV743 @ SY3478 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2388]) ).
thf(3043,plain,
! [SV744: $i,SV97: $i] :
( ( ( c_lessequals @ SV97 @ SV744 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV97 ) @ ( c_Suc @ SV744 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2389]) ).
thf(3044,plain,
! [SV745: $i,SV98: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV98 ) @ ( c_Suc @ SV745 ) @ tc_nat )
| ~ ( c_lessequals @ SV98 @ SV745 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2390]) ).
thf(3045,plain,
! [SV746: $i,SV99: $i] :
( ( ( c_lessequals @ SV99 @ SV746 @ tc_nat )
| ( c_lessequals @ SV746 @ SV99 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2391]) ).
thf(3046,plain,
! [SV747: $i,SV100: $i] :
( ( ! [SY3479: $i] :
( ~ ( class_Orderings_Olinorder @ SV100 )
| ( c_lessequals @ SV747 @ SY3479 @ SV100 )
| ( c_lessequals @ SY3479 @ SV747 @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2392]) ).
thf(3047,plain,
! [SV748: $i,SV101: $i] :
( ( ! [SY3480: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV101 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV748 @ ( c_Suc @ SY3480 ) @ SV101 ) @ ( c_HOL_Oone__class_Oone @ SV101 ) @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ SV748 @ ( c_HOL_Oone__class_Oone @ SV101 ) @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ SV748 @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2393]) ).
thf(3048,plain,
! [SV749: $i,SV102: $i] :
( ( ! [SY3481: $i,SY3482: $i] :
( ~ ( class_Orderings_Olinorder @ SV102 )
| ( c_lessequals @ SV749 @ SY3481 @ SV102 )
| ~ ( c_in @ SY3481 @ ( c_List_Oset @ SY3482 @ SV102 ) @ SV102 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV749 @ SY3482 @ SV102 ) @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2394]) ).
thf(3049,plain,
! [SV750: $i,SV103: $i] :
( ( ! [SY3483: $i,SY3484: $i,SY3485: $i] :
( ~ ( class_Orderings_Olinorder @ SV103 )
| ( c_lessequals @ SV750 @ SY3483 @ SV103 )
| ~ ( c_in @ SY3483 @ ( c_List_Oset @ SY3484 @ SV103 ) @ SV103 )
| ~ ( c_in @ SV750 @ ( c_List_Oset @ SY3485 @ SV103 ) @ SV103 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SY3485 @ SY3484 @ SV103 ) @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2395]) ).
thf(3050,plain,
! [SV751: $i,SV104: $i] :
( ( ! [SY3486: $i] :
( ( ( c_List_Olength__unique @ ( c_List_Olist_OCons @ SV104 @ SV751 @ SY3486 ) @ SY3486 )
= ( c_Suc @ ( c_List_Olength__unique @ SV751 @ SY3486 ) ) )
| ( c_in @ SV104 @ ( c_List_Oset @ SV751 @ SY3486 ) @ SY3486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2396]) ).
thf(3051,plain,
! [SV105: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV105 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV105 ) @ ( c_HOL_Ozero__class_Ozero @ SV105 ) @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2397]) ).
thf(3052,plain,
! [SV752: $i,SV106: $i] :
( ( ! [SY3487: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV106 )
| ( c_HOL_Oord__class_Oless @ SV752 @ SY3487 @ SV106 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV752 @ SY3487 @ SV106 ) @ ( c_HOL_Ozero__class_Ozero @ SV106 ) @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2398]) ).
thf(3053,plain,
! [SV753: $i,SV107: $i] :
( ( ! [SY3488: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV107 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV753 @ SY3488 @ SV107 ) @ ( c_HOL_Ozero__class_Ozero @ SV107 ) @ SV107 )
| ~ ( c_HOL_Oord__class_Oless @ SV753 @ SY3488 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2399]) ).
thf(3054,plain,
! [SV108: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV108 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV108 ) @ ( c_HOL_Oone__class_Oone @ SV108 ) @ SV108 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2400]) ).
thf(3055,plain,
! [SV754: $i,SV109: $i] :
( ( ! [SY3489: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV109 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ SV754 ) @ SY3489 ) @ SV109 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SY3489 @ SV109 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV754 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2401]) ).
thf(3056,plain,
! [SV110: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV110 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV110 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV110 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) )
= ( c_HOL_Ozero__class_Ozero @ SV110 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2402]) ).
thf(3057,plain,
! [SV755: $i,SV111: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV111 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV111 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV755 ) @ SV755 ) @ SV111 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV111 ) @ SV755 @ SV111 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2403]) ).
thf(3058,plain,
! [SV756: $i,SV112: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV112 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV112 ) @ SV756 @ SV112 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV112 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV756 ) @ SV756 ) @ SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(3059,plain,
! [SV757: $i,SV113: $i] :
( ( ! [SY3490: $i,SY3491: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV113 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV113 )
| ( c_lessequals @ SV757 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SY3490 ) @ SY3491 ) @ SV113 )
| ~ ( c_lessequals @ SV757 @ SY3491 @ SV113 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SY3490 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2405]) ).
thf(3060,plain,
! [SV758: $i,SV114: $i] :
( ( ! [SY3492: $i,SY3493: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV114 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV114 )
| ( c_lessequals @ SV758 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SY3492 ) @ SY3493 ) @ SV114 )
| ~ ( c_lessequals @ SV758 @ SY3492 @ SV114 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SY3493 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2406]) ).
thf(3061,plain,
! [SV759: $i,SV115: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV115 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV759 ) @ SV759 ) @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 )
| ~ ( c_lessequals @ SV759 @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2407]) ).
thf(3062,plain,
! [SV760: $i,SV116: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV116 )
| ( c_lessequals @ SV760 @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV760 ) @ SV760 ) @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2408]) ).
thf(3063,plain,
! [SV761: $i,SV117: $i] :
( ( ! [SY3494: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV117 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV761 ) @ SY3494 ) @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
| ~ ( c_lessequals @ SY3494 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
| ~ ( c_lessequals @ SV761 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2409]) ).
thf(3064,plain,
! [SV762: $i,SV118: $i] :
( ( ! [SY3495: $i,SY3496: $i,SY3497: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV118 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV762 ) @ SY3495 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SY3496 ) @ SY3497 ) @ SV118 )
| ~ ( c_lessequals @ SY3495 @ SY3497 @ SV118 )
| ~ ( c_HOL_Oord__class_Oless @ SV762 @ SY3496 @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2410]) ).
thf(3065,plain,
! [SV763: $i,SV119: $i] :
( ( ! [SY3498: $i,SY3499: $i,SY3500: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV119 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV119 ) @ SV763 ) @ SY3498 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV119 ) @ SY3499 ) @ SY3500 ) @ SV119 )
| ~ ( c_HOL_Oord__class_Oless @ SY3498 @ SY3500 @ SV119 )
| ~ ( c_lessequals @ SV763 @ SY3499 @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2411]) ).
thf(3066,plain,
! [SV764: $i,SV120: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV120 )
| ( c_HOL_Oord__class_Oless @ SV764 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV120 ) @ SV764 ) @ ( c_HOL_Oone__class_Oone @ SV120 ) ) @ SV120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2412]) ).
thf(3067,plain,
! [SV765: $i,SV121: $i] :
( ( ! [SY3501: $i] :
( ~ ( class_Orderings_Olinorder @ SV121 )
| ~ ( class_Int_Onumber @ SV121 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ SV765 @ SV121 ) @ ( c_Int_Onumber__class_Onumber__of @ SY3501 @ SV121 ) @ SV121 )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ SY3501 @ SV121 ) @ ( c_Int_Onumber__class_Onumber__of @ SV765 @ SV121 ) @ SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2413]) ).
thf(3068,plain,
! [SV766: $i,SV122: $i] :
( ( ! [SY3502: $i] :
( ~ ( class_Orderings_Olinorder @ SV122 )
| ~ ( class_Int_Onumber @ SV122 )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ SV766 @ SV122 ) @ ( c_Int_Onumber__class_Onumber__of @ SY3502 @ SV122 ) @ SV122 )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ SY3502 @ SV122 ) @ ( c_Int_Onumber__class_Onumber__of @ SV766 @ SV122 ) @ SV122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2414]) ).
thf(3069,plain,
! [SV767: $i,SV123: $i] :
( ( ! [SY3503: $i,SY3504: $i] :
( ( c_in @ SV123 @ ( c_List_Oset @ SV767 @ SY3503 ) @ SY3503 )
| ( SV123 = SY3504 )
| ~ ( c_in @ SV123 @ ( c_List_Oset @ ( c_List_Olist_OCons @ SY3504 @ SV767 @ SY3503 ) @ SY3503 ) @ SY3503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2415]) ).
thf(3070,plain,
! [SV768: $i,SV124: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV124 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV768 @ SV124 ) @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2416]) ).
thf(3071,plain,
! [SV769: $i,SV125: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV125 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV125 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV769 @ SV125 ) @ SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2417]) ).
thf(3072,plain,
! [SV128: $i] :
( ( ( SV128
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV128 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2420]) ).
thf(3073,plain,
! [SV770: $i,SV129: $i] :
( ( ! [SY3505: $i] :
( ( hBOOL @ ( hAPP @ SV129 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV770 @ SY3505 @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV129 @ ( c_HOL_Ominus__class_Ominus @ SV770 @ SY3505 @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2421]) ).
thf(3074,plain,
! [SV771: $i,SV130: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV130 @ SV771 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV771 @ SV130 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2422]) ).
thf(3075,plain,
! [SV772: $i,SV131: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV131 @ SV772 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV772 @ SV131 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2423]) ).
thf(3076,plain,
! [SV773: $i,SV132: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV132 @ SV773 @ tc_nat ) @ SV132 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV132 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV773 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2424]) ).
thf(3077,plain,
! [SV774: $i,SV133: $i] :
( ( ! [SY3506: $i,SY3507: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV133 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV774 @ SY3506 @ SV133 ) @ ( c_Power_Opower__class_Opower @ SY3507 @ SY3506 @ SV133 ) @ SV133 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV133 ) @ SV774 @ SV133 )
| ~ ( c_lessequals @ SV774 @ SY3507 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2425]) ).
thf(3078,plain,
! [SV775: $i,SV134: $i] :
( ( ! [SY3508: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV134 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV134 ) @ ( c_Power_Opower__class_Opower @ SV775 @ SY3508 @ SV134 ) @ SV134 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV134 ) @ SV775 @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2426]) ).
thf(3079,plain,
! [SV776: $i,SV135: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV135 )
| ~ ( class_Power_Opower @ SV135 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_Suc @ SV776 ) @ SV135 )
= ( c_HOL_Ozero__class_Ozero @ SV135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2427]) ).
thf(3080,plain,
! [SV777: $i,SV136: $i] :
( ( ! [SY3509: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV136 @ SV777 @ SY3509 ) @ ( tc_List_Olist @ SY3509 ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ SV777 @ ( tc_List_Olist @ SY3509 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2428]) ).
thf(3081,plain,
! [SV778: $i,SV137: $i] :
( ( ! [SY3510: $i] :
( ( c_Suc @ ( c_Nat_Osize__class_Osize @ SV137 @ ( tc_List_Olist @ SV778 ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SY3510 @ SV137 @ SV778 ) @ ( tc_List_Olist @ SV778 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2429]) ).
thf(3082,plain,
! [SV779: $i,SV138: $i] :
( ( ! [SY3511: $i] :
~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV138 @ SV779 @ SY3511 ) @ ( tc_List_Olist @ SY3511 ) ) @ ( c_Nat_Osize__class_Osize @ SV779 @ ( tc_List_Olist @ SY3511 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2430]) ).
thf(3083,plain,
! [SV780: $i,SV139: $i] :
( ( ~ ( class_Power_Opower @ SV139 )
| ( ( c_Power_Opower__class_Opower @ SV780 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV139 )
= ( c_HOL_Oone__class_Oone @ SV139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2431]) ).
thf(3084,plain,
! [SV781: $i,SV140: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV140 )
| ( ( c_Power_Opower__class_Opower @ SV781 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV140 )
= ( c_HOL_Oone__class_Oone @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2432]) ).
thf(3085,plain,
! [SV782: $i,SV141: $i] :
( ( ! [SY3512: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ SV141 @ SV782 @ SY3512 ) @ SY3512 )
= ( c_List_Ohd @ SV141 @ SY3512 ) )
| ( SV141
= ( c_List_Olist_ONil @ SY3512 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2433]) ).
thf(3086,plain,
! [SV783: $i,SV142: $i] :
( ( ( c_List_Ohd @ ( c_List_Oappend @ ( c_List_Olist_ONil @ SV142 ) @ SV783 @ SV142 ) @ SV142 )
= ( c_List_Ohd @ SV783 @ SV142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2434]) ).
thf(3087,plain,
! [SV784: $i,SV143: $i] :
( ( ! [SY3513: $i,SY3514: $i] :
( ( c_in @ SV143 @ ( c_List_Oset @ SV784 @ SY3513 ) @ SY3513 )
| ~ ( c_in @ SV143 @ ( c_List_Oset @ ( c_List_Otake @ SY3514 @ SV784 @ SY3513 ) @ SY3513 ) @ SY3513 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2435]) ).
thf(3088,plain,
! [SV785: $i,SV144: $i] :
( ( ! [SY3515: $i,SY3516: $i] :
( ( c_in @ SV144 @ ( c_List_Oset @ SV785 @ SY3515 ) @ SY3515 )
| ~ ( c_in @ SV144 @ ( c_List_Oset @ ( c_List_Odrop @ SY3516 @ SV785 @ SY3515 ) @ SY3515 ) @ SY3515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2436]) ).
thf(3089,plain,
! [SV786: $i,SV145: $i] :
( ( ! [SY3517: $i,SY3518: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ SV145 @ SV786 @ SY3517 ) @ ( c_Suc @ SY3518 ) @ SY3517 )
= ( c_List_Onth @ SV786 @ SY3518 @ SY3517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2437]) ).
thf(3090,plain,
! [SV787: $i,SV146: $i] :
( ( ! [SY3519: $i,SY3520: $i] :
( ( c_List_Otake @ ( c_Suc @ SV146 ) @ ( c_List_Olist_OCons @ SV787 @ SY3519 @ SY3520 ) @ SY3520 )
= ( c_List_Olist_OCons @ SV787 @ ( c_List_Otake @ SV146 @ SY3519 @ SY3520 ) @ SY3520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2438]) ).
thf(3091,plain,
! [SV788: $i,SV147: $i] :
( ( ! [SY3521: $i,SY3522: $i] :
( ( hBOOL @ ( hAPP @ SV147 @ SV788 ) )
| ~ ( c_in @ SV788 @ ( c_List_Oset @ ( c_List_OtakeWhile @ SV147 @ SY3521 @ SY3522 ) @ SY3522 ) @ SY3522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2439]) ).
thf(3092,plain,
! [SV789: $i,SV148: $i] :
( ( ! [SY3523: $i,SY3524: $i] :
( ( c_in @ SV148 @ ( c_List_Oset @ SV789 @ SY3523 ) @ SY3523 )
| ~ ( c_in @ SV148 @ ( c_List_Oset @ ( c_List_OtakeWhile @ SY3524 @ SV789 @ SY3523 ) @ SY3523 ) @ SY3523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2440]) ).
thf(3093,plain,
! [SV790: $i,SV149: $i] :
( ( ! [SY3525: $i,SY3526: $i] :
( ( hBOOL @ ( hAPP @ SV149 @ SV790 ) )
| ~ ( c_in @ SV790 @ ( c_List_Oset @ SY3525 @ SY3526 ) @ SY3526 )
| ~ ( c_List_Olistsp @ SV149 @ SY3525 @ SY3526 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2441]) ).
thf(3094,plain,
! [SV791: $i,SV150: $i] :
( ( ! [SY3527: $i,SY3528: $i] :
( ( SV150 = SV791 )
| ~ ( c_in @ SV150 @ ( c_List_Oset @ ( c_List_Oreplicate @ SY3527 @ SV791 @ SY3528 ) @ SY3528 ) @ SY3528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2442]) ).
thf(3095,plain,
! [SV792: $i,SV151: $i] :
( ( ! [SY3529: $i] :
( ( ( c_List_Onth @ ( c_List_Orev @ SV151 @ SV792 ) @ SY3529 @ SV792 )
= ( c_List_Onth @ SV151 @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SV151 @ ( tc_List_Olist @ SV792 ) ) @ ( c_Suc @ SY3529 ) @ tc_nat ) @ SV792 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3529 @ ( c_Nat_Osize__class_Osize @ SV151 @ ( tc_List_Olist @ SV792 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2443]) ).
thf(3096,plain,
! [SV793: $i,SV152: $i] :
( ( ! [SY3530: $i,SY3531: $i] :
( ~ ( class_Orderings_Olinorder @ SV152 )
| ( c_lessequals @ ( c_List_Onth @ SV793 @ SY3530 @ SV152 ) @ ( c_List_Onth @ SV793 @ SY3531 @ SV152 ) @ SV152 )
| ~ ( c_lessequals @ SY3530 @ SY3531 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY3531 @ ( c_Nat_Osize__class_Osize @ SV793 @ ( tc_List_Olist @ SV152 ) ) @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ SV793 @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2444]) ).
thf(3097,plain,
! [SV794: $i,SV153: $i] :
( ( ! [SY3532: $i,SY3533: $i] :
( ~ ( class_Orderings_Olinorder @ SV153 )
| ( c_lessequals @ ( c_List_Onth @ SV794 @ SY3532 @ SV153 ) @ ( c_List_Onth @ SV794 @ SY3533 @ SV153 ) @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SY3533 @ ( c_Nat_Osize__class_Osize @ SV794 @ ( tc_List_Olist @ SV153 ) ) @ tc_nat )
| ~ ( c_lessequals @ SY3532 @ SY3533 @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ SV794 @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2445]) ).
thf(3098,plain,
! [SV795: $i,SV154: $i] :
( ( ! [SY3534: $i,SY3535: $i] :
( ( c_List_Odrop @ ( c_Suc @ SV154 ) @ ( c_List_Olist_OCons @ SV795 @ SY3534 @ SY3535 ) @ SY3535 )
= ( c_List_Odrop @ SV154 @ SY3534 @ SY3535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2446]) ).
thf(3099,plain,
! [SV796: $i,SV155: $i] :
( ( ! [SY3536: $i] :
( ( ( c_List_Otake @ SV155 @ SV796 @ SY3536 )
= SV796 )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV796 @ ( tc_List_Olist @ SY3536 ) ) @ SV155 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2447]) ).
thf(3100,plain,
! [SV797: $i,SV156: $i] :
( ( ! [SY3537: $i,SY3538: $i] :
( ~ ( class_Orderings_Olinorder @ SV156 )
| ( c_lessequals @ SV797 @ SY3537 @ SV156 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV797 @ ( c_List_Olist_OCons @ SY3537 @ SY3538 @ SV156 ) @ SV156 ) @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2448]) ).
thf(3101,plain,
! [SV798: $i,SV157: $i] :
( ( ! [SY3539: $i,SY3540: $i] :
( ~ ( class_Orderings_Olinorder @ SV157 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV798 @ ( c_List_Olist_OCons @ SY3539 @ SY3540 @ SV157 ) @ SV157 ) @ SV157 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY3539 @ SY3540 @ SV157 ) @ SV157 )
| ~ ( c_lessequals @ SV798 @ SY3539 @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2449]) ).
thf(3102,plain,
! [SV799: $i,SV158: $i] :
( ( ! [SY3541: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Odrop @ SV158 @ SV799 @ SY3541 ) @ ( tc_List_Olist @ SY3541 ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SV799 @ ( tc_List_Olist @ SY3541 ) ) @ SV158 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2450]) ).
thf(3103,plain,
! [SV800: $i,SV159: $i] :
( ( ! [SY3542: $i,SY3543: $i,SY3544: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV159 @ SV800 @ SY3542 ) @ ( c_Suc @ SY3543 ) @ SY3544 @ SY3542 )
= ( c_List_Olist_OCons @ SV159 @ ( c_List_Olist__update @ SV800 @ SY3543 @ SY3544 @ SY3542 ) @ SY3542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2451]) ).
thf(3104,plain,
! [SV801: $i,SV160: $i] :
( ( ! [SY3545: $i] :
( ( ( c_List_Ohd @ ( c_List_Oreplicate @ SV160 @ SV801 @ SY3545 ) @ SY3545 )
= SV801 )
| ( SV160
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2452]) ).
thf(3105,plain,
! [SV802: $i,SV161: $i] :
( ( ! [SY3546: $i] :
( ( c_List_Oreplicate @ ( c_Suc @ SV161 ) @ SV802 @ SY3546 )
= ( c_List_Olist_OCons @ SV802 @ ( c_List_Oreplicate @ SV161 @ SV802 @ SY3546 ) @ SY3546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2453]) ).
thf(3106,plain,
! [SV803: $i,SV162: $i] :
( ( ! [SY3547: $i,SY3548: $i] :
( ( ( c_List_Olist__update @ SV162 @ SV803 @ SY3547 @ SY3548 )
= SV162 )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV162 @ ( tc_List_Olist @ SY3548 ) ) @ SV803 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2454]) ).
thf(3107,plain,
! [SV804: $i,SV163: $i] :
( ( ! [SY3549: $i] : ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ SV163 @ SV804 @ SY3549 ) @ ( tc_List_Olist @ SY3549 ) ) @ ( c_Nat_Osize__class_Osize @ SV804 @ ( tc_List_Olist @ SY3549 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2455]) ).
thf(3108,plain,
! [SV805: $i,SV164: $i] :
( ( ! [SY3550: $i] :
( ( c_in @ SV164 @ ( c_List_Oset @ SV805 @ SY3550 ) @ SY3550 )
| ~ ( c_in @ SV164 @ ( c_List_Oset @ ( c_List_Obutlast @ SV805 @ SY3550 ) @ SY3550 ) @ SY3550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2456]) ).
thf(3109,plain,
! [SV806: $i,SV165: $i] :
( ( ! [SY3551: $i,SY3552: $i] :
( ( c_List_Odrop @ SV165 @ ( c_List_Otake @ SV806 @ SY3551 @ SY3552 ) @ SY3552 )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ SV806 @ SV165 @ tc_nat ) @ ( c_List_Odrop @ SV165 @ SY3551 @ SY3552 ) @ SY3552 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2457]) ).
thf(3110,plain,
! [SV807: $i,SV166: $i] :
( ( ! [SY3553: $i,SY3554: $i] :
( ( c_in @ SV166 @ ( c_List_Oset @ SV807 @ SY3553 ) @ SY3553 )
| ~ ( c_in @ SV166 @ ( c_List_Oset @ ( c_List_Osublist @ SV807 @ SY3554 @ SY3553 ) @ SY3553 ) @ SY3553 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2458]) ).
thf(3111,plain,
! [SV808: $i,SV167: $i] :
( ( ! [SY3555: $i,SY3556: $i] :
( ~ ( c_in @ SV167 @ ( c_List_Oset @ ( c_List_Osublist @ SV808 @ SY3555 @ SY3556 ) @ SY3556 ) @ SY3556 )
| ( c_in @ SV167 @ ( c_List_Oset @ SV808 @ SY3556 ) @ SY3556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2459]) ).
thf(3112,plain,
! [SV809: $i,SV168: $i] :
( ( ! [SY3557: $i,SY3558: $i] :
( ( c_List_Odrop @ SV168 @ ( c_List_Oreplicate @ SV809 @ SY3557 @ SY3558 ) @ SY3558 )
= ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ SV809 @ SV168 @ tc_nat ) @ SY3557 @ SY3558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2460]) ).
thf(3113,plain,
! [SV810: $i,SV169: $i] :
( ( ! [SY3559: $i,SY3560: $i,SY3561: $i,SY3562: $i] :
( ~ ( class_Orderings_Olinorder @ SV169 )
| ( ( c_List_Olinorder__class_Oinsort__key @ SV810 @ SY3559 @ ( c_List_Olist_OCons @ SY3560 @ SY3561 @ SY3562 ) @ SY3562 @ SV169 )
= ( c_List_Olist_OCons @ SY3559 @ ( c_List_Olist_OCons @ SY3560 @ SY3561 @ SY3562 ) @ SY3562 ) )
| ~ ( c_lessequals @ ( hAPP @ SV810 @ SY3559 ) @ ( hAPP @ SV810 @ SY3560 ) @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2461]) ).
thf(3114,plain,
! [SV811: $i,SV170: $i] :
( ( ! [SY3563: $i,SY3564: $i,SY3565: $i,SY3566: $i] :
( ~ ( class_Orderings_Olinorder @ SV170 )
| ( ( c_List_Olinorder__class_Oinsort__key @ SV811 @ SY3563 @ ( c_List_Olist_OCons @ SY3564 @ SY3565 @ SY3566 ) @ SY3566 @ SV170 )
= ( c_List_Olist_OCons @ SY3564 @ ( c_List_Olinorder__class_Oinsort__key @ SV811 @ SY3563 @ SY3565 @ SY3566 @ SV170 ) @ SY3566 ) )
| ( c_lessequals @ ( hAPP @ SV811 @ SY3563 ) @ ( hAPP @ SV811 @ SY3564 ) @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2462]) ).
thf(3115,plain,
! [SV812: $i,SV171: $i] :
( ( ! [SY3567: $i,SY3568: $i,SY3569: $i] :
( ~ ( class_Orderings_Olinorder @ SV171 )
| ( ( c_Nat_Osize__class_Osize @ ( c_List_Olinorder__class_Oinsort__key @ SV812 @ SY3567 @ SY3568 @ SY3569 @ SV171 ) @ ( tc_List_Olist @ SY3569 ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ SY3568 @ ( tc_List_Olist @ SY3569 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2463]) ).
thf(3116,plain,
! [SV813: $i,SV172: $i] :
( ( ! [SY3570: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV172 @ SV813 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3570 @ SV813 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV172 @ SY3570 @ tc_nat )
| ~ ( c_lessequals @ SV813 @ SY3570 @ tc_nat )
| ~ ( c_lessequals @ SV813 @ SV172 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2464]) ).
thf(3117,plain,
! [SV814: $i,SV173: $i] :
( ( ! [SY3571: $i] :
( ( c_lessequals @ SV173 @ SV814 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV173 @ SY3571 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV814 @ SY3571 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SY3571 @ SV814 @ tc_nat )
| ~ ( c_lessequals @ SY3571 @ SV173 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2465]) ).
thf(3118,plain,
! [SV815: $i,SV174: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV174 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ SV815 ) @ SV174 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV174 ) @ ( c_HOL_Oone__class_Oone @ SV174 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV815 @ SV174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2466]) ).
thf(3119,plain,
! [SV816: $i,SV175: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV175 @ SV816 @ tc_nat ) @ SV175 @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2467]) ).
thf(3120,plain,
! [SV817: $i,SV176: $i] :
( ( ! [SY3572: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV176 @ SV817 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3572 @ SV817 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV176 @ SY3572 @ tc_nat ) )
| ~ ( c_lessequals @ SV817 @ SY3572 @ tc_nat )
| ~ ( c_lessequals @ SV817 @ SV176 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2468]) ).
thf(3121,plain,
! [SV818: $i,SV177: $i] :
( ( ! [SY3573: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV177 @ SV818 @ tc_nat ) @ SY3573 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV177 @ SY3573 @ tc_nat ) @ SV818 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2469]) ).
thf(3122,plain,
! [SV819: $i,SV178: $i] :
( ( ! [SY3574: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV178 @ SV819 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SY3574 @ SV819 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV819 @ SV178 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV178 @ SY3574 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2470]) ).
thf(3123,plain,
! [SV820: $i,SV179: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV179 ) @ SV820 @ tc_nat )
| ( ( c_Suc @ SV179 )
= SV820 )
| ~ ( c_HOL_Oord__class_Oless @ SV179 @ SV820 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2471]) ).
thf(3124,plain,
! [SV821: $i,SV180: $i] :
( ( ~ ( c_lessequals @ SV180 @ SV821 @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ SV821 ) @ SV180 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2472]) ).
thf(3125,plain,
! [SV822: $i,SV181: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV181 ) @ SV822 @ tc_nat )
| ( c_lessequals @ SV822 @ SV181 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2473]) ).
thf(3126,plain,
! [SV823: $i,SV182: $i] :
( ( ! [SY3575: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV182 ) @ SV823 @ tc_nat ) @ ( c_Suc @ SY3575 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV182 @ SV823 @ tc_nat ) @ SY3575 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2474]) ).
thf(3127,plain,
! [SV824: $i,SV184: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV184 @ ( c_HOL_Ominus__class_Ominus @ SV184 @ SV824 @ tc_nat ) @ tc_nat )
= SV824 )
| ~ ( c_lessequals @ SV824 @ SV184 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2476]) ).
thf(3128,plain,
! [SV825: $i,SV185: $i] :
( ( ( SV185
= ( c_Suc @ SV825 ) )
| ( c_lessequals @ SV185 @ SV825 @ tc_nat )
| ~ ( c_lessequals @ SV185 @ ( c_Suc @ SV825 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2477]) ).
thf(3129,plain,
! [SV186: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV186 @ SV186 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV186 @ ( c_Suc @ SV186 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2478]) ).
thf(3130,plain,
! [SV826: $i,SV187: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV187 @ SV826 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV826 @ ( c_Suc @ SV187 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2479]) ).
thf(3131,plain,
! [SV827: $i,SV188: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV188 @ ( c_Suc @ SV827 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV827 @ SV188 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2480]) ).
thf(3132,plain,
! [SV828: $i,SV189: $i] :
( ( ( c_in @ ( c_List_Ohd @ SV189 @ SV828 ) @ ( c_List_Oset @ SV189 @ SV828 ) @ SV828 )
| ( SV189
= ( c_List_Olist_ONil @ SV828 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2481]) ).
thf(3133,plain,
! [SV829: $i,SV190: $i] :
( ( ! [SY3576: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV190 )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV190 ) @ SV829 ) @ SY3576 ) @ SY3576 @ SV190 )
= SV829 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2482]) ).
thf(3134,plain,
! [SV830: $i,SV191: $i] :
( ( ! [SY3577: $i,SY3578: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV191 )
| ( c_lessequals @ SV830 @ SY3577 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY3578 @ SV830 @ SV191 ) @ ( c_Power_Opower__class_Opower @ SY3578 @ SY3577 @ SV191 ) @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV191 ) @ SY3578 @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2483]) ).
thf(3135,plain,
! [SV831: $i,SV192: $i] :
( ( ! [SY3579: $i,SY3580: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV192 )
| ( c_lessequals @ SV831 @ SY3579 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY3580 @ SV831 @ SV192 ) @ ( c_Power_Opower__class_Opower @ SY3580 @ SY3579 @ SV192 ) @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV192 ) @ SY3580 @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2484]) ).
thf(3136,plain,
! [SV832: $i,SV193: $i] :
( ( ! [SY3581: $i,SY3582: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV193 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV832 @ SY3581 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SV832 @ SY3582 @ SV193 ) @ SV193 )
| ~ ( c_lessequals @ SY3581 @ SY3582 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV193 ) @ SV832 @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2485]) ).
thf(3137,plain,
! [SV833: $i,SV194: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV194 ) @ ( c_Suc @ SV833 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV194 @ SV833 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2486]) ).
thf(3138,plain,
! [SV834: $i,SV195: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV195 @ SV834 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV195 ) @ ( c_Suc @ SV834 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2487]) ).
thf(3139,plain,
! [SV835: $i,SV196: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV196 ) @ ( c_Suc @ SV835 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV196 @ SV835 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2488]) ).
thf(3140,plain,
! [SV836: $i,SV197: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV197 )
| ~ ( class_Int_Onumber__ring @ SV197 )
| ( ( c_HOL_Ominus__class_Ominus @ SV836 @ SV836 @ SV197 )
= ( c_HOL_Ozero__class_Ozero @ SV197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2489]) ).
thf(3141,plain,
! [SV837: $i,SV198: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV198 )
| ( ( c_HOL_Ominus__class_Ominus @ SV837 @ SV837 @ SV198 )
= ( c_HOL_Ozero__class_Ozero @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2490]) ).
thf(3142,plain,
! [SV838: $i,SV199: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV199 )
| ( ( c_HOL_Ominus__class_Ominus @ SV838 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
= SV838 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2491]) ).
thf(3143,plain,
! [SV839: $i,SV200: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV200 )
| ( ( c_HOL_Ominus__class_Ominus @ SV839 @ SV839 @ SV200 )
= ( c_HOL_Ozero__class_Ozero @ SV200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2492]) ).
thf(3144,plain,
! [SV840: $i,SV201: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV201 )
| ( ( c_HOL_Ominus__class_Ominus @ SV840 @ SV840 @ SV201 )
= ( c_HOL_Ozero__class_Ozero @ SV201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2493]) ).
thf(3145,plain,
! [SV202: $i] :
( ( ( SV202
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV202 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2494]) ).
thf(3146,plain,
! [SV841: $i,SV207: $i] :
( ( ! [SY3583: $i] :
( ( c_List_Ohd @ ( c_List_Olist_OCons @ SV207 @ SV841 @ SY3583 ) @ SY3583 )
= SV207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2499]) ).
thf(3147,plain,
! [SV842: $i,SV208: $i] :
( ( ! [SY3584: $i,SY3585: $i,SY3586: $i] :
( ( c_ListOrder_Ostep1 @ SV208 @ ( c_List_Olist_OCons @ SV842 @ SY3584 @ SY3585 ) @ ( c_List_Olist_OCons @ SV842 @ SY3586 @ SY3585 ) @ SY3585 )
| ~ ( c_ListOrder_Ostep1 @ SV208 @ SY3584 @ SY3586 @ SY3585 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2500]) ).
thf(3148,plain,
! [SV843: $i,SV209: $i] :
( ( ! [SY3587: $i,SY3588: $i,SY3589: $i,SY3590: $i] :
( ( c_ListOrder_Ostep1 @ SV209 @ SV843 @ SY3587 @ SY3588 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV209 @ SY3589 ) @ SY3590 ) )
| ~ ( c_ListOrder_Ostep1 @ SV209 @ ( c_List_Olist_OCons @ SY3589 @ SV843 @ SY3588 ) @ ( c_List_Olist_OCons @ SY3590 @ SY3587 @ SY3588 ) @ SY3588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2501]) ).
thf(3149,plain,
! [SV844: $i,SV210: $i] :
( ( ! [SY3591: $i,SY3592: $i,SY3593: $i,SY3594: $i] :
( ( c_ListOrder_Ostep1 @ SV210 @ SV844 @ SY3591 @ SY3592 )
| ( SY3591 = SV844 )
| ~ ( c_ListOrder_Ostep1 @ SV210 @ ( c_List_Olist_OCons @ SY3593 @ SV844 @ SY3592 ) @ ( c_List_Olist_OCons @ SY3594 @ SY3591 @ SY3592 ) @ SY3592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2502]) ).
thf(3150,plain,
! [SV845: $i,SV211: $i] :
( ( ! [SY3595: $i,SY3596: $i,SY3597: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV211 @ SV845 ) @ SY3595 ) )
| ( c_ListOrder_Ostep1 @ SV211 @ ( c_List_Olist_OCons @ SV845 @ SY3596 @ SY3597 ) @ ( c_List_Olist_OCons @ SY3595 @ SY3596 @ SY3597 ) @ SY3597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2503]) ).
thf(3151,plain,
! [SV846: $i,SV212: $i] :
( ( ! [SY3598: $i,SY3599: $i,SY3600: $i,SY3601: $i] :
( ( SV212 = SV846 )
| ( SY3598 = SY3599 )
| ~ ( c_ListOrder_Ostep1 @ SY3600 @ ( c_List_Olist_OCons @ SV846 @ SY3599 @ SY3601 ) @ ( c_List_Olist_OCons @ SV212 @ SY3598 @ SY3601 ) @ SY3601 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2504]) ).
thf(3152,plain,
! [SV847: $i,SV213: $i] :
( ( ! [SY3602: $i,SY3603: $i,SY3604: $i,SY3605: $i] :
( ( SV213 = SV847 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY3602 @ SV847 ) @ SV213 ) )
| ~ ( c_ListOrder_Ostep1 @ SY3602 @ ( c_List_Olist_OCons @ SV847 @ SY3603 @ SY3604 ) @ ( c_List_Olist_OCons @ SV213 @ SY3605 @ SY3604 ) @ SY3604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2505]) ).
thf(3153,plain,
! [SV848: $i,SV214: $i] :
( ( ! [SY3606: $i] :
~ ( c_ListOrder_Ostep1 @ SV214 @ SV848 @ ( c_List_Olist_ONil @ SY3606 ) @ SY3606 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2506]) ).
thf(3154,plain,
! [SV849: $i,SV215: $i] :
( ( ! [SY3607: $i] :
~ ( c_ListOrder_Ostep1 @ SV215 @ ( c_List_Olist_ONil @ SV849 ) @ SY3607 @ SV849 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2507]) ).
thf(3155,plain,
! [SV850: $i,SV216: $i] :
( ( ! [SY3608: $i,SY3609: $i] :
( ~ ( class_Orderings_Olinorder @ SV216 )
| ( c_lessequals @ ( c_List_Onth @ SV850 @ SY3608 @ SV216 ) @ ( c_List_Onth @ SV850 @ SY3609 @ SV216 ) @ SV216 )
| ~ ( c_HOL_Oord__class_Oless @ SY3608 @ ( c_Nat_Osize__class_Osize @ SV850 @ ( tc_List_Olist @ SV216 ) ) @ tc_nat )
| ~ ( c_lessequals @ SY3609 @ SY3608 @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Orev @ SV850 @ SV216 ) @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2508]) ).
thf(3156,plain,
! [SV851: $i,SV217: $i] :
( ( ! [SY3610: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV217 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV217 ) @ SV851 ) @ SY3610 ) @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 )
| ~ ( c_lessequals @ SY3610 @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 )
| ~ ( c_HOL_Oord__class_Oless @ SV851 @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2509]) ).
thf(3157,plain,
! [SV852: $i,SV218: $i] :
( ( ! [SY3611: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV218 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV218 ) @ SV852 ) @ SY3611 ) @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
| ~ ( c_HOL_Oord__class_Oless @ SY3611 @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
| ~ ( c_lessequals @ SV852 @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2510]) ).
thf(3158,plain,
! [SV853: $i,SV219: $i] :
( ( ! [SY3612: $i,SY3613: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV219 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV219 )
| ( c_HOL_Oord__class_Oless @ SV853 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV219 ) @ SY3612 ) @ SY3613 ) @ SV219 )
| ~ ( c_lessequals @ SV853 @ SY3613 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SY3612 @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2511]) ).
thf(3159,plain,
! [SV854: $i,SV220: $i] :
( ( ! [SY3614: $i,SY3615: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV220 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV220 )
| ( c_HOL_Oord__class_Oless @ SV854 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV220 ) @ SY3614 ) @ SY3615 ) @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ SV854 @ SY3615 @ SV220 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SY3614 @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2512]) ).
thf(3160,plain,
! [SV855: $i,SV221: $i] :
( ( ! [SY3616: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV221 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SV855 ) @ SY3616 ) @ SV221 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ SY3616 @ SV221 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ SV855 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2513]) ).
thf(3161,plain,
! [SV856: $i,SV222: $i] :
( ( ! [SY3617: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV222 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SV856 ) @ SY3617 ) @ SV222 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ SY3617 @ SV222 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ SV856 @ SV222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2514]) ).
thf(3162,plain,
! [SV223: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV223 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV223 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV223 ) @ ( c_HOL_Oone__class_Oone @ SV223 ) ) @ ( c_HOL_Oone__class_Oone @ SV223 ) ) @ SV223 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2515]) ).
thf(3163,plain,
! [SV857: $i,SV224: $i] :
( ( ! [SY3618: $i,SY3619: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV224 )
| ( c_HOL_Oord__class_Oless @ SV857 @ SY3618 @ SV224 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV224 ) @ SY3618 @ SV224 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV857 @ SY3619 @ SV224 ) @ ( c_Power_Opower__class_Opower @ SY3618 @ SY3619 @ SV224 ) @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2516]) ).
thf(3164,plain,
! [SV858: $i,SV225: $i] :
( ( ! [SY3620: $i,SY3621: $i] :
( ( c_in @ SV225 @ ( c_List_Oset @ ( c_List_Oappend @ SV858 @ ( c_List_Olist_OCons @ SV225 @ SY3620 @ SY3621 ) @ SY3621 ) @ SY3621 ) @ SY3621 )
| ( c_in @ SV225 @ ( c_List_Oset @ SV858 @ SY3621 ) @ SY3621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2517]) ).
thf(3165,plain,
! [SV859: $i,SV226: $i] :
( ( ! [SY3622: $i,SY3623: $i] :
( ( c_in @ SV226 @ ( c_List_Oset @ ( c_List_Oappend @ SV859 @ ( c_List_Olist_OCons @ SV226 @ SY3622 @ SY3623 ) @ SY3623 ) @ SY3623 ) @ SY3623 )
| ( c_in @ SV226 @ ( c_List_Oset @ SY3622 @ SY3623 ) @ SY3623 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2518]) ).
thf(3166,plain,
! [SV860: $i,SV227: $i] :
( ( ! [SY3624: $i,SY3625: $i] : ( c_in @ SV227 @ ( c_List_Oset @ ( c_List_Oappend @ SV860 @ ( c_List_Olist_OCons @ SV227 @ SY3624 @ SY3625 ) @ SY3625 ) @ SY3625 ) @ SY3625 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2519]) ).
thf(3167,plain,
! [SV228: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV228 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV228 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV228 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV228 )
= ( c_HOL_Oone__class_Oone @ SV228 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2520]) ).
thf(3168,plain,
! [SV861: $i,SV229: $i] :
( ( ! [SY3626: $i,SY3627: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV229 )
| ( c_HOL_Oord__class_Oless @ SV861 @ SY3626 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY3627 @ SV861 @ SV229 ) @ ( c_Power_Opower__class_Opower @ SY3627 @ SY3626 @ SV229 ) @ SV229 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV229 ) @ SY3627 @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2521]) ).
thf(3169,plain,
! [SV862: $i,SV230: $i] :
( ( ! [SY3628: $i,SY3629: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV230 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV862 @ SY3628 @ SV230 ) @ ( c_Power_Opower__class_Opower @ SV862 @ SY3629 @ SV230 ) @ SV230 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV230 ) @ SV862 @ SV230 )
| ~ ( c_HOL_Oord__class_Oless @ SY3628 @ SY3629 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2522]) ).
thf(3170,plain,
! [SV863: $i,SV231: $i] :
( ( ! [SY3630: $i,SY3631: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV231 )
| ( c_HOL_Oord__class_Oless @ SV863 @ SY3630 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY3631 @ SV863 @ SV231 ) @ ( c_Power_Opower__class_Opower @ SY3631 @ SY3630 @ SV231 ) @ SV231 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV231 ) @ SY3631 @ SV231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2523]) ).
thf(3171,plain,
! [SV864: $i,SV232: $i] :
( ( ! [SY3632: $i,SY3633: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV232 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV864 @ SY3632 @ SV232 ) @ ( c_Power_Opower__class_Opower @ SV864 @ SY3633 @ SV232 ) @ SV232 )
| ~ ( c_HOL_Oord__class_Oless @ SY3632 @ SY3633 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV232 ) @ SV864 @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2524]) ).
thf(3172,plain,
! [SV865: $i,SV233: $i] :
( ( ! [SY3634: $i,SY3635: $i,SY3636: $i,SY3637: $i] :
( ( SV233 = SV865 )
| ( SY3634 = SY3635 )
| ~ ( c_ListOrder_Ostep1 @ SY3636 @ ( c_List_Oappend @ SV233 @ ( c_List_Olist_OCons @ SY3634 @ ( c_List_Olist_ONil @ SY3637 ) @ SY3637 ) @ SY3637 ) @ ( c_List_Oappend @ SV865 @ ( c_List_Olist_OCons @ SY3635 @ ( c_List_Olist_ONil @ SY3637 ) @ SY3637 ) @ SY3637 ) @ SY3637 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2525]) ).
thf(3173,plain,
! [SV866: $i,SV234: $i] :
( ( ! [SY3638: $i,SY3639: $i,SY3640: $i,SY3641: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV234 @ SV866 ) @ SY3638 ) )
| ( SV866 = SY3638 )
| ~ ( c_ListOrder_Ostep1 @ SV234 @ ( c_List_Oappend @ SY3639 @ ( c_List_Olist_OCons @ SV866 @ ( c_List_Olist_ONil @ SY3640 ) @ SY3640 ) @ SY3640 ) @ ( c_List_Oappend @ SY3641 @ ( c_List_Olist_OCons @ SY3638 @ ( c_List_Olist_ONil @ SY3640 ) @ SY3640 ) @ SY3640 ) @ SY3640 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2526]) ).
thf(3174,plain,
! [SV867: $i,SV235: $i] :
( ( ! [SY3642: $i,SY3643: $i,SY3644: $i,SY3645: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV867 ) @ SY3642 ) )
| ( c_ListOrder_Ostep1 @ SV235 @ SY3643 @ SY3644 @ SY3645 )
| ~ ( c_ListOrder_Ostep1 @ SV235 @ ( c_List_Oappend @ SY3643 @ ( c_List_Olist_OCons @ SV867 @ ( c_List_Olist_ONil @ SY3645 ) @ SY3645 ) @ SY3645 ) @ ( c_List_Oappend @ SY3644 @ ( c_List_Olist_OCons @ SY3642 @ ( c_List_Olist_ONil @ SY3645 ) @ SY3645 ) @ SY3645 ) @ SY3645 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2527]) ).
thf(3175,plain,
! [SV868: $i,SV236: $i] :
( ( ! [SY3646: $i,SY3647: $i,SY3648: $i,SY3649: $i] :
( ( SV236 = SV868 )
| ( c_ListOrder_Ostep1 @ SY3646 @ SV236 @ SV868 @ SY3647 )
| ~ ( c_ListOrder_Ostep1 @ SY3646 @ ( c_List_Oappend @ SV236 @ ( c_List_Olist_OCons @ SY3648 @ ( c_List_Olist_ONil @ SY3647 ) @ SY3647 ) @ SY3647 ) @ ( c_List_Oappend @ SV868 @ ( c_List_Olist_OCons @ SY3649 @ ( c_List_Olist_ONil @ SY3647 ) @ SY3647 ) @ SY3647 ) @ SY3647 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2528]) ).
thf(3176,plain,
! [SV869: $i,SV237: $i] :
( ( ( ( c_List_Ohd @ SV237 @ SV869 )
= ( c_List_Onth @ SV237 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV869 ) )
| ( SV237
= ( c_List_Olist_ONil @ SV869 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2529]) ).
thf(3177,plain,
! [SV870: $i,SV238: $i] :
( ( ! [SY3650: $i,SY3651: $i,SY3652: $i] :
( ( ( c_List_OtakeWhile @ SV238 @ ( c_List_Oappend @ SV870 @ SY3650 @ SY3651 ) @ SY3651 )
= ( c_List_OtakeWhile @ SV238 @ SV870 @ SY3651 ) )
| ( hBOOL @ ( hAPP @ SV238 @ SY3652 ) )
| ~ ( c_in @ SY3652 @ ( c_List_Oset @ SV870 @ SY3651 ) @ SY3651 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2530]) ).
thf(3178,plain,
! [SV871: $i,SV239: $i] :
( ( ! [SY3653: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV239 @ SV871 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV239 @ SY3653 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV871 @ SY3653 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2531]) ).
thf(3179,plain,
! [SV872: $i,SV240: $i] :
( ( ! [SY3654: $i] :
( ( ( c_List_Odrop @ SV240 @ SV872 @ SY3654 )
= ( c_List_Olist_ONil @ SY3654 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV872 @ ( tc_List_Olist @ SY3654 ) ) @ SV240 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2532]) ).
thf(3180,plain,
! [SV873: $i,SV241: $i] :
( ( ! [SY3655: $i,SY3656: $i] :
( ( c_List_Otake @ SV241 @ ( c_List_Oappend @ SV873 @ SY3655 @ SY3656 ) @ SY3656 )
= ( c_List_Oappend @ ( c_List_Otake @ SV241 @ SV873 @ SY3656 ) @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ SV241 @ ( c_Nat_Osize__class_Osize @ SV873 @ ( tc_List_Olist @ SY3656 ) ) @ tc_nat ) @ SY3655 @ SY3656 ) @ SY3656 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2533]) ).
thf(3181,plain,
! [SV874: $i,SV242: $i] :
( ( ! [SY3657: $i,SY3658: $i] :
( ( c_List_Odrop @ SV242 @ ( c_List_Oappend @ SV874 @ SY3657 @ SY3658 ) @ SY3658 )
= ( c_List_Oappend @ ( c_List_Odrop @ SV242 @ SV874 @ SY3658 ) @ ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ SV242 @ ( c_Nat_Osize__class_Osize @ SV874 @ ( tc_List_Olist @ SY3658 ) ) @ tc_nat ) @ SY3657 @ SY3658 ) @ SY3658 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2534]) ).
thf(3182,plain,
! [SV875: $i,SV243: $i] :
( ( ! [SY3659: $i,SY3660: $i] :
( ( c_in @ SV243 @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ SV875 @ SY3659 @ SY3660 ) @ SY3660 ) @ SY3660 ) @ SY3660 )
| ~ ( c_in @ SV243 @ ( c_List_Oset @ ( c_List_Obutlast @ SY3659 @ SY3660 ) @ SY3660 ) @ SY3660 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2535]) ).
thf(3183,plain,
! [SV876: $i,SV244: $i] :
( ( ! [SY3661: $i,SY3662: $i] :
( ( c_in @ SV244 @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ SV876 @ SY3661 @ SY3662 ) @ SY3662 ) @ SY3662 ) @ SY3662 )
| ~ ( c_in @ SV244 @ ( c_List_Oset @ ( c_List_Obutlast @ SV876 @ SY3662 ) @ SY3662 ) @ SY3662 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2536]) ).
thf(3184,plain,
! [SV877: $i,SV245: $i] :
( ( ( c_in @ ( c_List_Olast @ SV245 @ SV877 ) @ ( c_List_Oset @ SV245 @ SV877 ) @ SV877 )
| ( SV245
= ( c_List_Olist_ONil @ SV877 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2537]) ).
thf(3185,plain,
! [SV878: $i,SV246: $i] :
( ( ! [SY3663: $i,SY3664: $i,SY3665: $i] :
( ( c_HOL_Oord__class_Oless @ SV246 @ ( c_List_Olist_Olist__size @ SV878 @ SY3663 @ SY3664 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV246 @ ( hAPP @ SV878 @ SY3665 ) @ tc_nat )
| ~ ( c_in @ SY3665 @ ( c_List_Oset @ SY3663 @ SY3664 ) @ SY3664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2538]) ).
thf(3186,plain,
! [SV879: $i,SV247: $i] :
( ( ! [SY3666: $i,SY3667: $i] :
( ( ( c_List_OtakeWhile @ SV247 @ SV879 @ SY3666 )
= ( c_List_Otake @ SY3667 @ SV879 @ SY3666 ) )
| ( hBOOL @ ( hAPP @ SV247 @ ( c_List_Onth @ SV879 @ SY3667 @ SY3666 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV247 @ ( c_List_Onth @ SV879 @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV247 @ SY3667 @ SV879 @ SY3666 ) @ SY3666 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2539]) ).
thf(3187,plain,
! [SV880: $i,SV248: $i] :
( ( ( ( c_List_Ohd @ ( c_List_Orev @ SV248 @ SV880 ) @ SV880 )
= ( c_List_Olast @ SV248 @ SV880 ) )
| ( SV248
= ( c_List_Olist_ONil @ SV880 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2540]) ).
thf(3188,plain,
! [SV881: $i,SV249: $i] :
( ( ( ( c_List_Olast @ ( c_List_Orev @ SV249 @ SV881 ) @ SV881 )
= ( c_List_Ohd @ SV249 @ SV881 ) )
| ( SV249
= ( c_List_Olist_ONil @ SV881 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2541]) ).
thf(3189,plain,
! [SV882: $i,SV250: $i] :
( ( ! [SY3668: $i] :
( ( ( c_List_Olength__unique @ ( c_List_Olist_OCons @ SV250 @ SV882 @ SY3668 ) @ SY3668 )
= ( c_List_Olength__unique @ SV882 @ SY3668 ) )
| ~ ( c_in @ SV250 @ ( c_List_Oset @ SV882 @ SY3668 ) @ SY3668 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2542]) ).
thf(3190,plain,
! [SV883: $i,SV251: $i] :
( ( ! [SY3669: $i] :
( ( ( c_List_Oappend @ ( c_List_Otake @ SV251 @ SV883 @ SY3669 ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ ( c_List_Odrop @ SV251 @ SV883 @ SY3669 ) @ SY3669 ) @ ( c_List_Olist_ONil @ SY3669 ) @ SY3669 ) @ SY3669 )
= ( c_List_Otake @ ( c_Suc @ SV251 ) @ SV883 @ SY3669 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV251 @ ( c_Nat_Osize__class_Osize @ SV883 @ ( tc_List_Olist @ SY3669 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2543]) ).
thf(3191,plain,
! [SV884: $i,SV252: $i] :
( ( ! [SY3670: $i,SY3671: $i,SY3672: $i] :
( ~ ( class_Orderings_Olinorder @ SV252 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV884 @ ( c_List_Olinorder__class_Oinsort__key @ SV884 @ SY3670 @ SY3671 @ SY3672 @ SV252 ) @ SY3672 @ SV252 ) @ SV252 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV884 @ SY3671 @ SY3672 @ SV252 ) @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2544]) ).
thf(3192,plain,
! [SV885: $i,SV253: $i] :
( ( ! [SY3673: $i,SY3674: $i,SY3675: $i] :
( ~ ( class_Orderings_Olinorder @ SV253 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV885 @ SY3673 @ SY3674 @ SV253 ) @ SV253 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV885 @ ( c_List_Olinorder__class_Oinsort__key @ SV885 @ SY3675 @ SY3673 @ SY3674 @ SV253 ) @ SY3674 @ SV253 ) @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2545]) ).
thf(3193,plain,
! [SV886: $i,SV254: $i] :
( ( ! [SY3676: $i,SY3677: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ SV254 @ SV886 @ SY3676 @ SY3677 ) @ ( tc_List_Olist @ SY3677 ) )
= ( c_Nat_Osize__class_Osize @ SV254 @ ( tc_List_Olist @ SY3677 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2546]) ).
thf(3194,plain,
! [SV887: $i,SV255: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV255 @ ( c_List_Olist_ONil @ SV887 ) @ SV887 ) @ SV887 )
= ( c_List_Obutlast @ SV255 @ SV887 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2547]) ).
thf(3195,plain,
! [SV888: $i,SV256: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV256 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV888 @ SV256 ) @ ( c_HOL_Ozero__class_Ozero @ SV256 ) @ SV256 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2548]) ).
thf(3196,plain,
! [SV889: $i,SV257: $i] :
( ( ! [SY3678: $i,SY3679: $i,SY3680: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV257 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SV889 ) @ SY3678 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SY3679 ) @ SY3680 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SV889 ) @ SY3679 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SY3678 ) @ SY3680 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2549]) ).
thf(3197,plain,
! [SV890: $i,SV258: $i] :
( ( ! [SY3681: $i] :
( ( ( c_List_Olast @ ( c_List_Oreplicate @ SV258 @ SV890 @ SY3681 ) @ SY3681 )
= SV890 )
| ( SV258
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2550]) ).
thf(3198,plain,
! [SV891: $i,SV259: $i] :
( ( ! [SY3682: $i] :
( ( c_List_Obutlast @ ( c_List_Odrop @ SV259 @ SV891 @ SY3682 ) @ SY3682 )
= ( c_List_Odrop @ SV259 @ ( c_List_Obutlast @ SV891 @ SY3682 ) @ SY3682 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2551]) ).
thf(3199,plain,
! [SV892: $i,SV260: $i] :
( ( ! [SY3683: $i] :
( ( c_List_Oappend @ ( c_List_Otake @ SV260 @ SV892 @ SY3683 ) @ ( c_List_Odrop @ SV260 @ SV892 @ SY3683 ) @ SY3683 )
= SV892 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2552]) ).
thf(3200,plain,
! [SV893: $i,SV261: $i] :
( ( ! [SY3684: $i] :
( ~ ( class_Orderings_Olinorder @ SV261 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_OtakeWhile @ SV893 @ SY3684 @ SV261 ) @ SV261 )
| ~ ( c_List_Olinorder__class_Osorted @ SY3684 @ SV261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2553]) ).
thf(3201,plain,
! [SV894: $i,SV262: $i] :
( ( ! [SY3685: $i] :
( SV262
= ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV894 @ ( tc_List_Olist @ SY3685 ) ) @ ( c_List_Oappend @ SV894 @ SV262 @ SY3685 ) @ SY3685 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2554]) ).
thf(3202,plain,
! [SV895: $i,SV263: $i] :
( ( ! [SY3686: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV263 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV263 ) @ SV895 ) @ SY3686 ) @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ SY3686 @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ SV895 @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2555]) ).
thf(3203,plain,
! [SV896: $i,SV264: $i] :
( ( ! [SY3687: $i,SY3688: $i] :
( ( ( c_List_Onth @ ( c_List_OtakeWhile @ SV264 @ SV896 @ SY3687 ) @ SY3688 @ SY3687 )
= ( c_List_Onth @ SV896 @ SY3688 @ SY3687 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3688 @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ SV264 @ SV896 @ SY3687 ) @ ( tc_List_Olist @ SY3687 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2556]) ).
thf(3204,plain,
! [SV897: $i,SV265: $i] :
( ( ! [SY3689: $i] :
( ( c_List_Odrop @ SV265 @ ( c_List_Obutlast @ SV897 @ SY3689 ) @ SY3689 )
= ( c_List_Obutlast @ ( c_List_Odrop @ SV265 @ SV897 @ SY3689 ) @ SY3689 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2557]) ).
thf(3205,plain,
! [SV898: $i,SV266: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV266 @ SV266 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV266 ) ) @ SV898 ) @ SV266 )
= SV898 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2558]) ).
thf(3206,plain,
! [SV899: $i,SV267: $i] :
( ( ! [SY3690: $i,SY3691: $i,SY3692: $i,SY3693: $i] :
( ( hAPP @ ( c_COMBC @ SV267 @ SV899 @ SY3690 @ SY3691 @ SY3692 ) @ SY3693 )
= ( hAPP @ ( hAPP @ SV267 @ SY3693 ) @ SV899 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2559]) ).
thf(3207,plain,
! [SV900: $i,SV268: $i] :
( ( ! [SY3694: $i] :
( ( hBOOL @ ( hAPP @ SV268 @ SV900 ) )
| ~ ( c_in @ SV900 @ SV268 @ SY3694 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2560]) ).
thf(3208,plain,
! [SV901: $i,SV269: $i] :
( ( ! [SY3695: $i] :
( ( c_in @ SV269 @ SV901 @ SY3695 )
| ~ ( hBOOL @ ( hAPP @ SV901 @ SV269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2561]) ).
thf(3209,plain,
! [SV902: $i,SV270: $i] :
( ( ! [SY3696: $i,SY3697: $i,SY3698: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ SV270 @ SV902 @ SY3696 @ SY3697 ) @ SY3698 @ SY3697 )
= ( c_List_Onth @ SV270 @ SY3698 @ SY3697 ) )
| ( SV902 = SY3698 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2562]) ).
thf(3210,plain,
! [SV903: $i,SV271: $i] :
( ( ! [SY3699: $i,SY3700: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV271 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ SV903 ) @ SY3699 ) ) @ SY3700 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ SV903 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ SY3699 ) @ SY3700 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2563]) ).
thf(3211,plain,
! [SV904: $i,SV272: $i] :
( ( ! [SY3701: $i,SY3702: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV272 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV904 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SY3701 ) @ SY3702 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SY3701 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV904 ) @ SY3702 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2564]) ).
thf(3212,plain,
! [SV905: $i,SV273: $i] :
( ( ! [SY3703: $i,SY3704: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV273 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ SV905 ) @ SY3703 ) ) @ SY3704 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ SV905 ) @ SY3704 ) ) @ SY3703 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2565]) ).
thf(3213,plain,
! [SV906: $i,SV274: $i] :
( ( ! [SY3705: $i,SY3706: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV274 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ SV906 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ SY3705 ) @ SY3706 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ SV906 ) @ SY3705 ) ) @ SY3706 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2566]) ).
thf(3214,plain,
! [SV907: $i,SV275: $i] :
( ( ! [SY3707: $i,SY3708: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV275 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ SV907 ) @ SY3707 ) ) @ SY3708 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ SV907 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ SY3707 ) @ SY3708 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2567]) ).
thf(3215,plain,
! [SV908: $i,SV276: $i] :
( ( ! [SY3709: $i,SY3710: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV276 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ SV908 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ SY3709 ) @ SY3710 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ SY3709 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ SV908 ) @ SY3710 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2568]) ).
thf(3216,plain,
! [SV909: $i,SV277: $i] :
( ( ! [SY3711: $i,SY3712: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV277 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ SV909 ) @ SY3711 ) ) @ SY3712 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ SV909 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ SY3711 ) @ SY3712 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2569]) ).
thf(3217,plain,
! [SV910: $i,SV278: $i] :
( ( ! [SY3713: $i,SY3714: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV278 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV278 ) @ SV910 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV278 ) @ SY3713 ) @ SY3714 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV278 ) @ SY3713 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV278 ) @ SV910 ) @ SY3714 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2570]) ).
thf(3218,plain,
! [SV911: $i,SV279: $i] :
( ( ! [SY3715: $i,SY3716: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV279 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV279 ) @ SV911 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV279 ) @ SY3715 ) @ SY3716 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV279 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV279 ) @ SV911 ) @ SY3715 ) ) @ SY3716 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2571]) ).
thf(3219,plain,
! [SV912: $i,SV280: $i] :
( ( ! [SY3717: $i,SY3718: $i] :
( ( ( c_List_Onth @ ( c_List_Otake @ SV280 @ SV912 @ SY3717 ) @ SY3718 @ SY3717 )
= ( c_List_Onth @ SV912 @ SY3718 @ SY3717 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3718 @ SV280 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2572]) ).
thf(3220,plain,
! [SV913: $i,SV281: $i] :
( ( ! [SY3719: $i,SY3720: $i] :
( ~ ( class_Orderings_Oorder @ SV281 )
| ( c_HOL_Oord__class_Oless @ SV913 @ SY3719 @ SV281 )
| ~ ( c_HOL_Oord__class_Oless @ SV913 @ SY3720 @ SV281 )
| ~ ( c_HOL_Oord__class_Oless @ SY3720 @ SY3719 @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(3221,plain,
! [SV914: $i,SV282: $i] :
( ( ! [SY3721: $i,SY3722: $i] :
( ~ ( class_Orderings_Opreorder @ SV282 )
| ( c_HOL_Oord__class_Oless @ SV914 @ SY3721 @ SV282 )
| ~ ( c_HOL_Oord__class_Oless @ SY3722 @ SY3721 @ SV282 )
| ~ ( c_HOL_Oord__class_Oless @ SV914 @ SY3722 @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2574]) ).
thf(3222,plain,
! [SV915: $i,SV283: $i] :
( ( ! [SY3723: $i,SY3724: $i,SY3725: $i] :
( ( c_List_Otake @ SV283 @ ( c_List_Omap @ SV915 @ SY3723 @ SY3724 @ SY3725 ) @ SY3725 )
= ( c_List_Omap @ SV915 @ ( c_List_Otake @ SV283 @ SY3723 @ SY3724 ) @ SY3724 @ SY3725 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2575]) ).
thf(3223,plain,
! [SV916: $i,SV284: $i] :
( ( ! [SY3726: $i] :
( ~ ( class_Orderings_Olinorder @ SV284 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ SV916 @ SY3726 @ SV284 ) @ SV284 )
| ~ ( c_List_Olinorder__class_Osorted @ SY3726 @ SV284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2576]) ).
thf(3224,plain,
! [SV917: $i,SV285: $i] :
( ( ! [SY3727: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV285 ) ) @ SV917 ) @ SY3727 )
= ( c_Lambda_OdB_OVar @ SV285 ) )
| ( SV285 = SY3727 )
| ( c_HOL_Oord__class_Oless @ SY3727 @ SV285 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2577]) ).
thf(3225,plain,
! [SV918: $i,SV286: $i] :
( ( ! [SY3728: $i,SY3729: $i] :
( ( c_List_Olistsp @ SV286 @ SV918 @ SY3728 )
| ~ ( c_List_Olistsp @ SV286 @ ( c_List_Oappend @ SV918 @ SY3729 @ SY3728 ) @ SY3728 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2578]) ).
thf(3226,plain,
! [SV919: $i,SV287: $i] :
( ( ! [SY3730: $i,SY3731: $i] :
( ( c_List_Olistsp @ SV287 @ SV919 @ SY3730 )
| ~ ( c_List_Olistsp @ SV287 @ ( c_List_Oappend @ SY3731 @ SV919 @ SY3730 ) @ SY3730 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2579]) ).
thf(3227,plain,
! [SV920: $i,SV288: $i] :
( ( ! [SY3732: $i,SY3733: $i,SY3734: $i] :
( ( c_Lambda_OdB_OdB__case @ SV288 @ SV920 @ SY3732 @ ( c_Lambda_OdB_OAbs @ SY3733 ) @ SY3734 )
= ( hAPP @ SY3732 @ SY3733 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2580]) ).
thf(3228,plain,
! [SV921: $i,SV289: $i] :
( ( ! [SY3735: $i,SY3736: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV289 ) @ SV921 ) @ SY3735 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY3736 ) @ SV921 ) @ SY3735 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV289 ) @ SY3736 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2581]) ).
thf(3229,plain,
! [SV922: $i,SV290: $i] :
( ( ! [SY3737: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV290 @ ( c_Nat_Osize__class_Osize @ SV922 @ ( tc_List_Olist @ SY3737 ) ) @ tc_nat )
| ( ( c_List_Olist__update @ SV922 @ SV290 @ ( c_List_Onth @ SV922 @ SV290 @ SY3737 ) @ SY3737 )
= SV922 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2582]) ).
thf(3230,plain,
! [SV923: $i,SV291: $i] :
( ( ! [SY3738: $i,SY3739: $i] :
( ( ( c_List_Olist__update @ SV291 @ SV923 @ SY3738 @ SY3739 )
= ( c_List_Oappend @ ( c_List_Otake @ SV923 @ SV291 @ SY3739 ) @ ( c_List_Olist_OCons @ SY3738 @ ( c_List_Odrop @ ( c_Suc @ SV923 ) @ SV291 @ SY3739 ) @ SY3739 ) @ SY3739 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV923 @ ( c_Nat_Osize__class_Osize @ SV291 @ ( tc_List_Olist @ SY3739 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2583]) ).
thf(3231,plain,
! [SV924: $i,SV292: $i] :
( ( ! [SY3740: $i] :
( ( SV292
= ( c_List_Oappend @ ( c_List_Otake @ SV924 @ SV292 @ SY3740 ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ SV292 @ SV924 @ SY3740 ) @ ( c_List_Odrop @ ( c_Suc @ SV924 ) @ SV292 @ SY3740 ) @ SY3740 ) @ SY3740 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV924 @ ( c_Nat_Osize__class_Osize @ SV292 @ ( tc_List_Olist @ SY3740 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2584]) ).
thf(3232,plain,
! [SV925: $i,SV293: $i] :
( ( ! [SY3741: $i] :
( ( ( c_List_Otake @ ( c_Suc @ SV293 ) @ SV925 @ SY3741 )
= ( c_List_Oappend @ ( c_List_Otake @ SV293 @ SV925 @ SY3741 ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ SV925 @ SV293 @ SY3741 ) @ ( c_List_Olist_ONil @ SY3741 ) @ SY3741 ) @ SY3741 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV293 @ ( c_Nat_Osize__class_Osize @ SV925 @ ( tc_List_Olist @ SY3741 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2585]) ).
thf(3233,plain,
! [SV926: $i,SV294: $i] :
( ( ! [SY3742: $i,SY3743: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV294 @ SV926 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY3742 ) @ SY3743 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV294 ) @ SY3742 ) @ SY3743 ) @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SY3742 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SY3743 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV926 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2586]) ).
thf(3234,plain,
! [SV927: $i,SV295: $i] :
( ( ! [SY3744: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV295 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV927 @ SV295 @ SY3744 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV927 ) @ SV295 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY3744 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2587]) ).
thf(3235,plain,
! [SV928: $i,SV296: $i] :
( ( ! [SY3745: $i,SY3746: $i] :
( ( ( c_List_OtakeWhile @ SV296 @ SV928 @ SY3745 )
= ( c_List_Otake @ SY3746 @ SV928 @ SY3745 ) )
| ( c_HOL_Oord__class_Oless @ SY3746 @ ( c_Nat_Osize__class_Osize @ SV928 @ ( tc_List_Olist @ SY3745 ) ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV296 @ ( c_List_Onth @ SV928 @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV296 @ SY3746 @ SV928 @ SY3745 ) @ SY3745 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2588]) ).
thf(3236,plain,
! [SV929: $i,SV297: $i] :
( ( ! [SY3747: $i,SY3748: $i] :
( ( ( c_List_OtakeWhile @ SV297 @ SV929 @ SY3747 )
= ( c_List_Otake @ SY3748 @ SV929 @ SY3747 ) )
| ( hBOOL @ ( hAPP @ SV297 @ ( c_List_Onth @ SV929 @ SY3748 @ SY3747 ) ) )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV297 @ SY3748 @ SV929 @ SY3747 ) @ ( c_Nat_Osize__class_Osize @ SV929 @ ( tc_List_Olist @ SY3747 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2589]) ).
thf(3237,plain,
! [SV930: $i,SV298: $i] :
( ( ! [SY3749: $i] :
( ( ( c_List_Ohd @ ( c_List_Odrop @ SV298 @ SV930 @ SY3749 ) @ SY3749 )
= ( c_List_Onth @ SV930 @ SV298 @ SY3749 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV298 @ ( c_Nat_Osize__class_Osize @ SV930 @ ( tc_List_Olist @ SY3749 ) ) @ tc_nat )
| ( SV930
= ( c_List_Olist_ONil @ SY3749 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2590]) ).
thf(3238,plain,
! [SV931: $i,SV299: $i] :
( ( ! [SY3750: $i] :
( ( ( c_List_Olist_OCons @ ( c_List_Onth @ SV299 @ SV931 @ SY3750 ) @ ( c_List_Odrop @ ( c_Suc @ SV931 ) @ SV299 @ SY3750 ) @ SY3750 )
= ( c_List_Odrop @ SV931 @ SV299 @ SY3750 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV931 @ ( c_Nat_Osize__class_Osize @ SV299 @ ( tc_List_Olist @ SY3750 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2591]) ).
thf(3239,plain,
! [SV932: $i,SV300: $i] :
( ( ! [SY3751: $i,SY3752: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV300 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV932 @ SY3751 @ SV300 ) @ ( c_Power_Opower__class_Opower @ SY3752 @ SY3751 @ SV300 ) @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3751 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SV932 @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ SV932 @ SY3752 @ SV300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2592]) ).
thf(3240,plain,
! [SV933: $i,SV301: $i] :
( ( ! [SY3753: $i] :
( ( c_List_Orev @ ( c_List_Odrop @ SV301 @ SV933 @ SY3753 ) @ SY3753 )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SV933 @ ( tc_List_Olist @ SY3753 ) ) @ SV301 @ tc_nat ) @ ( c_List_Orev @ SV933 @ SY3753 ) @ SY3753 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2593]) ).
thf(3241,plain,
! [SV934: $i,SV302: $i] :
( ( ! [SY3754: $i] :
( ( c_List_Orev @ ( c_List_Otake @ SV302 @ SV934 @ SY3754 ) @ SY3754 )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SV934 @ ( tc_List_Olist @ SY3754 ) ) @ SV302 @ tc_nat ) @ ( c_List_Orev @ SV934 @ SY3754 ) @ SY3754 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2594]) ).
thf(3242,plain,
! [SV935: $i,SV303: $i] :
( ( ! [SY3755: $i,SY3756: $i] :
( ( ( c_List_OtakeWhile @ SV303 @ SV935 @ SY3755 )
= ( c_List_Otake @ SY3756 @ SV935 @ SY3755 ) )
| ( hBOOL @ ( hAPP @ SV303 @ ( c_List_Onth @ SV935 @ SY3756 @ SY3755 ) ) )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV303 @ SY3756 @ SV935 @ SY3755 ) @ SY3756 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2595]) ).
thf(3243,plain,
! [SV936: $i,SV304: $i] :
( ( ! [SY3757: $i,SY3758: $i] :
( ( ( c_List_OtakeWhile @ SV304 @ SV936 @ SY3757 )
= ( c_List_Otake @ SY3758 @ SV936 @ SY3757 ) )
| ( c_HOL_Oord__class_Oless @ SY3758 @ ( c_Nat_Osize__class_Osize @ SV936 @ ( tc_List_Olist @ SY3757 ) ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV304 @ SY3758 @ SV936 @ SY3757 ) @ ( c_Nat_Osize__class_Osize @ SV936 @ ( tc_List_Olist @ SY3757 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2596]) ).
thf(3244,plain,
! [SV937: $i,SV305: $i] :
( ( ! [SY3759: $i,SY3760: $i] :
( ( ( c_List_OtakeWhile @ SV305 @ SV937 @ SY3759 )
= ( c_List_Otake @ SY3760 @ SV937 @ SY3759 ) )
| ( c_HOL_Oord__class_Oless @ SY3760 @ ( c_Nat_Osize__class_Osize @ SV937 @ ( tc_List_Olist @ SY3759 ) ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV305 @ SY3760 @ SV937 @ SY3759 ) @ SY3760 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2597]) ).
thf(3245,plain,
! [SV938: $i,SV306: $i] :
( ( ! [SY3761: $i,SY3762: $i,SY3763: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV306 @ SV938 @ SY3761 ) @ SY3762 @ SY3763 @ SY3761 )
= ( c_List_Oappend @ SV306 @ ( c_List_Olist__update @ SV938 @ ( c_HOL_Ominus__class_Ominus @ SY3762 @ ( c_Nat_Osize__class_Osize @ SV306 @ ( tc_List_Olist @ SY3761 ) ) @ tc_nat ) @ SY3763 @ SY3761 ) @ SY3761 ) )
| ( c_HOL_Oord__class_Oless @ SY3762 @ ( c_Nat_Osize__class_Osize @ SV306 @ ( tc_List_Olist @ SY3761 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2598]) ).
thf(3246,plain,
! [SV939: $i,SV307: $i] :
( ( ! [SY3764: $i,SY3765: $i] :
( ( ( c_List_Onth @ ( c_List_Oappend @ SV307 @ SV939 @ SY3764 ) @ SY3765 @ SY3764 )
= ( c_List_Onth @ SV939 @ ( c_HOL_Ominus__class_Ominus @ SY3765 @ ( c_Nat_Osize__class_Osize @ SV307 @ ( tc_List_Olist @ SY3764 ) ) @ tc_nat ) @ SY3764 ) )
| ( c_HOL_Oord__class_Oless @ SY3765 @ ( c_Nat_Osize__class_Osize @ SV307 @ ( tc_List_Olist @ SY3764 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2599]) ).
thf(3247,plain,
! [SV940: $i,SV308: $i] :
( ( ! [SY3766: $i,SY3767: $i] :
( ( c_in @ SV308 @ ( c_List_Oset @ ( c_List_Olist__update @ SV940 @ SY3766 @ SV308 @ SY3767 ) @ SY3767 ) @ SY3767 )
| ~ ( c_HOL_Oord__class_Oless @ SY3766 @ ( c_Nat_Osize__class_Osize @ SV940 @ ( tc_List_Olist @ SY3767 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2600]) ).
thf(3248,plain,
! [SV941: $i,SV309: $i] :
( ( ! [SY3768: $i] :
( ( c_in @ ( c_List_Onth @ SV309 @ SV941 @ SY3768 ) @ ( c_List_Oset @ SV309 @ SY3768 ) @ SY3768 )
| ~ ( c_HOL_Oord__class_Oless @ SV941 @ ( c_Nat_Osize__class_Osize @ SV309 @ ( tc_List_Olist @ SY3768 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2601]) ).
thf(3249,plain,
! [SV942: $i,SV310: $i] :
( ( ! [SY3769: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV310 @ ( c_Nat_Osize__class_Osize @ SV942 @ ( tc_List_Olist @ SY3769 ) ) @ tc_nat )
| ( c_in @ ( c_List_Onth @ SV942 @ SV310 @ SY3769 ) @ ( c_List_Oset @ SV942 @ SY3769 ) @ SY3769 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2602]) ).
thf(3250,plain,
! [SV943: $i,SV311: $i] :
( ( ! [SY3770: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV311 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV311 ) @ ( c_Power_Opower__class_Opower @ SV943 @ SY3770 @ SV311 ) @ SV311 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3770 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV311 ) @ SV943 @ SV311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2603]) ).
thf(3251,plain,
! [SV944: $i,SV312: $i] :
( ( ! [SY3771: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV312 @ ( tc_List_Olist @ SV944 ) ) @ tc_nat )
| ~ ( c_in @ SY3771 @ ( c_List_Oset @ SV312 @ SV944 ) @ SV944 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2604]) ).
thf(3252,plain,
! [SV945: $i,SV313: $i] :
( ( ! [SY3772: $i,SY3773: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV313 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV945 @ SY3772 @ SV313 ) @ ( c_Power_Opower__class_Opower @ SV945 @ SY3773 @ SV313 ) @ SV313 )
| ~ ( c_HOL_Oord__class_Oless @ SV945 @ ( c_HOL_Oone__class_Oone @ SV313 ) @ SV313 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV313 ) @ SV945 @ SV313 )
| ~ ( c_HOL_Oord__class_Oless @ SY3773 @ SY3772 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2605]) ).
thf(3253,plain,
! [SV946: $i,SV314: $i] :
( ( ! [SY3774: $i,SY3775: $i,SY3776: $i,SY3777: $i] :
( ( c_List_Omap @ SV314 @ ( c_List_Olist__update @ SV946 @ SY3774 @ SY3775 @ SY3776 ) @ SY3776 @ SY3777 )
= ( c_List_Olist__update @ ( c_List_Omap @ SV314 @ SV946 @ SY3776 @ SY3777 ) @ SY3774 @ ( hAPP @ SV314 @ SY3775 ) @ SY3777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2606]) ).
thf(3254,plain,
! [SV947: $i,SV315: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV315 ) ) @ ( c_Lambda_OdB_OAbs @ SV947 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV315 ) @ SV947 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2607]) ).
thf(3255,plain,
! [SV948: $i,SV316: $i] :
( ( ! [SY3778: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ SV316 @ SV948 @ SY3778 ) @ SY3778 )
= ( c_List_Oappend @ ( c_List_Orev @ SV948 @ SY3778 ) @ ( c_List_Orev @ SV316 @ SY3778 ) @ SY3778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2608]) ).
thf(3256,plain,
! [SV949: $i,SV317: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV317 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ SV949 @ SV317 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV317 ) @ SV949 ) @ SV949 ) @ SV317 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2609]) ).
thf(3257,plain,
! [SV950: $i,SV318: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV318 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV318 ) @ SV950 ) @ SV950 ) @ SV318 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ SV950 @ SV318 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2610]) ).
thf(3258,plain,
! [SV319: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV319 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV319 ) @ ( c_HOL_Ozero__class_Ozero @ SV319 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV319 ) )
= ( c_HOL_Ozero__class_Ozero @ SV319 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2611]) ).
thf(3259,plain,
! [SV951: $i,SV320: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV320 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ ( c_HOL_Ozero__class_Ozero @ SV320 ) ) @ SV951 )
= SV951 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2612]) ).
thf(3260,plain,
! [SV952: $i,SV321: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV321 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV321 ) @ ( c_HOL_Ozero__class_Ozero @ SV321 ) ) @ SV952 )
= SV952 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2613]) ).
thf(3261,plain,
! [SV953: $i,SV322: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV322 )
| ~ ( class_Int_Onumber__ring @ SV322 )
| ( SV953
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV322 ) @ SV953 ) @ ( c_HOL_Ozero__class_Ozero @ SV322 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2614]) ).
thf(3262,plain,
! [SV954: $i,SV323: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV323 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV323 ) @ SV954 ) @ ( c_HOL_Ozero__class_Ozero @ SV323 ) )
= SV954 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2615]) ).
thf(3263,plain,
! [SV955: $i,SV324: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV324 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV324 ) @ ( c_HOL_Ozero__class_Ozero @ SV324 ) ) @ SV955 )
= SV955 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2616]) ).
thf(3264,plain,
! [SV956: $i,SV325: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV325 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV325 ) @ SV956 ) @ ( c_HOL_Ozero__class_Ozero @ SV325 ) )
= SV956 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2617]) ).
thf(3265,plain,
! [SV957: $i,SV326: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV326 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV326 ) @ SV957 ) @ ( c_HOL_Ozero__class_Ozero @ SV326 ) )
= SV957 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2618]) ).
thf(3266,plain,
! [SV958: $i,SV327: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV327 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ ( c_HOL_Ozero__class_Ozero @ SV327 ) ) @ SV958 )
= SV958 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(3267,plain,
! [SV328: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV328 @ tc_nat )
= $true )
| ( ( SV328
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2621]) ).
thf(3268,plain,
! [SV329: $i] :
( ( c_HOL_Oord__class_Oless @ SV329 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2622]) ).
thf(3269,plain,
! [SV330: $i] :
( ( c_HOL_Oord__class_Oless @ SV330 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2623]) ).
thf(3270,plain,
! [SV959: $i,SV331: $i] :
( ( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV331 @ SV959 )
= SV331 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2624]) ).
thf(3271,plain,
! [SV960: $i,SV332: $i] :
( ( ! [SY3779: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV332 @ SV960 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3779 @ SV960 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2625]) ).
thf(3272,plain,
! [SV961: $i,SV333: $i] :
( ( ! [SY3780: $i,SY3781: $i,SY3782: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV333 @ SV961 @ SY3780 ) @ ( c_List_Olist_OCons @ SY3781 @ SY3782 @ SY3780 ) @ SY3780 )
= ( c_List_Olist_OCons @ SV333 @ ( c_List_Olist_OCons @ SY3781 @ ( c_List_Osplice @ SV961 @ SY3782 @ SY3780 ) @ SY3780 ) @ SY3780 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2626]) ).
thf(3273,plain,
! [SV962: $i,SV334: $i] :
( ( ! [SY3783: $i,SY3784: $i] :
( ~ ( class_Orderings_Olinorder @ SV334 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV962 @ SY3783 @ SV334 ) @ SV334 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY3784 @ ( c_List_Olist_OCons @ SV962 @ SY3783 @ SV334 ) @ SV334 ) @ SV334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2627]) ).
thf(3274,plain,
! [SV963: $i,SV335: $i] :
( ( ! [SY3785: $i,SY3786: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV335 @ SV963 @ SY3785 ) @ SY3786 @ SY3785 )
= ( c_List_Olist_OCons @ SV335 @ ( c_List_Oappend @ SV963 @ SY3786 @ SY3785 ) @ SY3785 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2628]) ).
thf(3275,plain,
! [SV964: $i,SV336: $i] :
( ( ! [SY3787: $i,SY3788: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV336 @ SV964 @ SY3787 ) @ SY3788 @ SY3787 )
= ( c_List_Olist_OCons @ SV336 @ ( c_List_Oappend @ SV964 @ SY3788 @ SY3787 ) @ SY3787 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2629]) ).
thf(3276,plain,
! [SV965: $i,SV337: $i] :
( ( ! [SY3789: $i,SY3790: $i,SY3791: $i] :
( ( c_List_Omap @ SV337 @ ( c_List_Olist_OCons @ SV965 @ SY3789 @ SY3790 ) @ SY3790 @ SY3791 )
= ( c_List_Olist_OCons @ ( hAPP @ SV337 @ SV965 ) @ ( c_List_Omap @ SV337 @ SY3789 @ SY3790 @ SY3791 ) @ SY3791 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2630]) ).
thf(3277,plain,
! [SV966: $i,SV338: $i] :
( ( ! [SY3792: $i,SY3793: $i,SY3794: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ SV338 @ SV966 ) @ ( c_List_Omap @ SV338 @ SY3792 @ SY3793 @ SY3794 ) @ SY3794 )
= ( c_List_Omap @ SV338 @ ( c_List_Olist_OCons @ SV966 @ SY3792 @ SY3793 ) @ SY3793 @ SY3794 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2631]) ).
thf(3278,plain,
! [SV967: $i,SV339: $i] :
( ( ! [SY3795: $i,SY3796: $i,SY3797: $i] :
( ( c_List_Omap @ SV339 @ ( c_List_Olist_OCons @ SV967 @ SY3795 @ SY3796 ) @ SY3796 @ SY3797 )
= ( c_List_Olist_OCons @ ( hAPP @ SV339 @ SV967 ) @ ( c_List_Omap @ SV339 @ SY3795 @ SY3796 @ SY3797 ) @ SY3797 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2632]) ).
thf(3279,plain,
! [SV968: $i,SV340: $i] :
( ( ! [SY3798: $i,SY3799: $i] :
( ( c_List_Olist_OCons @ SV340 @ ( c_List_Oappend @ SV968 @ SY3798 @ SY3799 ) @ SY3799 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV340 @ SV968 @ SY3799 ) @ SY3798 @ SY3799 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2633]) ).
thf(3280,plain,
! [SV969: $i,SV341: $i] :
( ( ! [SY3800: $i,SY3801: $i] :
( ( c_List_Olist_OCons @ SV341 @ ( c_List_Oappend @ SV969 @ SY3800 @ SY3801 ) @ SY3801 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV341 @ SV969 @ SY3801 ) @ SY3800 @ SY3801 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2634]) ).
thf(3281,plain,
! [SV970: $i,SV342: $i] :
( ( ! [SY3802: $i] :
( ~ ( class_Orderings_Olinorder @ SV342 )
| ( c_List_Olinorder__class_Osorted @ SV970 @ SV342 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY3802 @ SV970 @ SV342 ) @ SV342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2635]) ).
thf(3282,plain,
! [SV971: $i,SV343: $i] :
( ( ! [SY3803: $i,SY3804: $i] :
( ( ( c_List_OtakeWhile @ SV343 @ ( c_List_Olist_OCons @ SV971 @ SY3803 @ SY3804 ) @ SY3804 )
= ( c_List_Olist_OCons @ SV971 @ ( c_List_OtakeWhile @ SV343 @ SY3803 @ SY3804 ) @ SY3804 ) )
| ~ ( hBOOL @ ( hAPP @ SV343 @ SV971 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2636]) ).
thf(3283,plain,
! [SV972: $i,SV344: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV344 @ ( tc_List_Olist @ SV972 ) ) @ tc_nat )
| ( SV344
= ( c_List_Olist_ONil @ SV972 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2637]) ).
thf(3284,plain,
! [SV345: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_ONil @ SV345 ) @ ( tc_List_Olist @ SV345 ) ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2638]) ).
thf(3285,plain,
! [SV973: $i,SV346: $i] :
( ( ! [SY3805: $i] :
( ( c_List_Olast @ ( c_List_Oappend @ SV346 @ ( c_List_Olist_OCons @ SV973 @ ( c_List_Olist_ONil @ SY3805 ) @ SY3805 ) @ SY3805 ) @ SY3805 )
= SV973 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2639]) ).
thf(3286,plain,
! [SV974: $i,SV347: $i] :
( ( ! [SY3806: $i] :
( ( c_List_Obutlast @ ( c_List_Oappend @ SV347 @ ( c_List_Olist_OCons @ SV974 @ ( c_List_Olist_ONil @ SY3806 ) @ SY3806 ) @ SY3806 ) @ SY3806 )
= SV347 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2640]) ).
thf(3287,plain,
! [SV975: $i,SV348: $i] :
( ( ! [SY3807: $i] :
( ( c_List_Orev @ ( c_List_Olist_OCons @ SV348 @ SV975 @ SY3807 ) @ SY3807 )
= ( c_List_Oappend @ ( c_List_Orev @ SV975 @ SY3807 ) @ ( c_List_Olist_OCons @ SV348 @ ( c_List_Olist_ONil @ SY3807 ) @ SY3807 ) @ SY3807 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2641]) ).
thf(3288,plain,
! [SV976: $i,SV349: $i] :
( ( ! [SY3808: $i] :
( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ SV349 @ SV976 ) @ ( c_List_Olist_OCons @ SY3808 @ ( c_List_Olist_ONil @ SV976 ) @ SV976 ) @ SV976 ) @ SV976 )
= ( c_List_Olist_OCons @ SY3808 @ SV349 @ SV976 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2642]) ).
thf(3289,plain,
! [SV977: $i,SV350: $i] :
( ( ! [SY3809: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV350 @ SV977 @ SY3809 ) @ ( c_List_Olist_OCons @ SV977 @ ( c_List_Olist_ONil @ SY3809 ) @ SY3809 ) @ SY3809 )
= ( c_List_Olist_OCons @ SV977 @ ( c_List_Oreplicate @ SV350 @ SV977 @ SY3809 ) @ SY3809 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2643]) ).
thf(3290,plain,
! [SV978: $i,SV354: $i] :
( ( ( c_List_OtakeWhile @ SV354 @ ( c_List_Olist_ONil @ SV978 ) @ SV978 )
= ( c_List_Olist_ONil @ SV978 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2647]) ).
thf(3291,plain,
! [SV979: $i,SV355: $i] :
( ( ( c_List_Osplice @ SV355 @ ( c_List_Olist_ONil @ SV979 ) @ SV979 )
= SV355 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2648]) ).
thf(3292,plain,
! [SV980: $i,SV356: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_ONil @ SV356 ) @ SV980 @ SV356 )
= SV980 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2649]) ).
thf(3293,plain,
! [SV981: $i,SV357: $i] :
( ( ( c_List_Odrop @ SV357 @ ( c_List_Olist_ONil @ SV981 ) @ SV981 )
= ( c_List_Olist_ONil @ SV981 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2650]) ).
thf(3294,plain,
! [SV982: $i,SV358: $i] :
( ( SV358
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV982 ) @ SV358 @ SV982 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2651]) ).
thf(3295,plain,
! [SV983: $i,SV359: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV359 ) @ SV983 @ SV359 )
= SV983 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2652]) ).
thf(3296,plain,
! [SV984: $i,SV360: $i] :
( ( SV360
= ( c_List_Oappend @ SV360 @ ( c_List_Olist_ONil @ SV984 ) @ SV984 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2653]) ).
thf(3297,plain,
! [SV985: $i,SV361: $i] :
( ( SV361
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV985 ) @ SV361 @ SV985 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2654]) ).
thf(3298,plain,
! [SV986: $i,SV362: $i] :
( ( ( c_List_Oappend @ SV362 @ ( c_List_Olist_ONil @ SV986 ) @ SV986 )
= SV362 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2655]) ).
thf(3299,plain,
! [SV987: $i,SV363: $i] :
( ( ( c_List_Otake @ SV363 @ ( c_List_Olist_ONil @ SV987 ) @ SV987 )
= ( c_List_Olist_ONil @ SV987 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2656]) ).
thf(3300,plain,
! [SV988: $i,SV364: $i] :
( ( c_List_Olistsp @ SV364 @ ( c_List_Olist_ONil @ SV988 ) @ SV988 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2657]) ).
thf(3301,plain,
! [SV989: $i,SV365: $i] :
( ( ! [SY3810: $i] :
( ( c_List_Omap @ SV365 @ ( c_List_Olist_ONil @ SV989 ) @ SV989 @ SY3810 )
= ( c_List_Olist_ONil @ SY3810 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2658]) ).
thf(3302,plain,
! [SV990: $i,SV366: $i] :
( ( ( c_List_Osublist @ ( c_List_Olist_ONil @ SV366 ) @ SV990 @ SV366 )
= ( c_List_Olist_ONil @ SV366 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2659]) ).
thf(3303,plain,
! [SV367: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV367 ) )
= $true )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ SV367 ) @ SV367 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2660]) ).
thf(3304,plain,
! [SV991: $i,SV368: $i] :
( ( ! [SY3811: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV368 ) @ SV991 @ SY3811 @ SV368 )
= ( c_List_Olist_ONil @ SV368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2661]) ).
thf(3305,plain,
! [SV992: $i,SV369: $i] :
( ( ! [SY3812: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV369 ) @ SV992 @ SY3812 @ SV369 )
= ( c_List_Olist_ONil @ SV369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2662]) ).
thf(3306,plain,
! [SV993: $i,SV370: $i] :
( ( ! [SY3813: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV370 ) @ SV993 @ SY3813 @ SV370 )
= ( c_List_Olist_ONil @ SV370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2663]) ).
thf(3307,plain,
! [SV994: $i,SV371: $i] :
( ( ! [SY3814: $i] :
( ( c_List_Olist_ONil @ SV371 )
= ( c_List_Omap @ SV994 @ ( c_List_Olist_ONil @ SY3814 ) @ SY3814 @ SV371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2664]) ).
thf(3308,plain,
! [SV995: $i,SV374: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV374 )
| ( ( c_List_Olistsum @ SV995 @ SV374 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV374 ) @ ( c_HOL_Ozero__class_Ozero @ SV374 ) @ SV995 @ SV374 @ SV374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2667]) ).
thf(3309,plain,
! [SV996: $i,SV375: $i] :
( ( ! [SY3815: $i,SY3816: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV375 ) @ SV996 ) ) @ SY3815 ) @ SY3816 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV375 ) @ SY3815 ) @ SY3816 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV996 ) @ SY3815 ) @ SY3816 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2668]) ).
thf(3310,plain,
! [SV997: $i,SV376: $i] :
( ( ! [SY3817: $i,SY3818: $i,SY3819: $i,SY3820: $i] :
( ~ ( hBOOL @ ( hAPP @ SV376 @ ( c_Lambda_OdB_OdB__case @ SV997 @ SY3817 @ SY3818 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3819 ) @ SY3820 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SY3817 @ SY3819 ) @ SY3820 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2669]) ).
thf(3311,plain,
! [SV998: $i,SV377: $i] :
( ( ! [SY3821: $i,SY3822: $i,SY3823: $i,SY3824: $i] :
( ~ ( hBOOL @ ( hAPP @ SV377 @ ( c_Lambda_OdB_OdB__case @ SV998 @ SY3821 @ SY3822 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3823 ) @ SY3824 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV377 @ ( hAPP @ ( hAPP @ SY3821 @ SY3823 ) @ SY3824 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2670]) ).
thf(3312,plain,
! [SV999: $i,SV378: $i] :
( ( ! [SY3825: $i,SY3826: $i,SY3827: $i,SY3828: $i] :
( ( c_Lambda_OdB_OdB__case @ SV378 @ SV999 @ SY3825 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3826 ) @ SY3827 ) @ SY3828 )
= ( hAPP @ ( hAPP @ SV999 @ SY3826 ) @ SY3827 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2671]) ).
thf(3313,plain,
! [SV1000: $i,SV379: $i] :
( ( ! [SY3829: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV379 ) @ SV1000 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV379 ) @ SY3829 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1000 ) @ SY3829 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2672]) ).
thf(3314,plain,
! [SV1001: $i,SV380: $i] :
( ( ! [SY3830: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV380 ) @ SV1001 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3830 ) @ SV1001 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV380 ) @ SY3830 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2673]) ).
thf(3315,plain,
! [SV1002: $i,SV381: $i] :
( ( ! [SY3831: $i,SY3832: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV381 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV1002 ) @ SY3831 ) @ SY3832 @ SV381 @ SV381 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV1002 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SY3831 @ SY3832 @ SV381 @ SV381 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2674]) ).
thf(3316,plain,
! [SV1003: $i,SV382: $i] :
( ( ! [SY3833: $i,SY3834: $i,SY3835: $i,SY3836: $i] :
( ( c_List_Ofoldl @ SV382 @ SV1003 @ ( c_List_Oappend @ SY3833 @ SY3834 @ SY3835 ) @ SY3836 @ SY3835 )
= ( c_List_Ofoldl @ SV382 @ ( c_List_Ofoldl @ SV382 @ SV1003 @ SY3833 @ SY3836 @ SY3835 ) @ SY3834 @ SY3836 @ SY3835 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2675]) ).
thf(3317,plain,
! [SV1004: $i,SV383: $i] :
( ( ! [SY3837: $i,SY3838: $i,SY3839: $i] :
( ~ ( hBOOL @ ( hAPP @ SV383 @ ( c_Lambda_OdB_OdB__case @ SV1004 @ SY3837 @ SY3838 @ ( c_Lambda_OdB_OVar @ SY3839 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV383 @ ( hAPP @ SV1004 @ SY3839 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2676]) ).
thf(3318,plain,
! [SV1005: $i,SV384: $i] :
( ( ! [SY3840: $i,SY3841: $i,SY3842: $i] :
( ~ ( hBOOL @ ( hAPP @ SV384 @ ( c_Lambda_OdB_OdB__case @ SV1005 @ SY3840 @ SY3841 @ ( c_Lambda_OdB_OVar @ SY3842 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV384 @ ( hAPP @ SV1005 @ SY3842 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2677]) ).
thf(3319,plain,
! [SV1006: $i,SV385: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV385 ) ) @ SV1006 ) @ SV385 )
= SV1006 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2678]) ).
thf(3320,plain,
! [SV1007: $i,SV386: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV386 ) ) @ SV1007 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2679]) ).
thf(3321,plain,
! [SV1008: $i,SV387: $i] :
( ( ! [SY3843: $i,SY3844: $i] :
( ( c_List_Orev @ ( c_List_Omap @ SV387 @ SV1008 @ SY3843 @ SY3844 ) @ SY3844 )
= ( c_List_Omap @ SV387 @ ( c_List_Orev @ SV1008 @ SY3843 ) @ SY3843 @ SY3844 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2680]) ).
thf(3322,plain,
! [SV1009: $i,SV388: $i] :
( ( ! [SY3845: $i] :
( ~ ( class_Orderings_Olinorder @ SV388 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ SV1009 @ SY3845 @ SV388 ) @ SV388 )
| ~ ( c_List_Olinorder__class_Osorted @ SY3845 @ SV388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2681]) ).
thf(3323,plain,
! [SV1010: $i,SV389: $i] :
( ( ! [SY3846: $i,SY3847: $i] :
( ( c_List_Onth @ ( c_List_Oappend @ SV389 @ ( c_List_Olist_OCons @ SV1010 @ SY3846 @ SY3847 ) @ SY3847 ) @ ( c_Nat_Osize__class_Osize @ SV389 @ ( tc_List_Olist @ SY3847 ) ) @ SY3847 )
= SV1010 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2682]) ).
thf(3324,plain,
! [SV1011: $i,SV390: $i] :
( ( ! [SY3848: $i] :
( ( c_List_OtakeWhile @ SV390 @ SV1011 @ SY3848 )
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ SV390 @ SV1011 @ SY3848 ) @ ( tc_List_Olist @ SY3848 ) ) @ SV1011 @ SY3848 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2683]) ).
thf(3325,plain,
! [SV1012: $i,SV391: $i] :
( ( ! [SY3849: $i] :
( ~ ( hBOOL @ ( hAPP @ SV391 @ ( c_List_Onth @ SV1012 @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ SV391 @ SV1012 @ SY3849 ) @ ( tc_List_Olist @ SY3849 ) ) @ SY3849 ) ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ SV391 @ SV1012 @ SY3849 ) @ ( tc_List_Olist @ SY3849 ) ) @ ( c_Nat_Osize__class_Osize @ SV1012 @ ( tc_List_Olist @ SY3849 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2684]) ).
thf(3326,plain,
! [SV1013: $i,SV392: $i] :
( ( SV392
= ( c_List_Orev @ ( c_List_Orev @ SV392 @ SV1013 ) @ SV1013 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2685]) ).
thf(3327,plain,
! [SV1014: $i,SV393: $i] :
( ( ( c_List_Orev @ ( c_List_Orev @ SV393 @ SV1014 ) @ SV1014 )
= SV393 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2686]) ).
thf(3328,plain,
! [SV1015: $i,SV394: $i] :
( ( ( c_List_Orev @ ( c_List_Orev @ SV394 @ SV1015 ) @ SV1015 )
= SV394 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2687]) ).
thf(3329,plain,
! [SV1016: $i,SV395: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Obutlast @ SV395 @ SV1016 ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ SV395 @ SV1016 ) @ ( c_List_Olist_ONil @ SV1016 ) @ SV1016 ) @ SV1016 )
= SV395 )
| ( SV395
= ( c_List_Olist_ONil @ SV1016 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2688]) ).
thf(3330,plain,
! [SV1017: $i,SV396: $i] :
( ( ! [SY3850: $i] :
( SV396
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV396 @ ( tc_List_Olist @ SV1017 ) ) @ ( c_List_Oappend @ SV396 @ SY3850 @ SV1017 ) @ SV1017 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2689]) ).
thf(3331,plain,
! [SV1018: $i,SV397: $i] :
( ( ! [SY3851: $i,SY3852: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ SV397 @ SV1018 @ SY3851 @ SY3852 ) @ ( tc_List_Olist @ SY3852 ) )
= ( c_Nat_Osize__class_Osize @ SV1018 @ ( tc_List_Olist @ SY3851 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2690]) ).
thf(3332,plain,
! [SV1019: $i,SV398: $i] :
( ( ! [SY3853: $i,SY3854: $i,SY3855: $i] :
( ( c_List_Omap @ SV398 @ ( c_List_Oreplicate @ SV1019 @ SY3853 @ SY3854 ) @ SY3854 @ SY3855 )
= ( c_List_Oreplicate @ SV1019 @ ( hAPP @ SV398 @ SY3853 ) @ SY3855 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2691]) ).
thf(3333,plain,
! [SV1020: $i,SV399: $i] :
( ( ! [SY3856: $i,SY3857: $i] :
( ( ( c_List_Onth @ ( c_List_Oappend @ SV399 @ SV1020 @ SY3856 ) @ SY3857 @ SY3856 )
= ( c_List_Onth @ SV399 @ SY3857 @ SY3856 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3857 @ ( c_Nat_Osize__class_Osize @ SV399 @ ( tc_List_Olist @ SY3856 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2692]) ).
thf(3334,plain,
! [SV1021: $i,SV400: $i] :
( ( ! [SY3858: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV400 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV400 ) @ SV1021 ) @ SY3858 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV400 ) @ SY3858 ) @ SV1021 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2693]) ).
thf(3335,plain,
! [SV1022: $i,SV401: $i] :
( ( ! [SY3859: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV401 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV401 ) @ SV1022 ) @ SY3859 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV401 ) @ SY3859 ) @ SV1022 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2694]) ).
thf(3336,plain,
! [SV1023: $i,SV402: $i] :
( ( ! [SY3860: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV402 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV402 ) @ SV1023 ) @ SY3860 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV402 ) @ SY3860 ) @ SV1023 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2695]) ).
thf(3337,plain,
! [SV1024: $i,SV403: $i] :
( ( ! [SY3861: $i] :
( ( c_List_Orev @ ( c_List_Oreplicate @ SV403 @ SV1024 @ SY3861 ) @ SY3861 )
= ( c_List_Oreplicate @ SV403 @ SV1024 @ SY3861 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2696]) ).
thf(3338,plain,
! [SV1025: $i,SV404: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV404 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV404 ) @ SV1025 ) @ SV1025 ) @ ( c_HOL_Ozero__class_Ozero @ SV404 ) @ SV404 )
| ~ ( c_HOL_Oord__class_Oless @ SV1025 @ ( c_HOL_Ozero__class_Ozero @ SV404 ) @ SV404 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2697]) ).
thf(3339,plain,
! [SV1026: $i,SV405: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV405 )
| ( c_HOL_Oord__class_Oless @ SV1026 @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SV405 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV405 ) @ SV1026 ) @ SV1026 ) @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SV405 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2698]) ).
thf(3340,plain,
! [SV1027: $i,SV406: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV406 )
| ( c_HOL_Oord__class_Oless @ SV1027 @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV406 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV406 ) @ SV1027 ) @ SV1027 ) @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV406 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2699]) ).
thf(3341,plain,
! [SV1028: $i,SV407: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV407 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV407 ) @ SV1028 ) @ SV1028 ) @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 )
| ~ ( c_HOL_Oord__class_Oless @ SV1028 @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2700]) ).
thf(3342,plain,
! [SV1029: $i,SV408: $i] :
( ( ! [SY3862: $i,SY3863: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV408 @ ( c_Nat_Osize__class_Osize @ SV1029 @ ( tc_List_Olist @ SY3862 ) ) @ tc_nat )
| ( ( c_List_Onth @ ( c_List_Olist__update @ SV1029 @ SV408 @ SY3863 @ SY3862 ) @ SV408 @ SY3862 )
= SY3863 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2701]) ).
thf(3343,plain,
! [SV1030: $i,SV409: $i] :
( ( ! [SY3864: $i,SY3865: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ SV409 @ SV1030 @ SY3864 @ SY3865 ) @ SV1030 @ SY3865 )
= SY3864 )
| ~ ( c_HOL_Oord__class_Oless @ SV1030 @ ( c_Nat_Osize__class_Osize @ SV409 @ ( tc_List_Olist @ SY3865 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2702]) ).
thf(3344,plain,
! [SV1031: $i,SV410: $i] :
( ( ! [SY3866: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV410 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV410 ) @ ( c_Power_Opower__class_Opower @ SV1031 @ SY3866 @ SV410 ) @ SV410 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV410 ) @ SV1031 @ SV410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2703]) ).
thf(3345,plain,
! [SV1032: $i,SV411: $i] :
( ( ! [SY3867: $i] :
( ( ( c_List_Olast @ ( c_List_Odrop @ SV411 @ SV1032 @ SY3867 ) @ SY3867 )
= ( c_List_Olast @ SV1032 @ SY3867 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV411 @ ( c_Nat_Osize__class_Osize @ SV1032 @ ( tc_List_Olist @ SY3867 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2704]) ).
thf(3346,plain,
! [SV1033: $i,SV412: $i] :
( ( ! [SY3868: $i] :
( ( ( c_List_Otake @ SV412 @ ( c_List_Obutlast @ SV1033 @ SY3868 ) @ SY3868 )
= ( c_List_Otake @ SV412 @ SV1033 @ SY3868 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV412 @ ( c_Nat_Osize__class_Osize @ SV1033 @ ( tc_List_Olist @ SY3868 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2705]) ).
thf(3347,plain,
! [SV1034: $i,SV413: $i] :
( ( ! [SY3869: $i,SY3870: $i,SY3871: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV413 @ SV1034 @ SY3869 ) @ SY3870 @ SY3871 @ SY3869 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV413 @ SY3870 @ SY3871 @ SY3869 ) @ SV1034 @ SY3869 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3870 @ ( c_Nat_Osize__class_Osize @ SV413 @ ( tc_List_Olist @ SY3869 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2706]) ).
thf(3348,plain,
! [SV1035: $i,SV414: $i] :
( ( ! [SY3872: $i,SY3873: $i,SY3874: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV414 @ SV1035 @ SY3872 ) @ SY3873 @ SY3874 @ SY3872 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV414 @ SY3873 @ SY3874 @ SY3872 ) @ SV1035 @ SY3872 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3873 @ ( c_Nat_Osize__class_Osize @ SV414 @ ( tc_List_Olist @ SY3872 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2707]) ).
thf(3349,plain,
! [SV1036: $i,SV415: $i] :
( ( ! [SY3875: $i,SY3876: $i] :
( ( ( c_List_Onth @ ( c_List_Oreplicate @ SV415 @ SV1036 @ SY3875 ) @ SY3876 @ SY3875 )
= SV1036 )
| ~ ( c_HOL_Oord__class_Oless @ SY3876 @ SV415 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2708]) ).
thf(3350,plain,
! [SV1037: $i,SV416: $i] :
( ( ! [SY3877: $i,SY3878: $i,SY3879: $i] :
( ( ( c_List_OtakeWhile @ SV416 @ ( c_List_Oappend @ SV1037 @ ( c_List_Olist_OCons @ SY3877 @ SY3878 @ SY3879 ) @ SY3879 ) @ SY3879 )
= ( c_List_OtakeWhile @ SV416 @ SV1037 @ SY3879 ) )
| ( hBOOL @ ( hAPP @ SV416 @ SY3877 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2709]) ).
thf(3351,plain,
! [SV417: $i] :
( ( c_HOL_Oord__class_Oless @ SV417 @ SV417 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2710]) ).
thf(3352,plain,
! [SV418: $i] :
( ( c_HOL_Oord__class_Oless @ SV418 @ SV418 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2711]) ).
thf(3353,plain,
! [SV1038: $i,SV419: $i] :
( ( ~ ( class_Orderings_Oorder @ SV419 )
| ~ ( c_HOL_Oord__class_Oless @ SV1038 @ SV1038 @ SV419 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2712]) ).
thf(3354,plain,
! [SV1039: $i,SV420: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV420 )
| ~ ( c_HOL_Oord__class_Oless @ SV1039 @ SV1039 @ SV420 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2713]) ).
thf(3355,plain,
! [SV1040: $i,SV421: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV421 )
| ~ ( c_HOL_Oord__class_Oless @ SV1040 @ SV1040 @ SV421 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2714]) ).
thf(3356,plain,
! [SV1041: $i,SV422: $i] :
( ( ! [SY3880: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ SV422 @ SV1041 @ SY3880 ) @ SY3880 )
= ( c_List_Olast @ SV1041 @ SY3880 ) )
| ( SV1041
= ( c_List_Olist_ONil @ SY3880 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2715]) ).
thf(3357,plain,
! [SV1042: $i,SV423: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV423 ) ) @ SV1042 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV423 ) @ SV1042 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2716]) ).
thf(3358,plain,
! [SV1043: $i,SV424: $i] :
( ( ! [SY3881: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV424 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SV1043 ) @ SY3881 ) @ SV424 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SY3881 @ SV424 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV1043 @ SV424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2717]) ).
thf(3359,plain,
! [SV1044: $i,SV425: $i] :
( ( ! [SY3882: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV425 )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SV1044 @ SY3882 @ SV425 ) @ SV425 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV425 ) @ SV1044 ) @ ( c_List_Olistsum @ SY3882 @ SV425 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2718]) ).
thf(3360,plain,
! [SV1045: $i,SV426: $i] :
( ( ! [SY3883: $i,SY3884: $i,SY3885: $i] :
( ( c_List_Omap @ SV426 @ ( c_List_Oappend @ SV1045 @ SY3883 @ SY3884 ) @ SY3884 @ SY3885 )
= ( c_List_Oappend @ ( c_List_Omap @ SV426 @ SV1045 @ SY3884 @ SY3885 ) @ ( c_List_Omap @ SV426 @ SY3883 @ SY3884 @ SY3885 ) @ SY3885 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2719]) ).
thf(3361,plain,
! [SV1046: $i,SV427: $i] :
( ( ! [SY3886: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV427 )
| ( c_HOL_Oord__class_Oless @ SV1046 @ SY3886 @ SV427 )
| ( c_HOL_Oord__class_Oless @ SY3886 @ SV1046 @ SV427 )
| ( SY3886 = SV1046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2720]) ).
thf(3362,plain,
! [SV1047: $i,SV428: $i] :
( ( ! [SY3887: $i] :
( ~ ( class_Orderings_Olinorder @ SV428 )
| ( SV1047 = SY3887 )
| ( c_HOL_Oord__class_Oless @ SY3887 @ SV1047 @ SV428 )
| ( c_HOL_Oord__class_Oless @ SV1047 @ SY3887 @ SV428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2721]) ).
thf(3363,plain,
! [SV1048: $i,SV429: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV429 @ SV1048 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV1048 @ SV429 @ tc_nat )
| ( SV1048 = SV429 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2722]) ).
thf(3364,plain,
! [SV1049: $i,SV430: $i] :
( ( ! [SY3888: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV430 @ SV1049 ) @ SY3888 ) )
| ( c_HOL_Oord__class_Oless @ SV1049 @ SY3888 @ tc_nat )
| ( SY3888 = SV1049 )
| ( c_HOL_Oord__class_Oless @ SY3888 @ SV1049 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2723]) ).
thf(3365,plain,
! [SV1050: $i,SV431: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV431 @ SV1050 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV1050 @ SV431 @ tc_nat )
| ( SV1050 = SV431 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2724]) ).
thf(3366,plain,
! [SV1051: $i,SV432: $i] :
( ( ! [SY3889: $i] :
( ~ ( class_Orderings_Olinorder @ SV432 )
| ( c_HOL_Oord__class_Oless @ SV1051 @ SY3889 @ SV432 )
| ( c_HOL_Oord__class_Oless @ SY3889 @ SV1051 @ SV432 )
| ( SY3889 = SV1051 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2725]) ).
thf(3367,plain,
! [SV1052: $i,SV433: $i] :
( ( ! [SY3890: $i,SY3891: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV433 @ SV1052 @ SY3890 ) @ ( c_List_Oreplicate @ SY3891 @ SV1052 @ SY3890 ) @ SY3890 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SY3891 @ SV1052 @ SY3890 ) @ ( c_List_Oreplicate @ SV433 @ SV1052 @ SY3890 ) @ SY3890 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2726]) ).
thf(3368,plain,
! [SV1053: $i,SV434: $i] :
( ( ! [SY3892: $i] :
( ~ ( class_Orderings_Olinorder @ SV434 )
| ( c_HOL_Oord__class_Oless @ SV1053 @ SY3892 @ SV434 )
| ( SY3892 = SV1053 )
| ( c_HOL_Oord__class_Oless @ SY3892 @ SV1053 @ SV434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2727]) ).
thf(3369,plain,
! [SV1054: $i,SV435: $i] :
( ( ! [SY3893: $i] :
( ~ ( class_Orderings_Olinorder @ SV435 )
| ( SV1054 = SY3893 )
| ( c_HOL_Oord__class_Oless @ SV1054 @ SY3893 @ SV435 )
| ( c_HOL_Oord__class_Oless @ SY3893 @ SV1054 @ SV435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2728]) ).
thf(3370,plain,
! [SV1055: $i,SV436: $i] :
( ( ! [SY3894: $i,SY3895: $i,SY3896: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV436 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV436 ) @ SV1055 ) @ SY3894 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV436 ) @ SY3895 ) @ SY3896 ) @ SV436 )
| ~ ( c_HOL_Oord__class_Oless @ SY3894 @ SY3896 @ SV436 )
| ~ ( c_HOL_Oord__class_Oless @ SV1055 @ SY3895 @ SV436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2729]) ).
thf(3371,plain,
! [SV1056: $i,SV437: $i] :
( ( ! [SY3897: $i,SY3898: $i,SY3899: $i] :
( ( ( c_List_Onth @ ( c_List_Omap @ SV437 @ SV1056 @ SY3897 @ SY3898 ) @ SY3899 @ SY3898 )
= ( hAPP @ SV437 @ ( c_List_Onth @ SV1056 @ SY3899 @ SY3897 ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3899 @ ( c_Nat_Osize__class_Osize @ SV1056 @ ( tc_List_Olist @ SY3897 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2730]) ).
thf(3372,plain,
! [SV1057: $i,SV438: $i] :
( ( ! [SY3900: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV438 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1057 @ SV438 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3900 @ SV438 ) @ SV438 )
| ~ ( c_HOL_Oord__class_Oless @ SV1057 @ SY3900 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2731]) ).
thf(3373,plain,
! [SV1058: $i,SV439: $i] :
( ( ! [SY3901: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV439 )
| ( c_HOL_Oord__class_Oless @ SV1058 @ SY3901 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1058 @ SV439 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3901 @ SV439 ) @ SV439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2732]) ).
thf(3374,plain,
! [SV1059: $i,SV440: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV440 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV440 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1059 @ SV440 ) @ SV440 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1059 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2733]) ).
thf(3375,plain,
! [SV1060: $i,SV441: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV441 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1060 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV441 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1060 @ SV441 ) @ SV441 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2734]) ).
thf(3376,plain,
! [SV1061: $i,SV442: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ SV442 @ ( c_List_Olist_ONil @ SV1061 ) @ SV1061 ) @ SV1061 )
= ( c_List_Olast @ SV442 @ SV1061 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2735]) ).
thf(3377,plain,
! [SV1062: $i,SV443: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV443 )
| ( ( c_List_Olistsum @ ( c_List_Orev @ SV1062 @ SV443 ) @ SV443 )
= ( c_List_Olistsum @ SV1062 @ SV443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2736]) ).
thf(3378,plain,
! [SV1063: $i,SV444: $i] :
( ( ! [SY3902: $i,SY3903: $i] :
( ( c_List_Olistsp @ SV444 @ ( c_List_Oappend @ SV1063 @ SY3902 @ SY3903 ) @ SY3903 )
| ~ ( c_List_Olistsp @ SV444 @ SY3902 @ SY3903 )
| ~ ( c_List_Olistsp @ SV444 @ SV1063 @ SY3903 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2737]) ).
thf(3379,plain,
! [SV1064: $i,SV445: $i] :
( ( ! [SY3904: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ SV445 @ SV1064 @ SY3904 ) @ ( tc_List_Olist @ SY3904 ) )
= SV445 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2738]) ).
thf(3380,plain,
! [SV1065: $i,SV446: $i] :
( ( ! [SY3905: $i] :
( ( c_List_Olist__update @ SV446 @ SV1065 @ ( c_List_Onth @ SV446 @ SV1065 @ SY3905 ) @ SY3905 )
= SV446 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2739]) ).
thf(3381,plain,
! [SV1066: $i,SV447: $i] :
( ( ! [SY3906: $i,SY3907: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV447 )
| ( c_HOL_Oord__class_Oless @ SV1066 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV447 ) @ SY3906 ) @ SY3907 ) @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ SV1066 @ SY3907 @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SY3906 @ SV447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2740]) ).
thf(3382,plain,
! [SV1067: $i,SV448: $i] :
( ( ! [SY3908: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV448 ) ) @ SV1067 ) @ SY3908 )
= ( c_Lambda_OdB_OVar @ SV448 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV448 @ SY3908 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2741]) ).
thf(3383,plain,
! [SV1068: $i,SV449: $i] :
( ( ! [SY3909: $i,SY3910: $i,SY3911: $i] :
( ~ ( hBOOL @ ( hAPP @ SV449 @ ( c_Lambda_OdB_OdB__case @ SV1068 @ SY3909 @ SY3910 @ ( c_Lambda_OdB_OAbs @ SY3911 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV449 @ ( hAPP @ SY3910 @ SY3911 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2742]) ).
thf(3384,plain,
! [SV1069: $i,SV450: $i] :
( ( ! [SY3912: $i,SY3913: $i,SY3914: $i] :
( ~ ( hBOOL @ ( hAPP @ SV450 @ ( c_Lambda_OdB_OdB__case @ SV1069 @ SY3912 @ SY3913 @ ( c_Lambda_OdB_OAbs @ SY3914 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV450 @ ( hAPP @ SY3913 @ SY3914 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2743]) ).
thf(3385,plain,
! [SV1070: $i,SV451: $i] :
( ( ! [SY3915: $i,SY3916: $i,SY3917: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV451 @ ( c_List_Olist_OCons @ SV1070 @ SY3915 @ SY3916 ) @ SY3916 ) @ ( c_Nat_Osize__class_Osize @ SV451 @ ( tc_List_Olist @ SY3916 ) ) @ SY3917 @ SY3916 )
= ( c_List_Oappend @ SV451 @ ( c_List_Olist_OCons @ SY3917 @ SY3915 @ SY3916 ) @ SY3916 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2744]) ).
thf(3386,plain,
! [SV1071: $i,SV452: $i] :
( ( ! [SY3918: $i,SY3919: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV452 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV452 ) @ SV1071 ) @ SY3918 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV452 ) @ SY3919 ) @ SY3918 ) @ SV452 )
| ~ ( c_HOL_Oord__class_Oless @ SV1071 @ SY3919 @ SV452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2745]) ).
thf(3387,plain,
! [SV1072: $i,SV453: $i] :
( ( ! [SY3920: $i,SY3921: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV453 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV453 ) @ SV1072 ) @ SY3920 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV453 ) @ SY3921 ) @ SY3920 ) @ SV453 )
| ~ ( c_HOL_Oord__class_Oless @ SV1072 @ SY3921 @ SV453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2746]) ).
thf(3388,plain,
! [SV1073: $i,SV454: $i] :
( ( ! [SY3922: $i,SY3923: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV454 )
| ( c_HOL_Oord__class_Oless @ SV1073 @ SY3922 @ SV454 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV454 ) @ SV1073 ) @ SY3923 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV454 ) @ SY3922 ) @ SY3923 ) @ SV454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2747]) ).
thf(3389,plain,
! [SV1074: $i,SV455: $i] :
( ( ! [SY3924: $i,SY3925: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV455 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV455 ) @ SV1074 ) @ SY3924 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV455 ) @ SV1074 ) @ SY3925 ) @ SV455 )
| ~ ( c_HOL_Oord__class_Oless @ SY3924 @ SY3925 @ SV455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2748]) ).
thf(3390,plain,
! [SV1075: $i,SV456: $i] :
( ( ! [SY3926: $i,SY3927: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV456 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV456 ) @ SV1075 ) @ SY3926 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV456 ) @ SV1075 ) @ SY3927 ) @ SV456 )
| ~ ( c_HOL_Oord__class_Oless @ SY3926 @ SY3927 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2749]) ).
thf(3391,plain,
! [SV1076: $i,SV457: $i] :
( ( ! [SY3928: $i,SY3929: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV457 )
| ( c_HOL_Oord__class_Oless @ SV1076 @ SY3928 @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SY3929 ) @ SV1076 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SY3929 ) @ SY3928 ) @ SV457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2750]) ).
thf(3392,plain,
! [SV1077: $i,SV458: $i] :
( ( ! [SY3930: $i,SY3931: $i] :
( ( c_Type_Otyping @ SV458 @ SV1077 @ SY3930 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY3931 ) @ SV1077 ) )
| ~ ( c_Type_Otyping @ SV458 @ SY3931 @ SY3930 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2751]) ).
thf(3393,plain,
! [SV1078: $i,SV459: $i] :
( ( ! [SY3932: $i] :
( ~ ( class_Orderings_Olinorder @ SV459 )
| ( c_List_Olinorder__class_Osorted @ SV1078 @ SV459 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1078 @ SY3932 @ SV459 ) @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2752]) ).
thf(3394,plain,
! [SV1079: $i,SV460: $i] :
( ( ! [SY3933: $i] :
( ~ ( class_Orderings_Olinorder @ SV460 )
| ( c_List_Olinorder__class_Osorted @ SV1079 @ SV460 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SY3933 @ SV1079 @ SV460 ) @ SV460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2753]) ).
thf(3395,plain,
! [SV1080: $i,SV461: $i] :
( ( ! [SY3934: $i,SY3935: $i,SY3936: $i,SY3937: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV461 @ SV1080 @ SY3934 @ SY3935 ) @ SY3936 @ SY3937 @ SY3935 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV461 @ SY3936 @ SY3937 @ SY3935 ) @ SV1080 @ SY3934 @ SY3935 ) )
| ( SV1080 = SY3936 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2754]) ).
thf(3396,plain,
! [SV1081: $i,SV462: $i] :
( ( ! [SY3938: $i,SY3939: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV462 @ SV1081 @ SY3938 ) @ ( c_List_Olist_OCons @ SV1081 @ SY3939 @ SY3938 ) @ SY3938 )
= ( c_List_Olist_OCons @ SV1081 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV462 @ SV1081 @ SY3938 ) @ SY3939 @ SY3938 ) @ SY3938 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2755]) ).
thf(3397,plain,
! [SV1082: $i,SV463: $i] :
( ( ! [SY3940: $i,SY3941: $i,SY3942: $i] :
( ( c_List_Odrop @ SV463 @ ( c_List_Omap @ SV1082 @ SY3940 @ SY3941 @ SY3942 ) @ SY3942 )
= ( c_List_Omap @ SV1082 @ ( c_List_Odrop @ SV463 @ SY3940 @ SY3941 ) @ SY3941 @ SY3942 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2756]) ).
thf(3398,plain,
! [SV1083: $i,SV464: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Orev @ SV464 @ SV1083 ) @ ( tc_List_Olist @ SV1083 ) )
= ( c_Nat_Osize__class_Osize @ SV464 @ ( tc_List_Olist @ SV1083 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2757]) ).
thf(3399,plain,
! [SV1084: $i,SV465: $i] :
( ( ! [SY3943: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV465 @ SV1084 @ SY3943 ) @ SY3943 )
= ( c_List_Oappend @ SV465 @ ( c_List_Obutlast @ SV1084 @ SY3943 ) @ SY3943 ) )
| ( SV1084
= ( c_List_Olist_ONil @ SY3943 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2758]) ).
thf(3400,plain,
! [SV1085: $i,SV466: $i] :
( ( ! [SY3944: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV466 )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ SV1085 @ SY3944 @ SV466 ) @ SV466 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV466 ) @ ( c_List_Olistsum @ SV1085 @ SV466 ) ) @ ( c_List_Olistsum @ SY3944 @ SV466 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2759]) ).
thf(3401,plain,
! [SV1086: $i,SV467: $i] :
( ( ! [SY3945: $i,SY3946: $i,SY3947: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ SV467 @ SV1086 @ SY3945 @ SY3946 ) @ SY3947 @ SY3946 )
= ( c_List_Onth @ SV467 @ SY3947 @ SY3946 ) )
| ( SV1086 = SY3947 )
| ~ ( c_HOL_Oord__class_Oless @ SV1086 @ ( c_Nat_Osize__class_Osize @ SV467 @ ( tc_List_Olist @ SY3946 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2760]) ).
thf(3402,plain,
! [SV1087: $i,SV468: $i] :
( ( ! [SY3948: $i,SY3949: $i,SY3950: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV468 @ SV1087 @ SY3948 @ SY3949 ) @ SV1087 @ SY3950 @ SY3949 )
= ( c_List_Olist__update @ SV468 @ SV1087 @ SY3950 @ SY3949 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2761]) ).
thf(3403,plain,
! [SV1088: $i,SV469: $i] :
( ( ! [SY3951: $i,SY3952: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV469 @ SV1088 @ SY3951 ) @ SY3952 @ SY3951 )
= ( c_List_Oappend @ SV469 @ ( c_List_Oappend @ SV1088 @ SY3952 @ SY3951 ) @ SY3951 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2762]) ).
thf(3404,plain,
! [SV1089: $i,SV470: $i] :
( ( ! [SY3953: $i,SY3954: $i] :
( ( c_List_Oappend @ SV470 @ ( c_List_Oappend @ SV1089 @ SY3953 @ SY3954 ) @ SY3954 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV470 @ SV1089 @ SY3954 ) @ SY3953 @ SY3954 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2763]) ).
thf(3405,plain,
! [SV1090: $i,SV471: $i] :
( ( ! [SY3955: $i,SY3956: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV471 @ SV1090 @ SY3955 ) @ SY3956 @ SY3955 )
= ( c_List_Oappend @ SV471 @ ( c_List_Oappend @ SV1090 @ SY3956 @ SY3955 ) @ SY3955 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2764]) ).
thf(3406,plain,
! [SV1091: $i,SV472: $i] :
( ( ! [SY3957: $i,SY3958: $i] :
( ( c_List_Oappend @ SV472 @ ( c_List_Oappend @ SV1091 @ SY3957 @ SY3958 ) @ SY3958 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV472 @ SV1091 @ SY3958 ) @ SY3957 @ SY3958 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2765]) ).
thf(3407,plain,
! [SV1092: $i,SV473: $i] :
( ( ! [SY3959: $i] :
( ~ ( class_Orderings_Oorder @ SV473 )
| ~ ( c_HOL_Oord__class_Oless @ SV1092 @ SY3959 @ SV473 )
| ~ ( c_HOL_Oord__class_Oless @ SY3959 @ SV1092 @ SV473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2766]) ).
thf(3408,plain,
! [SV1093: $i,SV474: $i] :
( ( ! [SY3960: $i] :
( ~ ( class_Orderings_Olinorder @ SV474 )
| ~ ( c_HOL_Oord__class_Oless @ SV1093 @ SY3960 @ SV474 )
| ~ ( c_HOL_Oord__class_Oless @ SY3960 @ SV1093 @ SV474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2767]) ).
thf(3409,plain,
! [SV1094: $i,SV475: $i] :
( ( ! [SY3961: $i] :
( ~ ( class_Orderings_Opreorder @ SV475 )
| ~ ( c_HOL_Oord__class_Oless @ SV1094 @ SY3961 @ SV475 )
| ~ ( c_HOL_Oord__class_Oless @ SY3961 @ SV1094 @ SV475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2768]) ).
thf(3410,plain,
! [SV1095: $i,SV476: $i] :
( ( ! [SY3962: $i] :
( ~ ( class_Orderings_Opreorder @ SV476 )
| ~ ( c_HOL_Oord__class_Oless @ SV1095 @ SY3962 @ SV476 )
| ~ ( c_HOL_Oord__class_Oless @ SY3962 @ SV1095 @ SV476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2769]) ).
thf(3411,plain,
! [SV1096: $i,SV477: $i] :
( ( ! [SY3963: $i] :
( ( ( hAPP @ SV477 @ SV1096 )
= SY3963 )
| ~ ( c_Type_Otyping @ SV477 @ ( c_Lambda_OdB_OVar @ SV1096 ) @ SY3963 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2770]) ).
thf(3412,plain,
! [SV1097: $i,SV478: $i] :
( ( ! [SY3964: $i,SY3965: $i,SY3966: $i] :
( ( c_Lambda_OdB_OdB__case @ SV478 @ SV1097 @ SY3964 @ ( c_Lambda_OdB_OVar @ SY3965 ) @ SY3966 )
= ( hAPP @ SV478 @ SY3965 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2771]) ).
thf(3413,plain,
! [SV1098: $i,SV479: $i] :
( ( c_Type_Otyping @ SV479 @ ( c_Lambda_OdB_OVar @ SV1098 ) @ ( hAPP @ SV479 @ SV1098 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2772]) ).
thf(3414,plain,
! [SV480: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV480 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV480 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2773]) ).
thf(3415,plain,
! [SV481: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV481 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV481 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2774]) ).
thf(3416,plain,
! [SV1099: $i,SV482: $i] :
( ( ! [SY3967: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV482 ) @ SV1099 ) ) @ SY3967 ) @ SV1099 )
= SV482 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2775]) ).
thf(3417,plain,
! [SV1100: $i,SV483: $i] :
( ( ! [SY3968: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV483 ) @ SV1100 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY3968 ) @ SV1100 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV483 ) @ SY3968 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2776]) ).
thf(3418,plain,
! [SV1101: $i,SV484: $i] :
( ( ! [SY3969: $i] :
( ( ( c_List_Osublist @ ( c_List_Olist_OCons @ SV484 @ ( c_List_Olist_ONil @ SV1101 ) @ SV1101 ) @ SY3969 @ SV1101 )
= ( c_List_Olist_OCons @ SV484 @ ( c_List_Olist_ONil @ SV1101 ) @ SV1101 ) )
| ~ ( c_in @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3969 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2777]) ).
thf(3419,plain,
! [SV1102: $i,SV485: $i] :
( ( ! [SY3970: $i] :
( ( ( c_List_Osublist @ ( c_List_Olist_OCons @ SV485 @ ( c_List_Olist_ONil @ SV1102 ) @ SV1102 ) @ SY3970 @ SV1102 )
= ( c_List_Olist_ONil @ SV1102 ) )
| ( c_in @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3970 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2778]) ).
thf(3420,plain,
! [SV1103: $i,SV486: $i] :
( ( ! [SY3971: $i] :
( ( SV486
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1103 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV1103 @ SY3971 @ SV486 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1103 ) @ SY3971 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV486 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2779]) ).
thf(3421,plain,
! [SV1104: $i,SV487: $i] :
( ( ! [SY3972: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV487 @ SV1104 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY3972 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV487 ) @ SY3972 ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ SY3972 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1104 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2780]) ).
thf(3422,plain,
! [SV1105: $i,SV488: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV488 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV488 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV488 )
| ~ ( class_Power_Opower @ SV488 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV488 ) @ SV1105 @ SV488 )
= ( c_HOL_Ozero__class_Ozero @ SV488 ) )
| ( SV1105
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2781]) ).
thf(3423,plain,
! [SV1106: $i,SV489: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV489 )
| ~ ( class_Power_Opower @ SV489 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV1106 @ SV489 )
= ( c_HOL_Ozero__class_Ozero @ SV489 ) )
| ( SV1106
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2782]) ).
thf(3424,plain,
! [SV490: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV490 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV490 )
= ( c_HOL_Ozero__class_Ozero @ SV490 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2783]) ).
thf(3425,plain,
! [SV491: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV491 ) )
= $true )
| ( ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ SV491 ) @ SV491 )
= ( c_HOL_Ozero__class_Ozero @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2784]) ).
thf(3426,plain,
! [SV1107: $i,SV492: $i] :
( ( ! [SY3973: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ SV492 @ SV1107 @ SY3973 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3973 )
= SV492 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2785]) ).
thf(3427,plain,
! [SV1108: $i,SV493: $i] :
( ( ! [SY3974: $i] :
( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ SV493 @ SV1108 @ SY3974 ) @ SY3974 )
= ( c_List_Olist_OCons @ SV493 @ SV1108 @ SY3974 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2786]) ).
thf(3428,plain,
! [SV1109: $i,SV494: $i] :
( ( ! [SY3975: $i,SY3976: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV494 @ SV1109 @ SY3975 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3976 @ SY3975 )
= ( c_List_Olist_OCons @ SY3976 @ SV1109 @ SY3975 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2787]) ).
thf(3429,plain,
! [SV1110: $i,SV495: $i] :
( ( ( c_List_Olist_Olist__size @ SV495 @ ( c_List_Olist_ONil @ SV1110 ) @ SV1110 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2788]) ).
thf(3430,plain,
! [SV1111: $i,SV496: $i] :
( ( ( c_List_Olist_Olist__size @ SV496 @ ( c_List_Olist_ONil @ SV1111 ) @ SV1111 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2789]) ).
thf(3431,plain,
! [SV1112: $i,SV497: $i] :
( ( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV497 @ SV1112 )
= ( c_List_Olist_ONil @ SV1112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2790]) ).
thf(3432,plain,
! [SV1113: $i,SV498: $i] :
( ( ( c_List_Olist_ONil @ SV498 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1113 @ SV498 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2791]) ).
thf(3433,plain,
! [SV1114: $i,SV501: $i] :
( ( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV501 @ SV1114 )
= ( c_List_Olist_ONil @ SV1114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2794]) ).
thf(3434,plain,
! [SV1115: $i,SV502: $i] :
( ( ! [SY3977: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV502 ) @ ( c_List_Olist_OCons @ SV1115 @ SY3977 @ SV502 ) @ SV502 )
= ( c_List_Olist_OCons @ SV1115 @ SY3977 @ SV502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2795]) ).
thf(3435,plain,
! [SV1116: $i,SV503: $i] :
( ( ! [SY3978: $i,SY3979: $i] :
( ~ ( class_Orderings_Olinorder @ SV503 )
| ( ( c_List_Olinorder__class_Oinsort__key @ SV1116 @ SY3978 @ ( c_List_Olist_ONil @ SY3979 ) @ SY3979 @ SV503 )
= ( c_List_Olist_OCons @ SY3978 @ ( c_List_Olist_ONil @ SY3979 ) @ SY3979 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2796]) ).
thf(3436,plain,
! [SV1117: $i,SV504: $i] :
( ( ! [SY3980: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV504 @ SV1117 @ SY3980 ) @ SY3980 )
= ( c_List_Olist_OCons @ SV504 @ ( c_List_Obutlast @ SV1117 @ SY3980 ) @ SY3980 ) )
| ( SV1117
= ( c_List_Olist_ONil @ SY3980 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2797]) ).
thf(3437,plain,
! [SV1118: $i,SV505: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV505 @ ( c_List_Olist_ONil @ SV1118 ) @ SV1118 ) @ SV1118 )
= SV505 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2798]) ).
thf(3438,plain,
! [SV1119: $i,SV506: $i] :
( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV506 @ ( c_List_Olist_ONil @ SV1119 ) @ SV1119 ) @ SV1119 )
= ( c_List_Olist_ONil @ SV1119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2799]) ).
thf(3439,plain,
! [SV1120: $i,SV507: $i] :
( ( ! [SY3981: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV507 @ SV1120 @ SY3981 ) @ ( c_List_Olist_ONil @ SY3981 ) @ SY3981 )
= ( c_List_Olist_OCons @ SV507 @ SV1120 @ SY3981 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2800]) ).
thf(3440,plain,
! [SV1121: $i,SV508: $i] :
( ( ! [SY3982: $i,SY3983: $i] :
( ( ( c_List_OtakeWhile @ SV508 @ ( c_List_Olist_OCons @ SV1121 @ SY3982 @ SY3983 ) @ SY3983 )
= ( c_List_Olist_ONil @ SY3983 ) )
| ( hBOOL @ ( hAPP @ SV508 @ SV1121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2801]) ).
thf(3441,plain,
! [SV1122: $i,SV509: $i] :
( ( ( c_List_Orev @ ( c_List_Olist_OCons @ SV509 @ ( c_List_Olist_ONil @ SV1122 ) @ SV1122 ) @ SV1122 )
= ( c_List_Olist_OCons @ SV509 @ ( c_List_Olist_ONil @ SV1122 ) @ SV1122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2802]) ).
thf(3442,plain,
! [SV1123: $i,SV510: $i] :
( ( ! [SY3984: $i] :
( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV510 @ SV1123 @ SY3984 ) @ SY3984 )
= ( c_List_Olast @ SV1123 @ SY3984 ) )
| ( SV1123
= ( c_List_Olist_ONil @ SY3984 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2803]) ).
thf(3443,plain,
! [SV1124: $i,SV511: $i] :
( ( ! [SY3985: $i] :
( ( c_List_Olist_OCons @ SV511 @ SV1124 @ SY3985 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY3985 ) @ ( c_List_Olist_OCons @ SV511 @ SV1124 @ SY3985 ) @ SY3985 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2804]) ).
thf(3444,plain,
! [SV1125: $i,SV512: $i] :
( ( ( c_List_Olist_OCons @ SV512 @ ( c_List_Olist_ONil @ SV1125 ) @ SV1125 )
= ( c_List_Orev @ ( c_List_Olist_OCons @ SV512 @ ( c_List_Olist_ONil @ SV1125 ) @ SV1125 ) @ SV1125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2805]) ).
thf(3445,plain,
! [SV1126: $i,SV513: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV513 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1126 @ ( c_List_Olist_ONil @ SV513 ) @ SV513 ) @ SV513 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2806]) ).
thf(3446,plain,
! [SV1127: $i,SV514: $i] :
( ( ! [SY3986: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV514 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1127 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ ( c_HOL_Ozero__class_Ozero @ SV514 ) @ SY3986 @ SV514 @ SV514 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1127 @ SY3986 @ SV514 @ SV514 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2807]) ).
thf(3447,plain,
! [SV1128: $i,SV517: $i] :
( ( ! [SY3987: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV517 @ SV1128 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3987 @ SV1128 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV517 ) @ SY3987 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2810]) ).
thf(3448,plain,
! [SV1129: $i,SV518: $i] :
( ( ! [SY3988: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV518 ) ) @ SV1129 ) @ SY3988 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1129 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV518 ) @ SV1129 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY3988 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2811]) ).
thf(3449,plain,
! [SV1130: $i,SV519: $i] :
( ( ! [SY3989: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV519 ) @ ( c_Lambda_OdB_OVar @ SV1130 ) ) @ SY3989 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV519 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2812]) ).
thf(3450,plain,
! [SV1131: $i,SV520: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV520 ) ) @ SV1131 )
= ( c_Lambda_OdB_OVar @ SV520 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV520 @ SV1131 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2813]) ).
thf(3451,plain,
! [SV1132: $i,SV521: $i] :
( ( ! [SY3990: $i] :
( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ SV521 @ SV1132 @ SY3990 ) @ SY3990 )
= ( c_List_Olist_ONil @ SY3990 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2814]) ).
thf(3452,plain,
! [SV1133: $i,SV522: $i] :
( ( ! [SY3991: $i,SY3992: $i,SY3993: $i] :
( ( SV522 = SV1133 )
| ~ ( c_Type_Otyping @ SY3991 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY3992 ) @ SY3993 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1133 )
| ~ ( c_Type_Otyping @ SY3991 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY3992 ) @ SY3993 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2815]) ).
thf(3453,plain,
! [SV1134: $i,SV525: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV525 ) @ SV1134 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV1134 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2818]) ).
thf(3454,plain,
! [SV1135: $i,SV526: $i] :
( ( ! [SY3994: $i] :
( ( ( c_List_Oappend @ SV526 @ ( c_List_Olist_OCons @ SV1135 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3994 @ SV526 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV1135 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3994 @ ( c_List_Oappend @ SV526 @ ( c_List_Olist_OCons @ SV1135 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2819]) ).
thf(3455,plain,
! [SV1136: $i,SV527: $i] :
( ( ! [SY3995: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV527 @ SV1136 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY3995 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV527 @ ( c_List_Oappend @ SV1136 @ ( c_List_Olist_OCons @ SY3995 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2820]) ).
thf(3456,plain,
! [SV1137: $i,SV528: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV528 ) @ SV1137 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV528 ) @ SV1137 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2821]) ).
thf(3457,plain,
! [SV1138: $i,SV529: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV529 ) @ SV1138 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV529 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2822]) ).
thf(3458,plain,
! [SV1139: $i,SV530: $i] :
( ( ! [SY3996: $i,SY3997: $i] :
( ( c_List_Ofoldl @ SV530 @ SV1139 @ ( c_List_Olist_ONil @ SY3996 ) @ SY3997 @ SY3996 )
= SV1139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2823]) ).
thf(3459,plain,
! [SV1140: $i,SV532: $i] :
( ( ! [SY3998: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV532 ) @ SV1140 ) ) @ SY3998 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV532 ) @ SY3998 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1140 ) @ SY3998 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2825]) ).
thf(3460,plain,
! [SV1141: $i,SV534: $i] :
( ( ! [SY3999: $i,SY4000: $i,SY4001: $i,SY4002: $i] :
( ( c_List_Ofoldl @ SV534 @ SV1141 @ ( c_List_Olist_OCons @ SY3999 @ SY4000 @ SY4001 ) @ SY4002 @ SY4001 )
= ( c_List_Ofoldl @ SV534 @ ( hAPP @ ( hAPP @ SV534 @ SV1141 ) @ SY3999 ) @ SY4000 @ SY4002 @ SY4001 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2827]) ).
thf(3461,plain,
! [SV1142: $i,SV535: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV535 ) @ ( c_Lambda_OdB_OVar @ SV1142 ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2828]) ).
thf(3462,plain,
! [SV1143: $i,SV536: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV536 @ SV1143 ) )
| ~ ( class_Orderings_Opreorder @ SV1143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2829]) ).
thf(3463,plain,
! [SV1144: $i,SV537: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV537 @ SV1144 ) )
| ~ ( class_Orderings_Oorder @ SV1144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2830]) ).
thf(3464,plain,
! [SV1145: $i,SV538: $i] :
( ( c_fequal @ SV538 @ SV538 @ SV1145 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2831]) ).
thf(3465,plain,
! [SV1146: $i,SV539: $i] :
( ( ! [SY4003: $i] :
( ( SV539 = SV1146 )
| ~ ( c_fequal @ SV539 @ SV1146 @ SY4003 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2832]) ).
thf(3466,plain,
! [SV1147: $i,SV540: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV540 )
!= ( c_Lambda_OdB_OAbs @ SV1147 ) )
| ( SV540 = SV1147 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2834]) ).
thf(3467,plain,
! [SV1148: $i,SV541: $i] :
( ( ! [SY4004: $i,SY4005: $i,SY4006: $i] :
( ( ( c_List_Oreplicate @ SV541 @ SV1148 @ SY4004 )
!= ( c_List_Oreplicate @ SY4005 @ SY4006 @ SY4004 ) )
| ( SV541 = SY4005 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2835]) ).
thf(3468,plain,
! [SV1149: $i,SV542: $i] :
( ( ! [SY4007: $i] :
( ( SV542
!= ( c_List_Oappend @ SV1149 @ SV542 @ SY4007 ) )
| ( SV1149
= ( c_List_Olist_ONil @ SY4007 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2836]) ).
thf(3469,plain,
! [SV1150: $i,SV543: $i] :
( ( ! [SY4008: $i,SY4009: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV543 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV543 ) @ SV1150 ) @ SY4008 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV543 ) @ SY4009 ) @ SY4008 ) )
| ( SV1150 = SY4009 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2837]) ).
thf(3470,plain,
! [SV1151: $i,SV544: $i] :
( ( ! [SY4010: $i] :
( ( c_List_Olist_OCons @ SV544 @ SV1151 @ SY4010 )
!= ( c_List_Olist_ONil @ SY4010 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2838]) ).
thf(3471,plain,
! [SV1152: $i,SV545: $i] :
( ( ! [SY4011: $i] :
( ( ( c_List_Odrop @ SV545 @ SV1152 @ SY4011 )
!= ( c_List_Olist_ONil @ SY4011 ) )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1152 @ ( tc_List_Olist @ SY4011 ) ) @ SV545 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2839]) ).
thf(3472,plain,
! [SV1153: $i,SV546: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV546 )
!= ( c_Lambda_OdB_OVar @ SV1153 ) )
| ( SV546 = SV1153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2840]) ).
thf(3473,plain,
! [SV1154: $i,SV547: $i] :
( ( ! [SY4012: $i] :
( ( ( c_Lambda_OdB_OVar @ SV547 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1154 @ SY4012 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV547 )
= SV1154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2841]) ).
thf(3474,plain,
! [SV1155: $i,SV548: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV548 )
!= ( c_Lambda_OdB_OVar @ SV1155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2842]) ).
thf(3475,plain,
! [SV1156: $i,SV549: $i] :
( ( ! [SY4013: $i] :
( ( SV549
!= ( c_List_Oappend @ SV549 @ SV1156 @ SY4013 ) )
| ( SV1156
= ( c_List_Olist_ONil @ SY4013 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2843]) ).
thf(3476,plain,
! [SV1157: $i,SV550: $i] :
( ( ! [SY4014: $i,SY4015: $i,SY4016: $i] :
( ( ( c_List_Oappend @ SV550 @ ( c_List_Olist_OCons @ SV1157 @ ( c_List_Olist_ONil @ SY4014 ) @ SY4014 ) @ SY4014 )
!= ( c_List_Oappend @ SY4015 @ ( c_List_Olist_OCons @ SY4016 @ ( c_List_Olist_ONil @ SY4014 ) @ SY4014 ) @ SY4014 ) )
| ( SV550 = SY4015 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2844]) ).
thf(3477,plain,
! [SV1158: $i,SV551: $i] :
( ( ! [SY4017: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV551 ) @ SV1158 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY4017 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV551 ) @ SV1158 )
= SY4017 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2845]) ).
thf(3478,plain,
! [SV1159: $i,SV552: $i] :
( ( ! [SY4018: $i,SY4019: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV552 ) @ SV1159 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY4018 @ SY4019 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY4019
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV552 @ SV1159 @ SY4018 @ SY4019 ) @ ( c_List_Olist_OCons @ SV1159 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SY4019
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2846]) ).
thf(3479,plain,
! [SV1160: $i,SV553: $i] :
( ( ! [SY4020: $i,SY4021: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV553 ) @ SV1160 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY4020 ) @ SY4021 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV553 = SY4020 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2847]) ).
thf(3480,plain,
! [SV1161: $i,SV554: $i] :
( ( ! [SY4022: $i,SY4023: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV554 )
| ( ( c_Power_Opower__class_Opower @ SV1161 @ SY4022 @ SV554 )
!= ( c_Power_Opower__class_Opower @ SY4023 @ SY4022 @ SV554 ) )
| ( SV1161 = SY4023 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4022 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SY4023 @ SV554 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SV1161 @ SV554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2848]) ).
thf(3481,plain,
! [SV1162: $i,SV555: $i] :
( ( ! [SY4024: $i] :
( ( c_List_Olist_ONil @ SV555 )
!= ( c_List_Olist_OCons @ SV1162 @ SY4024 @ SV555 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2849]) ).
thf(3482,plain,
! [SV556: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
= ( c_Suc @ SV556 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2850]) ).
thf(3483,plain,
! [SV1163: $i,SV557: $i] :
( ( ( ( c_Suc @ SV557 )
!= ( c_Suc @ SV1163 ) )
| ( SV557 = SV1163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2851]) ).
thf(3484,plain,
! [SV1164: $i,SV558: $i] :
( ( ! [SY4025: $i,SY4026: $i] :
( ( ( c_List_Oappend @ SV558 @ SV1164 @ SY4025 )
!= ( c_List_Oappend @ SV558 @ SY4026 @ SY4025 ) )
| ( SV1164 = SY4026 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2852]) ).
thf(3485,plain,
! [SV1165: $i,SV559: $i] :
( ( ! [SY4027: $i,SY4028: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV559 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1165 @ SY4027 @ SV559 )
!= ( c_HOL_Ominus__class_Ominus @ SY4028 @ SY4028 @ SV559 ) )
| ( SV1165 = SY4027 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2853]) ).
thf(3486,plain,
! [SV1166: $i,SV560: $i] :
( ( ! [SY4029: $i,SY4030: $i] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV560 @ ( tc_List_Olist @ SV1166 ) ) @ SY4029 @ SV1166 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SY4029 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) @ SY4030 @ SV1166 ) @ SV1166 )
!= SY4030 )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV560 @ ( tc_List_Olist @ SV1166 ) ) @ SY4029 @ SV1166 )
!= SV560 )
| ( SY4029
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SY4029 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) )
| ( ( c_List_Oappend @ SY4029 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SY4029 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) @ SY4030 @ SV1166 ) @ SV1166 )
= ( c_List_Oappend @ SV560 @ SY4030 @ SV1166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2854]) ).
thf(3487,plain,
! [SV1167: $i,SV561: $i] :
( ( ( ( c_Suc @ SV561 )
!= ( c_Suc @ SV1167 ) )
| ( SV561 = SV1167 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2855]) ).
thf(3488,plain,
! [SV1168: $i,SV562: $i] :
( ( ! [SY4031: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV562 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1168 @ SY4031 @ SV562 )
!= ( c_HOL_Ozero__class_Ozero @ SV562 ) )
| ( SV1168 = SY4031 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2856]) ).
thf(3489,plain,
! [SV1169: $i,SV563: $i] :
( ( ! [SY4032: $i] :
( ( ( c_List_Olist_ONil @ SV563 )
!= ( c_List_Oappend @ SV1169 @ SY4032 @ SV563 ) )
| ( SY4032
= ( c_List_Olist_ONil @ SV563 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2857]) ).
thf(3490,plain,
! [SV1170: $i,SV564: $i] :
( ( ! [SY4033: $i,SY4034: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV564 ) @ SV1170 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY4033 ) @ SY4034 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1170 = SY4034 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2858]) ).
thf(3491,plain,
! [SV1171: $i,SV565: $i] :
( ( ! [SY4035: $i] :
( ( ( c_Lambda_OdB_OVar @ SV565 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1171 @ SY4035 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY4035
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2859]) ).
thf(3492,plain,
! [SV1172: $i,SV566: $i] :
( ( ! [SY4036: $i] :
( ( c_Lambda_OdB_OVar @ SV566 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1172 ) @ SY4036 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2860]) ).
thf(3493,plain,
! [SV1173: $i,SV567: $i] :
( ( ! [SY4037: $i] :
( ( c_List_Olist_OCons @ SV567 @ SV1173 @ SY4037 )
!= ( c_List_Olist_ONil @ SY4037 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2861]) ).
thf(3494,plain,
! [SV568: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV568 ) )
= $true )
| ( ( ( c_HOL_Oone__class_Oone @ SV568 )
!= ( c_HOL_Ozero__class_Ozero @ SV568 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2862]) ).
thf(3495,plain,
! [SV1174: $i,SV569: $i] :
( ( ! [SY4038: $i,SY4039: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV569 ) @ SV1174 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY4038 ) @ SY4039 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV569 = SY4038 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2863]) ).
thf(3496,plain,
! [SV1175: $i,SV570: $i] :
( ( ! [SY4040: $i,SY4041: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV570 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV570 ) @ SV1175 ) @ SY4040 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV570 ) @ SV1175 ) @ SY4041 ) )
| ( SY4040 = SY4041 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2864]) ).
thf(3497,plain,
! [SV1176: $i,SV571: $i] :
( ( ! [SY4042: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV571 ) @ SV1176 )
!= ( c_Lambda_OdB_OVar @ SY4042 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2865]) ).
thf(3498,plain,
! [SV1177: $i,SV572: $i] :
( ( ! [SY4043: $i,SY4044: $i] :
( ( ( c_List_Oappend @ SV572 @ SV1177 @ SY4043 )
!= ( c_List_Oappend @ SY4044 @ SV1177 @ SY4043 ) )
| ( SV572 = SY4044 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2866]) ).
thf(3499,plain,
! [SV1178: $i,SV573: $i] :
( ( ! [SY4045: $i,SY4046: $i,SY4047: $i] :
( ( ( c_List_Oappend @ SV573 @ ( c_List_Olist_OCons @ SV1178 @ ( c_List_Olist_ONil @ SY4045 ) @ SY4045 ) @ SY4045 )
!= ( c_List_Oappend @ SY4046 @ ( c_List_Olist_OCons @ SY4047 @ ( c_List_Olist_ONil @ SY4045 ) @ SY4045 ) @ SY4045 ) )
| ( SV1178 = SY4047 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2867]) ).
thf(3500,plain,
! [SV1179: $i,SV574: $i] :
( ( ! [SY4048: $i,SY4049: $i,SY4050: $i] :
( ( ( c_List_Oappend @ SV574 @ SV1179 @ SY4048 )
!= ( c_List_Oappend @ SY4049 @ SY4050 @ SY4048 ) )
| ( SV1179
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV574 @ ( tc_List_Olist @ SY4048 ) ) @ SY4049 @ SY4048 ) @ SY4050 @ SY4048 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV574 @ ( tc_List_Olist @ SY4048 ) ) @ ( c_Nat_Osize__class_Osize @ SY4049 @ ( tc_List_Olist @ SY4048 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2868]) ).
thf(3501,plain,
! [SV1180: $i,SV575: $i] :
( ( ! [SY4051: $i] :
( ( ( c_List_Olist_OCons @ SV575 @ ( c_List_Olist_ONil @ SV1180 ) @ SV1180 )
!= ( c_List_Orev @ SY4051 @ SV1180 ) )
| ( SY4051
= ( c_List_Olist_OCons @ SV575 @ ( c_List_Olist_ONil @ SV1180 ) @ SV1180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2869]) ).
thf(3502,plain,
! [SV1181: $i,SV576: $i] :
( ( ! [SY4052: $i,SY4053: $i] :
( ( ( c_List_Orev @ SV576 @ SV1181 )
!= ( c_List_Olist_OCons @ SY4052 @ SY4053 @ SV1181 ) )
| ( SV576
= ( c_List_Oappend @ ( c_List_Orev @ SY4053 @ SV1181 ) @ ( c_List_Olist_OCons @ SY4052 @ ( c_List_Olist_ONil @ SV1181 ) @ SV1181 ) @ SV1181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2870]) ).
thf(3503,plain,
! [SV1182: $i,SV577: $i] :
( ( ! [SY4054: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV577 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV577 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV577 )
| ~ ( class_Power_Opower @ SV577 )
| ( ( c_Power_Opower__class_Opower @ SV1182 @ SY4054 @ SV577 )
!= ( c_HOL_Ozero__class_Ozero @ SV577 ) )
| ( SV1182
= ( c_HOL_Ozero__class_Ozero @ SV577 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2871]) ).
thf(3504,plain,
! [SV1183: $i,SV578: $i] :
( ( ! [SY4055: $i,SY4056: $i,SY4057: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV578 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1183 @ SY4055 @ SV578 )
!= ( c_HOL_Ominus__class_Ominus @ SY4056 @ SY4057 @ SV578 ) )
| ( c_HOL_Oord__class_Oless @ SY4056 @ SY4057 @ SV578 )
| ~ ( c_HOL_Oord__class_Oless @ SV1183 @ SY4055 @ SV578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2872]) ).
thf(3505,plain,
! [SV579: $i] :
( ( ( c_Suc @ SV579 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2873]) ).
thf(3506,plain,
! [SV1184: $i,SV580: $i] :
( ( ! [SY4058: $i,SY4059: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ SV580 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Onth @ ( c_List_Olist_OCons @ SV1184 @ SY4058 @ SY4059 ) @ ( c_Int_Onumber__class_Onumber__of @ SV580 @ tc_nat ) @ SY4059 )
= SV1184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2874]) ).
thf(3507,plain,
! [SV581: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV581 ) )
= $true )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV581 )
!= ( c_HOL_Oone__class_Oone @ SV581 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2875]) ).
thf(3508,plain,
! [SV1185: $i,SV582: $i] :
( ( ! [SY4060: $i,SY4061: $i,SY4062: $i] :
( ( ( c_List_Olist_OCons @ SV582 @ SV1185 @ SY4060 )
!= ( c_List_Olist_OCons @ SY4061 @ SY4062 @ SY4060 ) )
| ( SV1185 = SY4062 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2876]) ).
thf(3509,plain,
! [SV1186: $i,SV583: $i] :
( ( ! [SY4063: $i] :
( ( ( c_List_Oappend @ SV583 @ SV1186 @ SY4063 )
!= ( c_List_Olist_ONil @ SY4063 ) )
| ( SV583
= ( c_List_Olist_ONil @ SY4063 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2877]) ).
thf(3510,plain,
! [SV1187: $i,SV584: $i] :
( ( ! [SY4064: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV584 )
| ( ( c_Power_Opower__class_Opower @ SV1187 @ SY4064 @ SV584 )
!= ( c_HOL_Ozero__class_Ozero @ SV584 ) )
| ( SV1187
= ( c_HOL_Ozero__class_Ozero @ SV584 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2878]) ).
thf(3511,plain,
! [SV1188: $i,SV585: $i] :
( ( ! [SY4065: $i,SY4066: $i] :
( ( ( c_List_OtakeWhile @ SV585 @ SV1188 @ SY4065 )
!= SV1188 )
| ( hBOOL @ ( hAPP @ SV585 @ SY4066 ) )
| ~ ( c_in @ SY4066 @ ( c_List_Oset @ SV1188 @ SY4065 ) @ SY4065 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2879]) ).
thf(3512,plain,
! [SV1189: $i,SV586: $i] :
( ( ! [SY4067: $i] :
( ( c_Lambda_OdB_OAbs @ SV586 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1189 ) @ SY4067 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2880]) ).
thf(3513,plain,
! [SV1190: $i,SV587: $i] :
( ( ! [SY4068: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV587 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1190 @ SY4068 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV587 )
= SV1190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2881]) ).
thf(3514,plain,
! [SV1191: $i,SV588: $i] :
( ( ! [SY4069: $i,SY4070: $i] :
( ( ( c_List_Olist_ONil @ SV588 )
!= ( c_List_Omap @ SV1191 @ SY4069 @ SY4070 @ SV588 ) )
| ( SY4069
= ( c_List_Olist_ONil @ SY4070 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2882]) ).
thf(3515,plain,
! [SV1192: $i,SV589: $i] :
( ( ! [SY4071: $i] :
( ( ( c_List_Olist_ONil @ SV589 )
!= ( c_List_Oappend @ SV1192 @ SY4071 @ SV589 ) )
| ( SV1192
= ( c_List_Olist_ONil @ SV589 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2883]) ).
thf(3516,plain,
! [SV1193: $i,SV590: $i] :
( ( ( ( c_List_Olist_ONil @ SV590 )
!= ( c_List_Orev @ SV1193 @ SV590 ) )
| ( SV1193
= ( c_List_Olist_ONil @ SV590 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2884]) ).
thf(3517,plain,
! [SV1194: $i,SV591: $i] :
( ( ! [SY4072: $i] :
( ( ( c_List_Otake @ SV591 @ SV1194 @ SY4072 )
!= ( c_List_Olist_ONil @ SY4072 ) )
| ( SV1194
= ( c_List_Olist_ONil @ SY4072 ) )
| ( SV591
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2885]) ).
thf(3518,plain,
! [SV1195: $i,SV592: $i] :
( ( ! [SY4073: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV592 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1195 @ SY4073 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY4073
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2886]) ).
thf(3519,plain,
! [SV1196: $i,SV593: $i] :
( ( ( ( c_List_Orev @ SV593 @ SV1196 )
!= ( c_List_Olist_ONil @ SV1196 ) )
| ( SV593
= ( c_List_Olist_ONil @ SV1196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2887]) ).
thf(3520,plain,
! [SV1197: $i,SV594: $i] :
( ( ! [SY4074: $i,SY4075: $i,SY4076: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV594 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1197 @ SY4074 @ SV594 )
!= ( c_HOL_Ominus__class_Ominus @ SY4075 @ SY4076 @ SV594 ) )
| ( c_HOL_Oord__class_Oless @ SV1197 @ SY4074 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SY4075 @ SY4076 @ SV594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2888]) ).
thf(3521,plain,
! [SV1198: $i,SV595: $i] :
( ( ! [SY4077: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV595 @ SV1198 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY4077 ) )
| ( SV595
= ( c_Lambda_OdB_OAbs @ SY4077 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2889]) ).
thf(3522,plain,
! [SV1199: $i,SV596: $i] :
( ( ! [SY4078: $i,SY4079: $i,SY4080: $i] :
( ( ( c_List_Oappend @ SV596 @ SV1199 @ SY4078 )
!= ( c_List_Oappend @ SY4079 @ SY4080 @ SY4078 ) )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SY4079 @ ( tc_List_Olist @ SY4078 ) ) @ SV596 @ SY4078 )
= SY4079 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV596 @ ( tc_List_Olist @ SY4078 ) ) @ ( c_Nat_Osize__class_Osize @ SY4079 @ ( tc_List_Olist @ SY4078 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2890]) ).
thf(3523,plain,
! [SV1200: $i,SV597: $i] :
( ( ! [SY4081: $i] :
( ( c_List_Olist_OCons @ SV597 @ SV1200 @ SY4081 )
!= SV1200 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2891]) ).
thf(3524,plain,
! [SV1201: $i,SV598: $i] :
( ( ! [SY4082: $i] :
( ( SV598
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV598 @ ( tc_List_Olist @ SV1201 ) ) @ SY4082 @ SV1201 ) )
| ( ( c_List_Oappend @ SV598 @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV598 @ ( tc_List_Olist @ SV1201 ) ) @ SY4082 @ SV1201 ) @ SV1201 )
= SY4082 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2892]) ).
thf(3525,plain,
! [SV1202: $i,SV599: $i] :
( ( ! [SY4083: $i,SY4084: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ SV599 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ SV599 @ tc_nat ) @ ( c_List_Olist_OCons @ SV1202 @ SY4083 @ SY4084 ) @ SY4084 )
= ( c_List_Olist_OCons @ SV1202 @ SY4083 @ SY4084 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2893]) ).
thf(3526,plain,
! [SV1203: $i,SV600: $i] :
( ( ! [SY4085: $i] :
( ( ( c_List_Orev @ SV600 @ SV1203 )
!= ( c_List_Orev @ SY4085 @ SV1203 ) )
| ( SV600 = SY4085 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2894]) ).
thf(3527,plain,
! [SV1204: $i,SV601: $i] :
( ( ! [SY4086: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV601 @ SV1204 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY4086 ) )
| ( SV1204
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2895]) ).
thf(3528,plain,
! [SV602: $i] :
( ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
= ( c_Suc @ SV602 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2896]) ).
thf(3529,plain,
! [SV1205: $i,SV603: $i] :
( ( ! [SY4087: $i,SY4088: $i] :
( ( SV603
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV603 @ ( tc_List_Olist @ SV1205 ) ) @ SY4087 @ SV1205 ) )
| ( ( c_List_Oappend @ SV603 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV603 @ ( tc_List_Olist @ SV1205 ) ) @ SY4087 @ SV1205 ) @ SY4088 @ SV1205 ) @ SV1205 )
= ( c_List_Oappend @ SY4087 @ SY4088 @ SV1205 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV603 @ ( tc_List_Olist @ SV1205 ) ) @ ( c_Nat_Osize__class_Osize @ SY4087 @ ( tc_List_Olist @ SV1205 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2897]) ).
thf(3530,plain,
! [SV1206: $i,SV604: $i] :
( ( ! [SY4089: $i] :
( ( ( c_List_Olist_ONil @ SV604 )
!= ( c_List_Oreplicate @ SV1206 @ SY4089 @ SV604 ) )
| ( SV1206
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2898]) ).
thf(3531,plain,
! [SV1207: $i,SV605: $i] :
( ( ! [SY4090: $i] :
( ( ( c_List_Oappend @ SV605 @ SV1207 @ SY4090 )
!= SV1207 )
| ( SV605
= ( c_List_Olist_ONil @ SY4090 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2899]) ).
thf(3532,plain,
! [SV1208: $i,SV606: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV606 @ SV1208 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_lessequals @ SV606 @ SV1208 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2900]) ).
thf(3533,plain,
! [SV1209: $i,SV607: $i] :
( ( ! [SY4091: $i,SY4092: $i,SY4093: $i,SY4094: $i] :
( ( ( c_List_Omap @ SV607 @ SV1209 @ SY4091 @ SY4092 )
!= ( c_List_Omap @ SY4093 @ SV1209 @ SY4091 @ SY4092 ) )
| ( ( hAPP @ SV607 @ SY4094 )
= ( hAPP @ SY4093 @ SY4094 ) )
| ~ ( c_in @ SY4094 @ ( c_List_Oset @ SV1209 @ SY4091 ) @ SY4091 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2901]) ).
thf(3534,plain,
! [SV1210: $i,SV608: $i] :
( ( ! [SY4095: $i,SY4096: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV608 ) @ SV1210 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4095 ) @ SY4096 ) )
| ( SV608 = SY4095 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2902]) ).
thf(3535,plain,
! [SV1211: $i,SV609: $i] :
( ( ! [SY4097: $i,SY4098: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV609 ) @ SV1211 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4097 ) @ SY4098 ) )
| ( SV1211 = SY4098 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2903]) ).
thf(3536,plain,
! [SV1212: $i,SV610: $i] :
( ( ! [SY4099: $i] :
( ( ( c_List_Oappend @ SV610 @ SV1212 @ SY4099 )
!= ( c_List_Olist_ONil @ SY4099 ) )
| ( SV1212
= ( c_List_Olist_ONil @ SY4099 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2904]) ).
thf(3537,plain,
! [SV1213: $i,SV611: $i] :
( ( ! [SY4100: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV611 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1213 @ SV611 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY4100 @ SV611 ) )
| ( SV1213 = SY4100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2905]) ).
thf(3538,plain,
! [SV1214: $i,SV612: $i] :
( ( ! [SY4101: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ SV612 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1214 @ SY4101 @ SV612 )
!= ( c_HOL_Ozero__class_Ozero @ SV612 ) )
| ( SV1214 = SY4101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2906]) ).
thf(3539,plain,
! [SV1215: $i,SV613: $i] :
( ( ! [SY4102: $i,SY4103: $i,SY4104: $i] :
( ( ( c_List_Odrop @ SV613 @ SV1215 @ SY4102 )
!= ( c_List_Olist_OCons @ SY4103 @ SY4104 @ SY4102 ) )
| ( ( c_List_Onth @ SV1215 @ SV613 @ SY4102 )
= SY4103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2907]) ).
thf(3540,plain,
! [SV1216: $i,SV614: $i] :
( ( ! [SY4105: $i,SY4106: $i,SY4107: $i] :
( ( ( c_List_Oappend @ SV614 @ SV1216 @ SY4105 )
!= ( c_List_Oappend @ SY4106 @ SY4107 @ SY4105 ) )
| ( SV614
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV614 @ ( tc_List_Olist @ SY4105 ) ) @ SY4106 @ SY4105 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV614 @ ( tc_List_Olist @ SY4105 ) ) @ ( c_Nat_Osize__class_Osize @ SY4106 @ ( tc_List_Olist @ SY4105 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2908]) ).
thf(3541,plain,
! [SV1217: $i,SV615: $i] :
( ( ! [SY4108: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV615 )
| ~ ( class_Int_Onumber__ring @ SV615 )
| ( SV1217
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV615 ) @ SV1217 ) @ SY4108 ) )
| ( SY4108
= ( c_HOL_Ozero__class_Ozero @ SV615 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2909]) ).
thf(3542,plain,
! [SV1218: $i,SV616: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV616 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV616 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV616 )
| ~ ( class_Power_Opower @ SV616 )
| ( ( c_Power_Opower__class_Opower @ SV1218 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV616 )
!= ( c_HOL_Ozero__class_Ozero @ SV616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2910]) ).
thf(3543,plain,
! [SV1219: $i,SV617: $i] :
( ( ! [SY4109: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV617 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV617 ) @ SV1219 ) @ SY4109 )
!= ( c_HOL_Ozero__class_Ozero @ SV617 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV617 ) @ SY4109 @ SV617 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV617 ) @ SV1219 @ SV617 )
| ( SY4109
= ( c_HOL_Ozero__class_Ozero @ SV617 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2911]) ).
thf(3544,plain,
! [SV1220: $i,SV618: $i] :
( ( ! [SY4110: $i,SY4111: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV618 )
| ( ( c_Power_Opower__class_Opower @ SV1220 @ SY4110 @ SV618 )
!= ( c_Power_Opower__class_Opower @ SV1220 @ SY4111 @ SV618 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV618 ) @ SV1220 @ SV618 )
| ( SY4110 = SY4111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2912]) ).
thf(3545,plain,
! [SV1221: $i,SV619: $i] :
( ( ! [SY4112: $i] :
( ( ( c_List_Oreplicate @ SV619 @ SV1221 @ SY4112 )
!= ( c_List_Olist_ONil @ SY4112 ) )
| ( SV619
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2913]) ).
thf(3546,plain,
! [SV1222: $i,SV620: $i] :
( ( ! [SY4113: $i] :
( SV620
!= ( c_List_Olist_OCons @ SV1222 @ SV620 @ SY4113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2914]) ).
thf(3547,plain,
! [SV1223: $i,SV621: $i] :
( ( ! [SY4114: $i,SY4115: $i,SY4116: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV621 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1223 @ SY4114 @ SV621 )
!= ( c_HOL_Ominus__class_Ominus @ SY4115 @ SY4116 @ SV621 ) )
| ( c_lessequals @ SY4114 @ SV1223 @ SV621 )
| ~ ( c_lessequals @ SY4116 @ SY4115 @ SV621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2915]) ).
thf(3548,plain,
! [SV1224: $i,SV622: $i] :
( ( ! [SY4117: $i,SY4118: $i,SY4119: $i] :
( ( ( c_List_Oreplicate @ SV622 @ SV1224 @ SY4117 )
!= ( c_List_Oreplicate @ SY4118 @ SY4119 @ SY4117 ) )
| ( SV1224 = SY4119 )
| ( SV622
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2916]) ).
thf(3549,plain,
! [SV1225: $i,SV623: $i] :
( ( ! [SY4120: $i,SY4121: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV623 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1225 @ SV1225 @ SV623 )
!= ( c_HOL_Ominus__class_Ominus @ SY4120 @ SY4121 @ SV623 ) )
| ( SY4120 = SY4121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2917]) ).
thf(3550,plain,
! [SV1226: $i,SV624: $i] :
( ( ! [SY4122: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV624 )
| ~ ( class_Int_Onumber__ring @ SV624 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1226 @ SY4122 @ SV624 )
!= ( c_HOL_Ozero__class_Ozero @ SV624 ) )
| ( SV1226 = SY4122 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2918]) ).
thf(3551,plain,
! [SV1227: $i,SV625: $i] :
( ( ! [SY4123: $i,SY4124: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV625 )
| ( ( c_Power_Opower__class_Opower @ SV1227 @ ( c_Suc @ SY4123 ) @ SV625 )
!= ( c_Power_Opower__class_Opower @ SY4124 @ ( c_Suc @ SY4123 ) @ SV625 ) )
| ( SV1227 = SY4124 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV625 ) @ SY4124 @ SV625 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV625 ) @ SV1227 @ SV625 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2919]) ).
thf(3552,plain,
! [SV1228: $i,SV626: $i] :
( ( ! [SY4125: $i,SY4126: $i,SY4127: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV626 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1228 @ SY4125 @ SV626 )
!= ( c_HOL_Ominus__class_Ominus @ SY4126 @ SY4127 @ SV626 ) )
| ( c_lessequals @ SY4127 @ SY4126 @ SV626 )
| ~ ( c_lessequals @ SY4125 @ SV1228 @ SV626 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2920]) ).
thf(3553,plain,
! [SV627: $i] :
( ( SV627
= ( c_Suc @ SV627 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2921]) ).
thf(3554,plain,
! [SV1229: $i,SV628: $i] :
( ( ! [SY4128: $i] :
( ( SV628
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV628 ) @ SV1229 ) @ SY4128 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV628 ) @ SV1229 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV628 ) @ SV1229 ) @ ( c_List_Oappend @ SY4128 @ ( c_List_Olist_OCons @ SV1229 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2922]) ).
thf(3555,plain,
! [SV1230: $i,SV629: $i] :
( ( ! [SY4129: $i,SY4130: $i] :
( ( ( c_List_Olist__update @ SV629 @ SV1230 @ SY4129 @ SY4130 )
!= SV629 )
| ~ ( c_HOL_Oord__class_Oless @ SV1230 @ ( c_Nat_Osize__class_Osize @ SV629 @ ( tc_List_Olist @ SY4130 ) ) @ tc_nat )
| ( ( c_List_Onth @ SV629 @ SV1230 @ SY4130 )
= SY4129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2923]) ).
thf(3556,plain,
! [SV1231: $i,SV630: $i] :
( ( ! [SY4131: $i,SY4132: $i,SY4133: $i] :
( ( ( c_List_Oappend @ SV630 @ SV1231 @ SY4131 )
!= ( c_List_Oappend @ SY4132 @ SY4133 @ SY4131 ) )
| ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SY4132 @ ( tc_List_Olist @ SY4131 ) ) @ SV630 @ SY4131 ) @ SV1231 @ SY4131 )
= SY4133 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV630 @ ( tc_List_Olist @ SY4131 ) ) @ ( c_Nat_Osize__class_Osize @ SY4132 @ ( tc_List_Olist @ SY4131 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2924]) ).
thf(3557,plain,
! [SV1232: $i,SV631: $i] :
( ( ! [SY4134: $i,SY4135: $i,SY4136: $i] :
( ( ( c_List_Olist_OCons @ SV631 @ SV1232 @ SY4134 )
!= ( c_List_Olist_OCons @ SY4135 @ SY4136 @ SY4134 ) )
| ( SV631 = SY4135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2925]) ).
thf(3558,plain,
! [SV1233: $i,SV632: $i] :
( ( ! [SY4137: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV632 @ SV1233 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY4137 @ SV1233 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV632 = SY4137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2926]) ).
thf(3559,plain,
! [SV1234: $i,SV633: $i] :
( ( ! [SY4138: $i,SY4139: $i,SY4140: $i] :
( ( ( c_List_Omap @ SV633 @ SV1234 @ SY4138 @ SY4139 )
!= ( c_List_Omap @ SV633 @ SY4140 @ SY4138 @ SY4139 ) )
| ( ( c_Nat_Osize__class_Osize @ SV1234 @ ( tc_List_Olist @ SY4138 ) )
= ( c_Nat_Osize__class_Osize @ SY4140 @ ( tc_List_Olist @ SY4138 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2927]) ).
thf(3560,plain,
! [SV1235: $i,SV634: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV634 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV634 ) @ SV1235 ) @ SV1235 )
!= ( c_HOL_Ozero__class_Ozero @ SV634 ) )
| ( SV1235
= ( c_HOL_Ozero__class_Ozero @ SV634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2928]) ).
thf(3561,plain,
! [SV635: $i] :
( ( ( c_Suc @ SV635 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2929]) ).
thf(3562,plain,
! [SV1236: $i,SV636: $i] :
( ( ! [SY4141: $i] :
( ( ( c_List_Orev @ SV636 @ SV1236 )
!= ( c_List_Olist_OCons @ SY4141 @ ( c_List_Olist_ONil @ SV1236 ) @ SV1236 ) )
| ( SV636
= ( c_List_Olist_OCons @ SY4141 @ ( c_List_Olist_ONil @ SV1236 ) @ SV1236 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2930]) ).
thf(3563,plain,
! [SV1237: $i,SV637: $i] :
( ( ! [SY4142: $i,SY4143: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV637 )
| ~ ( class_Int_Onumber__ring @ SV637 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1237 ) @ SY4142 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1237 ) @ SY4143 ) )
| ( SY4142 = SY4143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2931]) ).
thf(3564,plain,
! [SV1238: $i,SV638: $i] :
( ( ! [SY4144: $i,SY4145: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV638 ) @ SV1238 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY4144 @ SY4145 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV638
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY4144 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV638 @ SV1238 @ SY4144 @ SY4145 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY4145
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2932]) ).
thf(3565,plain,
! [SV1239: $i,SV639: $i] :
( ( ! [SY4146: $i] :
( ~ ( class_Int_Oring__char__0 @ SV639 )
| ~ ( class_Int_Onumber__ring @ SV639 )
| ( ( c_Int_Onumber__class_Onumber__of @ SV1239 @ SV639 )
!= ( c_Int_Onumber__class_Onumber__of @ SY4146 @ SV639 ) )
| ( SV1239 = SY4146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2933]) ).
thf(3566,plain,
! [SV640: $i] :
( ( ( c_Suc @ SV640 )
= SV640 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2934]) ).
thf(3567,plain,
! [SV1240: $i,SV641: $i] :
( ( ! [SY4147: $i,SY4148: $i] :
( ( ( c_List_Olist__update @ SV641 @ SV1240 @ SY4147 @ SY4148 )
!= ( c_List_Olist_ONil @ SY4148 ) )
| ( SV641
= ( c_List_Olist_ONil @ SY4148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2935]) ).
thf(3568,plain,
! [SV1241: $i,SV642: $i] :
( ( ( c_Lambda_OdB_OVar @ SV642 )
!= ( c_Lambda_OdB_OAbs @ SV1241 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2936]) ).
thf(3569,plain,
! [SV1242: $i,SV643: $i] :
( ( ! [SY4149: $i,SY4150: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV643 ) @ SV1242 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY4149 ) @ SY4150 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1242 = SY4150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2937]) ).
thf(3570,plain,
! [SV1243: $i,SV644: $i] :
( ( ! [SY4151: $i,SY4152: $i] :
( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV644 @ ( tc_List_Olist @ SV1243 ) ) @ SY4151 @ SV1243 )
!= SV644 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SY4151 @ ( tc_List_Olist @ SV1243 ) ) @ ( c_Nat_Osize__class_Osize @ SV644 @ ( tc_List_Olist @ SV1243 ) ) @ tc_nat )
| ( ( c_List_Oappend @ SY4151 @ SY4152 @ SV1243 )
= ( c_List_Oappend @ SV644 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV644 @ ( tc_List_Olist @ SV1243 ) ) @ SY4151 @ SV1243 ) @ SY4152 @ SV1243 ) @ SV1243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2938]) ).
thf(3571,plain,
! [SV1244: $i,SV645: $i] :
( ( ! [SY4153: $i,SY4154: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ SV645 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ SV645 @ tc_nat ) @ ( c_List_Olist_OCons @ SV1244 @ SY4153 @ SY4154 ) @ SY4154 )
= ( c_List_Olist_ONil @ SY4154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2939]) ).
thf(3572,plain,
! [SV1245: $i,SV646: $i] :
( ( ! [SY4155: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ SV646 @ SV1245 @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ SY4155 @ SV1245 @ tc_nat ) )
| ~ ( c_lessequals @ SV1245 @ SY4155 @ tc_nat )
| ~ ( c_lessequals @ SV1245 @ SV646 @ tc_nat )
| ( SV646 = SY4155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2940]) ).
thf(3573,plain,
! [SV1246: $i,SV647: $i] :
( ( ! [SY4156: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV647 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV647 ) @ SV1246 ) @ SY4156 )
!= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV647 ) @ SY4156 @ SV647 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV647 ) @ SV1246 @ SV647 )
| ( SV1246
= ( c_HOL_Ozero__class_Ozero @ SV647 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2941]) ).
thf(3574,plain,
! [SV1247: $i,SV648: $i] :
( ( ! [SY4157: $i,SY4158: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV648 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV648 ) @ SV1247 ) @ SY4157 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV648 ) @ SV1247 ) @ SY4158 ) )
| ( SY4157 = SY4158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2942]) ).
thf(3575,plain,
! [SV1248: $i,SV649: $i] :
( ( ! [SY4159: $i,SY4160: $i,SY4161: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV649 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1248 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SY4159 ) @ SY4160 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SY4159 ) @ SY4161 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1248 ) @ SY4160 )
= SY4161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2943]) ).
thf(3576,plain,
! [SV1249: $i,SV650: $i] :
( ( ! [SY4162: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV650 ) @ SV1249 )
!= ( c_Lambda_OdB_OAbs @ SY4162 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2944]) ).
thf(3577,plain,
! [SV1250: $i,SV651: $i] :
( ( ! [SY4163: $i,SY4164: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV651 ) ) @ SV1250 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY4163 ) @ SY4164 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2945]) ).
thf(3578,plain,
! [SV1251: $i,SV652: $i] :
( ( ! [SY4165: $i,SY4166: $i] :
( ( ( c_List_Omap @ SV652 @ SV1251 @ SY4165 @ SY4166 )
!= ( c_List_Olist_ONil @ SY4166 ) )
| ( SV1251
= ( c_List_Olist_ONil @ SY4165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2946]) ).
thf(3579,plain,
! [SV1252: $i,SV653: $i] :
( ( ! [SY4167: $i] :
( ( ( c_List_Oappend @ SV653 @ SV1252 @ SY4167 )
!= SV653 )
| ( SV1252
= ( c_List_Olist_ONil @ SY4167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2947]) ).
thf(3580,plain,
! [SV1253: $i,SV654: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV654 @ SV1253 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_HOL_Ominus__class_Ominus @ SV1253 @ SV654 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1253 = SV654 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2948]) ).
thf(3581,plain,
! [SV1254: $i,SV655: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ SV655 @ ( tc_List_Olist @ SV1254 ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV655
= ( c_List_Olist_ONil @ SV1254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2949]) ).
thf(3582,plain,
! [SV1255: $i,SV656: $i] :
( ( ! [SY4168: $i,SY4169: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV656 ) @ SV1255 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY4168 ) @ SY4169 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2950]) ).
thf(3583,plain,
! [SV657: $i,SV1: $i] :
( ( ( SV1 = SV657 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1 @ ( c_Suc @ SV657 ) @ tc_nat )
| ~ ( c_lessequals @ SV657 @ SV1 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2951]) ).
thf(3584,plain,
! [SV1256: $i,SV658: $i,SV2: $i] :
( ( ! [SY4170: $i,SY4171: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV2 )
| ( c_lessequals @ SV658 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SV1256 ) @ SY4170 ) @ SV2 )
| ~ ( c_lessequals @ SY4171 @ SY4170 @ SV2 )
| ~ ( c_lessequals @ SV658 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SV1256 ) @ SY4171 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2952]) ).
thf(3585,plain,
! [SV1257: $i,SV659: $i,SV3: $i] :
( ( ! [SY4172: $i] :
( ~ ( class_Orderings_Opreorder @ SV3 )
| ( c_HOL_Oord__class_Oless @ SV659 @ SV1257 @ SV3 )
| ~ ( c_lessequals @ SY4172 @ SV1257 @ SV3 )
| ~ ( c_HOL_Oord__class_Oless @ SV659 @ SY4172 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2953]) ).
thf(3586,plain,
! [SV1258: $i,SV660: $i,SV4: $i] :
( ( ! [SY4173: $i] :
( ~ ( class_Orderings_Opreorder @ SV4 )
| ( c_HOL_Oord__class_Oless @ SV660 @ SV1258 @ SV4 )
| ~ ( c_HOL_Oord__class_Oless @ SY4173 @ SV1258 @ SV4 )
| ~ ( c_lessequals @ SV660 @ SY4173 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2954]) ).
thf(3587,plain,
! [SV661: $i,SV5: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV5 ) )
= $true )
| ( ( c_lessequals @ SV661 @ SV661 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2955]) ).
thf(3588,plain,
! [SV662: $i,SV6: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV6 ) )
= $true )
| ( ( c_lessequals @ SV662 @ SV662 @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2956]) ).
thf(3589,plain,
! [SV1259: $i,SV663: $i,SV8: $i] :
( ( ( c_lessequals @ SV8 @ SV663 @ tc_nat )
| ~ ( c_lessequals @ SV1259 @ SV663 @ tc_nat )
| ~ ( c_lessequals @ SV8 @ SV1259 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2957]) ).
thf(3590,plain,
! [SV1260: $i,SV664: $i,SV10: $i] :
( ( ! [SY4174: $i] :
( ~ ( class_Orderings_Opreorder @ SV10 )
| ( c_lessequals @ SV664 @ SV1260 @ SV10 )
| ~ ( c_lessequals @ SY4174 @ SV1260 @ SV10 )
| ~ ( c_lessequals @ SV664 @ SY4174 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2958]) ).
thf(3591,plain,
! [SV1261: $i,SV665: $i,SV11: $i] :
( ( ! [SY4175: $i] :
( ~ ( class_Orderings_Oorder @ SV11 )
| ( c_HOL_Oord__class_Oless @ SV665 @ SV1261 @ SV11 )
| ~ ( c_HOL_Oord__class_Oless @ SV665 @ SY4175 @ SV11 )
| ~ ( c_lessequals @ SY4175 @ SV1261 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2959]) ).
thf(3592,plain,
! [SV1262: $i,SV666: $i,SV12: $i] :
( ( ! [SY4176: $i] :
( ~ ( class_Orderings_Oorder @ SV12 )
| ( c_HOL_Oord__class_Oless @ SV666 @ SV1262 @ SV12 )
| ~ ( c_lessequals @ SV666 @ SY4176 @ SV12 )
| ~ ( c_HOL_Oord__class_Oless @ SY4176 @ SV1262 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2960]) ).
thf(3593,plain,
! [SV1263: $i,SV667: $i,SV13: $i] :
( ( ! [SY4177: $i] :
( ~ ( class_Orderings_Oorder @ SV13 )
| ( c_lessequals @ SV667 @ SV1263 @ SV13 )
| ~ ( c_lessequals @ SV667 @ SY4177 @ SV13 )
| ~ ( c_lessequals @ SY4177 @ SV1263 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2961]) ).
thf(3594,plain,
! [SV1264: $i,SV668: $i,SV14: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1 @ SV14 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV668 @ SV1264 @ tc_nat ) @ SV14 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV668 @ SV14 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1264 @ SV14 ) @ SV14 ) )
| ~ ( c_lessequals @ SV1264 @ SV668 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2962]) ).
thf(3595,plain,
! [SV1265: $i,SV669: $i,SV15: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV15 @ SV669 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1265 @ SV669 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV15 @ SV1265 @ tc_nat )
| ~ ( c_lessequals @ SV669 @ SV1265 @ tc_nat )
| ~ ( c_lessequals @ SV669 @ SV15 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2963]) ).
thf(3596,plain,
! [SV1266: $i,SV670: $i,SV16: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV16 @ SV670 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV16 @ SV1266 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV670 @ SV1266 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1266 @ SV670 @ tc_nat )
| ~ ( c_lessequals @ SV1266 @ SV16 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2964]) ).
thf(3597,plain,
! [SV671: $i,SV18: $i] :
( ( ( c_lessequals @ SV18 @ ( c_Suc @ SV671 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV18 @ SV671 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2966]) ).
thf(3598,plain,
! [SV672: $i,SV19: $i] :
( ( ( c_lessequals @ SV19 @ SV672 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV19 ) @ SV672 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2967]) ).
thf(3599,plain,
! [SV1267: $i,SV673: $i,SV20: $i] :
( ( ! [SY4178: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV20 )
| ( c_lessequals @ SV673 @ SV1267 @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV1267 @ SV20 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV673 @ ( c_Suc @ SY4178 ) @ SV20 ) @ ( c_Power_Opower__class_Opower @ SV1267 @ ( c_Suc @ SY4178 ) @ SV20 ) @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2968]) ).
thf(3600,plain,
! [SV1268: $i,SV674: $i,SV21: $i] :
( ( ! [SY4179: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV21 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SV674 ) @ SV1268 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SV674 ) @ SY4179 ) @ SV21 )
| ~ ( c_lessequals @ SV1268 @ SY4179 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2969]) ).
thf(3601,plain,
! [SV1269: $i,SV675: $i,SV22: $i] :
( ( ! [SY4180: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV22 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV675 ) @ SV1269 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SY4180 ) @ SV1269 ) @ SV22 )
| ~ ( c_lessequals @ SV675 @ SY4180 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2970]) ).
thf(3602,plain,
! [SV1270: $i,SV676: $i,SV23: $i] :
( ( ! [SY4181: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV23 )
| ( c_lessequals @ SV676 @ SV1270 @ SV23 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV23 ) @ SY4181 ) @ SV676 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV23 ) @ SY4181 ) @ SV1270 ) @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2971]) ).
thf(3603,plain,
! [SV1271: $i,SV677: $i,SV24: $i] :
( ( ! [SY4182: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV24 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ SV677 ) @ SV1271 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ SV677 ) @ SY4182 ) @ SV24 )
| ~ ( c_lessequals @ SV1271 @ SY4182 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2972]) ).
thf(3604,plain,
! [SV1272: $i,SV678: $i,SV25: $i] :
( ( ! [SY4183: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV25 )
| ( c_lessequals @ SV678 @ SV1272 @ SV25 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SV678 ) @ SY4183 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SV1272 ) @ SY4183 ) @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2973]) ).
thf(3605,plain,
! [SV1273: $i,SV679: $i,SV26: $i] :
( ( ! [SY4184: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV26 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV26 ) @ SV679 ) @ SV1273 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV26 ) @ SY4184 ) @ SV1273 ) @ SV26 )
| ~ ( c_lessequals @ SV679 @ SY4184 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2974]) ).
thf(3606,plain,
! [SV1274: $i,SV680: $i,SV27: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV27 ) @ SV680 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1274 @ SV680 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV27 @ SV1274 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2975]) ).
thf(3607,plain,
! [SV1275: $i,SV681: $i,SV30: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV30 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV30 ) @ ( c_Power_Opower__class_Opower @ SV681 @ ( c_Suc @ SV1275 ) @ SV30 ) @ SV30 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SV681 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2976]) ).
thf(3608,plain,
! [SV1276: $i,SV682: $i,SV31: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV31 )
| ( c_lessequals @ SV682 @ SV1276 @ SV31 )
| ~ ( c_HOL_Oord__class_Oless @ SV682 @ SV1276 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2977]) ).
thf(3609,plain,
! [SV1277: $i,SV683: $i,SV32: $i] :
( ( ~ ( class_Orderings_Oorder @ SV32 )
| ( c_lessequals @ SV683 @ SV1277 @ SV32 )
| ~ ( c_HOL_Oord__class_Oless @ SV683 @ SV1277 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2978]) ).
thf(3610,plain,
! [SV684: $i,SV33: $i] :
( ( ( c_lessequals @ SV33 @ SV684 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV33 @ SV684 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2979]) ).
thf(3611,plain,
! [SV685: $i,SV34: $i] :
( ( ( c_lessequals @ SV34 @ SV685 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV34 @ SV685 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2980]) ).
thf(3612,plain,
! [SV1278: $i,SV686: $i,SV35: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV35 )
| ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV686 @ SV1278 @ SV35 ) @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ SV35 )
| ~ ( c_lessequals @ SV686 @ SV1278 @ SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2981]) ).
thf(3613,plain,
! [SV1279: $i,SV687: $i,SV36: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV36 )
| ( c_lessequals @ SV687 @ SV1279 @ SV36 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV687 @ SV1279 @ SV36 ) @ ( c_HOL_Ozero__class_Ozero @ SV36 ) @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2982]) ).
thf(3614,plain,
! [SV1280: $i,SV688: $i,SV37: $i] :
( ( ~ ( class_Orderings_Oorder @ SV37 )
| ( SV688 = SV1280 )
| ~ ( c_lessequals @ SV688 @ SV1280 @ SV37 )
| ~ ( c_lessequals @ SV1280 @ SV688 @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2983]) ).
thf(3615,plain,
! [SV1281: $i,SV689: $i,SV38: $i] :
( ( ~ ( class_Orderings_Oorder @ SV38 )
| ( SV689 = SV1281 )
| ~ ( c_lessequals @ SV1281 @ SV689 @ SV38 )
| ~ ( c_lessequals @ SV689 @ SV1281 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2984]) ).
thf(3616,plain,
! [SV1282: $i,SV690: $i,SV39: $i] :
( ( ~ ( class_Orderings_Oorder @ SV39 )
| ( SV690 = SV1282 )
| ~ ( c_lessequals @ SV1282 @ SV690 @ SV39 )
| ~ ( c_lessequals @ SV690 @ SV1282 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2985]) ).
thf(3617,plain,
! [SV691: $i,SV40: $i] :
( ( ( SV40 = SV691 )
= $true )
| ( ( ~ ( c_lessequals @ SV691 @ SV40 @ tc_nat )
| ~ ( c_lessequals @ SV40 @ SV691 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2986]) ).
thf(3618,plain,
! [SV42: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV42 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV42 ) @ ( c_HOL_Ozero__class_Ozero @ SV42 ) @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2988]) ).
thf(3619,plain,
! [SV1283: $i,SV693: $i,SV43: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV43 )
| ( c_HOL_Oord__class_Oless @ SV693 @ SV1283 @ SV43 )
| ( c_lessequals @ SV1283 @ SV693 @ SV43 )
| ~ ( c_lessequals @ SV693 @ SV1283 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2989]) ).
thf(3620,plain,
! [SV1284: $i,SV694: $i,SV44: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV44 @ SV694 @ tc_nat ) @ SV1284 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV44 @ SV1284 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2990]) ).
thf(3621,plain,
! [SV45: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV45 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV45 ) @ ( c_HOL_Oone__class_Oone @ SV45 ) @ SV45 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2991]) ).
thf(3622,plain,
! [SV695: $i,SV46: $i] :
( ( ( SV46 = SV695 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV46 @ ( c_Suc @ SV695 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV46 @ SV695 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2992]) ).
thf(3623,plain,
! [SV696: $i,SV47: $i] :
( ( ( SV47 = SV696 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV696 @ ( c_Suc @ SV47 ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV696 @ SV47 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2993]) ).
thf(3624,plain,
! [SV697: $i,SV48: $i] :
( ( ( SV48 = SV697 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV48 @ SV697 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV48 @ ( c_Suc @ SV697 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2994]) ).
thf(3625,plain,
! [SV1285: $i,SV699: $i,SV50: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV50 @ SV699 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV50 @ SV1285 @ tc_nat ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1285 @ SV50 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1285 @ SV699 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2996]) ).
thf(3626,plain,
! [SV700: $i,SV51: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV51 ) @ SV700 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV51 @ SV700 @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_lessequals @ SV700 @ SV51 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2997]) ).
thf(3627,plain,
! [SV1286: $i,SV701: $i,SV52: $i] :
( ( ! [SY4185: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV52 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV701 @ SV1286 @ SV52 ) @ ( c_Power_Opower__class_Opower @ SV701 @ SY4185 @ SV52 ) @ SV52 )
| ~ ( c_lessequals @ SV701 @ ( c_HOL_Oone__class_Oone @ SV52 ) @ SV52 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV701 @ SV52 )
| ~ ( c_lessequals @ SY4185 @ SV1286 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2998]) ).
thf(3628,plain,
! [SV702: $i,SV53: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV53 @ SV702 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV53 ) @ SV702 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2999]) ).
thf(3629,plain,
! [SV703: $i,SV54: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV54 ) @ SV703 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV54 @ SV703 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3000]) ).
thf(3630,plain,
! [SV704: $i,SV55: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV55 @ SV704 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV55 ) @ SV704 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3001]) ).
thf(3631,plain,
! [SV705: $i,SV56: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV56 ) @ SV705 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV56 @ SV705 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3002]) ).
thf(3632,plain,
! [SV1287: $i,SV706: $i,SV57: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV57 )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV57 ) @ ( c_Power_Opower__class_Opower @ SV706 @ SV1287 @ SV57 ) @ SV57 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV57 ) @ SV706 @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3003]) ).
thf(3633,plain,
! [SV707: $i,SV58: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV58 @ SV707 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV58 @ SV707 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3004]) ).
thf(3634,plain,
! [SV1288: $i,SV708: $i,SV59: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV59 )
| ( c_lessequals @ SV708 @ SV1288 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV708 @ SV59 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1288 @ SV59 ) @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3005]) ).
thf(3635,plain,
! [SV1289: $i,SV709: $i,SV60: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV60 )
| ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV709 @ SV60 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1289 @ SV60 ) @ SV60 )
| ~ ( c_lessequals @ SV709 @ SV1289 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3006]) ).
thf(3636,plain,
! [SV1290: $i,SV710: $i,SV61: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV61 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ ( c_HOL_Ominus__class_Ominus @ SV710 @ SV1290 @ SV61 ) ) @ SV1290 )
= SV710 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3007]) ).
thf(3637,plain,
! [SV1291: $i,SV711: $i,SV62: $i] :
( ( ! [SY4186: $i,SY4187: $i] :
( ( c_ListOrder_Ostep1 @ SV62 @ ( c_List_Oappend @ SV711 @ SV1291 @ SY4186 ) @ ( c_List_Oappend @ SV711 @ SY4187 @ SY4186 ) @ SY4186 )
| ~ ( c_ListOrder_Ostep1 @ SV62 @ SV1291 @ SY4187 @ SY4186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3008]) ).
thf(3638,plain,
! [SV1292: $i,SV712: $i,SV63: $i] :
( ( ! [SY4188: $i,SY4189: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV63 @ SV712 @ SV1292 @ SY4188 )
| ( c_ListOrder_Ostep1 @ SV63 @ ( c_List_Oappend @ SV712 @ SY4189 @ SY4188 ) @ ( c_List_Oappend @ SV1292 @ SY4189 @ SY4188 ) @ SY4188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3009]) ).
thf(3639,plain,
! [SV1293: $i,SV713: $i,SV64: $i] :
( ( ! [SY4190: $i,SY4191: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV64 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV713 ) @ SV1293 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SY4190 ) @ SY4191 ) @ SV64 )
| ~ ( c_lessequals @ SV1293 @ SY4191 @ SV64 )
| ~ ( c_lessequals @ SV713 @ SY4190 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3010]) ).
thf(3640,plain,
! [SV1294: $i,SV714: $i,SV65: $i] :
( ( ! [SY4192: $i,SY4193: $i] :
( ( c_lessequals @ SV65 @ ( c_List_Olist_Olist__size @ SV714 @ SV1294 @ SY4192 ) @ tc_nat )
| ~ ( c_lessequals @ SV65 @ ( hAPP @ SV714 @ SY4193 ) @ tc_nat )
| ~ ( c_in @ SY4193 @ ( c_List_Oset @ SV1294 @ SY4192 ) @ SY4192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3011]) ).
thf(3641,plain,
! [SV715: $i,SV66: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV66 @ ( c_Suc @ SV715 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV66 @ SV715 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3012]) ).
thf(3642,plain,
! [SV716: $i,SV67: $i] :
( ( ( c_lessequals @ SV67 @ SV716 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV67 @ ( c_Suc @ SV716 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3013]) ).
thf(3643,plain,
! [SV68: $i] :
( ( ( c_lessequals @ SV68 @ SV68 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV68 @ ( c_Suc @ SV68 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3014]) ).
thf(3644,plain,
! [SV718: $i,SV70: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV70 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV70 ) @ SV718 @ SV70 )
= ( c_HOL_Oone__class_Oone @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3016]) ).
thf(3645,plain,
! [SV1295: $i,SV719: $i,SV71: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV71 )
| ( c_HOL_Oord__class_Oless @ SV719 @ SV1295 @ SV71 )
| ( c_lessequals @ SV1295 @ SV719 @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3017]) ).
thf(3646,plain,
! [SV720: $i,SV72: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV72 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV720 @ SV720 @ SV72 )
| ~ ( c_HOL_Oord__class_Oless @ SV720 @ SV720 @ SV72 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3018]) ).
thf(3647,plain,
! [SV721: $i,SV73: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV73 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV721 @ SV721 @ SV73 )
| ( c_lessequals @ SV721 @ SV721 @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3019]) ).
thf(3648,plain,
! [SV1296: $i,SV722: $i,SV74: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV74 )
| ~ ( c_HOL_Oord__class_Oless @ SV722 @ SV1296 @ SV74 )
| ~ ( c_lessequals @ SV1296 @ SV722 @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3020]) ).
thf(3649,plain,
! [SV1297: $i,SV723: $i,SV75: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV75 )
| ( c_lessequals @ SV723 @ SV1297 @ SV75 )
| ( c_HOL_Oord__class_Oless @ SV1297 @ SV723 @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3021]) ).
thf(3650,plain,
! [SV1298: $i,SV724: $i,SV76: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV76 )
| ~ ( c_lessequals @ SV724 @ SV1298 @ SV76 )
| ~ ( c_HOL_Oord__class_Oless @ SV1298 @ SV724 @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3022]) ).
thf(3651,plain,
! [SV1299: $i,SV725: $i,SV77: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV77 )
| ( c_HOL_Oord__class_Oless @ SV725 @ SV1299 @ SV77 )
| ( c_lessequals @ SV1299 @ SV725 @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3023]) ).
thf(3652,plain,
! [SV1300: $i,SV726: $i,SV78: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV78 )
| ~ ( c_lessequals @ SV726 @ SV1300 @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ SV1300 @ SV726 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3024]) ).
thf(3653,plain,
! [SV1301: $i,SV727: $i,SV79: $i] :
( ( ! [SY4194: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV79 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV727 @ SV1301 @ SV79 ) @ ( c_Power_Opower__class_Opower @ SV727 @ SY4194 @ SV79 ) @ SV79 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV79 ) @ SV727 @ SV79 )
| ~ ( c_lessequals @ SV1301 @ SY4194 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3025]) ).
thf(3654,plain,
! [SV1302: $i,SV728: $i,SV80: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV80 @ SV728 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV80 @ SV1302 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1302 @ SV728 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3026]) ).
thf(3655,plain,
! [SV1303: $i,SV729: $i,SV81: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV81 @ SV729 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1303 @ SV729 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV81 @ SV1303 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3027]) ).
thf(3656,plain,
! [SV730: $i,SV82: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV82 @ SV730 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV82 ) @ SV730 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3028]) ).
thf(3657,plain,
! [SV731: $i,SV83: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV83 @ ( c_Suc @ SV731 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV83 @ SV731 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3029]) ).
thf(3658,plain,
! [SV84: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV84 @ tc_nat )
= $false )
| ( ( ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV84 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) )
= SV84 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3030]) ).
thf(3659,plain,
! [SV732: $i,SV85: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV85 @ ( c_Suc @ SV732 ) @ tc_nat ) @ SV85 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV85 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3031]) ).
thf(3660,plain,
! [SV1304: $i,SV733: $i,SV86: $i] :
( ( ~ ( class_Orderings_Oorder @ SV86 )
| ( c_HOL_Oord__class_Oless @ SV733 @ SV1304 @ SV86 )
| ( SV1304 = SV733 )
| ~ ( c_lessequals @ SV733 @ SV1304 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3032]) ).
thf(3661,plain,
! [SV1305: $i,SV734: $i,SV87: $i] :
( ( ~ ( class_Orderings_Oorder @ SV87 )
| ( c_HOL_Oord__class_Oless @ SV734 @ SV1305 @ SV87 )
| ~ ( c_lessequals @ SV734 @ SV1305 @ SV87 )
| ( SV1305 = SV734 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3033]) ).
thf(3662,plain,
! [SV735: $i,SV88: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV88 @ SV735 @ tc_nat )
= $true )
| ( ( ( SV88 = SV735 )
| ~ ( c_lessequals @ SV88 @ SV735 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3034]) ).
thf(3663,plain,
! [SV736: $i,SV89: $i] :
( ( ( SV89 = SV736 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV89 @ SV736 @ tc_nat )
| ~ ( c_lessequals @ SV89 @ SV736 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3035]) ).
thf(3664,plain,
! [SV737: $i,SV90: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV90 @ SV737 @ tc_nat )
= $true )
| ( ( ( SV90 = SV737 )
| ~ ( c_lessequals @ SV90 @ SV737 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3036]) ).
thf(3665,plain,
! [SV1306: $i,SV738: $i,SV91: $i] :
( ( ~ ( class_Orderings_Oorder @ SV91 )
| ( SV738 = SV1306 )
| ( c_HOL_Oord__class_Oless @ SV738 @ SV1306 @ SV91 )
| ~ ( c_lessequals @ SV738 @ SV1306 @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3037]) ).
thf(3666,plain,
! [SV1307: $i,SV739: $i,SV92: $i] :
( ( ~ ( class_Orderings_Oorder @ SV92 )
| ( c_HOL_Oord__class_Oless @ SV739 @ SV1307 @ SV92 )
| ( SV739 = SV1307 )
| ~ ( c_lessequals @ SV739 @ SV1307 @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3038]) ).
thf(3667,plain,
! [SV1308: $i,SV740: $i,SV93: $i] :
( ( ~ ( class_Orderings_Oorder @ SV93 )
| ( c_HOL_Oord__class_Oless @ SV740 @ SV1308 @ SV93 )
| ( SV740 = SV1308 )
| ~ ( c_lessequals @ SV740 @ SV1308 @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3039]) ).
thf(3668,plain,
! [SV1309: $i,SV741: $i,SV94: $i] :
( ( ~ ( class_Orderings_Oorder @ SV94 )
| ( c_HOL_Oord__class_Oless @ SV741 @ SV1309 @ SV94 )
| ~ ( c_lessequals @ SV741 @ SV1309 @ SV94 )
| ( SV741 = SV1309 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3040]) ).
thf(3669,plain,
! [SV1310: $i,SV742: $i,SV95: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV95 )
| ( SV742 = SV1310 )
| ~ ( c_lessequals @ SV742 @ SV1310 @ SV95 )
| ( c_HOL_Oord__class_Oless @ SV742 @ SV1310 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3041]) ).
thf(3670,plain,
! [SV1311: $i,SV743: $i,SV96: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV96 )
| ( SV743 = SV1311 )
| ( c_HOL_Oord__class_Oless @ SV743 @ SV1311 @ SV96 )
| ~ ( c_lessequals @ SV743 @ SV1311 @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3042]) ).
thf(3671,plain,
! [SV744: $i,SV97: $i] :
( ( ( c_lessequals @ SV97 @ SV744 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV97 ) @ ( c_Suc @ SV744 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3043]) ).
thf(3672,plain,
! [SV745: $i,SV98: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV98 ) @ ( c_Suc @ SV745 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV98 @ SV745 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3044]) ).
thf(3673,plain,
! [SV746: $i,SV99: $i] :
( ( ( c_lessequals @ SV99 @ SV746 @ tc_nat )
= $true )
| ( ( c_lessequals @ SV746 @ SV99 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3045]) ).
thf(3674,plain,
! [SV1312: $i,SV747: $i,SV100: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV100 )
| ( c_lessequals @ SV747 @ SV1312 @ SV100 )
| ( c_lessequals @ SV1312 @ SV747 @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3046]) ).
thf(3675,plain,
! [SV1313: $i,SV748: $i,SV101: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV101 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV748 @ ( c_Suc @ SV1313 ) @ SV101 ) @ ( c_HOL_Oone__class_Oone @ SV101 ) @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ SV748 @ ( c_HOL_Oone__class_Oone @ SV101 ) @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ SV748 @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3047]) ).
thf(3676,plain,
! [SV1314: $i,SV749: $i,SV102: $i] :
( ( ! [SY4195: $i] :
( ~ ( class_Orderings_Olinorder @ SV102 )
| ( c_lessequals @ SV749 @ SV1314 @ SV102 )
| ~ ( c_in @ SV1314 @ ( c_List_Oset @ SY4195 @ SV102 ) @ SV102 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV749 @ SY4195 @ SV102 ) @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3048]) ).
thf(3677,plain,
! [SV1315: $i,SV750: $i,SV103: $i] :
( ( ! [SY4196: $i,SY4197: $i] :
( ~ ( class_Orderings_Olinorder @ SV103 )
| ( c_lessequals @ SV750 @ SV1315 @ SV103 )
| ~ ( c_in @ SV1315 @ ( c_List_Oset @ SY4196 @ SV103 ) @ SV103 )
| ~ ( c_in @ SV750 @ ( c_List_Oset @ SY4197 @ SV103 ) @ SV103 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SY4197 @ SY4196 @ SV103 ) @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3049]) ).
thf(3678,plain,
! [SV1316: $i,SV751: $i,SV104: $i] :
( ( ( ( c_List_Olength__unique @ ( c_List_Olist_OCons @ SV104 @ SV751 @ SV1316 ) @ SV1316 )
= ( c_Suc @ ( c_List_Olength__unique @ SV751 @ SV1316 ) ) )
| ( c_in @ SV104 @ ( c_List_Oset @ SV751 @ SV1316 ) @ SV1316 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3050]) ).
thf(3679,plain,
! [SV105: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV105 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV105 ) @ ( c_HOL_Ozero__class_Ozero @ SV105 ) @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3051]) ).
thf(3680,plain,
! [SV1317: $i,SV752: $i,SV106: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV106 )
| ( c_HOL_Oord__class_Oless @ SV752 @ SV1317 @ SV106 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV752 @ SV1317 @ SV106 ) @ ( c_HOL_Ozero__class_Ozero @ SV106 ) @ SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3052]) ).
thf(3681,plain,
! [SV1318: $i,SV753: $i,SV107: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV107 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV753 @ SV1318 @ SV107 ) @ ( c_HOL_Ozero__class_Ozero @ SV107 ) @ SV107 )
| ~ ( c_HOL_Oord__class_Oless @ SV753 @ SV1318 @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3053]) ).
thf(3682,plain,
! [SV108: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV108 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV108 ) @ ( c_HOL_Oone__class_Oone @ SV108 ) @ SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3054]) ).
thf(3683,plain,
! [SV1319: $i,SV754: $i,SV109: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV109 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ SV754 ) @ SV1319 ) @ SV109 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV1319 @ SV109 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV754 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3055]) ).
thf(3684,plain,
! [SV110: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV110 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV110 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV110 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) )
= ( c_HOL_Ozero__class_Ozero @ SV110 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3056]) ).
thf(3685,plain,
! [SV755: $i,SV111: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV111 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV111 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV755 ) @ SV755 ) @ SV111 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV111 ) @ SV755 @ SV111 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3057]) ).
thf(3686,plain,
! [SV756: $i,SV112: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV112 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV112 ) @ SV756 @ SV112 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV112 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV756 ) @ SV756 ) @ SV112 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3058]) ).
thf(3687,plain,
! [SV1320: $i,SV757: $i,SV113: $i] :
( ( ! [SY4198: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV113 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV113 )
| ( c_lessequals @ SV757 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV1320 ) @ SY4198 ) @ SV113 )
| ~ ( c_lessequals @ SV757 @ SY4198 @ SV113 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV1320 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3059]) ).
thf(3688,plain,
! [SV1321: $i,SV758: $i,SV114: $i] :
( ( ! [SY4199: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV114 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV114 )
| ( c_lessequals @ SV758 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SV1321 ) @ SY4199 ) @ SV114 )
| ~ ( c_lessequals @ SV758 @ SV1321 @ SV114 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SY4199 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3060]) ).
thf(3689,plain,
! [SV759: $i,SV115: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV115 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV759 ) @ SV759 ) @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 )
| ~ ( c_lessequals @ SV759 @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3061]) ).
thf(3690,plain,
! [SV760: $i,SV116: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV116 ) )
= $true )
| ( ( ( c_lessequals @ SV760 @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV760 ) @ SV760 ) @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3062]) ).
thf(3691,plain,
! [SV1322: $i,SV761: $i,SV117: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV117 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV761 ) @ SV1322 ) @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
| ~ ( c_lessequals @ SV1322 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
| ~ ( c_lessequals @ SV761 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3063]) ).
thf(3692,plain,
! [SV1323: $i,SV762: $i,SV118: $i] :
( ( ! [SY4200: $i,SY4201: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV118 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV762 ) @ SV1323 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SY4200 ) @ SY4201 ) @ SV118 )
| ~ ( c_lessequals @ SV1323 @ SY4201 @ SV118 )
| ~ ( c_HOL_Oord__class_Oless @ SV762 @ SY4200 @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3064]) ).
thf(3693,plain,
! [SV1324: $i,SV763: $i,SV119: $i] :
( ( ! [SY4202: $i,SY4203: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV119 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV119 ) @ SV763 ) @ SV1324 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV119 ) @ SY4202 ) @ SY4203 ) @ SV119 )
| ~ ( c_HOL_Oord__class_Oless @ SV1324 @ SY4203 @ SV119 )
| ~ ( c_lessequals @ SV763 @ SY4202 @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3065]) ).
thf(3694,plain,
! [SV764: $i,SV120: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV120 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV764 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV120 ) @ SV764 ) @ ( c_HOL_Oone__class_Oone @ SV120 ) ) @ SV120 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3066]) ).
thf(3695,plain,
! [SV1325: $i,SV765: $i,SV121: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV121 )
| ~ ( class_Int_Onumber @ SV121 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ SV765 @ SV121 ) @ ( c_Int_Onumber__class_Onumber__of @ SV1325 @ SV121 ) @ SV121 )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ SV1325 @ SV121 ) @ ( c_Int_Onumber__class_Onumber__of @ SV765 @ SV121 ) @ SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3067]) ).
thf(3696,plain,
! [SV1326: $i,SV766: $i,SV122: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV122 )
| ~ ( class_Int_Onumber @ SV122 )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ SV766 @ SV122 ) @ ( c_Int_Onumber__class_Onumber__of @ SV1326 @ SV122 ) @ SV122 )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ SV1326 @ SV122 ) @ ( c_Int_Onumber__class_Onumber__of @ SV766 @ SV122 ) @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3068]) ).
thf(3697,plain,
! [SV1327: $i,SV767: $i,SV123: $i] :
( ( ! [SY4204: $i] :
( ( c_in @ SV123 @ ( c_List_Oset @ SV767 @ SV1327 ) @ SV1327 )
| ( SV123 = SY4204 )
| ~ ( c_in @ SV123 @ ( c_List_Oset @ ( c_List_Olist_OCons @ SY4204 @ SV767 @ SV1327 ) @ SV1327 ) @ SV1327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3069]) ).
thf(3698,plain,
! [SV768: $i,SV124: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV124 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV768 @ SV124 ) @ SV124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3070]) ).
thf(3699,plain,
! [SV769: $i,SV125: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV125 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV125 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV769 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3071]) ).
thf(3700,plain,
! [SV128: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV128 @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat )
= $false )
| ( ( SV128
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3072]) ).
thf(3701,plain,
! [SV1328: $i,SV770: $i,SV129: $i] :
( ( ( hBOOL @ ( hAPP @ SV129 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV770 @ SV1328 @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV129 @ ( c_HOL_Ominus__class_Ominus @ SV770 @ SV1328 @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3073]) ).
thf(3702,plain,
! [SV771: $i,SV130: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV130 @ SV771 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV771 @ SV130 @ tc_nat ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3074]) ).
thf(3703,plain,
! [SV772: $i,SV131: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV131 @ SV772 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV772 @ SV131 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3075]) ).
thf(3704,plain,
! [SV773: $i,SV132: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV132 @ SV773 @ tc_nat ) @ SV132 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV132 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV773 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3076]) ).
thf(3705,plain,
! [SV1329: $i,SV774: $i,SV133: $i] :
( ( ! [SY4205: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV133 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV774 @ SV1329 @ SV133 ) @ ( c_Power_Opower__class_Opower @ SY4205 @ SV1329 @ SV133 ) @ SV133 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV133 ) @ SV774 @ SV133 )
| ~ ( c_lessequals @ SV774 @ SY4205 @ SV133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3077]) ).
thf(3706,plain,
! [SV1330: $i,SV775: $i,SV134: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV134 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV134 ) @ ( c_Power_Opower__class_Opower @ SV775 @ SV1330 @ SV134 ) @ SV134 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV134 ) @ SV775 @ SV134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3078]) ).
thf(3707,plain,
! [SV776: $i,SV135: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV135 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV135 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_Suc @ SV776 ) @ SV135 )
= ( c_HOL_Ozero__class_Ozero @ SV135 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3079]) ).
thf(3708,plain,
! [SV1331: $i,SV777: $i,SV136: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV136 @ SV777 @ SV1331 ) @ ( tc_List_Olist @ SV1331 ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ SV777 @ ( tc_List_Olist @ SV1331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3080]) ).
thf(3709,plain,
! [SV1332: $i,SV778: $i,SV137: $i] :
( ( ( c_Suc @ ( c_Nat_Osize__class_Osize @ SV137 @ ( tc_List_Olist @ SV778 ) ) )
= ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV1332 @ SV137 @ SV778 ) @ ( tc_List_Olist @ SV778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3081]) ).
thf(3710,plain,
! [SV1333: $i,SV779: $i,SV138: $i] :
( ( ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV138 @ SV779 @ SV1333 ) @ ( tc_List_Olist @ SV1333 ) ) @ ( c_Nat_Osize__class_Osize @ SV779 @ ( tc_List_Olist @ SV1333 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3082]) ).
thf(3711,plain,
! [SV780: $i,SV139: $i] :
( ( ( ~ ( class_Power_Opower @ SV139 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV780 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV139 )
= ( c_HOL_Oone__class_Oone @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3083]) ).
thf(3712,plain,
! [SV781: $i,SV140: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV140 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV781 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV140 )
= ( c_HOL_Oone__class_Oone @ SV140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3084]) ).
thf(3713,plain,
! [SV1334: $i,SV782: $i,SV141: $i] :
( ( ( ( c_List_Ohd @ ( c_List_Oappend @ SV141 @ SV782 @ SV1334 ) @ SV1334 )
= ( c_List_Ohd @ SV141 @ SV1334 ) )
| ( SV141
= ( c_List_Olist_ONil @ SV1334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3085]) ).
thf(3714,plain,
! [SV1335: $i,SV784: $i,SV143: $i] :
( ( ! [SY4206: $i] :
( ( c_in @ SV143 @ ( c_List_Oset @ SV784 @ SV1335 ) @ SV1335 )
| ~ ( c_in @ SV143 @ ( c_List_Oset @ ( c_List_Otake @ SY4206 @ SV784 @ SV1335 ) @ SV1335 ) @ SV1335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3087]) ).
thf(3715,plain,
! [SV1336: $i,SV785: $i,SV144: $i] :
( ( ! [SY4207: $i] :
( ( c_in @ SV144 @ ( c_List_Oset @ SV785 @ SV1336 ) @ SV1336 )
| ~ ( c_in @ SV144 @ ( c_List_Oset @ ( c_List_Odrop @ SY4207 @ SV785 @ SV1336 ) @ SV1336 ) @ SV1336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3088]) ).
thf(3716,plain,
! [SV1337: $i,SV786: $i,SV145: $i] :
( ( ! [SY4208: $i] :
( ( c_List_Onth @ ( c_List_Olist_OCons @ SV145 @ SV786 @ SV1337 ) @ ( c_Suc @ SY4208 ) @ SV1337 )
= ( c_List_Onth @ SV786 @ SY4208 @ SV1337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3089]) ).
thf(3717,plain,
! [SV1338: $i,SV787: $i,SV146: $i] :
( ( ! [SY4209: $i] :
( ( c_List_Otake @ ( c_Suc @ SV146 ) @ ( c_List_Olist_OCons @ SV787 @ SV1338 @ SY4209 ) @ SY4209 )
= ( c_List_Olist_OCons @ SV787 @ ( c_List_Otake @ SV146 @ SV1338 @ SY4209 ) @ SY4209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3090]) ).
thf(3718,plain,
! [SV1339: $i,SV788: $i,SV147: $i] :
( ( ! [SY4210: $i] :
( ( hBOOL @ ( hAPP @ SV147 @ SV788 ) )
| ~ ( c_in @ SV788 @ ( c_List_Oset @ ( c_List_OtakeWhile @ SV147 @ SV1339 @ SY4210 ) @ SY4210 ) @ SY4210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3091]) ).
thf(3719,plain,
! [SV1340: $i,SV789: $i,SV148: $i] :
( ( ! [SY4211: $i] :
( ( c_in @ SV148 @ ( c_List_Oset @ SV789 @ SV1340 ) @ SV1340 )
| ~ ( c_in @ SV148 @ ( c_List_Oset @ ( c_List_OtakeWhile @ SY4211 @ SV789 @ SV1340 ) @ SV1340 ) @ SV1340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3092]) ).
thf(3720,plain,
! [SV1341: $i,SV790: $i,SV149: $i] :
( ( ! [SY4212: $i] :
( ( hBOOL @ ( hAPP @ SV149 @ SV790 ) )
| ~ ( c_in @ SV790 @ ( c_List_Oset @ SV1341 @ SY4212 ) @ SY4212 )
| ~ ( c_List_Olistsp @ SV149 @ SV1341 @ SY4212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3093]) ).
thf(3721,plain,
! [SV1342: $i,SV791: $i,SV150: $i] :
( ( ! [SY4213: $i] :
( ( SV150 = SV791 )
| ~ ( c_in @ SV150 @ ( c_List_Oset @ ( c_List_Oreplicate @ SV1342 @ SV791 @ SY4213 ) @ SY4213 ) @ SY4213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3094]) ).
thf(3722,plain,
! [SV1343: $i,SV792: $i,SV151: $i] :
( ( ( ( c_List_Onth @ ( c_List_Orev @ SV151 @ SV792 ) @ SV1343 @ SV792 )
= ( c_List_Onth @ SV151 @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SV151 @ ( tc_List_Olist @ SV792 ) ) @ ( c_Suc @ SV1343 ) @ tc_nat ) @ SV792 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1343 @ ( c_Nat_Osize__class_Osize @ SV151 @ ( tc_List_Olist @ SV792 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3095]) ).
thf(3723,plain,
! [SV1344: $i,SV793: $i,SV152: $i] :
( ( ! [SY4214: $i] :
( ~ ( class_Orderings_Olinorder @ SV152 )
| ( c_lessequals @ ( c_List_Onth @ SV793 @ SV1344 @ SV152 ) @ ( c_List_Onth @ SV793 @ SY4214 @ SV152 ) @ SV152 )
| ~ ( c_lessequals @ SV1344 @ SY4214 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY4214 @ ( c_Nat_Osize__class_Osize @ SV793 @ ( tc_List_Olist @ SV152 ) ) @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ SV793 @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3096]) ).
thf(3724,plain,
! [SV1345: $i,SV794: $i,SV153: $i] :
( ( ! [SY4215: $i] :
( ~ ( class_Orderings_Olinorder @ SV153 )
| ( c_lessequals @ ( c_List_Onth @ SV794 @ SV1345 @ SV153 ) @ ( c_List_Onth @ SV794 @ SY4215 @ SV153 ) @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SY4215 @ ( c_Nat_Osize__class_Osize @ SV794 @ ( tc_List_Olist @ SV153 ) ) @ tc_nat )
| ~ ( c_lessequals @ SV1345 @ SY4215 @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ SV794 @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3097]) ).
thf(3725,plain,
! [SV1346: $i,SV795: $i,SV154: $i] :
( ( ! [SY4216: $i] :
( ( c_List_Odrop @ ( c_Suc @ SV154 ) @ ( c_List_Olist_OCons @ SV795 @ SV1346 @ SY4216 ) @ SY4216 )
= ( c_List_Odrop @ SV154 @ SV1346 @ SY4216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3098]) ).
thf(3726,plain,
! [SV1347: $i,SV796: $i,SV155: $i] :
( ( ( ( c_List_Otake @ SV155 @ SV796 @ SV1347 )
= SV796 )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV796 @ ( tc_List_Olist @ SV1347 ) ) @ SV155 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3099]) ).
thf(3727,plain,
! [SV1348: $i,SV797: $i,SV156: $i] :
( ( ! [SY4217: $i] :
( ~ ( class_Orderings_Olinorder @ SV156 )
| ( c_lessequals @ SV797 @ SV1348 @ SV156 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV797 @ ( c_List_Olist_OCons @ SV1348 @ SY4217 @ SV156 ) @ SV156 ) @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3100]) ).
thf(3728,plain,
! [SV1349: $i,SV798: $i,SV157: $i] :
( ( ! [SY4218: $i] :
( ~ ( class_Orderings_Olinorder @ SV157 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV798 @ ( c_List_Olist_OCons @ SV1349 @ SY4218 @ SV157 ) @ SV157 ) @ SV157 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1349 @ SY4218 @ SV157 ) @ SV157 )
| ~ ( c_lessequals @ SV798 @ SV1349 @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3101]) ).
thf(3729,plain,
! [SV1350: $i,SV799: $i,SV158: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Odrop @ SV158 @ SV799 @ SV1350 ) @ ( tc_List_Olist @ SV1350 ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SV799 @ ( tc_List_Olist @ SV1350 ) ) @ SV158 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3102]) ).
thf(3730,plain,
! [SV1351: $i,SV800: $i,SV159: $i] :
( ( ! [SY4219: $i,SY4220: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV159 @ SV800 @ SV1351 ) @ ( c_Suc @ SY4219 ) @ SY4220 @ SV1351 )
= ( c_List_Olist_OCons @ SV159 @ ( c_List_Olist__update @ SV800 @ SY4219 @ SY4220 @ SV1351 ) @ SV1351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3103]) ).
thf(3731,plain,
! [SV1352: $i,SV801: $i,SV160: $i] :
( ( ( ( c_List_Ohd @ ( c_List_Oreplicate @ SV160 @ SV801 @ SV1352 ) @ SV1352 )
= SV801 )
| ( SV160
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3104]) ).
thf(3732,plain,
! [SV1353: $i,SV802: $i,SV161: $i] :
( ( ( c_List_Oreplicate @ ( c_Suc @ SV161 ) @ SV802 @ SV1353 )
= ( c_List_Olist_OCons @ SV802 @ ( c_List_Oreplicate @ SV161 @ SV802 @ SV1353 ) @ SV1353 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3105]) ).
thf(3733,plain,
! [SV1354: $i,SV803: $i,SV162: $i] :
( ( ! [SY4221: $i] :
( ( ( c_List_Olist__update @ SV162 @ SV803 @ SV1354 @ SY4221 )
= SV162 )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV162 @ ( tc_List_Olist @ SY4221 ) ) @ SV803 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3106]) ).
thf(3734,plain,
! [SV1355: $i,SV804: $i,SV163: $i] :
( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ SV163 @ SV804 @ SV1355 ) @ ( tc_List_Olist @ SV1355 ) ) @ ( c_Nat_Osize__class_Osize @ SV804 @ ( tc_List_Olist @ SV1355 ) ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3107]) ).
thf(3735,plain,
! [SV1356: $i,SV805: $i,SV164: $i] :
( ( ( c_in @ SV164 @ ( c_List_Oset @ SV805 @ SV1356 ) @ SV1356 )
| ~ ( c_in @ SV164 @ ( c_List_Oset @ ( c_List_Obutlast @ SV805 @ SV1356 ) @ SV1356 ) @ SV1356 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3108]) ).
thf(3736,plain,
! [SV1357: $i,SV806: $i,SV165: $i] :
( ( ! [SY4222: $i] :
( ( c_List_Odrop @ SV165 @ ( c_List_Otake @ SV806 @ SV1357 @ SY4222 ) @ SY4222 )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ SV806 @ SV165 @ tc_nat ) @ ( c_List_Odrop @ SV165 @ SV1357 @ SY4222 ) @ SY4222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3109]) ).
thf(3737,plain,
! [SV1358: $i,SV807: $i,SV166: $i] :
( ( ! [SY4223: $i] :
( ( c_in @ SV166 @ ( c_List_Oset @ SV807 @ SV1358 ) @ SV1358 )
| ~ ( c_in @ SV166 @ ( c_List_Oset @ ( c_List_Osublist @ SV807 @ SY4223 @ SV1358 ) @ SV1358 ) @ SV1358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3110]) ).
thf(3738,plain,
! [SV1359: $i,SV808: $i,SV167: $i] :
( ( ! [SY4224: $i] :
( ~ ( c_in @ SV167 @ ( c_List_Oset @ ( c_List_Osublist @ SV808 @ SV1359 @ SY4224 ) @ SY4224 ) @ SY4224 )
| ( c_in @ SV167 @ ( c_List_Oset @ SV808 @ SY4224 ) @ SY4224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3111]) ).
thf(3739,plain,
! [SV1360: $i,SV809: $i,SV168: $i] :
( ( ! [SY4225: $i] :
( ( c_List_Odrop @ SV168 @ ( c_List_Oreplicate @ SV809 @ SV1360 @ SY4225 ) @ SY4225 )
= ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ SV809 @ SV168 @ tc_nat ) @ SV1360 @ SY4225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3112]) ).
thf(3740,plain,
! [SV1361: $i,SV810: $i,SV169: $i] :
( ( ! [SY4226: $i,SY4227: $i,SY4228: $i] :
( ~ ( class_Orderings_Olinorder @ SV169 )
| ( ( c_List_Olinorder__class_Oinsort__key @ SV810 @ SV1361 @ ( c_List_Olist_OCons @ SY4226 @ SY4227 @ SY4228 ) @ SY4228 @ SV169 )
= ( c_List_Olist_OCons @ SV1361 @ ( c_List_Olist_OCons @ SY4226 @ SY4227 @ SY4228 ) @ SY4228 ) )
| ~ ( c_lessequals @ ( hAPP @ SV810 @ SV1361 ) @ ( hAPP @ SV810 @ SY4226 ) @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3113]) ).
thf(3741,plain,
! [SV1362: $i,SV811: $i,SV170: $i] :
( ( ! [SY4229: $i,SY4230: $i,SY4231: $i] :
( ~ ( class_Orderings_Olinorder @ SV170 )
| ( ( c_List_Olinorder__class_Oinsort__key @ SV811 @ SV1362 @ ( c_List_Olist_OCons @ SY4229 @ SY4230 @ SY4231 ) @ SY4231 @ SV170 )
= ( c_List_Olist_OCons @ SY4229 @ ( c_List_Olinorder__class_Oinsort__key @ SV811 @ SV1362 @ SY4230 @ SY4231 @ SV170 ) @ SY4231 ) )
| ( c_lessequals @ ( hAPP @ SV811 @ SV1362 ) @ ( hAPP @ SV811 @ SY4229 ) @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3114]) ).
thf(3742,plain,
! [SV1363: $i,SV812: $i,SV171: $i] :
( ( ! [SY4232: $i,SY4233: $i] :
( ~ ( class_Orderings_Olinorder @ SV171 )
| ( ( c_Nat_Osize__class_Osize @ ( c_List_Olinorder__class_Oinsort__key @ SV812 @ SV1363 @ SY4232 @ SY4233 @ SV171 ) @ ( tc_List_Olist @ SY4233 ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ SY4232 @ ( tc_List_Olist @ SY4233 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3115]) ).
thf(3743,plain,
! [SV1364: $i,SV813: $i,SV172: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV172 @ SV813 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1364 @ SV813 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV172 @ SV1364 @ tc_nat )
| ~ ( c_lessequals @ SV813 @ SV1364 @ tc_nat )
| ~ ( c_lessequals @ SV813 @ SV172 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3116]) ).
thf(3744,plain,
! [SV1365: $i,SV814: $i,SV173: $i] :
( ( ( c_lessequals @ SV173 @ SV814 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV173 @ SV1365 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV814 @ SV1365 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1365 @ SV814 @ tc_nat )
| ~ ( c_lessequals @ SV1365 @ SV173 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3117]) ).
thf(3745,plain,
! [SV815: $i,SV174: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV174 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ SV815 ) @ SV174 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV174 ) @ ( c_HOL_Oone__class_Oone @ SV174 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV815 @ SV174 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3118]) ).
thf(3746,plain,
! [SV1366: $i,SV817: $i,SV176: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV176 @ SV817 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1366 @ SV817 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV176 @ SV1366 @ tc_nat ) )
| ~ ( c_lessequals @ SV817 @ SV1366 @ tc_nat )
| ~ ( c_lessequals @ SV817 @ SV176 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3120]) ).
thf(3747,plain,
! [SV1367: $i,SV818: $i,SV177: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV177 @ SV818 @ tc_nat ) @ SV1367 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV177 @ SV1367 @ tc_nat ) @ SV818 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3121]) ).
thf(3748,plain,
! [SV1368: $i,SV819: $i,SV178: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV178 @ SV819 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1368 @ SV819 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV819 @ SV178 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV178 @ SV1368 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3122]) ).
thf(3749,plain,
! [SV820: $i,SV179: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV179 ) @ SV820 @ tc_nat )
= $true )
| ( ( ( ( c_Suc @ SV179 )
= SV820 )
| ~ ( c_HOL_Oord__class_Oless @ SV179 @ SV820 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3123]) ).
thf(3750,plain,
! [SV821: $i,SV180: $i] :
( ( ( ~ ( c_lessequals @ SV180 @ SV821 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV821 ) @ SV180 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3124]) ).
thf(3751,plain,
! [SV822: $i,SV181: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV181 ) @ SV822 @ tc_nat )
= $true )
| ( ( c_lessequals @ SV822 @ SV181 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3125]) ).
thf(3752,plain,
! [SV1369: $i,SV823: $i,SV182: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV182 ) @ SV823 @ tc_nat ) @ ( c_Suc @ SV1369 ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV182 @ SV823 @ tc_nat ) @ SV1369 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3126]) ).
thf(3753,plain,
! [SV824: $i,SV184: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV184 @ ( c_HOL_Ominus__class_Ominus @ SV184 @ SV824 @ tc_nat ) @ tc_nat )
= SV824 )
= $true )
| ( ( ~ ( c_lessequals @ SV824 @ SV184 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3127]) ).
thf(3754,plain,
! [SV825: $i,SV185: $i] :
( ( ( SV185
= ( c_Suc @ SV825 ) )
= $true )
| ( ( ( c_lessequals @ SV185 @ SV825 @ tc_nat )
| ~ ( c_lessequals @ SV185 @ ( c_Suc @ SV825 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3128]) ).
thf(3755,plain,
! [SV826: $i,SV187: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV187 @ SV826 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV826 @ ( c_Suc @ SV187 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3130]) ).
thf(3756,plain,
! [SV827: $i,SV188: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV188 @ ( c_Suc @ SV827 ) @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV827 @ SV188 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3131]) ).
thf(3757,plain,
! [SV828: $i,SV189: $i] :
( ( ( c_in @ ( c_List_Ohd @ SV189 @ SV828 ) @ ( c_List_Oset @ SV189 @ SV828 ) @ SV828 )
= $true )
| ( ( SV189
= ( c_List_Olist_ONil @ SV828 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3132]) ).
thf(3758,plain,
! [SV1370: $i,SV829: $i,SV190: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV190 )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV190 ) @ SV829 ) @ SV1370 ) @ SV1370 @ SV190 )
= SV829 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3133]) ).
thf(3759,plain,
! [SV1371: $i,SV830: $i,SV191: $i] :
( ( ! [SY4234: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV191 )
| ( c_lessequals @ SV830 @ SV1371 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY4234 @ SV830 @ SV191 ) @ ( c_Power_Opower__class_Opower @ SY4234 @ SV1371 @ SV191 ) @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV191 ) @ SY4234 @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3134]) ).
thf(3760,plain,
! [SV1372: $i,SV831: $i,SV192: $i] :
( ( ! [SY4235: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV192 )
| ( c_lessequals @ SV831 @ SV1372 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY4235 @ SV831 @ SV192 ) @ ( c_Power_Opower__class_Opower @ SY4235 @ SV1372 @ SV192 ) @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV192 ) @ SY4235 @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3135]) ).
thf(3761,plain,
! [SV1373: $i,SV832: $i,SV193: $i] :
( ( ! [SY4236: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV193 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV832 @ SV1373 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SV832 @ SY4236 @ SV193 ) @ SV193 )
| ~ ( c_lessequals @ SV1373 @ SY4236 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV193 ) @ SV832 @ SV193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3136]) ).
thf(3762,plain,
! [SV833: $i,SV194: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV194 ) @ ( c_Suc @ SV833 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV194 @ SV833 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3137]) ).
thf(3763,plain,
! [SV834: $i,SV195: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV195 @ SV834 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV195 ) @ ( c_Suc @ SV834 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3138]) ).
thf(3764,plain,
! [SV835: $i,SV196: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV196 ) @ ( c_Suc @ SV835 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV196 @ SV835 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3139]) ).
thf(3765,plain,
! [SV836: $i,SV197: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV197 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV197 )
| ( ( c_HOL_Ominus__class_Ominus @ SV836 @ SV836 @ SV197 )
= ( c_HOL_Ozero__class_Ozero @ SV197 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3140]) ).
thf(3766,plain,
! [SV837: $i,SV198: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV198 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV837 @ SV837 @ SV198 )
= ( c_HOL_Ozero__class_Ozero @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3141]) ).
thf(3767,plain,
! [SV838: $i,SV199: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV199 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV838 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
= SV838 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3142]) ).
thf(3768,plain,
! [SV839: $i,SV200: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV200 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV839 @ SV839 @ SV200 )
= ( c_HOL_Ozero__class_Ozero @ SV200 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3143]) ).
thf(3769,plain,
! [SV840: $i,SV201: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV201 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV840 @ SV840 @ SV201 )
= ( c_HOL_Ozero__class_Ozero @ SV201 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3144]) ).
thf(3770,plain,
! [SV202: $i] :
( ( ( c_lessequals @ SV202 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false )
| ( ( SV202
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3145]) ).
thf(3771,plain,
! [SV1374: $i,SV841: $i,SV207: $i] :
( ( ( c_List_Ohd @ ( c_List_Olist_OCons @ SV207 @ SV841 @ SV1374 ) @ SV1374 )
= SV207 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3146]) ).
thf(3772,plain,
! [SV1375: $i,SV842: $i,SV208: $i] :
( ( ! [SY4237: $i,SY4238: $i] :
( ( c_ListOrder_Ostep1 @ SV208 @ ( c_List_Olist_OCons @ SV842 @ SV1375 @ SY4237 ) @ ( c_List_Olist_OCons @ SV842 @ SY4238 @ SY4237 ) @ SY4237 )
| ~ ( c_ListOrder_Ostep1 @ SV208 @ SV1375 @ SY4238 @ SY4237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3147]) ).
thf(3773,plain,
! [SV1376: $i,SV843: $i,SV209: $i] :
( ( ! [SY4239: $i,SY4240: $i,SY4241: $i] :
( ( c_ListOrder_Ostep1 @ SV209 @ SV843 @ SV1376 @ SY4239 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV209 @ SY4240 ) @ SY4241 ) )
| ~ ( c_ListOrder_Ostep1 @ SV209 @ ( c_List_Olist_OCons @ SY4240 @ SV843 @ SY4239 ) @ ( c_List_Olist_OCons @ SY4241 @ SV1376 @ SY4239 ) @ SY4239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3148]) ).
thf(3774,plain,
! [SV1377: $i,SV844: $i,SV210: $i] :
( ( ! [SY4242: $i,SY4243: $i,SY4244: $i] :
( ( c_ListOrder_Ostep1 @ SV210 @ SV844 @ SV1377 @ SY4242 )
| ( SV1377 = SV844 )
| ~ ( c_ListOrder_Ostep1 @ SV210 @ ( c_List_Olist_OCons @ SY4243 @ SV844 @ SY4242 ) @ ( c_List_Olist_OCons @ SY4244 @ SV1377 @ SY4242 ) @ SY4242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3149]) ).
thf(3775,plain,
! [SV1378: $i,SV845: $i,SV211: $i] :
( ( ! [SY4245: $i,SY4246: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV211 @ SV845 ) @ SV1378 ) )
| ( c_ListOrder_Ostep1 @ SV211 @ ( c_List_Olist_OCons @ SV845 @ SY4245 @ SY4246 ) @ ( c_List_Olist_OCons @ SV1378 @ SY4245 @ SY4246 ) @ SY4246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3150]) ).
thf(3776,plain,
! [SV1379: $i,SV846: $i,SV212: $i] :
( ( ! [SY4247: $i,SY4248: $i,SY4249: $i] :
( ( SV212 = SV846 )
| ( SV1379 = SY4247 )
| ~ ( c_ListOrder_Ostep1 @ SY4248 @ ( c_List_Olist_OCons @ SV846 @ SY4247 @ SY4249 ) @ ( c_List_Olist_OCons @ SV212 @ SV1379 @ SY4249 ) @ SY4249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3151]) ).
thf(3777,plain,
! [SV1380: $i,SV847: $i,SV213: $i] :
( ( ! [SY4250: $i,SY4251: $i,SY4252: $i] :
( ( SV213 = SV847 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV1380 @ SV847 ) @ SV213 ) )
| ~ ( c_ListOrder_Ostep1 @ SV1380 @ ( c_List_Olist_OCons @ SV847 @ SY4250 @ SY4251 ) @ ( c_List_Olist_OCons @ SV213 @ SY4252 @ SY4251 ) @ SY4251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3152]) ).
thf(3778,plain,
! [SV1381: $i,SV848: $i,SV214: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV214 @ SV848 @ ( c_List_Olist_ONil @ SV1381 ) @ SV1381 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3153]) ).
thf(3779,plain,
! [SV1382: $i,SV849: $i,SV215: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV215 @ ( c_List_Olist_ONil @ SV849 ) @ SV1382 @ SV849 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3154]) ).
thf(3780,plain,
! [SV1383: $i,SV850: $i,SV216: $i] :
( ( ! [SY4253: $i] :
( ~ ( class_Orderings_Olinorder @ SV216 )
| ( c_lessequals @ ( c_List_Onth @ SV850 @ SV1383 @ SV216 ) @ ( c_List_Onth @ SV850 @ SY4253 @ SV216 ) @ SV216 )
| ~ ( c_HOL_Oord__class_Oless @ SV1383 @ ( c_Nat_Osize__class_Osize @ SV850 @ ( tc_List_Olist @ SV216 ) ) @ tc_nat )
| ~ ( c_lessequals @ SY4253 @ SV1383 @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Orev @ SV850 @ SV216 ) @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3155]) ).
thf(3781,plain,
! [SV1384: $i,SV851: $i,SV217: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV217 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV217 ) @ SV851 ) @ SV1384 ) @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 )
| ~ ( c_lessequals @ SV1384 @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 )
| ~ ( c_HOL_Oord__class_Oless @ SV851 @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3156]) ).
thf(3782,plain,
! [SV1385: $i,SV852: $i,SV218: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV218 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV218 ) @ SV852 ) @ SV1385 ) @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
| ~ ( c_HOL_Oord__class_Oless @ SV1385 @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
| ~ ( c_lessequals @ SV852 @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3157]) ).
thf(3783,plain,
! [SV1386: $i,SV853: $i,SV219: $i] :
( ( ! [SY4254: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV219 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV219 )
| ( c_HOL_Oord__class_Oless @ SV853 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV219 ) @ SV1386 ) @ SY4254 ) @ SV219 )
| ~ ( c_lessequals @ SV853 @ SY4254 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV1386 @ SV219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3158]) ).
thf(3784,plain,
! [SV1387: $i,SV854: $i,SV220: $i] :
( ( ! [SY4255: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV220 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV220 )
| ( c_HOL_Oord__class_Oless @ SV854 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV220 ) @ SV1387 ) @ SY4255 ) @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ SV854 @ SY4255 @ SV220 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV1387 @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3159]) ).
thf(3785,plain,
! [SV1388: $i,SV855: $i,SV221: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV221 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SV855 ) @ SV1388 ) @ SV221 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ SV1388 @ SV221 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ SV855 @ SV221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3160]) ).
thf(3786,plain,
! [SV1389: $i,SV856: $i,SV222: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV222 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SV856 ) @ SV1389 ) @ SV222 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ SV1389 @ SV222 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ SV856 @ SV222 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3161]) ).
thf(3787,plain,
! [SV223: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV223 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV223 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV223 ) @ ( c_HOL_Oone__class_Oone @ SV223 ) ) @ ( c_HOL_Oone__class_Oone @ SV223 ) ) @ SV223 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3162]) ).
thf(3788,plain,
! [SV1390: $i,SV857: $i,SV224: $i] :
( ( ! [SY4256: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV224 )
| ( c_HOL_Oord__class_Oless @ SV857 @ SV1390 @ SV224 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV224 ) @ SV1390 @ SV224 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV857 @ SY4256 @ SV224 ) @ ( c_Power_Opower__class_Opower @ SV1390 @ SY4256 @ SV224 ) @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3163]) ).
thf(3789,plain,
! [SV1391: $i,SV858: $i,SV225: $i] :
( ( ! [SY4257: $i] :
( ( c_in @ SV225 @ ( c_List_Oset @ ( c_List_Oappend @ SV858 @ ( c_List_Olist_OCons @ SV225 @ SV1391 @ SY4257 ) @ SY4257 ) @ SY4257 ) @ SY4257 )
| ( c_in @ SV225 @ ( c_List_Oset @ SV858 @ SY4257 ) @ SY4257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3164]) ).
thf(3790,plain,
! [SV1392: $i,SV859: $i,SV226: $i] :
( ( ! [SY4258: $i] :
( ( c_in @ SV226 @ ( c_List_Oset @ ( c_List_Oappend @ SV859 @ ( c_List_Olist_OCons @ SV226 @ SV1392 @ SY4258 ) @ SY4258 ) @ SY4258 ) @ SY4258 )
| ( c_in @ SV226 @ ( c_List_Oset @ SV1392 @ SY4258 ) @ SY4258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3165]) ).
thf(3791,plain,
! [SV1393: $i,SV860: $i,SV227: $i] :
( ( ! [SY4259: $i] : ( c_in @ SV227 @ ( c_List_Oset @ ( c_List_Oappend @ SV860 @ ( c_List_Olist_OCons @ SV227 @ SV1393 @ SY4259 ) @ SY4259 ) @ SY4259 ) @ SY4259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3166]) ).
thf(3792,plain,
! [SV228: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV228 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV228 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV228 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV228 )
= ( c_HOL_Oone__class_Oone @ SV228 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3167]) ).
thf(3793,plain,
! [SV1394: $i,SV861: $i,SV229: $i] :
( ( ! [SY4260: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV229 )
| ( c_HOL_Oord__class_Oless @ SV861 @ SV1394 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY4260 @ SV861 @ SV229 ) @ ( c_Power_Opower__class_Opower @ SY4260 @ SV1394 @ SV229 ) @ SV229 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV229 ) @ SY4260 @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3168]) ).
thf(3794,plain,
! [SV1395: $i,SV862: $i,SV230: $i] :
( ( ! [SY4261: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV230 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV862 @ SV1395 @ SV230 ) @ ( c_Power_Opower__class_Opower @ SV862 @ SY4261 @ SV230 ) @ SV230 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV230 ) @ SV862 @ SV230 )
| ~ ( c_HOL_Oord__class_Oless @ SV1395 @ SY4261 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3169]) ).
thf(3795,plain,
! [SV1396: $i,SV863: $i,SV231: $i] :
( ( ! [SY4262: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV231 )
| ( c_HOL_Oord__class_Oless @ SV863 @ SV1396 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY4262 @ SV863 @ SV231 ) @ ( c_Power_Opower__class_Opower @ SY4262 @ SV1396 @ SV231 ) @ SV231 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV231 ) @ SY4262 @ SV231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3170]) ).
thf(3796,plain,
! [SV1397: $i,SV864: $i,SV232: $i] :
( ( ! [SY4263: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV232 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV864 @ SV1397 @ SV232 ) @ ( c_Power_Opower__class_Opower @ SV864 @ SY4263 @ SV232 ) @ SV232 )
| ~ ( c_HOL_Oord__class_Oless @ SV1397 @ SY4263 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV232 ) @ SV864 @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3171]) ).
thf(3797,plain,
! [SV1398: $i,SV865: $i,SV233: $i] :
( ( ! [SY4264: $i,SY4265: $i,SY4266: $i] :
( ( SV233 = SV865 )
| ( SV1398 = SY4264 )
| ~ ( c_ListOrder_Ostep1 @ SY4265 @ ( c_List_Oappend @ SV233 @ ( c_List_Olist_OCons @ SV1398 @ ( c_List_Olist_ONil @ SY4266 ) @ SY4266 ) @ SY4266 ) @ ( c_List_Oappend @ SV865 @ ( c_List_Olist_OCons @ SY4264 @ ( c_List_Olist_ONil @ SY4266 ) @ SY4266 ) @ SY4266 ) @ SY4266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3172]) ).
thf(3798,plain,
! [SV1399: $i,SV866: $i,SV234: $i] :
( ( ! [SY4267: $i,SY4268: $i,SY4269: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV234 @ SV866 ) @ SV1399 ) )
| ( SV866 = SV1399 )
| ~ ( c_ListOrder_Ostep1 @ SV234 @ ( c_List_Oappend @ SY4267 @ ( c_List_Olist_OCons @ SV866 @ ( c_List_Olist_ONil @ SY4268 ) @ SY4268 ) @ SY4268 ) @ ( c_List_Oappend @ SY4269 @ ( c_List_Olist_OCons @ SV1399 @ ( c_List_Olist_ONil @ SY4268 ) @ SY4268 ) @ SY4268 ) @ SY4268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3173]) ).
thf(3799,plain,
! [SV1400: $i,SV867: $i,SV235: $i] :
( ( ! [SY4270: $i,SY4271: $i,SY4272: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV867 ) @ SV1400 ) )
| ( c_ListOrder_Ostep1 @ SV235 @ SY4270 @ SY4271 @ SY4272 )
| ~ ( c_ListOrder_Ostep1 @ SV235 @ ( c_List_Oappend @ SY4270 @ ( c_List_Olist_OCons @ SV867 @ ( c_List_Olist_ONil @ SY4272 ) @ SY4272 ) @ SY4272 ) @ ( c_List_Oappend @ SY4271 @ ( c_List_Olist_OCons @ SV1400 @ ( c_List_Olist_ONil @ SY4272 ) @ SY4272 ) @ SY4272 ) @ SY4272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3174]) ).
thf(3800,plain,
! [SV1401: $i,SV868: $i,SV236: $i] :
( ( ! [SY4273: $i,SY4274: $i,SY4275: $i] :
( ( SV236 = SV868 )
| ( c_ListOrder_Ostep1 @ SV1401 @ SV236 @ SV868 @ SY4273 )
| ~ ( c_ListOrder_Ostep1 @ SV1401 @ ( c_List_Oappend @ SV236 @ ( c_List_Olist_OCons @ SY4274 @ ( c_List_Olist_ONil @ SY4273 ) @ SY4273 ) @ SY4273 ) @ ( c_List_Oappend @ SV868 @ ( c_List_Olist_OCons @ SY4275 @ ( c_List_Olist_ONil @ SY4273 ) @ SY4273 ) @ SY4273 ) @ SY4273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3175]) ).
thf(3801,plain,
! [SV869: $i,SV237: $i] :
( ( ( ( c_List_Ohd @ SV237 @ SV869 )
= ( c_List_Onth @ SV237 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV869 ) )
= $true )
| ( ( SV237
= ( c_List_Olist_ONil @ SV869 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3176]) ).
thf(3802,plain,
! [SV1402: $i,SV870: $i,SV238: $i] :
( ( ! [SY4276: $i,SY4277: $i] :
( ( ( c_List_OtakeWhile @ SV238 @ ( c_List_Oappend @ SV870 @ SV1402 @ SY4276 ) @ SY4276 )
= ( c_List_OtakeWhile @ SV238 @ SV870 @ SY4276 ) )
| ( hBOOL @ ( hAPP @ SV238 @ SY4277 ) )
| ~ ( c_in @ SY4277 @ ( c_List_Oset @ SV870 @ SY4276 ) @ SY4276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3177]) ).
thf(3803,plain,
! [SV1403: $i,SV871: $i,SV239: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV239 @ SV871 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV239 @ SV1403 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV871 @ SV1403 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3178]) ).
thf(3804,plain,
! [SV1404: $i,SV872: $i,SV240: $i] :
( ( ( ( c_List_Odrop @ SV240 @ SV872 @ SV1404 )
= ( c_List_Olist_ONil @ SV1404 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV872 @ ( tc_List_Olist @ SV1404 ) ) @ SV240 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3179]) ).
thf(3805,plain,
! [SV1405: $i,SV873: $i,SV241: $i] :
( ( ! [SY4278: $i] :
( ( c_List_Otake @ SV241 @ ( c_List_Oappend @ SV873 @ SV1405 @ SY4278 ) @ SY4278 )
= ( c_List_Oappend @ ( c_List_Otake @ SV241 @ SV873 @ SY4278 ) @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ SV241 @ ( c_Nat_Osize__class_Osize @ SV873 @ ( tc_List_Olist @ SY4278 ) ) @ tc_nat ) @ SV1405 @ SY4278 ) @ SY4278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3180]) ).
thf(3806,plain,
! [SV1406: $i,SV874: $i,SV242: $i] :
( ( ! [SY4279: $i] :
( ( c_List_Odrop @ SV242 @ ( c_List_Oappend @ SV874 @ SV1406 @ SY4279 ) @ SY4279 )
= ( c_List_Oappend @ ( c_List_Odrop @ SV242 @ SV874 @ SY4279 ) @ ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ SV242 @ ( c_Nat_Osize__class_Osize @ SV874 @ ( tc_List_Olist @ SY4279 ) ) @ tc_nat ) @ SV1406 @ SY4279 ) @ SY4279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3181]) ).
thf(3807,plain,
! [SV1407: $i,SV875: $i,SV243: $i] :
( ( ! [SY4280: $i] :
( ( c_in @ SV243 @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ SV875 @ SV1407 @ SY4280 ) @ SY4280 ) @ SY4280 ) @ SY4280 )
| ~ ( c_in @ SV243 @ ( c_List_Oset @ ( c_List_Obutlast @ SV1407 @ SY4280 ) @ SY4280 ) @ SY4280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3182]) ).
thf(3808,plain,
! [SV1408: $i,SV876: $i,SV244: $i] :
( ( ! [SY4281: $i] :
( ( c_in @ SV244 @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ SV876 @ SV1408 @ SY4281 ) @ SY4281 ) @ SY4281 ) @ SY4281 )
| ~ ( c_in @ SV244 @ ( c_List_Oset @ ( c_List_Obutlast @ SV876 @ SY4281 ) @ SY4281 ) @ SY4281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3183]) ).
thf(3809,plain,
! [SV877: $i,SV245: $i] :
( ( ( c_in @ ( c_List_Olast @ SV245 @ SV877 ) @ ( c_List_Oset @ SV245 @ SV877 ) @ SV877 )
= $true )
| ( ( SV245
= ( c_List_Olist_ONil @ SV877 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3184]) ).
thf(3810,plain,
! [SV1409: $i,SV878: $i,SV246: $i] :
( ( ! [SY4282: $i,SY4283: $i] :
( ( c_HOL_Oord__class_Oless @ SV246 @ ( c_List_Olist_Olist__size @ SV878 @ SV1409 @ SY4282 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV246 @ ( hAPP @ SV878 @ SY4283 ) @ tc_nat )
| ~ ( c_in @ SY4283 @ ( c_List_Oset @ SV1409 @ SY4282 ) @ SY4282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3185]) ).
thf(3811,plain,
! [SV1410: $i,SV879: $i,SV247: $i] :
( ( ! [SY4284: $i] :
( ( ( c_List_OtakeWhile @ SV247 @ SV879 @ SV1410 )
= ( c_List_Otake @ SY4284 @ SV879 @ SV1410 ) )
| ( hBOOL @ ( hAPP @ SV247 @ ( c_List_Onth @ SV879 @ SY4284 @ SV1410 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV247 @ ( c_List_Onth @ SV879 @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV247 @ SY4284 @ SV879 @ SV1410 ) @ SV1410 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3186]) ).
thf(3812,plain,
! [SV880: $i,SV248: $i] :
( ( ( ( c_List_Ohd @ ( c_List_Orev @ SV248 @ SV880 ) @ SV880 )
= ( c_List_Olast @ SV248 @ SV880 ) )
= $true )
| ( ( SV248
= ( c_List_Olist_ONil @ SV880 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3187]) ).
thf(3813,plain,
! [SV881: $i,SV249: $i] :
( ( ( ( c_List_Olast @ ( c_List_Orev @ SV249 @ SV881 ) @ SV881 )
= ( c_List_Ohd @ SV249 @ SV881 ) )
= $true )
| ( ( SV249
= ( c_List_Olist_ONil @ SV881 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3188]) ).
thf(3814,plain,
! [SV1411: $i,SV882: $i,SV250: $i] :
( ( ( ( c_List_Olength__unique @ ( c_List_Olist_OCons @ SV250 @ SV882 @ SV1411 ) @ SV1411 )
= ( c_List_Olength__unique @ SV882 @ SV1411 ) )
| ~ ( c_in @ SV250 @ ( c_List_Oset @ SV882 @ SV1411 ) @ SV1411 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3189]) ).
thf(3815,plain,
! [SV1412: $i,SV883: $i,SV251: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Otake @ SV251 @ SV883 @ SV1412 ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ ( c_List_Odrop @ SV251 @ SV883 @ SV1412 ) @ SV1412 ) @ ( c_List_Olist_ONil @ SV1412 ) @ SV1412 ) @ SV1412 )
= ( c_List_Otake @ ( c_Suc @ SV251 ) @ SV883 @ SV1412 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV251 @ ( c_Nat_Osize__class_Osize @ SV883 @ ( tc_List_Olist @ SV1412 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3190]) ).
thf(3816,plain,
! [SV1413: $i,SV884: $i,SV252: $i] :
( ( ! [SY4285: $i,SY4286: $i] :
( ~ ( class_Orderings_Olinorder @ SV252 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV884 @ ( c_List_Olinorder__class_Oinsort__key @ SV884 @ SV1413 @ SY4285 @ SY4286 @ SV252 ) @ SY4286 @ SV252 ) @ SV252 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV884 @ SY4285 @ SY4286 @ SV252 ) @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3191]) ).
thf(3817,plain,
! [SV1414: $i,SV885: $i,SV253: $i] :
( ( ! [SY4287: $i,SY4288: $i] :
( ~ ( class_Orderings_Olinorder @ SV253 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV885 @ SV1414 @ SY4287 @ SV253 ) @ SV253 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV885 @ ( c_List_Olinorder__class_Oinsort__key @ SV885 @ SY4288 @ SV1414 @ SY4287 @ SV253 ) @ SY4287 @ SV253 ) @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3192]) ).
thf(3818,plain,
! [SV1415: $i,SV886: $i,SV254: $i] :
( ( ! [SY4289: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ SV254 @ SV886 @ SV1415 @ SY4289 ) @ ( tc_List_Olist @ SY4289 ) )
= ( c_Nat_Osize__class_Osize @ SV254 @ ( tc_List_Olist @ SY4289 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3193]) ).
thf(3819,plain,
! [SV888: $i,SV256: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV256 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV888 @ SV256 ) @ ( c_HOL_Ozero__class_Ozero @ SV256 ) @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3195]) ).
thf(3820,plain,
! [SV1416: $i,SV889: $i,SV257: $i] :
( ( ! [SY4290: $i,SY4291: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV257 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SV889 ) @ SV1416 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SY4290 ) @ SY4291 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SV889 ) @ SY4290 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SV1416 ) @ SY4291 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3196]) ).
thf(3821,plain,
! [SV1417: $i,SV890: $i,SV258: $i] :
( ( ( ( c_List_Olast @ ( c_List_Oreplicate @ SV258 @ SV890 @ SV1417 ) @ SV1417 )
= SV890 )
| ( SV258
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3197]) ).
thf(3822,plain,
! [SV1418: $i,SV891: $i,SV259: $i] :
( ( ( c_List_Obutlast @ ( c_List_Odrop @ SV259 @ SV891 @ SV1418 ) @ SV1418 )
= ( c_List_Odrop @ SV259 @ ( c_List_Obutlast @ SV891 @ SV1418 ) @ SV1418 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3198]) ).
thf(3823,plain,
! [SV1419: $i,SV892: $i,SV260: $i] :
( ( ( c_List_Oappend @ ( c_List_Otake @ SV260 @ SV892 @ SV1419 ) @ ( c_List_Odrop @ SV260 @ SV892 @ SV1419 ) @ SV1419 )
= SV892 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3199]) ).
thf(3824,plain,
! [SV1420: $i,SV893: $i,SV261: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV261 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_OtakeWhile @ SV893 @ SV1420 @ SV261 ) @ SV261 )
| ~ ( c_List_Olinorder__class_Osorted @ SV1420 @ SV261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3200]) ).
thf(3825,plain,
! [SV1421: $i,SV894: $i,SV262: $i] :
( ( SV262
= ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV894 @ ( tc_List_Olist @ SV1421 ) ) @ ( c_List_Oappend @ SV894 @ SV262 @ SV1421 ) @ SV1421 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3201]) ).
thf(3826,plain,
! [SV1422: $i,SV895: $i,SV263: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV263 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV263 ) @ SV895 ) @ SV1422 ) @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ SV1422 @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ SV895 @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3202]) ).
thf(3827,plain,
! [SV1423: $i,SV896: $i,SV264: $i] :
( ( ! [SY4292: $i] :
( ( ( c_List_Onth @ ( c_List_OtakeWhile @ SV264 @ SV896 @ SV1423 ) @ SY4292 @ SV1423 )
= ( c_List_Onth @ SV896 @ SY4292 @ SV1423 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4292 @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ SV264 @ SV896 @ SV1423 ) @ ( tc_List_Olist @ SV1423 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3203]) ).
thf(3828,plain,
! [SV1424: $i,SV897: $i,SV265: $i] :
( ( ( c_List_Odrop @ SV265 @ ( c_List_Obutlast @ SV897 @ SV1424 ) @ SV1424 )
= ( c_List_Obutlast @ ( c_List_Odrop @ SV265 @ SV897 @ SV1424 ) @ SV1424 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3204]) ).
thf(3829,plain,
! [SV898: $i,SV266: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV266 @ SV266 @ tc_nat )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV266 ) ) @ SV898 ) @ SV266 )
= SV898 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3205]) ).
thf(3830,plain,
! [SV1425: $i,SV899: $i,SV267: $i] :
( ( ! [SY4293: $i,SY4294: $i,SY4295: $i] :
( ( hAPP @ ( c_COMBC @ SV267 @ SV899 @ SV1425 @ SY4293 @ SY4294 ) @ SY4295 )
= ( hAPP @ ( hAPP @ SV267 @ SY4295 ) @ SV899 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3206]) ).
thf(3831,plain,
! [SV1426: $i,SV900: $i,SV268: $i] :
( ( ( hBOOL @ ( hAPP @ SV268 @ SV900 ) )
| ~ ( c_in @ SV900 @ SV268 @ SV1426 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3207]) ).
thf(3832,plain,
! [SV1427: $i,SV901: $i,SV269: $i] :
( ( ( c_in @ SV269 @ SV901 @ SV1427 )
| ~ ( hBOOL @ ( hAPP @ SV901 @ SV269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3208]) ).
thf(3833,plain,
! [SV1428: $i,SV902: $i,SV270: $i] :
( ( ! [SY4296: $i,SY4297: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ SV270 @ SV902 @ SV1428 @ SY4296 ) @ SY4297 @ SY4296 )
= ( c_List_Onth @ SV270 @ SY4297 @ SY4296 ) )
| ( SV902 = SY4297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3209]) ).
thf(3834,plain,
! [SV1429: $i,SV903: $i,SV271: $i] :
( ( ! [SY4298: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV271 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ SV903 ) @ SV1429 ) ) @ SY4298 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ SV903 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ SV1429 ) @ SY4298 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3210]) ).
thf(3835,plain,
! [SV1430: $i,SV904: $i,SV272: $i] :
( ( ! [SY4299: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV272 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV904 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV1430 ) @ SY4299 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV1430 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV904 ) @ SY4299 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3211]) ).
thf(3836,plain,
! [SV1431: $i,SV905: $i,SV273: $i] :
( ( ! [SY4300: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV273 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ SV905 ) @ SV1431 ) ) @ SY4300 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ SV905 ) @ SY4300 ) ) @ SV1431 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3212]) ).
thf(3837,plain,
! [SV1432: $i,SV906: $i,SV274: $i] :
( ( ! [SY4301: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV274 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ SV906 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ SV1432 ) @ SY4301 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ SV906 ) @ SV1432 ) ) @ SY4301 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3213]) ).
thf(3838,plain,
! [SV1433: $i,SV907: $i,SV275: $i] :
( ( ! [SY4302: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV275 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ SV907 ) @ SV1433 ) ) @ SY4302 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ SV907 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ SV1433 ) @ SY4302 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3214]) ).
thf(3839,plain,
! [SV1434: $i,SV908: $i,SV276: $i] :
( ( ! [SY4303: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV276 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ SV908 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ SV1434 ) @ SY4303 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ SV1434 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ SV908 ) @ SY4303 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3215]) ).
thf(3840,plain,
! [SV1435: $i,SV909: $i,SV277: $i] :
( ( ! [SY4304: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV277 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ SV909 ) @ SV1435 ) ) @ SY4304 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ SV909 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ SV1435 ) @ SY4304 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3216]) ).
thf(3841,plain,
! [SV1436: $i,SV910: $i,SV278: $i] :
( ( ! [SY4305: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV278 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV278 ) @ SV910 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV278 ) @ SV1436 ) @ SY4305 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV278 ) @ SV1436 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV278 ) @ SV910 ) @ SY4305 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3217]) ).
thf(3842,plain,
! [SV1437: $i,SV911: $i,SV279: $i] :
( ( ! [SY4306: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV279 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV279 ) @ SV911 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV279 ) @ SV1437 ) @ SY4306 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV279 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV279 ) @ SV911 ) @ SV1437 ) ) @ SY4306 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3218]) ).
thf(3843,plain,
! [SV1438: $i,SV912: $i,SV280: $i] :
( ( ! [SY4307: $i] :
( ( ( c_List_Onth @ ( c_List_Otake @ SV280 @ SV912 @ SV1438 ) @ SY4307 @ SV1438 )
= ( c_List_Onth @ SV912 @ SY4307 @ SV1438 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4307 @ SV280 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3219]) ).
thf(3844,plain,
! [SV1439: $i,SV913: $i,SV281: $i] :
( ( ! [SY4308: $i] :
( ~ ( class_Orderings_Oorder @ SV281 )
| ( c_HOL_Oord__class_Oless @ SV913 @ SV1439 @ SV281 )
| ~ ( c_HOL_Oord__class_Oless @ SV913 @ SY4308 @ SV281 )
| ~ ( c_HOL_Oord__class_Oless @ SY4308 @ SV1439 @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3220]) ).
thf(3845,plain,
! [SV1440: $i,SV914: $i,SV282: $i] :
( ( ! [SY4309: $i] :
( ~ ( class_Orderings_Opreorder @ SV282 )
| ( c_HOL_Oord__class_Oless @ SV914 @ SV1440 @ SV282 )
| ~ ( c_HOL_Oord__class_Oless @ SY4309 @ SV1440 @ SV282 )
| ~ ( c_HOL_Oord__class_Oless @ SV914 @ SY4309 @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3221]) ).
thf(3846,plain,
! [SV1441: $i,SV915: $i,SV283: $i] :
( ( ! [SY4310: $i,SY4311: $i] :
( ( c_List_Otake @ SV283 @ ( c_List_Omap @ SV915 @ SV1441 @ SY4310 @ SY4311 ) @ SY4311 )
= ( c_List_Omap @ SV915 @ ( c_List_Otake @ SV283 @ SV1441 @ SY4310 ) @ SY4310 @ SY4311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3222]) ).
thf(3847,plain,
! [SV1442: $i,SV916: $i,SV284: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV284 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ SV916 @ SV1442 @ SV284 ) @ SV284 )
| ~ ( c_List_Olinorder__class_Osorted @ SV1442 @ SV284 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3223]) ).
thf(3848,plain,
! [SV1443: $i,SV917: $i,SV285: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV285 ) ) @ SV917 ) @ SV1443 )
= ( c_Lambda_OdB_OVar @ SV285 ) )
| ( SV285 = SV1443 )
| ( c_HOL_Oord__class_Oless @ SV1443 @ SV285 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3224]) ).
thf(3849,plain,
! [SV1444: $i,SV918: $i,SV286: $i] :
( ( ! [SY4312: $i] :
( ( c_List_Olistsp @ SV286 @ SV918 @ SV1444 )
| ~ ( c_List_Olistsp @ SV286 @ ( c_List_Oappend @ SV918 @ SY4312 @ SV1444 ) @ SV1444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3225]) ).
thf(3850,plain,
! [SV1445: $i,SV919: $i,SV287: $i] :
( ( ! [SY4313: $i] :
( ( c_List_Olistsp @ SV287 @ SV919 @ SV1445 )
| ~ ( c_List_Olistsp @ SV287 @ ( c_List_Oappend @ SY4313 @ SV919 @ SV1445 ) @ SV1445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3226]) ).
thf(3851,plain,
! [SV1446: $i,SV920: $i,SV288: $i] :
( ( ! [SY4314: $i,SY4315: $i] :
( ( c_Lambda_OdB_OdB__case @ SV288 @ SV920 @ SV1446 @ ( c_Lambda_OdB_OAbs @ SY4314 ) @ SY4315 )
= ( hAPP @ SV1446 @ SY4314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3227]) ).
thf(3852,plain,
! [SV1447: $i,SV921: $i,SV289: $i] :
( ( ! [SY4316: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV289 ) @ SV921 ) @ SV1447 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY4316 ) @ SV921 ) @ SV1447 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV289 ) @ SY4316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3228]) ).
thf(3853,plain,
! [SV1448: $i,SV922: $i,SV290: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV290 @ ( c_Nat_Osize__class_Osize @ SV922 @ ( tc_List_Olist @ SV1448 ) ) @ tc_nat )
| ( ( c_List_Olist__update @ SV922 @ SV290 @ ( c_List_Onth @ SV922 @ SV290 @ SV1448 ) @ SV1448 )
= SV922 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3229]) ).
thf(3854,plain,
! [SV1449: $i,SV923: $i,SV291: $i] :
( ( ! [SY4317: $i] :
( ( ( c_List_Olist__update @ SV291 @ SV923 @ SV1449 @ SY4317 )
= ( c_List_Oappend @ ( c_List_Otake @ SV923 @ SV291 @ SY4317 ) @ ( c_List_Olist_OCons @ SV1449 @ ( c_List_Odrop @ ( c_Suc @ SV923 ) @ SV291 @ SY4317 ) @ SY4317 ) @ SY4317 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV923 @ ( c_Nat_Osize__class_Osize @ SV291 @ ( tc_List_Olist @ SY4317 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3230]) ).
thf(3855,plain,
! [SV1450: $i,SV924: $i,SV292: $i] :
( ( ( SV292
= ( c_List_Oappend @ ( c_List_Otake @ SV924 @ SV292 @ SV1450 ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ SV292 @ SV924 @ SV1450 ) @ ( c_List_Odrop @ ( c_Suc @ SV924 ) @ SV292 @ SV1450 ) @ SV1450 ) @ SV1450 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV924 @ ( c_Nat_Osize__class_Osize @ SV292 @ ( tc_List_Olist @ SV1450 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3231]) ).
thf(3856,plain,
! [SV1451: $i,SV925: $i,SV293: $i] :
( ( ( ( c_List_Otake @ ( c_Suc @ SV293 ) @ SV925 @ SV1451 )
= ( c_List_Oappend @ ( c_List_Otake @ SV293 @ SV925 @ SV1451 ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ SV925 @ SV293 @ SV1451 ) @ ( c_List_Olist_ONil @ SV1451 ) @ SV1451 ) @ SV1451 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV293 @ ( c_Nat_Osize__class_Osize @ SV925 @ ( tc_List_Olist @ SV1451 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3232]) ).
thf(3857,plain,
! [SV1452: $i,SV926: $i,SV294: $i] :
( ( ! [SY4318: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV294 @ SV926 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV1452 ) @ SY4318 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV294 ) @ SV1452 ) @ SY4318 ) @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SV1452 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SY4318 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV926 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3233]) ).
thf(3858,plain,
! [SV1453: $i,SV927: $i,SV295: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV295 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV927 @ SV295 @ SV1453 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV927 ) @ SV295 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV1453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3234]) ).
thf(3859,plain,
! [SV1454: $i,SV928: $i,SV296: $i] :
( ( ! [SY4319: $i] :
( ( ( c_List_OtakeWhile @ SV296 @ SV928 @ SV1454 )
= ( c_List_Otake @ SY4319 @ SV928 @ SV1454 ) )
| ( c_HOL_Oord__class_Oless @ SY4319 @ ( c_Nat_Osize__class_Osize @ SV928 @ ( tc_List_Olist @ SV1454 ) ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV296 @ ( c_List_Onth @ SV928 @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV296 @ SY4319 @ SV928 @ SV1454 ) @ SV1454 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3235]) ).
thf(3860,plain,
! [SV1455: $i,SV929: $i,SV297: $i] :
( ( ! [SY4320: $i] :
( ( ( c_List_OtakeWhile @ SV297 @ SV929 @ SV1455 )
= ( c_List_Otake @ SY4320 @ SV929 @ SV1455 ) )
| ( hBOOL @ ( hAPP @ SV297 @ ( c_List_Onth @ SV929 @ SY4320 @ SV1455 ) ) )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV297 @ SY4320 @ SV929 @ SV1455 ) @ ( c_Nat_Osize__class_Osize @ SV929 @ ( tc_List_Olist @ SV1455 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3236]) ).
thf(3861,plain,
! [SV1456: $i,SV930: $i,SV298: $i] :
( ( ( ( c_List_Ohd @ ( c_List_Odrop @ SV298 @ SV930 @ SV1456 ) @ SV1456 )
= ( c_List_Onth @ SV930 @ SV298 @ SV1456 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV298 @ ( c_Nat_Osize__class_Osize @ SV930 @ ( tc_List_Olist @ SV1456 ) ) @ tc_nat )
| ( SV930
= ( c_List_Olist_ONil @ SV1456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3237]) ).
thf(3862,plain,
! [SV1457: $i,SV931: $i,SV299: $i] :
( ( ( ( c_List_Olist_OCons @ ( c_List_Onth @ SV299 @ SV931 @ SV1457 ) @ ( c_List_Odrop @ ( c_Suc @ SV931 ) @ SV299 @ SV1457 ) @ SV1457 )
= ( c_List_Odrop @ SV931 @ SV299 @ SV1457 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV931 @ ( c_Nat_Osize__class_Osize @ SV299 @ ( tc_List_Olist @ SV1457 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3238]) ).
thf(3863,plain,
! [SV1458: $i,SV932: $i,SV300: $i] :
( ( ! [SY4321: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV300 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV932 @ SV1458 @ SV300 ) @ ( c_Power_Opower__class_Opower @ SY4321 @ SV1458 @ SV300 ) @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1458 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SV932 @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ SV932 @ SY4321 @ SV300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3239]) ).
thf(3864,plain,
! [SV1459: $i,SV933: $i,SV301: $i] :
( ( ( c_List_Orev @ ( c_List_Odrop @ SV301 @ SV933 @ SV1459 ) @ SV1459 )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SV933 @ ( tc_List_Olist @ SV1459 ) ) @ SV301 @ tc_nat ) @ ( c_List_Orev @ SV933 @ SV1459 ) @ SV1459 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3240]) ).
thf(3865,plain,
! [SV1460: $i,SV934: $i,SV302: $i] :
( ( ( c_List_Orev @ ( c_List_Otake @ SV302 @ SV934 @ SV1460 ) @ SV1460 )
= ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SV934 @ ( tc_List_Olist @ SV1460 ) ) @ SV302 @ tc_nat ) @ ( c_List_Orev @ SV934 @ SV1460 ) @ SV1460 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3241]) ).
thf(3866,plain,
! [SV1461: $i,SV935: $i,SV303: $i] :
( ( ! [SY4322: $i] :
( ( ( c_List_OtakeWhile @ SV303 @ SV935 @ SV1461 )
= ( c_List_Otake @ SY4322 @ SV935 @ SV1461 ) )
| ( hBOOL @ ( hAPP @ SV303 @ ( c_List_Onth @ SV935 @ SY4322 @ SV1461 ) ) )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV303 @ SY4322 @ SV935 @ SV1461 ) @ SY4322 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3242]) ).
thf(3867,plain,
! [SV1462: $i,SV936: $i,SV304: $i] :
( ( ! [SY4323: $i] :
( ( ( c_List_OtakeWhile @ SV304 @ SV936 @ SV1462 )
= ( c_List_Otake @ SY4323 @ SV936 @ SV1462 ) )
| ( c_HOL_Oord__class_Oless @ SY4323 @ ( c_Nat_Osize__class_Osize @ SV936 @ ( tc_List_Olist @ SV1462 ) ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV304 @ SY4323 @ SV936 @ SV1462 ) @ ( c_Nat_Osize__class_Osize @ SV936 @ ( tc_List_Olist @ SV1462 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3243]) ).
thf(3868,plain,
! [SV1463: $i,SV937: $i,SV305: $i] :
( ( ! [SY4324: $i] :
( ( ( c_List_OtakeWhile @ SV305 @ SV937 @ SV1463 )
= ( c_List_Otake @ SY4324 @ SV937 @ SV1463 ) )
| ( c_HOL_Oord__class_Oless @ SY4324 @ ( c_Nat_Osize__class_Osize @ SV937 @ ( tc_List_Olist @ SV1463 ) ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV305 @ SY4324 @ SV937 @ SV1463 ) @ SY4324 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3244]) ).
thf(3869,plain,
! [SV1464: $i,SV938: $i,SV306: $i] :
( ( ! [SY4325: $i,SY4326: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV306 @ SV938 @ SV1464 ) @ SY4325 @ SY4326 @ SV1464 )
= ( c_List_Oappend @ SV306 @ ( c_List_Olist__update @ SV938 @ ( c_HOL_Ominus__class_Ominus @ SY4325 @ ( c_Nat_Osize__class_Osize @ SV306 @ ( tc_List_Olist @ SV1464 ) ) @ tc_nat ) @ SY4326 @ SV1464 ) @ SV1464 ) )
| ( c_HOL_Oord__class_Oless @ SY4325 @ ( c_Nat_Osize__class_Osize @ SV306 @ ( tc_List_Olist @ SV1464 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3245]) ).
thf(3870,plain,
! [SV1465: $i,SV939: $i,SV307: $i] :
( ( ! [SY4327: $i] :
( ( ( c_List_Onth @ ( c_List_Oappend @ SV307 @ SV939 @ SV1465 ) @ SY4327 @ SV1465 )
= ( c_List_Onth @ SV939 @ ( c_HOL_Ominus__class_Ominus @ SY4327 @ ( c_Nat_Osize__class_Osize @ SV307 @ ( tc_List_Olist @ SV1465 ) ) @ tc_nat ) @ SV1465 ) )
| ( c_HOL_Oord__class_Oless @ SY4327 @ ( c_Nat_Osize__class_Osize @ SV307 @ ( tc_List_Olist @ SV1465 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3246]) ).
thf(3871,plain,
! [SV1466: $i,SV940: $i,SV308: $i] :
( ( ! [SY4328: $i] :
( ( c_in @ SV308 @ ( c_List_Oset @ ( c_List_Olist__update @ SV940 @ SV1466 @ SV308 @ SY4328 ) @ SY4328 ) @ SY4328 )
| ~ ( c_HOL_Oord__class_Oless @ SV1466 @ ( c_Nat_Osize__class_Osize @ SV940 @ ( tc_List_Olist @ SY4328 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3247]) ).
thf(3872,plain,
! [SV1467: $i,SV941: $i,SV309: $i] :
( ( ( c_in @ ( c_List_Onth @ SV309 @ SV941 @ SV1467 ) @ ( c_List_Oset @ SV309 @ SV1467 ) @ SV1467 )
| ~ ( c_HOL_Oord__class_Oless @ SV941 @ ( c_Nat_Osize__class_Osize @ SV309 @ ( tc_List_Olist @ SV1467 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3248]) ).
thf(3873,plain,
! [SV1468: $i,SV942: $i,SV310: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV310 @ ( c_Nat_Osize__class_Osize @ SV942 @ ( tc_List_Olist @ SV1468 ) ) @ tc_nat )
| ( c_in @ ( c_List_Onth @ SV942 @ SV310 @ SV1468 ) @ ( c_List_Oset @ SV942 @ SV1468 ) @ SV1468 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3249]) ).
thf(3874,plain,
! [SV1469: $i,SV943: $i,SV311: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV311 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV311 ) @ ( c_Power_Opower__class_Opower @ SV943 @ SV1469 @ SV311 ) @ SV311 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1469 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV311 ) @ SV943 @ SV311 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3250]) ).
thf(3875,plain,
! [SV1470: $i,SV944: $i,SV312: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV312 @ ( tc_List_Olist @ SV944 ) ) @ tc_nat )
| ~ ( c_in @ SV1470 @ ( c_List_Oset @ SV312 @ SV944 ) @ SV944 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3251]) ).
thf(3876,plain,
! [SV1471: $i,SV945: $i,SV313: $i] :
( ( ! [SY4329: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV313 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV945 @ SV1471 @ SV313 ) @ ( c_Power_Opower__class_Opower @ SV945 @ SY4329 @ SV313 ) @ SV313 )
| ~ ( c_HOL_Oord__class_Oless @ SV945 @ ( c_HOL_Oone__class_Oone @ SV313 ) @ SV313 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV313 ) @ SV945 @ SV313 )
| ~ ( c_HOL_Oord__class_Oless @ SY4329 @ SV1471 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3252]) ).
thf(3877,plain,
! [SV1472: $i,SV946: $i,SV314: $i] :
( ( ! [SY4330: $i,SY4331: $i,SY4332: $i] :
( ( c_List_Omap @ SV314 @ ( c_List_Olist__update @ SV946 @ SV1472 @ SY4330 @ SY4331 ) @ SY4331 @ SY4332 )
= ( c_List_Olist__update @ ( c_List_Omap @ SV314 @ SV946 @ SY4331 @ SY4332 ) @ SV1472 @ ( hAPP @ SV314 @ SY4330 ) @ SY4332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3253]) ).
thf(3878,plain,
! [SV947: $i,SV315: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV315 ) ) @ ( c_Lambda_OdB_OAbs @ SV947 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV315 ) @ SV947 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3254]) ).
thf(3879,plain,
! [SV1473: $i,SV948: $i,SV316: $i] :
( ( ( c_List_Orev @ ( c_List_Oappend @ SV316 @ SV948 @ SV1473 ) @ SV1473 )
= ( c_List_Oappend @ ( c_List_Orev @ SV948 @ SV1473 ) @ ( c_List_Orev @ SV316 @ SV1473 ) @ SV1473 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3255]) ).
thf(3880,plain,
! [SV949: $i,SV317: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV317 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ SV949 @ SV317 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV317 ) @ SV949 ) @ SV949 ) @ SV317 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3256]) ).
thf(3881,plain,
! [SV950: $i,SV318: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV318 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV318 ) @ SV950 ) @ SV950 ) @ SV318 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ SV950 @ SV318 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3257]) ).
thf(3882,plain,
! [SV319: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV319 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV319 ) @ ( c_HOL_Ozero__class_Ozero @ SV319 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV319 ) )
= ( c_HOL_Ozero__class_Ozero @ SV319 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3258]) ).
thf(3883,plain,
! [SV951: $i,SV320: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV320 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ ( c_HOL_Ozero__class_Ozero @ SV320 ) ) @ SV951 )
= SV951 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3259]) ).
thf(3884,plain,
! [SV952: $i,SV321: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV321 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV321 ) @ ( c_HOL_Ozero__class_Ozero @ SV321 ) ) @ SV952 )
= SV952 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3260]) ).
thf(3885,plain,
! [SV953: $i,SV322: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV322 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV322 )
| ( SV953
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV322 ) @ SV953 ) @ ( c_HOL_Ozero__class_Ozero @ SV322 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3261]) ).
thf(3886,plain,
! [SV954: $i,SV323: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV323 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV323 ) @ SV954 ) @ ( c_HOL_Ozero__class_Ozero @ SV323 ) )
= SV954 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3262]) ).
thf(3887,plain,
! [SV955: $i,SV324: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV324 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV324 ) @ ( c_HOL_Ozero__class_Ozero @ SV324 ) ) @ SV955 )
= SV955 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3263]) ).
thf(3888,plain,
! [SV956: $i,SV325: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV325 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV325 ) @ SV956 ) @ ( c_HOL_Ozero__class_Ozero @ SV325 ) )
= SV956 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3264]) ).
thf(3889,plain,
! [SV957: $i,SV326: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV326 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV326 ) @ SV957 ) @ ( c_HOL_Ozero__class_Ozero @ SV326 ) )
= SV957 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3265]) ).
thf(3890,plain,
! [SV958: $i,SV327: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV327 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ ( c_HOL_Ozero__class_Ozero @ SV327 ) ) @ SV958 )
= SV958 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3266]) ).
thf(3891,plain,
! [SV1474: $i,SV960: $i,SV332: $i] :
( ( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV332 @ SV960 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1474 @ SV960 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3271]) ).
thf(3892,plain,
! [SV1475: $i,SV961: $i,SV333: $i] :
( ( ! [SY4333: $i,SY4334: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV333 @ SV961 @ SV1475 ) @ ( c_List_Olist_OCons @ SY4333 @ SY4334 @ SV1475 ) @ SV1475 )
= ( c_List_Olist_OCons @ SV333 @ ( c_List_Olist_OCons @ SY4333 @ ( c_List_Osplice @ SV961 @ SY4334 @ SV1475 ) @ SV1475 ) @ SV1475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3272]) ).
thf(3893,plain,
! [SV1476: $i,SV962: $i,SV334: $i] :
( ( ! [SY4335: $i] :
( ~ ( class_Orderings_Olinorder @ SV334 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV962 @ SV1476 @ SV334 ) @ SV334 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SY4335 @ ( c_List_Olist_OCons @ SV962 @ SV1476 @ SV334 ) @ SV334 ) @ SV334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3273]) ).
thf(3894,plain,
! [SV1477: $i,SV963: $i,SV335: $i] :
( ( ! [SY4336: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV335 @ SV963 @ SV1477 ) @ SY4336 @ SV1477 )
= ( c_List_Olist_OCons @ SV335 @ ( c_List_Oappend @ SV963 @ SY4336 @ SV1477 ) @ SV1477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3274]) ).
thf(3895,plain,
! [SV1478: $i,SV964: $i,SV336: $i] :
( ( ! [SY4337: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV336 @ SV964 @ SV1478 ) @ SY4337 @ SV1478 )
= ( c_List_Olist_OCons @ SV336 @ ( c_List_Oappend @ SV964 @ SY4337 @ SV1478 ) @ SV1478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3275]) ).
thf(3896,plain,
! [SV1479: $i,SV965: $i,SV337: $i] :
( ( ! [SY4338: $i,SY4339: $i] :
( ( c_List_Omap @ SV337 @ ( c_List_Olist_OCons @ SV965 @ SV1479 @ SY4338 ) @ SY4338 @ SY4339 )
= ( c_List_Olist_OCons @ ( hAPP @ SV337 @ SV965 ) @ ( c_List_Omap @ SV337 @ SV1479 @ SY4338 @ SY4339 ) @ SY4339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3276]) ).
thf(3897,plain,
! [SV1480: $i,SV966: $i,SV338: $i] :
( ( ! [SY4340: $i,SY4341: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ SV338 @ SV966 ) @ ( c_List_Omap @ SV338 @ SV1480 @ SY4340 @ SY4341 ) @ SY4341 )
= ( c_List_Omap @ SV338 @ ( c_List_Olist_OCons @ SV966 @ SV1480 @ SY4340 ) @ SY4340 @ SY4341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3277]) ).
thf(3898,plain,
! [SV1481: $i,SV967: $i,SV339: $i] :
( ( ! [SY4342: $i,SY4343: $i] :
( ( c_List_Omap @ SV339 @ ( c_List_Olist_OCons @ SV967 @ SV1481 @ SY4342 ) @ SY4342 @ SY4343 )
= ( c_List_Olist_OCons @ ( hAPP @ SV339 @ SV967 ) @ ( c_List_Omap @ SV339 @ SV1481 @ SY4342 @ SY4343 ) @ SY4343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3278]) ).
thf(3899,plain,
! [SV1482: $i,SV968: $i,SV340: $i] :
( ( ! [SY4344: $i] :
( ( c_List_Olist_OCons @ SV340 @ ( c_List_Oappend @ SV968 @ SV1482 @ SY4344 ) @ SY4344 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV340 @ SV968 @ SY4344 ) @ SV1482 @ SY4344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3279]) ).
thf(3900,plain,
! [SV1483: $i,SV969: $i,SV341: $i] :
( ( ! [SY4345: $i] :
( ( c_List_Olist_OCons @ SV341 @ ( c_List_Oappend @ SV969 @ SV1483 @ SY4345 ) @ SY4345 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV341 @ SV969 @ SY4345 ) @ SV1483 @ SY4345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3280]) ).
thf(3901,plain,
! [SV1484: $i,SV970: $i,SV342: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV342 )
| ( c_List_Olinorder__class_Osorted @ SV970 @ SV342 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1484 @ SV970 @ SV342 ) @ SV342 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3281]) ).
thf(3902,plain,
! [SV1485: $i,SV971: $i,SV343: $i] :
( ( ! [SY4346: $i] :
( ( ( c_List_OtakeWhile @ SV343 @ ( c_List_Olist_OCons @ SV971 @ SV1485 @ SY4346 ) @ SY4346 )
= ( c_List_Olist_OCons @ SV971 @ ( c_List_OtakeWhile @ SV343 @ SV1485 @ SY4346 ) @ SY4346 ) )
| ~ ( hBOOL @ ( hAPP @ SV343 @ SV971 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3282]) ).
thf(3903,plain,
! [SV972: $i,SV344: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV344 @ ( tc_List_Olist @ SV972 ) ) @ tc_nat )
= $true )
| ( ( SV344
= ( c_List_Olist_ONil @ SV972 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3283]) ).
thf(3904,plain,
! [SV1486: $i,SV973: $i,SV346: $i] :
( ( ( c_List_Olast @ ( c_List_Oappend @ SV346 @ ( c_List_Olist_OCons @ SV973 @ ( c_List_Olist_ONil @ SV1486 ) @ SV1486 ) @ SV1486 ) @ SV1486 )
= SV973 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3285]) ).
thf(3905,plain,
! [SV1487: $i,SV974: $i,SV347: $i] :
( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV347 @ ( c_List_Olist_OCons @ SV974 @ ( c_List_Olist_ONil @ SV1487 ) @ SV1487 ) @ SV1487 ) @ SV1487 )
= SV347 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3286]) ).
thf(3906,plain,
! [SV1488: $i,SV975: $i,SV348: $i] :
( ( ( c_List_Orev @ ( c_List_Olist_OCons @ SV348 @ SV975 @ SV1488 ) @ SV1488 )
= ( c_List_Oappend @ ( c_List_Orev @ SV975 @ SV1488 ) @ ( c_List_Olist_OCons @ SV348 @ ( c_List_Olist_ONil @ SV1488 ) @ SV1488 ) @ SV1488 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3287]) ).
thf(3907,plain,
! [SV1489: $i,SV976: $i,SV349: $i] :
( ( ( c_List_Orev @ ( c_List_Oappend @ ( c_List_Orev @ SV349 @ SV976 ) @ ( c_List_Olist_OCons @ SV1489 @ ( c_List_Olist_ONil @ SV976 ) @ SV976 ) @ SV976 ) @ SV976 )
= ( c_List_Olist_OCons @ SV1489 @ SV349 @ SV976 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3288]) ).
thf(3908,plain,
! [SV1490: $i,SV977: $i,SV350: $i] :
( ( ( c_List_Oappend @ ( c_List_Oreplicate @ SV350 @ SV977 @ SV1490 ) @ ( c_List_Olist_OCons @ SV977 @ ( c_List_Olist_ONil @ SV1490 ) @ SV1490 ) @ SV1490 )
= ( c_List_Olist_OCons @ SV977 @ ( c_List_Oreplicate @ SV350 @ SV977 @ SV1490 ) @ SV1490 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3289]) ).
thf(3909,plain,
! [SV1491: $i,SV989: $i,SV365: $i] :
( ( ( c_List_Omap @ SV365 @ ( c_List_Olist_ONil @ SV989 ) @ SV989 @ SV1491 )
= ( c_List_Olist_ONil @ SV1491 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3301]) ).
thf(3910,plain,
! [SV367: $i] :
( ( ( class_Orderings_Olinorder @ SV367 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_ONil @ SV367 ) @ SV367 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3303]) ).
thf(3911,plain,
! [SV1492: $i,SV991: $i,SV368: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV368 ) @ SV991 @ SV1492 @ SV368 )
= ( c_List_Olist_ONil @ SV368 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3304]) ).
thf(3912,plain,
! [SV1493: $i,SV992: $i,SV369: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV369 ) @ SV992 @ SV1493 @ SV369 )
= ( c_List_Olist_ONil @ SV369 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3305]) ).
thf(3913,plain,
! [SV1494: $i,SV993: $i,SV370: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist_ONil @ SV370 ) @ SV993 @ SV1494 @ SV370 )
= ( c_List_Olist_ONil @ SV370 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3306]) ).
thf(3914,plain,
! [SV1495: $i,SV994: $i,SV371: $i] :
( ( ( c_List_Olist_ONil @ SV371 )
= ( c_List_Omap @ SV994 @ ( c_List_Olist_ONil @ SV1495 ) @ SV1495 @ SV371 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3307]) ).
thf(3915,plain,
! [SV995: $i,SV374: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV374 ) )
= $true )
| ( ( ( c_List_Olistsum @ SV995 @ SV374 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV374 ) @ ( c_HOL_Ozero__class_Ozero @ SV374 ) @ SV995 @ SV374 @ SV374 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3308]) ).
thf(3916,plain,
! [SV1496: $i,SV996: $i,SV375: $i] :
( ( ! [SY4347: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV375 ) @ SV996 ) ) @ SV1496 ) @ SY4347 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV375 ) @ SV1496 ) @ SY4347 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV996 ) @ SV1496 ) @ SY4347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3309]) ).
thf(3917,plain,
! [SV1497: $i,SV997: $i,SV376: $i] :
( ( ! [SY4348: $i,SY4349: $i,SY4350: $i] :
( ~ ( hBOOL @ ( hAPP @ SV376 @ ( c_Lambda_OdB_OdB__case @ SV997 @ SV1497 @ SY4348 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4349 ) @ SY4350 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SV1497 @ SY4349 ) @ SY4350 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3310]) ).
thf(3918,plain,
! [SV1498: $i,SV998: $i,SV377: $i] :
( ( ! [SY4351: $i,SY4352: $i,SY4353: $i] :
( ~ ( hBOOL @ ( hAPP @ SV377 @ ( c_Lambda_OdB_OdB__case @ SV998 @ SV1498 @ SY4351 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4352 ) @ SY4353 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV377 @ ( hAPP @ ( hAPP @ SV1498 @ SY4352 ) @ SY4353 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3311]) ).
thf(3919,plain,
! [SV1499: $i,SV999: $i,SV378: $i] :
( ( ! [SY4354: $i,SY4355: $i,SY4356: $i] :
( ( c_Lambda_OdB_OdB__case @ SV378 @ SV999 @ SV1499 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4354 ) @ SY4355 ) @ SY4356 )
= ( hAPP @ ( hAPP @ SV999 @ SY4354 ) @ SY4355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3312]) ).
thf(3920,plain,
! [SV1500: $i,SV1000: $i,SV379: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV379 ) @ SV1000 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV379 ) @ SV1500 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1000 ) @ SV1500 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3313]) ).
thf(3921,plain,
! [SV1501: $i,SV1001: $i,SV380: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV380 ) @ SV1001 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1501 ) @ SV1001 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV380 ) @ SV1501 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3314]) ).
thf(3922,plain,
! [SV1502: $i,SV1002: $i,SV381: $i] :
( ( ! [SY4357: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV381 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV1002 ) @ SV1502 ) @ SY4357 @ SV381 @ SV381 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV1002 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV1502 @ SY4357 @ SV381 @ SV381 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3315]) ).
thf(3923,plain,
! [SV1503: $i,SV1003: $i,SV382: $i] :
( ( ! [SY4358: $i,SY4359: $i,SY4360: $i] :
( ( c_List_Ofoldl @ SV382 @ SV1003 @ ( c_List_Oappend @ SV1503 @ SY4358 @ SY4359 ) @ SY4360 @ SY4359 )
= ( c_List_Ofoldl @ SV382 @ ( c_List_Ofoldl @ SV382 @ SV1003 @ SV1503 @ SY4360 @ SY4359 ) @ SY4358 @ SY4360 @ SY4359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3316]) ).
thf(3924,plain,
! [SV1504: $i,SV1004: $i,SV383: $i] :
( ( ! [SY4361: $i,SY4362: $i] :
( ~ ( hBOOL @ ( hAPP @ SV383 @ ( c_Lambda_OdB_OdB__case @ SV1004 @ SV1504 @ SY4361 @ ( c_Lambda_OdB_OVar @ SY4362 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV383 @ ( hAPP @ SV1004 @ SY4362 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3317]) ).
thf(3925,plain,
! [SV1505: $i,SV1005: $i,SV384: $i] :
( ( ! [SY4363: $i,SY4364: $i] :
( ~ ( hBOOL @ ( hAPP @ SV384 @ ( c_Lambda_OdB_OdB__case @ SV1005 @ SV1505 @ SY4363 @ ( c_Lambda_OdB_OVar @ SY4364 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV384 @ ( hAPP @ SV1005 @ SY4364 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3318]) ).
thf(3926,plain,
! [SV1007: $i,SV386: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV386 ) ) @ SV1007 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3320]) ).
thf(3927,plain,
! [SV1506: $i,SV1008: $i,SV387: $i] :
( ( ! [SY4365: $i] :
( ( c_List_Orev @ ( c_List_Omap @ SV387 @ SV1008 @ SV1506 @ SY4365 ) @ SY4365 )
= ( c_List_Omap @ SV387 @ ( c_List_Orev @ SV1008 @ SV1506 ) @ SV1506 @ SY4365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3321]) ).
thf(3928,plain,
! [SV1507: $i,SV1009: $i,SV388: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV388 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ SV1009 @ SV1507 @ SV388 ) @ SV388 )
| ~ ( c_List_Olinorder__class_Osorted @ SV1507 @ SV388 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3322]) ).
thf(3929,plain,
! [SV1508: $i,SV1010: $i,SV389: $i] :
( ( ! [SY4366: $i] :
( ( c_List_Onth @ ( c_List_Oappend @ SV389 @ ( c_List_Olist_OCons @ SV1010 @ SV1508 @ SY4366 ) @ SY4366 ) @ ( c_Nat_Osize__class_Osize @ SV389 @ ( tc_List_Olist @ SY4366 ) ) @ SY4366 )
= SV1010 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3323]) ).
thf(3930,plain,
! [SV1509: $i,SV1011: $i,SV390: $i] :
( ( ( c_List_OtakeWhile @ SV390 @ SV1011 @ SV1509 )
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ SV390 @ SV1011 @ SV1509 ) @ ( tc_List_Olist @ SV1509 ) ) @ SV1011 @ SV1509 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3324]) ).
thf(3931,plain,
! [SV1510: $i,SV1012: $i,SV391: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV391 @ ( c_List_Onth @ SV1012 @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ SV391 @ SV1012 @ SV1510 ) @ ( tc_List_Olist @ SV1510 ) ) @ SV1510 ) ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ SV391 @ SV1012 @ SV1510 ) @ ( tc_List_Olist @ SV1510 ) ) @ ( c_Nat_Osize__class_Osize @ SV1012 @ ( tc_List_Olist @ SV1510 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3325]) ).
thf(3932,plain,
! [SV1016: $i,SV395: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Obutlast @ SV395 @ SV1016 ) @ ( c_List_Olist_OCons @ ( c_List_Olast @ SV395 @ SV1016 ) @ ( c_List_Olist_ONil @ SV1016 ) @ SV1016 ) @ SV1016 )
= SV395 )
= $true )
| ( ( SV395
= ( c_List_Olist_ONil @ SV1016 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3329]) ).
thf(3933,plain,
! [SV1511: $i,SV1017: $i,SV396: $i] :
( ( SV396
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV396 @ ( tc_List_Olist @ SV1017 ) ) @ ( c_List_Oappend @ SV396 @ SV1511 @ SV1017 ) @ SV1017 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3330]) ).
thf(3934,plain,
! [SV1512: $i,SV1018: $i,SV397: $i] :
( ( ! [SY4367: $i] :
( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ SV397 @ SV1018 @ SV1512 @ SY4367 ) @ ( tc_List_Olist @ SY4367 ) )
= ( c_Nat_Osize__class_Osize @ SV1018 @ ( tc_List_Olist @ SV1512 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3331]) ).
thf(3935,plain,
! [SV1513: $i,SV1019: $i,SV398: $i] :
( ( ! [SY4368: $i,SY4369: $i] :
( ( c_List_Omap @ SV398 @ ( c_List_Oreplicate @ SV1019 @ SV1513 @ SY4368 ) @ SY4368 @ SY4369 )
= ( c_List_Oreplicate @ SV1019 @ ( hAPP @ SV398 @ SV1513 ) @ SY4369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3332]) ).
thf(3936,plain,
! [SV1514: $i,SV1020: $i,SV399: $i] :
( ( ! [SY4370: $i] :
( ( ( c_List_Onth @ ( c_List_Oappend @ SV399 @ SV1020 @ SV1514 ) @ SY4370 @ SV1514 )
= ( c_List_Onth @ SV399 @ SY4370 @ SV1514 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4370 @ ( c_Nat_Osize__class_Osize @ SV399 @ ( tc_List_Olist @ SV1514 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3333]) ).
thf(3937,plain,
! [SV1515: $i,SV1021: $i,SV400: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV400 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV400 ) @ SV1021 ) @ SV1515 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV400 ) @ SV1515 ) @ SV1021 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3334]) ).
thf(3938,plain,
! [SV1516: $i,SV1022: $i,SV401: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV401 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV401 ) @ SV1022 ) @ SV1516 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV401 ) @ SV1516 ) @ SV1022 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3335]) ).
thf(3939,plain,
! [SV1517: $i,SV1023: $i,SV402: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV402 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV402 ) @ SV1023 ) @ SV1517 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV402 ) @ SV1517 ) @ SV1023 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3336]) ).
thf(3940,plain,
! [SV1518: $i,SV1024: $i,SV403: $i] :
( ( ( c_List_Orev @ ( c_List_Oreplicate @ SV403 @ SV1024 @ SV1518 ) @ SV1518 )
= ( c_List_Oreplicate @ SV403 @ SV1024 @ SV1518 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3337]) ).
thf(3941,plain,
! [SV1025: $i,SV404: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV404 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV404 ) @ SV1025 ) @ SV1025 ) @ ( c_HOL_Ozero__class_Ozero @ SV404 ) @ SV404 )
| ~ ( c_HOL_Oord__class_Oless @ SV1025 @ ( c_HOL_Ozero__class_Ozero @ SV404 ) @ SV404 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3338]) ).
thf(3942,plain,
! [SV1026: $i,SV405: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV405 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1026 @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SV405 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV405 ) @ SV1026 ) @ SV1026 ) @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SV405 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3339]) ).
thf(3943,plain,
! [SV1027: $i,SV406: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV406 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1027 @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV406 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV406 ) @ SV1027 ) @ SV1027 ) @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV406 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3340]) ).
thf(3944,plain,
! [SV1028: $i,SV407: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV407 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV407 ) @ SV1028 ) @ SV1028 ) @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 )
| ~ ( c_HOL_Oord__class_Oless @ SV1028 @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3341]) ).
thf(3945,plain,
! [SV1519: $i,SV1029: $i,SV408: $i] :
( ( ! [SY4371: $i] :
( ~ ( c_HOL_Oord__class_Oless @ SV408 @ ( c_Nat_Osize__class_Osize @ SV1029 @ ( tc_List_Olist @ SV1519 ) ) @ tc_nat )
| ( ( c_List_Onth @ ( c_List_Olist__update @ SV1029 @ SV408 @ SY4371 @ SV1519 ) @ SV408 @ SV1519 )
= SY4371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3342]) ).
thf(3946,plain,
! [SV1520: $i,SV1030: $i,SV409: $i] :
( ( ! [SY4372: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ SV409 @ SV1030 @ SV1520 @ SY4372 ) @ SV1030 @ SY4372 )
= SV1520 )
| ~ ( c_HOL_Oord__class_Oless @ SV1030 @ ( c_Nat_Osize__class_Osize @ SV409 @ ( tc_List_Olist @ SY4372 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3343]) ).
thf(3947,plain,
! [SV1521: $i,SV1031: $i,SV410: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV410 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV410 ) @ ( c_Power_Opower__class_Opower @ SV1031 @ SV1521 @ SV410 ) @ SV410 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV410 ) @ SV1031 @ SV410 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3344]) ).
thf(3948,plain,
! [SV1522: $i,SV1032: $i,SV411: $i] :
( ( ( ( c_List_Olast @ ( c_List_Odrop @ SV411 @ SV1032 @ SV1522 ) @ SV1522 )
= ( c_List_Olast @ SV1032 @ SV1522 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV411 @ ( c_Nat_Osize__class_Osize @ SV1032 @ ( tc_List_Olist @ SV1522 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3345]) ).
thf(3949,plain,
! [SV1523: $i,SV1033: $i,SV412: $i] :
( ( ( ( c_List_Otake @ SV412 @ ( c_List_Obutlast @ SV1033 @ SV1523 ) @ SV1523 )
= ( c_List_Otake @ SV412 @ SV1033 @ SV1523 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV412 @ ( c_Nat_Osize__class_Osize @ SV1033 @ ( tc_List_Olist @ SV1523 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3346]) ).
thf(3950,plain,
! [SV1524: $i,SV1034: $i,SV413: $i] :
( ( ! [SY4373: $i,SY4374: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV413 @ SV1034 @ SV1524 ) @ SY4373 @ SY4374 @ SV1524 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV413 @ SY4373 @ SY4374 @ SV1524 ) @ SV1034 @ SV1524 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4373 @ ( c_Nat_Osize__class_Osize @ SV413 @ ( tc_List_Olist @ SV1524 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3347]) ).
thf(3951,plain,
! [SV1525: $i,SV1035: $i,SV414: $i] :
( ( ! [SY4375: $i,SY4376: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV414 @ SV1035 @ SV1525 ) @ SY4375 @ SY4376 @ SV1525 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV414 @ SY4375 @ SY4376 @ SV1525 ) @ SV1035 @ SV1525 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4375 @ ( c_Nat_Osize__class_Osize @ SV414 @ ( tc_List_Olist @ SV1525 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3348]) ).
thf(3952,plain,
! [SV1526: $i,SV1036: $i,SV415: $i] :
( ( ! [SY4377: $i] :
( ( ( c_List_Onth @ ( c_List_Oreplicate @ SV415 @ SV1036 @ SV1526 ) @ SY4377 @ SV1526 )
= SV1036 )
| ~ ( c_HOL_Oord__class_Oless @ SY4377 @ SV415 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3349]) ).
thf(3953,plain,
! [SV1527: $i,SV1037: $i,SV416: $i] :
( ( ! [SY4378: $i,SY4379: $i] :
( ( ( c_List_OtakeWhile @ SV416 @ ( c_List_Oappend @ SV1037 @ ( c_List_Olist_OCons @ SV1527 @ SY4378 @ SY4379 ) @ SY4379 ) @ SY4379 )
= ( c_List_OtakeWhile @ SV416 @ SV1037 @ SY4379 ) )
| ( hBOOL @ ( hAPP @ SV416 @ SV1527 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3350]) ).
thf(3954,plain,
! [SV1038: $i,SV419: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV419 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1038 @ SV1038 @ SV419 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3353]) ).
thf(3955,plain,
! [SV1039: $i,SV420: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV420 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1039 @ SV1039 @ SV420 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3354]) ).
thf(3956,plain,
! [SV1040: $i,SV421: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV421 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1040 @ SV1040 @ SV421 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3355]) ).
thf(3957,plain,
! [SV1528: $i,SV1041: $i,SV422: $i] :
( ( ( ( c_List_Olast @ ( c_List_Oappend @ SV422 @ SV1041 @ SV1528 ) @ SV1528 )
= ( c_List_Olast @ SV1041 @ SV1528 ) )
| ( SV1041
= ( c_List_Olist_ONil @ SV1528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3356]) ).
thf(3958,plain,
! [SV1529: $i,SV1043: $i,SV424: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV424 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SV1043 ) @ SV1529 ) @ SV424 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV1529 @ SV424 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV1043 @ SV424 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3358]) ).
thf(3959,plain,
! [SV1530: $i,SV1044: $i,SV425: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV425 )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SV1044 @ SV1530 @ SV425 ) @ SV425 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV425 ) @ SV1044 ) @ ( c_List_Olistsum @ SV1530 @ SV425 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3359]) ).
thf(3960,plain,
! [SV1531: $i,SV1045: $i,SV426: $i] :
( ( ! [SY4380: $i,SY4381: $i] :
( ( c_List_Omap @ SV426 @ ( c_List_Oappend @ SV1045 @ SV1531 @ SY4380 ) @ SY4380 @ SY4381 )
= ( c_List_Oappend @ ( c_List_Omap @ SV426 @ SV1045 @ SY4380 @ SY4381 ) @ ( c_List_Omap @ SV426 @ SV1531 @ SY4380 @ SY4381 ) @ SY4381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3360]) ).
thf(3961,plain,
! [SV1532: $i,SV1046: $i,SV427: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV427 )
| ( c_HOL_Oord__class_Oless @ SV1046 @ SV1532 @ SV427 )
| ( c_HOL_Oord__class_Oless @ SV1532 @ SV1046 @ SV427 )
| ( SV1532 = SV1046 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3361]) ).
thf(3962,plain,
! [SV1533: $i,SV1047: $i,SV428: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV428 )
| ( SV1047 = SV1533 )
| ( c_HOL_Oord__class_Oless @ SV1533 @ SV1047 @ SV428 )
| ( c_HOL_Oord__class_Oless @ SV1047 @ SV1533 @ SV428 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3362]) ).
thf(3963,plain,
! [SV1048: $i,SV429: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV429 @ SV1048 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1048 @ SV429 @ tc_nat )
| ( SV1048 = SV429 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3363]) ).
thf(3964,plain,
! [SV1534: $i,SV1049: $i,SV430: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV430 @ SV1049 ) @ SV1534 ) )
| ( c_HOL_Oord__class_Oless @ SV1049 @ SV1534 @ tc_nat )
| ( SV1534 = SV1049 )
| ( c_HOL_Oord__class_Oless @ SV1534 @ SV1049 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3364]) ).
thf(3965,plain,
! [SV1050: $i,SV431: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV431 @ SV1050 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1050 @ SV431 @ tc_nat )
| ( SV1050 = SV431 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3365]) ).
thf(3966,plain,
! [SV1535: $i,SV1051: $i,SV432: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV432 )
| ( c_HOL_Oord__class_Oless @ SV1051 @ SV1535 @ SV432 )
| ( c_HOL_Oord__class_Oless @ SV1535 @ SV1051 @ SV432 )
| ( SV1535 = SV1051 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3366]) ).
thf(3967,plain,
! [SV1536: $i,SV1052: $i,SV433: $i] :
( ( ! [SY4382: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV433 @ SV1052 @ SV1536 ) @ ( c_List_Oreplicate @ SY4382 @ SV1052 @ SV1536 ) @ SV1536 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SY4382 @ SV1052 @ SV1536 ) @ ( c_List_Oreplicate @ SV433 @ SV1052 @ SV1536 ) @ SV1536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3367]) ).
thf(3968,plain,
! [SV1537: $i,SV1053: $i,SV434: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV434 )
| ( c_HOL_Oord__class_Oless @ SV1053 @ SV1537 @ SV434 )
| ( SV1537 = SV1053 )
| ( c_HOL_Oord__class_Oless @ SV1537 @ SV1053 @ SV434 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3368]) ).
thf(3969,plain,
! [SV1538: $i,SV1054: $i,SV435: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV435 )
| ( SV1054 = SV1538 )
| ( c_HOL_Oord__class_Oless @ SV1054 @ SV1538 @ SV435 )
| ( c_HOL_Oord__class_Oless @ SV1538 @ SV1054 @ SV435 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3369]) ).
thf(3970,plain,
! [SV1539: $i,SV1055: $i,SV436: $i] :
( ( ! [SY4383: $i,SY4384: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV436 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV436 ) @ SV1055 ) @ SV1539 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV436 ) @ SY4383 ) @ SY4384 ) @ SV436 )
| ~ ( c_HOL_Oord__class_Oless @ SV1539 @ SY4384 @ SV436 )
| ~ ( c_HOL_Oord__class_Oless @ SV1055 @ SY4383 @ SV436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3370]) ).
thf(3971,plain,
! [SV1540: $i,SV1056: $i,SV437: $i] :
( ( ! [SY4385: $i,SY4386: $i] :
( ( ( c_List_Onth @ ( c_List_Omap @ SV437 @ SV1056 @ SV1540 @ SY4385 ) @ SY4386 @ SY4385 )
= ( hAPP @ SV437 @ ( c_List_Onth @ SV1056 @ SY4386 @ SV1540 ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4386 @ ( c_Nat_Osize__class_Osize @ SV1056 @ ( tc_List_Olist @ SV1540 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3371]) ).
thf(3972,plain,
! [SV1541: $i,SV1057: $i,SV438: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV438 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1057 @ SV438 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1541 @ SV438 ) @ SV438 )
| ~ ( c_HOL_Oord__class_Oless @ SV1057 @ SV1541 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3372]) ).
thf(3973,plain,
! [SV1542: $i,SV1058: $i,SV439: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV439 )
| ( c_HOL_Oord__class_Oless @ SV1058 @ SV1542 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1058 @ SV439 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1542 @ SV439 ) @ SV439 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3373]) ).
thf(3974,plain,
! [SV1059: $i,SV440: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV440 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV440 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1059 @ SV440 ) @ SV440 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1059 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3374]) ).
thf(3975,plain,
! [SV1060: $i,SV441: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV441 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1060 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV441 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1060 @ SV441 ) @ SV441 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3375]) ).
thf(3976,plain,
! [SV1062: $i,SV443: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV443 ) )
= $true )
| ( ( ( c_List_Olistsum @ ( c_List_Orev @ SV1062 @ SV443 ) @ SV443 )
= ( c_List_Olistsum @ SV1062 @ SV443 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3377]) ).
thf(3977,plain,
! [SV1543: $i,SV1063: $i,SV444: $i] :
( ( ! [SY4387: $i] :
( ( c_List_Olistsp @ SV444 @ ( c_List_Oappend @ SV1063 @ SV1543 @ SY4387 ) @ SY4387 )
| ~ ( c_List_Olistsp @ SV444 @ SV1543 @ SY4387 )
| ~ ( c_List_Olistsp @ SV444 @ SV1063 @ SY4387 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3378]) ).
thf(3978,plain,
! [SV1544: $i,SV1064: $i,SV445: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Oreplicate @ SV445 @ SV1064 @ SV1544 ) @ ( tc_List_Olist @ SV1544 ) )
= SV445 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3379]) ).
thf(3979,plain,
! [SV1545: $i,SV1065: $i,SV446: $i] :
( ( ( c_List_Olist__update @ SV446 @ SV1065 @ ( c_List_Onth @ SV446 @ SV1065 @ SV1545 ) @ SV1545 )
= SV446 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3380]) ).
thf(3980,plain,
! [SV1546: $i,SV1066: $i,SV447: $i] :
( ( ! [SY4388: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV447 )
| ( c_HOL_Oord__class_Oless @ SV1066 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV447 ) @ SV1546 ) @ SY4388 ) @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ SV1066 @ SY4388 @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV1546 @ SV447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3381]) ).
thf(3981,plain,
! [SV1547: $i,SV1067: $i,SV448: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV448 ) ) @ SV1067 ) @ SV1547 )
= ( c_Lambda_OdB_OVar @ SV448 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV448 @ SV1547 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3382]) ).
thf(3982,plain,
! [SV1548: $i,SV1068: $i,SV449: $i] :
( ( ! [SY4389: $i,SY4390: $i] :
( ~ ( hBOOL @ ( hAPP @ SV449 @ ( c_Lambda_OdB_OdB__case @ SV1068 @ SV1548 @ SY4389 @ ( c_Lambda_OdB_OAbs @ SY4390 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV449 @ ( hAPP @ SY4389 @ SY4390 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3383]) ).
thf(3983,plain,
! [SV1549: $i,SV1069: $i,SV450: $i] :
( ( ! [SY4391: $i,SY4392: $i] :
( ~ ( hBOOL @ ( hAPP @ SV450 @ ( c_Lambda_OdB_OdB__case @ SV1069 @ SV1549 @ SY4391 @ ( c_Lambda_OdB_OAbs @ SY4392 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV450 @ ( hAPP @ SY4391 @ SY4392 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3384]) ).
thf(3984,plain,
! [SV1550: $i,SV1070: $i,SV451: $i] :
( ( ! [SY4393: $i,SY4394: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV451 @ ( c_List_Olist_OCons @ SV1070 @ SV1550 @ SY4393 ) @ SY4393 ) @ ( c_Nat_Osize__class_Osize @ SV451 @ ( tc_List_Olist @ SY4393 ) ) @ SY4394 @ SY4393 )
= ( c_List_Oappend @ SV451 @ ( c_List_Olist_OCons @ SY4394 @ SV1550 @ SY4393 ) @ SY4393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3385]) ).
thf(3985,plain,
! [SV1551: $i,SV1071: $i,SV452: $i] :
( ( ! [SY4395: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV452 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV452 ) @ SV1071 ) @ SV1551 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV452 ) @ SY4395 ) @ SV1551 ) @ SV452 )
| ~ ( c_HOL_Oord__class_Oless @ SV1071 @ SY4395 @ SV452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3386]) ).
thf(3986,plain,
! [SV1552: $i,SV1072: $i,SV453: $i] :
( ( ! [SY4396: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV453 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV453 ) @ SV1072 ) @ SV1552 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV453 ) @ SY4396 ) @ SV1552 ) @ SV453 )
| ~ ( c_HOL_Oord__class_Oless @ SV1072 @ SY4396 @ SV453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3387]) ).
thf(3987,plain,
! [SV1553: $i,SV1073: $i,SV454: $i] :
( ( ! [SY4397: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV454 )
| ( c_HOL_Oord__class_Oless @ SV1073 @ SV1553 @ SV454 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV454 ) @ SV1073 ) @ SY4397 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV454 ) @ SV1553 ) @ SY4397 ) @ SV454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3388]) ).
thf(3988,plain,
! [SV1554: $i,SV1074: $i,SV455: $i] :
( ( ! [SY4398: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV455 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV455 ) @ SV1074 ) @ SV1554 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV455 ) @ SV1074 ) @ SY4398 ) @ SV455 )
| ~ ( c_HOL_Oord__class_Oless @ SV1554 @ SY4398 @ SV455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3389]) ).
thf(3989,plain,
! [SV1555: $i,SV1075: $i,SV456: $i] :
( ( ! [SY4399: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV456 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV456 ) @ SV1075 ) @ SV1555 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV456 ) @ SV1075 ) @ SY4399 ) @ SV456 )
| ~ ( c_HOL_Oord__class_Oless @ SV1555 @ SY4399 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3390]) ).
thf(3990,plain,
! [SV1556: $i,SV1076: $i,SV457: $i] :
( ( ! [SY4400: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV457 )
| ( c_HOL_Oord__class_Oless @ SV1076 @ SV1556 @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SY4400 ) @ SV1076 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SY4400 ) @ SV1556 ) @ SV457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3391]) ).
thf(3991,plain,
! [SV1557: $i,SV1077: $i,SV458: $i] :
( ( ! [SY4401: $i] :
( ( c_Type_Otyping @ SV458 @ SV1077 @ SV1557 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY4401 ) @ SV1077 ) )
| ~ ( c_Type_Otyping @ SV458 @ SY4401 @ SV1557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3392]) ).
thf(3992,plain,
! [SV1558: $i,SV1078: $i,SV459: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV459 )
| ( c_List_Olinorder__class_Osorted @ SV1078 @ SV459 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1078 @ SV1558 @ SV459 ) @ SV459 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3393]) ).
thf(3993,plain,
! [SV1559: $i,SV1079: $i,SV460: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV460 )
| ( c_List_Olinorder__class_Osorted @ SV1079 @ SV460 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1559 @ SV1079 @ SV460 ) @ SV460 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3394]) ).
thf(3994,plain,
! [SV1560: $i,SV1080: $i,SV461: $i] :
( ( ! [SY4402: $i,SY4403: $i,SY4404: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV461 @ SV1080 @ SV1560 @ SY4402 ) @ SY4403 @ SY4404 @ SY4402 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV461 @ SY4403 @ SY4404 @ SY4402 ) @ SV1080 @ SV1560 @ SY4402 ) )
| ( SV1080 = SY4403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3395]) ).
thf(3995,plain,
! [SV1561: $i,SV1081: $i,SV462: $i] :
( ( ! [SY4405: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV462 @ SV1081 @ SV1561 ) @ ( c_List_Olist_OCons @ SV1081 @ SY4405 @ SV1561 ) @ SV1561 )
= ( c_List_Olist_OCons @ SV1081 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV462 @ SV1081 @ SV1561 ) @ SY4405 @ SV1561 ) @ SV1561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3396]) ).
thf(3996,plain,
! [SV1562: $i,SV1082: $i,SV463: $i] :
( ( ! [SY4406: $i,SY4407: $i] :
( ( c_List_Odrop @ SV463 @ ( c_List_Omap @ SV1082 @ SV1562 @ SY4406 @ SY4407 ) @ SY4407 )
= ( c_List_Omap @ SV1082 @ ( c_List_Odrop @ SV463 @ SV1562 @ SY4406 ) @ SY4406 @ SY4407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3397]) ).
thf(3997,plain,
! [SV1563: $i,SV1084: $i,SV465: $i] :
( ( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV465 @ SV1084 @ SV1563 ) @ SV1563 )
= ( c_List_Oappend @ SV465 @ ( c_List_Obutlast @ SV1084 @ SV1563 ) @ SV1563 ) )
| ( SV1084
= ( c_List_Olist_ONil @ SV1563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3399]) ).
thf(3998,plain,
! [SV1564: $i,SV1085: $i,SV466: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV466 )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ SV1085 @ SV1564 @ SV466 ) @ SV466 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV466 ) @ ( c_List_Olistsum @ SV1085 @ SV466 ) ) @ ( c_List_Olistsum @ SV1564 @ SV466 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3400]) ).
thf(3999,plain,
! [SV1565: $i,SV1086: $i,SV467: $i] :
( ( ! [SY4408: $i,SY4409: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ SV467 @ SV1086 @ SV1565 @ SY4408 ) @ SY4409 @ SY4408 )
= ( c_List_Onth @ SV467 @ SY4409 @ SY4408 ) )
| ( SV1086 = SY4409 )
| ~ ( c_HOL_Oord__class_Oless @ SV1086 @ ( c_Nat_Osize__class_Osize @ SV467 @ ( tc_List_Olist @ SY4408 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3401]) ).
thf(4000,plain,
! [SV1566: $i,SV1087: $i,SV468: $i] :
( ( ! [SY4410: $i,SY4411: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV468 @ SV1087 @ SV1566 @ SY4410 ) @ SV1087 @ SY4411 @ SY4410 )
= ( c_List_Olist__update @ SV468 @ SV1087 @ SY4411 @ SY4410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3402]) ).
thf(4001,plain,
! [SV1567: $i,SV1088: $i,SV469: $i] :
( ( ! [SY4412: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV469 @ SV1088 @ SV1567 ) @ SY4412 @ SV1567 )
= ( c_List_Oappend @ SV469 @ ( c_List_Oappend @ SV1088 @ SY4412 @ SV1567 ) @ SV1567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3403]) ).
thf(4002,plain,
! [SV1568: $i,SV1089: $i,SV470: $i] :
( ( ! [SY4413: $i] :
( ( c_List_Oappend @ SV470 @ ( c_List_Oappend @ SV1089 @ SV1568 @ SY4413 ) @ SY4413 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV470 @ SV1089 @ SY4413 ) @ SV1568 @ SY4413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3404]) ).
thf(4003,plain,
! [SV1569: $i,SV1090: $i,SV471: $i] :
( ( ! [SY4414: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV471 @ SV1090 @ SV1569 ) @ SY4414 @ SV1569 )
= ( c_List_Oappend @ SV471 @ ( c_List_Oappend @ SV1090 @ SY4414 @ SV1569 ) @ SV1569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3405]) ).
thf(4004,plain,
! [SV1570: $i,SV1091: $i,SV472: $i] :
( ( ! [SY4415: $i] :
( ( c_List_Oappend @ SV472 @ ( c_List_Oappend @ SV1091 @ SV1570 @ SY4415 ) @ SY4415 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV472 @ SV1091 @ SY4415 ) @ SV1570 @ SY4415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3406]) ).
thf(4005,plain,
! [SV1571: $i,SV1092: $i,SV473: $i] :
( ( ~ ( class_Orderings_Oorder @ SV473 )
| ~ ( c_HOL_Oord__class_Oless @ SV1092 @ SV1571 @ SV473 )
| ~ ( c_HOL_Oord__class_Oless @ SV1571 @ SV1092 @ SV473 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3407]) ).
thf(4006,plain,
! [SV1572: $i,SV1093: $i,SV474: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV474 )
| ~ ( c_HOL_Oord__class_Oless @ SV1093 @ SV1572 @ SV474 )
| ~ ( c_HOL_Oord__class_Oless @ SV1572 @ SV1093 @ SV474 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3408]) ).
thf(4007,plain,
! [SV1573: $i,SV1094: $i,SV475: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV475 )
| ~ ( c_HOL_Oord__class_Oless @ SV1094 @ SV1573 @ SV475 )
| ~ ( c_HOL_Oord__class_Oless @ SV1573 @ SV1094 @ SV475 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3409]) ).
thf(4008,plain,
! [SV1574: $i,SV1095: $i,SV476: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV476 )
| ~ ( c_HOL_Oord__class_Oless @ SV1095 @ SV1574 @ SV476 )
| ~ ( c_HOL_Oord__class_Oless @ SV1574 @ SV1095 @ SV476 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3410]) ).
thf(4009,plain,
! [SV1575: $i,SV1096: $i,SV477: $i] :
( ( ( ( hAPP @ SV477 @ SV1096 )
= SV1575 )
| ~ ( c_Type_Otyping @ SV477 @ ( c_Lambda_OdB_OVar @ SV1096 ) @ SV1575 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3411]) ).
thf(4010,plain,
! [SV1576: $i,SV1097: $i,SV478: $i] :
( ( ! [SY4416: $i,SY4417: $i] :
( ( c_Lambda_OdB_OdB__case @ SV478 @ SV1097 @ SV1576 @ ( c_Lambda_OdB_OVar @ SY4416 ) @ SY4417 )
= ( hAPP @ SV478 @ SY4416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3412]) ).
thf(4011,plain,
! [SV480: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ SV480 @ tc_Lambda_OdB )
= $false )
| ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV480 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3414]) ).
thf(4012,plain,
! [SV481: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV481 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV481 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3415]) ).
thf(4013,plain,
! [SV1577: $i,SV1099: $i,SV482: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV482 ) @ SV1099 ) ) @ SV1577 ) @ SV1099 )
= SV482 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3416]) ).
thf(4014,plain,
! [SV1578: $i,SV1100: $i,SV483: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV483 ) @ SV1100 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1578 ) @ SV1100 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV483 ) @ SV1578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3417]) ).
thf(4015,plain,
! [SV1579: $i,SV1101: $i,SV484: $i] :
( ( ( ( c_List_Osublist @ ( c_List_Olist_OCons @ SV484 @ ( c_List_Olist_ONil @ SV1101 ) @ SV1101 ) @ SV1579 @ SV1101 )
= ( c_List_Olist_OCons @ SV484 @ ( c_List_Olist_ONil @ SV1101 ) @ SV1101 ) )
| ~ ( c_in @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1579 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3418]) ).
thf(4016,plain,
! [SV1580: $i,SV1102: $i,SV485: $i] :
( ( ( ( c_List_Osublist @ ( c_List_Olist_OCons @ SV485 @ ( c_List_Olist_ONil @ SV1102 ) @ SV1102 ) @ SV1580 @ SV1102 )
= ( c_List_Olist_ONil @ SV1102 ) )
| ( c_in @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1580 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3419]) ).
thf(4017,plain,
! [SV1581: $i,SV1103: $i,SV486: $i] :
( ( ( SV486
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1103 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV1103 @ SV1581 @ SV486 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1103 ) @ SV1581 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3420]) ).
thf(4018,plain,
! [SV1582: $i,SV1104: $i,SV487: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV487 @ SV1104 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV1582 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV487 ) @ SV1582 ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ SV1582 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1104 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3421]) ).
thf(4019,plain,
! [SV1105: $i,SV488: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV488 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV488 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV488 )
| ~ ( class_Power_Opower @ SV488 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV488 ) @ SV1105 @ SV488 )
= ( c_HOL_Ozero__class_Ozero @ SV488 ) )
| ( SV1105
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3422]) ).
thf(4020,plain,
! [SV1106: $i,SV489: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV489 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV489 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV1106 @ SV489 )
= ( c_HOL_Ozero__class_Ozero @ SV489 ) )
| ( SV1106
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3423]) ).
thf(4021,plain,
! [SV490: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV490 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV490 )
= ( c_HOL_Ozero__class_Ozero @ SV490 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3424]) ).
thf(4022,plain,
! [SV491: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV491 )
= $false )
| ( ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ SV491 ) @ SV491 )
= ( c_HOL_Ozero__class_Ozero @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3425]) ).
thf(4023,plain,
! [SV1583: $i,SV1107: $i,SV492: $i] :
( ( ( c_List_Onth @ ( c_List_Olist_OCons @ SV492 @ SV1107 @ SV1583 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1583 )
= SV492 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3426]) ).
thf(4024,plain,
! [SV1584: $i,SV1108: $i,SV493: $i] :
( ( ( c_List_Odrop @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ SV493 @ SV1108 @ SV1584 ) @ SV1584 )
= ( c_List_Olist_OCons @ SV493 @ SV1108 @ SV1584 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3427]) ).
thf(4025,plain,
! [SV1585: $i,SV1109: $i,SV494: $i] :
( ( ! [SY4418: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV494 @ SV1109 @ SV1585 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY4418 @ SV1585 )
= ( c_List_Olist_OCons @ SY4418 @ SV1109 @ SV1585 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3428]) ).
thf(4026,plain,
! [SV1586: $i,SV1115: $i,SV502: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV502 ) @ ( c_List_Olist_OCons @ SV1115 @ SV1586 @ SV502 ) @ SV502 )
= ( c_List_Olist_OCons @ SV1115 @ SV1586 @ SV502 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3434]) ).
thf(4027,plain,
! [SV1587: $i,SV1116: $i,SV503: $i] :
( ( ! [SY4419: $i] :
( ~ ( class_Orderings_Olinorder @ SV503 )
| ( ( c_List_Olinorder__class_Oinsort__key @ SV1116 @ SV1587 @ ( c_List_Olist_ONil @ SY4419 ) @ SY4419 @ SV503 )
= ( c_List_Olist_OCons @ SV1587 @ ( c_List_Olist_ONil @ SY4419 ) @ SY4419 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3435]) ).
thf(4028,plain,
! [SV1588: $i,SV1117: $i,SV504: $i] :
( ( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV504 @ SV1117 @ SV1588 ) @ SV1588 )
= ( c_List_Olist_OCons @ SV504 @ ( c_List_Obutlast @ SV1117 @ SV1588 ) @ SV1588 ) )
| ( SV1117
= ( c_List_Olist_ONil @ SV1588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3436]) ).
thf(4029,plain,
! [SV1589: $i,SV1120: $i,SV507: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV507 @ SV1120 @ SV1589 ) @ ( c_List_Olist_ONil @ SV1589 ) @ SV1589 )
= ( c_List_Olist_OCons @ SV507 @ SV1120 @ SV1589 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3439]) ).
thf(4030,plain,
! [SV1590: $i,SV1121: $i,SV508: $i] :
( ( ! [SY4420: $i] :
( ( ( c_List_OtakeWhile @ SV508 @ ( c_List_Olist_OCons @ SV1121 @ SV1590 @ SY4420 ) @ SY4420 )
= ( c_List_Olist_ONil @ SY4420 ) )
| ( hBOOL @ ( hAPP @ SV508 @ SV1121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3440]) ).
thf(4031,plain,
! [SV1591: $i,SV1123: $i,SV510: $i] :
( ( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV510 @ SV1123 @ SV1591 ) @ SV1591 )
= ( c_List_Olast @ SV1123 @ SV1591 ) )
| ( SV1123
= ( c_List_Olist_ONil @ SV1591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3442]) ).
thf(4032,plain,
! [SV1592: $i,SV1124: $i,SV511: $i] :
( ( ( c_List_Olist_OCons @ SV511 @ SV1124 @ SV1592 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV1592 ) @ ( c_List_Olist_OCons @ SV511 @ SV1124 @ SV1592 ) @ SV1592 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3443]) ).
thf(4033,plain,
! [SV1126: $i,SV513: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV513 ) )
= $true )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1126 @ ( c_List_Olist_ONil @ SV513 ) @ SV513 ) @ SV513 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3445]) ).
thf(4034,plain,
! [SV1593: $i,SV1127: $i,SV514: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV514 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1127 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ ( c_HOL_Ozero__class_Ozero @ SV514 ) @ SV1593 @ SV514 @ SV514 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1127 @ SV1593 @ SV514 @ SV514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3446]) ).
thf(4035,plain,
! [SV1594: $i,SV1128: $i,SV517: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV517 @ SV1128 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1594 @ SV1128 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV517 ) @ SV1594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3447]) ).
thf(4036,plain,
! [SV1595: $i,SV1129: $i,SV518: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV518 ) ) @ SV1129 ) @ SV1595 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1129 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV518 ) @ SV1129 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1595 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3448]) ).
thf(4037,plain,
! [SV1596: $i,SV1130: $i,SV519: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV519 ) @ ( c_Lambda_OdB_OVar @ SV1130 ) ) @ SV1596 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3449]) ).
thf(4038,plain,
! [SV1131: $i,SV520: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV520 ) ) @ SV1131 )
= ( c_Lambda_OdB_OVar @ SV520 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV520 @ SV1131 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3450]) ).
thf(4039,plain,
! [SV1597: $i,SV1132: $i,SV521: $i] :
( ( ( c_List_Otake @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_List_Olist_OCons @ SV521 @ SV1132 @ SV1597 ) @ SV1597 )
= ( c_List_Olist_ONil @ SV1597 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3451]) ).
thf(4040,plain,
! [SV1598: $i,SV1133: $i,SV522: $i] :
( ( ! [SY4421: $i,SY4422: $i] :
( ( SV522 = SV1133 )
| ~ ( c_Type_Otyping @ SV1598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY4421 ) @ SY4422 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1133 )
| ~ ( c_Type_Otyping @ SV1598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY4421 ) @ SY4422 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3452]) ).
thf(4041,plain,
! [SV1134: $i,SV525: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV525 ) @ SV1134 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV1134 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3453]) ).
thf(4042,plain,
! [SV1599: $i,SV1135: $i,SV526: $i] :
( ( ( ( c_List_Oappend @ SV526 @ ( c_List_Olist_OCons @ SV1135 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1599 @ SV526 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV1135 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1599 @ ( c_List_Oappend @ SV526 @ ( c_List_Olist_OCons @ SV1135 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3454]) ).
thf(4043,plain,
! [SV1600: $i,SV1136: $i,SV527: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV527 @ SV1136 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV1600 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV527 @ ( c_List_Oappend @ SV1136 @ ( c_List_Olist_OCons @ SV1600 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3455]) ).
thf(4044,plain,
! [SV1138: $i,SV529: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV529 ) @ SV1138 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV529 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3457]) ).
thf(4045,plain,
! [SV1601: $i,SV1139: $i,SV530: $i] :
( ( ! [SY4423: $i] :
( ( c_List_Ofoldl @ SV530 @ SV1139 @ ( c_List_Olist_ONil @ SV1601 ) @ SY4423 @ SV1601 )
= SV1139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3458]) ).
thf(4046,plain,
! [SV1602: $i,SV1140: $i,SV532: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV532 ) @ SV1140 ) ) @ SV1602 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV532 ) @ SV1602 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1140 ) @ SV1602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3459]) ).
thf(4047,plain,
! [SV1603: $i,SV1141: $i,SV534: $i] :
( ( ! [SY4424: $i,SY4425: $i,SY4426: $i] :
( ( c_List_Ofoldl @ SV534 @ SV1141 @ ( c_List_Olist_OCons @ SV1603 @ SY4424 @ SY4425 ) @ SY4426 @ SY4425 )
= ( c_List_Ofoldl @ SV534 @ ( hAPP @ ( hAPP @ SV534 @ SV1141 ) @ SV1603 ) @ SY4424 @ SY4426 @ SY4425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3460]) ).
thf(4048,plain,
! [SV1142: $i,SV535: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV535 ) @ ( c_Lambda_OdB_OVar @ SV1142 ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV535 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3461]) ).
thf(4049,plain,
! [SV1143: $i,SV536: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV536 @ SV1143 ) )
= $true )
| ( ( ~ ( class_Orderings_Opreorder @ SV1143 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3462]) ).
thf(4050,plain,
! [SV1144: $i,SV537: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV537 @ SV1144 ) )
= $true )
| ( ( ~ ( class_Orderings_Oorder @ SV1144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3463]) ).
thf(4051,plain,
! [SV1604: $i,SV1146: $i,SV539: $i] :
( ( ( SV539 = SV1146 )
| ~ ( c_fequal @ SV539 @ SV1146 @ SV1604 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3465]) ).
thf(4052,plain,
! [SV1147: $i,SV540: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV540 )
!= ( c_Lambda_OdB_OAbs @ SV1147 ) )
= $true )
| ( ( SV540 = SV1147 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3466]) ).
thf(4053,plain,
! [SV1605: $i,SV1148: $i,SV541: $i] :
( ( ! [SY4427: $i,SY4428: $i] :
( ( ( c_List_Oreplicate @ SV541 @ SV1148 @ SV1605 )
!= ( c_List_Oreplicate @ SY4427 @ SY4428 @ SV1605 ) )
| ( SV541 = SY4427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3467]) ).
thf(4054,plain,
! [SV1606: $i,SV1149: $i,SV542: $i] :
( ( ( SV542
!= ( c_List_Oappend @ SV1149 @ SV542 @ SV1606 ) )
| ( SV1149
= ( c_List_Olist_ONil @ SV1606 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3468]) ).
thf(4055,plain,
! [SV1607: $i,SV1150: $i,SV543: $i] :
( ( ! [SY4429: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV543 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV543 ) @ SV1150 ) @ SV1607 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV543 ) @ SY4429 ) @ SV1607 ) )
| ( SV1150 = SY4429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3469]) ).
thf(4056,plain,
! [SV1608: $i,SV1151: $i,SV544: $i] :
( ( ( c_List_Olist_OCons @ SV544 @ SV1151 @ SV1608 )
!= ( c_List_Olist_ONil @ SV1608 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3470]) ).
thf(4057,plain,
! [SV1609: $i,SV1152: $i,SV545: $i] :
( ( ( ( c_List_Odrop @ SV545 @ SV1152 @ SV1609 )
!= ( c_List_Olist_ONil @ SV1609 ) )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1152 @ ( tc_List_Olist @ SV1609 ) ) @ SV545 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3471]) ).
thf(4058,plain,
! [SV1153: $i,SV546: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV546 )
!= ( c_Lambda_OdB_OVar @ SV1153 ) )
= $true )
| ( ( SV546 = SV1153 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3472]) ).
thf(4059,plain,
! [SV1610: $i,SV1154: $i,SV547: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV547 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1154 @ SV1610 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV547 )
= SV1154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3473]) ).
thf(4060,plain,
! [SV1155: $i,SV548: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV548 )
= ( c_Lambda_OdB_OVar @ SV1155 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3474]) ).
thf(4061,plain,
! [SV1611: $i,SV1156: $i,SV549: $i] :
( ( ( SV549
!= ( c_List_Oappend @ SV549 @ SV1156 @ SV1611 ) )
| ( SV1156
= ( c_List_Olist_ONil @ SV1611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3475]) ).
thf(4062,plain,
! [SV1612: $i,SV1157: $i,SV550: $i] :
( ( ! [SY4430: $i,SY4431: $i] :
( ( ( c_List_Oappend @ SV550 @ ( c_List_Olist_OCons @ SV1157 @ ( c_List_Olist_ONil @ SV1612 ) @ SV1612 ) @ SV1612 )
!= ( c_List_Oappend @ SY4430 @ ( c_List_Olist_OCons @ SY4431 @ ( c_List_Olist_ONil @ SV1612 ) @ SV1612 ) @ SV1612 ) )
| ( SV550 = SY4430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3476]) ).
thf(4063,plain,
! [SV1613: $i,SV1158: $i,SV551: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV551 ) @ SV1158 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1613 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV551 ) @ SV1158 )
= SV1613 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3477]) ).
thf(4064,plain,
! [SV1614: $i,SV1159: $i,SV552: $i] :
( ( ! [SY4432: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV552 ) @ SV1159 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1614 @ SY4432 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY4432
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV552 @ SV1159 @ SV1614 @ SY4432 ) @ ( c_List_Olist_OCons @ SV1159 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SY4432
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3478]) ).
thf(4065,plain,
! [SV1615: $i,SV1160: $i,SV553: $i] :
( ( ! [SY4433: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV553 ) @ SV1160 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1615 ) @ SY4433 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV553 = SV1615 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3479]) ).
thf(4066,plain,
! [SV1616: $i,SV1161: $i,SV554: $i] :
( ( ! [SY4434: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV554 )
| ( ( c_Power_Opower__class_Opower @ SV1161 @ SV1616 @ SV554 )
!= ( c_Power_Opower__class_Opower @ SY4434 @ SV1616 @ SV554 ) )
| ( SV1161 = SY4434 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1616 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SY4434 @ SV554 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SV1161 @ SV554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3480]) ).
thf(4067,plain,
! [SV1617: $i,SV1162: $i,SV555: $i] :
( ( ( c_List_Olist_ONil @ SV555 )
!= ( c_List_Olist_OCons @ SV1162 @ SV1617 @ SV555 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3481]) ).
thf(4068,plain,
! [SV1163: $i,SV557: $i] :
( ( ( ( c_Suc @ SV557 )
!= ( c_Suc @ SV1163 ) )
= $true )
| ( ( SV557 = SV1163 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3483]) ).
thf(4069,plain,
! [SV1618: $i,SV1164: $i,SV558: $i] :
( ( ! [SY4435: $i] :
( ( ( c_List_Oappend @ SV558 @ SV1164 @ SV1618 )
!= ( c_List_Oappend @ SV558 @ SY4435 @ SV1618 ) )
| ( SV1164 = SY4435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3484]) ).
thf(4070,plain,
! [SV1619: $i,SV1165: $i,SV559: $i] :
( ( ! [SY4436: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV559 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1165 @ SV1619 @ SV559 )
!= ( c_HOL_Ominus__class_Ominus @ SY4436 @ SY4436 @ SV559 ) )
| ( SV1165 = SV1619 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3485]) ).
thf(4071,plain,
! [SV1620: $i,SV1166: $i,SV560: $i] :
( ( ! [SY4437: $i] :
( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV560 @ ( tc_List_Olist @ SV1166 ) ) @ SV1620 @ SV1166 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1620 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) @ SY4437 @ SV1166 ) @ SV1166 )
!= SY4437 )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV560 @ ( tc_List_Olist @ SV1166 ) ) @ SV1620 @ SV1166 )
!= SV560 )
| ( SV1620
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV1620 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) )
| ( ( c_List_Oappend @ SV1620 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1620 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) @ SY4437 @ SV1166 ) @ SV1166 )
= ( c_List_Oappend @ SV560 @ SY4437 @ SV1166 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3486]) ).
thf(4072,plain,
! [SV1167: $i,SV561: $i] :
( ( ( ( c_Suc @ SV561 )
!= ( c_Suc @ SV1167 ) )
= $true )
| ( ( SV561 = SV1167 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3487]) ).
thf(4073,plain,
! [SV1621: $i,SV1168: $i,SV562: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV562 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1168 @ SV1621 @ SV562 )
!= ( c_HOL_Ozero__class_Ozero @ SV562 ) )
| ( SV1168 = SV1621 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3488]) ).
thf(4074,plain,
! [SV1622: $i,SV1169: $i,SV563: $i] :
( ( ( ( c_List_Olist_ONil @ SV563 )
!= ( c_List_Oappend @ SV1169 @ SV1622 @ SV563 ) )
| ( SV1622
= ( c_List_Olist_ONil @ SV563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3489]) ).
thf(4075,plain,
! [SV1623: $i,SV1170: $i,SV564: $i] :
( ( ! [SY4438: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV564 ) @ SV1170 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1623 ) @ SY4438 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1170 = SY4438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3490]) ).
thf(4076,plain,
! [SV1624: $i,SV1171: $i,SV565: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV565 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1171 @ SV1624 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1624
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3491]) ).
thf(4077,plain,
! [SV1625: $i,SV1172: $i,SV566: $i] :
( ( ( c_Lambda_OdB_OVar @ SV566 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1172 ) @ SV1625 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3492]) ).
thf(4078,plain,
! [SV1626: $i,SV1173: $i,SV567: $i] :
( ( ( c_List_Olist_OCons @ SV567 @ SV1173 @ SV1626 )
!= ( c_List_Olist_ONil @ SV1626 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3493]) ).
thf(4079,plain,
! [SV568: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV568 )
= $false )
| ( ( ( c_HOL_Oone__class_Oone @ SV568 )
!= ( c_HOL_Ozero__class_Ozero @ SV568 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3494]) ).
thf(4080,plain,
! [SV1627: $i,SV1174: $i,SV569: $i] :
( ( ! [SY4439: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV569 ) @ SV1174 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1627 ) @ SY4439 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV569 = SV1627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3495]) ).
thf(4081,plain,
! [SV1628: $i,SV1175: $i,SV570: $i] :
( ( ! [SY4440: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV570 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV570 ) @ SV1175 ) @ SV1628 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV570 ) @ SV1175 ) @ SY4440 ) )
| ( SV1628 = SY4440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3496]) ).
thf(4082,plain,
! [SV1629: $i,SV1176: $i,SV571: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV571 ) @ SV1176 )
!= ( c_Lambda_OdB_OVar @ SV1629 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3497]) ).
thf(4083,plain,
! [SV1630: $i,SV1177: $i,SV572: $i] :
( ( ! [SY4441: $i] :
( ( ( c_List_Oappend @ SV572 @ SV1177 @ SV1630 )
!= ( c_List_Oappend @ SY4441 @ SV1177 @ SV1630 ) )
| ( SV572 = SY4441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3498]) ).
thf(4084,plain,
! [SV1631: $i,SV1178: $i,SV573: $i] :
( ( ! [SY4442: $i,SY4443: $i] :
( ( ( c_List_Oappend @ SV573 @ ( c_List_Olist_OCons @ SV1178 @ ( c_List_Olist_ONil @ SV1631 ) @ SV1631 ) @ SV1631 )
!= ( c_List_Oappend @ SY4442 @ ( c_List_Olist_OCons @ SY4443 @ ( c_List_Olist_ONil @ SV1631 ) @ SV1631 ) @ SV1631 ) )
| ( SV1178 = SY4443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3499]) ).
thf(4085,plain,
! [SV1632: $i,SV1179: $i,SV574: $i] :
( ( ! [SY4444: $i,SY4445: $i] :
( ( ( c_List_Oappend @ SV574 @ SV1179 @ SV1632 )
!= ( c_List_Oappend @ SY4444 @ SY4445 @ SV1632 ) )
| ( SV1179
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV574 @ ( tc_List_Olist @ SV1632 ) ) @ SY4444 @ SV1632 ) @ SY4445 @ SV1632 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV574 @ ( tc_List_Olist @ SV1632 ) ) @ ( c_Nat_Osize__class_Osize @ SY4444 @ ( tc_List_Olist @ SV1632 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3500]) ).
thf(4086,plain,
! [SV1633: $i,SV1180: $i,SV575: $i] :
( ( ( ( c_List_Olist_OCons @ SV575 @ ( c_List_Olist_ONil @ SV1180 ) @ SV1180 )
!= ( c_List_Orev @ SV1633 @ SV1180 ) )
| ( SV1633
= ( c_List_Olist_OCons @ SV575 @ ( c_List_Olist_ONil @ SV1180 ) @ SV1180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3501]) ).
thf(4087,plain,
! [SV1634: $i,SV1181: $i,SV576: $i] :
( ( ! [SY4446: $i] :
( ( ( c_List_Orev @ SV576 @ SV1181 )
!= ( c_List_Olist_OCons @ SV1634 @ SY4446 @ SV1181 ) )
| ( SV576
= ( c_List_Oappend @ ( c_List_Orev @ SY4446 @ SV1181 ) @ ( c_List_Olist_OCons @ SV1634 @ ( c_List_Olist_ONil @ SV1181 ) @ SV1181 ) @ SV1181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3502]) ).
thf(4088,plain,
! [SV1635: $i,SV1182: $i,SV577: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV577 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV577 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV577 )
| ~ ( class_Power_Opower @ SV577 )
| ( ( c_Power_Opower__class_Opower @ SV1182 @ SV1635 @ SV577 )
!= ( c_HOL_Ozero__class_Ozero @ SV577 ) )
| ( SV1182
= ( c_HOL_Ozero__class_Ozero @ SV577 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3503]) ).
thf(4089,plain,
! [SV1636: $i,SV1183: $i,SV578: $i] :
( ( ! [SY4447: $i,SY4448: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV578 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1183 @ SV1636 @ SV578 )
!= ( c_HOL_Ominus__class_Ominus @ SY4447 @ SY4448 @ SV578 ) )
| ( c_HOL_Oord__class_Oless @ SY4447 @ SY4448 @ SV578 )
| ~ ( c_HOL_Oord__class_Oless @ SV1183 @ SV1636 @ SV578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3504]) ).
thf(4090,plain,
! [SV1637: $i,SV1184: $i,SV580: $i] :
( ( ! [SY4449: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ SV580 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Onth @ ( c_List_Olist_OCons @ SV1184 @ SV1637 @ SY4449 ) @ ( c_Int_Onumber__class_Onumber__of @ SV580 @ tc_nat ) @ SY4449 )
= SV1184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3506]) ).
thf(4091,plain,
! [SV581: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV581 )
= $false )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV581 )
!= ( c_HOL_Oone__class_Oone @ SV581 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3507]) ).
thf(4092,plain,
! [SV1638: $i,SV1185: $i,SV582: $i] :
( ( ! [SY4450: $i,SY4451: $i] :
( ( ( c_List_Olist_OCons @ SV582 @ SV1185 @ SV1638 )
!= ( c_List_Olist_OCons @ SY4450 @ SY4451 @ SV1638 ) )
| ( SV1185 = SY4451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3508]) ).
thf(4093,plain,
! [SV1639: $i,SV1186: $i,SV583: $i] :
( ( ( ( c_List_Oappend @ SV583 @ SV1186 @ SV1639 )
!= ( c_List_Olist_ONil @ SV1639 ) )
| ( SV583
= ( c_List_Olist_ONil @ SV1639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3509]) ).
thf(4094,plain,
! [SV1640: $i,SV1187: $i,SV584: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV584 )
| ( ( c_Power_Opower__class_Opower @ SV1187 @ SV1640 @ SV584 )
!= ( c_HOL_Ozero__class_Ozero @ SV584 ) )
| ( SV1187
= ( c_HOL_Ozero__class_Ozero @ SV584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3510]) ).
thf(4095,plain,
! [SV1641: $i,SV1188: $i,SV585: $i] :
( ( ! [SY4452: $i] :
( ( ( c_List_OtakeWhile @ SV585 @ SV1188 @ SV1641 )
!= SV1188 )
| ( hBOOL @ ( hAPP @ SV585 @ SY4452 ) )
| ~ ( c_in @ SY4452 @ ( c_List_Oset @ SV1188 @ SV1641 ) @ SV1641 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3511]) ).
thf(4096,plain,
! [SV1642: $i,SV1189: $i,SV586: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV586 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1189 ) @ SV1642 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3512]) ).
thf(4097,plain,
! [SV1643: $i,SV1190: $i,SV587: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV587 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1190 @ SV1643 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV587 )
= SV1190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3513]) ).
thf(4098,plain,
! [SV1644: $i,SV1191: $i,SV588: $i] :
( ( ! [SY4453: $i] :
( ( ( c_List_Olist_ONil @ SV588 )
!= ( c_List_Omap @ SV1191 @ SV1644 @ SY4453 @ SV588 ) )
| ( SV1644
= ( c_List_Olist_ONil @ SY4453 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3514]) ).
thf(4099,plain,
! [SV1645: $i,SV1192: $i,SV589: $i] :
( ( ( ( c_List_Olist_ONil @ SV589 )
!= ( c_List_Oappend @ SV1192 @ SV1645 @ SV589 ) )
| ( SV1192
= ( c_List_Olist_ONil @ SV589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3515]) ).
thf(4100,plain,
! [SV1193: $i,SV590: $i] :
( ( ( ( c_List_Olist_ONil @ SV590 )
!= ( c_List_Orev @ SV1193 @ SV590 ) )
= $true )
| ( ( SV1193
= ( c_List_Olist_ONil @ SV590 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3516]) ).
thf(4101,plain,
! [SV1646: $i,SV1194: $i,SV591: $i] :
( ( ( ( c_List_Otake @ SV591 @ SV1194 @ SV1646 )
!= ( c_List_Olist_ONil @ SV1646 ) )
| ( SV1194
= ( c_List_Olist_ONil @ SV1646 ) )
| ( SV591
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3517]) ).
thf(4102,plain,
! [SV1647: $i,SV1195: $i,SV592: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV592 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1195 @ SV1647 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1647
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3518]) ).
thf(4103,plain,
! [SV1196: $i,SV593: $i] :
( ( ( ( c_List_Orev @ SV593 @ SV1196 )
!= ( c_List_Olist_ONil @ SV1196 ) )
= $true )
| ( ( SV593
= ( c_List_Olist_ONil @ SV1196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3519]) ).
thf(4104,plain,
! [SV1648: $i,SV1197: $i,SV594: $i] :
( ( ! [SY4454: $i,SY4455: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV594 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1197 @ SV1648 @ SV594 )
!= ( c_HOL_Ominus__class_Ominus @ SY4454 @ SY4455 @ SV594 ) )
| ( c_HOL_Oord__class_Oless @ SV1197 @ SV1648 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SY4454 @ SY4455 @ SV594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3520]) ).
thf(4105,plain,
! [SV1649: $i,SV1198: $i,SV595: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV595 @ SV1198 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV1649 ) )
| ( SV595
= ( c_Lambda_OdB_OAbs @ SV1649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3521]) ).
thf(4106,plain,
! [SV1650: $i,SV1199: $i,SV596: $i] :
( ( ! [SY4456: $i,SY4457: $i] :
( ( ( c_List_Oappend @ SV596 @ SV1199 @ SV1650 )
!= ( c_List_Oappend @ SY4456 @ SY4457 @ SV1650 ) )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SY4456 @ ( tc_List_Olist @ SV1650 ) ) @ SV596 @ SV1650 )
= SY4456 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV596 @ ( tc_List_Olist @ SV1650 ) ) @ ( c_Nat_Osize__class_Osize @ SY4456 @ ( tc_List_Olist @ SV1650 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3522]) ).
thf(4107,plain,
! [SV1651: $i,SV1200: $i,SV597: $i] :
( ( ( c_List_Olist_OCons @ SV597 @ SV1200 @ SV1651 )
!= SV1200 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3523]) ).
thf(4108,plain,
! [SV1652: $i,SV1201: $i,SV598: $i] :
( ( ( SV598
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV598 @ ( tc_List_Olist @ SV1201 ) ) @ SV1652 @ SV1201 ) )
| ( ( c_List_Oappend @ SV598 @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV598 @ ( tc_List_Olist @ SV1201 ) ) @ SV1652 @ SV1201 ) @ SV1201 )
= SV1652 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3524]) ).
thf(4109,plain,
! [SV1653: $i,SV1202: $i,SV599: $i] :
( ( ! [SY4458: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ SV599 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ SV599 @ tc_nat ) @ ( c_List_Olist_OCons @ SV1202 @ SV1653 @ SY4458 ) @ SY4458 )
= ( c_List_Olist_OCons @ SV1202 @ SV1653 @ SY4458 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3525]) ).
thf(4110,plain,
! [SV1654: $i,SV1203: $i,SV600: $i] :
( ( ( ( c_List_Orev @ SV600 @ SV1203 )
!= ( c_List_Orev @ SV1654 @ SV1203 ) )
| ( SV600 = SV1654 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3526]) ).
thf(4111,plain,
! [SV1655: $i,SV1204: $i,SV601: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV601 @ SV1204 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV1655 ) )
| ( SV1204
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3527]) ).
thf(4112,plain,
! [SV1656: $i,SV1205: $i,SV603: $i] :
( ( ! [SY4459: $i] :
( ( SV603
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV603 @ ( tc_List_Olist @ SV1205 ) ) @ SV1656 @ SV1205 ) )
| ( ( c_List_Oappend @ SV603 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV603 @ ( tc_List_Olist @ SV1205 ) ) @ SV1656 @ SV1205 ) @ SY4459 @ SV1205 ) @ SV1205 )
= ( c_List_Oappend @ SV1656 @ SY4459 @ SV1205 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV603 @ ( tc_List_Olist @ SV1205 ) ) @ ( c_Nat_Osize__class_Osize @ SV1656 @ ( tc_List_Olist @ SV1205 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3529]) ).
thf(4113,plain,
! [SV1657: $i,SV1206: $i,SV604: $i] :
( ( ( ( c_List_Olist_ONil @ SV604 )
!= ( c_List_Oreplicate @ SV1206 @ SV1657 @ SV604 ) )
| ( SV1206
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3530]) ).
thf(4114,plain,
! [SV1658: $i,SV1207: $i,SV605: $i] :
( ( ( ( c_List_Oappend @ SV605 @ SV1207 @ SV1658 )
!= SV1207 )
| ( SV605
= ( c_List_Olist_ONil @ SV1658 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3531]) ).
thf(4115,plain,
! [SV1208: $i,SV606: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV606 @ SV1208 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV606 @ SV1208 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3532]) ).
thf(4116,plain,
! [SV1659: $i,SV1209: $i,SV607: $i] :
( ( ! [SY4460: $i,SY4461: $i,SY4462: $i] :
( ( ( c_List_Omap @ SV607 @ SV1209 @ SV1659 @ SY4460 )
!= ( c_List_Omap @ SY4461 @ SV1209 @ SV1659 @ SY4460 ) )
| ( ( hAPP @ SV607 @ SY4462 )
= ( hAPP @ SY4461 @ SY4462 ) )
| ~ ( c_in @ SY4462 @ ( c_List_Oset @ SV1209 @ SV1659 ) @ SV1659 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3533]) ).
thf(4117,plain,
! [SV1660: $i,SV1210: $i,SV608: $i] :
( ( ! [SY4463: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV608 ) @ SV1210 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1660 ) @ SY4463 ) )
| ( SV608 = SV1660 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3534]) ).
thf(4118,plain,
! [SV1661: $i,SV1211: $i,SV609: $i] :
( ( ! [SY4464: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV609 ) @ SV1211 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1661 ) @ SY4464 ) )
| ( SV1211 = SY4464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3535]) ).
thf(4119,plain,
! [SV1662: $i,SV1212: $i,SV610: $i] :
( ( ( ( c_List_Oappend @ SV610 @ SV1212 @ SV1662 )
!= ( c_List_Olist_ONil @ SV1662 ) )
| ( SV1212
= ( c_List_Olist_ONil @ SV1662 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3536]) ).
thf(4120,plain,
! [SV1663: $i,SV1213: $i,SV611: $i] :
( ( ~ ( class_Nat_Osemiring__char__0 @ SV611 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1213 @ SV611 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1663 @ SV611 ) )
| ( SV1213 = SV1663 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3537]) ).
thf(4121,plain,
! [SV1664: $i,SV1214: $i,SV612: $i] :
( ( ~ ( class_OrderedGroup_Ogroup__add @ SV612 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1214 @ SV1664 @ SV612 )
!= ( c_HOL_Ozero__class_Ozero @ SV612 ) )
| ( SV1214 = SV1664 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3538]) ).
thf(4122,plain,
! [SV1665: $i,SV1215: $i,SV613: $i] :
( ( ! [SY4465: $i,SY4466: $i] :
( ( ( c_List_Odrop @ SV613 @ SV1215 @ SV1665 )
!= ( c_List_Olist_OCons @ SY4465 @ SY4466 @ SV1665 ) )
| ( ( c_List_Onth @ SV1215 @ SV613 @ SV1665 )
= SY4465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3539]) ).
thf(4123,plain,
! [SV1666: $i,SV1216: $i,SV614: $i] :
( ( ! [SY4467: $i,SY4468: $i] :
( ( ( c_List_Oappend @ SV614 @ SV1216 @ SV1666 )
!= ( c_List_Oappend @ SY4467 @ SY4468 @ SV1666 ) )
| ( SV614
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV614 @ ( tc_List_Olist @ SV1666 ) ) @ SY4467 @ SV1666 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV614 @ ( tc_List_Olist @ SV1666 ) ) @ ( c_Nat_Osize__class_Osize @ SY4467 @ ( tc_List_Olist @ SV1666 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3540]) ).
thf(4124,plain,
! [SV1667: $i,SV1217: $i,SV615: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV615 )
| ~ ( class_Int_Onumber__ring @ SV615 )
| ( SV1217
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV615 ) @ SV1217 ) @ SV1667 ) )
| ( SV1667
= ( c_HOL_Ozero__class_Ozero @ SV615 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3541]) ).
thf(4125,plain,
! [SV1218: $i,SV616: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV616 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV616 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV616 )
| ~ ( class_Power_Opower @ SV616 )
| ( ( c_Power_Opower__class_Opower @ SV1218 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV616 )
!= ( c_HOL_Ozero__class_Ozero @ SV616 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3542]) ).
thf(4126,plain,
! [SV1668: $i,SV1219: $i,SV617: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV617 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV617 ) @ SV1219 ) @ SV1668 )
!= ( c_HOL_Ozero__class_Ozero @ SV617 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV617 ) @ SV1668 @ SV617 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV617 ) @ SV1219 @ SV617 )
| ( SV1668
= ( c_HOL_Ozero__class_Ozero @ SV617 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3543]) ).
thf(4127,plain,
! [SV1669: $i,SV1220: $i,SV618: $i] :
( ( ! [SY4469: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV618 )
| ( ( c_Power_Opower__class_Opower @ SV1220 @ SV1669 @ SV618 )
!= ( c_Power_Opower__class_Opower @ SV1220 @ SY4469 @ SV618 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV618 ) @ SV1220 @ SV618 )
| ( SV1669 = SY4469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3544]) ).
thf(4128,plain,
! [SV1670: $i,SV1221: $i,SV619: $i] :
( ( ( ( c_List_Oreplicate @ SV619 @ SV1221 @ SV1670 )
!= ( c_List_Olist_ONil @ SV1670 ) )
| ( SV619
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3545]) ).
thf(4129,plain,
! [SV1671: $i,SV1222: $i,SV620: $i] :
( ( SV620
!= ( c_List_Olist_OCons @ SV1222 @ SV620 @ SV1671 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3546]) ).
thf(4130,plain,
! [SV1672: $i,SV1223: $i,SV621: $i] :
( ( ! [SY4470: $i,SY4471: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV621 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1223 @ SV1672 @ SV621 )
!= ( c_HOL_Ominus__class_Ominus @ SY4470 @ SY4471 @ SV621 ) )
| ( c_lessequals @ SV1672 @ SV1223 @ SV621 )
| ~ ( c_lessequals @ SY4471 @ SY4470 @ SV621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3547]) ).
thf(4131,plain,
! [SV1673: $i,SV1224: $i,SV622: $i] :
( ( ! [SY4472: $i,SY4473: $i] :
( ( ( c_List_Oreplicate @ SV622 @ SV1224 @ SV1673 )
!= ( c_List_Oreplicate @ SY4472 @ SY4473 @ SV1673 ) )
| ( SV1224 = SY4473 )
| ( SV622
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3548]) ).
thf(4132,plain,
! [SV1674: $i,SV1225: $i,SV623: $i] :
( ( ! [SY4474: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV623 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1225 @ SV1225 @ SV623 )
!= ( c_HOL_Ominus__class_Ominus @ SV1674 @ SY4474 @ SV623 ) )
| ( SV1674 = SY4474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3549]) ).
thf(4133,plain,
! [SV1675: $i,SV1226: $i,SV624: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV624 )
| ~ ( class_Int_Onumber__ring @ SV624 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1226 @ SV1675 @ SV624 )
!= ( c_HOL_Ozero__class_Ozero @ SV624 ) )
| ( SV1226 = SV1675 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3550]) ).
thf(4134,plain,
! [SV1676: $i,SV1227: $i,SV625: $i] :
( ( ! [SY4475: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV625 )
| ( ( c_Power_Opower__class_Opower @ SV1227 @ ( c_Suc @ SV1676 ) @ SV625 )
!= ( c_Power_Opower__class_Opower @ SY4475 @ ( c_Suc @ SV1676 ) @ SV625 ) )
| ( SV1227 = SY4475 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV625 ) @ SY4475 @ SV625 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV625 ) @ SV1227 @ SV625 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3551]) ).
thf(4135,plain,
! [SV1677: $i,SV1228: $i,SV626: $i] :
( ( ! [SY4476: $i,SY4477: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV626 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1228 @ SV1677 @ SV626 )
!= ( c_HOL_Ominus__class_Ominus @ SY4476 @ SY4477 @ SV626 ) )
| ( c_lessequals @ SY4477 @ SY4476 @ SV626 )
| ~ ( c_lessequals @ SV1677 @ SV1228 @ SV626 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3552]) ).
thf(4136,plain,
! [SV1678: $i,SV1229: $i,SV628: $i] :
( ( ( SV628
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV628 ) @ SV1229 ) @ SV1678 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV628 ) @ SV1229 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV628 ) @ SV1229 ) @ ( c_List_Oappend @ SV1678 @ ( c_List_Olist_OCons @ SV1229 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3554]) ).
thf(4137,plain,
! [SV1679: $i,SV1230: $i,SV629: $i] :
( ( ! [SY4478: $i] :
( ( ( c_List_Olist__update @ SV629 @ SV1230 @ SV1679 @ SY4478 )
!= SV629 )
| ~ ( c_HOL_Oord__class_Oless @ SV1230 @ ( c_Nat_Osize__class_Osize @ SV629 @ ( tc_List_Olist @ SY4478 ) ) @ tc_nat )
| ( ( c_List_Onth @ SV629 @ SV1230 @ SY4478 )
= SV1679 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3555]) ).
thf(4138,plain,
! [SV1680: $i,SV1231: $i,SV630: $i] :
( ( ! [SY4479: $i,SY4480: $i] :
( ( ( c_List_Oappend @ SV630 @ SV1231 @ SV1680 )
!= ( c_List_Oappend @ SY4479 @ SY4480 @ SV1680 ) )
| ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SY4479 @ ( tc_List_Olist @ SV1680 ) ) @ SV630 @ SV1680 ) @ SV1231 @ SV1680 )
= SY4480 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV630 @ ( tc_List_Olist @ SV1680 ) ) @ ( c_Nat_Osize__class_Osize @ SY4479 @ ( tc_List_Olist @ SV1680 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3556]) ).
thf(4139,plain,
! [SV1681: $i,SV1232: $i,SV631: $i] :
( ( ! [SY4481: $i,SY4482: $i] :
( ( ( c_List_Olist_OCons @ SV631 @ SV1232 @ SV1681 )
!= ( c_List_Olist_OCons @ SY4481 @ SY4482 @ SV1681 ) )
| ( SV631 = SY4481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3557]) ).
thf(4140,plain,
! [SV1682: $i,SV1233: $i,SV632: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV632 @ SV1233 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1682 @ SV1233 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV632 = SV1682 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3558]) ).
thf(4141,plain,
! [SV1683: $i,SV1234: $i,SV633: $i] :
( ( ! [SY4483: $i,SY4484: $i] :
( ( ( c_List_Omap @ SV633 @ SV1234 @ SV1683 @ SY4483 )
!= ( c_List_Omap @ SV633 @ SY4484 @ SV1683 @ SY4483 ) )
| ( ( c_Nat_Osize__class_Osize @ SV1234 @ ( tc_List_Olist @ SV1683 ) )
= ( c_Nat_Osize__class_Osize @ SY4484 @ ( tc_List_Olist @ SV1683 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3559]) ).
thf(4142,plain,
! [SV1235: $i,SV634: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV634 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV634 ) @ SV1235 ) @ SV1235 )
!= ( c_HOL_Ozero__class_Ozero @ SV634 ) )
| ( SV1235
= ( c_HOL_Ozero__class_Ozero @ SV634 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3560]) ).
thf(4143,plain,
! [SV1684: $i,SV1236: $i,SV636: $i] :
( ( ( ( c_List_Orev @ SV636 @ SV1236 )
!= ( c_List_Olist_OCons @ SV1684 @ ( c_List_Olist_ONil @ SV1236 ) @ SV1236 ) )
| ( SV636
= ( c_List_Olist_OCons @ SV1684 @ ( c_List_Olist_ONil @ SV1236 ) @ SV1236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3562]) ).
thf(4144,plain,
! [SV1685: $i,SV1237: $i,SV637: $i] :
( ( ! [SY4485: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV637 )
| ~ ( class_Int_Onumber__ring @ SV637 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1237 ) @ SV1685 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1237 ) @ SY4485 ) )
| ( SV1685 = SY4485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3563]) ).
thf(4145,plain,
! [SV1686: $i,SV1238: $i,SV638: $i] :
( ( ! [SY4486: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV638 ) @ SV1238 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1686 @ SY4486 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV638
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1686 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV638 @ SV1238 @ SV1686 @ SY4486 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY4486
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3564]) ).
thf(4146,plain,
! [SV1687: $i,SV1239: $i,SV639: $i] :
( ( ~ ( class_Int_Oring__char__0 @ SV639 )
| ~ ( class_Int_Onumber__ring @ SV639 )
| ( ( c_Int_Onumber__class_Onumber__of @ SV1239 @ SV639 )
!= ( c_Int_Onumber__class_Onumber__of @ SV1687 @ SV639 ) )
| ( SV1239 = SV1687 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3565]) ).
thf(4147,plain,
! [SV1688: $i,SV1240: $i,SV641: $i] :
( ( ! [SY4487: $i] :
( ( ( c_List_Olist__update @ SV641 @ SV1240 @ SV1688 @ SY4487 )
!= ( c_List_Olist_ONil @ SY4487 ) )
| ( SV641
= ( c_List_Olist_ONil @ SY4487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3567]) ).
thf(4148,plain,
! [SV1241: $i,SV642: $i] :
( ( ( c_Lambda_OdB_OVar @ SV642 )
= ( c_Lambda_OdB_OAbs @ SV1241 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3568]) ).
thf(4149,plain,
! [SV1689: $i,SV1242: $i,SV643: $i] :
( ( ! [SY4488: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV643 ) @ SV1242 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1689 ) @ SY4488 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1242 = SY4488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3569]) ).
thf(4150,plain,
! [SV1690: $i,SV1243: $i,SV644: $i] :
( ( ! [SY4489: $i] :
( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV644 @ ( tc_List_Olist @ SV1243 ) ) @ SV1690 @ SV1243 )
!= SV644 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1690 @ ( tc_List_Olist @ SV1243 ) ) @ ( c_Nat_Osize__class_Osize @ SV644 @ ( tc_List_Olist @ SV1243 ) ) @ tc_nat )
| ( ( c_List_Oappend @ SV1690 @ SY4489 @ SV1243 )
= ( c_List_Oappend @ SV644 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV644 @ ( tc_List_Olist @ SV1243 ) ) @ SV1690 @ SV1243 ) @ SY4489 @ SV1243 ) @ SV1243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3570]) ).
thf(4151,plain,
! [SV1691: $i,SV1244: $i,SV645: $i] :
( ( ! [SY4490: $i] :
( ( ( c_Int_Onumber__class_Onumber__of @ SV645 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ SV645 @ tc_nat ) @ ( c_List_Olist_OCons @ SV1244 @ SV1691 @ SY4490 ) @ SY4490 )
= ( c_List_Olist_ONil @ SY4490 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3571]) ).
thf(4152,plain,
! [SV1692: $i,SV1245: $i,SV646: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV646 @ SV1245 @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ SV1692 @ SV1245 @ tc_nat ) )
| ~ ( c_lessequals @ SV1245 @ SV1692 @ tc_nat )
| ~ ( c_lessequals @ SV1245 @ SV646 @ tc_nat )
| ( SV646 = SV1692 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3572]) ).
thf(4153,plain,
! [SV1693: $i,SV1246: $i,SV647: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV647 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV647 ) @ SV1246 ) @ SV1693 )
!= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV647 ) @ SV1693 @ SV647 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV647 ) @ SV1246 @ SV647 )
| ( SV1246
= ( c_HOL_Ozero__class_Ozero @ SV647 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3573]) ).
thf(4154,plain,
! [SV1694: $i,SV1247: $i,SV648: $i] :
( ( ! [SY4491: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV648 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV648 ) @ SV1247 ) @ SV1694 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV648 ) @ SV1247 ) @ SY4491 ) )
| ( SV1694 = SY4491 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3574]) ).
thf(4155,plain,
! [SV1695: $i,SV1248: $i,SV649: $i] :
( ( ! [SY4492: $i,SY4493: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV649 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1248 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1695 ) @ SY4492 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1695 ) @ SY4493 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1248 ) @ SY4492 )
= SY4493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3575]) ).
thf(4156,plain,
! [SV1696: $i,SV1249: $i,SV650: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV650 ) @ SV1249 )
!= ( c_Lambda_OdB_OAbs @ SV1696 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3576]) ).
thf(4157,plain,
! [SV1697: $i,SV1250: $i,SV651: $i] :
( ( ! [SY4494: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV651 ) ) @ SV1250 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1697 ) @ SY4494 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3577]) ).
thf(4158,plain,
! [SV1698: $i,SV1251: $i,SV652: $i] :
( ( ! [SY4495: $i] :
( ( ( c_List_Omap @ SV652 @ SV1251 @ SV1698 @ SY4495 )
!= ( c_List_Olist_ONil @ SY4495 ) )
| ( SV1251
= ( c_List_Olist_ONil @ SV1698 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3578]) ).
thf(4159,plain,
! [SV1699: $i,SV1252: $i,SV653: $i] :
( ( ( ( c_List_Oappend @ SV653 @ SV1252 @ SV1699 )
!= SV653 )
| ( SV1252
= ( c_List_Olist_ONil @ SV1699 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3579]) ).
thf(4160,plain,
! [SV1253: $i,SV654: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV654 @ SV1253 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1253 @ SV654 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1253 = SV654 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3580]) ).
thf(4161,plain,
! [SV1254: $i,SV655: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ SV655 @ ( tc_List_Olist @ SV1254 ) )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV655
= ( c_List_Olist_ONil @ SV1254 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3581]) ).
thf(4162,plain,
! [SV1700: $i,SV1255: $i,SV656: $i] :
( ( ! [SY4496: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV656 ) @ SV1255 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1700 ) @ SY4496 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3582]) ).
thf(4163,plain,
! [SV657: $i,SV1: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1 @ ( c_Suc @ SV657 ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV657 @ SV1 @ tc_nat ) )
= $true )
| ( ( SV1 = SV657 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3583]) ).
thf(4164,plain,
! [SV1701: $i,SV1256: $i,SV658: $i,SV2: $i] :
( ( ! [SY4497: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV2 )
| ( c_lessequals @ SV658 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SV1256 ) @ SV1701 ) @ SV2 )
| ~ ( c_lessequals @ SY4497 @ SV1701 @ SV2 )
| ~ ( c_lessequals @ SV658 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SV1256 ) @ SY4497 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3584]) ).
thf(4165,plain,
! [SV1702: $i,SV1257: $i,SV659: $i,SV3: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV3 )
| ( c_HOL_Oord__class_Oless @ SV659 @ SV1257 @ SV3 )
| ~ ( c_lessequals @ SV1702 @ SV1257 @ SV3 )
| ~ ( c_HOL_Oord__class_Oless @ SV659 @ SV1702 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3585]) ).
thf(4166,plain,
! [SV1703: $i,SV1258: $i,SV660: $i,SV4: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV4 )
| ( c_HOL_Oord__class_Oless @ SV660 @ SV1258 @ SV4 )
| ~ ( c_HOL_Oord__class_Oless @ SV1703 @ SV1258 @ SV4 )
| ~ ( c_lessequals @ SV660 @ SV1703 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3586]) ).
thf(4167,plain,
! [SV661: $i,SV5: $i] :
( ( ( class_Orderings_Opreorder @ SV5 )
= $false )
| ( ( c_lessequals @ SV661 @ SV661 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3587]) ).
thf(4168,plain,
! [SV662: $i,SV6: $i] :
( ( ( class_Orderings_Oorder @ SV6 )
= $false )
| ( ( c_lessequals @ SV662 @ SV662 @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3588]) ).
thf(4169,plain,
! [SV1259: $i,SV663: $i,SV8: $i] :
( ( ( c_lessequals @ SV8 @ SV663 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1259 @ SV663 @ tc_nat )
| ~ ( c_lessequals @ SV8 @ SV1259 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3589]) ).
thf(4170,plain,
! [SV1704: $i,SV1260: $i,SV664: $i,SV10: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV10 )
| ( c_lessequals @ SV664 @ SV1260 @ SV10 )
| ~ ( c_lessequals @ SV1704 @ SV1260 @ SV10 )
| ~ ( c_lessequals @ SV664 @ SV1704 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3590]) ).
thf(4171,plain,
! [SV1705: $i,SV1261: $i,SV665: $i,SV11: $i] :
( ( ~ ( class_Orderings_Oorder @ SV11 )
| ( c_HOL_Oord__class_Oless @ SV665 @ SV1261 @ SV11 )
| ~ ( c_HOL_Oord__class_Oless @ SV665 @ SV1705 @ SV11 )
| ~ ( c_lessequals @ SV1705 @ SV1261 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3591]) ).
thf(4172,plain,
! [SV1706: $i,SV1262: $i,SV666: $i,SV12: $i] :
( ( ~ ( class_Orderings_Oorder @ SV12 )
| ( c_HOL_Oord__class_Oless @ SV666 @ SV1262 @ SV12 )
| ~ ( c_lessequals @ SV666 @ SV1706 @ SV12 )
| ~ ( c_HOL_Oord__class_Oless @ SV1706 @ SV1262 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3592]) ).
thf(4173,plain,
! [SV1707: $i,SV1263: $i,SV667: $i,SV13: $i] :
( ( ~ ( class_Orderings_Oorder @ SV13 )
| ( c_lessequals @ SV667 @ SV1263 @ SV13 )
| ~ ( c_lessequals @ SV667 @ SV1707 @ SV13 )
| ~ ( c_lessequals @ SV1707 @ SV1263 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3593]) ).
thf(4174,plain,
! [SV1264: $i,SV668: $i,SV14: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1 @ SV14 ) )
= $true )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV668 @ SV1264 @ tc_nat ) @ SV14 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV668 @ SV14 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1264 @ SV14 ) @ SV14 ) )
| ~ ( c_lessequals @ SV1264 @ SV668 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3594]) ).
thf(4175,plain,
! [SV1265: $i,SV669: $i,SV15: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV15 @ SV669 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1265 @ SV669 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV15 @ SV1265 @ tc_nat )
| ~ ( c_lessequals @ SV669 @ SV1265 @ tc_nat )
| ~ ( c_lessequals @ SV669 @ SV15 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3595]) ).
thf(4176,plain,
! [SV1266: $i,SV670: $i,SV16: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV16 @ SV670 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV16 @ SV1266 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV670 @ SV1266 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1266 @ SV670 @ tc_nat )
| ~ ( c_lessequals @ SV1266 @ SV16 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3596]) ).
thf(4177,plain,
! [SV671: $i,SV18: $i] :
( ( ( c_lessequals @ SV18 @ SV671 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV18 @ ( c_Suc @ SV671 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3597]) ).
thf(4178,plain,
! [SV672: $i,SV19: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV19 ) @ SV672 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV19 @ SV672 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3598]) ).
thf(4179,plain,
! [SV1708: $i,SV1267: $i,SV673: $i,SV20: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV20 )
| ( c_lessequals @ SV673 @ SV1267 @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV1267 @ SV20 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV673 @ ( c_Suc @ SV1708 ) @ SV20 ) @ ( c_Power_Opower__class_Opower @ SV1267 @ ( c_Suc @ SV1708 ) @ SV20 ) @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3599]) ).
thf(4180,plain,
! [SV1709: $i,SV1268: $i,SV674: $i,SV21: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV21 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SV674 ) @ SV1268 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SV674 ) @ SV1709 ) @ SV21 )
| ~ ( c_lessequals @ SV1268 @ SV1709 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3600]) ).
thf(4181,plain,
! [SV1710: $i,SV1269: $i,SV675: $i,SV22: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV22 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV675 ) @ SV1269 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV1710 ) @ SV1269 ) @ SV22 )
| ~ ( c_lessequals @ SV675 @ SV1710 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3601]) ).
thf(4182,plain,
! [SV1711: $i,SV1270: $i,SV676: $i,SV23: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV23 )
| ( c_lessequals @ SV676 @ SV1270 @ SV23 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV23 ) @ SV1711 ) @ SV676 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV23 ) @ SV1711 ) @ SV1270 ) @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3602]) ).
thf(4183,plain,
! [SV1712: $i,SV1271: $i,SV677: $i,SV24: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV24 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ SV677 ) @ SV1271 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ SV677 ) @ SV1712 ) @ SV24 )
| ~ ( c_lessequals @ SV1271 @ SV1712 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3603]) ).
thf(4184,plain,
! [SV1713: $i,SV1272: $i,SV678: $i,SV25: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV25 )
| ( c_lessequals @ SV678 @ SV1272 @ SV25 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SV678 ) @ SV1713 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SV1272 ) @ SV1713 ) @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3604]) ).
thf(4185,plain,
! [SV1714: $i,SV1273: $i,SV679: $i,SV26: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV26 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV26 ) @ SV679 ) @ SV1273 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV26 ) @ SV1714 ) @ SV1273 ) @ SV26 )
| ~ ( c_lessequals @ SV679 @ SV1714 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3605]) ).
thf(4186,plain,
! [SV1274: $i,SV680: $i,SV27: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV27 ) @ SV680 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1274 @ SV680 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV27 @ SV1274 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3606]) ).
thf(4187,plain,
! [SV1275: $i,SV681: $i,SV30: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV30 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV30 ) @ ( c_Power_Opower__class_Opower @ SV681 @ ( c_Suc @ SV1275 ) @ SV30 ) @ SV30 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SV681 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3607]) ).
thf(4188,plain,
! [SV1276: $i,SV682: $i,SV31: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV31 ) )
= $true )
| ( ( ( c_lessequals @ SV682 @ SV1276 @ SV31 )
| ~ ( c_HOL_Oord__class_Oless @ SV682 @ SV1276 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3608]) ).
thf(4189,plain,
! [SV1277: $i,SV683: $i,SV32: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV32 ) )
= $true )
| ( ( ( c_lessequals @ SV683 @ SV1277 @ SV32 )
| ~ ( c_HOL_Oord__class_Oless @ SV683 @ SV1277 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3609]) ).
thf(4190,plain,
! [SV684: $i,SV33: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV33 @ SV684 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV33 @ SV684 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3610]) ).
thf(4191,plain,
! [SV685: $i,SV34: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV34 @ SV685 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV34 @ SV685 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3611]) ).
thf(4192,plain,
! [SV1278: $i,SV686: $i,SV35: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV35 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV686 @ SV1278 @ SV35 ) @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ SV35 )
| ~ ( c_lessequals @ SV686 @ SV1278 @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3612]) ).
thf(4193,plain,
! [SV1279: $i,SV687: $i,SV36: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV36 ) )
= $true )
| ( ( ( c_lessequals @ SV687 @ SV1279 @ SV36 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV687 @ SV1279 @ SV36 ) @ ( c_HOL_Ozero__class_Ozero @ SV36 ) @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3613]) ).
thf(4194,plain,
! [SV1280: $i,SV688: $i,SV37: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV37 ) )
= $true )
| ( ( ( SV688 = SV1280 )
| ~ ( c_lessequals @ SV688 @ SV1280 @ SV37 )
| ~ ( c_lessequals @ SV1280 @ SV688 @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3614]) ).
thf(4195,plain,
! [SV1281: $i,SV689: $i,SV38: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV38 ) )
= $true )
| ( ( ( SV689 = SV1281 )
| ~ ( c_lessequals @ SV1281 @ SV689 @ SV38 )
| ~ ( c_lessequals @ SV689 @ SV1281 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3615]) ).
thf(4196,plain,
! [SV1282: $i,SV690: $i,SV39: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV39 ) )
= $true )
| ( ( ( SV690 = SV1282 )
| ~ ( c_lessequals @ SV1282 @ SV690 @ SV39 )
| ~ ( c_lessequals @ SV690 @ SV1282 @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3616]) ).
thf(4197,plain,
! [SV40: $i,SV691: $i] :
( ( ( ~ ( c_lessequals @ SV691 @ SV40 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV40 @ SV691 @ tc_nat ) )
= $true )
| ( ( SV40 = SV691 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3617]) ).
thf(4198,plain,
! [SV42: $i] :
( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV42 ) @ ( c_HOL_Ozero__class_Ozero @ SV42 ) @ SV42 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3618]) ).
thf(4199,plain,
! [SV1283: $i,SV693: $i,SV43: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV43 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV693 @ SV1283 @ SV43 )
| ( c_lessequals @ SV1283 @ SV693 @ SV43 )
| ~ ( c_lessequals @ SV693 @ SV1283 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3619]) ).
thf(4200,plain,
! [SV1284: $i,SV694: $i,SV44: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV44 @ SV694 @ tc_nat ) @ SV1284 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV44 @ SV1284 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3620]) ).
thf(4201,plain,
! [SV695: $i,SV46: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV46 @ ( c_Suc @ SV695 ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV46 @ SV695 @ tc_nat )
= $true )
| ( ( SV46 = SV695 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3622]) ).
thf(4202,plain,
! [SV47: $i,SV696: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV696 @ ( c_Suc @ SV47 ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV696 @ SV47 @ tc_nat )
= $true )
| ( ( SV47 = SV696 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3623]) ).
thf(4203,plain,
! [SV697: $i,SV48: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV48 @ SV697 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV48 @ ( c_Suc @ SV697 ) @ tc_nat ) )
= $true )
| ( ( SV48 = SV697 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3624]) ).
thf(4204,plain,
! [SV1285: $i,SV699: $i,SV50: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV50 @ SV699 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV50 @ SV1285 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1285 @ SV50 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1285 @ SV699 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3625]) ).
thf(4205,plain,
! [SV51: $i,SV700: $i] :
( ( ( c_lessequals @ SV700 @ SV51 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_Suc @ SV51 ) @ SV700 @ tc_nat )
= ( c_Suc @ ( c_HOL_Ominus__class_Ominus @ SV51 @ SV700 @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3626]) ).
thf(4206,plain,
! [SV1715: $i,SV1286: $i,SV701: $i,SV52: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV52 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV701 @ SV1286 @ SV52 ) @ ( c_Power_Opower__class_Opower @ SV701 @ SV1715 @ SV52 ) @ SV52 )
| ~ ( c_lessequals @ SV701 @ ( c_HOL_Oone__class_Oone @ SV52 ) @ SV52 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV701 @ SV52 )
| ~ ( c_lessequals @ SV1715 @ SV1286 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3627]) ).
thf(4207,plain,
! [SV702: $i,SV53: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV53 ) @ SV702 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV53 @ SV702 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3628]) ).
thf(4208,plain,
! [SV703: $i,SV54: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV54 @ SV703 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Suc @ SV54 ) @ SV703 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3629]) ).
thf(4209,plain,
! [SV704: $i,SV55: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV55 ) @ SV704 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV55 @ SV704 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3630]) ).
thf(4210,plain,
! [SV705: $i,SV56: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV56 @ SV705 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Suc @ SV56 ) @ SV705 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3631]) ).
thf(4211,plain,
! [SV1287: $i,SV706: $i,SV57: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV57 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV57 ) @ ( c_Power_Opower__class_Opower @ SV706 @ SV1287 @ SV57 ) @ SV57 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV57 ) @ SV706 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3632]) ).
thf(4212,plain,
! [SV707: $i,SV58: $i] :
( ( ( c_lessequals @ SV58 @ SV707 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV58 @ SV707 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3633]) ).
thf(4213,plain,
! [SV1288: $i,SV708: $i,SV59: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV59 ) )
= $true )
| ( ( ( c_lessequals @ SV708 @ SV1288 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV708 @ SV59 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1288 @ SV59 ) @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3634]) ).
thf(4214,plain,
! [SV1289: $i,SV709: $i,SV60: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV60 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV709 @ SV60 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1289 @ SV60 ) @ SV60 )
| ~ ( c_lessequals @ SV709 @ SV1289 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3635]) ).
thf(4215,plain,
! [SV1290: $i,SV710: $i,SV61: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV61 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ ( c_HOL_Ominus__class_Ominus @ SV710 @ SV1290 @ SV61 ) ) @ SV1290 )
= SV710 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3636]) ).
thf(4216,plain,
! [SV1716: $i,SV1291: $i,SV711: $i,SV62: $i] :
( ( ! [SY4498: $i] :
( ( c_ListOrder_Ostep1 @ SV62 @ ( c_List_Oappend @ SV711 @ SV1291 @ SV1716 ) @ ( c_List_Oappend @ SV711 @ SY4498 @ SV1716 ) @ SV1716 )
| ~ ( c_ListOrder_Ostep1 @ SV62 @ SV1291 @ SY4498 @ SV1716 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3637]) ).
thf(4217,plain,
! [SV1717: $i,SV1292: $i,SV712: $i,SV63: $i] :
( ( ! [SY4499: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV63 @ SV712 @ SV1292 @ SV1717 )
| ( c_ListOrder_Ostep1 @ SV63 @ ( c_List_Oappend @ SV712 @ SY4499 @ SV1717 ) @ ( c_List_Oappend @ SV1292 @ SY4499 @ SV1717 ) @ SV1717 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3638]) ).
thf(4218,plain,
! [SV1718: $i,SV1293: $i,SV713: $i,SV64: $i] :
( ( ! [SY4500: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV64 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV713 ) @ SV1293 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV1718 ) @ SY4500 ) @ SV64 )
| ~ ( c_lessequals @ SV1293 @ SY4500 @ SV64 )
| ~ ( c_lessequals @ SV713 @ SV1718 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3639]) ).
thf(4219,plain,
! [SV1719: $i,SV1294: $i,SV714: $i,SV65: $i] :
( ( ! [SY4501: $i] :
( ( c_lessequals @ SV65 @ ( c_List_Olist_Olist__size @ SV714 @ SV1294 @ SV1719 ) @ tc_nat )
| ~ ( c_lessequals @ SV65 @ ( hAPP @ SV714 @ SY4501 ) @ tc_nat )
| ~ ( c_in @ SY4501 @ ( c_List_Oset @ SV1294 @ SV1719 ) @ SV1719 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3640]) ).
thf(4220,plain,
! [SV715: $i,SV66: $i] :
( ( ( c_lessequals @ SV66 @ SV715 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV66 @ ( c_Suc @ SV715 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3641]) ).
thf(4221,plain,
! [SV716: $i,SV67: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV67 @ ( c_Suc @ SV716 ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV67 @ SV716 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3642]) ).
thf(4222,plain,
! [SV718: $i,SV70: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV70 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV70 ) @ SV718 @ SV70 )
= ( c_HOL_Oone__class_Oone @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3644]) ).
thf(4223,plain,
! [SV1295: $i,SV719: $i,SV71: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV71 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV719 @ SV1295 @ SV71 )
| ( c_lessequals @ SV1295 @ SV719 @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3645]) ).
thf(4224,plain,
! [SV720: $i,SV72: $i] :
( ( ( class_Orderings_Olinorder @ SV72 )
= $false )
| ( ( ~ ( c_lessequals @ SV720 @ SV720 @ SV72 )
| ~ ( c_HOL_Oord__class_Oless @ SV720 @ SV720 @ SV72 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3646]) ).
thf(4225,plain,
! [SV721: $i,SV73: $i] :
( ( ( class_Orderings_Olinorder @ SV73 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV721 @ SV721 @ SV73 )
| ( c_lessequals @ SV721 @ SV721 @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3647]) ).
thf(4226,plain,
! [SV1296: $i,SV722: $i,SV74: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV74 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV722 @ SV1296 @ SV74 )
| ~ ( c_lessequals @ SV1296 @ SV722 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3648]) ).
thf(4227,plain,
! [SV1297: $i,SV723: $i,SV75: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV75 ) )
= $true )
| ( ( ( c_lessequals @ SV723 @ SV1297 @ SV75 )
| ( c_HOL_Oord__class_Oless @ SV1297 @ SV723 @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3649]) ).
thf(4228,plain,
! [SV1298: $i,SV724: $i,SV76: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV76 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV724 @ SV1298 @ SV76 )
| ~ ( c_HOL_Oord__class_Oless @ SV1298 @ SV724 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3650]) ).
thf(4229,plain,
! [SV1299: $i,SV725: $i,SV77: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV77 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV725 @ SV1299 @ SV77 )
| ( c_lessequals @ SV1299 @ SV725 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3651]) ).
thf(4230,plain,
! [SV1300: $i,SV726: $i,SV78: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV78 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV726 @ SV1300 @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ SV1300 @ SV726 @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3652]) ).
thf(4231,plain,
! [SV1720: $i,SV1301: $i,SV727: $i,SV79: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV79 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV727 @ SV1301 @ SV79 ) @ ( c_Power_Opower__class_Opower @ SV727 @ SV1720 @ SV79 ) @ SV79 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV79 ) @ SV727 @ SV79 )
| ~ ( c_lessequals @ SV1301 @ SV1720 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3653]) ).
thf(4232,plain,
! [SV1302: $i,SV728: $i,SV80: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV80 @ SV728 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV80 @ SV1302 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV1302 @ SV728 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3654]) ).
thf(4233,plain,
! [SV1303: $i,SV729: $i,SV81: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV81 @ SV729 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1303 @ SV729 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV81 @ SV1303 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3655]) ).
thf(4234,plain,
! [SV730: $i,SV82: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV82 ) @ SV730 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV82 @ SV730 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3656]) ).
thf(4235,plain,
! [SV731: $i,SV83: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV83 @ SV731 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV83 @ ( c_Suc @ SV731 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3657]) ).
thf(4236,plain,
! [SV732: $i,SV85: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV85 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV85 @ ( c_Suc @ SV732 ) @ tc_nat ) @ SV85 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3659]) ).
thf(4237,plain,
! [SV1304: $i,SV733: $i,SV86: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV86 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV733 @ SV1304 @ SV86 )
| ( SV1304 = SV733 )
| ~ ( c_lessequals @ SV733 @ SV1304 @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3660]) ).
thf(4238,plain,
! [SV1305: $i,SV734: $i,SV87: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV87 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV734 @ SV1305 @ SV87 )
| ~ ( c_lessequals @ SV734 @ SV1305 @ SV87 )
| ( SV1305 = SV734 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3661]) ).
thf(4239,plain,
! [SV735: $i,SV88: $i] :
( ( ( SV88 = SV735 )
= $true )
| ( ( ~ ( c_lessequals @ SV88 @ SV735 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV88 @ SV735 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3662]) ).
thf(4240,plain,
! [SV736: $i,SV89: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV89 @ SV736 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV89 @ SV736 @ tc_nat ) )
= $true )
| ( ( SV89 = SV736 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3663]) ).
thf(4241,plain,
! [SV737: $i,SV90: $i] :
( ( ( SV90 = SV737 )
= $true )
| ( ( ~ ( c_lessequals @ SV90 @ SV737 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV90 @ SV737 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3664]) ).
thf(4242,plain,
! [SV1306: $i,SV738: $i,SV91: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV91 ) )
= $true )
| ( ( ( SV738 = SV1306 )
| ( c_HOL_Oord__class_Oless @ SV738 @ SV1306 @ SV91 )
| ~ ( c_lessequals @ SV738 @ SV1306 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3665]) ).
thf(4243,plain,
! [SV1307: $i,SV739: $i,SV92: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV92 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV739 @ SV1307 @ SV92 )
| ( SV739 = SV1307 )
| ~ ( c_lessequals @ SV739 @ SV1307 @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3666]) ).
thf(4244,plain,
! [SV1308: $i,SV740: $i,SV93: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV93 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV740 @ SV1308 @ SV93 )
| ( SV740 = SV1308 )
| ~ ( c_lessequals @ SV740 @ SV1308 @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3667]) ).
thf(4245,plain,
! [SV1309: $i,SV741: $i,SV94: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV94 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV741 @ SV1309 @ SV94 )
| ~ ( c_lessequals @ SV741 @ SV1309 @ SV94 )
| ( SV741 = SV1309 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3668]) ).
thf(4246,plain,
! [SV1310: $i,SV742: $i,SV95: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV95 ) )
= $true )
| ( ( ( SV742 = SV1310 )
| ~ ( c_lessequals @ SV742 @ SV1310 @ SV95 )
| ( c_HOL_Oord__class_Oless @ SV742 @ SV1310 @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3669]) ).
thf(4247,plain,
! [SV1311: $i,SV743: $i,SV96: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV96 ) )
= $true )
| ( ( ( SV743 = SV1311 )
| ( c_HOL_Oord__class_Oless @ SV743 @ SV1311 @ SV96 )
| ~ ( c_lessequals @ SV743 @ SV1311 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3670]) ).
thf(4248,plain,
! [SV744: $i,SV97: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV97 ) @ ( c_Suc @ SV744 ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV97 @ SV744 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3671]) ).
thf(4249,plain,
! [SV745: $i,SV98: $i] :
( ( ( c_lessequals @ SV98 @ SV745 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Suc @ SV98 ) @ ( c_Suc @ SV745 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3672]) ).
thf(4250,plain,
! [SV1312: $i,SV747: $i,SV100: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV100 ) )
= $true )
| ( ( ( c_lessequals @ SV747 @ SV1312 @ SV100 )
| ( c_lessequals @ SV1312 @ SV747 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3674]) ).
thf(4251,plain,
! [SV1313: $i,SV748: $i,SV101: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV101 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV748 @ ( c_Suc @ SV1313 ) @ SV101 ) @ ( c_HOL_Oone__class_Oone @ SV101 ) @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ SV748 @ ( c_HOL_Oone__class_Oone @ SV101 ) @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ SV748 @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3675]) ).
thf(4252,plain,
! [SV1721: $i,SV1314: $i,SV749: $i,SV102: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV102 )
| ( c_lessequals @ SV749 @ SV1314 @ SV102 )
| ~ ( c_in @ SV1314 @ ( c_List_Oset @ SV1721 @ SV102 ) @ SV102 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV749 @ SV1721 @ SV102 ) @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3676]) ).
thf(4253,plain,
! [SV1722: $i,SV1315: $i,SV750: $i,SV103: $i] :
( ( ! [SY4502: $i] :
( ~ ( class_Orderings_Olinorder @ SV103 )
| ( c_lessequals @ SV750 @ SV1315 @ SV103 )
| ~ ( c_in @ SV1315 @ ( c_List_Oset @ SV1722 @ SV103 ) @ SV103 )
| ~ ( c_in @ SV750 @ ( c_List_Oset @ SY4502 @ SV103 ) @ SV103 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SY4502 @ SV1722 @ SV103 ) @ SV103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3677]) ).
thf(4254,plain,
! [SV1316: $i,SV751: $i,SV104: $i] :
( ( ( ( c_List_Olength__unique @ ( c_List_Olist_OCons @ SV104 @ SV751 @ SV1316 ) @ SV1316 )
= ( c_Suc @ ( c_List_Olength__unique @ SV751 @ SV1316 ) ) )
= $true )
| ( ( c_in @ SV104 @ ( c_List_Oset @ SV751 @ SV1316 ) @ SV1316 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3678]) ).
thf(4255,plain,
! [SV105: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV105 ) @ ( c_HOL_Ozero__class_Ozero @ SV105 ) @ SV105 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3679]) ).
thf(4256,plain,
! [SV1317: $i,SV752: $i,SV106: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV106 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV752 @ SV1317 @ SV106 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV752 @ SV1317 @ SV106 ) @ ( c_HOL_Ozero__class_Ozero @ SV106 ) @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3680]) ).
thf(4257,plain,
! [SV1318: $i,SV753: $i,SV107: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV107 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV753 @ SV1318 @ SV107 ) @ ( c_HOL_Ozero__class_Ozero @ SV107 ) @ SV107 )
| ~ ( c_HOL_Oord__class_Oless @ SV753 @ SV1318 @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3681]) ).
thf(4258,plain,
! [SV1319: $i,SV754: $i,SV109: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV109 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ SV754 ) @ SV1319 ) @ SV109 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV1319 @ SV109 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV754 @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3683]) ).
thf(4259,plain,
! [SV110: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV110 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV110 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) )
= ( c_HOL_Ozero__class_Ozero @ SV110 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3684]) ).
thf(4260,plain,
! [SV755: $i,SV111: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV111 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV111 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV755 ) @ SV755 ) @ SV111 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV111 ) @ SV755 @ SV111 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3685]) ).
thf(4261,plain,
! [SV756: $i,SV112: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV112 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV112 ) @ SV756 @ SV112 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV112 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV756 ) @ SV756 ) @ SV112 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3686]) ).
thf(4262,plain,
! [SV1723: $i,SV1320: $i,SV757: $i,SV113: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV113 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV113 )
| ( c_lessequals @ SV757 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV1320 ) @ SV1723 ) @ SV113 )
| ~ ( c_lessequals @ SV757 @ SV1723 @ SV113 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV1320 @ SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3687]) ).
thf(4263,plain,
! [SV1724: $i,SV1321: $i,SV758: $i,SV114: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV114 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV114 )
| ( c_lessequals @ SV758 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SV1321 ) @ SV1724 ) @ SV114 )
| ~ ( c_lessequals @ SV758 @ SV1321 @ SV114 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV1724 @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3688]) ).
thf(4264,plain,
! [SV759: $i,SV115: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV115 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV759 ) @ SV759 ) @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 )
| ~ ( c_lessequals @ SV759 @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3689]) ).
thf(4265,plain,
! [SV760: $i,SV116: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV116 )
= $false )
| ( ( ( c_lessequals @ SV760 @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV760 ) @ SV760 ) @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3690]) ).
thf(4266,plain,
! [SV1322: $i,SV761: $i,SV117: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV117 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV761 ) @ SV1322 ) @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
| ~ ( c_lessequals @ SV1322 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
| ~ ( c_lessequals @ SV761 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3691]) ).
thf(4267,plain,
! [SV1725: $i,SV1323: $i,SV762: $i,SV118: $i] :
( ( ! [SY4503: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV118 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV762 ) @ SV1323 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV1725 ) @ SY4503 ) @ SV118 )
| ~ ( c_lessequals @ SV1323 @ SY4503 @ SV118 )
| ~ ( c_HOL_Oord__class_Oless @ SV762 @ SV1725 @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3692]) ).
thf(4268,plain,
! [SV1726: $i,SV1324: $i,SV763: $i,SV119: $i] :
( ( ! [SY4504: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV119 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV119 ) @ SV763 ) @ SV1324 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV119 ) @ SV1726 ) @ SY4504 ) @ SV119 )
| ~ ( c_HOL_Oord__class_Oless @ SV1324 @ SY4504 @ SV119 )
| ~ ( c_lessequals @ SV763 @ SV1726 @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3693]) ).
thf(4269,plain,
! [SV764: $i,SV120: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV120 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV764 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV120 ) @ SV764 ) @ ( c_HOL_Oone__class_Oone @ SV120 ) ) @ SV120 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3694]) ).
thf(4270,plain,
! [SV1325: $i,SV765: $i,SV121: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV121 ) )
= $true )
| ( ( ~ ( class_Int_Onumber @ SV121 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ SV765 @ SV121 ) @ ( c_Int_Onumber__class_Onumber__of @ SV1325 @ SV121 ) @ SV121 )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ SV1325 @ SV121 ) @ ( c_Int_Onumber__class_Onumber__of @ SV765 @ SV121 ) @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3695]) ).
thf(4271,plain,
! [SV1326: $i,SV766: $i,SV122: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV122 ) )
= $true )
| ( ( ~ ( class_Int_Onumber @ SV122 )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ SV766 @ SV122 ) @ ( c_Int_Onumber__class_Onumber__of @ SV1326 @ SV122 ) @ SV122 )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ SV1326 @ SV122 ) @ ( c_Int_Onumber__class_Onumber__of @ SV766 @ SV122 ) @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3696]) ).
thf(4272,plain,
! [SV1727: $i,SV1327: $i,SV767: $i,SV123: $i] :
( ( ( c_in @ SV123 @ ( c_List_Oset @ SV767 @ SV1327 ) @ SV1327 )
| ( SV123 = SV1727 )
| ~ ( c_in @ SV123 @ ( c_List_Oset @ ( c_List_Olist_OCons @ SV1727 @ SV767 @ SV1327 ) @ SV1327 ) @ SV1327 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3697]) ).
thf(4273,plain,
! [SV768: $i,SV124: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV124 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV124 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV768 @ SV124 ) @ SV124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3698]) ).
thf(4274,plain,
! [SV769: $i,SV125: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV125 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV125 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV769 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3699]) ).
thf(4275,plain,
! [SV1328: $i,SV770: $i,SV129: $i] :
( ( ( hBOOL @ ( hAPP @ SV129 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV770 @ SV1328 @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV129 @ ( c_HOL_Ominus__class_Ominus @ SV770 @ SV1328 @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3701]) ).
thf(4276,plain,
! [SV130: $i,SV771: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV771 @ SV130 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV130 @ SV771 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3702]) ).
thf(4277,plain,
! [SV131: $i,SV772: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV772 @ SV131 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV131 @ SV772 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3703]) ).
thf(4278,plain,
! [SV773: $i,SV132: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV132 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV773 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV132 @ SV773 @ tc_nat ) @ SV132 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3704]) ).
thf(4279,plain,
! [SV1728: $i,SV1329: $i,SV774: $i,SV133: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV133 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV774 @ SV1329 @ SV133 ) @ ( c_Power_Opower__class_Opower @ SV1728 @ SV1329 @ SV133 ) @ SV133 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV133 ) @ SV774 @ SV133 )
| ~ ( c_lessequals @ SV774 @ SV1728 @ SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3705]) ).
thf(4280,plain,
! [SV1330: $i,SV775: $i,SV134: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV134 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV134 ) @ ( c_Power_Opower__class_Opower @ SV775 @ SV1330 @ SV134 ) @ SV134 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV134 ) @ SV775 @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3706]) ).
thf(4281,plain,
! [SV776: $i,SV135: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV135 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV135 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_Suc @ SV776 ) @ SV135 )
= ( c_HOL_Ozero__class_Ozero @ SV135 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3707]) ).
thf(4282,plain,
! [SV1333: $i,SV779: $i,SV138: $i] :
( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ ( c_List_Olist_OCons @ SV138 @ SV779 @ SV1333 ) @ ( tc_List_Olist @ SV1333 ) ) @ ( c_Nat_Osize__class_Osize @ SV779 @ ( tc_List_Olist @ SV1333 ) ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3710]) ).
thf(4283,plain,
! [SV780: $i,SV139: $i] :
( ( ( class_Power_Opower @ SV139 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV780 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV139 )
= ( c_HOL_Oone__class_Oone @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3711]) ).
thf(4284,plain,
! [SV781: $i,SV140: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV140 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV781 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV140 )
= ( c_HOL_Oone__class_Oone @ SV140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3712]) ).
thf(4285,plain,
! [SV1334: $i,SV782: $i,SV141: $i] :
( ( ( ( c_List_Ohd @ ( c_List_Oappend @ SV141 @ SV782 @ SV1334 ) @ SV1334 )
= ( c_List_Ohd @ SV141 @ SV1334 ) )
= $true )
| ( ( SV141
= ( c_List_Olist_ONil @ SV1334 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3713]) ).
thf(4286,plain,
! [SV1729: $i,SV1335: $i,SV784: $i,SV143: $i] :
( ( ( c_in @ SV143 @ ( c_List_Oset @ SV784 @ SV1335 ) @ SV1335 )
| ~ ( c_in @ SV143 @ ( c_List_Oset @ ( c_List_Otake @ SV1729 @ SV784 @ SV1335 ) @ SV1335 ) @ SV1335 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3714]) ).
thf(4287,plain,
! [SV1730: $i,SV1336: $i,SV785: $i,SV144: $i] :
( ( ( c_in @ SV144 @ ( c_List_Oset @ SV785 @ SV1336 ) @ SV1336 )
| ~ ( c_in @ SV144 @ ( c_List_Oset @ ( c_List_Odrop @ SV1730 @ SV785 @ SV1336 ) @ SV1336 ) @ SV1336 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3715]) ).
thf(4288,plain,
! [SV1731: $i,SV1337: $i,SV786: $i,SV145: $i] :
( ( ( c_List_Onth @ ( c_List_Olist_OCons @ SV145 @ SV786 @ SV1337 ) @ ( c_Suc @ SV1731 ) @ SV1337 )
= ( c_List_Onth @ SV786 @ SV1731 @ SV1337 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3716]) ).
thf(4289,plain,
! [SV1732: $i,SV1338: $i,SV787: $i,SV146: $i] :
( ( ( c_List_Otake @ ( c_Suc @ SV146 ) @ ( c_List_Olist_OCons @ SV787 @ SV1338 @ SV1732 ) @ SV1732 )
= ( c_List_Olist_OCons @ SV787 @ ( c_List_Otake @ SV146 @ SV1338 @ SV1732 ) @ SV1732 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3717]) ).
thf(4290,plain,
! [SV1733: $i,SV1339: $i,SV788: $i,SV147: $i] :
( ( ( hBOOL @ ( hAPP @ SV147 @ SV788 ) )
| ~ ( c_in @ SV788 @ ( c_List_Oset @ ( c_List_OtakeWhile @ SV147 @ SV1339 @ SV1733 ) @ SV1733 ) @ SV1733 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3718]) ).
thf(4291,plain,
! [SV1734: $i,SV1340: $i,SV789: $i,SV148: $i] :
( ( ( c_in @ SV148 @ ( c_List_Oset @ SV789 @ SV1340 ) @ SV1340 )
| ~ ( c_in @ SV148 @ ( c_List_Oset @ ( c_List_OtakeWhile @ SV1734 @ SV789 @ SV1340 ) @ SV1340 ) @ SV1340 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3719]) ).
thf(4292,plain,
! [SV1735: $i,SV1341: $i,SV790: $i,SV149: $i] :
( ( ( hBOOL @ ( hAPP @ SV149 @ SV790 ) )
| ~ ( c_in @ SV790 @ ( c_List_Oset @ SV1341 @ SV1735 ) @ SV1735 )
| ~ ( c_List_Olistsp @ SV149 @ SV1341 @ SV1735 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3720]) ).
thf(4293,plain,
! [SV1736: $i,SV1342: $i,SV791: $i,SV150: $i] :
( ( ( SV150 = SV791 )
| ~ ( c_in @ SV150 @ ( c_List_Oset @ ( c_List_Oreplicate @ SV1342 @ SV791 @ SV1736 ) @ SV1736 ) @ SV1736 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3721]) ).
thf(4294,plain,
! [SV1343: $i,SV792: $i,SV151: $i] :
( ( ( ( c_List_Onth @ ( c_List_Orev @ SV151 @ SV792 ) @ SV1343 @ SV792 )
= ( c_List_Onth @ SV151 @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SV151 @ ( tc_List_Olist @ SV792 ) ) @ ( c_Suc @ SV1343 ) @ tc_nat ) @ SV792 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1343 @ ( c_Nat_Osize__class_Osize @ SV151 @ ( tc_List_Olist @ SV792 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3722]) ).
thf(4295,plain,
! [SV1737: $i,SV1344: $i,SV793: $i,SV152: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV152 )
| ( c_lessequals @ ( c_List_Onth @ SV793 @ SV1344 @ SV152 ) @ ( c_List_Onth @ SV793 @ SV1737 @ SV152 ) @ SV152 )
| ~ ( c_lessequals @ SV1344 @ SV1737 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1737 @ ( c_Nat_Osize__class_Osize @ SV793 @ ( tc_List_Olist @ SV152 ) ) @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ SV793 @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3723]) ).
thf(4296,plain,
! [SV1738: $i,SV1345: $i,SV794: $i,SV153: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV153 )
| ( c_lessequals @ ( c_List_Onth @ SV794 @ SV1345 @ SV153 ) @ ( c_List_Onth @ SV794 @ SV1738 @ SV153 ) @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SV1738 @ ( c_Nat_Osize__class_Osize @ SV794 @ ( tc_List_Olist @ SV153 ) ) @ tc_nat )
| ~ ( c_lessequals @ SV1345 @ SV1738 @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ SV794 @ SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3724]) ).
thf(4297,plain,
! [SV1739: $i,SV1346: $i,SV795: $i,SV154: $i] :
( ( ( c_List_Odrop @ ( c_Suc @ SV154 ) @ ( c_List_Olist_OCons @ SV795 @ SV1346 @ SV1739 ) @ SV1739 )
= ( c_List_Odrop @ SV154 @ SV1346 @ SV1739 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3725]) ).
thf(4298,plain,
! [SV1347: $i,SV796: $i,SV155: $i] :
( ( ( ( c_List_Otake @ SV155 @ SV796 @ SV1347 )
= SV796 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV796 @ ( tc_List_Olist @ SV1347 ) ) @ SV155 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3726]) ).
thf(4299,plain,
! [SV1740: $i,SV1348: $i,SV797: $i,SV156: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV156 )
| ( c_lessequals @ SV797 @ SV1348 @ SV156 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV797 @ ( c_List_Olist_OCons @ SV1348 @ SV1740 @ SV156 ) @ SV156 ) @ SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3727]) ).
thf(4300,plain,
! [SV1741: $i,SV1349: $i,SV798: $i,SV157: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV157 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV798 @ ( c_List_Olist_OCons @ SV1349 @ SV1741 @ SV157 ) @ SV157 ) @ SV157 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1349 @ SV1741 @ SV157 ) @ SV157 )
| ~ ( c_lessequals @ SV798 @ SV1349 @ SV157 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3728]) ).
thf(4301,plain,
! [SV1742: $i,SV1351: $i,SV800: $i,SV159: $i] :
( ( ! [SY4505: $i] :
( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV159 @ SV800 @ SV1351 ) @ ( c_Suc @ SV1742 ) @ SY4505 @ SV1351 )
= ( c_List_Olist_OCons @ SV159 @ ( c_List_Olist__update @ SV800 @ SV1742 @ SY4505 @ SV1351 ) @ SV1351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3730]) ).
thf(4302,plain,
! [SV1352: $i,SV801: $i,SV160: $i] :
( ( ( ( c_List_Ohd @ ( c_List_Oreplicate @ SV160 @ SV801 @ SV1352 ) @ SV1352 )
= SV801 )
= $true )
| ( ( SV160
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3731]) ).
thf(4303,plain,
! [SV1743: $i,SV1354: $i,SV803: $i,SV162: $i] :
( ( ( ( c_List_Olist__update @ SV162 @ SV803 @ SV1354 @ SV1743 )
= SV162 )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV162 @ ( tc_List_Olist @ SV1743 ) ) @ SV803 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3733]) ).
thf(4304,plain,
! [SV1356: $i,SV805: $i,SV164: $i] :
( ( ( c_in @ SV164 @ ( c_List_Oset @ SV805 @ SV1356 ) @ SV1356 )
= $true )
| ( ( ~ ( c_in @ SV164 @ ( c_List_Oset @ ( c_List_Obutlast @ SV805 @ SV1356 ) @ SV1356 ) @ SV1356 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3735]) ).
thf(4305,plain,
! [SV1744: $i,SV1357: $i,SV806: $i,SV165: $i] :
( ( ( c_List_Odrop @ SV165 @ ( c_List_Otake @ SV806 @ SV1357 @ SV1744 ) @ SV1744 )
= ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ SV806 @ SV165 @ tc_nat ) @ ( c_List_Odrop @ SV165 @ SV1357 @ SV1744 ) @ SV1744 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3736]) ).
thf(4306,plain,
! [SV1745: $i,SV1358: $i,SV807: $i,SV166: $i] :
( ( ( c_in @ SV166 @ ( c_List_Oset @ SV807 @ SV1358 ) @ SV1358 )
| ~ ( c_in @ SV166 @ ( c_List_Oset @ ( c_List_Osublist @ SV807 @ SV1745 @ SV1358 ) @ SV1358 ) @ SV1358 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3737]) ).
thf(4307,plain,
! [SV1746: $i,SV1359: $i,SV808: $i,SV167: $i] :
( ( ~ ( c_in @ SV167 @ ( c_List_Oset @ ( c_List_Osublist @ SV808 @ SV1359 @ SV1746 ) @ SV1746 ) @ SV1746 )
| ( c_in @ SV167 @ ( c_List_Oset @ SV808 @ SV1746 ) @ SV1746 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3738]) ).
thf(4308,plain,
! [SV1747: $i,SV1360: $i,SV809: $i,SV168: $i] :
( ( ( c_List_Odrop @ SV168 @ ( c_List_Oreplicate @ SV809 @ SV1360 @ SV1747 ) @ SV1747 )
= ( c_List_Oreplicate @ ( c_HOL_Ominus__class_Ominus @ SV809 @ SV168 @ tc_nat ) @ SV1360 @ SV1747 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3739]) ).
thf(4309,plain,
! [SV1748: $i,SV1361: $i,SV810: $i,SV169: $i] :
( ( ! [SY4506: $i,SY4507: $i] :
( ~ ( class_Orderings_Olinorder @ SV169 )
| ( ( c_List_Olinorder__class_Oinsort__key @ SV810 @ SV1361 @ ( c_List_Olist_OCons @ SV1748 @ SY4506 @ SY4507 ) @ SY4507 @ SV169 )
= ( c_List_Olist_OCons @ SV1361 @ ( c_List_Olist_OCons @ SV1748 @ SY4506 @ SY4507 ) @ SY4507 ) )
| ~ ( c_lessequals @ ( hAPP @ SV810 @ SV1361 ) @ ( hAPP @ SV810 @ SV1748 ) @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3740]) ).
thf(4310,plain,
! [SV1749: $i,SV1362: $i,SV811: $i,SV170: $i] :
( ( ! [SY4508: $i,SY4509: $i] :
( ~ ( class_Orderings_Olinorder @ SV170 )
| ( ( c_List_Olinorder__class_Oinsort__key @ SV811 @ SV1362 @ ( c_List_Olist_OCons @ SV1749 @ SY4508 @ SY4509 ) @ SY4509 @ SV170 )
= ( c_List_Olist_OCons @ SV1749 @ ( c_List_Olinorder__class_Oinsort__key @ SV811 @ SV1362 @ SY4508 @ SY4509 @ SV170 ) @ SY4509 ) )
| ( c_lessequals @ ( hAPP @ SV811 @ SV1362 ) @ ( hAPP @ SV811 @ SV1749 ) @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3741]) ).
thf(4311,plain,
! [SV1750: $i,SV1363: $i,SV812: $i,SV171: $i] :
( ( ! [SY4510: $i] :
( ~ ( class_Orderings_Olinorder @ SV171 )
| ( ( c_Nat_Osize__class_Osize @ ( c_List_Olinorder__class_Oinsort__key @ SV812 @ SV1363 @ SV1750 @ SY4510 @ SV171 ) @ ( tc_List_Olist @ SY4510 ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ SV1750 @ ( tc_List_Olist @ SY4510 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3742]) ).
thf(4312,plain,
! [SV1364: $i,SV813: $i,SV172: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV172 @ SV813 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1364 @ SV813 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV172 @ SV1364 @ tc_nat )
| ~ ( c_lessequals @ SV813 @ SV1364 @ tc_nat )
| ~ ( c_lessequals @ SV813 @ SV172 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3743]) ).
thf(4313,plain,
! [SV1365: $i,SV814: $i,SV173: $i] :
( ( ( c_lessequals @ SV173 @ SV814 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV173 @ SV1365 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV814 @ SV1365 @ tc_nat ) @ tc_nat )
| ~ ( c_lessequals @ SV1365 @ SV814 @ tc_nat )
| ~ ( c_lessequals @ SV1365 @ SV173 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3744]) ).
thf(4314,plain,
! [SV815: $i,SV174: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV174 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_Suc @ SV815 ) @ SV174 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV174 ) @ ( c_HOL_Oone__class_Oone @ SV174 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV815 @ SV174 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3745]) ).
thf(4315,plain,
! [SV1366: $i,SV817: $i,SV176: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV176 @ SV817 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1366 @ SV817 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV176 @ SV1366 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV817 @ SV1366 @ tc_nat )
| ~ ( c_lessequals @ SV817 @ SV176 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3746]) ).
thf(4316,plain,
! [SV1368: $i,SV819: $i,SV178: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV178 @ SV819 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1368 @ SV819 @ tc_nat ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV819 @ SV178 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV178 @ SV1368 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3748]) ).
thf(4317,plain,
! [SV820: $i,SV179: $i] :
( ( ( ( c_Suc @ SV179 )
= SV820 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV179 @ SV820 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV179 ) @ SV820 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3749]) ).
thf(4318,plain,
! [SV821: $i,SV180: $i] :
( ( ( c_lessequals @ SV180 @ SV821 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Suc @ SV821 ) @ SV180 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3750]) ).
thf(4319,plain,
! [SV184: $i,SV824: $i] :
( ( ( c_lessequals @ SV824 @ SV184 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV184 @ ( c_HOL_Ominus__class_Ominus @ SV184 @ SV824 @ tc_nat ) @ tc_nat )
= SV824 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3753]) ).
thf(4320,plain,
! [SV825: $i,SV185: $i] :
( ( ( c_lessequals @ SV185 @ SV825 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV185 @ ( c_Suc @ SV825 ) @ tc_nat ) )
= $true )
| ( ( SV185
= ( c_Suc @ SV825 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3754]) ).
thf(4321,plain,
! [SV826: $i,SV187: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV187 @ SV826 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV826 @ ( c_Suc @ SV187 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3755]) ).
thf(4322,plain,
! [SV1370: $i,SV829: $i,SV190: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV190 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV190 ) @ SV829 ) @ SV1370 ) @ SV1370 @ SV190 )
= SV829 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3758]) ).
thf(4323,plain,
! [SV1751: $i,SV1371: $i,SV830: $i,SV191: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV191 )
| ( c_lessequals @ SV830 @ SV1371 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1751 @ SV830 @ SV191 ) @ ( c_Power_Opower__class_Opower @ SV1751 @ SV1371 @ SV191 ) @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV191 ) @ SV1751 @ SV191 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3759]) ).
thf(4324,plain,
! [SV1752: $i,SV1372: $i,SV831: $i,SV192: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV192 )
| ( c_lessequals @ SV831 @ SV1372 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1752 @ SV831 @ SV192 ) @ ( c_Power_Opower__class_Opower @ SV1752 @ SV1372 @ SV192 ) @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV192 ) @ SV1752 @ SV192 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3760]) ).
thf(4325,plain,
! [SV1753: $i,SV1373: $i,SV832: $i,SV193: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV193 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV832 @ SV1373 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SV832 @ SV1753 @ SV193 ) @ SV193 )
| ~ ( c_lessequals @ SV1373 @ SV1753 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV193 ) @ SV832 @ SV193 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3761]) ).
thf(4326,plain,
! [SV833: $i,SV194: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV194 @ SV833 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV194 ) @ ( c_Suc @ SV833 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3762]) ).
thf(4327,plain,
! [SV834: $i,SV195: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV195 ) @ ( c_Suc @ SV834 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV195 @ SV834 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3763]) ).
thf(4328,plain,
! [SV835: $i,SV196: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV196 @ SV835 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV196 ) @ ( c_Suc @ SV835 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3764]) ).
thf(4329,plain,
! [SV836: $i,SV197: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV197 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV197 )
| ( ( c_HOL_Ominus__class_Ominus @ SV836 @ SV836 @ SV197 )
= ( c_HOL_Ozero__class_Ozero @ SV197 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3765]) ).
thf(4330,plain,
! [SV837: $i,SV198: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV198 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV837 @ SV837 @ SV198 )
= ( c_HOL_Ozero__class_Ozero @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3766]) ).
thf(4331,plain,
! [SV838: $i,SV199: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV199 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV838 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
= SV838 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3767]) ).
thf(4332,plain,
! [SV839: $i,SV200: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV200 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV839 @ SV839 @ SV200 )
= ( c_HOL_Ozero__class_Ozero @ SV200 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3768]) ).
thf(4333,plain,
! [SV840: $i,SV201: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV201 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV840 @ SV840 @ SV201 )
= ( c_HOL_Ozero__class_Ozero @ SV201 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3769]) ).
thf(4334,plain,
! [SV1754: $i,SV1375: $i,SV842: $i,SV208: $i] :
( ( ! [SY4511: $i] :
( ( c_ListOrder_Ostep1 @ SV208 @ ( c_List_Olist_OCons @ SV842 @ SV1375 @ SV1754 ) @ ( c_List_Olist_OCons @ SV842 @ SY4511 @ SV1754 ) @ SV1754 )
| ~ ( c_ListOrder_Ostep1 @ SV208 @ SV1375 @ SY4511 @ SV1754 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3772]) ).
thf(4335,plain,
! [SV1755: $i,SV1376: $i,SV843: $i,SV209: $i] :
( ( ! [SY4512: $i,SY4513: $i] :
( ( c_ListOrder_Ostep1 @ SV209 @ SV843 @ SV1376 @ SV1755 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV209 @ SY4512 ) @ SY4513 ) )
| ~ ( c_ListOrder_Ostep1 @ SV209 @ ( c_List_Olist_OCons @ SY4512 @ SV843 @ SV1755 ) @ ( c_List_Olist_OCons @ SY4513 @ SV1376 @ SV1755 ) @ SV1755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3773]) ).
thf(4336,plain,
! [SV1756: $i,SV1377: $i,SV844: $i,SV210: $i] :
( ( ! [SY4514: $i,SY4515: $i] :
( ( c_ListOrder_Ostep1 @ SV210 @ SV844 @ SV1377 @ SV1756 )
| ( SV1377 = SV844 )
| ~ ( c_ListOrder_Ostep1 @ SV210 @ ( c_List_Olist_OCons @ SY4514 @ SV844 @ SV1756 ) @ ( c_List_Olist_OCons @ SY4515 @ SV1377 @ SV1756 ) @ SV1756 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3774]) ).
thf(4337,plain,
! [SV1757: $i,SV1378: $i,SV845: $i,SV211: $i] :
( ( ! [SY4516: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV211 @ SV845 ) @ SV1378 ) )
| ( c_ListOrder_Ostep1 @ SV211 @ ( c_List_Olist_OCons @ SV845 @ SV1757 @ SY4516 ) @ ( c_List_Olist_OCons @ SV1378 @ SV1757 @ SY4516 ) @ SY4516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3775]) ).
thf(4338,plain,
! [SV1758: $i,SV1379: $i,SV846: $i,SV212: $i] :
( ( ! [SY4517: $i,SY4518: $i] :
( ( SV212 = SV846 )
| ( SV1379 = SV1758 )
| ~ ( c_ListOrder_Ostep1 @ SY4517 @ ( c_List_Olist_OCons @ SV846 @ SV1758 @ SY4518 ) @ ( c_List_Olist_OCons @ SV212 @ SV1379 @ SY4518 ) @ SY4518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3776]) ).
thf(4339,plain,
! [SV1759: $i,SV1380: $i,SV847: $i,SV213: $i] :
( ( ! [SY4519: $i,SY4520: $i] :
( ( SV213 = SV847 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV1380 @ SV847 ) @ SV213 ) )
| ~ ( c_ListOrder_Ostep1 @ SV1380 @ ( c_List_Olist_OCons @ SV847 @ SV1759 @ SY4519 ) @ ( c_List_Olist_OCons @ SV213 @ SY4520 @ SY4519 ) @ SY4519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3777]) ).
thf(4340,plain,
! [SV1381: $i,SV848: $i,SV214: $i] :
( ( c_ListOrder_Ostep1 @ SV214 @ SV848 @ ( c_List_Olist_ONil @ SV1381 ) @ SV1381 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3778]) ).
thf(4341,plain,
! [SV1382: $i,SV849: $i,SV215: $i] :
( ( c_ListOrder_Ostep1 @ SV215 @ ( c_List_Olist_ONil @ SV849 ) @ SV1382 @ SV849 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3779]) ).
thf(4342,plain,
! [SV1760: $i,SV1383: $i,SV850: $i,SV216: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV216 )
| ( c_lessequals @ ( c_List_Onth @ SV850 @ SV1383 @ SV216 ) @ ( c_List_Onth @ SV850 @ SV1760 @ SV216 ) @ SV216 )
| ~ ( c_HOL_Oord__class_Oless @ SV1383 @ ( c_Nat_Osize__class_Osize @ SV850 @ ( tc_List_Olist @ SV216 ) ) @ tc_nat )
| ~ ( c_lessequals @ SV1760 @ SV1383 @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Orev @ SV850 @ SV216 ) @ SV216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3780]) ).
thf(4343,plain,
! [SV1384: $i,SV851: $i,SV217: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV217 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV217 ) @ SV851 ) @ SV1384 ) @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 )
| ~ ( c_lessequals @ SV1384 @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 )
| ~ ( c_HOL_Oord__class_Oless @ SV851 @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3781]) ).
thf(4344,plain,
! [SV1385: $i,SV852: $i,SV218: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV218 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV218 ) @ SV852 ) @ SV1385 ) @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
| ~ ( c_HOL_Oord__class_Oless @ SV1385 @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
| ~ ( c_lessequals @ SV852 @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3782]) ).
thf(4345,plain,
! [SV1761: $i,SV1386: $i,SV853: $i,SV219: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV219 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV219 )
| ( c_HOL_Oord__class_Oless @ SV853 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV219 ) @ SV1386 ) @ SV1761 ) @ SV219 )
| ~ ( c_lessequals @ SV853 @ SV1761 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV1386 @ SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3783]) ).
thf(4346,plain,
! [SV1762: $i,SV1387: $i,SV854: $i,SV220: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV220 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV220 )
| ( c_HOL_Oord__class_Oless @ SV854 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV220 ) @ SV1387 ) @ SV1762 ) @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ SV854 @ SV1762 @ SV220 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV1387 @ SV220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3784]) ).
thf(4347,plain,
! [SV1388: $i,SV855: $i,SV221: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV221 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SV855 ) @ SV1388 ) @ SV221 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ SV1388 @ SV221 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ SV855 @ SV221 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3785]) ).
thf(4348,plain,
! [SV1389: $i,SV856: $i,SV222: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV222 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SV856 ) @ SV1389 ) @ SV222 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ SV1389 @ SV222 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ SV856 @ SV222 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3786]) ).
thf(4349,plain,
! [SV1763: $i,SV1390: $i,SV857: $i,SV224: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV224 )
| ( c_HOL_Oord__class_Oless @ SV857 @ SV1390 @ SV224 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV224 ) @ SV1390 @ SV224 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV857 @ SV1763 @ SV224 ) @ ( c_Power_Opower__class_Opower @ SV1390 @ SV1763 @ SV224 ) @ SV224 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3788]) ).
thf(4350,plain,
! [SV1764: $i,SV1391: $i,SV858: $i,SV225: $i] :
( ( ( c_in @ SV225 @ ( c_List_Oset @ ( c_List_Oappend @ SV858 @ ( c_List_Olist_OCons @ SV225 @ SV1391 @ SV1764 ) @ SV1764 ) @ SV1764 ) @ SV1764 )
| ( c_in @ SV225 @ ( c_List_Oset @ SV858 @ SV1764 ) @ SV1764 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3789]) ).
thf(4351,plain,
! [SV1765: $i,SV1392: $i,SV859: $i,SV226: $i] :
( ( ( c_in @ SV226 @ ( c_List_Oset @ ( c_List_Oappend @ SV859 @ ( c_List_Olist_OCons @ SV226 @ SV1392 @ SV1765 ) @ SV1765 ) @ SV1765 ) @ SV1765 )
| ( c_in @ SV226 @ ( c_List_Oset @ SV1392 @ SV1765 ) @ SV1765 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3790]) ).
thf(4352,plain,
! [SV1766: $i,SV1393: $i,SV860: $i,SV227: $i] :
( ( c_in @ SV227 @ ( c_List_Oset @ ( c_List_Oappend @ SV860 @ ( c_List_Olist_OCons @ SV227 @ SV1393 @ SV1766 ) @ SV1766 ) @ SV1766 ) @ SV1766 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3791]) ).
thf(4353,plain,
! [SV228: $i] :
( ( ( ~ ( class_Power_Opower @ SV228 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV228 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV228 )
= ( c_HOL_Oone__class_Oone @ SV228 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV228 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3792]) ).
thf(4354,plain,
! [SV1767: $i,SV1394: $i,SV861: $i,SV229: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV229 )
| ( c_HOL_Oord__class_Oless @ SV861 @ SV1394 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1767 @ SV861 @ SV229 ) @ ( c_Power_Opower__class_Opower @ SV1767 @ SV1394 @ SV229 ) @ SV229 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV229 ) @ SV1767 @ SV229 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3793]) ).
thf(4355,plain,
! [SV1768: $i,SV1395: $i,SV862: $i,SV230: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV230 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV862 @ SV1395 @ SV230 ) @ ( c_Power_Opower__class_Opower @ SV862 @ SV1768 @ SV230 ) @ SV230 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV230 ) @ SV862 @ SV230 )
| ~ ( c_HOL_Oord__class_Oless @ SV1395 @ SV1768 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3794]) ).
thf(4356,plain,
! [SV1769: $i,SV1396: $i,SV863: $i,SV231: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV231 )
| ( c_HOL_Oord__class_Oless @ SV863 @ SV1396 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1769 @ SV863 @ SV231 ) @ ( c_Power_Opower__class_Opower @ SV1769 @ SV1396 @ SV231 ) @ SV231 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV231 ) @ SV1769 @ SV231 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3795]) ).
thf(4357,plain,
! [SV1770: $i,SV1397: $i,SV864: $i,SV232: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV232 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV864 @ SV1397 @ SV232 ) @ ( c_Power_Opower__class_Opower @ SV864 @ SV1770 @ SV232 ) @ SV232 )
| ~ ( c_HOL_Oord__class_Oless @ SV1397 @ SV1770 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV232 ) @ SV864 @ SV232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3796]) ).
thf(4358,plain,
! [SV1771: $i,SV1398: $i,SV865: $i,SV233: $i] :
( ( ! [SY4521: $i,SY4522: $i] :
( ( SV233 = SV865 )
| ( SV1398 = SV1771 )
| ~ ( c_ListOrder_Ostep1 @ SY4521 @ ( c_List_Oappend @ SV233 @ ( c_List_Olist_OCons @ SV1398 @ ( c_List_Olist_ONil @ SY4522 ) @ SY4522 ) @ SY4522 ) @ ( c_List_Oappend @ SV865 @ ( c_List_Olist_OCons @ SV1771 @ ( c_List_Olist_ONil @ SY4522 ) @ SY4522 ) @ SY4522 ) @ SY4522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3797]) ).
thf(4359,plain,
! [SV1772: $i,SV1399: $i,SV866: $i,SV234: $i] :
( ( ! [SY4523: $i,SY4524: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV234 @ SV866 ) @ SV1399 ) )
| ( SV866 = SV1399 )
| ~ ( c_ListOrder_Ostep1 @ SV234 @ ( c_List_Oappend @ SV1772 @ ( c_List_Olist_OCons @ SV866 @ ( c_List_Olist_ONil @ SY4523 ) @ SY4523 ) @ SY4523 ) @ ( c_List_Oappend @ SY4524 @ ( c_List_Olist_OCons @ SV1399 @ ( c_List_Olist_ONil @ SY4523 ) @ SY4523 ) @ SY4523 ) @ SY4523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3798]) ).
thf(4360,plain,
! [SV1773: $i,SV1400: $i,SV867: $i,SV235: $i] :
( ( ! [SY4525: $i,SY4526: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV867 ) @ SV1400 ) )
| ( c_ListOrder_Ostep1 @ SV235 @ SV1773 @ SY4525 @ SY4526 )
| ~ ( c_ListOrder_Ostep1 @ SV235 @ ( c_List_Oappend @ SV1773 @ ( c_List_Olist_OCons @ SV867 @ ( c_List_Olist_ONil @ SY4526 ) @ SY4526 ) @ SY4526 ) @ ( c_List_Oappend @ SY4525 @ ( c_List_Olist_OCons @ SV1400 @ ( c_List_Olist_ONil @ SY4526 ) @ SY4526 ) @ SY4526 ) @ SY4526 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3799]) ).
thf(4361,plain,
! [SV1774: $i,SV1401: $i,SV868: $i,SV236: $i] :
( ( ! [SY4527: $i,SY4528: $i] :
( ( SV236 = SV868 )
| ( c_ListOrder_Ostep1 @ SV1401 @ SV236 @ SV868 @ SV1774 )
| ~ ( c_ListOrder_Ostep1 @ SV1401 @ ( c_List_Oappend @ SV236 @ ( c_List_Olist_OCons @ SY4527 @ ( c_List_Olist_ONil @ SV1774 ) @ SV1774 ) @ SV1774 ) @ ( c_List_Oappend @ SV868 @ ( c_List_Olist_OCons @ SY4528 @ ( c_List_Olist_ONil @ SV1774 ) @ SV1774 ) @ SV1774 ) @ SV1774 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3800]) ).
thf(4362,plain,
! [SV1775: $i,SV1402: $i,SV870: $i,SV238: $i] :
( ( ! [SY4529: $i] :
( ( ( c_List_OtakeWhile @ SV238 @ ( c_List_Oappend @ SV870 @ SV1402 @ SV1775 ) @ SV1775 )
= ( c_List_OtakeWhile @ SV238 @ SV870 @ SV1775 ) )
| ( hBOOL @ ( hAPP @ SV238 @ SY4529 ) )
| ~ ( c_in @ SY4529 @ ( c_List_Oset @ SV870 @ SV1775 ) @ SV1775 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3802]) ).
thf(4363,plain,
! [SV1403: $i,SV871: $i,SV239: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV239 @ SV871 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV239 @ SV1403 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV871 @ SV1403 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3803]) ).
thf(4364,plain,
! [SV1404: $i,SV872: $i,SV240: $i] :
( ( ( ( c_List_Odrop @ SV240 @ SV872 @ SV1404 )
= ( c_List_Olist_ONil @ SV1404 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV872 @ ( tc_List_Olist @ SV1404 ) ) @ SV240 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3804]) ).
thf(4365,plain,
! [SV1776: $i,SV1405: $i,SV873: $i,SV241: $i] :
( ( ( c_List_Otake @ SV241 @ ( c_List_Oappend @ SV873 @ SV1405 @ SV1776 ) @ SV1776 )
= ( c_List_Oappend @ ( c_List_Otake @ SV241 @ SV873 @ SV1776 ) @ ( c_List_Otake @ ( c_HOL_Ominus__class_Ominus @ SV241 @ ( c_Nat_Osize__class_Osize @ SV873 @ ( tc_List_Olist @ SV1776 ) ) @ tc_nat ) @ SV1405 @ SV1776 ) @ SV1776 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3805]) ).
thf(4366,plain,
! [SV1777: $i,SV1406: $i,SV874: $i,SV242: $i] :
( ( ( c_List_Odrop @ SV242 @ ( c_List_Oappend @ SV874 @ SV1406 @ SV1777 ) @ SV1777 )
= ( c_List_Oappend @ ( c_List_Odrop @ SV242 @ SV874 @ SV1777 ) @ ( c_List_Odrop @ ( c_HOL_Ominus__class_Ominus @ SV242 @ ( c_Nat_Osize__class_Osize @ SV874 @ ( tc_List_Olist @ SV1777 ) ) @ tc_nat ) @ SV1406 @ SV1777 ) @ SV1777 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3806]) ).
thf(4367,plain,
! [SV1778: $i,SV1407: $i,SV875: $i,SV243: $i] :
( ( ( c_in @ SV243 @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ SV875 @ SV1407 @ SV1778 ) @ SV1778 ) @ SV1778 ) @ SV1778 )
| ~ ( c_in @ SV243 @ ( c_List_Oset @ ( c_List_Obutlast @ SV1407 @ SV1778 ) @ SV1778 ) @ SV1778 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3807]) ).
thf(4368,plain,
! [SV1779: $i,SV1408: $i,SV876: $i,SV244: $i] :
( ( ( c_in @ SV244 @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ SV876 @ SV1408 @ SV1779 ) @ SV1779 ) @ SV1779 ) @ SV1779 )
| ~ ( c_in @ SV244 @ ( c_List_Oset @ ( c_List_Obutlast @ SV876 @ SV1779 ) @ SV1779 ) @ SV1779 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3808]) ).
thf(4369,plain,
! [SV1780: $i,SV1409: $i,SV878: $i,SV246: $i] :
( ( ! [SY4530: $i] :
( ( c_HOL_Oord__class_Oless @ SV246 @ ( c_List_Olist_Olist__size @ SV878 @ SV1409 @ SV1780 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV246 @ ( hAPP @ SV878 @ SY4530 ) @ tc_nat )
| ~ ( c_in @ SY4530 @ ( c_List_Oset @ SV1409 @ SV1780 ) @ SV1780 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3810]) ).
thf(4370,plain,
! [SV1781: $i,SV1410: $i,SV879: $i,SV247: $i] :
( ( ( ( c_List_OtakeWhile @ SV247 @ SV879 @ SV1410 )
= ( c_List_Otake @ SV1781 @ SV879 @ SV1410 ) )
| ( hBOOL @ ( hAPP @ SV247 @ ( c_List_Onth @ SV879 @ SV1781 @ SV1410 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV247 @ ( c_List_Onth @ SV879 @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV247 @ SV1781 @ SV879 @ SV1410 ) @ SV1410 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3811]) ).
thf(4371,plain,
! [SV1411: $i,SV882: $i,SV250: $i] :
( ( ( ( c_List_Olength__unique @ ( c_List_Olist_OCons @ SV250 @ SV882 @ SV1411 ) @ SV1411 )
= ( c_List_Olength__unique @ SV882 @ SV1411 ) )
= $true )
| ( ( ~ ( c_in @ SV250 @ ( c_List_Oset @ SV882 @ SV1411 ) @ SV1411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3814]) ).
thf(4372,plain,
! [SV1412: $i,SV883: $i,SV251: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Otake @ SV251 @ SV883 @ SV1412 ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ ( c_List_Odrop @ SV251 @ SV883 @ SV1412 ) @ SV1412 ) @ ( c_List_Olist_ONil @ SV1412 ) @ SV1412 ) @ SV1412 )
= ( c_List_Otake @ ( c_Suc @ SV251 ) @ SV883 @ SV1412 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV251 @ ( c_Nat_Osize__class_Osize @ SV883 @ ( tc_List_Olist @ SV1412 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3815]) ).
thf(4373,plain,
! [SV1782: $i,SV1413: $i,SV884: $i,SV252: $i] :
( ( ! [SY4531: $i] :
( ~ ( class_Orderings_Olinorder @ SV252 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV884 @ ( c_List_Olinorder__class_Oinsort__key @ SV884 @ SV1413 @ SV1782 @ SY4531 @ SV252 ) @ SY4531 @ SV252 ) @ SV252 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV884 @ SV1782 @ SY4531 @ SV252 ) @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3816]) ).
thf(4374,plain,
! [SV1783: $i,SV1414: $i,SV885: $i,SV253: $i] :
( ( ! [SY4532: $i] :
( ~ ( class_Orderings_Olinorder @ SV253 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV885 @ SV1414 @ SV1783 @ SV253 ) @ SV253 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV885 @ ( c_List_Olinorder__class_Oinsort__key @ SV885 @ SY4532 @ SV1414 @ SV1783 @ SV253 ) @ SV1783 @ SV253 ) @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3817]) ).
thf(4375,plain,
! [SV1784: $i,SV1415: $i,SV886: $i,SV254: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Olist__update @ SV254 @ SV886 @ SV1415 @ SV1784 ) @ ( tc_List_Olist @ SV1784 ) )
= ( c_Nat_Osize__class_Osize @ SV254 @ ( tc_List_Olist @ SV1784 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3818]) ).
thf(4376,plain,
! [SV888: $i,SV256: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV256 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV888 @ SV256 ) @ ( c_HOL_Ozero__class_Ozero @ SV256 ) @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3819]) ).
thf(4377,plain,
! [SV1785: $i,SV1416: $i,SV889: $i,SV257: $i] :
( ( ! [SY4533: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV257 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SV889 ) @ SV1416 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SV1785 ) @ SY4533 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SV889 ) @ SV1785 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SV1416 ) @ SY4533 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3820]) ).
thf(4378,plain,
! [SV1417: $i,SV890: $i,SV258: $i] :
( ( ( ( c_List_Olast @ ( c_List_Oreplicate @ SV258 @ SV890 @ SV1417 ) @ SV1417 )
= SV890 )
= $true )
| ( ( SV258
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3821]) ).
thf(4379,plain,
! [SV1420: $i,SV893: $i,SV261: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV261 ) )
= $true )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_OtakeWhile @ SV893 @ SV1420 @ SV261 ) @ SV261 )
| ~ ( c_List_Olinorder__class_Osorted @ SV1420 @ SV261 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3824]) ).
thf(4380,plain,
! [SV1422: $i,SV895: $i,SV263: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV263 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV263 ) @ SV895 ) @ SV1422 ) @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ SV1422 @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ SV895 @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3826]) ).
thf(4381,plain,
! [SV1786: $i,SV1423: $i,SV896: $i,SV264: $i] :
( ( ( ( c_List_Onth @ ( c_List_OtakeWhile @ SV264 @ SV896 @ SV1423 ) @ SV1786 @ SV1423 )
= ( c_List_Onth @ SV896 @ SV1786 @ SV1423 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1786 @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ SV264 @ SV896 @ SV1423 ) @ ( tc_List_Olist @ SV1423 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3827]) ).
thf(4382,plain,
! [SV1787: $i,SV1425: $i,SV899: $i,SV267: $i] :
( ( ! [SY4534: $i,SY4535: $i] :
( ( hAPP @ ( c_COMBC @ SV267 @ SV899 @ SV1425 @ SV1787 @ SY4534 ) @ SY4535 )
= ( hAPP @ ( hAPP @ SV267 @ SY4535 ) @ SV899 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3830]) ).
thf(4383,plain,
! [SV1426: $i,SV900: $i,SV268: $i] :
( ( ( hBOOL @ ( hAPP @ SV268 @ SV900 ) )
= $true )
| ( ( ~ ( c_in @ SV900 @ SV268 @ SV1426 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3831]) ).
thf(4384,plain,
! [SV1427: $i,SV901: $i,SV269: $i] :
( ( ( c_in @ SV269 @ SV901 @ SV1427 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV901 @ SV269 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3832]) ).
thf(4385,plain,
! [SV1788: $i,SV1428: $i,SV902: $i,SV270: $i] :
( ( ! [SY4536: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ SV270 @ SV902 @ SV1428 @ SV1788 ) @ SY4536 @ SV1788 )
= ( c_List_Onth @ SV270 @ SY4536 @ SV1788 ) )
| ( SV902 = SY4536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3833]) ).
thf(4386,plain,
! [SV1789: $i,SV1429: $i,SV903: $i,SV271: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV271 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ SV903 ) @ SV1429 ) ) @ SV1789 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ SV903 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ SV1429 ) @ SV1789 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3834]) ).
thf(4387,plain,
! [SV1790: $i,SV1430: $i,SV904: $i,SV272: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV272 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV904 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV1430 ) @ SV1790 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV1430 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV904 ) @ SV1790 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3835]) ).
thf(4388,plain,
! [SV1791: $i,SV1431: $i,SV905: $i,SV273: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV273 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ SV905 ) @ SV1431 ) ) @ SV1791 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ SV905 ) @ SV1791 ) ) @ SV1431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3836]) ).
thf(4389,plain,
! [SV1792: $i,SV1432: $i,SV906: $i,SV274: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV274 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ SV906 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ SV1432 ) @ SV1792 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ SV906 ) @ SV1432 ) ) @ SV1792 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3837]) ).
thf(4390,plain,
! [SV1793: $i,SV1433: $i,SV907: $i,SV275: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV275 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ SV907 ) @ SV1433 ) ) @ SV1793 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ SV907 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ SV1433 ) @ SV1793 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3838]) ).
thf(4391,plain,
! [SV1794: $i,SV1434: $i,SV908: $i,SV276: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV276 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ SV908 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ SV1434 ) @ SV1794 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ SV1434 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ SV908 ) @ SV1794 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3839]) ).
thf(4392,plain,
! [SV1795: $i,SV1435: $i,SV909: $i,SV277: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV277 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ SV909 ) @ SV1435 ) ) @ SV1795 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ SV909 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ SV1435 ) @ SV1795 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3840]) ).
thf(4393,plain,
! [SV1796: $i,SV1436: $i,SV910: $i,SV278: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV278 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV278 ) @ SV910 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV278 ) @ SV1436 ) @ SV1796 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV278 ) @ SV1436 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV278 ) @ SV910 ) @ SV1796 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3841]) ).
thf(4394,plain,
! [SV1797: $i,SV1437: $i,SV911: $i,SV279: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV279 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV279 ) @ SV911 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV279 ) @ SV1437 ) @ SV1797 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV279 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV279 ) @ SV911 ) @ SV1437 ) ) @ SV1797 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3842]) ).
thf(4395,plain,
! [SV1798: $i,SV1438: $i,SV912: $i,SV280: $i] :
( ( ( ( c_List_Onth @ ( c_List_Otake @ SV280 @ SV912 @ SV1438 ) @ SV1798 @ SV1438 )
= ( c_List_Onth @ SV912 @ SV1798 @ SV1438 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1798 @ SV280 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3843]) ).
thf(4396,plain,
! [SV1799: $i,SV1439: $i,SV913: $i,SV281: $i] :
( ( ~ ( class_Orderings_Oorder @ SV281 )
| ( c_HOL_Oord__class_Oless @ SV913 @ SV1439 @ SV281 )
| ~ ( c_HOL_Oord__class_Oless @ SV913 @ SV1799 @ SV281 )
| ~ ( c_HOL_Oord__class_Oless @ SV1799 @ SV1439 @ SV281 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3844]) ).
thf(4397,plain,
! [SV1800: $i,SV1440: $i,SV914: $i,SV282: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV282 )
| ( c_HOL_Oord__class_Oless @ SV914 @ SV1440 @ SV282 )
| ~ ( c_HOL_Oord__class_Oless @ SV1800 @ SV1440 @ SV282 )
| ~ ( c_HOL_Oord__class_Oless @ SV914 @ SV1800 @ SV282 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3845]) ).
thf(4398,plain,
! [SV1801: $i,SV1441: $i,SV915: $i,SV283: $i] :
( ( ! [SY4537: $i] :
( ( c_List_Otake @ SV283 @ ( c_List_Omap @ SV915 @ SV1441 @ SV1801 @ SY4537 ) @ SY4537 )
= ( c_List_Omap @ SV915 @ ( c_List_Otake @ SV283 @ SV1441 @ SV1801 ) @ SV1801 @ SY4537 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3846]) ).
thf(4399,plain,
! [SV1442: $i,SV916: $i,SV284: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV284 ) )
= $true )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ SV916 @ SV1442 @ SV284 ) @ SV284 )
| ~ ( c_List_Olinorder__class_Osorted @ SV1442 @ SV284 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3847]) ).
thf(4400,plain,
! [SV1443: $i,SV917: $i,SV285: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV285 ) ) @ SV917 ) @ SV1443 )
= ( c_Lambda_OdB_OVar @ SV285 ) )
= $true )
| ( ( ( SV285 = SV1443 )
| ( c_HOL_Oord__class_Oless @ SV1443 @ SV285 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3848]) ).
thf(4401,plain,
! [SV1802: $i,SV1444: $i,SV918: $i,SV286: $i] :
( ( ( c_List_Olistsp @ SV286 @ SV918 @ SV1444 )
| ~ ( c_List_Olistsp @ SV286 @ ( c_List_Oappend @ SV918 @ SV1802 @ SV1444 ) @ SV1444 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3849]) ).
thf(4402,plain,
! [SV1803: $i,SV1445: $i,SV919: $i,SV287: $i] :
( ( ( c_List_Olistsp @ SV287 @ SV919 @ SV1445 )
| ~ ( c_List_Olistsp @ SV287 @ ( c_List_Oappend @ SV1803 @ SV919 @ SV1445 ) @ SV1445 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3850]) ).
thf(4403,plain,
! [SV1804: $i,SV1446: $i,SV920: $i,SV288: $i] :
( ( ! [SY4538: $i] :
( ( c_Lambda_OdB_OdB__case @ SV288 @ SV920 @ SV1446 @ ( c_Lambda_OdB_OAbs @ SV1804 ) @ SY4538 )
= ( hAPP @ SV1446 @ SV1804 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3851]) ).
thf(4404,plain,
! [SV1805: $i,SV1447: $i,SV921: $i,SV289: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV289 ) @ SV921 ) @ SV1447 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1805 ) @ SV921 ) @ SV1447 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV289 ) @ SV1805 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3852]) ).
thf(4405,plain,
! [SV1448: $i,SV922: $i,SV290: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV290 @ ( c_Nat_Osize__class_Osize @ SV922 @ ( tc_List_Olist @ SV1448 ) ) @ tc_nat ) )
= $true )
| ( ( ( c_List_Olist__update @ SV922 @ SV290 @ ( c_List_Onth @ SV922 @ SV290 @ SV1448 ) @ SV1448 )
= SV922 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3853]) ).
thf(4406,plain,
! [SV1806: $i,SV1449: $i,SV923: $i,SV291: $i] :
( ( ( ( c_List_Olist__update @ SV291 @ SV923 @ SV1449 @ SV1806 )
= ( c_List_Oappend @ ( c_List_Otake @ SV923 @ SV291 @ SV1806 ) @ ( c_List_Olist_OCons @ SV1449 @ ( c_List_Odrop @ ( c_Suc @ SV923 ) @ SV291 @ SV1806 ) @ SV1806 ) @ SV1806 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV923 @ ( c_Nat_Osize__class_Osize @ SV291 @ ( tc_List_Olist @ SV1806 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3854]) ).
thf(4407,plain,
! [SV1450: $i,SV924: $i,SV292: $i] :
( ( ( SV292
= ( c_List_Oappend @ ( c_List_Otake @ SV924 @ SV292 @ SV1450 ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ SV292 @ SV924 @ SV1450 ) @ ( c_List_Odrop @ ( c_Suc @ SV924 ) @ SV292 @ SV1450 ) @ SV1450 ) @ SV1450 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV924 @ ( c_Nat_Osize__class_Osize @ SV292 @ ( tc_List_Olist @ SV1450 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3855]) ).
thf(4408,plain,
! [SV1451: $i,SV925: $i,SV293: $i] :
( ( ( ( c_List_Otake @ ( c_Suc @ SV293 ) @ SV925 @ SV1451 )
= ( c_List_Oappend @ ( c_List_Otake @ SV293 @ SV925 @ SV1451 ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ SV925 @ SV293 @ SV1451 ) @ ( c_List_Olist_ONil @ SV1451 ) @ SV1451 ) @ SV1451 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV293 @ ( c_Nat_Osize__class_Osize @ SV925 @ ( tc_List_Olist @ SV1451 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3856]) ).
thf(4409,plain,
! [SV1807: $i,SV1452: $i,SV926: $i,SV294: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV294 @ SV926 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV1452 ) @ SV1807 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV294 ) @ SV1452 ) @ SV1807 ) @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SV1452 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV1807 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV926 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3857]) ).
thf(4410,plain,
! [SV1453: $i,SV927: $i,SV295: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV295 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV927 @ SV295 @ SV1453 ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV927 ) @ SV295 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV1453 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3858]) ).
thf(4411,plain,
! [SV1808: $i,SV1454: $i,SV928: $i,SV296: $i] :
( ( ( ( c_List_OtakeWhile @ SV296 @ SV928 @ SV1454 )
= ( c_List_Otake @ SV1808 @ SV928 @ SV1454 ) )
| ( c_HOL_Oord__class_Oless @ SV1808 @ ( c_Nat_Osize__class_Osize @ SV928 @ ( tc_List_Olist @ SV1454 ) ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV296 @ ( c_List_Onth @ SV928 @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV296 @ SV1808 @ SV928 @ SV1454 ) @ SV1454 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3859]) ).
thf(4412,plain,
! [SV1809: $i,SV1455: $i,SV929: $i,SV297: $i] :
( ( ( ( c_List_OtakeWhile @ SV297 @ SV929 @ SV1455 )
= ( c_List_Otake @ SV1809 @ SV929 @ SV1455 ) )
| ( hBOOL @ ( hAPP @ SV297 @ ( c_List_Onth @ SV929 @ SV1809 @ SV1455 ) ) )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV297 @ SV1809 @ SV929 @ SV1455 ) @ ( c_Nat_Osize__class_Osize @ SV929 @ ( tc_List_Olist @ SV1455 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3860]) ).
thf(4413,plain,
! [SV1456: $i,SV930: $i,SV298: $i] :
( ( ( ( c_List_Ohd @ ( c_List_Odrop @ SV298 @ SV930 @ SV1456 ) @ SV1456 )
= ( c_List_Onth @ SV930 @ SV298 @ SV1456 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV298 @ ( c_Nat_Osize__class_Osize @ SV930 @ ( tc_List_Olist @ SV1456 ) ) @ tc_nat )
| ( SV930
= ( c_List_Olist_ONil @ SV1456 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3861]) ).
thf(4414,plain,
! [SV1457: $i,SV931: $i,SV299: $i] :
( ( ( ( c_List_Olist_OCons @ ( c_List_Onth @ SV299 @ SV931 @ SV1457 ) @ ( c_List_Odrop @ ( c_Suc @ SV931 ) @ SV299 @ SV1457 ) @ SV1457 )
= ( c_List_Odrop @ SV931 @ SV299 @ SV1457 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV931 @ ( c_Nat_Osize__class_Osize @ SV299 @ ( tc_List_Olist @ SV1457 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3862]) ).
thf(4415,plain,
! [SV1810: $i,SV1458: $i,SV932: $i,SV300: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV300 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV932 @ SV1458 @ SV300 ) @ ( c_Power_Opower__class_Opower @ SV1810 @ SV1458 @ SV300 ) @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1458 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SV932 @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ SV932 @ SV1810 @ SV300 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3863]) ).
thf(4416,plain,
! [SV1811: $i,SV1461: $i,SV935: $i,SV303: $i] :
( ( ( ( c_List_OtakeWhile @ SV303 @ SV935 @ SV1461 )
= ( c_List_Otake @ SV1811 @ SV935 @ SV1461 ) )
| ( hBOOL @ ( hAPP @ SV303 @ ( c_List_Onth @ SV935 @ SV1811 @ SV1461 ) ) )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV303 @ SV1811 @ SV935 @ SV1461 ) @ SV1811 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3866]) ).
thf(4417,plain,
! [SV1812: $i,SV1462: $i,SV936: $i,SV304: $i] :
( ( ( ( c_List_OtakeWhile @ SV304 @ SV936 @ SV1462 )
= ( c_List_Otake @ SV1812 @ SV936 @ SV1462 ) )
| ( c_HOL_Oord__class_Oless @ SV1812 @ ( c_Nat_Osize__class_Osize @ SV936 @ ( tc_List_Olist @ SV1462 ) ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV304 @ SV1812 @ SV936 @ SV1462 ) @ ( c_Nat_Osize__class_Osize @ SV936 @ ( tc_List_Olist @ SV1462 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3867]) ).
thf(4418,plain,
! [SV1813: $i,SV1463: $i,SV937: $i,SV305: $i] :
( ( ( ( c_List_OtakeWhile @ SV305 @ SV937 @ SV1463 )
= ( c_List_Otake @ SV1813 @ SV937 @ SV1463 ) )
| ( c_HOL_Oord__class_Oless @ SV1813 @ ( c_Nat_Osize__class_Osize @ SV937 @ ( tc_List_Olist @ SV1463 ) ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV305 @ SV1813 @ SV937 @ SV1463 ) @ SV1813 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3868]) ).
thf(4419,plain,
! [SV1814: $i,SV1464: $i,SV938: $i,SV306: $i] :
( ( ! [SY4539: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV306 @ SV938 @ SV1464 ) @ SV1814 @ SY4539 @ SV1464 )
= ( c_List_Oappend @ SV306 @ ( c_List_Olist__update @ SV938 @ ( c_HOL_Ominus__class_Ominus @ SV1814 @ ( c_Nat_Osize__class_Osize @ SV306 @ ( tc_List_Olist @ SV1464 ) ) @ tc_nat ) @ SY4539 @ SV1464 ) @ SV1464 ) )
| ( c_HOL_Oord__class_Oless @ SV1814 @ ( c_Nat_Osize__class_Osize @ SV306 @ ( tc_List_Olist @ SV1464 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3869]) ).
thf(4420,plain,
! [SV1815: $i,SV1465: $i,SV939: $i,SV307: $i] :
( ( ( ( c_List_Onth @ ( c_List_Oappend @ SV307 @ SV939 @ SV1465 ) @ SV1815 @ SV1465 )
= ( c_List_Onth @ SV939 @ ( c_HOL_Ominus__class_Ominus @ SV1815 @ ( c_Nat_Osize__class_Osize @ SV307 @ ( tc_List_Olist @ SV1465 ) ) @ tc_nat ) @ SV1465 ) )
| ( c_HOL_Oord__class_Oless @ SV1815 @ ( c_Nat_Osize__class_Osize @ SV307 @ ( tc_List_Olist @ SV1465 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3870]) ).
thf(4421,plain,
! [SV1816: $i,SV1466: $i,SV940: $i,SV308: $i] :
( ( ( c_in @ SV308 @ ( c_List_Oset @ ( c_List_Olist__update @ SV940 @ SV1466 @ SV308 @ SV1816 ) @ SV1816 ) @ SV1816 )
| ~ ( c_HOL_Oord__class_Oless @ SV1466 @ ( c_Nat_Osize__class_Osize @ SV940 @ ( tc_List_Olist @ SV1816 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3871]) ).
thf(4422,plain,
! [SV1467: $i,SV941: $i,SV309: $i] :
( ( ( c_in @ ( c_List_Onth @ SV309 @ SV941 @ SV1467 ) @ ( c_List_Oset @ SV309 @ SV1467 ) @ SV1467 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV941 @ ( c_Nat_Osize__class_Osize @ SV309 @ ( tc_List_Olist @ SV1467 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3872]) ).
thf(4423,plain,
! [SV1468: $i,SV942: $i,SV310: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV310 @ ( c_Nat_Osize__class_Osize @ SV942 @ ( tc_List_Olist @ SV1468 ) ) @ tc_nat ) )
= $true )
| ( ( c_in @ ( c_List_Onth @ SV942 @ SV310 @ SV1468 ) @ ( c_List_Oset @ SV942 @ SV1468 ) @ SV1468 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3873]) ).
thf(4424,plain,
! [SV1469: $i,SV943: $i,SV311: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV311 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV311 ) @ ( c_Power_Opower__class_Opower @ SV943 @ SV1469 @ SV311 ) @ SV311 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1469 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV311 ) @ SV943 @ SV311 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3874]) ).
thf(4425,plain,
! [SV1470: $i,SV944: $i,SV312: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV312 @ ( tc_List_Olist @ SV944 ) ) @ tc_nat )
= $true )
| ( ( ~ ( c_in @ SV1470 @ ( c_List_Oset @ SV312 @ SV944 ) @ SV944 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3875]) ).
thf(4426,plain,
! [SV1817: $i,SV1471: $i,SV945: $i,SV313: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV313 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV945 @ SV1471 @ SV313 ) @ ( c_Power_Opower__class_Opower @ SV945 @ SV1817 @ SV313 ) @ SV313 )
| ~ ( c_HOL_Oord__class_Oless @ SV945 @ ( c_HOL_Oone__class_Oone @ SV313 ) @ SV313 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV313 ) @ SV945 @ SV313 )
| ~ ( c_HOL_Oord__class_Oless @ SV1817 @ SV1471 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3876]) ).
thf(4427,plain,
! [SV1818: $i,SV1472: $i,SV946: $i,SV314: $i] :
( ( ! [SY4540: $i,SY4541: $i] :
( ( c_List_Omap @ SV314 @ ( c_List_Olist__update @ SV946 @ SV1472 @ SV1818 @ SY4540 ) @ SY4540 @ SY4541 )
= ( c_List_Olist__update @ ( c_List_Omap @ SV314 @ SV946 @ SY4540 @ SY4541 ) @ SV1472 @ ( hAPP @ SV314 @ SV1818 ) @ SY4541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3877]) ).
thf(4428,plain,
! [SV947: $i,SV315: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV315 ) @ SV947 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV315 ) ) @ ( c_Lambda_OdB_OAbs @ SV947 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3878]) ).
thf(4429,plain,
! [SV949: $i,SV317: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV317 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ SV949 @ SV317 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV317 ) @ SV949 ) @ SV949 ) @ SV317 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3880]) ).
thf(4430,plain,
! [SV950: $i,SV318: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV318 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV318 ) @ SV950 ) @ SV950 ) @ SV318 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ SV950 @ SV318 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3881]) ).
thf(4431,plain,
! [SV951: $i,SV320: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV320 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV320 ) @ ( c_HOL_Ozero__class_Ozero @ SV320 ) ) @ SV951 )
= SV951 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3883]) ).
thf(4432,plain,
! [SV952: $i,SV321: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV321 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV321 ) @ ( c_HOL_Ozero__class_Ozero @ SV321 ) ) @ SV952 )
= SV952 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3884]) ).
thf(4433,plain,
! [SV953: $i,SV322: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV322 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV322 )
| ( SV953
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV322 ) @ SV953 ) @ ( c_HOL_Ozero__class_Ozero @ SV322 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3885]) ).
thf(4434,plain,
! [SV954: $i,SV323: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV323 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV323 ) @ SV954 ) @ ( c_HOL_Ozero__class_Ozero @ SV323 ) )
= SV954 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3886]) ).
thf(4435,plain,
! [SV955: $i,SV324: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV324 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV324 ) @ ( c_HOL_Ozero__class_Ozero @ SV324 ) ) @ SV955 )
= SV955 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3887]) ).
thf(4436,plain,
! [SV956: $i,SV325: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV325 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV325 ) @ SV956 ) @ ( c_HOL_Ozero__class_Ozero @ SV325 ) )
= SV956 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3888]) ).
thf(4437,plain,
! [SV957: $i,SV326: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV326 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV326 ) @ SV957 ) @ ( c_HOL_Ozero__class_Ozero @ SV326 ) )
= SV957 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3889]) ).
thf(4438,plain,
! [SV958: $i,SV327: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV327 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV327 ) @ ( c_HOL_Ozero__class_Ozero @ SV327 ) ) @ SV958 )
= SV958 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3890]) ).
thf(4439,plain,
! [SV1819: $i,SV1475: $i,SV961: $i,SV333: $i] :
( ( ! [SY4542: $i] :
( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV333 @ SV961 @ SV1475 ) @ ( c_List_Olist_OCons @ SV1819 @ SY4542 @ SV1475 ) @ SV1475 )
= ( c_List_Olist_OCons @ SV333 @ ( c_List_Olist_OCons @ SV1819 @ ( c_List_Osplice @ SV961 @ SY4542 @ SV1475 ) @ SV1475 ) @ SV1475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3892]) ).
thf(4440,plain,
! [SV1820: $i,SV1476: $i,SV962: $i,SV334: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV334 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV962 @ SV1476 @ SV334 ) @ SV334 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1820 @ ( c_List_Olist_OCons @ SV962 @ SV1476 @ SV334 ) @ SV334 ) @ SV334 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3893]) ).
thf(4441,plain,
! [SV1821: $i,SV1477: $i,SV963: $i,SV335: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV335 @ SV963 @ SV1477 ) @ SV1821 @ SV1477 )
= ( c_List_Olist_OCons @ SV335 @ ( c_List_Oappend @ SV963 @ SV1821 @ SV1477 ) @ SV1477 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3894]) ).
thf(4442,plain,
! [SV1822: $i,SV1478: $i,SV964: $i,SV336: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV336 @ SV964 @ SV1478 ) @ SV1822 @ SV1478 )
= ( c_List_Olist_OCons @ SV336 @ ( c_List_Oappend @ SV964 @ SV1822 @ SV1478 ) @ SV1478 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3895]) ).
thf(4443,plain,
! [SV1823: $i,SV1479: $i,SV965: $i,SV337: $i] :
( ( ! [SY4543: $i] :
( ( c_List_Omap @ SV337 @ ( c_List_Olist_OCons @ SV965 @ SV1479 @ SV1823 ) @ SV1823 @ SY4543 )
= ( c_List_Olist_OCons @ ( hAPP @ SV337 @ SV965 ) @ ( c_List_Omap @ SV337 @ SV1479 @ SV1823 @ SY4543 ) @ SY4543 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3896]) ).
thf(4444,plain,
! [SV1824: $i,SV1480: $i,SV966: $i,SV338: $i] :
( ( ! [SY4544: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ SV338 @ SV966 ) @ ( c_List_Omap @ SV338 @ SV1480 @ SV1824 @ SY4544 ) @ SY4544 )
= ( c_List_Omap @ SV338 @ ( c_List_Olist_OCons @ SV966 @ SV1480 @ SV1824 ) @ SV1824 @ SY4544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3897]) ).
thf(4445,plain,
! [SV1825: $i,SV1481: $i,SV967: $i,SV339: $i] :
( ( ! [SY4545: $i] :
( ( c_List_Omap @ SV339 @ ( c_List_Olist_OCons @ SV967 @ SV1481 @ SV1825 ) @ SV1825 @ SY4545 )
= ( c_List_Olist_OCons @ ( hAPP @ SV339 @ SV967 ) @ ( c_List_Omap @ SV339 @ SV1481 @ SV1825 @ SY4545 ) @ SY4545 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3898]) ).
thf(4446,plain,
! [SV1826: $i,SV1482: $i,SV968: $i,SV340: $i] :
( ( ( c_List_Olist_OCons @ SV340 @ ( c_List_Oappend @ SV968 @ SV1482 @ SV1826 ) @ SV1826 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV340 @ SV968 @ SV1826 ) @ SV1482 @ SV1826 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3899]) ).
thf(4447,plain,
! [SV1827: $i,SV1483: $i,SV969: $i,SV341: $i] :
( ( ( c_List_Olist_OCons @ SV341 @ ( c_List_Oappend @ SV969 @ SV1483 @ SV1827 ) @ SV1827 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV341 @ SV969 @ SV1827 ) @ SV1483 @ SV1827 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3900]) ).
thf(4448,plain,
! [SV1484: $i,SV970: $i,SV342: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV342 ) )
= $true )
| ( ( ( c_List_Olinorder__class_Osorted @ SV970 @ SV342 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1484 @ SV970 @ SV342 ) @ SV342 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3901]) ).
thf(4449,plain,
! [SV1828: $i,SV1485: $i,SV971: $i,SV343: $i] :
( ( ( ( c_List_OtakeWhile @ SV343 @ ( c_List_Olist_OCons @ SV971 @ SV1485 @ SV1828 ) @ SV1828 )
= ( c_List_Olist_OCons @ SV971 @ ( c_List_OtakeWhile @ SV343 @ SV1485 @ SV1828 ) @ SV1828 ) )
| ~ ( hBOOL @ ( hAPP @ SV343 @ SV971 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3902]) ).
thf(4450,plain,
! [SV995: $i,SV374: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV374 )
= $false )
| ( ( ( c_List_Olistsum @ SV995 @ SV374 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV374 ) @ ( c_HOL_Ozero__class_Ozero @ SV374 ) @ SV995 @ SV374 @ SV374 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3915]) ).
thf(4451,plain,
! [SV1829: $i,SV1496: $i,SV996: $i,SV375: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV375 ) @ SV996 ) ) @ SV1496 ) @ SV1829 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV375 ) @ SV1496 ) @ SV1829 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV996 ) @ SV1496 ) @ SV1829 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3916]) ).
thf(4452,plain,
! [SV1830: $i,SV1497: $i,SV997: $i,SV376: $i] :
( ( ! [SY4546: $i,SY4547: $i] :
( ~ ( hBOOL @ ( hAPP @ SV376 @ ( c_Lambda_OdB_OdB__case @ SV997 @ SV1497 @ SV1830 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4546 ) @ SY4547 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SV1497 @ SY4546 ) @ SY4547 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3917]) ).
thf(4453,plain,
! [SV1831: $i,SV1498: $i,SV998: $i,SV377: $i] :
( ( ! [SY4548: $i,SY4549: $i] :
( ~ ( hBOOL @ ( hAPP @ SV377 @ ( c_Lambda_OdB_OdB__case @ SV998 @ SV1498 @ SV1831 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4548 ) @ SY4549 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV377 @ ( hAPP @ ( hAPP @ SV1498 @ SY4548 ) @ SY4549 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3918]) ).
thf(4454,plain,
! [SV1832: $i,SV1499: $i,SV999: $i,SV378: $i] :
( ( ! [SY4550: $i,SY4551: $i] :
( ( c_Lambda_OdB_OdB__case @ SV378 @ SV999 @ SV1499 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1832 ) @ SY4550 ) @ SY4551 )
= ( hAPP @ ( hAPP @ SV999 @ SV1832 ) @ SY4550 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3919]) ).
thf(4455,plain,
! [SV1500: $i,SV1000: $i,SV379: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV379 ) @ SV1000 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV379 ) @ SV1500 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1000 ) @ SV1500 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3920]) ).
thf(4456,plain,
! [SV1501: $i,SV1001: $i,SV380: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV380 ) @ SV1001 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1501 ) @ SV1001 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV380 ) @ SV1501 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3921]) ).
thf(4457,plain,
! [SV1833: $i,SV1502: $i,SV1002: $i,SV381: $i] :
( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV381 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV1002 ) @ SV1502 ) @ SV1833 @ SV381 @ SV381 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV1002 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV1502 @ SV1833 @ SV381 @ SV381 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3922]) ).
thf(4458,plain,
! [SV1834: $i,SV1503: $i,SV1003: $i,SV382: $i] :
( ( ! [SY4552: $i,SY4553: $i] :
( ( c_List_Ofoldl @ SV382 @ SV1003 @ ( c_List_Oappend @ SV1503 @ SV1834 @ SY4552 ) @ SY4553 @ SY4552 )
= ( c_List_Ofoldl @ SV382 @ ( c_List_Ofoldl @ SV382 @ SV1003 @ SV1503 @ SY4553 @ SY4552 ) @ SV1834 @ SY4553 @ SY4552 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3923]) ).
thf(4459,plain,
! [SV1835: $i,SV1504: $i,SV1004: $i,SV383: $i] :
( ( ! [SY4554: $i] :
( ~ ( hBOOL @ ( hAPP @ SV383 @ ( c_Lambda_OdB_OdB__case @ SV1004 @ SV1504 @ SV1835 @ ( c_Lambda_OdB_OVar @ SY4554 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV383 @ ( hAPP @ SV1004 @ SY4554 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3924]) ).
thf(4460,plain,
! [SV1836: $i,SV1505: $i,SV1005: $i,SV384: $i] :
( ( ! [SY4555: $i] :
( ~ ( hBOOL @ ( hAPP @ SV384 @ ( c_Lambda_OdB_OdB__case @ SV1005 @ SV1505 @ SV1836 @ ( c_Lambda_OdB_OVar @ SY4555 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV384 @ ( hAPP @ SV1005 @ SY4555 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3925]) ).
thf(4461,plain,
! [SV1837: $i,SV1506: $i,SV1008: $i,SV387: $i] :
( ( ( c_List_Orev @ ( c_List_Omap @ SV387 @ SV1008 @ SV1506 @ SV1837 ) @ SV1837 )
= ( c_List_Omap @ SV387 @ ( c_List_Orev @ SV1008 @ SV1506 ) @ SV1506 @ SV1837 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3927]) ).
thf(4462,plain,
! [SV1507: $i,SV1009: $i,SV388: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV388 ) )
= $true )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ SV1009 @ SV1507 @ SV388 ) @ SV388 )
| ~ ( c_List_Olinorder__class_Osorted @ SV1507 @ SV388 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3928]) ).
thf(4463,plain,
! [SV1838: $i,SV1508: $i,SV1010: $i,SV389: $i] :
( ( ( c_List_Onth @ ( c_List_Oappend @ SV389 @ ( c_List_Olist_OCons @ SV1010 @ SV1508 @ SV1838 ) @ SV1838 ) @ ( c_Nat_Osize__class_Osize @ SV389 @ ( tc_List_Olist @ SV1838 ) ) @ SV1838 )
= SV1010 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3929]) ).
thf(4464,plain,
! [SV1510: $i,SV1012: $i,SV391: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV391 @ ( c_List_Onth @ SV1012 @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ SV391 @ SV1012 @ SV1510 ) @ ( tc_List_Olist @ SV1510 ) ) @ SV1510 ) ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ SV391 @ SV1012 @ SV1510 ) @ ( tc_List_Olist @ SV1510 ) ) @ ( c_Nat_Osize__class_Osize @ SV1012 @ ( tc_List_Olist @ SV1510 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3931]) ).
thf(4465,plain,
! [SV1839: $i,SV1512: $i,SV1018: $i,SV397: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_List_Omap @ SV397 @ SV1018 @ SV1512 @ SV1839 ) @ ( tc_List_Olist @ SV1839 ) )
= ( c_Nat_Osize__class_Osize @ SV1018 @ ( tc_List_Olist @ SV1512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3934]) ).
thf(4466,plain,
! [SV1840: $i,SV1513: $i,SV1019: $i,SV398: $i] :
( ( ! [SY4556: $i] :
( ( c_List_Omap @ SV398 @ ( c_List_Oreplicate @ SV1019 @ SV1513 @ SV1840 ) @ SV1840 @ SY4556 )
= ( c_List_Oreplicate @ SV1019 @ ( hAPP @ SV398 @ SV1513 ) @ SY4556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3935]) ).
thf(4467,plain,
! [SV1841: $i,SV1514: $i,SV1020: $i,SV399: $i] :
( ( ( ( c_List_Onth @ ( c_List_Oappend @ SV399 @ SV1020 @ SV1514 ) @ SV1841 @ SV1514 )
= ( c_List_Onth @ SV399 @ SV1841 @ SV1514 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1841 @ ( c_Nat_Osize__class_Osize @ SV399 @ ( tc_List_Olist @ SV1514 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3936]) ).
thf(4468,plain,
! [SV1515: $i,SV1021: $i,SV400: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV400 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV400 ) @ SV1021 ) @ SV1515 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV400 ) @ SV1515 ) @ SV1021 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3937]) ).
thf(4469,plain,
! [SV1516: $i,SV1022: $i,SV401: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV401 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV401 ) @ SV1022 ) @ SV1516 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV401 ) @ SV1516 ) @ SV1022 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3938]) ).
thf(4470,plain,
! [SV1517: $i,SV1023: $i,SV402: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV402 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV402 ) @ SV1023 ) @ SV1517 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV402 ) @ SV1517 ) @ SV1023 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3939]) ).
thf(4471,plain,
! [SV1025: $i,SV404: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV404 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV404 ) @ SV1025 ) @ SV1025 ) @ ( c_HOL_Ozero__class_Ozero @ SV404 ) @ SV404 )
| ~ ( c_HOL_Oord__class_Oless @ SV1025 @ ( c_HOL_Ozero__class_Ozero @ SV404 ) @ SV404 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3941]) ).
thf(4472,plain,
! [SV1026: $i,SV405: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV405 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1026 @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SV405 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV405 ) @ SV1026 ) @ SV1026 ) @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SV405 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3942]) ).
thf(4473,plain,
! [SV1027: $i,SV406: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV406 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1027 @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV406 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV406 ) @ SV1027 ) @ SV1027 ) @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV406 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3943]) ).
thf(4474,plain,
! [SV1028: $i,SV407: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV407 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV407 ) @ SV1028 ) @ SV1028 ) @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 )
| ~ ( c_HOL_Oord__class_Oless @ SV1028 @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3944]) ).
thf(4475,plain,
! [SV1842: $i,SV1519: $i,SV1029: $i,SV408: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV408 @ ( c_Nat_Osize__class_Osize @ SV1029 @ ( tc_List_Olist @ SV1519 ) ) @ tc_nat )
| ( ( c_List_Onth @ ( c_List_Olist__update @ SV1029 @ SV408 @ SV1842 @ SV1519 ) @ SV408 @ SV1519 )
= SV1842 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3945]) ).
thf(4476,plain,
! [SV1843: $i,SV1520: $i,SV1030: $i,SV409: $i] :
( ( ( ( c_List_Onth @ ( c_List_Olist__update @ SV409 @ SV1030 @ SV1520 @ SV1843 ) @ SV1030 @ SV1843 )
= SV1520 )
| ~ ( c_HOL_Oord__class_Oless @ SV1030 @ ( c_Nat_Osize__class_Osize @ SV409 @ ( tc_List_Olist @ SV1843 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3946]) ).
thf(4477,plain,
! [SV1521: $i,SV1031: $i,SV410: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV410 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV410 ) @ ( c_Power_Opower__class_Opower @ SV1031 @ SV1521 @ SV410 ) @ SV410 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV410 ) @ SV1031 @ SV410 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3947]) ).
thf(4478,plain,
! [SV1522: $i,SV1032: $i,SV411: $i] :
( ( ( ( c_List_Olast @ ( c_List_Odrop @ SV411 @ SV1032 @ SV1522 ) @ SV1522 )
= ( c_List_Olast @ SV1032 @ SV1522 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV411 @ ( c_Nat_Osize__class_Osize @ SV1032 @ ( tc_List_Olist @ SV1522 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3948]) ).
thf(4479,plain,
! [SV1523: $i,SV1033: $i,SV412: $i] :
( ( ( ( c_List_Otake @ SV412 @ ( c_List_Obutlast @ SV1033 @ SV1523 ) @ SV1523 )
= ( c_List_Otake @ SV412 @ SV1033 @ SV1523 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV412 @ ( c_Nat_Osize__class_Osize @ SV1033 @ ( tc_List_Olist @ SV1523 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3949]) ).
thf(4480,plain,
! [SV1844: $i,SV1524: $i,SV1034: $i,SV413: $i] :
( ( ! [SY4557: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV413 @ SV1034 @ SV1524 ) @ SV1844 @ SY4557 @ SV1524 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV413 @ SV1844 @ SY4557 @ SV1524 ) @ SV1034 @ SV1524 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1844 @ ( c_Nat_Osize__class_Osize @ SV413 @ ( tc_List_Olist @ SV1524 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3950]) ).
thf(4481,plain,
! [SV1845: $i,SV1525: $i,SV1035: $i,SV414: $i] :
( ( ! [SY4558: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV414 @ SV1035 @ SV1525 ) @ SV1845 @ SY4558 @ SV1525 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV414 @ SV1845 @ SY4558 @ SV1525 ) @ SV1035 @ SV1525 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1845 @ ( c_Nat_Osize__class_Osize @ SV414 @ ( tc_List_Olist @ SV1525 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3951]) ).
thf(4482,plain,
! [SV1846: $i,SV1526: $i,SV1036: $i,SV415: $i] :
( ( ( ( c_List_Onth @ ( c_List_Oreplicate @ SV415 @ SV1036 @ SV1526 ) @ SV1846 @ SV1526 )
= SV1036 )
| ~ ( c_HOL_Oord__class_Oless @ SV1846 @ SV415 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3952]) ).
thf(4483,plain,
! [SV1847: $i,SV1527: $i,SV1037: $i,SV416: $i] :
( ( ! [SY4559: $i] :
( ( ( c_List_OtakeWhile @ SV416 @ ( c_List_Oappend @ SV1037 @ ( c_List_Olist_OCons @ SV1527 @ SV1847 @ SY4559 ) @ SY4559 ) @ SY4559 )
= ( c_List_OtakeWhile @ SV416 @ SV1037 @ SY4559 ) )
| ( hBOOL @ ( hAPP @ SV416 @ SV1527 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3953]) ).
thf(4484,plain,
! [SV1038: $i,SV419: $i] :
( ( ( class_Orderings_Oorder @ SV419 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1038 @ SV1038 @ SV419 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3954]) ).
thf(4485,plain,
! [SV1039: $i,SV420: $i] :
( ( ( class_Orderings_Olinorder @ SV420 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1039 @ SV1039 @ SV420 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3955]) ).
thf(4486,plain,
! [SV1040: $i,SV421: $i] :
( ( ( class_Orderings_Opreorder @ SV421 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1040 @ SV1040 @ SV421 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3956]) ).
thf(4487,plain,
! [SV1528: $i,SV1041: $i,SV422: $i] :
( ( ( ( c_List_Olast @ ( c_List_Oappend @ SV422 @ SV1041 @ SV1528 ) @ SV1528 )
= ( c_List_Olast @ SV1041 @ SV1528 ) )
= $true )
| ( ( SV1041
= ( c_List_Olist_ONil @ SV1528 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3957]) ).
thf(4488,plain,
! [SV1529: $i,SV1043: $i,SV424: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV424 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SV1043 ) @ SV1529 ) @ SV424 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV1529 @ SV424 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV1043 @ SV424 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3958]) ).
thf(4489,plain,
! [SV1530: $i,SV1044: $i,SV425: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV425 ) )
= $true )
| ( ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SV1044 @ SV1530 @ SV425 ) @ SV425 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV425 ) @ SV1044 ) @ ( c_List_Olistsum @ SV1530 @ SV425 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3959]) ).
thf(4490,plain,
! [SV1848: $i,SV1531: $i,SV1045: $i,SV426: $i] :
( ( ! [SY4560: $i] :
( ( c_List_Omap @ SV426 @ ( c_List_Oappend @ SV1045 @ SV1531 @ SV1848 ) @ SV1848 @ SY4560 )
= ( c_List_Oappend @ ( c_List_Omap @ SV426 @ SV1045 @ SV1848 @ SY4560 ) @ ( c_List_Omap @ SV426 @ SV1531 @ SV1848 @ SY4560 ) @ SY4560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3960]) ).
thf(4491,plain,
! [SV1532: $i,SV1046: $i,SV427: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV427 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1046 @ SV1532 @ SV427 )
| ( c_HOL_Oord__class_Oless @ SV1532 @ SV1046 @ SV427 )
| ( SV1532 = SV1046 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3961]) ).
thf(4492,plain,
! [SV1533: $i,SV1047: $i,SV428: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV428 ) )
= $true )
| ( ( ( SV1047 = SV1533 )
| ( c_HOL_Oord__class_Oless @ SV1533 @ SV1047 @ SV428 )
| ( c_HOL_Oord__class_Oless @ SV1047 @ SV1533 @ SV428 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3962]) ).
thf(4493,plain,
! [SV429: $i,SV1048: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1048 @ SV429 @ tc_nat )
= $true )
| ( ( SV1048 = SV429 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV429 @ SV1048 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3963]) ).
thf(4494,plain,
! [SV1534: $i,SV1049: $i,SV430: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV430 @ SV1049 ) @ SV1534 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1049 @ SV1534 @ tc_nat )
| ( SV1534 = SV1049 )
| ( c_HOL_Oord__class_Oless @ SV1534 @ SV1049 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3964]) ).
thf(4495,plain,
! [SV431: $i,SV1050: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1050 @ SV431 @ tc_nat )
= $true )
| ( ( SV1050 = SV431 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV431 @ SV1050 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3965]) ).
thf(4496,plain,
! [SV1535: $i,SV1051: $i,SV432: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV432 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1051 @ SV1535 @ SV432 )
| ( c_HOL_Oord__class_Oless @ SV1535 @ SV1051 @ SV432 )
| ( SV1535 = SV1051 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3966]) ).
thf(4497,plain,
! [SV1849: $i,SV1536: $i,SV1052: $i,SV433: $i] :
( ( ( c_List_Oappend @ ( c_List_Oreplicate @ SV433 @ SV1052 @ SV1536 ) @ ( c_List_Oreplicate @ SV1849 @ SV1052 @ SV1536 ) @ SV1536 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SV1849 @ SV1052 @ SV1536 ) @ ( c_List_Oreplicate @ SV433 @ SV1052 @ SV1536 ) @ SV1536 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3967]) ).
thf(4498,plain,
! [SV1537: $i,SV1053: $i,SV434: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV434 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1053 @ SV1537 @ SV434 )
| ( SV1537 = SV1053 )
| ( c_HOL_Oord__class_Oless @ SV1537 @ SV1053 @ SV434 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3968]) ).
thf(4499,plain,
! [SV1538: $i,SV1054: $i,SV435: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV435 ) )
= $true )
| ( ( ( SV1054 = SV1538 )
| ( c_HOL_Oord__class_Oless @ SV1054 @ SV1538 @ SV435 )
| ( c_HOL_Oord__class_Oless @ SV1538 @ SV1054 @ SV435 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3969]) ).
thf(4500,plain,
! [SV1850: $i,SV1539: $i,SV1055: $i,SV436: $i] :
( ( ! [SY4561: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV436 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV436 ) @ SV1055 ) @ SV1539 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV436 ) @ SV1850 ) @ SY4561 ) @ SV436 )
| ~ ( c_HOL_Oord__class_Oless @ SV1539 @ SY4561 @ SV436 )
| ~ ( c_HOL_Oord__class_Oless @ SV1055 @ SV1850 @ SV436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3970]) ).
thf(4501,plain,
! [SV1851: $i,SV1540: $i,SV1056: $i,SV437: $i] :
( ( ! [SY4562: $i] :
( ( ( c_List_Onth @ ( c_List_Omap @ SV437 @ SV1056 @ SV1540 @ SV1851 ) @ SY4562 @ SV1851 )
= ( hAPP @ SV437 @ ( c_List_Onth @ SV1056 @ SY4562 @ SV1540 ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4562 @ ( c_Nat_Osize__class_Osize @ SV1056 @ ( tc_List_Olist @ SV1540 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3971]) ).
thf(4502,plain,
! [SV1541: $i,SV1057: $i,SV438: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV438 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1057 @ SV438 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1541 @ SV438 ) @ SV438 )
| ~ ( c_HOL_Oord__class_Oless @ SV1057 @ SV1541 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3972]) ).
thf(4503,plain,
! [SV1542: $i,SV1058: $i,SV439: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV439 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1058 @ SV1542 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1058 @ SV439 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1542 @ SV439 ) @ SV439 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3973]) ).
thf(4504,plain,
! [SV1059: $i,SV440: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV440 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV440 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1059 @ SV440 ) @ SV440 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1059 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3974]) ).
thf(4505,plain,
! [SV1060: $i,SV441: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV441 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1060 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV441 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1060 @ SV441 ) @ SV441 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3975]) ).
thf(4506,plain,
! [SV1062: $i,SV443: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV443 )
= $false )
| ( ( ( c_List_Olistsum @ ( c_List_Orev @ SV1062 @ SV443 ) @ SV443 )
= ( c_List_Olistsum @ SV1062 @ SV443 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3976]) ).
thf(4507,plain,
! [SV1852: $i,SV1543: $i,SV1063: $i,SV444: $i] :
( ( ( c_List_Olistsp @ SV444 @ ( c_List_Oappend @ SV1063 @ SV1543 @ SV1852 ) @ SV1852 )
| ~ ( c_List_Olistsp @ SV444 @ SV1543 @ SV1852 )
| ~ ( c_List_Olistsp @ SV444 @ SV1063 @ SV1852 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3977]) ).
thf(4508,plain,
! [SV1853: $i,SV1546: $i,SV1066: $i,SV447: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV447 )
| ( c_HOL_Oord__class_Oless @ SV1066 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV447 ) @ SV1546 ) @ SV1853 ) @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ SV1066 @ SV1853 @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV1546 @ SV447 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3980]) ).
thf(4509,plain,
! [SV1547: $i,SV1067: $i,SV448: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV448 ) ) @ SV1067 ) @ SV1547 )
= ( c_Lambda_OdB_OVar @ SV448 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV448 @ SV1547 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3981]) ).
thf(4510,plain,
! [SV1854: $i,SV1548: $i,SV1068: $i,SV449: $i] :
( ( ! [SY4563: $i] :
( ~ ( hBOOL @ ( hAPP @ SV449 @ ( c_Lambda_OdB_OdB__case @ SV1068 @ SV1548 @ SV1854 @ ( c_Lambda_OdB_OAbs @ SY4563 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV449 @ ( hAPP @ SV1854 @ SY4563 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3982]) ).
thf(4511,plain,
! [SV1855: $i,SV1549: $i,SV1069: $i,SV450: $i] :
( ( ! [SY4564: $i] :
( ~ ( hBOOL @ ( hAPP @ SV450 @ ( c_Lambda_OdB_OdB__case @ SV1069 @ SV1549 @ SV1855 @ ( c_Lambda_OdB_OAbs @ SY4564 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV450 @ ( hAPP @ SV1855 @ SY4564 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3983]) ).
thf(4512,plain,
! [SV1856: $i,SV1550: $i,SV1070: $i,SV451: $i] :
( ( ! [SY4565: $i] :
( ( c_List_Olist__update @ ( c_List_Oappend @ SV451 @ ( c_List_Olist_OCons @ SV1070 @ SV1550 @ SV1856 ) @ SV1856 ) @ ( c_Nat_Osize__class_Osize @ SV451 @ ( tc_List_Olist @ SV1856 ) ) @ SY4565 @ SV1856 )
= ( c_List_Oappend @ SV451 @ ( c_List_Olist_OCons @ SY4565 @ SV1550 @ SV1856 ) @ SV1856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3984]) ).
thf(4513,plain,
! [SV1857: $i,SV1551: $i,SV1071: $i,SV452: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV452 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV452 ) @ SV1071 ) @ SV1551 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV452 ) @ SV1857 ) @ SV1551 ) @ SV452 )
| ~ ( c_HOL_Oord__class_Oless @ SV1071 @ SV1857 @ SV452 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3985]) ).
thf(4514,plain,
! [SV1858: $i,SV1552: $i,SV1072: $i,SV453: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV453 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV453 ) @ SV1072 ) @ SV1552 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV453 ) @ SV1858 ) @ SV1552 ) @ SV453 )
| ~ ( c_HOL_Oord__class_Oless @ SV1072 @ SV1858 @ SV453 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3986]) ).
thf(4515,plain,
! [SV1859: $i,SV1553: $i,SV1073: $i,SV454: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV454 )
| ( c_HOL_Oord__class_Oless @ SV1073 @ SV1553 @ SV454 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV454 ) @ SV1073 ) @ SV1859 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV454 ) @ SV1553 ) @ SV1859 ) @ SV454 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3987]) ).
thf(4516,plain,
! [SV1860: $i,SV1554: $i,SV1074: $i,SV455: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV455 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV455 ) @ SV1074 ) @ SV1554 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV455 ) @ SV1074 ) @ SV1860 ) @ SV455 )
| ~ ( c_HOL_Oord__class_Oless @ SV1554 @ SV1860 @ SV455 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3988]) ).
thf(4517,plain,
! [SV1861: $i,SV1555: $i,SV1075: $i,SV456: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV456 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV456 ) @ SV1075 ) @ SV1555 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV456 ) @ SV1075 ) @ SV1861 ) @ SV456 )
| ~ ( c_HOL_Oord__class_Oless @ SV1555 @ SV1861 @ SV456 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3989]) ).
thf(4518,plain,
! [SV1862: $i,SV1556: $i,SV1076: $i,SV457: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV457 )
| ( c_HOL_Oord__class_Oless @ SV1076 @ SV1556 @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV1862 ) @ SV1076 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV1862 ) @ SV1556 ) @ SV457 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3990]) ).
thf(4519,plain,
! [SV1863: $i,SV1557: $i,SV1077: $i,SV458: $i] :
( ( ( c_Type_Otyping @ SV458 @ SV1077 @ SV1557 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1863 ) @ SV1077 ) )
| ~ ( c_Type_Otyping @ SV458 @ SV1863 @ SV1557 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3991]) ).
thf(4520,plain,
! [SV1558: $i,SV1078: $i,SV459: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV459 ) )
= $true )
| ( ( ( c_List_Olinorder__class_Osorted @ SV1078 @ SV459 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1078 @ SV1558 @ SV459 ) @ SV459 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3992]) ).
thf(4521,plain,
! [SV1559: $i,SV1079: $i,SV460: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV460 ) )
= $true )
| ( ( ( c_List_Olinorder__class_Osorted @ SV1079 @ SV460 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1559 @ SV1079 @ SV460 ) @ SV460 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3993]) ).
thf(4522,plain,
! [SV1864: $i,SV1560: $i,SV1080: $i,SV461: $i] :
( ( ! [SY4566: $i,SY4567: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV461 @ SV1080 @ SV1560 @ SV1864 ) @ SY4566 @ SY4567 @ SV1864 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV461 @ SY4566 @ SY4567 @ SV1864 ) @ SV1080 @ SV1560 @ SV1864 ) )
| ( SV1080 = SY4566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3994]) ).
thf(4523,plain,
! [SV1865: $i,SV1561: $i,SV1081: $i,SV462: $i] :
( ( ( c_List_Oappend @ ( c_List_Oreplicate @ SV462 @ SV1081 @ SV1561 ) @ ( c_List_Olist_OCons @ SV1081 @ SV1865 @ SV1561 ) @ SV1561 )
= ( c_List_Olist_OCons @ SV1081 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV462 @ SV1081 @ SV1561 ) @ SV1865 @ SV1561 ) @ SV1561 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3995]) ).
thf(4524,plain,
! [SV1866: $i,SV1562: $i,SV1082: $i,SV463: $i] :
( ( ! [SY4568: $i] :
( ( c_List_Odrop @ SV463 @ ( c_List_Omap @ SV1082 @ SV1562 @ SV1866 @ SY4568 ) @ SY4568 )
= ( c_List_Omap @ SV1082 @ ( c_List_Odrop @ SV463 @ SV1562 @ SV1866 ) @ SV1866 @ SY4568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3996]) ).
thf(4525,plain,
! [SV1563: $i,SV1084: $i,SV465: $i] :
( ( ( ( c_List_Obutlast @ ( c_List_Oappend @ SV465 @ SV1084 @ SV1563 ) @ SV1563 )
= ( c_List_Oappend @ SV465 @ ( c_List_Obutlast @ SV1084 @ SV1563 ) @ SV1563 ) )
= $true )
| ( ( SV1084
= ( c_List_Olist_ONil @ SV1563 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3997]) ).
thf(4526,plain,
! [SV1564: $i,SV1085: $i,SV466: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV466 ) )
= $true )
| ( ( ( c_List_Olistsum @ ( c_List_Oappend @ SV1085 @ SV1564 @ SV466 ) @ SV466 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV466 ) @ ( c_List_Olistsum @ SV1085 @ SV466 ) ) @ ( c_List_Olistsum @ SV1564 @ SV466 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3998]) ).
thf(4527,plain,
! [SV1867: $i,SV1565: $i,SV1086: $i,SV467: $i] :
( ( ! [SY4569: $i] :
( ( ( c_List_Onth @ ( c_List_Olist__update @ SV467 @ SV1086 @ SV1565 @ SV1867 ) @ SY4569 @ SV1867 )
= ( c_List_Onth @ SV467 @ SY4569 @ SV1867 ) )
| ( SV1086 = SY4569 )
| ~ ( c_HOL_Oord__class_Oless @ SV1086 @ ( c_Nat_Osize__class_Osize @ SV467 @ ( tc_List_Olist @ SV1867 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3999]) ).
thf(4528,plain,
! [SV1868: $i,SV1566: $i,SV1087: $i,SV468: $i] :
( ( ! [SY4570: $i] :
( ( c_List_Olist__update @ ( c_List_Olist__update @ SV468 @ SV1087 @ SV1566 @ SV1868 ) @ SV1087 @ SY4570 @ SV1868 )
= ( c_List_Olist__update @ SV468 @ SV1087 @ SY4570 @ SV1868 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4000]) ).
thf(4529,plain,
! [SV1869: $i,SV1567: $i,SV1088: $i,SV469: $i] :
( ( ( c_List_Oappend @ ( c_List_Oappend @ SV469 @ SV1088 @ SV1567 ) @ SV1869 @ SV1567 )
= ( c_List_Oappend @ SV469 @ ( c_List_Oappend @ SV1088 @ SV1869 @ SV1567 ) @ SV1567 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4001]) ).
thf(4530,plain,
! [SV1870: $i,SV1568: $i,SV1089: $i,SV470: $i] :
( ( ( c_List_Oappend @ SV470 @ ( c_List_Oappend @ SV1089 @ SV1568 @ SV1870 ) @ SV1870 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV470 @ SV1089 @ SV1870 ) @ SV1568 @ SV1870 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4002]) ).
thf(4531,plain,
! [SV1871: $i,SV1569: $i,SV1090: $i,SV471: $i] :
( ( ( c_List_Oappend @ ( c_List_Oappend @ SV471 @ SV1090 @ SV1569 ) @ SV1871 @ SV1569 )
= ( c_List_Oappend @ SV471 @ ( c_List_Oappend @ SV1090 @ SV1871 @ SV1569 ) @ SV1569 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4003]) ).
thf(4532,plain,
! [SV1872: $i,SV1570: $i,SV1091: $i,SV472: $i] :
( ( ( c_List_Oappend @ SV472 @ ( c_List_Oappend @ SV1091 @ SV1570 @ SV1872 ) @ SV1872 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV472 @ SV1091 @ SV1872 ) @ SV1570 @ SV1872 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4004]) ).
thf(4533,plain,
! [SV1571: $i,SV1092: $i,SV473: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV473 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1092 @ SV1571 @ SV473 )
| ~ ( c_HOL_Oord__class_Oless @ SV1571 @ SV1092 @ SV473 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4005]) ).
thf(4534,plain,
! [SV1572: $i,SV1093: $i,SV474: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV474 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1093 @ SV1572 @ SV474 )
| ~ ( c_HOL_Oord__class_Oless @ SV1572 @ SV1093 @ SV474 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4006]) ).
thf(4535,plain,
! [SV1573: $i,SV1094: $i,SV475: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV475 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1094 @ SV1573 @ SV475 )
| ~ ( c_HOL_Oord__class_Oless @ SV1573 @ SV1094 @ SV475 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4007]) ).
thf(4536,plain,
! [SV1574: $i,SV1095: $i,SV476: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV476 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1095 @ SV1574 @ SV476 )
| ~ ( c_HOL_Oord__class_Oless @ SV1574 @ SV1095 @ SV476 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4008]) ).
thf(4537,plain,
! [SV1575: $i,SV1096: $i,SV477: $i] :
( ( ( ( hAPP @ SV477 @ SV1096 )
= SV1575 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV477 @ ( c_Lambda_OdB_OVar @ SV1096 ) @ SV1575 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4009]) ).
thf(4538,plain,
! [SV1873: $i,SV1576: $i,SV1097: $i,SV478: $i] :
( ( ! [SY4571: $i] :
( ( c_Lambda_OdB_OdB__case @ SV478 @ SV1097 @ SV1576 @ ( c_Lambda_OdB_OVar @ SV1873 ) @ SY4571 )
= ( hAPP @ SV478 @ SV1873 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4010]) ).
thf(4539,plain,
! [SV1578: $i,SV1100: $i,SV483: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV483 ) @ SV1100 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1578 ) @ SV1100 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV483 ) @ SV1578 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4014]) ).
thf(4540,plain,
! [SV1579: $i,SV1101: $i,SV484: $i] :
( ( ( ( c_List_Osublist @ ( c_List_Olist_OCons @ SV484 @ ( c_List_Olist_ONil @ SV1101 ) @ SV1101 ) @ SV1579 @ SV1101 )
= ( c_List_Olist_OCons @ SV484 @ ( c_List_Olist_ONil @ SV1101 ) @ SV1101 ) )
= $true )
| ( ( ~ ( c_in @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1579 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4015]) ).
thf(4541,plain,
! [SV1580: $i,SV1102: $i,SV485: $i] :
( ( ( ( c_List_Osublist @ ( c_List_Olist_OCons @ SV485 @ ( c_List_Olist_ONil @ SV1102 ) @ SV1102 ) @ SV1580 @ SV1102 )
= ( c_List_Olist_ONil @ SV1102 ) )
= $true )
| ( ( c_in @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1580 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4016]) ).
thf(4542,plain,
! [SV1581: $i,SV1103: $i,SV486: $i] :
( ( ( SV486
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1103 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV1103 @ SV1581 @ SV486 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1103 ) @ SV1581 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV486 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4017]) ).
thf(4543,plain,
! [SV1105: $i,SV488: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV488 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV488 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV488 )
| ~ ( class_Power_Opower @ SV488 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV488 ) @ SV1105 @ SV488 )
= ( c_HOL_Ozero__class_Ozero @ SV488 ) )
| ( SV1105
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4019]) ).
thf(4544,plain,
! [SV1106: $i,SV489: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV489 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV489 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV1106 @ SV489 )
= ( c_HOL_Ozero__class_Ozero @ SV489 ) )
| ( SV1106
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4020]) ).
thf(4545,plain,
! [SV1874: $i,SV1585: $i,SV1109: $i,SV494: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV494 @ SV1109 @ SV1585 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1874 @ SV1585 )
= ( c_List_Olist_OCons @ SV1874 @ SV1109 @ SV1585 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4025]) ).
thf(4546,plain,
! [SV1875: $i,SV1587: $i,SV1116: $i,SV503: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV503 )
| ( ( c_List_Olinorder__class_Oinsort__key @ SV1116 @ SV1587 @ ( c_List_Olist_ONil @ SV1875 ) @ SV1875 @ SV503 )
= ( c_List_Olist_OCons @ SV1587 @ ( c_List_Olist_ONil @ SV1875 ) @ SV1875 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4027]) ).
thf(4547,plain,
! [SV1588: $i,SV1117: $i,SV504: $i] :
( ( ( ( c_List_Obutlast @ ( c_List_Olist_OCons @ SV504 @ SV1117 @ SV1588 ) @ SV1588 )
= ( c_List_Olist_OCons @ SV504 @ ( c_List_Obutlast @ SV1117 @ SV1588 ) @ SV1588 ) )
= $true )
| ( ( SV1117
= ( c_List_Olist_ONil @ SV1588 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4028]) ).
thf(4548,plain,
! [SV1876: $i,SV1590: $i,SV1121: $i,SV508: $i] :
( ( ( ( c_List_OtakeWhile @ SV508 @ ( c_List_Olist_OCons @ SV1121 @ SV1590 @ SV1876 ) @ SV1876 )
= ( c_List_Olist_ONil @ SV1876 ) )
| ( hBOOL @ ( hAPP @ SV508 @ SV1121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4030]) ).
thf(4549,plain,
! [SV1591: $i,SV1123: $i,SV510: $i] :
( ( ( ( c_List_Olast @ ( c_List_Olist_OCons @ SV510 @ SV1123 @ SV1591 ) @ SV1591 )
= ( c_List_Olast @ SV1123 @ SV1591 ) )
= $true )
| ( ( SV1123
= ( c_List_Olist_ONil @ SV1591 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4031]) ).
thf(4550,plain,
! [SV1126: $i,SV513: $i] :
( ( ( class_Orderings_Olinorder @ SV513 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1126 @ ( c_List_Olist_ONil @ SV513 ) @ SV513 ) @ SV513 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4033]) ).
thf(4551,plain,
! [SV1593: $i,SV1127: $i,SV514: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV514 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1127 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ ( c_HOL_Ozero__class_Ozero @ SV514 ) @ SV1593 @ SV514 @ SV514 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1127 @ SV1593 @ SV514 @ SV514 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4034]) ).
thf(4552,plain,
! [SV1594: $i,SV1128: $i,SV517: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV517 @ SV1128 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1594 @ SV1128 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV517 ) @ SV1594 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4035]) ).
thf(4553,plain,
! [SV1595: $i,SV1129: $i,SV518: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV518 ) ) @ SV1129 ) @ SV1595 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1129 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV518 ) @ SV1129 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1595 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4036]) ).
thf(4554,plain,
! [SV1596: $i,SV1130: $i,SV519: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV519 ) @ ( c_Lambda_OdB_OVar @ SV1130 ) ) @ SV1596 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV519 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4037]) ).
thf(4555,plain,
! [SV1131: $i,SV520: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV520 @ SV1131 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV520 ) ) @ SV1131 )
= ( c_Lambda_OdB_OVar @ SV520 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4038]) ).
thf(4556,plain,
! [SV1877: $i,SV1598: $i,SV1133: $i,SV522: $i] :
( ( ! [SY4572: $i] :
( ( SV522 = SV1133 )
| ~ ( c_Type_Otyping @ SV1598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1877 ) @ SY4572 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1133 )
| ~ ( c_Type_Otyping @ SV1598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1877 ) @ SY4572 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4040]) ).
thf(4557,plain,
! [SV525: $i,SV1134: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ SV1134 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV525 ) @ SV1134 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4041]) ).
thf(4558,plain,
! [SV1599: $i,SV1135: $i,SV526: $i] :
( ( ( ( c_List_Oappend @ SV526 @ ( c_List_Olist_OCons @ SV1135 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1599 @ SV526 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV1135 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1599 @ ( c_List_Oappend @ SV526 @ ( c_List_Olist_OCons @ SV1135 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4042]) ).
thf(4559,plain,
! [SV1138: $i,SV529: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV529 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV529 ) @ SV1138 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4044]) ).
thf(4560,plain,
! [SV1878: $i,SV1601: $i,SV1139: $i,SV530: $i] :
( ( ( c_List_Ofoldl @ SV530 @ SV1139 @ ( c_List_Olist_ONil @ SV1601 ) @ SV1878 @ SV1601 )
= SV1139 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4045]) ).
thf(4561,plain,
! [SV1879: $i,SV1603: $i,SV1141: $i,SV534: $i] :
( ( ! [SY4573: $i,SY4574: $i] :
( ( c_List_Ofoldl @ SV534 @ SV1141 @ ( c_List_Olist_OCons @ SV1603 @ SV1879 @ SY4573 ) @ SY4574 @ SY4573 )
= ( c_List_Ofoldl @ SV534 @ ( hAPP @ ( hAPP @ SV534 @ SV1141 ) @ SV1603 ) @ SV1879 @ SY4574 @ SY4573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4047]) ).
thf(4562,plain,
! [SV1142: $i,SV535: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV535 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV535 ) @ ( c_Lambda_OdB_OVar @ SV1142 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4048]) ).
thf(4563,plain,
! [SV536: $i,SV1143: $i] :
( ( ( class_Orderings_Opreorder @ SV1143 )
= $false )
| ( ( class_Orderings_Opreorder @ ( tc_fun @ SV536 @ SV1143 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4049]) ).
thf(4564,plain,
! [SV537: $i,SV1144: $i] :
( ( ( class_Orderings_Oorder @ SV1144 )
= $false )
| ( ( class_Orderings_Oorder @ ( tc_fun @ SV537 @ SV1144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4050]) ).
thf(4565,plain,
! [SV1604: $i,SV1146: $i,SV539: $i] :
( ( ( SV539 = SV1146 )
= $true )
| ( ( ~ ( c_fequal @ SV539 @ SV1146 @ SV1604 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4051]) ).
thf(4566,plain,
! [SV1147: $i,SV540: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV540 )
= ( c_Lambda_OdB_OAbs @ SV1147 ) )
= $false )
| ( ( SV540 = SV1147 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4052]) ).
thf(4567,plain,
! [SV1880: $i,SV1605: $i,SV1148: $i,SV541: $i] :
( ( ! [SY4575: $i] :
( ( ( c_List_Oreplicate @ SV541 @ SV1148 @ SV1605 )
!= ( c_List_Oreplicate @ SV1880 @ SY4575 @ SV1605 ) )
| ( SV541 = SV1880 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4053]) ).
thf(4568,plain,
! [SV1606: $i,SV1149: $i,SV542: $i] :
( ( ( SV542
!= ( c_List_Oappend @ SV1149 @ SV542 @ SV1606 ) )
= $true )
| ( ( SV1149
= ( c_List_Olist_ONil @ SV1606 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4054]) ).
thf(4569,plain,
! [SV1881: $i,SV1607: $i,SV1150: $i,SV543: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV543 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV543 ) @ SV1150 ) @ SV1607 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV543 ) @ SV1881 ) @ SV1607 ) )
| ( SV1150 = SV1881 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4055]) ).
thf(4570,plain,
! [SV1608: $i,SV1151: $i,SV544: $i] :
( ( ( c_List_Olist_OCons @ SV544 @ SV1151 @ SV1608 )
= ( c_List_Olist_ONil @ SV1608 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4056]) ).
thf(4571,plain,
! [SV1609: $i,SV1152: $i,SV545: $i] :
( ( ( ( c_List_Odrop @ SV545 @ SV1152 @ SV1609 )
!= ( c_List_Olist_ONil @ SV1609 ) )
= $true )
| ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1152 @ ( tc_List_Olist @ SV1609 ) ) @ SV545 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4057]) ).
thf(4572,plain,
! [SV1153: $i,SV546: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV546 )
= ( c_Lambda_OdB_OVar @ SV1153 ) )
= $false )
| ( ( SV546 = SV1153 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4058]) ).
thf(4573,plain,
! [SV1610: $i,SV1154: $i,SV547: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV547 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1154 @ SV1610 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OVar @ SV547 )
= SV1154 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4059]) ).
thf(4574,plain,
! [SV1611: $i,SV1156: $i,SV549: $i] :
( ( ( SV549
!= ( c_List_Oappend @ SV549 @ SV1156 @ SV1611 ) )
= $true )
| ( ( SV1156
= ( c_List_Olist_ONil @ SV1611 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4061]) ).
thf(4575,plain,
! [SV1882: $i,SV1612: $i,SV1157: $i,SV550: $i] :
( ( ! [SY4576: $i] :
( ( ( c_List_Oappend @ SV550 @ ( c_List_Olist_OCons @ SV1157 @ ( c_List_Olist_ONil @ SV1612 ) @ SV1612 ) @ SV1612 )
!= ( c_List_Oappend @ SV1882 @ ( c_List_Olist_OCons @ SY4576 @ ( c_List_Olist_ONil @ SV1612 ) @ SV1612 ) @ SV1612 ) )
| ( SV550 = SV1882 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4062]) ).
thf(4576,plain,
! [SV1613: $i,SV1158: $i,SV551: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV551 ) @ SV1158 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1613 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV551 ) @ SV1158 )
= SV1613 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4063]) ).
thf(4577,plain,
! [SV1883: $i,SV1614: $i,SV1159: $i,SV552: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV552 ) @ SV1159 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1614 @ SV1883 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1883
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV552 @ SV1159 @ SV1614 @ SV1883 ) @ ( c_List_Olist_OCons @ SV1159 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SV1883
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4064]) ).
thf(4578,plain,
! [SV1884: $i,SV1615: $i,SV1160: $i,SV553: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV553 ) @ SV1160 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1615 ) @ SV1884 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV553 = SV1615 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4065]) ).
thf(4579,plain,
! [SV1885: $i,SV1616: $i,SV1161: $i,SV554: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV554 )
| ( ( c_Power_Opower__class_Opower @ SV1161 @ SV1616 @ SV554 )
!= ( c_Power_Opower__class_Opower @ SV1885 @ SV1616 @ SV554 ) )
| ( SV1161 = SV1885 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1616 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SV1885 @ SV554 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SV1161 @ SV554 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4066]) ).
thf(4580,plain,
! [SV1617: $i,SV1162: $i,SV555: $i] :
( ( ( c_List_Olist_ONil @ SV555 )
= ( c_List_Olist_OCons @ SV1162 @ SV1617 @ SV555 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4067]) ).
thf(4581,plain,
! [SV1163: $i,SV557: $i] :
( ( ( ( c_Suc @ SV557 )
= ( c_Suc @ SV1163 ) )
= $false )
| ( ( SV557 = SV1163 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4068]) ).
thf(4582,plain,
! [SV1886: $i,SV1618: $i,SV1164: $i,SV558: $i] :
( ( ( ( c_List_Oappend @ SV558 @ SV1164 @ SV1618 )
!= ( c_List_Oappend @ SV558 @ SV1886 @ SV1618 ) )
| ( SV1164 = SV1886 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4069]) ).
thf(4583,plain,
! [SV1887: $i,SV1619: $i,SV1165: $i,SV559: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV559 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1165 @ SV1619 @ SV559 )
!= ( c_HOL_Ominus__class_Ominus @ SV1887 @ SV1887 @ SV559 ) )
| ( SV1165 = SV1619 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4070]) ).
thf(4584,plain,
! [SV1888: $i,SV1620: $i,SV1166: $i,SV560: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV560 @ ( tc_List_Olist @ SV1166 ) ) @ SV1620 @ SV1166 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1620 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) @ SV1888 @ SV1166 ) @ SV1166 )
!= SV1888 )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV560 @ ( tc_List_Olist @ SV1166 ) ) @ SV1620 @ SV1166 )
!= SV560 )
| ( SV1620
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV1620 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) )
| ( ( c_List_Oappend @ SV1620 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1620 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) @ SV1888 @ SV1166 ) @ SV1166 )
= ( c_List_Oappend @ SV560 @ SV1888 @ SV1166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4071]) ).
thf(4585,plain,
! [SV1167: $i,SV561: $i] :
( ( ( ( c_Suc @ SV561 )
= ( c_Suc @ SV1167 ) )
= $false )
| ( ( SV561 = SV1167 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4072]) ).
thf(4586,plain,
! [SV1621: $i,SV1168: $i,SV562: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV562 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1168 @ SV1621 @ SV562 )
!= ( c_HOL_Ozero__class_Ozero @ SV562 ) )
| ( SV1168 = SV1621 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4073]) ).
thf(4587,plain,
! [SV1622: $i,SV1169: $i,SV563: $i] :
( ( ( ( c_List_Olist_ONil @ SV563 )
!= ( c_List_Oappend @ SV1169 @ SV1622 @ SV563 ) )
= $true )
| ( ( SV1622
= ( c_List_Olist_ONil @ SV563 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4074]) ).
thf(4588,plain,
! [SV1889: $i,SV1623: $i,SV1170: $i,SV564: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV564 ) @ SV1170 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1623 ) @ SV1889 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1170 = SV1889 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4075]) ).
thf(4589,plain,
! [SV1624: $i,SV1171: $i,SV565: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV565 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1171 @ SV1624 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV1624
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4076]) ).
thf(4590,plain,
! [SV1625: $i,SV1172: $i,SV566: $i] :
( ( ( c_Lambda_OdB_OVar @ SV566 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1172 ) @ SV1625 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4077]) ).
thf(4591,plain,
! [SV1626: $i,SV1173: $i,SV567: $i] :
( ( ( c_List_Olist_OCons @ SV567 @ SV1173 @ SV1626 )
= ( c_List_Olist_ONil @ SV1626 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4078]) ).
thf(4592,plain,
! [SV568: $i] :
( ( ( ( c_HOL_Oone__class_Oone @ SV568 )
= ( c_HOL_Ozero__class_Ozero @ SV568 ) )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV568 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4079]) ).
thf(4593,plain,
! [SV1890: $i,SV1627: $i,SV1174: $i,SV569: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV569 ) @ SV1174 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1627 ) @ SV1890 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV569 = SV1627 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4080]) ).
thf(4594,plain,
! [SV1891: $i,SV1628: $i,SV1175: $i,SV570: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV570 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV570 ) @ SV1175 ) @ SV1628 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV570 ) @ SV1175 ) @ SV1891 ) )
| ( SV1628 = SV1891 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4081]) ).
thf(4595,plain,
! [SV1629: $i,SV1176: $i,SV571: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV571 ) @ SV1176 )
= ( c_Lambda_OdB_OVar @ SV1629 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4082]) ).
thf(4596,plain,
! [SV1892: $i,SV1630: $i,SV1177: $i,SV572: $i] :
( ( ( ( c_List_Oappend @ SV572 @ SV1177 @ SV1630 )
!= ( c_List_Oappend @ SV1892 @ SV1177 @ SV1630 ) )
| ( SV572 = SV1892 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4083]) ).
thf(4597,plain,
! [SV1893: $i,SV1631: $i,SV1178: $i,SV573: $i] :
( ( ! [SY4577: $i] :
( ( ( c_List_Oappend @ SV573 @ ( c_List_Olist_OCons @ SV1178 @ ( c_List_Olist_ONil @ SV1631 ) @ SV1631 ) @ SV1631 )
!= ( c_List_Oappend @ SV1893 @ ( c_List_Olist_OCons @ SY4577 @ ( c_List_Olist_ONil @ SV1631 ) @ SV1631 ) @ SV1631 ) )
| ( SV1178 = SY4577 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4084]) ).
thf(4598,plain,
! [SV1894: $i,SV1632: $i,SV1179: $i,SV574: $i] :
( ( ! [SY4578: $i] :
( ( ( c_List_Oappend @ SV574 @ SV1179 @ SV1632 )
!= ( c_List_Oappend @ SV1894 @ SY4578 @ SV1632 ) )
| ( SV1179
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV574 @ ( tc_List_Olist @ SV1632 ) ) @ SV1894 @ SV1632 ) @ SY4578 @ SV1632 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV574 @ ( tc_List_Olist @ SV1632 ) ) @ ( c_Nat_Osize__class_Osize @ SV1894 @ ( tc_List_Olist @ SV1632 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4085]) ).
thf(4599,plain,
! [SV1633: $i,SV1180: $i,SV575: $i] :
( ( ( ( c_List_Olist_OCons @ SV575 @ ( c_List_Olist_ONil @ SV1180 ) @ SV1180 )
!= ( c_List_Orev @ SV1633 @ SV1180 ) )
= $true )
| ( ( SV1633
= ( c_List_Olist_OCons @ SV575 @ ( c_List_Olist_ONil @ SV1180 ) @ SV1180 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4086]) ).
thf(4600,plain,
! [SV1895: $i,SV1634: $i,SV1181: $i,SV576: $i] :
( ( ( ( c_List_Orev @ SV576 @ SV1181 )
!= ( c_List_Olist_OCons @ SV1634 @ SV1895 @ SV1181 ) )
| ( SV576
= ( c_List_Oappend @ ( c_List_Orev @ SV1895 @ SV1181 ) @ ( c_List_Olist_OCons @ SV1634 @ ( c_List_Olist_ONil @ SV1181 ) @ SV1181 ) @ SV1181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4087]) ).
thf(4601,plain,
! [SV1635: $i,SV1182: $i,SV577: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV577 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV577 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV577 )
| ~ ( class_Power_Opower @ SV577 )
| ( ( c_Power_Opower__class_Opower @ SV1182 @ SV1635 @ SV577 )
!= ( c_HOL_Ozero__class_Ozero @ SV577 ) )
| ( SV1182
= ( c_HOL_Ozero__class_Ozero @ SV577 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4088]) ).
thf(4602,plain,
! [SV1896: $i,SV1636: $i,SV1183: $i,SV578: $i] :
( ( ! [SY4579: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV578 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1183 @ SV1636 @ SV578 )
!= ( c_HOL_Ominus__class_Ominus @ SV1896 @ SY4579 @ SV578 ) )
| ( c_HOL_Oord__class_Oless @ SV1896 @ SY4579 @ SV578 )
| ~ ( c_HOL_Oord__class_Oless @ SV1183 @ SV1636 @ SV578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4089]) ).
thf(4603,plain,
! [SV1897: $i,SV1637: $i,SV1184: $i,SV580: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ SV580 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Onth @ ( c_List_Olist_OCons @ SV1184 @ SV1637 @ SV1897 ) @ ( c_Int_Onumber__class_Onumber__of @ SV580 @ tc_nat ) @ SV1897 )
= SV1184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4090]) ).
thf(4604,plain,
! [SV581: $i] :
( ( ( ( c_HOL_Ozero__class_Ozero @ SV581 )
= ( c_HOL_Oone__class_Oone @ SV581 ) )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV581 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4091]) ).
thf(4605,plain,
! [SV1898: $i,SV1638: $i,SV1185: $i,SV582: $i] :
( ( ! [SY4580: $i] :
( ( ( c_List_Olist_OCons @ SV582 @ SV1185 @ SV1638 )
!= ( c_List_Olist_OCons @ SV1898 @ SY4580 @ SV1638 ) )
| ( SV1185 = SY4580 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4092]) ).
thf(4606,plain,
! [SV1639: $i,SV1186: $i,SV583: $i] :
( ( ( ( c_List_Oappend @ SV583 @ SV1186 @ SV1639 )
!= ( c_List_Olist_ONil @ SV1639 ) )
= $true )
| ( ( SV583
= ( c_List_Olist_ONil @ SV1639 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4093]) ).
thf(4607,plain,
! [SV1640: $i,SV1187: $i,SV584: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV584 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1187 @ SV1640 @ SV584 )
!= ( c_HOL_Ozero__class_Ozero @ SV584 ) )
| ( SV1187
= ( c_HOL_Ozero__class_Ozero @ SV584 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4094]) ).
thf(4608,plain,
! [SV1899: $i,SV1641: $i,SV1188: $i,SV585: $i] :
( ( ( ( c_List_OtakeWhile @ SV585 @ SV1188 @ SV1641 )
!= SV1188 )
| ( hBOOL @ ( hAPP @ SV585 @ SV1899 ) )
| ~ ( c_in @ SV1899 @ ( c_List_Oset @ SV1188 @ SV1641 ) @ SV1641 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4095]) ).
thf(4609,plain,
! [SV1642: $i,SV1189: $i,SV586: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV586 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1189 ) @ SV1642 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4096]) ).
thf(4610,plain,
! [SV1643: $i,SV1190: $i,SV587: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV587 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1190 @ SV1643 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OAbs @ SV587 )
= SV1190 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4097]) ).
thf(4611,plain,
! [SV1900: $i,SV1644: $i,SV1191: $i,SV588: $i] :
( ( ( ( c_List_Olist_ONil @ SV588 )
!= ( c_List_Omap @ SV1191 @ SV1644 @ SV1900 @ SV588 ) )
| ( SV1644
= ( c_List_Olist_ONil @ SV1900 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4098]) ).
thf(4612,plain,
! [SV1645: $i,SV1192: $i,SV589: $i] :
( ( ( ( c_List_Olist_ONil @ SV589 )
!= ( c_List_Oappend @ SV1192 @ SV1645 @ SV589 ) )
= $true )
| ( ( SV1192
= ( c_List_Olist_ONil @ SV589 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4099]) ).
thf(4613,plain,
! [SV1193: $i,SV590: $i] :
( ( ( ( c_List_Olist_ONil @ SV590 )
= ( c_List_Orev @ SV1193 @ SV590 ) )
= $false )
| ( ( SV1193
= ( c_List_Olist_ONil @ SV590 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4100]) ).
thf(4614,plain,
! [SV1646: $i,SV1194: $i,SV591: $i] :
( ( ( ( c_List_Otake @ SV591 @ SV1194 @ SV1646 )
!= ( c_List_Olist_ONil @ SV1646 ) )
= $true )
| ( ( ( SV1194
= ( c_List_Olist_ONil @ SV1646 ) )
| ( SV591
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4101]) ).
thf(4615,plain,
! [SV1647: $i,SV1195: $i,SV592: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV592 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1195 @ SV1647 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV1647
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4102]) ).
thf(4616,plain,
! [SV1196: $i,SV593: $i] :
( ( ( ( c_List_Orev @ SV593 @ SV1196 )
= ( c_List_Olist_ONil @ SV1196 ) )
= $false )
| ( ( SV593
= ( c_List_Olist_ONil @ SV1196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4103]) ).
thf(4617,plain,
! [SV1901: $i,SV1648: $i,SV1197: $i,SV594: $i] :
( ( ! [SY4581: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV594 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1197 @ SV1648 @ SV594 )
!= ( c_HOL_Ominus__class_Ominus @ SV1901 @ SY4581 @ SV594 ) )
| ( c_HOL_Oord__class_Oless @ SV1197 @ SV1648 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV1901 @ SY4581 @ SV594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4104]) ).
thf(4618,plain,
! [SV1649: $i,SV1198: $i,SV595: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV595 @ SV1198 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV1649 ) )
= $true )
| ( ( SV595
= ( c_Lambda_OdB_OAbs @ SV1649 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4105]) ).
thf(4619,plain,
! [SV1902: $i,SV1650: $i,SV1199: $i,SV596: $i] :
( ( ! [SY4582: $i] :
( ( ( c_List_Oappend @ SV596 @ SV1199 @ SV1650 )
!= ( c_List_Oappend @ SV1902 @ SY4582 @ SV1650 ) )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV1902 @ ( tc_List_Olist @ SV1650 ) ) @ SV596 @ SV1650 )
= SV1902 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV596 @ ( tc_List_Olist @ SV1650 ) ) @ ( c_Nat_Osize__class_Osize @ SV1902 @ ( tc_List_Olist @ SV1650 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4106]) ).
thf(4620,plain,
! [SV1651: $i,SV1200: $i,SV597: $i] :
( ( ( c_List_Olist_OCons @ SV597 @ SV1200 @ SV1651 )
= SV1200 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4107]) ).
thf(4621,plain,
! [SV1652: $i,SV1201: $i,SV598: $i] :
( ( ( SV598
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV598 @ ( tc_List_Olist @ SV1201 ) ) @ SV1652 @ SV1201 ) )
= $true )
| ( ( ( c_List_Oappend @ SV598 @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV598 @ ( tc_List_Olist @ SV1201 ) ) @ SV1652 @ SV1201 ) @ SV1201 )
= SV1652 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4108]) ).
thf(4622,plain,
! [SV1903: $i,SV1653: $i,SV1202: $i,SV599: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ SV599 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ SV599 @ tc_nat ) @ ( c_List_Olist_OCons @ SV1202 @ SV1653 @ SV1903 ) @ SV1903 )
= ( c_List_Olist_OCons @ SV1202 @ SV1653 @ SV1903 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4109]) ).
thf(4623,plain,
! [SV1654: $i,SV1203: $i,SV600: $i] :
( ( ( ( c_List_Orev @ SV600 @ SV1203 )
!= ( c_List_Orev @ SV1654 @ SV1203 ) )
= $true )
| ( ( SV600 = SV1654 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4110]) ).
thf(4624,plain,
! [SV1655: $i,SV1204: $i,SV601: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV601 @ SV1204 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV1655 ) )
= $true )
| ( ( SV1204
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4111]) ).
thf(4625,plain,
! [SV1904: $i,SV1656: $i,SV1205: $i,SV603: $i] :
( ( ( SV603
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV603 @ ( tc_List_Olist @ SV1205 ) ) @ SV1656 @ SV1205 ) )
| ( ( c_List_Oappend @ SV603 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV603 @ ( tc_List_Olist @ SV1205 ) ) @ SV1656 @ SV1205 ) @ SV1904 @ SV1205 ) @ SV1205 )
= ( c_List_Oappend @ SV1656 @ SV1904 @ SV1205 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV603 @ ( tc_List_Olist @ SV1205 ) ) @ ( c_Nat_Osize__class_Osize @ SV1656 @ ( tc_List_Olist @ SV1205 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4112]) ).
thf(4626,plain,
! [SV1657: $i,SV1206: $i,SV604: $i] :
( ( ( ( c_List_Olist_ONil @ SV604 )
!= ( c_List_Oreplicate @ SV1206 @ SV1657 @ SV604 ) )
= $true )
| ( ( SV1206
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4113]) ).
thf(4627,plain,
! [SV1658: $i,SV1207: $i,SV605: $i] :
( ( ( ( c_List_Oappend @ SV605 @ SV1207 @ SV1658 )
!= SV1207 )
= $true )
| ( ( SV605
= ( c_List_Olist_ONil @ SV1658 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4114]) ).
thf(4628,plain,
! [SV1208: $i,SV606: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV606 @ SV1208 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( c_lessequals @ SV606 @ SV1208 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4115]) ).
thf(4629,plain,
! [SV1905: $i,SV1659: $i,SV1209: $i,SV607: $i] :
( ( ! [SY4583: $i,SY4584: $i] :
( ( ( c_List_Omap @ SV607 @ SV1209 @ SV1659 @ SV1905 )
!= ( c_List_Omap @ SY4583 @ SV1209 @ SV1659 @ SV1905 ) )
| ( ( hAPP @ SV607 @ SY4584 )
= ( hAPP @ SY4583 @ SY4584 ) )
| ~ ( c_in @ SY4584 @ ( c_List_Oset @ SV1209 @ SV1659 ) @ SV1659 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4116]) ).
thf(4630,plain,
! [SV1906: $i,SV1660: $i,SV1210: $i,SV608: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV608 ) @ SV1210 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1660 ) @ SV1906 ) )
| ( SV608 = SV1660 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4117]) ).
thf(4631,plain,
! [SV1907: $i,SV1661: $i,SV1211: $i,SV609: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV609 ) @ SV1211 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1661 ) @ SV1907 ) )
| ( SV1211 = SV1907 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4118]) ).
thf(4632,plain,
! [SV1662: $i,SV1212: $i,SV610: $i] :
( ( ( ( c_List_Oappend @ SV610 @ SV1212 @ SV1662 )
!= ( c_List_Olist_ONil @ SV1662 ) )
= $true )
| ( ( SV1212
= ( c_List_Olist_ONil @ SV1662 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4119]) ).
thf(4633,plain,
! [SV1663: $i,SV1213: $i,SV611: $i] :
( ( ( ~ ( class_Nat_Osemiring__char__0 @ SV611 ) )
= $true )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1213 @ SV611 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1663 @ SV611 ) )
| ( SV1213 = SV1663 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4120]) ).
thf(4634,plain,
! [SV1664: $i,SV1214: $i,SV612: $i] :
( ( ( ~ ( class_OrderedGroup_Ogroup__add @ SV612 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1214 @ SV1664 @ SV612 )
!= ( c_HOL_Ozero__class_Ozero @ SV612 ) )
| ( SV1214 = SV1664 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4121]) ).
thf(4635,plain,
! [SV1908: $i,SV1665: $i,SV1215: $i,SV613: $i] :
( ( ! [SY4585: $i] :
( ( ( c_List_Odrop @ SV613 @ SV1215 @ SV1665 )
!= ( c_List_Olist_OCons @ SV1908 @ SY4585 @ SV1665 ) )
| ( ( c_List_Onth @ SV1215 @ SV613 @ SV1665 )
= SV1908 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4122]) ).
thf(4636,plain,
! [SV1909: $i,SV1666: $i,SV1216: $i,SV614: $i] :
( ( ! [SY4586: $i] :
( ( ( c_List_Oappend @ SV614 @ SV1216 @ SV1666 )
!= ( c_List_Oappend @ SV1909 @ SY4586 @ SV1666 ) )
| ( SV614
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV614 @ ( tc_List_Olist @ SV1666 ) ) @ SV1909 @ SV1666 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV614 @ ( tc_List_Olist @ SV1666 ) ) @ ( c_Nat_Osize__class_Osize @ SV1909 @ ( tc_List_Olist @ SV1666 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4123]) ).
thf(4637,plain,
! [SV1667: $i,SV1217: $i,SV615: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV615 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV615 )
| ( SV1217
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV615 ) @ SV1217 ) @ SV1667 ) )
| ( SV1667
= ( c_HOL_Ozero__class_Ozero @ SV615 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4124]) ).
thf(4638,plain,
! [SV1218: $i,SV616: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV616 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV616 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV616 )
| ~ ( class_Power_Opower @ SV616 )
| ( ( c_Power_Opower__class_Opower @ SV1218 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV616 )
!= ( c_HOL_Ozero__class_Ozero @ SV616 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4125]) ).
thf(4639,plain,
! [SV1668: $i,SV1219: $i,SV617: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV617 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV617 ) @ SV1219 ) @ SV1668 )
!= ( c_HOL_Ozero__class_Ozero @ SV617 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV617 ) @ SV1668 @ SV617 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV617 ) @ SV1219 @ SV617 )
| ( SV1668
= ( c_HOL_Ozero__class_Ozero @ SV617 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4126]) ).
thf(4640,plain,
! [SV1910: $i,SV1669: $i,SV1220: $i,SV618: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV618 )
| ( ( c_Power_Opower__class_Opower @ SV1220 @ SV1669 @ SV618 )
!= ( c_Power_Opower__class_Opower @ SV1220 @ SV1910 @ SV618 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV618 ) @ SV1220 @ SV618 )
| ( SV1669 = SV1910 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4127]) ).
thf(4641,plain,
! [SV1670: $i,SV1221: $i,SV619: $i] :
( ( ( ( c_List_Oreplicate @ SV619 @ SV1221 @ SV1670 )
!= ( c_List_Olist_ONil @ SV1670 ) )
= $true )
| ( ( SV619
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4128]) ).
thf(4642,plain,
! [SV1671: $i,SV1222: $i,SV620: $i] :
( ( SV620
= ( c_List_Olist_OCons @ SV1222 @ SV620 @ SV1671 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4129]) ).
thf(4643,plain,
! [SV1911: $i,SV1672: $i,SV1223: $i,SV621: $i] :
( ( ! [SY4587: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV621 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1223 @ SV1672 @ SV621 )
!= ( c_HOL_Ominus__class_Ominus @ SV1911 @ SY4587 @ SV621 ) )
| ( c_lessequals @ SV1672 @ SV1223 @ SV621 )
| ~ ( c_lessequals @ SY4587 @ SV1911 @ SV621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4130]) ).
thf(4644,plain,
! [SV1912: $i,SV1673: $i,SV1224: $i,SV622: $i] :
( ( ! [SY4588: $i] :
( ( ( c_List_Oreplicate @ SV622 @ SV1224 @ SV1673 )
!= ( c_List_Oreplicate @ SV1912 @ SY4588 @ SV1673 ) )
| ( SV1224 = SY4588 )
| ( SV622
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4131]) ).
thf(4645,plain,
! [SV1913: $i,SV1674: $i,SV1225: $i,SV623: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV623 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1225 @ SV1225 @ SV623 )
!= ( c_HOL_Ominus__class_Ominus @ SV1674 @ SV1913 @ SV623 ) )
| ( SV1674 = SV1913 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4132]) ).
thf(4646,plain,
! [SV1675: $i,SV1226: $i,SV624: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV624 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV624 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1226 @ SV1675 @ SV624 )
!= ( c_HOL_Ozero__class_Ozero @ SV624 ) )
| ( SV1226 = SV1675 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4133]) ).
thf(4647,plain,
! [SV1914: $i,SV1676: $i,SV1227: $i,SV625: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV625 )
| ( ( c_Power_Opower__class_Opower @ SV1227 @ ( c_Suc @ SV1676 ) @ SV625 )
!= ( c_Power_Opower__class_Opower @ SV1914 @ ( c_Suc @ SV1676 ) @ SV625 ) )
| ( SV1227 = SV1914 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV625 ) @ SV1914 @ SV625 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV625 ) @ SV1227 @ SV625 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4134]) ).
thf(4648,plain,
! [SV1915: $i,SV1677: $i,SV1228: $i,SV626: $i] :
( ( ! [SY4589: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV626 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1228 @ SV1677 @ SV626 )
!= ( c_HOL_Ominus__class_Ominus @ SV1915 @ SY4589 @ SV626 ) )
| ( c_lessequals @ SY4589 @ SV1915 @ SV626 )
| ~ ( c_lessequals @ SV1677 @ SV1228 @ SV626 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4135]) ).
thf(4649,plain,
! [SV1678: $i,SV1229: $i,SV628: $i] :
( ( ( SV628
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV628 ) @ SV1229 ) @ SV1678 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV628 ) @ SV1229 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV628 ) @ SV1229 ) @ ( c_List_Oappend @ SV1678 @ ( c_List_Olist_OCons @ SV1229 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4136]) ).
thf(4650,plain,
! [SV1916: $i,SV1679: $i,SV1230: $i,SV629: $i] :
( ( ( ( c_List_Olist__update @ SV629 @ SV1230 @ SV1679 @ SV1916 )
!= SV629 )
| ~ ( c_HOL_Oord__class_Oless @ SV1230 @ ( c_Nat_Osize__class_Osize @ SV629 @ ( tc_List_Olist @ SV1916 ) ) @ tc_nat )
| ( ( c_List_Onth @ SV629 @ SV1230 @ SV1916 )
= SV1679 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4137]) ).
thf(4651,plain,
! [SV1917: $i,SV1680: $i,SV1231: $i,SV630: $i] :
( ( ! [SY4590: $i] :
( ( ( c_List_Oappend @ SV630 @ SV1231 @ SV1680 )
!= ( c_List_Oappend @ SV1917 @ SY4590 @ SV1680 ) )
| ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1917 @ ( tc_List_Olist @ SV1680 ) ) @ SV630 @ SV1680 ) @ SV1231 @ SV1680 )
= SY4590 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV630 @ ( tc_List_Olist @ SV1680 ) ) @ ( c_Nat_Osize__class_Osize @ SV1917 @ ( tc_List_Olist @ SV1680 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4138]) ).
thf(4652,plain,
! [SV1918: $i,SV1681: $i,SV1232: $i,SV631: $i] :
( ( ! [SY4591: $i] :
( ( ( c_List_Olist_OCons @ SV631 @ SV1232 @ SV1681 )
!= ( c_List_Olist_OCons @ SV1918 @ SY4591 @ SV1681 ) )
| ( SV631 = SV1918 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4139]) ).
thf(4653,plain,
! [SV1682: $i,SV1233: $i,SV632: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV632 @ SV1233 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1682 @ SV1233 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV632 = SV1682 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4140]) ).
thf(4654,plain,
! [SV1919: $i,SV1683: $i,SV1234: $i,SV633: $i] :
( ( ! [SY4592: $i] :
( ( ( c_List_Omap @ SV633 @ SV1234 @ SV1683 @ SV1919 )
!= ( c_List_Omap @ SV633 @ SY4592 @ SV1683 @ SV1919 ) )
| ( ( c_Nat_Osize__class_Osize @ SV1234 @ ( tc_List_Olist @ SV1683 ) )
= ( c_Nat_Osize__class_Osize @ SY4592 @ ( tc_List_Olist @ SV1683 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4141]) ).
thf(4655,plain,
! [SV1235: $i,SV634: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV634 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV634 ) @ SV1235 ) @ SV1235 )
!= ( c_HOL_Ozero__class_Ozero @ SV634 ) )
| ( SV1235
= ( c_HOL_Ozero__class_Ozero @ SV634 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4142]) ).
thf(4656,plain,
! [SV1684: $i,SV1236: $i,SV636: $i] :
( ( ( ( c_List_Orev @ SV636 @ SV1236 )
!= ( c_List_Olist_OCons @ SV1684 @ ( c_List_Olist_ONil @ SV1236 ) @ SV1236 ) )
= $true )
| ( ( SV636
= ( c_List_Olist_OCons @ SV1684 @ ( c_List_Olist_ONil @ SV1236 ) @ SV1236 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4143]) ).
thf(4657,plain,
! [SV1920: $i,SV1685: $i,SV1237: $i,SV637: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV637 )
| ~ ( class_Int_Onumber__ring @ SV637 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1237 ) @ SV1685 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1237 ) @ SV1920 ) )
| ( SV1685 = SV1920 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4144]) ).
thf(4658,plain,
! [SV1921: $i,SV1686: $i,SV1238: $i,SV638: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV638 ) @ SV1238 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1686 @ SV1921 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV638
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1686 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV638 @ SV1238 @ SV1686 @ SV1921 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1921
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4145]) ).
thf(4659,plain,
! [SV1687: $i,SV1239: $i,SV639: $i] :
( ( ( ~ ( class_Int_Oring__char__0 @ SV639 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV639 )
| ( ( c_Int_Onumber__class_Onumber__of @ SV1239 @ SV639 )
!= ( c_Int_Onumber__class_Onumber__of @ SV1687 @ SV639 ) )
| ( SV1239 = SV1687 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4146]) ).
thf(4660,plain,
! [SV1922: $i,SV1688: $i,SV1240: $i,SV641: $i] :
( ( ( ( c_List_Olist__update @ SV641 @ SV1240 @ SV1688 @ SV1922 )
!= ( c_List_Olist_ONil @ SV1922 ) )
| ( SV641
= ( c_List_Olist_ONil @ SV1922 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4147]) ).
thf(4661,plain,
! [SV1923: $i,SV1689: $i,SV1242: $i,SV643: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV643 ) @ SV1242 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1689 ) @ SV1923 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1242 = SV1923 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4149]) ).
thf(4662,plain,
! [SV1924: $i,SV1690: $i,SV1243: $i,SV644: $i] :
( ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV644 @ ( tc_List_Olist @ SV1243 ) ) @ SV1690 @ SV1243 )
!= SV644 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1690 @ ( tc_List_Olist @ SV1243 ) ) @ ( c_Nat_Osize__class_Osize @ SV644 @ ( tc_List_Olist @ SV1243 ) ) @ tc_nat )
| ( ( c_List_Oappend @ SV1690 @ SV1924 @ SV1243 )
= ( c_List_Oappend @ SV644 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV644 @ ( tc_List_Olist @ SV1243 ) ) @ SV1690 @ SV1243 ) @ SV1924 @ SV1243 ) @ SV1243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4150]) ).
thf(4663,plain,
! [SV1925: $i,SV1691: $i,SV1244: $i,SV645: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ SV645 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ SV645 @ tc_nat ) @ ( c_List_Olist_OCons @ SV1244 @ SV1691 @ SV1925 ) @ SV1925 )
= ( c_List_Olist_ONil @ SV1925 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4151]) ).
thf(4664,plain,
! [SV1692: $i,SV1245: $i,SV646: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV646 @ SV1245 @ tc_nat )
!= ( c_HOL_Ominus__class_Ominus @ SV1692 @ SV1245 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1245 @ SV1692 @ tc_nat )
| ~ ( c_lessequals @ SV1245 @ SV646 @ tc_nat )
| ( SV646 = SV1692 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4152]) ).
thf(4665,plain,
! [SV1693: $i,SV1246: $i,SV647: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV647 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV647 ) @ SV1246 ) @ SV1693 )
!= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV647 ) @ SV1693 @ SV647 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV647 ) @ SV1246 @ SV647 )
| ( SV1246
= ( c_HOL_Ozero__class_Ozero @ SV647 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4153]) ).
thf(4666,plain,
! [SV1926: $i,SV1694: $i,SV1247: $i,SV648: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV648 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV648 ) @ SV1247 ) @ SV1694 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV648 ) @ SV1247 ) @ SV1926 ) )
| ( SV1694 = SV1926 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4154]) ).
thf(4667,plain,
! [SV1927: $i,SV1695: $i,SV1248: $i,SV649: $i] :
( ( ! [SY4593: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV649 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1248 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1695 ) @ SV1927 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1695 ) @ SY4593 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1248 ) @ SV1927 )
= SY4593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4155]) ).
thf(4668,plain,
! [SV1696: $i,SV1249: $i,SV650: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV650 ) @ SV1249 )
= ( c_Lambda_OdB_OAbs @ SV1696 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4156]) ).
thf(4669,plain,
! [SV1928: $i,SV1697: $i,SV1250: $i,SV651: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV651 ) ) @ SV1250 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1697 ) @ SV1928 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4157]) ).
thf(4670,plain,
! [SV1929: $i,SV1698: $i,SV1251: $i,SV652: $i] :
( ( ( ( c_List_Omap @ SV652 @ SV1251 @ SV1698 @ SV1929 )
!= ( c_List_Olist_ONil @ SV1929 ) )
| ( SV1251
= ( c_List_Olist_ONil @ SV1698 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4158]) ).
thf(4671,plain,
! [SV1699: $i,SV1252: $i,SV653: $i] :
( ( ( ( c_List_Oappend @ SV653 @ SV1252 @ SV1699 )
!= SV653 )
= $true )
| ( ( SV1252
= ( c_List_Olist_ONil @ SV1699 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4159]) ).
thf(4672,plain,
! [SV1253: $i,SV654: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV654 @ SV1253 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1253 @ SV654 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV1253 = SV654 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4160]) ).
thf(4673,plain,
! [SV1254: $i,SV655: $i] :
( ( ( ( c_Nat_Osize__class_Osize @ SV655 @ ( tc_List_Olist @ SV1254 ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV655
= ( c_List_Olist_ONil @ SV1254 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4161]) ).
thf(4674,plain,
! [SV1930: $i,SV1700: $i,SV1255: $i,SV656: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV656 ) @ SV1255 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1700 ) @ SV1930 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4162]) ).
thf(4675,plain,
! [SV657: $i,SV1: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1 @ ( c_Suc @ SV657 ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV657 @ SV1 @ tc_nat ) )
= $true )
| ( ( SV1 = SV657 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4163]) ).
thf(4676,plain,
! [SV1931: $i,SV1701: $i,SV1256: $i,SV658: $i,SV2: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV2 )
| ( c_lessequals @ SV658 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SV1256 ) @ SV1701 ) @ SV2 )
| ~ ( c_lessequals @ SV1931 @ SV1701 @ SV2 )
| ~ ( c_lessequals @ SV658 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SV1256 ) @ SV1931 ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4164]) ).
thf(4677,plain,
! [SV1702: $i,SV1257: $i,SV659: $i,SV3: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV3 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV659 @ SV1257 @ SV3 )
| ~ ( c_lessequals @ SV1702 @ SV1257 @ SV3 )
| ~ ( c_HOL_Oord__class_Oless @ SV659 @ SV1702 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4165]) ).
thf(4678,plain,
! [SV1703: $i,SV1258: $i,SV660: $i,SV4: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV4 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV660 @ SV1258 @ SV4 )
| ~ ( c_HOL_Oord__class_Oless @ SV1703 @ SV1258 @ SV4 )
| ~ ( c_lessequals @ SV660 @ SV1703 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4166]) ).
thf(4679,plain,
! [SV8: $i,SV663: $i,SV1259: $i] :
( ( ( ~ ( c_lessequals @ SV1259 @ SV663 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV8 @ SV1259 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV8 @ SV663 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4169]) ).
thf(4680,plain,
! [SV1704: $i,SV1260: $i,SV664: $i,SV10: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV10 ) )
= $true )
| ( ( ( c_lessequals @ SV664 @ SV1260 @ SV10 )
| ~ ( c_lessequals @ SV1704 @ SV1260 @ SV10 )
| ~ ( c_lessequals @ SV664 @ SV1704 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4170]) ).
thf(4681,plain,
! [SV1705: $i,SV1261: $i,SV665: $i,SV11: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV11 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV665 @ SV1261 @ SV11 )
| ~ ( c_HOL_Oord__class_Oless @ SV665 @ SV1705 @ SV11 )
| ~ ( c_lessequals @ SV1705 @ SV1261 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4171]) ).
thf(4682,plain,
! [SV1706: $i,SV1262: $i,SV666: $i,SV12: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV12 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV666 @ SV1262 @ SV12 )
| ~ ( c_lessequals @ SV666 @ SV1706 @ SV12 )
| ~ ( c_HOL_Oord__class_Oless @ SV1706 @ SV1262 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4172]) ).
thf(4683,plain,
! [SV1707: $i,SV1263: $i,SV667: $i,SV13: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV13 ) )
= $true )
| ( ( ( c_lessequals @ SV667 @ SV1263 @ SV13 )
| ~ ( c_lessequals @ SV667 @ SV1707 @ SV13 )
| ~ ( c_lessequals @ SV1707 @ SV1263 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4173]) ).
thf(4684,plain,
! [SV1264: $i,SV668: $i,SV14: $i] :
( ( ( class_Ring__and__Field_Oring__1 @ SV14 )
= $false )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV668 @ SV1264 @ tc_nat ) @ SV14 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV668 @ SV14 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1264 @ SV14 ) @ SV14 ) )
| ~ ( c_lessequals @ SV1264 @ SV668 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4174]) ).
thf(4685,plain,
! [SV669: $i,SV1265: $i,SV15: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV15 @ SV1265 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV669 @ SV1265 @ tc_nat )
| ~ ( c_lessequals @ SV669 @ SV15 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV15 @ SV669 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1265 @ SV669 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4175]) ).
thf(4686,plain,
! [SV670: $i,SV1266: $i,SV16: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV16 @ SV1266 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV670 @ SV1266 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1266 @ SV670 @ tc_nat )
| ~ ( c_lessequals @ SV1266 @ SV16 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV16 @ SV670 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4176]) ).
thf(4687,plain,
! [SV1708: $i,SV1267: $i,SV673: $i,SV20: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV20 ) )
= $true )
| ( ( ( c_lessequals @ SV673 @ SV1267 @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV1267 @ SV20 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV673 @ ( c_Suc @ SV1708 ) @ SV20 ) @ ( c_Power_Opower__class_Opower @ SV1267 @ ( c_Suc @ SV1708 ) @ SV20 ) @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4179]) ).
thf(4688,plain,
! [SV1709: $i,SV1268: $i,SV674: $i,SV21: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV21 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SV674 ) @ SV1268 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SV674 ) @ SV1709 ) @ SV21 )
| ~ ( c_lessequals @ SV1268 @ SV1709 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4180]) ).
thf(4689,plain,
! [SV1710: $i,SV1269: $i,SV675: $i,SV22: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV22 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV675 ) @ SV1269 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV1710 ) @ SV1269 ) @ SV22 )
| ~ ( c_lessequals @ SV675 @ SV1710 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4181]) ).
thf(4690,plain,
! [SV1711: $i,SV1270: $i,SV676: $i,SV23: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV23 ) )
= $true )
| ( ( ( c_lessequals @ SV676 @ SV1270 @ SV23 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV23 ) @ SV1711 ) @ SV676 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV23 ) @ SV1711 ) @ SV1270 ) @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4182]) ).
thf(4691,plain,
! [SV1712: $i,SV1271: $i,SV677: $i,SV24: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV24 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ SV677 ) @ SV1271 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ SV677 ) @ SV1712 ) @ SV24 )
| ~ ( c_lessequals @ SV1271 @ SV1712 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4183]) ).
thf(4692,plain,
! [SV1713: $i,SV1272: $i,SV678: $i,SV25: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV25 ) )
= $true )
| ( ( ( c_lessequals @ SV678 @ SV1272 @ SV25 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SV678 ) @ SV1713 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SV1272 ) @ SV1713 ) @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4184]) ).
thf(4693,plain,
! [SV1714: $i,SV1273: $i,SV679: $i,SV26: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV26 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV26 ) @ SV679 ) @ SV1273 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV26 ) @ SV1714 ) @ SV1273 ) @ SV26 )
| ~ ( c_lessequals @ SV679 @ SV1714 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4185]) ).
thf(4694,plain,
! [SV27: $i,SV680: $i,SV1274: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1274 @ SV680 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV27 @ SV1274 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV27 ) @ SV680 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4186]) ).
thf(4695,plain,
! [SV1275: $i,SV681: $i,SV30: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV30 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV30 ) @ ( c_Power_Opower__class_Opower @ SV681 @ ( c_Suc @ SV1275 ) @ SV30 ) @ SV30 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SV681 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4187]) ).
thf(4696,plain,
! [SV1276: $i,SV682: $i,SV31: $i] :
( ( ( class_Orderings_Opreorder @ SV31 )
= $false )
| ( ( ( c_lessequals @ SV682 @ SV1276 @ SV31 )
| ~ ( c_HOL_Oord__class_Oless @ SV682 @ SV1276 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4188]) ).
thf(4697,plain,
! [SV1277: $i,SV683: $i,SV32: $i] :
( ( ( class_Orderings_Oorder @ SV32 )
= $false )
| ( ( ( c_lessequals @ SV683 @ SV1277 @ SV32 )
| ~ ( c_HOL_Oord__class_Oless @ SV683 @ SV1277 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4189]) ).
thf(4698,plain,
! [SV1278: $i,SV686: $i,SV35: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV35 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV686 @ SV1278 @ SV35 ) @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ SV35 )
| ~ ( c_lessequals @ SV686 @ SV1278 @ SV35 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4192]) ).
thf(4699,plain,
! [SV1279: $i,SV687: $i,SV36: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV36 )
= $false )
| ( ( ( c_lessequals @ SV687 @ SV1279 @ SV36 )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV687 @ SV1279 @ SV36 ) @ ( c_HOL_Ozero__class_Ozero @ SV36 ) @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4193]) ).
thf(4700,plain,
! [SV1280: $i,SV688: $i,SV37: $i] :
( ( ( class_Orderings_Oorder @ SV37 )
= $false )
| ( ( ( SV688 = SV1280 )
| ~ ( c_lessequals @ SV688 @ SV1280 @ SV37 )
| ~ ( c_lessequals @ SV1280 @ SV688 @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4194]) ).
thf(4701,plain,
! [SV1281: $i,SV689: $i,SV38: $i] :
( ( ( class_Orderings_Oorder @ SV38 )
= $false )
| ( ( ( SV689 = SV1281 )
| ~ ( c_lessequals @ SV1281 @ SV689 @ SV38 )
| ~ ( c_lessequals @ SV689 @ SV1281 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4195]) ).
thf(4702,plain,
! [SV1282: $i,SV690: $i,SV39: $i] :
( ( ( class_Orderings_Oorder @ SV39 )
= $false )
| ( ( ( SV690 = SV1282 )
| ~ ( c_lessequals @ SV1282 @ SV690 @ SV39 )
| ~ ( c_lessequals @ SV690 @ SV1282 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4196]) ).
thf(4703,plain,
! [SV40: $i,SV691: $i] :
( ( ( c_lessequals @ SV691 @ SV40 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV40 @ SV691 @ tc_nat ) )
= $true )
| ( ( SV40 = SV691 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4197]) ).
thf(4704,plain,
! [SV1283: $i,SV693: $i,SV43: $i] :
( ( ( class_Orderings_Opreorder @ SV43 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV693 @ SV1283 @ SV43 )
| ( c_lessequals @ SV1283 @ SV693 @ SV43 )
| ~ ( c_lessequals @ SV693 @ SV1283 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4199]) ).
thf(4705,plain,
! [SV694: $i,SV1284: $i,SV44: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV44 @ SV1284 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV44 @ SV694 @ tc_nat ) @ SV1284 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4200]) ).
thf(4706,plain,
! [SV695: $i,SV46: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV46 @ ( c_Suc @ SV695 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV46 @ SV695 @ tc_nat )
= $true )
| ( ( SV46 = SV695 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4201]) ).
thf(4707,plain,
! [SV47: $i,SV696: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV696 @ ( c_Suc @ SV47 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV696 @ SV47 @ tc_nat )
= $true )
| ( ( SV47 = SV696 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4202]) ).
thf(4708,plain,
! [SV697: $i,SV48: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV48 @ ( c_Suc @ SV697 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV48 @ SV697 @ tc_nat )
= $true )
| ( ( SV48 = SV697 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4203]) ).
thf(4709,plain,
! [SV699: $i,SV50: $i,SV1285: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1285 @ SV50 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1285 @ SV699 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV50 @ SV699 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV50 @ SV1285 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4204]) ).
thf(4710,plain,
! [SV1715: $i,SV1286: $i,SV701: $i,SV52: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV52 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV701 @ SV1286 @ SV52 ) @ ( c_Power_Opower__class_Opower @ SV701 @ SV1715 @ SV52 ) @ SV52 )
| ~ ( c_lessequals @ SV701 @ ( c_HOL_Oone__class_Oone @ SV52 ) @ SV52 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV701 @ SV52 )
| ~ ( c_lessequals @ SV1715 @ SV1286 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4206]) ).
thf(4711,plain,
! [SV1287: $i,SV706: $i,SV57: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV57 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV57 ) @ ( c_Power_Opower__class_Opower @ SV706 @ SV1287 @ SV57 ) @ SV57 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV57 ) @ SV706 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4211]) ).
thf(4712,plain,
! [SV1288: $i,SV708: $i,SV59: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV59 )
= $false )
| ( ( ( c_lessequals @ SV708 @ SV1288 @ tc_nat )
| ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV708 @ SV59 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1288 @ SV59 ) @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4213]) ).
thf(4713,plain,
! [SV1289: $i,SV709: $i,SV60: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV60 )
= $false )
| ( ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV709 @ SV60 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1289 @ SV60 ) @ SV60 )
| ~ ( c_lessequals @ SV709 @ SV1289 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4214]) ).
thf(4714,plain,
! [SV1290: $i,SV710: $i,SV61: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV61 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV61 ) @ ( c_HOL_Ominus__class_Ominus @ SV710 @ SV1290 @ SV61 ) ) @ SV1290 )
= SV710 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4215]) ).
thf(4715,plain,
! [SV1932: $i,SV1716: $i,SV1291: $i,SV711: $i,SV62: $i] :
( ( ( c_ListOrder_Ostep1 @ SV62 @ ( c_List_Oappend @ SV711 @ SV1291 @ SV1716 ) @ ( c_List_Oappend @ SV711 @ SV1932 @ SV1716 ) @ SV1716 )
| ~ ( c_ListOrder_Ostep1 @ SV62 @ SV1291 @ SV1932 @ SV1716 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4216]) ).
thf(4716,plain,
! [SV1933: $i,SV1717: $i,SV1292: $i,SV712: $i,SV63: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV63 @ SV712 @ SV1292 @ SV1717 )
| ( c_ListOrder_Ostep1 @ SV63 @ ( c_List_Oappend @ SV712 @ SV1933 @ SV1717 ) @ ( c_List_Oappend @ SV1292 @ SV1933 @ SV1717 ) @ SV1717 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4217]) ).
thf(4717,plain,
! [SV1934: $i,SV1718: $i,SV1293: $i,SV713: $i,SV64: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV64 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV713 ) @ SV1293 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV1718 ) @ SV1934 ) @ SV64 )
| ~ ( c_lessequals @ SV1293 @ SV1934 @ SV64 )
| ~ ( c_lessequals @ SV713 @ SV1718 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4218]) ).
thf(4718,plain,
! [SV1935: $i,SV1719: $i,SV1294: $i,SV714: $i,SV65: $i] :
( ( ( c_lessequals @ SV65 @ ( c_List_Olist_Olist__size @ SV714 @ SV1294 @ SV1719 ) @ tc_nat )
| ~ ( c_lessequals @ SV65 @ ( hAPP @ SV714 @ SV1935 ) @ tc_nat )
| ~ ( c_in @ SV1935 @ ( c_List_Oset @ SV1294 @ SV1719 ) @ SV1719 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4219]) ).
thf(4719,plain,
! [SV1295: $i,SV719: $i,SV71: $i] :
( ( ( class_Orderings_Olinorder @ SV71 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV719 @ SV1295 @ SV71 )
| ( c_lessequals @ SV1295 @ SV719 @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4223]) ).
thf(4720,plain,
! [SV72: $i,SV720: $i] :
( ( ( ~ ( c_lessequals @ SV720 @ SV720 @ SV72 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV720 @ SV720 @ SV72 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4224]) ).
thf(4721,plain,
! [SV73: $i,SV721: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV721 @ SV721 @ SV73 )
= $true )
| ( ( c_lessequals @ SV721 @ SV721 @ SV73 )
= $true )
| ( ( class_Orderings_Olinorder @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4225]) ).
thf(4722,plain,
! [SV1296: $i,SV722: $i,SV74: $i] :
( ( ( class_Orderings_Olinorder @ SV74 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV722 @ SV1296 @ SV74 )
| ~ ( c_lessequals @ SV1296 @ SV722 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4226]) ).
thf(4723,plain,
! [SV1297: $i,SV723: $i,SV75: $i] :
( ( ( class_Orderings_Olinorder @ SV75 )
= $false )
| ( ( ( c_lessequals @ SV723 @ SV1297 @ SV75 )
| ( c_HOL_Oord__class_Oless @ SV1297 @ SV723 @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4227]) ).
thf(4724,plain,
! [SV1298: $i,SV724: $i,SV76: $i] :
( ( ( class_Orderings_Olinorder @ SV76 )
= $false )
| ( ( ~ ( c_lessequals @ SV724 @ SV1298 @ SV76 )
| ~ ( c_HOL_Oord__class_Oless @ SV1298 @ SV724 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4228]) ).
thf(4725,plain,
! [SV1299: $i,SV725: $i,SV77: $i] :
( ( ( class_Orderings_Olinorder @ SV77 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV725 @ SV1299 @ SV77 )
| ( c_lessequals @ SV1299 @ SV725 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4229]) ).
thf(4726,plain,
! [SV1300: $i,SV726: $i,SV78: $i] :
( ( ( class_Orderings_Opreorder @ SV78 )
= $false )
| ( ( ~ ( c_lessequals @ SV726 @ SV1300 @ SV78 )
| ~ ( c_HOL_Oord__class_Oless @ SV1300 @ SV726 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4230]) ).
thf(4727,plain,
! [SV1720: $i,SV1301: $i,SV727: $i,SV79: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV79 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV727 @ SV1301 @ SV79 ) @ ( c_Power_Opower__class_Opower @ SV727 @ SV1720 @ SV79 ) @ SV79 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV79 ) @ SV727 @ SV79 )
| ~ ( c_lessequals @ SV1301 @ SV1720 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4231]) ).
thf(4728,plain,
! [SV80: $i,SV728: $i,SV1302: $i] :
( ( ( c_lessequals @ SV1302 @ SV728 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV80 @ SV728 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV80 @ SV1302 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4232]) ).
thf(4729,plain,
! [SV729: $i,SV1303: $i,SV81: $i] :
( ( ( c_lessequals @ SV81 @ SV1303 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV81 @ SV729 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1303 @ SV729 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4233]) ).
thf(4730,plain,
! [SV1304: $i,SV733: $i,SV86: $i] :
( ( ( class_Orderings_Oorder @ SV86 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV733 @ SV1304 @ SV86 )
| ( SV1304 = SV733 )
| ~ ( c_lessequals @ SV733 @ SV1304 @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4237]) ).
thf(4731,plain,
! [SV1305: $i,SV734: $i,SV87: $i] :
( ( ( class_Orderings_Oorder @ SV87 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV734 @ SV1305 @ SV87 )
| ~ ( c_lessequals @ SV734 @ SV1305 @ SV87 )
| ( SV1305 = SV734 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4238]) ).
thf(4732,plain,
! [SV735: $i,SV88: $i] :
( ( ( c_lessequals @ SV88 @ SV735 @ tc_nat )
= $false )
| ( ( SV88 = SV735 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV88 @ SV735 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4239]) ).
thf(4733,plain,
! [SV736: $i,SV89: $i] :
( ( ( c_lessequals @ SV89 @ SV736 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV89 @ SV736 @ tc_nat )
= $true )
| ( ( SV89 = SV736 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4240]) ).
thf(4734,plain,
! [SV737: $i,SV90: $i] :
( ( ( c_lessequals @ SV90 @ SV737 @ tc_nat )
= $false )
| ( ( SV90 = SV737 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV90 @ SV737 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4241]) ).
thf(4735,plain,
! [SV1306: $i,SV738: $i,SV91: $i] :
( ( ( class_Orderings_Oorder @ SV91 )
= $false )
| ( ( ( SV738 = SV1306 )
| ( c_HOL_Oord__class_Oless @ SV738 @ SV1306 @ SV91 )
| ~ ( c_lessequals @ SV738 @ SV1306 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4242]) ).
thf(4736,plain,
! [SV1307: $i,SV739: $i,SV92: $i] :
( ( ( class_Orderings_Oorder @ SV92 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV739 @ SV1307 @ SV92 )
| ( SV739 = SV1307 )
| ~ ( c_lessequals @ SV739 @ SV1307 @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4243]) ).
thf(4737,plain,
! [SV1308: $i,SV740: $i,SV93: $i] :
( ( ( class_Orderings_Oorder @ SV93 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV740 @ SV1308 @ SV93 )
| ( SV740 = SV1308 )
| ~ ( c_lessequals @ SV740 @ SV1308 @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4244]) ).
thf(4738,plain,
! [SV1309: $i,SV741: $i,SV94: $i] :
( ( ( class_Orderings_Oorder @ SV94 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV741 @ SV1309 @ SV94 )
| ~ ( c_lessequals @ SV741 @ SV1309 @ SV94 )
| ( SV741 = SV1309 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4245]) ).
thf(4739,plain,
! [SV1310: $i,SV742: $i,SV95: $i] :
( ( ( class_Orderings_Olinorder @ SV95 )
= $false )
| ( ( ( SV742 = SV1310 )
| ~ ( c_lessequals @ SV742 @ SV1310 @ SV95 )
| ( c_HOL_Oord__class_Oless @ SV742 @ SV1310 @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4246]) ).
thf(4740,plain,
! [SV1311: $i,SV743: $i,SV96: $i] :
( ( ( class_Orderings_Olinorder @ SV96 )
= $false )
| ( ( ( SV743 = SV1311 )
| ( c_HOL_Oord__class_Oless @ SV743 @ SV1311 @ SV96 )
| ~ ( c_lessequals @ SV743 @ SV1311 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4247]) ).
thf(4741,plain,
! [SV1312: $i,SV747: $i,SV100: $i] :
( ( ( class_Orderings_Olinorder @ SV100 )
= $false )
| ( ( ( c_lessequals @ SV747 @ SV1312 @ SV100 )
| ( c_lessequals @ SV1312 @ SV747 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4250]) ).
thf(4742,plain,
! [SV1313: $i,SV748: $i,SV101: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV101 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV748 @ ( c_Suc @ SV1313 ) @ SV101 ) @ ( c_HOL_Oone__class_Oone @ SV101 ) @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ SV748 @ ( c_HOL_Oone__class_Oone @ SV101 ) @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ SV748 @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4251]) ).
thf(4743,plain,
! [SV1721: $i,SV1314: $i,SV749: $i,SV102: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV102 ) )
= $true )
| ( ( ( c_lessequals @ SV749 @ SV1314 @ SV102 )
| ~ ( c_in @ SV1314 @ ( c_List_Oset @ SV1721 @ SV102 ) @ SV102 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV749 @ SV1721 @ SV102 ) @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4252]) ).
thf(4744,plain,
! [SV1936: $i,SV1722: $i,SV1315: $i,SV750: $i,SV103: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV103 )
| ( c_lessequals @ SV750 @ SV1315 @ SV103 )
| ~ ( c_in @ SV1315 @ ( c_List_Oset @ SV1722 @ SV103 ) @ SV103 )
| ~ ( c_in @ SV750 @ ( c_List_Oset @ SV1936 @ SV103 ) @ SV103 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1936 @ SV1722 @ SV103 ) @ SV103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4253]) ).
thf(4745,plain,
! [SV1317: $i,SV752: $i,SV106: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV106 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV752 @ SV1317 @ SV106 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV752 @ SV1317 @ SV106 ) @ ( c_HOL_Ozero__class_Ozero @ SV106 ) @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4256]) ).
thf(4746,plain,
! [SV1318: $i,SV753: $i,SV107: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV107 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV753 @ SV1318 @ SV107 ) @ ( c_HOL_Ozero__class_Ozero @ SV107 ) @ SV107 )
| ~ ( c_HOL_Oord__class_Oless @ SV753 @ SV1318 @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4257]) ).
thf(4747,plain,
! [SV1319: $i,SV754: $i,SV109: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV109 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ SV754 ) @ SV1319 ) @ SV109 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV1319 @ SV109 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV754 @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4258]) ).
thf(4748,plain,
! [SV110: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV110 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV110 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) )
= ( c_HOL_Ozero__class_Ozero @ SV110 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4259]) ).
thf(4749,plain,
! [SV755: $i,SV111: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV111 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV755 ) @ SV755 ) @ SV111 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV111 ) @ SV755 @ SV111 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV111 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4260]) ).
thf(4750,plain,
! [SV756: $i,SV112: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV112 ) @ SV756 @ SV112 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV112 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV756 ) @ SV756 ) @ SV112 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV112 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4261]) ).
thf(4751,plain,
! [SV1723: $i,SV1320: $i,SV757: $i,SV113: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV113 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV113 )
| ( c_lessequals @ SV757 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV1320 ) @ SV1723 ) @ SV113 )
| ~ ( c_lessequals @ SV757 @ SV1723 @ SV113 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV1320 @ SV113 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4262]) ).
thf(4752,plain,
! [SV1724: $i,SV1321: $i,SV758: $i,SV114: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV114 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV114 )
| ( c_lessequals @ SV758 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SV1321 ) @ SV1724 ) @ SV114 )
| ~ ( c_lessequals @ SV758 @ SV1321 @ SV114 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV1724 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4263]) ).
thf(4753,plain,
! [SV759: $i,SV115: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV759 ) @ SV759 ) @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 )
= $true )
| ( ( ~ ( c_lessequals @ SV759 @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4264]) ).
thf(4754,plain,
! [SV116: $i,SV760: $i] :
( ( ( c_lessequals @ SV760 @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV760 ) @ SV760 ) @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4265]) ).
thf(4755,plain,
! [SV1322: $i,SV761: $i,SV117: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV117 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV761 ) @ SV1322 ) @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
| ~ ( c_lessequals @ SV1322 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
| ~ ( c_lessequals @ SV761 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4266]) ).
thf(4756,plain,
! [SV1937: $i,SV1725: $i,SV1323: $i,SV762: $i,SV118: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV118 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV762 ) @ SV1323 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV1725 ) @ SV1937 ) @ SV118 )
| ~ ( c_lessequals @ SV1323 @ SV1937 @ SV118 )
| ~ ( c_HOL_Oord__class_Oless @ SV762 @ SV1725 @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4267]) ).
thf(4757,plain,
! [SV1938: $i,SV1726: $i,SV1324: $i,SV763: $i,SV119: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV119 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV119 ) @ SV763 ) @ SV1324 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV119 ) @ SV1726 ) @ SV1938 ) @ SV119 )
| ~ ( c_HOL_Oord__class_Oless @ SV1324 @ SV1938 @ SV119 )
| ~ ( c_lessequals @ SV763 @ SV1726 @ SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4268]) ).
thf(4758,plain,
! [SV1325: $i,SV765: $i,SV121: $i] :
( ( ( class_Orderings_Olinorder @ SV121 )
= $false )
| ( ( ~ ( class_Int_Onumber @ SV121 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ SV765 @ SV121 ) @ ( c_Int_Onumber__class_Onumber__of @ SV1325 @ SV121 ) @ SV121 )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ SV1325 @ SV121 ) @ ( c_Int_Onumber__class_Onumber__of @ SV765 @ SV121 ) @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4270]) ).
thf(4759,plain,
! [SV1326: $i,SV766: $i,SV122: $i] :
( ( ( class_Orderings_Olinorder @ SV122 )
= $false )
| ( ( ~ ( class_Int_Onumber @ SV122 )
| ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ SV766 @ SV122 ) @ ( c_Int_Onumber__class_Onumber__of @ SV1326 @ SV122 ) @ SV122 )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ SV1326 @ SV122 ) @ ( c_Int_Onumber__class_Onumber__of @ SV766 @ SV122 ) @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4271]) ).
thf(4760,plain,
! [SV1727: $i,SV1327: $i,SV767: $i,SV123: $i] :
( ( ( c_in @ SV123 @ ( c_List_Oset @ SV767 @ SV1327 ) @ SV1327 )
= $true )
| ( ( ( SV123 = SV1727 )
| ~ ( c_in @ SV123 @ ( c_List_Oset @ ( c_List_Olist_OCons @ SV1727 @ SV767 @ SV1327 ) @ SV1327 ) @ SV1327 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4272]) ).
thf(4761,plain,
! [SV129: $i,SV1328: $i,SV770: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV770 @ SV1328 @ tc_nat ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV129 @ ( c_HOL_Ominus__class_Ominus @ SV770 @ SV1328 @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV129 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4275]) ).
thf(4762,plain,
! [SV773: $i,SV132: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV132 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV773 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV132 @ SV773 @ tc_nat ) @ SV132 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4278]) ).
thf(4763,plain,
! [SV1728: $i,SV1329: $i,SV774: $i,SV133: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV133 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV774 @ SV1329 @ SV133 ) @ ( c_Power_Opower__class_Opower @ SV1728 @ SV1329 @ SV133 ) @ SV133 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV133 ) @ SV774 @ SV133 )
| ~ ( c_lessequals @ SV774 @ SV1728 @ SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4279]) ).
thf(4764,plain,
! [SV1330: $i,SV775: $i,SV134: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV134 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV134 ) @ ( c_Power_Opower__class_Opower @ SV775 @ SV1330 @ SV134 ) @ SV134 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV134 ) @ SV775 @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4280]) ).
thf(4765,plain,
! [SV776: $i,SV135: $i] :
( ( ( ~ ( class_Power_Opower @ SV135 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_Suc @ SV776 ) @ SV135 )
= ( c_HOL_Ozero__class_Ozero @ SV135 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4281]) ).
thf(4766,plain,
! [SV1729: $i,SV1335: $i,SV784: $i,SV143: $i] :
( ( ( c_in @ SV143 @ ( c_List_Oset @ SV784 @ SV1335 ) @ SV1335 )
= $true )
| ( ( ~ ( c_in @ SV143 @ ( c_List_Oset @ ( c_List_Otake @ SV1729 @ SV784 @ SV1335 ) @ SV1335 ) @ SV1335 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4286]) ).
thf(4767,plain,
! [SV1730: $i,SV1336: $i,SV785: $i,SV144: $i] :
( ( ( c_in @ SV144 @ ( c_List_Oset @ SV785 @ SV1336 ) @ SV1336 )
= $true )
| ( ( ~ ( c_in @ SV144 @ ( c_List_Oset @ ( c_List_Odrop @ SV1730 @ SV785 @ SV1336 ) @ SV1336 ) @ SV1336 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4287]) ).
thf(4768,plain,
! [SV1733: $i,SV1339: $i,SV788: $i,SV147: $i] :
( ( ( hBOOL @ ( hAPP @ SV147 @ SV788 ) )
= $true )
| ( ( ~ ( c_in @ SV788 @ ( c_List_Oset @ ( c_List_OtakeWhile @ SV147 @ SV1339 @ SV1733 ) @ SV1733 ) @ SV1733 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4290]) ).
thf(4769,plain,
! [SV1734: $i,SV1340: $i,SV789: $i,SV148: $i] :
( ( ( c_in @ SV148 @ ( c_List_Oset @ SV789 @ SV1340 ) @ SV1340 )
= $true )
| ( ( ~ ( c_in @ SV148 @ ( c_List_Oset @ ( c_List_OtakeWhile @ SV1734 @ SV789 @ SV1340 ) @ SV1340 ) @ SV1340 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4291]) ).
thf(4770,plain,
! [SV1735: $i,SV1341: $i,SV790: $i,SV149: $i] :
( ( ( hBOOL @ ( hAPP @ SV149 @ SV790 ) )
= $true )
| ( ( ~ ( c_in @ SV790 @ ( c_List_Oset @ SV1341 @ SV1735 ) @ SV1735 )
| ~ ( c_List_Olistsp @ SV149 @ SV1341 @ SV1735 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4292]) ).
thf(4771,plain,
! [SV1736: $i,SV1342: $i,SV791: $i,SV150: $i] :
( ( ( SV150 = SV791 )
= $true )
| ( ( ~ ( c_in @ SV150 @ ( c_List_Oset @ ( c_List_Oreplicate @ SV1342 @ SV791 @ SV1736 ) @ SV1736 ) @ SV1736 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4293]) ).
thf(4772,plain,
! [SV792: $i,SV151: $i,SV1343: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1343 @ ( c_Nat_Osize__class_Osize @ SV151 @ ( tc_List_Olist @ SV792 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Onth @ ( c_List_Orev @ SV151 @ SV792 ) @ SV1343 @ SV792 )
= ( c_List_Onth @ SV151 @ ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osize__class_Osize @ SV151 @ ( tc_List_Olist @ SV792 ) ) @ ( c_Suc @ SV1343 ) @ tc_nat ) @ SV792 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4294]) ).
thf(4773,plain,
! [SV1737: $i,SV1344: $i,SV793: $i,SV152: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV152 ) )
= $true )
| ( ( ( c_lessequals @ ( c_List_Onth @ SV793 @ SV1344 @ SV152 ) @ ( c_List_Onth @ SV793 @ SV1737 @ SV152 ) @ SV152 )
| ~ ( c_lessequals @ SV1344 @ SV1737 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1737 @ ( c_Nat_Osize__class_Osize @ SV793 @ ( tc_List_Olist @ SV152 ) ) @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ SV793 @ SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4295]) ).
thf(4774,plain,
! [SV1738: $i,SV1345: $i,SV794: $i,SV153: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV153 ) )
= $true )
| ( ( ( c_lessequals @ ( c_List_Onth @ SV794 @ SV1345 @ SV153 ) @ ( c_List_Onth @ SV794 @ SV1738 @ SV153 ) @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SV1738 @ ( c_Nat_Osize__class_Osize @ SV794 @ ( tc_List_Olist @ SV153 ) ) @ tc_nat )
| ~ ( c_lessequals @ SV1345 @ SV1738 @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ SV794 @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4296]) ).
thf(4775,plain,
! [SV155: $i,SV1347: $i,SV796: $i] :
( ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV796 @ ( tc_List_Olist @ SV1347 ) ) @ SV155 @ tc_nat )
= $false )
| ( ( ( c_List_Otake @ SV155 @ SV796 @ SV1347 )
= SV796 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4298]) ).
thf(4776,plain,
! [SV1740: $i,SV1348: $i,SV797: $i,SV156: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV156 ) )
= $true )
| ( ( ( c_lessequals @ SV797 @ SV1348 @ SV156 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV797 @ ( c_List_Olist_OCons @ SV1348 @ SV1740 @ SV156 ) @ SV156 ) @ SV156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4299]) ).
thf(4777,plain,
! [SV1741: $i,SV1349: $i,SV798: $i,SV157: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV157 ) )
= $true )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV798 @ ( c_List_Olist_OCons @ SV1349 @ SV1741 @ SV157 ) @ SV157 ) @ SV157 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1349 @ SV1741 @ SV157 ) @ SV157 )
| ~ ( c_lessequals @ SV798 @ SV1349 @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4300]) ).
thf(4778,plain,
! [SV1939: $i,SV1742: $i,SV1351: $i,SV800: $i,SV159: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist_OCons @ SV159 @ SV800 @ SV1351 ) @ ( c_Suc @ SV1742 ) @ SV1939 @ SV1351 )
= ( c_List_Olist_OCons @ SV159 @ ( c_List_Olist__update @ SV800 @ SV1742 @ SV1939 @ SV1351 ) @ SV1351 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4301]) ).
thf(4779,plain,
! [SV1743: $i,SV1354: $i,SV803: $i,SV162: $i] :
( ( ( ( c_List_Olist__update @ SV162 @ SV803 @ SV1354 @ SV1743 )
= SV162 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV162 @ ( tc_List_Olist @ SV1743 ) ) @ SV803 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4303]) ).
thf(4780,plain,
! [SV1356: $i,SV805: $i,SV164: $i] :
( ( ( c_in @ SV164 @ ( c_List_Oset @ ( c_List_Obutlast @ SV805 @ SV1356 ) @ SV1356 ) @ SV1356 )
= $false )
| ( ( c_in @ SV164 @ ( c_List_Oset @ SV805 @ SV1356 ) @ SV1356 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4304]) ).
thf(4781,plain,
! [SV1745: $i,SV1358: $i,SV807: $i,SV166: $i] :
( ( ( c_in @ SV166 @ ( c_List_Oset @ SV807 @ SV1358 ) @ SV1358 )
= $true )
| ( ( ~ ( c_in @ SV166 @ ( c_List_Oset @ ( c_List_Osublist @ SV807 @ SV1745 @ SV1358 ) @ SV1358 ) @ SV1358 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4306]) ).
thf(4782,plain,
! [SV1746: $i,SV1359: $i,SV808: $i,SV167: $i] :
( ( ( ~ ( c_in @ SV167 @ ( c_List_Oset @ ( c_List_Osublist @ SV808 @ SV1359 @ SV1746 ) @ SV1746 ) @ SV1746 ) )
= $true )
| ( ( c_in @ SV167 @ ( c_List_Oset @ SV808 @ SV1746 ) @ SV1746 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4307]) ).
thf(4783,plain,
! [SV1940: $i,SV1748: $i,SV1361: $i,SV810: $i,SV169: $i] :
( ( ! [SY4594: $i] :
( ~ ( class_Orderings_Olinorder @ SV169 )
| ( ( c_List_Olinorder__class_Oinsort__key @ SV810 @ SV1361 @ ( c_List_Olist_OCons @ SV1748 @ SV1940 @ SY4594 ) @ SY4594 @ SV169 )
= ( c_List_Olist_OCons @ SV1361 @ ( c_List_Olist_OCons @ SV1748 @ SV1940 @ SY4594 ) @ SY4594 ) )
| ~ ( c_lessequals @ ( hAPP @ SV810 @ SV1361 ) @ ( hAPP @ SV810 @ SV1748 ) @ SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4309]) ).
thf(4784,plain,
! [SV1941: $i,SV1749: $i,SV1362: $i,SV811: $i,SV170: $i] :
( ( ! [SY4595: $i] :
( ~ ( class_Orderings_Olinorder @ SV170 )
| ( ( c_List_Olinorder__class_Oinsort__key @ SV811 @ SV1362 @ ( c_List_Olist_OCons @ SV1749 @ SV1941 @ SY4595 ) @ SY4595 @ SV170 )
= ( c_List_Olist_OCons @ SV1749 @ ( c_List_Olinorder__class_Oinsort__key @ SV811 @ SV1362 @ SV1941 @ SY4595 @ SV170 ) @ SY4595 ) )
| ( c_lessequals @ ( hAPP @ SV811 @ SV1362 ) @ ( hAPP @ SV811 @ SV1749 ) @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4310]) ).
thf(4785,plain,
! [SV1942: $i,SV1750: $i,SV1363: $i,SV812: $i,SV171: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV171 )
| ( ( c_Nat_Osize__class_Osize @ ( c_List_Olinorder__class_Oinsort__key @ SV812 @ SV1363 @ SV1750 @ SV1942 @ SV171 ) @ ( tc_List_Olist @ SV1942 ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ SV1750 @ ( tc_List_Olist @ SV1942 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4311]) ).
thf(4786,plain,
! [SV813: $i,SV1364: $i,SV172: $i] :
( ( ( ~ ( c_lessequals @ SV172 @ SV1364 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV813 @ SV1364 @ tc_nat )
| ~ ( c_lessequals @ SV813 @ SV172 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV172 @ SV813 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1364 @ SV813 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4312]) ).
thf(4787,plain,
! [SV814: $i,SV1365: $i,SV173: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV173 @ SV1365 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV814 @ SV1365 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1365 @ SV814 @ tc_nat )
| ~ ( c_lessequals @ SV1365 @ SV173 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV173 @ SV814 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4313]) ).
thf(4788,plain,
! [SV176: $i,SV1366: $i,SV817: $i] :
( ( ( ~ ( c_lessequals @ SV817 @ SV1366 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV817 @ SV176 @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV176 @ SV817 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1366 @ SV817 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV176 @ SV1366 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4315]) ).
thf(4789,plain,
! [SV1368: $i,SV178: $i,SV819: $i] :
( ( ( ~ ( c_lessequals @ SV819 @ SV178 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV178 @ SV1368 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV178 @ SV819 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1368 @ SV819 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4316]) ).
thf(4790,plain,
! [SV820: $i,SV179: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV179 @ SV820 @ tc_nat )
= $false )
| ( ( ( c_Suc @ SV179 )
= SV820 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV179 ) @ SV820 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4317]) ).
thf(4791,plain,
! [SV180: $i,SV821: $i] :
( ( ( c_lessequals @ ( c_Suc @ SV821 ) @ SV180 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV180 @ SV821 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4318]) ).
thf(4792,plain,
! [SV825: $i,SV185: $i] :
( ( ( c_lessequals @ SV185 @ ( c_Suc @ SV825 ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV185 @ SV825 @ tc_nat )
= $true )
| ( ( SV185
= ( c_Suc @ SV825 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4320]) ).
thf(4793,plain,
! [SV187: $i,SV826: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV826 @ ( c_Suc @ SV187 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV187 @ SV826 @ tc_nat )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4321]) ).
thf(4794,plain,
! [SV1370: $i,SV829: $i,SV190: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV190 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV190 ) @ SV829 ) @ SV1370 ) @ SV1370 @ SV190 )
= SV829 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4322]) ).
thf(4795,plain,
! [SV1751: $i,SV1371: $i,SV830: $i,SV191: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV191 ) )
= $true )
| ( ( ( c_lessequals @ SV830 @ SV1371 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1751 @ SV830 @ SV191 ) @ ( c_Power_Opower__class_Opower @ SV1751 @ SV1371 @ SV191 ) @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV191 ) @ SV1751 @ SV191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4323]) ).
thf(4796,plain,
! [SV1752: $i,SV1372: $i,SV831: $i,SV192: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV192 ) )
= $true )
| ( ( ( c_lessequals @ SV831 @ SV1372 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1752 @ SV831 @ SV192 ) @ ( c_Power_Opower__class_Opower @ SV1752 @ SV1372 @ SV192 ) @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV192 ) @ SV1752 @ SV192 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4324]) ).
thf(4797,plain,
! [SV1753: $i,SV1373: $i,SV832: $i,SV193: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV193 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV832 @ SV1373 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SV832 @ SV1753 @ SV193 ) @ SV193 )
| ~ ( c_lessequals @ SV1373 @ SV1753 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV193 ) @ SV832 @ SV193 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4325]) ).
thf(4798,plain,
! [SV836: $i,SV197: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV197 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV836 @ SV836 @ SV197 )
= ( c_HOL_Ozero__class_Ozero @ SV197 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4329]) ).
thf(4799,plain,
! [SV1943: $i,SV1754: $i,SV1375: $i,SV842: $i,SV208: $i] :
( ( ( c_ListOrder_Ostep1 @ SV208 @ ( c_List_Olist_OCons @ SV842 @ SV1375 @ SV1754 ) @ ( c_List_Olist_OCons @ SV842 @ SV1943 @ SV1754 ) @ SV1754 )
| ~ ( c_ListOrder_Ostep1 @ SV208 @ SV1375 @ SV1943 @ SV1754 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4334]) ).
thf(4800,plain,
! [SV1944: $i,SV1755: $i,SV1376: $i,SV843: $i,SV209: $i] :
( ( ! [SY4596: $i] :
( ( c_ListOrder_Ostep1 @ SV209 @ SV843 @ SV1376 @ SV1755 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV209 @ SV1944 ) @ SY4596 ) )
| ~ ( c_ListOrder_Ostep1 @ SV209 @ ( c_List_Olist_OCons @ SV1944 @ SV843 @ SV1755 ) @ ( c_List_Olist_OCons @ SY4596 @ SV1376 @ SV1755 ) @ SV1755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4335]) ).
thf(4801,plain,
! [SV1945: $i,SV1756: $i,SV1377: $i,SV844: $i,SV210: $i] :
( ( ! [SY4597: $i] :
( ( c_ListOrder_Ostep1 @ SV210 @ SV844 @ SV1377 @ SV1756 )
| ( SV1377 = SV844 )
| ~ ( c_ListOrder_Ostep1 @ SV210 @ ( c_List_Olist_OCons @ SV1945 @ SV844 @ SV1756 ) @ ( c_List_Olist_OCons @ SY4597 @ SV1377 @ SV1756 ) @ SV1756 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4336]) ).
thf(4802,plain,
! [SV1946: $i,SV1757: $i,SV1378: $i,SV845: $i,SV211: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV211 @ SV845 ) @ SV1378 ) )
| ( c_ListOrder_Ostep1 @ SV211 @ ( c_List_Olist_OCons @ SV845 @ SV1757 @ SV1946 ) @ ( c_List_Olist_OCons @ SV1378 @ SV1757 @ SV1946 ) @ SV1946 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4337]) ).
thf(4803,plain,
! [SV1947: $i,SV1758: $i,SV1379: $i,SV846: $i,SV212: $i] :
( ( ! [SY4598: $i] :
( ( SV212 = SV846 )
| ( SV1379 = SV1758 )
| ~ ( c_ListOrder_Ostep1 @ SV1947 @ ( c_List_Olist_OCons @ SV846 @ SV1758 @ SY4598 ) @ ( c_List_Olist_OCons @ SV212 @ SV1379 @ SY4598 ) @ SY4598 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4338]) ).
thf(4804,plain,
! [SV1948: $i,SV1759: $i,SV1380: $i,SV847: $i,SV213: $i] :
( ( ! [SY4599: $i] :
( ( SV213 = SV847 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV1380 @ SV847 ) @ SV213 ) )
| ~ ( c_ListOrder_Ostep1 @ SV1380 @ ( c_List_Olist_OCons @ SV847 @ SV1759 @ SV1948 ) @ ( c_List_Olist_OCons @ SV213 @ SY4599 @ SV1948 ) @ SV1948 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4339]) ).
thf(4805,plain,
! [SV1760: $i,SV1383: $i,SV850: $i,SV216: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV216 ) )
= $true )
| ( ( ( c_lessequals @ ( c_List_Onth @ SV850 @ SV1383 @ SV216 ) @ ( c_List_Onth @ SV850 @ SV1760 @ SV216 ) @ SV216 )
| ~ ( c_HOL_Oord__class_Oless @ SV1383 @ ( c_Nat_Osize__class_Osize @ SV850 @ ( tc_List_Olist @ SV216 ) ) @ tc_nat )
| ~ ( c_lessequals @ SV1760 @ SV1383 @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Orev @ SV850 @ SV216 ) @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4342]) ).
thf(4806,plain,
! [SV1384: $i,SV851: $i,SV217: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV217 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV217 ) @ SV851 ) @ SV1384 ) @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 )
| ~ ( c_lessequals @ SV1384 @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 )
| ~ ( c_HOL_Oord__class_Oless @ SV851 @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4343]) ).
thf(4807,plain,
! [SV1385: $i,SV852: $i,SV218: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV218 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV218 ) @ SV852 ) @ SV1385 ) @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
| ~ ( c_HOL_Oord__class_Oless @ SV1385 @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
| ~ ( c_lessequals @ SV852 @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4344]) ).
thf(4808,plain,
! [SV1761: $i,SV1386: $i,SV853: $i,SV219: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV219 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV219 )
| ( c_HOL_Oord__class_Oless @ SV853 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV219 ) @ SV1386 ) @ SV1761 ) @ SV219 )
| ~ ( c_lessequals @ SV853 @ SV1761 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV1386 @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4345]) ).
thf(4809,plain,
! [SV1762: $i,SV1387: $i,SV854: $i,SV220: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV220 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV220 )
| ( c_HOL_Oord__class_Oless @ SV854 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV220 ) @ SV1387 ) @ SV1762 ) @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ SV854 @ SV1762 @ SV220 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV1387 @ SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4346]) ).
thf(4810,plain,
! [SV1388: $i,SV855: $i,SV221: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV221 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SV855 ) @ SV1388 ) @ SV221 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ SV1388 @ SV221 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ SV855 @ SV221 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4347]) ).
thf(4811,plain,
! [SV1389: $i,SV856: $i,SV222: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV222 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SV856 ) @ SV1389 ) @ SV222 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ SV1389 @ SV222 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ SV856 @ SV222 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4348]) ).
thf(4812,plain,
! [SV1763: $i,SV1390: $i,SV857: $i,SV224: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV224 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV857 @ SV1390 @ SV224 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV224 ) @ SV1390 @ SV224 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV857 @ SV1763 @ SV224 ) @ ( c_Power_Opower__class_Opower @ SV1390 @ SV1763 @ SV224 ) @ SV224 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4349]) ).
thf(4813,plain,
! [SV1764: $i,SV1391: $i,SV858: $i,SV225: $i] :
( ( ( c_in @ SV225 @ ( c_List_Oset @ ( c_List_Oappend @ SV858 @ ( c_List_Olist_OCons @ SV225 @ SV1391 @ SV1764 ) @ SV1764 ) @ SV1764 ) @ SV1764 )
= $true )
| ( ( c_in @ SV225 @ ( c_List_Oset @ SV858 @ SV1764 ) @ SV1764 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4350]) ).
thf(4814,plain,
! [SV1765: $i,SV1392: $i,SV859: $i,SV226: $i] :
( ( ( c_in @ SV226 @ ( c_List_Oset @ ( c_List_Oappend @ SV859 @ ( c_List_Olist_OCons @ SV226 @ SV1392 @ SV1765 ) @ SV1765 ) @ SV1765 ) @ SV1765 )
= $true )
| ( ( c_in @ SV226 @ ( c_List_Oset @ SV1392 @ SV1765 ) @ SV1765 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4351]) ).
thf(4815,plain,
! [SV228: $i] :
( ( ( class_Power_Opower @ SV228 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV228 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV228 )
= ( c_HOL_Oone__class_Oone @ SV228 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV228 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4353]) ).
thf(4816,plain,
! [SV1767: $i,SV1394: $i,SV861: $i,SV229: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV229 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV861 @ SV1394 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1767 @ SV861 @ SV229 ) @ ( c_Power_Opower__class_Opower @ SV1767 @ SV1394 @ SV229 ) @ SV229 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV229 ) @ SV1767 @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4354]) ).
thf(4817,plain,
! [SV1768: $i,SV1395: $i,SV862: $i,SV230: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV230 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV862 @ SV1395 @ SV230 ) @ ( c_Power_Opower__class_Opower @ SV862 @ SV1768 @ SV230 ) @ SV230 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV230 ) @ SV862 @ SV230 )
| ~ ( c_HOL_Oord__class_Oless @ SV1395 @ SV1768 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4355]) ).
thf(4818,plain,
! [SV1769: $i,SV1396: $i,SV863: $i,SV231: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV231 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV863 @ SV1396 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1769 @ SV863 @ SV231 ) @ ( c_Power_Opower__class_Opower @ SV1769 @ SV1396 @ SV231 ) @ SV231 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV231 ) @ SV1769 @ SV231 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4356]) ).
thf(4819,plain,
! [SV1770: $i,SV1397: $i,SV864: $i,SV232: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV232 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV864 @ SV1397 @ SV232 ) @ ( c_Power_Opower__class_Opower @ SV864 @ SV1770 @ SV232 ) @ SV232 )
| ~ ( c_HOL_Oord__class_Oless @ SV1397 @ SV1770 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV232 ) @ SV864 @ SV232 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4357]) ).
thf(4820,plain,
! [SV1949: $i,SV1771: $i,SV1398: $i,SV865: $i,SV233: $i] :
( ( ! [SY4600: $i] :
( ( SV233 = SV865 )
| ( SV1398 = SV1771 )
| ~ ( c_ListOrder_Ostep1 @ SV1949 @ ( c_List_Oappend @ SV233 @ ( c_List_Olist_OCons @ SV1398 @ ( c_List_Olist_ONil @ SY4600 ) @ SY4600 ) @ SY4600 ) @ ( c_List_Oappend @ SV865 @ ( c_List_Olist_OCons @ SV1771 @ ( c_List_Olist_ONil @ SY4600 ) @ SY4600 ) @ SY4600 ) @ SY4600 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4358]) ).
thf(4821,plain,
! [SV1950: $i,SV1772: $i,SV1399: $i,SV866: $i,SV234: $i] :
( ( ! [SY4601: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV234 @ SV866 ) @ SV1399 ) )
| ( SV866 = SV1399 )
| ~ ( c_ListOrder_Ostep1 @ SV234 @ ( c_List_Oappend @ SV1772 @ ( c_List_Olist_OCons @ SV866 @ ( c_List_Olist_ONil @ SV1950 ) @ SV1950 ) @ SV1950 ) @ ( c_List_Oappend @ SY4601 @ ( c_List_Olist_OCons @ SV1399 @ ( c_List_Olist_ONil @ SV1950 ) @ SV1950 ) @ SV1950 ) @ SV1950 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4359]) ).
thf(4822,plain,
! [SV1951: $i,SV1773: $i,SV1400: $i,SV867: $i,SV235: $i] :
( ( ! [SY4602: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV867 ) @ SV1400 ) )
| ( c_ListOrder_Ostep1 @ SV235 @ SV1773 @ SV1951 @ SY4602 )
| ~ ( c_ListOrder_Ostep1 @ SV235 @ ( c_List_Oappend @ SV1773 @ ( c_List_Olist_OCons @ SV867 @ ( c_List_Olist_ONil @ SY4602 ) @ SY4602 ) @ SY4602 ) @ ( c_List_Oappend @ SV1951 @ ( c_List_Olist_OCons @ SV1400 @ ( c_List_Olist_ONil @ SY4602 ) @ SY4602 ) @ SY4602 ) @ SY4602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4360]) ).
thf(4823,plain,
! [SV1952: $i,SV1774: $i,SV1401: $i,SV868: $i,SV236: $i] :
( ( ! [SY4603: $i] :
( ( SV236 = SV868 )
| ( c_ListOrder_Ostep1 @ SV1401 @ SV236 @ SV868 @ SV1774 )
| ~ ( c_ListOrder_Ostep1 @ SV1401 @ ( c_List_Oappend @ SV236 @ ( c_List_Olist_OCons @ SV1952 @ ( c_List_Olist_ONil @ SV1774 ) @ SV1774 ) @ SV1774 ) @ ( c_List_Oappend @ SV868 @ ( c_List_Olist_OCons @ SY4603 @ ( c_List_Olist_ONil @ SV1774 ) @ SV1774 ) @ SV1774 ) @ SV1774 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4361]) ).
thf(4824,plain,
! [SV1953: $i,SV1775: $i,SV1402: $i,SV870: $i,SV238: $i] :
( ( ( ( c_List_OtakeWhile @ SV238 @ ( c_List_Oappend @ SV870 @ SV1402 @ SV1775 ) @ SV1775 )
= ( c_List_OtakeWhile @ SV238 @ SV870 @ SV1775 ) )
| ( hBOOL @ ( hAPP @ SV238 @ SV1953 ) )
| ~ ( c_in @ SV1953 @ ( c_List_Oset @ SV870 @ SV1775 ) @ SV1775 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4362]) ).
thf(4825,plain,
! [SV239: $i,SV1403: $i,SV871: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV871 @ SV1403 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV239 @ SV871 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV239 @ SV1403 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4363]) ).
thf(4826,plain,
! [SV240: $i,SV1404: $i,SV872: $i] :
( ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV872 @ ( tc_List_Olist @ SV1404 ) ) @ SV240 @ tc_nat )
= $false )
| ( ( ( c_List_Odrop @ SV240 @ SV872 @ SV1404 )
= ( c_List_Olist_ONil @ SV1404 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4364]) ).
thf(4827,plain,
! [SV1778: $i,SV1407: $i,SV875: $i,SV243: $i] :
( ( ( c_in @ SV243 @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ SV875 @ SV1407 @ SV1778 ) @ SV1778 ) @ SV1778 ) @ SV1778 )
= $true )
| ( ( ~ ( c_in @ SV243 @ ( c_List_Oset @ ( c_List_Obutlast @ SV1407 @ SV1778 ) @ SV1778 ) @ SV1778 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4367]) ).
thf(4828,plain,
! [SV1779: $i,SV1408: $i,SV876: $i,SV244: $i] :
( ( ( c_in @ SV244 @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ SV876 @ SV1408 @ SV1779 ) @ SV1779 ) @ SV1779 ) @ SV1779 )
= $true )
| ( ( ~ ( c_in @ SV244 @ ( c_List_Oset @ ( c_List_Obutlast @ SV876 @ SV1779 ) @ SV1779 ) @ SV1779 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4368]) ).
thf(4829,plain,
! [SV1954: $i,SV1780: $i,SV1409: $i,SV878: $i,SV246: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV246 @ ( c_List_Olist_Olist__size @ SV878 @ SV1409 @ SV1780 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV246 @ ( hAPP @ SV878 @ SV1954 ) @ tc_nat )
| ~ ( c_in @ SV1954 @ ( c_List_Oset @ SV1409 @ SV1780 ) @ SV1780 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4369]) ).
thf(4830,plain,
! [SV1781: $i,SV1410: $i,SV879: $i,SV247: $i] :
( ( ( ( c_List_OtakeWhile @ SV247 @ SV879 @ SV1410 )
= ( c_List_Otake @ SV1781 @ SV879 @ SV1410 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV247 @ ( c_List_Onth @ SV879 @ SV1781 @ SV1410 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV247 @ ( c_List_Onth @ SV879 @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV247 @ SV1781 @ SV879 @ SV1410 ) @ SV1410 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4370]) ).
thf(4831,plain,
! [SV1411: $i,SV882: $i,SV250: $i] :
( ( ( c_in @ SV250 @ ( c_List_Oset @ SV882 @ SV1411 ) @ SV1411 )
= $false )
| ( ( ( c_List_Olength__unique @ ( c_List_Olist_OCons @ SV250 @ SV882 @ SV1411 ) @ SV1411 )
= ( c_List_Olength__unique @ SV882 @ SV1411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4371]) ).
thf(4832,plain,
! [SV1412: $i,SV883: $i,SV251: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV251 @ ( c_Nat_Osize__class_Osize @ SV883 @ ( tc_List_Olist @ SV1412 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Oappend @ ( c_List_Otake @ SV251 @ SV883 @ SV1412 ) @ ( c_List_Olist_OCons @ ( c_List_Ohd @ ( c_List_Odrop @ SV251 @ SV883 @ SV1412 ) @ SV1412 ) @ ( c_List_Olist_ONil @ SV1412 ) @ SV1412 ) @ SV1412 )
= ( c_List_Otake @ ( c_Suc @ SV251 ) @ SV883 @ SV1412 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4372]) ).
thf(4833,plain,
! [SV1955: $i,SV1782: $i,SV1413: $i,SV884: $i,SV252: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV252 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV884 @ ( c_List_Olinorder__class_Oinsort__key @ SV884 @ SV1413 @ SV1782 @ SV1955 @ SV252 ) @ SV1955 @ SV252 ) @ SV252 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV884 @ SV1782 @ SV1955 @ SV252 ) @ SV252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4373]) ).
thf(4834,plain,
! [SV1956: $i,SV1783: $i,SV1414: $i,SV885: $i,SV253: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV253 )
| ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV885 @ SV1414 @ SV1783 @ SV253 ) @ SV253 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV885 @ ( c_List_Olinorder__class_Oinsort__key @ SV885 @ SV1956 @ SV1414 @ SV1783 @ SV253 ) @ SV1783 @ SV253 ) @ SV253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4374]) ).
thf(4835,plain,
! [SV256: $i,SV888: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV888 @ SV256 ) @ ( c_HOL_Ozero__class_Ozero @ SV256 ) @ SV256 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV256 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4376]) ).
thf(4836,plain,
! [SV1957: $i,SV1785: $i,SV1416: $i,SV889: $i,SV257: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV257 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SV889 ) @ SV1416 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SV1785 ) @ SV1957 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SV889 ) @ SV1785 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SV1416 ) @ SV1957 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4377]) ).
thf(4837,plain,
! [SV1420: $i,SV893: $i,SV261: $i] :
( ( ( class_Orderings_Olinorder @ SV261 )
= $false )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_OtakeWhile @ SV893 @ SV1420 @ SV261 ) @ SV261 )
| ~ ( c_List_Olinorder__class_Osorted @ SV1420 @ SV261 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4379]) ).
thf(4838,plain,
! [SV1422: $i,SV895: $i,SV263: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV263 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV263 ) @ SV895 ) @ SV1422 ) @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ SV1422 @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ SV895 @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4380]) ).
thf(4839,plain,
! [SV1786: $i,SV1423: $i,SV896: $i,SV264: $i] :
( ( ( ( c_List_Onth @ ( c_List_OtakeWhile @ SV264 @ SV896 @ SV1423 ) @ SV1786 @ SV1423 )
= ( c_List_Onth @ SV896 @ SV1786 @ SV1423 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1786 @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ SV264 @ SV896 @ SV1423 ) @ ( tc_List_Olist @ SV1423 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4381]) ).
thf(4840,plain,
! [SV1958: $i,SV1787: $i,SV1425: $i,SV899: $i,SV267: $i] :
( ( ! [SY4604: $i] :
( ( hAPP @ ( c_COMBC @ SV267 @ SV899 @ SV1425 @ SV1787 @ SV1958 ) @ SY4604 )
= ( hAPP @ ( hAPP @ SV267 @ SY4604 ) @ SV899 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4382]) ).
thf(4841,plain,
! [SV1426: $i,SV268: $i,SV900: $i] :
( ( ( c_in @ SV900 @ SV268 @ SV1426 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV268 @ SV900 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4383]) ).
thf(4842,plain,
! [SV1427: $i,SV269: $i,SV901: $i] :
( ( ( hBOOL @ ( hAPP @ SV901 @ SV269 ) )
= $false )
| ( ( c_in @ SV269 @ SV901 @ SV1427 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4384]) ).
thf(4843,plain,
! [SV1959: $i,SV1788: $i,SV1428: $i,SV902: $i,SV270: $i] :
( ( ( ( c_List_Onth @ ( c_List_Olist__update @ SV270 @ SV902 @ SV1428 @ SV1788 ) @ SV1959 @ SV1788 )
= ( c_List_Onth @ SV270 @ SV1959 @ SV1788 ) )
| ( SV902 = SV1959 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4385]) ).
thf(4844,plain,
! [SV1789: $i,SV1429: $i,SV903: $i,SV271: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV271 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ SV903 ) @ SV1429 ) ) @ SV1789 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ SV903 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ SV1429 ) @ SV1789 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4386]) ).
thf(4845,plain,
! [SV1790: $i,SV1430: $i,SV904: $i,SV272: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV272 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV904 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV1430 ) @ SV1790 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV1430 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV904 ) @ SV1790 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4387]) ).
thf(4846,plain,
! [SV1791: $i,SV1431: $i,SV905: $i,SV273: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV273 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ SV905 ) @ SV1431 ) ) @ SV1791 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ SV905 ) @ SV1791 ) ) @ SV1431 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4388]) ).
thf(4847,plain,
! [SV1792: $i,SV1432: $i,SV906: $i,SV274: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV274 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ SV906 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ SV1432 ) @ SV1792 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ SV906 ) @ SV1432 ) ) @ SV1792 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4389]) ).
thf(4848,plain,
! [SV1793: $i,SV1433: $i,SV907: $i,SV275: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV275 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ SV907 ) @ SV1433 ) ) @ SV1793 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ SV907 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ SV1433 ) @ SV1793 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4390]) ).
thf(4849,plain,
! [SV1794: $i,SV1434: $i,SV908: $i,SV276: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV276 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ SV908 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ SV1434 ) @ SV1794 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ SV1434 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ SV908 ) @ SV1794 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4391]) ).
thf(4850,plain,
! [SV1795: $i,SV1435: $i,SV909: $i,SV277: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV277 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ SV909 ) @ SV1435 ) ) @ SV1795 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ SV909 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ SV1435 ) @ SV1795 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4392]) ).
thf(4851,plain,
! [SV1796: $i,SV1436: $i,SV910: $i,SV278: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV278 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV278 ) @ SV910 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV278 ) @ SV1436 ) @ SV1796 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV278 ) @ SV1436 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV278 ) @ SV910 ) @ SV1796 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4393]) ).
thf(4852,plain,
! [SV1797: $i,SV1437: $i,SV911: $i,SV279: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV279 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV279 ) @ SV911 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV279 ) @ SV1437 ) @ SV1797 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV279 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV279 ) @ SV911 ) @ SV1437 ) ) @ SV1797 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4394]) ).
thf(4853,plain,
! [SV1798: $i,SV1438: $i,SV912: $i,SV280: $i] :
( ( ( ( c_List_Onth @ ( c_List_Otake @ SV280 @ SV912 @ SV1438 ) @ SV1798 @ SV1438 )
= ( c_List_Onth @ SV912 @ SV1798 @ SV1438 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1798 @ SV280 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4395]) ).
thf(4854,plain,
! [SV1799: $i,SV1439: $i,SV913: $i,SV281: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV281 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV913 @ SV1439 @ SV281 )
| ~ ( c_HOL_Oord__class_Oless @ SV913 @ SV1799 @ SV281 )
| ~ ( c_HOL_Oord__class_Oless @ SV1799 @ SV1439 @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4396]) ).
thf(4855,plain,
! [SV1800: $i,SV1440: $i,SV914: $i,SV282: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV282 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV914 @ SV1440 @ SV282 )
| ~ ( c_HOL_Oord__class_Oless @ SV1800 @ SV1440 @ SV282 )
| ~ ( c_HOL_Oord__class_Oless @ SV914 @ SV1800 @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4397]) ).
thf(4856,plain,
! [SV1960: $i,SV1801: $i,SV1441: $i,SV915: $i,SV283: $i] :
( ( ( c_List_Otake @ SV283 @ ( c_List_Omap @ SV915 @ SV1441 @ SV1801 @ SV1960 ) @ SV1960 )
= ( c_List_Omap @ SV915 @ ( c_List_Otake @ SV283 @ SV1441 @ SV1801 ) @ SV1801 @ SV1960 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4398]) ).
thf(4857,plain,
! [SV1442: $i,SV916: $i,SV284: $i] :
( ( ( class_Orderings_Olinorder @ SV284 )
= $false )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ SV916 @ SV1442 @ SV284 ) @ SV284 )
| ~ ( c_List_Olinorder__class_Osorted @ SV1442 @ SV284 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4399]) ).
thf(4858,plain,
! [SV917: $i,SV1443: $i,SV285: $i] :
( ( ( SV285 = SV1443 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1443 @ SV285 @ tc_nat )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV285 ) ) @ SV917 ) @ SV1443 )
= ( c_Lambda_OdB_OVar @ SV285 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4400]) ).
thf(4859,plain,
! [SV1802: $i,SV1444: $i,SV918: $i,SV286: $i] :
( ( ( c_List_Olistsp @ SV286 @ SV918 @ SV1444 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV286 @ ( c_List_Oappend @ SV918 @ SV1802 @ SV1444 ) @ SV1444 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4401]) ).
thf(4860,plain,
! [SV1803: $i,SV1445: $i,SV919: $i,SV287: $i] :
( ( ( c_List_Olistsp @ SV287 @ SV919 @ SV1445 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV287 @ ( c_List_Oappend @ SV1803 @ SV919 @ SV1445 ) @ SV1445 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4402]) ).
thf(4861,plain,
! [SV1961: $i,SV1804: $i,SV1446: $i,SV920: $i,SV288: $i] :
( ( ( c_Lambda_OdB_OdB__case @ SV288 @ SV920 @ SV1446 @ ( c_Lambda_OdB_OAbs @ SV1804 ) @ SV1961 )
= ( hAPP @ SV1446 @ SV1804 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4403]) ).
thf(4862,plain,
! [SV1805: $i,SV1447: $i,SV921: $i,SV289: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV289 ) @ SV921 ) @ SV1447 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1805 ) @ SV921 ) @ SV1447 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV289 ) @ SV1805 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4404]) ).
thf(4863,plain,
! [SV1448: $i,SV922: $i,SV290: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV290 @ ( c_Nat_Osize__class_Osize @ SV922 @ ( tc_List_Olist @ SV1448 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Olist__update @ SV922 @ SV290 @ ( c_List_Onth @ SV922 @ SV290 @ SV1448 ) @ SV1448 )
= SV922 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4405]) ).
thf(4864,plain,
! [SV1806: $i,SV1449: $i,SV923: $i,SV291: $i] :
( ( ( ( c_List_Olist__update @ SV291 @ SV923 @ SV1449 @ SV1806 )
= ( c_List_Oappend @ ( c_List_Otake @ SV923 @ SV291 @ SV1806 ) @ ( c_List_Olist_OCons @ SV1449 @ ( c_List_Odrop @ ( c_Suc @ SV923 ) @ SV291 @ SV1806 ) @ SV1806 ) @ SV1806 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV923 @ ( c_Nat_Osize__class_Osize @ SV291 @ ( tc_List_Olist @ SV1806 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4406]) ).
thf(4865,plain,
! [SV1450: $i,SV292: $i,SV924: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV924 @ ( c_Nat_Osize__class_Osize @ SV292 @ ( tc_List_Olist @ SV1450 ) ) @ tc_nat )
= $false )
| ( ( SV292
= ( c_List_Oappend @ ( c_List_Otake @ SV924 @ SV292 @ SV1450 ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ SV292 @ SV924 @ SV1450 ) @ ( c_List_Odrop @ ( c_Suc @ SV924 ) @ SV292 @ SV1450 ) @ SV1450 ) @ SV1450 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4407]) ).
thf(4866,plain,
! [SV1451: $i,SV925: $i,SV293: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV293 @ ( c_Nat_Osize__class_Osize @ SV925 @ ( tc_List_Olist @ SV1451 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Otake @ ( c_Suc @ SV293 ) @ SV925 @ SV1451 )
= ( c_List_Oappend @ ( c_List_Otake @ SV293 @ SV925 @ SV1451 ) @ ( c_List_Olist_OCons @ ( c_List_Onth @ SV925 @ SV293 @ SV1451 ) @ ( c_List_Olist_ONil @ SV1451 ) @ SV1451 ) @ SV1451 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4408]) ).
thf(4867,plain,
! [SV1453: $i,SV295: $i,SV927: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV927 ) @ SV295 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV1453 ) )
= $false )
| ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV295 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV927 @ SV295 @ SV1453 ) @ tc_Lambda_OdB )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4410]) ).
thf(4868,plain,
! [SV1808: $i,SV1454: $i,SV928: $i,SV296: $i] :
( ( ( ( c_List_OtakeWhile @ SV296 @ SV928 @ SV1454 )
= ( c_List_Otake @ SV1808 @ SV928 @ SV1454 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1808 @ ( c_Nat_Osize__class_Osize @ SV928 @ ( tc_List_Olist @ SV1454 ) ) @ tc_nat )
| ~ ( hBOOL @ ( hAPP @ SV296 @ ( c_List_Onth @ SV928 @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV296 @ SV1808 @ SV928 @ SV1454 ) @ SV1454 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4411]) ).
thf(4869,plain,
! [SV1809: $i,SV1455: $i,SV929: $i,SV297: $i] :
( ( ( ( c_List_OtakeWhile @ SV297 @ SV929 @ SV1455 )
= ( c_List_Otake @ SV1809 @ SV929 @ SV1455 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV297 @ ( c_List_Onth @ SV929 @ SV1809 @ SV1455 ) ) )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV297 @ SV1809 @ SV929 @ SV1455 ) @ ( c_Nat_Osize__class_Osize @ SV929 @ ( tc_List_Olist @ SV1455 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4412]) ).
thf(4870,plain,
! [SV1456: $i,SV930: $i,SV298: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV298 @ ( c_Nat_Osize__class_Osize @ SV930 @ ( tc_List_Olist @ SV1456 ) ) @ tc_nat ) )
= $true )
| ( ( SV930
= ( c_List_Olist_ONil @ SV1456 ) )
= $true )
| ( ( ( c_List_Ohd @ ( c_List_Odrop @ SV298 @ SV930 @ SV1456 ) @ SV1456 )
= ( c_List_Onth @ SV930 @ SV298 @ SV1456 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4413]) ).
thf(4871,plain,
! [SV1457: $i,SV299: $i,SV931: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV931 @ ( c_Nat_Osize__class_Osize @ SV299 @ ( tc_List_Olist @ SV1457 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Olist_OCons @ ( c_List_Onth @ SV299 @ SV931 @ SV1457 ) @ ( c_List_Odrop @ ( c_Suc @ SV931 ) @ SV299 @ SV1457 ) @ SV1457 )
= ( c_List_Odrop @ SV931 @ SV299 @ SV1457 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4414]) ).
thf(4872,plain,
! [SV1810: $i,SV1458: $i,SV932: $i,SV300: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV300 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV932 @ SV1458 @ SV300 ) @ ( c_Power_Opower__class_Opower @ SV1810 @ SV1458 @ SV300 ) @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1458 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SV932 @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ SV932 @ SV1810 @ SV300 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4415]) ).
thf(4873,plain,
! [SV1811: $i,SV1461: $i,SV935: $i,SV303: $i] :
( ( ( ( c_List_OtakeWhile @ SV303 @ SV935 @ SV1461 )
= ( c_List_Otake @ SV1811 @ SV935 @ SV1461 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV303 @ ( c_List_Onth @ SV935 @ SV1811 @ SV1461 ) ) )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV303 @ SV1811 @ SV935 @ SV1461 ) @ SV1811 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4416]) ).
thf(4874,plain,
! [SV1812: $i,SV1462: $i,SV936: $i,SV304: $i] :
( ( ( ( c_List_OtakeWhile @ SV304 @ SV936 @ SV1462 )
= ( c_List_Otake @ SV1812 @ SV936 @ SV1462 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1812 @ ( c_Nat_Osize__class_Osize @ SV936 @ ( tc_List_Olist @ SV1462 ) ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV304 @ SV1812 @ SV936 @ SV1462 ) @ ( c_Nat_Osize__class_Osize @ SV936 @ ( tc_List_Olist @ SV1462 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4417]) ).
thf(4875,plain,
! [SV1813: $i,SV1463: $i,SV937: $i,SV305: $i] :
( ( ( ( c_List_OtakeWhile @ SV305 @ SV937 @ SV1463 )
= ( c_List_Otake @ SV1813 @ SV937 @ SV1463 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1813 @ ( c_Nat_Osize__class_Osize @ SV937 @ ( tc_List_Olist @ SV1463 ) ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV305 @ SV1813 @ SV937 @ SV1463 ) @ SV1813 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4418]) ).
thf(4876,plain,
! [SV1962: $i,SV1814: $i,SV1464: $i,SV938: $i,SV306: $i] :
( ( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV306 @ SV938 @ SV1464 ) @ SV1814 @ SV1962 @ SV1464 )
= ( c_List_Oappend @ SV306 @ ( c_List_Olist__update @ SV938 @ ( c_HOL_Ominus__class_Ominus @ SV1814 @ ( c_Nat_Osize__class_Osize @ SV306 @ ( tc_List_Olist @ SV1464 ) ) @ tc_nat ) @ SV1962 @ SV1464 ) @ SV1464 ) )
| ( c_HOL_Oord__class_Oless @ SV1814 @ ( c_Nat_Osize__class_Osize @ SV306 @ ( tc_List_Olist @ SV1464 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4419]) ).
thf(4877,plain,
! [SV1815: $i,SV1465: $i,SV939: $i,SV307: $i] :
( ( ( ( c_List_Onth @ ( c_List_Oappend @ SV307 @ SV939 @ SV1465 ) @ SV1815 @ SV1465 )
= ( c_List_Onth @ SV939 @ ( c_HOL_Ominus__class_Ominus @ SV1815 @ ( c_Nat_Osize__class_Osize @ SV307 @ ( tc_List_Olist @ SV1465 ) ) @ tc_nat ) @ SV1465 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1815 @ ( c_Nat_Osize__class_Osize @ SV307 @ ( tc_List_Olist @ SV1465 ) ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4420]) ).
thf(4878,plain,
! [SV1816: $i,SV1466: $i,SV940: $i,SV308: $i] :
( ( ( c_in @ SV308 @ ( c_List_Oset @ ( c_List_Olist__update @ SV940 @ SV1466 @ SV308 @ SV1816 ) @ SV1816 ) @ SV1816 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1466 @ ( c_Nat_Osize__class_Osize @ SV940 @ ( tc_List_Olist @ SV1816 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4421]) ).
thf(4879,plain,
! [SV1467: $i,SV309: $i,SV941: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV941 @ ( c_Nat_Osize__class_Osize @ SV309 @ ( tc_List_Olist @ SV1467 ) ) @ tc_nat )
= $false )
| ( ( c_in @ ( c_List_Onth @ SV309 @ SV941 @ SV1467 ) @ ( c_List_Oset @ SV309 @ SV1467 ) @ SV1467 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4422]) ).
thf(4880,plain,
! [SV1468: $i,SV942: $i,SV310: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV310 @ ( c_Nat_Osize__class_Osize @ SV942 @ ( tc_List_Olist @ SV1468 ) ) @ tc_nat )
= $false )
| ( ( c_in @ ( c_List_Onth @ SV942 @ SV310 @ SV1468 ) @ ( c_List_Oset @ SV942 @ SV1468 ) @ SV1468 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4423]) ).
thf(4881,plain,
! [SV1469: $i,SV943: $i,SV311: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV311 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV311 ) @ ( c_Power_Opower__class_Opower @ SV943 @ SV1469 @ SV311 ) @ SV311 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1469 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV311 ) @ SV943 @ SV311 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4424]) ).
thf(4882,plain,
! [SV944: $i,SV312: $i,SV1470: $i] :
( ( ( c_in @ SV1470 @ ( c_List_Oset @ SV312 @ SV944 ) @ SV944 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Nat_Osize__class_Osize @ SV312 @ ( tc_List_Olist @ SV944 ) ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4425]) ).
thf(4883,plain,
! [SV1817: $i,SV1471: $i,SV945: $i,SV313: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV313 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV945 @ SV1471 @ SV313 ) @ ( c_Power_Opower__class_Opower @ SV945 @ SV1817 @ SV313 ) @ SV313 )
| ~ ( c_HOL_Oord__class_Oless @ SV945 @ ( c_HOL_Oone__class_Oone @ SV313 ) @ SV313 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV313 ) @ SV945 @ SV313 )
| ~ ( c_HOL_Oord__class_Oless @ SV1817 @ SV1471 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4426]) ).
thf(4884,plain,
! [SV1963: $i,SV1818: $i,SV1472: $i,SV946: $i,SV314: $i] :
( ( ! [SY4605: $i] :
( ( c_List_Omap @ SV314 @ ( c_List_Olist__update @ SV946 @ SV1472 @ SV1818 @ SV1963 ) @ SV1963 @ SY4605 )
= ( c_List_Olist__update @ ( c_List_Omap @ SV314 @ SV946 @ SV1963 @ SY4605 ) @ SV1472 @ ( hAPP @ SV314 @ SV1818 ) @ SY4605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4427]) ).
thf(4885,plain,
! [SV949: $i,SV317: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ SV949 @ SV317 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV317 ) @ SV949 ) @ SV949 ) @ SV317 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV317 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4429]) ).
thf(4886,plain,
! [SV950: $i,SV318: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV318 ) @ SV950 ) @ SV950 ) @ SV318 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ SV950 @ SV318 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV318 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4430]) ).
thf(4887,plain,
! [SV953: $i,SV322: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV322 ) )
= $true )
| ( ( SV953
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV322 ) @ SV953 ) @ ( c_HOL_Ozero__class_Ozero @ SV322 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV322 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4433]) ).
thf(4888,plain,
! [SV1964: $i,SV1819: $i,SV1475: $i,SV961: $i,SV333: $i] :
( ( ( c_List_Osplice @ ( c_List_Olist_OCons @ SV333 @ SV961 @ SV1475 ) @ ( c_List_Olist_OCons @ SV1819 @ SV1964 @ SV1475 ) @ SV1475 )
= ( c_List_Olist_OCons @ SV333 @ ( c_List_Olist_OCons @ SV1819 @ ( c_List_Osplice @ SV961 @ SV1964 @ SV1475 ) @ SV1475 ) @ SV1475 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4439]) ).
thf(4889,plain,
! [SV1820: $i,SV1476: $i,SV962: $i,SV334: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV334 ) )
= $true )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV962 @ SV1476 @ SV334 ) @ SV334 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1820 @ ( c_List_Olist_OCons @ SV962 @ SV1476 @ SV334 ) @ SV334 ) @ SV334 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4440]) ).
thf(4890,plain,
! [SV1965: $i,SV1823: $i,SV1479: $i,SV965: $i,SV337: $i] :
( ( ( c_List_Omap @ SV337 @ ( c_List_Olist_OCons @ SV965 @ SV1479 @ SV1823 ) @ SV1823 @ SV1965 )
= ( c_List_Olist_OCons @ ( hAPP @ SV337 @ SV965 ) @ ( c_List_Omap @ SV337 @ SV1479 @ SV1823 @ SV1965 ) @ SV1965 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4443]) ).
thf(4891,plain,
! [SV1966: $i,SV1824: $i,SV1480: $i,SV966: $i,SV338: $i] :
( ( ( c_List_Olist_OCons @ ( hAPP @ SV338 @ SV966 ) @ ( c_List_Omap @ SV338 @ SV1480 @ SV1824 @ SV1966 ) @ SV1966 )
= ( c_List_Omap @ SV338 @ ( c_List_Olist_OCons @ SV966 @ SV1480 @ SV1824 ) @ SV1824 @ SV1966 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4444]) ).
thf(4892,plain,
! [SV1967: $i,SV1825: $i,SV1481: $i,SV967: $i,SV339: $i] :
( ( ( c_List_Omap @ SV339 @ ( c_List_Olist_OCons @ SV967 @ SV1481 @ SV1825 ) @ SV1825 @ SV1967 )
= ( c_List_Olist_OCons @ ( hAPP @ SV339 @ SV967 ) @ ( c_List_Omap @ SV339 @ SV1481 @ SV1825 @ SV1967 ) @ SV1967 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4445]) ).
thf(4893,plain,
! [SV1484: $i,SV970: $i,SV342: $i] :
( ( ( class_Orderings_Olinorder @ SV342 )
= $false )
| ( ( ( c_List_Olinorder__class_Osorted @ SV970 @ SV342 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1484 @ SV970 @ SV342 ) @ SV342 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4448]) ).
thf(4894,plain,
! [SV1828: $i,SV1485: $i,SV971: $i,SV343: $i] :
( ( ( ( c_List_OtakeWhile @ SV343 @ ( c_List_Olist_OCons @ SV971 @ SV1485 @ SV1828 ) @ SV1828 )
= ( c_List_Olist_OCons @ SV971 @ ( c_List_OtakeWhile @ SV343 @ SV1485 @ SV1828 ) @ SV1828 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV343 @ SV971 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4449]) ).
thf(4895,plain,
! [SV1968: $i,SV1830: $i,SV1497: $i,SV997: $i,SV376: $i] :
( ( ! [SY4606: $i] :
( ~ ( hBOOL @ ( hAPP @ SV376 @ ( c_Lambda_OdB_OdB__case @ SV997 @ SV1497 @ SV1830 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1968 ) @ SY4606 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SV1497 @ SV1968 ) @ SY4606 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4452]) ).
thf(4896,plain,
! [SV1969: $i,SV1831: $i,SV1498: $i,SV998: $i,SV377: $i] :
( ( ! [SY4607: $i] :
( ~ ( hBOOL @ ( hAPP @ SV377 @ ( c_Lambda_OdB_OdB__case @ SV998 @ SV1498 @ SV1831 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1969 ) @ SY4607 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV377 @ ( hAPP @ ( hAPP @ SV1498 @ SV1969 ) @ SY4607 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4453]) ).
thf(4897,plain,
! [SV1970: $i,SV1832: $i,SV1499: $i,SV999: $i,SV378: $i] :
( ( ! [SY4608: $i] :
( ( c_Lambda_OdB_OdB__case @ SV378 @ SV999 @ SV1499 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1832 ) @ SV1970 ) @ SY4608 )
= ( hAPP @ ( hAPP @ SV999 @ SV1832 ) @ SV1970 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4454]) ).
thf(4898,plain,
! [SV379: $i,SV1500: $i,SV1000: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1000 ) @ SV1500 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV379 ) @ SV1000 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV379 ) @ SV1500 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4455]) ).
thf(4899,plain,
! [SV1001: $i,SV1501: $i,SV380: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV380 ) @ SV1501 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV380 ) @ SV1001 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1501 ) @ SV1001 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4456]) ).
thf(4900,plain,
! [SV1833: $i,SV1502: $i,SV1002: $i,SV381: $i] :
( ( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV381 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV1002 ) @ SV1502 ) @ SV1833 @ SV381 @ SV381 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV1002 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV1502 @ SV1833 @ SV381 @ SV381 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4457]) ).
thf(4901,plain,
! [SV1971: $i,SV1834: $i,SV1503: $i,SV1003: $i,SV382: $i] :
( ( ! [SY4609: $i] :
( ( c_List_Ofoldl @ SV382 @ SV1003 @ ( c_List_Oappend @ SV1503 @ SV1834 @ SV1971 ) @ SY4609 @ SV1971 )
= ( c_List_Ofoldl @ SV382 @ ( c_List_Ofoldl @ SV382 @ SV1003 @ SV1503 @ SY4609 @ SV1971 ) @ SV1834 @ SY4609 @ SV1971 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4458]) ).
thf(4902,plain,
! [SV1972: $i,SV1835: $i,SV1504: $i,SV1004: $i,SV383: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV383 @ ( c_Lambda_OdB_OdB__case @ SV1004 @ SV1504 @ SV1835 @ ( c_Lambda_OdB_OVar @ SV1972 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV383 @ ( hAPP @ SV1004 @ SV1972 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4459]) ).
thf(4903,plain,
! [SV1973: $i,SV1836: $i,SV1505: $i,SV1005: $i,SV384: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV384 @ ( c_Lambda_OdB_OdB__case @ SV1005 @ SV1505 @ SV1836 @ ( c_Lambda_OdB_OVar @ SV1973 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV384 @ ( hAPP @ SV1005 @ SV1973 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4460]) ).
thf(4904,plain,
! [SV1507: $i,SV1009: $i,SV388: $i] :
( ( ( class_Orderings_Olinorder @ SV388 )
= $false )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ SV1009 @ SV1507 @ SV388 ) @ SV388 )
| ~ ( c_List_Olinorder__class_Osorted @ SV1507 @ SV388 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4462]) ).
thf(4905,plain,
! [SV1510: $i,SV1012: $i,SV391: $i] :
( ( ( hBOOL @ ( hAPP @ SV391 @ ( c_List_Onth @ SV1012 @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ SV391 @ SV1012 @ SV1510 ) @ ( tc_List_Olist @ SV1510 ) ) @ SV1510 ) ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ SV391 @ SV1012 @ SV1510 ) @ ( tc_List_Olist @ SV1510 ) ) @ ( c_Nat_Osize__class_Osize @ SV1012 @ ( tc_List_Olist @ SV1510 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4464]) ).
thf(4906,plain,
! [SV1974: $i,SV1840: $i,SV1513: $i,SV1019: $i,SV398: $i] :
( ( ( c_List_Omap @ SV398 @ ( c_List_Oreplicate @ SV1019 @ SV1513 @ SV1840 ) @ SV1840 @ SV1974 )
= ( c_List_Oreplicate @ SV1019 @ ( hAPP @ SV398 @ SV1513 ) @ SV1974 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4466]) ).
thf(4907,plain,
! [SV1841: $i,SV1514: $i,SV1020: $i,SV399: $i] :
( ( ( ( c_List_Onth @ ( c_List_Oappend @ SV399 @ SV1020 @ SV1514 ) @ SV1841 @ SV1514 )
= ( c_List_Onth @ SV399 @ SV1841 @ SV1514 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1841 @ ( c_Nat_Osize__class_Osize @ SV399 @ ( tc_List_Olist @ SV1514 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4467]) ).
thf(4908,plain,
! [SV1515: $i,SV1021: $i,SV400: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV400 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV400 ) @ SV1021 ) @ SV1515 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV400 ) @ SV1515 ) @ SV1021 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4468]) ).
thf(4909,plain,
! [SV1516: $i,SV1022: $i,SV401: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV401 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV401 ) @ SV1022 ) @ SV1516 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV401 ) @ SV1516 ) @ SV1022 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4469]) ).
thf(4910,plain,
! [SV1517: $i,SV1023: $i,SV402: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV402 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV402 ) @ SV1023 ) @ SV1517 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV402 ) @ SV1517 ) @ SV1023 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4470]) ).
thf(4911,plain,
! [SV1025: $i,SV404: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV404 ) @ SV1025 ) @ SV1025 ) @ ( c_HOL_Ozero__class_Ozero @ SV404 ) @ SV404 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1025 @ ( c_HOL_Ozero__class_Ozero @ SV404 ) @ SV404 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV404 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4471]) ).
thf(4912,plain,
! [SV405: $i,SV1026: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1026 @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SV405 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV405 ) @ SV1026 ) @ SV1026 ) @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SV405 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV405 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4472]) ).
thf(4913,plain,
! [SV406: $i,SV1027: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1027 @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV406 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV406 ) @ SV1027 ) @ SV1027 ) @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV406 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV406 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4473]) ).
thf(4914,plain,
! [SV1028: $i,SV407: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV407 ) @ SV1028 ) @ SV1028 ) @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1028 @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV407 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4474]) ).
thf(4915,plain,
! [SV1842: $i,SV1519: $i,SV1029: $i,SV408: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV408 @ ( c_Nat_Osize__class_Osize @ SV1029 @ ( tc_List_Olist @ SV1519 ) ) @ tc_nat ) )
= $true )
| ( ( ( c_List_Onth @ ( c_List_Olist__update @ SV1029 @ SV408 @ SV1842 @ SV1519 ) @ SV408 @ SV1519 )
= SV1842 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4475]) ).
thf(4916,plain,
! [SV1843: $i,SV1520: $i,SV1030: $i,SV409: $i] :
( ( ( ( c_List_Onth @ ( c_List_Olist__update @ SV409 @ SV1030 @ SV1520 @ SV1843 ) @ SV1030 @ SV1843 )
= SV1520 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1030 @ ( c_Nat_Osize__class_Osize @ SV409 @ ( tc_List_Olist @ SV1843 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4476]) ).
thf(4917,plain,
! [SV1521: $i,SV1031: $i,SV410: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV410 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV410 ) @ ( c_Power_Opower__class_Opower @ SV1031 @ SV1521 @ SV410 ) @ SV410 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV410 ) @ SV1031 @ SV410 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4477]) ).
thf(4918,plain,
! [SV1522: $i,SV1032: $i,SV411: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV411 @ ( c_Nat_Osize__class_Osize @ SV1032 @ ( tc_List_Olist @ SV1522 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Olast @ ( c_List_Odrop @ SV411 @ SV1032 @ SV1522 ) @ SV1522 )
= ( c_List_Olast @ SV1032 @ SV1522 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4478]) ).
thf(4919,plain,
! [SV1523: $i,SV1033: $i,SV412: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV412 @ ( c_Nat_Osize__class_Osize @ SV1033 @ ( tc_List_Olist @ SV1523 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Otake @ SV412 @ ( c_List_Obutlast @ SV1033 @ SV1523 ) @ SV1523 )
= ( c_List_Otake @ SV412 @ SV1033 @ SV1523 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4479]) ).
thf(4920,plain,
! [SV1975: $i,SV1844: $i,SV1524: $i,SV1034: $i,SV413: $i] :
( ( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV413 @ SV1034 @ SV1524 ) @ SV1844 @ SV1975 @ SV1524 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV413 @ SV1844 @ SV1975 @ SV1524 ) @ SV1034 @ SV1524 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1844 @ ( c_Nat_Osize__class_Osize @ SV413 @ ( tc_List_Olist @ SV1524 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4480]) ).
thf(4921,plain,
! [SV1976: $i,SV1845: $i,SV1525: $i,SV1035: $i,SV414: $i] :
( ( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV414 @ SV1035 @ SV1525 ) @ SV1845 @ SV1976 @ SV1525 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV414 @ SV1845 @ SV1976 @ SV1525 ) @ SV1035 @ SV1525 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1845 @ ( c_Nat_Osize__class_Osize @ SV414 @ ( tc_List_Olist @ SV1525 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4481]) ).
thf(4922,plain,
! [SV1846: $i,SV1526: $i,SV1036: $i,SV415: $i] :
( ( ( ( c_List_Onth @ ( c_List_Oreplicate @ SV415 @ SV1036 @ SV1526 ) @ SV1846 @ SV1526 )
= SV1036 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1846 @ SV415 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4482]) ).
thf(4923,plain,
! [SV1977: $i,SV1847: $i,SV1527: $i,SV1037: $i,SV416: $i] :
( ( ( ( c_List_OtakeWhile @ SV416 @ ( c_List_Oappend @ SV1037 @ ( c_List_Olist_OCons @ SV1527 @ SV1847 @ SV1977 ) @ SV1977 ) @ SV1977 )
= ( c_List_OtakeWhile @ SV416 @ SV1037 @ SV1977 ) )
| ( hBOOL @ ( hAPP @ SV416 @ SV1527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4483]) ).
thf(4924,plain,
! [SV419: $i,SV1038: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1038 @ SV1038 @ SV419 )
= $false )
| ( ( class_Orderings_Oorder @ SV419 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4484]) ).
thf(4925,plain,
! [SV420: $i,SV1039: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1039 @ SV1039 @ SV420 )
= $false )
| ( ( class_Orderings_Olinorder @ SV420 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4485]) ).
thf(4926,plain,
! [SV421: $i,SV1040: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1040 @ SV1040 @ SV421 )
= $false )
| ( ( class_Orderings_Opreorder @ SV421 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4486]) ).
thf(4927,plain,
! [SV1529: $i,SV1043: $i,SV424: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV424 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SV1043 ) @ SV1529 ) @ SV424 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV1529 @ SV424 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV1043 @ SV424 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4488]) ).
thf(4928,plain,
! [SV1530: $i,SV1044: $i,SV425: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV425 )
= $false )
| ( ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SV1044 @ SV1530 @ SV425 ) @ SV425 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV425 ) @ SV1044 ) @ ( c_List_Olistsum @ SV1530 @ SV425 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4489]) ).
thf(4929,plain,
! [SV1978: $i,SV1848: $i,SV1531: $i,SV1045: $i,SV426: $i] :
( ( ( c_List_Omap @ SV426 @ ( c_List_Oappend @ SV1045 @ SV1531 @ SV1848 ) @ SV1848 @ SV1978 )
= ( c_List_Oappend @ ( c_List_Omap @ SV426 @ SV1045 @ SV1848 @ SV1978 ) @ ( c_List_Omap @ SV426 @ SV1531 @ SV1848 @ SV1978 ) @ SV1978 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4490]) ).
thf(4930,plain,
! [SV1532: $i,SV1046: $i,SV427: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV427 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1046 @ SV1532 @ SV427 )
| ( c_HOL_Oord__class_Oless @ SV1532 @ SV1046 @ SV427 )
| ( SV1532 = SV1046 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4491]) ).
thf(4931,plain,
! [SV1533: $i,SV1047: $i,SV428: $i] :
( ( ( class_Orderings_Olinorder @ SV428 )
= $false )
| ( ( ( SV1047 = SV1533 )
| ( c_HOL_Oord__class_Oless @ SV1533 @ SV1047 @ SV428 )
| ( c_HOL_Oord__class_Oless @ SV1047 @ SV1533 @ SV428 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4492]) ).
thf(4932,plain,
! [SV430: $i,SV1534: $i,SV1049: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1049 @ SV1534 @ tc_nat )
= $true )
| ( ( ( SV1534 = SV1049 )
| ( c_HOL_Oord__class_Oless @ SV1534 @ SV1049 @ tc_nat ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV430 @ SV1049 ) @ SV1534 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4494]) ).
thf(4933,plain,
! [SV1535: $i,SV1051: $i,SV432: $i] :
( ( ( class_Orderings_Olinorder @ SV432 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1051 @ SV1535 @ SV432 )
| ( c_HOL_Oord__class_Oless @ SV1535 @ SV1051 @ SV432 )
| ( SV1535 = SV1051 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4496]) ).
thf(4934,plain,
! [SV1537: $i,SV1053: $i,SV434: $i] :
( ( ( class_Orderings_Olinorder @ SV434 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1053 @ SV1537 @ SV434 )
| ( SV1537 = SV1053 )
| ( c_HOL_Oord__class_Oless @ SV1537 @ SV1053 @ SV434 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4498]) ).
thf(4935,plain,
! [SV1538: $i,SV1054: $i,SV435: $i] :
( ( ( class_Orderings_Olinorder @ SV435 )
= $false )
| ( ( ( SV1054 = SV1538 )
| ( c_HOL_Oord__class_Oless @ SV1054 @ SV1538 @ SV435 )
| ( c_HOL_Oord__class_Oless @ SV1538 @ SV1054 @ SV435 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4499]) ).
thf(4936,plain,
! [SV1979: $i,SV1850: $i,SV1539: $i,SV1055: $i,SV436: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV436 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV436 ) @ SV1055 ) @ SV1539 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV436 ) @ SV1850 ) @ SV1979 ) @ SV436 )
| ~ ( c_HOL_Oord__class_Oless @ SV1539 @ SV1979 @ SV436 )
| ~ ( c_HOL_Oord__class_Oless @ SV1055 @ SV1850 @ SV436 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4500]) ).
thf(4937,plain,
! [SV1980: $i,SV1851: $i,SV1540: $i,SV1056: $i,SV437: $i] :
( ( ( ( c_List_Onth @ ( c_List_Omap @ SV437 @ SV1056 @ SV1540 @ SV1851 ) @ SV1980 @ SV1851 )
= ( hAPP @ SV437 @ ( c_List_Onth @ SV1056 @ SV1980 @ SV1540 ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1980 @ ( c_Nat_Osize__class_Osize @ SV1056 @ ( tc_List_Olist @ SV1540 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4501]) ).
thf(4938,plain,
! [SV1541: $i,SV1057: $i,SV438: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV438 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1057 @ SV438 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1541 @ SV438 ) @ SV438 )
| ~ ( c_HOL_Oord__class_Oless @ SV1057 @ SV1541 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4502]) ).
thf(4939,plain,
! [SV1542: $i,SV1058: $i,SV439: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV439 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1058 @ SV1542 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1058 @ SV439 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1542 @ SV439 ) @ SV439 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4503]) ).
thf(4940,plain,
! [SV1059: $i,SV440: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV440 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1059 @ SV440 ) @ SV440 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1059 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV440 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4504]) ).
thf(4941,plain,
! [SV441: $i,SV1060: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1060 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV441 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1060 @ SV441 ) @ SV441 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV441 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4505]) ).
thf(4942,plain,
! [SV1852: $i,SV1543: $i,SV1063: $i,SV444: $i] :
( ( ( c_List_Olistsp @ SV444 @ ( c_List_Oappend @ SV1063 @ SV1543 @ SV1852 ) @ SV1852 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV444 @ SV1543 @ SV1852 )
| ~ ( c_List_Olistsp @ SV444 @ SV1063 @ SV1852 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4507]) ).
thf(4943,plain,
! [SV1853: $i,SV1546: $i,SV1066: $i,SV447: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV447 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1066 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV447 ) @ SV1546 ) @ SV1853 ) @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ SV1066 @ SV1853 @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV1546 @ SV447 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4508]) ).
thf(4944,plain,
! [SV1067: $i,SV1547: $i,SV448: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV448 @ SV1547 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV448 ) ) @ SV1067 ) @ SV1547 )
= ( c_Lambda_OdB_OVar @ SV448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4509]) ).
thf(4945,plain,
! [SV1981: $i,SV1854: $i,SV1548: $i,SV1068: $i,SV449: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV449 @ ( c_Lambda_OdB_OdB__case @ SV1068 @ SV1548 @ SV1854 @ ( c_Lambda_OdB_OAbs @ SV1981 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV449 @ ( hAPP @ SV1854 @ SV1981 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4510]) ).
thf(4946,plain,
! [SV1982: $i,SV1855: $i,SV1549: $i,SV1069: $i,SV450: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV450 @ ( c_Lambda_OdB_OdB__case @ SV1069 @ SV1549 @ SV1855 @ ( c_Lambda_OdB_OAbs @ SV1982 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV450 @ ( hAPP @ SV1855 @ SV1982 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4511]) ).
thf(4947,plain,
! [SV1983: $i,SV1856: $i,SV1550: $i,SV1070: $i,SV451: $i] :
( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV451 @ ( c_List_Olist_OCons @ SV1070 @ SV1550 @ SV1856 ) @ SV1856 ) @ ( c_Nat_Osize__class_Osize @ SV451 @ ( tc_List_Olist @ SV1856 ) ) @ SV1983 @ SV1856 )
= ( c_List_Oappend @ SV451 @ ( c_List_Olist_OCons @ SV1983 @ SV1550 @ SV1856 ) @ SV1856 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4512]) ).
thf(4948,plain,
! [SV1857: $i,SV1551: $i,SV1071: $i,SV452: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV452 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV452 ) @ SV1071 ) @ SV1551 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV452 ) @ SV1857 ) @ SV1551 ) @ SV452 )
| ~ ( c_HOL_Oord__class_Oless @ SV1071 @ SV1857 @ SV452 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4513]) ).
thf(4949,plain,
! [SV1858: $i,SV1552: $i,SV1072: $i,SV453: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV453 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV453 ) @ SV1072 ) @ SV1552 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV453 ) @ SV1858 ) @ SV1552 ) @ SV453 )
| ~ ( c_HOL_Oord__class_Oless @ SV1072 @ SV1858 @ SV453 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4514]) ).
thf(4950,plain,
! [SV1859: $i,SV1553: $i,SV1073: $i,SV454: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV454 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1073 @ SV1553 @ SV454 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV454 ) @ SV1073 ) @ SV1859 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV454 ) @ SV1553 ) @ SV1859 ) @ SV454 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4515]) ).
thf(4951,plain,
! [SV1860: $i,SV1554: $i,SV1074: $i,SV455: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV455 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV455 ) @ SV1074 ) @ SV1554 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV455 ) @ SV1074 ) @ SV1860 ) @ SV455 )
| ~ ( c_HOL_Oord__class_Oless @ SV1554 @ SV1860 @ SV455 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4516]) ).
thf(4952,plain,
! [SV1861: $i,SV1555: $i,SV1075: $i,SV456: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV456 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV456 ) @ SV1075 ) @ SV1555 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV456 ) @ SV1075 ) @ SV1861 ) @ SV456 )
| ~ ( c_HOL_Oord__class_Oless @ SV1555 @ SV1861 @ SV456 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4517]) ).
thf(4953,plain,
! [SV1862: $i,SV1556: $i,SV1076: $i,SV457: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV457 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1076 @ SV1556 @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV1862 ) @ SV1076 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV1862 ) @ SV1556 ) @ SV457 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4518]) ).
thf(4954,plain,
! [SV1863: $i,SV1557: $i,SV1077: $i,SV458: $i] :
( ( ( c_Type_Otyping @ SV458 @ SV1077 @ SV1557 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1863 ) @ SV1077 ) )
| ~ ( c_Type_Otyping @ SV458 @ SV1863 @ SV1557 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4519]) ).
thf(4955,plain,
! [SV1558: $i,SV1078: $i,SV459: $i] :
( ( ( class_Orderings_Olinorder @ SV459 )
= $false )
| ( ( ( c_List_Olinorder__class_Osorted @ SV1078 @ SV459 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1078 @ SV1558 @ SV459 ) @ SV459 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4520]) ).
thf(4956,plain,
! [SV1559: $i,SV1079: $i,SV460: $i] :
( ( ( class_Orderings_Olinorder @ SV460 )
= $false )
| ( ( ( c_List_Olinorder__class_Osorted @ SV1079 @ SV460 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1559 @ SV1079 @ SV460 ) @ SV460 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4521]) ).
thf(4957,plain,
! [SV1984: $i,SV1864: $i,SV1560: $i,SV1080: $i,SV461: $i] :
( ( ! [SY4610: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV461 @ SV1080 @ SV1560 @ SV1864 ) @ SV1984 @ SY4610 @ SV1864 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV461 @ SV1984 @ SY4610 @ SV1864 ) @ SV1080 @ SV1560 @ SV1864 ) )
| ( SV1080 = SV1984 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4522]) ).
thf(4958,plain,
! [SV1985: $i,SV1866: $i,SV1562: $i,SV1082: $i,SV463: $i] :
( ( ( c_List_Odrop @ SV463 @ ( c_List_Omap @ SV1082 @ SV1562 @ SV1866 @ SV1985 ) @ SV1985 )
= ( c_List_Omap @ SV1082 @ ( c_List_Odrop @ SV463 @ SV1562 @ SV1866 ) @ SV1866 @ SV1985 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4524]) ).
thf(4959,plain,
! [SV1564: $i,SV1085: $i,SV466: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV466 )
= $false )
| ( ( ( c_List_Olistsum @ ( c_List_Oappend @ SV1085 @ SV1564 @ SV466 ) @ SV466 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV466 ) @ ( c_List_Olistsum @ SV1085 @ SV466 ) ) @ ( c_List_Olistsum @ SV1564 @ SV466 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4526]) ).
thf(4960,plain,
! [SV1986: $i,SV1867: $i,SV1565: $i,SV1086: $i,SV467: $i] :
( ( ( ( c_List_Onth @ ( c_List_Olist__update @ SV467 @ SV1086 @ SV1565 @ SV1867 ) @ SV1986 @ SV1867 )
= ( c_List_Onth @ SV467 @ SV1986 @ SV1867 ) )
| ( SV1086 = SV1986 )
| ~ ( c_HOL_Oord__class_Oless @ SV1086 @ ( c_Nat_Osize__class_Osize @ SV467 @ ( tc_List_Olist @ SV1867 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4527]) ).
thf(4961,plain,
! [SV1987: $i,SV1868: $i,SV1566: $i,SV1087: $i,SV468: $i] :
( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV468 @ SV1087 @ SV1566 @ SV1868 ) @ SV1087 @ SV1987 @ SV1868 )
= ( c_List_Olist__update @ SV468 @ SV1087 @ SV1987 @ SV1868 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4528]) ).
thf(4962,plain,
! [SV1571: $i,SV1092: $i,SV473: $i] :
( ( ( class_Orderings_Oorder @ SV473 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1092 @ SV1571 @ SV473 )
| ~ ( c_HOL_Oord__class_Oless @ SV1571 @ SV1092 @ SV473 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4533]) ).
thf(4963,plain,
! [SV1572: $i,SV1093: $i,SV474: $i] :
( ( ( class_Orderings_Olinorder @ SV474 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1093 @ SV1572 @ SV474 )
| ~ ( c_HOL_Oord__class_Oless @ SV1572 @ SV1093 @ SV474 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4534]) ).
thf(4964,plain,
! [SV1573: $i,SV1094: $i,SV475: $i] :
( ( ( class_Orderings_Opreorder @ SV475 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1094 @ SV1573 @ SV475 )
| ~ ( c_HOL_Oord__class_Oless @ SV1573 @ SV1094 @ SV475 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4535]) ).
thf(4965,plain,
! [SV1574: $i,SV1095: $i,SV476: $i] :
( ( ( class_Orderings_Opreorder @ SV476 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1095 @ SV1574 @ SV476 )
| ~ ( c_HOL_Oord__class_Oless @ SV1574 @ SV1095 @ SV476 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4536]) ).
thf(4966,plain,
! [SV1575: $i,SV1096: $i,SV477: $i] :
( ( ( c_Type_Otyping @ SV477 @ ( c_Lambda_OdB_OVar @ SV1096 ) @ SV1575 )
= $false )
| ( ( ( hAPP @ SV477 @ SV1096 )
= SV1575 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4537]) ).
thf(4967,plain,
! [SV1988: $i,SV1873: $i,SV1576: $i,SV1097: $i,SV478: $i] :
( ( ( c_Lambda_OdB_OdB__case @ SV478 @ SV1097 @ SV1576 @ ( c_Lambda_OdB_OVar @ SV1873 ) @ SV1988 )
= ( hAPP @ SV478 @ SV1873 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4538]) ).
thf(4968,plain,
! [SV1100: $i,SV1578: $i,SV483: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV483 ) @ SV1578 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV483 ) @ SV1100 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1578 ) @ SV1100 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4539]) ).
thf(4969,plain,
! [SV1101: $i,SV484: $i,SV1579: $i] :
( ( ( c_in @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1579 @ tc_nat )
= $false )
| ( ( ( c_List_Osublist @ ( c_List_Olist_OCons @ SV484 @ ( c_List_Olist_ONil @ SV1101 ) @ SV1101 ) @ SV1579 @ SV1101 )
= ( c_List_Olist_OCons @ SV484 @ ( c_List_Olist_ONil @ SV1101 ) @ SV1101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4540]) ).
thf(4970,plain,
! [SV486: $i,SV1581: $i,SV1103: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1103 ) @ SV1581 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV486 ) )
= $false )
| ( ( SV486
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1103 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV1103 @ SV1581 @ SV486 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4542]) ).
thf(4971,plain,
! [SV1105: $i,SV488: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV488 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV488 )
| ~ ( class_Power_Opower @ SV488 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV488 ) @ SV1105 @ SV488 )
= ( c_HOL_Ozero__class_Ozero @ SV488 ) )
| ( SV1105
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV488 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4543]) ).
thf(4972,plain,
! [SV1106: $i,SV489: $i] :
( ( ( ~ ( class_Power_Opower @ SV489 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV1106 @ SV489 )
= ( c_HOL_Ozero__class_Ozero @ SV489 ) )
| ( SV1106
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV489 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4544]) ).
thf(4973,plain,
! [SV1875: $i,SV1587: $i,SV1116: $i,SV503: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV503 ) )
= $true )
| ( ( ( c_List_Olinorder__class_Oinsort__key @ SV1116 @ SV1587 @ ( c_List_Olist_ONil @ SV1875 ) @ SV1875 @ SV503 )
= ( c_List_Olist_OCons @ SV1587 @ ( c_List_Olist_ONil @ SV1875 ) @ SV1875 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4546]) ).
thf(4974,plain,
! [SV1876: $i,SV1590: $i,SV1121: $i,SV508: $i] :
( ( ( ( c_List_OtakeWhile @ SV508 @ ( c_List_Olist_OCons @ SV1121 @ SV1590 @ SV1876 ) @ SV1876 )
= ( c_List_Olist_ONil @ SV1876 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV508 @ SV1121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4548]) ).
thf(4975,plain,
! [SV1593: $i,SV1127: $i,SV514: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV514 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1127 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ ( c_HOL_Ozero__class_Ozero @ SV514 ) @ SV1593 @ SV514 @ SV514 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV514 ) @ SV1127 @ SV1593 @ SV514 @ SV514 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4551]) ).
thf(4976,plain,
! [SV1128: $i,SV1594: $i,SV517: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV517 ) @ SV1594 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV517 @ SV1128 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1594 @ SV1128 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4552]) ).
thf(4977,plain,
! [SV1595: $i,SV518: $i,SV1129: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1129 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV518 ) @ SV1129 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1595 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV518 ) ) @ SV1129 ) @ SV1595 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4553]) ).
thf(4978,plain,
! [SV1596: $i,SV1130: $i,SV519: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV519 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV519 ) @ ( c_Lambda_OdB_OVar @ SV1130 ) ) @ SV1596 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4554]) ).
thf(4979,plain,
! [SV1989: $i,SV1877: $i,SV1598: $i,SV1133: $i,SV522: $i] :
( ( ( SV522 = SV1133 )
| ~ ( c_Type_Otyping @ SV1598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1877 ) @ SV1989 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1133 )
| ~ ( c_Type_Otyping @ SV1598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1877 ) @ SV1989 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV522 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4556]) ).
thf(4980,plain,
! [SV1990: $i,SV1879: $i,SV1603: $i,SV1141: $i,SV534: $i] :
( ( ! [SY4611: $i] :
( ( c_List_Ofoldl @ SV534 @ SV1141 @ ( c_List_Olist_OCons @ SV1603 @ SV1879 @ SV1990 ) @ SY4611 @ SV1990 )
= ( c_List_Ofoldl @ SV534 @ ( hAPP @ ( hAPP @ SV534 @ SV1141 ) @ SV1603 ) @ SV1879 @ SY4611 @ SV1990 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4561]) ).
thf(4981,plain,
! [SV1604: $i,SV1146: $i,SV539: $i] :
( ( ( c_fequal @ SV539 @ SV1146 @ SV1604 )
= $false )
| ( ( SV539 = SV1146 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4565]) ).
thf(4982,plain,
! [SV1991: $i,SV1880: $i,SV1605: $i,SV1148: $i,SV541: $i] :
( ( ( ( c_List_Oreplicate @ SV541 @ SV1148 @ SV1605 )
!= ( c_List_Oreplicate @ SV1880 @ SV1991 @ SV1605 ) )
| ( SV541 = SV1880 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4567]) ).
thf(4983,plain,
! [SV1606: $i,SV1149: $i,SV542: $i] :
( ( ( SV542
= ( c_List_Oappend @ SV1149 @ SV542 @ SV1606 ) )
= $false )
| ( ( SV1149
= ( c_List_Olist_ONil @ SV1606 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4568]) ).
thf(4984,plain,
! [SV1881: $i,SV1607: $i,SV1150: $i,SV543: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV543 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV543 ) @ SV1150 ) @ SV1607 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV543 ) @ SV1881 ) @ SV1607 ) )
| ( SV1150 = SV1881 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4569]) ).
thf(4985,plain,
! [SV1609: $i,SV1152: $i,SV545: $i] :
( ( ( ( c_List_Odrop @ SV545 @ SV1152 @ SV1609 )
= ( c_List_Olist_ONil @ SV1609 ) )
= $false )
| ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1152 @ ( tc_List_Olist @ SV1609 ) ) @ SV545 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4571]) ).
thf(4986,plain,
! [SV1610: $i,SV1154: $i,SV547: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV547 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1154 @ SV1610 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OVar @ SV547 )
= SV1154 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4573]) ).
thf(4987,plain,
! [SV1611: $i,SV1156: $i,SV549: $i] :
( ( ( SV549
= ( c_List_Oappend @ SV549 @ SV1156 @ SV1611 ) )
= $false )
| ( ( SV1156
= ( c_List_Olist_ONil @ SV1611 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4574]) ).
thf(4988,plain,
! [SV1992: $i,SV1882: $i,SV1612: $i,SV1157: $i,SV550: $i] :
( ( ( ( c_List_Oappend @ SV550 @ ( c_List_Olist_OCons @ SV1157 @ ( c_List_Olist_ONil @ SV1612 ) @ SV1612 ) @ SV1612 )
!= ( c_List_Oappend @ SV1882 @ ( c_List_Olist_OCons @ SV1992 @ ( c_List_Olist_ONil @ SV1612 ) @ SV1612 ) @ SV1612 ) )
| ( SV550 = SV1882 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4575]) ).
thf(4989,plain,
! [SV1613: $i,SV1158: $i,SV551: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV551 ) @ SV1158 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1613 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV551 ) @ SV1158 )
= SV1613 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4576]) ).
thf(4990,plain,
! [SV1883: $i,SV1614: $i,SV1159: $i,SV552: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV552 ) @ SV1159 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1614 @ SV1883 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( SV1883
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV552 @ SV1159 @ SV1614 @ SV1883 ) @ ( c_List_Olist_OCons @ SV1159 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SV1883
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4577]) ).
thf(4991,plain,
! [SV1884: $i,SV1615: $i,SV1160: $i,SV553: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV553 ) @ SV1160 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1615 ) @ SV1884 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV553 = SV1615 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4578]) ).
thf(4992,plain,
! [SV1885: $i,SV1616: $i,SV1161: $i,SV554: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV554 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1161 @ SV1616 @ SV554 )
!= ( c_Power_Opower__class_Opower @ SV1885 @ SV1616 @ SV554 ) )
| ( SV1161 = SV1885 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1616 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SV1885 @ SV554 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SV1161 @ SV554 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4579]) ).
thf(4993,plain,
! [SV1886: $i,SV1618: $i,SV1164: $i,SV558: $i] :
( ( ( ( c_List_Oappend @ SV558 @ SV1164 @ SV1618 )
!= ( c_List_Oappend @ SV558 @ SV1886 @ SV1618 ) )
= $true )
| ( ( SV1164 = SV1886 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4582]) ).
thf(4994,plain,
! [SV1887: $i,SV1619: $i,SV1165: $i,SV559: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV559 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1165 @ SV1619 @ SV559 )
!= ( c_HOL_Ominus__class_Ominus @ SV1887 @ SV1887 @ SV559 ) )
| ( SV1165 = SV1619 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4583]) ).
thf(4995,plain,
! [SV1888: $i,SV1620: $i,SV1166: $i,SV560: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV560 @ ( tc_List_Olist @ SV1166 ) ) @ SV1620 @ SV1166 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1620 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) @ SV1888 @ SV1166 ) @ SV1166 )
!= SV1888 )
= $true )
| ( ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV560 @ ( tc_List_Olist @ SV1166 ) ) @ SV1620 @ SV1166 )
!= SV560 )
| ( SV1620
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV1620 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) )
| ( ( c_List_Oappend @ SV1620 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1620 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) @ SV1888 @ SV1166 ) @ SV1166 )
= ( c_List_Oappend @ SV560 @ SV1888 @ SV1166 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4584]) ).
thf(4996,plain,
! [SV1621: $i,SV1168: $i,SV562: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV562 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1168 @ SV1621 @ SV562 )
!= ( c_HOL_Ozero__class_Ozero @ SV562 ) )
| ( SV1168 = SV1621 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4586]) ).
thf(4997,plain,
! [SV1622: $i,SV1169: $i,SV563: $i] :
( ( ( ( c_List_Olist_ONil @ SV563 )
= ( c_List_Oappend @ SV1169 @ SV1622 @ SV563 ) )
= $false )
| ( ( SV1622
= ( c_List_Olist_ONil @ SV563 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4587]) ).
thf(4998,plain,
! [SV1889: $i,SV1623: $i,SV1170: $i,SV564: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV564 ) @ SV1170 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1623 ) @ SV1889 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV1170 = SV1889 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4588]) ).
thf(4999,plain,
! [SV1624: $i,SV1171: $i,SV565: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV565 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1171 @ SV1624 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV1624
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4589]) ).
thf(5000,plain,
! [SV1890: $i,SV1627: $i,SV1174: $i,SV569: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV569 ) @ SV1174 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1627 ) @ SV1890 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV569 = SV1627 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4593]) ).
thf(5001,plain,
! [SV1891: $i,SV1628: $i,SV1175: $i,SV570: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV570 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV570 ) @ SV1175 ) @ SV1628 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV570 ) @ SV1175 ) @ SV1891 ) )
| ( SV1628 = SV1891 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4594]) ).
thf(5002,plain,
! [SV1892: $i,SV1630: $i,SV1177: $i,SV572: $i] :
( ( ( ( c_List_Oappend @ SV572 @ SV1177 @ SV1630 )
!= ( c_List_Oappend @ SV1892 @ SV1177 @ SV1630 ) )
= $true )
| ( ( SV572 = SV1892 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4596]) ).
thf(5003,plain,
! [SV1993: $i,SV1893: $i,SV1631: $i,SV1178: $i,SV573: $i] :
( ( ( ( c_List_Oappend @ SV573 @ ( c_List_Olist_OCons @ SV1178 @ ( c_List_Olist_ONil @ SV1631 ) @ SV1631 ) @ SV1631 )
!= ( c_List_Oappend @ SV1893 @ ( c_List_Olist_OCons @ SV1993 @ ( c_List_Olist_ONil @ SV1631 ) @ SV1631 ) @ SV1631 ) )
| ( SV1178 = SV1993 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4597]) ).
thf(5004,plain,
! [SV1994: $i,SV1894: $i,SV1632: $i,SV1179: $i,SV574: $i] :
( ( ( ( c_List_Oappend @ SV574 @ SV1179 @ SV1632 )
!= ( c_List_Oappend @ SV1894 @ SV1994 @ SV1632 ) )
| ( SV1179
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV574 @ ( tc_List_Olist @ SV1632 ) ) @ SV1894 @ SV1632 ) @ SV1994 @ SV1632 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV574 @ ( tc_List_Olist @ SV1632 ) ) @ ( c_Nat_Osize__class_Osize @ SV1894 @ ( tc_List_Olist @ SV1632 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4598]) ).
thf(5005,plain,
! [SV1633: $i,SV1180: $i,SV575: $i] :
( ( ( ( c_List_Olist_OCons @ SV575 @ ( c_List_Olist_ONil @ SV1180 ) @ SV1180 )
= ( c_List_Orev @ SV1633 @ SV1180 ) )
= $false )
| ( ( SV1633
= ( c_List_Olist_OCons @ SV575 @ ( c_List_Olist_ONil @ SV1180 ) @ SV1180 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4599]) ).
thf(5006,plain,
! [SV1895: $i,SV1634: $i,SV1181: $i,SV576: $i] :
( ( ( ( c_List_Orev @ SV576 @ SV1181 )
!= ( c_List_Olist_OCons @ SV1634 @ SV1895 @ SV1181 ) )
= $true )
| ( ( SV576
= ( c_List_Oappend @ ( c_List_Orev @ SV1895 @ SV1181 ) @ ( c_List_Olist_OCons @ SV1634 @ ( c_List_Olist_ONil @ SV1181 ) @ SV1181 ) @ SV1181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4600]) ).
thf(5007,plain,
! [SV1635: $i,SV1182: $i,SV577: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV577 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV577 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV577 )
| ~ ( class_Power_Opower @ SV577 )
| ( ( c_Power_Opower__class_Opower @ SV1182 @ SV1635 @ SV577 )
!= ( c_HOL_Ozero__class_Ozero @ SV577 ) )
| ( SV1182
= ( c_HOL_Ozero__class_Ozero @ SV577 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4601]) ).
thf(5008,plain,
! [SV1995: $i,SV1896: $i,SV1636: $i,SV1183: $i,SV578: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV578 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1183 @ SV1636 @ SV578 )
!= ( c_HOL_Ominus__class_Ominus @ SV1896 @ SV1995 @ SV578 ) )
| ( c_HOL_Oord__class_Oless @ SV1896 @ SV1995 @ SV578 )
| ~ ( c_HOL_Oord__class_Oless @ SV1183 @ SV1636 @ SV578 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4602]) ).
thf(5009,plain,
! [SV1897: $i,SV1637: $i,SV1184: $i,SV580: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ SV580 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_List_Onth @ ( c_List_Olist_OCons @ SV1184 @ SV1637 @ SV1897 ) @ ( c_Int_Onumber__class_Onumber__of @ SV580 @ tc_nat ) @ SV1897 )
= SV1184 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4603]) ).
thf(5010,plain,
! [SV1996: $i,SV1898: $i,SV1638: $i,SV1185: $i,SV582: $i] :
( ( ( ( c_List_Olist_OCons @ SV582 @ SV1185 @ SV1638 )
!= ( c_List_Olist_OCons @ SV1898 @ SV1996 @ SV1638 ) )
| ( SV1185 = SV1996 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4605]) ).
thf(5011,plain,
! [SV1639: $i,SV1186: $i,SV583: $i] :
( ( ( ( c_List_Oappend @ SV583 @ SV1186 @ SV1639 )
= ( c_List_Olist_ONil @ SV1639 ) )
= $false )
| ( ( SV583
= ( c_List_Olist_ONil @ SV1639 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4606]) ).
thf(5012,plain,
! [SV1640: $i,SV1187: $i,SV584: $i] :
( ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV584 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1187 @ SV1640 @ SV584 )
!= ( c_HOL_Ozero__class_Ozero @ SV584 ) )
| ( SV1187
= ( c_HOL_Ozero__class_Ozero @ SV584 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4607]) ).
thf(5013,plain,
! [SV1899: $i,SV1641: $i,SV1188: $i,SV585: $i] :
( ( ( ( c_List_OtakeWhile @ SV585 @ SV1188 @ SV1641 )
!= SV1188 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV585 @ SV1899 ) )
| ~ ( c_in @ SV1899 @ ( c_List_Oset @ SV1188 @ SV1641 ) @ SV1641 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4608]) ).
thf(5014,plain,
! [SV1643: $i,SV1190: $i,SV587: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV587 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1190 @ SV1643 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OAbs @ SV587 )
= SV1190 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4610]) ).
thf(5015,plain,
! [SV1900: $i,SV1644: $i,SV1191: $i,SV588: $i] :
( ( ( ( c_List_Olist_ONil @ SV588 )
!= ( c_List_Omap @ SV1191 @ SV1644 @ SV1900 @ SV588 ) )
= $true )
| ( ( SV1644
= ( c_List_Olist_ONil @ SV1900 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4611]) ).
thf(5016,plain,
! [SV1645: $i,SV1192: $i,SV589: $i] :
( ( ( ( c_List_Olist_ONil @ SV589 )
= ( c_List_Oappend @ SV1192 @ SV1645 @ SV589 ) )
= $false )
| ( ( SV1192
= ( c_List_Olist_ONil @ SV589 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4612]) ).
thf(5017,plain,
! [SV1646: $i,SV1194: $i,SV591: $i] :
( ( ( ( c_List_Otake @ SV591 @ SV1194 @ SV1646 )
= ( c_List_Olist_ONil @ SV1646 ) )
= $false )
| ( ( ( SV1194
= ( c_List_Olist_ONil @ SV1646 ) )
| ( SV591
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4614]) ).
thf(5018,plain,
! [SV1647: $i,SV1195: $i,SV592: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV592 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1195 @ SV1647 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV1647
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4615]) ).
thf(5019,plain,
! [SV1997: $i,SV1901: $i,SV1648: $i,SV1197: $i,SV594: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV594 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1197 @ SV1648 @ SV594 )
!= ( c_HOL_Ominus__class_Ominus @ SV1901 @ SV1997 @ SV594 ) )
| ( c_HOL_Oord__class_Oless @ SV1197 @ SV1648 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV1901 @ SV1997 @ SV594 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4617]) ).
thf(5020,plain,
! [SV1649: $i,SV1198: $i,SV595: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV595 @ SV1198 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV1649 ) )
= $false )
| ( ( SV595
= ( c_Lambda_OdB_OAbs @ SV1649 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4618]) ).
thf(5021,plain,
! [SV1998: $i,SV1902: $i,SV1650: $i,SV1199: $i,SV596: $i] :
( ( ( ( c_List_Oappend @ SV596 @ SV1199 @ SV1650 )
!= ( c_List_Oappend @ SV1902 @ SV1998 @ SV1650 ) )
| ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV1902 @ ( tc_List_Olist @ SV1650 ) ) @ SV596 @ SV1650 )
= SV1902 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV596 @ ( tc_List_Olist @ SV1650 ) ) @ ( c_Nat_Osize__class_Osize @ SV1902 @ ( tc_List_Olist @ SV1650 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4619]) ).
thf(5022,plain,
! [SV1652: $i,SV1201: $i,SV598: $i] :
( ( ( SV598
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV598 @ ( tc_List_Olist @ SV1201 ) ) @ SV1652 @ SV1201 ) )
= $false )
| ( ( ( c_List_Oappend @ SV598 @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV598 @ ( tc_List_Olist @ SV1201 ) ) @ SV1652 @ SV1201 ) @ SV1201 )
= SV1652 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4621]) ).
thf(5023,plain,
! [SV1903: $i,SV1653: $i,SV1202: $i,SV599: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ SV599 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ SV599 @ tc_nat ) @ ( c_List_Olist_OCons @ SV1202 @ SV1653 @ SV1903 ) @ SV1903 )
= ( c_List_Olist_OCons @ SV1202 @ SV1653 @ SV1903 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4622]) ).
thf(5024,plain,
! [SV1654: $i,SV1203: $i,SV600: $i] :
( ( ( ( c_List_Orev @ SV600 @ SV1203 )
= ( c_List_Orev @ SV1654 @ SV1203 ) )
= $false )
| ( ( SV600 = SV1654 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4623]) ).
thf(5025,plain,
! [SV1655: $i,SV1204: $i,SV601: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV601 @ SV1204 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV1655 ) )
= $false )
| ( ( SV1204
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4624]) ).
thf(5026,plain,
! [SV1904: $i,SV1656: $i,SV1205: $i,SV603: $i] :
( ( ( SV603
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV603 @ ( tc_List_Olist @ SV1205 ) ) @ SV1656 @ SV1205 ) )
= $true )
| ( ( ( ( c_List_Oappend @ SV603 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV603 @ ( tc_List_Olist @ SV1205 ) ) @ SV1656 @ SV1205 ) @ SV1904 @ SV1205 ) @ SV1205 )
= ( c_List_Oappend @ SV1656 @ SV1904 @ SV1205 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV603 @ ( tc_List_Olist @ SV1205 ) ) @ ( c_Nat_Osize__class_Osize @ SV1656 @ ( tc_List_Olist @ SV1205 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4625]) ).
thf(5027,plain,
! [SV1657: $i,SV1206: $i,SV604: $i] :
( ( ( ( c_List_Olist_ONil @ SV604 )
= ( c_List_Oreplicate @ SV1206 @ SV1657 @ SV604 ) )
= $false )
| ( ( SV1206
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4626]) ).
thf(5028,plain,
! [SV1658: $i,SV1207: $i,SV605: $i] :
( ( ( ( c_List_Oappend @ SV605 @ SV1207 @ SV1658 )
= SV1207 )
= $false )
| ( ( SV605
= ( c_List_Olist_ONil @ SV1658 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4627]) ).
thf(5029,plain,
! [SV1999: $i,SV1905: $i,SV1659: $i,SV1209: $i,SV607: $i] :
( ( ! [SY4612: $i] :
( ( ( c_List_Omap @ SV607 @ SV1209 @ SV1659 @ SV1905 )
!= ( c_List_Omap @ SV1999 @ SV1209 @ SV1659 @ SV1905 ) )
| ( ( hAPP @ SV607 @ SY4612 )
= ( hAPP @ SV1999 @ SY4612 ) )
| ~ ( c_in @ SY4612 @ ( c_List_Oset @ SV1209 @ SV1659 ) @ SV1659 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4629]) ).
thf(5030,plain,
! [SV1906: $i,SV1660: $i,SV1210: $i,SV608: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV608 ) @ SV1210 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1660 ) @ SV1906 ) )
= $true )
| ( ( SV608 = SV1660 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4630]) ).
thf(5031,plain,
! [SV1907: $i,SV1661: $i,SV1211: $i,SV609: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV609 ) @ SV1211 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1661 ) @ SV1907 ) )
= $true )
| ( ( SV1211 = SV1907 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4631]) ).
thf(5032,plain,
! [SV1662: $i,SV1212: $i,SV610: $i] :
( ( ( ( c_List_Oappend @ SV610 @ SV1212 @ SV1662 )
= ( c_List_Olist_ONil @ SV1662 ) )
= $false )
| ( ( SV1212
= ( c_List_Olist_ONil @ SV1662 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4632]) ).
thf(5033,plain,
! [SV1663: $i,SV1213: $i,SV611: $i] :
( ( ( class_Nat_Osemiring__char__0 @ SV611 )
= $false )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1213 @ SV611 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1663 @ SV611 ) )
| ( SV1213 = SV1663 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4633]) ).
thf(5034,plain,
! [SV1664: $i,SV1214: $i,SV612: $i] :
( ( ( class_OrderedGroup_Ogroup__add @ SV612 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1214 @ SV1664 @ SV612 )
!= ( c_HOL_Ozero__class_Ozero @ SV612 ) )
| ( SV1214 = SV1664 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4634]) ).
thf(5035,plain,
! [SV2000: $i,SV1908: $i,SV1665: $i,SV1215: $i,SV613: $i] :
( ( ( ( c_List_Odrop @ SV613 @ SV1215 @ SV1665 )
!= ( c_List_Olist_OCons @ SV1908 @ SV2000 @ SV1665 ) )
| ( ( c_List_Onth @ SV1215 @ SV613 @ SV1665 )
= SV1908 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4635]) ).
thf(5036,plain,
! [SV2001: $i,SV1909: $i,SV1666: $i,SV1216: $i,SV614: $i] :
( ( ( ( c_List_Oappend @ SV614 @ SV1216 @ SV1666 )
!= ( c_List_Oappend @ SV1909 @ SV2001 @ SV1666 ) )
| ( SV614
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV614 @ ( tc_List_Olist @ SV1666 ) ) @ SV1909 @ SV1666 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV614 @ ( tc_List_Olist @ SV1666 ) ) @ ( c_Nat_Osize__class_Osize @ SV1909 @ ( tc_List_Olist @ SV1666 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4636]) ).
thf(5037,plain,
! [SV1667: $i,SV1217: $i,SV615: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV615 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV615 )
| ( SV1217
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV615 ) @ SV1217 ) @ SV1667 ) )
| ( SV1667
= ( c_HOL_Ozero__class_Ozero @ SV615 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4637]) ).
thf(5038,plain,
! [SV1218: $i,SV616: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV616 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV616 )
| ~ ( class_Power_Opower @ SV616 )
| ( ( c_Power_Opower__class_Opower @ SV1218 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV616 )
!= ( c_HOL_Ozero__class_Ozero @ SV616 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV616 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4638]) ).
thf(5039,plain,
! [SV1668: $i,SV1219: $i,SV617: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV617 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV617 ) @ SV1219 ) @ SV1668 )
!= ( c_HOL_Ozero__class_Ozero @ SV617 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV617 ) @ SV1668 @ SV617 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV617 ) @ SV1219 @ SV617 )
| ( SV1668
= ( c_HOL_Ozero__class_Ozero @ SV617 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4639]) ).
thf(5040,plain,
! [SV1910: $i,SV1669: $i,SV1220: $i,SV618: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV618 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1220 @ SV1669 @ SV618 )
!= ( c_Power_Opower__class_Opower @ SV1220 @ SV1910 @ SV618 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV618 ) @ SV1220 @ SV618 )
| ( SV1669 = SV1910 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4640]) ).
thf(5041,plain,
! [SV1670: $i,SV1221: $i,SV619: $i] :
( ( ( ( c_List_Oreplicate @ SV619 @ SV1221 @ SV1670 )
= ( c_List_Olist_ONil @ SV1670 ) )
= $false )
| ( ( SV619
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4641]) ).
thf(5042,plain,
! [SV2002: $i,SV1911: $i,SV1672: $i,SV1223: $i,SV621: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV621 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1223 @ SV1672 @ SV621 )
!= ( c_HOL_Ominus__class_Ominus @ SV1911 @ SV2002 @ SV621 ) )
| ( c_lessequals @ SV1672 @ SV1223 @ SV621 )
| ~ ( c_lessequals @ SV2002 @ SV1911 @ SV621 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4643]) ).
thf(5043,plain,
! [SV2003: $i,SV1912: $i,SV1673: $i,SV1224: $i,SV622: $i] :
( ( ( ( c_List_Oreplicate @ SV622 @ SV1224 @ SV1673 )
!= ( c_List_Oreplicate @ SV1912 @ SV2003 @ SV1673 ) )
| ( SV1224 = SV2003 )
| ( SV622
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4644]) ).
thf(5044,plain,
! [SV1913: $i,SV1674: $i,SV1225: $i,SV623: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV623 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1225 @ SV1225 @ SV623 )
!= ( c_HOL_Ominus__class_Ominus @ SV1674 @ SV1913 @ SV623 ) )
| ( SV1674 = SV1913 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4645]) ).
thf(5045,plain,
! [SV1675: $i,SV1226: $i,SV624: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV624 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV624 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1226 @ SV1675 @ SV624 )
!= ( c_HOL_Ozero__class_Ozero @ SV624 ) )
| ( SV1226 = SV1675 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4646]) ).
thf(5046,plain,
! [SV1914: $i,SV1676: $i,SV1227: $i,SV625: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV625 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1227 @ ( c_Suc @ SV1676 ) @ SV625 )
!= ( c_Power_Opower__class_Opower @ SV1914 @ ( c_Suc @ SV1676 ) @ SV625 ) )
| ( SV1227 = SV1914 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV625 ) @ SV1914 @ SV625 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV625 ) @ SV1227 @ SV625 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4647]) ).
thf(5047,plain,
! [SV2004: $i,SV1915: $i,SV1677: $i,SV1228: $i,SV626: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV626 )
| ( ( c_HOL_Ominus__class_Ominus @ SV1228 @ SV1677 @ SV626 )
!= ( c_HOL_Ominus__class_Ominus @ SV1915 @ SV2004 @ SV626 ) )
| ( c_lessequals @ SV2004 @ SV1915 @ SV626 )
| ~ ( c_lessequals @ SV1677 @ SV1228 @ SV626 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4648]) ).
thf(5048,plain,
! [SV1678: $i,SV1229: $i,SV628: $i] :
( ( ( SV628
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV628 ) @ SV1229 ) @ SV1678 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV628 ) @ SV1229 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV628 ) @ SV1229 ) @ ( c_List_Oappend @ SV1678 @ ( c_List_Olist_OCons @ SV1229 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4649]) ).
thf(5049,plain,
! [SV1916: $i,SV1679: $i,SV1230: $i,SV629: $i] :
( ( ( ( c_List_Olist__update @ SV629 @ SV1230 @ SV1679 @ SV1916 )
!= SV629 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1230 @ ( c_Nat_Osize__class_Osize @ SV629 @ ( tc_List_Olist @ SV1916 ) ) @ tc_nat )
| ( ( c_List_Onth @ SV629 @ SV1230 @ SV1916 )
= SV1679 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4650]) ).
thf(5050,plain,
! [SV2005: $i,SV1917: $i,SV1680: $i,SV1231: $i,SV630: $i] :
( ( ( ( c_List_Oappend @ SV630 @ SV1231 @ SV1680 )
!= ( c_List_Oappend @ SV1917 @ SV2005 @ SV1680 ) )
| ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1917 @ ( tc_List_Olist @ SV1680 ) ) @ SV630 @ SV1680 ) @ SV1231 @ SV1680 )
= SV2005 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV630 @ ( tc_List_Olist @ SV1680 ) ) @ ( c_Nat_Osize__class_Osize @ SV1917 @ ( tc_List_Olist @ SV1680 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4651]) ).
thf(5051,plain,
! [SV2006: $i,SV1918: $i,SV1681: $i,SV1232: $i,SV631: $i] :
( ( ( ( c_List_Olist_OCons @ SV631 @ SV1232 @ SV1681 )
!= ( c_List_Olist_OCons @ SV1918 @ SV2006 @ SV1681 ) )
| ( SV631 = SV1918 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4652]) ).
thf(5052,plain,
! [SV1682: $i,SV1233: $i,SV632: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV632 @ SV1233 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1682 @ SV1233 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV632 = SV1682 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4653]) ).
thf(5053,plain,
! [SV2007: $i,SV1919: $i,SV1683: $i,SV1234: $i,SV633: $i] :
( ( ( ( c_List_Omap @ SV633 @ SV1234 @ SV1683 @ SV1919 )
!= ( c_List_Omap @ SV633 @ SV2007 @ SV1683 @ SV1919 ) )
| ( ( c_Nat_Osize__class_Osize @ SV1234 @ ( tc_List_Olist @ SV1683 ) )
= ( c_Nat_Osize__class_Osize @ SV2007 @ ( tc_List_Olist @ SV1683 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4654]) ).
thf(5054,plain,
! [SV1235: $i,SV634: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV634 ) @ SV1235 ) @ SV1235 )
!= ( c_HOL_Ozero__class_Ozero @ SV634 ) )
= $true )
| ( ( SV1235
= ( c_HOL_Ozero__class_Ozero @ SV634 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV634 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4655]) ).
thf(5055,plain,
! [SV1684: $i,SV1236: $i,SV636: $i] :
( ( ( ( c_List_Orev @ SV636 @ SV1236 )
= ( c_List_Olist_OCons @ SV1684 @ ( c_List_Olist_ONil @ SV1236 ) @ SV1236 ) )
= $false )
| ( ( SV636
= ( c_List_Olist_OCons @ SV1684 @ ( c_List_Olist_ONil @ SV1236 ) @ SV1236 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4656]) ).
thf(5056,plain,
! [SV1920: $i,SV1685: $i,SV1237: $i,SV637: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV637 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV637 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1237 ) @ SV1685 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1237 ) @ SV1920 ) )
| ( SV1685 = SV1920 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4657]) ).
thf(5057,plain,
! [SV1921: $i,SV1686: $i,SV1238: $i,SV638: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV638 ) @ SV1238 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1686 @ SV1921 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( SV638
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1686 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV638 @ SV1238 @ SV1686 @ SV1921 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1921
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4658]) ).
thf(5058,plain,
! [SV1687: $i,SV1239: $i,SV639: $i] :
( ( ( class_Int_Oring__char__0 @ SV639 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV639 )
| ( ( c_Int_Onumber__class_Onumber__of @ SV1239 @ SV639 )
!= ( c_Int_Onumber__class_Onumber__of @ SV1687 @ SV639 ) )
| ( SV1239 = SV1687 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4659]) ).
thf(5059,plain,
! [SV1922: $i,SV1688: $i,SV1240: $i,SV641: $i] :
( ( ( ( c_List_Olist__update @ SV641 @ SV1240 @ SV1688 @ SV1922 )
!= ( c_List_Olist_ONil @ SV1922 ) )
= $true )
| ( ( SV641
= ( c_List_Olist_ONil @ SV1922 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4660]) ).
thf(5060,plain,
! [SV1923: $i,SV1689: $i,SV1242: $i,SV643: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV643 ) @ SV1242 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1689 ) @ SV1923 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV1242 = SV1923 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4661]) ).
thf(5061,plain,
! [SV1924: $i,SV1690: $i,SV1243: $i,SV644: $i] :
( ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV644 @ ( tc_List_Olist @ SV1243 ) ) @ SV1690 @ SV1243 )
!= SV644 )
= $true )
| ( ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1690 @ ( tc_List_Olist @ SV1243 ) ) @ ( c_Nat_Osize__class_Osize @ SV644 @ ( tc_List_Olist @ SV1243 ) ) @ tc_nat )
| ( ( c_List_Oappend @ SV1690 @ SV1924 @ SV1243 )
= ( c_List_Oappend @ SV644 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV644 @ ( tc_List_Olist @ SV1243 ) ) @ SV1690 @ SV1243 ) @ SV1924 @ SV1243 ) @ SV1243 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4662]) ).
thf(5062,plain,
! [SV1925: $i,SV1691: $i,SV1244: $i,SV645: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ SV645 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ SV645 @ tc_nat ) @ ( c_List_Olist_OCons @ SV1244 @ SV1691 @ SV1925 ) @ SV1925 )
= ( c_List_Olist_ONil @ SV1925 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4663]) ).
thf(5063,plain,
! [SV1692: $i,SV1245: $i,SV646: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV646 @ SV1245 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1692 @ SV1245 @ tc_nat ) )
= $false )
| ( ( ~ ( c_lessequals @ SV1245 @ SV1692 @ tc_nat )
| ~ ( c_lessequals @ SV1245 @ SV646 @ tc_nat )
| ( SV646 = SV1692 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4664]) ).
thf(5064,plain,
! [SV1693: $i,SV1246: $i,SV647: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV647 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV647 ) @ SV1246 ) @ SV1693 )
!= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV647 ) @ SV1693 @ SV647 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV647 ) @ SV1246 @ SV647 )
| ( SV1246
= ( c_HOL_Ozero__class_Ozero @ SV647 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4665]) ).
thf(5065,plain,
! [SV1926: $i,SV1694: $i,SV1247: $i,SV648: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV648 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV648 ) @ SV1247 ) @ SV1694 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV648 ) @ SV1247 ) @ SV1926 ) )
| ( SV1694 = SV1926 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4666]) ).
thf(5066,plain,
! [SV2008: $i,SV1927: $i,SV1695: $i,SV1248: $i,SV649: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV649 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1248 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1695 ) @ SV1927 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1695 ) @ SV2008 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1248 ) @ SV1927 )
= SV2008 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4667]) ).
thf(5067,plain,
! [SV1928: $i,SV1697: $i,SV1250: $i,SV651: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV651 ) ) @ SV1250 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1697 ) @ SV1928 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4669]) ).
thf(5068,plain,
! [SV1929: $i,SV1698: $i,SV1251: $i,SV652: $i] :
( ( ( ( c_List_Omap @ SV652 @ SV1251 @ SV1698 @ SV1929 )
!= ( c_List_Olist_ONil @ SV1929 ) )
= $true )
| ( ( SV1251
= ( c_List_Olist_ONil @ SV1698 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4670]) ).
thf(5069,plain,
! [SV1699: $i,SV1252: $i,SV653: $i] :
( ( ( ( c_List_Oappend @ SV653 @ SV1252 @ SV1699 )
= SV653 )
= $false )
| ( ( SV1252
= ( c_List_Olist_ONil @ SV1699 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4671]) ).
thf(5070,plain,
! [SV654: $i,SV1253: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1253 @ SV654 @ tc_nat )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV1253 = SV654 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV654 @ SV1253 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4672]) ).
thf(5071,plain,
! [SV1930: $i,SV1700: $i,SV1255: $i,SV656: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV656 ) @ SV1255 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1700 ) @ SV1930 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[4674]) ).
thf(5072,plain,
! [SV1: $i,SV657: $i] :
( ( ( c_lessequals @ SV657 @ SV1 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1 @ ( c_Suc @ SV657 ) @ tc_nat )
= $false )
| ( ( SV1 = SV657 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4675]) ).
thf(5073,plain,
! [SV1931: $i,SV1701: $i,SV1256: $i,SV658: $i,SV2: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV2 ) )
= $true )
| ( ( ( c_lessequals @ SV658 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SV1256 ) @ SV1701 ) @ SV2 )
| ~ ( c_lessequals @ SV1931 @ SV1701 @ SV2 )
| ~ ( c_lessequals @ SV658 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SV1256 ) @ SV1931 ) @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4676]) ).
thf(5074,plain,
! [SV1702: $i,SV1257: $i,SV659: $i,SV3: $i] :
( ( ( class_Orderings_Opreorder @ SV3 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV659 @ SV1257 @ SV3 )
| ~ ( c_lessequals @ SV1702 @ SV1257 @ SV3 )
| ~ ( c_HOL_Oord__class_Oless @ SV659 @ SV1702 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4677]) ).
thf(5075,plain,
! [SV1703: $i,SV1258: $i,SV660: $i,SV4: $i] :
( ( ( class_Orderings_Opreorder @ SV4 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV660 @ SV1258 @ SV4 )
| ~ ( c_HOL_Oord__class_Oless @ SV1703 @ SV1258 @ SV4 )
| ~ ( c_lessequals @ SV660 @ SV1703 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4678]) ).
thf(5076,plain,
! [SV8: $i,SV663: $i,SV1259: $i] :
( ( ( c_lessequals @ SV1259 @ SV663 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV8 @ SV1259 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV8 @ SV663 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4679]) ).
thf(5077,plain,
! [SV1704: $i,SV1260: $i,SV664: $i,SV10: $i] :
( ( ( class_Orderings_Opreorder @ SV10 )
= $false )
| ( ( ( c_lessequals @ SV664 @ SV1260 @ SV10 )
| ~ ( c_lessequals @ SV1704 @ SV1260 @ SV10 )
| ~ ( c_lessequals @ SV664 @ SV1704 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4680]) ).
thf(5078,plain,
! [SV1705: $i,SV1261: $i,SV665: $i,SV11: $i] :
( ( ( class_Orderings_Oorder @ SV11 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV665 @ SV1261 @ SV11 )
| ~ ( c_HOL_Oord__class_Oless @ SV665 @ SV1705 @ SV11 )
| ~ ( c_lessequals @ SV1705 @ SV1261 @ SV11 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4681]) ).
thf(5079,plain,
! [SV1706: $i,SV1262: $i,SV666: $i,SV12: $i] :
( ( ( class_Orderings_Oorder @ SV12 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV666 @ SV1262 @ SV12 )
| ~ ( c_lessequals @ SV666 @ SV1706 @ SV12 )
| ~ ( c_HOL_Oord__class_Oless @ SV1706 @ SV1262 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4682]) ).
thf(5080,plain,
! [SV1707: $i,SV1263: $i,SV667: $i,SV13: $i] :
( ( ( class_Orderings_Oorder @ SV13 )
= $false )
| ( ( ( c_lessequals @ SV667 @ SV1263 @ SV13 )
| ~ ( c_lessequals @ SV667 @ SV1707 @ SV13 )
| ~ ( c_lessequals @ SV1707 @ SV1263 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4683]) ).
thf(5081,plain,
! [SV14: $i,SV1264: $i,SV668: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV668 @ SV1264 @ tc_nat ) @ SV14 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV668 @ SV14 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1264 @ SV14 ) @ SV14 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1264 @ SV668 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4684]) ).
thf(5082,plain,
! [SV669: $i,SV1265: $i,SV15: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV15 @ SV1265 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV669 @ SV1265 @ tc_nat )
| ~ ( c_lessequals @ SV669 @ SV15 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV15 @ SV669 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1265 @ SV669 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4685]) ).
thf(5083,plain,
! [SV670: $i,SV1266: $i,SV16: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV16 @ SV1266 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV670 @ SV1266 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1266 @ SV670 @ tc_nat )
| ~ ( c_lessequals @ SV1266 @ SV16 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV16 @ SV670 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4686]) ).
thf(5084,plain,
! [SV1708: $i,SV1267: $i,SV673: $i,SV20: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV20 )
= $false )
| ( ( ( c_lessequals @ SV673 @ SV1267 @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV1267 @ SV20 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV673 @ ( c_Suc @ SV1708 ) @ SV20 ) @ ( c_Power_Opower__class_Opower @ SV1267 @ ( c_Suc @ SV1708 ) @ SV20 ) @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4687]) ).
thf(5085,plain,
! [SV1709: $i,SV1268: $i,SV674: $i,SV21: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV21 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SV674 ) @ SV1268 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SV674 ) @ SV1709 ) @ SV21 )
| ~ ( c_lessequals @ SV1268 @ SV1709 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4688]) ).
thf(5086,plain,
! [SV1710: $i,SV1269: $i,SV675: $i,SV22: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV22 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV675 ) @ SV1269 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV1710 ) @ SV1269 ) @ SV22 )
| ~ ( c_lessequals @ SV675 @ SV1710 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4689]) ).
thf(5087,plain,
! [SV1711: $i,SV1270: $i,SV676: $i,SV23: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV23 )
= $false )
| ( ( ( c_lessequals @ SV676 @ SV1270 @ SV23 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV23 ) @ SV1711 ) @ SV676 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV23 ) @ SV1711 ) @ SV1270 ) @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4690]) ).
thf(5088,plain,
! [SV1712: $i,SV1271: $i,SV677: $i,SV24: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV24 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ SV677 ) @ SV1271 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ SV677 ) @ SV1712 ) @ SV24 )
| ~ ( c_lessequals @ SV1271 @ SV1712 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4691]) ).
thf(5089,plain,
! [SV1713: $i,SV1272: $i,SV678: $i,SV25: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV25 )
= $false )
| ( ( ( c_lessequals @ SV678 @ SV1272 @ SV25 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SV678 ) @ SV1713 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SV1272 ) @ SV1713 ) @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4692]) ).
thf(5090,plain,
! [SV1714: $i,SV1273: $i,SV679: $i,SV26: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV26 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV26 ) @ SV679 ) @ SV1273 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV26 ) @ SV1714 ) @ SV1273 ) @ SV26 )
| ~ ( c_lessequals @ SV679 @ SV1714 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4693]) ).
thf(5091,plain,
! [SV27: $i,SV680: $i,SV1274: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1274 @ SV680 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV27 @ SV1274 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV27 ) @ SV680 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4694]) ).
thf(5092,plain,
! [SV1275: $i,SV681: $i,SV30: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV30 ) @ ( c_Power_Opower__class_Opower @ SV681 @ ( c_Suc @ SV1275 ) @ SV30 ) @ SV30 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SV681 @ SV30 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4695]) ).
thf(5093,plain,
! [SV31: $i,SV1276: $i,SV682: $i] :
( ( ( c_lessequals @ SV682 @ SV1276 @ SV31 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV682 @ SV1276 @ SV31 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4696]) ).
thf(5094,plain,
! [SV32: $i,SV1277: $i,SV683: $i] :
( ( ( c_lessequals @ SV683 @ SV1277 @ SV32 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV683 @ SV1277 @ SV32 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4697]) ).
thf(5095,plain,
! [SV35: $i,SV1278: $i,SV686: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV686 @ SV1278 @ SV35 ) @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ SV35 )
= $true )
| ( ( ~ ( c_lessequals @ SV686 @ SV1278 @ SV35 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4698]) ).
thf(5096,plain,
! [SV36: $i,SV1279: $i,SV687: $i] :
( ( ( c_lessequals @ SV687 @ SV1279 @ SV36 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV687 @ SV1279 @ SV36 ) @ ( c_HOL_Ozero__class_Ozero @ SV36 ) @ SV36 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4699]) ).
thf(5097,plain,
! [SV37: $i,SV1280: $i,SV688: $i] :
( ( ( SV688 = SV1280 )
= $true )
| ( ( ~ ( c_lessequals @ SV688 @ SV1280 @ SV37 )
| ~ ( c_lessequals @ SV1280 @ SV688 @ SV37 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4700]) ).
thf(5098,plain,
! [SV38: $i,SV1281: $i,SV689: $i] :
( ( ( SV689 = SV1281 )
= $true )
| ( ( ~ ( c_lessequals @ SV1281 @ SV689 @ SV38 )
| ~ ( c_lessequals @ SV689 @ SV1281 @ SV38 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4701]) ).
thf(5099,plain,
! [SV39: $i,SV1282: $i,SV690: $i] :
( ( ( SV690 = SV1282 )
= $true )
| ( ( ~ ( c_lessequals @ SV1282 @ SV690 @ SV39 )
| ~ ( c_lessequals @ SV690 @ SV1282 @ SV39 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4702]) ).
thf(5100,plain,
! [SV691: $i,SV40: $i] :
( ( ( c_lessequals @ SV40 @ SV691 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV691 @ SV40 @ tc_nat )
= $false )
| ( ( SV40 = SV691 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4703]) ).
thf(5101,plain,
! [SV43: $i,SV1283: $i,SV693: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV693 @ SV1283 @ SV43 )
= $true )
| ( ( ( c_lessequals @ SV1283 @ SV693 @ SV43 )
| ~ ( c_lessequals @ SV693 @ SV1283 @ SV43 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4704]) ).
thf(5102,plain,
! [SV699: $i,SV50: $i,SV1285: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1285 @ SV50 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1285 @ SV699 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV50 @ SV699 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV50 @ SV1285 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4709]) ).
thf(5103,plain,
! [SV1715: $i,SV1286: $i,SV701: $i,SV52: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV52 )
= $false )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV701 @ SV1286 @ SV52 ) @ ( c_Power_Opower__class_Opower @ SV701 @ SV1715 @ SV52 ) @ SV52 )
| ~ ( c_lessequals @ SV701 @ ( c_HOL_Oone__class_Oone @ SV52 ) @ SV52 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV701 @ SV52 )
| ~ ( c_lessequals @ SV1715 @ SV1286 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4710]) ).
thf(5104,plain,
! [SV1287: $i,SV706: $i,SV57: $i] :
( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV57 ) @ ( c_Power_Opower__class_Opower @ SV706 @ SV1287 @ SV57 ) @ SV57 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV57 ) @ SV706 @ SV57 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4711]) ).
thf(5105,plain,
! [SV59: $i,SV1288: $i,SV708: $i] :
( ( ( c_lessequals @ SV708 @ SV1288 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV708 @ SV59 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1288 @ SV59 ) @ SV59 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4712]) ).
thf(5106,plain,
! [SV1289: $i,SV60: $i,SV709: $i] :
( ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV709 @ SV60 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1289 @ SV60 ) @ SV60 )
= $true )
| ( ( ~ ( c_lessequals @ SV709 @ SV1289 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4713]) ).
thf(5107,plain,
! [SV1932: $i,SV1716: $i,SV1291: $i,SV711: $i,SV62: $i] :
( ( ( c_ListOrder_Ostep1 @ SV62 @ ( c_List_Oappend @ SV711 @ SV1291 @ SV1716 ) @ ( c_List_Oappend @ SV711 @ SV1932 @ SV1716 ) @ SV1716 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV62 @ SV1291 @ SV1932 @ SV1716 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4715]) ).
thf(5108,plain,
! [SV1933: $i,SV1717: $i,SV1292: $i,SV712: $i,SV63: $i] :
( ( ( ~ ( c_ListOrder_Ostep1 @ SV63 @ SV712 @ SV1292 @ SV1717 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV63 @ ( c_List_Oappend @ SV712 @ SV1933 @ SV1717 ) @ ( c_List_Oappend @ SV1292 @ SV1933 @ SV1717 ) @ SV1717 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4716]) ).
thf(5109,plain,
! [SV1934: $i,SV1718: $i,SV1293: $i,SV713: $i,SV64: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV64 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV713 ) @ SV1293 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV1718 ) @ SV1934 ) @ SV64 )
| ~ ( c_lessequals @ SV1293 @ SV1934 @ SV64 )
| ~ ( c_lessequals @ SV713 @ SV1718 @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4717]) ).
thf(5110,plain,
! [SV1935: $i,SV1719: $i,SV1294: $i,SV714: $i,SV65: $i] :
( ( ( c_lessequals @ SV65 @ ( c_List_Olist_Olist__size @ SV714 @ SV1294 @ SV1719 ) @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ SV65 @ ( hAPP @ SV714 @ SV1935 ) @ tc_nat )
| ~ ( c_in @ SV1935 @ ( c_List_Oset @ SV1294 @ SV1719 ) @ SV1719 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4718]) ).
thf(5111,plain,
! [SV71: $i,SV1295: $i,SV719: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV719 @ SV1295 @ SV71 )
= $true )
| ( ( c_lessequals @ SV1295 @ SV719 @ SV71 )
= $true )
| ( ( class_Orderings_Olinorder @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4719]) ).
thf(5112,plain,
! [SV72: $i,SV720: $i] :
( ( ( c_lessequals @ SV720 @ SV720 @ SV72 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV720 @ SV720 @ SV72 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4720]) ).
thf(5113,plain,
! [SV74: $i,SV1296: $i,SV722: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV722 @ SV1296 @ SV74 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1296 @ SV722 @ SV74 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4722]) ).
thf(5114,plain,
! [SV75: $i,SV1297: $i,SV723: $i] :
( ( ( c_lessequals @ SV723 @ SV1297 @ SV75 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1297 @ SV723 @ SV75 )
= $true )
| ( ( class_Orderings_Olinorder @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4723]) ).
thf(5115,plain,
! [SV76: $i,SV1298: $i,SV724: $i] :
( ( ( ~ ( c_lessequals @ SV724 @ SV1298 @ SV76 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1298 @ SV724 @ SV76 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4724]) ).
thf(5116,plain,
! [SV77: $i,SV1299: $i,SV725: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV725 @ SV1299 @ SV77 )
= $true )
| ( ( c_lessequals @ SV1299 @ SV725 @ SV77 )
= $true )
| ( ( class_Orderings_Olinorder @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4725]) ).
thf(5117,plain,
! [SV78: $i,SV1300: $i,SV726: $i] :
( ( ( ~ ( c_lessequals @ SV726 @ SV1300 @ SV78 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1300 @ SV726 @ SV78 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4726]) ).
thf(5118,plain,
! [SV1720: $i,SV1301: $i,SV727: $i,SV79: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV79 )
= $false )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV727 @ SV1301 @ SV79 ) @ ( c_Power_Opower__class_Opower @ SV727 @ SV1720 @ SV79 ) @ SV79 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV79 ) @ SV727 @ SV79 )
| ~ ( c_lessequals @ SV1301 @ SV1720 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4727]) ).
thf(5119,plain,
! [SV86: $i,SV1304: $i,SV733: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV733 @ SV1304 @ SV86 )
= $true )
| ( ( ( SV1304 = SV733 )
| ~ ( c_lessequals @ SV733 @ SV1304 @ SV86 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4730]) ).
thf(5120,plain,
! [SV87: $i,SV1305: $i,SV734: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV734 @ SV1305 @ SV87 )
= $true )
| ( ( ~ ( c_lessequals @ SV734 @ SV1305 @ SV87 )
| ( SV1305 = SV734 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4731]) ).
thf(5121,plain,
! [SV91: $i,SV1306: $i,SV738: $i] :
( ( ( SV738 = SV1306 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV738 @ SV1306 @ SV91 )
| ~ ( c_lessequals @ SV738 @ SV1306 @ SV91 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4735]) ).
thf(5122,plain,
! [SV92: $i,SV1307: $i,SV739: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV739 @ SV1307 @ SV92 )
= $true )
| ( ( ( SV739 = SV1307 )
| ~ ( c_lessequals @ SV739 @ SV1307 @ SV92 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4736]) ).
thf(5123,plain,
! [SV93: $i,SV1308: $i,SV740: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV740 @ SV1308 @ SV93 )
= $true )
| ( ( ( SV740 = SV1308 )
| ~ ( c_lessequals @ SV740 @ SV1308 @ SV93 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4737]) ).
thf(5124,plain,
! [SV94: $i,SV1309: $i,SV741: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV741 @ SV1309 @ SV94 )
= $true )
| ( ( ~ ( c_lessequals @ SV741 @ SV1309 @ SV94 )
| ( SV741 = SV1309 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4738]) ).
thf(5125,plain,
! [SV95: $i,SV1310: $i,SV742: $i] :
( ( ( SV742 = SV1310 )
= $true )
| ( ( ~ ( c_lessequals @ SV742 @ SV1310 @ SV95 )
| ( c_HOL_Oord__class_Oless @ SV742 @ SV1310 @ SV95 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4739]) ).
thf(5126,plain,
! [SV96: $i,SV1311: $i,SV743: $i] :
( ( ( SV743 = SV1311 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV743 @ SV1311 @ SV96 )
| ~ ( c_lessequals @ SV743 @ SV1311 @ SV96 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4740]) ).
thf(5127,plain,
! [SV100: $i,SV1312: $i,SV747: $i] :
( ( ( c_lessequals @ SV747 @ SV1312 @ SV100 )
= $true )
| ( ( c_lessequals @ SV1312 @ SV747 @ SV100 )
= $true )
| ( ( class_Orderings_Olinorder @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4741]) ).
thf(5128,plain,
! [SV101: $i,SV1313: $i,SV748: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV748 @ ( c_Suc @ SV1313 ) @ SV101 ) @ ( c_HOL_Oone__class_Oone @ SV101 ) @ SV101 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV748 @ ( c_HOL_Oone__class_Oone @ SV101 ) @ SV101 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ SV748 @ SV101 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4742]) ).
thf(5129,plain,
! [SV1721: $i,SV1314: $i,SV749: $i,SV102: $i] :
( ( ( class_Orderings_Olinorder @ SV102 )
= $false )
| ( ( ( c_lessequals @ SV749 @ SV1314 @ SV102 )
| ~ ( c_in @ SV1314 @ ( c_List_Oset @ SV1721 @ SV102 ) @ SV102 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV749 @ SV1721 @ SV102 ) @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4743]) ).
thf(5130,plain,
! [SV1936: $i,SV1722: $i,SV1315: $i,SV750: $i,SV103: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV103 ) )
= $true )
| ( ( ( c_lessequals @ SV750 @ SV1315 @ SV103 )
| ~ ( c_in @ SV1315 @ ( c_List_Oset @ SV1722 @ SV103 ) @ SV103 )
| ~ ( c_in @ SV750 @ ( c_List_Oset @ SV1936 @ SV103 ) @ SV103 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1936 @ SV1722 @ SV103 ) @ SV103 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4744]) ).
thf(5131,plain,
! [SV106: $i,SV1317: $i,SV752: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV752 @ SV1317 @ SV106 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV752 @ SV1317 @ SV106 ) @ ( c_HOL_Ozero__class_Ozero @ SV106 ) @ SV106 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4745]) ).
thf(5132,plain,
! [SV107: $i,SV1318: $i,SV753: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV753 @ SV1318 @ SV107 ) @ ( c_HOL_Ozero__class_Ozero @ SV107 ) @ SV107 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV753 @ SV1318 @ SV107 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4746]) ).
thf(5133,plain,
! [SV1319: $i,SV754: $i,SV109: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ SV754 ) @ SV1319 ) @ SV109 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV1319 @ SV109 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV754 @ SV109 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4747]) ).
thf(5134,plain,
! [SV110: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV110 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) )
= ( c_HOL_Ozero__class_Ozero @ SV110 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV110 )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4748]) ).
thf(5135,plain,
! [SV755: $i,SV111: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV111 ) @ SV755 @ SV111 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV111 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV111 ) @ SV755 ) @ SV755 ) @ SV111 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4749]) ).
thf(5136,plain,
! [SV756: $i,SV112: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV112 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV112 ) @ SV756 ) @ SV756 ) @ SV112 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV112 ) @ SV756 @ SV112 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV112 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4750]) ).
thf(5137,plain,
! [SV1723: $i,SV1320: $i,SV757: $i,SV113: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV113 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV113 )
| ( c_lessequals @ SV757 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV1320 ) @ SV1723 ) @ SV113 )
| ~ ( c_lessequals @ SV757 @ SV1723 @ SV113 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV1320 @ SV113 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4751]) ).
thf(5138,plain,
! [SV1724: $i,SV1321: $i,SV758: $i,SV114: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV114 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV114 )
| ( c_lessequals @ SV758 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SV1321 ) @ SV1724 ) @ SV114 )
| ~ ( c_lessequals @ SV758 @ SV1321 @ SV114 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV1724 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4752]) ).
thf(5139,plain,
! [SV115: $i,SV759: $i] :
( ( ( c_lessequals @ SV759 @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV115 ) @ SV759 ) @ SV759 ) @ ( c_HOL_Ozero__class_Ozero @ SV115 ) @ SV115 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4753]) ).
thf(5140,plain,
! [SV760: $i,SV116: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV116 ) @ SV760 ) @ SV760 ) @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 )
= $false )
| ( ( c_lessequals @ SV760 @ ( c_HOL_Ozero__class_Ozero @ SV116 ) @ SV116 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4754]) ).
thf(5141,plain,
! [SV1322: $i,SV761: $i,SV117: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV761 ) @ SV1322 ) @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
= $true )
| ( ( ~ ( c_lessequals @ SV1322 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
| ~ ( c_lessequals @ SV761 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4755]) ).
thf(5142,plain,
! [SV1937: $i,SV1725: $i,SV1323: $i,SV762: $i,SV118: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV118 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV762 ) @ SV1323 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV1725 ) @ SV1937 ) @ SV118 )
| ~ ( c_lessequals @ SV1323 @ SV1937 @ SV118 )
| ~ ( c_HOL_Oord__class_Oless @ SV762 @ SV1725 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4756]) ).
thf(5143,plain,
! [SV1938: $i,SV1726: $i,SV1324: $i,SV763: $i,SV119: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV119 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV119 ) @ SV763 ) @ SV1324 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV119 ) @ SV1726 ) @ SV1938 ) @ SV119 )
| ~ ( c_HOL_Oord__class_Oless @ SV1324 @ SV1938 @ SV119 )
| ~ ( c_lessequals @ SV763 @ SV1726 @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4757]) ).
thf(5144,plain,
! [SV1325: $i,SV765: $i,SV121: $i] :
( ( ( ~ ( class_Int_Onumber @ SV121 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ SV765 @ SV121 ) @ ( c_Int_Onumber__class_Onumber__of @ SV1325 @ SV121 ) @ SV121 )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ SV1325 @ SV121 ) @ ( c_Int_Onumber__class_Onumber__of @ SV765 @ SV121 ) @ SV121 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4758]) ).
thf(5145,plain,
! [SV1326: $i,SV766: $i,SV122: $i] :
( ( ( ~ ( class_Int_Onumber @ SV122 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ SV766 @ SV122 ) @ ( c_Int_Onumber__class_Onumber__of @ SV1326 @ SV122 ) @ SV122 )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ SV1326 @ SV122 ) @ ( c_Int_Onumber__class_Onumber__of @ SV766 @ SV122 ) @ SV122 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4759]) ).
thf(5146,plain,
! [SV1327: $i,SV767: $i,SV1727: $i,SV123: $i] :
( ( ( SV123 = SV1727 )
= $true )
| ( ( ~ ( c_in @ SV123 @ ( c_List_Oset @ ( c_List_Olist_OCons @ SV1727 @ SV767 @ SV1327 ) @ SV1327 ) @ SV1327 ) )
= $true )
| ( ( c_in @ SV123 @ ( c_List_Oset @ SV767 @ SV1327 ) @ SV1327 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4760]) ).
thf(5147,plain,
! [SV129: $i,SV1328: $i,SV770: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV770 @ SV1328 @ tc_nat )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV129 @ ( c_HOL_Ominus__class_Ominus @ SV770 @ SV1328 @ tc_nat ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV129 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4761]) ).
thf(5148,plain,
! [SV132: $i,SV773: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV773 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV132 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV132 @ SV773 @ tc_nat ) @ SV132 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4762]) ).
thf(5149,plain,
! [SV1728: $i,SV1329: $i,SV774: $i,SV133: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV133 )
= $false )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV774 @ SV1329 @ SV133 ) @ ( c_Power_Opower__class_Opower @ SV1728 @ SV1329 @ SV133 ) @ SV133 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV133 ) @ SV774 @ SV133 )
| ~ ( c_lessequals @ SV774 @ SV1728 @ SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4763]) ).
thf(5150,plain,
! [SV1330: $i,SV775: $i,SV134: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV134 ) @ ( c_Power_Opower__class_Opower @ SV775 @ SV1330 @ SV134 ) @ SV134 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV134 ) @ SV775 @ SV134 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4764]) ).
thf(5151,plain,
! [SV776: $i,SV135: $i] :
( ( ( class_Power_Opower @ SV135 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV135 ) @ ( c_Suc @ SV776 ) @ SV135 )
= ( c_HOL_Ozero__class_Ozero @ SV135 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV135 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4765]) ).
thf(5152,plain,
! [SV1335: $i,SV784: $i,SV1729: $i,SV143: $i] :
( ( ( c_in @ SV143 @ ( c_List_Oset @ ( c_List_Otake @ SV1729 @ SV784 @ SV1335 ) @ SV1335 ) @ SV1335 )
= $false )
| ( ( c_in @ SV143 @ ( c_List_Oset @ SV784 @ SV1335 ) @ SV1335 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4766]) ).
thf(5153,plain,
! [SV1336: $i,SV785: $i,SV1730: $i,SV144: $i] :
( ( ( c_in @ SV144 @ ( c_List_Oset @ ( c_List_Odrop @ SV1730 @ SV785 @ SV1336 ) @ SV1336 ) @ SV1336 )
= $false )
| ( ( c_in @ SV144 @ ( c_List_Oset @ SV785 @ SV1336 ) @ SV1336 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4767]) ).
thf(5154,plain,
! [SV1733: $i,SV1339: $i,SV147: $i,SV788: $i] :
( ( ( c_in @ SV788 @ ( c_List_Oset @ ( c_List_OtakeWhile @ SV147 @ SV1339 @ SV1733 ) @ SV1733 ) @ SV1733 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV147 @ SV788 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4768]) ).
thf(5155,plain,
! [SV1340: $i,SV789: $i,SV1734: $i,SV148: $i] :
( ( ( c_in @ SV148 @ ( c_List_Oset @ ( c_List_OtakeWhile @ SV1734 @ SV789 @ SV1340 ) @ SV1340 ) @ SV1340 )
= $false )
| ( ( c_in @ SV148 @ ( c_List_Oset @ SV789 @ SV1340 ) @ SV1340 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4769]) ).
thf(5156,plain,
! [SV149: $i,SV1735: $i,SV1341: $i,SV790: $i] :
( ( ( ~ ( c_in @ SV790 @ ( c_List_Oset @ SV1341 @ SV1735 ) @ SV1735 ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV149 @ SV1341 @ SV1735 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV149 @ SV790 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4770]) ).
thf(5157,plain,
! [SV1736: $i,SV791: $i,SV1342: $i,SV150: $i] :
( ( ( c_in @ SV150 @ ( c_List_Oset @ ( c_List_Oreplicate @ SV1342 @ SV791 @ SV1736 ) @ SV1736 ) @ SV1736 )
= $false )
| ( ( SV150 = SV791 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4771]) ).
thf(5158,plain,
! [SV1737: $i,SV1344: $i,SV793: $i,SV152: $i] :
( ( ( class_Orderings_Olinorder @ SV152 )
= $false )
| ( ( ( c_lessequals @ ( c_List_Onth @ SV793 @ SV1344 @ SV152 ) @ ( c_List_Onth @ SV793 @ SV1737 @ SV152 ) @ SV152 )
| ~ ( c_lessequals @ SV1344 @ SV1737 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1737 @ ( c_Nat_Osize__class_Osize @ SV793 @ ( tc_List_Olist @ SV152 ) ) @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ SV793 @ SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4773]) ).
thf(5159,plain,
! [SV1738: $i,SV1345: $i,SV794: $i,SV153: $i] :
( ( ( class_Orderings_Olinorder @ SV153 )
= $false )
| ( ( ( c_lessequals @ ( c_List_Onth @ SV794 @ SV1345 @ SV153 ) @ ( c_List_Onth @ SV794 @ SV1738 @ SV153 ) @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SV1738 @ ( c_Nat_Osize__class_Osize @ SV794 @ ( tc_List_Olist @ SV153 ) ) @ tc_nat )
| ~ ( c_lessequals @ SV1345 @ SV1738 @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ SV794 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4774]) ).
thf(5160,plain,
! [SV1740: $i,SV1348: $i,SV797: $i,SV156: $i] :
( ( ( class_Orderings_Olinorder @ SV156 )
= $false )
| ( ( ( c_lessequals @ SV797 @ SV1348 @ SV156 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV797 @ ( c_List_Olist_OCons @ SV1348 @ SV1740 @ SV156 ) @ SV156 ) @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4776]) ).
thf(5161,plain,
! [SV1741: $i,SV1349: $i,SV798: $i,SV157: $i] :
( ( ( class_Orderings_Olinorder @ SV157 )
= $false )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV798 @ ( c_List_Olist_OCons @ SV1349 @ SV1741 @ SV157 ) @ SV157 ) @ SV157 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1349 @ SV1741 @ SV157 ) @ SV157 )
| ~ ( c_lessequals @ SV798 @ SV1349 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4777]) ).
thf(5162,plain,
! [SV1354: $i,SV803: $i,SV1743: $i,SV162: $i] :
( ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV162 @ ( tc_List_Olist @ SV1743 ) ) @ SV803 @ tc_nat )
= $false )
| ( ( ( c_List_Olist__update @ SV162 @ SV803 @ SV1354 @ SV1743 )
= SV162 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4779]) ).
thf(5163,plain,
! [SV1358: $i,SV1745: $i,SV807: $i,SV166: $i] :
( ( ( c_in @ SV166 @ ( c_List_Oset @ ( c_List_Osublist @ SV807 @ SV1745 @ SV1358 ) @ SV1358 ) @ SV1358 )
= $false )
| ( ( c_in @ SV166 @ ( c_List_Oset @ SV807 @ SV1358 ) @ SV1358 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4781]) ).
thf(5164,plain,
! [SV1746: $i,SV1359: $i,SV808: $i,SV167: $i] :
( ( ( c_in @ SV167 @ ( c_List_Oset @ ( c_List_Osublist @ SV808 @ SV1359 @ SV1746 ) @ SV1746 ) @ SV1746 )
= $false )
| ( ( c_in @ SV167 @ ( c_List_Oset @ SV808 @ SV1746 ) @ SV1746 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4782]) ).
thf(5165,plain,
! [SV2009: $i,SV1940: $i,SV1748: $i,SV1361: $i,SV810: $i,SV169: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV169 )
| ( ( c_List_Olinorder__class_Oinsort__key @ SV810 @ SV1361 @ ( c_List_Olist_OCons @ SV1748 @ SV1940 @ SV2009 ) @ SV2009 @ SV169 )
= ( c_List_Olist_OCons @ SV1361 @ ( c_List_Olist_OCons @ SV1748 @ SV1940 @ SV2009 ) @ SV2009 ) )
| ~ ( c_lessequals @ ( hAPP @ SV810 @ SV1361 ) @ ( hAPP @ SV810 @ SV1748 ) @ SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4783]) ).
thf(5166,plain,
! [SV2010: $i,SV1941: $i,SV1749: $i,SV1362: $i,SV811: $i,SV170: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV170 )
| ( ( c_List_Olinorder__class_Oinsort__key @ SV811 @ SV1362 @ ( c_List_Olist_OCons @ SV1749 @ SV1941 @ SV2010 ) @ SV2010 @ SV170 )
= ( c_List_Olist_OCons @ SV1749 @ ( c_List_Olinorder__class_Oinsort__key @ SV811 @ SV1362 @ SV1941 @ SV2010 @ SV170 ) @ SV2010 ) )
| ( c_lessequals @ ( hAPP @ SV811 @ SV1362 ) @ ( hAPP @ SV811 @ SV1749 ) @ SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4784]) ).
thf(5167,plain,
! [SV1942: $i,SV1750: $i,SV1363: $i,SV812: $i,SV171: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV171 ) )
= $true )
| ( ( ( c_Nat_Osize__class_Osize @ ( c_List_Olinorder__class_Oinsort__key @ SV812 @ SV1363 @ SV1750 @ SV1942 @ SV171 ) @ ( tc_List_Olist @ SV1942 ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ SV1750 @ ( tc_List_Olist @ SV1942 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4785]) ).
thf(5168,plain,
! [SV813: $i,SV1364: $i,SV172: $i] :
( ( ( c_lessequals @ SV172 @ SV1364 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV813 @ SV1364 @ tc_nat )
| ~ ( c_lessequals @ SV813 @ SV172 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV172 @ SV813 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1364 @ SV813 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4786]) ).
thf(5169,plain,
! [SV814: $i,SV1365: $i,SV173: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV173 @ SV1365 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV814 @ SV1365 @ tc_nat ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1365 @ SV814 @ tc_nat )
| ~ ( c_lessequals @ SV1365 @ SV173 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV173 @ SV814 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4787]) ).
thf(5170,plain,
! [SV176: $i,SV1366: $i,SV817: $i] :
( ( ( c_lessequals @ SV817 @ SV1366 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV817 @ SV176 @ tc_nat ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV176 @ SV817 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1366 @ SV817 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV176 @ SV1366 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4788]) ).
thf(5171,plain,
! [SV1368: $i,SV178: $i,SV819: $i] :
( ( ( c_lessequals @ SV819 @ SV178 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV178 @ SV1368 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV178 @ SV819 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1368 @ SV819 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4789]) ).
thf(5172,plain,
! [SV1751: $i,SV1371: $i,SV830: $i,SV191: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV191 )
= $false )
| ( ( ( c_lessequals @ SV830 @ SV1371 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1751 @ SV830 @ SV191 ) @ ( c_Power_Opower__class_Opower @ SV1751 @ SV1371 @ SV191 ) @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV191 ) @ SV1751 @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4795]) ).
thf(5173,plain,
! [SV1752: $i,SV1372: $i,SV831: $i,SV192: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV192 )
= $false )
| ( ( ( c_lessequals @ SV831 @ SV1372 @ tc_nat )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1752 @ SV831 @ SV192 ) @ ( c_Power_Opower__class_Opower @ SV1752 @ SV1372 @ SV192 ) @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV192 ) @ SV1752 @ SV192 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4796]) ).
thf(5174,plain,
! [SV1753: $i,SV1373: $i,SV832: $i,SV193: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV193 )
= $false )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV832 @ SV1373 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SV832 @ SV1753 @ SV193 ) @ SV193 )
| ~ ( c_lessequals @ SV1373 @ SV1753 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV193 ) @ SV832 @ SV193 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4797]) ).
thf(5175,plain,
! [SV836: $i,SV197: $i] :
( ( ( class_Int_Onumber__ring @ SV197 )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV836 @ SV836 @ SV197 )
= ( c_HOL_Ozero__class_Ozero @ SV197 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4798]) ).
thf(5176,plain,
! [SV1943: $i,SV1754: $i,SV1375: $i,SV842: $i,SV208: $i] :
( ( ( c_ListOrder_Ostep1 @ SV208 @ ( c_List_Olist_OCons @ SV842 @ SV1375 @ SV1754 ) @ ( c_List_Olist_OCons @ SV842 @ SV1943 @ SV1754 ) @ SV1754 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV208 @ SV1375 @ SV1943 @ SV1754 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4799]) ).
thf(5177,plain,
! [SV2011: $i,SV1944: $i,SV1755: $i,SV1376: $i,SV843: $i,SV209: $i] :
( ( ( c_ListOrder_Ostep1 @ SV209 @ SV843 @ SV1376 @ SV1755 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV209 @ SV1944 ) @ SV2011 ) )
| ~ ( c_ListOrder_Ostep1 @ SV209 @ ( c_List_Olist_OCons @ SV1944 @ SV843 @ SV1755 ) @ ( c_List_Olist_OCons @ SV2011 @ SV1376 @ SV1755 ) @ SV1755 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4800]) ).
thf(5178,plain,
! [SV2012: $i,SV1945: $i,SV1756: $i,SV1377: $i,SV844: $i,SV210: $i] :
( ( ( c_ListOrder_Ostep1 @ SV210 @ SV844 @ SV1377 @ SV1756 )
| ( SV1377 = SV844 )
| ~ ( c_ListOrder_Ostep1 @ SV210 @ ( c_List_Olist_OCons @ SV1945 @ SV844 @ SV1756 ) @ ( c_List_Olist_OCons @ SV2012 @ SV1377 @ SV1756 ) @ SV1756 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4801]) ).
thf(5179,plain,
! [SV1946: $i,SV1757: $i,SV1378: $i,SV845: $i,SV211: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV211 @ SV845 ) @ SV1378 ) ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV211 @ ( c_List_Olist_OCons @ SV845 @ SV1757 @ SV1946 ) @ ( c_List_Olist_OCons @ SV1378 @ SV1757 @ SV1946 ) @ SV1946 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4802]) ).
thf(5180,plain,
! [SV2013: $i,SV1947: $i,SV1758: $i,SV1379: $i,SV846: $i,SV212: $i] :
( ( ( SV212 = SV846 )
| ( SV1379 = SV1758 )
| ~ ( c_ListOrder_Ostep1 @ SV1947 @ ( c_List_Olist_OCons @ SV846 @ SV1758 @ SV2013 ) @ ( c_List_Olist_OCons @ SV212 @ SV1379 @ SV2013 ) @ SV2013 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4803]) ).
thf(5181,plain,
! [SV2014: $i,SV1948: $i,SV1759: $i,SV1380: $i,SV847: $i,SV213: $i] :
( ( ( SV213 = SV847 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV1380 @ SV847 ) @ SV213 ) )
| ~ ( c_ListOrder_Ostep1 @ SV1380 @ ( c_List_Olist_OCons @ SV847 @ SV1759 @ SV1948 ) @ ( c_List_Olist_OCons @ SV213 @ SV2014 @ SV1948 ) @ SV1948 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4804]) ).
thf(5182,plain,
! [SV1760: $i,SV1383: $i,SV850: $i,SV216: $i] :
( ( ( class_Orderings_Olinorder @ SV216 )
= $false )
| ( ( ( c_lessequals @ ( c_List_Onth @ SV850 @ SV1383 @ SV216 ) @ ( c_List_Onth @ SV850 @ SV1760 @ SV216 ) @ SV216 )
| ~ ( c_HOL_Oord__class_Oless @ SV1383 @ ( c_Nat_Osize__class_Osize @ SV850 @ ( tc_List_Olist @ SV216 ) ) @ tc_nat )
| ~ ( c_lessequals @ SV1760 @ SV1383 @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Orev @ SV850 @ SV216 ) @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4805]) ).
thf(5183,plain,
! [SV1384: $i,SV851: $i,SV217: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV217 ) @ SV851 ) @ SV1384 ) @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 )
= $true )
| ( ( ~ ( c_lessequals @ SV1384 @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 )
| ~ ( c_HOL_Oord__class_Oless @ SV851 @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV217 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4806]) ).
thf(5184,plain,
! [SV1385: $i,SV852: $i,SV218: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV218 ) @ SV852 ) @ SV1385 ) @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1385 @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
| ~ ( c_lessequals @ SV852 @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV218 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4807]) ).
thf(5185,plain,
! [SV1761: $i,SV1386: $i,SV853: $i,SV219: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV219 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV219 )
| ( c_HOL_Oord__class_Oless @ SV853 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV219 ) @ SV1386 ) @ SV1761 ) @ SV219 )
| ~ ( c_lessequals @ SV853 @ SV1761 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV1386 @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4808]) ).
thf(5186,plain,
! [SV1762: $i,SV1387: $i,SV854: $i,SV220: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV220 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV220 )
| ( c_HOL_Oord__class_Oless @ SV854 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV220 ) @ SV1387 ) @ SV1762 ) @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ SV854 @ SV1762 @ SV220 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV1387 @ SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4809]) ).
thf(5187,plain,
! [SV1388: $i,SV855: $i,SV221: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SV855 ) @ SV1388 ) @ SV221 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ SV1388 @ SV221 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ SV855 @ SV221 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV221 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4810]) ).
thf(5188,plain,
! [SV1389: $i,SV856: $i,SV222: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SV856 ) @ SV1389 ) @ SV222 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ SV1389 @ SV222 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ SV856 @ SV222 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV222 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4811]) ).
thf(5189,plain,
! [SV1763: $i,SV1390: $i,SV857: $i,SV224: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV224 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV857 @ SV1390 @ SV224 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV224 ) @ SV1390 @ SV224 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV857 @ SV1763 @ SV224 ) @ ( c_Power_Opower__class_Opower @ SV1390 @ SV1763 @ SV224 ) @ SV224 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4812]) ).
thf(5190,plain,
! [SV1767: $i,SV1394: $i,SV861: $i,SV229: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV229 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV861 @ SV1394 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1767 @ SV861 @ SV229 ) @ ( c_Power_Opower__class_Opower @ SV1767 @ SV1394 @ SV229 ) @ SV229 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV229 ) @ SV1767 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4816]) ).
thf(5191,plain,
! [SV1768: $i,SV1395: $i,SV862: $i,SV230: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV230 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV862 @ SV1395 @ SV230 ) @ ( c_Power_Opower__class_Opower @ SV862 @ SV1768 @ SV230 ) @ SV230 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV230 ) @ SV862 @ SV230 )
| ~ ( c_HOL_Oord__class_Oless @ SV1395 @ SV1768 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4817]) ).
thf(5192,plain,
! [SV1769: $i,SV1396: $i,SV863: $i,SV231: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV231 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV863 @ SV1396 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1769 @ SV863 @ SV231 ) @ ( c_Power_Opower__class_Opower @ SV1769 @ SV1396 @ SV231 ) @ SV231 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV231 ) @ SV1769 @ SV231 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4818]) ).
thf(5193,plain,
! [SV1770: $i,SV1397: $i,SV864: $i,SV232: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV232 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV864 @ SV1397 @ SV232 ) @ ( c_Power_Opower__class_Opower @ SV864 @ SV1770 @ SV232 ) @ SV232 )
| ~ ( c_HOL_Oord__class_Oless @ SV1397 @ SV1770 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV232 ) @ SV864 @ SV232 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4819]) ).
thf(5194,plain,
! [SV2015: $i,SV1949: $i,SV1771: $i,SV1398: $i,SV865: $i,SV233: $i] :
( ( ( SV233 = SV865 )
| ( SV1398 = SV1771 )
| ~ ( c_ListOrder_Ostep1 @ SV1949 @ ( c_List_Oappend @ SV233 @ ( c_List_Olist_OCons @ SV1398 @ ( c_List_Olist_ONil @ SV2015 ) @ SV2015 ) @ SV2015 ) @ ( c_List_Oappend @ SV865 @ ( c_List_Olist_OCons @ SV1771 @ ( c_List_Olist_ONil @ SV2015 ) @ SV2015 ) @ SV2015 ) @ SV2015 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4820]) ).
thf(5195,plain,
! [SV2016: $i,SV1950: $i,SV1772: $i,SV1399: $i,SV866: $i,SV234: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV234 @ SV866 ) @ SV1399 ) )
| ( SV866 = SV1399 )
| ~ ( c_ListOrder_Ostep1 @ SV234 @ ( c_List_Oappend @ SV1772 @ ( c_List_Olist_OCons @ SV866 @ ( c_List_Olist_ONil @ SV1950 ) @ SV1950 ) @ SV1950 ) @ ( c_List_Oappend @ SV2016 @ ( c_List_Olist_OCons @ SV1399 @ ( c_List_Olist_ONil @ SV1950 ) @ SV1950 ) @ SV1950 ) @ SV1950 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4821]) ).
thf(5196,plain,
! [SV2017: $i,SV1951: $i,SV1773: $i,SV1400: $i,SV867: $i,SV235: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV867 ) @ SV1400 ) )
| ( c_ListOrder_Ostep1 @ SV235 @ SV1773 @ SV1951 @ SV2017 )
| ~ ( c_ListOrder_Ostep1 @ SV235 @ ( c_List_Oappend @ SV1773 @ ( c_List_Olist_OCons @ SV867 @ ( c_List_Olist_ONil @ SV2017 ) @ SV2017 ) @ SV2017 ) @ ( c_List_Oappend @ SV1951 @ ( c_List_Olist_OCons @ SV1400 @ ( c_List_Olist_ONil @ SV2017 ) @ SV2017 ) @ SV2017 ) @ SV2017 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4822]) ).
thf(5197,plain,
! [SV2018: $i,SV1952: $i,SV1774: $i,SV1401: $i,SV868: $i,SV236: $i] :
( ( ( SV236 = SV868 )
| ( c_ListOrder_Ostep1 @ SV1401 @ SV236 @ SV868 @ SV1774 )
| ~ ( c_ListOrder_Ostep1 @ SV1401 @ ( c_List_Oappend @ SV236 @ ( c_List_Olist_OCons @ SV1952 @ ( c_List_Olist_ONil @ SV1774 ) @ SV1774 ) @ SV1774 ) @ ( c_List_Oappend @ SV868 @ ( c_List_Olist_OCons @ SV2018 @ ( c_List_Olist_ONil @ SV1774 ) @ SV1774 ) @ SV1774 ) @ SV1774 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4823]) ).
thf(5198,plain,
! [SV1953: $i,SV1775: $i,SV1402: $i,SV870: $i,SV238: $i] :
( ( ( ( c_List_OtakeWhile @ SV238 @ ( c_List_Oappend @ SV870 @ SV1402 @ SV1775 ) @ SV1775 )
= ( c_List_OtakeWhile @ SV238 @ SV870 @ SV1775 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV238 @ SV1953 ) )
| ~ ( c_in @ SV1953 @ ( c_List_Oset @ SV870 @ SV1775 ) @ SV1775 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4824]) ).
thf(5199,plain,
! [SV875: $i,SV1778: $i,SV1407: $i,SV243: $i] :
( ( ( c_in @ SV243 @ ( c_List_Oset @ ( c_List_Obutlast @ SV1407 @ SV1778 ) @ SV1778 ) @ SV1778 )
= $false )
| ( ( c_in @ SV243 @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ SV875 @ SV1407 @ SV1778 ) @ SV1778 ) @ SV1778 ) @ SV1778 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4827]) ).
thf(5200,plain,
! [SV1408: $i,SV1779: $i,SV876: $i,SV244: $i] :
( ( ( c_in @ SV244 @ ( c_List_Oset @ ( c_List_Obutlast @ SV876 @ SV1779 ) @ SV1779 ) @ SV1779 )
= $false )
| ( ( c_in @ SV244 @ ( c_List_Oset @ ( c_List_Obutlast @ ( c_List_Oappend @ SV876 @ SV1408 @ SV1779 ) @ SV1779 ) @ SV1779 ) @ SV1779 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4828]) ).
thf(5201,plain,
! [SV1954: $i,SV1780: $i,SV1409: $i,SV878: $i,SV246: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV246 @ ( c_List_Olist_Olist__size @ SV878 @ SV1409 @ SV1780 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV246 @ ( hAPP @ SV878 @ SV1954 ) @ tc_nat )
| ~ ( c_in @ SV1954 @ ( c_List_Oset @ SV1409 @ SV1780 ) @ SV1780 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4829]) ).
thf(5202,plain,
! [SV1410: $i,SV1781: $i,SV879: $i,SV247: $i] :
( ( ( hBOOL @ ( hAPP @ SV247 @ ( c_List_Onth @ SV879 @ SV1781 @ SV1410 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV247 @ ( c_List_Onth @ SV879 @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV247 @ SV1781 @ SV879 @ SV1410 ) @ SV1410 ) ) ) )
= $true )
| ( ( ( c_List_OtakeWhile @ SV247 @ SV879 @ SV1410 )
= ( c_List_Otake @ SV1781 @ SV879 @ SV1410 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4830]) ).
thf(5203,plain,
! [SV1955: $i,SV1782: $i,SV1413: $i,SV884: $i,SV252: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV252 ) )
= $true )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV884 @ ( c_List_Olinorder__class_Oinsort__key @ SV884 @ SV1413 @ SV1782 @ SV1955 @ SV252 ) @ SV1955 @ SV252 ) @ SV252 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV884 @ SV1782 @ SV1955 @ SV252 ) @ SV252 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4833]) ).
thf(5204,plain,
! [SV1956: $i,SV1783: $i,SV1414: $i,SV885: $i,SV253: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV253 ) )
= $true )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV885 @ SV1414 @ SV1783 @ SV253 ) @ SV253 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV885 @ ( c_List_Olinorder__class_Oinsort__key @ SV885 @ SV1956 @ SV1414 @ SV1783 @ SV253 ) @ SV1783 @ SV253 ) @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4834]) ).
thf(5205,plain,
! [SV1957: $i,SV1785: $i,SV1416: $i,SV889: $i,SV257: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV257 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SV889 ) @ SV1416 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SV1785 ) @ SV1957 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SV889 ) @ SV1785 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SV1416 ) @ SV1957 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4836]) ).
thf(5206,plain,
! [SV261: $i,SV1420: $i,SV893: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_OtakeWhile @ SV893 @ SV1420 @ SV261 ) @ SV261 )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ SV1420 @ SV261 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV261 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4837]) ).
thf(5207,plain,
! [SV1422: $i,SV895: $i,SV263: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV263 ) @ SV895 ) @ SV1422 ) @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1422 @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ SV895 @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV263 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4838]) ).
thf(5208,plain,
! [SV1423: $i,SV896: $i,SV264: $i,SV1786: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1786 @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ SV264 @ SV896 @ SV1423 ) @ ( tc_List_Olist @ SV1423 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Onth @ ( c_List_OtakeWhile @ SV264 @ SV896 @ SV1423 ) @ SV1786 @ SV1423 )
= ( c_List_Onth @ SV896 @ SV1786 @ SV1423 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4839]) ).
thf(5209,plain,
! [SV2019: $i,SV1958: $i,SV1787: $i,SV1425: $i,SV899: $i,SV267: $i] :
( ( ( hAPP @ ( c_COMBC @ SV267 @ SV899 @ SV1425 @ SV1787 @ SV1958 ) @ SV2019 )
= ( hAPP @ ( hAPP @ SV267 @ SV2019 ) @ SV899 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4840]) ).
thf(5210,plain,
! [SV1959: $i,SV1788: $i,SV1428: $i,SV902: $i,SV270: $i] :
( ( ( ( c_List_Onth @ ( c_List_Olist__update @ SV270 @ SV902 @ SV1428 @ SV1788 ) @ SV1959 @ SV1788 )
= ( c_List_Onth @ SV270 @ SV1959 @ SV1788 ) )
= $true )
| ( ( SV902 = SV1959 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4843]) ).
thf(5211,plain,
! [SV1789: $i,SV1429: $i,SV903: $i,SV271: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV271 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ SV903 ) @ SV1429 ) ) @ SV1789 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ SV903 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ SV1429 ) @ SV1789 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4844]) ).
thf(5212,plain,
! [SV1790: $i,SV1430: $i,SV904: $i,SV272: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV272 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV904 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV1430 ) @ SV1790 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV1430 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV904 ) @ SV1790 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4845]) ).
thf(5213,plain,
! [SV1791: $i,SV1431: $i,SV905: $i,SV273: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV273 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ SV905 ) @ SV1431 ) ) @ SV1791 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ SV905 ) @ SV1791 ) ) @ SV1431 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4846]) ).
thf(5214,plain,
! [SV1792: $i,SV1432: $i,SV906: $i,SV274: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV274 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ SV906 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ SV1432 ) @ SV1792 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ SV906 ) @ SV1432 ) ) @ SV1792 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4847]) ).
thf(5215,plain,
! [SV1793: $i,SV1433: $i,SV907: $i,SV275: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ SV275 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ SV907 ) @ SV1433 ) ) @ SV1793 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ SV907 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ SV1433 ) @ SV1793 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4848]) ).
thf(5216,plain,
! [SV1794: $i,SV1434: $i,SV908: $i,SV276: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV276 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ SV908 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ SV1434 ) @ SV1794 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ SV1434 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ SV908 ) @ SV1794 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4849]) ).
thf(5217,plain,
! [SV1795: $i,SV1435: $i,SV909: $i,SV277: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV277 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ SV909 ) @ SV1435 ) ) @ SV1795 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ SV909 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV277 ) @ SV1435 ) @ SV1795 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4850]) ).
thf(5218,plain,
! [SV1796: $i,SV1436: $i,SV910: $i,SV278: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV278 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV278 ) @ SV910 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV278 ) @ SV1436 ) @ SV1796 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV278 ) @ SV1436 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV278 ) @ SV910 ) @ SV1796 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4851]) ).
thf(5219,plain,
! [SV1797: $i,SV1437: $i,SV911: $i,SV279: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV279 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV279 ) @ SV911 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV279 ) @ SV1437 ) @ SV1797 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV279 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV279 ) @ SV911 ) @ SV1437 ) ) @ SV1797 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4852]) ).
thf(5220,plain,
! [SV1438: $i,SV912: $i,SV280: $i,SV1798: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1798 @ SV280 @ tc_nat )
= $false )
| ( ( ( c_List_Onth @ ( c_List_Otake @ SV280 @ SV912 @ SV1438 ) @ SV1798 @ SV1438 )
= ( c_List_Onth @ SV912 @ SV1798 @ SV1438 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4853]) ).
thf(5221,plain,
! [SV1799: $i,SV1439: $i,SV913: $i,SV281: $i] :
( ( ( class_Orderings_Oorder @ SV281 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV913 @ SV1439 @ SV281 )
| ~ ( c_HOL_Oord__class_Oless @ SV913 @ SV1799 @ SV281 )
| ~ ( c_HOL_Oord__class_Oless @ SV1799 @ SV1439 @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4854]) ).
thf(5222,plain,
! [SV1800: $i,SV1440: $i,SV914: $i,SV282: $i] :
( ( ( class_Orderings_Opreorder @ SV282 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV914 @ SV1440 @ SV282 )
| ~ ( c_HOL_Oord__class_Oless @ SV1800 @ SV1440 @ SV282 )
| ~ ( c_HOL_Oord__class_Oless @ SV914 @ SV1800 @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4855]) ).
thf(5223,plain,
! [SV284: $i,SV1442: $i,SV916: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ SV916 @ SV1442 @ SV284 ) @ SV284 )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ SV1442 @ SV284 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV284 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4857]) ).
thf(5224,plain,
! [SV1444: $i,SV1802: $i,SV918: $i,SV286: $i] :
( ( ( c_List_Olistsp @ SV286 @ ( c_List_Oappend @ SV918 @ SV1802 @ SV1444 ) @ SV1444 )
= $false )
| ( ( c_List_Olistsp @ SV286 @ SV918 @ SV1444 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4859]) ).
thf(5225,plain,
! [SV1445: $i,SV919: $i,SV1803: $i,SV287: $i] :
( ( ( c_List_Olistsp @ SV287 @ ( c_List_Oappend @ SV1803 @ SV919 @ SV1445 ) @ SV1445 )
= $false )
| ( ( c_List_Olistsp @ SV287 @ SV919 @ SV1445 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4860]) ).
thf(5226,plain,
! [SV1447: $i,SV921: $i,SV1805: $i,SV289: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV289 ) @ SV1805 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV289 ) @ SV921 ) @ SV1447 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1805 ) @ SV921 ) @ SV1447 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4862]) ).
thf(5227,plain,
! [SV1449: $i,SV1806: $i,SV291: $i,SV923: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV923 @ ( c_Nat_Osize__class_Osize @ SV291 @ ( tc_List_Olist @ SV1806 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Olist__update @ SV291 @ SV923 @ SV1449 @ SV1806 )
= ( c_List_Oappend @ ( c_List_Otake @ SV923 @ SV291 @ SV1806 ) @ ( c_List_Olist_OCons @ SV1449 @ ( c_List_Odrop @ ( c_Suc @ SV923 ) @ SV291 @ SV1806 ) @ SV1806 ) @ SV1806 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4864]) ).
thf(5228,plain,
! [SV296: $i,SV1454: $i,SV928: $i,SV1808: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1808 @ ( c_Nat_Osize__class_Osize @ SV928 @ ( tc_List_Olist @ SV1454 ) ) @ tc_nat )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV296 @ ( c_List_Onth @ SV928 @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV296 @ SV1808 @ SV928 @ SV1454 ) @ SV1454 ) ) ) )
= $true )
| ( ( ( c_List_OtakeWhile @ SV296 @ SV928 @ SV1454 )
= ( c_List_Otake @ SV1808 @ SV928 @ SV1454 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4868]) ).
thf(5229,plain,
! [SV1455: $i,SV1809: $i,SV929: $i,SV297: $i] :
( ( ( hBOOL @ ( hAPP @ SV297 @ ( c_List_Onth @ SV929 @ SV1809 @ SV1455 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV297 @ SV1809 @ SV929 @ SV1455 ) @ ( c_Nat_Osize__class_Osize @ SV929 @ ( tc_List_Olist @ SV1455 ) ) @ tc_nat )
= $true )
| ( ( ( c_List_OtakeWhile @ SV297 @ SV929 @ SV1455 )
= ( c_List_Otake @ SV1809 @ SV929 @ SV1455 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4869]) ).
thf(5230,plain,
! [SV1456: $i,SV930: $i,SV298: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV298 @ ( c_Nat_Osize__class_Osize @ SV930 @ ( tc_List_Olist @ SV1456 ) ) @ tc_nat )
= $false )
| ( ( SV930
= ( c_List_Olist_ONil @ SV1456 ) )
= $true )
| ( ( ( c_List_Ohd @ ( c_List_Odrop @ SV298 @ SV930 @ SV1456 ) @ SV1456 )
= ( c_List_Onth @ SV930 @ SV298 @ SV1456 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4870]) ).
thf(5231,plain,
! [SV1810: $i,SV1458: $i,SV932: $i,SV300: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV300 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV932 @ SV1458 @ SV300 ) @ ( c_Power_Opower__class_Opower @ SV1810 @ SV1458 @ SV300 ) @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1458 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SV932 @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ SV932 @ SV1810 @ SV300 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4872]) ).
thf(5232,plain,
! [SV1461: $i,SV1811: $i,SV935: $i,SV303: $i] :
( ( ( hBOOL @ ( hAPP @ SV303 @ ( c_List_Onth @ SV935 @ SV1811 @ SV1461 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV303 @ SV1811 @ SV935 @ SV1461 ) @ SV1811 @ tc_nat )
= $true )
| ( ( ( c_List_OtakeWhile @ SV303 @ SV935 @ SV1461 )
= ( c_List_Otake @ SV1811 @ SV935 @ SV1461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4873]) ).
thf(5233,plain,
! [SV304: $i,SV1462: $i,SV936: $i,SV1812: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1812 @ ( c_Nat_Osize__class_Osize @ SV936 @ ( tc_List_Olist @ SV1462 ) ) @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV304 @ SV1812 @ SV936 @ SV1462 ) @ ( c_Nat_Osize__class_Osize @ SV936 @ ( tc_List_Olist @ SV1462 ) ) @ tc_nat )
= $true )
| ( ( ( c_List_OtakeWhile @ SV304 @ SV936 @ SV1462 )
= ( c_List_Otake @ SV1812 @ SV936 @ SV1462 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4874]) ).
thf(5234,plain,
! [SV305: $i,SV1463: $i,SV937: $i,SV1813: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1813 @ ( c_Nat_Osize__class_Osize @ SV937 @ ( tc_List_Olist @ SV1463 ) ) @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV305 @ SV1813 @ SV937 @ SV1463 ) @ SV1813 @ tc_nat )
= $true )
| ( ( ( c_List_OtakeWhile @ SV305 @ SV937 @ SV1463 )
= ( c_List_Otake @ SV1813 @ SV937 @ SV1463 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4875]) ).
thf(5235,plain,
! [SV1962: $i,SV1814: $i,SV1464: $i,SV938: $i,SV306: $i] :
( ( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV306 @ SV938 @ SV1464 ) @ SV1814 @ SV1962 @ SV1464 )
= ( c_List_Oappend @ SV306 @ ( c_List_Olist__update @ SV938 @ ( c_HOL_Ominus__class_Ominus @ SV1814 @ ( c_Nat_Osize__class_Osize @ SV306 @ ( tc_List_Olist @ SV1464 ) ) @ tc_nat ) @ SV1962 @ SV1464 ) @ SV1464 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1814 @ ( c_Nat_Osize__class_Osize @ SV306 @ ( tc_List_Olist @ SV1464 ) ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4876]) ).
thf(5236,plain,
! [SV308: $i,SV1816: $i,SV940: $i,SV1466: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1466 @ ( c_Nat_Osize__class_Osize @ SV940 @ ( tc_List_Olist @ SV1816 ) ) @ tc_nat )
= $false )
| ( ( c_in @ SV308 @ ( c_List_Oset @ ( c_List_Olist__update @ SV940 @ SV1466 @ SV308 @ SV1816 ) @ SV1816 ) @ SV1816 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4878]) ).
thf(5237,plain,
! [SV1469: $i,SV943: $i,SV311: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV311 ) @ ( c_Power_Opower__class_Opower @ SV943 @ SV1469 @ SV311 ) @ SV311 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1469 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV311 ) @ SV943 @ SV311 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV311 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4881]) ).
thf(5238,plain,
! [SV1817: $i,SV1471: $i,SV945: $i,SV313: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV313 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV945 @ SV1471 @ SV313 ) @ ( c_Power_Opower__class_Opower @ SV945 @ SV1817 @ SV313 ) @ SV313 )
| ~ ( c_HOL_Oord__class_Oless @ SV945 @ ( c_HOL_Oone__class_Oone @ SV313 ) @ SV313 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV313 ) @ SV945 @ SV313 )
| ~ ( c_HOL_Oord__class_Oless @ SV1817 @ SV1471 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4883]) ).
thf(5239,plain,
! [SV2020: $i,SV1963: $i,SV1818: $i,SV1472: $i,SV946: $i,SV314: $i] :
( ( ( c_List_Omap @ SV314 @ ( c_List_Olist__update @ SV946 @ SV1472 @ SV1818 @ SV1963 ) @ SV1963 @ SV2020 )
= ( c_List_Olist__update @ ( c_List_Omap @ SV314 @ SV946 @ SV1963 @ SV2020 ) @ SV1472 @ ( hAPP @ SV314 @ SV1818 ) @ SV2020 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4884]) ).
thf(5240,plain,
! [SV949: $i,SV317: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV317 ) @ SV949 ) @ SV949 ) @ SV317 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV317 ) @ SV949 @ SV317 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV317 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4885]) ).
thf(5241,plain,
! [SV950: $i,SV318: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ SV950 @ SV318 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV318 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV318 ) @ SV950 ) @ SV950 ) @ SV318 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV318 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4886]) ).
thf(5242,plain,
! [SV953: $i,SV322: $i] :
( ( ( class_Int_Onumber__ring @ SV322 )
= $false )
| ( ( SV953
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV322 ) @ SV953 ) @ ( c_HOL_Ozero__class_Ozero @ SV322 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV322 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4887]) ).
thf(5243,plain,
! [SV1820: $i,SV1476: $i,SV962: $i,SV334: $i] :
( ( ( class_Orderings_Olinorder @ SV334 )
= $false )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV962 @ SV1476 @ SV334 ) @ SV334 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1820 @ ( c_List_Olist_OCons @ SV962 @ SV1476 @ SV334 ) @ SV334 ) @ SV334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4889]) ).
thf(5244,plain,
! [SV1484: $i,SV342: $i,SV970: $i] :
( ( ( c_List_Olinorder__class_Osorted @ SV970 @ SV342 )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1484 @ SV970 @ SV342 ) @ SV342 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV342 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4893]) ).
thf(5245,plain,
! [SV1828: $i,SV1485: $i,SV971: $i,SV343: $i] :
( ( ( hBOOL @ ( hAPP @ SV343 @ SV971 ) )
= $false )
| ( ( ( c_List_OtakeWhile @ SV343 @ ( c_List_Olist_OCons @ SV971 @ SV1485 @ SV1828 ) @ SV1828 )
= ( c_List_Olist_OCons @ SV971 @ ( c_List_OtakeWhile @ SV343 @ SV1485 @ SV1828 ) @ SV1828 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4894]) ).
thf(5246,plain,
! [SV2021: $i,SV1968: $i,SV1830: $i,SV1497: $i,SV997: $i,SV376: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV376 @ ( c_Lambda_OdB_OdB__case @ SV997 @ SV1497 @ SV1830 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1968 ) @ SV2021 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SV1497 @ SV1968 ) @ SV2021 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4895]) ).
thf(5247,plain,
! [SV2022: $i,SV1969: $i,SV1831: $i,SV1498: $i,SV998: $i,SV377: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV377 @ ( c_Lambda_OdB_OdB__case @ SV998 @ SV1498 @ SV1831 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1969 ) @ SV2022 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV377 @ ( hAPP @ ( hAPP @ SV1498 @ SV1969 ) @ SV2022 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4896]) ).
thf(5248,plain,
! [SV2023: $i,SV1970: $i,SV1832: $i,SV1499: $i,SV999: $i,SV378: $i] :
( ( ( c_Lambda_OdB_OdB__case @ SV378 @ SV999 @ SV1499 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1832 ) @ SV1970 ) @ SV2023 )
= ( hAPP @ ( hAPP @ SV999 @ SV1832 ) @ SV1970 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4897]) ).
thf(5249,plain,
! [SV1833: $i,SV1502: $i,SV1002: $i,SV381: $i] :
( ( ( class_OrderedGroup_Osemigroup__add @ SV381 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV1002 ) @ SV1502 ) @ SV1833 @ SV381 @ SV381 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV1002 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV381 ) @ SV1502 @ SV1833 @ SV381 @ SV381 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4900]) ).
thf(5250,plain,
! [SV2024: $i,SV1971: $i,SV1834: $i,SV1503: $i,SV1003: $i,SV382: $i] :
( ( ( c_List_Ofoldl @ SV382 @ SV1003 @ ( c_List_Oappend @ SV1503 @ SV1834 @ SV1971 ) @ SV2024 @ SV1971 )
= ( c_List_Ofoldl @ SV382 @ ( c_List_Ofoldl @ SV382 @ SV1003 @ SV1503 @ SV2024 @ SV1971 ) @ SV1834 @ SV2024 @ SV1971 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4901]) ).
thf(5251,plain,
! [SV1972: $i,SV1835: $i,SV1504: $i,SV1004: $i,SV383: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV383 @ ( c_Lambda_OdB_OdB__case @ SV1004 @ SV1504 @ SV1835 @ ( c_Lambda_OdB_OVar @ SV1972 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV383 @ ( hAPP @ SV1004 @ SV1972 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4902]) ).
thf(5252,plain,
! [SV1973: $i,SV1836: $i,SV1505: $i,SV1005: $i,SV384: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV384 @ ( c_Lambda_OdB_OdB__case @ SV1005 @ SV1505 @ SV1836 @ ( c_Lambda_OdB_OVar @ SV1973 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV384 @ ( hAPP @ SV1005 @ SV1973 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4903]) ).
thf(5253,plain,
! [SV388: $i,SV1507: $i,SV1009: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ SV1009 @ SV1507 @ SV388 ) @ SV388 )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ SV1507 @ SV388 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV388 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4904]) ).
thf(5254,plain,
! [SV1510: $i,SV1012: $i,SV391: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ SV391 @ SV1012 @ SV1510 ) @ ( tc_List_Olist @ SV1510 ) ) @ ( c_Nat_Osize__class_Osize @ SV1012 @ ( tc_List_Olist @ SV1510 ) ) @ tc_nat )
= $false )
| ( ( hBOOL @ ( hAPP @ SV391 @ ( c_List_Onth @ SV1012 @ ( c_Nat_Osize__class_Osize @ ( c_List_OtakeWhile @ SV391 @ SV1012 @ SV1510 ) @ ( tc_List_Olist @ SV1510 ) ) @ SV1510 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4905]) ).
thf(5255,plain,
! [SV1020: $i,SV1514: $i,SV399: $i,SV1841: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1841 @ ( c_Nat_Osize__class_Osize @ SV399 @ ( tc_List_Olist @ SV1514 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Onth @ ( c_List_Oappend @ SV399 @ SV1020 @ SV1514 ) @ SV1841 @ SV1514 )
= ( c_List_Onth @ SV399 @ SV1841 @ SV1514 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4907]) ).
thf(5256,plain,
! [SV404: $i,SV1025: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1025 @ ( c_HOL_Ozero__class_Ozero @ SV404 ) @ SV404 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV404 ) @ SV1025 ) @ SV1025 ) @ ( c_HOL_Ozero__class_Ozero @ SV404 ) @ SV404 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV404 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4911]) ).
thf(5257,plain,
! [SV1026: $i,SV405: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV405 ) @ SV1026 ) @ SV1026 ) @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SV405 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1026 @ ( c_HOL_Ozero__class_Ozero @ SV405 ) @ SV405 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV405 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4912]) ).
thf(5258,plain,
! [SV1027: $i,SV406: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV406 ) @ SV1027 ) @ SV1027 ) @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV406 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1027 @ ( c_HOL_Ozero__class_Ozero @ SV406 ) @ SV406 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV406 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4913]) ).
thf(5259,plain,
! [SV407: $i,SV1028: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1028 @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV407 ) @ SV1028 ) @ SV1028 ) @ ( c_HOL_Ozero__class_Ozero @ SV407 ) @ SV407 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV407 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4914]) ).
thf(5260,plain,
! [SV1842: $i,SV1519: $i,SV1029: $i,SV408: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV408 @ ( c_Nat_Osize__class_Osize @ SV1029 @ ( tc_List_Olist @ SV1519 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Onth @ ( c_List_Olist__update @ SV1029 @ SV408 @ SV1842 @ SV1519 ) @ SV408 @ SV1519 )
= SV1842 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4915]) ).
thf(5261,plain,
! [SV1520: $i,SV1843: $i,SV409: $i,SV1030: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1030 @ ( c_Nat_Osize__class_Osize @ SV409 @ ( tc_List_Olist @ SV1843 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Onth @ ( c_List_Olist__update @ SV409 @ SV1030 @ SV1520 @ SV1843 ) @ SV1030 @ SV1843 )
= SV1520 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4916]) ).
thf(5262,plain,
! [SV1521: $i,SV1031: $i,SV410: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV410 ) @ ( c_Power_Opower__class_Opower @ SV1031 @ SV1521 @ SV410 ) @ SV410 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV410 ) @ SV1031 @ SV410 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV410 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4917]) ).
thf(5263,plain,
! [SV1975: $i,SV1844: $i,SV1524: $i,SV1034: $i,SV413: $i] :
( ( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV413 @ SV1034 @ SV1524 ) @ SV1844 @ SV1975 @ SV1524 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV413 @ SV1844 @ SV1975 @ SV1524 ) @ SV1034 @ SV1524 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1844 @ ( c_Nat_Osize__class_Osize @ SV413 @ ( tc_List_Olist @ SV1524 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4920]) ).
thf(5264,plain,
! [SV1976: $i,SV1845: $i,SV1525: $i,SV1035: $i,SV414: $i] :
( ( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV414 @ SV1035 @ SV1525 ) @ SV1845 @ SV1976 @ SV1525 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV414 @ SV1845 @ SV1976 @ SV1525 ) @ SV1035 @ SV1525 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1845 @ ( c_Nat_Osize__class_Osize @ SV414 @ ( tc_List_Olist @ SV1525 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4921]) ).
thf(5265,plain,
! [SV1526: $i,SV1036: $i,SV415: $i,SV1846: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1846 @ SV415 @ tc_nat )
= $false )
| ( ( ( c_List_Onth @ ( c_List_Oreplicate @ SV415 @ SV1036 @ SV1526 ) @ SV1846 @ SV1526 )
= SV1036 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4922]) ).
thf(5266,plain,
! [SV1977: $i,SV1847: $i,SV1527: $i,SV1037: $i,SV416: $i] :
( ( ( ( c_List_OtakeWhile @ SV416 @ ( c_List_Oappend @ SV1037 @ ( c_List_Olist_OCons @ SV1527 @ SV1847 @ SV1977 ) @ SV1977 ) @ SV1977 )
= ( c_List_OtakeWhile @ SV416 @ SV1037 @ SV1977 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV416 @ SV1527 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4923]) ).
thf(5267,plain,
! [SV1529: $i,SV1043: $i,SV424: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SV1043 ) @ SV1529 ) @ SV424 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV1529 @ SV424 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV1043 @ SV424 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV424 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4927]) ).
thf(5268,plain,
! [SV427: $i,SV1532: $i,SV1046: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1046 @ SV1532 @ SV427 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1532 @ SV1046 @ SV427 )
| ( SV1532 = SV1046 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV427 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4930]) ).
thf(5269,plain,
! [SV428: $i,SV1533: $i,SV1047: $i] :
( ( ( SV1047 = SV1533 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1533 @ SV1047 @ SV428 )
| ( c_HOL_Oord__class_Oless @ SV1047 @ SV1533 @ SV428 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV428 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4931]) ).
thf(5270,plain,
! [SV430: $i,SV1049: $i,SV1534: $i] :
( ( ( SV1534 = SV1049 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1534 @ SV1049 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1049 @ SV1534 @ tc_nat )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV430 @ SV1049 ) @ SV1534 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4932]) ).
thf(5271,plain,
! [SV432: $i,SV1535: $i,SV1051: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1051 @ SV1535 @ SV432 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1535 @ SV1051 @ SV432 )
| ( SV1535 = SV1051 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV432 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4933]) ).
thf(5272,plain,
! [SV434: $i,SV1537: $i,SV1053: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1053 @ SV1537 @ SV434 )
= $true )
| ( ( ( SV1537 = SV1053 )
| ( c_HOL_Oord__class_Oless @ SV1537 @ SV1053 @ SV434 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV434 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4934]) ).
thf(5273,plain,
! [SV435: $i,SV1538: $i,SV1054: $i] :
( ( ( SV1054 = SV1538 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1054 @ SV1538 @ SV435 )
| ( c_HOL_Oord__class_Oless @ SV1538 @ SV1054 @ SV435 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV435 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4935]) ).
thf(5274,plain,
! [SV1979: $i,SV1850: $i,SV1539: $i,SV1055: $i,SV436: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV436 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV436 ) @ SV1055 ) @ SV1539 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV436 ) @ SV1850 ) @ SV1979 ) @ SV436 )
| ~ ( c_HOL_Oord__class_Oless @ SV1539 @ SV1979 @ SV436 )
| ~ ( c_HOL_Oord__class_Oless @ SV1055 @ SV1850 @ SV436 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4936]) ).
thf(5275,plain,
! [SV1980: $i,SV1851: $i,SV1540: $i,SV1056: $i,SV437: $i] :
( ( ( ( c_List_Onth @ ( c_List_Omap @ SV437 @ SV1056 @ SV1540 @ SV1851 ) @ SV1980 @ SV1851 )
= ( hAPP @ SV437 @ ( c_List_Onth @ SV1056 @ SV1980 @ SV1540 ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1980 @ ( c_Nat_Osize__class_Osize @ SV1056 @ ( tc_List_Olist @ SV1540 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4937]) ).
thf(5276,plain,
! [SV1541: $i,SV438: $i,SV1057: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1057 @ SV438 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1541 @ SV438 ) @ SV438 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1057 @ SV1541 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV438 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4938]) ).
thf(5277,plain,
! [SV439: $i,SV1542: $i,SV1058: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1058 @ SV1542 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1058 @ SV439 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1542 @ SV439 ) @ SV439 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV439 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4939]) ).
thf(5278,plain,
! [SV440: $i,SV1059: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1059 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV440 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1059 @ SV440 ) @ SV440 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV440 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4940]) ).
thf(5279,plain,
! [SV1060: $i,SV441: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV441 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1060 @ SV441 ) @ SV441 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1060 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV441 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4941]) ).
thf(5280,plain,
! [SV1063: $i,SV1852: $i,SV1543: $i,SV444: $i] :
( ( ( ~ ( c_List_Olistsp @ SV444 @ SV1543 @ SV1852 ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV444 @ SV1063 @ SV1852 ) )
= $true )
| ( ( c_List_Olistsp @ SV444 @ ( c_List_Oappend @ SV1063 @ SV1543 @ SV1852 ) @ SV1852 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4942]) ).
thf(5281,plain,
! [SV1853: $i,SV1546: $i,SV1066: $i,SV447: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV447 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1066 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV447 ) @ SV1546 ) @ SV1853 ) @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ SV1066 @ SV1853 @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV1546 @ SV447 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4943]) ).
thf(5282,plain,
! [SV1981: $i,SV1854: $i,SV1548: $i,SV1068: $i,SV449: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV449 @ ( c_Lambda_OdB_OdB__case @ SV1068 @ SV1548 @ SV1854 @ ( c_Lambda_OdB_OAbs @ SV1981 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV449 @ ( hAPP @ SV1854 @ SV1981 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4945]) ).
thf(5283,plain,
! [SV1982: $i,SV1855: $i,SV1549: $i,SV1069: $i,SV450: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV450 @ ( c_Lambda_OdB_OdB__case @ SV1069 @ SV1549 @ SV1855 @ ( c_Lambda_OdB_OAbs @ SV1982 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV450 @ ( hAPP @ SV1855 @ SV1982 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4946]) ).
thf(5284,plain,
! [SV1857: $i,SV1551: $i,SV1071: $i,SV452: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV452 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV452 ) @ SV1071 ) @ SV1551 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV452 ) @ SV1857 ) @ SV1551 ) @ SV452 )
| ~ ( c_HOL_Oord__class_Oless @ SV1071 @ SV1857 @ SV452 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4948]) ).
thf(5285,plain,
! [SV1858: $i,SV1552: $i,SV1072: $i,SV453: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV453 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV453 ) @ SV1072 ) @ SV1552 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV453 ) @ SV1858 ) @ SV1552 ) @ SV453 )
| ~ ( c_HOL_Oord__class_Oless @ SV1072 @ SV1858 @ SV453 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4949]) ).
thf(5286,plain,
! [SV1859: $i,SV1553: $i,SV1073: $i,SV454: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV454 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1073 @ SV1553 @ SV454 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV454 ) @ SV1073 ) @ SV1859 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV454 ) @ SV1553 ) @ SV1859 ) @ SV454 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4950]) ).
thf(5287,plain,
! [SV1860: $i,SV1554: $i,SV1074: $i,SV455: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV455 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV455 ) @ SV1074 ) @ SV1554 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV455 ) @ SV1074 ) @ SV1860 ) @ SV455 )
| ~ ( c_HOL_Oord__class_Oless @ SV1554 @ SV1860 @ SV455 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4951]) ).
thf(5288,plain,
! [SV1861: $i,SV1555: $i,SV1075: $i,SV456: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV456 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV456 ) @ SV1075 ) @ SV1555 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV456 ) @ SV1075 ) @ SV1861 ) @ SV456 )
| ~ ( c_HOL_Oord__class_Oless @ SV1555 @ SV1861 @ SV456 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4952]) ).
thf(5289,plain,
! [SV1862: $i,SV1556: $i,SV1076: $i,SV457: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV457 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1076 @ SV1556 @ SV457 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV1862 ) @ SV1076 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV1862 ) @ SV1556 ) @ SV457 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4953]) ).
thf(5290,plain,
! [SV1557: $i,SV458: $i,SV1077: $i,SV1863: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1863 ) @ SV1077 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV458 @ SV1863 @ SV1557 ) )
= $true )
| ( ( c_Type_Otyping @ SV458 @ SV1077 @ SV1557 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4954]) ).
thf(5291,plain,
! [SV1558: $i,SV459: $i,SV1078: $i] :
( ( ( c_List_Olinorder__class_Osorted @ SV1078 @ SV459 )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1078 @ SV1558 @ SV459 ) @ SV459 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV459 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4955]) ).
thf(5292,plain,
! [SV1559: $i,SV460: $i,SV1079: $i] :
( ( ( c_List_Olinorder__class_Osorted @ SV1079 @ SV460 )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1559 @ SV1079 @ SV460 ) @ SV460 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV460 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4956]) ).
thf(5293,plain,
! [SV2025: $i,SV1984: $i,SV1864: $i,SV1560: $i,SV1080: $i,SV461: $i] :
( ( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV461 @ SV1080 @ SV1560 @ SV1864 ) @ SV1984 @ SV2025 @ SV1864 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV461 @ SV1984 @ SV2025 @ SV1864 ) @ SV1080 @ SV1560 @ SV1864 ) )
| ( SV1080 = SV1984 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4957]) ).
thf(5294,plain,
! [SV1986: $i,SV1867: $i,SV1565: $i,SV1086: $i,SV467: $i] :
( ( ( ( c_List_Onth @ ( c_List_Olist__update @ SV467 @ SV1086 @ SV1565 @ SV1867 ) @ SV1986 @ SV1867 )
= ( c_List_Onth @ SV467 @ SV1986 @ SV1867 ) )
= $true )
| ( ( ( SV1086 = SV1986 )
| ~ ( c_HOL_Oord__class_Oless @ SV1086 @ ( c_Nat_Osize__class_Osize @ SV467 @ ( tc_List_Olist @ SV1867 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4960]) ).
thf(5295,plain,
! [SV473: $i,SV1571: $i,SV1092: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1092 @ SV1571 @ SV473 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1571 @ SV1092 @ SV473 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV473 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4962]) ).
thf(5296,plain,
! [SV474: $i,SV1572: $i,SV1093: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1093 @ SV1572 @ SV474 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1572 @ SV1093 @ SV474 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV474 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4963]) ).
thf(5297,plain,
! [SV475: $i,SV1573: $i,SV1094: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1094 @ SV1573 @ SV475 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1573 @ SV1094 @ SV475 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV475 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4964]) ).
thf(5298,plain,
! [SV476: $i,SV1574: $i,SV1095: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1095 @ SV1574 @ SV476 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1574 @ SV1095 @ SV476 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV476 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4965]) ).
thf(5299,plain,
! [SV1105: $i,SV488: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV488 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV488 )
| ~ ( class_Power_Opower @ SV488 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV488 ) @ SV1105 @ SV488 )
= ( c_HOL_Ozero__class_Ozero @ SV488 ) )
| ( SV1105
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV488 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4971]) ).
thf(5300,plain,
! [SV1106: $i,SV489: $i] :
( ( ( class_Power_Opower @ SV489 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV1106 @ SV489 )
= ( c_HOL_Ozero__class_Ozero @ SV489 ) )
| ( SV1106
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV489 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4972]) ).
thf(5301,plain,
! [SV1875: $i,SV1587: $i,SV1116: $i,SV503: $i] :
( ( ( class_Orderings_Olinorder @ SV503 )
= $false )
| ( ( ( c_List_Olinorder__class_Oinsort__key @ SV1116 @ SV1587 @ ( c_List_Olist_ONil @ SV1875 ) @ SV1875 @ SV503 )
= ( c_List_Olist_OCons @ SV1587 @ ( c_List_Olist_ONil @ SV1875 ) @ SV1875 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4973]) ).
thf(5302,plain,
! [SV1595: $i,SV518: $i,SV1129: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1129 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV518 ) @ SV1129 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1595 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV518 ) ) @ SV1129 ) @ SV1595 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4977]) ).
thf(5303,plain,
! [SV1989: $i,SV1877: $i,SV1598: $i,SV1133: $i,SV522: $i] :
( ( ( SV522 = SV1133 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV1598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1877 ) @ SV1989 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1133 )
| ~ ( c_Type_Otyping @ SV1598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1877 ) @ SV1989 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV522 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4979]) ).
thf(5304,plain,
! [SV2026: $i,SV1990: $i,SV1879: $i,SV1603: $i,SV1141: $i,SV534: $i] :
( ( ( c_List_Ofoldl @ SV534 @ SV1141 @ ( c_List_Olist_OCons @ SV1603 @ SV1879 @ SV1990 ) @ SV2026 @ SV1990 )
= ( c_List_Ofoldl @ SV534 @ ( hAPP @ ( hAPP @ SV534 @ SV1141 ) @ SV1603 ) @ SV1879 @ SV2026 @ SV1990 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4980]) ).
thf(5305,plain,
! [SV1991: $i,SV1880: $i,SV1605: $i,SV1148: $i,SV541: $i] :
( ( ( ( c_List_Oreplicate @ SV541 @ SV1148 @ SV1605 )
!= ( c_List_Oreplicate @ SV1880 @ SV1991 @ SV1605 ) )
= $true )
| ( ( SV541 = SV1880 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4982]) ).
thf(5306,plain,
! [SV1881: $i,SV1607: $i,SV1150: $i,SV543: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV543 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV543 ) @ SV1150 ) @ SV1607 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV543 ) @ SV1881 ) @ SV1607 ) )
| ( SV1150 = SV1881 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4984]) ).
thf(5307,plain,
! [SV1992: $i,SV1882: $i,SV1612: $i,SV1157: $i,SV550: $i] :
( ( ( ( c_List_Oappend @ SV550 @ ( c_List_Olist_OCons @ SV1157 @ ( c_List_Olist_ONil @ SV1612 ) @ SV1612 ) @ SV1612 )
!= ( c_List_Oappend @ SV1882 @ ( c_List_Olist_OCons @ SV1992 @ ( c_List_Olist_ONil @ SV1612 ) @ SV1612 ) @ SV1612 ) )
= $true )
| ( ( SV550 = SV1882 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4988]) ).
thf(5308,plain,
! [SV1883: $i,SV1614: $i,SV1159: $i,SV552: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV552 ) @ SV1159 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1614 @ SV1883 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( SV1883
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV552 @ SV1159 @ SV1614 @ SV1883 ) @ ( c_List_Olist_OCons @ SV1159 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
| ( SV1883
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4990]) ).
thf(5309,plain,
! [SV1884: $i,SV1615: $i,SV1160: $i,SV553: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV553 ) @ SV1160 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1615 ) @ SV1884 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV553 = SV1615 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4991]) ).
thf(5310,plain,
! [SV1885: $i,SV1616: $i,SV1161: $i,SV554: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV554 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1161 @ SV1616 @ SV554 )
!= ( c_Power_Opower__class_Opower @ SV1885 @ SV1616 @ SV554 ) )
| ( SV1161 = SV1885 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1616 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SV1885 @ SV554 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SV1161 @ SV554 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4992]) ).
thf(5311,plain,
! [SV1886: $i,SV1618: $i,SV1164: $i,SV558: $i] :
( ( ( ( c_List_Oappend @ SV558 @ SV1164 @ SV1618 )
= ( c_List_Oappend @ SV558 @ SV1886 @ SV1618 ) )
= $false )
| ( ( SV1164 = SV1886 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4993]) ).
thf(5312,plain,
! [SV1887: $i,SV1619: $i,SV1165: $i,SV559: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV559 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1165 @ SV1619 @ SV559 )
!= ( c_HOL_Ominus__class_Ominus @ SV1887 @ SV1887 @ SV559 ) )
| ( SV1165 = SV1619 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4994]) ).
thf(5313,plain,
! [SV1888: $i,SV1620: $i,SV1166: $i,SV560: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV560 @ ( tc_List_Olist @ SV1166 ) ) @ SV1620 @ SV1166 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1620 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) @ SV1888 @ SV1166 ) @ SV1166 )
= SV1888 )
= $false )
| ( ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV560 @ ( tc_List_Olist @ SV1166 ) ) @ SV1620 @ SV1166 )
!= SV560 )
| ( SV1620
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV1620 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) )
| ( ( c_List_Oappend @ SV1620 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1620 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) @ SV1888 @ SV1166 ) @ SV1166 )
= ( c_List_Oappend @ SV560 @ SV1888 @ SV1166 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4995]) ).
thf(5314,plain,
! [SV562: $i,SV1621: $i,SV1168: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1168 @ SV1621 @ SV562 )
!= ( c_HOL_Ozero__class_Ozero @ SV562 ) )
= $true )
| ( ( SV1168 = SV1621 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV562 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4996]) ).
thf(5315,plain,
! [SV1889: $i,SV1623: $i,SV1170: $i,SV564: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV564 ) @ SV1170 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1623 ) @ SV1889 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV1170 = SV1889 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4998]) ).
thf(5316,plain,
! [SV1890: $i,SV1627: $i,SV1174: $i,SV569: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV569 ) @ SV1174 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1627 ) @ SV1890 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV569 = SV1627 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5000]) ).
thf(5317,plain,
! [SV1891: $i,SV1628: $i,SV1175: $i,SV570: $i] :
( ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV570 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV570 ) @ SV1175 ) @ SV1628 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV570 ) @ SV1175 ) @ SV1891 ) )
| ( SV1628 = SV1891 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5001]) ).
thf(5318,plain,
! [SV1892: $i,SV1630: $i,SV1177: $i,SV572: $i] :
( ( ( ( c_List_Oappend @ SV572 @ SV1177 @ SV1630 )
= ( c_List_Oappend @ SV1892 @ SV1177 @ SV1630 ) )
= $false )
| ( ( SV572 = SV1892 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5002]) ).
thf(5319,plain,
! [SV1993: $i,SV1893: $i,SV1631: $i,SV1178: $i,SV573: $i] :
( ( ( ( c_List_Oappend @ SV573 @ ( c_List_Olist_OCons @ SV1178 @ ( c_List_Olist_ONil @ SV1631 ) @ SV1631 ) @ SV1631 )
!= ( c_List_Oappend @ SV1893 @ ( c_List_Olist_OCons @ SV1993 @ ( c_List_Olist_ONil @ SV1631 ) @ SV1631 ) @ SV1631 ) )
= $true )
| ( ( SV1178 = SV1993 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5003]) ).
thf(5320,plain,
! [SV1994: $i,SV1894: $i,SV1632: $i,SV1179: $i,SV574: $i] :
( ( ( ( c_List_Oappend @ SV574 @ SV1179 @ SV1632 )
!= ( c_List_Oappend @ SV1894 @ SV1994 @ SV1632 ) )
= $true )
| ( ( ( SV1179
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV574 @ ( tc_List_Olist @ SV1632 ) ) @ SV1894 @ SV1632 ) @ SV1994 @ SV1632 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV574 @ ( tc_List_Olist @ SV1632 ) ) @ ( c_Nat_Osize__class_Osize @ SV1894 @ ( tc_List_Olist @ SV1632 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5004]) ).
thf(5321,plain,
! [SV1895: $i,SV1634: $i,SV1181: $i,SV576: $i] :
( ( ( ( c_List_Orev @ SV576 @ SV1181 )
= ( c_List_Olist_OCons @ SV1634 @ SV1895 @ SV1181 ) )
= $false )
| ( ( SV576
= ( c_List_Oappend @ ( c_List_Orev @ SV1895 @ SV1181 ) @ ( c_List_Olist_OCons @ SV1634 @ ( c_List_Olist_ONil @ SV1181 ) @ SV1181 ) @ SV1181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5006]) ).
thf(5322,plain,
! [SV1635: $i,SV1182: $i,SV577: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV577 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV577 )
| ~ ( class_Power_Opower @ SV577 )
| ( ( c_Power_Opower__class_Opower @ SV1182 @ SV1635 @ SV577 )
!= ( c_HOL_Ozero__class_Ozero @ SV577 ) )
| ( SV1182
= ( c_HOL_Ozero__class_Ozero @ SV577 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV577 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5007]) ).
thf(5323,plain,
! [SV1995: $i,SV1896: $i,SV1636: $i,SV1183: $i,SV578: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV578 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1183 @ SV1636 @ SV578 )
!= ( c_HOL_Ominus__class_Ominus @ SV1896 @ SV1995 @ SV578 ) )
| ( c_HOL_Oord__class_Oless @ SV1896 @ SV1995 @ SV578 )
| ~ ( c_HOL_Oord__class_Oless @ SV1183 @ SV1636 @ SV578 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5008]) ).
thf(5324,plain,
! [SV1897: $i,SV1637: $i,SV1184: $i,SV580: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ SV580 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( ( c_List_Onth @ ( c_List_Olist_OCons @ SV1184 @ SV1637 @ SV1897 ) @ ( c_Int_Onumber__class_Onumber__of @ SV580 @ tc_nat ) @ SV1897 )
= SV1184 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5009]) ).
thf(5325,plain,
! [SV1996: $i,SV1898: $i,SV1638: $i,SV1185: $i,SV582: $i] :
( ( ( ( c_List_Olist_OCons @ SV582 @ SV1185 @ SV1638 )
!= ( c_List_Olist_OCons @ SV1898 @ SV1996 @ SV1638 ) )
= $true )
| ( ( SV1185 = SV1996 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5010]) ).
thf(5326,plain,
! [SV584: $i,SV1640: $i,SV1187: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1187 @ SV1640 @ SV584 )
!= ( c_HOL_Ozero__class_Ozero @ SV584 ) )
= $true )
| ( ( SV1187
= ( c_HOL_Ozero__class_Ozero @ SV584 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV584 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5012]) ).
thf(5327,plain,
! [SV1899: $i,SV1641: $i,SV1188: $i,SV585: $i] :
( ( ( ( c_List_OtakeWhile @ SV585 @ SV1188 @ SV1641 )
= SV1188 )
= $false )
| ( ( ( hBOOL @ ( hAPP @ SV585 @ SV1899 ) )
| ~ ( c_in @ SV1899 @ ( c_List_Oset @ SV1188 @ SV1641 ) @ SV1641 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5013]) ).
thf(5328,plain,
! [SV1900: $i,SV1644: $i,SV1191: $i,SV588: $i] :
( ( ( ( c_List_Olist_ONil @ SV588 )
= ( c_List_Omap @ SV1191 @ SV1644 @ SV1900 @ SV588 ) )
= $false )
| ( ( SV1644
= ( c_List_Olist_ONil @ SV1900 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5015]) ).
thf(5329,plain,
! [SV591: $i,SV1646: $i,SV1194: $i] :
( ( ( SV1194
= ( c_List_Olist_ONil @ SV1646 ) )
= $true )
| ( ( SV591
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_List_Otake @ SV591 @ SV1194 @ SV1646 )
= ( c_List_Olist_ONil @ SV1646 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5017]) ).
thf(5330,plain,
! [SV1997: $i,SV1901: $i,SV1648: $i,SV1197: $i,SV594: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV594 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1197 @ SV1648 @ SV594 )
!= ( c_HOL_Ominus__class_Ominus @ SV1901 @ SV1997 @ SV594 ) )
| ( c_HOL_Oord__class_Oless @ SV1197 @ SV1648 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV1901 @ SV1997 @ SV594 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5019]) ).
thf(5331,plain,
! [SV1998: $i,SV1902: $i,SV1650: $i,SV1199: $i,SV596: $i] :
( ( ( ( c_List_Oappend @ SV596 @ SV1199 @ SV1650 )
!= ( c_List_Oappend @ SV1902 @ SV1998 @ SV1650 ) )
= $true )
| ( ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV1902 @ ( tc_List_Olist @ SV1650 ) ) @ SV596 @ SV1650 )
= SV1902 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV596 @ ( tc_List_Olist @ SV1650 ) ) @ ( c_Nat_Osize__class_Osize @ SV1902 @ ( tc_List_Olist @ SV1650 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5021]) ).
thf(5332,plain,
! [SV1903: $i,SV1653: $i,SV1202: $i,SV599: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ SV599 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( ( c_List_Odrop @ ( c_Int_Onumber__class_Onumber__of @ SV599 @ tc_nat ) @ ( c_List_Olist_OCons @ SV1202 @ SV1653 @ SV1903 ) @ SV1903 )
= ( c_List_Olist_OCons @ SV1202 @ SV1653 @ SV1903 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5023]) ).
thf(5333,plain,
! [SV1904: $i,SV1656: $i,SV1205: $i,SV603: $i] :
( ( ( SV603
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV603 @ ( tc_List_Olist @ SV1205 ) ) @ SV1656 @ SV1205 ) )
= $false )
| ( ( ( ( c_List_Oappend @ SV603 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV603 @ ( tc_List_Olist @ SV1205 ) ) @ SV1656 @ SV1205 ) @ SV1904 @ SV1205 ) @ SV1205 )
= ( c_List_Oappend @ SV1656 @ SV1904 @ SV1205 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV603 @ ( tc_List_Olist @ SV1205 ) ) @ ( c_Nat_Osize__class_Osize @ SV1656 @ ( tc_List_Olist @ SV1205 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5026]) ).
thf(5334,plain,
! [SV2027: $i,SV1999: $i,SV1905: $i,SV1659: $i,SV1209: $i,SV607: $i] :
( ( ( ( c_List_Omap @ SV607 @ SV1209 @ SV1659 @ SV1905 )
!= ( c_List_Omap @ SV1999 @ SV1209 @ SV1659 @ SV1905 ) )
| ( ( hAPP @ SV607 @ SV2027 )
= ( hAPP @ SV1999 @ SV2027 ) )
| ~ ( c_in @ SV2027 @ ( c_List_Oset @ SV1209 @ SV1659 ) @ SV1659 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[5029]) ).
thf(5335,plain,
! [SV1906: $i,SV1660: $i,SV1210: $i,SV608: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV608 ) @ SV1210 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1660 ) @ SV1906 ) )
= $false )
| ( ( SV608 = SV1660 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5030]) ).
thf(5336,plain,
! [SV1907: $i,SV1661: $i,SV1211: $i,SV609: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV609 ) @ SV1211 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1661 ) @ SV1907 ) )
= $false )
| ( ( SV1211 = SV1907 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5031]) ).
thf(5337,plain,
! [SV1663: $i,SV611: $i,SV1213: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1213 @ SV611 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1663 @ SV611 ) )
= $true )
| ( ( SV1213 = SV1663 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV611 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5033]) ).
thf(5338,plain,
! [SV612: $i,SV1664: $i,SV1214: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1214 @ SV1664 @ SV612 )
!= ( c_HOL_Ozero__class_Ozero @ SV612 ) )
= $true )
| ( ( SV1214 = SV1664 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV612 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5034]) ).
thf(5339,plain,
! [SV2000: $i,SV1908: $i,SV1665: $i,SV1215: $i,SV613: $i] :
( ( ( ( c_List_Odrop @ SV613 @ SV1215 @ SV1665 )
!= ( c_List_Olist_OCons @ SV1908 @ SV2000 @ SV1665 ) )
= $true )
| ( ( ( c_List_Onth @ SV1215 @ SV613 @ SV1665 )
= SV1908 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5035]) ).
thf(5340,plain,
! [SV2001: $i,SV1909: $i,SV1666: $i,SV1216: $i,SV614: $i] :
( ( ( ( c_List_Oappend @ SV614 @ SV1216 @ SV1666 )
!= ( c_List_Oappend @ SV1909 @ SV2001 @ SV1666 ) )
= $true )
| ( ( ( SV614
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV614 @ ( tc_List_Olist @ SV1666 ) ) @ SV1909 @ SV1666 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV614 @ ( tc_List_Olist @ SV1666 ) ) @ ( c_Nat_Osize__class_Osize @ SV1909 @ ( tc_List_Olist @ SV1666 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5036]) ).
thf(5341,plain,
! [SV1667: $i,SV1217: $i,SV615: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV615 ) )
= $true )
| ( ( ( SV1217
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV615 ) @ SV1217 ) @ SV1667 ) )
| ( SV1667
= ( c_HOL_Ozero__class_Ozero @ SV615 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV615 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5037]) ).
thf(5342,plain,
! [SV1218: $i,SV616: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV616 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV616 )
| ~ ( class_Power_Opower @ SV616 )
| ( ( c_Power_Opower__class_Opower @ SV1218 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV616 )
!= ( c_HOL_Ozero__class_Ozero @ SV616 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV616 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5038]) ).
thf(5343,plain,
! [SV1668: $i,SV1219: $i,SV617: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV617 ) @ SV1219 ) @ SV1668 )
!= ( c_HOL_Ozero__class_Ozero @ SV617 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV617 ) @ SV1668 @ SV617 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV617 ) @ SV1219 @ SV617 )
| ( SV1668
= ( c_HOL_Ozero__class_Ozero @ SV617 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV617 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5039]) ).
thf(5344,plain,
! [SV1910: $i,SV1669: $i,SV1220: $i,SV618: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV618 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1220 @ SV1669 @ SV618 )
!= ( c_Power_Opower__class_Opower @ SV1220 @ SV1910 @ SV618 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV618 ) @ SV1220 @ SV618 )
| ( SV1669 = SV1910 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5040]) ).
thf(5345,plain,
! [SV2002: $i,SV1911: $i,SV1672: $i,SV1223: $i,SV621: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV621 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1223 @ SV1672 @ SV621 )
!= ( c_HOL_Ominus__class_Ominus @ SV1911 @ SV2002 @ SV621 ) )
| ( c_lessequals @ SV1672 @ SV1223 @ SV621 )
| ~ ( c_lessequals @ SV2002 @ SV1911 @ SV621 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5042]) ).
thf(5346,plain,
! [SV2003: $i,SV1912: $i,SV1673: $i,SV1224: $i,SV622: $i] :
( ( ( ( c_List_Oreplicate @ SV622 @ SV1224 @ SV1673 )
!= ( c_List_Oreplicate @ SV1912 @ SV2003 @ SV1673 ) )
= $true )
| ( ( ( SV1224 = SV2003 )
| ( SV622
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5043]) ).
thf(5347,plain,
! [SV1913: $i,SV1674: $i,SV1225: $i,SV623: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV623 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1225 @ SV1225 @ SV623 )
!= ( c_HOL_Ominus__class_Ominus @ SV1674 @ SV1913 @ SV623 ) )
| ( SV1674 = SV1913 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5044]) ).
thf(5348,plain,
! [SV1675: $i,SV1226: $i,SV624: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV624 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1226 @ SV1675 @ SV624 )
!= ( c_HOL_Ozero__class_Ozero @ SV624 ) )
| ( SV1226 = SV1675 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV624 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5045]) ).
thf(5349,plain,
! [SV1914: $i,SV1676: $i,SV1227: $i,SV625: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV625 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1227 @ ( c_Suc @ SV1676 ) @ SV625 )
!= ( c_Power_Opower__class_Opower @ SV1914 @ ( c_Suc @ SV1676 ) @ SV625 ) )
| ( SV1227 = SV1914 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV625 ) @ SV1914 @ SV625 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV625 ) @ SV1227 @ SV625 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5046]) ).
thf(5350,plain,
! [SV2004: $i,SV1915: $i,SV1677: $i,SV1228: $i,SV626: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV626 ) )
= $true )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1228 @ SV1677 @ SV626 )
!= ( c_HOL_Ominus__class_Ominus @ SV1915 @ SV2004 @ SV626 ) )
| ( c_lessequals @ SV2004 @ SV1915 @ SV626 )
| ~ ( c_lessequals @ SV1677 @ SV1228 @ SV626 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5047]) ).
thf(5351,plain,
! [SV1916: $i,SV1679: $i,SV1230: $i,SV629: $i] :
( ( ( ( c_List_Olist__update @ SV629 @ SV1230 @ SV1679 @ SV1916 )
= SV629 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1230 @ ( c_Nat_Osize__class_Osize @ SV629 @ ( tc_List_Olist @ SV1916 ) ) @ tc_nat )
| ( ( c_List_Onth @ SV629 @ SV1230 @ SV1916 )
= SV1679 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5049]) ).
thf(5352,plain,
! [SV2005: $i,SV1917: $i,SV1680: $i,SV1231: $i,SV630: $i] :
( ( ( ( c_List_Oappend @ SV630 @ SV1231 @ SV1680 )
!= ( c_List_Oappend @ SV1917 @ SV2005 @ SV1680 ) )
= $true )
| ( ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1917 @ ( tc_List_Olist @ SV1680 ) ) @ SV630 @ SV1680 ) @ SV1231 @ SV1680 )
= SV2005 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV630 @ ( tc_List_Olist @ SV1680 ) ) @ ( c_Nat_Osize__class_Osize @ SV1917 @ ( tc_List_Olist @ SV1680 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5050]) ).
thf(5353,plain,
! [SV2006: $i,SV1918: $i,SV1681: $i,SV1232: $i,SV631: $i] :
( ( ( ( c_List_Olist_OCons @ SV631 @ SV1232 @ SV1681 )
!= ( c_List_Olist_OCons @ SV1918 @ SV2006 @ SV1681 ) )
= $true )
| ( ( SV631 = SV1918 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5051]) ).
thf(5354,plain,
! [SV2007: $i,SV1919: $i,SV1683: $i,SV1234: $i,SV633: $i] :
( ( ( ( c_List_Omap @ SV633 @ SV1234 @ SV1683 @ SV1919 )
!= ( c_List_Omap @ SV633 @ SV2007 @ SV1683 @ SV1919 ) )
= $true )
| ( ( ( c_Nat_Osize__class_Osize @ SV1234 @ ( tc_List_Olist @ SV1683 ) )
= ( c_Nat_Osize__class_Osize @ SV2007 @ ( tc_List_Olist @ SV1683 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5053]) ).
thf(5355,plain,
! [SV1235: $i,SV634: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV634 ) @ SV1235 ) @ SV1235 )
= ( c_HOL_Ozero__class_Ozero @ SV634 ) )
= $false )
| ( ( SV1235
= ( c_HOL_Ozero__class_Ozero @ SV634 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV634 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5054]) ).
thf(5356,plain,
! [SV1920: $i,SV1685: $i,SV1237: $i,SV637: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV637 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV637 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1237 ) @ SV1685 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1237 ) @ SV1920 ) )
| ( SV1685 = SV1920 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5056]) ).
thf(5357,plain,
! [SV1921: $i,SV1686: $i,SV1238: $i,SV638: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV638 ) @ SV1238 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1686 @ SV1921 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( SV638
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1686 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV638 @ SV1238 @ SV1686 @ SV1921 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1921
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5057]) ).
thf(5358,plain,
! [SV1687: $i,SV1239: $i,SV639: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV639 ) )
= $true )
| ( ( ( ( c_Int_Onumber__class_Onumber__of @ SV1239 @ SV639 )
!= ( c_Int_Onumber__class_Onumber__of @ SV1687 @ SV639 ) )
| ( SV1239 = SV1687 ) )
= $true )
| ( ( class_Int_Oring__char__0 @ SV639 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5058]) ).
thf(5359,plain,
! [SV1922: $i,SV1688: $i,SV1240: $i,SV641: $i] :
( ( ( ( c_List_Olist__update @ SV641 @ SV1240 @ SV1688 @ SV1922 )
= ( c_List_Olist_ONil @ SV1922 ) )
= $false )
| ( ( SV641
= ( c_List_Olist_ONil @ SV1922 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5059]) ).
thf(5360,plain,
! [SV1923: $i,SV1689: $i,SV1242: $i,SV643: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV643 ) @ SV1242 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1689 ) @ SV1923 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV1242 = SV1923 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5060]) ).
thf(5361,plain,
! [SV1924: $i,SV1690: $i,SV1243: $i,SV644: $i] :
( ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV644 @ ( tc_List_Olist @ SV1243 ) ) @ SV1690 @ SV1243 )
= SV644 )
= $false )
| ( ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1690 @ ( tc_List_Olist @ SV1243 ) ) @ ( c_Nat_Osize__class_Osize @ SV644 @ ( tc_List_Olist @ SV1243 ) ) @ tc_nat )
| ( ( c_List_Oappend @ SV1690 @ SV1924 @ SV1243 )
= ( c_List_Oappend @ SV644 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV644 @ ( tc_List_Olist @ SV1243 ) ) @ SV1690 @ SV1243 ) @ SV1924 @ SV1243 ) @ SV1243 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5061]) ).
thf(5362,plain,
! [SV1925: $i,SV1691: $i,SV1244: $i,SV645: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ SV645 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( ( c_List_Otake @ ( c_Int_Onumber__class_Onumber__of @ SV645 @ tc_nat ) @ ( c_List_Olist_OCons @ SV1244 @ SV1691 @ SV1925 ) @ SV1925 )
= ( c_List_Olist_ONil @ SV1925 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5062]) ).
thf(5363,plain,
! [SV646: $i,SV1692: $i,SV1245: $i] :
( ( ( ~ ( c_lessequals @ SV1245 @ SV1692 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1245 @ SV646 @ tc_nat )
| ( SV646 = SV1692 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV646 @ SV1245 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1692 @ SV1245 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5063]) ).
thf(5364,plain,
! [SV1693: $i,SV1246: $i,SV647: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV647 ) @ SV1246 ) @ SV1693 )
!= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV647 ) @ SV1693 @ SV647 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV647 ) @ SV1246 @ SV647 )
| ( SV1246
= ( c_HOL_Ozero__class_Ozero @ SV647 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV647 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5064]) ).
thf(5365,plain,
! [SV1926: $i,SV1694: $i,SV1247: $i,SV648: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV648 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV648 ) @ SV1247 ) @ SV1694 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV648 ) @ SV1247 ) @ SV1926 ) )
| ( SV1694 = SV1926 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5065]) ).
thf(5366,plain,
! [SV2008: $i,SV1927: $i,SV1695: $i,SV1248: $i,SV649: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV649 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1248 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1695 ) @ SV1927 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1695 ) @ SV2008 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1248 ) @ SV1927 )
= SV2008 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5066]) ).
thf(5367,plain,
! [SV1929: $i,SV1698: $i,SV1251: $i,SV652: $i] :
( ( ( ( c_List_Omap @ SV652 @ SV1251 @ SV1698 @ SV1929 )
= ( c_List_Olist_ONil @ SV1929 ) )
= $false )
| ( ( SV1251
= ( c_List_Olist_ONil @ SV1698 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5068]) ).
thf(5368,plain,
! [SV654: $i,SV1253: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1253 @ SV654 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV1253 = SV654 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV654 @ SV1253 @ tc_nat )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5070]) ).
thf(5369,plain,
! [SV1931: $i,SV1701: $i,SV1256: $i,SV658: $i,SV2: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV2 )
= $false )
| ( ( ( c_lessequals @ SV658 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SV1256 ) @ SV1701 ) @ SV2 )
| ~ ( c_lessequals @ SV1931 @ SV1701 @ SV2 )
| ~ ( c_lessequals @ SV658 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SV1256 ) @ SV1931 ) @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5073]) ).
thf(5370,plain,
! [SV1702: $i,SV3: $i,SV1257: $i,SV659: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV659 @ SV1257 @ SV3 )
= $true )
| ( ( ~ ( c_lessequals @ SV1702 @ SV1257 @ SV3 )
| ~ ( c_HOL_Oord__class_Oless @ SV659 @ SV1702 @ SV3 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5074]) ).
thf(5371,plain,
! [SV1703: $i,SV4: $i,SV1258: $i,SV660: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV660 @ SV1258 @ SV4 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1703 @ SV1258 @ SV4 )
| ~ ( c_lessequals @ SV660 @ SV1703 @ SV4 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5075]) ).
thf(5372,plain,
! [SV663: $i,SV1259: $i,SV8: $i] :
( ( ( c_lessequals @ SV8 @ SV1259 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1259 @ SV663 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV8 @ SV663 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5076]) ).
thf(5373,plain,
! [SV1704: $i,SV10: $i,SV1260: $i,SV664: $i] :
( ( ( c_lessequals @ SV664 @ SV1260 @ SV10 )
= $true )
| ( ( ~ ( c_lessequals @ SV1704 @ SV1260 @ SV10 )
| ~ ( c_lessequals @ SV664 @ SV1704 @ SV10 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5077]) ).
thf(5374,plain,
! [SV1705: $i,SV11: $i,SV1261: $i,SV665: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV665 @ SV1261 @ SV11 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV665 @ SV1705 @ SV11 )
| ~ ( c_lessequals @ SV1705 @ SV1261 @ SV11 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5078]) ).
thf(5375,plain,
! [SV1706: $i,SV12: $i,SV1262: $i,SV666: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV666 @ SV1262 @ SV12 )
= $true )
| ( ( ~ ( c_lessequals @ SV666 @ SV1706 @ SV12 )
| ~ ( c_HOL_Oord__class_Oless @ SV1706 @ SV1262 @ SV12 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5079]) ).
thf(5376,plain,
! [SV1707: $i,SV13: $i,SV1263: $i,SV667: $i] :
( ( ( c_lessequals @ SV667 @ SV1263 @ SV13 )
= $true )
| ( ( ~ ( c_lessequals @ SV667 @ SV1707 @ SV13 )
| ~ ( c_lessequals @ SV1707 @ SV1263 @ SV13 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5080]) ).
thf(5377,plain,
! [SV14: $i,SV668: $i,SV1264: $i] :
( ( ( c_lessequals @ SV1264 @ SV668 @ tc_nat )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ominus__class_Ominus @ SV668 @ SV1264 @ tc_nat ) @ SV14 )
= ( c_HOL_Ominus__class_Ominus @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV668 @ SV14 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1264 @ SV14 ) @ SV14 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5081]) ).
thf(5378,plain,
! [SV15: $i,SV1265: $i,SV669: $i] :
( ( ( ~ ( c_lessequals @ SV669 @ SV1265 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV669 @ SV15 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV15 @ SV1265 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV15 @ SV669 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1265 @ SV669 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5082]) ).
thf(5379,plain,
! [SV16: $i,SV670: $i,SV1266: $i] :
( ( ( ~ ( c_lessequals @ SV1266 @ SV670 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1266 @ SV16 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV16 @ SV1266 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV670 @ SV1266 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV16 @ SV670 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5083]) ).
thf(5380,plain,
! [SV1708: $i,SV20: $i,SV1267: $i,SV673: $i] :
( ( ( c_lessequals @ SV673 @ SV1267 @ SV20 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV1267 @ SV20 )
| ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV673 @ ( c_Suc @ SV1708 ) @ SV20 ) @ ( c_Power_Opower__class_Opower @ SV1267 @ ( c_Suc @ SV1708 ) @ SV20 ) @ SV20 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5084]) ).
thf(5381,plain,
! [SV1709: $i,SV1268: $i,SV674: $i,SV21: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SV674 ) @ SV1268 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SV674 ) @ SV1709 ) @ SV21 )
= $true )
| ( ( ~ ( c_lessequals @ SV1268 @ SV1709 @ SV21 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5085]) ).
thf(5382,plain,
! [SV1710: $i,SV1269: $i,SV675: $i,SV22: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV675 ) @ SV1269 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV1710 ) @ SV1269 ) @ SV22 )
= $true )
| ( ( ~ ( c_lessequals @ SV675 @ SV1710 @ SV22 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5086]) ).
thf(5383,plain,
! [SV1711: $i,SV23: $i,SV1270: $i,SV676: $i] :
( ( ( c_lessequals @ SV676 @ SV1270 @ SV23 )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV23 ) @ SV1711 ) @ SV676 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV23 ) @ SV1711 ) @ SV1270 ) @ SV23 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5087]) ).
thf(5384,plain,
! [SV1712: $i,SV1271: $i,SV677: $i,SV24: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ SV677 ) @ SV1271 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ SV677 ) @ SV1712 ) @ SV24 )
= $true )
| ( ( ~ ( c_lessequals @ SV1271 @ SV1712 @ SV24 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5088]) ).
thf(5385,plain,
! [SV1713: $i,SV25: $i,SV1272: $i,SV678: $i] :
( ( ( c_lessequals @ SV678 @ SV1272 @ SV25 )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SV678 ) @ SV1713 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SV1272 ) @ SV1713 ) @ SV25 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5089]) ).
thf(5386,plain,
! [SV1714: $i,SV1273: $i,SV679: $i,SV26: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV26 ) @ SV679 ) @ SV1273 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV26 ) @ SV1714 ) @ SV1273 ) @ SV26 )
= $true )
| ( ( ~ ( c_lessequals @ SV679 @ SV1714 @ SV26 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5090]) ).
thf(5387,plain,
! [SV680: $i,SV1274: $i,SV27: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV27 @ SV1274 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1274 @ SV680 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Suc @ SV27 ) @ SV680 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5091]) ).
thf(5388,plain,
! [SV1275: $i,SV681: $i,SV30: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV30 ) @ SV681 @ SV30 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV30 ) @ ( c_Power_Opower__class_Opower @ SV681 @ ( c_Suc @ SV1275 ) @ SV30 ) @ SV30 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5092]) ).
thf(5389,plain,
! [SV31: $i,SV1276: $i,SV682: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV682 @ SV1276 @ SV31 )
= $false )
| ( ( c_lessequals @ SV682 @ SV1276 @ SV31 )
= $true )
| ( ( class_Orderings_Opreorder @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5093]) ).
thf(5390,plain,
! [SV32: $i,SV1277: $i,SV683: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV683 @ SV1277 @ SV32 )
= $false )
| ( ( c_lessequals @ SV683 @ SV1277 @ SV32 )
= $true )
| ( ( class_Orderings_Oorder @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5094]) ).
thf(5391,plain,
! [SV35: $i,SV1278: $i,SV686: $i] :
( ( ( c_lessequals @ SV686 @ SV1278 @ SV35 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV686 @ SV1278 @ SV35 ) @ ( c_HOL_Ozero__class_Ozero @ SV35 ) @ SV35 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5095]) ).
thf(5392,plain,
! [SV36: $i,SV1279: $i,SV687: $i] :
( ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV687 @ SV1279 @ SV36 ) @ ( c_HOL_Ozero__class_Ozero @ SV36 ) @ SV36 )
= $false )
| ( ( c_lessequals @ SV687 @ SV1279 @ SV36 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5096]) ).
thf(5393,plain,
! [SV37: $i,SV1280: $i,SV688: $i] :
( ( ( ~ ( c_lessequals @ SV688 @ SV1280 @ SV37 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1280 @ SV688 @ SV37 ) )
= $true )
| ( ( SV688 = SV1280 )
= $true )
| ( ( class_Orderings_Oorder @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5097]) ).
thf(5394,plain,
! [SV38: $i,SV689: $i,SV1281: $i] :
( ( ( ~ ( c_lessequals @ SV1281 @ SV689 @ SV38 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV689 @ SV1281 @ SV38 ) )
= $true )
| ( ( SV689 = SV1281 )
= $true )
| ( ( class_Orderings_Oorder @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5098]) ).
thf(5395,plain,
! [SV39: $i,SV690: $i,SV1282: $i] :
( ( ( ~ ( c_lessequals @ SV1282 @ SV690 @ SV39 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV690 @ SV1282 @ SV39 ) )
= $true )
| ( ( SV690 = SV1282 )
= $true )
| ( ( class_Orderings_Oorder @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5099]) ).
thf(5396,plain,
! [SV43: $i,SV693: $i,SV1283: $i] :
( ( ( c_lessequals @ SV1283 @ SV693 @ SV43 )
= $true )
| ( ( ~ ( c_lessequals @ SV693 @ SV1283 @ SV43 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV693 @ SV1283 @ SV43 )
= $true )
| ( ( class_Orderings_Opreorder @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5101]) ).
thf(5397,plain,
! [SV50: $i,SV699: $i,SV1285: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1285 @ SV699 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1285 @ SV50 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV50 @ SV699 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV50 @ SV1285 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5102]) ).
thf(5398,plain,
! [SV1715: $i,SV52: $i,SV1286: $i,SV701: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV701 @ SV1286 @ SV52 ) @ ( c_Power_Opower__class_Opower @ SV701 @ SV1715 @ SV52 ) @ SV52 )
= $true )
| ( ( ~ ( c_lessequals @ SV701 @ ( c_HOL_Oone__class_Oone @ SV52 ) @ SV52 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV701 @ SV52 )
| ~ ( c_lessequals @ SV1715 @ SV1286 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5103]) ).
thf(5399,plain,
! [SV1287: $i,SV706: $i,SV57: $i] :
( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV57 ) @ SV706 @ SV57 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV57 ) @ ( c_Power_Opower__class_Opower @ SV706 @ SV1287 @ SV57 ) @ SV57 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5104]) ).
thf(5400,plain,
! [SV1288: $i,SV59: $i,SV708: $i] :
( ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV708 @ SV59 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1288 @ SV59 ) @ SV59 )
= $false )
| ( ( c_lessequals @ SV708 @ SV1288 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5105]) ).
thf(5401,plain,
! [SV60: $i,SV1289: $i,SV709: $i] :
( ( ( c_lessequals @ SV709 @ SV1289 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV709 @ SV60 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1289 @ SV60 ) @ SV60 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5106]) ).
thf(5402,plain,
! [SV711: $i,SV1716: $i,SV1932: $i,SV1291: $i,SV62: $i] :
( ( ( c_ListOrder_Ostep1 @ SV62 @ SV1291 @ SV1932 @ SV1716 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV62 @ ( c_List_Oappend @ SV711 @ SV1291 @ SV1716 ) @ ( c_List_Oappend @ SV711 @ SV1932 @ SV1716 ) @ SV1716 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5107]) ).
thf(5403,plain,
! [SV1933: $i,SV1717: $i,SV1292: $i,SV712: $i,SV63: $i] :
( ( ( c_ListOrder_Ostep1 @ SV63 @ SV712 @ SV1292 @ SV1717 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV63 @ ( c_List_Oappend @ SV712 @ SV1933 @ SV1717 ) @ ( c_List_Oappend @ SV1292 @ SV1933 @ SV1717 ) @ SV1717 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5108]) ).
thf(5404,plain,
! [SV1934: $i,SV1718: $i,SV1293: $i,SV713: $i,SV64: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV64 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV713 ) @ SV1293 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV1718 ) @ SV1934 ) @ SV64 )
| ~ ( c_lessequals @ SV1293 @ SV1934 @ SV64 )
| ~ ( c_lessequals @ SV713 @ SV1718 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5109]) ).
thf(5405,plain,
! [SV1719: $i,SV1294: $i,SV1935: $i,SV714: $i,SV65: $i] :
( ( ( ~ ( c_lessequals @ SV65 @ ( hAPP @ SV714 @ SV1935 ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_in @ SV1935 @ ( c_List_Oset @ SV1294 @ SV1719 ) @ SV1719 ) )
= $true )
| ( ( c_lessequals @ SV65 @ ( c_List_Olist_Olist__size @ SV714 @ SV1294 @ SV1719 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5110]) ).
thf(5406,plain,
! [SV72: $i,SV720: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV720 @ SV720 @ SV72 )
= $false )
| ( ( c_lessequals @ SV720 @ SV720 @ SV72 )
= $false )
| ( ( class_Orderings_Olinorder @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5112]) ).
thf(5407,plain,
! [SV74: $i,SV1296: $i,SV722: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV722 @ SV1296 @ SV74 )
= $false )
| ( ( ~ ( c_lessequals @ SV1296 @ SV722 @ SV74 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5113]) ).
thf(5408,plain,
! [SV76: $i,SV1298: $i,SV724: $i] :
( ( ( c_lessequals @ SV724 @ SV1298 @ SV76 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1298 @ SV724 @ SV76 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5115]) ).
thf(5409,plain,
! [SV78: $i,SV1300: $i,SV726: $i] :
( ( ( c_lessequals @ SV726 @ SV1300 @ SV78 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1300 @ SV726 @ SV78 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5117]) ).
thf(5410,plain,
! [SV1720: $i,SV79: $i,SV1301: $i,SV727: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV727 @ SV1301 @ SV79 ) @ ( c_Power_Opower__class_Opower @ SV727 @ SV1720 @ SV79 ) @ SV79 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV79 ) @ SV727 @ SV79 )
| ~ ( c_lessequals @ SV1301 @ SV1720 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5118]) ).
thf(5411,plain,
! [SV86: $i,SV733: $i,SV1304: $i] :
( ( ( SV1304 = SV733 )
= $true )
| ( ( ~ ( c_lessequals @ SV733 @ SV1304 @ SV86 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV733 @ SV1304 @ SV86 )
= $true )
| ( ( class_Orderings_Oorder @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5119]) ).
thf(5412,plain,
! [SV87: $i,SV1305: $i,SV734: $i] :
( ( ( ~ ( c_lessequals @ SV734 @ SV1305 @ SV87 ) )
= $true )
| ( ( SV1305 = SV734 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV734 @ SV1305 @ SV87 )
= $true )
| ( ( class_Orderings_Oorder @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5120]) ).
thf(5413,plain,
! [SV91: $i,SV1306: $i,SV738: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV738 @ SV1306 @ SV91 )
= $true )
| ( ( ~ ( c_lessequals @ SV738 @ SV1306 @ SV91 ) )
= $true )
| ( ( SV738 = SV1306 )
= $true )
| ( ( class_Orderings_Oorder @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5121]) ).
thf(5414,plain,
! [SV92: $i,SV1307: $i,SV739: $i] :
( ( ( SV739 = SV1307 )
= $true )
| ( ( ~ ( c_lessequals @ SV739 @ SV1307 @ SV92 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV739 @ SV1307 @ SV92 )
= $true )
| ( ( class_Orderings_Oorder @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5122]) ).
thf(5415,plain,
! [SV93: $i,SV1308: $i,SV740: $i] :
( ( ( SV740 = SV1308 )
= $true )
| ( ( ~ ( c_lessequals @ SV740 @ SV1308 @ SV93 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV740 @ SV1308 @ SV93 )
= $true )
| ( ( class_Orderings_Oorder @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5123]) ).
thf(5416,plain,
! [SV94: $i,SV1309: $i,SV741: $i] :
( ( ( ~ ( c_lessequals @ SV741 @ SV1309 @ SV94 ) )
= $true )
| ( ( SV741 = SV1309 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV741 @ SV1309 @ SV94 )
= $true )
| ( ( class_Orderings_Oorder @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5124]) ).
thf(5417,plain,
! [SV95: $i,SV1310: $i,SV742: $i] :
( ( ( ~ ( c_lessequals @ SV742 @ SV1310 @ SV95 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV742 @ SV1310 @ SV95 )
= $true )
| ( ( SV742 = SV1310 )
= $true )
| ( ( class_Orderings_Olinorder @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5125]) ).
thf(5418,plain,
! [SV96: $i,SV1311: $i,SV743: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV743 @ SV1311 @ SV96 )
= $true )
| ( ( ~ ( c_lessequals @ SV743 @ SV1311 @ SV96 ) )
= $true )
| ( ( SV743 = SV1311 )
= $true )
| ( ( class_Orderings_Olinorder @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5126]) ).
thf(5419,plain,
! [SV1313: $i,SV101: $i,SV748: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV748 @ ( c_HOL_Oone__class_Oone @ SV101 ) @ SV101 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ SV748 @ SV101 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV748 @ ( c_Suc @ SV1313 ) @ SV101 ) @ ( c_HOL_Oone__class_Oone @ SV101 ) @ SV101 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5128]) ).
thf(5420,plain,
! [SV1721: $i,SV102: $i,SV1314: $i,SV749: $i] :
( ( ( c_lessequals @ SV749 @ SV1314 @ SV102 )
= $true )
| ( ( ~ ( c_in @ SV1314 @ ( c_List_Oset @ SV1721 @ SV102 ) @ SV102 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV749 @ SV1721 @ SV102 ) @ SV102 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5129]) ).
thf(5421,plain,
! [SV1936: $i,SV1722: $i,SV1315: $i,SV750: $i,SV103: $i] :
( ( ( class_Orderings_Olinorder @ SV103 )
= $false )
| ( ( ( c_lessequals @ SV750 @ SV1315 @ SV103 )
| ~ ( c_in @ SV1315 @ ( c_List_Oset @ SV1722 @ SV103 ) @ SV103 )
| ~ ( c_in @ SV750 @ ( c_List_Oset @ SV1936 @ SV103 ) @ SV103 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1936 @ SV1722 @ SV103 ) @ SV103 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5130]) ).
thf(5422,plain,
! [SV106: $i,SV1317: $i,SV752: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV752 @ SV1317 @ SV106 ) @ ( c_HOL_Ozero__class_Ozero @ SV106 ) @ SV106 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV752 @ SV1317 @ SV106 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5131]) ).
thf(5423,plain,
! [SV107: $i,SV1318: $i,SV753: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV753 @ SV1318 @ SV107 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV753 @ SV1318 @ SV107 ) @ ( c_HOL_Ozero__class_Ozero @ SV107 ) @ SV107 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5132]) ).
thf(5424,plain,
! [SV754: $i,SV1319: $i,SV109: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV1319 @ SV109 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV754 @ SV109 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ SV754 ) @ SV1319 ) @ SV109 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5133]) ).
thf(5425,plain,
! [SV110: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV110 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) )
= ( c_HOL_Ozero__class_Ozero @ SV110 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ ( c_HOL_Ozero__class_Ozero @ SV110 ) @ SV110 )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5134]) ).
thf(5426,plain,
! [SV1723: $i,SV1320: $i,SV757: $i,SV113: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV113 ) )
= $true )
| ( ( ( c_lessequals @ SV757 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV1320 ) @ SV1723 ) @ SV113 )
| ~ ( c_lessequals @ SV757 @ SV1723 @ SV113 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV1320 @ SV113 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5137]) ).
thf(5427,plain,
! [SV1724: $i,SV1321: $i,SV758: $i,SV114: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV114 ) )
= $true )
| ( ( ( c_lessequals @ SV758 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SV1321 ) @ SV1724 ) @ SV114 )
| ~ ( c_lessequals @ SV758 @ SV1321 @ SV114 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV1724 @ SV114 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5138]) ).
thf(5428,plain,
! [SV761: $i,SV117: $i,SV1322: $i] :
( ( ( ~ ( c_lessequals @ SV1322 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV761 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV761 ) @ SV1322 ) @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5141]) ).
thf(5429,plain,
! [SV1937: $i,SV1725: $i,SV1323: $i,SV762: $i,SV118: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV118 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV762 ) @ SV1323 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV1725 ) @ SV1937 ) @ SV118 )
| ~ ( c_lessequals @ SV1323 @ SV1937 @ SV118 )
| ~ ( c_HOL_Oord__class_Oless @ SV762 @ SV1725 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5142]) ).
thf(5430,plain,
! [SV1938: $i,SV1726: $i,SV1324: $i,SV763: $i,SV119: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV119 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV119 ) @ SV763 ) @ SV1324 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV119 ) @ SV1726 ) @ SV1938 ) @ SV119 )
| ~ ( c_HOL_Oord__class_Oless @ SV1324 @ SV1938 @ SV119 )
| ~ ( c_lessequals @ SV763 @ SV1726 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5143]) ).
thf(5431,plain,
! [SV1325: $i,SV765: $i,SV121: $i] :
( ( ( class_Int_Onumber @ SV121 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ SV765 @ SV121 ) @ ( c_Int_Onumber__class_Onumber__of @ SV1325 @ SV121 ) @ SV121 )
| ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ SV1325 @ SV121 ) @ ( c_Int_Onumber__class_Onumber__of @ SV765 @ SV121 ) @ SV121 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5144]) ).
thf(5432,plain,
! [SV1326: $i,SV766: $i,SV122: $i] :
( ( ( class_Int_Onumber @ SV122 )
= $false )
| ( ( ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ SV766 @ SV122 ) @ ( c_Int_Onumber__class_Onumber__of @ SV1326 @ SV122 ) @ SV122 )
| ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ SV1326 @ SV122 ) @ ( c_Int_Onumber__class_Onumber__of @ SV766 @ SV122 ) @ SV122 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5145]) ).
thf(5433,plain,
! [SV1327: $i,SV767: $i,SV1727: $i,SV123: $i] :
( ( ( c_in @ SV123 @ ( c_List_Oset @ ( c_List_Olist_OCons @ SV1727 @ SV767 @ SV1327 ) @ SV1327 ) @ SV1327 )
= $false )
| ( ( SV123 = SV1727 )
= $true )
| ( ( c_in @ SV123 @ ( c_List_Oset @ SV767 @ SV1327 ) @ SV1327 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5146]) ).
thf(5434,plain,
! [SV1328: $i,SV770: $i,SV129: $i] :
( ( ( hBOOL @ ( hAPP @ SV129 @ ( c_HOL_Ominus__class_Ominus @ SV770 @ SV1328 @ tc_nat ) ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV770 @ SV1328 @ tc_nat )
= $false )
| ( ( hBOOL @ ( hAPP @ SV129 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5147]) ).
thf(5435,plain,
! [SV1728: $i,SV133: $i,SV1329: $i,SV774: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV774 @ SV1329 @ SV133 ) @ ( c_Power_Opower__class_Opower @ SV1728 @ SV1329 @ SV133 ) @ SV133 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV133 ) @ SV774 @ SV133 )
| ~ ( c_lessequals @ SV774 @ SV1728 @ SV133 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5149]) ).
thf(5436,plain,
! [SV1330: $i,SV775: $i,SV134: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV134 ) @ SV775 @ SV134 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV134 ) @ ( c_Power_Opower__class_Opower @ SV775 @ SV1330 @ SV134 ) @ SV134 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5150]) ).
thf(5437,plain,
! [SV149: $i,SV1735: $i,SV1341: $i,SV790: $i] :
( ( ( c_in @ SV790 @ ( c_List_Oset @ SV1341 @ SV1735 ) @ SV1735 )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV149 @ SV1341 @ SV1735 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV149 @ SV790 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5156]) ).
thf(5438,plain,
! [SV1737: $i,SV152: $i,SV1344: $i,SV793: $i] :
( ( ( c_lessequals @ ( c_List_Onth @ SV793 @ SV1344 @ SV152 ) @ ( c_List_Onth @ SV793 @ SV1737 @ SV152 ) @ SV152 )
= $true )
| ( ( ~ ( c_lessequals @ SV1344 @ SV1737 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV1737 @ ( c_Nat_Osize__class_Osize @ SV793 @ ( tc_List_Olist @ SV152 ) ) @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ SV793 @ SV152 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV152 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5158]) ).
thf(5439,plain,
! [SV1738: $i,SV153: $i,SV1345: $i,SV794: $i] :
( ( ( c_lessequals @ ( c_List_Onth @ SV794 @ SV1345 @ SV153 ) @ ( c_List_Onth @ SV794 @ SV1738 @ SV153 ) @ SV153 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1738 @ ( c_Nat_Osize__class_Osize @ SV794 @ ( tc_List_Olist @ SV153 ) ) @ tc_nat )
| ~ ( c_lessequals @ SV1345 @ SV1738 @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ SV794 @ SV153 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5159]) ).
thf(5440,plain,
! [SV1740: $i,SV156: $i,SV1348: $i,SV797: $i] :
( ( ( c_lessequals @ SV797 @ SV1348 @ SV156 )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV797 @ ( c_List_Olist_OCons @ SV1348 @ SV1740 @ SV156 ) @ SV156 ) @ SV156 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV156 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5160]) ).
thf(5441,plain,
! [SV157: $i,SV1741: $i,SV1349: $i,SV798: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV798 @ ( c_List_Olist_OCons @ SV1349 @ SV1741 @ SV157 ) @ SV157 ) @ SV157 )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1349 @ SV1741 @ SV157 ) @ SV157 )
| ~ ( c_lessequals @ SV798 @ SV1349 @ SV157 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5161]) ).
thf(5442,plain,
! [SV2009: $i,SV1940: $i,SV1748: $i,SV1361: $i,SV810: $i,SV169: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV169 ) )
= $true )
| ( ( ( ( c_List_Olinorder__class_Oinsort__key @ SV810 @ SV1361 @ ( c_List_Olist_OCons @ SV1748 @ SV1940 @ SV2009 ) @ SV2009 @ SV169 )
= ( c_List_Olist_OCons @ SV1361 @ ( c_List_Olist_OCons @ SV1748 @ SV1940 @ SV2009 ) @ SV2009 ) )
| ~ ( c_lessequals @ ( hAPP @ SV810 @ SV1361 ) @ ( hAPP @ SV810 @ SV1748 ) @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5165]) ).
thf(5443,plain,
! [SV2010: $i,SV1941: $i,SV1749: $i,SV1362: $i,SV811: $i,SV170: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV170 ) )
= $true )
| ( ( ( ( c_List_Olinorder__class_Oinsort__key @ SV811 @ SV1362 @ ( c_List_Olist_OCons @ SV1749 @ SV1941 @ SV2010 ) @ SV2010 @ SV170 )
= ( c_List_Olist_OCons @ SV1749 @ ( c_List_Olinorder__class_Oinsort__key @ SV811 @ SV1362 @ SV1941 @ SV2010 @ SV170 ) @ SV2010 ) )
| ( c_lessequals @ ( hAPP @ SV811 @ SV1362 ) @ ( hAPP @ SV811 @ SV1749 ) @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5166]) ).
thf(5444,plain,
! [SV1942: $i,SV1750: $i,SV1363: $i,SV812: $i,SV171: $i] :
( ( ( class_Orderings_Olinorder @ SV171 )
= $false )
| ( ( ( c_Nat_Osize__class_Osize @ ( c_List_Olinorder__class_Oinsort__key @ SV812 @ SV1363 @ SV1750 @ SV1942 @ SV171 ) @ ( tc_List_Olist @ SV1942 ) )
= ( c_Suc @ ( c_Nat_Osize__class_Osize @ SV1750 @ ( tc_List_Olist @ SV1942 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5167]) ).
thf(5445,plain,
! [SV172: $i,SV1364: $i,SV813: $i] :
( ( ( ~ ( c_lessequals @ SV813 @ SV1364 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV813 @ SV172 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV172 @ SV1364 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV172 @ SV813 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1364 @ SV813 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5168]) ).
thf(5446,plain,
! [SV173: $i,SV814: $i,SV1365: $i] :
( ( ( ~ ( c_lessequals @ SV1365 @ SV814 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1365 @ SV173 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV173 @ SV1365 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV814 @ SV1365 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV173 @ SV814 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5169]) ).
thf(5447,plain,
! [SV1366: $i,SV176: $i,SV817: $i] :
( ( ( c_lessequals @ SV817 @ SV176 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV817 @ SV1366 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ SV176 @ SV817 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1366 @ SV817 @ tc_nat ) @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV176 @ SV1366 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5170]) ).
thf(5448,plain,
! [SV819: $i,SV1368: $i,SV178: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV178 @ SV1368 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV819 @ SV178 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV178 @ SV819 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1368 @ SV819 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5171]) ).
thf(5449,plain,
! [SV191: $i,SV1751: $i,SV1371: $i,SV830: $i] :
( ( ( c_lessequals @ SV830 @ SV1371 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1751 @ SV830 @ SV191 ) @ ( c_Power_Opower__class_Opower @ SV1751 @ SV1371 @ SV191 ) @ SV191 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV191 ) @ SV1751 @ SV191 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5172]) ).
thf(5450,plain,
! [SV192: $i,SV1752: $i,SV1372: $i,SV831: $i] :
( ( ( c_lessequals @ SV831 @ SV1372 @ tc_nat )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1752 @ SV831 @ SV192 ) @ ( c_Power_Opower__class_Opower @ SV1752 @ SV1372 @ SV192 ) @ SV192 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV192 ) @ SV1752 @ SV192 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5173]) ).
thf(5451,plain,
! [SV1753: $i,SV193: $i,SV1373: $i,SV832: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV832 @ SV1373 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SV832 @ SV1753 @ SV193 ) @ SV193 )
= $true )
| ( ( ~ ( c_lessequals @ SV1373 @ SV1753 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV193 ) @ SV832 @ SV193 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5174]) ).
thf(5452,plain,
! [SV842: $i,SV1754: $i,SV1943: $i,SV1375: $i,SV208: $i] :
( ( ( c_ListOrder_Ostep1 @ SV208 @ SV1375 @ SV1943 @ SV1754 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV208 @ ( c_List_Olist_OCons @ SV842 @ SV1375 @ SV1754 ) @ ( c_List_Olist_OCons @ SV842 @ SV1943 @ SV1754 ) @ SV1754 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5176]) ).
thf(5453,plain,
! [SV2011: $i,SV1944: $i,SV1755: $i,SV1376: $i,SV843: $i,SV209: $i] :
( ( ( c_ListOrder_Ostep1 @ SV209 @ SV843 @ SV1376 @ SV1755 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV209 @ SV1944 ) @ SV2011 ) )
| ~ ( c_ListOrder_Ostep1 @ SV209 @ ( c_List_Olist_OCons @ SV1944 @ SV843 @ SV1755 ) @ ( c_List_Olist_OCons @ SV2011 @ SV1376 @ SV1755 ) @ SV1755 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5177]) ).
thf(5454,plain,
! [SV2012: $i,SV1945: $i,SV1756: $i,SV1377: $i,SV844: $i,SV210: $i] :
( ( ( c_ListOrder_Ostep1 @ SV210 @ SV844 @ SV1377 @ SV1756 )
= $true )
| ( ( ( SV1377 = SV844 )
| ~ ( c_ListOrder_Ostep1 @ SV210 @ ( c_List_Olist_OCons @ SV1945 @ SV844 @ SV1756 ) @ ( c_List_Olist_OCons @ SV2012 @ SV1377 @ SV1756 ) @ SV1756 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5178]) ).
thf(5455,plain,
! [SV1946: $i,SV1757: $i,SV1378: $i,SV845: $i,SV211: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV211 @ SV845 ) @ SV1378 ) )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV211 @ ( c_List_Olist_OCons @ SV845 @ SV1757 @ SV1946 ) @ ( c_List_Olist_OCons @ SV1378 @ SV1757 @ SV1946 ) @ SV1946 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5179]) ).
thf(5456,plain,
! [SV2013: $i,SV1947: $i,SV1758: $i,SV1379: $i,SV846: $i,SV212: $i] :
( ( ( SV212 = SV846 )
= $true )
| ( ( ( SV1379 = SV1758 )
| ~ ( c_ListOrder_Ostep1 @ SV1947 @ ( c_List_Olist_OCons @ SV846 @ SV1758 @ SV2013 ) @ ( c_List_Olist_OCons @ SV212 @ SV1379 @ SV2013 ) @ SV2013 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5180]) ).
thf(5457,plain,
! [SV2014: $i,SV1948: $i,SV1759: $i,SV1380: $i,SV847: $i,SV213: $i] :
( ( ( SV213 = SV847 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1380 @ SV847 ) @ SV213 ) )
| ~ ( c_ListOrder_Ostep1 @ SV1380 @ ( c_List_Olist_OCons @ SV847 @ SV1759 @ SV1948 ) @ ( c_List_Olist_OCons @ SV213 @ SV2014 @ SV1948 ) @ SV1948 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5181]) ).
thf(5458,plain,
! [SV1760: $i,SV216: $i,SV1383: $i,SV850: $i] :
( ( ( c_lessequals @ ( c_List_Onth @ SV850 @ SV1383 @ SV216 ) @ ( c_List_Onth @ SV850 @ SV1760 @ SV216 ) @ SV216 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1383 @ ( c_Nat_Osize__class_Osize @ SV850 @ ( tc_List_Olist @ SV216 ) ) @ tc_nat )
| ~ ( c_lessequals @ SV1760 @ SV1383 @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Orev @ SV850 @ SV216 ) @ SV216 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV216 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5182]) ).
thf(5459,plain,
! [SV851: $i,SV217: $i,SV1384: $i] :
( ( ( ~ ( c_lessequals @ SV1384 @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV851 @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV217 ) @ SV851 ) @ SV1384 ) @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV217 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5183]) ).
thf(5460,plain,
! [SV852: $i,SV218: $i,SV1385: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1385 @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV852 @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV218 ) @ SV852 ) @ SV1385 ) @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV218 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5184]) ).
thf(5461,plain,
! [SV1761: $i,SV1386: $i,SV853: $i,SV219: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV219 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV853 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV219 ) @ SV1386 ) @ SV1761 ) @ SV219 )
| ~ ( c_lessequals @ SV853 @ SV1761 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV1386 @ SV219 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5185]) ).
thf(5462,plain,
! [SV1762: $i,SV1387: $i,SV854: $i,SV220: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV220 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV854 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV220 ) @ SV1387 ) @ SV1762 ) @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ SV854 @ SV1762 @ SV220 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV1387 @ SV220 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV220 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5186]) ).
thf(5463,plain,
! [SV855: $i,SV1388: $i,SV221: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ SV1388 @ SV221 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ SV855 @ SV221 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SV855 ) @ SV1388 ) @ SV221 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV221 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5187]) ).
thf(5464,plain,
! [SV856: $i,SV1389: $i,SV222: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ SV1389 @ SV222 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ SV856 @ SV222 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SV856 ) @ SV1389 ) @ SV222 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV222 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5188]) ).
thf(5465,plain,
! [SV1763: $i,SV224: $i,SV1390: $i,SV857: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV857 @ SV1390 @ SV224 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV224 ) @ SV1390 @ SV224 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV857 @ SV1763 @ SV224 ) @ ( c_Power_Opower__class_Opower @ SV1390 @ SV1763 @ SV224 ) @ SV224 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5189]) ).
thf(5466,plain,
! [SV229: $i,SV1767: $i,SV1394: $i,SV861: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV861 @ SV1394 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1767 @ SV861 @ SV229 ) @ ( c_Power_Opower__class_Opower @ SV1767 @ SV1394 @ SV229 ) @ SV229 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV229 ) @ SV1767 @ SV229 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV229 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5190]) ).
thf(5467,plain,
! [SV1768: $i,SV230: $i,SV1395: $i,SV862: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV862 @ SV1395 @ SV230 ) @ ( c_Power_Opower__class_Opower @ SV862 @ SV1768 @ SV230 ) @ SV230 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV230 ) @ SV862 @ SV230 )
| ~ ( c_HOL_Oord__class_Oless @ SV1395 @ SV1768 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5191]) ).
thf(5468,plain,
! [SV231: $i,SV1769: $i,SV1396: $i,SV863: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV863 @ SV1396 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1769 @ SV863 @ SV231 ) @ ( c_Power_Opower__class_Opower @ SV1769 @ SV1396 @ SV231 ) @ SV231 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV231 ) @ SV1769 @ SV231 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV231 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5192]) ).
thf(5469,plain,
! [SV1770: $i,SV232: $i,SV1397: $i,SV864: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV864 @ SV1397 @ SV232 ) @ ( c_Power_Opower__class_Opower @ SV864 @ SV1770 @ SV232 ) @ SV232 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1397 @ SV1770 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV232 ) @ SV864 @ SV232 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5193]) ).
thf(5470,plain,
! [SV2015: $i,SV1949: $i,SV1771: $i,SV1398: $i,SV865: $i,SV233: $i] :
( ( ( SV233 = SV865 )
= $true )
| ( ( ( SV1398 = SV1771 )
| ~ ( c_ListOrder_Ostep1 @ SV1949 @ ( c_List_Oappend @ SV233 @ ( c_List_Olist_OCons @ SV1398 @ ( c_List_Olist_ONil @ SV2015 ) @ SV2015 ) @ SV2015 ) @ ( c_List_Oappend @ SV865 @ ( c_List_Olist_OCons @ SV1771 @ ( c_List_Olist_ONil @ SV2015 ) @ SV2015 ) @ SV2015 ) @ SV2015 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5194]) ).
thf(5471,plain,
! [SV2016: $i,SV1950: $i,SV1772: $i,SV1399: $i,SV866: $i,SV234: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV234 @ SV866 ) @ SV1399 ) )
= $true )
| ( ( ( SV866 = SV1399 )
| ~ ( c_ListOrder_Ostep1 @ SV234 @ ( c_List_Oappend @ SV1772 @ ( c_List_Olist_OCons @ SV866 @ ( c_List_Olist_ONil @ SV1950 ) @ SV1950 ) @ SV1950 ) @ ( c_List_Oappend @ SV2016 @ ( c_List_Olist_OCons @ SV1399 @ ( c_List_Olist_ONil @ SV1950 ) @ SV1950 ) @ SV1950 ) @ SV1950 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5195]) ).
thf(5472,plain,
! [SV2017: $i,SV1951: $i,SV1773: $i,SV1400: $i,SV867: $i,SV235: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV867 ) @ SV1400 ) )
= $true )
| ( ( ( c_ListOrder_Ostep1 @ SV235 @ SV1773 @ SV1951 @ SV2017 )
| ~ ( c_ListOrder_Ostep1 @ SV235 @ ( c_List_Oappend @ SV1773 @ ( c_List_Olist_OCons @ SV867 @ ( c_List_Olist_ONil @ SV2017 ) @ SV2017 ) @ SV2017 ) @ ( c_List_Oappend @ SV1951 @ ( c_List_Olist_OCons @ SV1400 @ ( c_List_Olist_ONil @ SV2017 ) @ SV2017 ) @ SV2017 ) @ SV2017 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5196]) ).
thf(5473,plain,
! [SV2018: $i,SV1952: $i,SV1774: $i,SV1401: $i,SV868: $i,SV236: $i] :
( ( ( SV236 = SV868 )
= $true )
| ( ( ( c_ListOrder_Ostep1 @ SV1401 @ SV236 @ SV868 @ SV1774 )
| ~ ( c_ListOrder_Ostep1 @ SV1401 @ ( c_List_Oappend @ SV236 @ ( c_List_Olist_OCons @ SV1952 @ ( c_List_Olist_ONil @ SV1774 ) @ SV1774 ) @ SV1774 ) @ ( c_List_Oappend @ SV868 @ ( c_List_Olist_OCons @ SV2018 @ ( c_List_Olist_ONil @ SV1774 ) @ SV1774 ) @ SV1774 ) @ SV1774 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5197]) ).
thf(5474,plain,
! [SV1402: $i,SV1775: $i,SV870: $i,SV1953: $i,SV238: $i] :
( ( ( hBOOL @ ( hAPP @ SV238 @ SV1953 ) )
= $true )
| ( ( ~ ( c_in @ SV1953 @ ( c_List_Oset @ SV870 @ SV1775 ) @ SV1775 ) )
= $true )
| ( ( ( c_List_OtakeWhile @ SV238 @ ( c_List_Oappend @ SV870 @ SV1402 @ SV1775 ) @ SV1775 )
= ( c_List_OtakeWhile @ SV238 @ SV870 @ SV1775 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5198]) ).
thf(5475,plain,
! [SV1780: $i,SV1409: $i,SV1954: $i,SV878: $i,SV246: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV246 @ ( hAPP @ SV878 @ SV1954 ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_in @ SV1954 @ ( c_List_Oset @ SV1409 @ SV1780 ) @ SV1780 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV246 @ ( c_List_Olist_Olist__size @ SV878 @ SV1409 @ SV1780 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5201]) ).
thf(5476,plain,
! [SV1410: $i,SV1781: $i,SV879: $i,SV247: $i] :
( ( ( hBOOL @ ( hAPP @ SV247 @ ( c_List_Onth @ SV879 @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV247 @ SV1781 @ SV879 @ SV1410 ) @ SV1410 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV247 @ ( c_List_Onth @ SV879 @ SV1781 @ SV1410 ) ) )
= $true )
| ( ( ( c_List_OtakeWhile @ SV247 @ SV879 @ SV1410 )
= ( c_List_Otake @ SV1781 @ SV879 @ SV1410 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5202]) ).
thf(5477,plain,
! [SV1955: $i,SV1782: $i,SV1413: $i,SV884: $i,SV252: $i] :
( ( ( class_Orderings_Olinorder @ SV252 )
= $false )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV884 @ ( c_List_Olinorder__class_Oinsort__key @ SV884 @ SV1413 @ SV1782 @ SV1955 @ SV252 ) @ SV1955 @ SV252 ) @ SV252 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV884 @ SV1782 @ SV1955 @ SV252 ) @ SV252 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5203]) ).
thf(5478,plain,
! [SV1956: $i,SV1783: $i,SV1414: $i,SV885: $i,SV253: $i] :
( ( ( class_Orderings_Olinorder @ SV253 )
= $false )
| ( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV885 @ SV1414 @ SV1783 @ SV253 ) @ SV253 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV885 @ ( c_List_Olinorder__class_Oinsort__key @ SV885 @ SV1956 @ SV1414 @ SV1783 @ SV253 ) @ SV1783 @ SV253 ) @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5204]) ).
thf(5479,plain,
! [SV1957: $i,SV1785: $i,SV1416: $i,SV889: $i,SV257: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV257 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SV889 ) @ SV1416 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SV1785 ) @ SV1957 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SV889 ) @ SV1785 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV257 ) @ SV1416 ) @ SV1957 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5205]) ).
thf(5480,plain,
! [SV893: $i,SV261: $i,SV1420: $i] :
( ( ( c_List_Olinorder__class_Osorted @ SV1420 @ SV261 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_OtakeWhile @ SV893 @ SV1420 @ SV261 ) @ SV261 )
= $true )
| ( ( class_Orderings_Olinorder @ SV261 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5206]) ).
thf(5481,plain,
! [SV895: $i,SV263: $i,SV1422: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1422 @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV895 @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV263 ) @ SV895 ) @ SV1422 ) @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV263 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5207]) ).
thf(5482,plain,
! [SV1799: $i,SV281: $i,SV1439: $i,SV913: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV913 @ SV1439 @ SV281 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV913 @ SV1799 @ SV281 )
| ~ ( c_HOL_Oord__class_Oless @ SV1799 @ SV1439 @ SV281 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV281 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5221]) ).
thf(5483,plain,
! [SV1800: $i,SV282: $i,SV1440: $i,SV914: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV914 @ SV1440 @ SV282 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1800 @ SV1440 @ SV282 )
| ~ ( c_HOL_Oord__class_Oless @ SV914 @ SV1800 @ SV282 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5222]) ).
thf(5484,plain,
! [SV916: $i,SV284: $i,SV1442: $i] :
( ( ( c_List_Olinorder__class_Osorted @ SV1442 @ SV284 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Odrop @ SV916 @ SV1442 @ SV284 ) @ SV284 )
= $true )
| ( ( class_Orderings_Olinorder @ SV284 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5223]) ).
thf(5485,plain,
! [SV1454: $i,SV1808: $i,SV928: $i,SV296: $i] :
( ( ( hBOOL @ ( hAPP @ SV296 @ ( c_List_Onth @ SV928 @ ( c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 @ SV296 @ SV1808 @ SV928 @ SV1454 ) @ SV1454 ) ) )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1808 @ ( c_Nat_Osize__class_Osize @ SV928 @ ( tc_List_Olist @ SV1454 ) ) @ tc_nat )
= $true )
| ( ( ( c_List_OtakeWhile @ SV296 @ SV928 @ SV1454 )
= ( c_List_Otake @ SV1808 @ SV928 @ SV1454 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5228]) ).
thf(5486,plain,
! [SV1810: $i,SV300: $i,SV1458: $i,SV932: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV932 @ SV1458 @ SV300 ) @ ( c_Power_Opower__class_Opower @ SV1810 @ SV1458 @ SV300 ) @ SV300 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1458 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SV932 @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ SV932 @ SV1810 @ SV300 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV300 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5231]) ).
thf(5487,plain,
! [SV943: $i,SV311: $i,SV1469: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1469 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV311 ) @ SV943 @ SV311 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV311 ) @ ( c_Power_Opower__class_Opower @ SV943 @ SV1469 @ SV311 ) @ SV311 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV311 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5237]) ).
thf(5488,plain,
! [SV1817: $i,SV313: $i,SV1471: $i,SV945: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV945 @ SV1471 @ SV313 ) @ ( c_Power_Opower__class_Opower @ SV945 @ SV1817 @ SV313 ) @ SV313 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV945 @ ( c_HOL_Oone__class_Oone @ SV313 ) @ SV313 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV313 ) @ SV945 @ SV313 )
| ~ ( c_HOL_Oord__class_Oless @ SV1817 @ SV1471 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV313 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5238]) ).
thf(5489,plain,
! [SV1820: $i,SV334: $i,SV1476: $i,SV962: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV962 @ SV1476 @ SV334 ) @ SV334 )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1820 @ ( c_List_Olist_OCons @ SV962 @ SV1476 @ SV334 ) @ SV334 ) @ SV334 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV334 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5243]) ).
thf(5490,plain,
! [SV342: $i,SV970: $i,SV1484: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1484 @ SV970 @ SV342 ) @ SV342 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ SV970 @ SV342 )
= $true )
| ( ( class_Orderings_Olinorder @ SV342 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5244]) ).
thf(5491,plain,
! [SV2021: $i,SV1968: $i,SV1830: $i,SV1497: $i,SV997: $i,SV376: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV376 @ ( c_Lambda_OdB_OdB__case @ SV997 @ SV1497 @ SV1830 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1968 ) @ SV2021 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SV1497 @ SV1968 ) @ SV2021 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5246]) ).
thf(5492,plain,
! [SV2022: $i,SV1969: $i,SV1831: $i,SV1498: $i,SV998: $i,SV377: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV377 @ ( c_Lambda_OdB_OdB__case @ SV998 @ SV1498 @ SV1831 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1969 ) @ SV2022 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV377 @ ( hAPP @ ( hAPP @ SV1498 @ SV1969 ) @ SV2022 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5247]) ).
thf(5493,plain,
! [SV1972: $i,SV1835: $i,SV1504: $i,SV1004: $i,SV383: $i] :
( ( ( hBOOL @ ( hAPP @ SV383 @ ( c_Lambda_OdB_OdB__case @ SV1004 @ SV1504 @ SV1835 @ ( c_Lambda_OdB_OVar @ SV1972 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV383 @ ( hAPP @ SV1004 @ SV1972 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5251]) ).
thf(5494,plain,
! [SV1973: $i,SV1836: $i,SV1505: $i,SV1005: $i,SV384: $i] :
( ( ( hBOOL @ ( hAPP @ SV384 @ ( c_Lambda_OdB_OdB__case @ SV1005 @ SV1505 @ SV1836 @ ( c_Lambda_OdB_OVar @ SV1973 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV384 @ ( hAPP @ SV1005 @ SV1973 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5252]) ).
thf(5495,plain,
! [SV1009: $i,SV388: $i,SV1507: $i] :
( ( ( c_List_Olinorder__class_Osorted @ SV1507 @ SV388 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Otake @ SV1009 @ SV1507 @ SV388 ) @ SV388 )
= $true )
| ( ( class_Orderings_Olinorder @ SV388 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5253]) ).
thf(5496,plain,
! [SV1521: $i,SV1031: $i,SV410: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV410 ) @ SV1031 @ SV410 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV410 ) @ ( c_Power_Opower__class_Opower @ SV1031 @ SV1521 @ SV410 ) @ SV410 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV410 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5262]) ).
thf(5497,plain,
! [SV1975: $i,SV1034: $i,SV1524: $i,SV413: $i,SV1844: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1844 @ ( c_Nat_Osize__class_Osize @ SV413 @ ( tc_List_Olist @ SV1524 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV413 @ SV1034 @ SV1524 ) @ SV1844 @ SV1975 @ SV1524 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV413 @ SV1844 @ SV1975 @ SV1524 ) @ SV1034 @ SV1524 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5263]) ).
thf(5498,plain,
! [SV1976: $i,SV1035: $i,SV1525: $i,SV414: $i,SV1845: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1845 @ ( c_Nat_Osize__class_Osize @ SV414 @ ( tc_List_Olist @ SV1525 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Olist__update @ ( c_List_Oappend @ SV414 @ SV1035 @ SV1525 ) @ SV1845 @ SV1976 @ SV1525 )
= ( c_List_Oappend @ ( c_List_Olist__update @ SV414 @ SV1845 @ SV1976 @ SV1525 ) @ SV1035 @ SV1525 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5264]) ).
thf(5499,plain,
! [SV1043: $i,SV1529: $i,SV424: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV1529 @ SV424 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV1043 @ SV424 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SV1043 ) @ SV1529 ) @ SV424 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV424 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5267]) ).
thf(5500,plain,
! [SV427: $i,SV1046: $i,SV1532: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1532 @ SV1046 @ SV427 )
= $true )
| ( ( SV1532 = SV1046 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1046 @ SV1532 @ SV427 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV427 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5268]) ).
thf(5501,plain,
! [SV428: $i,SV1047: $i,SV1533: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1533 @ SV1047 @ SV428 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1047 @ SV1533 @ SV428 )
= $true )
| ( ( SV1047 = SV1533 )
= $true )
| ( ( class_Orderings_Olinorder @ SV428 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5269]) ).
thf(5502,plain,
! [SV432: $i,SV1051: $i,SV1535: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1535 @ SV1051 @ SV432 )
= $true )
| ( ( SV1535 = SV1051 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1051 @ SV1535 @ SV432 )
= $true )
| ( ( class_Orderings_Olinorder @ SV432 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5271]) ).
thf(5503,plain,
! [SV434: $i,SV1053: $i,SV1537: $i] :
( ( ( SV1537 = SV1053 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1537 @ SV1053 @ SV434 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1053 @ SV1537 @ SV434 )
= $true )
| ( ( class_Orderings_Olinorder @ SV434 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5272]) ).
thf(5504,plain,
! [SV435: $i,SV1538: $i,SV1054: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1054 @ SV1538 @ SV435 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1538 @ SV1054 @ SV435 )
= $true )
| ( ( SV1054 = SV1538 )
= $true )
| ( ( class_Orderings_Olinorder @ SV435 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5273]) ).
thf(5505,plain,
! [SV1979: $i,SV1850: $i,SV1539: $i,SV1055: $i,SV436: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV436 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV436 ) @ SV1055 ) @ SV1539 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV436 ) @ SV1850 ) @ SV1979 ) @ SV436 )
| ~ ( c_HOL_Oord__class_Oless @ SV1539 @ SV1979 @ SV436 )
| ~ ( c_HOL_Oord__class_Oless @ SV1055 @ SV1850 @ SV436 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5274]) ).
thf(5506,plain,
! [SV1851: $i,SV437: $i,SV1540: $i,SV1056: $i,SV1980: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1980 @ ( c_Nat_Osize__class_Osize @ SV1056 @ ( tc_List_Olist @ SV1540 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Onth @ ( c_List_Omap @ SV437 @ SV1056 @ SV1540 @ SV1851 ) @ SV1980 @ SV1851 )
= ( hAPP @ SV437 @ ( c_List_Onth @ SV1056 @ SV1980 @ SV1540 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5275]) ).
thf(5507,plain,
! [SV438: $i,SV1541: $i,SV1057: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1057 @ SV1541 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1057 @ SV438 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1541 @ SV438 ) @ SV438 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV438 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5276]) ).
thf(5508,plain,
! [SV1542: $i,SV439: $i,SV1058: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1058 @ SV439 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1542 @ SV439 ) @ SV439 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1058 @ SV1542 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV439 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5277]) ).
thf(5509,plain,
! [SV1063: $i,SV1852: $i,SV1543: $i,SV444: $i] :
( ( ( c_List_Olistsp @ SV444 @ SV1543 @ SV1852 )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV444 @ SV1063 @ SV1852 ) )
= $true )
| ( ( c_List_Olistsp @ SV444 @ ( c_List_Oappend @ SV1063 @ SV1543 @ SV1852 ) @ SV1852 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5280]) ).
thf(5510,plain,
! [SV1853: $i,SV1546: $i,SV447: $i,SV1066: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1066 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV447 ) @ SV1546 ) @ SV1853 ) @ SV447 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1066 @ SV1853 @ SV447 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV1546 @ SV447 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV447 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5281]) ).
thf(5511,plain,
! [SV1981: $i,SV1854: $i,SV1548: $i,SV1068: $i,SV449: $i] :
( ( ( hBOOL @ ( hAPP @ SV449 @ ( c_Lambda_OdB_OdB__case @ SV1068 @ SV1548 @ SV1854 @ ( c_Lambda_OdB_OAbs @ SV1981 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV449 @ ( hAPP @ SV1854 @ SV1981 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5282]) ).
thf(5512,plain,
! [SV1982: $i,SV1855: $i,SV1549: $i,SV1069: $i,SV450: $i] :
( ( ( hBOOL @ ( hAPP @ SV450 @ ( c_Lambda_OdB_OdB__case @ SV1069 @ SV1549 @ SV1855 @ ( c_Lambda_OdB_OAbs @ SV1982 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV450 @ ( hAPP @ SV1855 @ SV1982 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5283]) ).
thf(5513,plain,
! [SV1857: $i,SV1551: $i,SV1071: $i,SV452: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV452 ) @ SV1071 ) @ SV1551 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV452 ) @ SV1857 ) @ SV1551 ) @ SV452 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1071 @ SV1857 @ SV452 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV452 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5284]) ).
thf(5514,plain,
! [SV1858: $i,SV1552: $i,SV1072: $i,SV453: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV453 ) @ SV1072 ) @ SV1552 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV453 ) @ SV1858 ) @ SV1552 ) @ SV453 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1072 @ SV1858 @ SV453 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV453 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5285]) ).
thf(5515,plain,
! [SV1859: $i,SV454: $i,SV1553: $i,SV1073: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1073 @ SV1553 @ SV454 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV454 ) @ SV1073 ) @ SV1859 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV454 ) @ SV1553 ) @ SV1859 ) @ SV454 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV454 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5286]) ).
thf(5516,plain,
! [SV1860: $i,SV1554: $i,SV1074: $i,SV455: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV455 ) @ SV1074 ) @ SV1554 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV455 ) @ SV1074 ) @ SV1860 ) @ SV455 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1554 @ SV1860 @ SV455 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV455 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5287]) ).
thf(5517,plain,
! [SV1861: $i,SV1555: $i,SV1075: $i,SV456: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV456 ) @ SV1075 ) @ SV1555 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV456 ) @ SV1075 ) @ SV1861 ) @ SV456 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1555 @ SV1861 @ SV456 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV456 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5288]) ).
thf(5518,plain,
! [SV1862: $i,SV457: $i,SV1556: $i,SV1076: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1076 @ SV1556 @ SV457 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV1862 ) @ SV1076 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV1862 ) @ SV1556 ) @ SV457 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV457 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5289]) ).
thf(5519,plain,
! [SV1557: $i,SV458: $i,SV1077: $i,SV1863: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1863 ) @ SV1077 ) )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV458 @ SV1863 @ SV1557 ) )
= $true )
| ( ( c_Type_Otyping @ SV458 @ SV1077 @ SV1557 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5290]) ).
thf(5520,plain,
! [SV459: $i,SV1558: $i,SV1078: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1078 @ SV1558 @ SV459 ) @ SV459 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ SV1078 @ SV459 )
= $true )
| ( ( class_Orderings_Olinorder @ SV459 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5291]) ).
thf(5521,plain,
! [SV460: $i,SV1079: $i,SV1559: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1559 @ SV1079 @ SV460 ) @ SV460 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ SV1079 @ SV460 )
= $true )
| ( ( class_Orderings_Olinorder @ SV460 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5292]) ).
thf(5522,plain,
! [SV2025: $i,SV1984: $i,SV1864: $i,SV1560: $i,SV1080: $i,SV461: $i] :
( ( ( ( c_List_Olist__update @ ( c_List_Olist__update @ SV461 @ SV1080 @ SV1560 @ SV1864 ) @ SV1984 @ SV2025 @ SV1864 )
= ( c_List_Olist__update @ ( c_List_Olist__update @ SV461 @ SV1984 @ SV2025 @ SV1864 ) @ SV1080 @ SV1560 @ SV1864 ) )
= $true )
| ( ( SV1080 = SV1984 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5293]) ).
thf(5523,plain,
! [SV1565: $i,SV1867: $i,SV467: $i,SV1986: $i,SV1086: $i] :
( ( ( SV1086 = SV1986 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1086 @ ( c_Nat_Osize__class_Osize @ SV467 @ ( tc_List_Olist @ SV1867 ) ) @ tc_nat ) )
= $true )
| ( ( ( c_List_Onth @ ( c_List_Olist__update @ SV467 @ SV1086 @ SV1565 @ SV1867 ) @ SV1986 @ SV1867 )
= ( c_List_Onth @ SV467 @ SV1986 @ SV1867 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5294]) ).
thf(5524,plain,
! [SV473: $i,SV1571: $i,SV1092: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1092 @ SV1571 @ SV473 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1571 @ SV1092 @ SV473 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV473 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5295]) ).
thf(5525,plain,
! [SV474: $i,SV1572: $i,SV1093: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1093 @ SV1572 @ SV474 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1572 @ SV1093 @ SV474 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV474 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5296]) ).
thf(5526,plain,
! [SV475: $i,SV1573: $i,SV1094: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1094 @ SV1573 @ SV475 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1573 @ SV1094 @ SV475 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV475 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5297]) ).
thf(5527,plain,
! [SV476: $i,SV1574: $i,SV1095: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1095 @ SV1574 @ SV476 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1574 @ SV1095 @ SV476 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV476 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5298]) ).
thf(5528,plain,
! [SV1105: $i,SV488: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV488 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV488 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV488 ) @ SV1105 @ SV488 )
= ( c_HOL_Ozero__class_Ozero @ SV488 ) )
| ( SV1105
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV488 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV488 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5299]) ).
thf(5529,plain,
! [SV1106: $i,SV489: $i] :
( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV1106 @ SV489 )
= ( c_HOL_Ozero__class_Ozero @ SV489 ) )
= $true )
| ( ( SV1106
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( class_Power_Opower @ SV489 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV489 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5300]) ).
thf(5530,plain,
! [SV1595: $i,SV1129: $i,SV518: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV518 ) @ SV1129 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1595 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV1129 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV518 ) ) @ SV1129 ) @ SV1595 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5302]) ).
thf(5531,plain,
! [SV522: $i,SV1133: $i,SV1989: $i,SV1877: $i,SV1598: $i] :
( ( ( ~ ( c_Type_Otyping @ SV1598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1877 ) @ SV1989 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1133 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV1598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1877 ) @ SV1989 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV522 ) )
= $true )
| ( ( SV522 = SV1133 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5303]) ).
thf(5532,plain,
! [SV1991: $i,SV1880: $i,SV1605: $i,SV1148: $i,SV541: $i] :
( ( ( ( c_List_Oreplicate @ SV541 @ SV1148 @ SV1605 )
= ( c_List_Oreplicate @ SV1880 @ SV1991 @ SV1605 ) )
= $false )
| ( ( SV541 = SV1880 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5305]) ).
thf(5533,plain,
! [SV1881: $i,SV1607: $i,SV1150: $i,SV543: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV543 ) @ SV1150 ) @ SV1607 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV543 ) @ SV1881 ) @ SV1607 ) )
= $true )
| ( ( SV1150 = SV1881 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV543 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5306]) ).
thf(5534,plain,
! [SV1992: $i,SV1882: $i,SV1612: $i,SV1157: $i,SV550: $i] :
( ( ( ( c_List_Oappend @ SV550 @ ( c_List_Olist_OCons @ SV1157 @ ( c_List_Olist_ONil @ SV1612 ) @ SV1612 ) @ SV1612 )
= ( c_List_Oappend @ SV1882 @ ( c_List_Olist_OCons @ SV1992 @ ( c_List_Olist_ONil @ SV1612 ) @ SV1612 ) @ SV1612 ) )
= $false )
| ( ( SV550 = SV1882 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5307]) ).
thf(5535,plain,
! [SV1614: $i,SV1159: $i,SV552: $i,SV1883: $i] :
( ( ( SV1883
= ( c_List_Oappend @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV552 @ SV1159 @ SV1614 @ SV1883 ) @ ( c_List_Olist_OCons @ SV1159 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true )
| ( ( SV1883
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV552 ) @ SV1159 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1614 @ SV1883 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5308]) ).
thf(5536,plain,
! [SV1885: $i,SV554: $i,SV1616: $i,SV1161: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1161 @ SV1616 @ SV554 )
!= ( c_Power_Opower__class_Opower @ SV1885 @ SV1616 @ SV554 ) )
= $true )
| ( ( ( SV1161 = SV1885 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1616 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SV1885 @ SV554 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SV1161 @ SV554 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV554 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5310]) ).
thf(5537,plain,
! [SV1887: $i,SV559: $i,SV1619: $i,SV1165: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1165 @ SV1619 @ SV559 )
!= ( c_HOL_Ominus__class_Ominus @ SV1887 @ SV1887 @ SV559 ) )
= $true )
| ( ( SV1165 = SV1619 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV559 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5312]) ).
thf(5538,plain,
! [SV1888: $i,SV1620: $i,SV1166: $i,SV560: $i] :
( ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV560 @ ( tc_List_Olist @ SV1166 ) ) @ SV1620 @ SV1166 )
!= SV560 )
= $true )
| ( ( ( SV1620
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV1620 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) )
| ( ( c_List_Oappend @ SV1620 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1620 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) @ SV1888 @ SV1166 ) @ SV1166 )
= ( c_List_Oappend @ SV560 @ SV1888 @ SV1166 ) ) )
= $true )
| ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV560 @ ( tc_List_Olist @ SV1166 ) ) @ SV1620 @ SV1166 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1620 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) @ SV1888 @ SV1166 ) @ SV1166 )
= SV1888 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5313]) ).
thf(5539,plain,
! [SV562: $i,SV1621: $i,SV1168: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1168 @ SV1621 @ SV562 )
= ( c_HOL_Ozero__class_Ozero @ SV562 ) )
= $false )
| ( ( SV1168 = SV1621 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV562 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5314]) ).
thf(5540,plain,
! [SV1891: $i,SV1628: $i,SV1175: $i,SV570: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV570 ) @ SV1175 ) @ SV1628 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV570 ) @ SV1175 ) @ SV1891 ) )
= $true )
| ( ( SV1628 = SV1891 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV570 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5317]) ).
thf(5541,plain,
! [SV1993: $i,SV1893: $i,SV1631: $i,SV1178: $i,SV573: $i] :
( ( ( ( c_List_Oappend @ SV573 @ ( c_List_Olist_OCons @ SV1178 @ ( c_List_Olist_ONil @ SV1631 ) @ SV1631 ) @ SV1631 )
= ( c_List_Oappend @ SV1893 @ ( c_List_Olist_OCons @ SV1993 @ ( c_List_Olist_ONil @ SV1631 ) @ SV1631 ) @ SV1631 ) )
= $false )
| ( ( SV1178 = SV1993 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5319]) ).
thf(5542,plain,
! [SV1994: $i,SV1894: $i,SV1632: $i,SV1179: $i,SV574: $i] :
( ( ( ( c_List_Oappend @ SV574 @ SV1179 @ SV1632 )
= ( c_List_Oappend @ SV1894 @ SV1994 @ SV1632 ) )
= $false )
| ( ( ( SV1179
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV574 @ ( tc_List_Olist @ SV1632 ) ) @ SV1894 @ SV1632 ) @ SV1994 @ SV1632 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV574 @ ( tc_List_Olist @ SV1632 ) ) @ ( c_Nat_Osize__class_Osize @ SV1894 @ ( tc_List_Olist @ SV1632 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5320]) ).
thf(5543,plain,
! [SV1635: $i,SV1182: $i,SV577: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV577 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV577 )
| ~ ( class_Power_Opower @ SV577 )
| ( ( c_Power_Opower__class_Opower @ SV1182 @ SV1635 @ SV577 )
!= ( c_HOL_Ozero__class_Ozero @ SV577 ) )
| ( SV1182
= ( c_HOL_Ozero__class_Ozero @ SV577 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV577 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5322]) ).
thf(5544,plain,
! [SV1995: $i,SV1896: $i,SV1636: $i,SV1183: $i,SV578: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV578 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1183 @ SV1636 @ SV578 )
!= ( c_HOL_Ominus__class_Ominus @ SV1896 @ SV1995 @ SV578 ) )
| ( c_HOL_Oord__class_Oless @ SV1896 @ SV1995 @ SV578 )
| ~ ( c_HOL_Oord__class_Oless @ SV1183 @ SV1636 @ SV578 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5323]) ).
thf(5545,plain,
! [SV1996: $i,SV1898: $i,SV1638: $i,SV1185: $i,SV582: $i] :
( ( ( ( c_List_Olist_OCons @ SV582 @ SV1185 @ SV1638 )
= ( c_List_Olist_OCons @ SV1898 @ SV1996 @ SV1638 ) )
= $false )
| ( ( SV1185 = SV1996 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5325]) ).
thf(5546,plain,
! [SV584: $i,SV1640: $i,SV1187: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1187 @ SV1640 @ SV584 )
= ( c_HOL_Ozero__class_Ozero @ SV584 ) )
= $false )
| ( ( SV1187
= ( c_HOL_Ozero__class_Ozero @ SV584 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV584 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5326]) ).
thf(5547,plain,
! [SV1641: $i,SV1188: $i,SV1899: $i,SV585: $i] :
( ( ( hBOOL @ ( hAPP @ SV585 @ SV1899 ) )
= $true )
| ( ( ~ ( c_in @ SV1899 @ ( c_List_Oset @ SV1188 @ SV1641 ) @ SV1641 ) )
= $true )
| ( ( ( c_List_OtakeWhile @ SV585 @ SV1188 @ SV1641 )
= SV1188 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5327]) ).
thf(5548,plain,
! [SV1997: $i,SV1901: $i,SV1648: $i,SV1197: $i,SV594: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV594 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1197 @ SV1648 @ SV594 )
!= ( c_HOL_Ominus__class_Ominus @ SV1901 @ SV1997 @ SV594 ) )
| ( c_HOL_Oord__class_Oless @ SV1197 @ SV1648 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV1901 @ SV1997 @ SV594 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5330]) ).
thf(5549,plain,
! [SV1998: $i,SV1902: $i,SV1650: $i,SV1199: $i,SV596: $i] :
( ( ( ( c_List_Oappend @ SV596 @ SV1199 @ SV1650 )
= ( c_List_Oappend @ SV1902 @ SV1998 @ SV1650 ) )
= $false )
| ( ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV1902 @ ( tc_List_Olist @ SV1650 ) ) @ SV596 @ SV1650 )
= SV1902 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV596 @ ( tc_List_Olist @ SV1650 ) ) @ ( c_Nat_Osize__class_Osize @ SV1902 @ ( tc_List_Olist @ SV1650 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5331]) ).
thf(5550,plain,
! [SV1904: $i,SV1656: $i,SV1205: $i,SV603: $i] :
( ( ( ( c_List_Oappend @ SV603 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV603 @ ( tc_List_Olist @ SV1205 ) ) @ SV1656 @ SV1205 ) @ SV1904 @ SV1205 ) @ SV1205 )
= ( c_List_Oappend @ SV1656 @ SV1904 @ SV1205 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV603 @ ( tc_List_Olist @ SV1205 ) ) @ ( c_Nat_Osize__class_Osize @ SV1656 @ ( tc_List_Olist @ SV1205 ) ) @ tc_nat ) )
= $true )
| ( ( SV603
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV603 @ ( tc_List_Olist @ SV1205 ) ) @ SV1656 @ SV1205 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5333]) ).
thf(5551,plain,
! [SV2027: $i,SV1999: $i,SV1905: $i,SV1659: $i,SV1209: $i,SV607: $i] :
( ( ( ( c_List_Omap @ SV607 @ SV1209 @ SV1659 @ SV1905 )
!= ( c_List_Omap @ SV1999 @ SV1209 @ SV1659 @ SV1905 ) )
= $true )
| ( ( ( ( hAPP @ SV607 @ SV2027 )
= ( hAPP @ SV1999 @ SV2027 ) )
| ~ ( c_in @ SV2027 @ ( c_List_Oset @ SV1209 @ SV1659 ) @ SV1659 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5334]) ).
thf(5552,plain,
! [SV1663: $i,SV611: $i,SV1213: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV1213 @ SV611 )
= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1663 @ SV611 ) )
= $false )
| ( ( SV1213 = SV1663 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV611 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5337]) ).
thf(5553,plain,
! [SV612: $i,SV1664: $i,SV1214: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1214 @ SV1664 @ SV612 )
= ( c_HOL_Ozero__class_Ozero @ SV612 ) )
= $false )
| ( ( SV1214 = SV1664 )
= $true )
| ( ( class_OrderedGroup_Ogroup__add @ SV612 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5338]) ).
thf(5554,plain,
! [SV2000: $i,SV1908: $i,SV1665: $i,SV1215: $i,SV613: $i] :
( ( ( ( c_List_Odrop @ SV613 @ SV1215 @ SV1665 )
= ( c_List_Olist_OCons @ SV1908 @ SV2000 @ SV1665 ) )
= $false )
| ( ( ( c_List_Onth @ SV1215 @ SV613 @ SV1665 )
= SV1908 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5339]) ).
thf(5555,plain,
! [SV2001: $i,SV1909: $i,SV1666: $i,SV1216: $i,SV614: $i] :
( ( ( ( c_List_Oappend @ SV614 @ SV1216 @ SV1666 )
= ( c_List_Oappend @ SV1909 @ SV2001 @ SV1666 ) )
= $false )
| ( ( ( SV614
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV614 @ ( tc_List_Olist @ SV1666 ) ) @ SV1909 @ SV1666 ) )
| ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV614 @ ( tc_List_Olist @ SV1666 ) ) @ ( c_Nat_Osize__class_Osize @ SV1909 @ ( tc_List_Olist @ SV1666 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5340]) ).
thf(5556,plain,
! [SV1667: $i,SV1217: $i,SV615: $i] :
( ( ( class_Int_Onumber__ring @ SV615 )
= $false )
| ( ( ( SV1217
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV615 ) @ SV1217 ) @ SV1667 ) )
| ( SV1667
= ( c_HOL_Ozero__class_Ozero @ SV615 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV615 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5341]) ).
thf(5557,plain,
! [SV1218: $i,SV616: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV616 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV616 )
| ( ( c_Power_Opower__class_Opower @ SV1218 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV616 )
!= ( c_HOL_Ozero__class_Ozero @ SV616 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV616 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV616 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5342]) ).
thf(5558,plain,
! [SV1668: $i,SV1219: $i,SV617: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV617 ) @ SV1219 ) @ SV1668 )
= ( c_HOL_Ozero__class_Ozero @ SV617 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV617 ) @ SV1668 @ SV617 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV617 ) @ SV1219 @ SV617 )
| ( SV1668
= ( c_HOL_Ozero__class_Ozero @ SV617 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV617 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5343]) ).
thf(5559,plain,
! [SV1910: $i,SV618: $i,SV1669: $i,SV1220: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1220 @ SV1669 @ SV618 )
!= ( c_Power_Opower__class_Opower @ SV1220 @ SV1910 @ SV618 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV618 ) @ SV1220 @ SV618 )
| ( SV1669 = SV1910 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV618 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5344]) ).
thf(5560,plain,
! [SV2002: $i,SV1911: $i,SV1672: $i,SV1223: $i,SV621: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV621 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1223 @ SV1672 @ SV621 )
!= ( c_HOL_Ominus__class_Ominus @ SV1911 @ SV2002 @ SV621 ) )
| ( c_lessequals @ SV1672 @ SV1223 @ SV621 )
| ~ ( c_lessequals @ SV2002 @ SV1911 @ SV621 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5345]) ).
thf(5561,plain,
! [SV2003: $i,SV1912: $i,SV1673: $i,SV1224: $i,SV622: $i] :
( ( ( ( c_List_Oreplicate @ SV622 @ SV1224 @ SV1673 )
= ( c_List_Oreplicate @ SV1912 @ SV2003 @ SV1673 ) )
= $false )
| ( ( ( SV1224 = SV2003 )
| ( SV622
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5346]) ).
thf(5562,plain,
! [SV1913: $i,SV1674: $i,SV623: $i,SV1225: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1225 @ SV1225 @ SV623 )
!= ( c_HOL_Ominus__class_Ominus @ SV1674 @ SV1913 @ SV623 ) )
= $true )
| ( ( SV1674 = SV1913 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV623 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5347]) ).
thf(5563,plain,
! [SV1675: $i,SV1226: $i,SV624: $i] :
( ( ( class_Int_Onumber__ring @ SV624 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1226 @ SV1675 @ SV624 )
!= ( c_HOL_Ozero__class_Ozero @ SV624 ) )
| ( SV1226 = SV1675 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV624 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5348]) ).
thf(5564,plain,
! [SV1914: $i,SV625: $i,SV1676: $i,SV1227: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1227 @ ( c_Suc @ SV1676 ) @ SV625 )
!= ( c_Power_Opower__class_Opower @ SV1914 @ ( c_Suc @ SV1676 ) @ SV625 ) )
= $true )
| ( ( ( SV1227 = SV1914 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV625 ) @ SV1914 @ SV625 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV625 ) @ SV1227 @ SV625 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV625 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5349]) ).
thf(5565,plain,
! [SV2004: $i,SV1915: $i,SV1677: $i,SV1228: $i,SV626: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV626 )
= $false )
| ( ( ( ( c_HOL_Ominus__class_Ominus @ SV1228 @ SV1677 @ SV626 )
!= ( c_HOL_Ominus__class_Ominus @ SV1915 @ SV2004 @ SV626 ) )
| ( c_lessequals @ SV2004 @ SV1915 @ SV626 )
| ~ ( c_lessequals @ SV1677 @ SV1228 @ SV626 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5350]) ).
thf(5566,plain,
! [SV1679: $i,SV1916: $i,SV629: $i,SV1230: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1230 @ ( c_Nat_Osize__class_Osize @ SV629 @ ( tc_List_Olist @ SV1916 ) ) @ tc_nat ) )
= $true )
| ( ( ( c_List_Onth @ SV629 @ SV1230 @ SV1916 )
= SV1679 )
= $true )
| ( ( ( c_List_Olist__update @ SV629 @ SV1230 @ SV1679 @ SV1916 )
= SV629 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5351]) ).
thf(5567,plain,
! [SV2005: $i,SV1917: $i,SV1680: $i,SV1231: $i,SV630: $i] :
( ( ( ( c_List_Oappend @ SV630 @ SV1231 @ SV1680 )
= ( c_List_Oappend @ SV1917 @ SV2005 @ SV1680 ) )
= $false )
| ( ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1917 @ ( tc_List_Olist @ SV1680 ) ) @ SV630 @ SV1680 ) @ SV1231 @ SV1680 )
= SV2005 )
| ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV630 @ ( tc_List_Olist @ SV1680 ) ) @ ( c_Nat_Osize__class_Osize @ SV1917 @ ( tc_List_Olist @ SV1680 ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5352]) ).
thf(5568,plain,
! [SV2006: $i,SV1918: $i,SV1681: $i,SV1232: $i,SV631: $i] :
( ( ( ( c_List_Olist_OCons @ SV631 @ SV1232 @ SV1681 )
= ( c_List_Olist_OCons @ SV1918 @ SV2006 @ SV1681 ) )
= $false )
| ( ( SV631 = SV1918 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5353]) ).
thf(5569,plain,
! [SV2007: $i,SV1919: $i,SV1683: $i,SV1234: $i,SV633: $i] :
( ( ( ( c_List_Omap @ SV633 @ SV1234 @ SV1683 @ SV1919 )
= ( c_List_Omap @ SV633 @ SV2007 @ SV1683 @ SV1919 ) )
= $false )
| ( ( ( c_Nat_Osize__class_Osize @ SV1234 @ ( tc_List_Olist @ SV1683 ) )
= ( c_Nat_Osize__class_Osize @ SV2007 @ ( tc_List_Olist @ SV1683 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5354]) ).
thf(5570,plain,
! [SV1920: $i,SV1685: $i,SV1237: $i,SV637: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV637 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1237 ) @ SV1685 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1237 ) @ SV1920 ) )
| ( SV1685 = SV1920 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV637 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5356]) ).
thf(5571,plain,
! [SV1921: $i,SV1238: $i,SV1686: $i,SV638: $i] :
( ( ( SV638
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1686 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV638 @ SV1238 @ SV1686 @ SV1921 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV1921
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV638 ) @ SV1238 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1686 @ SV1921 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5357]) ).
thf(5572,plain,
! [SV1687: $i,SV1239: $i,SV639: $i] :
( ( ( class_Int_Onumber__ring @ SV639 )
= $false )
| ( ( ( ( c_Int_Onumber__class_Onumber__of @ SV1239 @ SV639 )
!= ( c_Int_Onumber__class_Onumber__of @ SV1687 @ SV639 ) )
| ( SV1239 = SV1687 ) )
= $true )
| ( ( class_Int_Oring__char__0 @ SV639 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5358]) ).
thf(5573,plain,
! [SV1924: $i,SV644: $i,SV1243: $i,SV1690: $i] :
( ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV1690 @ ( tc_List_Olist @ SV1243 ) ) @ ( c_Nat_Osize__class_Osize @ SV644 @ ( tc_List_Olist @ SV1243 ) ) @ tc_nat )
= $true )
| ( ( ( c_List_Oappend @ SV1690 @ SV1924 @ SV1243 )
= ( c_List_Oappend @ SV644 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV644 @ ( tc_List_Olist @ SV1243 ) ) @ SV1690 @ SV1243 ) @ SV1924 @ SV1243 ) @ SV1243 ) )
= $true )
| ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV644 @ ( tc_List_Olist @ SV1243 ) ) @ SV1690 @ SV1243 )
= SV644 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5361]) ).
thf(5574,plain,
! [SV646: $i,SV1692: $i,SV1245: $i] :
( ( ( c_lessequals @ SV1245 @ SV1692 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1245 @ SV646 @ tc_nat )
| ( SV646 = SV1692 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV646 @ SV1245 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1692 @ SV1245 @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5363]) ).
thf(5575,plain,
! [SV1693: $i,SV1246: $i,SV647: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV647 ) @ SV1246 ) @ SV1693 )
= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV647 ) @ SV1693 @ SV647 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV647 ) @ SV1246 @ SV647 )
| ( SV1246
= ( c_HOL_Ozero__class_Ozero @ SV647 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV647 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5364]) ).
thf(5576,plain,
! [SV1926: $i,SV1694: $i,SV1247: $i,SV648: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV648 ) @ SV1247 ) @ SV1694 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV648 ) @ SV1247 ) @ SV1926 ) )
= $true )
| ( ( SV1694 = SV1926 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV648 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5365]) ).
thf(5577,plain,
! [SV2008: $i,SV1927: $i,SV1695: $i,SV1248: $i,SV649: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV649 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1248 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1695 ) @ SV1927 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1695 ) @ SV2008 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1248 ) @ SV1927 )
= SV2008 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5366]) ).
thf(5578,plain,
! [SV1931: $i,SV1701: $i,SV1256: $i,SV2: $i,SV658: $i] :
( ( ( c_lessequals @ SV658 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SV1256 ) @ SV1701 ) @ SV2 )
= $true )
| ( ( ~ ( c_lessequals @ SV1931 @ SV1701 @ SV2 )
| ~ ( c_lessequals @ SV658 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SV1256 ) @ SV1931 ) @ SV2 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5369]) ).
thf(5579,plain,
! [SV659: $i,SV3: $i,SV1257: $i,SV1702: $i] :
( ( ( ~ ( c_lessequals @ SV1702 @ SV1257 @ SV3 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV659 @ SV1702 @ SV3 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV659 @ SV1257 @ SV3 )
= $true )
| ( ( class_Orderings_Opreorder @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5370]) ).
thf(5580,plain,
! [SV660: $i,SV4: $i,SV1258: $i,SV1703: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1703 @ SV1258 @ SV4 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV660 @ SV1703 @ SV4 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV660 @ SV1258 @ SV4 )
= $true )
| ( ( class_Orderings_Opreorder @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5371]) ).
thf(5581,plain,
! [SV664: $i,SV10: $i,SV1260: $i,SV1704: $i] :
( ( ( ~ ( c_lessequals @ SV1704 @ SV1260 @ SV10 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV664 @ SV1704 @ SV10 ) )
= $true )
| ( ( c_lessequals @ SV664 @ SV1260 @ SV10 )
= $true )
| ( ( class_Orderings_Opreorder @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5373]) ).
thf(5582,plain,
! [SV1261: $i,SV11: $i,SV1705: $i,SV665: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV665 @ SV1705 @ SV11 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1705 @ SV1261 @ SV11 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV665 @ SV1261 @ SV11 )
= $true )
| ( ( class_Orderings_Oorder @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5374]) ).
thf(5583,plain,
! [SV1262: $i,SV12: $i,SV1706: $i,SV666: $i] :
( ( ( ~ ( c_lessequals @ SV666 @ SV1706 @ SV12 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1706 @ SV1262 @ SV12 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV666 @ SV1262 @ SV12 )
= $true )
| ( ( class_Orderings_Oorder @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5375]) ).
thf(5584,plain,
! [SV1263: $i,SV13: $i,SV1707: $i,SV667: $i] :
( ( ( ~ ( c_lessequals @ SV667 @ SV1707 @ SV13 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1707 @ SV1263 @ SV13 ) )
= $true )
| ( ( c_lessequals @ SV667 @ SV1263 @ SV13 )
= $true )
| ( ( class_Orderings_Oorder @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5376]) ).
thf(5585,plain,
! [SV15: $i,SV1265: $i,SV669: $i] :
( ( ( c_lessequals @ SV669 @ SV1265 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV669 @ SV15 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV15 @ SV1265 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV15 @ SV669 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1265 @ SV669 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5378]) ).
thf(5586,plain,
! [SV16: $i,SV670: $i,SV1266: $i] :
( ( ( c_lessequals @ SV1266 @ SV670 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1266 @ SV16 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV16 @ SV1266 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV670 @ SV1266 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV16 @ SV670 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5379]) ).
thf(5587,plain,
! [SV1708: $i,SV673: $i,SV1267: $i,SV20: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV1267 @ SV20 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV673 @ ( c_Suc @ SV1708 ) @ SV20 ) @ ( c_Power_Opower__class_Opower @ SV1267 @ ( c_Suc @ SV1708 ) @ SV20 ) @ SV20 ) )
= $true )
| ( ( c_lessequals @ SV673 @ SV1267 @ SV20 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5380]) ).
thf(5588,plain,
! [SV674: $i,SV21: $i,SV1709: $i,SV1268: $i] :
( ( ( c_lessequals @ SV1268 @ SV1709 @ SV21 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SV674 ) @ SV1268 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SV674 ) @ SV1709 ) @ SV21 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5381]) ).
thf(5589,plain,
! [SV1269: $i,SV22: $i,SV1710: $i,SV675: $i] :
( ( ( c_lessequals @ SV675 @ SV1710 @ SV22 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV675 ) @ SV1269 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV1710 ) @ SV1269 ) @ SV22 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5382]) ).
thf(5590,plain,
! [SV1270: $i,SV676: $i,SV1711: $i,SV23: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV23 ) @ SV1711 ) @ SV676 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV23 ) @ SV1711 ) @ SV1270 ) @ SV23 )
= $false )
| ( ( c_lessequals @ SV676 @ SV1270 @ SV23 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5383]) ).
thf(5591,plain,
! [SV677: $i,SV24: $i,SV1712: $i,SV1271: $i] :
( ( ( c_lessequals @ SV1271 @ SV1712 @ SV24 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ SV677 ) @ SV1271 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ SV677 ) @ SV1712 ) @ SV24 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5384]) ).
thf(5592,plain,
! [SV1272: $i,SV1713: $i,SV678: $i,SV25: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SV678 ) @ SV1713 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SV1272 ) @ SV1713 ) @ SV25 )
= $false )
| ( ( c_lessequals @ SV678 @ SV1272 @ SV25 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5385]) ).
thf(5593,plain,
! [SV1273: $i,SV26: $i,SV1714: $i,SV679: $i] :
( ( ( c_lessequals @ SV679 @ SV1714 @ SV26 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV26 ) @ SV679 ) @ SV1273 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV26 ) @ SV1714 ) @ SV1273 ) @ SV26 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV26 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5386]) ).
thf(5594,plain,
! [SV37: $i,SV1280: $i,SV688: $i] :
( ( ( c_lessequals @ SV688 @ SV1280 @ SV37 )
= $false )
| ( ( ~ ( c_lessequals @ SV1280 @ SV688 @ SV37 ) )
= $true )
| ( ( SV688 = SV1280 )
= $true )
| ( ( class_Orderings_Oorder @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5393]) ).
thf(5595,plain,
! [SV38: $i,SV689: $i,SV1281: $i] :
( ( ( c_lessequals @ SV1281 @ SV689 @ SV38 )
= $false )
| ( ( ~ ( c_lessequals @ SV689 @ SV1281 @ SV38 ) )
= $true )
| ( ( SV689 = SV1281 )
= $true )
| ( ( class_Orderings_Oorder @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5394]) ).
thf(5596,plain,
! [SV39: $i,SV690: $i,SV1282: $i] :
( ( ( c_lessequals @ SV1282 @ SV690 @ SV39 )
= $false )
| ( ( ~ ( c_lessequals @ SV690 @ SV1282 @ SV39 ) )
= $true )
| ( ( SV690 = SV1282 )
= $true )
| ( ( class_Orderings_Oorder @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5395]) ).
thf(5597,plain,
! [SV43: $i,SV1283: $i,SV693: $i] :
( ( ( c_lessequals @ SV693 @ SV1283 @ SV43 )
= $false )
| ( ( c_lessequals @ SV1283 @ SV693 @ SV43 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV693 @ SV1283 @ SV43 )
= $true )
| ( ( class_Orderings_Opreorder @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5396]) ).
thf(5598,plain,
! [SV1286: $i,SV1715: $i,SV52: $i,SV701: $i] :
( ( ( ~ ( c_lessequals @ SV701 @ ( c_HOL_Oone__class_Oone @ SV52 ) @ SV52 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV701 @ SV52 )
| ~ ( c_lessequals @ SV1715 @ SV1286 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV701 @ SV1286 @ SV52 ) @ ( c_Power_Opower__class_Opower @ SV701 @ SV1715 @ SV52 ) @ SV52 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5398]) ).
thf(5599,plain,
! [SV1934: $i,SV1718: $i,SV1293: $i,SV713: $i,SV64: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV713 ) @ SV1293 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV1718 ) @ SV1934 ) @ SV64 )
= $true )
| ( ( ~ ( c_lessequals @ SV1293 @ SV1934 @ SV64 )
| ~ ( c_lessequals @ SV713 @ SV1718 @ SV64 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5404]) ).
thf(5600,plain,
! [SV1719: $i,SV1294: $i,SV1935: $i,SV714: $i,SV65: $i] :
( ( ( c_lessequals @ SV65 @ ( hAPP @ SV714 @ SV1935 ) @ tc_nat )
= $false )
| ( ( ~ ( c_in @ SV1935 @ ( c_List_Oset @ SV1294 @ SV1719 ) @ SV1719 ) )
= $true )
| ( ( c_lessequals @ SV65 @ ( c_List_Olist_Olist__size @ SV714 @ SV1294 @ SV1719 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5405]) ).
thf(5601,plain,
! [SV74: $i,SV722: $i,SV1296: $i] :
( ( ( c_lessequals @ SV1296 @ SV722 @ SV74 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV722 @ SV1296 @ SV74 )
= $false )
| ( ( class_Orderings_Olinorder @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5407]) ).
thf(5602,plain,
! [SV76: $i,SV724: $i,SV1298: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1298 @ SV724 @ SV76 )
= $false )
| ( ( c_lessequals @ SV724 @ SV1298 @ SV76 )
= $false )
| ( ( class_Orderings_Olinorder @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5408]) ).
thf(5603,plain,
! [SV78: $i,SV726: $i,SV1300: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1300 @ SV726 @ SV78 )
= $false )
| ( ( c_lessequals @ SV726 @ SV1300 @ SV78 )
= $false )
| ( ( class_Orderings_Opreorder @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5409]) ).
thf(5604,plain,
! [SV1720: $i,SV1301: $i,SV727: $i,SV79: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV79 ) @ SV727 @ SV79 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1301 @ SV1720 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV727 @ SV1301 @ SV79 ) @ ( c_Power_Opower__class_Opower @ SV727 @ SV1720 @ SV79 ) @ SV79 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5410]) ).
thf(5605,plain,
! [SV86: $i,SV1304: $i,SV733: $i] :
( ( ( c_lessequals @ SV733 @ SV1304 @ SV86 )
= $false )
| ( ( SV1304 = SV733 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV733 @ SV1304 @ SV86 )
= $true )
| ( ( class_Orderings_Oorder @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5411]) ).
thf(5606,plain,
! [SV87: $i,SV1305: $i,SV734: $i] :
( ( ( c_lessequals @ SV734 @ SV1305 @ SV87 )
= $false )
| ( ( SV1305 = SV734 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV734 @ SV1305 @ SV87 )
= $true )
| ( ( class_Orderings_Oorder @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5412]) ).
thf(5607,plain,
! [SV91: $i,SV1306: $i,SV738: $i] :
( ( ( c_lessequals @ SV738 @ SV1306 @ SV91 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV738 @ SV1306 @ SV91 )
= $true )
| ( ( SV738 = SV1306 )
= $true )
| ( ( class_Orderings_Oorder @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5413]) ).
thf(5608,plain,
! [SV92: $i,SV1307: $i,SV739: $i] :
( ( ( c_lessequals @ SV739 @ SV1307 @ SV92 )
= $false )
| ( ( SV739 = SV1307 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV739 @ SV1307 @ SV92 )
= $true )
| ( ( class_Orderings_Oorder @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5414]) ).
thf(5609,plain,
! [SV93: $i,SV1308: $i,SV740: $i] :
( ( ( c_lessequals @ SV740 @ SV1308 @ SV93 )
= $false )
| ( ( SV740 = SV1308 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV740 @ SV1308 @ SV93 )
= $true )
| ( ( class_Orderings_Oorder @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5415]) ).
thf(5610,plain,
! [SV94: $i,SV1309: $i,SV741: $i] :
( ( ( c_lessequals @ SV741 @ SV1309 @ SV94 )
= $false )
| ( ( SV741 = SV1309 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV741 @ SV1309 @ SV94 )
= $true )
| ( ( class_Orderings_Oorder @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5416]) ).
thf(5611,plain,
! [SV95: $i,SV1310: $i,SV742: $i] :
( ( ( c_lessequals @ SV742 @ SV1310 @ SV95 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV742 @ SV1310 @ SV95 )
= $true )
| ( ( SV742 = SV1310 )
= $true )
| ( ( class_Orderings_Olinorder @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5417]) ).
thf(5612,plain,
! [SV96: $i,SV1311: $i,SV743: $i] :
( ( ( c_lessequals @ SV743 @ SV1311 @ SV96 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV743 @ SV1311 @ SV96 )
= $true )
| ( ( SV743 = SV1311 )
= $true )
| ( ( class_Orderings_Olinorder @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5418]) ).
thf(5613,plain,
! [SV1313: $i,SV101: $i,SV748: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV748 @ ( c_HOL_Oone__class_Oone @ SV101 ) @ SV101 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ SV748 @ SV101 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV748 @ ( c_Suc @ SV1313 ) @ SV101 ) @ ( c_HOL_Oone__class_Oone @ SV101 ) @ SV101 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5419]) ).
thf(5614,plain,
! [SV749: $i,SV102: $i,SV1721: $i,SV1314: $i] :
( ( ( ~ ( c_in @ SV1314 @ ( c_List_Oset @ SV1721 @ SV102 ) @ SV102 ) )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV749 @ SV1721 @ SV102 ) @ SV102 ) )
= $true )
| ( ( c_lessequals @ SV749 @ SV1314 @ SV102 )
= $true )
| ( ( class_Orderings_Olinorder @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5420]) ).
thf(5615,plain,
! [SV1936: $i,SV1722: $i,SV103: $i,SV1315: $i,SV750: $i] :
( ( ( c_lessequals @ SV750 @ SV1315 @ SV103 )
= $true )
| ( ( ~ ( c_in @ SV1315 @ ( c_List_Oset @ SV1722 @ SV103 ) @ SV103 )
| ~ ( c_in @ SV750 @ ( c_List_Oset @ SV1936 @ SV103 ) @ SV103 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1936 @ SV1722 @ SV103 ) @ SV103 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5421]) ).
thf(5616,plain,
! [SV754: $i,SV1319: $i,SV109: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV1319 @ SV109 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV754 @ SV109 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ SV754 ) @ SV1319 ) @ SV109 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5424]) ).
thf(5617,plain,
! [SV1723: $i,SV1320: $i,SV757: $i,SV113: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV113 )
= $false )
| ( ( ( c_lessequals @ SV757 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV1320 ) @ SV1723 ) @ SV113 )
| ~ ( c_lessequals @ SV757 @ SV1723 @ SV113 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV1320 @ SV113 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5426]) ).
thf(5618,plain,
! [SV1724: $i,SV1321: $i,SV758: $i,SV114: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV114 )
= $false )
| ( ( ( c_lessequals @ SV758 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SV1321 ) @ SV1724 ) @ SV114 )
| ~ ( c_lessequals @ SV758 @ SV1321 @ SV114 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV1724 @ SV114 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5427]) ).
thf(5619,plain,
! [SV761: $i,SV117: $i,SV1322: $i] :
( ( ( c_lessequals @ SV1322 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
= $false )
| ( ( ~ ( c_lessequals @ SV761 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV761 ) @ SV1322 ) @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5428]) ).
thf(5620,plain,
! [SV1937: $i,SV1725: $i,SV1323: $i,SV762: $i,SV118: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV762 ) @ SV1323 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV1725 ) @ SV1937 ) @ SV118 )
= $true )
| ( ( ~ ( c_lessequals @ SV1323 @ SV1937 @ SV118 )
| ~ ( c_HOL_Oord__class_Oless @ SV762 @ SV1725 @ SV118 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5429]) ).
thf(5621,plain,
! [SV1938: $i,SV1726: $i,SV1324: $i,SV763: $i,SV119: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV119 ) @ SV763 ) @ SV1324 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV119 ) @ SV1726 ) @ SV1938 ) @ SV119 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1324 @ SV1938 @ SV119 )
| ~ ( c_lessequals @ SV763 @ SV1726 @ SV119 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5430]) ).
thf(5622,plain,
! [SV1325: $i,SV121: $i,SV765: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ SV765 @ SV121 ) @ ( c_Int_Onumber__class_Onumber__of @ SV1325 @ SV121 ) @ SV121 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ SV1325 @ SV121 ) @ ( c_Int_Onumber__class_Onumber__of @ SV765 @ SV121 ) @ SV121 ) )
= $true )
| ( ( class_Int_Onumber @ SV121 )
= $false )
| ( ( class_Orderings_Olinorder @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5431]) ).
thf(5623,plain,
! [SV1326: $i,SV122: $i,SV766: $i] :
( ( ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ SV766 @ SV122 ) @ ( c_Int_Onumber__class_Onumber__of @ SV1326 @ SV122 ) @ SV122 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ SV1326 @ SV122 ) @ ( c_Int_Onumber__class_Onumber__of @ SV766 @ SV122 ) @ SV122 )
= $true )
| ( ( class_Int_Onumber @ SV122 )
= $false )
| ( ( class_Orderings_Olinorder @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5432]) ).
thf(5624,plain,
! [SV1329: $i,SV1728: $i,SV774: $i,SV133: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV133 ) @ SV774 @ SV133 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV774 @ SV1728 @ SV133 ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV774 @ SV1329 @ SV133 ) @ ( c_Power_Opower__class_Opower @ SV1728 @ SV1329 @ SV133 ) @ SV133 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5435]) ).
thf(5625,plain,
! [SV790: $i,SV1735: $i,SV1341: $i,SV149: $i] :
( ( ( c_List_Olistsp @ SV149 @ SV1341 @ SV1735 )
= $false )
| ( ( c_in @ SV790 @ ( c_List_Oset @ SV1341 @ SV1735 ) @ SV1735 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV149 @ SV790 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5437]) ).
thf(5626,plain,
! [SV152: $i,SV793: $i,SV1737: $i,SV1344: $i] :
( ( ( ~ ( c_lessequals @ SV1344 @ SV1737 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1737 @ ( c_Nat_Osize__class_Osize @ SV793 @ ( tc_List_Olist @ SV152 ) ) @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ SV793 @ SV152 ) )
= $true )
| ( ( c_lessequals @ ( c_List_Onth @ SV793 @ SV1344 @ SV152 ) @ ( c_List_Onth @ SV793 @ SV1737 @ SV152 ) @ SV152 )
= $true )
| ( ( class_Orderings_Olinorder @ SV152 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5438]) ).
thf(5627,plain,
! [SV1345: $i,SV153: $i,SV794: $i,SV1738: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1738 @ ( c_Nat_Osize__class_Osize @ SV794 @ ( tc_List_Olist @ SV153 ) ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1345 @ SV1738 @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ SV794 @ SV153 ) )
= $true )
| ( ( c_lessequals @ ( c_List_Onth @ SV794 @ SV1345 @ SV153 ) @ ( c_List_Onth @ SV794 @ SV1738 @ SV153 ) @ SV153 )
= $true )
| ( ( class_Orderings_Olinorder @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5439]) ).
thf(5628,plain,
! [SV156: $i,SV1740: $i,SV1348: $i,SV797: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV797 @ ( c_List_Olist_OCons @ SV1348 @ SV1740 @ SV156 ) @ SV156 ) @ SV156 )
= $false )
| ( ( c_lessequals @ SV797 @ SV1348 @ SV156 )
= $true )
| ( ( class_Orderings_Olinorder @ SV156 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5440]) ).
thf(5629,plain,
! [SV798: $i,SV157: $i,SV1741: $i,SV1349: $i] :
( ( ( ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1349 @ SV1741 @ SV157 ) @ SV157 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV798 @ SV1349 @ SV157 ) )
= $true )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV798 @ ( c_List_Olist_OCons @ SV1349 @ SV1741 @ SV157 ) @ SV157 ) @ SV157 )
= $true )
| ( ( class_Orderings_Olinorder @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5441]) ).
thf(5630,plain,
! [SV2009: $i,SV1940: $i,SV1748: $i,SV1361: $i,SV810: $i,SV169: $i] :
( ( ( class_Orderings_Olinorder @ SV169 )
= $false )
| ( ( ( ( c_List_Olinorder__class_Oinsort__key @ SV810 @ SV1361 @ ( c_List_Olist_OCons @ SV1748 @ SV1940 @ SV2009 ) @ SV2009 @ SV169 )
= ( c_List_Olist_OCons @ SV1361 @ ( c_List_Olist_OCons @ SV1748 @ SV1940 @ SV2009 ) @ SV2009 ) )
| ~ ( c_lessequals @ ( hAPP @ SV810 @ SV1361 ) @ ( hAPP @ SV810 @ SV1748 ) @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5442]) ).
thf(5631,plain,
! [SV2010: $i,SV1941: $i,SV1749: $i,SV1362: $i,SV811: $i,SV170: $i] :
( ( ( class_Orderings_Olinorder @ SV170 )
= $false )
| ( ( ( ( c_List_Olinorder__class_Oinsort__key @ SV811 @ SV1362 @ ( c_List_Olist_OCons @ SV1749 @ SV1941 @ SV2010 ) @ SV2010 @ SV170 )
= ( c_List_Olist_OCons @ SV1749 @ ( c_List_Olinorder__class_Oinsort__key @ SV811 @ SV1362 @ SV1941 @ SV2010 @ SV170 ) @ SV2010 ) )
| ( c_lessequals @ ( hAPP @ SV811 @ SV1362 ) @ ( hAPP @ SV811 @ SV1749 ) @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5443]) ).
thf(5632,plain,
! [SV172: $i,SV1364: $i,SV813: $i] :
( ( ( c_lessequals @ SV813 @ SV1364 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV813 @ SV172 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV172 @ SV1364 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV172 @ SV813 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1364 @ SV813 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5445]) ).
thf(5633,plain,
! [SV173: $i,SV814: $i,SV1365: $i] :
( ( ( c_lessequals @ SV1365 @ SV814 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1365 @ SV173 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV173 @ SV1365 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV814 @ SV1365 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV173 @ SV814 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5446]) ).
thf(5634,plain,
! [SV1371: $i,SV191: $i,SV830: $i,SV1751: $i] :
( ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1751 @ SV830 @ SV191 ) @ ( c_Power_Opower__class_Opower @ SV1751 @ SV1371 @ SV191 ) @ SV191 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV191 ) @ SV1751 @ SV191 ) )
= $true )
| ( ( c_lessequals @ SV830 @ SV1371 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5449]) ).
thf(5635,plain,
! [SV1372: $i,SV192: $i,SV831: $i,SV1752: $i] :
( ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1752 @ SV831 @ SV192 ) @ ( c_Power_Opower__class_Opower @ SV1752 @ SV1372 @ SV192 ) @ SV192 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV192 ) @ SV1752 @ SV192 ) )
= $true )
| ( ( c_lessequals @ SV831 @ SV1372 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5450]) ).
thf(5636,plain,
! [SV832: $i,SV193: $i,SV1753: $i,SV1373: $i] :
( ( ( ~ ( c_lessequals @ SV1373 @ SV1753 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV193 ) @ SV832 @ SV193 ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV832 @ SV1373 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SV832 @ SV1753 @ SV193 ) @ SV193 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5451]) ).
thf(5637,plain,
! [SV1376: $i,SV1755: $i,SV843: $i,SV2011: $i,SV1944: $i,SV209: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV209 @ SV1944 ) @ SV2011 ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV209 @ ( c_List_Olist_OCons @ SV1944 @ SV843 @ SV1755 ) @ ( c_List_Olist_OCons @ SV2011 @ SV1376 @ SV1755 ) @ SV1755 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV209 @ SV843 @ SV1376 @ SV1755 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5453]) ).
thf(5638,plain,
! [SV2012: $i,SV1756: $i,SV1945: $i,SV210: $i,SV844: $i,SV1377: $i] :
( ( ( SV1377 = SV844 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV210 @ ( c_List_Olist_OCons @ SV1945 @ SV844 @ SV1756 ) @ ( c_List_Olist_OCons @ SV2012 @ SV1377 @ SV1756 ) @ SV1756 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV210 @ SV844 @ SV1377 @ SV1756 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5454]) ).
thf(5639,plain,
! [SV212: $i,SV2013: $i,SV846: $i,SV1947: $i,SV1758: $i,SV1379: $i] :
( ( ( SV1379 = SV1758 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV1947 @ ( c_List_Olist_OCons @ SV846 @ SV1758 @ SV2013 ) @ ( c_List_Olist_OCons @ SV212 @ SV1379 @ SV2013 ) @ SV2013 ) )
= $true )
| ( ( SV212 = SV846 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5456]) ).
thf(5640,plain,
! [SV2014: $i,SV1948: $i,SV1759: $i,SV213: $i,SV847: $i,SV1380: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1380 @ SV847 ) @ SV213 ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV1380 @ ( c_List_Olist_OCons @ SV847 @ SV1759 @ SV1948 ) @ ( c_List_Olist_OCons @ SV213 @ SV2014 @ SV1948 ) @ SV1948 ) )
= $true )
| ( ( SV213 = SV847 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5457]) ).
thf(5641,plain,
! [SV1760: $i,SV216: $i,SV850: $i,SV1383: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1383 @ ( c_Nat_Osize__class_Osize @ SV850 @ ( tc_List_Olist @ SV216 ) ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1760 @ SV1383 @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Orev @ SV850 @ SV216 ) @ SV216 ) )
= $true )
| ( ( c_lessequals @ ( c_List_Onth @ SV850 @ SV1383 @ SV216 ) @ ( c_List_Onth @ SV850 @ SV1760 @ SV216 ) @ SV216 )
= $true )
| ( ( class_Orderings_Olinorder @ SV216 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5458]) ).
thf(5642,plain,
! [SV851: $i,SV217: $i,SV1384: $i] :
( ( ( c_lessequals @ SV1384 @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV851 @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV217 ) @ SV851 ) @ SV1384 ) @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV217 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5459]) ).
thf(5643,plain,
! [SV852: $i,SV218: $i,SV1385: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1385 @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
= $false )
| ( ( ~ ( c_lessequals @ SV852 @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV218 ) @ SV852 ) @ SV1385 ) @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5460]) ).
thf(5644,plain,
! [SV1761: $i,SV1386: $i,SV853: $i,SV219: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV219 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV853 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV219 ) @ SV1386 ) @ SV1761 ) @ SV219 )
| ~ ( c_lessequals @ SV853 @ SV1761 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV1386 @ SV219 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5461]) ).
thf(5645,plain,
! [SV1762: $i,SV1387: $i,SV854: $i,SV220: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV220 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV854 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV220 ) @ SV1387 ) @ SV1762 ) @ SV220 )
| ~ ( c_HOL_Oord__class_Oless @ SV854 @ SV1762 @ SV220 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV1387 @ SV220 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV220 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5462]) ).
thf(5646,plain,
! [SV855: $i,SV1388: $i,SV221: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ SV1388 @ SV221 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ SV855 @ SV221 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SV855 ) @ SV1388 ) @ SV221 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5463]) ).
thf(5647,plain,
! [SV856: $i,SV1389: $i,SV222: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ SV1389 @ SV222 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ SV856 @ SV222 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SV856 ) @ SV1389 ) @ SV222 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV222 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5464]) ).
thf(5648,plain,
! [SV1763: $i,SV857: $i,SV1390: $i,SV224: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV224 ) @ SV1390 @ SV224 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV857 @ SV1763 @ SV224 ) @ ( c_Power_Opower__class_Opower @ SV1390 @ SV1763 @ SV224 ) @ SV224 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV857 @ SV1390 @ SV224 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5465]) ).
thf(5649,plain,
! [SV1394: $i,SV229: $i,SV861: $i,SV1767: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1767 @ SV861 @ SV229 ) @ ( c_Power_Opower__class_Opower @ SV1767 @ SV1394 @ SV229 ) @ SV229 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV229 ) @ SV1767 @ SV229 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV861 @ SV1394 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV229 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5466]) ).
thf(5650,plain,
! [SV1768: $i,SV1395: $i,SV862: $i,SV230: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV230 ) @ SV862 @ SV230 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1395 @ SV1768 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV862 @ SV1395 @ SV230 ) @ ( c_Power_Opower__class_Opower @ SV862 @ SV1768 @ SV230 ) @ SV230 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5467]) ).
thf(5651,plain,
! [SV1396: $i,SV231: $i,SV863: $i,SV1769: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1769 @ SV863 @ SV231 ) @ ( c_Power_Opower__class_Opower @ SV1769 @ SV1396 @ SV231 ) @ SV231 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV231 ) @ SV1769 @ SV231 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV863 @ SV1396 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV231 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5468]) ).
thf(5652,plain,
! [SV864: $i,SV232: $i,SV1770: $i,SV1397: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1397 @ SV1770 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV232 ) @ SV864 @ SV232 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV864 @ SV1397 @ SV232 ) @ ( c_Power_Opower__class_Opower @ SV864 @ SV1770 @ SV232 ) @ SV232 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5469]) ).
thf(5653,plain,
! [SV865: $i,SV2015: $i,SV233: $i,SV1949: $i,SV1771: $i,SV1398: $i] :
( ( ( SV1398 = SV1771 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV1949 @ ( c_List_Oappend @ SV233 @ ( c_List_Olist_OCons @ SV1398 @ ( c_List_Olist_ONil @ SV2015 ) @ SV2015 ) @ SV2015 ) @ ( c_List_Oappend @ SV865 @ ( c_List_Olist_OCons @ SV1771 @ ( c_List_Olist_ONil @ SV2015 ) @ SV2015 ) @ SV2015 ) @ SV2015 ) )
= $true )
| ( ( SV233 = SV865 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5470]) ).
thf(5654,plain,
! [SV2016: $i,SV1950: $i,SV1772: $i,SV234: $i,SV1399: $i,SV866: $i] :
( ( ( SV866 = SV1399 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV234 @ ( c_List_Oappend @ SV1772 @ ( c_List_Olist_OCons @ SV866 @ ( c_List_Olist_ONil @ SV1950 ) @ SV1950 ) @ SV1950 ) @ ( c_List_Oappend @ SV2016 @ ( c_List_Olist_OCons @ SV1399 @ ( c_List_Olist_ONil @ SV1950 ) @ SV1950 ) @ SV1950 ) @ SV1950 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV234 @ SV866 ) @ SV1399 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5471]) ).
thf(5655,plain,
! [SV1400: $i,SV867: $i,SV2017: $i,SV1951: $i,SV1773: $i,SV235: $i] :
( ( ( c_ListOrder_Ostep1 @ SV235 @ SV1773 @ SV1951 @ SV2017 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV235 @ ( c_List_Oappend @ SV1773 @ ( c_List_Olist_OCons @ SV867 @ ( c_List_Olist_ONil @ SV2017 ) @ SV2017 ) @ SV2017 ) @ ( c_List_Oappend @ SV1951 @ ( c_List_Olist_OCons @ SV1400 @ ( c_List_Olist_ONil @ SV2017 ) @ SV2017 ) @ SV2017 ) @ SV2017 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV867 ) @ SV1400 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5472]) ).
thf(5656,plain,
! [SV2018: $i,SV1952: $i,SV1774: $i,SV868: $i,SV236: $i,SV1401: $i] :
( ( ( c_ListOrder_Ostep1 @ SV1401 @ SV236 @ SV868 @ SV1774 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV1401 @ ( c_List_Oappend @ SV236 @ ( c_List_Olist_OCons @ SV1952 @ ( c_List_Olist_ONil @ SV1774 ) @ SV1774 ) @ SV1774 ) @ ( c_List_Oappend @ SV868 @ ( c_List_Olist_OCons @ SV2018 @ ( c_List_Olist_ONil @ SV1774 ) @ SV1774 ) @ SV1774 ) @ SV1774 ) )
= $true )
| ( ( SV236 = SV868 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5473]) ).
thf(5657,plain,
! [SV1402: $i,SV238: $i,SV1775: $i,SV870: $i,SV1953: $i] :
( ( ( c_in @ SV1953 @ ( c_List_Oset @ SV870 @ SV1775 ) @ SV1775 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV238 @ SV1953 ) )
= $true )
| ( ( ( c_List_OtakeWhile @ SV238 @ ( c_List_Oappend @ SV870 @ SV1402 @ SV1775 ) @ SV1775 )
= ( c_List_OtakeWhile @ SV238 @ SV870 @ SV1775 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5474]) ).
thf(5658,plain,
! [SV1780: $i,SV1409: $i,SV1954: $i,SV878: $i,SV246: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV246 @ ( hAPP @ SV878 @ SV1954 ) @ tc_nat )
= $false )
| ( ( ~ ( c_in @ SV1954 @ ( c_List_Oset @ SV1409 @ SV1780 ) @ SV1780 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV246 @ ( c_List_Olist_Olist__size @ SV878 @ SV1409 @ SV1780 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5475]) ).
thf(5659,plain,
! [SV252: $i,SV1955: $i,SV1782: $i,SV1413: $i,SV884: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV884 @ ( c_List_Olinorder__class_Oinsort__key @ SV884 @ SV1413 @ SV1782 @ SV1955 @ SV252 ) @ SV1955 @ SV252 ) @ SV252 )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV884 @ SV1782 @ SV1955 @ SV252 ) @ SV252 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5477]) ).
thf(5660,plain,
! [SV1956: $i,SV253: $i,SV1783: $i,SV1414: $i,SV885: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV885 @ SV1414 @ SV1783 @ SV253 ) @ SV253 )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV885 @ ( c_List_Olinorder__class_Oinsort__key @ SV885 @ SV1956 @ SV1414 @ SV1783 @ SV253 ) @ SV1783 @ SV253 ) @ SV253 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV253 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5478]) ).
thf(5661,plain,
! [SV895: $i,SV263: $i,SV1422: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1422 @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV895 @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV263 ) @ SV895 ) @ SV1422 ) @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV263 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5481]) ).
thf(5662,plain,
! [SV1439: $i,SV281: $i,SV1799: $i,SV913: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV913 @ SV1799 @ SV281 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1799 @ SV1439 @ SV281 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV913 @ SV1439 @ SV281 )
= $true )
| ( ( class_Orderings_Oorder @ SV281 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5482]) ).
thf(5663,plain,
! [SV914: $i,SV282: $i,SV1440: $i,SV1800: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1800 @ SV1440 @ SV282 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV914 @ SV1800 @ SV282 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV914 @ SV1440 @ SV282 )
= $true )
| ( ( class_Orderings_Opreorder @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5483]) ).
thf(5664,plain,
! [SV1810: $i,SV932: $i,SV300: $i,SV1458: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1458 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SV932 @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ SV932 @ SV1810 @ SV300 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV932 @ SV1458 @ SV300 ) @ ( c_Power_Opower__class_Opower @ SV1810 @ SV1458 @ SV300 ) @ SV300 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV300 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5486]) ).
thf(5665,plain,
! [SV943: $i,SV311: $i,SV1469: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1469 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV311 ) @ SV943 @ SV311 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV311 ) @ ( c_Power_Opower__class_Opower @ SV943 @ SV1469 @ SV311 ) @ SV311 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5487]) ).
thf(5666,plain,
! [SV1471: $i,SV1817: $i,SV313: $i,SV945: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV945 @ ( c_HOL_Oone__class_Oone @ SV313 ) @ SV313 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV313 ) @ SV945 @ SV313 )
| ~ ( c_HOL_Oord__class_Oless @ SV1817 @ SV1471 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV945 @ SV1471 @ SV313 ) @ ( c_Power_Opower__class_Opower @ SV945 @ SV1817 @ SV313 ) @ SV313 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV313 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5488]) ).
thf(5667,plain,
! [SV334: $i,SV1476: $i,SV962: $i,SV1820: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1820 @ ( c_List_Olist_OCons @ SV962 @ SV1476 @ SV334 ) @ SV334 ) @ SV334 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV962 @ SV1476 @ SV334 ) @ SV334 )
= $true )
| ( ( class_Orderings_Olinorder @ SV334 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5489]) ).
thf(5668,plain,
! [SV2021: $i,SV1968: $i,SV1830: $i,SV1497: $i,SV997: $i,SV376: $i] :
( ( ( hBOOL @ ( hAPP @ SV376 @ ( c_Lambda_OdB_OdB__case @ SV997 @ SV1497 @ SV1830 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1968 ) @ SV2021 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SV1497 @ SV1968 ) @ SV2021 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5491]) ).
thf(5669,plain,
! [SV2022: $i,SV1969: $i,SV1831: $i,SV1498: $i,SV998: $i,SV377: $i] :
( ( ( hBOOL @ ( hAPP @ SV377 @ ( c_Lambda_OdB_OdB__case @ SV998 @ SV1498 @ SV1831 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1969 ) @ SV2022 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV377 @ ( hAPP @ ( hAPP @ SV1498 @ SV1969 ) @ SV2022 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5492]) ).
thf(5670,plain,
! [SV1043: $i,SV1529: $i,SV424: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV1529 @ SV424 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV1043 @ SV424 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SV1043 ) @ SV1529 ) @ SV424 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV424 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5499]) ).
thf(5671,plain,
! [SV1979: $i,SV1850: $i,SV1539: $i,SV1055: $i,SV436: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV436 ) @ SV1055 ) @ SV1539 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV436 ) @ SV1850 ) @ SV1979 ) @ SV436 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1539 @ SV1979 @ SV436 )
| ~ ( c_HOL_Oord__class_Oless @ SV1055 @ SV1850 @ SV436 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV436 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5505]) ).
thf(5672,plain,
! [SV1543: $i,SV1852: $i,SV1063: $i,SV444: $i] :
( ( ( c_List_Olistsp @ SV444 @ SV1063 @ SV1852 )
= $false )
| ( ( c_List_Olistsp @ SV444 @ SV1543 @ SV1852 )
= $false )
| ( ( c_List_Olistsp @ SV444 @ ( c_List_Oappend @ SV1063 @ SV1543 @ SV1852 ) @ SV1852 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5509]) ).
thf(5673,plain,
! [SV1546: $i,SV447: $i,SV1853: $i,SV1066: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1066 @ SV1853 @ SV447 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV1546 @ SV447 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1066 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV447 ) @ SV1546 ) @ SV1853 ) @ SV447 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV447 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5510]) ).
thf(5674,plain,
! [SV1551: $i,SV452: $i,SV1857: $i,SV1071: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1071 @ SV1857 @ SV452 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV452 ) @ SV1071 ) @ SV1551 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV452 ) @ SV1857 ) @ SV1551 ) @ SV452 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV452 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5513]) ).
thf(5675,plain,
! [SV1552: $i,SV453: $i,SV1858: $i,SV1072: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1072 @ SV1858 @ SV453 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV453 ) @ SV1072 ) @ SV1552 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV453 ) @ SV1858 ) @ SV1552 ) @ SV453 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV453 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5514]) ).
thf(5676,plain,
! [SV1553: $i,SV1859: $i,SV1073: $i,SV454: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV454 ) @ SV1073 ) @ SV1859 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV454 ) @ SV1553 ) @ SV1859 ) @ SV454 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1073 @ SV1553 @ SV454 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV454 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5515]) ).
thf(5677,plain,
! [SV1074: $i,SV455: $i,SV1860: $i,SV1554: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1554 @ SV1860 @ SV455 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV455 ) @ SV1074 ) @ SV1554 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV455 ) @ SV1074 ) @ SV1860 ) @ SV455 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV455 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5516]) ).
thf(5678,plain,
! [SV1075: $i,SV456: $i,SV1861: $i,SV1555: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1555 @ SV1861 @ SV456 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV456 ) @ SV1075 ) @ SV1555 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV456 ) @ SV1075 ) @ SV1861 ) @ SV456 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV456 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5517]) ).
thf(5679,plain,
! [SV1556: $i,SV1076: $i,SV1862: $i,SV457: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV1862 ) @ SV1076 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV457 ) @ SV1862 ) @ SV1556 ) @ SV457 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1076 @ SV1556 @ SV457 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV457 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5518]) ).
thf(5680,plain,
! [SV1077: $i,SV1557: $i,SV1863: $i,SV458: $i] :
( ( ( c_Type_Otyping @ SV458 @ SV1863 @ SV1557 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1863 ) @ SV1077 ) )
= $false )
| ( ( c_Type_Otyping @ SV458 @ SV1077 @ SV1557 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5519]) ).
thf(5681,plain,
! [SV1565: $i,SV1986: $i,SV1867: $i,SV467: $i,SV1086: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1086 @ ( c_Nat_Osize__class_Osize @ SV467 @ ( tc_List_Olist @ SV1867 ) ) @ tc_nat )
= $false )
| ( ( SV1086 = SV1986 )
= $true )
| ( ( ( c_List_Onth @ ( c_List_Olist__update @ SV467 @ SV1086 @ SV1565 @ SV1867 ) @ SV1986 @ SV1867 )
= ( c_List_Onth @ SV467 @ SV1986 @ SV1867 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5523]) ).
thf(5682,plain,
! [SV473: $i,SV1092: $i,SV1571: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1571 @ SV1092 @ SV473 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1092 @ SV1571 @ SV473 )
= $false )
| ( ( class_Orderings_Oorder @ SV473 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5524]) ).
thf(5683,plain,
! [SV474: $i,SV1093: $i,SV1572: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1572 @ SV1093 @ SV474 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1093 @ SV1572 @ SV474 )
= $false )
| ( ( class_Orderings_Olinorder @ SV474 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5525]) ).
thf(5684,plain,
! [SV475: $i,SV1094: $i,SV1573: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1573 @ SV1094 @ SV475 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1094 @ SV1573 @ SV475 )
= $false )
| ( ( class_Orderings_Opreorder @ SV475 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5526]) ).
thf(5685,plain,
! [SV476: $i,SV1095: $i,SV1574: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1574 @ SV1095 @ SV476 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1095 @ SV1574 @ SV476 )
= $false )
| ( ( class_Orderings_Opreorder @ SV476 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5527]) ).
thf(5686,plain,
! [SV1105: $i,SV488: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV488 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV488 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV488 ) @ SV1105 @ SV488 )
= ( c_HOL_Ozero__class_Ozero @ SV488 ) )
| ( SV1105
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV488 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV488 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5528]) ).
thf(5687,plain,
! [SV522: $i,SV1133: $i,SV1989: $i,SV1877: $i,SV1598: $i] :
( ( ( c_Type_Otyping @ SV1598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1877 ) @ SV1989 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1133 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV1598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1877 ) @ SV1989 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV522 ) )
= $true )
| ( ( SV522 = SV1133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5531]) ).
thf(5688,plain,
! [SV1881: $i,SV1607: $i,SV1150: $i,SV543: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV543 ) @ SV1150 ) @ SV1607 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV543 ) @ SV1881 ) @ SV1607 ) )
= $false )
| ( ( SV1150 = SV1881 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV543 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5533]) ).
thf(5689,plain,
! [SV1885: $i,SV554: $i,SV1616: $i,SV1161: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1161 @ SV1616 @ SV554 )
= ( c_Power_Opower__class_Opower @ SV1885 @ SV1616 @ SV554 ) )
= $false )
| ( ( ( SV1161 = SV1885 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1616 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SV1885 @ SV554 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SV1161 @ SV554 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV554 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5536]) ).
thf(5690,plain,
! [SV1887: $i,SV559: $i,SV1619: $i,SV1165: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1165 @ SV1619 @ SV559 )
= ( c_HOL_Ominus__class_Ominus @ SV1887 @ SV1887 @ SV559 ) )
= $false )
| ( ( SV1165 = SV1619 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV559 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5537]) ).
thf(5691,plain,
! [SV1888: $i,SV1620: $i,SV1166: $i,SV560: $i] :
( ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV560 @ ( tc_List_Olist @ SV1166 ) ) @ SV1620 @ SV1166 )
= SV560 )
= $false )
| ( ( ( SV1620
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV1620 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) )
| ( ( c_List_Oappend @ SV1620 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1620 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) @ SV1888 @ SV1166 ) @ SV1166 )
= ( c_List_Oappend @ SV560 @ SV1888 @ SV1166 ) ) )
= $true )
| ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV560 @ ( tc_List_Olist @ SV1166 ) ) @ SV1620 @ SV1166 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1620 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) @ SV1888 @ SV1166 ) @ SV1166 )
= SV1888 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5538]) ).
thf(5692,plain,
! [SV1891: $i,SV1628: $i,SV1175: $i,SV570: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV570 ) @ SV1175 ) @ SV1628 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV570 ) @ SV1175 ) @ SV1891 ) )
= $false )
| ( ( SV1628 = SV1891 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV570 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5540]) ).
thf(5693,plain,
! [SV1994: $i,SV1894: $i,SV1632: $i,SV574: $i,SV1179: $i] :
( ( ( SV1179
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV574 @ ( tc_List_Olist @ SV1632 ) ) @ SV1894 @ SV1632 ) @ SV1994 @ SV1632 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV574 @ ( tc_List_Olist @ SV1632 ) ) @ ( c_Nat_Osize__class_Osize @ SV1894 @ ( tc_List_Olist @ SV1632 ) ) @ tc_nat ) )
= $true )
| ( ( ( c_List_Oappend @ SV574 @ SV1179 @ SV1632 )
= ( c_List_Oappend @ SV1894 @ SV1994 @ SV1632 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5542]) ).
thf(5694,plain,
! [SV1635: $i,SV1182: $i,SV577: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV577 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV577 )
| ( ( c_Power_Opower__class_Opower @ SV1182 @ SV1635 @ SV577 )
!= ( c_HOL_Ozero__class_Ozero @ SV577 ) )
| ( SV1182
= ( c_HOL_Ozero__class_Ozero @ SV577 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV577 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV577 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5543]) ).
thf(5695,plain,
! [SV1995: $i,SV1896: $i,SV578: $i,SV1636: $i,SV1183: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1183 @ SV1636 @ SV578 )
!= ( c_HOL_Ominus__class_Ominus @ SV1896 @ SV1995 @ SV578 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1896 @ SV1995 @ SV578 )
| ~ ( c_HOL_Oord__class_Oless @ SV1183 @ SV1636 @ SV578 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV578 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5544]) ).
thf(5696,plain,
! [SV585: $i,SV1641: $i,SV1188: $i,SV1899: $i] :
( ( ( c_in @ SV1899 @ ( c_List_Oset @ SV1188 @ SV1641 ) @ SV1641 )
= $false )
| ( ( hBOOL @ ( hAPP @ SV585 @ SV1899 ) )
= $true )
| ( ( ( c_List_OtakeWhile @ SV585 @ SV1188 @ SV1641 )
= SV1188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5547]) ).
thf(5697,plain,
! [SV1997: $i,SV1901: $i,SV594: $i,SV1648: $i,SV1197: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1197 @ SV1648 @ SV594 )
!= ( c_HOL_Ominus__class_Ominus @ SV1901 @ SV1997 @ SV594 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1197 @ SV1648 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV1901 @ SV1997 @ SV594 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV594 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5548]) ).
thf(5698,plain,
! [SV1998: $i,SV1199: $i,SV596: $i,SV1650: $i,SV1902: $i] :
( ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV1902 @ ( tc_List_Olist @ SV1650 ) ) @ SV596 @ SV1650 )
= SV1902 )
= $true )
| ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV596 @ ( tc_List_Olist @ SV1650 ) ) @ ( c_Nat_Osize__class_Osize @ SV1902 @ ( tc_List_Olist @ SV1650 ) ) @ tc_nat )
= $true )
| ( ( ( c_List_Oappend @ SV596 @ SV1199 @ SV1650 )
= ( c_List_Oappend @ SV1902 @ SV1998 @ SV1650 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5549]) ).
thf(5699,plain,
! [SV1904: $i,SV1656: $i,SV1205: $i,SV603: $i] :
( ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV603 @ ( tc_List_Olist @ SV1205 ) ) @ ( c_Nat_Osize__class_Osize @ SV1656 @ ( tc_List_Olist @ SV1205 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Oappend @ SV603 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV603 @ ( tc_List_Olist @ SV1205 ) ) @ SV1656 @ SV1205 ) @ SV1904 @ SV1205 ) @ SV1205 )
= ( c_List_Oappend @ SV1656 @ SV1904 @ SV1205 ) )
= $true )
| ( ( SV603
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV603 @ ( tc_List_Olist @ SV1205 ) ) @ SV1656 @ SV1205 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5550]) ).
thf(5700,plain,
! [SV2027: $i,SV1999: $i,SV1905: $i,SV1659: $i,SV1209: $i,SV607: $i] :
( ( ( ( c_List_Omap @ SV607 @ SV1209 @ SV1659 @ SV1905 )
= ( c_List_Omap @ SV1999 @ SV1209 @ SV1659 @ SV1905 ) )
= $false )
| ( ( ( ( hAPP @ SV607 @ SV2027 )
= ( hAPP @ SV1999 @ SV2027 ) )
| ~ ( c_in @ SV2027 @ ( c_List_Oset @ SV1209 @ SV1659 ) @ SV1659 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5551]) ).
thf(5701,plain,
! [SV2001: $i,SV1216: $i,SV1909: $i,SV1666: $i,SV614: $i] :
( ( ( SV614
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV614 @ ( tc_List_Olist @ SV1666 ) ) @ SV1909 @ SV1666 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV614 @ ( tc_List_Olist @ SV1666 ) ) @ ( c_Nat_Osize__class_Osize @ SV1909 @ ( tc_List_Olist @ SV1666 ) ) @ tc_nat ) )
= $true )
| ( ( ( c_List_Oappend @ SV614 @ SV1216 @ SV1666 )
= ( c_List_Oappend @ SV1909 @ SV2001 @ SV1666 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5555]) ).
thf(5702,plain,
! [SV1667: $i,SV615: $i,SV1217: $i] :
( ( ( SV1217
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV615 ) @ SV1217 ) @ SV1667 ) )
= $true )
| ( ( SV1667
= ( c_HOL_Ozero__class_Ozero @ SV615 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV615 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV615 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5556]) ).
thf(5703,plain,
! [SV1218: $i,SV616: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV616 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV616 )
| ( ( c_Power_Opower__class_Opower @ SV1218 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV616 )
!= ( c_HOL_Ozero__class_Ozero @ SV616 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV616 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV616 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5557]) ).
thf(5704,plain,
! [SV1219: $i,SV1668: $i,SV617: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV617 ) @ SV1668 @ SV617 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV617 ) @ SV1219 @ SV617 )
| ( SV1668
= ( c_HOL_Ozero__class_Ozero @ SV617 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV617 ) @ SV1219 ) @ SV1668 )
= ( c_HOL_Ozero__class_Ozero @ SV617 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV617 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5558]) ).
thf(5705,plain,
! [SV1910: $i,SV618: $i,SV1669: $i,SV1220: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1220 @ SV1669 @ SV618 )
= ( c_Power_Opower__class_Opower @ SV1220 @ SV1910 @ SV618 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV618 ) @ SV1220 @ SV618 )
| ( SV1669 = SV1910 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV618 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5559]) ).
thf(5706,plain,
! [SV2002: $i,SV1911: $i,SV621: $i,SV1672: $i,SV1223: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1223 @ SV1672 @ SV621 )
!= ( c_HOL_Ominus__class_Ominus @ SV1911 @ SV2002 @ SV621 ) )
= $true )
| ( ( ( c_lessequals @ SV1672 @ SV1223 @ SV621 )
| ~ ( c_lessequals @ SV2002 @ SV1911 @ SV621 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV621 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5560]) ).
thf(5707,plain,
! [SV1912: $i,SV1673: $i,SV622: $i,SV2003: $i,SV1224: $i] :
( ( ( SV1224 = SV2003 )
= $true )
| ( ( SV622
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_List_Oreplicate @ SV622 @ SV1224 @ SV1673 )
= ( c_List_Oreplicate @ SV1912 @ SV2003 @ SV1673 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5561]) ).
thf(5708,plain,
! [SV1913: $i,SV1674: $i,SV623: $i,SV1225: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1225 @ SV1225 @ SV623 )
= ( c_HOL_Ominus__class_Ominus @ SV1674 @ SV1913 @ SV623 ) )
= $false )
| ( ( SV1674 = SV1913 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV623 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5562]) ).
thf(5709,plain,
! [SV624: $i,SV1675: $i,SV1226: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1226 @ SV1675 @ SV624 )
!= ( c_HOL_Ozero__class_Ozero @ SV624 ) )
= $true )
| ( ( SV1226 = SV1675 )
= $true )
| ( ( class_Int_Onumber__ring @ SV624 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV624 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5563]) ).
thf(5710,plain,
! [SV1914: $i,SV625: $i,SV1676: $i,SV1227: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1227 @ ( c_Suc @ SV1676 ) @ SV625 )
= ( c_Power_Opower__class_Opower @ SV1914 @ ( c_Suc @ SV1676 ) @ SV625 ) )
= $false )
| ( ( ( SV1227 = SV1914 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV625 ) @ SV1914 @ SV625 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV625 ) @ SV1227 @ SV625 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV625 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5564]) ).
thf(5711,plain,
! [SV2004: $i,SV1915: $i,SV626: $i,SV1677: $i,SV1228: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1228 @ SV1677 @ SV626 )
!= ( c_HOL_Ominus__class_Ominus @ SV1915 @ SV2004 @ SV626 ) )
= $true )
| ( ( ( c_lessequals @ SV2004 @ SV1915 @ SV626 )
| ~ ( c_lessequals @ SV1677 @ SV1228 @ SV626 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV626 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5565]) ).
thf(5712,plain,
! [SV1679: $i,SV1916: $i,SV629: $i,SV1230: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1230 @ ( c_Nat_Osize__class_Osize @ SV629 @ ( tc_List_Olist @ SV1916 ) ) @ tc_nat )
= $false )
| ( ( ( c_List_Onth @ SV629 @ SV1230 @ SV1916 )
= SV1679 )
= $true )
| ( ( ( c_List_Olist__update @ SV629 @ SV1230 @ SV1679 @ SV1916 )
= SV629 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5566]) ).
thf(5713,plain,
! [SV2005: $i,SV1231: $i,SV630: $i,SV1680: $i,SV1917: $i] :
( ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1917 @ ( tc_List_Olist @ SV1680 ) ) @ SV630 @ SV1680 ) @ SV1231 @ SV1680 )
= SV2005 )
= $true )
| ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV630 @ ( tc_List_Olist @ SV1680 ) ) @ ( c_Nat_Osize__class_Osize @ SV1917 @ ( tc_List_Olist @ SV1680 ) ) @ tc_nat )
= $true )
| ( ( ( c_List_Oappend @ SV630 @ SV1231 @ SV1680 )
= ( c_List_Oappend @ SV1917 @ SV2005 @ SV1680 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5567]) ).
thf(5714,plain,
! [SV1920: $i,SV1685: $i,SV1237: $i,SV637: $i] :
( ( ( class_Int_Onumber__ring @ SV637 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1237 ) @ SV1685 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1237 ) @ SV1920 ) )
| ( SV1685 = SV1920 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV637 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5570]) ).
thf(5715,plain,
! [SV1687: $i,SV639: $i,SV1239: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ SV1239 @ SV639 )
!= ( c_Int_Onumber__class_Onumber__of @ SV1687 @ SV639 ) )
= $true )
| ( ( SV1239 = SV1687 )
= $true )
| ( ( class_Int_Onumber__ring @ SV639 )
= $false )
| ( ( class_Int_Oring__char__0 @ SV639 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5572]) ).
thf(5716,plain,
! [SV1692: $i,SV646: $i,SV1245: $i] :
( ( ( ~ ( c_lessequals @ SV1245 @ SV646 @ tc_nat ) )
= $true )
| ( ( SV646 = SV1692 )
= $true )
| ( ( c_lessequals @ SV1245 @ SV1692 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV646 @ SV1245 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1692 @ SV1245 @ tc_nat ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5574]) ).
thf(5717,plain,
! [SV1246: $i,SV1693: $i,SV647: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV647 ) @ SV1693 @ SV647 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV647 ) @ SV1246 @ SV647 )
| ( SV1246
= ( c_HOL_Ozero__class_Ozero @ SV647 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV647 ) @ SV1246 ) @ SV1693 )
= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV647 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5575]) ).
thf(5718,plain,
! [SV1926: $i,SV1694: $i,SV1247: $i,SV648: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV648 ) @ SV1247 ) @ SV1694 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV648 ) @ SV1247 ) @ SV1926 ) )
= $false )
| ( ( SV1694 = SV1926 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV648 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5576]) ).
thf(5719,plain,
! [SV2008: $i,SV1927: $i,SV1695: $i,SV1248: $i,SV649: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1248 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1695 ) @ SV1927 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1695 ) @ SV2008 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1248 ) @ SV1927 )
= SV2008 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV649 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5577]) ).
thf(5720,plain,
! [SV1256: $i,SV658: $i,SV2: $i,SV1701: $i,SV1931: $i] :
( ( ( ~ ( c_lessequals @ SV1931 @ SV1701 @ SV2 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV658 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SV1256 ) @ SV1931 ) @ SV2 ) )
= $true )
| ( ( c_lessequals @ SV658 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SV1256 ) @ SV1701 ) @ SV2 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5578]) ).
thf(5721,plain,
! [SV659: $i,SV3: $i,SV1257: $i,SV1702: $i] :
( ( ( c_lessequals @ SV1702 @ SV1257 @ SV3 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV659 @ SV1702 @ SV3 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV659 @ SV1257 @ SV3 )
= $true )
| ( ( class_Orderings_Opreorder @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5579]) ).
thf(5722,plain,
! [SV660: $i,SV4: $i,SV1258: $i,SV1703: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1703 @ SV1258 @ SV4 )
= $false )
| ( ( ~ ( c_lessequals @ SV660 @ SV1703 @ SV4 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV660 @ SV1258 @ SV4 )
= $true )
| ( ( class_Orderings_Opreorder @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5580]) ).
thf(5723,plain,
! [SV664: $i,SV10: $i,SV1260: $i,SV1704: $i] :
( ( ( c_lessequals @ SV1704 @ SV1260 @ SV10 )
= $false )
| ( ( ~ ( c_lessequals @ SV664 @ SV1704 @ SV10 ) )
= $true )
| ( ( c_lessequals @ SV664 @ SV1260 @ SV10 )
= $true )
| ( ( class_Orderings_Opreorder @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5581]) ).
thf(5724,plain,
! [SV1261: $i,SV11: $i,SV1705: $i,SV665: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV665 @ SV1705 @ SV11 )
= $false )
| ( ( ~ ( c_lessequals @ SV1705 @ SV1261 @ SV11 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV665 @ SV1261 @ SV11 )
= $true )
| ( ( class_Orderings_Oorder @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5582]) ).
thf(5725,plain,
! [SV1262: $i,SV12: $i,SV1706: $i,SV666: $i] :
( ( ( c_lessequals @ SV666 @ SV1706 @ SV12 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1706 @ SV1262 @ SV12 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV666 @ SV1262 @ SV12 )
= $true )
| ( ( class_Orderings_Oorder @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5583]) ).
thf(5726,plain,
! [SV1263: $i,SV13: $i,SV1707: $i,SV667: $i] :
( ( ( c_lessequals @ SV667 @ SV1707 @ SV13 )
= $false )
| ( ( ~ ( c_lessequals @ SV1707 @ SV1263 @ SV13 ) )
= $true )
| ( ( c_lessequals @ SV667 @ SV1263 @ SV13 )
= $true )
| ( ( class_Orderings_Oorder @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5584]) ).
thf(5727,plain,
! [SV1265: $i,SV15: $i,SV669: $i] :
( ( ( c_lessequals @ SV669 @ SV15 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV669 @ SV1265 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV15 @ SV1265 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV15 @ SV669 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1265 @ SV669 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5585]) ).
thf(5728,plain,
! [SV670: $i,SV16: $i,SV1266: $i] :
( ( ( c_lessequals @ SV1266 @ SV16 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1266 @ SV670 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ SV16 @ SV1266 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV670 @ SV1266 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV16 @ SV670 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5586]) ).
thf(5729,plain,
! [SV1708: $i,SV673: $i,SV1267: $i,SV20: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV1267 @ SV20 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV673 @ ( c_Suc @ SV1708 ) @ SV20 ) @ ( c_Power_Opower__class_Opower @ SV1267 @ ( c_Suc @ SV1708 ) @ SV20 ) @ SV20 ) )
= $true )
| ( ( c_lessequals @ SV673 @ SV1267 @ SV20 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5587]) ).
thf(5730,plain,
! [SV37: $i,SV688: $i,SV1280: $i] :
( ( ( c_lessequals @ SV1280 @ SV688 @ SV37 )
= $false )
| ( ( c_lessequals @ SV688 @ SV1280 @ SV37 )
= $false )
| ( ( SV688 = SV1280 )
= $true )
| ( ( class_Orderings_Oorder @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5594]) ).
thf(5731,plain,
! [SV38: $i,SV1281: $i,SV689: $i] :
( ( ( c_lessequals @ SV689 @ SV1281 @ SV38 )
= $false )
| ( ( c_lessequals @ SV1281 @ SV689 @ SV38 )
= $false )
| ( ( SV689 = SV1281 )
= $true )
| ( ( class_Orderings_Oorder @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5595]) ).
thf(5732,plain,
! [SV39: $i,SV1282: $i,SV690: $i] :
( ( ( c_lessequals @ SV690 @ SV1282 @ SV39 )
= $false )
| ( ( c_lessequals @ SV1282 @ SV690 @ SV39 )
= $false )
| ( ( SV690 = SV1282 )
= $true )
| ( ( class_Orderings_Oorder @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5596]) ).
thf(5733,plain,
! [SV1286: $i,SV1715: $i,SV52: $i,SV701: $i] :
( ( ( c_lessequals @ SV701 @ ( c_HOL_Oone__class_Oone @ SV52 ) @ SV52 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV701 @ SV52 )
| ~ ( c_lessequals @ SV1715 @ SV1286 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV701 @ SV1286 @ SV52 ) @ ( c_Power_Opower__class_Opower @ SV701 @ SV1715 @ SV52 ) @ SV52 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5598]) ).
thf(5734,plain,
! [SV1718: $i,SV713: $i,SV64: $i,SV1934: $i,SV1293: $i] :
( ( ( ~ ( c_lessequals @ SV1293 @ SV1934 @ SV64 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV713 @ SV1718 @ SV64 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV713 ) @ SV1293 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV1718 ) @ SV1934 ) @ SV64 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5599]) ).
thf(5735,plain,
! [SV714: $i,SV65: $i,SV1719: $i,SV1294: $i,SV1935: $i] :
( ( ( c_in @ SV1935 @ ( c_List_Oset @ SV1294 @ SV1719 ) @ SV1719 )
= $false )
| ( ( c_lessequals @ SV65 @ ( hAPP @ SV714 @ SV1935 ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV65 @ ( c_List_Olist_Olist__size @ SV714 @ SV1294 @ SV1719 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5600]) ).
thf(5736,plain,
! [SV1720: $i,SV1301: $i,SV727: $i,SV79: $i] :
( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV79 ) @ SV727 @ SV79 )
= $false )
| ( ( ~ ( c_lessequals @ SV1301 @ SV1720 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV727 @ SV1301 @ SV79 ) @ ( c_Power_Opower__class_Opower @ SV727 @ SV1720 @ SV79 ) @ SV79 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5604]) ).
thf(5737,plain,
! [SV1313: $i,SV748: $i,SV101: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ SV748 @ SV101 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV748 @ ( c_HOL_Oone__class_Oone @ SV101 ) @ SV101 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV748 @ ( c_Suc @ SV1313 ) @ SV101 ) @ ( c_HOL_Oone__class_Oone @ SV101 ) @ SV101 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5613]) ).
thf(5738,plain,
! [SV749: $i,SV102: $i,SV1721: $i,SV1314: $i] :
( ( ( c_in @ SV1314 @ ( c_List_Oset @ SV1721 @ SV102 ) @ SV102 )
= $false )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV749 @ SV1721 @ SV102 ) @ SV102 ) )
= $true )
| ( ( c_lessequals @ SV749 @ SV1314 @ SV102 )
= $true )
| ( ( class_Orderings_Olinorder @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5614]) ).
thf(5739,plain,
! [SV1936: $i,SV750: $i,SV103: $i,SV1722: $i,SV1315: $i] :
( ( ( ~ ( c_in @ SV1315 @ ( c_List_Oset @ SV1722 @ SV103 ) @ SV103 ) )
= $true )
| ( ( ~ ( c_in @ SV750 @ ( c_List_Oset @ SV1936 @ SV103 ) @ SV103 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1936 @ SV1722 @ SV103 ) @ SV103 ) )
= $true )
| ( ( c_lessequals @ SV750 @ SV1315 @ SV103 )
= $true )
| ( ( class_Orderings_Olinorder @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5615]) ).
thf(5740,plain,
! [SV1319: $i,SV754: $i,SV109: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV754 @ SV109 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV1319 @ SV109 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV109 ) @ SV754 ) @ SV1319 ) @ SV109 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5616]) ).
thf(5741,plain,
! [SV1723: $i,SV1320: $i,SV113: $i,SV757: $i] :
( ( ( c_lessequals @ SV757 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV1320 ) @ SV1723 ) @ SV113 )
= $true )
| ( ( ~ ( c_lessequals @ SV757 @ SV1723 @ SV113 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV1320 @ SV113 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV113 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5617]) ).
thf(5742,plain,
! [SV1724: $i,SV1321: $i,SV114: $i,SV758: $i] :
( ( ( c_lessequals @ SV758 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SV1321 ) @ SV1724 ) @ SV114 )
= $true )
| ( ( ~ ( c_lessequals @ SV758 @ SV1321 @ SV114 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV1724 @ SV114 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV114 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5618]) ).
thf(5743,plain,
! [SV1322: $i,SV117: $i,SV761: $i] :
( ( ( c_lessequals @ SV761 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
= $false )
| ( ( c_lessequals @ SV1322 @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV117 ) @ SV761 ) @ SV1322 ) @ ( c_HOL_Ozero__class_Ozero @ SV117 ) @ SV117 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5619]) ).
thf(5744,plain,
! [SV1725: $i,SV762: $i,SV118: $i,SV1937: $i,SV1323: $i] :
( ( ( ~ ( c_lessequals @ SV1323 @ SV1937 @ SV118 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV762 @ SV1725 @ SV118 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV762 ) @ SV1323 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV1725 ) @ SV1937 ) @ SV118 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5620]) ).
thf(5745,plain,
! [SV1726: $i,SV763: $i,SV119: $i,SV1938: $i,SV1324: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1324 @ SV1938 @ SV119 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV763 @ SV1726 @ SV119 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV119 ) @ SV763 ) @ SV1324 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV119 ) @ SV1726 ) @ SV1938 ) @ SV119 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5621]) ).
thf(5746,plain,
! [SV1325: $i,SV121: $i,SV765: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ SV765 @ SV121 ) @ ( c_Int_Onumber__class_Onumber__of @ SV1325 @ SV121 ) @ SV121 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ SV1325 @ SV121 ) @ ( c_Int_Onumber__class_Onumber__of @ SV765 @ SV121 ) @ SV121 ) )
= $true )
| ( ( class_Int_Onumber @ SV121 )
= $false )
| ( ( class_Orderings_Olinorder @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5622]) ).
thf(5747,plain,
! [SV1329: $i,SV1728: $i,SV774: $i,SV133: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV133 ) @ SV774 @ SV133 )
= $false )
| ( ( ~ ( c_lessequals @ SV774 @ SV1728 @ SV133 ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV774 @ SV1329 @ SV133 ) @ ( c_Power_Opower__class_Opower @ SV1728 @ SV1329 @ SV133 ) @ SV133 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5624]) ).
thf(5748,plain,
! [SV152: $i,SV793: $i,SV1737: $i,SV1344: $i] :
( ( ( c_lessequals @ SV1344 @ SV1737 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1737 @ ( c_Nat_Osize__class_Osize @ SV793 @ ( tc_List_Olist @ SV152 ) ) @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ SV793 @ SV152 ) )
= $true )
| ( ( c_lessequals @ ( c_List_Onth @ SV793 @ SV1344 @ SV152 ) @ ( c_List_Onth @ SV793 @ SV1737 @ SV152 ) @ SV152 )
= $true )
| ( ( class_Orderings_Olinorder @ SV152 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5626]) ).
thf(5749,plain,
! [SV1345: $i,SV153: $i,SV794: $i,SV1738: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1738 @ ( c_Nat_Osize__class_Osize @ SV794 @ ( tc_List_Olist @ SV153 ) ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1345 @ SV1738 @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ SV794 @ SV153 ) )
= $true )
| ( ( c_lessequals @ ( c_List_Onth @ SV794 @ SV1345 @ SV153 ) @ ( c_List_Onth @ SV794 @ SV1738 @ SV153 ) @ SV153 )
= $true )
| ( ( class_Orderings_Olinorder @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5627]) ).
thf(5750,plain,
! [SV798: $i,SV157: $i,SV1741: $i,SV1349: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1349 @ SV1741 @ SV157 ) @ SV157 )
= $false )
| ( ( ~ ( c_lessequals @ SV798 @ SV1349 @ SV157 ) )
= $true )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV798 @ ( c_List_Olist_OCons @ SV1349 @ SV1741 @ SV157 ) @ SV157 ) @ SV157 )
= $true )
| ( ( class_Orderings_Olinorder @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5629]) ).
thf(5751,plain,
! [SV169: $i,SV2009: $i,SV1940: $i,SV1748: $i,SV1361: $i,SV810: $i] :
( ( ( ( c_List_Olinorder__class_Oinsort__key @ SV810 @ SV1361 @ ( c_List_Olist_OCons @ SV1748 @ SV1940 @ SV2009 ) @ SV2009 @ SV169 )
= ( c_List_Olist_OCons @ SV1361 @ ( c_List_Olist_OCons @ SV1748 @ SV1940 @ SV2009 ) @ SV2009 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ SV810 @ SV1361 ) @ ( hAPP @ SV810 @ SV1748 ) @ SV169 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5630]) ).
thf(5752,plain,
! [SV170: $i,SV2010: $i,SV1941: $i,SV1749: $i,SV1362: $i,SV811: $i] :
( ( ( ( c_List_Olinorder__class_Oinsort__key @ SV811 @ SV1362 @ ( c_List_Olist_OCons @ SV1749 @ SV1941 @ SV2010 ) @ SV2010 @ SV170 )
= ( c_List_Olist_OCons @ SV1749 @ ( c_List_Olinorder__class_Oinsort__key @ SV811 @ SV1362 @ SV1941 @ SV2010 @ SV170 ) @ SV2010 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ SV811 @ SV1362 ) @ ( hAPP @ SV811 @ SV1749 ) @ SV170 )
= $true )
| ( ( class_Orderings_Olinorder @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5631]) ).
thf(5753,plain,
! [SV1364: $i,SV172: $i,SV813: $i] :
( ( ( c_lessequals @ SV813 @ SV172 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV813 @ SV1364 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV172 @ SV1364 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV172 @ SV813 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV1364 @ SV813 @ tc_nat ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5632]) ).
thf(5754,plain,
! [SV814: $i,SV173: $i,SV1365: $i] :
( ( ( c_lessequals @ SV1365 @ SV173 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1365 @ SV814 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ SV173 @ SV1365 @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ SV814 @ SV1365 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV173 @ SV814 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5633]) ).
thf(5755,plain,
! [SV1371: $i,SV191: $i,SV830: $i,SV1751: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1751 @ SV830 @ SV191 ) @ ( c_Power_Opower__class_Opower @ SV1751 @ SV1371 @ SV191 ) @ SV191 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV191 ) @ SV1751 @ SV191 ) )
= $true )
| ( ( c_lessequals @ SV830 @ SV1371 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5634]) ).
thf(5756,plain,
! [SV1372: $i,SV192: $i,SV831: $i,SV1752: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1752 @ SV831 @ SV192 ) @ ( c_Power_Opower__class_Opower @ SV1752 @ SV1372 @ SV192 ) @ SV192 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV192 ) @ SV1752 @ SV192 ) )
= $true )
| ( ( c_lessequals @ SV831 @ SV1372 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5635]) ).
thf(5757,plain,
! [SV832: $i,SV193: $i,SV1753: $i,SV1373: $i] :
( ( ( c_lessequals @ SV1373 @ SV1753 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV193 ) @ SV832 @ SV193 ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV832 @ SV1373 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SV832 @ SV1753 @ SV193 ) @ SV193 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5636]) ).
thf(5758,plain,
! [SV1376: $i,SV2011: $i,SV1755: $i,SV843: $i,SV1944: $i,SV209: $i] :
( ( ( c_ListOrder_Ostep1 @ SV209 @ ( c_List_Olist_OCons @ SV1944 @ SV843 @ SV1755 ) @ ( c_List_Olist_OCons @ SV2011 @ SV1376 @ SV1755 ) @ SV1755 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV209 @ SV1944 ) @ SV2011 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV209 @ SV843 @ SV1376 @ SV1755 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5637]) ).
thf(5759,plain,
! [SV1377: $i,SV2012: $i,SV1756: $i,SV844: $i,SV1945: $i,SV210: $i] :
( ( ( c_ListOrder_Ostep1 @ SV210 @ ( c_List_Olist_OCons @ SV1945 @ SV844 @ SV1756 ) @ ( c_List_Olist_OCons @ SV2012 @ SV1377 @ SV1756 ) @ SV1756 )
= $false )
| ( ( SV1377 = SV844 )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV210 @ SV844 @ SV1377 @ SV1756 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5638]) ).
thf(5760,plain,
! [SV1379: $i,SV212: $i,SV2013: $i,SV1758: $i,SV846: $i,SV1947: $i] :
( ( ( c_ListOrder_Ostep1 @ SV1947 @ ( c_List_Olist_OCons @ SV846 @ SV1758 @ SV2013 ) @ ( c_List_Olist_OCons @ SV212 @ SV1379 @ SV2013 ) @ SV2013 )
= $false )
| ( ( SV1379 = SV1758 )
= $true )
| ( ( SV212 = SV846 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5639]) ).
thf(5761,plain,
! [SV2014: $i,SV213: $i,SV1948: $i,SV1759: $i,SV847: $i,SV1380: $i] :
( ( ( c_ListOrder_Ostep1 @ SV1380 @ ( c_List_Olist_OCons @ SV847 @ SV1759 @ SV1948 ) @ ( c_List_Olist_OCons @ SV213 @ SV2014 @ SV1948 ) @ SV1948 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1380 @ SV847 ) @ SV213 ) )
= $true )
| ( ( SV213 = SV847 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5640]) ).
thf(5762,plain,
! [SV1760: $i,SV216: $i,SV850: $i,SV1383: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1383 @ ( c_Nat_Osize__class_Osize @ SV850 @ ( tc_List_Olist @ SV216 ) ) @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ SV1760 @ SV1383 @ tc_nat )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Orev @ SV850 @ SV216 ) @ SV216 ) )
= $true )
| ( ( c_lessequals @ ( c_List_Onth @ SV850 @ SV1383 @ SV216 ) @ ( c_List_Onth @ SV850 @ SV1760 @ SV216 ) @ SV216 )
= $true )
| ( ( class_Orderings_Olinorder @ SV216 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5641]) ).
thf(5763,plain,
! [SV1384: $i,SV217: $i,SV851: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV851 @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 )
= $false )
| ( ( c_lessequals @ SV1384 @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV217 ) @ SV851 ) @ SV1384 ) @ ( c_HOL_Ozero__class_Ozero @ SV217 ) @ SV217 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV217 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5642]) ).
thf(5764,plain,
! [SV1385: $i,SV218: $i,SV852: $i] :
( ( ( c_lessequals @ SV852 @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1385 @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV218 ) @ SV852 ) @ SV1385 ) @ ( c_HOL_Ozero__class_Ozero @ SV218 ) @ SV218 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5643]) ).
thf(5765,plain,
! [SV1761: $i,SV1386: $i,SV219: $i,SV853: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV853 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV219 ) @ SV1386 ) @ SV1761 ) @ SV219 )
= $true )
| ( ( ~ ( c_lessequals @ SV853 @ SV1761 @ SV219 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV1386 @ SV219 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV219 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5644]) ).
thf(5766,plain,
! [SV1762: $i,SV1387: $i,SV220: $i,SV854: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV854 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV220 ) @ SV1387 ) @ SV1762 ) @ SV220 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV854 @ SV1762 @ SV220 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV1387 @ SV220 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV220 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV220 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5645]) ).
thf(5767,plain,
! [SV1388: $i,SV855: $i,SV221: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ SV855 @ SV221 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ SV1388 @ SV221 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV221 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV221 ) @ SV855 ) @ SV1388 ) @ SV221 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5646]) ).
thf(5768,plain,
! [SV1389: $i,SV856: $i,SV222: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ SV856 @ SV222 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ SV1389 @ SV222 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV222 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV222 ) @ SV856 ) @ SV1389 ) @ SV222 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV222 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5647]) ).
thf(5769,plain,
! [SV1763: $i,SV857: $i,SV1390: $i,SV224: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV224 ) @ SV1390 @ SV224 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV857 @ SV1763 @ SV224 ) @ ( c_Power_Opower__class_Opower @ SV1390 @ SV1763 @ SV224 ) @ SV224 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV857 @ SV1390 @ SV224 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5648]) ).
thf(5770,plain,
! [SV1394: $i,SV229: $i,SV861: $i,SV1767: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1767 @ SV861 @ SV229 ) @ ( c_Power_Opower__class_Opower @ SV1767 @ SV1394 @ SV229 ) @ SV229 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV229 ) @ SV1767 @ SV229 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV861 @ SV1394 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV229 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5649]) ).
thf(5771,plain,
! [SV1768: $i,SV1395: $i,SV862: $i,SV230: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV230 ) @ SV862 @ SV230 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1395 @ SV1768 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV862 @ SV1395 @ SV230 ) @ ( c_Power_Opower__class_Opower @ SV862 @ SV1768 @ SV230 ) @ SV230 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5650]) ).
thf(5772,plain,
! [SV1396: $i,SV231: $i,SV863: $i,SV1769: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1769 @ SV863 @ SV231 ) @ ( c_Power_Opower__class_Opower @ SV1769 @ SV1396 @ SV231 ) @ SV231 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV231 ) @ SV1769 @ SV231 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV863 @ SV1396 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV231 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5651]) ).
thf(5773,plain,
! [SV864: $i,SV232: $i,SV1770: $i,SV1397: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1397 @ SV1770 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV232 ) @ SV864 @ SV232 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV864 @ SV1397 @ SV232 ) @ ( c_Power_Opower__class_Opower @ SV864 @ SV1770 @ SV232 ) @ SV232 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5652]) ).
thf(5774,plain,
! [SV1771: $i,SV865: $i,SV2015: $i,SV1398: $i,SV233: $i,SV1949: $i] :
( ( ( c_ListOrder_Ostep1 @ SV1949 @ ( c_List_Oappend @ SV233 @ ( c_List_Olist_OCons @ SV1398 @ ( c_List_Olist_ONil @ SV2015 ) @ SV2015 ) @ SV2015 ) @ ( c_List_Oappend @ SV865 @ ( c_List_Olist_OCons @ SV1771 @ ( c_List_Olist_ONil @ SV2015 ) @ SV2015 ) @ SV2015 ) @ SV2015 )
= $false )
| ( ( SV1398 = SV1771 )
= $true )
| ( ( SV233 = SV865 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5653]) ).
thf(5775,plain,
! [SV1399: $i,SV2016: $i,SV1950: $i,SV866: $i,SV1772: $i,SV234: $i] :
( ( ( c_ListOrder_Ostep1 @ SV234 @ ( c_List_Oappend @ SV1772 @ ( c_List_Olist_OCons @ SV866 @ ( c_List_Olist_ONil @ SV1950 ) @ SV1950 ) @ SV1950 ) @ ( c_List_Oappend @ SV2016 @ ( c_List_Olist_OCons @ SV1399 @ ( c_List_Olist_ONil @ SV1950 ) @ SV1950 ) @ SV1950 ) @ SV1950 )
= $false )
| ( ( SV866 = SV1399 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV234 @ SV866 ) @ SV1399 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5654]) ).
thf(5776,plain,
! [SV1400: $i,SV1951: $i,SV2017: $i,SV867: $i,SV1773: $i,SV235: $i] :
( ( ( c_ListOrder_Ostep1 @ SV235 @ ( c_List_Oappend @ SV1773 @ ( c_List_Olist_OCons @ SV867 @ ( c_List_Olist_ONil @ SV2017 ) @ SV2017 ) @ SV2017 ) @ ( c_List_Oappend @ SV1951 @ ( c_List_Olist_OCons @ SV1400 @ ( c_List_Olist_ONil @ SV2017 ) @ SV2017 ) @ SV2017 ) @ SV2017 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV235 @ SV1773 @ SV1951 @ SV2017 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV235 @ SV867 ) @ SV1400 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5655]) ).
thf(5777,plain,
! [SV2018: $i,SV868: $i,SV1774: $i,SV1952: $i,SV236: $i,SV1401: $i] :
( ( ( c_ListOrder_Ostep1 @ SV1401 @ ( c_List_Oappend @ SV236 @ ( c_List_Olist_OCons @ SV1952 @ ( c_List_Olist_ONil @ SV1774 ) @ SV1774 ) @ SV1774 ) @ ( c_List_Oappend @ SV868 @ ( c_List_Olist_OCons @ SV2018 @ ( c_List_Olist_ONil @ SV1774 ) @ SV1774 ) @ SV1774 ) @ SV1774 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV1401 @ SV236 @ SV868 @ SV1774 )
= $true )
| ( ( SV236 = SV868 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5656]) ).
thf(5778,plain,
! [SV878: $i,SV246: $i,SV1780: $i,SV1409: $i,SV1954: $i] :
( ( ( c_in @ SV1954 @ ( c_List_Oset @ SV1409 @ SV1780 ) @ SV1780 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV246 @ ( hAPP @ SV878 @ SV1954 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV246 @ ( c_List_Olist_Olist__size @ SV878 @ SV1409 @ SV1780 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5658]) ).
thf(5779,plain,
! [SV1413: $i,SV252: $i,SV1955: $i,SV1782: $i,SV884: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV884 @ SV1782 @ SV1955 @ SV252 ) @ SV252 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV884 @ ( c_List_Olinorder__class_Oinsort__key @ SV884 @ SV1413 @ SV1782 @ SV1955 @ SV252 ) @ SV1955 @ SV252 ) @ SV252 )
= $true )
| ( ( class_Orderings_Olinorder @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5659]) ).
thf(5780,plain,
! [SV253: $i,SV1783: $i,SV1414: $i,SV1956: $i,SV885: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV885 @ ( c_List_Olinorder__class_Oinsort__key @ SV885 @ SV1956 @ SV1414 @ SV1783 @ SV253 ) @ SV1783 @ SV253 ) @ SV253 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Omap @ SV885 @ SV1414 @ SV1783 @ SV253 ) @ SV253 )
= $true )
| ( ( class_Orderings_Olinorder @ SV253 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5660]) ).
thf(5781,plain,
! [SV1422: $i,SV263: $i,SV895: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV895 @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1422 @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV263 ) @ SV895 ) @ SV1422 ) @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV263 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV263 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5661]) ).
thf(5782,plain,
! [SV1439: $i,SV281: $i,SV1799: $i,SV913: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV913 @ SV1799 @ SV281 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1799 @ SV1439 @ SV281 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV913 @ SV1439 @ SV281 )
= $true )
| ( ( class_Orderings_Oorder @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5662]) ).
thf(5783,plain,
! [SV914: $i,SV282: $i,SV1440: $i,SV1800: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1800 @ SV1440 @ SV282 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV914 @ SV1800 @ SV282 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV914 @ SV1440 @ SV282 )
= $true )
| ( ( class_Orderings_Opreorder @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5663]) ).
thf(5784,plain,
! [SV1810: $i,SV932: $i,SV300: $i,SV1458: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1458 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SV932 @ SV300 )
| ~ ( c_HOL_Oord__class_Oless @ SV932 @ SV1810 @ SV300 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV932 @ SV1458 @ SV300 ) @ ( c_Power_Opower__class_Opower @ SV1810 @ SV1458 @ SV300 ) @ SV300 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV300 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5664]) ).
thf(5785,plain,
! [SV1469: $i,SV943: $i,SV311: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV311 ) @ SV943 @ SV311 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1469 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV311 ) @ ( c_Power_Opower__class_Opower @ SV943 @ SV1469 @ SV311 ) @ SV311 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5665]) ).
thf(5786,plain,
! [SV1471: $i,SV1817: $i,SV313: $i,SV945: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV945 @ ( c_HOL_Oone__class_Oone @ SV313 ) @ SV313 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV313 ) @ SV945 @ SV313 )
| ~ ( c_HOL_Oord__class_Oless @ SV1817 @ SV1471 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV945 @ SV1471 @ SV313 ) @ ( c_Power_Opower__class_Opower @ SV945 @ SV1817 @ SV313 ) @ SV313 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV313 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5666]) ).
thf(5787,plain,
! [SV1529: $i,SV1043: $i,SV424: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV1043 @ SV424 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ SV1529 @ SV424 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV424 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV424 ) @ SV1043 ) @ SV1529 ) @ SV424 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV424 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5670]) ).
thf(5788,plain,
! [SV1850: $i,SV1055: $i,SV436: $i,SV1979: $i,SV1539: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1539 @ SV1979 @ SV436 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1055 @ SV1850 @ SV436 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV436 ) @ SV1055 ) @ SV1539 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV436 ) @ SV1850 ) @ SV1979 ) @ SV436 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV436 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5671]) ).
thf(5789,plain,
! [SV1546: $i,SV447: $i,SV1853: $i,SV1066: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1066 @ SV1853 @ SV447 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV1546 @ SV447 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1066 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV447 ) @ SV1546 ) @ SV1853 ) @ SV447 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV447 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5673]) ).
thf(5790,plain,
! [SV1105: $i,SV488: $i] :
( ( ( ~ ( class_Power_Opower @ SV488 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV488 ) @ SV1105 @ SV488 )
= ( c_HOL_Ozero__class_Ozero @ SV488 ) )
| ( SV1105
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV488 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV488 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV488 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5686]) ).
thf(5791,plain,
! [SV1133: $i,SV522: $i,SV1989: $i,SV1877: $i,SV1598: $i] :
( ( ( c_Type_Otyping @ SV1598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1877 ) @ SV1989 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV522 )
= $false )
| ( ( c_Type_Otyping @ SV1598 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1877 ) @ SV1989 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1133 )
= $false )
| ( ( SV522 = SV1133 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5687]) ).
thf(5792,plain,
! [SV554: $i,SV1616: $i,SV1885: $i,SV1161: $i] :
( ( ( SV1161 = SV1885 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1616 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SV1885 @ SV554 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SV1161 @ SV554 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1161 @ SV1616 @ SV554 )
= ( c_Power_Opower__class_Opower @ SV1885 @ SV1616 @ SV554 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV554 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5689]) ).
thf(5793,plain,
! [SV1888: $i,SV560: $i,SV1166: $i,SV1620: $i] :
( ( ( SV1620
!= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV1620 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) )
= $true )
| ( ( ( c_List_Oappend @ SV1620 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1620 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) @ SV1888 @ SV1166 ) @ SV1166 )
= ( c_List_Oappend @ SV560 @ SV1888 @ SV1166 ) )
= $true )
| ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV560 @ ( tc_List_Olist @ SV1166 ) ) @ SV1620 @ SV1166 )
= SV560 )
= $false )
| ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV560 @ ( tc_List_Olist @ SV1166 ) ) @ SV1620 @ SV1166 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1620 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) @ SV1888 @ SV1166 ) @ SV1166 )
= SV1888 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5691]) ).
thf(5794,plain,
! [SV1994: $i,SV1179: $i,SV1894: $i,SV1632: $i,SV574: $i] :
( ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV574 @ ( tc_List_Olist @ SV1632 ) ) @ ( c_Nat_Osize__class_Osize @ SV1894 @ ( tc_List_Olist @ SV1632 ) ) @ tc_nat )
= $false )
| ( ( SV1179
= ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV574 @ ( tc_List_Olist @ SV1632 ) ) @ SV1894 @ SV1632 ) @ SV1994 @ SV1632 ) )
= $true )
| ( ( ( c_List_Oappend @ SV574 @ SV1179 @ SV1632 )
= ( c_List_Oappend @ SV1894 @ SV1994 @ SV1632 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5693]) ).
thf(5795,plain,
! [SV1635: $i,SV1182: $i,SV577: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV577 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV577 )
| ( ( c_Power_Opower__class_Opower @ SV1182 @ SV1635 @ SV577 )
!= ( c_HOL_Ozero__class_Ozero @ SV577 ) )
| ( SV1182
= ( c_HOL_Ozero__class_Ozero @ SV577 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV577 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV577 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5694]) ).
thf(5796,plain,
! [SV1995: $i,SV1896: $i,SV578: $i,SV1636: $i,SV1183: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1183 @ SV1636 @ SV578 )
= ( c_HOL_Ominus__class_Ominus @ SV1896 @ SV1995 @ SV578 ) )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1896 @ SV1995 @ SV578 )
| ~ ( c_HOL_Oord__class_Oless @ SV1183 @ SV1636 @ SV578 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV578 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5695]) ).
thf(5797,plain,
! [SV1997: $i,SV1901: $i,SV594: $i,SV1648: $i,SV1197: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1197 @ SV1648 @ SV594 )
= ( c_HOL_Ominus__class_Ominus @ SV1901 @ SV1997 @ SV594 ) )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV1197 @ SV1648 @ SV594 )
| ~ ( c_HOL_Oord__class_Oless @ SV1901 @ SV1997 @ SV594 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV594 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5697]) ).
thf(5798,plain,
! [SV1905: $i,SV1659: $i,SV1209: $i,SV1999: $i,SV2027: $i,SV607: $i] :
( ( ( ( hAPP @ SV607 @ SV2027 )
= ( hAPP @ SV1999 @ SV2027 ) )
= $true )
| ( ( ~ ( c_in @ SV2027 @ ( c_List_Oset @ SV1209 @ SV1659 ) @ SV1659 ) )
= $true )
| ( ( ( c_List_Omap @ SV607 @ SV1209 @ SV1659 @ SV1905 )
= ( c_List_Omap @ SV1999 @ SV1209 @ SV1659 @ SV1905 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5700]) ).
thf(5799,plain,
! [SV2001: $i,SV1216: $i,SV1909: $i,SV1666: $i,SV614: $i] :
( ( ( c_lessequals @ ( c_Nat_Osize__class_Osize @ SV614 @ ( tc_List_Olist @ SV1666 ) ) @ ( c_Nat_Osize__class_Osize @ SV1909 @ ( tc_List_Olist @ SV1666 ) ) @ tc_nat )
= $false )
| ( ( SV614
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV614 @ ( tc_List_Olist @ SV1666 ) ) @ SV1909 @ SV1666 ) )
= $true )
| ( ( ( c_List_Oappend @ SV614 @ SV1216 @ SV1666 )
= ( c_List_Oappend @ SV1909 @ SV2001 @ SV1666 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5701]) ).
thf(5800,plain,
! [SV1667: $i,SV615: $i,SV1217: $i] :
( ( ( SV1217
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV615 ) @ SV1217 ) @ SV1667 ) )
= $false )
| ( ( SV1667
= ( c_HOL_Ozero__class_Ozero @ SV615 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV615 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV615 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5702]) ).
thf(5801,plain,
! [SV1218: $i,SV616: $i] :
( ( ( ~ ( class_Power_Opower @ SV616 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1218 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV616 )
!= ( c_HOL_Ozero__class_Ozero @ SV616 ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV616 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV616 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV616 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5703]) ).
thf(5802,plain,
! [SV1219: $i,SV1668: $i,SV617: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV617 ) @ SV1668 @ SV617 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV617 ) @ SV1219 @ SV617 )
| ( SV1668
= ( c_HOL_Ozero__class_Ozero @ SV617 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV617 ) @ SV1219 ) @ SV1668 )
= ( c_HOL_Ozero__class_Ozero @ SV617 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV617 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5704]) ).
thf(5803,plain,
! [SV1910: $i,SV1669: $i,SV1220: $i,SV618: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV618 ) @ SV1220 @ SV618 ) )
= $true )
| ( ( SV1669 = SV1910 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1220 @ SV1669 @ SV618 )
= ( c_Power_Opower__class_Opower @ SV1220 @ SV1910 @ SV618 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV618 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5705]) ).
thf(5804,plain,
! [SV2002: $i,SV1911: $i,SV621: $i,SV1672: $i,SV1223: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1223 @ SV1672 @ SV621 )
= ( c_HOL_Ominus__class_Ominus @ SV1911 @ SV2002 @ SV621 ) )
= $false )
| ( ( ( c_lessequals @ SV1672 @ SV1223 @ SV621 )
| ~ ( c_lessequals @ SV2002 @ SV1911 @ SV621 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV621 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5706]) ).
thf(5805,plain,
! [SV624: $i,SV1675: $i,SV1226: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1226 @ SV1675 @ SV624 )
= ( c_HOL_Ozero__class_Ozero @ SV624 ) )
= $false )
| ( ( SV1226 = SV1675 )
= $true )
| ( ( class_Int_Onumber__ring @ SV624 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV624 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5709]) ).
thf(5806,plain,
! [SV1676: $i,SV625: $i,SV1914: $i,SV1227: $i] :
( ( ( SV1227 = SV1914 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV625 ) @ SV1914 @ SV625 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV625 ) @ SV1227 @ SV625 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1227 @ ( c_Suc @ SV1676 ) @ SV625 )
= ( c_Power_Opower__class_Opower @ SV1914 @ ( c_Suc @ SV1676 ) @ SV625 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV625 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5710]) ).
thf(5807,plain,
! [SV2004: $i,SV1915: $i,SV626: $i,SV1677: $i,SV1228: $i] :
( ( ( ( c_HOL_Ominus__class_Ominus @ SV1228 @ SV1677 @ SV626 )
= ( c_HOL_Ominus__class_Ominus @ SV1915 @ SV2004 @ SV626 ) )
= $false )
| ( ( ( c_lessequals @ SV2004 @ SV1915 @ SV626 )
| ~ ( c_lessequals @ SV1677 @ SV1228 @ SV626 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV626 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5711]) ).
thf(5808,plain,
! [SV1920: $i,SV1685: $i,SV1237: $i,SV637: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1237 ) @ SV1685 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1237 ) @ SV1920 ) )
= $true )
| ( ( SV1685 = SV1920 )
= $true )
| ( ( class_Int_Onumber__ring @ SV637 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV637 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5714]) ).
thf(5809,plain,
! [SV1687: $i,SV639: $i,SV1239: $i] :
( ( ( ( c_Int_Onumber__class_Onumber__of @ SV1239 @ SV639 )
= ( c_Int_Onumber__class_Onumber__of @ SV1687 @ SV639 ) )
= $false )
| ( ( SV1239 = SV1687 )
= $true )
| ( ( class_Int_Onumber__ring @ SV639 )
= $false )
| ( ( class_Int_Oring__char__0 @ SV639 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5715]) ).
thf(5810,plain,
! [SV1692: $i,SV646: $i,SV1245: $i] :
( ( ( c_lessequals @ SV1245 @ SV646 @ tc_nat )
= $false )
| ( ( SV646 = SV1692 )
= $true )
| ( ( c_lessequals @ SV1245 @ SV1692 @ tc_nat )
= $false )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV646 @ SV1245 @ tc_nat )
= ( c_HOL_Ominus__class_Ominus @ SV1692 @ SV1245 @ tc_nat ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5716]) ).
thf(5811,plain,
! [SV1246: $i,SV1693: $i,SV647: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV647 ) @ SV1693 @ SV647 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV647 ) @ SV1246 @ SV647 )
| ( SV1246
= ( c_HOL_Ozero__class_Ozero @ SV647 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV647 ) @ SV1246 ) @ SV1693 )
= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV647 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5717]) ).
thf(5812,plain,
! [SV2008: $i,SV1927: $i,SV1695: $i,SV1248: $i,SV649: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1248 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1695 ) @ SV1927 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1695 ) @ SV2008 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV649 ) @ SV1248 ) @ SV1927 )
= SV2008 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV649 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5719]) ).
thf(5813,plain,
! [SV1256: $i,SV658: $i,SV2: $i,SV1701: $i,SV1931: $i] :
( ( ( c_lessequals @ SV1931 @ SV1701 @ SV2 )
= $false )
| ( ( ~ ( c_lessequals @ SV658 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SV1256 ) @ SV1931 ) @ SV2 ) )
= $true )
| ( ( c_lessequals @ SV658 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SV1256 ) @ SV1701 ) @ SV2 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5720]) ).
thf(5814,plain,
! [SV1257: $i,SV3: $i,SV1702: $i,SV659: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV659 @ SV1702 @ SV3 )
= $false )
| ( ( c_lessequals @ SV1702 @ SV1257 @ SV3 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV659 @ SV1257 @ SV3 )
= $true )
| ( ( class_Orderings_Opreorder @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5721]) ).
thf(5815,plain,
! [SV1258: $i,SV4: $i,SV1703: $i,SV660: $i] :
( ( ( c_lessequals @ SV660 @ SV1703 @ SV4 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1703 @ SV1258 @ SV4 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV660 @ SV1258 @ SV4 )
= $true )
| ( ( class_Orderings_Opreorder @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5722]) ).
thf(5816,plain,
! [SV1260: $i,SV10: $i,SV1704: $i,SV664: $i] :
( ( ( c_lessequals @ SV664 @ SV1704 @ SV10 )
= $false )
| ( ( c_lessequals @ SV1704 @ SV1260 @ SV10 )
= $false )
| ( ( c_lessequals @ SV664 @ SV1260 @ SV10 )
= $true )
| ( ( class_Orderings_Opreorder @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5723]) ).
thf(5817,plain,
! [SV665: $i,SV11: $i,SV1261: $i,SV1705: $i] :
( ( ( c_lessequals @ SV1705 @ SV1261 @ SV11 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV665 @ SV1705 @ SV11 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV665 @ SV1261 @ SV11 )
= $true )
| ( ( class_Orderings_Oorder @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5724]) ).
thf(5818,plain,
! [SV666: $i,SV12: $i,SV1262: $i,SV1706: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1706 @ SV1262 @ SV12 )
= $false )
| ( ( c_lessequals @ SV666 @ SV1706 @ SV12 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV666 @ SV1262 @ SV12 )
= $true )
| ( ( class_Orderings_Oorder @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5725]) ).
thf(5819,plain,
! [SV667: $i,SV13: $i,SV1263: $i,SV1707: $i] :
( ( ( c_lessequals @ SV1707 @ SV1263 @ SV13 )
= $false )
| ( ( c_lessequals @ SV667 @ SV1707 @ SV13 )
= $false )
| ( ( c_lessequals @ SV667 @ SV1263 @ SV13 )
= $true )
| ( ( class_Orderings_Oorder @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5726]) ).
thf(5820,plain,
! [SV1267: $i,SV20: $i,SV1708: $i,SV673: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV673 @ ( c_Suc @ SV1708 ) @ SV20 ) @ ( c_Power_Opower__class_Opower @ SV1267 @ ( c_Suc @ SV1708 ) @ SV20 ) @ SV20 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV1267 @ SV20 )
= $false )
| ( ( c_lessequals @ SV673 @ SV1267 @ SV20 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5729]) ).
thf(5821,plain,
! [SV1286: $i,SV1715: $i,SV701: $i,SV52: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV701 @ SV52 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1715 @ SV1286 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV701 @ ( c_HOL_Oone__class_Oone @ SV52 ) @ SV52 )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV701 @ SV1286 @ SV52 ) @ ( c_Power_Opower__class_Opower @ SV701 @ SV1715 @ SV52 ) @ SV52 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5733]) ).
thf(5822,plain,
! [SV1718: $i,SV713: $i,SV64: $i,SV1934: $i,SV1293: $i] :
( ( ( c_lessequals @ SV1293 @ SV1934 @ SV64 )
= $false )
| ( ( ~ ( c_lessequals @ SV713 @ SV1718 @ SV64 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV713 ) @ SV1293 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV1718 ) @ SV1934 ) @ SV64 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5734]) ).
thf(5823,plain,
! [SV727: $i,SV79: $i,SV1720: $i,SV1301: $i] :
( ( ( c_lessequals @ SV1301 @ SV1720 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV79 ) @ SV727 @ SV79 )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV727 @ SV1301 @ SV79 ) @ ( c_Power_Opower__class_Opower @ SV727 @ SV1720 @ SV79 ) @ SV79 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5736]) ).
thf(5824,plain,
! [SV1314: $i,SV102: $i,SV1721: $i,SV749: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV749 @ SV1721 @ SV102 ) @ SV102 )
= $false )
| ( ( c_in @ SV1314 @ ( c_List_Oset @ SV1721 @ SV102 ) @ SV102 )
= $false )
| ( ( c_lessequals @ SV749 @ SV1314 @ SV102 )
= $true )
| ( ( class_Orderings_Olinorder @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5738]) ).
thf(5825,plain,
! [SV1936: $i,SV750: $i,SV103: $i,SV1722: $i,SV1315: $i] :
( ( ( c_in @ SV1315 @ ( c_List_Oset @ SV1722 @ SV103 ) @ SV103 )
= $false )
| ( ( ~ ( c_in @ SV750 @ ( c_List_Oset @ SV1936 @ SV103 ) @ SV103 )
| ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1936 @ SV1722 @ SV103 ) @ SV103 ) )
= $true )
| ( ( c_lessequals @ SV750 @ SV1315 @ SV103 )
= $true )
| ( ( class_Orderings_Olinorder @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5739]) ).
thf(5826,plain,
! [SV1320: $i,SV113: $i,SV1723: $i,SV757: $i] :
( ( ( ~ ( c_lessequals @ SV757 @ SV1723 @ SV113 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV1320 @ SV113 ) )
= $true )
| ( ( c_lessequals @ SV757 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV1320 ) @ SV1723 ) @ SV113 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV113 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5741]) ).
thf(5827,plain,
! [SV1724: $i,SV114: $i,SV1321: $i,SV758: $i] :
( ( ( ~ ( c_lessequals @ SV758 @ SV1321 @ SV114 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV1724 @ SV114 ) )
= $true )
| ( ( c_lessequals @ SV758 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SV1321 ) @ SV1724 ) @ SV114 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV114 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5742]) ).
thf(5828,plain,
! [SV1725: $i,SV762: $i,SV118: $i,SV1937: $i,SV1323: $i] :
( ( ( c_lessequals @ SV1323 @ SV1937 @ SV118 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV762 @ SV1725 @ SV118 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV762 ) @ SV1323 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV1725 ) @ SV1937 ) @ SV118 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5744]) ).
thf(5829,plain,
! [SV1726: $i,SV763: $i,SV119: $i,SV1938: $i,SV1324: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1324 @ SV1938 @ SV119 )
= $false )
| ( ( ~ ( c_lessequals @ SV763 @ SV1726 @ SV119 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV119 ) @ SV763 ) @ SV1324 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV119 ) @ SV1726 ) @ SV1938 ) @ SV119 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5745]) ).
thf(5830,plain,
! [SV765: $i,SV121: $i,SV1325: $i] :
( ( ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ SV1325 @ SV121 ) @ ( c_Int_Onumber__class_Onumber__of @ SV765 @ SV121 ) @ SV121 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ SV765 @ SV121 ) @ ( c_Int_Onumber__class_Onumber__of @ SV1325 @ SV121 ) @ SV121 )
= $false )
| ( ( class_Int_Onumber @ SV121 )
= $false )
| ( ( class_Orderings_Olinorder @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5746]) ).
thf(5831,plain,
! [SV1329: $i,SV133: $i,SV1728: $i,SV774: $i] :
( ( ( c_lessequals @ SV774 @ SV1728 @ SV133 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV133 ) @ SV774 @ SV133 )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV774 @ SV1329 @ SV133 ) @ ( c_Power_Opower__class_Opower @ SV1728 @ SV1329 @ SV133 ) @ SV133 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5747]) ).
thf(5832,plain,
! [SV1344: $i,SV152: $i,SV793: $i,SV1737: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1737 @ ( c_Nat_Osize__class_Osize @ SV793 @ ( tc_List_Olist @ SV152 ) ) @ tc_nat ) )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ SV793 @ SV152 ) )
= $true )
| ( ( c_lessequals @ SV1344 @ SV1737 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_List_Onth @ SV793 @ SV1344 @ SV152 ) @ ( c_List_Onth @ SV793 @ SV1737 @ SV152 ) @ SV152 )
= $true )
| ( ( class_Orderings_Olinorder @ SV152 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5748]) ).
thf(5833,plain,
! [SV153: $i,SV794: $i,SV1738: $i,SV1345: $i] :
( ( ( ~ ( c_lessequals @ SV1345 @ SV1738 @ tc_nat ) )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ SV794 @ SV153 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1738 @ ( c_Nat_Osize__class_Osize @ SV794 @ ( tc_List_Olist @ SV153 ) ) @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_List_Onth @ SV794 @ SV1345 @ SV153 ) @ ( c_List_Onth @ SV794 @ SV1738 @ SV153 ) @ SV153 )
= $true )
| ( ( class_Orderings_Olinorder @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5749]) ).
thf(5834,plain,
! [SV1741: $i,SV157: $i,SV1349: $i,SV798: $i] :
( ( ( c_lessequals @ SV798 @ SV1349 @ SV157 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV1349 @ SV1741 @ SV157 ) @ SV157 )
= $false )
| ( ( c_List_Olinorder__class_Osorted @ ( c_List_Olist_OCons @ SV798 @ ( c_List_Olist_OCons @ SV1349 @ SV1741 @ SV157 ) @ SV157 ) @ SV157 )
= $true )
| ( ( class_Orderings_Olinorder @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5750]) ).
thf(5835,plain,
! [SV2009: $i,SV1940: $i,SV169: $i,SV1748: $i,SV1361: $i,SV810: $i] :
( ( ( c_lessequals @ ( hAPP @ SV810 @ SV1361 ) @ ( hAPP @ SV810 @ SV1748 ) @ SV169 )
= $false )
| ( ( ( c_List_Olinorder__class_Oinsort__key @ SV810 @ SV1361 @ ( c_List_Olist_OCons @ SV1748 @ SV1940 @ SV2009 ) @ SV2009 @ SV169 )
= ( c_List_Olist_OCons @ SV1361 @ ( c_List_Olist_OCons @ SV1748 @ SV1940 @ SV2009 ) @ SV2009 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5751]) ).
thf(5836,plain,
! [SV1371: $i,SV830: $i,SV1751: $i,SV191: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV191 ) @ SV1751 @ SV191 )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1751 @ SV830 @ SV191 ) @ ( c_Power_Opower__class_Opower @ SV1751 @ SV1371 @ SV191 ) @ SV191 )
= $false )
| ( ( c_lessequals @ SV830 @ SV1371 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5755]) ).
thf(5837,plain,
! [SV1372: $i,SV831: $i,SV1752: $i,SV192: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV192 ) @ SV1752 @ SV192 )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV1752 @ SV831 @ SV192 ) @ ( c_Power_Opower__class_Opower @ SV1752 @ SV1372 @ SV192 ) @ SV192 )
= $false )
| ( ( c_lessequals @ SV831 @ SV1372 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5756]) ).
thf(5838,plain,
! [SV1753: $i,SV1373: $i,SV832: $i,SV193: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV193 ) @ SV832 @ SV193 )
= $false )
| ( ( c_lessequals @ SV1373 @ SV1753 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV832 @ SV1373 @ SV193 ) @ ( c_Power_Opower__class_Opower @ SV832 @ SV1753 @ SV193 ) @ SV193 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5757]) ).
thf(5839,plain,
! [SV216: $i,SV850: $i,SV1383: $i,SV1760: $i] :
( ( ( ~ ( c_lessequals @ SV1760 @ SV1383 @ tc_nat ) )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Orev @ SV850 @ SV216 ) @ SV216 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1383 @ ( c_Nat_Osize__class_Osize @ SV850 @ ( tc_List_Olist @ SV216 ) ) @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_List_Onth @ SV850 @ SV1383 @ SV216 ) @ ( c_List_Onth @ SV850 @ SV1760 @ SV216 ) @ SV216 )
= $true )
| ( ( class_Orderings_Olinorder @ SV216 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5762]) ).
thf(5840,plain,
! [SV1386: $i,SV219: $i,SV1761: $i,SV853: $i] :
( ( ( ~ ( c_lessequals @ SV853 @ SV1761 @ SV219 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV1386 @ SV219 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV853 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV219 ) @ SV1386 ) @ SV1761 ) @ SV219 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV219 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5765]) ).
thf(5841,plain,
! [SV1387: $i,SV220: $i,SV1762: $i,SV854: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV854 @ SV1762 @ SV220 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV1387 @ SV220 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV854 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV220 ) @ SV1387 ) @ SV1762 ) @ SV220 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV220 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV220 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5766]) ).
thf(5842,plain,
! [SV1390: $i,SV224: $i,SV1763: $i,SV857: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV857 @ SV1763 @ SV224 ) @ ( c_Power_Opower__class_Opower @ SV1390 @ SV1763 @ SV224 ) @ SV224 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV224 ) @ SV1390 @ SV224 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV857 @ SV1390 @ SV224 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5769]) ).
thf(5843,plain,
! [SV1394: $i,SV861: $i,SV1767: $i,SV229: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV229 ) @ SV1767 @ SV229 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1767 @ SV861 @ SV229 ) @ ( c_Power_Opower__class_Opower @ SV1767 @ SV1394 @ SV229 ) @ SV229 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV861 @ SV1394 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV229 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5770]) ).
thf(5844,plain,
! [SV862: $i,SV230: $i,SV1768: $i,SV1395: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1395 @ SV1768 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV230 ) @ SV862 @ SV230 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV862 @ SV1395 @ SV230 ) @ ( c_Power_Opower__class_Opower @ SV862 @ SV1768 @ SV230 ) @ SV230 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5771]) ).
thf(5845,plain,
! [SV1396: $i,SV863: $i,SV1769: $i,SV231: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV231 ) @ SV1769 @ SV231 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1769 @ SV863 @ SV231 ) @ ( c_Power_Opower__class_Opower @ SV1769 @ SV1396 @ SV231 ) @ SV231 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV863 @ SV1396 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV231 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5772]) ).
thf(5846,plain,
! [SV1770: $i,SV1397: $i,SV864: $i,SV232: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV232 ) @ SV864 @ SV232 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1397 @ SV1770 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV864 @ SV1397 @ SV232 ) @ ( c_Power_Opower__class_Opower @ SV864 @ SV1770 @ SV232 ) @ SV232 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5773]) ).
thf(5847,plain,
! [SV913: $i,SV281: $i,SV1439: $i,SV1799: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1799 @ SV1439 @ SV281 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV913 @ SV1799 @ SV281 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV913 @ SV1439 @ SV281 )
= $true )
| ( ( class_Orderings_Oorder @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5782]) ).
thf(5848,plain,
! [SV1440: $i,SV282: $i,SV1800: $i,SV914: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV914 @ SV1800 @ SV282 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1800 @ SV1440 @ SV282 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV914 @ SV1440 @ SV282 )
= $true )
| ( ( class_Orderings_Opreorder @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5783]) ).
thf(5849,plain,
! [SV1458: $i,SV1810: $i,SV932: $i,SV300: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SV932 @ SV300 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV932 @ SV1810 @ SV300 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1458 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV932 @ SV1458 @ SV300 ) @ ( c_Power_Opower__class_Opower @ SV1810 @ SV1458 @ SV300 ) @ SV300 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV300 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5784]) ).
thf(5850,plain,
! [SV1471: $i,SV1817: $i,SV945: $i,SV313: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV313 ) @ SV945 @ SV313 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1817 @ SV1471 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV945 @ ( c_HOL_Oone__class_Oone @ SV313 ) @ SV313 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV945 @ SV1471 @ SV313 ) @ ( c_Power_Opower__class_Opower @ SV945 @ SV1817 @ SV313 ) @ SV313 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV313 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5786]) ).
thf(5851,plain,
! [SV1850: $i,SV1055: $i,SV436: $i,SV1979: $i,SV1539: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1539 @ SV1979 @ SV436 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1055 @ SV1850 @ SV436 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV436 ) @ SV1055 ) @ SV1539 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV436 ) @ SV1850 ) @ SV1979 ) @ SV436 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV436 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5788]) ).
thf(5852,plain,
! [SV1853: $i,SV1066: $i,SV1546: $i,SV447: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV447 ) @ SV1546 @ SV447 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1066 @ SV1853 @ SV447 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1066 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV447 ) @ SV1546 ) @ SV1853 ) @ SV447 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV447 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5789]) ).
thf(5853,plain,
! [SV1105: $i,SV488: $i] :
( ( ( class_Power_Opower @ SV488 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV488 ) @ SV1105 @ SV488 )
= ( c_HOL_Ozero__class_Ozero @ SV488 ) )
| ( SV1105
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV488 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV488 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV488 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5790]) ).
thf(5854,plain,
! [SV1161: $i,SV1885: $i,SV554: $i,SV1616: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1616 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SV1885 @ SV554 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SV1161 @ SV554 ) )
= $true )
| ( ( SV1161 = SV1885 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1161 @ SV1616 @ SV554 )
= ( c_Power_Opower__class_Opower @ SV1885 @ SV1616 @ SV554 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV554 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5792]) ).
thf(5855,plain,
! [SV1888: $i,SV560: $i,SV1166: $i,SV1620: $i] :
( ( ( SV1620
= ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV1620 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) )
= $false )
| ( ( ( c_List_Oappend @ SV1620 @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1620 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) @ SV1888 @ SV1166 ) @ SV1166 )
= ( c_List_Oappend @ SV560 @ SV1888 @ SV1166 ) )
= $true )
| ( ( ( c_List_Otake @ ( c_Nat_Osize__class_Osize @ SV560 @ ( tc_List_Olist @ SV1166 ) ) @ SV1620 @ SV1166 )
= SV560 )
= $false )
| ( ( ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV560 @ ( tc_List_Olist @ SV1166 ) ) @ SV1620 @ SV1166 ) @ ( c_List_Oappend @ ( c_List_Odrop @ ( c_Nat_Osize__class_Osize @ SV1620 @ ( tc_List_Olist @ SV1166 ) ) @ SV560 @ SV1166 ) @ SV1888 @ SV1166 ) @ SV1166 )
= SV1888 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5793]) ).
thf(5856,plain,
! [SV1635: $i,SV1182: $i,SV577: $i] :
( ( ( ~ ( class_Power_Opower @ SV577 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1182 @ SV1635 @ SV577 )
!= ( c_HOL_Ozero__class_Ozero @ SV577 ) )
| ( SV1182
= ( c_HOL_Ozero__class_Ozero @ SV577 ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV577 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV577 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV577 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5795]) ).
thf(5857,plain,
! [SV1636: $i,SV1183: $i,SV578: $i,SV1995: $i,SV1896: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1896 @ SV1995 @ SV578 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1183 @ SV1636 @ SV578 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1183 @ SV1636 @ SV578 )
= ( c_HOL_Ominus__class_Ominus @ SV1896 @ SV1995 @ SV578 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV578 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5796]) ).
thf(5858,plain,
! [SV1997: $i,SV1901: $i,SV594: $i,SV1648: $i,SV1197: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1197 @ SV1648 @ SV594 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1901 @ SV1997 @ SV594 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1197 @ SV1648 @ SV594 )
= ( c_HOL_Ominus__class_Ominus @ SV1901 @ SV1997 @ SV594 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV594 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5797]) ).
thf(5859,plain,
! [SV1905: $i,SV1999: $i,SV607: $i,SV1659: $i,SV1209: $i,SV2027: $i] :
( ( ( c_in @ SV2027 @ ( c_List_Oset @ SV1209 @ SV1659 ) @ SV1659 )
= $false )
| ( ( ( hAPP @ SV607 @ SV2027 )
= ( hAPP @ SV1999 @ SV2027 ) )
= $true )
| ( ( ( c_List_Omap @ SV607 @ SV1209 @ SV1659 @ SV1905 )
= ( c_List_Omap @ SV1999 @ SV1209 @ SV1659 @ SV1905 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5798]) ).
thf(5860,plain,
! [SV1218: $i,SV616: $i] :
( ( ( class_Power_Opower @ SV616 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV1218 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV616 )
!= ( c_HOL_Ozero__class_Ozero @ SV616 ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV616 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV616 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV616 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5801]) ).
thf(5861,plain,
! [SV1668: $i,SV1219: $i,SV617: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV617 ) @ SV1219 @ SV617 ) )
= $true )
| ( ( SV1668
= ( c_HOL_Ozero__class_Ozero @ SV617 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV617 ) @ SV1668 @ SV617 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV617 ) @ SV1219 ) @ SV1668 )
= ( c_HOL_Ozero__class_Ozero @ SV617 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV617 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5802]) ).
thf(5862,plain,
! [SV1910: $i,SV1669: $i,SV1220: $i,SV618: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV618 ) @ SV1220 @ SV618 )
= $false )
| ( ( SV1669 = SV1910 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1220 @ SV1669 @ SV618 )
= ( c_Power_Opower__class_Opower @ SV1220 @ SV1910 @ SV618 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV618 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5803]) ).
thf(5863,plain,
! [SV1911: $i,SV2002: $i,SV621: $i,SV1223: $i,SV1672: $i] :
( ( ( c_lessequals @ SV1672 @ SV1223 @ SV621 )
= $true )
| ( ( ~ ( c_lessequals @ SV2002 @ SV1911 @ SV621 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1223 @ SV1672 @ SV621 )
= ( c_HOL_Ominus__class_Ominus @ SV1911 @ SV2002 @ SV621 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV621 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5804]) ).
thf(5864,plain,
! [SV1676: $i,SV1227: $i,SV1914: $i,SV625: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV625 ) @ SV1914 @ SV625 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV625 ) @ SV1227 @ SV625 ) )
= $true )
| ( ( SV1227 = SV1914 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1227 @ ( c_Suc @ SV1676 ) @ SV625 )
= ( c_Power_Opower__class_Opower @ SV1914 @ ( c_Suc @ SV1676 ) @ SV625 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV625 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5806]) ).
thf(5865,plain,
! [SV1228: $i,SV1677: $i,SV626: $i,SV1915: $i,SV2004: $i] :
( ( ( c_lessequals @ SV2004 @ SV1915 @ SV626 )
= $true )
| ( ( ~ ( c_lessequals @ SV1677 @ SV1228 @ SV626 ) )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1228 @ SV1677 @ SV626 )
= ( c_HOL_Ominus__class_Ominus @ SV1915 @ SV2004 @ SV626 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV626 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5807]) ).
thf(5866,plain,
! [SV1920: $i,SV1685: $i,SV1237: $i,SV637: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1237 ) @ SV1685 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV637 ) @ SV1237 ) @ SV1920 ) )
= $false )
| ( ( SV1685 = SV1920 )
= $true )
| ( ( class_Int_Onumber__ring @ SV637 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV637 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5808]) ).
thf(5867,plain,
! [SV1693: $i,SV1246: $i,SV647: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV647 ) @ SV1246 @ SV647 ) )
= $true )
| ( ( SV1246
= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV647 ) @ SV1693 @ SV647 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV647 ) @ SV1246 ) @ SV1693 )
= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV647 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5811]) ).
thf(5868,plain,
! [SV1701: $i,SV1931: $i,SV1256: $i,SV2: $i,SV658: $i] :
( ( ( c_lessequals @ SV658 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SV1256 ) @ SV1931 ) @ SV2 )
= $false )
| ( ( c_lessequals @ SV1931 @ SV1701 @ SV2 )
= $false )
| ( ( c_lessequals @ SV658 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV2 ) @ SV1256 ) @ SV1701 ) @ SV2 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5813]) ).
thf(5869,plain,
! [SV1286: $i,SV1715: $i,SV701: $i,SV52: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV701 @ SV52 )
= $false )
| ( ( ~ ( c_lessequals @ SV1715 @ SV1286 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV701 @ ( c_HOL_Oone__class_Oone @ SV52 ) @ SV52 )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV701 @ SV1286 @ SV52 ) @ ( c_Power_Opower__class_Opower @ SV701 @ SV1715 @ SV52 ) @ SV52 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5821]) ).
thf(5870,plain,
! [SV1934: $i,SV1293: $i,SV64: $i,SV1718: $i,SV713: $i] :
( ( ( c_lessequals @ SV713 @ SV1718 @ SV64 )
= $false )
| ( ( c_lessequals @ SV1293 @ SV1934 @ SV64 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV713 ) @ SV1293 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV64 ) @ SV1718 ) @ SV1934 ) @ SV64 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5822]) ).
thf(5871,plain,
! [SV1315: $i,SV1722: $i,SV103: $i,SV1936: $i,SV750: $i] :
( ( ( ~ ( c_in @ SV750 @ ( c_List_Oset @ SV1936 @ SV103 ) @ SV103 ) )
= $true )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1936 @ SV1722 @ SV103 ) @ SV103 ) )
= $true )
| ( ( c_in @ SV1315 @ ( c_List_Oset @ SV1722 @ SV103 ) @ SV103 )
= $false )
| ( ( c_lessequals @ SV750 @ SV1315 @ SV103 )
= $true )
| ( ( class_Orderings_Olinorder @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5825]) ).
thf(5872,plain,
! [SV1320: $i,SV113: $i,SV1723: $i,SV757: $i] :
( ( ( c_lessequals @ SV757 @ SV1723 @ SV113 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV1320 @ SV113 ) )
= $true )
| ( ( c_lessequals @ SV757 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV1320 ) @ SV1723 ) @ SV113 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV113 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5826]) ).
thf(5873,plain,
! [SV1724: $i,SV114: $i,SV1321: $i,SV758: $i] :
( ( ( c_lessequals @ SV758 @ SV1321 @ SV114 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV1724 @ SV114 ) )
= $true )
| ( ( c_lessequals @ SV758 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SV1321 ) @ SV1724 ) @ SV114 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV114 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5827]) ).
thf(5874,plain,
! [SV1937: $i,SV1323: $i,SV118: $i,SV1725: $i,SV762: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV762 @ SV1725 @ SV118 )
= $false )
| ( ( c_lessequals @ SV1323 @ SV1937 @ SV118 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV762 ) @ SV1323 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV118 ) @ SV1725 ) @ SV1937 ) @ SV118 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5828]) ).
thf(5875,plain,
! [SV1938: $i,SV1324: $i,SV119: $i,SV1726: $i,SV763: $i] :
( ( ( c_lessequals @ SV763 @ SV1726 @ SV119 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1324 @ SV1938 @ SV119 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV119 ) @ SV763 ) @ SV1324 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV119 ) @ SV1726 ) @ SV1938 ) @ SV119 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5829]) ).
thf(5876,plain,
! [SV1344: $i,SV152: $i,SV793: $i,SV1737: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1737 @ ( c_Nat_Osize__class_Osize @ SV793 @ ( tc_List_Olist @ SV152 ) ) @ tc_nat )
= $false )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ SV793 @ SV152 ) )
= $true )
| ( ( c_lessequals @ SV1344 @ SV1737 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_List_Onth @ SV793 @ SV1344 @ SV152 ) @ ( c_List_Onth @ SV793 @ SV1737 @ SV152 ) @ SV152 )
= $true )
| ( ( class_Orderings_Olinorder @ SV152 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5832]) ).
thf(5877,plain,
! [SV153: $i,SV794: $i,SV1738: $i,SV1345: $i] :
( ( ( c_lessequals @ SV1345 @ SV1738 @ tc_nat )
= $false )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ SV794 @ SV153 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1738 @ ( c_Nat_Osize__class_Osize @ SV794 @ ( tc_List_Olist @ SV153 ) ) @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_List_Onth @ SV794 @ SV1345 @ SV153 ) @ ( c_List_Onth @ SV794 @ SV1738 @ SV153 ) @ SV153 )
= $true )
| ( ( class_Orderings_Olinorder @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5833]) ).
thf(5878,plain,
! [SV216: $i,SV850: $i,SV1383: $i,SV1760: $i] :
( ( ( c_lessequals @ SV1760 @ SV1383 @ tc_nat )
= $false )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Orev @ SV850 @ SV216 ) @ SV216 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1383 @ ( c_Nat_Osize__class_Osize @ SV850 @ ( tc_List_Olist @ SV216 ) ) @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_List_Onth @ SV850 @ SV1383 @ SV216 ) @ ( c_List_Onth @ SV850 @ SV1760 @ SV216 ) @ SV216 )
= $true )
| ( ( class_Orderings_Olinorder @ SV216 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5839]) ).
thf(5879,plain,
! [SV1386: $i,SV219: $i,SV1761: $i,SV853: $i] :
( ( ( c_lessequals @ SV853 @ SV1761 @ SV219 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV1386 @ SV219 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV853 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV219 ) @ SV1386 ) @ SV1761 ) @ SV219 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV219 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5840]) ).
thf(5880,plain,
! [SV1387: $i,SV220: $i,SV1762: $i,SV854: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV854 @ SV1762 @ SV220 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV1387 @ SV220 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV854 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV220 ) @ SV1387 ) @ SV1762 ) @ SV220 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV220 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV220 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5841]) ).
thf(5881,plain,
! [SV1458: $i,SV1810: $i,SV932: $i,SV300: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SV932 @ SV300 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV932 @ SV1810 @ SV300 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1458 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV932 @ SV1458 @ SV300 ) @ ( c_Power_Opower__class_Opower @ SV1810 @ SV1458 @ SV300 ) @ SV300 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV300 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5849]) ).
thf(5882,plain,
! [SV1471: $i,SV1817: $i,SV945: $i,SV313: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV313 ) @ SV945 @ SV313 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1817 @ SV1471 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV945 @ ( c_HOL_Oone__class_Oone @ SV313 ) @ SV313 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV945 @ SV1471 @ SV313 ) @ ( c_Power_Opower__class_Opower @ SV945 @ SV1817 @ SV313 ) @ SV313 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV313 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5850]) ).
thf(5883,plain,
! [SV1979: $i,SV1539: $i,SV436: $i,SV1850: $i,SV1055: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1055 @ SV1850 @ SV436 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1539 @ SV1979 @ SV436 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV436 ) @ SV1055 ) @ SV1539 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV436 ) @ SV1850 ) @ SV1979 ) @ SV436 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV436 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5851]) ).
thf(5884,plain,
! [SV1105: $i,SV488: $i] :
( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV488 ) @ SV1105 @ SV488 )
= ( c_HOL_Ozero__class_Ozero @ SV488 ) )
= $true )
| ( ( SV1105
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( class_Power_Opower @ SV488 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV488 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV488 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV488 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5853]) ).
thf(5885,plain,
! [SV1161: $i,SV1885: $i,SV554: $i,SV1616: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1616 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SV1885 @ SV554 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SV1161 @ SV554 ) )
= $true )
| ( ( SV1161 = SV1885 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1161 @ SV1616 @ SV554 )
= ( c_Power_Opower__class_Opower @ SV1885 @ SV1616 @ SV554 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV554 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5854]) ).
thf(5886,plain,
! [SV1635: $i,SV1182: $i,SV577: $i] :
( ( ( class_Power_Opower @ SV577 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV1182 @ SV1635 @ SV577 )
!= ( c_HOL_Ozero__class_Ozero @ SV577 ) )
| ( SV1182
= ( c_HOL_Ozero__class_Ozero @ SV577 ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV577 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV577 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV577 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5856]) ).
thf(5887,plain,
! [SV1995: $i,SV1896: $i,SV578: $i,SV1636: $i,SV1183: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1183 @ SV1636 @ SV578 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1896 @ SV1995 @ SV578 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1183 @ SV1636 @ SV578 )
= ( c_HOL_Ominus__class_Ominus @ SV1896 @ SV1995 @ SV578 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV578 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5857]) ).
thf(5888,plain,
! [SV1648: $i,SV1197: $i,SV594: $i,SV1997: $i,SV1901: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1901 @ SV1997 @ SV594 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1197 @ SV1648 @ SV594 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1197 @ SV1648 @ SV594 )
= ( c_HOL_Ominus__class_Ominus @ SV1901 @ SV1997 @ SV594 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV594 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5858]) ).
thf(5889,plain,
! [SV616: $i,SV1218: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1218 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV616 )
= ( c_HOL_Ozero__class_Ozero @ SV616 ) )
= $false )
| ( ( class_Power_Opower @ SV616 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV616 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV616 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV616 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5860]) ).
thf(5890,plain,
! [SV1668: $i,SV1219: $i,SV617: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV617 ) @ SV1219 @ SV617 )
= $false )
| ( ( SV1668
= ( c_HOL_Ozero__class_Ozero @ SV617 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV617 ) @ SV1668 @ SV617 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV617 ) @ SV1219 ) @ SV1668 )
= ( c_HOL_Ozero__class_Ozero @ SV617 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV617 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5861]) ).
thf(5891,plain,
! [SV1223: $i,SV1672: $i,SV621: $i,SV1911: $i,SV2002: $i] :
( ( ( c_lessequals @ SV2002 @ SV1911 @ SV621 )
= $false )
| ( ( c_lessequals @ SV1672 @ SV1223 @ SV621 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1223 @ SV1672 @ SV621 )
= ( c_HOL_Ominus__class_Ominus @ SV1911 @ SV2002 @ SV621 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV621 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5863]) ).
thf(5892,plain,
! [SV1676: $i,SV1227: $i,SV1914: $i,SV625: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV625 ) @ SV1914 @ SV625 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV625 ) @ SV1227 @ SV625 ) )
= $true )
| ( ( SV1227 = SV1914 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1227 @ ( c_Suc @ SV1676 ) @ SV625 )
= ( c_Power_Opower__class_Opower @ SV1914 @ ( c_Suc @ SV1676 ) @ SV625 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV625 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5864]) ).
thf(5893,plain,
! [SV1915: $i,SV2004: $i,SV626: $i,SV1228: $i,SV1677: $i] :
( ( ( c_lessequals @ SV1677 @ SV1228 @ SV626 )
= $false )
| ( ( c_lessequals @ SV2004 @ SV1915 @ SV626 )
= $true )
| ( ( ( c_HOL_Ominus__class_Ominus @ SV1228 @ SV1677 @ SV626 )
= ( c_HOL_Ominus__class_Ominus @ SV1915 @ SV2004 @ SV626 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV626 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5865]) ).
thf(5894,plain,
! [SV1693: $i,SV1246: $i,SV647: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV647 ) @ SV1246 @ SV647 )
= $false )
| ( ( SV1246
= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV647 ) @ SV1693 @ SV647 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV647 ) @ SV1246 ) @ SV1693 )
= ( c_HOL_Ozero__class_Ozero @ SV647 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV647 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5867]) ).
thf(5895,plain,
! [SV701: $i,SV52: $i,SV1286: $i,SV1715: $i] :
( ( ( c_lessequals @ SV1715 @ SV1286 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV52 ) @ SV701 @ SV52 )
= $false )
| ( ( c_lessequals @ SV701 @ ( c_HOL_Oone__class_Oone @ SV52 ) @ SV52 )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV701 @ SV1286 @ SV52 ) @ ( c_Power_Opower__class_Opower @ SV701 @ SV1715 @ SV52 ) @ SV52 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5869]) ).
thf(5896,plain,
! [SV1315: $i,SV1722: $i,SV103: $i,SV1936: $i,SV750: $i] :
( ( ( c_in @ SV750 @ ( c_List_Oset @ SV1936 @ SV103 ) @ SV103 )
= $false )
| ( ( ~ ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1936 @ SV1722 @ SV103 ) @ SV103 ) )
= $true )
| ( ( c_in @ SV1315 @ ( c_List_Oset @ SV1722 @ SV103 ) @ SV103 )
= $false )
| ( ( c_lessequals @ SV750 @ SV1315 @ SV103 )
= $true )
| ( ( class_Orderings_Olinorder @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5871]) ).
thf(5897,plain,
! [SV1723: $i,SV757: $i,SV1320: $i,SV113: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV113 ) @ SV1320 @ SV113 )
= $false )
| ( ( c_lessequals @ SV757 @ SV1723 @ SV113 )
= $false )
| ( ( c_lessequals @ SV757 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV113 ) @ SV1320 ) @ SV1723 ) @ SV113 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV113 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5872]) ).
thf(5898,plain,
! [SV1321: $i,SV758: $i,SV1724: $i,SV114: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV114 ) @ SV1724 @ SV114 )
= $false )
| ( ( c_lessequals @ SV758 @ SV1321 @ SV114 )
= $false )
| ( ( c_lessequals @ SV758 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV114 ) @ SV1321 ) @ SV1724 ) @ SV114 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV114 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5873]) ).
thf(5899,plain,
! [SV1344: $i,SV1737: $i,SV152: $i,SV793: $i] :
( ( ( c_List_Olinorder__class_Osorted @ SV793 @ SV152 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1737 @ ( c_Nat_Osize__class_Osize @ SV793 @ ( tc_List_Olist @ SV152 ) ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV1344 @ SV1737 @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_List_Onth @ SV793 @ SV1344 @ SV152 ) @ ( c_List_Onth @ SV793 @ SV1737 @ SV152 ) @ SV152 )
= $true )
| ( ( class_Orderings_Olinorder @ SV152 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5876]) ).
thf(5900,plain,
! [SV1738: $i,SV1345: $i,SV153: $i,SV794: $i] :
( ( ( c_List_Olinorder__class_Osorted @ SV794 @ SV153 )
= $false )
| ( ( c_lessequals @ SV1345 @ SV1738 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1738 @ ( c_Nat_Osize__class_Osize @ SV794 @ ( tc_List_Olist @ SV153 ) ) @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_List_Onth @ SV794 @ SV1345 @ SV153 ) @ ( c_List_Onth @ SV794 @ SV1738 @ SV153 ) @ SV153 )
= $true )
| ( ( class_Orderings_Olinorder @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5877]) ).
thf(5901,plain,
! [SV1383: $i,SV1760: $i,SV216: $i,SV850: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Orev @ SV850 @ SV216 ) @ SV216 )
= $false )
| ( ( c_lessequals @ SV1760 @ SV1383 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1383 @ ( c_Nat_Osize__class_Osize @ SV850 @ ( tc_List_Olist @ SV216 ) ) @ tc_nat )
= $false )
| ( ( c_lessequals @ ( c_List_Onth @ SV850 @ SV1383 @ SV216 ) @ ( c_List_Onth @ SV850 @ SV1760 @ SV216 ) @ SV216 )
= $true )
| ( ( class_Orderings_Olinorder @ SV216 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5878]) ).
thf(5902,plain,
! [SV1761: $i,SV853: $i,SV1386: $i,SV219: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV219 ) @ SV1386 @ SV219 )
= $false )
| ( ( c_lessequals @ SV853 @ SV1761 @ SV219 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV853 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV219 ) @ SV1386 ) @ SV1761 ) @ SV219 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV219 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5879]) ).
thf(5903,plain,
! [SV1762: $i,SV854: $i,SV1387: $i,SV220: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV220 ) @ SV1387 @ SV220 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV854 @ SV1762 @ SV220 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV854 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV220 ) @ SV1387 ) @ SV1762 ) @ SV220 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV220 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV220 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5880]) ).
thf(5904,plain,
! [SV1458: $i,SV300: $i,SV1810: $i,SV932: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV932 @ SV1810 @ SV300 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV300 ) @ SV932 @ SV300 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1458 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV932 @ SV1458 @ SV300 ) @ ( c_Power_Opower__class_Opower @ SV1810 @ SV1458 @ SV300 ) @ SV300 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV300 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5881]) ).
thf(5905,plain,
! [SV945: $i,SV313: $i,SV1471: $i,SV1817: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1817 @ SV1471 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV313 ) @ SV945 @ SV313 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV945 @ ( c_HOL_Oone__class_Oone @ SV313 ) @ SV313 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV945 @ SV1471 @ SV313 ) @ ( c_Power_Opower__class_Opower @ SV945 @ SV1817 @ SV313 ) @ SV313 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV313 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5882]) ).
thf(5906,plain,
! [SV1616: $i,SV1161: $i,SV1885: $i,SV554: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SV1885 @ SV554 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SV1161 @ SV554 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1616 @ tc_nat )
= $false )
| ( ( SV1161 = SV1885 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1161 @ SV1616 @ SV554 )
= ( c_Power_Opower__class_Opower @ SV1885 @ SV1616 @ SV554 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV554 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5885]) ).
thf(5907,plain,
! [SV577: $i,SV1635: $i,SV1182: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1182 @ SV1635 @ SV577 )
!= ( c_HOL_Ozero__class_Ozero @ SV577 ) )
= $true )
| ( ( SV1182
= ( c_HOL_Ozero__class_Ozero @ SV577 ) )
= $true )
| ( ( class_Power_Opower @ SV577 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV577 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV577 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV577 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5886]) ).
thf(5908,plain,
! [SV1676: $i,SV1914: $i,SV1227: $i,SV625: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV625 ) @ SV1227 @ SV625 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV625 ) @ SV1914 @ SV625 )
= $false )
| ( ( SV1227 = SV1914 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1227 @ ( c_Suc @ SV1676 ) @ SV625 )
= ( c_Power_Opower__class_Opower @ SV1914 @ ( c_Suc @ SV1676 ) @ SV625 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV625 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5892]) ).
thf(5909,plain,
! [SV1315: $i,SV750: $i,SV103: $i,SV1722: $i,SV1936: $i] :
( ( ( c_List_Olinorder__class_Osorted @ ( c_List_Oappend @ SV1936 @ SV1722 @ SV103 ) @ SV103 )
= $false )
| ( ( c_in @ SV750 @ ( c_List_Oset @ SV1936 @ SV103 ) @ SV103 )
= $false )
| ( ( c_in @ SV1315 @ ( c_List_Oset @ SV1722 @ SV103 ) @ SV103 )
= $false )
| ( ( c_lessequals @ SV750 @ SV1315 @ SV103 )
= $true )
| ( ( class_Orderings_Olinorder @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5896]) ).
thf(5910,plain,
! [SV1616: $i,SV1161: $i,SV1885: $i,SV554: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SV1885 @ SV554 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SV1161 @ SV554 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1616 @ tc_nat )
= $false )
| ( ( SV1161 = SV1885 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1161 @ SV1616 @ SV554 )
= ( c_Power_Opower__class_Opower @ SV1885 @ SV1616 @ SV554 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV554 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5906]) ).
thf(5911,plain,
! [SV577: $i,SV1635: $i,SV1182: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV1182 @ SV1635 @ SV577 )
= ( c_HOL_Ozero__class_Ozero @ SV577 ) )
= $false )
| ( ( SV1182
= ( c_HOL_Ozero__class_Ozero @ SV577 ) )
= $true )
| ( ( class_Power_Opower @ SV577 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV577 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV577 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV577 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5907]) ).
thf(5912,plain,
! [SV1616: $i,SV1885: $i,SV1161: $i,SV554: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SV1161 @ SV554 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV554 ) @ SV1885 @ SV554 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1616 @ tc_nat )
= $false )
| ( ( SV1161 = SV1885 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV1161 @ SV1616 @ SV554 )
= ( c_Power_Opower__class_Opower @ SV1885 @ SV1616 @ SV554 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV554 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5910]) ).
thf(5913,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1591,5912,5911,5909,5908,5905,5904,5903,5902,5901,5900,5899,5898,5897,5895,5894,5893,5891,5890,5889,5888,5887,5884,5883,5875,5874,5870,5868,5866,5862,5859,5855,5852,5848,5847,5846,5845,5844,5843,5842,5838,5837,5836,5835,5834,5831,5830,5824,5823,5820,5819,5818,5817,5816,5815,5814,5812,5810,5809,5805,5800,5799,5794,5791,5787,5785,5781,5780,5779,5778,5777,5776,5775,5774,5768,5767,5764,5763,5761,5760,5759,5758,5754,5753,5752,5743,5740,5737,5735,5732,5731,5730,5728,5727,5718,5713,5712,5708,5707,5699,5698,5696,5692,5690,5688,5685,5684,5683,5682,5681,5680,5679,5678,5677,5676,5675,5674,5672,5669,5668,5667,5657,5628,5625,5623,5612,5611,5610,5609,5608,5607,5606,5605,5603,5602,5601,5597,5593,5592,5591,5590,5589,5588,5573,5571,5569,5568,5554,5553,5552,5546,5545,5541,5539,5535,5534,5532,5530,5529,5522,5521,5520,5512,5511,5508,5507,5506,5504,5503,5502,5501,5500,5498,5497,5496,5495,5494,5493,5490,5485,5484,5480,5479,5476,5455,5452,5448,5447,5444,5436,5434,5433,5425,5423,5422,5406,5403,5402,5401,5400,5399,5397,5392,5391,5390,5389,5388,5387,5377,5372,5368,5367,5362,5360,5359,5355,5336,5335,5332,5329,5328,5324,5321,5318,5316,5315,5311,5309,5304,5301,5279,5278,5270,5266,5265,5261,5260,5259,5258,5257,5256,5255,5254,5250,5249,5248,5245,5242,5241,5240,5239,5236,5235,5234,5233,5232,5230,5229,5227,5226,5225,5224,5220,5219,5218,5217,5216,5215,5214,5213,5212,5211,5210,5209,5208,5200,5199,5175,5164,5163,5162,5157,5155,5154,5153,5152,5151,5148,5140,5139,5136,5135,5127,5116,5114,5111,5100,5072,5071,5069,5067,5055,5052,5048,5041,5032,5028,5027,5025,5024,5022,5020,5018,5016,5014,5011,5005,4999,4997,4989,4987,4986,4985,4983,4981,4978,4976,4975,4974,4970,4969,4968,4967,4966,4961,4959,4958,4947,4944,4929,4928,4926,4925,4924,4919,4918,4910,4909,4908,4906,4899,4898,4892,4891,4890,4888,4882,4880,4879,4877,4871,4867,4866,4865,4863,4861,4858,4856,4842,4841,4835,4832,4831,4826,4825,4815,4814,4813,4794,4793,4792,4791,4790,4780,4778,4775,4772,4734,4733,4732,4729,4728,4721,4714,4708,4707,4706,4705,4673,4668,4642,4628,4620,4616,4613,4609,4604,4595,4592,4591,4590,4585,4581,4580,4572,4570,4566,4564,4563,4562,4560,4559,4558,4557,4555,4550,4549,4547,4545,4541,4532,4531,4530,4529,4525,4523,4506,4497,4495,4493,4487,4465,4463,4461,4451,4450,4447,4446,4442,4441,4438,4437,4436,4435,4434,4432,4431,4428,4409,4378,4375,4366,4365,4352,4341,4340,4333,4332,4331,4330,4328,4327,4326,4319,4314,4308,4305,4302,4297,4289,4288,4285,4284,4283,4282,4277,4276,4274,4273,4269,4255,4254,4249,4248,4236,4235,4234,4222,4221,4220,4212,4210,4209,4208,4207,4205,4198,4191,4190,4178,4177,4168,4167,4148,4060,4046,4043,4039,4032,4029,4026,4024,4023,4022,4021,4018,4013,4012,4011,3979,3978,3940,3933,3932,3930,3926,3914,3913,3912,3911,3910,3909,3908,3907,3906,3905,3904,3903,3891,3882,3879,3865,3864,3829,3828,3825,3823,3822,3813,3812,3809,3801,3787,3771,3770,3757,3756,3752,3751,3747,3734,3732,3729,3709,3708,3700,3682,3673,3658,3643,3621,3566,3561,3553,3528,3505,3482,3464,3456,3444,3441,3438,3437,3433,3432,3431,3430,3429,3413,3398,3376,3357,3352,3351,3328,3327,3326,3319,3302,3300,3299,3298,3297,3296,3295,3294,3293,3292,3291,3290,3284,3270,3269,3268,3267,3194,3129,3119,3086,3015,2995,2987,2965,2833,2826,2824,2817,2816,2809,2808,2793,2792,2666,2665,2646,2645,2644,2620,2498,2497,2496,2495,2475,2419,2418,2321,2320,2301,2299,2292,2171,2170,2169,2168,2167,2166,2165,2164,2163,2162,2161,2160,2159,2158,2157,2156,2155,2154,2153,2152,2151,2150,2149,2148,2147,2146,2145,2144,2143,2142,2141,2140,2139,2138,2137,2136,2135,2134,2133,2132,2131,2130,2129,2128,2127,2126,2125,2124,2123,2122,2121,2120,2119,2118,2117,2116,2115,2114,2113,2112,2109,2098,2013,1677]) ).
thf(5914,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[5913]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL848-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n013.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 12:35:06 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 216.65/36.32 .....
% 216.65/36.32
% 216.65/36.32 No.of.Axioms: 723
% 216.65/36.32
% 216.65/36.32 Length.of.Defs: 0
% 216.65/36.32
% 216.65/36.32 Contains.Choice.Funs: false
% 216.65/36.32 .......................................................................................................................................................................................................
% 216.65/36.32
% 216.65/36.32 ********************************
% 216.65/36.32 * All subproblems solved! *
% 216.65/36.32 ********************************
% 216.65/36.32 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:723,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:297,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:5913,loop_count:0,foatp_calls:1,translation:fof_full)
% 216.65/36.32
% 216.65/36.32 %**** Beginning of derivation protocol ****
% 216.65/36.32 % SZS output start CNFRefutation
% See solution above
% 216.65/36.35
% 216.65/36.35 %**** End of derivation protocol ****
% 216.65/36.35 %**** no. of clauses in derivation: 5914 ****
% 216.65/36.35 %**** clause counter: 5913 ****
% 216.65/36.35
% 216.65/36.35 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:723,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:297,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:5913,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------