%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL778-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 10:30:27 AM UTC 2026
% Result : Unsatisfiable 118.39s 20.08s
% Output : CNFRefutation 118.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 550
% Syntax : Number of formulae : 4914 (3175 unt; 0 typ; 0 def)
% Number of atoms : 25432 (9949 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 78354 (5814 ~;7482 |; 0 &;65058 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 108 ( 105 usr; 17 con; 0-6 aty)
% Number of variables : 18733 ( 0 ^;18733 !; 0 ?;18733 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_COMBC,type,
c_COMBC: $i > $i > $i > $i > $i > $i ).
thf(tp_c_Groebner__Basis_Ogb__semiring,type,
c_Groebner__Basis_Ogb__semiring: $i > $i > $i > $i > $i > $i > $o ).
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_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__rec,type,
c_Lambda_OdB_OdB__rec: $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_Oliftn,type,
c_Lambda_Oliftn: $i > $i > $i > $i ).
thf(tp_c_Lambda_Osubst,type,
c_Lambda_Osubst: $i ).
thf(tp_c_Lambda_Osubstn,type,
c_Lambda_Osubstn: $i > $i > $i > $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_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1,type,
c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1: $i > $i ).
thf(tp_c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2,type,
c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2: $i > $i ).
thf(tp_c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3,type,
c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3: $i > $i ).
thf(tp_c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4,type,
c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4: $i > $i ).
thf(tp_c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1,type,
c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1: $i > $i ).
thf(tp_c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2,type,
c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2: $i > $i ).
thf(tp_c_ListApplication_Osko__ListApplication__Xlem__1__1,type,
c_ListApplication_Osko__ListApplication__Xlem__1__1: $i > $i ).
thf(tp_c_ListApplication_Osko__ListApplication__Xlem__1__2,type,
c_ListApplication_Osko__ListApplication__Xlem__1__2: $i > $i ).
thf(tp_c_ListApplication_Osko__ListApplication__Xlem__1__3,type,
c_ListApplication_Osko__ListApplication__Xlem__1__3: $i > $i ).
thf(tp_c_ListApplication_Osko__ListApplication__Xlem__1__4,type,
c_ListApplication_Osko__ListApplication__Xlem__1__4: $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_Ofoldl,type,
c_List_Ofoldl: $i > $i > $i > $i > $i > $i ).
thf(tp_c_List_Ofoldr,type,
c_List_Ofoldr: $i > $i > $i > $i > $i > $i ).
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_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_Oreplicate,type,
c_List_Oreplicate: $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_OrderedGroup_Omonoid__add,type,
c_OrderedGroup_Omonoid__add: $i > $i > $i > $o ).
thf(tp_c_OrderedGroup_Osemigroup__add,type,
c_OrderedGroup_Osemigroup__add: $i > $i > $o ).
thf(tp_c_Orderings_Oord__class_Omax,type,
c_Orderings_Oord__class_Omax: $i > $i > $i > $i ).
thf(tp_c_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: $i > $i > $i > $i ).
thf(tp_c_Predicate_Oconversep,type,
c_Predicate_Oconversep: $i > $i > $i > $i ).
thf(tp_c_Transitive__Closure_Ortranclp,type,
c_Transitive__Closure_Ortranclp: $i > $i > $i ).
thf(tp_c_Type_Oshift,type,
c_Type_Oshift: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xvar__app__typesE__1__1,type,
c_Type_Osko__Type__Xvar__app__typesE__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Osko__Type__Xvar__app__types__1__1,type,
c_Type_Osko__Type__Xvar__app__types__1__1: $i > $i > $i > $i > $i ).
thf(tp_c_Type_Otyping,type,
c_Type_Otyping: $i > $i > $i > $o ).
thf(tp_c_Type_Otypings,type,
c_Type_Otypings: $i > $i > $i > $o ).
thf(tp_c_Wellfounded_Oaccp,type,
c_Wellfounded_Oaccp: $i > $i > $i > $o ).
thf(tp_c_fequal,type,
c_fequal: $i > $i ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $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_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__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_Lambda_OdB,type,
tc_Lambda_OdB: $i ).
thf(tp_tc_String_Ochar,type,
tc_String_Ochar: $i ).
thf(tp_tc_Type_Otype,type,
tc_Type_Otype: $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_i,type,
v_i: $i ).
thf(tp_v_r,type,
v_r: $i ).
thf(tp_v_s,type,
v_s: $i ).
thf(tp_v_sko__InductTermi__XIT__Xcases__1,type,
v_sko__InductTermi__XIT__Xcases__1: $i > $i ).
thf(tp_v_sko__InductTermi__XIT__Xcases__2,type,
v_sko__InductTermi__XIT__Xcases__2: $i > $i ).
thf(tp_v_sko__InductTermi__XIT__Xcases__3,type,
v_sko__InductTermi__XIT__Xcases__3: $i > $i ).
thf(tp_v_sko__InductTermi__XIT__Xcases__4,type,
v_sko__InductTermi__XIT__Xcases__4: $i > $i ).
thf(tp_v_sko__InductTermi__XIT__Xcases__5,type,
v_sko__InductTermi__XIT__Xcases__5: $i > $i ).
thf(tp_v_sko__InductTermi__XIT__Xcases__6,type,
v_sko__InductTermi__XIT__Xcases__6: $i > $i ).
thf(tp_v_ss,type,
v_ss: $i ).
thf(1,axiom,
! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(2,axiom,
! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(3,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(4,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(5,axiom,
class_Power_Opower @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
thf(6,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(7,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(8,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(9,axiom,
class_Nat_Osemiring__char__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(10,axiom,
class_OrderedGroup_Omonoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
thf(11,axiom,
class_OrderedGroup_Omonoid__mult @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
thf(12,axiom,
class_Ring__and__Field_Omult__zero @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
thf(13,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(14,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(15,axiom,
class_OrderedGroup_Osemigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
thf(16,axiom,
class_Ring__and__Field_Ozero__neq__one @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
thf(17,axiom,
class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
thf(18,axiom,
class_OrderedGroup_Oab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
thf(19,axiom,
class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
thf(20,axiom,
class_Ring__and__Field_Oordered__semidom @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
thf(21,axiom,
class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
thf(22,axiom,
class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
thf(23,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
thf(24,axiom,
class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
thf(25,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
thf(26,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
thf(27,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
thf(28,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Oorder @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(29,axiom,
! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(30,axiom,
! [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/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
thf(31,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/sandbox/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).
thf(32,axiom,
! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__IT_0) ).
thf(33,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
thf(34,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/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
thf(35,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
thf(36,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
thf(37,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/sandbox/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
thf(38,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/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).
thf(39,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/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).
thf(40,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/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).
thf(41,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
thf(42,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/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).
thf(43,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/sandbox/benchmark/theBenchmark.p',cls_Beta_0) ).
thf(44,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/sandbox/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
thf(45,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/sandbox/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
thf(46,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/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).
thf(47,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/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_2) ).
thf(48,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/sandbox/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
thf(49,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/sandbox/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).
thf(50,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/sandbox/benchmark/theBenchmark.p',cls_subst__Var_1) ).
thf(51,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/sandbox/benchmark/theBenchmark.p',cls_subst__Var_2) ).
thf(52,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/sandbox/benchmark/theBenchmark.p',cls_subst__lt_0) ).
thf(53,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/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).
thf(54,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/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
thf(55,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/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).
thf(56,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/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).
thf(57,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/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
thf(58,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/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_0) ).
thf(59,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/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_4) ).
thf(60,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I1_J_0) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osize_I4_J_0) ).
thf(62,axiom,
! [V_t: $i,V_s: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn__subst__0_0) ).
thf(63,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/sandbox/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).
thf(64,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/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
thf(65,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/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
thf(66,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/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).
thf(67,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/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
thf(68,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/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).
thf(69,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/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).
thf(70,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/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).
thf(71,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/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).
thf(72,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/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
thf(73,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I10_J_0) ).
thf(74,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/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
thf(75,axiom,
! [V_nat: $i,V_dB_H: $i] :
( ( c_Lambda_OdB_OVar @ V_nat )
!= ( c_Lambda_OdB_OAbs @ V_dB_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
thf(76,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_nat: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Orecs_I1_J_0) ).
thf(77,axiom,
! [V_i: $i,V_t: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
thf(78,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit_0) ).
thf(79,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit__asm_0) ).
thf(80,axiom,
! [V_dB_H: $i,V_nat: $i] :
( ( c_Lambda_OdB_OAbs @ V_dB_H )
!= ( c_Lambda_OdB_OVar @ V_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
thf(81,axiom,
! [V_a: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_Ocases_5) ).
thf(82,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/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).
thf(83,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/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
thf(84,axiom,
! [V_a: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_Ocases_4) ).
thf(85,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/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_0) ).
thf(86,axiom,
! [V_e: $i,V_us: $i,V_T: $i,V_U: $i,V_i: $i,V_ts: $i,V_Ts: $i] :
( ( c_Type_Otypings @ V_e @ V_us @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ V_T @ V_U @ V_e @ V_us ) )
| ~ ( 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_Otypings @ V_e @ V_ts @ V_Ts )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_us @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__types_1) ).
thf(87,axiom,
! [V_P: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_t ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ V_P ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ V_P ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Apps__dB__induct_3) ).
thf(88,axiom,
! [V_e: $i,V_ts: $i,V_T: $i,V_i: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ V_T @ V_e @ V_i @ V_ts ) )
| ~ ( 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/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_1) ).
thf(89,axiom,
! [V_P: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ V_P ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ V_P ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ V_P @ V_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lem_3) ).
thf(90,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/sandbox/benchmark/theBenchmark.p',cls_subst__map_0) ).
thf(91,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/sandbox/benchmark/theBenchmark.p',cls_foldl__append_0) ).
thf(92,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/sandbox/benchmark/theBenchmark.p',cls_foldl__Cons_0) ).
thf(93,axiom,
! [V_plus: $i,V_x: $i,V_zero: $i,V_zs: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_plus @ V_x ) @ ( c_List_Ofoldl @ V_plus @ V_zero @ V_zs @ T_a @ T_a ) )
= ( c_List_Ofoldl @ V_plus @ V_x @ V_zs @ T_a @ T_a ) )
| ~ ( c_OrderedGroup_Omonoid__add @ V_zero @ V_plus @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add_Ofoldl__absorb0_0) ).
thf(94,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/sandbox/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).
thf(95,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/sandbox/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
thf(96,axiom,
! [V_plus: $i,V_x: $i,V_y: $i,V_zs: $i,T_a: $i] :
( ( ( c_List_Ofoldl @ V_plus @ ( hAPP @ ( hAPP @ V_plus @ V_x ) @ V_y ) @ V_zs @ T_a @ T_a )
= ( hAPP @ ( hAPP @ V_plus @ V_x ) @ ( c_List_Ofoldl @ V_plus @ V_y @ V_zs @ T_a @ T_a ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ V_plus @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_semigroup__add_Ofoldl__assoc_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).
thf(99,axiom,
! [V_t: $i] :
( V_t
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2 @ V_t ) @ ( c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1 @ V_t ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__head__tail_0) ).
thf(100,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/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_2) ).
thf(101,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/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_2) ).
thf(102,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/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_1) ).
thf(103,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/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__betas_0) ).
thf(104,axiom,
! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( 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_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta2_0) ).
thf(105,axiom,
! [V_r: $i,V_s: $i,V_ss: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( 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 ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_s @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( 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 ) @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__induction__lemma_0) ).
thf(106,axiom,
! [V_t: $i,V_s: $i,V_n: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ V_n )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ ( c_Lambda_Oliftn @ V_n @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn__subst__n_0) ).
thf(107,axiom,
! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_s @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ V_t @ V_s @ V_k ) ) @ ( c_Lambda_Osubstn @ V_u @ V_s @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I2_J_0) ).
thf(108,axiom,
! [V_n: $i,V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ V_n @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ V_n @ V_s @ V_k ) ) @ ( c_Lambda_Oliftn @ V_n @ V_t @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).
thf(109,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/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).
thf(110,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/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).
thf(111,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB1: $i,V_dB2: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ V_f2 @ V_dB1 ) @ V_dB2 ) @ ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ V_dB1 @ T_a ) ) @ ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ V_dB2 @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Orecs_I2_J_0) ).
thf(112,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I11_J_0) ).
thf(113,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/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
thf(114,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit_1) ).
thf(115,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit__asm_1) ).
thf(116,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
thf(117,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
thf(118,axiom,
! [T_a: $i,V_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a @ V_xs @ T_a @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__foldr1__lemma_0) ).
thf(119,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/sandbox/benchmark/theBenchmark.p',cls_listsum_0) ).
thf(120,axiom,
! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ 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 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__foldr1_0) ).
thf(121,axiom,
! [V_pwr: $i,V_x: $i,V_r1: $i,V_add: $i,V_mul: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= V_r1 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__0_0) ).
thf(122,axiom,
! [V_m: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= V_m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
thf(123,axiom,
! [V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n )
= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
thf(124,axiom,
! [V_x: $i] :
( V_x
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
thf(125,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/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_1) ).
thf(126,axiom,
! [V_n: $i] :
( ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__0L_0) ).
thf(127,axiom,
! [V_n: $i] :
( ( c_Orderings_Oord__class_Omax @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= V_n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__0R_0) ).
thf(128,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/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_2) ).
thf(129,axiom,
! [V_c: $i] :
( ( c_Nat_Osize__class_Osize @ V_c @ tc_String_Ochar )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_size__char_0) ).
thf(130,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(131,axiom,
! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__downward_0) ).
thf(132,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(133,axiom,
! [V_r: $i,V_y: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_y @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp_Ocases_0) ).
thf(134,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(135,axiom,
! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__into__rtrancl_0) ).
thf(136,axiom,
! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclp__into__rtranclp_0) ).
thf(137,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(138,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/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_5) ).
thf(139,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/sandbox/benchmark/theBenchmark.p',cls_append__eq__append__conv2_4) ).
thf(140,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/sandbox/benchmark/theBenchmark.p',cls_append__eq__appendI_0) ).
thf(141,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/sandbox/benchmark/theBenchmark.p',cls_append__assoc_0) ).
thf(142,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/sandbox/benchmark/theBenchmark.p',cls_lifts__IT_0) ).
thf(143,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/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_2) ).
thf(144,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/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_1) ).
thf(145,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/sandbox/benchmark/theBenchmark.p',cls_append1__eq__conv_0) ).
thf(146,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/sandbox/benchmark/theBenchmark.p',cls_listsum__append_0) ).
thf(147,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/sandbox/benchmark/theBenchmark.p',cls_map__is__Nil__conv_0) ).
thf(148,axiom,
! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__add_0) ).
thf(149,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/sandbox/benchmark/theBenchmark.p',cls_replicate__app__Cons__same_0) ).
thf(150,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/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_5) ).
thf(151,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/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_1) ).
thf(152,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/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
thf(153,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/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_1) ).
thf(154,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/sandbox/benchmark/theBenchmark.p',cls_list_Oinject_0) ).
thf(155,axiom,
! [V_a: $i] :
( ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ V_a ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_Ocases_9) ).
thf(156,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
thf(157,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
thf(158,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_k ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
thf(159,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/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
thf(160,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/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
thf(161,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/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
thf(162,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/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
thf(163,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/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
thf(164,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/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
thf(165,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/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_4) ).
thf(166,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/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_0) ).
thf(167,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/sandbox/benchmark/theBenchmark.p',cls_append__self__conv2_0) ).
thf(168,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/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_0) ).
thf(169,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/sandbox/benchmark/theBenchmark.p',cls_append__self__conv_0) ).
thf(170,axiom,
! [V_j: $i,V_i: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_i ) @ V_i @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
thf(171,axiom,
! [V_i: $i,V_j: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_i @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
thf(172,axiom,
! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ T_b @ T_a )
= V_r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__conversep_0) ).
thf(173,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit__asm_2) ).
thf(174,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osplit_2) ).
thf(175,axiom,
! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ V_a @ T_b @ T_a )
= ( hAPP @ ( hAPP @ V_f @ V_x ) @ ( c_List_Ofoldr @ V_f @ V_xs @ V_a @ T_b @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I2_J_0) ).
thf(176,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/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
thf(177,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/sandbox/benchmark/theBenchmark.p',cls_empty__replicate_0) ).
thf(178,axiom,
! [T_a: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ T_a )
| ( c_OrderedGroup_Osemigroup__add @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_semigroup__add__class_Oaxioms_0) ).
thf(179,axiom,
! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_dB ) @ T_a )
= ( hAPP @ ( hAPP @ V_f3 @ V_dB ) @ ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ V_dB @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Orecs_I3_J_0) ).
thf(180,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/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_2) ).
thf(181,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/sandbox/benchmark/theBenchmark.p',cls_replicate__empty_0) ).
thf(182,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/sandbox/benchmark/theBenchmark.p',cls_lift__map_0) ).
thf(183,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/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_2) ).
thf(184,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/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
thf(185,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/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
thf(186,axiom,
! [V_n: $i,V_m: $i,V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_m @ V_x @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_replicate__add_0) ).
thf(187,axiom,
! [V_a: $i] :
( ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ V_a ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_a
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_Ocases_0) ).
thf(188,axiom,
! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ V_xs @ T_a )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsum__foldr_0) ).
thf(189,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/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
thf(190,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/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
thf(191,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/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I2_J_0) ).
thf(192,axiom,
! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_l ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
thf(193,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/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
thf(194,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_x @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).
thf(195,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(196,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(197,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/sandbox/benchmark/theBenchmark.p',cls_append__replicate__commute_0) ).
thf(198,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(199,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/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(200,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/sandbox/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
thf(201,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/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(202,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(203,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(204,axiom,
! [V_a: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( V_a
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_Ocases_7) ).
thf(205,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/sandbox/benchmark/theBenchmark.p',cls_map__append_0) ).
thf(206,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/sandbox/benchmark/theBenchmark.p',cls_listsum_Osimps_I2_J_0) ).
thf(207,axiom,
! [V_plus: $i,V_a: $i,V_b: $i,V_c: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_plus @ ( hAPP @ ( hAPP @ V_plus @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_plus @ V_a ) @ ( hAPP @ ( hAPP @ V_plus @ V_b ) @ V_c ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ V_plus @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_semigroup__add_Oadd__assoc_0) ).
thf(208,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/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_3) ).
thf(209,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/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
thf(210,axiom,
! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_r ) @ V_i ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_H_0) ).
thf(211,axiom,
! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_n ) ) )
| ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_1) ).
thf(212,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(213,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(214,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(215,axiom,
! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(216,axiom,
! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(217,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/sandbox/benchmark/theBenchmark.p',cls_empty__replicate_1) ).
thf(218,axiom,
! [V_a: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_Ocases_11) ).
thf(219,axiom,
! [T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_fequal @ T_a ) @ T_a @ T_a )
= ( c_fequal @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__eq_0) ).
thf(220,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/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_1) ).
thf(221,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/sandbox/benchmark/theBenchmark.p',cls_append__is__Nil__conv_0) ).
thf(222,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
thf(223,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/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_1) ).
thf(224,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/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_0) ).
thf(225,axiom,
! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubstn @ ( 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/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_2) ).
thf(226,axiom,
! [T_a: $i,V_z: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_0) ).
thf(227,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/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
thf(228,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/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
thf(229,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/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
thf(230,axiom,
! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(231,axiom,
! [V_m: $i] :
~ ( c_HOL_Oord__class_Oless @ V_m @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(232,axiom,
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_2) ).
thf(233,axiom,
! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= V_m )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
thf(234,axiom,
! [V_x: $i,V_a: $i] :
( ( V_x
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
thf(235,axiom,
! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).
thf(236,axiom,
! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).
thf(237,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/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(238,axiom,
! [V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_t @ V_k )
= V_t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__0_0) ).
thf(239,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/sandbox/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(240,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
thf(241,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
thf(242,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/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
thf(243,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/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
thf(244,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/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
thf(245,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/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
thf(246,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/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
thf(247,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
thf(248,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/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
thf(249,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/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
thf(250,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/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
thf(251,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/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
thf(252,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/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
thf(253,axiom,
! [V_a: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( V_a
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_Ocases_1) ).
thf(254,axiom,
! [V_a: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_Ocases_10) ).
thf(255,axiom,
! [V_a: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) )
| ( V_a
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_Ocases_2) ).
thf(256,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/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
thf(257,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/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
thf(258,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_1) ).
thf(259,axiom,
! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_2) ).
thf(260,axiom,
! [V_plus: $i,V_zero: $i,V_a: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_plus @ V_zero ) @ V_a )
= V_a )
| ~ ( c_OrderedGroup_Omonoid__add @ V_zero @ V_plus @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add_Oadd__0__left_0) ).
thf(261,axiom,
! [V_plus: $i,V_a: $i,V_zero: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_plus @ V_a ) @ V_zero )
= V_a )
| ~ ( c_OrderedGroup_Omonoid__add @ V_zero @ V_plus @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add_Oadd__0__right_0) ).
thf(262,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/sandbox/benchmark/theBenchmark.p',cls_replicate__append__same_0) ).
thf(263,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).
thf(264,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/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).
thf(265,axiom,
! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__idemp_0) ).
thf(266,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/sandbox/benchmark/theBenchmark.p',cls_Nil__is__append__conv_2) ).
thf(267,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omax @ V_y @ ( c_Orderings_Oord__class_Omax @ V_x @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__left__commute_0) ).
thf(268,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__assoc_0) ).
thf(269,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/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_0) ).
thf(270,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/sandbox/benchmark/theBenchmark.p',cls_Nil__is__map__conv_1) ).
thf(271,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) ) @ V_z )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__add__distrib__left_0) ).
thf(272,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/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_4) ).
thf(273,axiom,
! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= ( c_Lambda_Oliftn @ V_x @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I1_J_1) ).
thf(274,axiom,
! [V_a: $i] :
( ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ V_a ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_Ocases_3) ).
thf(275,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/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self_0) ).
thf(276,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/sandbox/benchmark/theBenchmark.p',cls_not__Cons__self2_0) ).
thf(277,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/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
thf(278,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/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
thf(279,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/sandbox/benchmark/theBenchmark.p',cls_replicate__empty_1) ).
thf(280,axiom,
! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_H_0) ).
thf(281,axiom,
! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( 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/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).
thf(282,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a )
= ( c_Orderings_Oord__class_Omax @ V_y @ V_x @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).
thf(283,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/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
thf(284,axiom,
! [V_s: $i,V_t: $i,V_s_H: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__App_0) ).
thf(285,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
thf(286,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/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_0) ).
thf(287,axiom,
! [V_add: $i,V_mul: $i,V_a: $i,V_m: $i,V_b: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_m ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_b ) @ V_m ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ V_m ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I1_J_0) ).
thf(288,axiom,
! [V_add: $i,V_mul: $i,V_a: $i,V_m: $i,V_r1: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_m ) ) @ V_m )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_r1 ) ) @ V_m ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I2_J_0) ).
thf(289,axiom,
! [V_add: $i,V_m: $i,V_mul: $i,V_a: $i,V_r1: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_m ) @ ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_m ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_r1 ) ) @ V_m ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I3_J_0) ).
thf(290,axiom,
! [V_add: $i,V_m: $i,V_mul: $i,V_r1: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_m ) @ V_m )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_r1 ) @ V_r1 ) ) @ V_m ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I4_J_0) ).
thf(291,axiom,
! [V_add: $i,V_r0: $i,V_a: $i,V_mul: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_r0 ) @ V_a )
= V_a )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I5_J_0) ).
thf(292,axiom,
! [V_add: $i,V_a: $i,V_r0: $i,V_mul: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_r0 )
= V_a )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I6_J_0) ).
thf(293,axiom,
! [V_mul: $i,V_a: $i,V_b: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ V_mul @ V_b ) @ V_a ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I7_J_0) ).
thf(294,axiom,
! [V_mul: $i,V_add: $i,V_a: $i,V_b: $i,V_c: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_b ) @ V_c ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I8_J_0) ).
thf(295,axiom,
! [V_mul: $i,V_r0: $i,V_a: $i,V_add: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_r0 ) @ V_a )
= V_r0 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I9_J_0) ).
thf(296,axiom,
! [V_mul: $i,V_a: $i,V_r0: $i,V_add: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_r0 )
= V_r0 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I10_J_0) ).
thf(297,axiom,
! [V_mul: $i,V_r1: $i,V_a: $i,V_add: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_r1 ) @ V_a )
= V_a )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I11_J_0) ).
thf(298,axiom,
! [V_mul: $i,V_a: $i,V_r1: $i,V_add: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_r1 )
= V_a )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I12_J_0) ).
thf(299,axiom,
! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_rx ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_ly ) @ V_ry ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I13_J_0) ).
thf(300,axiom,
! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ ( hAPP @ ( hAPP @ V_mul @ V_ly ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I14_J_0) ).
thf(301,axiom,
! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ V_ry ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I15_J_0) ).
thf(302,axiom,
! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ V_rx )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_rx ) ) @ V_ly ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I16_J_0) ).
thf(303,axiom,
! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ V_rx )
= ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ ( hAPP @ ( hAPP @ V_mul @ V_ly ) @ V_rx ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I17_J_0) ).
thf(304,axiom,
! [V_mul: $i,V_lx: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_rx ) ) @ V_ry ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I18_J_0) ).
thf(305,axiom,
! [V_mul: $i,V_lx: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ry ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I19_J_0) ).
thf(306,axiom,
! [V_add: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ V_add @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ V_add @ V_b ) @ V_d ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I20_J_0) ).
thf(307,axiom,
! [V_add: $i,V_a: $i,V_b: $i,V_c: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_add @ V_a ) @ ( hAPP @ ( hAPP @ V_add @ V_b ) @ V_c ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I21_J_0) ).
thf(308,axiom,
! [V_add: $i,V_a: $i,V_c: $i,V_d: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_a ) @ ( hAPP @ ( hAPP @ V_add @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ V_add @ V_c ) @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_d ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I22_J_0) ).
thf(309,axiom,
! [V_add: $i,V_a: $i,V_b: $i,V_c: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_c ) ) @ V_b ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I23_J_0) ).
thf(310,axiom,
! [V_add: $i,V_a: $i,V_c: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_c )
= ( hAPP @ ( hAPP @ V_add @ V_c ) @ V_a ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I24_J_0) ).
thf(311,axiom,
! [V_add: $i,V_a: $i,V_c: $i,V_d: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_a ) @ ( hAPP @ ( hAPP @ V_add @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_c ) ) @ V_d ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I25_J_0) ).
thf(312,axiom,
! [V_add: $i,V_r0: $i,V_x: $i,V_mul: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_r0 ) @ V_x )
= V_x )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__0_0) ).
thf(313,axiom,
! [V_add: $i,V_x: $i,V_y: $i,V_z: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_x ) @ ( hAPP @ ( hAPP @ V_add @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_x ) @ V_y ) ) @ V_z ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__a_0) ).
thf(314,axiom,
! [V_add: $i,V_x: $i,V_y: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ V_add @ V_y ) @ V_x ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Oadd__c_0) ).
thf(315,axiom,
! [V_mul: $i,V_r0: $i,V_x: $i,V_add: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_r0 ) @ V_x )
= V_r0 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Omul__0_0) ).
thf(316,axiom,
! [V_mul: $i,V_r1: $i,V_x: $i,V_add: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_r1 ) @ V_x )
= V_x )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Omul__1_0) ).
thf(317,axiom,
! [V_mul: $i,V_x: $i,V_y: $i,V_z: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_x ) @ ( hAPP @ ( hAPP @ V_mul @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_y ) ) @ V_z ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Omul__a_0) ).
thf(318,axiom,
! [V_mul: $i,V_x: $i,V_y: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ V_mul @ V_y ) @ V_x ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Omul__c_0) ).
thf(319,axiom,
! [V_mul: $i,V_x: $i,V_add: $i,V_y: $i,V_z: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_x ) @ ( hAPP @ ( hAPP @ V_add @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_y ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_z ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Omul__d_0) ).
thf(320,axiom,
! [V_pwr: $i,V_mul: $i,V_x: $i,V_y: $i,V_q: $i,V_add: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_y ) ) @ V_q )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_q ) ) @ ( hAPP @ ( hAPP @ V_pwr @ V_y ) @ V_q ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Opwr__mul_0) ).
thf(321,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/sandbox/benchmark/theBenchmark.p',cls_list_Osimps_I3_J_0) ).
thf(322,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/sandbox/benchmark/theBenchmark.p',cls_neq__Nil__conv_1) ).
thf(323,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/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__appendI_0) ).
thf(324,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/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__append__conv_5) ).
thf(325,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/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
thf(326,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/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
thf(327,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/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
thf(328,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/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
thf(329,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
thf(330,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/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
thf(331,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/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
thf(332,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/sandbox/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).
thf(333,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/sandbox/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).
thf(334,axiom,
! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtranclp_0) ).
thf(335,axiom,
! [T_a: $i,V_xs: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ V_a @ T_a @ T_a )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a @ V_xs @ T_a @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__conv__foldl_0) ).
thf(336,axiom,
! [V_t: $i,V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_r ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_H_0) ).
thf(337,axiom,
! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( 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_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_H_0) ).
thf(338,axiom,
! [V_mul: $i,V_pwr: $i,V_x: $i,V_p: $i,V_q: $i,V_add: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_p ) ) @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_q ) )
= ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_p ) @ V_q ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Omul__pwr_0) ).
thf(339,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/sandbox/benchmark/theBenchmark.p',cls_Nil__is__map__conv_0) ).
thf(340,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/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
thf(341,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/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_3) ).
thf(342,axiom,
! [V_f: $i,V_xs: $i,V_ys: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ V_a @ T_b @ T_a )
= ( c_List_Ofoldr @ V_f @ V_xs @ ( c_List_Ofoldr @ V_f @ V_ys @ V_a @ T_b @ T_a ) @ T_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__append_0) ).
thf(343,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
thf(344,axiom,
! [V_m: $i,V_l: $i,V_k: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_l )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
thf(345,axiom,
! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
thf(346,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/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
thf(347,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
thf(348,axiom,
! [V_i: $i,V_m: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_j ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
thf(349,axiom,
! [V_i: $i,V_j: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_m ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
thf(350,axiom,
! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
thf(351,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_z @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).
thf(352,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
thf(353,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/sandbox/benchmark/theBenchmark.p',cls_map__replicate_0) ).
thf(354,axiom,
! [V_t: $i,V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_r ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_0) ).
thf(355,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/sandbox/benchmark/theBenchmark.p',cls_self__append__conv2_1) ).
thf(356,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/sandbox/benchmark/theBenchmark.p',cls_append__Nil_0) ).
thf(357,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/sandbox/benchmark/theBenchmark.p',cls_self__append__conv_1) ).
thf(358,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/sandbox/benchmark/theBenchmark.p',cls_eq__Nil__appendI_0) ).
thf(359,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/sandbox/benchmark/theBenchmark.p',cls_append__Nil2_0) ).
thf(360,axiom,
! [V_a: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) )
| ( V_a
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_Ocases_8) ).
thf(361,axiom,
! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_r @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termi__implies__IT_0) ).
thf(362,axiom,
! [V_t: $i] :
( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_t @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT__implies__termi_0) ).
thf(363,axiom,
! [V_r: $i,T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__trans_0) ).
thf(364,axiom,
! [V_r: $i,V_b: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__downwards__aux_0) ).
thf(365,axiom,
! [V_r: $i,V_b: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__downwards_0) ).
thf(366,axiom,
! [V_r: $i,T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_1) ).
thf(367,axiom,
! [V_r: $i,T_a: $i,V_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__refl_0) ).
thf(368,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_2) ).
thf(369,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/sandbox/benchmark/theBenchmark.p',cls_same__append__eq_0) ).
thf(370,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/sandbox/benchmark/theBenchmark.p',cls_append__same__eq_0) ).
thf(371,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/sandbox/benchmark/theBenchmark.p',cls_replicate__eq__replicate_0) ).
thf(372,axiom,
! [V_A: $i,T_a: $i] : ( c_List_Olistsp @ V_A @ ( c_List_Olist_ONil @ T_a ) @ T_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
thf(373,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/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_4) ).
thf(374,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/sandbox/benchmark/theBenchmark.p',cls_Cons__step1__Cons_2) ).
thf(375,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/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I12_J_0) ).
thf(376,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/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_1) ).
thf(377,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/sandbox/benchmark/theBenchmark.p',cls_append__in__listsp__conv_0) ).
thf(378,axiom,
! [V_s: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_s_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__Abs_0) ).
thf(379,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/sandbox/benchmark/theBenchmark.p',cls_append__step1I_1) ).
thf(380,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/sandbox/benchmark/theBenchmark.p',cls_append__step1I_0) ).
thf(381,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(382,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(383,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
thf(384,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/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
thf(385,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
thf(386,axiom,
! [V_m: $i,V_n: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) @ V_k )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
thf(387,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/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
thf(388,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/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
thf(389,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/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
thf(390,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
thf(391,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
thf(392,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
thf(393,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
thf(394,axiom,
! [V_n: $i,V_m: $i] :
( ( 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 @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
thf(395,axiom,
! [V_r: $i,T_a: $i,T_b: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep_Ointros_0) ).
thf(396,axiom,
! [V_r: $i,V_a2: $i,V_a1: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a2 ) @ V_a1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a1 ) @ V_a2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep_Ocases_0) ).
thf(397,axiom,
! [V_r: $i,T_a: $i,T_b: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__iff_1) ).
thf(398,axiom,
! [V_r: $i,V_b: $i,V_a: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversepD_0) ).
thf(399,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/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
thf(400,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/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(401,axiom,
! [V_f: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Olist_ONil @ T_b ) @ V_a @ T_b @ T_a )
= V_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr_Osimps_I1_J_0) ).
thf(402,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/sandbox/benchmark/theBenchmark.p',cls_map__is__Nil__conv_1) ).
thf(403,axiom,
! [V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__converseD_0) ).
thf(404,axiom,
! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_x ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__converseI_0) ).
thf(405,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/sandbox/benchmark/theBenchmark.p',cls_Snoc__step1__SnocD_1) ).
thf(406,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__supI1_0) ).
thf(407,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__supI2_0) ).
thf(408,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_1) ).
thf(409,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_2) ).
thf(410,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).
thf(411,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).
thf(412,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/sandbox/benchmark/theBenchmark.p',cls_listsum_Osimps_I1_J_0) ).
thf(413,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/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
thf(414,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/sandbox/benchmark/theBenchmark.p',cls_append__eq__Cons__conv_5) ).
thf(415,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/sandbox/benchmark/theBenchmark.p',cls_append__Cons_0) ).
thf(416,axiom,
! [V_s: $i,V_t: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppR_0) ).
thf(417,axiom,
! [V_s: $i,V_t: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppL_0) ).
thf(418,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/sandbox/benchmark/theBenchmark.p',cls_map__eq__Cons__conv_3) ).
thf(419,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/sandbox/benchmark/theBenchmark.p',cls_Cons__eq__map__conv_3) ).
thf(420,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/sandbox/benchmark/theBenchmark.p',cls_map_Osimps_I2_J_0) ).
thf(421,axiom,
! [V_a: $i] :
( ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ V_a ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_a
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_Ocases_6) ).
thf(422,axiom,
! [V_x: $i,V_y: $i,V_z: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
thf(423,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
thf(424,axiom,
! [V_P: $i,V_t: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ V_P ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__4 @ V_P ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ V_P ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ V_P ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ V_P @ V_t ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lem_5) ).
thf(425,axiom,
! [V_P: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_t ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ V_P ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @ V_P ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ V_P ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ V_P ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Apps__dB__induct_5) ).
thf(426,axiom,
! [V_e: $i,V_u: $i,V_i: $i,V_ts: $i,V_Ts: $i,V_T: $i] :
( ( c_Type_Otypings @ V_e @ ( 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 ) @ V_Ts )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ V_e @ V_i @ V_T @ tc_Type_Otype ) @ V_ts @ V_Ts )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substs__lemma_0) ).
thf(427,axiom,
! [V_e: $i,V_i: $i,V_U: $i,V_ts: $i,V_Ts: $i] :
( ( c_Type_Otypings @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ tc_Type_Otype ) @ ( 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 ) @ V_Ts )
| ~ ( c_Type_Otypings @ V_e @ V_ts @ V_Ts ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__types_0) ).
thf(428,axiom,
! [V_t: $i,V_s: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ V_t ) ) @ V_s ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Abs_0) ).
thf(429,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/sandbox/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).
thf(430,axiom,
! [V_t: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_s @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubstn @ V_t @ V_s @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substn_Osimps_I3_J_0) ).
thf(431,axiom,
! [V_n: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Oliftn @ V_n @ V_s @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I3_J_0) ).
thf(432,axiom,
! [V_s: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I3_J_0) ).
thf(433,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/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).
thf(434,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/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).
thf(435,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/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).
thf(436,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/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).
thf(437,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/sandbox/benchmark/theBenchmark.p',cls_power__0__left_0) ).
thf(438,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/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).
thf(439,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/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
thf(440,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/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
thf(441,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/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
thf(442,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/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
thf(443,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/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
thf(444,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/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
thf(445,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/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
thf(446,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/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
thf(447,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/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
thf(448,axiom,
! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__1_0) ).
thf(449,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(450,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(451,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(452,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(453,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(454,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(455,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ~ ( c_lessequals @ V_x @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(456,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(457,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/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).
thf(458,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
thf(459,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).
thf(460,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
thf(461,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/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).
thf(462,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/sandbox/benchmark/theBenchmark.p',cls_one__le__power_0) ).
thf(463,axiom,
! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_2) ).
thf(464,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__least_0) ).
thf(465,axiom,
! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI_0) ).
thf(466,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__maxI1_0) ).
thf(467,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__maxI2_0) ).
thf(468,axiom,
! [T_a: $i,V_z: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_z @ V_y @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_0) ).
thf(469,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_Oone__class_Oone @ tc_nat ) @ T_a )
= V_x ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I33_J_0) ).
thf(470,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= V_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__right_0) ).
thf(471,axiom,
! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_1) ).
thf(472,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_0) ).
thf(473,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_2) ).
thf(474,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_1) ).
thf(475,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI2_0) ).
thf(476,axiom,
! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI1_0) ).
thf(477,axiom,
! [T_a: $i,V_b: $i,V_x: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supE_1) ).
thf(478,axiom,
! [T_a: $i,V_a: $i,V_x: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_a @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supE_0) ).
thf(479,axiom,
! [V_e: $i,V_x: $i,V_T: $i,T_a: $i] :
( ( hAPP @ ( c_Type_Oshift @ V_e @ V_x @ V_T @ T_a ) @ V_x )
= V_T ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__eq_0) ).
thf(480,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/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
thf(481,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(482,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/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
thf(483,axiom,
! [V_pwr: $i,V_x: $i,V_add: $i,V_mul: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= V_x )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gb__semiring_Osemiring__rules_I33_J_0) ).
thf(484,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(485,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_y @ V_x @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(486,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(487,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(488,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(489,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/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
thf(490,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/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
thf(491,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/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
thf(492,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/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
thf(493,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/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
thf(494,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/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
thf(495,axiom,
! [V_e: $i,V_i: $i,V_T: $i,T_a: $i,V_j: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ V_e @ V_i @ V_T @ T_a ) @ V_j )
= ( hAPP @ V_e @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__gt_0) ).
thf(496,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(497,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(498,axiom,
! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(499,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(500,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(501,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(502,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(503,axiom,
! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Opreorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(504,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/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
thf(505,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_b @ V_a @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(506,axiom,
! [T_a: $i,V_b: $i,V_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_b @ V_a @ T_a )
| ~ ( c_lessequals @ V_b @ V_a @ T_a )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(507,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(508,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(509,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ( V_a = V_b )
| ~ ( c_lessequals @ V_a @ V_b @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(510,axiom,
! [T_a: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_a @ V_b @ T_a )
| ~ ( c_lessequals @ V_a @ V_b @ T_a )
| ( V_a = V_b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(511,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(512,axiom,
! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( V_x = V_y )
| ( c_HOL_Oord__class_Oless @ V_x @ V_y @ T_a )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(513,axiom,
! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_x @ T_a )
| ( c_lessequals @ V_x @ V_y @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(514,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/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
thf(515,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/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
thf(516,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/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
thf(517,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/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
thf(518,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/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
thf(519,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/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
thf(520,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/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).
thf(521,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/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
thf(522,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/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
thf(523,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/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
thf(524,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/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
thf(525,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/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
thf(526,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/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
thf(527,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/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
thf(528,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/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
thf(529,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/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).
thf(530,axiom,
! [V_i: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_k )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_1) ).
thf(531,axiom,
! [V_t: $i,V_s: $i,V_j: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_j ) ) @ V_i )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__subst__lt_0) ).
thf(532,axiom,
! [V_t: $i,V_s: $i,V_j: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_j ) ) @ V_i )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_i ) ) @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__subst_0) ).
thf(533,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/sandbox/benchmark/theBenchmark.p',cls_one__less__power_0) ).
thf(534,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/sandbox/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).
thf(535,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/sandbox/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).
thf(536,axiom,
! [V_e: $i,V_i: $i,V_U: $i,V_t: $i,V_T: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__type_0) ).
thf(537,axiom,
! [V_e_H: $i,V_u: $i,V_U: $i,V_i: $i,V_t: $i,V_T: $i] :
( ~ ( c_Type_Otyping @ V_e_H @ V_u @ V_U )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e_H @ V_i @ V_U @ tc_Type_Otype ) @ V_t @ V_T )
| ( c_Type_Otyping @ V_e_H @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) @ V_T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lemma_0) ).
thf(538,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
thf(539,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/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).
thf(540,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/sandbox/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
thf(541,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/sandbox/benchmark/theBenchmark.p',cls_zero__le__power_0) ).
thf(542,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/sandbox/benchmark/theBenchmark.p',cls_power__mono_0) ).
thf(543,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/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).
thf(544,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/sandbox/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).
thf(545,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(546,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[545]) ).
thf(547,negated_conjecture,
~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( 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 ) ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(548,negated_conjecture,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ v_s ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(549,negated_conjecture,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_s ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(550,negated_conjecture,
hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( 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 ) ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(551,negated_conjecture,
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/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(552,plain,
$false = $false,
inference(unfold_def,[status(thm)],[546]) ).
thf(553,plain,
( ( ! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(554,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(555,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(556,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(557,plain,
( ( class_Power_Opower @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(558,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(559,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(560,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(561,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(562,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(563,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(564,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(565,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(566,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(567,plain,
( ( class_OrderedGroup_Osemigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(568,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(569,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(570,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(571,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(572,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(573,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(574,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(575,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(576,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(577,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(578,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(579,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(580,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)],[28]) ).
thf(581,plain,
( ( ! [T_2: $i,T_1: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ T_2 @ T_1 ) )
| ~ ( class_Orderings_Opreorder @ T_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(582,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)],[30]) ).
thf(583,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)],[31]) ).
thf(584,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(585,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)],[33]) ).
thf(586,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)],[34]) ).
thf(587,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)],[35]) ).
thf(588,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)],[36]) ).
thf(589,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)],[37]) ).
thf(590,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)],[38]) ).
thf(591,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)],[39]) ).
thf(592,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)],[40]) ).
thf(593,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)],[41]) ).
thf(594,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)],[42]) ).
thf(595,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)],[43]) ).
thf(596,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)],[44]) ).
thf(597,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)],[45]) ).
thf(598,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)],[46]) ).
thf(599,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)],[47]) ).
thf(600,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)],[48]) ).
thf(601,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)],[49]) ).
thf(602,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)],[50]) ).
thf(603,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)],[51]) ).
thf(604,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)],[52]) ).
thf(605,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)],[53]) ).
thf(606,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)],[54]) ).
thf(607,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)],[55]) ).
thf(608,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)],[56]) ).
thf(609,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)],[57]) ).
thf(610,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)],[58]) ).
thf(611,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)],[59]) ).
thf(612,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)],[60]) ).
thf(613,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)],[61]) ).
thf(614,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(615,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)],[63]) ).
thf(616,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)],[64]) ).
thf(617,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)],[65]) ).
thf(618,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)],[66]) ).
thf(619,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)],[67]) ).
thf(620,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)],[68]) ).
thf(621,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)],[69]) ).
thf(622,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)],[70]) ).
thf(623,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)],[71]) ).
thf(624,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)],[72]) ).
thf(625,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)],[73]) ).
thf(626,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)],[74]) ).
thf(627,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)],[75]) ).
thf(628,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_nat: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__rec @ 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)],[76]) ).
thf(629,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)],[77]) ).
thf(630,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)],[78]) ).
thf(631,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)],[79]) ).
thf(632,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)],[80]) ).
thf(633,plain,
( ( ! [V_a: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(634,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)],[82]) ).
thf(635,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)],[83]) ).
thf(636,plain,
( ( ! [V_a: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(637,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)],[85]) ).
thf(638,plain,
( ( ! [V_e: $i,V_us: $i,V_T: $i,V_U: $i,V_i: $i,V_ts: $i,V_Ts: $i] :
( ( c_Type_Otypings @ V_e @ V_us @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ V_T @ V_U @ V_e @ V_us ) )
| ~ ( 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_Otypings @ V_e @ V_ts @ V_Ts )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_us @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(639,plain,
( ( ! [V_P: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_t ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ V_P ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ V_P ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(640,plain,
( ( ! [V_e: $i,V_ts: $i,V_T: $i,V_i: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ V_T @ V_e @ V_i @ V_ts ) )
| ~ ( 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)],[88]) ).
thf(641,plain,
( ( ! [V_P: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ V_P ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ V_P ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ V_P @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(642,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)],[90]) ).
thf(643,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)],[91]) ).
thf(644,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)],[92]) ).
thf(645,plain,
( ( ! [V_plus: $i,V_x: $i,V_zero: $i,V_zs: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_plus @ V_x ) @ ( c_List_Ofoldl @ V_plus @ V_zero @ V_zs @ T_a @ T_a ) )
= ( c_List_Ofoldl @ V_plus @ V_x @ V_zs @ T_a @ T_a ) )
| ~ ( c_OrderedGroup_Omonoid__add @ V_zero @ V_plus @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(646,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)],[94]) ).
thf(647,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)],[95]) ).
thf(648,plain,
( ( ! [V_plus: $i,V_x: $i,V_y: $i,V_zs: $i,T_a: $i] :
( ( ( c_List_Ofoldl @ V_plus @ ( hAPP @ ( hAPP @ V_plus @ V_x ) @ V_y ) @ V_zs @ T_a @ T_a )
= ( hAPP @ ( hAPP @ V_plus @ V_x ) @ ( c_List_Ofoldl @ V_plus @ V_y @ V_zs @ T_a @ T_a ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ V_plus @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(649,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(650,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(651,plain,
( ( ! [V_t: $i] :
( V_t
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2 @ V_t ) @ ( c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1 @ V_t ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(652,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)],[100]) ).
thf(653,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)],[101]) ).
thf(654,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)],[102]) ).
thf(655,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)],[103]) ).
thf(656,plain,
( ( ! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( 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_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(657,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( 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 ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_s @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( 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 ) @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(658,plain,
( ( ! [V_t: $i,V_s: $i,V_n: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ V_n )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ ( c_Lambda_Oliftn @ V_n @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(659,plain,
( ( ! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_s @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ V_t @ V_s @ V_k ) ) @ ( c_Lambda_Osubstn @ V_u @ V_s @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(660,plain,
( ( ! [V_n: $i,V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ V_n @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ V_n @ V_s @ V_k ) ) @ ( c_Lambda_Oliftn @ V_n @ V_t @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(661,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)],[109]) ).
thf(662,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)],[110]) ).
thf(663,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB1: $i,V_dB2: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ V_f2 @ V_dB1 ) @ V_dB2 ) @ ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ V_dB1 @ T_a ) ) @ ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ V_dB2 @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(664,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)],[112]) ).
thf(665,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)],[113]) ).
thf(666,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)],[114]) ).
thf(667,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)],[115]) ).
thf(668,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)],[116]) ).
thf(669,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)],[117]) ).
thf(670,plain,
( ( ! [T_a: $i,V_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a @ V_xs @ T_a @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[118]) ).
thf(671,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)],[119]) ).
thf(672,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ 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 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(673,plain,
( ( ! [V_pwr: $i,V_x: $i,V_r1: $i,V_add: $i,V_mul: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= V_r1 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(674,plain,
( ( ! [V_m: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= V_m ) )
= $true ),
inference(unfold_def,[status(thm)],[122]) ).
thf(675,plain,
( ( ! [V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n )
= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(676,plain,
( ( ! [V_x: $i] :
( V_x
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(677,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)],[125]) ).
thf(678,plain,
( ( ! [V_n: $i] :
( ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(679,plain,
( ( ! [V_n: $i] :
( ( c_Orderings_Oord__class_Omax @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= V_n ) )
= $true ),
inference(unfold_def,[status(thm)],[127]) ).
thf(680,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)],[128]) ).
thf(681,plain,
( ( ! [V_c: $i] :
( ( c_Nat_Osize__class_Osize @ V_c @ tc_String_Ochar )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(682,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)],[130]) ).
thf(683,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[131]) ).
thf(684,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)],[132]) ).
thf(685,plain,
( ( ! [V_r: $i,V_y: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_y @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[133]) ).
thf(686,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)],[134]) ).
thf(687,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(688,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(689,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)],[137]) ).
thf(690,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)],[138]) ).
thf(691,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)],[139]) ).
thf(692,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)],[140]) ).
thf(693,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)],[141]) ).
thf(694,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)],[142]) ).
thf(695,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)],[143]) ).
thf(696,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)],[144]) ).
thf(697,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)],[145]) ).
thf(698,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)],[146]) ).
thf(699,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)],[147]) ).
thf(700,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(701,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)],[149]) ).
thf(702,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)],[150]) ).
thf(703,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)],[151]) ).
thf(704,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)],[152]) ).
thf(705,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)],[153]) ).
thf(706,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)],[154]) ).
thf(707,plain,
( ( ! [V_a: $i] :
( ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ V_a ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(708,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(709,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[157]) ).
thf(710,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_k ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[158]) ).
thf(711,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)],[159]) ).
thf(712,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)],[160]) ).
thf(713,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)],[161]) ).
thf(714,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)],[162]) ).
thf(715,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)],[163]) ).
thf(716,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)],[164]) ).
thf(717,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)],[165]) ).
thf(718,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)],[166]) ).
thf(719,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)],[167]) ).
thf(720,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)],[168]) ).
thf(721,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)],[169]) ).
thf(722,plain,
( ( ! [V_j: $i,V_i: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_i ) @ V_i @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(723,plain,
( ( ! [V_i: $i,V_j: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_i @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[171]) ).
thf(724,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ T_b @ T_a )
= V_r ) )
= $true ),
inference(unfold_def,[status(thm)],[172]) ).
thf(725,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)],[173]) ).
thf(726,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)],[174]) ).
thf(727,plain,
( ( ! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ V_a @ T_b @ T_a )
= ( hAPP @ ( hAPP @ V_f @ V_x ) @ ( c_List_Ofoldr @ V_f @ V_xs @ V_a @ T_b @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[175]) ).
thf(728,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)],[176]) ).
thf(729,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)],[177]) ).
thf(730,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ T_a )
| ( c_OrderedGroup_Osemigroup__add @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[178]) ).
thf(731,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_dB ) @ T_a )
= ( hAPP @ ( hAPP @ V_f3 @ V_dB ) @ ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ V_dB @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[179]) ).
thf(732,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)],[180]) ).
thf(733,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)],[181]) ).
thf(734,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)],[182]) ).
thf(735,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)],[183]) ).
thf(736,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)],[184]) ).
thf(737,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)],[185]) ).
thf(738,plain,
( ( ! [V_n: $i,V_m: $i,V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_m @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(739,plain,
( ( ! [V_a: $i] :
( ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ V_a ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_a
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(740,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ V_xs @ T_a )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[188]) ).
thf(741,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)],[189]) ).
thf(742,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)],[190]) ).
thf(743,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)],[191]) ).
thf(744,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_l ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(745,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)],[193]) ).
thf(746,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[194]) ).
thf(747,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)],[195]) ).
thf(748,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)],[196]) ).
thf(749,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)],[197]) ).
thf(750,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)],[198]) ).
thf(751,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)],[199]) ).
thf(752,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)],[200]) ).
thf(753,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)],[201]) ).
thf(754,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)],[202]) ).
thf(755,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)],[203]) ).
thf(756,plain,
( ( ! [V_a: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( V_a
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[204]) ).
thf(757,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)],[205]) ).
thf(758,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)],[206]) ).
thf(759,plain,
( ( ! [V_plus: $i,V_a: $i,V_b: $i,V_c: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_plus @ ( hAPP @ ( hAPP @ V_plus @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_plus @ V_a ) @ ( hAPP @ ( hAPP @ V_plus @ V_b ) @ V_c ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ V_plus @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[207]) ).
thf(760,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)],[208]) ).
thf(761,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)],[209]) ).
thf(762,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_r ) @ V_i ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[210]) ).
thf(763,plain,
( ( ! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_n ) ) )
| ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[211]) ).
thf(764,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)],[212]) ).
thf(765,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)],[213]) ).
thf(766,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)],[214]) ).
thf(767,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(768,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(769,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)],[217]) ).
thf(770,plain,
( ( ! [V_a: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(771,plain,
( ( ! [T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_fequal @ T_a ) @ T_a @ T_a )
= ( c_fequal @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219]) ).
thf(772,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)],[220]) ).
thf(773,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)],[221]) ).
thf(774,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)],[222]) ).
thf(775,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)],[223]) ).
thf(776,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)],[224]) ).
thf(777,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubstn @ ( 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)],[225]) ).
thf(778,plain,
( ( ! [T_a: $i,V_z: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(779,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)],[227]) ).
thf(780,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)],[228]) ).
thf(781,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)],[229]) ).
thf(782,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)],[230]) ).
thf(783,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)],[231]) ).
thf(784,plain,
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[232]) ).
thf(785,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= V_m )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233]) ).
thf(786,plain,
( ( ! [V_x: $i,V_a: $i] :
( ( V_x
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(787,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(788,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(789,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)],[237]) ).
thf(790,plain,
( ( ! [V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_t @ V_k )
= V_t ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(791,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)],[239]) ).
thf(792,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)],[240]) ).
thf(793,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)],[241]) ).
thf(794,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)],[242]) ).
thf(795,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)],[243]) ).
thf(796,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)],[244]) ).
thf(797,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)],[245]) ).
thf(798,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)],[246]) ).
thf(799,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)],[247]) ).
thf(800,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)],[248]) ).
thf(801,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)],[249]) ).
thf(802,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)],[250]) ).
thf(803,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)],[251]) ).
thf(804,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)],[252]) ).
thf(805,plain,
( ( ! [V_a: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( V_a
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(806,plain,
( ( ! [V_a: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(807,plain,
( ( ! [V_a: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) )
| ( V_a
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(808,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)],[256]) ).
thf(809,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)],[257]) ).
thf(810,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(811,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ 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)],[259]) ).
thf(812,plain,
( ( ! [V_plus: $i,V_zero: $i,V_a: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_plus @ V_zero ) @ V_a )
= V_a )
| ~ ( c_OrderedGroup_Omonoid__add @ V_zero @ V_plus @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(813,plain,
( ( ! [V_plus: $i,V_a: $i,V_zero: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_plus @ V_a ) @ V_zero )
= V_a )
| ~ ( c_OrderedGroup_Omonoid__add @ V_zero @ V_plus @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(814,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)],[262]) ).
thf(815,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(816,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)],[264]) ).
thf(817,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[265]) ).
thf(818,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)],[266]) ).
thf(819,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omax @ V_y @ ( c_Orderings_Oord__class_Omax @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[267]) ).
thf(820,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[268]) ).
thf(821,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)],[269]) ).
thf(822,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)],[270]) ).
thf(823,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) ) @ V_z )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271]) ).
thf(824,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)],[272]) ).
thf(825,plain,
( ( ! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= ( c_Lambda_Oliftn @ V_x @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273]) ).
thf(826,plain,
( ( ! [V_a: $i] :
( ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ V_a ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274]) ).
thf(827,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)],[275]) ).
thf(828,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)],[276]) ).
thf(829,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)],[277]) ).
thf(830,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)],[278]) ).
thf(831,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)],[279]) ).
thf(832,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280]) ).
thf(833,plain,
( ( ! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( 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)],[281]) ).
thf(834,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a )
= ( c_Orderings_Oord__class_Omax @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282]) ).
thf(835,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)],[283]) ).
thf(836,plain,
( ( ! [V_s: $i,V_t: $i,V_s_H: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284]) ).
thf(837,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)],[285]) ).
thf(838,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)],[286]) ).
thf(839,plain,
( ( ! [V_add: $i,V_mul: $i,V_a: $i,V_m: $i,V_b: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_m ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_b ) @ V_m ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ V_m ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287]) ).
thf(840,plain,
( ( ! [V_add: $i,V_mul: $i,V_a: $i,V_m: $i,V_r1: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_m ) ) @ V_m )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_r1 ) ) @ V_m ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(841,plain,
( ( ! [V_add: $i,V_m: $i,V_mul: $i,V_a: $i,V_r1: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_m ) @ ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_m ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_r1 ) ) @ V_m ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(842,plain,
( ( ! [V_add: $i,V_m: $i,V_mul: $i,V_r1: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_m ) @ V_m )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_r1 ) @ V_r1 ) ) @ V_m ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(843,plain,
( ( ! [V_add: $i,V_r0: $i,V_a: $i,V_mul: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_r0 ) @ V_a )
= V_a )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(844,plain,
( ( ! [V_add: $i,V_a: $i,V_r0: $i,V_mul: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_r0 )
= V_a )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(845,plain,
( ( ! [V_mul: $i,V_a: $i,V_b: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ V_mul @ V_b ) @ V_a ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(846,plain,
( ( ! [V_mul: $i,V_add: $i,V_a: $i,V_b: $i,V_c: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_b ) @ V_c ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(847,plain,
( ( ! [V_mul: $i,V_r0: $i,V_a: $i,V_add: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_r0 ) @ V_a )
= V_r0 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(848,plain,
( ( ! [V_mul: $i,V_a: $i,V_r0: $i,V_add: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_r0 )
= V_r0 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(849,plain,
( ( ! [V_mul: $i,V_r1: $i,V_a: $i,V_add: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_r1 ) @ V_a )
= V_a )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(850,plain,
( ( ! [V_mul: $i,V_a: $i,V_r1: $i,V_add: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_r1 )
= V_a )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(851,plain,
( ( ! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_rx ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_ly ) @ V_ry ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(852,plain,
( ( ! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ ( hAPP @ ( hAPP @ V_mul @ V_ly ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(853,plain,
( ( ! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ V_ry ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(854,plain,
( ( ! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ V_rx )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_rx ) ) @ V_ly ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(855,plain,
( ( ! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ V_rx )
= ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ ( hAPP @ ( hAPP @ V_mul @ V_ly ) @ V_rx ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(856,plain,
( ( ! [V_mul: $i,V_lx: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_rx ) ) @ V_ry ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(857,plain,
( ( ! [V_mul: $i,V_lx: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ry ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(858,plain,
( ( ! [V_add: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ V_add @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ V_add @ V_b ) @ V_d ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(859,plain,
( ( ! [V_add: $i,V_a: $i,V_b: $i,V_c: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_add @ V_a ) @ ( hAPP @ ( hAPP @ V_add @ V_b ) @ V_c ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(860,plain,
( ( ! [V_add: $i,V_a: $i,V_c: $i,V_d: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_a ) @ ( hAPP @ ( hAPP @ V_add @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ V_add @ V_c ) @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_d ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(861,plain,
( ( ! [V_add: $i,V_a: $i,V_b: $i,V_c: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_c ) ) @ V_b ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(862,plain,
( ( ! [V_add: $i,V_a: $i,V_c: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_c )
= ( hAPP @ ( hAPP @ V_add @ V_c ) @ V_a ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(863,plain,
( ( ! [V_add: $i,V_a: $i,V_c: $i,V_d: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_a ) @ ( hAPP @ ( hAPP @ V_add @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_c ) ) @ V_d ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(864,plain,
( ( ! [V_add: $i,V_r0: $i,V_x: $i,V_mul: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_r0 ) @ V_x )
= V_x )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(865,plain,
( ( ! [V_add: $i,V_x: $i,V_y: $i,V_z: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_x ) @ ( hAPP @ ( hAPP @ V_add @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_x ) @ V_y ) ) @ V_z ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(866,plain,
( ( ! [V_add: $i,V_x: $i,V_y: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ V_add @ V_y ) @ V_x ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(867,plain,
( ( ! [V_mul: $i,V_r0: $i,V_x: $i,V_add: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_r0 ) @ V_x )
= V_r0 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(868,plain,
( ( ! [V_mul: $i,V_r1: $i,V_x: $i,V_add: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_r1 ) @ V_x )
= V_x )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(869,plain,
( ( ! [V_mul: $i,V_x: $i,V_y: $i,V_z: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_x ) @ ( hAPP @ ( hAPP @ V_mul @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_y ) ) @ V_z ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317]) ).
thf(870,plain,
( ( ! [V_mul: $i,V_x: $i,V_y: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ V_mul @ V_y ) @ V_x ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318]) ).
thf(871,plain,
( ( ! [V_mul: $i,V_x: $i,V_add: $i,V_y: $i,V_z: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_x ) @ ( hAPP @ ( hAPP @ V_add @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_y ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_z ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319]) ).
thf(872,plain,
( ( ! [V_pwr: $i,V_mul: $i,V_x: $i,V_y: $i,V_q: $i,V_add: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_y ) ) @ V_q )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_q ) ) @ ( hAPP @ ( hAPP @ V_pwr @ V_y ) @ V_q ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320]) ).
thf(873,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)],[321]) ).
thf(874,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)],[322]) ).
thf(875,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)],[323]) ).
thf(876,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)],[324]) ).
thf(877,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)],[325]) ).
thf(878,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)],[326]) ).
thf(879,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)],[327]) ).
thf(880,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)],[328]) ).
thf(881,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329]) ).
thf(882,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)],[330]) ).
thf(883,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)],[331]) ).
thf(884,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)],[332]) ).
thf(885,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)],[333]) ).
thf(886,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334]) ).
thf(887,plain,
( ( ! [T_a: $i,V_xs: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ V_a @ T_a @ T_a )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a @ V_xs @ T_a @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335]) ).
thf(888,plain,
( ( ! [V_t: $i,V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_r ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336]) ).
thf(889,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( 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_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337]) ).
thf(890,plain,
( ( ! [V_mul: $i,V_pwr: $i,V_x: $i,V_p: $i,V_q: $i,V_add: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_p ) ) @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_q ) )
= ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_p ) @ V_q ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338]) ).
thf(891,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)],[339]) ).
thf(892,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)],[340]) ).
thf(893,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)],[341]) ).
thf(894,plain,
( ( ! [V_f: $i,V_xs: $i,V_ys: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ V_a @ T_b @ T_a )
= ( c_List_Ofoldr @ V_f @ V_xs @ ( c_List_Ofoldr @ V_f @ V_ys @ V_a @ T_b @ T_a ) @ T_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342]) ).
thf(895,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)],[343]) ).
thf(896,plain,
( ( ! [V_m: $i,V_l: $i,V_k: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_l )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344]) ).
thf(897,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345]) ).
thf(898,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)],[346]) ).
thf(899,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)],[347]) ).
thf(900,plain,
( ( ! [V_i: $i,V_m: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_j ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348]) ).
thf(901,plain,
( ( ! [V_i: $i,V_j: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_m ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349]) ).
thf(902,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350]) ).
thf(903,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_z @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351]) ).
thf(904,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352]) ).
thf(905,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)],[353]) ).
thf(906,plain,
( ( ! [V_t: $i,V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_r ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354]) ).
thf(907,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)],[355]) ).
thf(908,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)],[356]) ).
thf(909,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)],[357]) ).
thf(910,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)],[358]) ).
thf(911,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)],[359]) ).
thf(912,plain,
( ( ! [V_a: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) )
| ( V_a
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360]) ).
thf(913,plain,
( ( ! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_r @ tc_Lambda_OdB ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361]) ).
thf(914,plain,
( ( ! [V_t: $i] :
( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_t @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362]) ).
thf(915,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363]) ).
thf(916,plain,
( ( ! [V_r: $i,V_b: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364]) ).
thf(917,plain,
( ( ! [V_r: $i,V_b: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365]) ).
thf(918,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366]) ).
thf(919,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367]) ).
thf(920,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368]) ).
thf(921,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)],[369]) ).
thf(922,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)],[370]) ).
thf(923,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)],[371]) ).
thf(924,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)],[372]) ).
thf(925,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)],[373]) ).
thf(926,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)],[374]) ).
thf(927,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)],[375]) ).
thf(928,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)],[376]) ).
thf(929,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)],[377]) ).
thf(930,plain,
( ( ! [V_s: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_s_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378]) ).
thf(931,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)],[379]) ).
thf(932,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)],[380]) ).
thf(933,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)],[381]) ).
thf(934,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)],[382]) ).
thf(935,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)],[383]) ).
thf(936,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)],[384]) ).
thf(937,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385]) ).
thf(938,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) @ V_k )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386]) ).
thf(939,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)],[387]) ).
thf(940,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)],[388]) ).
thf(941,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)],[389]) ).
thf(942,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)],[390]) ).
thf(943,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)],[391]) ).
thf(944,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)],[392]) ).
thf(945,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)],[393]) ).
thf(946,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( 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 @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394]) ).
thf(947,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395]) ).
thf(948,plain,
( ( ! [V_r: $i,V_a2: $i,V_a1: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a2 ) @ V_a1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a1 ) @ V_a2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396]) ).
thf(949,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397]) ).
thf(950,plain,
( ( ! [V_r: $i,V_b: $i,V_a: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398]) ).
thf(951,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)],[399]) ).
thf(952,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)],[400]) ).
thf(953,plain,
( ( ! [V_f: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Olist_ONil @ T_b ) @ V_a @ T_b @ T_a )
= V_a ) )
= $true ),
inference(unfold_def,[status(thm)],[401]) ).
thf(954,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)],[402]) ).
thf(955,plain,
( ( ! [V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403]) ).
thf(956,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404]) ).
thf(957,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)],[405]) ).
thf(958,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406]) ).
thf(959,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407]) ).
thf(960,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[408]) ).
thf(961,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409]) ).
thf(962,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410]) ).
thf(963,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411]) ).
thf(964,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)],[412]) ).
thf(965,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)],[413]) ).
thf(966,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)],[414]) ).
thf(967,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)],[415]) ).
thf(968,plain,
( ( ! [V_s: $i,V_t: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416]) ).
thf(969,plain,
( ( ! [V_s: $i,V_t: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417]) ).
thf(970,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)],[418]) ).
thf(971,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)],[419]) ).
thf(972,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)],[420]) ).
thf(973,plain,
( ( ! [V_a: $i] :
( ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ V_a ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_a
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421]) ).
thf(974,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[422]) ).
thf(975,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423]) ).
thf(976,plain,
( ( ! [V_P: $i,V_t: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ V_P ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__4 @ V_P ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ V_P ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ V_P ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ V_P @ V_t ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424]) ).
thf(977,plain,
( ( ! [V_P: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_t ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ V_P ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @ V_P ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ V_P ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ V_P ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[425]) ).
thf(978,plain,
( ( ! [V_e: $i,V_u: $i,V_i: $i,V_ts: $i,V_Ts: $i,V_T: $i] :
( ( c_Type_Otypings @ V_e @ ( 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 ) @ V_Ts )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ V_e @ V_i @ V_T @ tc_Type_Otype ) @ V_ts @ V_Ts )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[426]) ).
thf(979,plain,
( ( ! [V_e: $i,V_i: $i,V_U: $i,V_ts: $i,V_Ts: $i] :
( ( c_Type_Otypings @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ tc_Type_Otype ) @ ( 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 ) @ V_Ts )
| ~ ( c_Type_Otypings @ V_e @ V_ts @ V_Ts ) ) )
= $true ),
inference(unfold_def,[status(thm)],[427]) ).
thf(980,plain,
( ( ! [V_t: $i,V_s: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ V_t ) ) @ V_s ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[428]) ).
thf(981,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)],[429]) ).
thf(982,plain,
( ( ! [V_t: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_s @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubstn @ V_t @ V_s @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[430]) ).
thf(983,plain,
( ( ! [V_n: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Oliftn @ V_n @ V_s @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(984,plain,
( ( ! [V_s: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[432]) ).
thf(985,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)],[433]) ).
thf(986,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)],[434]) ).
thf(987,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)],[435]) ).
thf(988,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)],[436]) ).
thf(989,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)],[437]) ).
thf(990,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)],[438]) ).
thf(991,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)],[439]) ).
thf(992,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)],[440]) ).
thf(993,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)],[441]) ).
thf(994,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)],[442]) ).
thf(995,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)],[443]) ).
thf(996,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)],[444]) ).
thf(997,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)],[445]) ).
thf(998,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)],[446]) ).
thf(999,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)],[447]) ).
thf(1000,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448]) ).
thf(1001,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)],[449]) ).
thf(1002,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)],[450]) ).
thf(1003,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)],[451]) ).
thf(1004,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)],[452]) ).
thf(1005,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)],[453]) ).
thf(1006,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)],[454]) ).
thf(1007,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)],[455]) ).
thf(1008,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)],[456]) ).
thf(1009,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)],[457]) ).
thf(1010,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458]) ).
thf(1011,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[459]) ).
thf(1012,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[460]) ).
thf(1013,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)],[461]) ).
thf(1014,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)],[462]) ).
thf(1015,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463]) ).
thf(1016,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464]) ).
thf(1017,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465]) ).
thf(1018,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[466]) ).
thf(1019,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467]) ).
thf(1020,plain,
( ( ! [T_a: $i,V_z: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_z @ V_y @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468]) ).
thf(1021,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_Oone__class_Oone @ tc_nat ) @ T_a )
= V_x ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469]) ).
thf(1022,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= V_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470]) ).
thf(1023,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471]) ).
thf(1024,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472]) ).
thf(1025,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473]) ).
thf(1026,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474]) ).
thf(1027,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475]) ).
thf(1028,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[476]) ).
thf(1029,plain,
( ( ! [T_a: $i,V_b: $i,V_x: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[477]) ).
thf(1030,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_a @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[478]) ).
thf(1031,plain,
( ( ! [V_e: $i,V_x: $i,V_T: $i,T_a: $i] :
( ( hAPP @ ( c_Type_Oshift @ V_e @ V_x @ V_T @ T_a ) @ V_x )
= V_T ) )
= $true ),
inference(unfold_def,[status(thm)],[479]) ).
thf(1032,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)],[480]) ).
thf(1033,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)],[481]) ).
thf(1034,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)],[482]) ).
thf(1035,plain,
( ( ! [V_pwr: $i,V_x: $i,V_add: $i,V_mul: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= V_x )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[483]) ).
thf(1036,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)],[484]) ).
thf(1037,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)],[485]) ).
thf(1038,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)],[486]) ).
thf(1039,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)],[487]) ).
thf(1040,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)],[488]) ).
thf(1041,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)],[489]) ).
thf(1042,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)],[490]) ).
thf(1043,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)],[491]) ).
thf(1044,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)],[492]) ).
thf(1045,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)],[493]) ).
thf(1046,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)],[494]) ).
thf(1047,plain,
( ( ! [V_e: $i,V_i: $i,V_T: $i,T_a: $i,V_j: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ V_e @ V_i @ V_T @ T_a ) @ V_j )
= ( hAPP @ V_e @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495]) ).
thf(1048,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)],[496]) ).
thf(1049,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)],[497]) ).
thf(1050,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)],[498]) ).
thf(1051,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)],[499]) ).
thf(1052,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)],[500]) ).
thf(1053,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)],[501]) ).
thf(1054,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)],[502]) ).
thf(1055,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)],[503]) ).
thf(1056,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)],[504]) ).
thf(1057,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)],[505]) ).
thf(1058,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)],[506]) ).
thf(1059,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)],[507]) ).
thf(1060,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)],[508]) ).
thf(1061,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)],[509]) ).
thf(1062,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)],[510]) ).
thf(1063,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)],[511]) ).
thf(1064,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)],[512]) ).
thf(1065,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)],[513]) ).
thf(1066,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)],[514]) ).
thf(1067,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)],[515]) ).
thf(1068,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)],[516]) ).
thf(1069,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)],[517]) ).
thf(1070,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)],[518]) ).
thf(1071,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)],[519]) ).
thf(1072,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)],[520]) ).
thf(1073,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)],[521]) ).
thf(1074,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)],[522]) ).
thf(1075,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)],[523]) ).
thf(1076,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)],[524]) ).
thf(1077,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)],[525]) ).
thf(1078,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)],[526]) ).
thf(1079,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)],[527]) ).
thf(1080,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)],[528]) ).
thf(1081,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)],[529]) ).
thf(1082,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_k )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530]) ).
thf(1083,plain,
( ( ! [V_t: $i,V_s: $i,V_j: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_j ) ) @ V_i )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[531]) ).
thf(1084,plain,
( ( ! [V_t: $i,V_s: $i,V_j: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_j ) ) @ V_i )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_i ) ) @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[532]) ).
thf(1085,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)],[533]) ).
thf(1086,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)],[534]) ).
thf(1087,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)],[535]) ).
thf(1088,plain,
( ( ! [V_e: $i,V_i: $i,V_U: $i,V_t: $i,V_T: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[536]) ).
thf(1089,plain,
( ( ! [V_e_H: $i,V_u: $i,V_U: $i,V_i: $i,V_t: $i,V_T: $i] :
( ~ ( c_Type_Otyping @ V_e_H @ V_u @ V_U )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e_H @ V_i @ V_U @ tc_Type_Otype ) @ V_t @ V_T )
| ( c_Type_Otyping @ V_e_H @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) @ V_T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[537]) ).
thf(1090,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)],[538]) ).
thf(1091,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)],[539]) ).
thf(1092,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)],[540]) ).
thf(1093,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)],[541]) ).
thf(1094,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)],[542]) ).
thf(1095,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)],[543]) ).
thf(1096,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)],[544]) ).
thf(1097,plain,
( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( 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 ) ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[547]) ).
thf(1098,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ v_s ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[548]) ).
thf(1099,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_s ) )
= $true ),
inference(unfold_def,[status(thm)],[549]) ).
thf(1100,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( 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 ) ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[550]) ).
thf(1101,plain,
( ( 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)],[551]) ).
thf(1102,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[552]) ).
thf(1103,plain,
( ( 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)],[1101]) ).
thf(1104,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( 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 ) ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ) )
= $true ),
inference(copy,[status(thm)],[1100]) ).
thf(1105,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ v_s ) )
= $true ),
inference(copy,[status(thm)],[1099]) ).
thf(1106,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ v_s ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ) )
= $true ),
inference(copy,[status(thm)],[1098]) ).
thf(1107,plain,
( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( 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 ) ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1097]) ).
thf(1108,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)],[1096]) ).
thf(1109,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)],[1095]) ).
thf(1110,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)],[1094]) ).
thf(1111,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)],[1093]) ).
thf(1112,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)],[1092]) ).
thf(1113,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)],[1091]) ).
thf(1114,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)],[1090]) ).
thf(1115,plain,
( ( ! [V_e_H: $i,V_u: $i,V_U: $i,V_i: $i,V_t: $i,V_T: $i] :
( ~ ( c_Type_Otyping @ V_e_H @ V_u @ V_U )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ V_e_H @ V_i @ V_U @ tc_Type_Otype ) @ V_t @ V_T )
| ( c_Type_Otyping @ V_e_H @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_u ) @ V_i ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[1089]) ).
thf(1116,plain,
( ( ! [V_e: $i,V_i: $i,V_U: $i,V_t: $i,V_T: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[1088]) ).
thf(1117,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)],[1087]) ).
thf(1118,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)],[1086]) ).
thf(1119,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)],[1085]) ).
thf(1120,plain,
( ( ! [V_t: $i,V_s: $i,V_j: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_j ) ) @ V_i )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_i ) ) @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1084]) ).
thf(1121,plain,
( ( ! [V_t: $i,V_s: $i,V_j: $i,V_i: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_j ) ) @ V_i )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_t ) @ V_i ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1083]) ).
thf(1122,plain,
( ( ! [V_i: $i,V_k: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ V_i ) ) @ V_k )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1082]) ).
thf(1123,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)],[1081]) ).
thf(1124,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)],[1080]) ).
thf(1125,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)],[1079]) ).
thf(1126,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)],[1078]) ).
thf(1127,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)],[1077]) ).
thf(1128,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)],[1076]) ).
thf(1129,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)],[1075]) ).
thf(1130,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)],[1074]) ).
thf(1131,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)],[1073]) ).
thf(1132,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)],[1072]) ).
thf(1133,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)],[1071]) ).
thf(1134,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)],[1070]) ).
thf(1135,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)],[1069]) ).
thf(1136,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)],[1068]) ).
thf(1137,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)],[1067]) ).
thf(1138,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)],[1066]) ).
thf(1139,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)],[1065]) ).
thf(1140,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)],[1064]) ).
thf(1141,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)],[1063]) ).
thf(1142,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)],[1062]) ).
thf(1143,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)],[1061]) ).
thf(1144,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)],[1060]) ).
thf(1145,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)],[1059]) ).
thf(1146,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)],[1058]) ).
thf(1147,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)],[1057]) ).
thf(1148,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)],[1056]) ).
thf(1149,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)],[1055]) ).
thf(1150,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)],[1054]) ).
thf(1151,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)],[1053]) ).
thf(1152,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)],[1052]) ).
thf(1153,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)],[1051]) ).
thf(1154,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)],[1050]) ).
thf(1155,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)],[1049]) ).
thf(1156,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)],[1048]) ).
thf(1157,plain,
( ( ! [V_e: $i,V_i: $i,V_T: $i,T_a: $i,V_j: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ V_e @ V_i @ V_T @ T_a ) @ V_j )
= ( hAPP @ V_e @ V_j ) )
| ~ ( c_HOL_Oord__class_Oless @ V_j @ V_i @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[1047]) ).
thf(1158,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)],[1046]) ).
thf(1159,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)],[1045]) ).
thf(1160,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)],[1044]) ).
thf(1161,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)],[1043]) ).
thf(1162,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)],[1042]) ).
thf(1163,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)],[1041]) ).
thf(1164,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)],[1040]) ).
thf(1165,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)],[1039]) ).
thf(1166,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)],[1038]) ).
thf(1167,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)],[1037]) ).
thf(1168,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)],[1036]) ).
thf(1169,plain,
( ( ! [V_pwr: $i,V_x: $i,V_add: $i,V_mul: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= V_x )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1035]) ).
thf(1170,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)],[1034]) ).
thf(1171,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)],[1033]) ).
thf(1172,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)],[1032]) ).
thf(1173,plain,
( ( ! [V_e: $i,V_x: $i,V_T: $i,T_a: $i] :
( ( hAPP @ ( c_Type_Oshift @ V_e @ V_x @ V_T @ T_a ) @ V_x )
= V_T ) )
= $true ),
inference(copy,[status(thm)],[1031]) ).
thf(1174,plain,
( ( ! [T_a: $i,V_a: $i,V_x: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_a @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1030]) ).
thf(1175,plain,
( ( ! [T_a: $i,V_b: $i,V_x: $i,V_a: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1029]) ).
thf(1176,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1028]) ).
thf(1177,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_x @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1027]) ).
thf(1178,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1026]) ).
thf(1179,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_lessequals @ V_z @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1025]) ).
thf(1180,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1024]) ).
thf(1181,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1023]) ).
thf(1182,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ T_a )
| ( ( c_Power_Opower__class_Opower @ V_a @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= V_a ) ) )
= $true ),
inference(copy,[status(thm)],[1022]) ).
thf(1183,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_Oone__class_Oone @ tc_nat ) @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[1021]) ).
thf(1184,plain,
( ( ! [T_a: $i,V_z: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_z @ V_y @ T_a )
| ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1020]) ).
thf(1185,plain,
( ( ! [T_a: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_y @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1019]) ).
thf(1186,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ V_x @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1018]) ).
thf(1187,plain,
( ( ! [T_a: $i,V_a: $i,V_b: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_b @ V_x @ T_a )
| ~ ( c_lessequals @ V_a @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1017]) ).
thf(1188,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ V_x @ T_a )
| ~ ( c_lessequals @ V_z @ V_x @ T_a )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1016]) ).
thf(1189,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_lessequals @ V_y @ V_z @ T_a )
| ~ ( c_lessequals @ V_x @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1015]) ).
thf(1190,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)],[1014]) ).
thf(1191,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)],[1013]) ).
thf(1192,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a )
= V_y )
| ~ ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1012]) ).
thf(1193,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a )
!= V_y )
| ( c_lessequals @ V_x @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1011]) ).
thf(1194,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a )
= V_x )
| ~ ( c_lessequals @ V_y @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[1010]) ).
thf(1195,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)],[1009]) ).
thf(1196,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)],[1008]) ).
thf(1197,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)],[1007]) ).
thf(1198,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)],[1006]) ).
thf(1199,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)],[1005]) ).
thf(1200,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)],[1004]) ).
thf(1201,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)],[1003]) ).
thf(1202,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)],[1002]) ).
thf(1203,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)],[1001]) ).
thf(1204,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ T_a )
= ( c_HOL_Oone__class_Oone @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[1000]) ).
thf(1205,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)],[999]) ).
thf(1206,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)],[998]) ).
thf(1207,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)],[997]) ).
thf(1208,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)],[996]) ).
thf(1209,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)],[995]) ).
thf(1210,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)],[994]) ).
thf(1211,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)],[993]) ).
thf(1212,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)],[992]) ).
thf(1213,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)],[991]) ).
thf(1214,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)],[990]) ).
thf(1215,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)],[989]) ).
thf(1216,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)],[988]) ).
thf(1217,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)],[987]) ).
thf(1218,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)],[986]) ).
thf(1219,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)],[985]) ).
thf(1220,plain,
( ( ! [V_s: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[984]) ).
thf(1221,plain,
( ( ! [V_n: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OAbs @ V_s ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Oliftn @ V_n @ V_s @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[983]) ).
thf(1222,plain,
( ( ! [V_t: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OAbs @ V_t ) @ V_s @ V_k )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubstn @ V_t @ V_s @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[982]) ).
thf(1223,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)],[981]) ).
thf(1224,plain,
( ( ! [V_t: $i,V_s: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ V_t ) ) @ V_s ) @ V_k )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[980]) ).
thf(1225,plain,
( ( ! [V_e: $i,V_i: $i,V_U: $i,V_ts: $i,V_Ts: $i] :
( ( c_Type_Otypings @ ( c_Type_Oshift @ V_e @ V_i @ V_U @ tc_Type_Otype ) @ ( 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 ) @ V_Ts )
| ~ ( c_Type_Otypings @ V_e @ V_ts @ V_Ts ) ) )
= $true ),
inference(copy,[status(thm)],[979]) ).
thf(1226,plain,
( ( ! [V_e: $i,V_u: $i,V_i: $i,V_ts: $i,V_Ts: $i,V_T: $i] :
( ( c_Type_Otypings @ V_e @ ( 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 ) @ V_Ts )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ V_e @ V_i @ V_T @ tc_Type_Otype ) @ V_ts @ V_Ts )
| ~ ( c_Type_Otyping @ V_e @ V_u @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[978]) ).
thf(1227,plain,
( ( ! [V_P: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_t ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ V_P ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @ V_P ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ V_P ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ V_P ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[977]) ).
thf(1228,plain,
( ( ! [V_P: $i,V_t: $i] :
( ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ V_P ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__4 @ V_P ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ V_P ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ V_P ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ V_P @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[976]) ).
thf(1229,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_k )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[975]) ).
thf(1230,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_y )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) )
| ( V_y = V_z ) ) )
= $true ),
inference(copy,[status(thm)],[974]) ).
thf(1231,plain,
( ( ! [V_a: $i] :
( ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ V_a ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_a
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[973]) ).
thf(1232,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)],[972]) ).
thf(1233,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)],[971]) ).
thf(1234,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)],[970]) ).
thf(1235,plain,
( ( ! [V_s: $i,V_t: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[969]) ).
thf(1236,plain,
( ( ! [V_s: $i,V_t: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[968]) ).
thf(1237,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)],[967]) ).
thf(1238,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)],[966]) ).
thf(1239,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)],[965]) ).
thf(1240,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)],[964]) ).
thf(1241,plain,
( ( ! [T_a: $i,V_y: $i,V_z: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[963]) ).
thf(1242,plain,
( ( ! [T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[962]) ).
thf(1243,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[961]) ).
thf(1244,plain,
( ( ! [T_a: $i,V_z: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[960]) ).
thf(1245,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[959]) ).
thf(1246,plain,
( ( ! [T_a: $i,V_x: $i,V_a: $i,V_b: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_x @ ( c_Orderings_Oord__class_Omax @ V_a @ V_b @ T_a ) @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[958]) ).
thf(1247,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)],[957]) ).
thf(1248,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_x ) ) ) )
= $true ),
inference(copy,[status(thm)],[956]) ).
thf(1249,plain,
( ( ! [V_r: $i,T_a: $i,V_y: $i,V_x: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_x ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_a ) @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[955]) ).
thf(1250,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)],[954]) ).
thf(1251,plain,
( ( ! [V_f: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Olist_ONil @ T_b ) @ V_a @ T_b @ T_a )
= V_a ) )
= $true ),
inference(copy,[status(thm)],[953]) ).
thf(1252,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)],[952]) ).
thf(1253,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)],[951]) ).
thf(1254,plain,
( ( ! [V_r: $i,V_b: $i,V_a: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[950]) ).
thf(1255,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i,V_a: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a ) @ V_b ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[949]) ).
thf(1256,plain,
( ( ! [V_r: $i,V_a2: $i,V_a1: $i,T_a: $i,T_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a2 ) @ V_a1 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_a1 ) @ V_a2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[948]) ).
thf(1257,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i,V_b: $i,V_a: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ V_b ) @ V_a ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[947]) ).
thf(1258,plain,
( ( ! [V_n: $i,V_m: $i] :
( ( 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 @ tc_nat ) @ V_m @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[946]) ).
thf(1259,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)],[945]) ).
thf(1260,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)],[944]) ).
thf(1261,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)],[943]) ).
thf(1262,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)],[942]) ).
thf(1263,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)],[941]) ).
thf(1264,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)],[940]) ).
thf(1265,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)],[939]) ).
thf(1266,plain,
( ( ! [V_m: $i,V_n: $i,V_k: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) ) @ V_k )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[938]) ).
thf(1267,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_z ) ) ) )
= $true ),
inference(copy,[status(thm)],[937]) ).
thf(1268,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)],[936]) ).
thf(1269,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)],[935]) ).
thf(1270,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)],[934]) ).
thf(1271,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)],[933]) ).
thf(1272,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)],[932]) ).
thf(1273,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)],[931]) ).
thf(1274,plain,
( ( ! [V_s: $i,V_s_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ V_s ) ) @ ( c_Lambda_OdB_OAbs @ V_s_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[930]) ).
thf(1275,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)],[929]) ).
thf(1276,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)],[928]) ).
thf(1277,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)],[927]) ).
thf(1278,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)],[926]) ).
thf(1279,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)],[925]) ).
thf(1280,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)],[924]) ).
thf(1281,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)],[923]) ).
thf(1282,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)],[922]) ).
thf(1283,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)],[921]) ).
thf(1284,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_y @ V_z @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_z @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[920]) ).
thf(1285,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_a ) ) )
= $true ),
inference(copy,[status(thm)],[919]) ).
thf(1286,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[918]) ).
thf(1287,plain,
( ( ! [V_r: $i,V_b: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[917]) ).
thf(1288,plain,
( ( ! [V_r: $i,V_b: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[916]) ).
thf(1289,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_z: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_y ) @ V_z ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[915]) ).
thf(1290,plain,
( ( ! [V_t: $i] :
( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_t @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[914]) ).
thf(1291,plain,
( ( ! [V_r: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_r ) )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_r @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[913]) ).
thf(1292,plain,
( ( ! [V_a: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) )
| ( V_a
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[912]) ).
thf(1293,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)],[911]) ).
thf(1294,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)],[910]) ).
thf(1295,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)],[909]) ).
thf(1296,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)],[908]) ).
thf(1297,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)],[907]) ).
thf(1298,plain,
( ( ! [V_t: $i,V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_r ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[906]) ).
thf(1299,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)],[905]) ).
thf(1300,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_y @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[904]) ).
thf(1301,plain,
( ( ! [V_x: $i,V_y: $i,V_z: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_y ) @ V_z ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_x @ V_z @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[903]) ).
thf(1302,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[902]) ).
thf(1303,plain,
( ( ! [V_i: $i,V_j: $i,V_m: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_m ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[901]) ).
thf(1304,plain,
( ( ! [V_i: $i,V_m: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ V_i @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_j ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[900]) ).
thf(1305,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)],[899]) ).
thf(1306,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)],[898]) ).
thf(1307,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) ) )
= $true ),
inference(copy,[status(thm)],[897]) ).
thf(1308,plain,
( ( ! [V_m: $i,V_l: $i,V_k: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_l )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ tc_nat )
| ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[896]) ).
thf(1309,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)],[895]) ).
thf(1310,plain,
( ( ! [V_f: $i,V_xs: $i,V_ys: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Oappend @ V_xs @ V_ys @ T_b ) @ V_a @ T_b @ T_a )
= ( c_List_Ofoldr @ V_f @ V_xs @ ( c_List_Ofoldr @ V_f @ V_ys @ V_a @ T_b @ T_a ) @ T_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[894]) ).
thf(1311,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)],[893]) ).
thf(1312,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)],[892]) ).
thf(1313,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)],[891]) ).
thf(1314,plain,
( ( ! [V_mul: $i,V_pwr: $i,V_x: $i,V_p: $i,V_q: $i,V_add: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_p ) ) @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_q ) )
= ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_p ) @ V_q ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[890]) ).
thf(1315,plain,
( ( ! [V_r: $i,V_t: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( 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_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[889]) ).
thf(1316,plain,
( ( ! [V_t: $i,V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_r ) @ V_i ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[888]) ).
thf(1317,plain,
( ( ! [T_a: $i,V_xs: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ T_a )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ V_a @ T_a @ T_a )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a @ V_xs @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[887]) ).
thf(1318,plain,
( ( ! [V_r: $i,T_a: $i,V_x: $i,V_y: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_x ) @ V_y ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_x ) @ V_y ) ) ) )
= $true ),
inference(copy,[status(thm)],[886]) ).
thf(1319,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)],[885]) ).
thf(1320,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)],[884]) ).
thf(1321,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)],[883]) ).
thf(1322,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)],[882]) ).
thf(1323,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[881]) ).
thf(1324,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)],[880]) ).
thf(1325,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)],[879]) ).
thf(1326,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)],[878]) ).
thf(1327,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)],[877]) ).
thf(1328,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)],[876]) ).
thf(1329,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)],[875]) ).
thf(1330,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)],[874]) ).
thf(1331,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)],[873]) ).
thf(1332,plain,
( ( ! [V_pwr: $i,V_mul: $i,V_x: $i,V_y: $i,V_q: $i,V_add: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_y ) ) @ V_q )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ V_q ) ) @ ( hAPP @ ( hAPP @ V_pwr @ V_y ) @ V_q ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[872]) ).
thf(1333,plain,
( ( ! [V_mul: $i,V_x: $i,V_add: $i,V_y: $i,V_z: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_x ) @ ( hAPP @ ( hAPP @ V_add @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_y ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_z ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[871]) ).
thf(1334,plain,
( ( ! [V_mul: $i,V_x: $i,V_y: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ V_mul @ V_y ) @ V_x ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[870]) ).
thf(1335,plain,
( ( ! [V_mul: $i,V_x: $i,V_y: $i,V_z: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_x ) @ ( hAPP @ ( hAPP @ V_mul @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_x ) @ V_y ) ) @ V_z ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[869]) ).
thf(1336,plain,
( ( ! [V_mul: $i,V_r1: $i,V_x: $i,V_add: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_r1 ) @ V_x )
= V_x )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[868]) ).
thf(1337,plain,
( ( ! [V_mul: $i,V_r0: $i,V_x: $i,V_add: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_r0 ) @ V_x )
= V_r0 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[867]) ).
thf(1338,plain,
( ( ! [V_add: $i,V_x: $i,V_y: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_x ) @ V_y )
= ( hAPP @ ( hAPP @ V_add @ V_y ) @ V_x ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[866]) ).
thf(1339,plain,
( ( ! [V_add: $i,V_x: $i,V_y: $i,V_z: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_x ) @ ( hAPP @ ( hAPP @ V_add @ V_y ) @ V_z ) )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_x ) @ V_y ) ) @ V_z ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[865]) ).
thf(1340,plain,
( ( ! [V_add: $i,V_r0: $i,V_x: $i,V_mul: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_r0 ) @ V_x )
= V_x )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[864]) ).
thf(1341,plain,
( ( ! [V_add: $i,V_a: $i,V_c: $i,V_d: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_a ) @ ( hAPP @ ( hAPP @ V_add @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_c ) ) @ V_d ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[863]) ).
thf(1342,plain,
( ( ! [V_add: $i,V_a: $i,V_c: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_c )
= ( hAPP @ ( hAPP @ V_add @ V_c ) @ V_a ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[862]) ).
thf(1343,plain,
( ( ! [V_add: $i,V_a: $i,V_b: $i,V_c: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_c ) ) @ V_b ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[861]) ).
thf(1344,plain,
( ( ! [V_add: $i,V_a: $i,V_c: $i,V_d: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_a ) @ ( hAPP @ ( hAPP @ V_add @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ V_add @ V_c ) @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_d ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[860]) ).
thf(1345,plain,
( ( ! [V_add: $i,V_a: $i,V_b: $i,V_c: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_add @ V_a ) @ ( hAPP @ ( hAPP @ V_add @ V_b ) @ V_c ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[859]) ).
thf(1346,plain,
( ( ! [V_add: $i,V_a: $i,V_b: $i,V_c: $i,V_d: $i,V_mul: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ ( hAPP @ ( hAPP @ V_add @ V_c ) @ V_d ) )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ V_add @ V_b ) @ V_d ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[858]) ).
thf(1347,plain,
( ( ! [V_mul: $i,V_lx: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ry ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[857]) ).
thf(1348,plain,
( ( ! [V_mul: $i,V_lx: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_rx ) ) @ V_ry ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[856]) ).
thf(1349,plain,
( ( ! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ V_rx )
= ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ ( hAPP @ ( hAPP @ V_mul @ V_ly ) @ V_rx ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[855]) ).
thf(1350,plain,
( ( ! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ V_rx )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_rx ) ) @ V_ly ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[854]) ).
thf(1351,plain,
( ( ! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ V_ry ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[853]) ).
thf(1352,plain,
( ( ! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ ( hAPP @ ( hAPP @ V_mul @ V_ly ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[852]) ).
thf(1353,plain,
( ( ! [V_mul: $i,V_lx: $i,V_ly: $i,V_rx: $i,V_ry: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_ly ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_rx ) @ V_ry ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_mul @ V_lx ) @ V_rx ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_ly ) @ V_ry ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[851]) ).
thf(1354,plain,
( ( ! [V_mul: $i,V_a: $i,V_r1: $i,V_add: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_r1 )
= V_a )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[850]) ).
thf(1355,plain,
( ( ! [V_mul: $i,V_r1: $i,V_a: $i,V_add: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_r1 ) @ V_a )
= V_a )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[849]) ).
thf(1356,plain,
( ( ! [V_mul: $i,V_a: $i,V_r0: $i,V_add: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_r0 )
= V_r0 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[848]) ).
thf(1357,plain,
( ( ! [V_mul: $i,V_r0: $i,V_a: $i,V_add: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_r0 ) @ V_a )
= V_r0 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[847]) ).
thf(1358,plain,
( ( ! [V_mul: $i,V_add: $i,V_a: $i,V_b: $i,V_c: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_c ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_b ) @ V_c ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[846]) ).
thf(1359,plain,
( ( ! [V_mul: $i,V_a: $i,V_b: $i,V_add: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ V_mul @ V_b ) @ V_a ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[845]) ).
thf(1360,plain,
( ( ! [V_add: $i,V_a: $i,V_r0: $i,V_mul: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_r0 )
= V_a )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[844]) ).
thf(1361,plain,
( ( ! [V_add: $i,V_r0: $i,V_a: $i,V_mul: $i,V_pwr: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_r0 ) @ V_a )
= V_a )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[843]) ).
thf(1362,plain,
( ( ! [V_add: $i,V_m: $i,V_mul: $i,V_r1: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_m ) @ V_m )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_r1 ) @ V_r1 ) ) @ V_m ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[842]) ).
thf(1363,plain,
( ( ! [V_add: $i,V_m: $i,V_mul: $i,V_a: $i,V_r1: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ V_m ) @ ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_m ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_r1 ) ) @ V_m ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[841]) ).
thf(1364,plain,
( ( ! [V_add: $i,V_mul: $i,V_a: $i,V_m: $i,V_r1: $i,V_pwr: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_m ) ) @ V_m )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_r1 ) ) @ V_m ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[840]) ).
thf(1365,plain,
( ( ! [V_add: $i,V_mul: $i,V_a: $i,V_m: $i,V_b: $i,V_pwr: $i,V_r0: $i,V_r1: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_add @ ( hAPP @ ( hAPP @ V_mul @ V_a ) @ V_m ) ) @ ( hAPP @ ( hAPP @ V_mul @ V_b ) @ V_m ) )
= ( hAPP @ ( hAPP @ V_mul @ ( hAPP @ ( hAPP @ V_add @ V_a ) @ V_b ) ) @ V_m ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[839]) ).
thf(1366,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)],[838]) ).
thf(1367,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)],[837]) ).
thf(1368,plain,
( ( ! [V_s: $i,V_t: $i,V_s_H: $i,V_t_H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s_H ) @ V_t_H ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_s ) @ V_s_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[836]) ).
thf(1369,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)],[835]) ).
thf(1370,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a )
= ( c_Orderings_Oord__class_Omax @ V_y @ V_x @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[834]) ).
thf(1371,plain,
( ( ! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( 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(1372,plain,
( ( ! [V_e: $i,V_t_H: $i,V_T: $i,V_t: $i] :
( ( c_Type_Otyping @ V_e @ V_t_H @ V_T )
| ~ ( c_Type_Otyping @ V_e @ V_t @ V_T )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_t ) @ V_t_H ) ) ) )
= $true ),
inference(copy,[status(thm)],[832]) ).
thf(1373,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)],[831]) ).
thf(1374,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)],[830]) ).
thf(1375,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)],[829]) ).
thf(1376,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)],[828]) ).
thf(1377,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)],[827]) ).
thf(1378,plain,
( ( ! [V_a: $i] :
( ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ V_a ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[826]) ).
thf(1379,plain,
( ( ! [V_x: $i,V_s: $i] :
( ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ V_x ) @ V_s @ V_x )
= ( c_Lambda_Oliftn @ V_x @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[825]) ).
thf(1380,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)],[824]) ).
thf(1381,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ T_a )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) ) @ V_z )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_x ) @ V_z ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_y ) @ V_z ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[823]) ).
thf(1382,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)],[822]) ).
thf(1383,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)],[821]) ).
thf(1384,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ V_z @ T_a )
= ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[820]) ).
thf(1385,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i,V_z: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omax @ V_y @ V_z @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omax @ V_y @ ( c_Orderings_Oord__class_Omax @ V_x @ V_z @ T_a ) @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[819]) ).
thf(1386,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)],[818]) ).
thf(1387,plain,
( ( ! [V_r: $i,T_a: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ T_a )
= ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[817]) ).
thf(1388,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)],[816]) ).
thf(1389,plain,
( ( ! [T_a: $i,V_x: $i,V_y: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a )
= ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[815]) ).
thf(1390,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)],[814]) ).
thf(1391,plain,
( ( ! [V_plus: $i,V_a: $i,V_zero: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_plus @ V_a ) @ V_zero )
= V_a )
| ~ ( c_OrderedGroup_Omonoid__add @ V_zero @ V_plus @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[813]) ).
thf(1392,plain,
( ( ! [V_plus: $i,V_zero: $i,V_a: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_plus @ V_zero ) @ V_a )
= V_a )
| ~ ( c_OrderedGroup_Omonoid__add @ V_zero @ V_plus @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[812]) ).
thf(1393,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ 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)],[811]) ).
thf(1394,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_m @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[810]) ).
thf(1395,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)],[809]) ).
thf(1396,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)],[808]) ).
thf(1397,plain,
( ( ! [V_a: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) )
| ( V_a
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[807]) ).
thf(1398,plain,
( ( ! [V_a: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[806]) ).
thf(1399,plain,
( ( ! [V_a: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( V_a
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[805]) ).
thf(1400,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)],[804]) ).
thf(1401,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)],[803]) ).
thf(1402,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)],[802]) ).
thf(1403,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)],[801]) ).
thf(1404,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)],[800]) ).
thf(1405,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)],[799]) ).
thf(1406,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)],[798]) ).
thf(1407,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)],[797]) ).
thf(1408,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)],[796]) ).
thf(1409,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)],[795]) ).
thf(1410,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)],[794]) ).
thf(1411,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)],[793]) ).
thf(1412,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)],[792]) ).
thf(1413,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)],[791]) ).
thf(1414,plain,
( ( ! [V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_t @ V_k )
= V_t ) )
= $true ),
inference(copy,[status(thm)],[790]) ).
thf(1415,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)],[789]) ).
thf(1416,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[788]) ).
thf(1417,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( V_m
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[787]) ).
thf(1418,plain,
( ( ! [V_x: $i,V_a: $i] :
( ( V_x
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ V_a ) )
| ( V_a
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[786]) ).
thf(1419,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n )
!= V_m )
| ( V_n
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[785]) ).
thf(1420,plain,
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[784]) ).
thf(1421,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)],[783]) ).
thf(1422,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)],[782]) ).
thf(1423,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)],[781]) ).
thf(1424,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)],[780]) ).
thf(1425,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)],[779]) ).
thf(1426,plain,
( ( ! [T_a: $i,V_z: $i,V_y: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_y @ T_a )
| ( c_HOL_Oord__class_Oless @ V_z @ V_x @ T_a )
| ~ ( c_HOL_Oord__class_Oless @ V_z @ ( c_Orderings_Oord__class_Omax @ V_x @ V_y @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[778]) ).
thf(1427,plain,
( ( ! [V_i: $i,V_s: $i,V_k: $i] :
( ( ( c_Lambda_Osubstn @ ( 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)],[777]) ).
thf(1428,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)],[776]) ).
thf(1429,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)],[775]) ).
thf(1430,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)],[774]) ).
thf(1431,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)],[773]) ).
thf(1432,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)],[772]) ).
thf(1433,plain,
( ( ! [T_a: $i] :
( ( c_Predicate_Oconversep @ ( c_fequal @ T_a ) @ T_a @ T_a )
= ( c_fequal @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[771]) ).
thf(1434,plain,
( ( ! [V_a: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[770]) ).
thf(1435,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)],[769]) ).
thf(1436,plain,
( ( ! [V_x: $i] :
~ ( c_HOL_Oord__class_Oless @ V_x @ V_x @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[768]) ).
thf(1437,plain,
( ( ! [V_n: $i] :
~ ( c_HOL_Oord__class_Oless @ V_n @ V_n @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[767]) ).
thf(1438,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)],[766]) ).
thf(1439,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)],[765]) ).
thf(1440,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)],[764]) ).
thf(1441,plain,
( ( ! [V_n: $i,V_i: $i,V_k: $i] :
( ( ( c_Lambda_Oliftn @ V_n @ ( c_Lambda_OdB_OVar @ V_i ) @ V_k )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_n ) ) )
| ( c_HOL_Oord__class_Oless @ V_i @ V_k @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[763]) ).
thf(1442,plain,
( ( ! [V_r: $i,V_i: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_r ) @ V_i ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ V_s ) @ V_i ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[762]) ).
thf(1443,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)],[761]) ).
thf(1444,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)],[760]) ).
thf(1445,plain,
( ( ! [V_plus: $i,V_a: $i,V_b: $i,V_c: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_plus @ ( hAPP @ ( hAPP @ V_plus @ V_a ) @ V_b ) ) @ V_c )
= ( hAPP @ ( hAPP @ V_plus @ V_a ) @ ( hAPP @ ( hAPP @ V_plus @ V_b ) @ V_c ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ V_plus @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[759]) ).
thf(1446,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)],[758]) ).
thf(1447,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)],[757]) ).
thf(1448,plain,
( ( ! [V_a: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( V_a
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[756]) ).
thf(1449,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)],[755]) ).
thf(1450,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)],[754]) ).
thf(1451,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)],[753]) ).
thf(1452,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)],[752]) ).
thf(1453,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)],[751]) ).
thf(1454,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)],[750]) ).
thf(1455,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)],[749]) ).
thf(1456,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)],[748]) ).
thf(1457,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)],[747]) ).
thf(1458,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Olinorder @ T_a )
| ( ( c_Orderings_Oord__class_Omax @ V_x @ V_x @ T_a )
= V_x ) ) )
= $true ),
inference(copy,[status(thm)],[746]) ).
thf(1459,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)],[745]) ).
thf(1460,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i,V_l: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_l ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_k @ V_l @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[744]) ).
thf(1461,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)],[743]) ).
thf(1462,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)],[742]) ).
thf(1463,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)],[741]) ).
thf(1464,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Olistsum @ V_xs @ T_a )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[740]) ).
thf(1465,plain,
( ( ! [V_a: $i] :
( ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ V_a ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( V_a
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[739]) ).
thf(1466,plain,
( ( ! [V_n: $i,V_m: $i,V_x: $i,T_a: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_n ) @ V_m ) @ V_x @ T_a )
= ( c_List_Oappend @ ( c_List_Oreplicate @ V_n @ V_x @ T_a ) @ ( c_List_Oreplicate @ V_m @ V_x @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[738]) ).
thf(1467,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)],[737]) ).
thf(1468,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)],[736]) ).
thf(1469,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)],[735]) ).
thf(1470,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)],[734]) ).
thf(1471,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)],[733]) ).
thf(1472,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)],[732]) ).
thf(1473,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OAbs @ V_dB ) @ T_a )
= ( hAPP @ ( hAPP @ V_f3 @ V_dB ) @ ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ V_dB @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[731]) ).
thf(1474,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ T_a )
| ( c_OrderedGroup_Osemigroup__add @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[730]) ).
thf(1475,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)],[729]) ).
thf(1476,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)],[728]) ).
thf(1477,plain,
( ( ! [V_f: $i,V_x: $i,V_xs: $i,T_b: $i,V_a: $i,T_a: $i] :
( ( c_List_Ofoldr @ V_f @ ( c_List_Olist_OCons @ V_x @ V_xs @ T_b ) @ V_a @ T_b @ T_a )
= ( hAPP @ ( hAPP @ V_f @ V_x ) @ ( c_List_Ofoldr @ V_f @ V_xs @ V_a @ T_b @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[727]) ).
thf(1478,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)],[726]) ).
thf(1479,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)],[725]) ).
thf(1480,plain,
( ( ! [V_r: $i,T_a: $i,T_b: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ V_r @ T_a @ T_b ) @ T_b @ T_a )
= V_r ) )
= $true ),
inference(copy,[status(thm)],[724]) ).
thf(1481,plain,
( ( ! [V_i: $i,V_j: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_j ) @ V_i @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[723]) ).
thf(1482,plain,
( ( ! [V_j: $i,V_i: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_i ) @ V_i @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[722]) ).
thf(1483,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)],[721]) ).
thf(1484,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)],[720]) ).
thf(1485,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)],[719]) ).
thf(1486,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)],[718]) ).
thf(1487,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)],[717]) ).
thf(1488,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)],[716]) ).
thf(1489,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)],[715]) ).
thf(1490,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)],[714]) ).
thf(1491,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)],[713]) ).
thf(1492,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)],[712]) ).
thf(1493,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)],[711]) ).
thf(1494,plain,
( ( ! [V_i: $i,V_k: $i,V_j: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_i ) @ V_k ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_j ) @ V_k ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_i @ V_j @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[710]) ).
thf(1495,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 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[709]) ).
thf(1496,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_m ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_k ) @ V_n ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[708]) ).
thf(1497,plain,
( ( ! [V_a: $i] :
( ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ V_a ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[707]) ).
thf(1498,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)],[706]) ).
thf(1499,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)],[705]) ).
thf(1500,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)],[704]) ).
thf(1501,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)],[703]) ).
thf(1502,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)],[702]) ).
thf(1503,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)],[701]) ).
thf(1504,plain,
( ( ! [T_a: $i,V_m: $i,V_n: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ T_a )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ V_n ) @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_m @ T_a ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ V_n @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[700]) ).
thf(1505,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)],[699]) ).
thf(1506,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)],[698]) ).
thf(1507,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)],[697]) ).
thf(1508,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)],[696]) ).
thf(1509,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)],[695]) ).
thf(1510,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)],[694]) ).
thf(1511,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)],[693]) ).
thf(1512,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)],[692]) ).
thf(1513,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)],[691]) ).
thf(1514,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)],[690]) ).
thf(1515,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)],[689]) ).
thf(1516,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[688]) ).
thf(1517,plain,
( ( ! [V_r: $i,T_a: $i,V_a: $i,V_c: $i,V_b: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_b ) @ V_c ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ V_r @ T_a ) @ V_a ) @ V_b ) ) ) )
= $true ),
inference(copy,[status(thm)],[687]) ).
thf(1518,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)],[686]) ).
thf(1519,plain,
( ( ! [V_r: $i,V_y: $i,T_a: $i,V_a: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_y @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_y ) @ V_a ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[685]) ).
thf(1520,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)],[684]) ).
thf(1521,plain,
( ( ! [V_r: $i,V_a: $i,T_a: $i,V_b: $i] :
( ( c_Wellfounded_Oaccp @ V_r @ V_a @ T_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ V_r @ V_a ) @ V_b ) )
| ~ ( c_Wellfounded_Oaccp @ V_r @ V_b @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[683]) ).
thf(1522,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)],[682]) ).
thf(1523,plain,
( ( ! [V_c: $i] :
( ( c_Nat_Osize__class_Osize @ V_c @ tc_String_Ochar )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[681]) ).
thf(1524,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)],[680]) ).
thf(1525,plain,
( ( ! [V_n: $i] :
( ( c_Orderings_Oord__class_Omax @ V_n @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= V_n ) )
= $true ),
inference(copy,[status(thm)],[679]) ).
thf(1526,plain,
( ( ! [V_n: $i] :
( ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat )
= V_n ) )
= $true ),
inference(copy,[status(thm)],[678]) ).
thf(1527,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)],[677]) ).
thf(1528,plain,
( ( ! [V_x: $i] :
( V_x
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[676]) ).
thf(1529,plain,
( ( ! [V_n: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ V_n )
= V_n ) )
= $true ),
inference(copy,[status(thm)],[675]) ).
thf(1530,plain,
( ( ! [V_m: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ V_m ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= V_m ) )
= $true ),
inference(copy,[status(thm)],[674]) ).
thf(1531,plain,
( ( ! [V_pwr: $i,V_x: $i,V_r1: $i,V_add: $i,V_mul: $i,V_r0: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_pwr @ V_x ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= V_r1 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ V_add @ V_mul @ V_pwr @ V_r0 @ V_r1 @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[673]) ).
thf(1532,plain,
( ( ! [T_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ 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 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[672]) ).
thf(1533,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)],[671]) ).
thf(1534,plain,
( ( ! [T_a: $i,V_a: $i,V_xs: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ T_a )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a @ V_xs @ T_a @ T_a )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_a ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ T_a ) @ V_xs @ ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a @ T_a ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[670]) ).
thf(1535,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)],[669]) ).
thf(1536,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)],[668]) ).
thf(1537,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)],[667]) ).
thf(1538,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)],[666]) ).
thf(1539,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)],[665]) ).
thf(1540,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)],[664]) ).
thf(1541,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_dB1: $i,V_dB2: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_dB1 ) @ V_dB2 ) @ T_a )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ V_f2 @ V_dB1 ) @ V_dB2 ) @ ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ V_dB1 @ T_a ) ) @ ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ V_dB2 @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[663]) ).
thf(1542,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)],[662]) ).
thf(1543,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)],[661]) ).
thf(1544,plain,
( ( ! [V_n: $i,V_s: $i,V_t: $i,V_k: $i] :
( ( c_Lambda_Oliftn @ V_n @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_s ) @ V_t ) @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ V_n @ V_s @ V_k ) ) @ ( c_Lambda_Oliftn @ V_n @ V_t @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[660]) ).
thf(1545,plain,
( ( ! [V_t: $i,V_u: $i,V_s: $i,V_k: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ V_t ) @ V_u ) @ V_s @ V_k )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ V_t @ V_s @ V_k ) ) @ ( c_Lambda_Osubstn @ V_u @ V_s @ V_k ) ) ) )
= $true ),
inference(copy,[status(thm)],[659]) ).
thf(1546,plain,
( ( ! [V_t: $i,V_s: $i,V_n: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ V_n )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ ( c_Lambda_Oliftn @ V_n @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ V_n ) ) )
= $true ),
inference(copy,[status(thm)],[658]) ).
thf(1547,plain,
( ( ! [V_r: $i,V_s: $i,V_ss: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( 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 ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_s @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( 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 ) @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[657]) ).
thf(1548,plain,
( ( ! [V_r: $i,V_ss: $i,V_s: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( 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_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ V_r ) @ V_s ) ) ) )
= $true ),
inference(copy,[status(thm)],[656]) ).
thf(1549,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)],[655]) ).
thf(1550,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)],[654]) ).
thf(1551,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)],[653]) ).
thf(1552,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)],[652]) ).
thf(1553,plain,
( ( ! [V_t: $i] :
( V_t
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2 @ V_t ) @ ( c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1 @ V_t ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(copy,[status(thm)],[651]) ).
thf(1554,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)],[650]) ).
thf(1555,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)],[649]) ).
thf(1556,plain,
( ( ! [V_plus: $i,V_x: $i,V_y: $i,V_zs: $i,T_a: $i] :
( ( ( c_List_Ofoldl @ V_plus @ ( hAPP @ ( hAPP @ V_plus @ V_x ) @ V_y ) @ V_zs @ T_a @ T_a )
= ( hAPP @ ( hAPP @ V_plus @ V_x ) @ ( c_List_Ofoldl @ V_plus @ V_y @ V_zs @ T_a @ T_a ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ V_plus @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[648]) ).
thf(1557,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)],[647]) ).
thf(1558,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)],[646]) ).
thf(1559,plain,
( ( ! [V_plus: $i,V_x: $i,V_zero: $i,V_zs: $i,T_a: $i] :
( ( ( hAPP @ ( hAPP @ V_plus @ V_x ) @ ( c_List_Ofoldl @ V_plus @ V_zero @ V_zs @ T_a @ T_a ) )
= ( c_List_Ofoldl @ V_plus @ V_x @ V_zs @ T_a @ T_a ) )
| ~ ( c_OrderedGroup_Omonoid__add @ V_zero @ V_plus @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[645]) ).
thf(1560,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)],[644]) ).
thf(1561,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)],[643]) ).
thf(1562,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)],[642]) ).
thf(1563,plain,
( ( ! [V_P: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ V_P @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ V_P ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ V_P ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ V_P @ V_t ) ) ) )
= $true ),
inference(copy,[status(thm)],[641]) ).
thf(1564,plain,
( ( ! [V_e: $i,V_ts: $i,V_T: $i,V_i: $i] :
( ( c_Type_Otypings @ V_e @ V_ts @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ V_T @ V_e @ V_i @ V_ts ) )
| ~ ( 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)],[640]) ).
thf(1565,plain,
( ( ! [V_P: $i,V_t: $i] :
( ( hBOOL @ ( hAPP @ V_P @ V_t ) )
| ( hBOOL @ ( hAPP @ V_P @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ V_P ) ) )
| ~ ( hBOOL @ ( hAPP @ V_P @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ V_P ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ V_P ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[639]) ).
thf(1566,plain,
( ( ! [V_e: $i,V_us: $i,V_T: $i,V_U: $i,V_i: $i,V_ts: $i,V_Ts: $i] :
( ( c_Type_Otypings @ V_e @ V_us @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ V_T @ V_U @ V_e @ V_us ) )
| ~ ( 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_Otypings @ V_e @ V_ts @ V_Ts )
| ~ ( c_Type_Otyping @ V_e @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ V_i ) @ V_ts @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_us @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ V_T ) ) )
= $true ),
inference(copy,[status(thm)],[638]) ).
thf(1567,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)],[637]) ).
thf(1568,plain,
( ( ! [V_a: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[636]) ).
thf(1569,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)],[635]) ).
thf(1570,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)],[634]) ).
thf(1571,plain,
( ( ! [V_a: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ V_a ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ V_a ) ) )
| ( V_a
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ V_a ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ V_a ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ V_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[633]) ).
thf(1572,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)],[632]) ).
thf(1573,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)],[631]) ).
thf(1574,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)],[630]) ).
thf(1575,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)],[629]) ).
thf(1576,plain,
( ( ! [V_f1: $i,V_f2: $i,V_f3: $i,V_nat: $i,T_a: $i] :
( ( c_Lambda_OdB_OdB__rec @ V_f1 @ V_f2 @ V_f3 @ ( c_Lambda_OdB_OVar @ V_nat ) @ T_a )
= ( hAPP @ V_f1 @ V_nat ) ) )
= $true ),
inference(copy,[status(thm)],[628]) ).
thf(1577,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)],[627]) ).
thf(1578,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)],[626]) ).
thf(1579,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)],[625]) ).
thf(1580,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)],[624]) ).
thf(1581,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)],[623]) ).
thf(1582,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)],[622]) ).
thf(1583,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)],[621]) ).
thf(1584,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)],[620]) ).
thf(1585,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)],[619]) ).
thf(1586,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)],[618]) ).
thf(1587,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)],[617]) ).
thf(1588,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)],[616]) ).
thf(1589,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)],[615]) ).
thf(1590,plain,
( ( ! [V_t: $i,V_s: $i] :
( ( c_Lambda_Osubstn @ V_t @ V_s @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ V_t ) @ V_s ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[614]) ).
thf(1591,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)],[613]) ).
thf(1592,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)],[612]) ).
thf(1593,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)],[611]) ).
thf(1594,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)],[610]) ).
thf(1595,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)],[609]) ).
thf(1596,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)],[608]) ).
thf(1597,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)],[607]) ).
thf(1598,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)],[606]) ).
thf(1599,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)],[605]) ).
thf(1600,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)],[604]) ).
thf(1601,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)],[603]) ).
thf(1602,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)],[602]) ).
thf(1603,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)],[601]) ).
thf(1604,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)],[600]) ).
thf(1605,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)],[599]) ).
thf(1606,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)],[598]) ).
thf(1607,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)],[597]) ).
thf(1608,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)],[596]) ).
thf(1609,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)],[595]) ).
thf(1610,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)],[594]) ).
thf(1611,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)],[593]) ).
thf(1612,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)],[592]) ).
thf(1613,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)],[591]) ).
thf(1614,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)],[590]) ).
thf(1615,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)],[589]) ).
thf(1616,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)],[588]) ).
thf(1617,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)],[587]) ).
thf(1618,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)],[586]) ).
thf(1619,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)],[585]) ).
thf(1620,plain,
( ( ! [V_n: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ V_n ) ) ) )
= $true ),
inference(copy,[status(thm)],[584]) ).
thf(1621,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)],[583]) ).
thf(1622,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)],[582]) ).
thf(1623,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)],[581]) ).
thf(1624,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)],[580]) ).
thf(1625,plain,
( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[579]) ).
thf(1626,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat )
= $true ),
inference(copy,[status(thm)],[578]) ).
thf(1627,plain,
( ( class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[577]) ).
thf(1628,plain,
( ( class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[576]) ).
thf(1629,plain,
( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[575]) ).
thf(1630,plain,
( ( class_OrderedGroup_Ocancel__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[574]) ).
thf(1631,plain,
( ( class_Ring__and__Field_Ono__zero__divisors @ tc_nat )
= $true ),
inference(copy,[status(thm)],[573]) ).
thf(1632,plain,
( ( class_Ring__and__Field_Oordered__semidom @ tc_nat )
= $true ),
inference(copy,[status(thm)],[572]) ).
thf(1633,plain,
( ( class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[571]) ).
thf(1634,plain,
( ( class_OrderedGroup_Oab__semigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[570]) ).
thf(1635,plain,
( ( class_OrderedGroup_Ocomm__monoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[569]) ).
thf(1636,plain,
( ( class_Ring__and__Field_Ozero__neq__one @ tc_nat )
= $true ),
inference(copy,[status(thm)],[568]) ).
thf(1637,plain,
( ( class_OrderedGroup_Osemigroup__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[567]) ).
thf(1638,plain,
( ( class_Ring__and__Field_Osemiring__1 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[566]) ).
thf(1639,plain,
( ( class_Ring__and__Field_Osemiring__0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[565]) ).
thf(1640,plain,
( ( class_Ring__and__Field_Omult__zero @ tc_nat )
= $true ),
inference(copy,[status(thm)],[564]) ).
thf(1641,plain,
( ( class_OrderedGroup_Omonoid__mult @ tc_nat )
= $true ),
inference(copy,[status(thm)],[563]) ).
thf(1642,plain,
( ( class_OrderedGroup_Omonoid__add @ tc_nat )
= $true ),
inference(copy,[status(thm)],[562]) ).
thf(1643,plain,
( ( class_Nat_Osemiring__char__0 @ tc_nat )
= $true ),
inference(copy,[status(thm)],[561]) ).
thf(1644,plain,
( ( class_Orderings_Opreorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[560]) ).
thf(1645,plain,
( ( class_Orderings_Olinorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[559]) ).
thf(1646,plain,
( ( class_Orderings_Oorder @ tc_nat )
= $true ),
inference(copy,[status(thm)],[558]) ).
thf(1647,plain,
( ( class_Power_Opower @ tc_nat )
= $true ),
inference(copy,[status(thm)],[557]) ).
thf(1648,plain,
( ( class_Orderings_Opreorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[556]) ).
thf(1649,plain,
( ( class_Orderings_Oorder @ tc_bool )
= $true ),
inference(copy,[status(thm)],[555]) ).
thf(1650,plain,
( ( ! [T_a: $i,V_x: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_x ) @ V_x ) ) )
= $true ),
inference(copy,[status(thm)],[554]) ).
thf(1651,plain,
( ( ! [V_X: $i,V_Y: $i,T_a: $i] :
( ( V_X = V_Y )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ T_a ) @ V_X ) @ V_Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[553]) ).
thf(1652,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[1102]) ).
thf(1653,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OVar @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1611]) ).
thf(1654,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)],[1498]) ).
thf(1655,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)],[1253]) ).
thf(1656,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)],[1619]) ).
thf(1657,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)],[1324]) ).
thf(1658,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)],[1616]) ).
thf(1659,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)],[1331]) ).
thf(1660,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( class_Orderings_Olinorder @ SX0 )
| ( ( c_Orderings_Oord__class_Omax @ SX1 @ SX2 @ SX0 )
!= SX2 )
| ( c_lessequals @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1193]) ).
thf(1661,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)],[1507]) ).
thf(1662,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)],[1402]) ).
thf(1663,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)],[1486]) ).
thf(1664,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)],[1461]) ).
thf(1665,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1418]) ).
thf(1666,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1416]) ).
thf(1667,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)],[1118]) ).
thf(1668,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)],[1281]) ).
thf(1669,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)],[1594]) ).
thf(1670,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)],[1130]) ).
thf(1671,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)],[1613]) ).
thf(1672,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= SX0 )
| ( SX1
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1419]) ).
thf(1673,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)],[1599]) ).
thf(1674,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)],[1606]) ).
thf(1675,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)],[1499]) ).
thf(1676,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)],[1527]) ).
thf(1677,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)],[1536]) ).
thf(1678,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)],[1403]) ).
thf(1679,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)],[1617]) ).
thf(1680,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)],[1484]) ).
thf(1681,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)],[1604]) ).
thf(1682,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)],[1400]) ).
thf(1683,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)],[1621]) ).
thf(1684,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1430]) ).
thf(1685,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)],[1283]) ).
thf(1686,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX2 ) @ SX1 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1229]) ).
thf(1687,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)],[1313]) ).
thf(1688,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)],[1312]) ).
thf(1689,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)],[1330]) ).
thf(1690,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)],[1550]) ).
thf(1691,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)],[1554]) ).
thf(1692,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1323]) ).
thf(1693,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)],[1206]) ).
thf(1694,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)],[1595]) ).
thf(1695,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)],[1401]) ).
thf(1696,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)],[1327]) ).
thf(1697,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Lambda_OdB_OAbs @ SX0 )
!= ( c_Lambda_OdB_OVar @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1572]) ).
thf(1698,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)],[1587]) ).
thf(1699,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)],[1475]) ).
thf(1700,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)],[1129]) ).
thf(1701,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)],[1471]) ).
thf(1702,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)],[1428]) ).
thf(1703,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX2 ) @ SX3 ) )
| ~ ( c_HOL_Oord__class_Oless @ SX2 @ SX1 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SX0 @ SX3 @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1308]) ).
thf(1704,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)],[1326]) ).
thf(1705,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)],[1596]) ).
thf(1706,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)],[1535]) ).
thf(1707,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)],[1112]) ).
thf(1708,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)],[1325]) ).
thf(1709,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)],[1607]) ).
thf(1710,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)],[1429]) ).
thf(1711,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)],[1622]) ).
thf(1712,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)],[1508]) ).
thf(1713,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)],[1432]) ).
thf(1714,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)],[1505]) ).
thf(1715,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)],[1552]) ).
thf(1716,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)],[1597]) ).
thf(1717,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)],[1618]) ).
thf(1718,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)],[1205]) ).
thf(1719,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 )
!= SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[1376]) ).
thf(1720,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SX0
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1417]) ).
thf(1721,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)],[1485]) ).
thf(1722,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( c_Lambda_OdB_OVar @ SX0 )
!= ( c_Lambda_OdB_OAbs @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1577]) ).
thf(1723,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)],[1431]) ).
thf(1724,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)],[1483]) ).
thf(1725,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)],[1282]) ).
thf(1726,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX1 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SX0 ) @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1230]) ).
thf(1727,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)],[1612]) ).
thf(1728,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( SX0
!= ( c_List_Olist_OCons @ SX1 @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1377]) ).
thf(1729,plain,
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( 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 ) ) @ ( c_Lambda_OdB_OVar @ v_i ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1730,plain,
! [SV1: $i] :
( ( ! [SY1829: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV1 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1829 @ SV1 ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1731,plain,
! [SV2: $i] :
( ( ! [SY1830: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV2 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY1830 @ SV2 ) @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1732,plain,
! [SV3: $i] :
( ( ! [SY1831: $i,SY1832: $i,SY1833: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV3 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SY1831 @ SY1832 @ SV3 ) @ ( c_Power_Opower__class_Opower @ SY1833 @ SY1832 @ SV3 ) @ SV3 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SY1831 @ SV3 )
| ~ ( c_lessequals @ SY1831 @ SY1833 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1733,plain,
! [SV4: $i] :
( ( ! [SY1834: $i,SY1835: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV4 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV4 ) @ ( c_Power_Opower__class_Opower @ SY1834 @ SY1835 @ SV4 ) @ SV4 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV4 ) @ SY1834 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1734,plain,
! [SV5: $i] :
( ( ! [SY1836: $i] :
( ~ ( class_Power_Opower @ SV5 )
| ( ( c_Power_Opower__class_Opower @ SY1836 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV5 )
= ( c_HOL_Oone__class_Oone @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1735,plain,
! [SV6: $i] :
( ( ! [SY1837: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV6 )
| ( ( c_Power_Opower__class_Opower @ SY1837 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV6 )
= ( c_HOL_Oone__class_Oone @ SV6 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1736,plain,
! [SV7: $i] :
( ( ! [SY1838: $i,SY1839: $i,SY1840: $i,SY1841: $i,SY1842: $i] :
( ~ ( c_Type_Otyping @ SV7 @ SY1838 @ SY1839 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV7 @ SY1840 @ SY1839 @ tc_Type_Otype ) @ SY1841 @ SY1842 )
| ( c_Type_Otyping @ SV7 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY1841 ) @ SY1838 ) @ SY1840 ) @ SY1842 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1737,plain,
! [SV8: $i] :
( ( ! [SY1843: $i,SY1844: $i,SY1845: $i,SY1846: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV8 @ SY1843 @ SY1844 @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY1845 ) @ SY1843 ) @ SY1846 )
| ~ ( c_Type_Otyping @ SV8 @ SY1845 @ SY1846 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1738,plain,
! [SV9: $i] :
( ( ! [SY1847: $i,SY1848: $i,SY1849: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV9 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY1847 @ SY1848 @ SV9 ) @ ( c_Power_Opower__class_Opower @ SY1847 @ SY1849 @ SV9 ) @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SY1847 @ ( c_HOL_Oone__class_Oone @ SV9 ) @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SY1847 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SY1849 @ SY1848 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1739,plain,
! [SV10: $i] :
( ( ! [SY1850: $i,SY1851: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV10 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV10 ) @ ( c_Power_Opower__class_Opower @ SY1850 @ SY1851 @ SV10 ) @ SV10 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY1851 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV10 ) @ SY1850 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1740,plain,
! [SV11: $i] :
( ( ! [SY1852: $i,SY1853: $i,SY1854: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV11 ) @ SY1852 ) @ SY1853 ) ) @ SY1854 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV11 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1854 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY1852 ) @ SY1854 ) ) @ SY1853 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1853 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1854 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1741,plain,
! [SV12: $i] :
( ( ! [SY1855: $i,SY1856: $i,SY1857: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV12 ) @ SY1855 ) @ SY1856 ) ) @ SY1857 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV12 ) @ SY1857 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY1855 ) @ SY1857 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1856 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1857 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY1856 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1742,plain,
! [SV13: $i] :
( ( ! [SY1858: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV13 ) ) @ SY1858 )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV13 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ( c_HOL_Oord__class_Oless @ SV13 @ SY1858 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1743,plain,
! [SV14: $i] :
( ( ! [SY1859: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV14 )
| ( c_HOL_Oord__class_Oless @ SY1859 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV14 ) @ SY1859 ) @ ( c_HOL_Oone__class_Oone @ SV14 ) ) @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1744,plain,
! [SV15: $i] :
( ( ! [SY1860: $i,SY1861: $i,SY1862: $i,SY1863: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV15 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SY1860 ) @ SY1861 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SY1862 ) @ SY1863 ) @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SY1861 @ SY1863 @ SV15 )
| ~ ( c_lessequals @ SY1860 @ SY1862 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1745,plain,
! [SV16: $i] :
( ( ! [SY1864: $i,SY1865: $i,SY1866: $i,SY1867: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV16 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SY1864 ) @ SY1865 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SY1866 ) @ SY1867 ) @ SV16 )
| ~ ( c_lessequals @ SY1865 @ SY1867 @ SV16 )
| ~ ( c_HOL_Oord__class_Oless @ SY1864 @ SY1866 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1746,plain,
! [SV17: $i] :
( ( ! [SY1868: $i,SY1869: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV17 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV17 ) @ SY1868 ) @ SY1869 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
| ~ ( c_lessequals @ SY1869 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
| ~ ( c_lessequals @ SY1868 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1747,plain,
! [SV18: $i] :
( ( ! [SY1870: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV18 )
| ( c_lessequals @ SY1870 @ ( c_HOL_Ozero__class_Ozero @ SV18 ) @ SV18 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV18 ) @ SY1870 ) @ SY1870 ) @ ( c_HOL_Ozero__class_Ozero @ SV18 ) @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1748,plain,
! [SV19: $i] :
( ( ! [SY1871: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV19 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV19 ) @ SY1871 ) @ SY1871 ) @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 )
| ~ ( c_lessequals @ SY1871 @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1749,plain,
! [SV20: $i] :
( ( ! [SY1872: $i,SY1873: $i,SY1874: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV20 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV20 )
| ( c_lessequals @ SY1872 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV20 ) @ SY1873 ) @ SY1874 ) @ SV20 )
| ~ ( c_lessequals @ SY1872 @ SY1873 @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SY1874 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1750,plain,
! [SV21: $i] :
( ( ! [SY1875: $i,SY1876: $i,SY1877: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV21 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV21 )
| ( c_lessequals @ SY1875 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SY1876 ) @ SY1877 ) @ SV21 )
| ~ ( c_lessequals @ SY1875 @ SY1877 @ SV21 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ SY1876 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1751,plain,
! [SV22: $i] :
( ( ! [SY1878: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV22 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV22 ) @ SY1878 @ SV22 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV22 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SY1878 ) @ SY1878 ) @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1752,plain,
! [SV23: $i] :
( ( ! [SY1879: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV23 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV23 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV23 ) @ SY1879 ) @ SY1879 ) @ SV23 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV23 ) @ SY1879 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1753,plain,
! [SV24: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV24 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ SV24 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ SV24 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) )
= ( c_HOL_Ozero__class_Ozero @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1754,plain,
! [SV25: $i] :
( ( ! [SY1880: $i,SY1881: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV25 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SY1880 ) @ SY1881 ) @ SV25 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SY1881 @ SV25 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SY1880 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1755,plain,
! [SV26: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV26 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ ( c_HOL_Oone__class_Oone @ SV26 ) @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1756,plain,
! [SV27: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV27 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV27 ) @ ( c_HOL_Ozero__class_Ozero @ SV27 ) @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1757,plain,
! [SV28: $i] :
( ( ! [SY1882: $i,SY1883: $i] :
( ~ ( class_Orderings_Olinorder @ SV28 )
| ( c_lessequals @ SY1882 @ SY1883 @ SV28 )
| ( c_lessequals @ SY1883 @ SY1882 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1758,plain,
! [SV29: $i] :
( ( ! [SY1884: $i,SY1885: $i] :
( ~ ( class_Orderings_Olinorder @ SV29 )
| ( SY1884 = SY1885 )
| ( c_HOL_Oord__class_Oless @ SY1884 @ SY1885 @ SV29 )
| ~ ( c_lessequals @ SY1884 @ SY1885 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1759,plain,
! [SV30: $i] :
( ( ! [SY1886: $i,SY1887: $i] :
( ~ ( class_Orderings_Olinorder @ SV30 )
| ( SY1886 = SY1887 )
| ~ ( c_lessequals @ SY1886 @ SY1887 @ SV30 )
| ( c_HOL_Oord__class_Oless @ SY1886 @ SY1887 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1760,plain,
! [SV31: $i] :
( ( ! [SY1888: $i,SY1889: $i] :
( ~ ( class_Orderings_Oorder @ SV31 )
| ( c_HOL_Oord__class_Oless @ SY1888 @ SY1889 @ SV31 )
| ~ ( c_lessequals @ SY1888 @ SY1889 @ SV31 )
| ( SY1888 = SY1889 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1761,plain,
! [SV32: $i] :
( ( ! [SY1890: $i,SY1891: $i] :
( ~ ( class_Orderings_Oorder @ SV32 )
| ( c_HOL_Oord__class_Oless @ SY1890 @ SY1891 @ SV32 )
| ( SY1890 = SY1891 )
| ~ ( c_lessequals @ SY1890 @ SY1891 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1762,plain,
! [SV33: $i] :
( ( ! [SY1892: $i,SY1893: $i] :
( ~ ( class_Orderings_Oorder @ SV33 )
| ( c_HOL_Oord__class_Oless @ SY1892 @ SY1893 @ SV33 )
| ( SY1892 = SY1893 )
| ~ ( c_lessequals @ SY1892 @ SY1893 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1763,plain,
! [SV34: $i] :
( ( ! [SY1894: $i,SY1895: $i] :
( ~ ( class_Orderings_Oorder @ SV34 )
| ( SY1894 = SY1895 )
| ( c_HOL_Oord__class_Oless @ SY1894 @ SY1895 @ SV34 )
| ~ ( c_lessequals @ SY1894 @ SY1895 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1764,plain,
! [SV35: $i] :
( ( ! [SY1896: $i,SY1897: $i] :
( ~ ( class_Orderings_Oorder @ SV35 )
| ( c_HOL_Oord__class_Oless @ SY1896 @ SY1897 @ SV35 )
| ~ ( c_lessequals @ SY1896 @ SY1897 @ SV35 )
| ( SY1897 = SY1896 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1765,plain,
! [SV36: $i] :
( ( ! [SY1898: $i,SY1899: $i] :
( ~ ( class_Orderings_Oorder @ SV36 )
| ( c_HOL_Oord__class_Oless @ SY1898 @ SY1899 @ SV36 )
| ( SY1899 = SY1898 )
| ~ ( c_lessequals @ SY1898 @ SY1899 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1766,plain,
! [SV37: $i] :
( ( ! [SY1900: $i,SY1901: $i,SY1902: $i,SY1903: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV37 )
| ( c_lessequals @ SY1900 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SY1901 ) @ SY1902 ) @ SV37 )
| ~ ( c_lessequals @ SY1903 @ SY1902 @ SV37 )
| ~ ( c_lessequals @ SY1900 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SY1901 ) @ SY1903 ) @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1767,plain,
! [SV38: $i] :
( ( ! [SY1904: $i,SY1905: $i,SY1906: $i] :
( ~ ( class_Orderings_Opreorder @ SV38 )
| ( c_HOL_Oord__class_Oless @ SY1904 @ SY1905 @ SV38 )
| ~ ( c_lessequals @ SY1906 @ SY1905 @ SV38 )
| ~ ( c_HOL_Oord__class_Oless @ SY1904 @ SY1906 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1768,plain,
! [SV39: $i] :
( ( ! [SY1907: $i,SY1908: $i,SY1909: $i] :
( ~ ( class_Orderings_Opreorder @ SV39 )
| ( c_HOL_Oord__class_Oless @ SY1907 @ SY1908 @ SV39 )
| ~ ( c_HOL_Oord__class_Oless @ SY1909 @ SY1908 @ SV39 )
| ~ ( c_lessequals @ SY1907 @ SY1909 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1769,plain,
! [SV40: $i] :
( ( ! [SY1910: $i] :
( ~ ( class_Orderings_Opreorder @ SV40 )
| ( c_lessequals @ SY1910 @ SY1910 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1770,plain,
! [SV41: $i] :
( ( ! [SY1911: $i] :
( ~ ( class_Orderings_Oorder @ SV41 )
| ( c_lessequals @ SY1911 @ SY1911 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1771,plain,
! [SV42: $i] :
( ( ! [SY1912: $i,SY1913: $i,SY1914: $i] :
( ~ ( class_Orderings_Opreorder @ SV42 )
| ( c_lessequals @ SY1912 @ SY1913 @ SV42 )
| ~ ( c_lessequals @ SY1914 @ SY1913 @ SV42 )
| ~ ( c_lessequals @ SY1912 @ SY1914 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1772,plain,
! [SV43: $i] :
( ( ! [SY1915: $i,SY1916: $i,SY1917: $i] :
( ~ ( class_Orderings_Oorder @ SV43 )
| ( c_HOL_Oord__class_Oless @ SY1915 @ SY1916 @ SV43 )
| ~ ( c_HOL_Oord__class_Oless @ SY1915 @ SY1917 @ SV43 )
| ~ ( c_lessequals @ SY1917 @ SY1916 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1773,plain,
! [SV44: $i] :
( ( ! [SY1918: $i,SY1919: $i,SY1920: $i] :
( ~ ( class_Orderings_Oorder @ SV44 )
| ( c_HOL_Oord__class_Oless @ SY1918 @ SY1919 @ SV44 )
| ~ ( c_lessequals @ SY1918 @ SY1920 @ SV44 )
| ~ ( c_HOL_Oord__class_Oless @ SY1920 @ SY1919 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1774,plain,
! [SV45: $i] :
( ( ! [SY1921: $i,SY1922: $i,SY1923: $i] :
( ~ ( class_Orderings_Oorder @ SV45 )
| ( c_lessequals @ SY1921 @ SY1922 @ SV45 )
| ~ ( c_lessequals @ SY1921 @ SY1923 @ SV45 )
| ~ ( c_lessequals @ SY1923 @ SY1922 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1775,plain,
! [SV46: $i] :
( ( ! [SY1924: $i,SY1925: $i,SY1926: $i,SY1927: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV46 @ SY1924 @ SY1925 @ SY1926 ) @ SY1927 )
= ( hAPP @ SV46 @ SY1927 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY1927 @ SY1924 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1776,plain,
! [SV47: $i] :
( ( ! [SY1928: $i,SY1929: $i,SY1930: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV47 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ SY1928 ) @ SY1929 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ SY1928 ) @ SY1930 ) @ SV47 )
| ~ ( c_lessequals @ SY1929 @ SY1930 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1777,plain,
! [SV48: $i] :
( ( ! [SY1931: $i,SY1932: $i,SY1933: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV48 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV48 ) @ SY1931 ) @ SY1932 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV48 ) @ SY1933 ) @ SY1932 ) @ SV48 )
| ~ ( c_lessequals @ SY1931 @ SY1933 @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1778,plain,
! [SV49: $i] :
( ( ! [SY1934: $i,SY1935: $i,SY1936: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV49 )
| ( c_lessequals @ SY1934 @ SY1935 @ SV49 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SY1936 ) @ SY1934 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SY1936 ) @ SY1935 ) @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1779,plain,
! [SV50: $i] :
( ( ! [SY1937: $i,SY1938: $i,SY1939: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SY1937 ) @ SY1938 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SY1937 ) @ SY1939 ) @ SV50 )
| ~ ( c_lessequals @ SY1938 @ SY1939 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1780,plain,
! [SV51: $i] :
( ( ! [SY1940: $i,SY1941: $i,SY1942: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV51 )
| ( c_lessequals @ SY1940 @ SY1941 @ SV51 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV51 ) @ SY1940 ) @ SY1942 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV51 ) @ SY1941 ) @ SY1942 ) @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1781,plain,
! [SV52: $i] :
( ( ! [SY1943: $i,SY1944: $i,SY1945: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV52 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SY1943 ) @ SY1944 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SY1945 ) @ SY1944 ) @ SV52 )
| ~ ( c_lessequals @ SY1943 @ SY1945 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1782,plain,
! [SV53: $i] :
( ( ! [SY1946: $i,SY1947: $i] :
( ~ ( class_Orderings_Opreorder @ SV53 )
| ( c_lessequals @ SY1946 @ SY1947 @ SV53 )
| ~ ( c_HOL_Oord__class_Oless @ SY1946 @ SY1947 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1783,plain,
! [SV54: $i] :
( ( ! [SY1948: $i,SY1949: $i] :
( ~ ( class_Orderings_Oorder @ SV54 )
| ( c_lessequals @ SY1948 @ SY1949 @ SV54 )
| ~ ( c_HOL_Oord__class_Oless @ SY1948 @ SY1949 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1784,plain,
! [SV55: $i] :
( ( ! [SY1950: $i,SY1951: $i] :
( ~ ( class_Orderings_Oorder @ SV55 )
| ( SY1950 = SY1951 )
| ~ ( c_lessequals @ SY1950 @ SY1951 @ SV55 )
| ~ ( c_lessequals @ SY1951 @ SY1950 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1785,plain,
! [SV56: $i] :
( ( ! [SY1952: $i,SY1953: $i] :
( ~ ( class_Orderings_Oorder @ SV56 )
| ( SY1952 = SY1953 )
| ~ ( c_lessequals @ SY1953 @ SY1952 @ SV56 )
| ~ ( c_lessequals @ SY1952 @ SY1953 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1167]) ).
thf(1786,plain,
! [SV57: $i] :
( ( ! [SY1954: $i,SY1955: $i] :
( ~ ( class_Orderings_Oorder @ SV57 )
| ( SY1954 = SY1955 )
| ~ ( c_lessequals @ SY1955 @ SY1954 @ SV57 )
| ~ ( c_lessequals @ SY1954 @ SY1955 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1787,plain,
! [SV58: $i] :
( ( ! [SY1956: $i,SY1957: $i,SY1958: $i,SY1959: $i,SY1960: $i,SY1961: $i] :
( ( ( hAPP @ ( hAPP @ SV58 @ SY1956 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= SY1956 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY1957 @ SY1958 @ SV58 @ SY1959 @ SY1960 @ SY1961 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1788,plain,
! [SV59: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV59 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1789,plain,
! [SV60: $i] :
( ( ! [SY1962: $i,SY1963: $i] :
( ~ ( class_Orderings_Opreorder @ SV60 )
| ( c_HOL_Oord__class_Oless @ SY1962 @ SY1963 @ SV60 )
| ( c_lessequals @ SY1963 @ SY1962 @ SV60 )
| ~ ( c_lessequals @ SY1962 @ SY1963 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1790,plain,
! [SV61: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV61 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ ( c_HOL_Oone__class_Oone @ SV61 ) @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1791,plain,
! [SV62: $i] :
( ( ! [SY1964: $i,SY1965: $i,SY1966: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV62 @ SY1964 @ SY1965 @ SY1966 ) @ SY1964 )
= SY1965 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1173]) ).
thf(1792,plain,
! [SV63: $i] :
( ( ! [SY1967: $i,SY1968: $i,SY1969: $i] :
( ~ ( class_Orderings_Olinorder @ SV63 )
| ( c_lessequals @ SY1967 @ SY1968 @ SV63 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY1967 @ SY1969 @ SV63 ) @ SY1968 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1793,plain,
! [SV64: $i] :
( ( ! [SY1970: $i,SY1971: $i,SY1972: $i] :
( ~ ( class_Orderings_Olinorder @ SV64 )
| ( c_lessequals @ SY1970 @ SY1971 @ SV64 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY1972 @ SY1970 @ SV64 ) @ SY1971 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1794,plain,
! [SV65: $i] :
( ( ! [SY1973: $i,SY1974: $i,SY1975: $i] :
( ~ ( class_Orderings_Olinorder @ SV65 )
| ( c_lessequals @ SY1973 @ ( c_Orderings_Oord__class_Omax @ SY1974 @ SY1975 @ SV65 ) @ SV65 )
| ~ ( c_lessequals @ SY1973 @ SY1974 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1795,plain,
! [SV66: $i] :
( ( ! [SY1976: $i,SY1977: $i,SY1978: $i] :
( ~ ( class_Orderings_Olinorder @ SV66 )
| ( c_lessequals @ SY1976 @ ( c_Orderings_Oord__class_Omax @ SY1977 @ SY1978 @ SV66 ) @ SV66 )
| ~ ( c_lessequals @ SY1976 @ SY1978 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1796,plain,
! [SV67: $i] :
( ( ! [SY1979: $i,SY1980: $i,SY1981: $i] :
( ~ ( class_Orderings_Olinorder @ SV67 )
| ( c_lessequals @ SY1979 @ ( c_Orderings_Oord__class_Omax @ SY1980 @ SY1981 @ SV67 ) @ SV67 )
| ~ ( c_lessequals @ SY1979 @ SY1980 @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1797,plain,
! [SV68: $i] :
( ( ! [SY1982: $i,SY1983: $i,SY1984: $i] :
( ~ ( class_Orderings_Olinorder @ SV68 )
| ( c_lessequals @ SY1982 @ ( c_Orderings_Oord__class_Omax @ SY1983 @ SY1984 @ SV68 ) @ SV68 )
| ~ ( c_lessequals @ SY1982 @ SY1984 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1798,plain,
! [SV69: $i] :
( ( ! [SY1985: $i,SY1986: $i,SY1987: $i] :
( ~ ( class_Orderings_Olinorder @ SV69 )
| ( c_lessequals @ SY1985 @ SY1986 @ SV69 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY1985 @ SY1987 @ SV69 ) @ SY1986 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1180]) ).
thf(1799,plain,
! [SV70: $i] :
( ( ! [SY1988: $i,SY1989: $i,SY1990: $i] :
( ~ ( class_Orderings_Olinorder @ SV70 )
| ( c_lessequals @ SY1988 @ SY1989 @ SV70 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY1990 @ SY1988 @ SV70 ) @ SY1989 @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1800,plain,
! [SV71: $i] :
( ( ! [SY1991: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV71 )
| ( ( c_Power_Opower__class_Opower @ SY1991 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV71 )
= SY1991 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1801,plain,
! [SV72: $i] :
( ( ! [SY1992: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV72 )
| ( ( c_Power_Opower__class_Opower @ SY1992 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV72 )
= SY1992 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1802,plain,
! [SV73: $i] :
( ( ! [SY1993: $i,SY1994: $i,SY1995: $i] :
( ~ ( class_Orderings_Olinorder @ SV73 )
| ( c_lessequals @ SY1993 @ SY1994 @ SV73 )
| ( c_lessequals @ SY1993 @ SY1995 @ SV73 )
| ~ ( c_lessequals @ SY1993 @ ( c_Orderings_Oord__class_Omax @ SY1995 @ SY1994 @ SV73 ) @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1803,plain,
! [SV74: $i] :
( ( ! [SY1996: $i,SY1997: $i] :
( ~ ( class_Orderings_Olinorder @ SV74 )
| ( c_lessequals @ SY1996 @ ( c_Orderings_Oord__class_Omax @ SY1997 @ SY1996 @ SV74 ) @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1804,plain,
! [SV75: $i] :
( ( ! [SY1998: $i,SY1999: $i] :
( ~ ( class_Orderings_Olinorder @ SV75 )
| ( c_lessequals @ SY1998 @ ( c_Orderings_Oord__class_Omax @ SY1998 @ SY1999 @ SV75 ) @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1805,plain,
! [SV76: $i] :
( ( ! [SY2000: $i,SY2001: $i,SY2002: $i] :
( ~ ( class_Orderings_Olinorder @ SV76 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY2000 @ SY2001 @ SV76 ) @ SY2002 @ SV76 )
| ~ ( c_lessequals @ SY2001 @ SY2002 @ SV76 )
| ~ ( c_lessequals @ SY2000 @ SY2002 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1187]) ).
thf(1806,plain,
! [SV77: $i] :
( ( ! [SY2003: $i,SY2004: $i,SY2005: $i] :
( ~ ( class_Orderings_Olinorder @ SV77 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY2003 @ SY2004 @ SV77 ) @ SY2005 @ SV77 )
| ~ ( c_lessequals @ SY2004 @ SY2005 @ SV77 )
| ~ ( c_lessequals @ SY2003 @ SY2005 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1807,plain,
! [SV78: $i] :
( ( ! [SY2006: $i,SY2007: $i,SY2008: $i] :
( ~ ( class_Orderings_Olinorder @ SV78 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY2006 @ SY2007 @ SV78 ) @ SY2008 @ SV78 )
| ~ ( c_lessequals @ SY2007 @ SY2008 @ SV78 )
| ~ ( c_lessequals @ SY2006 @ SY2008 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1808,plain,
! [SV79: $i] :
( ( ! [SY2009: $i,SY2010: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV79 )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV79 ) @ ( c_Power_Opower__class_Opower @ SY2009 @ SY2010 @ SV79 ) @ SV79 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV79 ) @ SY2009 @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1809,plain,
! [SV80: $i] :
( ( ! [SY2011: $i,SY2012: $i,SY2013: $i,SY2014: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV80 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SY2011 ) @ SY2012 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SY2013 ) @ SY2014 ) @ SV80 )
| ~ ( c_lessequals @ SY2012 @ SY2014 @ SV80 )
| ~ ( c_lessequals @ SY2011 @ SY2013 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1810,plain,
! [SV81: $i] :
( ( ! [SY2015: $i,SY2016: $i] :
( ~ ( class_Orderings_Olinorder @ SV81 )
| ( ( c_Orderings_Oord__class_Omax @ SY2015 @ SY2016 @ SV81 )
= SY2016 )
| ~ ( c_lessequals @ SY2015 @ SY2016 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1811,plain,
! [SV82: $i] :
( ( ! [SY2017: $i,SY2018: $i] :
( ~ ( class_Orderings_Olinorder @ SV82 )
| ( ( c_Orderings_Oord__class_Omax @ SY2017 @ SY2018 @ SV82 )
= SY2017 )
| ~ ( c_lessequals @ SY2018 @ SY2017 @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1812,plain,
! [SV83: $i] :
( ( ! [SY2019: $i] :
( ~ ( class_OrderedGroup_Omonoid__mult @ SV83 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV83 ) @ SY2019 @ SV83 )
= ( c_HOL_Oone__class_Oone @ SV83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1813,plain,
! [SV84: $i] :
( ( ! [SY2020: $i,SY2021: $i] :
( ~ ( class_Orderings_Olinorder @ SV84 )
| ( c_HOL_Oord__class_Oless @ SY2020 @ SY2021 @ SV84 )
| ( c_lessequals @ SY2021 @ SY2020 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1814,plain,
! [SV85: $i] :
( ( ! [SY2022: $i] :
( ~ ( class_Orderings_Olinorder @ SV85 )
| ~ ( c_lessequals @ SY2022 @ SY2022 @ SV85 )
| ~ ( c_HOL_Oord__class_Oless @ SY2022 @ SY2022 @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1815,plain,
! [SV86: $i] :
( ( ! [SY2023: $i] :
( ~ ( class_Orderings_Olinorder @ SV86 )
| ( c_HOL_Oord__class_Oless @ SY2023 @ SY2023 @ SV86 )
| ( c_lessequals @ SY2023 @ SY2023 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1816,plain,
! [SV87: $i] :
( ( ! [SY2024: $i,SY2025: $i] :
( ~ ( class_Orderings_Olinorder @ SV87 )
| ~ ( c_HOL_Oord__class_Oless @ SY2024 @ SY2025 @ SV87 )
| ~ ( c_lessequals @ SY2025 @ SY2024 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1817,plain,
! [SV88: $i] :
( ( ! [SY2026: $i,SY2027: $i] :
( ~ ( class_Orderings_Olinorder @ SV88 )
| ( c_lessequals @ SY2026 @ SY2027 @ SV88 )
| ( c_HOL_Oord__class_Oless @ SY2027 @ SY2026 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1818,plain,
! [SV89: $i] :
( ( ! [SY2028: $i,SY2029: $i] :
( ~ ( class_Orderings_Olinorder @ SV89 )
| ~ ( c_lessequals @ SY2028 @ SY2029 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SY2029 @ SY2028 @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1819,plain,
! [SV90: $i] :
( ( ! [SY2030: $i,SY2031: $i] :
( ~ ( class_Orderings_Olinorder @ SV90 )
| ( c_HOL_Oord__class_Oless @ SY2030 @ SY2031 @ SV90 )
| ( c_lessequals @ SY2031 @ SY2030 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1202]) ).
thf(1820,plain,
! [SV91: $i] :
( ( ! [SY2032: $i,SY2033: $i] :
( ~ ( class_Orderings_Opreorder @ SV91 )
| ~ ( c_lessequals @ SY2032 @ SY2033 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SY2033 @ SY2032 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1821,plain,
! [SV92: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV92 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV92 )
= ( c_HOL_Oone__class_Oone @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1822,plain,
! [SV93: $i] :
( ( ! [SY2034: $i,SY2035: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV93 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SY2034 ) @ SY2035 ) @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 )
| ~ ( c_lessequals @ SY2035 @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ SY2034 @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1823,plain,
! [SV94: $i] :
( ( ! [SY2036: $i,SY2037: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV94 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SY2036 ) @ SY2037 ) @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 )
| ~ ( c_HOL_Oord__class_Oless @ SY2037 @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 )
| ~ ( c_lessequals @ SY2036 @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1824,plain,
! [SV95: $i] :
( ( ! [SY2038: $i,SY2039: $i,SY2040: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV95 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV95 )
| ( c_HOL_Oord__class_Oless @ SY2038 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SY2039 ) @ SY2040 ) @ SV95 )
| ~ ( c_lessequals @ SY2038 @ SY2040 @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SY2039 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1825,plain,
! [SV96: $i] :
( ( ! [SY2041: $i,SY2042: $i,SY2043: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV96 )
| ( c_HOL_Oord__class_Oless @ SY2041 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SY2042 ) @ SY2043 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ SY2041 @ SY2043 @ SV96 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SY2042 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1826,plain,
! [SV97: $i] :
( ( ! [SY2044: $i,SY2045: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV97 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SY2044 ) @ SY2045 ) @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SY2045 @ SV97 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SY2044 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1827,plain,
! [SV98: $i] :
( ( ! [SY2046: $i,SY2047: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV98 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV98 ) @ SY2046 ) @ SY2047 ) @ SV98 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ SY2047 @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ SY2046 @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1828,plain,
! [SV99: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV99 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV99 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV99 ) @ ( c_HOL_Oone__class_Oone @ SV99 ) ) @ ( c_HOL_Oone__class_Oone @ SV99 ) ) @ SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1829,plain,
! [SV100: $i] :
( ( ! [SY2048: $i,SY2049: $i,SY2050: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV100 )
| ( c_HOL_Oord__class_Oless @ SY2048 @ SY2049 @ SV100 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV100 ) @ SY2049 @ SV100 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2048 @ SY2050 @ SV100 ) @ ( c_Power_Opower__class_Opower @ SY2049 @ SY2050 @ SV100 ) @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1830,plain,
! [SV101: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV101 )
| ~ ( class_Power_Opower @ SV101 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV101 )
= ( c_HOL_Oone__class_Oone @ SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1831,plain,
! [SV102: $i] :
( ( ! [SY2051: $i,SY2052: $i,SY2053: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV102 )
| ( c_HOL_Oord__class_Oless @ SY2051 @ SY2052 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2053 @ SY2051 @ SV102 ) @ ( c_Power_Opower__class_Opower @ SY2053 @ SY2052 @ SV102 ) @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV102 ) @ SY2053 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1216]) ).
thf(1832,plain,
! [SV103: $i] :
( ( ! [SY2054: $i,SY2055: $i,SY2056: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV103 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2054 @ SY2055 @ SV103 ) @ ( c_Power_Opower__class_Opower @ SY2054 @ SY2056 @ SV103 ) @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV103 ) @ SY2054 @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ SY2055 @ SY2056 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1833,plain,
! [SV104: $i] :
( ( ! [SY2057: $i,SY2058: $i,SY2059: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV104 )
| ( c_HOL_Oord__class_Oless @ SY2057 @ SY2058 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2059 @ SY2057 @ SV104 ) @ ( c_Power_Opower__class_Opower @ SY2059 @ SY2058 @ SV104 ) @ SV104 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV104 ) @ SY2059 @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1834,plain,
! [SV105: $i] :
( ( ! [SY2060: $i,SY2061: $i,SY2062: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV105 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2060 @ SY2061 @ SV105 ) @ ( c_Power_Opower__class_Opower @ SY2060 @ SY2062 @ SV105 ) @ SV105 )
| ~ ( c_HOL_Oord__class_Oless @ SY2061 @ SY2062 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV105 ) @ SY2060 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1835,plain,
! [SV106: $i] :
( ( ! [SY2063: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ SV106 ) ) @ SY2063 )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV106 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2063 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1836,plain,
! [SV107: $i] :
( ( ! [SY2064: $i,SY2065: $i] :
( ( c_Lambda_Oliftn @ SV107 @ ( c_Lambda_OdB_OAbs @ SY2064 ) @ SY2065 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Oliftn @ SV107 @ SY2064 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2065 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1837,plain,
! [SV108: $i] :
( ( ! [SY2066: $i,SY2067: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OAbs @ SV108 ) @ SY2066 @ SY2067 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubstn @ SV108 @ SY2066 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2067 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1838,plain,
! [SV109: $i] :
( ( ! [SY2068: $i,SY2069: $i,SY2070: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV109 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY2068 @ SY2069 @ SV109 ) @ ( c_Power_Opower__class_Opower @ SY2070 @ SY2069 @ SV109 ) @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2069 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SY2068 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SY2068 @ SY2070 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1839,plain,
! [SV110: $i] :
( ( ! [SY2071: $i,SY2072: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ SV110 ) ) @ SY2071 ) @ SY2072 )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV110 ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY2071 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2072 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1840,plain,
! [SV111: $i] :
( ( ! [SY2073: $i,SY2074: $i,SY2075: $i,SY2076: $i] :
( ( c_Type_Otypings @ ( c_Type_Oshift @ SV111 @ SY2073 @ SY2074 @ tc_Type_Otype ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ SY2073 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY2075 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2076 )
| ~ ( c_Type_Otypings @ SV111 @ SY2075 @ SY2076 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1841,plain,
! [SV112: $i] :
( ( ! [SY2077: $i,SY2078: $i,SY2079: $i,SY2080: $i,SY2081: $i] :
( ( c_Type_Otypings @ SV112 @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SY2077 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SY2078 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY2079 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2080 )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ SV112 @ SY2078 @ SY2081 @ tc_Type_Otype ) @ SY2079 @ SY2080 )
| ~ ( c_Type_Otyping @ SV112 @ SY2077 @ SY2081 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1842,plain,
! [SV113: $i] :
( ( ! [SY2082: $i] :
( ( hBOOL @ ( hAPP @ SV113 @ SY2082 ) )
| ~ ( hBOOL @ ( hAPP @ SV113 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV113 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @ SV113 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ SV113 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV113 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV113 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1843,plain,
! [SV114: $i] :
( ( ! [SY2083: $i] :
( ~ ( hBOOL @ ( hAPP @ SV114 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV114 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__4 @ SV114 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ SV114 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV114 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV114 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ SV114 @ SY2083 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1844,plain,
! [SV115: $i] :
( ( ( SV115
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV115 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV115 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV115 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV115
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV115 ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV115 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1845,plain,
! [SV116: $i] :
( ( ! [SY2084: $i,SY2085: $i,SY2086: $i,SY2087: $i] :
( ( c_List_Omap @ SV116 @ ( c_List_Olist_OCons @ SY2084 @ SY2085 @ SY2086 ) @ SY2086 @ SY2087 )
= ( c_List_Olist_OCons @ ( hAPP @ SV116 @ SY2084 ) @ ( c_List_Omap @ SV116 @ SY2085 @ SY2086 @ SY2087 ) @ SY2087 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1846,plain,
! [SV117: $i] :
( ( ! [SY2088: $i,SY2089: $i,SY2090: $i,SY2091: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ SV117 @ SY2088 ) @ ( c_List_Omap @ SV117 @ SY2089 @ SY2090 @ SY2091 ) @ SY2091 )
= ( c_List_Omap @ SV117 @ ( c_List_Olist_OCons @ SY2088 @ SY2089 @ SY2090 ) @ SY2090 @ SY2091 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1847,plain,
! [SV118: $i] :
( ( ! [SY2092: $i,SY2093: $i,SY2094: $i,SY2095: $i] :
( ( c_List_Omap @ SV118 @ ( c_List_Olist_OCons @ SY2092 @ SY2093 @ SY2094 ) @ SY2094 @ SY2095 )
= ( c_List_Olist_OCons @ ( hAPP @ SV118 @ SY2092 ) @ ( c_List_Omap @ SV118 @ SY2093 @ SY2094 @ SY2095 ) @ SY2095 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1848,plain,
! [SV119: $i] :
( ( ! [SY2096: $i,SY2097: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV119 ) @ SY2096 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2097 ) @ SY2096 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV119 ) @ SY2097 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1849,plain,
! [SV120: $i] :
( ( ! [SY2098: $i,SY2099: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV120 ) @ SY2098 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV120 ) @ SY2099 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY2098 ) @ SY2099 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1850,plain,
! [SV121: $i] :
( ( ! [SY2100: $i,SY2101: $i,SY2102: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV121 @ SY2100 @ SY2101 ) @ SY2102 @ SY2101 )
= ( c_List_Olist_OCons @ SV121 @ ( c_List_Oappend @ SY2100 @ SY2102 @ SY2101 ) @ SY2101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1851,plain,
! [SV122: $i] :
( ( ! [SY2103: $i,SY2104: $i,SY2105: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV122 @ SY2103 @ SY2104 ) @ SY2105 @ SY2104 )
= ( c_List_Olist_OCons @ SV122 @ ( c_List_Oappend @ SY2103 @ SY2105 @ SY2104 ) @ SY2104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1852,plain,
! [SV123: $i] :
( ( ! [SY2106: $i,SY2107: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV123 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV123 ) @ SY2106 ) @ SY2107 ) @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 )
| ~ ( c_HOL_Oord__class_Oless @ SY2107 @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 )
| ~ ( c_HOL_Oord__class_Oless @ SY2106 @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1853,plain,
! [SV124: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV124 )
| ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ SV124 ) @ SV124 )
= ( c_HOL_Ozero__class_Ozero @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1854,plain,
! [SV125: $i] :
( ( ! [SY2108: $i,SY2109: $i,SY2110: $i] :
( ~ ( class_Orderings_Olinorder @ SV125 )
| ( c_HOL_Oord__class_Oless @ SY2108 @ SY2109 @ SV125 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SY2110 @ SY2108 @ SV125 ) @ SY2109 @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1855,plain,
! [SV126: $i] :
( ( ! [SY2111: $i,SY2112: $i,SY2113: $i] :
( ~ ( class_Orderings_Olinorder @ SV126 )
| ( c_HOL_Oord__class_Oless @ SY2111 @ SY2112 @ SV126 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SY2111 @ SY2113 @ SV126 ) @ SY2112 @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1856,plain,
! [SV127: $i] :
( ( ! [SY2114: $i,SY2115: $i,SY2116: $i] :
( ~ ( class_Orderings_Olinorder @ SV127 )
| ( c_HOL_Oord__class_Oless @ SY2114 @ ( c_Orderings_Oord__class_Omax @ SY2115 @ SY2116 @ SV127 ) @ SV127 )
| ~ ( c_HOL_Oord__class_Oless @ SY2114 @ SY2116 @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1243]) ).
thf(1857,plain,
! [SV128: $i] :
( ( ! [SY2117: $i,SY2118: $i,SY2119: $i] :
( ~ ( class_Orderings_Olinorder @ SV128 )
| ( c_HOL_Oord__class_Oless @ SY2117 @ ( c_Orderings_Oord__class_Omax @ SY2118 @ SY2119 @ SV128 ) @ SV128 )
| ~ ( c_HOL_Oord__class_Oless @ SY2117 @ SY2118 @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1858,plain,
! [SV129: $i] :
( ( ! [SY2120: $i,SY2121: $i,SY2122: $i] :
( ~ ( class_Orderings_Olinorder @ SV129 )
| ( c_HOL_Oord__class_Oless @ SY2120 @ ( c_Orderings_Oord__class_Omax @ SY2121 @ SY2122 @ SV129 ) @ SV129 )
| ~ ( c_HOL_Oord__class_Oless @ SY2120 @ SY2122 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1859,plain,
! [SV130: $i] :
( ( ! [SY2123: $i,SY2124: $i,SY2125: $i] :
( ~ ( class_Orderings_Olinorder @ SV130 )
| ( c_HOL_Oord__class_Oless @ SY2123 @ ( c_Orderings_Oord__class_Omax @ SY2124 @ SY2125 @ SV130 ) @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SY2123 @ SY2124 @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1860,plain,
! [SV131: $i] :
( ( ! [SY2126: $i,SY2127: $i,SY2128: $i,SY2129: $i,SY2130: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SY2126 ) @ SY2127 ) )
| ( c_ListOrder_Ostep1 @ SV131 @ SY2128 @ SY2129 @ SY2130 )
| ~ ( c_ListOrder_Ostep1 @ SV131 @ ( c_List_Oappend @ SY2128 @ ( c_List_Olist_OCons @ SY2126 @ ( c_List_Olist_ONil @ SY2130 ) @ SY2130 ) @ SY2130 ) @ ( c_List_Oappend @ SY2129 @ ( c_List_Olist_OCons @ SY2127 @ ( c_List_Olist_ONil @ SY2130 ) @ SY2130 ) @ SY2130 ) @ SY2130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1861,plain,
! [SV132: $i] :
( ( ! [SY2131: $i,SY2132: $i,SY2133: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV132 @ SY2131 @ SY2131 ) @ SY2131 ) @ SY2132 ) @ SY2133 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV132 @ SY2131 ) @ SY2133 ) @ SY2132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1862,plain,
! [SV133: $i] :
( ( ! [SY2134: $i,SY2135: $i,SY2136: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV133 @ SY2134 ) @ SY2135 ) @ SY2136 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV133 @ SY2134 @ SY2134 ) @ SY2134 ) @ SY2136 ) @ SY2135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1863,plain,
! [SV134: $i] :
( ( ! [SY2137: $i,SY2138: $i] :
( ( c_List_Omap @ SV134 @ ( c_List_Olist_ONil @ SY2137 ) @ SY2137 @ SY2138 )
= ( c_List_Olist_ONil @ SY2138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1864,plain,
! [SV135: $i] :
( ( ! [SY2139: $i,SY2140: $i,SY2141: $i] :
( ( c_List_Ofoldr @ SV135 @ ( c_List_Olist_ONil @ SY2139 ) @ SY2140 @ SY2139 @ SY2141 )
= SY2140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1865,plain,
! [SV136: $i] :
( ( ! [SY2142: $i,SY2143: $i,SY2144: $i,SY2145: $i,SY2146: $i] :
( ( hAPP @ ( c_COMBC @ SV136 @ SY2142 @ SY2143 @ SY2144 @ SY2145 ) @ SY2146 )
= ( hAPP @ ( hAPP @ SV136 @ SY2146 ) @ SY2142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1866,plain,
! [SV137: $i] :
( ( ! [SY2147: $i,SY2148: $i,SY2149: $i,SY2150: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SY2147 ) @ SY2148 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV137 @ SY2149 @ SY2150 ) @ SY2148 ) @ SY2147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1867,plain,
! [SV138: $i] :
( ( ! [SY2151: $i,SY2152: $i,SY2153: $i,SY2154: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV138 @ SY2151 @ SY2152 ) @ SY2153 ) @ SY2154 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV138 @ SY2154 ) @ SY2153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1868,plain,
! [SV139: $i] :
( ( ! [SY2155: $i,SY2156: $i,SY2157: $i,SY2158: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV139 @ SY2155 ) @ SY2156 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV139 @ SY2157 @ SY2158 ) @ SY2156 ) @ SY2155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1869,plain,
! [SV140: $i] :
( ( ! [SY2159: $i,SY2160: $i,SY2161: $i,SY2162: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV140 @ SY2159 @ SY2160 ) @ SY2161 ) @ SY2162 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV140 @ SY2162 ) @ SY2161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1870,plain,
! [SV141: $i] :
( ( ! [SY2163: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV141 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2163 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2163 ) @ SV141 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1871,plain,
! [SV142: $i] :
( ( ! [SY2164: $i,SY2165: $i,SY2166: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV142 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ SY2164 ) @ SY2165 ) ) @ SY2166 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ SY2164 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ SY2165 ) @ SY2166 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1872,plain,
! [SV143: $i] :
( ( ! [SY2167: $i,SY2168: $i,SY2169: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV143 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ SY2167 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ SY2168 ) @ SY2169 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ SY2168 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ SY2167 ) @ SY2169 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1873,plain,
! [SV144: $i] :
( ( ! [SY2170: $i,SY2171: $i,SY2172: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV144 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ SY2170 ) @ SY2171 ) ) @ SY2172 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ SY2170 ) @ SY2172 ) ) @ SY2171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1874,plain,
! [SV145: $i] :
( ( ! [SY2173: $i,SY2174: $i,SY2175: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV145 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV145 ) @ SY2173 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV145 ) @ SY2174 ) @ SY2175 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV145 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV145 ) @ SY2173 ) @ SY2174 ) ) @ SY2175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1875,plain,
! [SV146: $i] :
( ( ! [SY2176: $i,SY2177: $i,SY2178: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV146 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ SY2176 ) @ SY2177 ) ) @ SY2178 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ SY2176 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ SY2177 ) @ SY2178 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1876,plain,
! [SV147: $i] :
( ( ! [SY2179: $i,SY2180: $i,SY2181: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV147 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SY2179 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SY2180 ) @ SY2181 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SY2180 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SY2179 ) @ SY2181 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1877,plain,
! [SV148: $i] :
( ( ! [SY2182: $i,SY2183: $i,SY2184: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV148 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SY2182 ) @ SY2183 ) ) @ SY2184 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SY2182 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SY2183 ) @ SY2184 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1878,plain,
! [SV149: $i] :
( ( ! [SY2185: $i,SY2186: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV149 ) @ SY2185 ) ) @ SY2186 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV149 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2185 ) @ SY2186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1879,plain,
! [SV150: $i] :
( ( ! [SY2187: $i,SY2188: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV150 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2187 ) @ SY2188 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2187 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV150 ) @ SY2188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1880,plain,
! [SV151: $i] :
( ( ! [SY2189: $i,SY2190: $i,SY2191: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV151 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SY2189 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SY2190 ) @ SY2191 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SY2190 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SY2189 ) @ SY2191 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1881,plain,
! [SV152: $i] :
( ( ! [SY2192: $i,SY2193: $i,SY2194: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV152 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SY2192 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SY2193 ) @ SY2194 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SY2192 ) @ SY2193 ) ) @ SY2194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1882,plain,
! [SV153: $i] :
( ( ! [SY2195: $i,SY2196: $i,SY2197: $i] :
( ~ ( class_Orderings_Oorder @ SV153 )
| ( c_HOL_Oord__class_Oless @ SY2195 @ SY2196 @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SY2195 @ SY2197 @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SY2197 @ SY2196 @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1883,plain,
! [SV154: $i] :
( ( ! [SY2198: $i,SY2199: $i,SY2200: $i] :
( ~ ( class_Orderings_Opreorder @ SV154 )
| ( c_HOL_Oord__class_Oless @ SY2198 @ SY2199 @ SV154 )
| ~ ( c_HOL_Oord__class_Oless @ SY2200 @ SY2199 @ SV154 )
| ~ ( c_HOL_Oord__class_Oless @ SY2198 @ SY2200 @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1884,plain,
! [SV155: $i] :
( ( ! [SY2201: $i,SY2202: $i,SY2203: $i,SY2204: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV155 @ SY2201 @ SY2202 @ SY2203 )
| ( c_ListOrder_Ostep1 @ SV155 @ ( c_List_Oappend @ SY2201 @ SY2204 @ SY2203 ) @ ( c_List_Oappend @ SY2202 @ SY2204 @ SY2203 ) @ SY2203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1885,plain,
! [SV156: $i] :
( ( ! [SY2205: $i,SY2206: $i,SY2207: $i,SY2208: $i] :
( ( c_ListOrder_Ostep1 @ SV156 @ ( c_List_Oappend @ SY2205 @ SY2206 @ SY2207 ) @ ( c_List_Oappend @ SY2205 @ SY2208 @ SY2207 ) @ SY2207 )
| ~ ( c_ListOrder_Ostep1 @ SV156 @ SY2206 @ SY2208 @ SY2207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1886,plain,
! [SV157: $i] :
( ( ! [SY2209: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV157 ) ) @ ( c_Lambda_OdB_OAbs @ SY2209 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV157 ) @ SY2209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1887,plain,
! [SV158: $i] :
( ( ! [SY2210: $i,SY2211: $i,SY2212: $i] :
( ( c_List_Olistsp @ SV158 @ SY2210 @ SY2211 )
| ~ ( c_List_Olistsp @ SV158 @ ( c_List_Oappend @ SY2210 @ SY2212 @ SY2211 ) @ SY2211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1888,plain,
! [SV159: $i] :
( ( ! [SY2213: $i,SY2214: $i,SY2215: $i] :
( ( c_List_Olistsp @ SV159 @ SY2213 @ SY2214 )
| ~ ( c_List_Olistsp @ SV159 @ ( c_List_Oappend @ SY2215 @ SY2213 @ SY2214 ) @ SY2214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1889,plain,
! [SV160: $i] :
( ( ! [SY2216: $i,SY2217: $i,SY2218: $i,SY2219: $i] :
( ( c_Lambda_OdB_OdB__case @ SV160 @ SY2216 @ SY2217 @ ( c_Lambda_OdB_OAbs @ SY2218 ) @ SY2219 )
= ( hAPP @ SY2217 @ SY2218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1890,plain,
! [SV161: $i] :
( ( ! [SY2220: $i,SY2221: $i,SY2222: $i,SY2223: $i,SY2224: $i] :
( ( SV161 = SY2220 )
| ( SY2221 = SY2222 )
| ~ ( c_ListOrder_Ostep1 @ SY2223 @ ( c_List_Olist_OCons @ SY2220 @ SY2222 @ SY2224 ) @ ( c_List_Olist_OCons @ SV161 @ SY2221 @ SY2224 ) @ SY2224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1891,plain,
! [SV162: $i] :
( ( ! [SY2225: $i,SY2226: $i,SY2227: $i,SY2228: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV162 @ SY2225 ) @ SY2226 ) )
| ( c_ListOrder_Ostep1 @ SV162 @ ( c_List_Olist_OCons @ SY2225 @ SY2227 @ SY2228 ) @ ( c_List_Olist_OCons @ SY2226 @ SY2227 @ SY2228 ) @ SY2228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1892,plain,
! [SV163: $i] :
( ( ! [SY2229: $i] : ( c_List_Olistsp @ SV163 @ ( c_List_Olist_ONil @ SY2229 ) @ SY2229 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1280]) ).
thf(1893,plain,
! [SV164: $i] :
( ( ! [SY2230: $i,SY2231: $i,SY2232: $i] :
( ~ ( class_Orderings_Olinorder @ SV164 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SY2230 @ SY2231 @ SV164 ) @ SY2232 @ SV164 )
| ~ ( c_HOL_Oord__class_Oless @ SY2231 @ SY2232 @ SV164 )
| ~ ( c_HOL_Oord__class_Oless @ SY2230 @ SY2232 @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1894,plain,
! [SV165: $i] :
( ( ! [SY2233: $i,SY2234: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV165 @ SY2233 ) @ SY2234 ) @ SY2234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1895,plain,
! [SV166: $i] :
( ( ! [SY2235: $i,SY2236: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV166 @ SY2235 ) @ SY2236 ) @ SY2236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1896,plain,
! [SV167: $i] :
( ( ! [SY2237: $i,SY2238: $i,SY2239: $i] :
( ( c_Wellfounded_Oaccp @ SV167 @ SY2237 @ SY2238 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SY2238 ) @ SY2237 ) @ SY2239 ) )
| ~ ( c_Wellfounded_Oaccp @ SV167 @ SY2239 @ SY2238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1897,plain,
! [SV168: $i] :
( ( ! [SY2240: $i,SY2241: $i,SY2242: $i] :
( ( c_Wellfounded_Oaccp @ SV168 @ SY2240 @ SY2241 )
| ~ ( c_Wellfounded_Oaccp @ SV168 @ SY2242 @ SY2241 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SY2241 ) @ SY2240 ) @ SY2242 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1898,plain,
! [SV169: $i] :
( ( ! [SY2243: $i,SY2244: $i,SY2245: $i,SY2246: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SY2243 ) @ SY2244 ) @ SY2245 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SY2243 ) @ SY2246 ) @ SY2245 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SY2243 ) @ SY2244 ) @ SY2246 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1899,plain,
! [SV170: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV170 @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1900,plain,
! [SV171: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV171 ) )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV171 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1901,plain,
! [SV172: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV172 ) ) )
| ( SV172
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV172 ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV172 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1902,plain,
! [SV173: $i] :
( ( ! [SY2247: $i] :
( ( c_List_Oappend @ SV173 @ ( c_List_Olist_ONil @ SY2247 ) @ SY2247 )
= SV173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1903,plain,
! [SV174: $i] :
( ( ! [SY2248: $i] :
( SV174
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY2248 ) @ SV174 @ SY2248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1904,plain,
! [SV175: $i] :
( ( ! [SY2249: $i] :
( SV175
= ( c_List_Oappend @ SV175 @ ( c_List_Olist_ONil @ SY2249 ) @ SY2249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1905,plain,
! [SV176: $i] :
( ( ! [SY2250: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV176 ) @ SY2250 @ SV176 )
= SY2250 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1906,plain,
! [SV177: $i] :
( ( ! [SY2251: $i] :
( SV177
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY2251 ) @ SV177 @ SY2251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1907,plain,
! [SV178: $i] :
( ( ! [SY2252: $i,SY2253: $i,SY2254: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV178 ) @ SY2252 ) @ SY2253 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV178 ) @ SY2254 ) @ SY2253 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY2252 ) @ SY2254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1298]) ).
thf(1908,plain,
! [SV179: $i] :
( ( ! [SY2255: $i,SY2256: $i,SY2257: $i,SY2258: $i] :
( ( c_List_Omap @ SV179 @ ( c_List_Oreplicate @ SY2255 @ SY2256 @ SY2257 ) @ SY2257 @ SY2258 )
= ( c_List_Oreplicate @ SY2255 @ ( hAPP @ SV179 @ SY2256 ) @ SY2258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1909,plain,
! [SV180: $i] :
( ( ! [SY2259: $i,SY2260: $i] :
( ( c_HOL_Oord__class_Oless @ SV180 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2259 ) @ SY2260 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV180 @ SY2259 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1910,plain,
! [SV181: $i] :
( ( ! [SY2261: $i,SY2262: $i] :
( ( c_HOL_Oord__class_Oless @ SV181 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2261 ) @ SY2262 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV181 @ SY2262 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1911,plain,
! [SV182: $i] :
( ( ! [SY2263: $i,SY2264: $i] :
( ( c_HOL_Oord__class_Oless @ SV182 @ SY2263 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV182 ) @ SY2264 ) @ SY2263 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1912,plain,
! [SV183: $i] :
( ( ! [SY2265: $i,SY2266: $i] :
( ( c_HOL_Oord__class_Oless @ SV183 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2265 ) @ SY2266 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV183 @ SY2265 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1913,plain,
! [SV184: $i] :
( ( ! [SY2267: $i,SY2268: $i] :
( ( c_HOL_Oord__class_Oless @ SV184 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2267 ) @ SY2268 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV184 @ SY2268 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1914,plain,
! [SV185: $i] :
( ( ! [SY2269: $i,SY2270: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV185 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV185 ) @ SY2269 ) @ SY2270 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV185 ) @ SY2270 ) @ SY2269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1915,plain,
! [SV186: $i] :
( ( ! [SY2271: $i,SY2272: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV186 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV186 ) @ SY2271 ) @ SY2272 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV186 ) @ SY2272 ) @ SY2271 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1916,plain,
! [SV187: $i] :
( ( ! [SY2273: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV187 ) @ SY2273 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2273 ) @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1917,plain,
! [SV188: $i] :
( ( ! [SY2274: $i,SY2275: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV188 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV188 ) @ SY2274 ) @ SY2275 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV188 ) @ SY2275 ) @ SY2274 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1918,plain,
! [SV189: $i] :
( ( ! [SY2276: $i,SY2277: $i,SY2278: $i,SY2279: $i,SY2280: $i] :
( ( c_List_Ofoldr @ SV189 @ ( c_List_Oappend @ SY2276 @ SY2277 @ SY2278 ) @ SY2279 @ SY2278 @ SY2280 )
= ( c_List_Ofoldr @ SV189 @ SY2276 @ ( c_List_Ofoldr @ SV189 @ SY2277 @ SY2279 @ SY2278 @ SY2280 ) @ SY2278 @ SY2280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1919,plain,
! [SV190: $i] :
( ( ! [SY2281: $i,SY2282: $i,SY2283: $i,SY2284: $i,SY2285: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV190 @ SY2281 ) @ SY2282 ) )
| ( SY2281 = SY2282 )
| ~ ( c_ListOrder_Ostep1 @ SV190 @ ( c_List_Oappend @ SY2283 @ ( c_List_Olist_OCons @ SY2281 @ ( c_List_Olist_ONil @ SY2284 ) @ SY2284 ) @ SY2284 ) @ ( c_List_Oappend @ SY2285 @ ( c_List_Olist_OCons @ SY2282 @ ( c_List_Olist_ONil @ SY2284 ) @ SY2284 ) @ SY2284 ) @ SY2284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1920,plain,
! [SV191: $i] :
( ( ! [SY2286: $i,SY2287: $i,SY2288: $i,SY2289: $i,SY2290: $i,SY2291: $i,SY2292: $i,SY2293: $i] :
( ( ( hAPP @ ( hAPP @ SV191 @ ( hAPP @ ( hAPP @ SY2286 @ SY2287 ) @ SY2288 ) ) @ ( hAPP @ ( hAPP @ SY2286 @ SY2287 ) @ SY2289 ) )
= ( hAPP @ ( hAPP @ SY2286 @ SY2287 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2288 ) @ SY2289 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY2290 @ SV191 @ SY2286 @ SY2291 @ SY2292 @ SY2293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1921,plain,
! [SV192: $i] :
( ( ! [SY2294: $i,SY2295: $i,SY2296: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV192 ) @ SY2294 ) @ SY2295 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY2296 ) @ SY2294 ) @ SY2295 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV192 ) @ SY2296 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1922,plain,
! [SV193: $i] :
( ( ! [SY2297: $i,SY2298: $i,SY2299: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV193 ) @ SY2297 ) @ SY2298 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV193 ) @ SY2299 ) @ SY2298 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY2297 ) @ SY2299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1923,plain,
! [SV194: $i] :
( ( ! [SY2300: $i,SY2301: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV194 )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV194 ) @ SY2300 @ SY2301 @ SV194 @ SV194 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV194 ) @ SY2301 @ SY2300 @ SV194 @ SV194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1924,plain,
! [SV195: $i] :
( ( ! [SY2302: $i,SY2303: $i,SY2304: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV195 @ SY2302 ) @ SY2303 ) @ SY2304 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV195 @ SY2303 ) @ SY2304 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1925,plain,
! [SV196: $i] :
( ( ! [SY2305: $i,SY2306: $i] :
~ ( c_ListOrder_Ostep1 @ SV196 @ ( c_List_Olist_ONil @ SY2305 ) @ SY2306 @ SY2305 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1926,plain,
! [SV197: $i] :
( ( ! [SY2307: $i,SY2308: $i] :
~ ( c_ListOrder_Ostep1 @ SV197 @ SY2307 @ ( c_List_Olist_ONil @ SY2308 ) @ SY2308 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1927,plain,
! [SV198: $i] :
( ( ! [SY2309: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV198 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ SY2309 ) @ SY2309 ) @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
| ~ ( c_HOL_Oord__class_Oless @ SY2309 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1928,plain,
! [SV199: $i] :
( ( ! [SY2310: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV199 )
| ( c_HOL_Oord__class_Oless @ SY2310 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV199 ) @ SY2310 ) @ SY2310 ) @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1929,plain,
! [SV200: $i] :
( ( ! [SY2311: $i,SY2312: $i,SY2313: $i] :
( ( c_List_Olist_OCons @ SV200 @ ( c_List_Oappend @ SY2311 @ SY2312 @ SY2313 ) @ SY2313 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV200 @ SY2311 @ SY2313 ) @ SY2312 @ SY2313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1930,plain,
! [SV201: $i] :
( ( ! [SY2314: $i,SY2315: $i,SY2316: $i] :
( ( c_List_Olist_OCons @ SV201 @ ( c_List_Oappend @ SY2314 @ SY2315 @ SY2316 ) @ SY2316 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV201 @ SY2314 @ SY2316 ) @ SY2315 @ SY2316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1931,plain,
! [SV202: $i] :
( ( ! [SY2317: $i,SY2318: $i,SY2319: $i,SY2320: $i,SY2321: $i,SY2322: $i,SY2323: $i,SY2324: $i] :
( ( ( hAPP @ ( hAPP @ SV202 @ ( hAPP @ ( hAPP @ SY2317 @ SY2318 ) @ SY2319 ) ) @ SY2320 )
= ( hAPP @ ( hAPP @ SY2317 @ ( hAPP @ ( hAPP @ SV202 @ SY2318 ) @ SY2320 ) ) @ ( hAPP @ ( hAPP @ SV202 @ SY2319 ) @ SY2320 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY2321 @ SY2317 @ SV202 @ SY2322 @ SY2323 @ SY2324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1932,plain,
! [SV203: $i] :
( ( ! [SY2325: $i,SY2326: $i,SY2327: $i,SY2328: $i,SY2329: $i,SY2330: $i,SY2331: $i,SY2332: $i] :
( ( ( hAPP @ ( hAPP @ SV203 @ SY2325 ) @ ( hAPP @ ( hAPP @ SY2326 @ SY2327 ) @ SY2328 ) )
= ( hAPP @ ( hAPP @ SY2326 @ ( hAPP @ ( hAPP @ SV203 @ SY2325 ) @ SY2327 ) ) @ ( hAPP @ ( hAPP @ SV203 @ SY2325 ) @ SY2328 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY2326 @ SV203 @ SY2329 @ SY2330 @ SY2331 @ SY2332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1933,plain,
! [SV204: $i] :
( ( ! [SY2333: $i,SY2334: $i,SY2335: $i,SY2336: $i,SY2337: $i,SY2338: $i,SY2339: $i] :
( ( ( hAPP @ ( hAPP @ SV204 @ SY2333 ) @ SY2334 )
= ( hAPP @ ( hAPP @ SV204 @ SY2334 ) @ SY2333 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY2335 @ SV204 @ SY2336 @ SY2337 @ SY2338 @ SY2339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1934,plain,
! [SV205: $i] :
( ( ! [SY2340: $i,SY2341: $i,SY2342: $i,SY2343: $i,SY2344: $i,SY2345: $i,SY2346: $i,SY2347: $i] :
( ( ( hAPP @ ( hAPP @ SV205 @ SY2340 ) @ ( hAPP @ ( hAPP @ SV205 @ SY2341 ) @ SY2342 ) )
= ( hAPP @ ( hAPP @ SV205 @ ( hAPP @ ( hAPP @ SV205 @ SY2340 ) @ SY2341 ) ) @ SY2342 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY2343 @ SV205 @ SY2344 @ SY2345 @ SY2346 @ SY2347 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1335]) ).
thf(1935,plain,
! [SV206: $i] :
( ( ! [SY2348: $i,SY2349: $i,SY2350: $i,SY2351: $i,SY2352: $i,SY2353: $i] :
( ( ( hAPP @ ( hAPP @ SV206 @ SY2348 ) @ SY2349 )
= SY2349 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY2350 @ SV206 @ SY2351 @ SY2352 @ SY2348 @ SY2353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1936,plain,
! [SV207: $i] :
( ( ! [SY2354: $i,SY2355: $i,SY2356: $i,SY2357: $i,SY2358: $i,SY2359: $i] :
( ( ( hAPP @ ( hAPP @ SV207 @ SY2354 ) @ SY2355 )
= SY2354 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY2356 @ SV207 @ SY2357 @ SY2354 @ SY2358 @ SY2359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1937,plain,
! [SV208: $i] :
( ( ! [SY2360: $i,SY2361: $i,SY2362: $i,SY2363: $i,SY2364: $i,SY2365: $i,SY2366: $i] :
( ( ( hAPP @ ( hAPP @ SV208 @ SY2360 ) @ SY2361 )
= ( hAPP @ ( hAPP @ SV208 @ SY2361 ) @ SY2360 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV208 @ SY2362 @ SY2363 @ SY2364 @ SY2365 @ SY2366 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1938,plain,
! [SV209: $i] :
( ( ! [SY2367: $i,SY2368: $i,SY2369: $i,SY2370: $i,SY2371: $i,SY2372: $i,SY2373: $i,SY2374: $i] :
( ( ( hAPP @ ( hAPP @ SV209 @ SY2367 ) @ ( hAPP @ ( hAPP @ SV209 @ SY2368 ) @ SY2369 ) )
= ( hAPP @ ( hAPP @ SV209 @ ( hAPP @ ( hAPP @ SV209 @ SY2367 ) @ SY2368 ) ) @ SY2369 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV209 @ SY2370 @ SY2371 @ SY2372 @ SY2373 @ SY2374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1939,plain,
! [SV210: $i] :
( ( ! [SY2375: $i,SY2376: $i,SY2377: $i,SY2378: $i,SY2379: $i,SY2380: $i] :
( ( ( hAPP @ ( hAPP @ SV210 @ SY2375 ) @ SY2376 )
= SY2376 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV210 @ SY2377 @ SY2378 @ SY2375 @ SY2379 @ SY2380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1940,plain,
! [SV211: $i] :
( ( ! [SY2381: $i,SY2382: $i,SY2383: $i,SY2384: $i,SY2385: $i,SY2386: $i,SY2387: $i,SY2388: $i] :
( ( ( hAPP @ ( hAPP @ SV211 @ SY2381 ) @ ( hAPP @ ( hAPP @ SV211 @ SY2382 ) @ SY2383 ) )
= ( hAPP @ ( hAPP @ SV211 @ ( hAPP @ ( hAPP @ SV211 @ SY2381 ) @ SY2382 ) ) @ SY2383 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV211 @ SY2384 @ SY2385 @ SY2386 @ SY2387 @ SY2388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1941,plain,
! [SV212: $i] :
( ( ! [SY2389: $i,SY2390: $i,SY2391: $i,SY2392: $i,SY2393: $i,SY2394: $i,SY2395: $i] :
( ( ( hAPP @ ( hAPP @ SV212 @ SY2389 ) @ SY2390 )
= ( hAPP @ ( hAPP @ SV212 @ SY2390 ) @ SY2389 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV212 @ SY2391 @ SY2392 @ SY2393 @ SY2394 @ SY2395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1342]) ).
thf(1942,plain,
! [SV213: $i] :
( ( ! [SY2396: $i,SY2397: $i,SY2398: $i,SY2399: $i,SY2400: $i,SY2401: $i,SY2402: $i,SY2403: $i] :
( ( ( hAPP @ ( hAPP @ SV213 @ ( hAPP @ ( hAPP @ SV213 @ SY2396 ) @ SY2397 ) ) @ SY2398 )
= ( hAPP @ ( hAPP @ SV213 @ ( hAPP @ ( hAPP @ SV213 @ SY2396 ) @ SY2398 ) ) @ SY2397 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV213 @ SY2399 @ SY2400 @ SY2401 @ SY2402 @ SY2403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1943,plain,
! [SV214: $i] :
( ( ! [SY2404: $i,SY2405: $i,SY2406: $i,SY2407: $i,SY2408: $i,SY2409: $i,SY2410: $i,SY2411: $i] :
( ( ( hAPP @ ( hAPP @ SV214 @ SY2404 ) @ ( hAPP @ ( hAPP @ SV214 @ SY2405 ) @ SY2406 ) )
= ( hAPP @ ( hAPP @ SV214 @ SY2405 ) @ ( hAPP @ ( hAPP @ SV214 @ SY2404 ) @ SY2406 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV214 @ SY2407 @ SY2408 @ SY2409 @ SY2410 @ SY2411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1944,plain,
! [SV215: $i] :
( ( ! [SY2412: $i,SY2413: $i,SY2414: $i,SY2415: $i,SY2416: $i,SY2417: $i,SY2418: $i,SY2419: $i] :
( ( ( hAPP @ ( hAPP @ SV215 @ ( hAPP @ ( hAPP @ SV215 @ SY2412 ) @ SY2413 ) ) @ SY2414 )
= ( hAPP @ ( hAPP @ SV215 @ SY2412 ) @ ( hAPP @ ( hAPP @ SV215 @ SY2413 ) @ SY2414 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV215 @ SY2415 @ SY2416 @ SY2417 @ SY2418 @ SY2419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1945,plain,
! [SV216: $i] :
( ( ! [SY2420: $i,SY2421: $i,SY2422: $i,SY2423: $i,SY2424: $i,SY2425: $i,SY2426: $i,SY2427: $i,SY2428: $i] :
( ( ( hAPP @ ( hAPP @ SV216 @ ( hAPP @ ( hAPP @ SV216 @ SY2420 ) @ SY2421 ) ) @ ( hAPP @ ( hAPP @ SV216 @ SY2422 ) @ SY2423 ) )
= ( hAPP @ ( hAPP @ SV216 @ ( hAPP @ ( hAPP @ SV216 @ SY2420 ) @ SY2422 ) ) @ ( hAPP @ ( hAPP @ SV216 @ SY2421 ) @ SY2423 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV216 @ SY2424 @ SY2425 @ SY2426 @ SY2427 @ SY2428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1946,plain,
! [SV217: $i] :
( ( ! [SY2429: $i,SY2430: $i,SY2431: $i,SY2432: $i,SY2433: $i,SY2434: $i,SY2435: $i,SY2436: $i] :
( ( ( hAPP @ ( hAPP @ SV217 @ SY2429 ) @ ( hAPP @ ( hAPP @ SV217 @ SY2430 ) @ SY2431 ) )
= ( hAPP @ ( hAPP @ SV217 @ SY2430 ) @ ( hAPP @ ( hAPP @ SV217 @ SY2429 ) @ SY2431 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY2432 @ SV217 @ SY2433 @ SY2434 @ SY2435 @ SY2436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(1947,plain,
! [SV218: $i] :
( ( ! [SY2437: $i,SY2438: $i,SY2439: $i,SY2440: $i,SY2441: $i,SY2442: $i,SY2443: $i,SY2444: $i] :
( ( ( hAPP @ ( hAPP @ SV218 @ SY2437 ) @ ( hAPP @ ( hAPP @ SV218 @ SY2438 ) @ SY2439 ) )
= ( hAPP @ ( hAPP @ SV218 @ ( hAPP @ ( hAPP @ SV218 @ SY2437 ) @ SY2438 ) ) @ SY2439 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY2440 @ SV218 @ SY2441 @ SY2442 @ SY2443 @ SY2444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1348]) ).
thf(1948,plain,
! [SV219: $i] :
( ( ! [SY2445: $i,SY2446: $i,SY2447: $i,SY2448: $i,SY2449: $i,SY2450: $i,SY2451: $i,SY2452: $i] :
( ( ( hAPP @ ( hAPP @ SV219 @ ( hAPP @ ( hAPP @ SV219 @ SY2445 ) @ SY2446 ) ) @ SY2447 )
= ( hAPP @ ( hAPP @ SV219 @ SY2445 ) @ ( hAPP @ ( hAPP @ SV219 @ SY2446 ) @ SY2447 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY2448 @ SV219 @ SY2449 @ SY2450 @ SY2451 @ SY2452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1949,plain,
! [SV220: $i] :
( ( ! [SY2453: $i,SY2454: $i,SY2455: $i,SY2456: $i,SY2457: $i,SY2458: $i,SY2459: $i,SY2460: $i] :
( ( ( hAPP @ ( hAPP @ SV220 @ ( hAPP @ ( hAPP @ SV220 @ SY2453 ) @ SY2454 ) ) @ SY2455 )
= ( hAPP @ ( hAPP @ SV220 @ ( hAPP @ ( hAPP @ SV220 @ SY2453 ) @ SY2455 ) ) @ SY2454 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY2456 @ SV220 @ SY2457 @ SY2458 @ SY2459 @ SY2460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(1950,plain,
! [SV221: $i] :
( ( ! [SY2461: $i,SY2462: $i,SY2463: $i,SY2464: $i,SY2465: $i,SY2466: $i,SY2467: $i,SY2468: $i,SY2469: $i] :
( ( ( hAPP @ ( hAPP @ SV221 @ ( hAPP @ ( hAPP @ SV221 @ SY2461 ) @ SY2462 ) ) @ ( hAPP @ ( hAPP @ SV221 @ SY2463 ) @ SY2464 ) )
= ( hAPP @ ( hAPP @ SV221 @ SY2463 ) @ ( hAPP @ ( hAPP @ SV221 @ ( hAPP @ ( hAPP @ SV221 @ SY2461 ) @ SY2462 ) ) @ SY2464 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY2465 @ SV221 @ SY2466 @ SY2467 @ SY2468 @ SY2469 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1351]) ).
thf(1951,plain,
! [SV222: $i] :
( ( ! [SY2470: $i,SY2471: $i,SY2472: $i,SY2473: $i,SY2474: $i,SY2475: $i,SY2476: $i,SY2477: $i,SY2478: $i] :
( ( ( hAPP @ ( hAPP @ SV222 @ ( hAPP @ ( hAPP @ SV222 @ SY2470 ) @ SY2471 ) ) @ ( hAPP @ ( hAPP @ SV222 @ SY2472 ) @ SY2473 ) )
= ( hAPP @ ( hAPP @ SV222 @ SY2470 ) @ ( hAPP @ ( hAPP @ SV222 @ SY2471 ) @ ( hAPP @ ( hAPP @ SV222 @ SY2472 ) @ SY2473 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY2474 @ SV222 @ SY2475 @ SY2476 @ SY2477 @ SY2478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1352]) ).
thf(1952,plain,
! [SV223: $i] :
( ( ! [SY2479: $i,SY2480: $i,SY2481: $i,SY2482: $i,SY2483: $i,SY2484: $i,SY2485: $i,SY2486: $i,SY2487: $i] :
( ( ( hAPP @ ( hAPP @ SV223 @ ( hAPP @ ( hAPP @ SV223 @ SY2479 ) @ SY2480 ) ) @ ( hAPP @ ( hAPP @ SV223 @ SY2481 ) @ SY2482 ) )
= ( hAPP @ ( hAPP @ SV223 @ ( hAPP @ ( hAPP @ SV223 @ SY2479 ) @ SY2481 ) ) @ ( hAPP @ ( hAPP @ SV223 @ SY2480 ) @ SY2482 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY2483 @ SV223 @ SY2484 @ SY2485 @ SY2486 @ SY2487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1353]) ).
thf(1953,plain,
! [SV224: $i] :
( ( ! [SY2488: $i,SY2489: $i,SY2490: $i,SY2491: $i,SY2492: $i,SY2493: $i] :
( ( ( hAPP @ ( hAPP @ SV224 @ SY2488 ) @ SY2489 )
= SY2488 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY2490 @ SV224 @ SY2491 @ SY2492 @ SY2489 @ SY2493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1954,plain,
! [SV225: $i] :
( ( ! [SY2494: $i,SY2495: $i,SY2496: $i,SY2497: $i,SY2498: $i,SY2499: $i] :
( ( ( hAPP @ ( hAPP @ SV225 @ SY2494 ) @ SY2495 )
= SY2495 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY2496 @ SV225 @ SY2497 @ SY2498 @ SY2494 @ SY2499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1355]) ).
thf(1955,plain,
! [SV226: $i] :
( ( ! [SY2500: $i,SY2501: $i,SY2502: $i,SY2503: $i,SY2504: $i,SY2505: $i] :
( ( ( hAPP @ ( hAPP @ SV226 @ SY2500 ) @ SY2501 )
= SY2501 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY2502 @ SV226 @ SY2503 @ SY2501 @ SY2504 @ SY2505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1356]) ).
thf(1956,plain,
! [SV227: $i] :
( ( ! [SY2506: $i,SY2507: $i,SY2508: $i,SY2509: $i,SY2510: $i,SY2511: $i] :
( ( ( hAPP @ ( hAPP @ SV227 @ SY2506 ) @ SY2507 )
= SY2506 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY2508 @ SV227 @ SY2509 @ SY2506 @ SY2510 @ SY2511 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1357]) ).
thf(1957,plain,
! [SV228: $i] :
( ( ! [SY2512: $i,SY2513: $i,SY2514: $i,SY2515: $i,SY2516: $i,SY2517: $i,SY2518: $i,SY2519: $i] :
( ( ( hAPP @ ( hAPP @ SV228 @ ( hAPP @ ( hAPP @ SY2512 @ SY2513 ) @ SY2514 ) ) @ SY2515 )
= ( hAPP @ ( hAPP @ SY2512 @ ( hAPP @ ( hAPP @ SV228 @ SY2513 ) @ SY2515 ) ) @ ( hAPP @ ( hAPP @ SV228 @ SY2514 ) @ SY2515 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY2512 @ SV228 @ SY2516 @ SY2517 @ SY2518 @ SY2519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(1958,plain,
! [SV229: $i] :
( ( ! [SY2520: $i,SY2521: $i,SY2522: $i,SY2523: $i,SY2524: $i,SY2525: $i,SY2526: $i] :
( ( ( hAPP @ ( hAPP @ SV229 @ SY2520 ) @ SY2521 )
= ( hAPP @ ( hAPP @ SV229 @ SY2521 ) @ SY2520 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY2522 @ SV229 @ SY2523 @ SY2524 @ SY2525 @ SY2526 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(1959,plain,
! [SV230: $i] :
( ( ! [SY2527: $i,SY2528: $i,SY2529: $i,SY2530: $i,SY2531: $i,SY2532: $i] :
( ( ( hAPP @ ( hAPP @ SV230 @ SY2527 ) @ SY2528 )
= SY2527 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV230 @ SY2529 @ SY2530 @ SY2528 @ SY2531 @ SY2532 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(1960,plain,
! [SV231: $i] :
( ( ! [SY2533: $i,SY2534: $i,SY2535: $i,SY2536: $i,SY2537: $i,SY2538: $i] :
( ( ( hAPP @ ( hAPP @ SV231 @ SY2533 ) @ SY2534 )
= SY2534 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV231 @ SY2535 @ SY2536 @ SY2533 @ SY2537 @ SY2538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1961,plain,
! [SV232: $i] :
( ( ! [SY2539: $i,SY2540: $i,SY2541: $i,SY2542: $i,SY2543: $i,SY2544: $i] :
( ( ( hAPP @ ( hAPP @ SV232 @ SY2539 ) @ SY2539 )
= ( hAPP @ ( hAPP @ SY2540 @ ( hAPP @ ( hAPP @ SV232 @ SY2541 ) @ SY2541 ) ) @ SY2539 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV232 @ SY2540 @ SY2542 @ SY2543 @ SY2541 @ SY2544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1362]) ).
thf(1962,plain,
! [SV233: $i] :
( ( ! [SY2545: $i,SY2546: $i,SY2547: $i,SY2548: $i,SY2549: $i,SY2550: $i,SY2551: $i] :
( ( ( hAPP @ ( hAPP @ SV233 @ SY2545 ) @ ( hAPP @ ( hAPP @ SY2546 @ SY2547 ) @ SY2545 ) )
= ( hAPP @ ( hAPP @ SY2546 @ ( hAPP @ ( hAPP @ SV233 @ SY2547 ) @ SY2548 ) ) @ SY2545 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV233 @ SY2546 @ SY2549 @ SY2550 @ SY2548 @ SY2551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1363]) ).
thf(1963,plain,
! [SV234: $i] :
( ( ! [SY2552: $i,SY2553: $i,SY2554: $i,SY2555: $i,SY2556: $i,SY2557: $i,SY2558: $i] :
( ( ( hAPP @ ( hAPP @ SV234 @ ( hAPP @ ( hAPP @ SY2552 @ SY2553 ) @ SY2554 ) ) @ SY2554 )
= ( hAPP @ ( hAPP @ SY2552 @ ( hAPP @ ( hAPP @ SV234 @ SY2553 ) @ SY2555 ) ) @ SY2554 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV234 @ SY2552 @ SY2556 @ SY2557 @ SY2555 @ SY2558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1364]) ).
thf(1964,plain,
! [SV235: $i] :
( ( ! [SY2559: $i,SY2560: $i,SY2561: $i,SY2562: $i,SY2563: $i,SY2564: $i,SY2565: $i,SY2566: $i] :
( ( ( hAPP @ ( hAPP @ SV235 @ ( hAPP @ ( hAPP @ SY2559 @ SY2560 ) @ SY2561 ) ) @ ( hAPP @ ( hAPP @ SY2559 @ SY2562 ) @ SY2561 ) )
= ( hAPP @ ( hAPP @ SY2559 @ ( hAPP @ ( hAPP @ SV235 @ SY2560 ) @ SY2562 ) ) @ SY2561 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV235 @ SY2559 @ SY2563 @ SY2564 @ SY2565 @ SY2566 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1365]) ).
thf(1965,plain,
! [SV236: $i] :
( ( ! [SY2567: $i,SY2568: $i,SY2569: $i,SY2570: $i,SY2571: $i] :
( ( SV236 = SY2567 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY2568 @ SY2567 ) @ SV236 ) )
| ~ ( c_ListOrder_Ostep1 @ SY2568 @ ( c_List_Olist_OCons @ SY2567 @ SY2569 @ SY2570 ) @ ( c_List_Olist_OCons @ SV236 @ SY2571 @ SY2570 ) @ SY2570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1966,plain,
! [SV237: $i] :
( ( ! [SY2572: $i,SY2573: $i,SY2574: $i,SY2575: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV237 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SY2572 ) @ SY2573 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SY2574 ) @ SY2575 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SY2572 ) @ SY2574 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SY2573 ) @ SY2575 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1367]) ).
thf(1967,plain,
! [SV238: $i] :
( ( ! [SY2576: $i,SY2577: $i,SY2578: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV238 ) @ SY2576 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2577 ) @ SY2578 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY2576 ) @ SY2578 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV238 ) @ SY2577 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1368]) ).
thf(1968,plain,
! [SV239: $i] :
( ( ! [SY2579: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV239 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2579 @ SV239 ) @ ( c_HOL_Ozero__class_Ozero @ SV239 ) @ SV239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1969,plain,
! [SV240: $i] :
( ( ! [SY2580: $i,SY2581: $i] :
( ~ ( class_Orderings_Olinorder @ SV240 )
| ( ( c_Orderings_Oord__class_Omax @ SY2580 @ SY2581 @ SV240 )
= ( c_Orderings_Oord__class_Omax @ SY2581 @ SY2580 @ SV240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1970,plain,
! [SV241: $i] :
( ( ! [SY2582: $i,SY2583: $i] :
( ( ( c_Lambda_Oliftn @ SV241 @ ( c_Lambda_OdB_OVar @ SY2582 ) @ SY2583 )
= ( c_Lambda_OdB_OVar @ SY2582 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY2582 @ SY2583 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1971,plain,
! [SV242: $i] :
( ( ! [SY2584: $i,SY2585: $i,SY2586: $i] :
( ( c_Type_Otyping @ SV242 @ SY2584 @ SY2585 )
| ~ ( c_Type_Otyping @ SV242 @ SY2586 @ SY2585 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY2586 ) @ SY2584 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(1972,plain,
! [SV243: $i] :
( ( ! [SY2587: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV243 @ SY2587 )
= ( c_List_Olist_ONil @ SY2587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1373]) ).
thf(1973,plain,
! [SV244: $i] :
( ( ! [SY2588: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV244 ) ) @ SY2588 )
= ( c_Lambda_OdB_OVar @ SV244 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV244 @ SY2588 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1974,plain,
! [SV245: $i] :
( ( ! [SY2589: $i,SY2590: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV245 ) @ SY2589 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY2590 ) @ SY2589 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV245 ) @ SY2590 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1975,plain,
! [SV246: $i] :
( ( ( SV246
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV246 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV246 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV246 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV246 ) ) )
| ( SV246
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV246 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV246 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1378]) ).
thf(1976,plain,
! [SV247: $i] :
( ( ! [SY2591: $i] :
( ( c_HOL_Oord__class_Oless @ SV247 @ SV247 @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV247 ) @ SY2591 @ SV247 )
= ( c_Lambda_Oliftn @ SV247 @ SY2591 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1379]) ).
thf(1977,plain,
! [SV248: $i] :
( ( ! [SY2592: $i,SY2593: $i] :
( ( c_List_Olist_OCons @ SV248 @ SY2592 @ SY2593 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY2593 ) @ ( c_List_Olist_OCons @ SV248 @ SY2592 @ SY2593 ) @ SY2593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1380]) ).
thf(1978,plain,
! [SV249: $i] :
( ( ! [SY2594: $i,SY2595: $i,SY2596: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV249 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV249 ) @ ( c_Orderings_Oord__class_Omax @ SY2594 @ SY2595 @ SV249 ) ) @ SY2596 )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV249 ) @ SY2594 ) @ SY2596 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV249 ) @ SY2595 ) @ SY2596 ) @ SV249 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1381]) ).
thf(1979,plain,
! [SV250: $i] :
( ( ! [SY2597: $i,SY2598: $i] :
( ( c_List_Olist_ONil @ SV250 )
= ( c_List_Omap @ SY2597 @ ( c_List_Olist_ONil @ SY2598 ) @ SY2598 @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1382]) ).
thf(1980,plain,
! [SV251: $i] :
( ( ! [SY2599: $i,SY2600: $i,SY2601: $i,SY2602: $i,SY2603: $i] :
( ( SV251 = SY2599 )
| ( c_ListOrder_Ostep1 @ SY2600 @ SV251 @ SY2599 @ SY2601 )
| ~ ( c_ListOrder_Ostep1 @ SY2600 @ ( c_List_Oappend @ SV251 @ ( c_List_Olist_OCons @ SY2602 @ ( c_List_Olist_ONil @ SY2601 ) @ SY2601 ) @ SY2601 ) @ ( c_List_Oappend @ SY2599 @ ( c_List_Olist_OCons @ SY2603 @ ( c_List_Olist_ONil @ SY2601 ) @ SY2601 ) @ SY2601 ) @ SY2601 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1383]) ).
thf(1981,plain,
! [SV252: $i] :
( ( ! [SY2604: $i,SY2605: $i,SY2606: $i] :
( ~ ( class_Orderings_Olinorder @ SV252 )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ SY2604 @ SY2605 @ SV252 ) @ SY2606 @ SV252 )
= ( c_Orderings_Oord__class_Omax @ SY2604 @ ( c_Orderings_Oord__class_Omax @ SY2605 @ SY2606 @ SV252 ) @ SV252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1384]) ).
thf(1982,plain,
! [SV253: $i] :
( ( ! [SY2607: $i,SY2608: $i,SY2609: $i] :
( ~ ( class_Orderings_Olinorder @ SV253 )
| ( ( c_Orderings_Oord__class_Omax @ SY2607 @ ( c_Orderings_Oord__class_Omax @ SY2608 @ SY2609 @ SV253 ) @ SV253 )
= ( c_Orderings_Oord__class_Omax @ SY2608 @ ( c_Orderings_Oord__class_Omax @ SY2607 @ SY2609 @ SV253 ) @ SV253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1983,plain,
! [SV254: $i] :
( ( ( c_List_Olist_ONil @ SV254 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV254 ) @ ( c_List_Olist_ONil @ SV254 ) @ SV254 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1984,plain,
! [SV255: $i] :
( ( ! [SY2610: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ SV255 @ SY2610 ) @ SY2610 )
= ( c_Transitive__Closure_Ortranclp @ SV255 @ SY2610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1387]) ).
thf(1985,plain,
! [SV256: $i] :
( ( ! [SY2611: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV256 ) ) @ ( c_Lambda_OdB_OAbs @ SY2611 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV256 ) @ SY2611 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(1986,plain,
! [SV257: $i] :
( ( ! [SY2612: $i,SY2613: $i] :
( ~ ( class_Orderings_Olinorder @ SV257 )
| ( ( c_Orderings_Oord__class_Omax @ SY2612 @ ( c_Orderings_Oord__class_Omax @ SY2612 @ SY2613 @ SV257 ) @ SV257 )
= ( c_Orderings_Oord__class_Omax @ SY2612 @ SY2613 @ SV257 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(1987,plain,
! [SV258: $i] :
( ( ! [SY2614: $i,SY2615: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV258 @ SY2614 @ SY2615 ) @ ( c_List_Olist_OCons @ SY2614 @ ( c_List_Olist_ONil @ SY2615 ) @ SY2615 ) @ SY2615 )
= ( c_List_Olist_OCons @ SY2614 @ ( c_List_Oreplicate @ SV258 @ SY2614 @ SY2615 ) @ SY2615 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1390]) ).
thf(1988,plain,
! [SV259: $i] :
( ( ! [SY2616: $i,SY2617: $i,SY2618: $i] :
( ( ( hAPP @ ( hAPP @ SV259 @ SY2616 ) @ SY2617 )
= SY2616 )
| ~ ( c_OrderedGroup_Omonoid__add @ SY2617 @ SV259 @ SY2618 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1391]) ).
thf(1989,plain,
! [SV260: $i] :
( ( ! [SY2619: $i,SY2620: $i,SY2621: $i] :
( ( ( hAPP @ ( hAPP @ SV260 @ SY2619 ) @ SY2620 )
= SY2620 )
| ~ ( c_OrderedGroup_Omonoid__add @ SY2619 @ SV260 @ SY2621 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1392]) ).
thf(1990,plain,
! [SV261: $i] :
( ( ! [SY2622: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV261 ) @ SY2622 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2622 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1991,plain,
! [SV262: $i] :
( ( ! [SY2623: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV262 ) @ SY2623 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV262 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1992,plain,
! [SV263: $i] :
( ( ! [SY2624: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV263 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SY2624 @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV263 ) @ SY2624 ) @ SY2624 ) @ SV263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1993,plain,
! [SV264: $i] :
( ( ! [SY2625: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV264 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV264 ) @ SY2625 ) @ SY2625 ) @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SY2625 @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1396]) ).
thf(1994,plain,
! [SV265: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV265 ) ) )
| ( SV265
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV265 ) ) )
| ( SV265
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV265 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV265 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(1995,plain,
! [SV266: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV266 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV266 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV266 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV266 ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV266 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1996,plain,
! [SV267: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV267 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV267 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV267 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( SV267
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV267 ) ) )
| ( SV267
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV267 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV267 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(1997,plain,
! [SV268: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV268 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV268 ) @ ( c_HOL_Ozero__class_Ozero @ SV268 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV268 ) )
= ( c_HOL_Ozero__class_Ozero @ SV268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1404]) ).
thf(1998,plain,
! [SV269: $i] :
( ( ! [SY2626: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV269 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ ( c_HOL_Ozero__class_Ozero @ SV269 ) ) @ SY2626 )
= SY2626 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1405]) ).
thf(1999,plain,
! [SV270: $i] :
( ( ! [SY2627: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV270 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV270 ) @ ( c_HOL_Ozero__class_Ozero @ SV270 ) ) @ SY2627 )
= SY2627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(2000,plain,
! [SV271: $i] :
( ( ! [SY2628: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV271 )
| ~ ( class_Int_Onumber__ring @ SV271 )
| ( SY2628
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ SY2628 ) @ ( c_HOL_Ozero__class_Ozero @ SV271 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(2001,plain,
! [SV272: $i] :
( ( ! [SY2629: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV272 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SY2629 ) @ ( c_HOL_Ozero__class_Ozero @ SV272 ) )
= SY2629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(2002,plain,
! [SV273: $i] :
( ( ! [SY2630: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV273 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ ( c_HOL_Ozero__class_Ozero @ SV273 ) ) @ SY2630 )
= SY2630 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1409]) ).
thf(2003,plain,
! [SV274: $i] :
( ( ! [SY2631: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV274 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ SY2631 ) @ ( c_HOL_Ozero__class_Ozero @ SV274 ) )
= SY2631 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(2004,plain,
! [SV275: $i] :
( ( ! [SY2632: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV275 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ SY2632 ) @ ( c_HOL_Ozero__class_Ozero @ SV275 ) )
= SY2632 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(2005,plain,
! [SV276: $i] :
( ( ! [SY2633: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV276 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ ( c_HOL_Ozero__class_Ozero @ SV276 ) ) @ SY2633 )
= SY2633 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1412]) ).
thf(2006,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)],[1413]) ).
thf(2007,plain,
! [SV277: $i] :
( ( ! [SY2634: $i] :
( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV277 @ SY2634 )
= SV277 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1414]) ).
thf(2008,plain,
! [SV278: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV278 @ tc_nat )
| ( SV278
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(2009,plain,
! [SV279: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV279 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(2010,plain,
! [SV280: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV280 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1422]) ).
thf(2011,plain,
! [SV281: $i] :
( ( ! [SY2635: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV281 )
| ( c_HOL_Oord__class_Oless @ SY2635 @ ( c_HOL_Ozero__class_Ozero @ SV281 ) @ SV281 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV281 ) @ SY2635 ) @ SY2635 ) @ ( c_HOL_Ozero__class_Ozero @ SV281 ) @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(2012,plain,
! [SV282: $i] :
( ( ! [SY2636: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV282 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV282 ) @ SY2636 ) @ SY2636 ) @ ( c_HOL_Ozero__class_Ozero @ SV282 ) @ SV282 )
| ~ ( c_HOL_Oord__class_Oless @ SY2636 @ ( c_HOL_Ozero__class_Ozero @ SV282 ) @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(2013,plain,
! [SV283: $i] :
( ( ! [SY2637: $i,SY2638: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV283 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV283 ) @ ( c_Power_Opower__class_Opower @ SY2637 @ SY2638 @ SV283 ) @ SV283 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV283 ) @ SY2637 @ SV283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(2014,plain,
! [SV284: $i] :
( ( ! [SY2639: $i,SY2640: $i,SY2641: $i] :
( ~ ( class_Orderings_Olinorder @ SV284 )
| ( c_HOL_Oord__class_Oless @ SY2639 @ SY2640 @ SV284 )
| ( c_HOL_Oord__class_Oless @ SY2639 @ SY2641 @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ SY2639 @ ( c_Orderings_Oord__class_Omax @ SY2641 @ SY2640 @ SV284 ) @ SV284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1426]) ).
thf(2015,plain,
! [SV285: $i] :
( ( ! [SY2642: $i,SY2643: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV285 ) @ SY2642 @ SY2643 )
= ( c_Lambda_OdB_OVar @ SV285 ) )
| ( SV285 = SY2643 )
| ( c_HOL_Oord__class_Oless @ SY2643 @ SV285 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1427]) ).
thf(2016,plain,
! [SV286: $i] :
( ( ( c_Predicate_Oconversep @ ( c_fequal @ SV286 ) @ SV286 @ SV286 )
= ( c_fequal @ SV286 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(2017,plain,
! [SV287: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV287 ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV287 ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV287 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(2018,plain,
! [SV288: $i] :
( ( ! [SY2644: $i] :
( ( c_List_Olist_ONil @ SV288 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2644 @ SV288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(2019,plain,
! [SV289: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV289 @ SV289 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1436]) ).
thf(2020,plain,
! [SV290: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ SV290 @ SV290 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1437]) ).
thf(2021,plain,
! [SV291: $i] :
( ( ! [SY2645: $i] :
( ~ ( class_Orderings_Oorder @ SV291 )
| ~ ( c_HOL_Oord__class_Oless @ SY2645 @ SY2645 @ SV291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(2022,plain,
! [SV292: $i] :
( ( ! [SY2646: $i] :
( ~ ( class_Orderings_Olinorder @ SV292 )
| ~ ( c_HOL_Oord__class_Oless @ SY2646 @ SY2646 @ SV292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(2023,plain,
! [SV293: $i] :
( ( ! [SY2647: $i] :
( ~ ( class_Orderings_Opreorder @ SV293 )
| ~ ( c_HOL_Oord__class_Oless @ SY2647 @ SY2647 @ SV293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1440]) ).
thf(2024,plain,
! [SV294: $i] :
( ( ! [SY2648: $i,SY2649: $i] :
( ( ( c_Lambda_Oliftn @ SV294 @ ( c_Lambda_OdB_OVar @ SY2648 ) @ SY2649 )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2648 ) @ SV294 ) ) )
| ( c_HOL_Oord__class_Oless @ SY2648 @ SY2649 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(2025,plain,
! [SV295: $i] :
( ( ! [SY2650: $i,SY2651: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV295 ) @ SY2650 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY2651 ) @ SY2650 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV295 ) @ SY2651 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(2026,plain,
! [SV296: $i] :
( ( ! [SY2652: $i,SY2653: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV296 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV296 ) @ SY2652 ) @ SY2653 ) @ SV296 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SY2653 @ SV296 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SY2652 @ SV296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(2027,plain,
! [SV297: $i] :
( ( ! [SY2654: $i,SY2655: $i,SY2656: $i,SY2657: $i,SY2658: $i] :
( ( c_ListOrder_Ostep1 @ SV297 @ SY2654 @ SY2655 @ SY2656 )
| ( SY2655 = SY2654 )
| ~ ( c_ListOrder_Ostep1 @ SV297 @ ( c_List_Olist_OCons @ SY2657 @ SY2654 @ SY2656 ) @ ( c_List_Olist_OCons @ SY2658 @ SY2655 @ SY2656 ) @ SY2656 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(2028,plain,
! [SV298: $i] :
( ( ! [SY2659: $i,SY2660: $i,SY2661: $i,SY2662: $i] :
( ( ( hAPP @ ( hAPP @ SV298 @ ( hAPP @ ( hAPP @ SV298 @ SY2659 ) @ SY2660 ) ) @ SY2661 )
= ( hAPP @ ( hAPP @ SV298 @ SY2659 ) @ ( hAPP @ ( hAPP @ SV298 @ SY2660 ) @ SY2661 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV298 @ SY2662 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1445]) ).
thf(2029,plain,
! [SV299: $i] :
( ( ! [SY2663: $i,SY2664: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV299 )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SY2663 @ SY2664 @ SV299 ) @ SV299 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV299 ) @ SY2663 ) @ ( c_List_Olistsum @ SY2664 @ SV299 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(2030,plain,
! [SV300: $i] :
( ( ! [SY2665: $i,SY2666: $i,SY2667: $i,SY2668: $i] :
( ( c_List_Omap @ SV300 @ ( c_List_Oappend @ SY2665 @ SY2666 @ SY2667 ) @ SY2667 @ SY2668 )
= ( c_List_Oappend @ ( c_List_Omap @ SV300 @ SY2665 @ SY2667 @ SY2668 ) @ ( c_List_Omap @ SV300 @ SY2666 @ SY2667 @ SY2668 ) @ SY2668 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(2031,plain,
! [SV301: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV301 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV301 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV301 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( SV301
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV301 ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV301 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1448]) ).
thf(2032,plain,
! [SV302: $i] :
( ( ! [SY2669: $i,SY2670: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV302 )
| ( c_HOL_Oord__class_Oless @ SY2669 @ SY2670 @ SV302 )
| ( c_HOL_Oord__class_Oless @ SY2670 @ SY2669 @ SV302 )
| ( SY2670 = SY2669 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1449]) ).
thf(2033,plain,
! [SV303: $i] :
( ( ! [SY2671: $i,SY2672: $i] :
( ~ ( class_Orderings_Olinorder @ SV303 )
| ( SY2671 = SY2672 )
| ( c_HOL_Oord__class_Oless @ SY2672 @ SY2671 @ SV303 )
| ( c_HOL_Oord__class_Oless @ SY2671 @ SY2672 @ SV303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(2034,plain,
! [SV304: $i] :
( ( ! [SY2673: $i] :
( ( c_HOL_Oord__class_Oless @ SV304 @ SY2673 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY2673 @ SV304 @ tc_nat )
| ( SY2673 = SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(2035,plain,
! [SV305: $i] :
( ( ! [SY2674: $i,SY2675: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV305 @ SY2674 ) @ SY2675 ) )
| ( c_HOL_Oord__class_Oless @ SY2674 @ SY2675 @ tc_nat )
| ( SY2675 = SY2674 )
| ( c_HOL_Oord__class_Oless @ SY2675 @ SY2674 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(2036,plain,
! [SV306: $i] :
( ( ! [SY2676: $i] :
( ( c_HOL_Oord__class_Oless @ SV306 @ SY2676 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SY2676 @ SV306 @ tc_nat )
| ( SY2676 = SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1453]) ).
thf(2037,plain,
! [SV307: $i] :
( ( ! [SY2677: $i,SY2678: $i] :
( ~ ( class_Orderings_Olinorder @ SV307 )
| ( c_HOL_Oord__class_Oless @ SY2677 @ SY2678 @ SV307 )
| ( c_HOL_Oord__class_Oless @ SY2678 @ SY2677 @ SV307 )
| ( SY2678 = SY2677 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1454]) ).
thf(2038,plain,
! [SV308: $i] :
( ( ! [SY2679: $i,SY2680: $i,SY2681: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV308 @ SY2679 @ SY2680 ) @ ( c_List_Oreplicate @ SY2681 @ SY2679 @ SY2680 ) @ SY2680 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SY2681 @ SY2679 @ SY2680 ) @ ( c_List_Oreplicate @ SV308 @ SY2679 @ SY2680 ) @ SY2680 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1455]) ).
thf(2039,plain,
! [SV309: $i] :
( ( ! [SY2682: $i,SY2683: $i] :
( ~ ( class_Orderings_Olinorder @ SV309 )
| ( c_HOL_Oord__class_Oless @ SY2682 @ SY2683 @ SV309 )
| ( SY2683 = SY2682 )
| ( c_HOL_Oord__class_Oless @ SY2683 @ SY2682 @ SV309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1456]) ).
thf(2040,plain,
! [SV310: $i] :
( ( ! [SY2684: $i,SY2685: $i] :
( ~ ( class_Orderings_Olinorder @ SV310 )
| ( SY2684 = SY2685 )
| ( c_HOL_Oord__class_Oless @ SY2684 @ SY2685 @ SV310 )
| ( c_HOL_Oord__class_Oless @ SY2685 @ SY2684 @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(2041,plain,
! [SV311: $i] :
( ( ! [SY2686: $i] :
( ~ ( class_Orderings_Olinorder @ SV311 )
| ( ( c_Orderings_Oord__class_Omax @ SY2686 @ SY2686 @ SV311 )
= SY2686 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(2042,plain,
! [SV312: $i] :
( ( ! [SY2687: $i,SY2688: $i,SY2689: $i,SY2690: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV312 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV312 ) @ SY2687 ) @ SY2688 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV312 ) @ SY2689 ) @ SY2690 ) @ SV312 )
| ~ ( c_HOL_Oord__class_Oless @ SY2688 @ SY2690 @ SV312 )
| ~ ( c_HOL_Oord__class_Oless @ SY2687 @ SY2689 @ SV312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(2043,plain,
! [SV313: $i] :
( ( ! [SY2691: $i,SY2692: $i,SY2693: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV313 ) @ SY2691 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2692 ) @ SY2693 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2691 @ SY2693 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV313 @ SY2692 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(2044,plain,
! [SV314: $i] :
( ( ! [SY2694: $i,SY2695: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV314 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2694 @ SV314 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2695 @ SV314 ) @ SV314 )
| ~ ( c_HOL_Oord__class_Oless @ SY2694 @ SY2695 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(2045,plain,
! [SV315: $i] :
( ( ! [SY2696: $i,SY2697: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV315 )
| ( c_HOL_Oord__class_Oless @ SY2696 @ SY2697 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2696 @ SV315 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2697 @ SV315 ) @ SV315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(2046,plain,
! [SV316: $i] :
( ( ! [SY2698: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV316 )
| ( ( c_List_Olistsum @ SY2698 @ SV316 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV316 ) @ SY2698 @ ( c_HOL_Ozero__class_Ozero @ SV316 ) @ SV316 @ SV316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(2047,plain,
! [SV317: $i] :
( ( ( SV317
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV317 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV317 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV317 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV317
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV317 ) ) )
| ( SV317
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV317 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV317 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(2048,plain,
! [SV318: $i] :
( ( ! [SY2699: $i,SY2700: $i,SY2701: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV318 ) @ SY2699 ) @ SY2700 @ SY2701 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SV318 @ SY2700 @ SY2701 ) @ ( c_List_Oreplicate @ SY2699 @ SY2700 @ SY2701 ) @ SY2701 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(2049,plain,
! [SV319: $i] :
( ( ! [SY2702: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV319 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV319 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2702 @ SV319 ) @ SV319 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2702 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(2050,plain,
! [SV320: $i] :
( ( ! [SY2703: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV320 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2703 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV320 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2703 @ SV320 ) @ SV320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(2051,plain,
! [SV321: $i] :
( ( ! [SY2704: $i,SY2705: $i,SY2706: $i,SY2707: $i,SY2708: $i] :
( ( SV321 = SY2704 )
| ( SY2705 = SY2706 )
| ~ ( c_ListOrder_Ostep1 @ SY2707 @ ( c_List_Oappend @ SV321 @ ( c_List_Olist_OCons @ SY2705 @ ( c_List_Olist_ONil @ SY2708 ) @ SY2708 ) @ SY2708 ) @ ( c_List_Oappend @ SY2704 @ ( c_List_Olist_OCons @ SY2706 @ ( c_List_Olist_ONil @ SY2708 ) @ SY2708 ) @ SY2708 ) @ SY2708 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(2052,plain,
! [SV322: $i] :
( ( ! [SY2709: $i,SY2710: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV322 @ SY2709 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY2710 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV322 ) @ SY2710 ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ SY2710 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY2709 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(2053,plain,
! [SV323: $i] :
( ( ! [SY2711: $i,SY2712: $i,SY2713: $i] :
( ( c_List_Olistsp @ SV323 @ ( c_List_Oappend @ SY2711 @ SY2712 @ SY2713 ) @ SY2713 )
| ~ ( c_List_Olistsp @ SV323 @ SY2712 @ SY2713 )
| ~ ( c_List_Olistsp @ SV323 @ SY2711 @ SY2713 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1472]) ).
thf(2054,plain,
! [SV324: $i] :
( ( ! [SY2714: $i,SY2715: $i,SY2716: $i,SY2717: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV324 @ SY2714 @ SY2715 @ ( c_Lambda_OdB_OAbs @ SY2716 ) @ SY2717 )
= ( hAPP @ ( hAPP @ SY2715 @ SY2716 ) @ ( c_Lambda_OdB_OdB__rec @ SV324 @ SY2714 @ SY2715 @ SY2716 @ SY2717 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(2055,plain,
! [SV325: $i] :
( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV325 )
| ( c_OrderedGroup_Osemigroup__add @ ( c_HOL_Oplus__class_Oplus @ SV325 ) @ SV325 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(2056,plain,
! [SV326: $i] :
( ( ! [SY2718: $i,SY2719: $i,SY2720: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV326 )
| ( c_HOL_Oord__class_Oless @ SY2718 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV326 ) @ SY2719 ) @ SY2720 ) @ SV326 )
| ~ ( c_HOL_Oord__class_Oless @ SY2718 @ SY2720 @ SV326 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SY2719 @ SV326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(2057,plain,
! [SV327: $i] :
( ( ! [SY2721: $i,SY2722: $i,SY2723: $i,SY2724: $i,SY2725: $i] :
( ( c_List_Ofoldr @ SV327 @ ( c_List_Olist_OCons @ SY2721 @ SY2722 @ SY2723 ) @ SY2724 @ SY2723 @ SY2725 )
= ( hAPP @ ( hAPP @ SV327 @ SY2721 ) @ ( c_List_Ofoldr @ SV327 @ SY2722 @ SY2724 @ SY2723 @ SY2725 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(2058,plain,
! [SV328: $i] :
( ( ! [SY2726: $i,SY2727: $i,SY2728: $i,SY2729: $i] :
( ~ ( hBOOL @ ( hAPP @ SV328 @ ( c_Lambda_OdB_OdB__case @ SY2726 @ SY2727 @ SY2728 @ ( c_Lambda_OdB_OAbs @ SY2729 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV328 @ ( hAPP @ SY2728 @ SY2729 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(2059,plain,
! [SV329: $i] :
( ( ! [SY2730: $i,SY2731: $i,SY2732: $i,SY2733: $i] :
( ~ ( hBOOL @ ( hAPP @ SV329 @ ( c_Lambda_OdB_OdB__case @ SY2730 @ SY2731 @ SY2732 @ ( c_Lambda_OdB_OAbs @ SY2733 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV329 @ ( hAPP @ SY2732 @ SY2733 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1479]) ).
thf(2060,plain,
! [SV330: $i] :
( ( ! [SY2734: $i,SY2735: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ SV330 @ SY2734 @ SY2735 ) @ SY2735 @ SY2734 )
= SV330 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(2061,plain,
! [SV331: $i] :
( ( ! [SY2736: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV331 ) @ SY2736 ) @ SV331 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1481]) ).
thf(2062,plain,
! [SV332: $i] :
( ( ! [SY2737: $i] :
~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV332 ) @ SY2737 ) @ SY2737 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(2063,plain,
! [SV333: $i] :
( ( ! [SY2738: $i,SY2739: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV333 ) @ ( c_List_Olist_OCons @ SY2738 @ SY2739 @ SV333 ) @ SV333 )
= ( c_List_Olist_OCons @ SY2738 @ SY2739 @ SV333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1487]) ).
thf(2064,plain,
! [SV334: $i] :
( ( ! [SY2740: $i,SY2741: $i,SY2742: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV334 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV334 ) @ SY2740 ) @ SY2741 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV334 ) @ SY2742 ) @ SY2741 ) @ SV334 )
| ~ ( c_HOL_Oord__class_Oless @ SY2740 @ SY2742 @ SV334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1488]) ).
thf(2065,plain,
! [SV335: $i] :
( ( ! [SY2743: $i,SY2744: $i,SY2745: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV335 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV335 ) @ SY2743 ) @ SY2744 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV335 ) @ SY2745 ) @ SY2744 ) @ SV335 )
| ~ ( c_HOL_Oord__class_Oless @ SY2743 @ SY2745 @ SV335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(2066,plain,
! [SV336: $i] :
( ( ! [SY2746: $i,SY2747: $i,SY2748: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV336 )
| ( c_HOL_Oord__class_Oless @ SY2746 @ SY2747 @ SV336 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV336 ) @ SY2746 ) @ SY2748 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV336 ) @ SY2747 ) @ SY2748 ) @ SV336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(2067,plain,
! [SV337: $i] :
( ( ! [SY2749: $i,SY2750: $i,SY2751: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV337 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV337 ) @ SY2749 ) @ SY2750 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV337 ) @ SY2749 ) @ SY2751 ) @ SV337 )
| ~ ( c_HOL_Oord__class_Oless @ SY2750 @ SY2751 @ SV337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1491]) ).
thf(2068,plain,
! [SV338: $i] :
( ( ! [SY2752: $i,SY2753: $i,SY2754: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV338 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV338 ) @ SY2752 ) @ SY2753 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV338 ) @ SY2752 ) @ SY2754 ) @ SV338 )
| ~ ( c_HOL_Oord__class_Oless @ SY2753 @ SY2754 @ SV338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(2069,plain,
! [SV339: $i] :
( ( ! [SY2755: $i,SY2756: $i,SY2757: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV339 )
| ( c_HOL_Oord__class_Oless @ SY2755 @ SY2756 @ SV339 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SY2757 ) @ SY2755 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SY2757 ) @ SY2756 ) @ SV339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(2070,plain,
! [SV340: $i] :
( ( ! [SY2758: $i,SY2759: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV340 ) @ SY2758 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2759 ) @ SY2758 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV340 @ SY2759 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(2071,plain,
! [SV341: $i] :
( ( ! [SY2760: $i,SY2761: $i] :
( ( c_HOL_Oord__class_Oless @ SV341 @ SY2760 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2761 ) @ SV341 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2761 ) @ SY2760 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(2072,plain,
! [SV342: $i] :
( ( ! [SY2762: $i,SY2763: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV342 ) @ SY2762 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV342 ) @ SY2763 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SY2762 @ SY2763 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(2073,plain,
! [SV343: $i] :
( ( ( SV343
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV343 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV343 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV343 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV343 ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV343 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(2074,plain,
! [SV344: $i] :
( ( ! [SY2764: $i,SY2765: $i,SY2766: $i] :
( ( c_Type_Otyping @ SV344 @ SY2764 @ SY2765 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY2766 ) @ SY2764 ) )
| ~ ( c_Type_Otyping @ SV344 @ SY2766 @ SY2765 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1500]) ).
thf(2075,plain,
! [SV345: $i] :
( ( ! [SY2767: $i,SY2768: $i,SY2769: $i,SY2770: $i,SY2771: $i] :
( ( c_ListOrder_Ostep1 @ SV345 @ SY2767 @ SY2768 @ SY2769 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV345 @ SY2770 ) @ SY2771 ) )
| ~ ( c_ListOrder_Ostep1 @ SV345 @ ( c_List_Olist_OCons @ SY2770 @ SY2767 @ SY2769 ) @ ( c_List_Olist_OCons @ SY2771 @ SY2768 @ SY2769 ) @ SY2769 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1501]) ).
thf(2076,plain,
! [SV346: $i] :
( ( ! [SY2772: $i,SY2773: $i,SY2774: $i,SY2775: $i] :
( ( c_ListOrder_Ostep1 @ SV346 @ ( c_List_Olist_OCons @ SY2772 @ SY2773 @ SY2774 ) @ ( c_List_Olist_OCons @ SY2772 @ SY2775 @ SY2774 ) @ SY2774 )
| ~ ( c_ListOrder_Ostep1 @ SV346 @ SY2773 @ SY2775 @ SY2774 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(2077,plain,
! [SV347: $i] :
( ( ! [SY2776: $i,SY2777: $i,SY2778: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV347 @ SY2776 @ SY2777 ) @ ( c_List_Olist_OCons @ SY2776 @ SY2778 @ SY2777 ) @ SY2777 )
= ( c_List_Olist_OCons @ SY2776 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV347 @ SY2776 @ SY2777 ) @ SY2778 @ SY2777 ) @ SY2777 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(2078,plain,
! [SV348: $i] :
( ( ! [SY2779: $i,SY2780: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV348 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY2779 ) @ SY2780 ) @ SV348 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV348 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2779 @ SV348 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY2780 @ SV348 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(2079,plain,
! [SV349: $i] :
( ( ! [SY2781: $i,SY2782: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV349 )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ SY2781 @ SY2782 @ SV349 ) @ SV349 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV349 ) @ ( c_List_Olistsum @ SY2781 @ SV349 ) ) @ ( c_List_Olistsum @ SY2782 @ SV349 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(2080,plain,
! [SV350: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV350 ) @ ( c_List_Olist_ONil @ SV350 ) @ SV350 )
= ( c_List_Olist_ONil @ SV350 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1509]) ).
thf(2081,plain,
! [SV351: $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 ) @ SV351 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV351 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(2082,plain,
! [SV352: $i] :
( ( ! [SY2783: $i,SY2784: $i,SY2785: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV352 @ SY2783 @ SY2784 ) @ SY2785 @ SY2784 )
= ( c_List_Oappend @ SV352 @ ( c_List_Oappend @ SY2783 @ SY2785 @ SY2784 ) @ SY2784 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1511]) ).
thf(2083,plain,
! [SV353: $i] :
( ( ! [SY2786: $i,SY2787: $i,SY2788: $i] :
( ( c_List_Oappend @ SV353 @ ( c_List_Oappend @ SY2786 @ SY2787 @ SY2788 ) @ SY2788 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV353 @ SY2786 @ SY2788 ) @ SY2787 @ SY2788 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1512]) ).
thf(2084,plain,
! [SV354: $i] :
( ( ! [SY2789: $i,SY2790: $i,SY2791: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV354 @ SY2789 @ SY2790 ) @ SY2791 @ SY2790 )
= ( c_List_Oappend @ SV354 @ ( c_List_Oappend @ SY2789 @ SY2791 @ SY2790 ) @ SY2790 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(2085,plain,
! [SV355: $i] :
( ( ! [SY2792: $i,SY2793: $i,SY2794: $i] :
( ( c_List_Oappend @ SV355 @ ( c_List_Oappend @ SY2792 @ SY2793 @ SY2794 ) @ SY2794 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV355 @ SY2792 @ SY2794 ) @ SY2793 @ SY2794 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(2086,plain,
! [SV356: $i] :
( ( ! [SY2795: $i,SY2796: $i] :
( ~ ( class_Orderings_Oorder @ SV356 )
| ~ ( c_HOL_Oord__class_Oless @ SY2795 @ SY2796 @ SV356 )
| ~ ( c_HOL_Oord__class_Oless @ SY2796 @ SY2795 @ SV356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(2087,plain,
! [SV357: $i] :
( ( ! [SY2797: $i,SY2798: $i,SY2799: $i,SY2800: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV357 @ SY2797 ) @ SY2798 ) @ SY2799 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV357 @ SY2797 ) @ SY2800 ) @ SY2799 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV357 @ SY2798 ) @ SY2800 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1516]) ).
thf(2088,plain,
! [SV358: $i] :
( ( ! [SY2801: $i,SY2802: $i,SY2803: $i,SY2804: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV358 @ SY2801 ) @ SY2802 ) @ SY2803 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SY2804 ) @ SY2803 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV358 @ SY2801 ) @ SY2802 ) @ SY2804 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(2089,plain,
! [SV359: $i] :
( ( ! [SY2805: $i,SY2806: $i] :
( ~ ( class_Orderings_Olinorder @ SV359 )
| ~ ( c_HOL_Oord__class_Oless @ SY2805 @ SY2806 @ SV359 )
| ~ ( c_HOL_Oord__class_Oless @ SY2806 @ SY2805 @ SV359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(2090,plain,
! [SV360: $i] :
( ( ! [SY2807: $i,SY2808: $i,SY2809: $i] :
( ( c_Wellfounded_Oaccp @ SV360 @ SY2807 @ SY2808 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV360 @ SY2807 ) @ SY2809 ) )
| ~ ( c_Wellfounded_Oaccp @ SV360 @ SY2809 @ SY2808 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(2091,plain,
! [SV361: $i] :
( ( ! [SY2810: $i,SY2811: $i] :
( ~ ( class_Orderings_Opreorder @ SV361 )
| ~ ( c_HOL_Oord__class_Oless @ SY2810 @ SY2811 @ SV361 )
| ~ ( c_HOL_Oord__class_Oless @ SY2811 @ SY2810 @ SV361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(2092,plain,
! [SV362: $i] :
( ( ! [SY2812: $i,SY2813: $i,SY2814: $i] :
( ( c_Wellfounded_Oaccp @ SV362 @ SY2812 @ SY2813 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV362 @ SY2812 ) @ SY2814 ) )
| ~ ( c_Wellfounded_Oaccp @ SV362 @ SY2814 @ SY2813 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(2093,plain,
! [SV363: $i] :
( ( ! [SY2815: $i,SY2816: $i] :
( ~ ( class_Orderings_Opreorder @ SV363 )
| ~ ( c_HOL_Oord__class_Oless @ SY2815 @ SY2816 @ SV363 )
| ~ ( c_HOL_Oord__class_Oless @ SY2816 @ SY2815 @ SV363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(2094,plain,
! [SV364: $i] :
( ( ( c_Nat_Osize__class_Osize @ SV364 @ tc_String_Ochar )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(2095,plain,
! [SV365: $i] :
( ( ! [SY2817: $i,SY2818: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV365 @ SY2817 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY2818 @ SY2817 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1524]) ).
thf(2096,plain,
! [SV366: $i] :
( ( ( c_Orderings_Oord__class_Omax @ SV366 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= SV366 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1525]) ).
thf(2097,plain,
! [SV367: $i] :
( ( ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV367 @ tc_nat )
= SV367 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(2098,plain,
! [SV368: $i] :
( ( SV368
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV368 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(2099,plain,
! [SV369: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV369 )
= SV369 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(2100,plain,
! [SV370: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV370 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV370 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(2101,plain,
! [SV371: $i] :
( ( ! [SY2819: $i,SY2820: $i,SY2821: $i,SY2822: $i,SY2823: $i,SY2824: $i] :
( ( ( hAPP @ ( hAPP @ SV371 @ SY2819 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SY2820 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY2821 @ SY2822 @ SV371 @ SY2823 @ SY2820 @ SY2824 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(2102,plain,
! [SV372: $i] :
( ( ! [SY2825: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV372 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV372 ) @ ( c_HOL_Ozero__class_Ozero @ SV372 ) @ SY2825 @ SV372 @ SV372 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV372 ) @ SY2825 @ ( c_HOL_Ozero__class_Ozero @ SV372 ) @ SV372 @ SV372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(2103,plain,
! [SV373: $i] :
( ( ! [SY2826: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV373 )
| ( ( c_List_Olistsum @ SY2826 @ SV373 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV373 ) @ ( c_HOL_Ozero__class_Ozero @ SV373 ) @ SY2826 @ SV373 @ SV373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(2104,plain,
! [SV374: $i] :
( ( ! [SY2827: $i,SY2828: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV374 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV374 ) @ SY2827 @ SY2828 @ SV374 @ SV374 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV374 ) @ SY2827 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV374 ) @ SY2828 @ ( c_HOL_Ozero__class_Ozero @ SV374 ) @ SV374 @ SV374 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1534]) ).
thf(2105,plain,
! [SV375: $i] :
( ( ! [SY2829: $i,SY2830: $i,SY2831: $i,SY2832: $i,SY2833: $i] :
( ~ ( hBOOL @ ( hAPP @ SV375 @ ( c_Lambda_OdB_OdB__case @ SY2829 @ SY2830 @ SY2831 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2832 ) @ SY2833 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV375 @ ( hAPP @ ( hAPP @ SY2830 @ SY2832 ) @ SY2833 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(2106,plain,
! [SV376: $i] :
( ( ! [SY2834: $i,SY2835: $i,SY2836: $i,SY2837: $i,SY2838: $i] :
( ~ ( hBOOL @ ( hAPP @ SV376 @ ( c_Lambda_OdB_OdB__case @ SY2834 @ SY2835 @ SY2836 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2837 ) @ SY2838 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SY2835 @ SY2837 ) @ SY2838 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1538]) ).
thf(2107,plain,
! [SV377: $i] :
( ( ! [SY2839: $i,SY2840: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV377 ) @ SY2839 ) ) @ SY2840 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV377 ) @ SY2840 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY2839 ) @ SY2840 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(2108,plain,
! [SV378: $i] :
( ( ! [SY2841: $i,SY2842: $i,SY2843: $i,SY2844: $i,SY2845: $i] :
( ( c_Lambda_OdB_OdB__case @ SV378 @ SY2841 @ SY2842 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2843 ) @ SY2844 ) @ SY2845 )
= ( hAPP @ ( hAPP @ SY2841 @ SY2843 ) @ SY2844 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(2109,plain,
! [SV379: $i] :
( ( ! [SY2846: $i,SY2847: $i,SY2848: $i,SY2849: $i,SY2850: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV379 @ SY2846 @ SY2847 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2848 ) @ SY2849 ) @ SY2850 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SY2846 @ SY2848 ) @ SY2849 ) @ ( c_Lambda_OdB_OdB__rec @ SV379 @ SY2846 @ SY2847 @ SY2848 @ SY2850 ) ) @ ( c_Lambda_OdB_OdB__rec @ SV379 @ SY2846 @ SY2847 @ SY2849 @ SY2850 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1541]) ).
thf(2110,plain,
! [SV380: $i] :
( ( ! [SY2851: $i,SY2852: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV380 ) @ SY2851 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV380 ) @ SY2852 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY2851 ) @ SY2852 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(2111,plain,
! [SV381: $i] :
( ( ! [SY2853: $i,SY2854: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV381 ) @ SY2853 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2854 ) @ SY2853 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV381 ) @ SY2854 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1543]) ).
thf(2112,plain,
! [SV382: $i] :
( ( ! [SY2855: $i,SY2856: $i,SY2857: $i] :
( ( c_Lambda_Oliftn @ SV382 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2855 ) @ SY2856 ) @ SY2857 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV382 @ SY2855 @ SY2857 ) ) @ ( c_Lambda_Oliftn @ SV382 @ SY2856 @ SY2857 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(2113,plain,
! [SV383: $i] :
( ( ! [SY2858: $i,SY2859: $i,SY2860: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV383 ) @ SY2858 ) @ SY2859 @ SY2860 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV383 @ SY2859 @ SY2860 ) ) @ ( c_Lambda_Osubstn @ SY2858 @ SY2859 @ SY2860 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(2114,plain,
! [SV384: $i] :
( ( ! [SY2861: $i,SY2862: $i] :
( ( c_Lambda_Osubstn @ SV384 @ SY2861 @ SY2862 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV384 ) @ ( c_Lambda_Oliftn @ SY2862 @ SY2861 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ SY2862 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(2115,plain,
! [SV385: $i] :
( ( ! [SY2863: $i,SY2864: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV385 ) @ SY2863 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY2864 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2863 @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV385 ) ) @ SY2863 ) @ SY2864 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(2116,plain,
! [SV386: $i] :
( ( ! [SY2865: $i,SY2866: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV386 @ SY2865 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2866 @ SY2865 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV386 ) @ SY2866 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1548]) ).
thf(2117,plain,
! [SV387: $i] :
( ( ! [SY2867: $i,SY2868: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV387 @ SY2867 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV387 @ SY2868 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SY2867 @ SY2868 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1549]) ).
thf(2118,plain,
! [SV388: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV388 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV388 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(2119,plain,
! [SV389: $i] :
( ( SV389
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2 @ SV389 ) @ ( c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1 @ SV389 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1553]) ).
thf(2120,plain,
! [SV390: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV390 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV390 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(2121,plain,
! [SV391: $i] :
( ( ! [SY2869: $i,SY2870: $i,SY2871: $i,SY2872: $i] :
( ( ( c_List_Ofoldl @ SV391 @ ( hAPP @ ( hAPP @ SV391 @ SY2869 ) @ SY2870 ) @ SY2871 @ SY2872 @ SY2872 )
= ( hAPP @ ( hAPP @ SV391 @ SY2869 ) @ ( c_List_Ofoldl @ SV391 @ SY2870 @ SY2871 @ SY2872 @ SY2872 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV391 @ SY2872 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(2122,plain,
! [SV392: $i] :
( ( ! [SY2873: $i,SY2874: $i,SY2875: $i] :
( ( c_List_Ofoldl @ SV392 @ SY2873 @ ( c_List_Olist_ONil @ SY2874 ) @ SY2875 @ SY2874 )
= SY2873 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(2123,plain,
! [SV393: $i] :
( ( ! [SY2876: $i,SY2877: $i,SY2878: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV393 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV393 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV393 ) @ SY2876 ) @ SY2877 ) @ SY2878 @ SV393 @ SV393 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV393 ) @ SY2876 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV393 ) @ SY2877 @ SY2878 @ SV393 @ SV393 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(2124,plain,
! [SV394: $i] :
( ( ! [SY2879: $i,SY2880: $i,SY2881: $i,SY2882: $i] :
( ( ( hAPP @ ( hAPP @ SV394 @ SY2879 ) @ ( c_List_Ofoldl @ SV394 @ SY2880 @ SY2881 @ SY2882 @ SY2882 ) )
= ( c_List_Ofoldl @ SV394 @ SY2879 @ SY2881 @ SY2882 @ SY2882 ) )
| ~ ( c_OrderedGroup_Omonoid__add @ SY2880 @ SV394 @ SY2882 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(2125,plain,
! [SV395: $i] :
( ( ! [SY2883: $i,SY2884: $i,SY2885: $i,SY2886: $i,SY2887: $i] :
( ( c_List_Ofoldl @ SV395 @ SY2883 @ ( c_List_Olist_OCons @ SY2884 @ SY2885 @ SY2886 ) @ SY2887 @ SY2886 )
= ( c_List_Ofoldl @ SV395 @ ( hAPP @ ( hAPP @ SV395 @ SY2883 ) @ SY2884 ) @ SY2885 @ SY2887 @ SY2886 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(2126,plain,
! [SV396: $i] :
( ( ! [SY2888: $i,SY2889: $i,SY2890: $i,SY2891: $i,SY2892: $i] :
( ( c_List_Ofoldl @ SV396 @ SY2888 @ ( c_List_Oappend @ SY2889 @ SY2890 @ SY2891 ) @ SY2892 @ SY2891 )
= ( c_List_Ofoldl @ SV396 @ ( c_List_Ofoldl @ SV396 @ SY2888 @ SY2889 @ SY2892 @ SY2891 ) @ SY2890 @ SY2892 @ SY2891 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1561]) ).
thf(2127,plain,
! [SV397: $i] :
( ( ! [SY2893: $i,SY2894: $i,SY2895: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV397 @ SY2893 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY2894 ) @ SY2895 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV397 ) @ SY2894 ) @ SY2895 ) @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SY2894 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SY2895 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY2893 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1562]) ).
thf(2128,plain,
! [SV398: $i] :
( ( ! [SY2896: $i] :
( ( hBOOL @ ( hAPP @ SV398 @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV398 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV398 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV398 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV398 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ SV398 @ SY2896 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(2129,plain,
! [SV399: $i] :
( ( ! [SY2897: $i,SY2898: $i,SY2899: $i] :
( ( c_Type_Otypings @ SV399 @ SY2897 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY2898 @ SV399 @ SY2899 @ SY2897 ) )
| ~ ( c_Type_Otyping @ SV399 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2899 ) @ SY2897 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2898 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1564]) ).
thf(2130,plain,
! [SV400: $i] :
( ( ! [SY2900: $i] :
( ( hBOOL @ ( hAPP @ SV400 @ SY2900 ) )
| ( hBOOL @ ( hAPP @ SV400 @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV400 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV400 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV400 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV400 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(2131,plain,
! [SV401: $i] :
( ( ! [SY2901: $i,SY2902: $i,SY2903: $i,SY2904: $i,SY2905: $i,SY2906: $i] :
( ( c_Type_Otypings @ SV401 @ SY2901 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SY2902 @ SY2903 @ SV401 @ SY2901 ) )
| ~ ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2904 ) @ SY2905 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2903 )
| ~ ( c_Type_Otypings @ SV401 @ SY2905 @ SY2906 )
| ~ ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2904 ) @ SY2905 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2901 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2902 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1566]) ).
thf(2132,plain,
! [SV402: $i] :
( ( ! [SY2907: $i,SY2908: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV402 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SY2907 @ SV402 @ SY2908 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2907 ) @ SV402 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY2908 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(2133,plain,
! [SV403: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV403 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV403 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV403 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV403 ) ) )
| ( SV403
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV403 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV403 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1568]) ).
thf(2134,plain,
! [SV404: $i] :
( ( ! [SY2909: $i,SY2910: $i,SY2911: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV404 ) @ SY2909 ) @ SY2910 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY2911 ) @ SY2909 ) @ SY2910 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV404 ) @ SY2911 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1569]) ).
thf(2135,plain,
! [SV405: $i] :
( ( ! [SY2912: $i,SY2913: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV405 ) @ SY2912 ) ) @ SY2913 ) @ SY2912 )
= SV405 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1570]) ).
thf(2136,plain,
! [SV406: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV406 ) ) )
| ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV406 ) ) )
| ( SV406
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV406 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV406 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1571]) ).
thf(2137,plain,
! [SV407: $i] :
( ( ! [SY2914: $i,SY2915: $i,SY2916: $i,SY2917: $i] :
( ~ ( hBOOL @ ( hAPP @ SV407 @ ( c_Lambda_OdB_OdB__case @ SY2914 @ SY2915 @ SY2916 @ ( c_Lambda_OdB_OVar @ SY2917 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV407 @ ( hAPP @ SY2914 @ SY2917 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1573]) ).
thf(2138,plain,
! [SV408: $i] :
( ( ! [SY2918: $i,SY2919: $i,SY2920: $i,SY2921: $i] :
( ~ ( hBOOL @ ( hAPP @ SV408 @ ( c_Lambda_OdB_OdB__case @ SY2918 @ SY2919 @ SY2920 @ ( c_Lambda_OdB_OVar @ SY2921 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV408 @ ( hAPP @ SY2918 @ SY2921 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1574]) ).
thf(2139,plain,
! [SV409: $i] :
( ( ! [SY2922: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV409 ) ) @ SY2922 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(2140,plain,
! [SV410: $i] :
( ( ! [SY2923: $i,SY2924: $i,SY2925: $i,SY2926: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV410 @ SY2923 @ SY2924 @ ( c_Lambda_OdB_OVar @ SY2925 ) @ SY2926 )
= ( hAPP @ SV410 @ SY2925 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1576]) ).
thf(2141,plain,
! [SV411: $i] :
( ( ! [SY2927: $i,SY2928: $i] :
( ( ( hAPP @ SV411 @ SY2927 )
= SY2928 )
| ~ ( c_Type_Otyping @ SV411 @ ( c_Lambda_OdB_OVar @ SY2927 ) @ SY2928 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(2142,plain,
! [SV412: $i] :
( ( ! [SY2929: $i,SY2930: $i,SY2931: $i,SY2932: $i] :
( ( c_Lambda_OdB_OdB__case @ SV412 @ SY2929 @ SY2930 @ ( c_Lambda_OdB_OVar @ SY2931 ) @ SY2932 )
= ( hAPP @ SV412 @ SY2931 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(2143,plain,
! [SV413: $i] :
( ( ! [SY2933: $i] : ( c_Type_Otyping @ SV413 @ ( c_Lambda_OdB_OVar @ SY2933 ) @ ( hAPP @ SV413 @ SY2933 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(2144,plain,
! [SV414: $i] :
( ( ! [SY2934: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV414 ) @ SY2934 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV414 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(2145,plain,
! [SV415: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV415 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1582]) ).
thf(2146,plain,
! [SV416: $i] :
( ( ! [SY2935: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV416 ) ) @ SY2935 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV416 ) @ SY2935 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(2147,plain,
! [SV417: $i] :
( ( ! [SY2936: $i,SY2937: $i] :
( ( SV417
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2936 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SY2936 @ SY2937 @ SV417 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2936 ) @ SY2937 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV417 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(2148,plain,
! [SV418: $i] :
( ( ! [SY2938: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV418 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV418 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV418 )
| ~ ( class_Power_Opower @ SV418 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV418 ) @ SY2938 @ SV418 )
= ( c_HOL_Ozero__class_Ozero @ SV418 ) )
| ( SY2938
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(2149,plain,
! [SV419: $i] :
( ( ! [SY2939: $i] :
( ~ ( class_Ring__and__Field_Osemiring__0 @ SV419 )
| ~ ( class_Power_Opower @ SV419 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV419 ) @ SY2939 @ SV419 )
= ( c_HOL_Ozero__class_Ozero @ SV419 ) )
| ( SY2939
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1586]) ).
thf(2150,plain,
! [SV420: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV420 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV420 )
= ( c_HOL_Ozero__class_Ozero @ SV420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1588]) ).
thf(2151,plain,
! [SV421: $i] :
( ( ! [SY2940: $i,SY2941: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV421 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SY2940 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ ( c_HOL_Ozero__class_Ozero @ SV421 ) @ SY2941 @ SV421 @ SV421 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SY2940 @ SY2941 @ SV421 @ SV421 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1589]) ).
thf(2152,plain,
! [SV422: $i] :
( ( ! [SY2942: $i] :
( ( c_Lambda_Osubstn @ SV422 @ SY2942 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV422 ) @ SY2942 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(2153,plain,
! [SV423: $i] :
( ( ( c_Nat_Osize__class_Osize @ ( c_Lambda_OdB_OVar @ SV423 ) @ tc_Lambda_OdB )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1591]) ).
thf(2154,plain,
! [SV424: $i] :
( ( ( c_Lambda_OdB_OdB__size @ ( c_Lambda_OdB_OVar @ SV424 ) )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1592]) ).
thf(2155,plain,
! [SV425: $i] :
( ( ! [SY2943: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV425 ) @ SY2943 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV425 ) @ SY2943 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1593]) ).
thf(2156,plain,
! [SV426: $i] :
( ( ! [SY2944: $i,SY2945: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV426 @ SY2944 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY2945 @ SY2944 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV426 ) @ SY2945 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1598]) ).
thf(2157,plain,
! [SV427: $i] :
( ( ! [SY2946: $i,SY2947: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV427 ) ) @ SY2946 ) @ SY2947 )
= ( c_Lambda_OdB_OVar @ SV427 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV427 @ SY2947 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(2158,plain,
! [SV428: $i] :
( ( ! [SY2948: $i,SY2949: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV428 ) ) @ SY2948 ) @ SY2949 )
= ( c_Lambda_OdB_OVar @ SV428 ) )
| ( SV428 = SY2949 )
| ( c_HOL_Oord__class_Oless @ SY2949 @ SV428 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(2159,plain,
! [SV429: $i] :
( ( ! [SY2950: $i] :
( ( c_HOL_Oord__class_Oless @ SV429 @ SV429 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV429 ) ) @ SY2950 ) @ SV429 )
= SY2950 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(2160,plain,
! [SV430: $i] :
( ( ! [SY2951: $i,SY2952: $i,SY2953: $i,SY2954: $i] :
( ( SV430 = SY2951 )
| ~ ( c_Type_Otyping @ SY2952 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2953 ) @ SY2954 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY2951 )
| ~ ( c_Type_Otyping @ SY2952 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY2953 ) @ SY2954 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(2161,plain,
! [SV431: $i] :
( ( ( c_Lambda_OdB_OVar @ SV431 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV431 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(2162,plain,
! [SV432: $i] :
( ( ! [SY2955: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV432 ) @ SY2955 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SY2955 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(2163,plain,
! [SV433: $i] :
( ( ! [SY2956: $i,SY2957: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV433 ) ) @ SY2956 ) @ SY2957 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SY2956 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV433 ) @ SY2956 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY2957 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1609]) ).
thf(2164,plain,
! [SV434: $i] :
( ( ! [SY2958: $i,SY2959: $i,SY2960: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV434 ) @ SY2958 ) ) @ SY2959 ) @ SY2960 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV434 ) @ SY2959 ) @ SY2960 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY2958 ) @ SY2959 ) @ SY2960 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1610]) ).
thf(2165,plain,
! [SV435: $i] :
( ( ! [SY2961: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV435 ) ) @ SY2961 ) @ SV435 )
= SY2961 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1614]) ).
thf(2166,plain,
! [SV436: $i] :
( ( ! [SY2962: $i,SY2963: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV436 ) @ ( c_Lambda_OdB_OVar @ SY2962 ) ) @ SY2963 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV436 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1615]) ).
thf(2167,plain,
! [SV437: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ SV437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1620]) ).
thf(2168,plain,
! [SV438: $i] :
( ( ! [SY2964: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ SV438 @ SY2964 ) )
| ~ ( class_Orderings_Opreorder @ SY2964 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(2169,plain,
! [SV439: $i] :
( ( ! [SY2965: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ SV439 @ SY2965 ) )
| ~ ( class_Orderings_Oorder @ SY2965 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(2170,plain,
! [SV440: $i] :
( ( ! [SY2966: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV440 ) @ SY2966 ) @ SY2966 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1650]) ).
thf(2171,plain,
! [SV441: $i] :
( ( ! [SY2967: $i,SY2968: $i] :
( ( SV441 = SY2967 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY2968 ) @ SV441 ) @ SY2967 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1651]) ).
thf(2172,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[1652]) ).
thf(2173,plain,
! [SV442: $i] :
( ( ! [SY2969: $i] :
( ( ( c_Lambda_OdB_OVar @ SV442 )
!= ( c_Lambda_OdB_OVar @ SY2969 ) )
| ( SV442 = SY2969 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(2174,plain,
! [SV443: $i] :
( ( ! [SY2970: $i,SY2971: $i,SY2972: $i,SY2973: $i] :
( ( ( c_List_Olist_OCons @ SV443 @ SY2970 @ SY2971 )
!= ( c_List_Olist_OCons @ SY2972 @ SY2973 @ SY2971 ) )
| ( SV443 = SY2972 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(2175,plain,
! [SV444: $i] :
( ( ! [SY2974: $i,SY2975: $i,SY2976: $i,SY2977: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV444 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SY2974 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SY2975 ) @ SY2976 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SY2975 ) @ SY2977 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SY2974 ) @ SY2976 )
= SY2977 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1655]) ).
thf(2176,plain,
! [SV445: $i] :
( ( ! [SY2978: $i,SY2979: $i] :
( ( c_Lambda_OdB_OVar @ SV445 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2978 ) @ SY2979 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(2177,plain,
! [SV446: $i] :
( ( ! [SY2980: $i,SY2981: $i,SY2982: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV446 )
| ~ ( class_Int_Onumber__ring @ SV446 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV446 ) @ SY2980 ) @ SY2981 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV446 ) @ SY2980 ) @ SY2982 ) )
| ( SY2981 = SY2982 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1657]) ).
thf(2178,plain,
! [SV447: $i] :
( ( ! [SY2983: $i,SY2984: $i,SY2985: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV447 ) @ SY2983 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY2984 ) @ SY2985 ) )
| ( SV447 = SY2984 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(2179,plain,
! [SV448: $i] :
( ( ! [SY2986: $i,SY2987: $i] :
( ( c_List_Olist_OCons @ SV448 @ SY2986 @ SY2987 )
!= ( c_List_Olist_ONil @ SY2987 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1659]) ).
thf(2180,plain,
! [SV449: $i] :
( ( ! [SY2988: $i,SY2989: $i] :
( ~ ( class_Orderings_Olinorder @ SV449 )
| ( ( c_Orderings_Oord__class_Omax @ SY2988 @ SY2989 @ SV449 )
!= SY2989 )
| ( c_lessequals @ SY2988 @ SY2989 @ SV449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(2181,plain,
! [SV450: $i] :
( ( ! [SY2990: $i,SY2991: $i,SY2992: $i,SY2993: $i] :
( ( ( c_List_Oappend @ SV450 @ ( c_List_Olist_OCons @ SY2990 @ ( c_List_Olist_ONil @ SY2991 ) @ SY2991 ) @ SY2991 )
!= ( c_List_Oappend @ SY2992 @ ( c_List_Olist_OCons @ SY2993 @ ( c_List_Olist_ONil @ SY2991 ) @ SY2991 ) @ SY2991 ) )
| ( SV450 = SY2992 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(2182,plain,
! [SV451: $i] :
( ( ! [SY2994: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV451 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV451 ) @ SY2994 ) @ SY2994 )
!= ( c_HOL_Ozero__class_Ozero @ SV451 ) )
| ( SY2994
= ( c_HOL_Ozero__class_Ozero @ SV451 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1662]) ).
thf(2183,plain,
! [SV452: $i] :
( ( ! [SY2995: $i,SY2996: $i] :
( ( SV452
!= ( c_List_Oappend @ SY2995 @ SV452 @ SY2996 ) )
| ( SY2995
= ( c_List_Olist_ONil @ SY2996 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1663]) ).
thf(2184,plain,
! [SV453: $i] :
( ( ! [SY2997: $i,SY2998: $i] :
( ( c_List_Olist_ONil @ SV453 )
!= ( c_List_Olist_OCons @ SY2997 @ SY2998 @ SV453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1664]) ).
thf(2185,plain,
! [SV454: $i] :
( ( ! [SY2999: $i] :
( ( SV454
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV454 ) @ SY2999 ) )
| ( SY2999
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1665]) ).
thf(2186,plain,
! [SV455: $i] :
( ( ! [SY3000: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV455 ) @ SY3000 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SY3000
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(2187,plain,
! [SV456: $i] :
( ( ! [SY3001: $i,SY3002: $i,SY3003: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV456 )
| ( ( c_Power_Opower__class_Opower @ SY3001 @ SY3002 @ SV456 )
!= ( c_Power_Opower__class_Opower @ SY3003 @ SY3002 @ SV456 ) )
| ( SY3001 = SY3003 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3002 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SY3003 @ SV456 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SY3001 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(2188,plain,
! [SV457: $i] :
( ( ! [SY3004: $i,SY3005: $i,SY3006: $i,SY3007: $i] :
( ( ( c_List_Oreplicate @ SV457 @ SY3004 @ SY3005 )
!= ( c_List_Oreplicate @ SY3006 @ SY3007 @ SY3005 ) )
| ( SV457 = SY3006 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(2189,plain,
! [SV458: $i] :
( ( ! [SY3008: $i,SY3009: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV458 ) @ SY3008 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3009 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV458 ) @ SY3008 )
= SY3009 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(2190,plain,
! [SV459: $i] :
( ( ! [SY3010: $i,SY3011: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV459 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV459 ) @ SY3010 ) @ SY3011 )
!= ( c_HOL_Ozero__class_Ozero @ SV459 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV459 ) @ SY3011 @ SV459 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV459 ) @ SY3010 @ SV459 )
| ( SY3011
= ( c_HOL_Ozero__class_Ozero @ SV459 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1670]) ).
thf(2191,plain,
! [SV460: $i] :
( ( ! [SY3012: $i,SY3013: $i,SY3014: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV460 ) @ SY3012 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY3013 ) @ SY3014 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY3012 = SY3014 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1671]) ).
thf(2192,plain,
! [SV461: $i] :
( ( ! [SY3015: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV461 ) @ SY3015 )
!= SV461 )
| ( SY3015
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(2193,plain,
! [SV462: $i] :
( ( ! [SY3016: $i,SY3017: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV462 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3016 @ SY3017 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV462 )
= SY3016 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1673]) ).
thf(2194,plain,
! [SV463: $i] :
( ( ! [SY3018: $i,SY3019: $i] :
( ( ( c_Lambda_OdB_OVar @ SV463 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3018 @ SY3019 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY3019
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(2195,plain,
! [SV464: $i] :
( ( ! [SY3020: $i,SY3021: $i,SY3022: $i,SY3023: $i] :
( ( ( c_List_Olist_OCons @ SV464 @ SY3020 @ SY3021 )
!= ( c_List_Olist_OCons @ SY3022 @ SY3023 @ SY3021 ) )
| ( SY3020 = SY3023 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(2196,plain,
! [SV465: $i] :
( ( ! [SY3024: $i,SY3025: $i,SY3026: $i,SY3027: $i] :
( ( ( c_List_Oreplicate @ SV465 @ SY3024 @ SY3025 )
!= ( c_List_Oreplicate @ SY3026 @ SY3027 @ SY3025 ) )
| ( SY3024 = SY3027 )
| ( SV465
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(2197,plain,
! [SV466: $i] :
( ( ! [SY3028: $i,SY3029: $i] :
( ( c_Lambda_OdB_OAbs @ SV466 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3028 ) @ SY3029 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1677]) ).
thf(2198,plain,
! [SV467: $i] :
( ( ! [SY3030: $i,SY3031: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV467 )
| ~ ( class_Int_Onumber__ring @ SV467 )
| ( SY3030
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV467 ) @ SY3030 ) @ SY3031 ) )
| ( SY3031
= ( c_HOL_Ozero__class_Ozero @ SV467 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1678]) ).
thf(2199,plain,
! [SV468: $i] :
( ( ! [SY3032: $i,SY3033: $i,SY3034: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV468 ) @ SY3032 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3033 ) @ SY3034 ) )
| ( SY3032 = SY3034 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1679]) ).
thf(2200,plain,
! [SV469: $i] :
( ( ! [SY3035: $i,SY3036: $i] :
( ( SV469
!= ( c_List_Oappend @ SV469 @ SY3035 @ SY3036 ) )
| ( SY3035
= ( c_List_Olist_ONil @ SY3036 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(2201,plain,
! [SV470: $i] :
( ( ! [SY3037: $i,SY3038: $i,SY3039: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV470 ) @ SY3037 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY3038 ) @ SY3039 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(2202,plain,
! [SV471: $i] :
( ( ! [SY3040: $i,SY3041: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV471 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV471 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV471 )
| ~ ( class_Power_Opower @ SV471 )
| ( ( c_Power_Opower__class_Opower @ SY3040 @ SY3041 @ SV471 )
!= ( c_HOL_Ozero__class_Ozero @ SV471 ) )
| ( SY3040
= ( c_HOL_Ozero__class_Ozero @ SV471 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(2203,plain,
! [SV472: $i] :
( ( ! [SY3042: $i,SY3043: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV472 @ SY3042 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3043 @ SY3042 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV472 = SY3043 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1683]) ).
thf(2204,plain,
! [SV473: $i] :
( ( ! [SY3044: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV473 )
!= ( c_Lambda_OdB_OAbs @ SY3044 ) )
| ( SV473 = SY3044 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1684]) ).
thf(2205,plain,
! [SV474: $i] :
( ( ! [SY3045: $i,SY3046: $i,SY3047: $i] :
( ( ( c_List_Oappend @ SV474 @ SY3045 @ SY3046 )
!= ( c_List_Oappend @ SV474 @ SY3047 @ SY3046 ) )
| ( SY3045 = SY3047 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1685]) ).
thf(2206,plain,
! [SV475: $i] :
( ( ! [SY3048: $i,SY3049: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV475 ) @ SY3048 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3049 ) @ SY3048 ) )
| ( SV475 = SY3049 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1686]) ).
thf(2207,plain,
! [SV476: $i] :
( ( ! [SY3050: $i,SY3051: $i,SY3052: $i] :
( ( ( c_List_Olist_ONil @ SV476 )
!= ( c_List_Omap @ SY3050 @ SY3051 @ SY3052 @ SV476 ) )
| ( SY3051
= ( c_List_Olist_ONil @ SY3052 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1687]) ).
thf(2208,plain,
! [SV477: $i] :
( ( ! [SY3053: $i,SY3054: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV477 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SY3053 @ SV477 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY3054 @ SV477 ) )
| ( SY3053 = SY3054 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1688]) ).
thf(2209,plain,
! [SV478: $i] :
( ( ! [SY3055: $i,SY3056: $i] :
( ( c_List_Olist_OCons @ SV478 @ SY3055 @ SY3056 )
!= ( c_List_Olist_ONil @ SY3056 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(2210,plain,
! [SV479: $i] :
( ( ! [SY3057: $i,SY3058: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV479 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3057 @ SY3058 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY3058
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1690]) ).
thf(2211,plain,
! [SV480: $i] :
( ( ! [SY3059: $i,SY3060: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV480 @ SY3059 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY3060 ) )
| ( SY3059
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(2212,plain,
! [SV481: $i] :
( ( ! [SY3061: $i,SY3062: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV481 ) @ SY3061 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV481 ) @ SY3062 ) )
| ( SY3061 = SY3062 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(2213,plain,
! [SV482: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV482 )
| ( ( c_HOL_Ozero__class_Ozero @ SV482 )
!= ( c_HOL_Oone__class_Oone @ SV482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(2214,plain,
! [SV483: $i] :
( ( ! [SY3063: $i,SY3064: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV483 @ SY3063 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY3064 ) )
| ( SV483
= ( c_Lambda_OdB_OAbs @ SY3064 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1694]) ).
thf(2215,plain,
! [SV484: $i] :
( ( ! [SY3065: $i,SY3066: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV484 )
| ( ( c_Power_Opower__class_Opower @ SY3065 @ SY3066 @ SV484 )
!= ( c_HOL_Ozero__class_Ozero @ SV484 ) )
| ( SY3065
= ( c_HOL_Ozero__class_Ozero @ SV484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1695]) ).
thf(2216,plain,
! [SV485: $i] :
( ( ! [SY3067: $i,SY3068: $i,SY3069: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV485 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SY3067 ) @ SY3068 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SY3069 ) @ SY3068 ) )
| ( SY3067 = SY3069 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1696]) ).
thf(2217,plain,
! [SV486: $i] :
( ( ! [SY3070: $i] :
( ( c_Lambda_OdB_OAbs @ SV486 )
!= ( c_Lambda_OdB_OVar @ SY3070 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1697]) ).
thf(2218,plain,
! [SV487: $i] :
( ( ! [SY3071: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV487 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV487 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV487 )
| ~ ( class_Power_Opower @ SV487 )
| ( ( c_Power_Opower__class_Opower @ SY3071 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV487 )
!= ( c_HOL_Ozero__class_Ozero @ SV487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1698]) ).
thf(2219,plain,
! [SV488: $i] :
( ( ! [SY3072: $i,SY3073: $i] :
( ( ( c_List_Olist_ONil @ SV488 )
!= ( c_List_Oreplicate @ SY3072 @ SY3073 @ SV488 ) )
| ( SY3072
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(2220,plain,
! [SV489: $i] :
( ( ! [SY3074: $i,SY3075: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV489 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV489 ) @ SY3074 ) @ SY3075 )
!= ( c_HOL_Ozero__class_Ozero @ SV489 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SY3075 @ SV489 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SY3074 @ SV489 )
| ( SY3074
= ( c_HOL_Ozero__class_Ozero @ SV489 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1700]) ).
thf(2221,plain,
! [SV490: $i] :
( ( ! [SY3076: $i,SY3077: $i] :
( ( ( c_List_Oreplicate @ SV490 @ SY3076 @ SY3077 )
!= ( c_List_Olist_ONil @ SY3077 ) )
| ( SV490
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1701]) ).
thf(2222,plain,
! [SV491: $i] :
( ( ! [SY3078: $i,SY3079: $i] :
( ( ( c_List_Olist_ONil @ SV491 )
!= ( c_List_Oappend @ SY3078 @ SY3079 @ SV491 ) )
| ( SY3078
= ( c_List_Olist_ONil @ SV491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1702]) ).
thf(2223,plain,
! [SV492: $i] :
( ( ! [SY3080: $i,SY3081: $i,SY3082: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV492 ) @ SY3080 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3081 ) @ SY3082 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3081 @ SY3080 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV492 @ SY3082 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1703]) ).
thf(2224,plain,
! [SV493: $i] :
( ( ! [SY3083: $i,SY3084: $i,SY3085: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV493 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SY3083 ) @ SY3084 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SY3083 ) @ SY3085 ) )
| ( SY3084 = SY3085 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1704]) ).
thf(2225,plain,
! [SV494: $i] :
( ( ! [SY3086: $i,SY3087: $i,SY3088: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV494 ) @ SY3086 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY3087 ) @ SY3088 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV494 = SY3087 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1705]) ).
thf(2226,plain,
! [SV495: $i] :
( ( ! [SY3089: $i,SY3090: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV495 ) @ SY3089 )
!= ( c_Lambda_OdB_OAbs @ SY3090 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1706]) ).
thf(2227,plain,
! [SV496: $i] :
( ( ! [SY3091: $i,SY3092: $i,SY3093: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV496 )
| ( ( c_Power_Opower__class_Opower @ SY3091 @ SY3092 @ SV496 )
!= ( c_Power_Opower__class_Opower @ SY3091 @ SY3093 @ SV496 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV496 ) @ SY3091 @ SV496 )
| ( SY3092 = SY3093 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1707]) ).
thf(2228,plain,
! [SV497: $i] :
( ( ! [SY3094: $i,SY3095: $i,SY3096: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV497 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SY3094 ) @ SY3095 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SY3094 ) @ SY3096 ) )
| ( SY3095 = SY3096 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1708]) ).
thf(2229,plain,
! [SV498: $i] :
( ( ! [SY3097: $i,SY3098: $i,SY3099: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV498 ) ) @ SY3097 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY3098 ) @ SY3099 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1709]) ).
thf(2230,plain,
! [SV499: $i] :
( ( ! [SY3100: $i,SY3101: $i] :
( ( ( c_List_Olist_ONil @ SV499 )
!= ( c_List_Oappend @ SY3100 @ SY3101 @ SV499 ) )
| ( SY3101
= ( c_List_Olist_ONil @ SV499 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(2231,plain,
! [SV500: $i] :
( ( ! [SY3102: $i,SY3103: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV500 ) @ SY3102 )
!= ( c_Lambda_OdB_OVar @ SY3103 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1711]) ).
thf(2232,plain,
! [SV501: $i] :
( ( ! [SY3104: $i,SY3105: $i,SY3106: $i,SY3107: $i] :
( ( ( c_List_Oappend @ SV501 @ ( c_List_Olist_OCons @ SY3104 @ ( c_List_Olist_ONil @ SY3105 ) @ SY3105 ) @ SY3105 )
!= ( c_List_Oappend @ SY3106 @ ( c_List_Olist_OCons @ SY3107 @ ( c_List_Olist_ONil @ SY3105 ) @ SY3105 ) @ SY3105 ) )
| ( SY3104 = SY3107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1712]) ).
thf(2233,plain,
! [SV502: $i] :
( ( ! [SY3108: $i,SY3109: $i] :
( ( ( c_List_Oappend @ SV502 @ SY3108 @ SY3109 )
!= ( c_List_Olist_ONil @ SY3109 ) )
| ( SY3108
= ( c_List_Olist_ONil @ SY3109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1713]) ).
thf(2234,plain,
! [SV503: $i] :
( ( ! [SY3110: $i,SY3111: $i,SY3112: $i] :
( ( ( c_List_Omap @ SV503 @ SY3110 @ SY3111 @ SY3112 )
!= ( c_List_Olist_ONil @ SY3112 ) )
| ( SY3110
= ( c_List_Olist_ONil @ SY3111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1714]) ).
thf(2235,plain,
! [SV504: $i] :
( ( ! [SY3113: $i,SY3114: $i,SY3115: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV504 ) @ SY3113 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3114 @ SY3115 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV504
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3114 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV504 @ SY3113 @ SY3114 @ SY3115 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY3115
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(2236,plain,
! [SV505: $i] :
( ( ! [SY3116: $i,SY3117: $i,SY3118: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV505 ) @ SY3116 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY3117 ) @ SY3118 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY3116 = SY3118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1716]) ).
thf(2237,plain,
! [SV506: $i] :
( ( ! [SY3119: $i,SY3120: $i] :
( ( ( c_Lambda_OdB_OVar @ SV506 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3119 @ SY3120 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV506 )
= SY3119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1717]) ).
thf(2238,plain,
! [SV507: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV507 )
| ( ( c_HOL_Oone__class_Oone @ SV507 )
!= ( c_HOL_Ozero__class_Ozero @ SV507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1718]) ).
thf(2239,plain,
! [SV508: $i] :
( ( ! [SY3121: $i,SY3122: $i] :
( ( c_List_Olist_OCons @ SV508 @ SY3121 @ SY3122 )
!= SY3121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1719]) ).
thf(2240,plain,
! [SV509: $i] :
( ( ! [SY3123: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV509 ) @ SY3123 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV509
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1720]) ).
thf(2241,plain,
! [SV510: $i] :
( ( ! [SY3124: $i,SY3125: $i] :
( ( ( c_List_Oappend @ SV510 @ SY3124 @ SY3125 )
!= SY3124 )
| ( SV510
= ( c_List_Olist_ONil @ SY3125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1721]) ).
thf(2242,plain,
! [SV511: $i] :
( ( ! [SY3126: $i] :
( ( c_Lambda_OdB_OVar @ SV511 )
!= ( c_Lambda_OdB_OAbs @ SY3126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1722]) ).
thf(2243,plain,
! [SV512: $i] :
( ( ! [SY3127: $i,SY3128: $i] :
( ( ( c_List_Oappend @ SV512 @ SY3127 @ SY3128 )
!= ( c_List_Olist_ONil @ SY3128 ) )
| ( SV512
= ( c_List_Olist_ONil @ SY3128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1723]) ).
thf(2244,plain,
! [SV513: $i] :
( ( ! [SY3129: $i,SY3130: $i] :
( ( ( c_List_Oappend @ SV513 @ SY3129 @ SY3130 )
!= SV513 )
| ( SY3129
= ( c_List_Olist_ONil @ SY3130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1724]) ).
thf(2245,plain,
! [SV514: $i] :
( ( ! [SY3131: $i,SY3132: $i,SY3133: $i] :
( ( ( c_List_Oappend @ SV514 @ SY3131 @ SY3132 )
!= ( c_List_Oappend @ SY3133 @ SY3131 @ SY3132 ) )
| ( SV514 = SY3133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1725]) ).
thf(2246,plain,
! [SV515: $i] :
( ( ! [SY3134: $i,SY3135: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV515 ) @ SY3134 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV515 ) @ SY3135 ) )
| ( SY3134 = SY3135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1726]) ).
thf(2247,plain,
! [SV516: $i] :
( ( ! [SY3136: $i,SY3137: $i,SY3138: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV516 ) @ SY3136 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY3137 ) @ SY3138 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV516 = SY3137 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1727]) ).
thf(2248,plain,
! [SV517: $i] :
( ( ! [SY3139: $i,SY3140: $i] :
( SV517
!= ( c_List_Olist_OCons @ SY3139 @ SV517 @ SY3140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1728]) ).
thf(2249,plain,
! [SV518: $i,SV1: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV1 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV518 @ SV1 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1730]) ).
thf(2250,plain,
! [SV519: $i,SV2: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV2 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV519 @ SV2 ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(2251,plain,
! [SV520: $i,SV3: $i] :
( ( ! [SY3141: $i,SY3142: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV3 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV520 @ SY3141 @ SV3 ) @ ( c_Power_Opower__class_Opower @ SY3142 @ SY3141 @ SV3 ) @ SV3 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV520 @ SV3 )
| ~ ( c_lessequals @ SV520 @ SY3142 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1732]) ).
thf(2252,plain,
! [SV521: $i,SV4: $i] :
( ( ! [SY3143: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV4 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV4 ) @ ( c_Power_Opower__class_Opower @ SV521 @ SY3143 @ SV4 ) @ SV4 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV4 ) @ SV521 @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1733]) ).
thf(2253,plain,
! [SV522: $i,SV5: $i] :
( ( ~ ( class_Power_Opower @ SV5 )
| ( ( c_Power_Opower__class_Opower @ SV522 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV5 )
= ( c_HOL_Oone__class_Oone @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1734]) ).
thf(2254,plain,
! [SV523: $i,SV6: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV6 )
| ( ( c_Power_Opower__class_Opower @ SV523 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV6 )
= ( c_HOL_Oone__class_Oone @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1735]) ).
thf(2255,plain,
! [SV524: $i,SV7: $i] :
( ( ! [SY3144: $i,SY3145: $i,SY3146: $i,SY3147: $i] :
( ~ ( c_Type_Otyping @ SV7 @ SV524 @ SY3144 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV7 @ SY3145 @ SY3144 @ tc_Type_Otype ) @ SY3146 @ SY3147 )
| ( c_Type_Otyping @ SV7 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY3146 ) @ SV524 ) @ SY3145 ) @ SY3147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1736]) ).
thf(2256,plain,
! [SV525: $i,SV8: $i] :
( ( ! [SY3148: $i,SY3149: $i,SY3150: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV8 @ SV525 @ SY3148 @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY3149 ) @ SV525 ) @ SY3150 )
| ~ ( c_Type_Otyping @ SV8 @ SY3149 @ SY3150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1737]) ).
thf(2257,plain,
! [SV526: $i,SV9: $i] :
( ( ! [SY3151: $i,SY3152: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV9 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV526 @ SY3151 @ SV9 ) @ ( c_Power_Opower__class_Opower @ SV526 @ SY3152 @ SV9 ) @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV526 @ ( c_HOL_Oone__class_Oone @ SV9 ) @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV526 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SY3152 @ SY3151 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(2258,plain,
! [SV527: $i,SV10: $i] :
( ( ! [SY3153: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV10 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV10 ) @ ( c_Power_Opower__class_Opower @ SV527 @ SY3153 @ SV10 ) @ SV10 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3153 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV10 ) @ SV527 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1739]) ).
thf(2259,plain,
! [SV528: $i,SV11: $i] :
( ( ! [SY3154: $i,SY3155: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV11 ) @ SV528 ) @ SY3154 ) ) @ SY3155 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV11 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3155 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV528 ) @ SY3155 ) ) @ SY3154 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3154 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3155 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(2260,plain,
! [SV529: $i,SV12: $i] :
( ( ! [SY3156: $i,SY3157: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV12 ) @ SV529 ) @ SY3156 ) ) @ SY3157 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV12 ) @ SY3157 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV529 ) @ SY3157 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3156 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3157 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3156 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(2261,plain,
! [SV530: $i,SV13: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV13 ) ) @ SV530 )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV13 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ( c_HOL_Oord__class_Oless @ SV13 @ SV530 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1742]) ).
thf(2262,plain,
! [SV531: $i,SV14: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV14 )
| ( c_HOL_Oord__class_Oless @ SV531 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV14 ) @ SV531 ) @ ( c_HOL_Oone__class_Oone @ SV14 ) ) @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1743]) ).
thf(2263,plain,
! [SV532: $i,SV15: $i] :
( ( ! [SY3158: $i,SY3159: $i,SY3160: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV15 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SV532 ) @ SY3158 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SY3159 ) @ SY3160 ) @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SY3158 @ SY3160 @ SV15 )
| ~ ( c_lessequals @ SV532 @ SY3159 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1744]) ).
thf(2264,plain,
! [SV533: $i,SV16: $i] :
( ( ! [SY3161: $i,SY3162: $i,SY3163: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV16 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SV533 ) @ SY3161 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SY3162 ) @ SY3163 ) @ SV16 )
| ~ ( c_lessequals @ SY3161 @ SY3163 @ SV16 )
| ~ ( c_HOL_Oord__class_Oless @ SV533 @ SY3162 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1745]) ).
thf(2265,plain,
! [SV534: $i,SV17: $i] :
( ( ! [SY3164: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV17 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV17 ) @ SV534 ) @ SY3164 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
| ~ ( c_lessequals @ SY3164 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
| ~ ( c_lessequals @ SV534 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1746]) ).
thf(2266,plain,
! [SV535: $i,SV18: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV18 )
| ( c_lessequals @ SV535 @ ( c_HOL_Ozero__class_Ozero @ SV18 ) @ SV18 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV18 ) @ SV535 ) @ SV535 ) @ ( c_HOL_Ozero__class_Ozero @ SV18 ) @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(2267,plain,
! [SV536: $i,SV19: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV19 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV19 ) @ SV536 ) @ SV536 ) @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 )
| ~ ( c_lessequals @ SV536 @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1748]) ).
thf(2268,plain,
! [SV537: $i,SV20: $i] :
( ( ! [SY3165: $i,SY3166: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV20 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV20 )
| ( c_lessequals @ SV537 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV20 ) @ SY3165 ) @ SY3166 ) @ SV20 )
| ~ ( c_lessequals @ SV537 @ SY3165 @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SY3166 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1749]) ).
thf(2269,plain,
! [SV538: $i,SV21: $i] :
( ( ! [SY3167: $i,SY3168: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV21 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV21 )
| ( c_lessequals @ SV538 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SY3167 ) @ SY3168 ) @ SV21 )
| ~ ( c_lessequals @ SV538 @ SY3168 @ SV21 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ SY3167 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(2270,plain,
! [SV539: $i,SV22: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV22 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV22 ) @ SV539 @ SV22 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV22 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV539 ) @ SV539 ) @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1751]) ).
thf(2271,plain,
! [SV540: $i,SV23: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV23 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV23 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV23 ) @ SV540 ) @ SV540 ) @ SV23 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV23 ) @ SV540 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(2272,plain,
! [SV24: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV24 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ SV24 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ SV24 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) )
= ( c_HOL_Ozero__class_Ozero @ SV24 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1753]) ).
thf(2273,plain,
! [SV541: $i,SV25: $i] :
( ( ! [SY3169: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV25 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SV541 ) @ SY3169 ) @ SV25 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SY3169 @ SV25 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV541 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(2274,plain,
! [SV26: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV26 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ ( c_HOL_Oone__class_Oone @ SV26 ) @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1755]) ).
thf(2275,plain,
! [SV27: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV27 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV27 ) @ ( c_HOL_Ozero__class_Ozero @ SV27 ) @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1756]) ).
thf(2276,plain,
! [SV542: $i,SV28: $i] :
( ( ! [SY3170: $i] :
( ~ ( class_Orderings_Olinorder @ SV28 )
| ( c_lessequals @ SV542 @ SY3170 @ SV28 )
| ( c_lessequals @ SY3170 @ SV542 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1757]) ).
thf(2277,plain,
! [SV543: $i,SV29: $i] :
( ( ! [SY3171: $i] :
( ~ ( class_Orderings_Olinorder @ SV29 )
| ( SV543 = SY3171 )
| ( c_HOL_Oord__class_Oless @ SV543 @ SY3171 @ SV29 )
| ~ ( c_lessequals @ SV543 @ SY3171 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1758]) ).
thf(2278,plain,
! [SV544: $i,SV30: $i] :
( ( ! [SY3172: $i] :
( ~ ( class_Orderings_Olinorder @ SV30 )
| ( SV544 = SY3172 )
| ~ ( c_lessequals @ SV544 @ SY3172 @ SV30 )
| ( c_HOL_Oord__class_Oless @ SV544 @ SY3172 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1759]) ).
thf(2279,plain,
! [SV545: $i,SV31: $i] :
( ( ! [SY3173: $i] :
( ~ ( class_Orderings_Oorder @ SV31 )
| ( c_HOL_Oord__class_Oless @ SV545 @ SY3173 @ SV31 )
| ~ ( c_lessequals @ SV545 @ SY3173 @ SV31 )
| ( SV545 = SY3173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1760]) ).
thf(2280,plain,
! [SV546: $i,SV32: $i] :
( ( ! [SY3174: $i] :
( ~ ( class_Orderings_Oorder @ SV32 )
| ( c_HOL_Oord__class_Oless @ SV546 @ SY3174 @ SV32 )
| ( SV546 = SY3174 )
| ~ ( c_lessequals @ SV546 @ SY3174 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(2281,plain,
! [SV547: $i,SV33: $i] :
( ( ! [SY3175: $i] :
( ~ ( class_Orderings_Oorder @ SV33 )
| ( c_HOL_Oord__class_Oless @ SV547 @ SY3175 @ SV33 )
| ( SV547 = SY3175 )
| ~ ( c_lessequals @ SV547 @ SY3175 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(2282,plain,
! [SV548: $i,SV34: $i] :
( ( ! [SY3176: $i] :
( ~ ( class_Orderings_Oorder @ SV34 )
| ( SV548 = SY3176 )
| ( c_HOL_Oord__class_Oless @ SV548 @ SY3176 @ SV34 )
| ~ ( c_lessequals @ SV548 @ SY3176 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1763]) ).
thf(2283,plain,
! [SV549: $i,SV35: $i] :
( ( ! [SY3177: $i] :
( ~ ( class_Orderings_Oorder @ SV35 )
| ( c_HOL_Oord__class_Oless @ SV549 @ SY3177 @ SV35 )
| ~ ( c_lessequals @ SV549 @ SY3177 @ SV35 )
| ( SY3177 = SV549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(2284,plain,
! [SV550: $i,SV36: $i] :
( ( ! [SY3178: $i] :
( ~ ( class_Orderings_Oorder @ SV36 )
| ( c_HOL_Oord__class_Oless @ SV550 @ SY3178 @ SV36 )
| ( SY3178 = SV550 )
| ~ ( c_lessequals @ SV550 @ SY3178 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1765]) ).
thf(2285,plain,
! [SV551: $i,SV37: $i] :
( ( ! [SY3179: $i,SY3180: $i,SY3181: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV37 )
| ( c_lessequals @ SV551 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SY3179 ) @ SY3180 ) @ SV37 )
| ~ ( c_lessequals @ SY3181 @ SY3180 @ SV37 )
| ~ ( c_lessequals @ SV551 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SY3179 ) @ SY3181 ) @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(2286,plain,
! [SV552: $i,SV38: $i] :
( ( ! [SY3182: $i,SY3183: $i] :
( ~ ( class_Orderings_Opreorder @ SV38 )
| ( c_HOL_Oord__class_Oless @ SV552 @ SY3182 @ SV38 )
| ~ ( c_lessequals @ SY3183 @ SY3182 @ SV38 )
| ~ ( c_HOL_Oord__class_Oless @ SV552 @ SY3183 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1767]) ).
thf(2287,plain,
! [SV553: $i,SV39: $i] :
( ( ! [SY3184: $i,SY3185: $i] :
( ~ ( class_Orderings_Opreorder @ SV39 )
| ( c_HOL_Oord__class_Oless @ SV553 @ SY3184 @ SV39 )
| ~ ( c_HOL_Oord__class_Oless @ SY3185 @ SY3184 @ SV39 )
| ~ ( c_lessequals @ SV553 @ SY3185 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(2288,plain,
! [SV554: $i,SV40: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV40 )
| ( c_lessequals @ SV554 @ SV554 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1769]) ).
thf(2289,plain,
! [SV555: $i,SV41: $i] :
( ( ~ ( class_Orderings_Oorder @ SV41 )
| ( c_lessequals @ SV555 @ SV555 @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(2290,plain,
! [SV556: $i,SV42: $i] :
( ( ! [SY3186: $i,SY3187: $i] :
( ~ ( class_Orderings_Opreorder @ SV42 )
| ( c_lessequals @ SV556 @ SY3186 @ SV42 )
| ~ ( c_lessequals @ SY3187 @ SY3186 @ SV42 )
| ~ ( c_lessequals @ SV556 @ SY3187 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1771]) ).
thf(2291,plain,
! [SV557: $i,SV43: $i] :
( ( ! [SY3188: $i,SY3189: $i] :
( ~ ( class_Orderings_Oorder @ SV43 )
| ( c_HOL_Oord__class_Oless @ SV557 @ SY3188 @ SV43 )
| ~ ( c_HOL_Oord__class_Oless @ SV557 @ SY3189 @ SV43 )
| ~ ( c_lessequals @ SY3189 @ SY3188 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1772]) ).
thf(2292,plain,
! [SV558: $i,SV44: $i] :
( ( ! [SY3190: $i,SY3191: $i] :
( ~ ( class_Orderings_Oorder @ SV44 )
| ( c_HOL_Oord__class_Oless @ SV558 @ SY3190 @ SV44 )
| ~ ( c_lessequals @ SV558 @ SY3191 @ SV44 )
| ~ ( c_HOL_Oord__class_Oless @ SY3191 @ SY3190 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(2293,plain,
! [SV559: $i,SV45: $i] :
( ( ! [SY3192: $i,SY3193: $i] :
( ~ ( class_Orderings_Oorder @ SV45 )
| ( c_lessequals @ SV559 @ SY3192 @ SV45 )
| ~ ( c_lessequals @ SV559 @ SY3193 @ SV45 )
| ~ ( c_lessequals @ SY3193 @ SY3192 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(2294,plain,
! [SV560: $i,SV46: $i] :
( ( ! [SY3194: $i,SY3195: $i,SY3196: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV46 @ SV560 @ SY3194 @ SY3195 ) @ SY3196 )
= ( hAPP @ SV46 @ SY3196 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3196 @ SV560 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(2295,plain,
! [SV561: $i,SV47: $i] :
( ( ! [SY3197: $i,SY3198: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV47 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ SV561 ) @ SY3197 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ SV561 ) @ SY3198 ) @ SV47 )
| ~ ( c_lessequals @ SY3197 @ SY3198 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1776]) ).
thf(2296,plain,
! [SV562: $i,SV48: $i] :
( ( ! [SY3199: $i,SY3200: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV48 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV48 ) @ SV562 ) @ SY3199 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV48 ) @ SY3200 ) @ SY3199 ) @ SV48 )
| ~ ( c_lessequals @ SV562 @ SY3200 @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1777]) ).
thf(2297,plain,
! [SV563: $i,SV49: $i] :
( ( ! [SY3201: $i,SY3202: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV49 )
| ( c_lessequals @ SV563 @ SY3201 @ SV49 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SY3202 ) @ SV563 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SY3202 ) @ SY3201 ) @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(2298,plain,
! [SV564: $i,SV50: $i] :
( ( ! [SY3203: $i,SY3204: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV564 ) @ SY3203 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV564 ) @ SY3204 ) @ SV50 )
| ~ ( c_lessequals @ SY3203 @ SY3204 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1779]) ).
thf(2299,plain,
! [SV565: $i,SV51: $i] :
( ( ! [SY3205: $i,SY3206: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV51 )
| ( c_lessequals @ SV565 @ SY3205 @ SV51 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV51 ) @ SV565 ) @ SY3206 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV51 ) @ SY3205 ) @ SY3206 ) @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(2300,plain,
! [SV566: $i,SV52: $i] :
( ( ! [SY3207: $i,SY3208: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV52 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV566 ) @ SY3207 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SY3208 ) @ SY3207 ) @ SV52 )
| ~ ( c_lessequals @ SV566 @ SY3208 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1781]) ).
thf(2301,plain,
! [SV567: $i,SV53: $i] :
( ( ! [SY3209: $i] :
( ~ ( class_Orderings_Opreorder @ SV53 )
| ( c_lessequals @ SV567 @ SY3209 @ SV53 )
| ~ ( c_HOL_Oord__class_Oless @ SV567 @ SY3209 @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(2302,plain,
! [SV568: $i,SV54: $i] :
( ( ! [SY3210: $i] :
( ~ ( class_Orderings_Oorder @ SV54 )
| ( c_lessequals @ SV568 @ SY3210 @ SV54 )
| ~ ( c_HOL_Oord__class_Oless @ SV568 @ SY3210 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1783]) ).
thf(2303,plain,
! [SV569: $i,SV55: $i] :
( ( ! [SY3211: $i] :
( ~ ( class_Orderings_Oorder @ SV55 )
| ( SV569 = SY3211 )
| ~ ( c_lessequals @ SV569 @ SY3211 @ SV55 )
| ~ ( c_lessequals @ SY3211 @ SV569 @ SV55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(2304,plain,
! [SV570: $i,SV56: $i] :
( ( ! [SY3212: $i] :
( ~ ( class_Orderings_Oorder @ SV56 )
| ( SV570 = SY3212 )
| ~ ( c_lessequals @ SY3212 @ SV570 @ SV56 )
| ~ ( c_lessequals @ SV570 @ SY3212 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1785]) ).
thf(2305,plain,
! [SV571: $i,SV57: $i] :
( ( ! [SY3213: $i] :
( ~ ( class_Orderings_Oorder @ SV57 )
| ( SV571 = SY3213 )
| ~ ( c_lessequals @ SY3213 @ SV571 @ SV57 )
| ~ ( c_lessequals @ SV571 @ SY3213 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(2306,plain,
! [SV572: $i,SV58: $i] :
( ( ! [SY3214: $i,SY3215: $i,SY3216: $i,SY3217: $i,SY3218: $i] :
( ( ( hAPP @ ( hAPP @ SV58 @ SV572 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= SV572 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3214 @ SY3215 @ SV58 @ SY3216 @ SY3217 @ SY3218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(2307,plain,
! [SV59: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV59 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1788]) ).
thf(2308,plain,
! [SV573: $i,SV60: $i] :
( ( ! [SY3219: $i] :
( ~ ( class_Orderings_Opreorder @ SV60 )
| ( c_HOL_Oord__class_Oless @ SV573 @ SY3219 @ SV60 )
| ( c_lessequals @ SY3219 @ SV573 @ SV60 )
| ~ ( c_lessequals @ SV573 @ SY3219 @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(2309,plain,
! [SV61: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV61 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ ( c_HOL_Oone__class_Oone @ SV61 ) @ SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1790]) ).
thf(2310,plain,
! [SV574: $i,SV62: $i] :
( ( ! [SY3220: $i,SY3221: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV62 @ SV574 @ SY3220 @ SY3221 ) @ SV574 )
= SY3220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1791]) ).
thf(2311,plain,
! [SV575: $i,SV63: $i] :
( ( ! [SY3222: $i,SY3223: $i] :
( ~ ( class_Orderings_Olinorder @ SV63 )
| ( c_lessequals @ SV575 @ SY3222 @ SV63 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV575 @ SY3223 @ SV63 ) @ SY3222 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1792]) ).
thf(2312,plain,
! [SV576: $i,SV64: $i] :
( ( ! [SY3224: $i,SY3225: $i] :
( ~ ( class_Orderings_Olinorder @ SV64 )
| ( c_lessequals @ SV576 @ SY3224 @ SV64 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY3225 @ SV576 @ SV64 ) @ SY3224 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(2313,plain,
! [SV577: $i,SV65: $i] :
( ( ! [SY3226: $i,SY3227: $i] :
( ~ ( class_Orderings_Olinorder @ SV65 )
| ( c_lessequals @ SV577 @ ( c_Orderings_Oord__class_Omax @ SY3226 @ SY3227 @ SV65 ) @ SV65 )
| ~ ( c_lessequals @ SV577 @ SY3226 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1794]) ).
thf(2314,plain,
! [SV578: $i,SV66: $i] :
( ( ! [SY3228: $i,SY3229: $i] :
( ~ ( class_Orderings_Olinorder @ SV66 )
| ( c_lessequals @ SV578 @ ( c_Orderings_Oord__class_Omax @ SY3228 @ SY3229 @ SV66 ) @ SV66 )
| ~ ( c_lessequals @ SV578 @ SY3229 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1795]) ).
thf(2315,plain,
! [SV579: $i,SV67: $i] :
( ( ! [SY3230: $i,SY3231: $i] :
( ~ ( class_Orderings_Olinorder @ SV67 )
| ( c_lessequals @ SV579 @ ( c_Orderings_Oord__class_Omax @ SY3230 @ SY3231 @ SV67 ) @ SV67 )
| ~ ( c_lessequals @ SV579 @ SY3230 @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1796]) ).
thf(2316,plain,
! [SV580: $i,SV68: $i] :
( ( ! [SY3232: $i,SY3233: $i] :
( ~ ( class_Orderings_Olinorder @ SV68 )
| ( c_lessequals @ SV580 @ ( c_Orderings_Oord__class_Omax @ SY3232 @ SY3233 @ SV68 ) @ SV68 )
| ~ ( c_lessequals @ SV580 @ SY3233 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(2317,plain,
! [SV581: $i,SV69: $i] :
( ( ! [SY3234: $i,SY3235: $i] :
( ~ ( class_Orderings_Olinorder @ SV69 )
| ( c_lessequals @ SV581 @ SY3234 @ SV69 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV581 @ SY3235 @ SV69 ) @ SY3234 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(2318,plain,
! [SV582: $i,SV70: $i] :
( ( ! [SY3236: $i,SY3237: $i] :
( ~ ( class_Orderings_Olinorder @ SV70 )
| ( c_lessequals @ SV582 @ SY3236 @ SV70 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY3237 @ SV582 @ SV70 ) @ SY3236 @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(2319,plain,
! [SV583: $i,SV71: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV71 )
| ( ( c_Power_Opower__class_Opower @ SV583 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV71 )
= SV583 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1800]) ).
thf(2320,plain,
! [SV584: $i,SV72: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV72 )
| ( ( c_Power_Opower__class_Opower @ SV584 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV72 )
= SV584 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1801]) ).
thf(2321,plain,
! [SV585: $i,SV73: $i] :
( ( ! [SY3238: $i,SY3239: $i] :
( ~ ( class_Orderings_Olinorder @ SV73 )
| ( c_lessequals @ SV585 @ SY3238 @ SV73 )
| ( c_lessequals @ SV585 @ SY3239 @ SV73 )
| ~ ( c_lessequals @ SV585 @ ( c_Orderings_Oord__class_Omax @ SY3239 @ SY3238 @ SV73 ) @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2322,plain,
! [SV586: $i,SV74: $i] :
( ( ! [SY3240: $i] :
( ~ ( class_Orderings_Olinorder @ SV74 )
| ( c_lessequals @ SV586 @ ( c_Orderings_Oord__class_Omax @ SY3240 @ SV586 @ SV74 ) @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1803]) ).
thf(2323,plain,
! [SV587: $i,SV75: $i] :
( ( ! [SY3241: $i] :
( ~ ( class_Orderings_Olinorder @ SV75 )
| ( c_lessequals @ SV587 @ ( c_Orderings_Oord__class_Omax @ SV587 @ SY3241 @ SV75 ) @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(2324,plain,
! [SV588: $i,SV76: $i] :
( ( ! [SY3242: $i,SY3243: $i] :
( ~ ( class_Orderings_Olinorder @ SV76 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV588 @ SY3242 @ SV76 ) @ SY3243 @ SV76 )
| ~ ( c_lessequals @ SY3242 @ SY3243 @ SV76 )
| ~ ( c_lessequals @ SV588 @ SY3243 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(2325,plain,
! [SV589: $i,SV77: $i] :
( ( ! [SY3244: $i,SY3245: $i] :
( ~ ( class_Orderings_Olinorder @ SV77 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV589 @ SY3244 @ SV77 ) @ SY3245 @ SV77 )
| ~ ( c_lessequals @ SY3244 @ SY3245 @ SV77 )
| ~ ( c_lessequals @ SV589 @ SY3245 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1806]) ).
thf(2326,plain,
! [SV590: $i,SV78: $i] :
( ( ! [SY3246: $i,SY3247: $i] :
( ~ ( class_Orderings_Olinorder @ SV78 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV590 @ SY3246 @ SV78 ) @ SY3247 @ SV78 )
| ~ ( c_lessequals @ SY3246 @ SY3247 @ SV78 )
| ~ ( c_lessequals @ SV590 @ SY3247 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1807]) ).
thf(2327,plain,
! [SV591: $i,SV79: $i] :
( ( ! [SY3248: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV79 )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV79 ) @ ( c_Power_Opower__class_Opower @ SV591 @ SY3248 @ SV79 ) @ SV79 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV79 ) @ SV591 @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(2328,plain,
! [SV592: $i,SV80: $i] :
( ( ! [SY3249: $i,SY3250: $i,SY3251: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV80 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SV592 ) @ SY3249 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SY3250 ) @ SY3251 ) @ SV80 )
| ~ ( c_lessequals @ SY3249 @ SY3251 @ SV80 )
| ~ ( c_lessequals @ SV592 @ SY3250 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(2329,plain,
! [SV593: $i,SV81: $i] :
( ( ! [SY3252: $i] :
( ~ ( class_Orderings_Olinorder @ SV81 )
| ( ( c_Orderings_Oord__class_Omax @ SV593 @ SY3252 @ SV81 )
= SY3252 )
| ~ ( c_lessequals @ SV593 @ SY3252 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2330,plain,
! [SV594: $i,SV82: $i] :
( ( ! [SY3253: $i] :
( ~ ( class_Orderings_Olinorder @ SV82 )
| ( ( c_Orderings_Oord__class_Omax @ SV594 @ SY3253 @ SV82 )
= SV594 )
| ~ ( c_lessequals @ SY3253 @ SV594 @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(2331,plain,
! [SV595: $i,SV83: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV83 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV83 ) @ SV595 @ SV83 )
= ( c_HOL_Oone__class_Oone @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1812]) ).
thf(2332,plain,
! [SV596: $i,SV84: $i] :
( ( ! [SY3254: $i] :
( ~ ( class_Orderings_Olinorder @ SV84 )
| ( c_HOL_Oord__class_Oless @ SV596 @ SY3254 @ SV84 )
| ( c_lessequals @ SY3254 @ SV596 @ SV84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(2333,plain,
! [SV597: $i,SV85: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV85 )
| ~ ( c_lessequals @ SV597 @ SV597 @ SV85 )
| ~ ( c_HOL_Oord__class_Oless @ SV597 @ SV597 @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1814]) ).
thf(2334,plain,
! [SV598: $i,SV86: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV86 )
| ( c_HOL_Oord__class_Oless @ SV598 @ SV598 @ SV86 )
| ( c_lessequals @ SV598 @ SV598 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1815]) ).
thf(2335,plain,
! [SV599: $i,SV87: $i] :
( ( ! [SY3255: $i] :
( ~ ( class_Orderings_Olinorder @ SV87 )
| ~ ( c_HOL_Oord__class_Oless @ SV599 @ SY3255 @ SV87 )
| ~ ( c_lessequals @ SY3255 @ SV599 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1816]) ).
thf(2336,plain,
! [SV600: $i,SV88: $i] :
( ( ! [SY3256: $i] :
( ~ ( class_Orderings_Olinorder @ SV88 )
| ( c_lessequals @ SV600 @ SY3256 @ SV88 )
| ( c_HOL_Oord__class_Oless @ SY3256 @ SV600 @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1817]) ).
thf(2337,plain,
! [SV601: $i,SV89: $i] :
( ( ! [SY3257: $i] :
( ~ ( class_Orderings_Olinorder @ SV89 )
| ~ ( c_lessequals @ SV601 @ SY3257 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SY3257 @ SV601 @ SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1818]) ).
thf(2338,plain,
! [SV602: $i,SV90: $i] :
( ( ! [SY3258: $i] :
( ~ ( class_Orderings_Olinorder @ SV90 )
| ( c_HOL_Oord__class_Oless @ SV602 @ SY3258 @ SV90 )
| ( c_lessequals @ SY3258 @ SV602 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(2339,plain,
! [SV603: $i,SV91: $i] :
( ( ! [SY3259: $i] :
( ~ ( class_Orderings_Opreorder @ SV91 )
| ~ ( c_lessequals @ SV603 @ SY3259 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SY3259 @ SV603 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1820]) ).
thf(2340,plain,
! [SV92: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV92 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV92 )
= ( c_HOL_Oone__class_Oone @ SV92 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1821]) ).
thf(2341,plain,
! [SV604: $i,SV93: $i] :
( ( ! [SY3260: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV93 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV604 ) @ SY3260 ) @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 )
| ~ ( c_lessequals @ SY3260 @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ SV604 @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1822]) ).
thf(2342,plain,
! [SV605: $i,SV94: $i] :
( ( ! [SY3261: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV94 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV605 ) @ SY3261 ) @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 )
| ~ ( c_HOL_Oord__class_Oless @ SY3261 @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 )
| ~ ( c_lessequals @ SV605 @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1823]) ).
thf(2343,plain,
! [SV606: $i,SV95: $i] :
( ( ! [SY3262: $i,SY3263: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV95 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV95 )
| ( c_HOL_Oord__class_Oless @ SV606 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SY3262 ) @ SY3263 ) @ SV95 )
| ~ ( c_lessequals @ SV606 @ SY3263 @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SY3262 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(2344,plain,
! [SV607: $i,SV96: $i] :
( ( ! [SY3264: $i,SY3265: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV96 )
| ( c_HOL_Oord__class_Oless @ SV607 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SY3264 ) @ SY3265 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ SV607 @ SY3265 @ SV96 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SY3264 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(2345,plain,
! [SV608: $i,SV97: $i] :
( ( ! [SY3266: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV97 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV608 ) @ SY3266 ) @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SY3266 @ SV97 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV608 @ SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2346,plain,
! [SV609: $i,SV98: $i] :
( ( ! [SY3267: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV98 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV98 ) @ SV609 ) @ SY3267 ) @ SV98 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ SY3267 @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ SV609 @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(2347,plain,
! [SV99: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV99 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV99 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV99 ) @ ( c_HOL_Oone__class_Oone @ SV99 ) ) @ ( c_HOL_Oone__class_Oone @ SV99 ) ) @ SV99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1828]) ).
thf(2348,plain,
! [SV610: $i,SV100: $i] :
( ( ! [SY3268: $i,SY3269: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV100 )
| ( c_HOL_Oord__class_Oless @ SV610 @ SY3268 @ SV100 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV100 ) @ SY3268 @ SV100 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV610 @ SY3269 @ SV100 ) @ ( c_Power_Opower__class_Opower @ SY3268 @ SY3269 @ SV100 ) @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1829]) ).
thf(2349,plain,
! [SV101: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV101 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV101 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV101 )
= ( c_HOL_Oone__class_Oone @ SV101 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1830]) ).
thf(2350,plain,
! [SV611: $i,SV102: $i] :
( ( ! [SY3270: $i,SY3271: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV102 )
| ( c_HOL_Oord__class_Oless @ SV611 @ SY3270 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY3271 @ SV611 @ SV102 ) @ ( c_Power_Opower__class_Opower @ SY3271 @ SY3270 @ SV102 ) @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV102 ) @ SY3271 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(2351,plain,
! [SV612: $i,SV103: $i] :
( ( ! [SY3272: $i,SY3273: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV103 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV612 @ SY3272 @ SV103 ) @ ( c_Power_Opower__class_Opower @ SV612 @ SY3273 @ SV103 ) @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV103 ) @ SV612 @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ SY3272 @ SY3273 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(2352,plain,
! [SV613: $i,SV104: $i] :
( ( ! [SY3274: $i,SY3275: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV104 )
| ( c_HOL_Oord__class_Oless @ SV613 @ SY3274 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY3275 @ SV613 @ SV104 ) @ ( c_Power_Opower__class_Opower @ SY3275 @ SY3274 @ SV104 ) @ SV104 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV104 ) @ SY3275 @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1833]) ).
thf(2353,plain,
! [SV614: $i,SV105: $i] :
( ( ! [SY3276: $i,SY3277: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV105 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV614 @ SY3276 @ SV105 ) @ ( c_Power_Opower__class_Opower @ SV614 @ SY3277 @ SV105 ) @ SV105 )
| ~ ( c_HOL_Oord__class_Oless @ SY3276 @ SY3277 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV105 ) @ SV614 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1834]) ).
thf(2354,plain,
! [SV615: $i,SV106: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OAbs @ SV106 ) ) @ SV615 )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV106 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV615 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(2355,plain,
! [SV616: $i,SV107: $i] :
( ( ! [SY3278: $i] :
( ( c_Lambda_Oliftn @ SV107 @ ( c_Lambda_OdB_OAbs @ SV616 ) @ SY3278 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Oliftn @ SV107 @ SV616 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3278 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1836]) ).
thf(2356,plain,
! [SV617: $i,SV108: $i] :
( ( ! [SY3279: $i] :
( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OAbs @ SV108 ) @ SV617 @ SY3279 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubstn @ SV108 @ SV617 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3279 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(2357,plain,
! [SV618: $i,SV109: $i] :
( ( ! [SY3280: $i,SY3281: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV109 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV618 @ SY3280 @ SV109 ) @ ( c_Power_Opower__class_Opower @ SY3281 @ SY3280 @ SV109 ) @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3280 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV618 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SV618 @ SY3281 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1838]) ).
thf(2358,plain,
! [SV619: $i,SV110: $i] :
( ( ! [SY3282: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ SV110 ) ) @ SV619 ) @ SY3282 )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV110 ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV619 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3282 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(2359,plain,
! [SV620: $i,SV111: $i] :
( ( ! [SY3283: $i,SY3284: $i,SY3285: $i] :
( ( c_Type_Otypings @ ( c_Type_Oshift @ SV111 @ SV620 @ SY3283 @ tc_Type_Otype ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ SV620 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY3284 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY3285 )
| ~ ( c_Type_Otypings @ SV111 @ SY3284 @ SY3285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(2360,plain,
! [SV621: $i,SV112: $i] :
( ( ! [SY3286: $i,SY3287: $i,SY3288: $i,SY3289: $i] :
( ( c_Type_Otypings @ SV112 @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SV621 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SY3286 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY3287 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY3288 )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ SV112 @ SY3286 @ SY3289 @ tc_Type_Otype ) @ SY3287 @ SY3288 )
| ~ ( c_Type_Otyping @ SV112 @ SV621 @ SY3289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(2361,plain,
! [SV622: $i,SV113: $i] :
( ( ( hBOOL @ ( hAPP @ SV113 @ SV622 ) )
| ~ ( hBOOL @ ( hAPP @ SV113 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV113 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @ SV113 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ SV113 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV113 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV113 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1842]) ).
thf(2362,plain,
! [SV623: $i,SV114: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV114 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV114 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__4 @ SV114 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ SV114 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV114 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV114 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ SV114 @ SV623 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1843]) ).
thf(2363,plain,
! [SV115: $i] :
( ( ( SV115
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV115 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV115 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV115 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( SV115
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV115 ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV115 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV115 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1844]) ).
thf(2364,plain,
! [SV624: $i,SV116: $i] :
( ( ! [SY3290: $i,SY3291: $i,SY3292: $i] :
( ( c_List_Omap @ SV116 @ ( c_List_Olist_OCons @ SV624 @ SY3290 @ SY3291 ) @ SY3291 @ SY3292 )
= ( c_List_Olist_OCons @ ( hAPP @ SV116 @ SV624 ) @ ( c_List_Omap @ SV116 @ SY3290 @ SY3291 @ SY3292 ) @ SY3292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(2365,plain,
! [SV625: $i,SV117: $i] :
( ( ! [SY3293: $i,SY3294: $i,SY3295: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ SV117 @ SV625 ) @ ( c_List_Omap @ SV117 @ SY3293 @ SY3294 @ SY3295 ) @ SY3295 )
= ( c_List_Omap @ SV117 @ ( c_List_Olist_OCons @ SV625 @ SY3293 @ SY3294 ) @ SY3294 @ SY3295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(2366,plain,
! [SV626: $i,SV118: $i] :
( ( ! [SY3296: $i,SY3297: $i,SY3298: $i] :
( ( c_List_Omap @ SV118 @ ( c_List_Olist_OCons @ SV626 @ SY3296 @ SY3297 ) @ SY3297 @ SY3298 )
= ( c_List_Olist_OCons @ ( hAPP @ SV118 @ SV626 ) @ ( c_List_Omap @ SV118 @ SY3296 @ SY3297 @ SY3298 ) @ SY3298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(2367,plain,
! [SV627: $i,SV119: $i] :
( ( ! [SY3299: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV119 ) @ SV627 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3299 ) @ SV627 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV119 ) @ SY3299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(2368,plain,
! [SV628: $i,SV120: $i] :
( ( ! [SY3300: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV120 ) @ SV628 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV120 ) @ SY3300 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV628 ) @ SY3300 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(2369,plain,
! [SV629: $i,SV121: $i] :
( ( ! [SY3301: $i,SY3302: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV121 @ SV629 @ SY3301 ) @ SY3302 @ SY3301 )
= ( c_List_Olist_OCons @ SV121 @ ( c_List_Oappend @ SV629 @ SY3302 @ SY3301 ) @ SY3301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1850]) ).
thf(2370,plain,
! [SV630: $i,SV122: $i] :
( ( ! [SY3303: $i,SY3304: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV122 @ SV630 @ SY3303 ) @ SY3304 @ SY3303 )
= ( c_List_Olist_OCons @ SV122 @ ( c_List_Oappend @ SV630 @ SY3304 @ SY3303 ) @ SY3303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(2371,plain,
! [SV631: $i,SV123: $i] :
( ( ! [SY3305: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV123 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV123 ) @ SV631 ) @ SY3305 ) @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 )
| ~ ( c_HOL_Oord__class_Oless @ SY3305 @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 )
| ~ ( c_HOL_Oord__class_Oless @ SV631 @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(2372,plain,
! [SV124: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV124 ) )
= $true )
| ( ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ SV124 ) @ SV124 )
= ( c_HOL_Ozero__class_Ozero @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1853]) ).
thf(2373,plain,
! [SV632: $i,SV125: $i] :
( ( ! [SY3306: $i,SY3307: $i] :
( ~ ( class_Orderings_Olinorder @ SV125 )
| ( c_HOL_Oord__class_Oless @ SV632 @ SY3306 @ SV125 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SY3307 @ SV632 @ SV125 ) @ SY3306 @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2374,plain,
! [SV633: $i,SV126: $i] :
( ( ! [SY3308: $i,SY3309: $i] :
( ~ ( class_Orderings_Olinorder @ SV126 )
| ( c_HOL_Oord__class_Oless @ SV633 @ SY3308 @ SV126 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV633 @ SY3309 @ SV126 ) @ SY3308 @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1855]) ).
thf(2375,plain,
! [SV634: $i,SV127: $i] :
( ( ! [SY3310: $i,SY3311: $i] :
( ~ ( class_Orderings_Olinorder @ SV127 )
| ( c_HOL_Oord__class_Oless @ SV634 @ ( c_Orderings_Oord__class_Omax @ SY3310 @ SY3311 @ SV127 ) @ SV127 )
| ~ ( c_HOL_Oord__class_Oless @ SV634 @ SY3311 @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2376,plain,
! [SV635: $i,SV128: $i] :
( ( ! [SY3312: $i,SY3313: $i] :
( ~ ( class_Orderings_Olinorder @ SV128 )
| ( c_HOL_Oord__class_Oless @ SV635 @ ( c_Orderings_Oord__class_Omax @ SY3312 @ SY3313 @ SV128 ) @ SV128 )
| ~ ( c_HOL_Oord__class_Oless @ SV635 @ SY3312 @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(2377,plain,
! [SV636: $i,SV129: $i] :
( ( ! [SY3314: $i,SY3315: $i] :
( ~ ( class_Orderings_Olinorder @ SV129 )
| ( c_HOL_Oord__class_Oless @ SV636 @ ( c_Orderings_Oord__class_Omax @ SY3314 @ SY3315 @ SV129 ) @ SV129 )
| ~ ( c_HOL_Oord__class_Oless @ SV636 @ SY3315 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1858]) ).
thf(2378,plain,
! [SV637: $i,SV130: $i] :
( ( ! [SY3316: $i,SY3317: $i] :
( ~ ( class_Orderings_Olinorder @ SV130 )
| ( c_HOL_Oord__class_Oless @ SV637 @ ( c_Orderings_Oord__class_Omax @ SY3316 @ SY3317 @ SV130 ) @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SV637 @ SY3316 @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(2379,plain,
! [SV638: $i,SV131: $i] :
( ( ! [SY3318: $i,SY3319: $i,SY3320: $i,SY3321: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV638 ) @ SY3318 ) )
| ( c_ListOrder_Ostep1 @ SV131 @ SY3319 @ SY3320 @ SY3321 )
| ~ ( c_ListOrder_Ostep1 @ SV131 @ ( c_List_Oappend @ SY3319 @ ( c_List_Olist_OCons @ SV638 @ ( c_List_Olist_ONil @ SY3321 ) @ SY3321 ) @ SY3321 ) @ ( c_List_Oappend @ SY3320 @ ( c_List_Olist_OCons @ SY3318 @ ( c_List_Olist_ONil @ SY3321 ) @ SY3321 ) @ SY3321 ) @ SY3321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(2380,plain,
! [SV639: $i,SV132: $i] :
( ( ! [SY3322: $i,SY3323: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV132 @ SV639 @ SV639 ) @ SV639 ) @ SY3322 ) @ SY3323 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV132 @ SV639 ) @ SY3323 ) @ SY3322 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(2381,plain,
! [SV640: $i,SV133: $i] :
( ( ! [SY3324: $i,SY3325: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV133 @ SV640 ) @ SY3324 ) @ SY3325 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV133 @ SV640 @ SV640 ) @ SV640 ) @ SY3325 ) @ SY3324 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(2382,plain,
! [SV641: $i,SV134: $i] :
( ( ! [SY3326: $i] :
( ( c_List_Omap @ SV134 @ ( c_List_Olist_ONil @ SV641 ) @ SV641 @ SY3326 )
= ( c_List_Olist_ONil @ SY3326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(2383,plain,
! [SV642: $i,SV135: $i] :
( ( ! [SY3327: $i,SY3328: $i] :
( ( c_List_Ofoldr @ SV135 @ ( c_List_Olist_ONil @ SV642 ) @ SY3327 @ SV642 @ SY3328 )
= SY3327 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2384,plain,
! [SV643: $i,SV136: $i] :
( ( ! [SY3329: $i,SY3330: $i,SY3331: $i,SY3332: $i] :
( ( hAPP @ ( c_COMBC @ SV136 @ SV643 @ SY3329 @ SY3330 @ SY3331 ) @ SY3332 )
= ( hAPP @ ( hAPP @ SV136 @ SY3332 ) @ SV643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1865]) ).
thf(2385,plain,
! [SV644: $i,SV137: $i] :
( ( ! [SY3333: $i,SY3334: $i,SY3335: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV644 ) @ SY3333 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV137 @ SY3334 @ SY3335 ) @ SY3333 ) @ SV644 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(2386,plain,
! [SV645: $i,SV138: $i] :
( ( ! [SY3336: $i,SY3337: $i,SY3338: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV138 @ SV645 @ SY3336 ) @ SY3337 ) @ SY3338 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV138 @ SY3338 ) @ SY3337 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1867]) ).
thf(2387,plain,
! [SV646: $i,SV139: $i] :
( ( ! [SY3339: $i,SY3340: $i,SY3341: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV139 @ SV646 ) @ SY3339 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV139 @ SY3340 @ SY3341 ) @ SY3339 ) @ SV646 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(2388,plain,
! [SV647: $i,SV140: $i] :
( ( ! [SY3342: $i,SY3343: $i,SY3344: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV140 @ SV647 @ SY3342 ) @ SY3343 ) @ SY3344 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV140 @ SY3344 ) @ SY3343 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1869]) ).
thf(2389,plain,
! [SV648: $i,SV141: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV141 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV648 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV648 ) @ SV141 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1870]) ).
thf(2390,plain,
! [SV649: $i,SV142: $i] :
( ( ! [SY3345: $i,SY3346: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV142 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ SV649 ) @ SY3345 ) ) @ SY3346 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ SV649 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ SY3345 ) @ SY3346 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(2391,plain,
! [SV650: $i,SV143: $i] :
( ( ! [SY3347: $i,SY3348: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV143 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ SV650 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ SY3347 ) @ SY3348 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ SY3347 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ SV650 ) @ SY3348 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1872]) ).
thf(2392,plain,
! [SV651: $i,SV144: $i] :
( ( ! [SY3349: $i,SY3350: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV144 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ SV651 ) @ SY3349 ) ) @ SY3350 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ SV651 ) @ SY3350 ) ) @ SY3349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(2393,plain,
! [SV652: $i,SV145: $i] :
( ( ! [SY3351: $i,SY3352: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV145 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV145 ) @ SV652 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV145 ) @ SY3351 ) @ SY3352 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV145 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV145 ) @ SV652 ) @ SY3351 ) ) @ SY3352 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(2394,plain,
! [SV653: $i,SV146: $i] :
( ( ! [SY3353: $i,SY3354: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV146 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ SV653 ) @ SY3353 ) ) @ SY3354 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ SV653 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ SY3353 ) @ SY3354 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(2395,plain,
! [SV654: $i,SV147: $i] :
( ( ! [SY3355: $i,SY3356: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV147 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV654 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SY3355 ) @ SY3356 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SY3355 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV654 ) @ SY3356 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1876]) ).
thf(2396,plain,
! [SV655: $i,SV148: $i] :
( ( ! [SY3357: $i,SY3358: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV148 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV655 ) @ SY3357 ) ) @ SY3358 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV655 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SY3357 ) @ SY3358 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(2397,plain,
! [SV656: $i,SV149: $i] :
( ( ! [SY3359: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV149 ) @ SV656 ) ) @ SY3359 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV149 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV656 ) @ SY3359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(2398,plain,
! [SV657: $i,SV150: $i] :
( ( ! [SY3360: $i] :
( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV150 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV657 ) @ SY3360 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV657 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV150 ) @ SY3360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(2399,plain,
! [SV658: $i,SV151: $i] :
( ( ! [SY3361: $i,SY3362: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV151 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV658 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SY3361 ) @ SY3362 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SY3361 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV658 ) @ SY3362 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(2400,plain,
! [SV659: $i,SV152: $i] :
( ( ! [SY3363: $i,SY3364: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV152 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV659 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SY3363 ) @ SY3364 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV659 ) @ SY3363 ) ) @ SY3364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2401,plain,
! [SV660: $i,SV153: $i] :
( ( ! [SY3365: $i,SY3366: $i] :
( ~ ( class_Orderings_Oorder @ SV153 )
| ( c_HOL_Oord__class_Oless @ SV660 @ SY3365 @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SV660 @ SY3366 @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SY3366 @ SY3365 @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2402,plain,
! [SV661: $i,SV154: $i] :
( ( ! [SY3367: $i,SY3368: $i] :
( ~ ( class_Orderings_Opreorder @ SV154 )
| ( c_HOL_Oord__class_Oless @ SV661 @ SY3367 @ SV154 )
| ~ ( c_HOL_Oord__class_Oless @ SY3368 @ SY3367 @ SV154 )
| ~ ( c_HOL_Oord__class_Oless @ SV661 @ SY3368 @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2403,plain,
! [SV662: $i,SV155: $i] :
( ( ! [SY3369: $i,SY3370: $i,SY3371: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV155 @ SV662 @ SY3369 @ SY3370 )
| ( c_ListOrder_Ostep1 @ SV155 @ ( c_List_Oappend @ SV662 @ SY3371 @ SY3370 ) @ ( c_List_Oappend @ SY3369 @ SY3371 @ SY3370 ) @ SY3370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2404,plain,
! [SV663: $i,SV156: $i] :
( ( ! [SY3372: $i,SY3373: $i,SY3374: $i] :
( ( c_ListOrder_Ostep1 @ SV156 @ ( c_List_Oappend @ SV663 @ SY3372 @ SY3373 ) @ ( c_List_Oappend @ SV663 @ SY3374 @ SY3373 ) @ SY3373 )
| ~ ( c_ListOrder_Ostep1 @ SV156 @ SY3372 @ SY3374 @ SY3373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2405,plain,
! [SV664: $i,SV157: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV157 ) ) @ ( c_Lambda_OdB_OAbs @ SV664 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV157 ) @ SV664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2406,plain,
! [SV665: $i,SV158: $i] :
( ( ! [SY3375: $i,SY3376: $i] :
( ( c_List_Olistsp @ SV158 @ SV665 @ SY3375 )
| ~ ( c_List_Olistsp @ SV158 @ ( c_List_Oappend @ SV665 @ SY3376 @ SY3375 ) @ SY3375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(2407,plain,
! [SV666: $i,SV159: $i] :
( ( ! [SY3377: $i,SY3378: $i] :
( ( c_List_Olistsp @ SV159 @ SV666 @ SY3377 )
| ~ ( c_List_Olistsp @ SV159 @ ( c_List_Oappend @ SY3378 @ SV666 @ SY3377 ) @ SY3377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(2408,plain,
! [SV667: $i,SV160: $i] :
( ( ! [SY3379: $i,SY3380: $i,SY3381: $i] :
( ( c_Lambda_OdB_OdB__case @ SV160 @ SV667 @ SY3379 @ ( c_Lambda_OdB_OAbs @ SY3380 ) @ SY3381 )
= ( hAPP @ SY3379 @ SY3380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2409,plain,
! [SV668: $i,SV161: $i] :
( ( ! [SY3382: $i,SY3383: $i,SY3384: $i,SY3385: $i] :
( ( SV161 = SV668 )
| ( SY3382 = SY3383 )
| ~ ( c_ListOrder_Ostep1 @ SY3384 @ ( c_List_Olist_OCons @ SV668 @ SY3383 @ SY3385 ) @ ( c_List_Olist_OCons @ SV161 @ SY3382 @ SY3385 ) @ SY3385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1890]) ).
thf(2410,plain,
! [SV669: $i,SV162: $i] :
( ( ! [SY3386: $i,SY3387: $i,SY3388: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV162 @ SV669 ) @ SY3386 ) )
| ( c_ListOrder_Ostep1 @ SV162 @ ( c_List_Olist_OCons @ SV669 @ SY3387 @ SY3388 ) @ ( c_List_Olist_OCons @ SY3386 @ SY3387 @ SY3388 ) @ SY3388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1891]) ).
thf(2411,plain,
! [SV670: $i,SV163: $i] :
( ( c_List_Olistsp @ SV163 @ ( c_List_Olist_ONil @ SV670 ) @ SV670 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(2412,plain,
! [SV671: $i,SV164: $i] :
( ( ! [SY3389: $i,SY3390: $i] :
( ~ ( class_Orderings_Olinorder @ SV164 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV671 @ SY3389 @ SV164 ) @ SY3390 @ SV164 )
| ~ ( c_HOL_Oord__class_Oless @ SY3389 @ SY3390 @ SV164 )
| ~ ( c_HOL_Oord__class_Oless @ SV671 @ SY3390 @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2413,plain,
! [SV672: $i,SV165: $i] :
( ( ! [SY3391: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV165 @ SV672 ) @ SY3391 ) @ SY3391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2414,plain,
! [SV673: $i,SV166: $i] :
( ( ! [SY3392: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV166 @ SV673 ) @ SY3392 ) @ SY3392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2415,plain,
! [SV674: $i,SV167: $i] :
( ( ! [SY3393: $i,SY3394: $i] :
( ( c_Wellfounded_Oaccp @ SV167 @ SV674 @ SY3393 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SY3393 ) @ SV674 ) @ SY3394 ) )
| ~ ( c_Wellfounded_Oaccp @ SV167 @ SY3394 @ SY3393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2416,plain,
! [SV675: $i,SV168: $i] :
( ( ! [SY3395: $i,SY3396: $i] :
( ( c_Wellfounded_Oaccp @ SV168 @ SV675 @ SY3395 )
| ~ ( c_Wellfounded_Oaccp @ SV168 @ SY3396 @ SY3395 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SY3395 ) @ SV675 ) @ SY3396 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1897]) ).
thf(2417,plain,
! [SV676: $i,SV169: $i] :
( ( ! [SY3397: $i,SY3398: $i,SY3399: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SV676 ) @ SY3397 ) @ SY3398 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SV676 ) @ SY3399 ) @ SY3398 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SV676 ) @ SY3397 ) @ SY3399 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2418,plain,
! [SV170: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV170 @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV170 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1899]) ).
thf(2419,plain,
! [SV171: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV171 ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV171 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1900]) ).
thf(2420,plain,
! [SV172: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV172 ) ) )
= $true )
| ( ( ( SV172
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV172 ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV172 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV172 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1901]) ).
thf(2421,plain,
! [SV677: $i,SV173: $i] :
( ( ( c_List_Oappend @ SV173 @ ( c_List_Olist_ONil @ SV677 ) @ SV677 )
= SV173 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2422,plain,
! [SV678: $i,SV174: $i] :
( ( SV174
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV678 ) @ SV174 @ SV678 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(2423,plain,
! [SV679: $i,SV175: $i] :
( ( SV175
= ( c_List_Oappend @ SV175 @ ( c_List_Olist_ONil @ SV679 ) @ SV679 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(2424,plain,
! [SV680: $i,SV176: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV176 ) @ SV680 @ SV176 )
= SV680 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2425,plain,
! [SV681: $i,SV177: $i] :
( ( SV177
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV681 ) @ SV177 @ SV681 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2426,plain,
! [SV682: $i,SV178: $i] :
( ( ! [SY3400: $i,SY3401: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV178 ) @ SV682 ) @ SY3400 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV178 ) @ SY3401 ) @ SY3400 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV682 ) @ SY3401 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(2427,plain,
! [SV683: $i,SV179: $i] :
( ( ! [SY3402: $i,SY3403: $i,SY3404: $i] :
( ( c_List_Omap @ SV179 @ ( c_List_Oreplicate @ SV683 @ SY3402 @ SY3403 ) @ SY3403 @ SY3404 )
= ( c_List_Oreplicate @ SV683 @ ( hAPP @ SV179 @ SY3402 ) @ SY3404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2428,plain,
! [SV684: $i,SV180: $i] :
( ( ! [SY3405: $i] :
( ( c_HOL_Oord__class_Oless @ SV180 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV684 ) @ SY3405 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV180 @ SV684 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(2429,plain,
! [SV685: $i,SV181: $i] :
( ( ! [SY3406: $i] :
( ( c_HOL_Oord__class_Oless @ SV181 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV685 ) @ SY3406 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV181 @ SY3406 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(2430,plain,
! [SV686: $i,SV182: $i] :
( ( ! [SY3407: $i] :
( ( c_HOL_Oord__class_Oless @ SV182 @ SV686 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV182 ) @ SY3407 ) @ SV686 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(2431,plain,
! [SV687: $i,SV183: $i] :
( ( ! [SY3408: $i] :
( ( c_HOL_Oord__class_Oless @ SV183 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV687 ) @ SY3408 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV183 @ SV687 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1912]) ).
thf(2432,plain,
! [SV688: $i,SV184: $i] :
( ( ! [SY3409: $i] :
( ( c_HOL_Oord__class_Oless @ SV184 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV688 ) @ SY3409 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV184 @ SY3409 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2433,plain,
! [SV689: $i,SV185: $i] :
( ( ! [SY3410: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV185 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV185 ) @ SV689 ) @ SY3410 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV185 ) @ SY3410 ) @ SV689 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(2434,plain,
! [SV690: $i,SV186: $i] :
( ( ! [SY3411: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV186 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV186 ) @ SV690 ) @ SY3411 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV186 ) @ SY3411 ) @ SV690 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2435,plain,
! [SV691: $i,SV187: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV187 ) @ SV691 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV691 ) @ SV187 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2436,plain,
! [SV692: $i,SV188: $i] :
( ( ! [SY3412: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV188 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV188 ) @ SV692 ) @ SY3412 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV188 ) @ SY3412 ) @ SV692 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2437,plain,
! [SV693: $i,SV189: $i] :
( ( ! [SY3413: $i,SY3414: $i,SY3415: $i,SY3416: $i] :
( ( c_List_Ofoldr @ SV189 @ ( c_List_Oappend @ SV693 @ SY3413 @ SY3414 ) @ SY3415 @ SY3414 @ SY3416 )
= ( c_List_Ofoldr @ SV189 @ SV693 @ ( c_List_Ofoldr @ SV189 @ SY3413 @ SY3415 @ SY3414 @ SY3416 ) @ SY3414 @ SY3416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2438,plain,
! [SV694: $i,SV190: $i] :
( ( ! [SY3417: $i,SY3418: $i,SY3419: $i,SY3420: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV190 @ SV694 ) @ SY3417 ) )
| ( SV694 = SY3417 )
| ~ ( c_ListOrder_Ostep1 @ SV190 @ ( c_List_Oappend @ SY3418 @ ( c_List_Olist_OCons @ SV694 @ ( c_List_Olist_ONil @ SY3419 ) @ SY3419 ) @ SY3419 ) @ ( c_List_Oappend @ SY3420 @ ( c_List_Olist_OCons @ SY3417 @ ( c_List_Olist_ONil @ SY3419 ) @ SY3419 ) @ SY3419 ) @ SY3419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2439,plain,
! [SV695: $i,SV191: $i] :
( ( ! [SY3421: $i,SY3422: $i,SY3423: $i,SY3424: $i,SY3425: $i,SY3426: $i,SY3427: $i] :
( ( ( hAPP @ ( hAPP @ SV191 @ ( hAPP @ ( hAPP @ SV695 @ SY3421 ) @ SY3422 ) ) @ ( hAPP @ ( hAPP @ SV695 @ SY3421 ) @ SY3423 ) )
= ( hAPP @ ( hAPP @ SV695 @ SY3421 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3422 ) @ SY3423 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3424 @ SV191 @ SV695 @ SY3425 @ SY3426 @ SY3427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(2440,plain,
! [SV696: $i,SV192: $i] :
( ( ! [SY3428: $i,SY3429: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV192 ) @ SV696 ) @ SY3428 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY3429 ) @ SV696 ) @ SY3428 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV192 ) @ SY3429 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2441,plain,
! [SV697: $i,SV193: $i] :
( ( ! [SY3430: $i,SY3431: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV193 ) @ SV697 ) @ SY3430 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV193 ) @ SY3431 ) @ SY3430 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV697 ) @ SY3431 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2442,plain,
! [SV698: $i,SV194: $i] :
( ( ! [SY3432: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV194 )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV194 ) @ SV698 @ SY3432 @ SV194 @ SV194 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV194 ) @ SY3432 @ SV698 @ SV194 @ SV194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2443,plain,
! [SV699: $i,SV195: $i] :
( ( ! [SY3433: $i,SY3434: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV195 @ SV699 ) @ SY3433 ) @ SY3434 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV195 @ SY3433 ) @ SY3434 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2444,plain,
! [SV700: $i,SV196: $i] :
( ( ! [SY3435: $i] :
~ ( c_ListOrder_Ostep1 @ SV196 @ ( c_List_Olist_ONil @ SV700 ) @ SY3435 @ SV700 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1925]) ).
thf(2445,plain,
! [SV701: $i,SV197: $i] :
( ( ! [SY3436: $i] :
~ ( c_ListOrder_Ostep1 @ SV197 @ SV701 @ ( c_List_Olist_ONil @ SY3436 ) @ SY3436 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1926]) ).
thf(2446,plain,
! [SV702: $i,SV198: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV198 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ SV702 ) @ SV702 ) @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
| ~ ( c_HOL_Oord__class_Oless @ SV702 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2447,plain,
! [SV703: $i,SV199: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV199 )
| ( c_HOL_Oord__class_Oless @ SV703 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV199 ) @ SV703 ) @ SV703 ) @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2448,plain,
! [SV704: $i,SV200: $i] :
( ( ! [SY3437: $i,SY3438: $i] :
( ( c_List_Olist_OCons @ SV200 @ ( c_List_Oappend @ SV704 @ SY3437 @ SY3438 ) @ SY3438 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV200 @ SV704 @ SY3438 ) @ SY3437 @ SY3438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(2449,plain,
! [SV705: $i,SV201: $i] :
( ( ! [SY3439: $i,SY3440: $i] :
( ( c_List_Olist_OCons @ SV201 @ ( c_List_Oappend @ SV705 @ SY3439 @ SY3440 ) @ SY3440 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV201 @ SV705 @ SY3440 ) @ SY3439 @ SY3440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2450,plain,
! [SV706: $i,SV202: $i] :
( ( ! [SY3441: $i,SY3442: $i,SY3443: $i,SY3444: $i,SY3445: $i,SY3446: $i,SY3447: $i] :
( ( ( hAPP @ ( hAPP @ SV202 @ ( hAPP @ ( hAPP @ SV706 @ SY3441 ) @ SY3442 ) ) @ SY3443 )
= ( hAPP @ ( hAPP @ SV706 @ ( hAPP @ ( hAPP @ SV202 @ SY3441 ) @ SY3443 ) ) @ ( hAPP @ ( hAPP @ SV202 @ SY3442 ) @ SY3443 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3444 @ SV706 @ SV202 @ SY3445 @ SY3446 @ SY3447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2451,plain,
! [SV707: $i,SV203: $i] :
( ( ! [SY3448: $i,SY3449: $i,SY3450: $i,SY3451: $i,SY3452: $i,SY3453: $i,SY3454: $i] :
( ( ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ ( hAPP @ ( hAPP @ SY3448 @ SY3449 ) @ SY3450 ) )
= ( hAPP @ ( hAPP @ SY3448 @ ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ SY3449 ) ) @ ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ SY3450 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3448 @ SV203 @ SY3451 @ SY3452 @ SY3453 @ SY3454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2452,plain,
! [SV708: $i,SV204: $i] :
( ( ! [SY3455: $i,SY3456: $i,SY3457: $i,SY3458: $i,SY3459: $i,SY3460: $i] :
( ( ( hAPP @ ( hAPP @ SV204 @ SV708 ) @ SY3455 )
= ( hAPP @ ( hAPP @ SV204 @ SY3455 ) @ SV708 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3456 @ SV204 @ SY3457 @ SY3458 @ SY3459 @ SY3460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2453,plain,
! [SV709: $i,SV205: $i] :
( ( ! [SY3461: $i,SY3462: $i,SY3463: $i,SY3464: $i,SY3465: $i,SY3466: $i,SY3467: $i] :
( ( ( hAPP @ ( hAPP @ SV205 @ SV709 ) @ ( hAPP @ ( hAPP @ SV205 @ SY3461 ) @ SY3462 ) )
= ( hAPP @ ( hAPP @ SV205 @ ( hAPP @ ( hAPP @ SV205 @ SV709 ) @ SY3461 ) ) @ SY3462 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3463 @ SV205 @ SY3464 @ SY3465 @ SY3466 @ SY3467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2454,plain,
! [SV710: $i,SV206: $i] :
( ( ! [SY3468: $i,SY3469: $i,SY3470: $i,SY3471: $i,SY3472: $i] :
( ( ( hAPP @ ( hAPP @ SV206 @ SV710 ) @ SY3468 )
= SY3468 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3469 @ SV206 @ SY3470 @ SY3471 @ SV710 @ SY3472 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2455,plain,
! [SV711: $i,SV207: $i] :
( ( ! [SY3473: $i,SY3474: $i,SY3475: $i,SY3476: $i,SY3477: $i] :
( ( ( hAPP @ ( hAPP @ SV207 @ SV711 ) @ SY3473 )
= SV711 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3474 @ SV207 @ SY3475 @ SV711 @ SY3476 @ SY3477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2456,plain,
! [SV712: $i,SV208: $i] :
( ( ! [SY3478: $i,SY3479: $i,SY3480: $i,SY3481: $i,SY3482: $i,SY3483: $i] :
( ( ( hAPP @ ( hAPP @ SV208 @ SV712 ) @ SY3478 )
= ( hAPP @ ( hAPP @ SV208 @ SY3478 ) @ SV712 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV208 @ SY3479 @ SY3480 @ SY3481 @ SY3482 @ SY3483 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2457,plain,
! [SV713: $i,SV209: $i] :
( ( ! [SY3484: $i,SY3485: $i,SY3486: $i,SY3487: $i,SY3488: $i,SY3489: $i,SY3490: $i] :
( ( ( hAPP @ ( hAPP @ SV209 @ SV713 ) @ ( hAPP @ ( hAPP @ SV209 @ SY3484 ) @ SY3485 ) )
= ( hAPP @ ( hAPP @ SV209 @ ( hAPP @ ( hAPP @ SV209 @ SV713 ) @ SY3484 ) ) @ SY3485 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV209 @ SY3486 @ SY3487 @ SY3488 @ SY3489 @ SY3490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2458,plain,
! [SV714: $i,SV210: $i] :
( ( ! [SY3491: $i,SY3492: $i,SY3493: $i,SY3494: $i,SY3495: $i] :
( ( ( hAPP @ ( hAPP @ SV210 @ SV714 ) @ SY3491 )
= SY3491 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV210 @ SY3492 @ SY3493 @ SV714 @ SY3494 @ SY3495 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2459,plain,
! [SV715: $i,SV211: $i] :
( ( ! [SY3496: $i,SY3497: $i,SY3498: $i,SY3499: $i,SY3500: $i,SY3501: $i,SY3502: $i] :
( ( ( hAPP @ ( hAPP @ SV211 @ SV715 ) @ ( hAPP @ ( hAPP @ SV211 @ SY3496 ) @ SY3497 ) )
= ( hAPP @ ( hAPP @ SV211 @ ( hAPP @ ( hAPP @ SV211 @ SV715 ) @ SY3496 ) ) @ SY3497 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV211 @ SY3498 @ SY3499 @ SY3500 @ SY3501 @ SY3502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2460,plain,
! [SV716: $i,SV212: $i] :
( ( ! [SY3503: $i,SY3504: $i,SY3505: $i,SY3506: $i,SY3507: $i,SY3508: $i] :
( ( ( hAPP @ ( hAPP @ SV212 @ SV716 ) @ SY3503 )
= ( hAPP @ ( hAPP @ SV212 @ SY3503 ) @ SV716 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV212 @ SY3504 @ SY3505 @ SY3506 @ SY3507 @ SY3508 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(2461,plain,
! [SV717: $i,SV213: $i] :
( ( ! [SY3509: $i,SY3510: $i,SY3511: $i,SY3512: $i,SY3513: $i,SY3514: $i,SY3515: $i] :
( ( ( hAPP @ ( hAPP @ SV213 @ ( hAPP @ ( hAPP @ SV213 @ SV717 ) @ SY3509 ) ) @ SY3510 )
= ( hAPP @ ( hAPP @ SV213 @ ( hAPP @ ( hAPP @ SV213 @ SV717 ) @ SY3510 ) ) @ SY3509 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV213 @ SY3511 @ SY3512 @ SY3513 @ SY3514 @ SY3515 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2462,plain,
! [SV718: $i,SV214: $i] :
( ( ! [SY3516: $i,SY3517: $i,SY3518: $i,SY3519: $i,SY3520: $i,SY3521: $i,SY3522: $i] :
( ( ( hAPP @ ( hAPP @ SV214 @ SV718 ) @ ( hAPP @ ( hAPP @ SV214 @ SY3516 ) @ SY3517 ) )
= ( hAPP @ ( hAPP @ SV214 @ SY3516 ) @ ( hAPP @ ( hAPP @ SV214 @ SV718 ) @ SY3517 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV214 @ SY3518 @ SY3519 @ SY3520 @ SY3521 @ SY3522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2463,plain,
! [SV719: $i,SV215: $i] :
( ( ! [SY3523: $i,SY3524: $i,SY3525: $i,SY3526: $i,SY3527: $i,SY3528: $i,SY3529: $i] :
( ( ( hAPP @ ( hAPP @ SV215 @ ( hAPP @ ( hAPP @ SV215 @ SV719 ) @ SY3523 ) ) @ SY3524 )
= ( hAPP @ ( hAPP @ SV215 @ SV719 ) @ ( hAPP @ ( hAPP @ SV215 @ SY3523 ) @ SY3524 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV215 @ SY3525 @ SY3526 @ SY3527 @ SY3528 @ SY3529 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2464,plain,
! [SV720: $i,SV216: $i] :
( ( ! [SY3530: $i,SY3531: $i,SY3532: $i,SY3533: $i,SY3534: $i,SY3535: $i,SY3536: $i,SY3537: $i] :
( ( ( hAPP @ ( hAPP @ SV216 @ ( hAPP @ ( hAPP @ SV216 @ SV720 ) @ SY3530 ) ) @ ( hAPP @ ( hAPP @ SV216 @ SY3531 ) @ SY3532 ) )
= ( hAPP @ ( hAPP @ SV216 @ ( hAPP @ ( hAPP @ SV216 @ SV720 ) @ SY3531 ) ) @ ( hAPP @ ( hAPP @ SV216 @ SY3530 ) @ SY3532 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV216 @ SY3533 @ SY3534 @ SY3535 @ SY3536 @ SY3537 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2465,plain,
! [SV721: $i,SV217: $i] :
( ( ! [SY3538: $i,SY3539: $i,SY3540: $i,SY3541: $i,SY3542: $i,SY3543: $i,SY3544: $i] :
( ( ( hAPP @ ( hAPP @ SV217 @ SV721 ) @ ( hAPP @ ( hAPP @ SV217 @ SY3538 ) @ SY3539 ) )
= ( hAPP @ ( hAPP @ SV217 @ SY3538 ) @ ( hAPP @ ( hAPP @ SV217 @ SV721 ) @ SY3539 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3540 @ SV217 @ SY3541 @ SY3542 @ SY3543 @ SY3544 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2466,plain,
! [SV722: $i,SV218: $i] :
( ( ! [SY3545: $i,SY3546: $i,SY3547: $i,SY3548: $i,SY3549: $i,SY3550: $i,SY3551: $i] :
( ( ( hAPP @ ( hAPP @ SV218 @ SV722 ) @ ( hAPP @ ( hAPP @ SV218 @ SY3545 ) @ SY3546 ) )
= ( hAPP @ ( hAPP @ SV218 @ ( hAPP @ ( hAPP @ SV218 @ SV722 ) @ SY3545 ) ) @ SY3546 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3547 @ SV218 @ SY3548 @ SY3549 @ SY3550 @ SY3551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2467,plain,
! [SV723: $i,SV219: $i] :
( ( ! [SY3552: $i,SY3553: $i,SY3554: $i,SY3555: $i,SY3556: $i,SY3557: $i,SY3558: $i] :
( ( ( hAPP @ ( hAPP @ SV219 @ ( hAPP @ ( hAPP @ SV219 @ SV723 ) @ SY3552 ) ) @ SY3553 )
= ( hAPP @ ( hAPP @ SV219 @ SV723 ) @ ( hAPP @ ( hAPP @ SV219 @ SY3552 ) @ SY3553 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3554 @ SV219 @ SY3555 @ SY3556 @ SY3557 @ SY3558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2468,plain,
! [SV724: $i,SV220: $i] :
( ( ! [SY3559: $i,SY3560: $i,SY3561: $i,SY3562: $i,SY3563: $i,SY3564: $i,SY3565: $i] :
( ( ( hAPP @ ( hAPP @ SV220 @ ( hAPP @ ( hAPP @ SV220 @ SV724 ) @ SY3559 ) ) @ SY3560 )
= ( hAPP @ ( hAPP @ SV220 @ ( hAPP @ ( hAPP @ SV220 @ SV724 ) @ SY3560 ) ) @ SY3559 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3561 @ SV220 @ SY3562 @ SY3563 @ SY3564 @ SY3565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2469,plain,
! [SV725: $i,SV221: $i] :
( ( ! [SY3566: $i,SY3567: $i,SY3568: $i,SY3569: $i,SY3570: $i,SY3571: $i,SY3572: $i,SY3573: $i] :
( ( ( hAPP @ ( hAPP @ SV221 @ ( hAPP @ ( hAPP @ SV221 @ SV725 ) @ SY3566 ) ) @ ( hAPP @ ( hAPP @ SV221 @ SY3567 ) @ SY3568 ) )
= ( hAPP @ ( hAPP @ SV221 @ SY3567 ) @ ( hAPP @ ( hAPP @ SV221 @ ( hAPP @ ( hAPP @ SV221 @ SV725 ) @ SY3566 ) ) @ SY3568 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3569 @ SV221 @ SY3570 @ SY3571 @ SY3572 @ SY3573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2470,plain,
! [SV726: $i,SV222: $i] :
( ( ! [SY3574: $i,SY3575: $i,SY3576: $i,SY3577: $i,SY3578: $i,SY3579: $i,SY3580: $i,SY3581: $i] :
( ( ( hAPP @ ( hAPP @ SV222 @ ( hAPP @ ( hAPP @ SV222 @ SV726 ) @ SY3574 ) ) @ ( hAPP @ ( hAPP @ SV222 @ SY3575 ) @ SY3576 ) )
= ( hAPP @ ( hAPP @ SV222 @ SV726 ) @ ( hAPP @ ( hAPP @ SV222 @ SY3574 ) @ ( hAPP @ ( hAPP @ SV222 @ SY3575 ) @ SY3576 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3577 @ SV222 @ SY3578 @ SY3579 @ SY3580 @ SY3581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2471,plain,
! [SV727: $i,SV223: $i] :
( ( ! [SY3582: $i,SY3583: $i,SY3584: $i,SY3585: $i,SY3586: $i,SY3587: $i,SY3588: $i,SY3589: $i] :
( ( ( hAPP @ ( hAPP @ SV223 @ ( hAPP @ ( hAPP @ SV223 @ SV727 ) @ SY3582 ) ) @ ( hAPP @ ( hAPP @ SV223 @ SY3583 ) @ SY3584 ) )
= ( hAPP @ ( hAPP @ SV223 @ ( hAPP @ ( hAPP @ SV223 @ SV727 ) @ SY3583 ) ) @ ( hAPP @ ( hAPP @ SV223 @ SY3582 ) @ SY3584 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3585 @ SV223 @ SY3586 @ SY3587 @ SY3588 @ SY3589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2472,plain,
! [SV728: $i,SV224: $i] :
( ( ! [SY3590: $i,SY3591: $i,SY3592: $i,SY3593: $i,SY3594: $i] :
( ( ( hAPP @ ( hAPP @ SV224 @ SV728 ) @ SY3590 )
= SV728 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3591 @ SV224 @ SY3592 @ SY3593 @ SY3590 @ SY3594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(2473,plain,
! [SV729: $i,SV225: $i] :
( ( ! [SY3595: $i,SY3596: $i,SY3597: $i,SY3598: $i,SY3599: $i] :
( ( ( hAPP @ ( hAPP @ SV225 @ SV729 ) @ SY3595 )
= SY3595 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3596 @ SV225 @ SY3597 @ SY3598 @ SV729 @ SY3599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2474,plain,
! [SV730: $i,SV226: $i] :
( ( ! [SY3600: $i,SY3601: $i,SY3602: $i,SY3603: $i,SY3604: $i] :
( ( ( hAPP @ ( hAPP @ SV226 @ SV730 ) @ SY3600 )
= SY3600 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3601 @ SV226 @ SY3602 @ SY3600 @ SY3603 @ SY3604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2475,plain,
! [SV731: $i,SV227: $i] :
( ( ! [SY3605: $i,SY3606: $i,SY3607: $i,SY3608: $i,SY3609: $i] :
( ( ( hAPP @ ( hAPP @ SV227 @ SV731 ) @ SY3605 )
= SV731 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3606 @ SV227 @ SY3607 @ SV731 @ SY3608 @ SY3609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2476,plain,
! [SV732: $i,SV228: $i] :
( ( ! [SY3610: $i,SY3611: $i,SY3612: $i,SY3613: $i,SY3614: $i,SY3615: $i,SY3616: $i] :
( ( ( hAPP @ ( hAPP @ SV228 @ ( hAPP @ ( hAPP @ SV732 @ SY3610 ) @ SY3611 ) ) @ SY3612 )
= ( hAPP @ ( hAPP @ SV732 @ ( hAPP @ ( hAPP @ SV228 @ SY3610 ) @ SY3612 ) ) @ ( hAPP @ ( hAPP @ SV228 @ SY3611 ) @ SY3612 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV732 @ SV228 @ SY3613 @ SY3614 @ SY3615 @ SY3616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2477,plain,
! [SV733: $i,SV229: $i] :
( ( ! [SY3617: $i,SY3618: $i,SY3619: $i,SY3620: $i,SY3621: $i,SY3622: $i] :
( ( ( hAPP @ ( hAPP @ SV229 @ SV733 ) @ SY3617 )
= ( hAPP @ ( hAPP @ SV229 @ SY3617 ) @ SV733 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3618 @ SV229 @ SY3619 @ SY3620 @ SY3621 @ SY3622 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2478,plain,
! [SV734: $i,SV230: $i] :
( ( ! [SY3623: $i,SY3624: $i,SY3625: $i,SY3626: $i,SY3627: $i] :
( ( ( hAPP @ ( hAPP @ SV230 @ SV734 ) @ SY3623 )
= SV734 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV230 @ SY3624 @ SY3625 @ SY3623 @ SY3626 @ SY3627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2479,plain,
! [SV735: $i,SV231: $i] :
( ( ! [SY3628: $i,SY3629: $i,SY3630: $i,SY3631: $i,SY3632: $i] :
( ( ( hAPP @ ( hAPP @ SV231 @ SV735 ) @ SY3628 )
= SY3628 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV231 @ SY3629 @ SY3630 @ SV735 @ SY3631 @ SY3632 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2480,plain,
! [SV736: $i,SV232: $i] :
( ( ! [SY3633: $i,SY3634: $i,SY3635: $i,SY3636: $i,SY3637: $i] :
( ( ( hAPP @ ( hAPP @ SV232 @ SV736 ) @ SV736 )
= ( hAPP @ ( hAPP @ SY3633 @ ( hAPP @ ( hAPP @ SV232 @ SY3634 ) @ SY3634 ) ) @ SV736 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV232 @ SY3633 @ SY3635 @ SY3636 @ SY3634 @ SY3637 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(2481,plain,
! [SV737: $i,SV233: $i] :
( ( ! [SY3638: $i,SY3639: $i,SY3640: $i,SY3641: $i,SY3642: $i,SY3643: $i] :
( ( ( hAPP @ ( hAPP @ SV233 @ SV737 ) @ ( hAPP @ ( hAPP @ SY3638 @ SY3639 ) @ SV737 ) )
= ( hAPP @ ( hAPP @ SY3638 @ ( hAPP @ ( hAPP @ SV233 @ SY3639 ) @ SY3640 ) ) @ SV737 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV233 @ SY3638 @ SY3641 @ SY3642 @ SY3640 @ SY3643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2482,plain,
! [SV738: $i,SV234: $i] :
( ( ! [SY3644: $i,SY3645: $i,SY3646: $i,SY3647: $i,SY3648: $i,SY3649: $i] :
( ( ( hAPP @ ( hAPP @ SV234 @ ( hAPP @ ( hAPP @ SV738 @ SY3644 ) @ SY3645 ) ) @ SY3645 )
= ( hAPP @ ( hAPP @ SV738 @ ( hAPP @ ( hAPP @ SV234 @ SY3644 ) @ SY3646 ) ) @ SY3645 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV234 @ SV738 @ SY3647 @ SY3648 @ SY3646 @ SY3649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2483,plain,
! [SV739: $i,SV235: $i] :
( ( ! [SY3650: $i,SY3651: $i,SY3652: $i,SY3653: $i,SY3654: $i,SY3655: $i,SY3656: $i] :
( ( ( hAPP @ ( hAPP @ SV235 @ ( hAPP @ ( hAPP @ SV739 @ SY3650 ) @ SY3651 ) ) @ ( hAPP @ ( hAPP @ SV739 @ SY3652 ) @ SY3651 ) )
= ( hAPP @ ( hAPP @ SV739 @ ( hAPP @ ( hAPP @ SV235 @ SY3650 ) @ SY3652 ) ) @ SY3651 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV235 @ SV739 @ SY3653 @ SY3654 @ SY3655 @ SY3656 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2484,plain,
! [SV740: $i,SV236: $i] :
( ( ! [SY3657: $i,SY3658: $i,SY3659: $i,SY3660: $i] :
( ( SV236 = SV740 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SY3657 @ SV740 ) @ SV236 ) )
| ~ ( c_ListOrder_Ostep1 @ SY3657 @ ( c_List_Olist_OCons @ SV740 @ SY3658 @ SY3659 ) @ ( c_List_Olist_OCons @ SV236 @ SY3660 @ SY3659 ) @ SY3659 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2485,plain,
! [SV741: $i,SV237: $i] :
( ( ! [SY3661: $i,SY3662: $i,SY3663: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV237 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SV741 ) @ SY3661 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SY3662 ) @ SY3663 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SV741 ) @ SY3662 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SY3661 ) @ SY3663 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(2486,plain,
! [SV742: $i,SV238: $i] :
( ( ! [SY3664: $i,SY3665: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV238 ) @ SV742 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3664 ) @ SY3665 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV742 ) @ SY3665 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV238 ) @ SY3664 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2487,plain,
! [SV743: $i,SV239: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV239 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV743 @ SV239 ) @ ( c_HOL_Ozero__class_Ozero @ SV239 ) @ SV239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2488,plain,
! [SV744: $i,SV240: $i] :
( ( ! [SY3666: $i] :
( ~ ( class_Orderings_Olinorder @ SV240 )
| ( ( c_Orderings_Oord__class_Omax @ SV744 @ SY3666 @ SV240 )
= ( c_Orderings_Oord__class_Omax @ SY3666 @ SV744 @ SV240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1969]) ).
thf(2489,plain,
! [SV745: $i,SV241: $i] :
( ( ! [SY3667: $i] :
( ( ( c_Lambda_Oliftn @ SV241 @ ( c_Lambda_OdB_OVar @ SV745 ) @ SY3667 )
= ( c_Lambda_OdB_OVar @ SV745 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV745 @ SY3667 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2490,plain,
! [SV746: $i,SV242: $i] :
( ( ! [SY3668: $i,SY3669: $i] :
( ( c_Type_Otyping @ SV242 @ SV746 @ SY3668 )
| ~ ( c_Type_Otyping @ SV242 @ SY3669 @ SY3668 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY3669 ) @ SV746 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2491,plain,
! [SV747: $i,SV243: $i] :
( ( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV243 @ SV747 )
= ( c_List_Olist_ONil @ SV747 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2492,plain,
! [SV748: $i,SV244: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV244 ) ) @ SV748 )
= ( c_Lambda_OdB_OVar @ SV244 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV244 @ SV748 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2493,plain,
! [SV749: $i,SV245: $i] :
( ( ! [SY3670: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV245 ) @ SV749 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY3670 ) @ SV749 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV245 ) @ SY3670 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2494,plain,
! [SV246: $i] :
( ( ( SV246
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV246 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV246 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV246 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV246 ) ) )
| ( SV246
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV246 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV246 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV246 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1975]) ).
thf(2495,plain,
! [SV750: $i,SV247: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV247 @ SV247 @ tc_nat )
| ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV247 ) @ SV750 @ SV247 )
= ( c_Lambda_Oliftn @ SV247 @ SV750 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2496,plain,
! [SV751: $i,SV248: $i] :
( ( ! [SY3671: $i] :
( ( c_List_Olist_OCons @ SV248 @ SV751 @ SY3671 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SY3671 ) @ ( c_List_Olist_OCons @ SV248 @ SV751 @ SY3671 ) @ SY3671 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2497,plain,
! [SV752: $i,SV249: $i] :
( ( ! [SY3672: $i,SY3673: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV249 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV249 ) @ ( c_Orderings_Oord__class_Omax @ SV752 @ SY3672 @ SV249 ) ) @ SY3673 )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV249 ) @ SV752 ) @ SY3673 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV249 ) @ SY3672 ) @ SY3673 ) @ SV249 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2498,plain,
! [SV753: $i,SV250: $i] :
( ( ! [SY3674: $i] :
( ( c_List_Olist_ONil @ SV250 )
= ( c_List_Omap @ SV753 @ ( c_List_Olist_ONil @ SY3674 ) @ SY3674 @ SV250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2499,plain,
! [SV754: $i,SV251: $i] :
( ( ! [SY3675: $i,SY3676: $i,SY3677: $i,SY3678: $i] :
( ( SV251 = SV754 )
| ( c_ListOrder_Ostep1 @ SY3675 @ SV251 @ SV754 @ SY3676 )
| ~ ( c_ListOrder_Ostep1 @ SY3675 @ ( c_List_Oappend @ SV251 @ ( c_List_Olist_OCons @ SY3677 @ ( c_List_Olist_ONil @ SY3676 ) @ SY3676 ) @ SY3676 ) @ ( c_List_Oappend @ SV754 @ ( c_List_Olist_OCons @ SY3678 @ ( c_List_Olist_ONil @ SY3676 ) @ SY3676 ) @ SY3676 ) @ SY3676 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2500,plain,
! [SV755: $i,SV252: $i] :
( ( ! [SY3679: $i,SY3680: $i] :
( ~ ( class_Orderings_Olinorder @ SV252 )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ SV755 @ SY3679 @ SV252 ) @ SY3680 @ SV252 )
= ( c_Orderings_Oord__class_Omax @ SV755 @ ( c_Orderings_Oord__class_Omax @ SY3679 @ SY3680 @ SV252 ) @ SV252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2501,plain,
! [SV756: $i,SV253: $i] :
( ( ! [SY3681: $i,SY3682: $i] :
( ~ ( class_Orderings_Olinorder @ SV253 )
| ( ( c_Orderings_Oord__class_Omax @ SV756 @ ( c_Orderings_Oord__class_Omax @ SY3681 @ SY3682 @ SV253 ) @ SV253 )
= ( c_Orderings_Oord__class_Omax @ SY3681 @ ( c_Orderings_Oord__class_Omax @ SV756 @ SY3682 @ SV253 ) @ SV253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2502,plain,
! [SV757: $i,SV255: $i] :
( ( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ SV255 @ SV757 ) @ SV757 )
= ( c_Transitive__Closure_Ortranclp @ SV255 @ SV757 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1984]) ).
thf(2503,plain,
! [SV758: $i,SV256: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV256 ) ) @ ( c_Lambda_OdB_OAbs @ SV758 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV256 ) @ SV758 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(2504,plain,
! [SV759: $i,SV257: $i] :
( ( ! [SY3683: $i] :
( ~ ( class_Orderings_Olinorder @ SV257 )
| ( ( c_Orderings_Oord__class_Omax @ SV759 @ ( c_Orderings_Oord__class_Omax @ SV759 @ SY3683 @ SV257 ) @ SV257 )
= ( c_Orderings_Oord__class_Omax @ SV759 @ SY3683 @ SV257 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2505,plain,
! [SV760: $i,SV258: $i] :
( ( ! [SY3684: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV258 @ SV760 @ SY3684 ) @ ( c_List_Olist_OCons @ SV760 @ ( c_List_Olist_ONil @ SY3684 ) @ SY3684 ) @ SY3684 )
= ( c_List_Olist_OCons @ SV760 @ ( c_List_Oreplicate @ SV258 @ SV760 @ SY3684 ) @ SY3684 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2506,plain,
! [SV761: $i,SV259: $i] :
( ( ! [SY3685: $i,SY3686: $i] :
( ( ( hAPP @ ( hAPP @ SV259 @ SV761 ) @ SY3685 )
= SV761 )
| ~ ( c_OrderedGroup_Omonoid__add @ SY3685 @ SV259 @ SY3686 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1988]) ).
thf(2507,plain,
! [SV762: $i,SV260: $i] :
( ( ! [SY3687: $i,SY3688: $i] :
( ( ( hAPP @ ( hAPP @ SV260 @ SV762 ) @ SY3687 )
= SY3687 )
| ~ ( c_OrderedGroup_Omonoid__add @ SV762 @ SV260 @ SY3688 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2508,plain,
! [SV763: $i,SV261: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV261 ) @ SV763 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV763 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1990]) ).
thf(2509,plain,
! [SV764: $i,SV262: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV262 ) @ SV764 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV262 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2510,plain,
! [SV765: $i,SV263: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV263 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV765 @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV263 ) @ SV765 ) @ SV765 ) @ SV263 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2511,plain,
! [SV766: $i,SV264: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV264 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV264 ) @ SV766 ) @ SV766 ) @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SV766 @ SV264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2512,plain,
! [SV265: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV265 ) ) )
= $true )
| ( ( ( SV265
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV265 ) ) )
| ( SV265
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV265 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV265 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV265 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1994]) ).
thf(2513,plain,
! [SV266: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV266 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV266 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV266 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV266 ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV266 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV266 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1995]) ).
thf(2514,plain,
! [SV267: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV267 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV267 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV267 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ( SV267
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV267 ) ) )
| ( SV267
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV267 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV267 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV267 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1996]) ).
thf(2515,plain,
! [SV268: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV268 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV268 ) @ ( c_HOL_Ozero__class_Ozero @ SV268 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV268 ) )
= ( c_HOL_Ozero__class_Ozero @ SV268 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1997]) ).
thf(2516,plain,
! [SV767: $i,SV269: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV269 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ ( c_HOL_Ozero__class_Ozero @ SV269 ) ) @ SV767 )
= SV767 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2517,plain,
! [SV768: $i,SV270: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV270 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV270 ) @ ( c_HOL_Ozero__class_Ozero @ SV270 ) ) @ SV768 )
= SV768 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2518,plain,
! [SV769: $i,SV271: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV271 )
| ~ ( class_Int_Onumber__ring @ SV271 )
| ( SV769
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ SV769 ) @ ( c_HOL_Ozero__class_Ozero @ SV271 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2519,plain,
! [SV770: $i,SV272: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV272 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV770 ) @ ( c_HOL_Ozero__class_Ozero @ SV272 ) )
= SV770 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(2520,plain,
! [SV771: $i,SV273: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV273 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ ( c_HOL_Ozero__class_Ozero @ SV273 ) ) @ SV771 )
= SV771 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2521,plain,
! [SV772: $i,SV274: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV274 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ SV772 ) @ ( c_HOL_Ozero__class_Ozero @ SV274 ) )
= SV772 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2522,plain,
! [SV773: $i,SV275: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV275 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ SV773 ) @ ( c_HOL_Ozero__class_Ozero @ SV275 ) )
= SV773 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2523,plain,
! [SV774: $i,SV276: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV276 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ ( c_HOL_Ozero__class_Ozero @ SV276 ) ) @ SV774 )
= SV774 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2524,plain,
! [SV775: $i,SV277: $i] :
( ( ( c_Lambda_Oliftn @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV277 @ SV775 )
= SV277 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2525,plain,
! [SV278: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV278 @ tc_nat )
= $true )
| ( ( SV278
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2008]) ).
thf(2526,plain,
! [SV279: $i] :
( ( c_HOL_Oord__class_Oless @ SV279 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2009]) ).
thf(2527,plain,
! [SV280: $i] :
( ( c_HOL_Oord__class_Oless @ SV280 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2010]) ).
thf(2528,plain,
! [SV776: $i,SV281: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV281 )
| ( c_HOL_Oord__class_Oless @ SV776 @ ( c_HOL_Ozero__class_Ozero @ SV281 ) @ SV281 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV281 ) @ SV776 ) @ SV776 ) @ ( c_HOL_Ozero__class_Ozero @ SV281 ) @ SV281 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2011]) ).
thf(2529,plain,
! [SV777: $i,SV282: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV282 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV282 ) @ SV777 ) @ SV777 ) @ ( c_HOL_Ozero__class_Ozero @ SV282 ) @ SV282 )
| ~ ( c_HOL_Oord__class_Oless @ SV777 @ ( c_HOL_Ozero__class_Ozero @ SV282 ) @ SV282 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2530,plain,
! [SV778: $i,SV283: $i] :
( ( ! [SY3689: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV283 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV283 ) @ ( c_Power_Opower__class_Opower @ SV778 @ SY3689 @ SV283 ) @ SV283 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV283 ) @ SV778 @ SV283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2531,plain,
! [SV779: $i,SV284: $i] :
( ( ! [SY3690: $i,SY3691: $i] :
( ~ ( class_Orderings_Olinorder @ SV284 )
| ( c_HOL_Oord__class_Oless @ SV779 @ SY3690 @ SV284 )
| ( c_HOL_Oord__class_Oless @ SV779 @ SY3691 @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ SV779 @ ( c_Orderings_Oord__class_Omax @ SY3691 @ SY3690 @ SV284 ) @ SV284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2532,plain,
! [SV780: $i,SV285: $i] :
( ( ! [SY3692: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV285 ) @ SV780 @ SY3692 )
= ( c_Lambda_OdB_OVar @ SV285 ) )
| ( SV285 = SY3692 )
| ( c_HOL_Oord__class_Oless @ SY3692 @ SV285 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2015]) ).
thf(2533,plain,
! [SV287: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV287 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV287 ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV287 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV287 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2017]) ).
thf(2534,plain,
! [SV781: $i,SV288: $i] :
( ( ( c_List_Olist_ONil @ SV288 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV781 @ SV288 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2018]) ).
thf(2535,plain,
! [SV289: $i] :
( ( c_HOL_Oord__class_Oless @ SV289 @ SV289 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2019]) ).
thf(2536,plain,
! [SV290: $i] :
( ( c_HOL_Oord__class_Oless @ SV290 @ SV290 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2020]) ).
thf(2537,plain,
! [SV782: $i,SV291: $i] :
( ( ~ ( class_Orderings_Oorder @ SV291 )
| ~ ( c_HOL_Oord__class_Oless @ SV782 @ SV782 @ SV291 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2021]) ).
thf(2538,plain,
! [SV783: $i,SV292: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV292 )
| ~ ( c_HOL_Oord__class_Oless @ SV783 @ SV783 @ SV292 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2022]) ).
thf(2539,plain,
! [SV784: $i,SV293: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV293 )
| ~ ( c_HOL_Oord__class_Oless @ SV784 @ SV784 @ SV293 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2540,plain,
! [SV785: $i,SV294: $i] :
( ( ! [SY3693: $i] :
( ( ( c_Lambda_Oliftn @ SV294 @ ( c_Lambda_OdB_OVar @ SV785 ) @ SY3693 )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV785 ) @ SV294 ) ) )
| ( c_HOL_Oord__class_Oless @ SV785 @ SY3693 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2541,plain,
! [SV786: $i,SV295: $i] :
( ( ! [SY3694: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV295 ) @ SV786 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY3694 ) @ SV786 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV295 ) @ SY3694 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2542,plain,
! [SV787: $i,SV296: $i] :
( ( ! [SY3695: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV296 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV296 ) @ SV787 ) @ SY3695 ) @ SV296 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SY3695 @ SV296 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SV787 @ SV296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2543,plain,
! [SV788: $i,SV297: $i] :
( ( ! [SY3696: $i,SY3697: $i,SY3698: $i,SY3699: $i] :
( ( c_ListOrder_Ostep1 @ SV297 @ SV788 @ SY3696 @ SY3697 )
| ( SY3696 = SV788 )
| ~ ( c_ListOrder_Ostep1 @ SV297 @ ( c_List_Olist_OCons @ SY3698 @ SV788 @ SY3697 ) @ ( c_List_Olist_OCons @ SY3699 @ SY3696 @ SY3697 ) @ SY3697 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2544,plain,
! [SV789: $i,SV298: $i] :
( ( ! [SY3700: $i,SY3701: $i,SY3702: $i] :
( ( ( hAPP @ ( hAPP @ SV298 @ ( hAPP @ ( hAPP @ SV298 @ SV789 ) @ SY3700 ) ) @ SY3701 )
= ( hAPP @ ( hAPP @ SV298 @ SV789 ) @ ( hAPP @ ( hAPP @ SV298 @ SY3700 ) @ SY3701 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV298 @ SY3702 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2545,plain,
! [SV790: $i,SV299: $i] :
( ( ! [SY3703: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV299 )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SV790 @ SY3703 @ SV299 ) @ SV299 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV299 ) @ SV790 ) @ ( c_List_Olistsum @ SY3703 @ SV299 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2546,plain,
! [SV791: $i,SV300: $i] :
( ( ! [SY3704: $i,SY3705: $i,SY3706: $i] :
( ( c_List_Omap @ SV300 @ ( c_List_Oappend @ SV791 @ SY3704 @ SY3705 ) @ SY3705 @ SY3706 )
= ( c_List_Oappend @ ( c_List_Omap @ SV300 @ SV791 @ SY3705 @ SY3706 ) @ ( c_List_Omap @ SV300 @ SY3704 @ SY3705 @ SY3706 ) @ SY3706 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2030]) ).
thf(2547,plain,
! [SV301: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV301 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV301 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV301 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ( SV301
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV301 ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV301 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV301 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2031]) ).
thf(2548,plain,
! [SV792: $i,SV302: $i] :
( ( ! [SY3707: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ SV302 )
| ( c_HOL_Oord__class_Oless @ SV792 @ SY3707 @ SV302 )
| ( c_HOL_Oord__class_Oless @ SY3707 @ SV792 @ SV302 )
| ( SY3707 = SV792 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2549,plain,
! [SV793: $i,SV303: $i] :
( ( ! [SY3708: $i] :
( ~ ( class_Orderings_Olinorder @ SV303 )
| ( SV793 = SY3708 )
| ( c_HOL_Oord__class_Oless @ SY3708 @ SV793 @ SV303 )
| ( c_HOL_Oord__class_Oless @ SV793 @ SY3708 @ SV303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2550,plain,
! [SV794: $i,SV304: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV304 @ SV794 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV794 @ SV304 @ tc_nat )
| ( SV794 = SV304 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2034]) ).
thf(2551,plain,
! [SV795: $i,SV305: $i] :
( ( ! [SY3709: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV305 @ SV795 ) @ SY3709 ) )
| ( c_HOL_Oord__class_Oless @ SV795 @ SY3709 @ tc_nat )
| ( SY3709 = SV795 )
| ( c_HOL_Oord__class_Oless @ SY3709 @ SV795 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2552,plain,
! [SV796: $i,SV306: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV306 @ SV796 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV796 @ SV306 @ tc_nat )
| ( SV796 = SV306 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(2553,plain,
! [SV797: $i,SV307: $i] :
( ( ! [SY3710: $i] :
( ~ ( class_Orderings_Olinorder @ SV307 )
| ( c_HOL_Oord__class_Oless @ SV797 @ SY3710 @ SV307 )
| ( c_HOL_Oord__class_Oless @ SY3710 @ SV797 @ SV307 )
| ( SY3710 = SV797 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2554,plain,
! [SV798: $i,SV308: $i] :
( ( ! [SY3711: $i,SY3712: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV308 @ SV798 @ SY3711 ) @ ( c_List_Oreplicate @ SY3712 @ SV798 @ SY3711 ) @ SY3711 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SY3712 @ SV798 @ SY3711 ) @ ( c_List_Oreplicate @ SV308 @ SV798 @ SY3711 ) @ SY3711 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2038]) ).
thf(2555,plain,
! [SV799: $i,SV309: $i] :
( ( ! [SY3713: $i] :
( ~ ( class_Orderings_Olinorder @ SV309 )
| ( c_HOL_Oord__class_Oless @ SV799 @ SY3713 @ SV309 )
| ( SY3713 = SV799 )
| ( c_HOL_Oord__class_Oless @ SY3713 @ SV799 @ SV309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2556,plain,
! [SV800: $i,SV310: $i] :
( ( ! [SY3714: $i] :
( ~ ( class_Orderings_Olinorder @ SV310 )
| ( SV800 = SY3714 )
| ( c_HOL_Oord__class_Oless @ SV800 @ SY3714 @ SV310 )
| ( c_HOL_Oord__class_Oless @ SY3714 @ SV800 @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2557,plain,
! [SV801: $i,SV311: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV311 )
| ( ( c_Orderings_Oord__class_Omax @ SV801 @ SV801 @ SV311 )
= SV801 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2558,plain,
! [SV802: $i,SV312: $i] :
( ( ! [SY3715: $i,SY3716: $i,SY3717: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV312 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV312 ) @ SV802 ) @ SY3715 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV312 ) @ SY3716 ) @ SY3717 ) @ SV312 )
| ~ ( c_HOL_Oord__class_Oless @ SY3715 @ SY3717 @ SV312 )
| ~ ( c_HOL_Oord__class_Oless @ SV802 @ SY3716 @ SV312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2559,plain,
! [SV803: $i,SV313: $i] :
( ( ! [SY3718: $i,SY3719: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV313 ) @ SV803 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3718 ) @ SY3719 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV803 @ SY3719 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV313 @ SY3718 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2560,plain,
! [SV804: $i,SV314: $i] :
( ( ! [SY3720: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV314 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV804 @ SV314 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3720 @ SV314 ) @ SV314 )
| ~ ( c_HOL_Oord__class_Oless @ SV804 @ SY3720 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2561,plain,
! [SV805: $i,SV315: $i] :
( ( ! [SY3721: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV315 )
| ( c_HOL_Oord__class_Oless @ SV805 @ SY3721 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV805 @ SV315 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3721 @ SV315 ) @ SV315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2562,plain,
! [SV806: $i,SV316: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV316 )
| ( ( c_List_Olistsum @ SV806 @ SV316 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV316 ) @ SV806 @ ( c_HOL_Ozero__class_Ozero @ SV316 ) @ SV316 @ SV316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2563,plain,
! [SV317: $i] :
( ( ( SV317
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV317 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV317 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV317 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( SV317
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV317 ) ) )
| ( SV317
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV317 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV317 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV317 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2047]) ).
thf(2564,plain,
! [SV807: $i,SV318: $i] :
( ( ! [SY3722: $i,SY3723: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV318 ) @ SV807 ) @ SY3722 @ SY3723 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SV318 @ SY3722 @ SY3723 ) @ ( c_List_Oreplicate @ SV807 @ SY3722 @ SY3723 ) @ SY3723 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2565,plain,
! [SV808: $i,SV319: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV319 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV319 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV808 @ SV319 ) @ SV319 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV808 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2049]) ).
thf(2566,plain,
! [SV809: $i,SV320: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV320 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV809 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV320 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV809 @ SV320 ) @ SV320 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2567,plain,
! [SV810: $i,SV321: $i] :
( ( ! [SY3724: $i,SY3725: $i,SY3726: $i,SY3727: $i] :
( ( SV321 = SV810 )
| ( SY3724 = SY3725 )
| ~ ( c_ListOrder_Ostep1 @ SY3726 @ ( c_List_Oappend @ SV321 @ ( c_List_Olist_OCons @ SY3724 @ ( c_List_Olist_ONil @ SY3727 ) @ SY3727 ) @ SY3727 ) @ ( c_List_Oappend @ SV810 @ ( c_List_Olist_OCons @ SY3725 @ ( c_List_Olist_ONil @ SY3727 ) @ SY3727 ) @ SY3727 ) @ SY3727 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2051]) ).
thf(2568,plain,
! [SV811: $i,SV322: $i] :
( ( ! [SY3728: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV322 @ SV811 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY3728 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV322 ) @ SY3728 ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ SY3728 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV811 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2569,plain,
! [SV812: $i,SV323: $i] :
( ( ! [SY3729: $i,SY3730: $i] :
( ( c_List_Olistsp @ SV323 @ ( c_List_Oappend @ SV812 @ SY3729 @ SY3730 ) @ SY3730 )
| ~ ( c_List_Olistsp @ SV323 @ SY3729 @ SY3730 )
| ~ ( c_List_Olistsp @ SV323 @ SV812 @ SY3730 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2570,plain,
! [SV813: $i,SV324: $i] :
( ( ! [SY3731: $i,SY3732: $i,SY3733: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV324 @ SV813 @ SY3731 @ ( c_Lambda_OdB_OAbs @ SY3732 ) @ SY3733 )
= ( hAPP @ ( hAPP @ SY3731 @ SY3732 ) @ ( c_Lambda_OdB_OdB__rec @ SV324 @ SV813 @ SY3731 @ SY3732 @ SY3733 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2054]) ).
thf(2571,plain,
! [SV325: $i] :
( ( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV325 ) )
= $true )
| ( ( c_OrderedGroup_Osemigroup__add @ ( c_HOL_Oplus__class_Oplus @ SV325 ) @ SV325 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2055]) ).
thf(2572,plain,
! [SV814: $i,SV326: $i] :
( ( ! [SY3734: $i,SY3735: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV326 )
| ( c_HOL_Oord__class_Oless @ SV814 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV326 ) @ SY3734 ) @ SY3735 ) @ SV326 )
| ~ ( c_HOL_Oord__class_Oless @ SV814 @ SY3735 @ SV326 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SY3734 @ SV326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2056]) ).
thf(2573,plain,
! [SV815: $i,SV327: $i] :
( ( ! [SY3736: $i,SY3737: $i,SY3738: $i,SY3739: $i] :
( ( c_List_Ofoldr @ SV327 @ ( c_List_Olist_OCons @ SV815 @ SY3736 @ SY3737 ) @ SY3738 @ SY3737 @ SY3739 )
= ( hAPP @ ( hAPP @ SV327 @ SV815 ) @ ( c_List_Ofoldr @ SV327 @ SY3736 @ SY3738 @ SY3737 @ SY3739 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2057]) ).
thf(2574,plain,
! [SV816: $i,SV328: $i] :
( ( ! [SY3740: $i,SY3741: $i,SY3742: $i] :
( ~ ( hBOOL @ ( hAPP @ SV328 @ ( c_Lambda_OdB_OdB__case @ SV816 @ SY3740 @ SY3741 @ ( c_Lambda_OdB_OAbs @ SY3742 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV328 @ ( hAPP @ SY3741 @ SY3742 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2058]) ).
thf(2575,plain,
! [SV817: $i,SV329: $i] :
( ( ! [SY3743: $i,SY3744: $i,SY3745: $i] :
( ~ ( hBOOL @ ( hAPP @ SV329 @ ( c_Lambda_OdB_OdB__case @ SV817 @ SY3743 @ SY3744 @ ( c_Lambda_OdB_OAbs @ SY3745 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV329 @ ( hAPP @ SY3744 @ SY3745 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2576,plain,
! [SV818: $i,SV330: $i] :
( ( ! [SY3746: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ SV330 @ SV818 @ SY3746 ) @ SY3746 @ SV818 )
= SV330 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2577,plain,
! [SV819: $i,SV331: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV331 ) @ SV819 ) @ SV331 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2578,plain,
! [SV820: $i,SV332: $i] :
( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV332 ) @ SV820 ) @ SV820 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2062]) ).
thf(2579,plain,
! [SV821: $i,SV333: $i] :
( ( ! [SY3747: $i] :
( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV333 ) @ ( c_List_Olist_OCons @ SV821 @ SY3747 @ SV333 ) @ SV333 )
= ( c_List_Olist_OCons @ SV821 @ SY3747 @ SV333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2580,plain,
! [SV822: $i,SV334: $i] :
( ( ! [SY3748: $i,SY3749: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV334 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV334 ) @ SV822 ) @ SY3748 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV334 ) @ SY3749 ) @ SY3748 ) @ SV334 )
| ~ ( c_HOL_Oord__class_Oless @ SV822 @ SY3749 @ SV334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2064]) ).
thf(2581,plain,
! [SV823: $i,SV335: $i] :
( ( ! [SY3750: $i,SY3751: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV335 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV335 ) @ SV823 ) @ SY3750 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV335 ) @ SY3751 ) @ SY3750 ) @ SV335 )
| ~ ( c_HOL_Oord__class_Oless @ SV823 @ SY3751 @ SV335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2582,plain,
! [SV824: $i,SV336: $i] :
( ( ! [SY3752: $i,SY3753: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV336 )
| ( c_HOL_Oord__class_Oless @ SV824 @ SY3752 @ SV336 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV336 ) @ SV824 ) @ SY3753 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV336 ) @ SY3752 ) @ SY3753 ) @ SV336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2583,plain,
! [SV825: $i,SV337: $i] :
( ( ! [SY3754: $i,SY3755: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV337 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV337 ) @ SV825 ) @ SY3754 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV337 ) @ SV825 ) @ SY3755 ) @ SV337 )
| ~ ( c_HOL_Oord__class_Oless @ SY3754 @ SY3755 @ SV337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2584,plain,
! [SV826: $i,SV338: $i] :
( ( ! [SY3756: $i,SY3757: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV338 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV338 ) @ SV826 ) @ SY3756 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV338 ) @ SV826 ) @ SY3757 ) @ SV338 )
| ~ ( c_HOL_Oord__class_Oless @ SY3756 @ SY3757 @ SV338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2585,plain,
! [SV827: $i,SV339: $i] :
( ( ! [SY3758: $i,SY3759: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV339 )
| ( c_HOL_Oord__class_Oless @ SV827 @ SY3758 @ SV339 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SY3759 ) @ SV827 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SY3759 ) @ SY3758 ) @ SV339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2586,plain,
! [SV828: $i,SV340: $i] :
( ( ! [SY3760: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV340 ) @ SV828 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3760 ) @ SV828 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV340 @ SY3760 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(2587,plain,
! [SV829: $i,SV341: $i] :
( ( ! [SY3761: $i] :
( ( c_HOL_Oord__class_Oless @ SV341 @ SV829 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3761 ) @ SV341 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3761 ) @ SV829 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2071]) ).
thf(2588,plain,
! [SV830: $i,SV342: $i] :
( ( ! [SY3762: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV342 ) @ SV830 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV342 ) @ SY3762 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV830 @ SY3762 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2589,plain,
! [SV343: $i] :
( ( ( SV343
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV343 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV343 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV343 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV343 ) ) )
| ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV343 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV343 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2073]) ).
thf(2590,plain,
! [SV831: $i,SV344: $i] :
( ( ! [SY3763: $i,SY3764: $i] :
( ( c_Type_Otyping @ SV344 @ SV831 @ SY3763 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY3764 ) @ SV831 ) )
| ~ ( c_Type_Otyping @ SV344 @ SY3764 @ SY3763 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2591,plain,
! [SV832: $i,SV345: $i] :
( ( ! [SY3765: $i,SY3766: $i,SY3767: $i,SY3768: $i] :
( ( c_ListOrder_Ostep1 @ SV345 @ SV832 @ SY3765 @ SY3766 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV345 @ SY3767 ) @ SY3768 ) )
| ~ ( c_ListOrder_Ostep1 @ SV345 @ ( c_List_Olist_OCons @ SY3767 @ SV832 @ SY3766 ) @ ( c_List_Olist_OCons @ SY3768 @ SY3765 @ SY3766 ) @ SY3766 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2592,plain,
! [SV833: $i,SV346: $i] :
( ( ! [SY3769: $i,SY3770: $i,SY3771: $i] :
( ( c_ListOrder_Ostep1 @ SV346 @ ( c_List_Olist_OCons @ SV833 @ SY3769 @ SY3770 ) @ ( c_List_Olist_OCons @ SV833 @ SY3771 @ SY3770 ) @ SY3770 )
| ~ ( c_ListOrder_Ostep1 @ SV346 @ SY3769 @ SY3771 @ SY3770 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2076]) ).
thf(2593,plain,
! [SV834: $i,SV347: $i] :
( ( ! [SY3772: $i,SY3773: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV347 @ SV834 @ SY3772 ) @ ( c_List_Olist_OCons @ SV834 @ SY3773 @ SY3772 ) @ SY3772 )
= ( c_List_Olist_OCons @ SV834 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV347 @ SV834 @ SY3772 ) @ SY3773 @ SY3772 ) @ SY3772 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2594,plain,
! [SV835: $i,SV348: $i] :
( ( ! [SY3774: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ SV348 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV835 ) @ SY3774 ) @ SV348 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV348 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV835 @ SV348 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SY3774 @ SV348 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2595,plain,
! [SV836: $i,SV349: $i] :
( ( ! [SY3775: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV349 )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ SV836 @ SY3775 @ SV349 ) @ SV349 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV349 ) @ ( c_List_Olistsum @ SV836 @ SV349 ) ) @ ( c_List_Olistsum @ SY3775 @ SV349 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2079]) ).
thf(2596,plain,
! [SV351: $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 ) @ SV351 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV351 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2081]) ).
thf(2597,plain,
! [SV837: $i,SV352: $i] :
( ( ! [SY3776: $i,SY3777: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV352 @ SV837 @ SY3776 ) @ SY3777 @ SY3776 )
= ( c_List_Oappend @ SV352 @ ( c_List_Oappend @ SV837 @ SY3777 @ SY3776 ) @ SY3776 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2598,plain,
! [SV838: $i,SV353: $i] :
( ( ! [SY3778: $i,SY3779: $i] :
( ( c_List_Oappend @ SV353 @ ( c_List_Oappend @ SV838 @ SY3778 @ SY3779 ) @ SY3779 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV353 @ SV838 @ SY3779 ) @ SY3778 @ SY3779 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2599,plain,
! [SV839: $i,SV354: $i] :
( ( ! [SY3780: $i,SY3781: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV354 @ SV839 @ SY3780 ) @ SY3781 @ SY3780 )
= ( c_List_Oappend @ SV354 @ ( c_List_Oappend @ SV839 @ SY3781 @ SY3780 ) @ SY3780 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2600,plain,
! [SV840: $i,SV355: $i] :
( ( ! [SY3782: $i,SY3783: $i] :
( ( c_List_Oappend @ SV355 @ ( c_List_Oappend @ SV840 @ SY3782 @ SY3783 ) @ SY3783 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV355 @ SV840 @ SY3783 ) @ SY3782 @ SY3783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(2601,plain,
! [SV841: $i,SV356: $i] :
( ( ! [SY3784: $i] :
( ~ ( class_Orderings_Oorder @ SV356 )
| ~ ( c_HOL_Oord__class_Oless @ SV841 @ SY3784 @ SV356 )
| ~ ( c_HOL_Oord__class_Oless @ SY3784 @ SV841 @ SV356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2602,plain,
! [SV842: $i,SV357: $i] :
( ( ! [SY3785: $i,SY3786: $i,SY3787: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV357 @ SV842 ) @ SY3785 ) @ SY3786 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV357 @ SV842 ) @ SY3787 ) @ SY3786 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV357 @ SY3785 ) @ SY3787 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2603,plain,
! [SV843: $i,SV358: $i] :
( ( ! [SY3788: $i,SY3789: $i,SY3790: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV358 @ SV843 ) @ SY3788 ) @ SY3789 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SY3790 ) @ SY3789 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV358 @ SV843 ) @ SY3788 ) @ SY3790 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2604,plain,
! [SV844: $i,SV359: $i] :
( ( ! [SY3791: $i] :
( ~ ( class_Orderings_Olinorder @ SV359 )
| ~ ( c_HOL_Oord__class_Oless @ SV844 @ SY3791 @ SV359 )
| ~ ( c_HOL_Oord__class_Oless @ SY3791 @ SV844 @ SV359 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2605,plain,
! [SV845: $i,SV360: $i] :
( ( ! [SY3792: $i,SY3793: $i] :
( ( c_Wellfounded_Oaccp @ SV360 @ SV845 @ SY3792 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV360 @ SV845 ) @ SY3793 ) )
| ~ ( c_Wellfounded_Oaccp @ SV360 @ SY3793 @ SY3792 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(2606,plain,
! [SV846: $i,SV361: $i] :
( ( ! [SY3794: $i] :
( ~ ( class_Orderings_Opreorder @ SV361 )
| ~ ( c_HOL_Oord__class_Oless @ SV846 @ SY3794 @ SV361 )
| ~ ( c_HOL_Oord__class_Oless @ SY3794 @ SV846 @ SV361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2091]) ).
thf(2607,plain,
! [SV847: $i,SV362: $i] :
( ( ! [SY3795: $i,SY3796: $i] :
( ( c_Wellfounded_Oaccp @ SV362 @ SV847 @ SY3795 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV362 @ SV847 ) @ SY3796 ) )
| ~ ( c_Wellfounded_Oaccp @ SV362 @ SY3796 @ SY3795 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2092]) ).
thf(2608,plain,
! [SV848: $i,SV363: $i] :
( ( ! [SY3797: $i] :
( ~ ( class_Orderings_Opreorder @ SV363 )
| ~ ( c_HOL_Oord__class_Oless @ SV848 @ SY3797 @ SV363 )
| ~ ( c_HOL_Oord__class_Oless @ SY3797 @ SV848 @ SV363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2093]) ).
thf(2609,plain,
! [SV849: $i,SV365: $i] :
( ( ! [SY3798: $i] :
( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV365 @ SV849 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3798 @ SV849 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2095]) ).
thf(2610,plain,
! [SV850: $i,SV371: $i] :
( ( ! [SY3799: $i,SY3800: $i,SY3801: $i,SY3802: $i,SY3803: $i] :
( ( ( hAPP @ ( hAPP @ SV371 @ SV850 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SY3799 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY3800 @ SY3801 @ SV371 @ SY3802 @ SY3799 @ SY3803 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2611,plain,
! [SV851: $i,SV372: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV372 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV372 ) @ ( c_HOL_Ozero__class_Ozero @ SV372 ) @ SV851 @ SV372 @ SV372 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV372 ) @ SV851 @ ( c_HOL_Ozero__class_Ozero @ SV372 ) @ SV372 @ SV372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2102]) ).
thf(2612,plain,
! [SV852: $i,SV373: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV373 )
| ( ( c_List_Olistsum @ SV852 @ SV373 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV373 ) @ ( c_HOL_Ozero__class_Ozero @ SV373 ) @ SV852 @ SV373 @ SV373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2103]) ).
thf(2613,plain,
! [SV853: $i,SV374: $i] :
( ( ! [SY3804: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV374 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV374 ) @ SV853 @ SY3804 @ SV374 @ SV374 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV374 ) @ SV853 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV374 ) @ SY3804 @ ( c_HOL_Ozero__class_Ozero @ SV374 ) @ SV374 @ SV374 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2104]) ).
thf(2614,plain,
! [SV854: $i,SV375: $i] :
( ( ! [SY3805: $i,SY3806: $i,SY3807: $i,SY3808: $i] :
( ~ ( hBOOL @ ( hAPP @ SV375 @ ( c_Lambda_OdB_OdB__case @ SV854 @ SY3805 @ SY3806 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3807 ) @ SY3808 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV375 @ ( hAPP @ ( hAPP @ SY3805 @ SY3807 ) @ SY3808 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2105]) ).
thf(2615,plain,
! [SV855: $i,SV376: $i] :
( ( ! [SY3809: $i,SY3810: $i,SY3811: $i,SY3812: $i] :
( ~ ( hBOOL @ ( hAPP @ SV376 @ ( c_Lambda_OdB_OdB__case @ SV855 @ SY3809 @ SY3810 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3811 ) @ SY3812 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SY3809 @ SY3811 ) @ SY3812 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(2616,plain,
! [SV856: $i,SV377: $i] :
( ( ! [SY3813: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV377 ) @ SV856 ) ) @ SY3813 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV377 ) @ SY3813 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV856 ) @ SY3813 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2107]) ).
thf(2617,plain,
! [SV857: $i,SV378: $i] :
( ( ! [SY3814: $i,SY3815: $i,SY3816: $i,SY3817: $i] :
( ( c_Lambda_OdB_OdB__case @ SV378 @ SV857 @ SY3814 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3815 ) @ SY3816 ) @ SY3817 )
= ( hAPP @ ( hAPP @ SV857 @ SY3815 ) @ SY3816 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2108]) ).
thf(2618,plain,
! [SV858: $i,SV379: $i] :
( ( ! [SY3818: $i,SY3819: $i,SY3820: $i,SY3821: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV379 @ SV858 @ SY3818 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3819 ) @ SY3820 ) @ SY3821 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV858 @ SY3819 ) @ SY3820 ) @ ( c_Lambda_OdB_OdB__rec @ SV379 @ SV858 @ SY3818 @ SY3819 @ SY3821 ) ) @ ( c_Lambda_OdB_OdB__rec @ SV379 @ SV858 @ SY3818 @ SY3820 @ SY3821 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2109]) ).
thf(2619,plain,
! [SV859: $i,SV380: $i] :
( ( ! [SY3822: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV380 ) @ SV859 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV380 ) @ SY3822 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV859 ) @ SY3822 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2110]) ).
thf(2620,plain,
! [SV860: $i,SV381: $i] :
( ( ! [SY3823: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV381 ) @ SV860 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3823 ) @ SV860 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV381 ) @ SY3823 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2111]) ).
thf(2621,plain,
! [SV861: $i,SV382: $i] :
( ( ! [SY3824: $i,SY3825: $i] :
( ( c_Lambda_Oliftn @ SV382 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV861 ) @ SY3824 ) @ SY3825 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV382 @ SV861 @ SY3825 ) ) @ ( c_Lambda_Oliftn @ SV382 @ SY3824 @ SY3825 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2112]) ).
thf(2622,plain,
! [SV862: $i,SV383: $i] :
( ( ! [SY3826: $i,SY3827: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV383 ) @ SV862 ) @ SY3826 @ SY3827 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV383 @ SY3826 @ SY3827 ) ) @ ( c_Lambda_Osubstn @ SV862 @ SY3826 @ SY3827 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2623,plain,
! [SV863: $i,SV384: $i] :
( ( ! [SY3828: $i] :
( ( c_Lambda_Osubstn @ SV384 @ SV863 @ SY3828 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV384 ) @ ( c_Lambda_Oliftn @ SY3828 @ SV863 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ SY3828 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2114]) ).
thf(2624,plain,
! [SV864: $i,SV385: $i] :
( ( ! [SY3829: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV385 ) @ SV864 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY3829 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV864 @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV385 ) ) @ SV864 ) @ SY3829 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2115]) ).
thf(2625,plain,
! [SV865: $i,SV386: $i] :
( ( ! [SY3830: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV386 @ SV865 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3830 @ SV865 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV386 ) @ SY3830 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2116]) ).
thf(2626,plain,
! [SV866: $i,SV387: $i] :
( ( ! [SY3831: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV387 @ SV866 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV387 @ SY3831 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV866 @ SY3831 @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2627,plain,
! [SV867: $i,SV391: $i] :
( ( ! [SY3832: $i,SY3833: $i,SY3834: $i] :
( ( ( c_List_Ofoldl @ SV391 @ ( hAPP @ ( hAPP @ SV391 @ SV867 ) @ SY3832 ) @ SY3833 @ SY3834 @ SY3834 )
= ( hAPP @ ( hAPP @ SV391 @ SV867 ) @ ( c_List_Ofoldl @ SV391 @ SY3832 @ SY3833 @ SY3834 @ SY3834 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV391 @ SY3834 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2121]) ).
thf(2628,plain,
! [SV868: $i,SV392: $i] :
( ( ! [SY3835: $i,SY3836: $i] :
( ( c_List_Ofoldl @ SV392 @ SV868 @ ( c_List_Olist_ONil @ SY3835 ) @ SY3836 @ SY3835 )
= SV868 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2122]) ).
thf(2629,plain,
! [SV869: $i,SV393: $i] :
( ( ! [SY3837: $i,SY3838: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV393 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV393 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV393 ) @ SV869 ) @ SY3837 ) @ SY3838 @ SV393 @ SV393 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV393 ) @ SV869 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV393 ) @ SY3837 @ SY3838 @ SV393 @ SV393 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2123]) ).
thf(2630,plain,
! [SV870: $i,SV394: $i] :
( ( ! [SY3839: $i,SY3840: $i,SY3841: $i] :
( ( ( hAPP @ ( hAPP @ SV394 @ SV870 ) @ ( c_List_Ofoldl @ SV394 @ SY3839 @ SY3840 @ SY3841 @ SY3841 ) )
= ( c_List_Ofoldl @ SV394 @ SV870 @ SY3840 @ SY3841 @ SY3841 ) )
| ~ ( c_OrderedGroup_Omonoid__add @ SY3839 @ SV394 @ SY3841 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2124]) ).
thf(2631,plain,
! [SV871: $i,SV395: $i] :
( ( ! [SY3842: $i,SY3843: $i,SY3844: $i,SY3845: $i] :
( ( c_List_Ofoldl @ SV395 @ SV871 @ ( c_List_Olist_OCons @ SY3842 @ SY3843 @ SY3844 ) @ SY3845 @ SY3844 )
= ( c_List_Ofoldl @ SV395 @ ( hAPP @ ( hAPP @ SV395 @ SV871 ) @ SY3842 ) @ SY3843 @ SY3845 @ SY3844 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2125]) ).
thf(2632,plain,
! [SV872: $i,SV396: $i] :
( ( ! [SY3846: $i,SY3847: $i,SY3848: $i,SY3849: $i] :
( ( c_List_Ofoldl @ SV396 @ SV872 @ ( c_List_Oappend @ SY3846 @ SY3847 @ SY3848 ) @ SY3849 @ SY3848 )
= ( c_List_Ofoldl @ SV396 @ ( c_List_Ofoldl @ SV396 @ SV872 @ SY3846 @ SY3849 @ SY3848 ) @ SY3847 @ SY3849 @ SY3848 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2126]) ).
thf(2633,plain,
! [SV873: $i,SV397: $i] :
( ( ! [SY3850: $i,SY3851: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV397 @ SV873 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY3850 ) @ SY3851 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV397 ) @ SY3850 ) @ SY3851 ) @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SY3850 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SY3851 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV873 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2127]) ).
thf(2634,plain,
! [SV874: $i,SV398: $i] :
( ( ( hBOOL @ ( hAPP @ SV398 @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV398 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV398 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV398 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV398 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ SV398 @ SV874 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(2635,plain,
! [SV875: $i,SV399: $i] :
( ( ! [SY3852: $i,SY3853: $i] :
( ( c_Type_Otypings @ SV399 @ SV875 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SY3852 @ SV399 @ SY3853 @ SV875 ) )
| ~ ( c_Type_Otyping @ SV399 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY3853 ) @ SV875 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY3852 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2129]) ).
thf(2636,plain,
! [SV876: $i,SV400: $i] :
( ( ( hBOOL @ ( hAPP @ SV400 @ SV876 ) )
| ( hBOOL @ ( hAPP @ SV400 @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV400 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV400 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV400 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV400 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2130]) ).
thf(2637,plain,
! [SV877: $i,SV401: $i] :
( ( ! [SY3854: $i,SY3855: $i,SY3856: $i,SY3857: $i,SY3858: $i] :
( ( c_Type_Otypings @ SV401 @ SV877 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SY3854 @ SY3855 @ SV401 @ SV877 ) )
| ~ ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY3856 ) @ SY3857 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY3855 )
| ~ ( c_Type_Otypings @ SV401 @ SY3857 @ SY3858 )
| ~ ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY3856 ) @ SY3857 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV877 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY3854 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2131]) ).
thf(2638,plain,
! [SV878: $i,SV402: $i] :
( ( ! [SY3859: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV402 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV878 @ SV402 @ SY3859 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV878 ) @ SV402 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SY3859 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2132]) ).
thf(2639,plain,
! [SV403: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV403 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV403 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV403 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV403 ) ) )
| ( SV403
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV403 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV403 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV403 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2133]) ).
thf(2640,plain,
! [SV879: $i,SV404: $i] :
( ( ! [SY3860: $i,SY3861: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV404 ) @ SV879 ) @ SY3860 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY3861 ) @ SV879 ) @ SY3860 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV404 ) @ SY3861 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2134]) ).
thf(2641,plain,
! [SV880: $i,SV405: $i] :
( ( ! [SY3862: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV405 ) @ SV880 ) ) @ SY3862 ) @ SV880 )
= SV405 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2135]) ).
thf(2642,plain,
! [SV406: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV406 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV406 ) ) )
| ( SV406
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV406 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV406 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV406 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2136]) ).
thf(2643,plain,
! [SV881: $i,SV407: $i] :
( ( ! [SY3863: $i,SY3864: $i,SY3865: $i] :
( ~ ( hBOOL @ ( hAPP @ SV407 @ ( c_Lambda_OdB_OdB__case @ SV881 @ SY3863 @ SY3864 @ ( c_Lambda_OdB_OVar @ SY3865 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV407 @ ( hAPP @ SV881 @ SY3865 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2137]) ).
thf(2644,plain,
! [SV882: $i,SV408: $i] :
( ( ! [SY3866: $i,SY3867: $i,SY3868: $i] :
( ~ ( hBOOL @ ( hAPP @ SV408 @ ( c_Lambda_OdB_OdB__case @ SV882 @ SY3866 @ SY3867 @ ( c_Lambda_OdB_OVar @ SY3868 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV408 @ ( hAPP @ SV882 @ SY3868 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2138]) ).
thf(2645,plain,
! [SV883: $i,SV409: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV409 ) ) @ SV883 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2139]) ).
thf(2646,plain,
! [SV884: $i,SV410: $i] :
( ( ! [SY3869: $i,SY3870: $i,SY3871: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV410 @ SV884 @ SY3869 @ ( c_Lambda_OdB_OVar @ SY3870 ) @ SY3871 )
= ( hAPP @ SV410 @ SY3870 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2140]) ).
thf(2647,plain,
! [SV885: $i,SV411: $i] :
( ( ! [SY3872: $i] :
( ( ( hAPP @ SV411 @ SV885 )
= SY3872 )
| ~ ( c_Type_Otyping @ SV411 @ ( c_Lambda_OdB_OVar @ SV885 ) @ SY3872 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2141]) ).
thf(2648,plain,
! [SV886: $i,SV412: $i] :
( ( ! [SY3873: $i,SY3874: $i,SY3875: $i] :
( ( c_Lambda_OdB_OdB__case @ SV412 @ SV886 @ SY3873 @ ( c_Lambda_OdB_OVar @ SY3874 ) @ SY3875 )
= ( hAPP @ SV412 @ SY3874 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2142]) ).
thf(2649,plain,
! [SV887: $i,SV413: $i] :
( ( c_Type_Otyping @ SV413 @ ( c_Lambda_OdB_OVar @ SV887 ) @ ( hAPP @ SV413 @ SV887 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2143]) ).
thf(2650,plain,
! [SV888: $i,SV414: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV414 ) @ SV888 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2144]) ).
thf(2651,plain,
! [SV415: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV415 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV415 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2145]) ).
thf(2652,plain,
! [SV889: $i,SV416: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV416 ) ) @ SV889 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV416 ) @ SV889 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2146]) ).
thf(2653,plain,
! [SV890: $i,SV417: $i] :
( ( ! [SY3876: $i] :
( ( SV417
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV890 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV890 @ SY3876 @ SV417 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV890 ) @ SY3876 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV417 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2147]) ).
thf(2654,plain,
! [SV891: $i,SV418: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV418 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV418 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV418 )
| ~ ( class_Power_Opower @ SV418 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV418 ) @ SV891 @ SV418 )
= ( c_HOL_Ozero__class_Ozero @ SV418 ) )
| ( SV891
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2148]) ).
thf(2655,plain,
! [SV892: $i,SV419: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV419 )
| ~ ( class_Power_Opower @ SV419 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV419 ) @ SV892 @ SV419 )
= ( c_HOL_Ozero__class_Ozero @ SV419 ) )
| ( SV892
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2149]) ).
thf(2656,plain,
! [SV420: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV420 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV420 )
= ( c_HOL_Ozero__class_Ozero @ SV420 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2150]) ).
thf(2657,plain,
! [SV893: $i,SV421: $i] :
( ( ! [SY3877: $i] :
( ~ ( class_OrderedGroup_Omonoid__add @ SV421 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SV893 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ ( c_HOL_Ozero__class_Ozero @ SV421 ) @ SY3877 @ SV421 @ SV421 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SV893 @ SY3877 @ SV421 @ SV421 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2151]) ).
thf(2658,plain,
! [SV894: $i,SV422: $i] :
( ( ( c_Lambda_Osubstn @ SV422 @ SV894 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV422 ) @ SV894 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2152]) ).
thf(2659,plain,
! [SV895: $i,SV425: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV425 ) @ SV895 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV425 ) @ SV895 ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2155]) ).
thf(2660,plain,
! [SV896: $i,SV426: $i] :
( ( ! [SY3878: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV426 @ SV896 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3878 @ SV896 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV426 ) @ SY3878 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2156]) ).
thf(2661,plain,
! [SV897: $i,SV427: $i] :
( ( ! [SY3879: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV427 ) ) @ SV897 ) @ SY3879 )
= ( c_Lambda_OdB_OVar @ SV427 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV427 @ SY3879 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2157]) ).
thf(2662,plain,
! [SV898: $i,SV428: $i] :
( ( ! [SY3880: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV428 ) ) @ SV898 ) @ SY3880 )
= ( c_Lambda_OdB_OVar @ SV428 ) )
| ( SV428 = SY3880 )
| ( c_HOL_Oord__class_Oless @ SY3880 @ SV428 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2158]) ).
thf(2663,plain,
! [SV899: $i,SV429: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV429 @ SV429 @ tc_nat )
| ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV429 ) ) @ SV899 ) @ SV429 )
= SV899 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2159]) ).
thf(2664,plain,
! [SV900: $i,SV430: $i] :
( ( ! [SY3881: $i,SY3882: $i,SY3883: $i] :
( ( SV430 = SV900 )
| ~ ( c_Type_Otyping @ SY3881 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY3882 ) @ SY3883 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV900 )
| ~ ( c_Type_Otyping @ SY3881 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY3882 ) @ SY3883 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2160]) ).
thf(2665,plain,
! [SV901: $i,SV432: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV432 ) @ SV901 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV901 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2162]) ).
thf(2666,plain,
! [SV902: $i,SV433: $i] :
( ( ! [SY3884: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV433 ) ) @ SV902 ) @ SY3884 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV902 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV433 ) @ SV902 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SY3884 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2163]) ).
thf(2667,plain,
! [SV903: $i,SV434: $i] :
( ( ! [SY3885: $i,SY3886: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV434 ) @ SV903 ) ) @ SY3885 ) @ SY3886 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV434 ) @ SY3885 ) @ SY3886 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV903 ) @ SY3885 ) @ SY3886 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2164]) ).
thf(2668,plain,
! [SV904: $i,SV435: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV435 ) ) @ SV904 ) @ SV435 )
= SV904 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2165]) ).
thf(2669,plain,
! [SV905: $i,SV436: $i] :
( ( ! [SY3887: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV436 ) @ ( c_Lambda_OdB_OVar @ SV905 ) ) @ SY3887 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV436 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2166]) ).
thf(2670,plain,
! [SV906: $i,SV438: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV438 @ SV906 ) )
| ~ ( class_Orderings_Opreorder @ SV906 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2168]) ).
thf(2671,plain,
! [SV907: $i,SV439: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV439 @ SV907 ) )
| ~ ( class_Orderings_Oorder @ SV907 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(2672,plain,
! [SV908: $i,SV440: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV440 ) @ SV908 ) @ SV908 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2170]) ).
thf(2673,plain,
! [SV909: $i,SV441: $i] :
( ( ! [SY3888: $i] :
( ( SV441 = SV909 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SY3888 ) @ SV441 ) @ SV909 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2171]) ).
thf(2674,plain,
! [SV910: $i,SV442: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV442 )
!= ( c_Lambda_OdB_OVar @ SV910 ) )
| ( SV442 = SV910 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2173]) ).
thf(2675,plain,
! [SV911: $i,SV443: $i] :
( ( ! [SY3889: $i,SY3890: $i,SY3891: $i] :
( ( ( c_List_Olist_OCons @ SV443 @ SV911 @ SY3889 )
!= ( c_List_Olist_OCons @ SY3890 @ SY3891 @ SY3889 ) )
| ( SV443 = SY3890 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2174]) ).
thf(2676,plain,
! [SV912: $i,SV444: $i] :
( ( ! [SY3892: $i,SY3893: $i,SY3894: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV444 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV912 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SY3892 ) @ SY3893 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SY3892 ) @ SY3894 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV912 ) @ SY3893 )
= SY3894 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2175]) ).
thf(2677,plain,
! [SV913: $i,SV445: $i] :
( ( ! [SY3895: $i] :
( ( c_Lambda_OdB_OVar @ SV445 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV913 ) @ SY3895 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2176]) ).
thf(2678,plain,
! [SV914: $i,SV446: $i] :
( ( ! [SY3896: $i,SY3897: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV446 )
| ~ ( class_Int_Onumber__ring @ SV446 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV446 ) @ SV914 ) @ SY3896 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV446 ) @ SV914 ) @ SY3897 ) )
| ( SY3896 = SY3897 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2177]) ).
thf(2679,plain,
! [SV915: $i,SV447: $i] :
( ( ! [SY3898: $i,SY3899: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV447 ) @ SV915 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3898 ) @ SY3899 ) )
| ( SV447 = SY3898 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2680,plain,
! [SV916: $i,SV448: $i] :
( ( ! [SY3900: $i] :
( ( c_List_Olist_OCons @ SV448 @ SV916 @ SY3900 )
!= ( c_List_Olist_ONil @ SY3900 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(2681,plain,
! [SV917: $i,SV449: $i] :
( ( ! [SY3901: $i] :
( ~ ( class_Orderings_Olinorder @ SV449 )
| ( ( c_Orderings_Oord__class_Omax @ SV917 @ SY3901 @ SV449 )
!= SY3901 )
| ( c_lessequals @ SV917 @ SY3901 @ SV449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2180]) ).
thf(2682,plain,
! [SV918: $i,SV450: $i] :
( ( ! [SY3902: $i,SY3903: $i,SY3904: $i] :
( ( ( c_List_Oappend @ SV450 @ ( c_List_Olist_OCons @ SV918 @ ( c_List_Olist_ONil @ SY3902 ) @ SY3902 ) @ SY3902 )
!= ( c_List_Oappend @ SY3903 @ ( c_List_Olist_OCons @ SY3904 @ ( c_List_Olist_ONil @ SY3902 ) @ SY3902 ) @ SY3902 ) )
| ( SV450 = SY3903 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2181]) ).
thf(2683,plain,
! [SV919: $i,SV451: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV451 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV451 ) @ SV919 ) @ SV919 )
!= ( c_HOL_Ozero__class_Ozero @ SV451 ) )
| ( SV919
= ( c_HOL_Ozero__class_Ozero @ SV451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2182]) ).
thf(2684,plain,
! [SV920: $i,SV452: $i] :
( ( ! [SY3905: $i] :
( ( SV452
!= ( c_List_Oappend @ SV920 @ SV452 @ SY3905 ) )
| ( SV920
= ( c_List_Olist_ONil @ SY3905 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2183]) ).
thf(2685,plain,
! [SV921: $i,SV453: $i] :
( ( ! [SY3906: $i] :
( ( c_List_Olist_ONil @ SV453 )
!= ( c_List_Olist_OCons @ SV921 @ SY3906 @ SV453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2184]) ).
thf(2686,plain,
! [SV922: $i,SV454: $i] :
( ( ( SV454
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV454 ) @ SV922 ) )
| ( SV922
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2185]) ).
thf(2687,plain,
! [SV923: $i,SV455: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV455 ) @ SV923 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV923
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2688,plain,
! [SV924: $i,SV456: $i] :
( ( ! [SY3907: $i,SY3908: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV456 )
| ( ( c_Power_Opower__class_Opower @ SV924 @ SY3907 @ SV456 )
!= ( c_Power_Opower__class_Opower @ SY3908 @ SY3907 @ SV456 ) )
| ( SV924 = SY3908 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SY3907 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SY3908 @ SV456 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV924 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2187]) ).
thf(2689,plain,
! [SV925: $i,SV457: $i] :
( ( ! [SY3909: $i,SY3910: $i,SY3911: $i] :
( ( ( c_List_Oreplicate @ SV457 @ SV925 @ SY3909 )
!= ( c_List_Oreplicate @ SY3910 @ SY3911 @ SY3909 ) )
| ( SV457 = SY3910 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2188]) ).
thf(2690,plain,
! [SV926: $i,SV458: $i] :
( ( ! [SY3912: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV458 ) @ SV926 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3912 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV458 ) @ SV926 )
= SY3912 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(2691,plain,
! [SV927: $i,SV459: $i] :
( ( ! [SY3913: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV459 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV459 ) @ SV927 ) @ SY3913 )
!= ( c_HOL_Ozero__class_Ozero @ SV459 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV459 ) @ SY3913 @ SV459 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV459 ) @ SV927 @ SV459 )
| ( SY3913
= ( c_HOL_Ozero__class_Ozero @ SV459 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2190]) ).
thf(2692,plain,
! [SV928: $i,SV460: $i] :
( ( ! [SY3914: $i,SY3915: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV460 ) @ SV928 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY3914 ) @ SY3915 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV928 = SY3915 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(2693,plain,
! [SV929: $i,SV461: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV461 ) @ SV929 )
!= SV461 )
| ( SV929
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(2694,plain,
! [SV930: $i,SV462: $i] :
( ( ! [SY3916: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV462 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV930 @ SY3916 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV462 )
= SV930 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2193]) ).
thf(2695,plain,
! [SV931: $i,SV463: $i] :
( ( ! [SY3917: $i] :
( ( ( c_Lambda_OdB_OVar @ SV463 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV931 @ SY3917 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY3917
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(2696,plain,
! [SV932: $i,SV464: $i] :
( ( ! [SY3918: $i,SY3919: $i,SY3920: $i] :
( ( ( c_List_Olist_OCons @ SV464 @ SV932 @ SY3918 )
!= ( c_List_Olist_OCons @ SY3919 @ SY3920 @ SY3918 ) )
| ( SV932 = SY3920 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2195]) ).
thf(2697,plain,
! [SV933: $i,SV465: $i] :
( ( ! [SY3921: $i,SY3922: $i,SY3923: $i] :
( ( ( c_List_Oreplicate @ SV465 @ SV933 @ SY3921 )
!= ( c_List_Oreplicate @ SY3922 @ SY3923 @ SY3921 ) )
| ( SV933 = SY3923 )
| ( SV465
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2196]) ).
thf(2698,plain,
! [SV934: $i,SV466: $i] :
( ( ! [SY3924: $i] :
( ( c_Lambda_OdB_OAbs @ SV466 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV934 ) @ SY3924 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2699,plain,
! [SV935: $i,SV467: $i] :
( ( ! [SY3925: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV467 )
| ~ ( class_Int_Onumber__ring @ SV467 )
| ( SV935
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV467 ) @ SV935 ) @ SY3925 ) )
| ( SY3925
= ( c_HOL_Ozero__class_Ozero @ SV467 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2198]) ).
thf(2700,plain,
! [SV936: $i,SV468: $i] :
( ( ! [SY3926: $i,SY3927: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV468 ) @ SV936 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY3926 ) @ SY3927 ) )
| ( SV936 = SY3927 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2199]) ).
thf(2701,plain,
! [SV937: $i,SV469: $i] :
( ( ! [SY3928: $i] :
( ( SV469
!= ( c_List_Oappend @ SV469 @ SV937 @ SY3928 ) )
| ( SV937
= ( c_List_Olist_ONil @ SY3928 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(2702,plain,
! [SV938: $i,SV470: $i] :
( ( ! [SY3929: $i,SY3930: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV470 ) @ SV938 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY3929 ) @ SY3930 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2201]) ).
thf(2703,plain,
! [SV939: $i,SV471: $i] :
( ( ! [SY3931: $i] :
( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV471 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV471 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV471 )
| ~ ( class_Power_Opower @ SV471 )
| ( ( c_Power_Opower__class_Opower @ SV939 @ SY3931 @ SV471 )
!= ( c_HOL_Ozero__class_Ozero @ SV471 ) )
| ( SV939
= ( c_HOL_Ozero__class_Ozero @ SV471 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2202]) ).
thf(2704,plain,
! [SV940: $i,SV472: $i] :
( ( ! [SY3932: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV472 @ SV940 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3932 @ SV940 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV472 = SY3932 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2203]) ).
thf(2705,plain,
! [SV941: $i,SV473: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV473 )
!= ( c_Lambda_OdB_OAbs @ SV941 ) )
| ( SV473 = SV941 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2204]) ).
thf(2706,plain,
! [SV942: $i,SV474: $i] :
( ( ! [SY3933: $i,SY3934: $i] :
( ( ( c_List_Oappend @ SV474 @ SV942 @ SY3933 )
!= ( c_List_Oappend @ SV474 @ SY3934 @ SY3933 ) )
| ( SV942 = SY3934 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2707,plain,
! [SV943: $i,SV475: $i] :
( ( ! [SY3935: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV475 ) @ SV943 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3935 ) @ SV943 ) )
| ( SV475 = SY3935 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2206]) ).
thf(2708,plain,
! [SV944: $i,SV476: $i] :
( ( ! [SY3936: $i,SY3937: $i] :
( ( ( c_List_Olist_ONil @ SV476 )
!= ( c_List_Omap @ SV944 @ SY3936 @ SY3937 @ SV476 ) )
| ( SY3936
= ( c_List_Olist_ONil @ SY3937 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(2709,plain,
! [SV945: $i,SV477: $i] :
( ( ! [SY3938: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ SV477 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV945 @ SV477 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SY3938 @ SV477 ) )
| ( SV945 = SY3938 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2208]) ).
thf(2710,plain,
! [SV946: $i,SV478: $i] :
( ( ! [SY3939: $i] :
( ( c_List_Olist_OCons @ SV478 @ SV946 @ SY3939 )
!= ( c_List_Olist_ONil @ SY3939 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2209]) ).
thf(2711,plain,
! [SV947: $i,SV479: $i] :
( ( ! [SY3940: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV479 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV947 @ SY3940 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY3940
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2210]) ).
thf(2712,plain,
! [SV948: $i,SV480: $i] :
( ( ! [SY3941: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV480 @ SV948 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY3941 ) )
| ( SV948
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2211]) ).
thf(2713,plain,
! [SV949: $i,SV481: $i] :
( ( ! [SY3942: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV481 ) @ SV949 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV481 ) @ SY3942 ) )
| ( SV949 = SY3942 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2212]) ).
thf(2714,plain,
! [SV482: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV482 ) )
= $true )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV482 )
!= ( c_HOL_Oone__class_Oone @ SV482 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2213]) ).
thf(2715,plain,
! [SV950: $i,SV483: $i] :
( ( ! [SY3943: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV483 @ SV950 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SY3943 ) )
| ( SV483
= ( c_Lambda_OdB_OAbs @ SY3943 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2214]) ).
thf(2716,plain,
! [SV951: $i,SV484: $i] :
( ( ! [SY3944: $i] :
( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV484 )
| ( ( c_Power_Opower__class_Opower @ SV951 @ SY3944 @ SV484 )
!= ( c_HOL_Ozero__class_Ozero @ SV484 ) )
| ( SV951
= ( c_HOL_Ozero__class_Ozero @ SV484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2215]) ).
thf(2717,plain,
! [SV952: $i,SV485: $i] :
( ( ! [SY3945: $i,SY3946: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV485 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV952 ) @ SY3945 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SY3946 ) @ SY3945 ) )
| ( SV952 = SY3946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2216]) ).
thf(2718,plain,
! [SV953: $i,SV486: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV486 )
!= ( c_Lambda_OdB_OVar @ SV953 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2217]) ).
thf(2719,plain,
! [SV954: $i,SV487: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV487 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV487 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV487 )
| ~ ( class_Power_Opower @ SV487 )
| ( ( c_Power_Opower__class_Opower @ SV954 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV487 )
!= ( c_HOL_Ozero__class_Ozero @ SV487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(2720,plain,
! [SV955: $i,SV488: $i] :
( ( ! [SY3947: $i] :
( ( ( c_List_Olist_ONil @ SV488 )
!= ( c_List_Oreplicate @ SV955 @ SY3947 @ SV488 ) )
| ( SV955
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2219]) ).
thf(2721,plain,
! [SV956: $i,SV489: $i] :
( ( ! [SY3948: $i] :
( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV489 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV489 ) @ SV956 ) @ SY3948 )
!= ( c_HOL_Ozero__class_Ozero @ SV489 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SY3948 @ SV489 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV956 @ SV489 )
| ( SV956
= ( c_HOL_Ozero__class_Ozero @ SV489 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2220]) ).
thf(2722,plain,
! [SV957: $i,SV490: $i] :
( ( ! [SY3949: $i] :
( ( ( c_List_Oreplicate @ SV490 @ SV957 @ SY3949 )
!= ( c_List_Olist_ONil @ SY3949 ) )
| ( SV490
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2221]) ).
thf(2723,plain,
! [SV958: $i,SV491: $i] :
( ( ! [SY3950: $i] :
( ( ( c_List_Olist_ONil @ SV491 )
!= ( c_List_Oappend @ SV958 @ SY3950 @ SV491 ) )
| ( SV958
= ( c_List_Olist_ONil @ SV491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2222]) ).
thf(2724,plain,
! [SV959: $i,SV492: $i] :
( ( ! [SY3951: $i,SY3952: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV492 ) @ SV959 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3951 ) @ SY3952 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3951 @ SV959 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV492 @ SY3952 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2223]) ).
thf(2725,plain,
! [SV960: $i,SV493: $i] :
( ( ! [SY3953: $i,SY3954: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV493 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV960 ) @ SY3953 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV960 ) @ SY3954 ) )
| ( SY3953 = SY3954 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2224]) ).
thf(2726,plain,
! [SV961: $i,SV494: $i] :
( ( ! [SY3955: $i,SY3956: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV494 ) @ SV961 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY3955 ) @ SY3956 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV494 = SY3955 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(2727,plain,
! [SV962: $i,SV495: $i] :
( ( ! [SY3957: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV495 ) @ SV962 )
!= ( c_Lambda_OdB_OAbs @ SY3957 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2226]) ).
thf(2728,plain,
! [SV963: $i,SV496: $i] :
( ( ! [SY3958: $i,SY3959: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV496 )
| ( ( c_Power_Opower__class_Opower @ SV963 @ SY3958 @ SV496 )
!= ( c_Power_Opower__class_Opower @ SV963 @ SY3959 @ SV496 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV496 ) @ SV963 @ SV496 )
| ( SY3958 = SY3959 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(2729,plain,
! [SV964: $i,SV497: $i] :
( ( ! [SY3960: $i,SY3961: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV497 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV964 ) @ SY3960 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV964 ) @ SY3961 ) )
| ( SY3960 = SY3961 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2228]) ).
thf(2730,plain,
! [SV965: $i,SV498: $i] :
( ( ! [SY3962: $i,SY3963: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV498 ) ) @ SV965 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY3962 ) @ SY3963 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2229]) ).
thf(2731,plain,
! [SV966: $i,SV499: $i] :
( ( ! [SY3964: $i] :
( ( ( c_List_Olist_ONil @ SV499 )
!= ( c_List_Oappend @ SV966 @ SY3964 @ SV499 ) )
| ( SY3964
= ( c_List_Olist_ONil @ SV499 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2230]) ).
thf(2732,plain,
! [SV967: $i,SV500: $i] :
( ( ! [SY3965: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV500 ) @ SV967 )
!= ( c_Lambda_OdB_OVar @ SY3965 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2231]) ).
thf(2733,plain,
! [SV968: $i,SV501: $i] :
( ( ! [SY3966: $i,SY3967: $i,SY3968: $i] :
( ( ( c_List_Oappend @ SV501 @ ( c_List_Olist_OCons @ SV968 @ ( c_List_Olist_ONil @ SY3966 ) @ SY3966 ) @ SY3966 )
!= ( c_List_Oappend @ SY3967 @ ( c_List_Olist_OCons @ SY3968 @ ( c_List_Olist_ONil @ SY3966 ) @ SY3966 ) @ SY3966 ) )
| ( SV968 = SY3968 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2232]) ).
thf(2734,plain,
! [SV969: $i,SV502: $i] :
( ( ! [SY3969: $i] :
( ( ( c_List_Oappend @ SV502 @ SV969 @ SY3969 )
!= ( c_List_Olist_ONil @ SY3969 ) )
| ( SV969
= ( c_List_Olist_ONil @ SY3969 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2233]) ).
thf(2735,plain,
! [SV970: $i,SV503: $i] :
( ( ! [SY3970: $i,SY3971: $i] :
( ( ( c_List_Omap @ SV503 @ SV970 @ SY3970 @ SY3971 )
!= ( c_List_Olist_ONil @ SY3971 ) )
| ( SV970
= ( c_List_Olist_ONil @ SY3970 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2234]) ).
thf(2736,plain,
! [SV971: $i,SV504: $i] :
( ( ! [SY3972: $i,SY3973: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV504 ) @ SV971 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3972 @ SY3973 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV504
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SY3972 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV504 @ SV971 @ SY3972 @ SY3973 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY3973
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2235]) ).
thf(2737,plain,
! [SV972: $i,SV505: $i] :
( ( ! [SY3974: $i,SY3975: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV505 ) @ SV972 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SY3974 ) @ SY3975 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV972 = SY3975 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(2738,plain,
! [SV973: $i,SV506: $i] :
( ( ! [SY3976: $i] :
( ( ( c_Lambda_OdB_OVar @ SV506 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV973 @ SY3976 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV506 )
= SV973 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2237]) ).
thf(2739,plain,
! [SV507: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV507 ) )
= $true )
| ( ( ( c_HOL_Oone__class_Oone @ SV507 )
!= ( c_HOL_Ozero__class_Ozero @ SV507 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2238]) ).
thf(2740,plain,
! [SV974: $i,SV508: $i] :
( ( ! [SY3977: $i] :
( ( c_List_Olist_OCons @ SV508 @ SV974 @ SY3977 )
!= SV974 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2239]) ).
thf(2741,plain,
! [SV975: $i,SV509: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV509 ) @ SV975 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( SV509
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2240]) ).
thf(2742,plain,
! [SV976: $i,SV510: $i] :
( ( ! [SY3978: $i] :
( ( ( c_List_Oappend @ SV510 @ SV976 @ SY3978 )
!= SV976 )
| ( SV510
= ( c_List_Olist_ONil @ SY3978 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2241]) ).
thf(2743,plain,
! [SV977: $i,SV511: $i] :
( ( ( c_Lambda_OdB_OVar @ SV511 )
!= ( c_Lambda_OdB_OAbs @ SV977 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2242]) ).
thf(2744,plain,
! [SV978: $i,SV512: $i] :
( ( ! [SY3979: $i] :
( ( ( c_List_Oappend @ SV512 @ SV978 @ SY3979 )
!= ( c_List_Olist_ONil @ SY3979 ) )
| ( SV512
= ( c_List_Olist_ONil @ SY3979 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(2745,plain,
! [SV979: $i,SV513: $i] :
( ( ! [SY3980: $i] :
( ( ( c_List_Oappend @ SV513 @ SV979 @ SY3980 )
!= SV513 )
| ( SV979
= ( c_List_Olist_ONil @ SY3980 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(2746,plain,
! [SV980: $i,SV514: $i] :
( ( ! [SY3981: $i,SY3982: $i] :
( ( ( c_List_Oappend @ SV514 @ SV980 @ SY3981 )
!= ( c_List_Oappend @ SY3982 @ SV980 @ SY3981 ) )
| ( SV514 = SY3982 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2245]) ).
thf(2747,plain,
! [SV981: $i,SV515: $i] :
( ( ! [SY3983: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV515 ) @ SV981 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV515 ) @ SY3983 ) )
| ( SV981 = SY3983 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2246]) ).
thf(2748,plain,
! [SV982: $i,SV516: $i] :
( ( ! [SY3984: $i,SY3985: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV516 ) @ SV982 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY3984 ) @ SY3985 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV516 = SY3984 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2247]) ).
thf(2749,plain,
! [SV983: $i,SV517: $i] :
( ( ! [SY3986: $i] :
( SV517
!= ( c_List_Olist_OCons @ SV983 @ SV517 @ SY3986 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2248]) ).
thf(2750,plain,
! [SV518: $i,SV1: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV1 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV518 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2249]) ).
thf(2751,plain,
! [SV519: $i,SV2: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV2 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV519 @ SV2 ) @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2250]) ).
thf(2752,plain,
! [SV984: $i,SV520: $i,SV3: $i] :
( ( ! [SY3987: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV3 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV520 @ SV984 @ SV3 ) @ ( c_Power_Opower__class_Opower @ SY3987 @ SV984 @ SV3 ) @ SV3 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV520 @ SV3 )
| ~ ( c_lessequals @ SV520 @ SY3987 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(2753,plain,
! [SV985: $i,SV521: $i,SV4: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV4 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV4 ) @ ( c_Power_Opower__class_Opower @ SV521 @ SV985 @ SV4 ) @ SV4 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV4 ) @ SV521 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2252]) ).
thf(2754,plain,
! [SV522: $i,SV5: $i] :
( ( ( ~ ( class_Power_Opower @ SV5 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV522 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV5 )
= ( c_HOL_Oone__class_Oone @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2253]) ).
thf(2755,plain,
! [SV523: $i,SV6: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV6 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV523 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV6 )
= ( c_HOL_Oone__class_Oone @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2254]) ).
thf(2756,plain,
! [SV986: $i,SV524: $i,SV7: $i] :
( ( ! [SY3988: $i,SY3989: $i,SY3990: $i] :
( ~ ( c_Type_Otyping @ SV7 @ SV524 @ SV986 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV7 @ SY3988 @ SV986 @ tc_Type_Otype ) @ SY3989 @ SY3990 )
| ( c_Type_Otyping @ SV7 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY3989 ) @ SV524 ) @ SY3988 ) @ SY3990 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2255]) ).
thf(2757,plain,
! [SV987: $i,SV525: $i,SV8: $i] :
( ( ! [SY3991: $i,SY3992: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV8 @ SV525 @ SV987 @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SY3991 ) @ SV525 ) @ SY3992 )
| ~ ( c_Type_Otyping @ SV8 @ SY3991 @ SY3992 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2256]) ).
thf(2758,plain,
! [SV988: $i,SV526: $i,SV9: $i] :
( ( ! [SY3993: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV9 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV526 @ SV988 @ SV9 ) @ ( c_Power_Opower__class_Opower @ SV526 @ SY3993 @ SV9 ) @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV526 @ ( c_HOL_Oone__class_Oone @ SV9 ) @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV526 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SY3993 @ SV988 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2257]) ).
thf(2759,plain,
! [SV989: $i,SV527: $i,SV10: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV10 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV10 ) @ ( c_Power_Opower__class_Opower @ SV527 @ SV989 @ SV10 ) @ SV10 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV989 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV10 ) @ SV527 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(2760,plain,
! [SV990: $i,SV528: $i,SV11: $i] :
( ( ! [SY3994: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV11 ) @ SV528 ) @ SV990 ) ) @ SY3994 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV11 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3994 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV528 ) @ SY3994 ) ) @ SV990 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV990 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY3994 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2259]) ).
thf(2761,plain,
! [SV991: $i,SV529: $i,SV12: $i] :
( ( ! [SY3995: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV12 ) @ SV529 ) @ SV991 ) ) @ SY3995 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV12 ) @ SY3995 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV529 ) @ SY3995 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV991 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SY3995 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV991 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2260]) ).
thf(2762,plain,
! [SV530: $i,SV13: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV13 ) ) @ SV530 )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV13 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV13 @ SV530 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2261]) ).
thf(2763,plain,
! [SV531: $i,SV14: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV14 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV531 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV14 ) @ SV531 ) @ ( c_HOL_Oone__class_Oone @ SV14 ) ) @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2262]) ).
thf(2764,plain,
! [SV992: $i,SV532: $i,SV15: $i] :
( ( ! [SY3996: $i,SY3997: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV15 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SV532 ) @ SV992 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SY3996 ) @ SY3997 ) @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV992 @ SY3997 @ SV15 )
| ~ ( c_lessequals @ SV532 @ SY3996 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2263]) ).
thf(2765,plain,
! [SV993: $i,SV533: $i,SV16: $i] :
( ( ! [SY3998: $i,SY3999: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV16 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SV533 ) @ SV993 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SY3998 ) @ SY3999 ) @ SV16 )
| ~ ( c_lessequals @ SV993 @ SY3999 @ SV16 )
| ~ ( c_HOL_Oord__class_Oless @ SV533 @ SY3998 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2264]) ).
thf(2766,plain,
! [SV994: $i,SV534: $i,SV17: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV17 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV17 ) @ SV534 ) @ SV994 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
| ~ ( c_lessequals @ SV994 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
| ~ ( c_lessequals @ SV534 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2265]) ).
thf(2767,plain,
! [SV535: $i,SV18: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV18 ) )
= $true )
| ( ( ( c_lessequals @ SV535 @ ( c_HOL_Ozero__class_Ozero @ SV18 ) @ SV18 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV18 ) @ SV535 ) @ SV535 ) @ ( c_HOL_Ozero__class_Ozero @ SV18 ) @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2266]) ).
thf(2768,plain,
! [SV536: $i,SV19: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV19 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV19 ) @ SV536 ) @ SV536 ) @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 )
| ~ ( c_lessequals @ SV536 @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2267]) ).
thf(2769,plain,
! [SV995: $i,SV537: $i,SV20: $i] :
( ( ! [SY4000: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV20 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV20 )
| ( c_lessequals @ SV537 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV20 ) @ SV995 ) @ SY4000 ) @ SV20 )
| ~ ( c_lessequals @ SV537 @ SV995 @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SY4000 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2268]) ).
thf(2770,plain,
! [SV996: $i,SV538: $i,SV21: $i] :
( ( ! [SY4001: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV21 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV21 )
| ( c_lessequals @ SV538 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SV996 ) @ SY4001 ) @ SV21 )
| ~ ( c_lessequals @ SV538 @ SY4001 @ SV21 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ SV996 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2269]) ).
thf(2771,plain,
! [SV539: $i,SV22: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV22 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV22 ) @ SV539 @ SV22 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV22 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV539 ) @ SV539 ) @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2270]) ).
thf(2772,plain,
! [SV540: $i,SV23: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV23 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV23 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV23 ) @ SV540 ) @ SV540 ) @ SV23 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV23 ) @ SV540 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2271]) ).
thf(2773,plain,
! [SV24: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV24 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ SV24 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ SV24 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) )
= ( c_HOL_Ozero__class_Ozero @ SV24 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2272]) ).
thf(2774,plain,
! [SV997: $i,SV541: $i,SV25: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV25 )
| ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SV541 ) @ SV997 ) @ SV25 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV997 @ SV25 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV541 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2273]) ).
thf(2775,plain,
! [SV26: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV26 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV26 ) @ ( c_HOL_Oone__class_Oone @ SV26 ) @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2274]) ).
thf(2776,plain,
! [SV27: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV27 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV27 ) @ ( c_HOL_Ozero__class_Ozero @ SV27 ) @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2275]) ).
thf(2777,plain,
! [SV998: $i,SV542: $i,SV28: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV28 )
| ( c_lessequals @ SV542 @ SV998 @ SV28 )
| ( c_lessequals @ SV998 @ SV542 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2276]) ).
thf(2778,plain,
! [SV999: $i,SV543: $i,SV29: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV29 )
| ( SV543 = SV999 )
| ( c_HOL_Oord__class_Oless @ SV543 @ SV999 @ SV29 )
| ~ ( c_lessequals @ SV543 @ SV999 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2277]) ).
thf(2779,plain,
! [SV1000: $i,SV544: $i,SV30: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV30 )
| ( SV544 = SV1000 )
| ~ ( c_lessequals @ SV544 @ SV1000 @ SV30 )
| ( c_HOL_Oord__class_Oless @ SV544 @ SV1000 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2278]) ).
thf(2780,plain,
! [SV1001: $i,SV545: $i,SV31: $i] :
( ( ~ ( class_Orderings_Oorder @ SV31 )
| ( c_HOL_Oord__class_Oless @ SV545 @ SV1001 @ SV31 )
| ~ ( c_lessequals @ SV545 @ SV1001 @ SV31 )
| ( SV545 = SV1001 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2279]) ).
thf(2781,plain,
! [SV1002: $i,SV546: $i,SV32: $i] :
( ( ~ ( class_Orderings_Oorder @ SV32 )
| ( c_HOL_Oord__class_Oless @ SV546 @ SV1002 @ SV32 )
| ( SV546 = SV1002 )
| ~ ( c_lessequals @ SV546 @ SV1002 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2280]) ).
thf(2782,plain,
! [SV1003: $i,SV547: $i,SV33: $i] :
( ( ~ ( class_Orderings_Oorder @ SV33 )
| ( c_HOL_Oord__class_Oless @ SV547 @ SV1003 @ SV33 )
| ( SV547 = SV1003 )
| ~ ( c_lessequals @ SV547 @ SV1003 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2281]) ).
thf(2783,plain,
! [SV1004: $i,SV548: $i,SV34: $i] :
( ( ~ ( class_Orderings_Oorder @ SV34 )
| ( SV548 = SV1004 )
| ( c_HOL_Oord__class_Oless @ SV548 @ SV1004 @ SV34 )
| ~ ( c_lessequals @ SV548 @ SV1004 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2282]) ).
thf(2784,plain,
! [SV1005: $i,SV549: $i,SV35: $i] :
( ( ~ ( class_Orderings_Oorder @ SV35 )
| ( c_HOL_Oord__class_Oless @ SV549 @ SV1005 @ SV35 )
| ~ ( c_lessequals @ SV549 @ SV1005 @ SV35 )
| ( SV1005 = SV549 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(2785,plain,
! [SV1006: $i,SV550: $i,SV36: $i] :
( ( ~ ( class_Orderings_Oorder @ SV36 )
| ( c_HOL_Oord__class_Oless @ SV550 @ SV1006 @ SV36 )
| ( SV1006 = SV550 )
| ~ ( c_lessequals @ SV550 @ SV1006 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(2786,plain,
! [SV1007: $i,SV551: $i,SV37: $i] :
( ( ! [SY4002: $i,SY4003: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV37 )
| ( c_lessequals @ SV551 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV1007 ) @ SY4002 ) @ SV37 )
| ~ ( c_lessequals @ SY4003 @ SY4002 @ SV37 )
| ~ ( c_lessequals @ SV551 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV1007 ) @ SY4003 ) @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2285]) ).
thf(2787,plain,
! [SV1008: $i,SV552: $i,SV38: $i] :
( ( ! [SY4004: $i] :
( ~ ( class_Orderings_Opreorder @ SV38 )
| ( c_HOL_Oord__class_Oless @ SV552 @ SV1008 @ SV38 )
| ~ ( c_lessequals @ SY4004 @ SV1008 @ SV38 )
| ~ ( c_HOL_Oord__class_Oless @ SV552 @ SY4004 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2286]) ).
thf(2788,plain,
! [SV1009: $i,SV553: $i,SV39: $i] :
( ( ! [SY4005: $i] :
( ~ ( class_Orderings_Opreorder @ SV39 )
| ( c_HOL_Oord__class_Oless @ SV553 @ SV1009 @ SV39 )
| ~ ( c_HOL_Oord__class_Oless @ SY4005 @ SV1009 @ SV39 )
| ~ ( c_lessequals @ SV553 @ SY4005 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2287]) ).
thf(2789,plain,
! [SV554: $i,SV40: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV40 ) )
= $true )
| ( ( c_lessequals @ SV554 @ SV554 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2288]) ).
thf(2790,plain,
! [SV555: $i,SV41: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV41 ) )
= $true )
| ( ( c_lessequals @ SV555 @ SV555 @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2289]) ).
thf(2791,plain,
! [SV1010: $i,SV556: $i,SV42: $i] :
( ( ! [SY4006: $i] :
( ~ ( class_Orderings_Opreorder @ SV42 )
| ( c_lessequals @ SV556 @ SV1010 @ SV42 )
| ~ ( c_lessequals @ SY4006 @ SV1010 @ SV42 )
| ~ ( c_lessequals @ SV556 @ SY4006 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2290]) ).
thf(2792,plain,
! [SV1011: $i,SV557: $i,SV43: $i] :
( ( ! [SY4007: $i] :
( ~ ( class_Orderings_Oorder @ SV43 )
| ( c_HOL_Oord__class_Oless @ SV557 @ SV1011 @ SV43 )
| ~ ( c_HOL_Oord__class_Oless @ SV557 @ SY4007 @ SV43 )
| ~ ( c_lessequals @ SY4007 @ SV1011 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2291]) ).
thf(2793,plain,
! [SV1012: $i,SV558: $i,SV44: $i] :
( ( ! [SY4008: $i] :
( ~ ( class_Orderings_Oorder @ SV44 )
| ( c_HOL_Oord__class_Oless @ SV558 @ SV1012 @ SV44 )
| ~ ( c_lessequals @ SV558 @ SY4008 @ SV44 )
| ~ ( c_HOL_Oord__class_Oless @ SY4008 @ SV1012 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(2794,plain,
! [SV1013: $i,SV559: $i,SV45: $i] :
( ( ! [SY4009: $i] :
( ~ ( class_Orderings_Oorder @ SV45 )
| ( c_lessequals @ SV559 @ SV1013 @ SV45 )
| ~ ( c_lessequals @ SV559 @ SY4009 @ SV45 )
| ~ ( c_lessequals @ SY4009 @ SV1013 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2293]) ).
thf(2795,plain,
! [SV1014: $i,SV560: $i,SV46: $i] :
( ( ! [SY4010: $i,SY4011: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV46 @ SV560 @ SV1014 @ SY4010 ) @ SY4011 )
= ( hAPP @ SV46 @ SY4011 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4011 @ SV560 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2294]) ).
thf(2796,plain,
! [SV1015: $i,SV561: $i,SV47: $i] :
( ( ! [SY4012: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV47 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ SV561 ) @ SV1015 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ SV561 ) @ SY4012 ) @ SV47 )
| ~ ( c_lessequals @ SV1015 @ SY4012 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2295]) ).
thf(2797,plain,
! [SV1016: $i,SV562: $i,SV48: $i] :
( ( ! [SY4013: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV48 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV48 ) @ SV562 ) @ SV1016 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV48 ) @ SY4013 ) @ SV1016 ) @ SV48 )
| ~ ( c_lessequals @ SV562 @ SY4013 @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2296]) ).
thf(2798,plain,
! [SV1017: $i,SV563: $i,SV49: $i] :
( ( ! [SY4014: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV49 )
| ( c_lessequals @ SV563 @ SV1017 @ SV49 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SY4014 ) @ SV563 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SY4014 ) @ SV1017 ) @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2297]) ).
thf(2799,plain,
! [SV1018: $i,SV564: $i,SV50: $i] :
( ( ! [SY4015: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV564 ) @ SV1018 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV564 ) @ SY4015 ) @ SV50 )
| ~ ( c_lessequals @ SV1018 @ SY4015 @ SV50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2298]) ).
thf(2800,plain,
! [SV1019: $i,SV565: $i,SV51: $i] :
( ( ! [SY4016: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV51 )
| ( c_lessequals @ SV565 @ SV1019 @ SV51 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV51 ) @ SV565 ) @ SY4016 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV51 ) @ SV1019 ) @ SY4016 ) @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2299]) ).
thf(2801,plain,
! [SV1020: $i,SV566: $i,SV52: $i] :
( ( ! [SY4017: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV52 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV566 ) @ SV1020 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SY4017 ) @ SV1020 ) @ SV52 )
| ~ ( c_lessequals @ SV566 @ SY4017 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2300]) ).
thf(2802,plain,
! [SV1021: $i,SV567: $i,SV53: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV53 )
| ( c_lessequals @ SV567 @ SV1021 @ SV53 )
| ~ ( c_HOL_Oord__class_Oless @ SV567 @ SV1021 @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2301]) ).
thf(2803,plain,
! [SV1022: $i,SV568: $i,SV54: $i] :
( ( ~ ( class_Orderings_Oorder @ SV54 )
| ( c_lessequals @ SV568 @ SV1022 @ SV54 )
| ~ ( c_HOL_Oord__class_Oless @ SV568 @ SV1022 @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2302]) ).
thf(2804,plain,
! [SV1023: $i,SV569: $i,SV55: $i] :
( ( ~ ( class_Orderings_Oorder @ SV55 )
| ( SV569 = SV1023 )
| ~ ( c_lessequals @ SV569 @ SV1023 @ SV55 )
| ~ ( c_lessequals @ SV1023 @ SV569 @ SV55 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2303]) ).
thf(2805,plain,
! [SV1024: $i,SV570: $i,SV56: $i] :
( ( ~ ( class_Orderings_Oorder @ SV56 )
| ( SV570 = SV1024 )
| ~ ( c_lessequals @ SV1024 @ SV570 @ SV56 )
| ~ ( c_lessequals @ SV570 @ SV1024 @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2304]) ).
thf(2806,plain,
! [SV1025: $i,SV571: $i,SV57: $i] :
( ( ~ ( class_Orderings_Oorder @ SV57 )
| ( SV571 = SV1025 )
| ~ ( c_lessequals @ SV1025 @ SV571 @ SV57 )
| ~ ( c_lessequals @ SV571 @ SV1025 @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2305]) ).
thf(2807,plain,
! [SV1026: $i,SV572: $i,SV58: $i] :
( ( ! [SY4018: $i,SY4019: $i,SY4020: $i,SY4021: $i] :
( ( ( hAPP @ ( hAPP @ SV58 @ SV572 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= SV572 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1026 @ SY4018 @ SV58 @ SY4019 @ SY4020 @ SY4021 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2306]) ).
thf(2808,plain,
! [SV59: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV59 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2307]) ).
thf(2809,plain,
! [SV1027: $i,SV573: $i,SV60: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV60 )
| ( c_HOL_Oord__class_Oless @ SV573 @ SV1027 @ SV60 )
| ( c_lessequals @ SV1027 @ SV573 @ SV60 )
| ~ ( c_lessequals @ SV573 @ SV1027 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2308]) ).
thf(2810,plain,
! [SV61: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV61 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV61 ) @ ( c_HOL_Oone__class_Oone @ SV61 ) @ SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2309]) ).
thf(2811,plain,
! [SV1028: $i,SV574: $i,SV62: $i] :
( ( ! [SY4022: $i] :
( ( hAPP @ ( c_Type_Oshift @ SV62 @ SV574 @ SV1028 @ SY4022 ) @ SV574 )
= SV1028 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2310]) ).
thf(2812,plain,
! [SV1029: $i,SV575: $i,SV63: $i] :
( ( ! [SY4023: $i] :
( ~ ( class_Orderings_Olinorder @ SV63 )
| ( c_lessequals @ SV575 @ SV1029 @ SV63 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV575 @ SY4023 @ SV63 ) @ SV1029 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2311]) ).
thf(2813,plain,
! [SV1030: $i,SV576: $i,SV64: $i] :
( ( ! [SY4024: $i] :
( ~ ( class_Orderings_Olinorder @ SV64 )
| ( c_lessequals @ SV576 @ SV1030 @ SV64 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY4024 @ SV576 @ SV64 ) @ SV1030 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2312]) ).
thf(2814,plain,
! [SV1031: $i,SV577: $i,SV65: $i] :
( ( ! [SY4025: $i] :
( ~ ( class_Orderings_Olinorder @ SV65 )
| ( c_lessequals @ SV577 @ ( c_Orderings_Oord__class_Omax @ SV1031 @ SY4025 @ SV65 ) @ SV65 )
| ~ ( c_lessequals @ SV577 @ SV1031 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2313]) ).
thf(2815,plain,
! [SV1032: $i,SV578: $i,SV66: $i] :
( ( ! [SY4026: $i] :
( ~ ( class_Orderings_Olinorder @ SV66 )
| ( c_lessequals @ SV578 @ ( c_Orderings_Oord__class_Omax @ SV1032 @ SY4026 @ SV66 ) @ SV66 )
| ~ ( c_lessequals @ SV578 @ SY4026 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2314]) ).
thf(2816,plain,
! [SV1033: $i,SV579: $i,SV67: $i] :
( ( ! [SY4027: $i] :
( ~ ( class_Orderings_Olinorder @ SV67 )
| ( c_lessequals @ SV579 @ ( c_Orderings_Oord__class_Omax @ SV1033 @ SY4027 @ SV67 ) @ SV67 )
| ~ ( c_lessequals @ SV579 @ SV1033 @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2315]) ).
thf(2817,plain,
! [SV1034: $i,SV580: $i,SV68: $i] :
( ( ! [SY4028: $i] :
( ~ ( class_Orderings_Olinorder @ SV68 )
| ( c_lessequals @ SV580 @ ( c_Orderings_Oord__class_Omax @ SV1034 @ SY4028 @ SV68 ) @ SV68 )
| ~ ( c_lessequals @ SV580 @ SY4028 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2316]) ).
thf(2818,plain,
! [SV1035: $i,SV581: $i,SV69: $i] :
( ( ! [SY4029: $i] :
( ~ ( class_Orderings_Olinorder @ SV69 )
| ( c_lessequals @ SV581 @ SV1035 @ SV69 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV581 @ SY4029 @ SV69 ) @ SV1035 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2317]) ).
thf(2819,plain,
! [SV1036: $i,SV582: $i,SV70: $i] :
( ( ! [SY4030: $i] :
( ~ ( class_Orderings_Olinorder @ SV70 )
| ( c_lessequals @ SV582 @ SV1036 @ SV70 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SY4030 @ SV582 @ SV70 ) @ SV1036 @ SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2318]) ).
thf(2820,plain,
! [SV583: $i,SV71: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV71 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV583 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV71 )
= SV583 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2319]) ).
thf(2821,plain,
! [SV584: $i,SV72: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV72 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV584 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV72 )
= SV584 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2320]) ).
thf(2822,plain,
! [SV1037: $i,SV585: $i,SV73: $i] :
( ( ! [SY4031: $i] :
( ~ ( class_Orderings_Olinorder @ SV73 )
| ( c_lessequals @ SV585 @ SV1037 @ SV73 )
| ( c_lessequals @ SV585 @ SY4031 @ SV73 )
| ~ ( c_lessequals @ SV585 @ ( c_Orderings_Oord__class_Omax @ SY4031 @ SV1037 @ SV73 ) @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2321]) ).
thf(2823,plain,
! [SV1038: $i,SV586: $i,SV74: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV74 )
| ( c_lessequals @ SV586 @ ( c_Orderings_Oord__class_Omax @ SV1038 @ SV586 @ SV74 ) @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2322]) ).
thf(2824,plain,
! [SV1039: $i,SV587: $i,SV75: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV75 )
| ( c_lessequals @ SV587 @ ( c_Orderings_Oord__class_Omax @ SV587 @ SV1039 @ SV75 ) @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2323]) ).
thf(2825,plain,
! [SV1040: $i,SV588: $i,SV76: $i] :
( ( ! [SY4032: $i] :
( ~ ( class_Orderings_Olinorder @ SV76 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV588 @ SV1040 @ SV76 ) @ SY4032 @ SV76 )
| ~ ( c_lessequals @ SV1040 @ SY4032 @ SV76 )
| ~ ( c_lessequals @ SV588 @ SY4032 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2324]) ).
thf(2826,plain,
! [SV1041: $i,SV589: $i,SV77: $i] :
( ( ! [SY4033: $i] :
( ~ ( class_Orderings_Olinorder @ SV77 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV589 @ SV1041 @ SV77 ) @ SY4033 @ SV77 )
| ~ ( c_lessequals @ SV1041 @ SY4033 @ SV77 )
| ~ ( c_lessequals @ SV589 @ SY4033 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2325]) ).
thf(2827,plain,
! [SV1042: $i,SV590: $i,SV78: $i] :
( ( ! [SY4034: $i] :
( ~ ( class_Orderings_Olinorder @ SV78 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV590 @ SV1042 @ SV78 ) @ SY4034 @ SV78 )
| ~ ( c_lessequals @ SV1042 @ SY4034 @ SV78 )
| ~ ( c_lessequals @ SV590 @ SY4034 @ SV78 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2326]) ).
thf(2828,plain,
! [SV1043: $i,SV591: $i,SV79: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV79 )
| ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV79 ) @ ( c_Power_Opower__class_Opower @ SV591 @ SV1043 @ SV79 ) @ SV79 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV79 ) @ SV591 @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2327]) ).
thf(2829,plain,
! [SV1044: $i,SV592: $i,SV80: $i] :
( ( ! [SY4035: $i,SY4036: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV80 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SV592 ) @ SV1044 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SY4035 ) @ SY4036 ) @ SV80 )
| ~ ( c_lessequals @ SV1044 @ SY4036 @ SV80 )
| ~ ( c_lessequals @ SV592 @ SY4035 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2328]) ).
thf(2830,plain,
! [SV1045: $i,SV593: $i,SV81: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV81 )
| ( ( c_Orderings_Oord__class_Omax @ SV593 @ SV1045 @ SV81 )
= SV1045 )
| ~ ( c_lessequals @ SV593 @ SV1045 @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2329]) ).
thf(2831,plain,
! [SV1046: $i,SV594: $i,SV82: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV82 )
| ( ( c_Orderings_Oord__class_Omax @ SV594 @ SV1046 @ SV82 )
= SV594 )
| ~ ( c_lessequals @ SV1046 @ SV594 @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2330]) ).
thf(2832,plain,
! [SV595: $i,SV83: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__mult @ SV83 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV83 ) @ SV595 @ SV83 )
= ( c_HOL_Oone__class_Oone @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2331]) ).
thf(2833,plain,
! [SV1047: $i,SV596: $i,SV84: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV84 )
| ( c_HOL_Oord__class_Oless @ SV596 @ SV1047 @ SV84 )
| ( c_lessequals @ SV1047 @ SV596 @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2332]) ).
thf(2834,plain,
! [SV597: $i,SV85: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV85 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV597 @ SV597 @ SV85 )
| ~ ( c_HOL_Oord__class_Oless @ SV597 @ SV597 @ SV85 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2333]) ).
thf(2835,plain,
! [SV598: $i,SV86: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV86 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV598 @ SV598 @ SV86 )
| ( c_lessequals @ SV598 @ SV598 @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2334]) ).
thf(2836,plain,
! [SV1048: $i,SV599: $i,SV87: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV87 )
| ~ ( c_HOL_Oord__class_Oless @ SV599 @ SV1048 @ SV87 )
| ~ ( c_lessequals @ SV1048 @ SV599 @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2335]) ).
thf(2837,plain,
! [SV1049: $i,SV600: $i,SV88: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV88 )
| ( c_lessequals @ SV600 @ SV1049 @ SV88 )
| ( c_HOL_Oord__class_Oless @ SV1049 @ SV600 @ SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2336]) ).
thf(2838,plain,
! [SV1050: $i,SV601: $i,SV89: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV89 )
| ~ ( c_lessequals @ SV601 @ SV1050 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV1050 @ SV601 @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2337]) ).
thf(2839,plain,
! [SV1051: $i,SV602: $i,SV90: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV90 )
| ( c_HOL_Oord__class_Oless @ SV602 @ SV1051 @ SV90 )
| ( c_lessequals @ SV1051 @ SV602 @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2338]) ).
thf(2840,plain,
! [SV1052: $i,SV603: $i,SV91: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV91 )
| ~ ( c_lessequals @ SV603 @ SV1052 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV1052 @ SV603 @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2339]) ).
thf(2841,plain,
! [SV92: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV92 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV92 )
= ( c_HOL_Oone__class_Oone @ SV92 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2340]) ).
thf(2842,plain,
! [SV1053: $i,SV604: $i,SV93: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV93 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV604 ) @ SV1053 ) @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 )
| ~ ( c_lessequals @ SV1053 @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ SV604 @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2341]) ).
thf(2843,plain,
! [SV1054: $i,SV605: $i,SV94: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV94 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV605 ) @ SV1054 ) @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 )
| ~ ( c_HOL_Oord__class_Oless @ SV1054 @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 )
| ~ ( c_lessequals @ SV605 @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2342]) ).
thf(2844,plain,
! [SV1055: $i,SV606: $i,SV95: $i] :
( ( ! [SY4037: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV95 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV95 )
| ( c_HOL_Oord__class_Oless @ SV606 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV1055 ) @ SY4037 ) @ SV95 )
| ~ ( c_lessequals @ SV606 @ SY4037 @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV1055 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(2845,plain,
! [SV1056: $i,SV607: $i,SV96: $i] :
( ( ! [SY4038: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV96 )
| ( c_HOL_Oord__class_Oless @ SV607 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SV1056 ) @ SY4038 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ SV607 @ SY4038 @ SV96 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV1056 @ SV96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2344]) ).
thf(2846,plain,
! [SV1057: $i,SV608: $i,SV97: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV97 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV608 ) @ SV1057 ) @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV1057 @ SV97 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV608 @ SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2345]) ).
thf(2847,plain,
! [SV1058: $i,SV609: $i,SV98: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV98 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV98 ) @ SV609 ) @ SV1058 ) @ SV98 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ SV1058 @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ SV609 @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2346]) ).
thf(2848,plain,
! [SV99: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV99 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV99 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV99 ) @ ( c_HOL_Oone__class_Oone @ SV99 ) ) @ ( c_HOL_Oone__class_Oone @ SV99 ) ) @ SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2347]) ).
thf(2849,plain,
! [SV1059: $i,SV610: $i,SV100: $i] :
( ( ! [SY4039: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV100 )
| ( c_HOL_Oord__class_Oless @ SV610 @ SV1059 @ SV100 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV100 ) @ SV1059 @ SV100 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV610 @ SY4039 @ SV100 ) @ ( c_Power_Opower__class_Opower @ SV1059 @ SY4039 @ SV100 ) @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2348]) ).
thf(2850,plain,
! [SV101: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV101 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV101 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV101 )
= ( c_HOL_Oone__class_Oone @ SV101 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2349]) ).
thf(2851,plain,
! [SV1060: $i,SV611: $i,SV102: $i] :
( ( ! [SY4040: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV102 )
| ( c_HOL_Oord__class_Oless @ SV611 @ SV1060 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY4040 @ SV611 @ SV102 ) @ ( c_Power_Opower__class_Opower @ SY4040 @ SV1060 @ SV102 ) @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV102 ) @ SY4040 @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2350]) ).
thf(2852,plain,
! [SV1061: $i,SV612: $i,SV103: $i] :
( ( ! [SY4041: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV103 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV612 @ SV1061 @ SV103 ) @ ( c_Power_Opower__class_Opower @ SV612 @ SY4041 @ SV103 ) @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV103 ) @ SV612 @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ SV1061 @ SY4041 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2351]) ).
thf(2853,plain,
! [SV1062: $i,SV613: $i,SV104: $i] :
( ( ! [SY4042: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV104 )
| ( c_HOL_Oord__class_Oless @ SV613 @ SV1062 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SY4042 @ SV613 @ SV104 ) @ ( c_Power_Opower__class_Opower @ SY4042 @ SV1062 @ SV104 ) @ SV104 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV104 ) @ SY4042 @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2352]) ).
thf(2854,plain,
! [SV1063: $i,SV614: $i,SV105: $i] :
( ( ! [SY4043: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV105 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV614 @ SV1063 @ SV105 ) @ ( c_Power_Opower__class_Opower @ SV614 @ SY4043 @ SV105 ) @ SV105 )
| ~ ( c_HOL_Oord__class_Oless @ SV1063 @ SY4043 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV105 ) @ SV614 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2353]) ).
thf(2855,plain,
! [SV1064: $i,SV616: $i,SV107: $i] :
( ( ( c_Lambda_Oliftn @ SV107 @ ( c_Lambda_OdB_OAbs @ SV616 ) @ SV1064 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Oliftn @ SV107 @ SV616 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1064 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2355]) ).
thf(2856,plain,
! [SV1065: $i,SV617: $i,SV108: $i] :
( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OAbs @ SV108 ) @ SV617 @ SV1065 )
= ( c_Lambda_OdB_OAbs @ ( c_Lambda_Osubstn @ SV108 @ SV617 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1065 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2356]) ).
thf(2857,plain,
! [SV1066: $i,SV618: $i,SV109: $i] :
( ( ! [SY4044: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV109 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV618 @ SV1066 @ SV109 ) @ ( c_Power_Opower__class_Opower @ SY4044 @ SV1066 @ SV109 ) @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1066 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV618 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SV618 @ SY4044 @ SV109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2357]) ).
thf(2858,plain,
! [SV1067: $i,SV619: $i,SV110: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OAbs @ SV110 ) ) @ SV619 ) @ SV1067 )
= ( c_Lambda_OdB_OAbs @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV110 ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV619 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1067 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2358]) ).
thf(2859,plain,
! [SV1068: $i,SV620: $i,SV111: $i] :
( ( ! [SY4045: $i,SY4046: $i] :
( ( c_Type_Otypings @ ( c_Type_Oshift @ SV111 @ SV620 @ SV1068 @ tc_Type_Otype ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ SV620 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY4045 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY4046 )
| ~ ( c_Type_Otypings @ SV111 @ SY4045 @ SY4046 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2359]) ).
thf(2860,plain,
! [SV1069: $i,SV621: $i,SV112: $i] :
( ( ! [SY4047: $i,SY4048: $i,SY4049: $i] :
( ( c_Type_Otypings @ SV112 @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SV621 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV1069 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SY4047 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY4048 )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ SV112 @ SV1069 @ SY4049 @ tc_Type_Otype ) @ SY4047 @ SY4048 )
| ~ ( c_Type_Otyping @ SV112 @ SV621 @ SY4049 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2360]) ).
thf(2861,plain,
! [SV622: $i,SV113: $i] :
( ( ( hBOOL @ ( hAPP @ SV113 @ SV622 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV113 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV113 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @ SV113 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ SV113 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV113 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV113 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2361]) ).
thf(2862,plain,
! [SV623: $i,SV114: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV114 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV114 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__4 @ SV114 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV114 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV114 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV114 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ SV114 @ SV623 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2362]) ).
thf(2863,plain,
! [SV115: $i] :
( ( ( SV115
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV115 ) ) )
= $true )
| ( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV115 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV115 ) ) )
= $true )
| ( ( SV115
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV115 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV115 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV115 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2363]) ).
thf(2864,plain,
! [SV1070: $i,SV624: $i,SV116: $i] :
( ( ! [SY4050: $i,SY4051: $i] :
( ( c_List_Omap @ SV116 @ ( c_List_Olist_OCons @ SV624 @ SV1070 @ SY4050 ) @ SY4050 @ SY4051 )
= ( c_List_Olist_OCons @ ( hAPP @ SV116 @ SV624 ) @ ( c_List_Omap @ SV116 @ SV1070 @ SY4050 @ SY4051 ) @ SY4051 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2364]) ).
thf(2865,plain,
! [SV1071: $i,SV625: $i,SV117: $i] :
( ( ! [SY4052: $i,SY4053: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ SV117 @ SV625 ) @ ( c_List_Omap @ SV117 @ SV1071 @ SY4052 @ SY4053 ) @ SY4053 )
= ( c_List_Omap @ SV117 @ ( c_List_Olist_OCons @ SV625 @ SV1071 @ SY4052 ) @ SY4052 @ SY4053 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2365]) ).
thf(2866,plain,
! [SV1072: $i,SV626: $i,SV118: $i] :
( ( ! [SY4054: $i,SY4055: $i] :
( ( c_List_Omap @ SV118 @ ( c_List_Olist_OCons @ SV626 @ SV1072 @ SY4054 ) @ SY4054 @ SY4055 )
= ( c_List_Olist_OCons @ ( hAPP @ SV118 @ SV626 ) @ ( c_List_Omap @ SV118 @ SV1072 @ SY4054 @ SY4055 ) @ SY4055 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2366]) ).
thf(2867,plain,
! [SV1073: $i,SV627: $i,SV119: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV119 ) @ SV627 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1073 ) @ SV627 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV119 ) @ SV1073 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2367]) ).
thf(2868,plain,
! [SV1074: $i,SV628: $i,SV120: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV120 ) @ SV628 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV120 ) @ SV1074 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV628 ) @ SV1074 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2368]) ).
thf(2869,plain,
! [SV1075: $i,SV629: $i,SV121: $i] :
( ( ! [SY4056: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV121 @ SV629 @ SV1075 ) @ SY4056 @ SV1075 )
= ( c_List_Olist_OCons @ SV121 @ ( c_List_Oappend @ SV629 @ SY4056 @ SV1075 ) @ SV1075 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2369]) ).
thf(2870,plain,
! [SV1076: $i,SV630: $i,SV122: $i] :
( ( ! [SY4057: $i] :
( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV122 @ SV630 @ SV1076 ) @ SY4057 @ SV1076 )
= ( c_List_Olist_OCons @ SV122 @ ( c_List_Oappend @ SV630 @ SY4057 @ SV1076 ) @ SV1076 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2370]) ).
thf(2871,plain,
! [SV1077: $i,SV631: $i,SV123: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV123 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV123 ) @ SV631 ) @ SV1077 ) @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 )
| ~ ( c_HOL_Oord__class_Oless @ SV1077 @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 )
| ~ ( c_HOL_Oord__class_Oless @ SV631 @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2371]) ).
thf(2872,plain,
! [SV124: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV124 )
= $false )
| ( ( ( c_List_Olistsum @ ( c_List_Olist_ONil @ SV124 ) @ SV124 )
= ( c_HOL_Ozero__class_Ozero @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2372]) ).
thf(2873,plain,
! [SV1078: $i,SV632: $i,SV125: $i] :
( ( ! [SY4058: $i] :
( ~ ( class_Orderings_Olinorder @ SV125 )
| ( c_HOL_Oord__class_Oless @ SV632 @ SV1078 @ SV125 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SY4058 @ SV632 @ SV125 ) @ SV1078 @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2373]) ).
thf(2874,plain,
! [SV1079: $i,SV633: $i,SV126: $i] :
( ( ! [SY4059: $i] :
( ~ ( class_Orderings_Olinorder @ SV126 )
| ( c_HOL_Oord__class_Oless @ SV633 @ SV1079 @ SV126 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV633 @ SY4059 @ SV126 ) @ SV1079 @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2374]) ).
thf(2875,plain,
! [SV1080: $i,SV634: $i,SV127: $i] :
( ( ! [SY4060: $i] :
( ~ ( class_Orderings_Olinorder @ SV127 )
| ( c_HOL_Oord__class_Oless @ SV634 @ ( c_Orderings_Oord__class_Omax @ SV1080 @ SY4060 @ SV127 ) @ SV127 )
| ~ ( c_HOL_Oord__class_Oless @ SV634 @ SY4060 @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2375]) ).
thf(2876,plain,
! [SV1081: $i,SV635: $i,SV128: $i] :
( ( ! [SY4061: $i] :
( ~ ( class_Orderings_Olinorder @ SV128 )
| ( c_HOL_Oord__class_Oless @ SV635 @ ( c_Orderings_Oord__class_Omax @ SV1081 @ SY4061 @ SV128 ) @ SV128 )
| ~ ( c_HOL_Oord__class_Oless @ SV635 @ SV1081 @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2376]) ).
thf(2877,plain,
! [SV1082: $i,SV636: $i,SV129: $i] :
( ( ! [SY4062: $i] :
( ~ ( class_Orderings_Olinorder @ SV129 )
| ( c_HOL_Oord__class_Oless @ SV636 @ ( c_Orderings_Oord__class_Omax @ SV1082 @ SY4062 @ SV129 ) @ SV129 )
| ~ ( c_HOL_Oord__class_Oless @ SV636 @ SY4062 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2377]) ).
thf(2878,plain,
! [SV1083: $i,SV637: $i,SV130: $i] :
( ( ! [SY4063: $i] :
( ~ ( class_Orderings_Olinorder @ SV130 )
| ( c_HOL_Oord__class_Oless @ SV637 @ ( c_Orderings_Oord__class_Omax @ SV1083 @ SY4063 @ SV130 ) @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SV637 @ SV1083 @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2378]) ).
thf(2879,plain,
! [SV1084: $i,SV638: $i,SV131: $i] :
( ( ! [SY4064: $i,SY4065: $i,SY4066: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV638 ) @ SV1084 ) )
| ( c_ListOrder_Ostep1 @ SV131 @ SY4064 @ SY4065 @ SY4066 )
| ~ ( c_ListOrder_Ostep1 @ SV131 @ ( c_List_Oappend @ SY4064 @ ( c_List_Olist_OCons @ SV638 @ ( c_List_Olist_ONil @ SY4066 ) @ SY4066 ) @ SY4066 ) @ ( c_List_Oappend @ SY4065 @ ( c_List_Olist_OCons @ SV1084 @ ( c_List_Olist_ONil @ SY4066 ) @ SY4066 ) @ SY4066 ) @ SY4066 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2379]) ).
thf(2880,plain,
! [SV1085: $i,SV639: $i,SV132: $i] :
( ( ! [SY4067: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV132 @ SV639 @ SV639 ) @ SV639 ) @ SV1085 ) @ SY4067 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV132 @ SV639 ) @ SY4067 ) @ SV1085 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2380]) ).
thf(2881,plain,
! [SV1086: $i,SV640: $i,SV133: $i] :
( ( ! [SY4068: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV133 @ SV640 ) @ SV1086 ) @ SY4068 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV133 @ SV640 @ SV640 ) @ SV640 ) @ SY4068 ) @ SV1086 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2381]) ).
thf(2882,plain,
! [SV1087: $i,SV641: $i,SV134: $i] :
( ( ( c_List_Omap @ SV134 @ ( c_List_Olist_ONil @ SV641 ) @ SV641 @ SV1087 )
= ( c_List_Olist_ONil @ SV1087 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2382]) ).
thf(2883,plain,
! [SV1088: $i,SV642: $i,SV135: $i] :
( ( ! [SY4069: $i] :
( ( c_List_Ofoldr @ SV135 @ ( c_List_Olist_ONil @ SV642 ) @ SV1088 @ SV642 @ SY4069 )
= SV1088 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2383]) ).
thf(2884,plain,
! [SV1089: $i,SV643: $i,SV136: $i] :
( ( ! [SY4070: $i,SY4071: $i,SY4072: $i] :
( ( hAPP @ ( c_COMBC @ SV136 @ SV643 @ SV1089 @ SY4070 @ SY4071 ) @ SY4072 )
= ( hAPP @ ( hAPP @ SV136 @ SY4072 ) @ SV643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2384]) ).
thf(2885,plain,
! [SV1090: $i,SV644: $i,SV137: $i] :
( ( ! [SY4073: $i,SY4074: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV644 ) @ SV1090 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV137 @ SY4073 @ SY4074 ) @ SV1090 ) @ SV644 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2385]) ).
thf(2886,plain,
! [SV1091: $i,SV645: $i,SV138: $i] :
( ( ! [SY4075: $i,SY4076: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV138 @ SV645 @ SV1091 ) @ SY4075 ) @ SY4076 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV138 @ SY4076 ) @ SY4075 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2386]) ).
thf(2887,plain,
! [SV1092: $i,SV646: $i,SV139: $i] :
( ( ! [SY4077: $i,SY4078: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV139 @ SV646 ) @ SV1092 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV139 @ SY4077 @ SY4078 ) @ SV1092 ) @ SV646 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2387]) ).
thf(2888,plain,
! [SV1093: $i,SV647: $i,SV140: $i] :
( ( ! [SY4079: $i,SY4080: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV140 @ SV647 @ SV1093 ) @ SY4079 ) @ SY4080 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV140 @ SY4080 ) @ SY4079 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2388]) ).
thf(2889,plain,
! [SV648: $i,SV141: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV141 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV648 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV648 ) @ SV141 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2389]) ).
thf(2890,plain,
! [SV1094: $i,SV649: $i,SV142: $i] :
( ( ! [SY4081: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV142 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ SV649 ) @ SV1094 ) ) @ SY4081 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ SV649 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ SV1094 ) @ SY4081 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2390]) ).
thf(2891,plain,
! [SV1095: $i,SV650: $i,SV143: $i] :
( ( ! [SY4082: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV143 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ SV650 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ SV1095 ) @ SY4082 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ SV1095 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ SV650 ) @ SY4082 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2391]) ).
thf(2892,plain,
! [SV1096: $i,SV651: $i,SV144: $i] :
( ( ! [SY4083: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV144 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ SV651 ) @ SV1096 ) ) @ SY4083 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ SV651 ) @ SY4083 ) ) @ SV1096 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2392]) ).
thf(2893,plain,
! [SV1097: $i,SV652: $i,SV145: $i] :
( ( ! [SY4084: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV145 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV145 ) @ SV652 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV145 ) @ SV1097 ) @ SY4084 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV145 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV145 ) @ SV652 ) @ SV1097 ) ) @ SY4084 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2393]) ).
thf(2894,plain,
! [SV1098: $i,SV653: $i,SV146: $i] :
( ( ! [SY4085: $i] :
( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV146 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ SV653 ) @ SV1098 ) ) @ SY4085 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ SV653 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ SV1098 ) @ SY4085 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2394]) ).
thf(2895,plain,
! [SV1099: $i,SV654: $i,SV147: $i] :
( ( ! [SY4086: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV147 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV654 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV1099 ) @ SY4086 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV1099 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV654 ) @ SY4086 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2395]) ).
thf(2896,plain,
! [SV1100: $i,SV655: $i,SV148: $i] :
( ( ! [SY4087: $i] :
( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV148 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV655 ) @ SV1100 ) ) @ SY4087 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV655 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV1100 ) @ SY4087 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2396]) ).
thf(2897,plain,
! [SV1101: $i,SV656: $i,SV149: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV149 ) @ SV656 ) ) @ SV1101 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV149 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV656 ) @ SV1101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2397]) ).
thf(2898,plain,
! [SV1102: $i,SV657: $i,SV150: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV150 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV657 ) @ SV1102 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV657 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV150 ) @ SV1102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2398]) ).
thf(2899,plain,
! [SV1103: $i,SV658: $i,SV151: $i] :
( ( ! [SY4088: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV151 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV658 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV1103 ) @ SY4088 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV1103 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV658 ) @ SY4088 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2399]) ).
thf(2900,plain,
! [SV1104: $i,SV659: $i,SV152: $i] :
( ( ! [SY4089: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV152 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV659 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV1104 ) @ SY4089 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV659 ) @ SV1104 ) ) @ SY4089 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2400]) ).
thf(2901,plain,
! [SV1105: $i,SV660: $i,SV153: $i] :
( ( ! [SY4090: $i] :
( ~ ( class_Orderings_Oorder @ SV153 )
| ( c_HOL_Oord__class_Oless @ SV660 @ SV1105 @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SV660 @ SY4090 @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SY4090 @ SV1105 @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2401]) ).
thf(2902,plain,
! [SV1106: $i,SV661: $i,SV154: $i] :
( ( ! [SY4091: $i] :
( ~ ( class_Orderings_Opreorder @ SV154 )
| ( c_HOL_Oord__class_Oless @ SV661 @ SV1106 @ SV154 )
| ~ ( c_HOL_Oord__class_Oless @ SY4091 @ SV1106 @ SV154 )
| ~ ( c_HOL_Oord__class_Oless @ SV661 @ SY4091 @ SV154 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2402]) ).
thf(2903,plain,
! [SV1107: $i,SV662: $i,SV155: $i] :
( ( ! [SY4092: $i,SY4093: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV155 @ SV662 @ SV1107 @ SY4092 )
| ( c_ListOrder_Ostep1 @ SV155 @ ( c_List_Oappend @ SV662 @ SY4093 @ SY4092 ) @ ( c_List_Oappend @ SV1107 @ SY4093 @ SY4092 ) @ SY4092 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2403]) ).
thf(2904,plain,
! [SV1108: $i,SV663: $i,SV156: $i] :
( ( ! [SY4094: $i,SY4095: $i] :
( ( c_ListOrder_Ostep1 @ SV156 @ ( c_List_Oappend @ SV663 @ SV1108 @ SY4094 ) @ ( c_List_Oappend @ SV663 @ SY4095 @ SY4094 ) @ SY4094 )
| ~ ( c_ListOrder_Ostep1 @ SV156 @ SV1108 @ SY4095 @ SY4094 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(2905,plain,
! [SV664: $i,SV157: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV157 ) ) @ ( c_Lambda_OdB_OAbs @ SV664 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV157 ) @ SV664 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2405]) ).
thf(2906,plain,
! [SV1109: $i,SV665: $i,SV158: $i] :
( ( ! [SY4096: $i] :
( ( c_List_Olistsp @ SV158 @ SV665 @ SV1109 )
| ~ ( c_List_Olistsp @ SV158 @ ( c_List_Oappend @ SV665 @ SY4096 @ SV1109 ) @ SV1109 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2406]) ).
thf(2907,plain,
! [SV1110: $i,SV666: $i,SV159: $i] :
( ( ! [SY4097: $i] :
( ( c_List_Olistsp @ SV159 @ SV666 @ SV1110 )
| ~ ( c_List_Olistsp @ SV159 @ ( c_List_Oappend @ SY4097 @ SV666 @ SV1110 ) @ SV1110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2407]) ).
thf(2908,plain,
! [SV1111: $i,SV667: $i,SV160: $i] :
( ( ! [SY4098: $i,SY4099: $i] :
( ( c_Lambda_OdB_OdB__case @ SV160 @ SV667 @ SV1111 @ ( c_Lambda_OdB_OAbs @ SY4098 ) @ SY4099 )
= ( hAPP @ SV1111 @ SY4098 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2408]) ).
thf(2909,plain,
! [SV1112: $i,SV668: $i,SV161: $i] :
( ( ! [SY4100: $i,SY4101: $i,SY4102: $i] :
( ( SV161 = SV668 )
| ( SV1112 = SY4100 )
| ~ ( c_ListOrder_Ostep1 @ SY4101 @ ( c_List_Olist_OCons @ SV668 @ SY4100 @ SY4102 ) @ ( c_List_Olist_OCons @ SV161 @ SV1112 @ SY4102 ) @ SY4102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2409]) ).
thf(2910,plain,
! [SV1113: $i,SV669: $i,SV162: $i] :
( ( ! [SY4103: $i,SY4104: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV162 @ SV669 ) @ SV1113 ) )
| ( c_ListOrder_Ostep1 @ SV162 @ ( c_List_Olist_OCons @ SV669 @ SY4103 @ SY4104 ) @ ( c_List_Olist_OCons @ SV1113 @ SY4103 @ SY4104 ) @ SY4104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2410]) ).
thf(2911,plain,
! [SV1114: $i,SV671: $i,SV164: $i] :
( ( ! [SY4105: $i] :
( ~ ( class_Orderings_Olinorder @ SV164 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV671 @ SV1114 @ SV164 ) @ SY4105 @ SV164 )
| ~ ( c_HOL_Oord__class_Oless @ SV1114 @ SY4105 @ SV164 )
| ~ ( c_HOL_Oord__class_Oless @ SV671 @ SY4105 @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2412]) ).
thf(2912,plain,
! [SV1115: $i,SV672: $i,SV165: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV165 @ SV672 ) @ SV1115 ) @ SV1115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2413]) ).
thf(2913,plain,
! [SV1116: $i,SV673: $i,SV166: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV166 @ SV673 ) @ SV1116 ) @ SV1116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2414]) ).
thf(2914,plain,
! [SV1117: $i,SV674: $i,SV167: $i] :
( ( ! [SY4106: $i] :
( ( c_Wellfounded_Oaccp @ SV167 @ SV674 @ SV1117 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SV1117 ) @ SV674 ) @ SY4106 ) )
| ~ ( c_Wellfounded_Oaccp @ SV167 @ SY4106 @ SV1117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2415]) ).
thf(2915,plain,
! [SV1118: $i,SV675: $i,SV168: $i] :
( ( ! [SY4107: $i] :
( ( c_Wellfounded_Oaccp @ SV168 @ SV675 @ SV1118 )
| ~ ( c_Wellfounded_Oaccp @ SV168 @ SY4107 @ SV1118 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SV1118 ) @ SV675 ) @ SY4107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2416]) ).
thf(2916,plain,
! [SV1119: $i,SV676: $i,SV169: $i] :
( ( ! [SY4108: $i,SY4109: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SV676 ) @ SV1119 ) @ SY4108 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SV676 ) @ SY4109 ) @ SY4108 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SV676 ) @ SV1119 ) @ SY4109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2417]) ).
thf(2917,plain,
! [SV170: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV170 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV170 @ tc_Lambda_OdB )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2418]) ).
thf(2918,plain,
! [SV171: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV171 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2419]) ).
thf(2919,plain,
! [SV172: $i] :
( ( ( SV172
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV172 ) ) )
= $true )
| ( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV172 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV172 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV172 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2420]) ).
thf(2920,plain,
! [SV1120: $i,SV682: $i,SV178: $i] :
( ( ! [SY4110: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV178 ) @ SV682 ) @ SV1120 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV178 ) @ SY4110 ) @ SV1120 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV682 ) @ SY4110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2426]) ).
thf(2921,plain,
! [SV1121: $i,SV683: $i,SV179: $i] :
( ( ! [SY4111: $i,SY4112: $i] :
( ( c_List_Omap @ SV179 @ ( c_List_Oreplicate @ SV683 @ SV1121 @ SY4111 ) @ SY4111 @ SY4112 )
= ( c_List_Oreplicate @ SV683 @ ( hAPP @ SV179 @ SV1121 ) @ SY4112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2427]) ).
thf(2922,plain,
! [SV1122: $i,SV684: $i,SV180: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV180 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV684 ) @ SV1122 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV180 @ SV684 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2428]) ).
thf(2923,plain,
! [SV1123: $i,SV685: $i,SV181: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV181 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV685 ) @ SV1123 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV181 @ SV1123 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2429]) ).
thf(2924,plain,
! [SV1124: $i,SV686: $i,SV182: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV182 @ SV686 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV182 ) @ SV1124 ) @ SV686 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2430]) ).
thf(2925,plain,
! [SV1125: $i,SV687: $i,SV183: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV183 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV687 ) @ SV1125 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV183 @ SV687 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2431]) ).
thf(2926,plain,
! [SV1126: $i,SV688: $i,SV184: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV184 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV688 ) @ SV1126 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV184 @ SV1126 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2432]) ).
thf(2927,plain,
! [SV1127: $i,SV689: $i,SV185: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV185 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV185 ) @ SV689 ) @ SV1127 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV185 ) @ SV1127 ) @ SV689 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2433]) ).
thf(2928,plain,
! [SV1128: $i,SV690: $i,SV186: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV186 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV186 ) @ SV690 ) @ SV1128 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV186 ) @ SV1128 ) @ SV690 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2434]) ).
thf(2929,plain,
! [SV1129: $i,SV692: $i,SV188: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV188 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV188 ) @ SV692 ) @ SV1129 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV188 ) @ SV1129 ) @ SV692 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2436]) ).
thf(2930,plain,
! [SV1130: $i,SV693: $i,SV189: $i] :
( ( ! [SY4113: $i,SY4114: $i,SY4115: $i] :
( ( c_List_Ofoldr @ SV189 @ ( c_List_Oappend @ SV693 @ SV1130 @ SY4113 ) @ SY4114 @ SY4113 @ SY4115 )
= ( c_List_Ofoldr @ SV189 @ SV693 @ ( c_List_Ofoldr @ SV189 @ SV1130 @ SY4114 @ SY4113 @ SY4115 ) @ SY4113 @ SY4115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2437]) ).
thf(2931,plain,
! [SV1131: $i,SV694: $i,SV190: $i] :
( ( ! [SY4116: $i,SY4117: $i,SY4118: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV190 @ SV694 ) @ SV1131 ) )
| ( SV694 = SV1131 )
| ~ ( c_ListOrder_Ostep1 @ SV190 @ ( c_List_Oappend @ SY4116 @ ( c_List_Olist_OCons @ SV694 @ ( c_List_Olist_ONil @ SY4117 ) @ SY4117 ) @ SY4117 ) @ ( c_List_Oappend @ SY4118 @ ( c_List_Olist_OCons @ SV1131 @ ( c_List_Olist_ONil @ SY4117 ) @ SY4117 ) @ SY4117 ) @ SY4117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2438]) ).
thf(2932,plain,
! [SV1132: $i,SV695: $i,SV191: $i] :
( ( ! [SY4119: $i,SY4120: $i,SY4121: $i,SY4122: $i,SY4123: $i,SY4124: $i] :
( ( ( hAPP @ ( hAPP @ SV191 @ ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ SY4119 ) ) @ ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ SY4120 ) )
= ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SY4119 ) @ SY4120 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4121 @ SV191 @ SV695 @ SY4122 @ SY4123 @ SY4124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2439]) ).
thf(2933,plain,
! [SV1133: $i,SV696: $i,SV192: $i] :
( ( ! [SY4125: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV192 ) @ SV696 ) @ SV1133 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY4125 ) @ SV696 ) @ SV1133 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV192 ) @ SY4125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2440]) ).
thf(2934,plain,
! [SV1134: $i,SV697: $i,SV193: $i] :
( ( ! [SY4126: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV193 ) @ SV697 ) @ SV1134 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV193 ) @ SY4126 ) @ SV1134 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV697 ) @ SY4126 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2441]) ).
thf(2935,plain,
! [SV1135: $i,SV698: $i,SV194: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV194 )
| ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV194 ) @ SV698 @ SV1135 @ SV194 @ SV194 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV194 ) @ SV1135 @ SV698 @ SV194 @ SV194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2442]) ).
thf(2936,plain,
! [SV1136: $i,SV699: $i,SV195: $i] :
( ( ! [SY4127: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV195 @ SV699 ) @ SV1136 ) @ SY4127 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV195 @ SV1136 ) @ SY4127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2443]) ).
thf(2937,plain,
! [SV1137: $i,SV700: $i,SV196: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV196 @ ( c_List_Olist_ONil @ SV700 ) @ SV1137 @ SV700 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2444]) ).
thf(2938,plain,
! [SV1138: $i,SV701: $i,SV197: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV197 @ SV701 @ ( c_List_Olist_ONil @ SV1138 ) @ SV1138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2445]) ).
thf(2939,plain,
! [SV702: $i,SV198: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV198 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ SV702 ) @ SV702 ) @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
| ~ ( c_HOL_Oord__class_Oless @ SV702 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2446]) ).
thf(2940,plain,
! [SV703: $i,SV199: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV199 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV703 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV199 ) @ SV703 ) @ SV703 ) @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2447]) ).
thf(2941,plain,
! [SV1139: $i,SV704: $i,SV200: $i] :
( ( ! [SY4128: $i] :
( ( c_List_Olist_OCons @ SV200 @ ( c_List_Oappend @ SV704 @ SV1139 @ SY4128 ) @ SY4128 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV200 @ SV704 @ SY4128 ) @ SV1139 @ SY4128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2448]) ).
thf(2942,plain,
! [SV1140: $i,SV705: $i,SV201: $i] :
( ( ! [SY4129: $i] :
( ( c_List_Olist_OCons @ SV201 @ ( c_List_Oappend @ SV705 @ SV1140 @ SY4129 ) @ SY4129 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV201 @ SV705 @ SY4129 ) @ SV1140 @ SY4129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2449]) ).
thf(2943,plain,
! [SV1141: $i,SV706: $i,SV202: $i] :
( ( ! [SY4130: $i,SY4131: $i,SY4132: $i,SY4133: $i,SY4134: $i,SY4135: $i] :
( ( ( hAPP @ ( hAPP @ SV202 @ ( hAPP @ ( hAPP @ SV706 @ SV1141 ) @ SY4130 ) ) @ SY4131 )
= ( hAPP @ ( hAPP @ SV706 @ ( hAPP @ ( hAPP @ SV202 @ SV1141 ) @ SY4131 ) ) @ ( hAPP @ ( hAPP @ SV202 @ SY4130 ) @ SY4131 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4132 @ SV706 @ SV202 @ SY4133 @ SY4134 @ SY4135 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2450]) ).
thf(2944,plain,
! [SV1142: $i,SV707: $i,SV203: $i] :
( ( ! [SY4136: $i,SY4137: $i,SY4138: $i,SY4139: $i,SY4140: $i,SY4141: $i] :
( ( ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ ( hAPP @ ( hAPP @ SV1142 @ SY4136 ) @ SY4137 ) )
= ( hAPP @ ( hAPP @ SV1142 @ ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ SY4136 ) ) @ ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ SY4137 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1142 @ SV203 @ SY4138 @ SY4139 @ SY4140 @ SY4141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2451]) ).
thf(2945,plain,
! [SV1143: $i,SV708: $i,SV204: $i] :
( ( ! [SY4142: $i,SY4143: $i,SY4144: $i,SY4145: $i,SY4146: $i] :
( ( ( hAPP @ ( hAPP @ SV204 @ SV708 ) @ SV1143 )
= ( hAPP @ ( hAPP @ SV204 @ SV1143 ) @ SV708 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4142 @ SV204 @ SY4143 @ SY4144 @ SY4145 @ SY4146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2452]) ).
thf(2946,plain,
! [SV1144: $i,SV709: $i,SV205: $i] :
( ( ! [SY4147: $i,SY4148: $i,SY4149: $i,SY4150: $i,SY4151: $i,SY4152: $i] :
( ( ( hAPP @ ( hAPP @ SV205 @ SV709 ) @ ( hAPP @ ( hAPP @ SV205 @ SV1144 ) @ SY4147 ) )
= ( hAPP @ ( hAPP @ SV205 @ ( hAPP @ ( hAPP @ SV205 @ SV709 ) @ SV1144 ) ) @ SY4147 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4148 @ SV205 @ SY4149 @ SY4150 @ SY4151 @ SY4152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2453]) ).
thf(2947,plain,
! [SV1145: $i,SV710: $i,SV206: $i] :
( ( ! [SY4153: $i,SY4154: $i,SY4155: $i,SY4156: $i] :
( ( ( hAPP @ ( hAPP @ SV206 @ SV710 ) @ SV1145 )
= SV1145 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4153 @ SV206 @ SY4154 @ SY4155 @ SV710 @ SY4156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2454]) ).
thf(2948,plain,
! [SV1146: $i,SV711: $i,SV207: $i] :
( ( ! [SY4157: $i,SY4158: $i,SY4159: $i,SY4160: $i] :
( ( ( hAPP @ ( hAPP @ SV207 @ SV711 ) @ SV1146 )
= SV711 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4157 @ SV207 @ SY4158 @ SV711 @ SY4159 @ SY4160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2455]) ).
thf(2949,plain,
! [SV1147: $i,SV712: $i,SV208: $i] :
( ( ! [SY4161: $i,SY4162: $i,SY4163: $i,SY4164: $i,SY4165: $i] :
( ( ( hAPP @ ( hAPP @ SV208 @ SV712 ) @ SV1147 )
= ( hAPP @ ( hAPP @ SV208 @ SV1147 ) @ SV712 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV208 @ SY4161 @ SY4162 @ SY4163 @ SY4164 @ SY4165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2456]) ).
thf(2950,plain,
! [SV1148: $i,SV713: $i,SV209: $i] :
( ( ! [SY4166: $i,SY4167: $i,SY4168: $i,SY4169: $i,SY4170: $i,SY4171: $i] :
( ( ( hAPP @ ( hAPP @ SV209 @ SV713 ) @ ( hAPP @ ( hAPP @ SV209 @ SV1148 ) @ SY4166 ) )
= ( hAPP @ ( hAPP @ SV209 @ ( hAPP @ ( hAPP @ SV209 @ SV713 ) @ SV1148 ) ) @ SY4166 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV209 @ SY4167 @ SY4168 @ SY4169 @ SY4170 @ SY4171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2457]) ).
thf(2951,plain,
! [SV1149: $i,SV714: $i,SV210: $i] :
( ( ! [SY4172: $i,SY4173: $i,SY4174: $i,SY4175: $i] :
( ( ( hAPP @ ( hAPP @ SV210 @ SV714 ) @ SV1149 )
= SV1149 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV210 @ SY4172 @ SY4173 @ SV714 @ SY4174 @ SY4175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2458]) ).
thf(2952,plain,
! [SV1150: $i,SV715: $i,SV211: $i] :
( ( ! [SY4176: $i,SY4177: $i,SY4178: $i,SY4179: $i,SY4180: $i,SY4181: $i] :
( ( ( hAPP @ ( hAPP @ SV211 @ SV715 ) @ ( hAPP @ ( hAPP @ SV211 @ SV1150 ) @ SY4176 ) )
= ( hAPP @ ( hAPP @ SV211 @ ( hAPP @ ( hAPP @ SV211 @ SV715 ) @ SV1150 ) ) @ SY4176 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV211 @ SY4177 @ SY4178 @ SY4179 @ SY4180 @ SY4181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2459]) ).
thf(2953,plain,
! [SV1151: $i,SV716: $i,SV212: $i] :
( ( ! [SY4182: $i,SY4183: $i,SY4184: $i,SY4185: $i,SY4186: $i] :
( ( ( hAPP @ ( hAPP @ SV212 @ SV716 ) @ SV1151 )
= ( hAPP @ ( hAPP @ SV212 @ SV1151 ) @ SV716 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV212 @ SY4182 @ SY4183 @ SY4184 @ SY4185 @ SY4186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2460]) ).
thf(2954,plain,
! [SV1152: $i,SV717: $i,SV213: $i] :
( ( ! [SY4187: $i,SY4188: $i,SY4189: $i,SY4190: $i,SY4191: $i,SY4192: $i] :
( ( ( hAPP @ ( hAPP @ SV213 @ ( hAPP @ ( hAPP @ SV213 @ SV717 ) @ SV1152 ) ) @ SY4187 )
= ( hAPP @ ( hAPP @ SV213 @ ( hAPP @ ( hAPP @ SV213 @ SV717 ) @ SY4187 ) ) @ SV1152 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV213 @ SY4188 @ SY4189 @ SY4190 @ SY4191 @ SY4192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2461]) ).
thf(2955,plain,
! [SV1153: $i,SV718: $i,SV214: $i] :
( ( ! [SY4193: $i,SY4194: $i,SY4195: $i,SY4196: $i,SY4197: $i,SY4198: $i] :
( ( ( hAPP @ ( hAPP @ SV214 @ SV718 ) @ ( hAPP @ ( hAPP @ SV214 @ SV1153 ) @ SY4193 ) )
= ( hAPP @ ( hAPP @ SV214 @ SV1153 ) @ ( hAPP @ ( hAPP @ SV214 @ SV718 ) @ SY4193 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV214 @ SY4194 @ SY4195 @ SY4196 @ SY4197 @ SY4198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2462]) ).
thf(2956,plain,
! [SV1154: $i,SV719: $i,SV215: $i] :
( ( ! [SY4199: $i,SY4200: $i,SY4201: $i,SY4202: $i,SY4203: $i,SY4204: $i] :
( ( ( hAPP @ ( hAPP @ SV215 @ ( hAPP @ ( hAPP @ SV215 @ SV719 ) @ SV1154 ) ) @ SY4199 )
= ( hAPP @ ( hAPP @ SV215 @ SV719 ) @ ( hAPP @ ( hAPP @ SV215 @ SV1154 ) @ SY4199 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV215 @ SY4200 @ SY4201 @ SY4202 @ SY4203 @ SY4204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2463]) ).
thf(2957,plain,
! [SV1155: $i,SV720: $i,SV216: $i] :
( ( ! [SY4205: $i,SY4206: $i,SY4207: $i,SY4208: $i,SY4209: $i,SY4210: $i,SY4211: $i] :
( ( ( hAPP @ ( hAPP @ SV216 @ ( hAPP @ ( hAPP @ SV216 @ SV720 ) @ SV1155 ) ) @ ( hAPP @ ( hAPP @ SV216 @ SY4205 ) @ SY4206 ) )
= ( hAPP @ ( hAPP @ SV216 @ ( hAPP @ ( hAPP @ SV216 @ SV720 ) @ SY4205 ) ) @ ( hAPP @ ( hAPP @ SV216 @ SV1155 ) @ SY4206 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV216 @ SY4207 @ SY4208 @ SY4209 @ SY4210 @ SY4211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2464]) ).
thf(2958,plain,
! [SV1156: $i,SV721: $i,SV217: $i] :
( ( ! [SY4212: $i,SY4213: $i,SY4214: $i,SY4215: $i,SY4216: $i,SY4217: $i] :
( ( ( hAPP @ ( hAPP @ SV217 @ SV721 ) @ ( hAPP @ ( hAPP @ SV217 @ SV1156 ) @ SY4212 ) )
= ( hAPP @ ( hAPP @ SV217 @ SV1156 ) @ ( hAPP @ ( hAPP @ SV217 @ SV721 ) @ SY4212 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4213 @ SV217 @ SY4214 @ SY4215 @ SY4216 @ SY4217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2465]) ).
thf(2959,plain,
! [SV1157: $i,SV722: $i,SV218: $i] :
( ( ! [SY4218: $i,SY4219: $i,SY4220: $i,SY4221: $i,SY4222: $i,SY4223: $i] :
( ( ( hAPP @ ( hAPP @ SV218 @ SV722 ) @ ( hAPP @ ( hAPP @ SV218 @ SV1157 ) @ SY4218 ) )
= ( hAPP @ ( hAPP @ SV218 @ ( hAPP @ ( hAPP @ SV218 @ SV722 ) @ SV1157 ) ) @ SY4218 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4219 @ SV218 @ SY4220 @ SY4221 @ SY4222 @ SY4223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2466]) ).
thf(2960,plain,
! [SV1158: $i,SV723: $i,SV219: $i] :
( ( ! [SY4224: $i,SY4225: $i,SY4226: $i,SY4227: $i,SY4228: $i,SY4229: $i] :
( ( ( hAPP @ ( hAPP @ SV219 @ ( hAPP @ ( hAPP @ SV219 @ SV723 ) @ SV1158 ) ) @ SY4224 )
= ( hAPP @ ( hAPP @ SV219 @ SV723 ) @ ( hAPP @ ( hAPP @ SV219 @ SV1158 ) @ SY4224 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4225 @ SV219 @ SY4226 @ SY4227 @ SY4228 @ SY4229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2467]) ).
thf(2961,plain,
! [SV1159: $i,SV724: $i,SV220: $i] :
( ( ! [SY4230: $i,SY4231: $i,SY4232: $i,SY4233: $i,SY4234: $i,SY4235: $i] :
( ( ( hAPP @ ( hAPP @ SV220 @ ( hAPP @ ( hAPP @ SV220 @ SV724 ) @ SV1159 ) ) @ SY4230 )
= ( hAPP @ ( hAPP @ SV220 @ ( hAPP @ ( hAPP @ SV220 @ SV724 ) @ SY4230 ) ) @ SV1159 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4231 @ SV220 @ SY4232 @ SY4233 @ SY4234 @ SY4235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2468]) ).
thf(2962,plain,
! [SV1160: $i,SV725: $i,SV221: $i] :
( ( ! [SY4236: $i,SY4237: $i,SY4238: $i,SY4239: $i,SY4240: $i,SY4241: $i,SY4242: $i] :
( ( ( hAPP @ ( hAPP @ SV221 @ ( hAPP @ ( hAPP @ SV221 @ SV725 ) @ SV1160 ) ) @ ( hAPP @ ( hAPP @ SV221 @ SY4236 ) @ SY4237 ) )
= ( hAPP @ ( hAPP @ SV221 @ SY4236 ) @ ( hAPP @ ( hAPP @ SV221 @ ( hAPP @ ( hAPP @ SV221 @ SV725 ) @ SV1160 ) ) @ SY4237 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4238 @ SV221 @ SY4239 @ SY4240 @ SY4241 @ SY4242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2469]) ).
thf(2963,plain,
! [SV1161: $i,SV726: $i,SV222: $i] :
( ( ! [SY4243: $i,SY4244: $i,SY4245: $i,SY4246: $i,SY4247: $i,SY4248: $i,SY4249: $i] :
( ( ( hAPP @ ( hAPP @ SV222 @ ( hAPP @ ( hAPP @ SV222 @ SV726 ) @ SV1161 ) ) @ ( hAPP @ ( hAPP @ SV222 @ SY4243 ) @ SY4244 ) )
= ( hAPP @ ( hAPP @ SV222 @ SV726 ) @ ( hAPP @ ( hAPP @ SV222 @ SV1161 ) @ ( hAPP @ ( hAPP @ SV222 @ SY4243 ) @ SY4244 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4245 @ SV222 @ SY4246 @ SY4247 @ SY4248 @ SY4249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2470]) ).
thf(2964,plain,
! [SV1162: $i,SV727: $i,SV223: $i] :
( ( ! [SY4250: $i,SY4251: $i,SY4252: $i,SY4253: $i,SY4254: $i,SY4255: $i,SY4256: $i] :
( ( ( hAPP @ ( hAPP @ SV223 @ ( hAPP @ ( hAPP @ SV223 @ SV727 ) @ SV1162 ) ) @ ( hAPP @ ( hAPP @ SV223 @ SY4250 ) @ SY4251 ) )
= ( hAPP @ ( hAPP @ SV223 @ ( hAPP @ ( hAPP @ SV223 @ SV727 ) @ SY4250 ) ) @ ( hAPP @ ( hAPP @ SV223 @ SV1162 ) @ SY4251 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4252 @ SV223 @ SY4253 @ SY4254 @ SY4255 @ SY4256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2471]) ).
thf(2965,plain,
! [SV1163: $i,SV728: $i,SV224: $i] :
( ( ! [SY4257: $i,SY4258: $i,SY4259: $i,SY4260: $i] :
( ( ( hAPP @ ( hAPP @ SV224 @ SV728 ) @ SV1163 )
= SV728 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4257 @ SV224 @ SY4258 @ SY4259 @ SV1163 @ SY4260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2472]) ).
thf(2966,plain,
! [SV1164: $i,SV729: $i,SV225: $i] :
( ( ! [SY4261: $i,SY4262: $i,SY4263: $i,SY4264: $i] :
( ( ( hAPP @ ( hAPP @ SV225 @ SV729 ) @ SV1164 )
= SV1164 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4261 @ SV225 @ SY4262 @ SY4263 @ SV729 @ SY4264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2473]) ).
thf(2967,plain,
! [SV1165: $i,SV730: $i,SV226: $i] :
( ( ! [SY4265: $i,SY4266: $i,SY4267: $i,SY4268: $i] :
( ( ( hAPP @ ( hAPP @ SV226 @ SV730 ) @ SV1165 )
= SV1165 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4265 @ SV226 @ SY4266 @ SV1165 @ SY4267 @ SY4268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2474]) ).
thf(2968,plain,
! [SV1166: $i,SV731: $i,SV227: $i] :
( ( ! [SY4269: $i,SY4270: $i,SY4271: $i,SY4272: $i] :
( ( ( hAPP @ ( hAPP @ SV227 @ SV731 ) @ SV1166 )
= SV731 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4269 @ SV227 @ SY4270 @ SV731 @ SY4271 @ SY4272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2475]) ).
thf(2969,plain,
! [SV1167: $i,SV732: $i,SV228: $i] :
( ( ! [SY4273: $i,SY4274: $i,SY4275: $i,SY4276: $i,SY4277: $i,SY4278: $i] :
( ( ( hAPP @ ( hAPP @ SV228 @ ( hAPP @ ( hAPP @ SV732 @ SV1167 ) @ SY4273 ) ) @ SY4274 )
= ( hAPP @ ( hAPP @ SV732 @ ( hAPP @ ( hAPP @ SV228 @ SV1167 ) @ SY4274 ) ) @ ( hAPP @ ( hAPP @ SV228 @ SY4273 ) @ SY4274 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV732 @ SV228 @ SY4275 @ SY4276 @ SY4277 @ SY4278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2476]) ).
thf(2970,plain,
! [SV1168: $i,SV733: $i,SV229: $i] :
( ( ! [SY4279: $i,SY4280: $i,SY4281: $i,SY4282: $i,SY4283: $i] :
( ( ( hAPP @ ( hAPP @ SV229 @ SV733 ) @ SV1168 )
= ( hAPP @ ( hAPP @ SV229 @ SV1168 ) @ SV733 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4279 @ SV229 @ SY4280 @ SY4281 @ SY4282 @ SY4283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2477]) ).
thf(2971,plain,
! [SV1169: $i,SV734: $i,SV230: $i] :
( ( ! [SY4284: $i,SY4285: $i,SY4286: $i,SY4287: $i] :
( ( ( hAPP @ ( hAPP @ SV230 @ SV734 ) @ SV1169 )
= SV734 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV230 @ SY4284 @ SY4285 @ SV1169 @ SY4286 @ SY4287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2478]) ).
thf(2972,plain,
! [SV1170: $i,SV735: $i,SV231: $i] :
( ( ! [SY4288: $i,SY4289: $i,SY4290: $i,SY4291: $i] :
( ( ( hAPP @ ( hAPP @ SV231 @ SV735 ) @ SV1170 )
= SV1170 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV231 @ SY4288 @ SY4289 @ SV735 @ SY4290 @ SY4291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2479]) ).
thf(2973,plain,
! [SV1171: $i,SV736: $i,SV232: $i] :
( ( ! [SY4292: $i,SY4293: $i,SY4294: $i,SY4295: $i] :
( ( ( hAPP @ ( hAPP @ SV232 @ SV736 ) @ SV736 )
= ( hAPP @ ( hAPP @ SV1171 @ ( hAPP @ ( hAPP @ SV232 @ SY4292 ) @ SY4292 ) ) @ SV736 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV232 @ SV1171 @ SY4293 @ SY4294 @ SY4292 @ SY4295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2480]) ).
thf(2974,plain,
! [SV1172: $i,SV737: $i,SV233: $i] :
( ( ! [SY4296: $i,SY4297: $i,SY4298: $i,SY4299: $i,SY4300: $i] :
( ( ( hAPP @ ( hAPP @ SV233 @ SV737 ) @ ( hAPP @ ( hAPP @ SV1172 @ SY4296 ) @ SV737 ) )
= ( hAPP @ ( hAPP @ SV1172 @ ( hAPP @ ( hAPP @ SV233 @ SY4296 ) @ SY4297 ) ) @ SV737 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV233 @ SV1172 @ SY4298 @ SY4299 @ SY4297 @ SY4300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2481]) ).
thf(2975,plain,
! [SV1173: $i,SV738: $i,SV234: $i] :
( ( ! [SY4301: $i,SY4302: $i,SY4303: $i,SY4304: $i,SY4305: $i] :
( ( ( hAPP @ ( hAPP @ SV234 @ ( hAPP @ ( hAPP @ SV738 @ SV1173 ) @ SY4301 ) ) @ SY4301 )
= ( hAPP @ ( hAPP @ SV738 @ ( hAPP @ ( hAPP @ SV234 @ SV1173 ) @ SY4302 ) ) @ SY4301 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV234 @ SV738 @ SY4303 @ SY4304 @ SY4302 @ SY4305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2482]) ).
thf(2976,plain,
! [SV1174: $i,SV739: $i,SV235: $i] :
( ( ! [SY4306: $i,SY4307: $i,SY4308: $i,SY4309: $i,SY4310: $i,SY4311: $i] :
( ( ( hAPP @ ( hAPP @ SV235 @ ( hAPP @ ( hAPP @ SV739 @ SV1174 ) @ SY4306 ) ) @ ( hAPP @ ( hAPP @ SV739 @ SY4307 ) @ SY4306 ) )
= ( hAPP @ ( hAPP @ SV739 @ ( hAPP @ ( hAPP @ SV235 @ SV1174 ) @ SY4307 ) ) @ SY4306 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV235 @ SV739 @ SY4308 @ SY4309 @ SY4310 @ SY4311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2483]) ).
thf(2977,plain,
! [SV1175: $i,SV740: $i,SV236: $i] :
( ( ! [SY4312: $i,SY4313: $i,SY4314: $i] :
( ( SV236 = SV740 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV1175 @ SV740 ) @ SV236 ) )
| ~ ( c_ListOrder_Ostep1 @ SV1175 @ ( c_List_Olist_OCons @ SV740 @ SY4312 @ SY4313 ) @ ( c_List_Olist_OCons @ SV236 @ SY4314 @ SY4313 ) @ SY4313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2484]) ).
thf(2978,plain,
! [SV1176: $i,SV741: $i,SV237: $i] :
( ( ! [SY4315: $i,SY4316: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV237 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SV741 ) @ SV1176 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SY4315 ) @ SY4316 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SV741 ) @ SY4315 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SV1176 ) @ SY4316 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2485]) ).
thf(2979,plain,
! [SV1177: $i,SV742: $i,SV238: $i] :
( ( ! [SY4317: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV238 ) @ SV742 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1177 ) @ SY4317 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV742 ) @ SY4317 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV238 ) @ SV1177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2486]) ).
thf(2980,plain,
! [SV743: $i,SV239: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV239 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV743 @ SV239 ) @ ( c_HOL_Ozero__class_Ozero @ SV239 ) @ SV239 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2487]) ).
thf(2981,plain,
! [SV1178: $i,SV744: $i,SV240: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV240 )
| ( ( c_Orderings_Oord__class_Omax @ SV744 @ SV1178 @ SV240 )
= ( c_Orderings_Oord__class_Omax @ SV1178 @ SV744 @ SV240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2488]) ).
thf(2982,plain,
! [SV1179: $i,SV745: $i,SV241: $i] :
( ( ( ( c_Lambda_Oliftn @ SV241 @ ( c_Lambda_OdB_OVar @ SV745 ) @ SV1179 )
= ( c_Lambda_OdB_OVar @ SV745 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV745 @ SV1179 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2489]) ).
thf(2983,plain,
! [SV1180: $i,SV746: $i,SV242: $i] :
( ( ! [SY4318: $i] :
( ( c_Type_Otyping @ SV242 @ SV746 @ SV1180 )
| ~ ( c_Type_Otyping @ SV242 @ SY4318 @ SV1180 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SY4318 ) @ SV746 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2490]) ).
thf(2984,plain,
! [SV748: $i,SV244: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV244 ) ) @ SV748 )
= ( c_Lambda_OdB_OVar @ SV244 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV244 @ SV748 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2492]) ).
thf(2985,plain,
! [SV1181: $i,SV749: $i,SV245: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV245 ) @ SV749 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1181 ) @ SV749 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV245 ) @ SV1181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2493]) ).
thf(2986,plain,
! [SV246: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV246 ) ) )
= $true )
| ( ( ( SV246
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV246 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV246 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV246 ) ) )
= $true )
| ( ( SV246
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV246 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV246 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV246 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2494]) ).
thf(2987,plain,
! [SV750: $i,SV247: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV247 @ SV247 @ tc_nat )
= $true )
| ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV247 ) @ SV750 @ SV247 )
= ( c_Lambda_Oliftn @ SV247 @ SV750 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2495]) ).
thf(2988,plain,
! [SV1182: $i,SV751: $i,SV248: $i] :
( ( ( c_List_Olist_OCons @ SV248 @ SV751 @ SV1182 )
= ( c_List_Oappend @ ( c_List_Olist_ONil @ SV1182 ) @ ( c_List_Olist_OCons @ SV248 @ SV751 @ SV1182 ) @ SV1182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2496]) ).
thf(2989,plain,
! [SV1183: $i,SV752: $i,SV249: $i] :
( ( ! [SY4319: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV249 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV249 ) @ ( c_Orderings_Oord__class_Omax @ SV752 @ SV1183 @ SV249 ) ) @ SY4319 )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV249 ) @ SV752 ) @ SY4319 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV249 ) @ SV1183 ) @ SY4319 ) @ SV249 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2497]) ).
thf(2990,plain,
! [SV1184: $i,SV753: $i,SV250: $i] :
( ( ( c_List_Olist_ONil @ SV250 )
= ( c_List_Omap @ SV753 @ ( c_List_Olist_ONil @ SV1184 ) @ SV1184 @ SV250 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2498]) ).
thf(2991,plain,
! [SV1185: $i,SV754: $i,SV251: $i] :
( ( ! [SY4320: $i,SY4321: $i,SY4322: $i] :
( ( SV251 = SV754 )
| ( c_ListOrder_Ostep1 @ SV1185 @ SV251 @ SV754 @ SY4320 )
| ~ ( c_ListOrder_Ostep1 @ SV1185 @ ( c_List_Oappend @ SV251 @ ( c_List_Olist_OCons @ SY4321 @ ( c_List_Olist_ONil @ SY4320 ) @ SY4320 ) @ SY4320 ) @ ( c_List_Oappend @ SV754 @ ( c_List_Olist_OCons @ SY4322 @ ( c_List_Olist_ONil @ SY4320 ) @ SY4320 ) @ SY4320 ) @ SY4320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2499]) ).
thf(2992,plain,
! [SV1186: $i,SV755: $i,SV252: $i] :
( ( ! [SY4323: $i] :
( ~ ( class_Orderings_Olinorder @ SV252 )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ SV755 @ SV1186 @ SV252 ) @ SY4323 @ SV252 )
= ( c_Orderings_Oord__class_Omax @ SV755 @ ( c_Orderings_Oord__class_Omax @ SV1186 @ SY4323 @ SV252 ) @ SV252 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2500]) ).
thf(2993,plain,
! [SV1187: $i,SV756: $i,SV253: $i] :
( ( ! [SY4324: $i] :
( ~ ( class_Orderings_Olinorder @ SV253 )
| ( ( c_Orderings_Oord__class_Omax @ SV756 @ ( c_Orderings_Oord__class_Omax @ SV1187 @ SY4324 @ SV253 ) @ SV253 )
= ( c_Orderings_Oord__class_Omax @ SV1187 @ ( c_Orderings_Oord__class_Omax @ SV756 @ SY4324 @ SV253 ) @ SV253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2501]) ).
thf(2994,plain,
! [SV758: $i,SV256: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV256 ) ) @ ( c_Lambda_OdB_OAbs @ SV758 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV256 ) @ SV758 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2503]) ).
thf(2995,plain,
! [SV1188: $i,SV759: $i,SV257: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV257 )
| ( ( c_Orderings_Oord__class_Omax @ SV759 @ ( c_Orderings_Oord__class_Omax @ SV759 @ SV1188 @ SV257 ) @ SV257 )
= ( c_Orderings_Oord__class_Omax @ SV759 @ SV1188 @ SV257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2504]) ).
thf(2996,plain,
! [SV1189: $i,SV760: $i,SV258: $i] :
( ( ( c_List_Oappend @ ( c_List_Oreplicate @ SV258 @ SV760 @ SV1189 ) @ ( c_List_Olist_OCons @ SV760 @ ( c_List_Olist_ONil @ SV1189 ) @ SV1189 ) @ SV1189 )
= ( c_List_Olist_OCons @ SV760 @ ( c_List_Oreplicate @ SV258 @ SV760 @ SV1189 ) @ SV1189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2505]) ).
thf(2997,plain,
! [SV1190: $i,SV761: $i,SV259: $i] :
( ( ! [SY4325: $i] :
( ( ( hAPP @ ( hAPP @ SV259 @ SV761 ) @ SV1190 )
= SV761 )
| ~ ( c_OrderedGroup_Omonoid__add @ SV1190 @ SV259 @ SY4325 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2506]) ).
thf(2998,plain,
! [SV1191: $i,SV762: $i,SV260: $i] :
( ( ! [SY4326: $i] :
( ( ( hAPP @ ( hAPP @ SV260 @ SV762 ) @ SV1191 )
= SV1191 )
| ~ ( c_OrderedGroup_Omonoid__add @ SV762 @ SV260 @ SY4326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2507]) ).
thf(2999,plain,
! [SV763: $i,SV261: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV261 ) @ SV763 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV763 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2508]) ).
thf(3000,plain,
! [SV764: $i,SV262: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV262 ) @ SV764 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV262 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2509]) ).
thf(3001,plain,
! [SV765: $i,SV263: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV263 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV765 @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV263 ) @ SV765 ) @ SV765 ) @ SV263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2510]) ).
thf(3002,plain,
! [SV766: $i,SV264: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV264 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV264 ) @ SV766 ) @ SV766 ) @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SV766 @ SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2511]) ).
thf(3003,plain,
! [SV265: $i] :
( ( ( SV265
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV265 ) ) )
= $true )
| ( ( ( SV265
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV265 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV265 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV265 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV265 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2512]) ).
thf(3004,plain,
! [SV266: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV266 ) ) )
= $true )
| ( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV266 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV266 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV266 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV266 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV266 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2513]) ).
thf(3005,plain,
! [SV267: $i] :
( ( ( SV267
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV267 ) ) )
= $true )
| ( ( ( SV267
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV267 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV267 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV267 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV267 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV267 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV267 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2514]) ).
thf(3006,plain,
! [SV268: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV268 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV268 ) @ ( c_HOL_Ozero__class_Ozero @ SV268 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV268 ) )
= ( c_HOL_Ozero__class_Ozero @ SV268 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2515]) ).
thf(3007,plain,
! [SV767: $i,SV269: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV269 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ ( c_HOL_Ozero__class_Ozero @ SV269 ) ) @ SV767 )
= SV767 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2516]) ).
thf(3008,plain,
! [SV768: $i,SV270: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV270 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV270 ) @ ( c_HOL_Ozero__class_Ozero @ SV270 ) ) @ SV768 )
= SV768 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2517]) ).
thf(3009,plain,
! [SV769: $i,SV271: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV271 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV271 )
| ( SV769
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ SV769 ) @ ( c_HOL_Ozero__class_Ozero @ SV271 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2518]) ).
thf(3010,plain,
! [SV770: $i,SV272: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV272 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV770 ) @ ( c_HOL_Ozero__class_Ozero @ SV272 ) )
= SV770 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2519]) ).
thf(3011,plain,
! [SV771: $i,SV273: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV273 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ ( c_HOL_Ozero__class_Ozero @ SV273 ) ) @ SV771 )
= SV771 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2520]) ).
thf(3012,plain,
! [SV772: $i,SV274: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV274 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ SV772 ) @ ( c_HOL_Ozero__class_Ozero @ SV274 ) )
= SV772 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2521]) ).
thf(3013,plain,
! [SV773: $i,SV275: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV275 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ SV773 ) @ ( c_HOL_Ozero__class_Ozero @ SV275 ) )
= SV773 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2522]) ).
thf(3014,plain,
! [SV774: $i,SV276: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV276 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ ( c_HOL_Ozero__class_Ozero @ SV276 ) ) @ SV774 )
= SV774 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2523]) ).
thf(3015,plain,
! [SV776: $i,SV281: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV281 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV776 @ ( c_HOL_Ozero__class_Ozero @ SV281 ) @ SV281 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV281 ) @ SV776 ) @ SV776 ) @ ( c_HOL_Ozero__class_Ozero @ SV281 ) @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2528]) ).
thf(3016,plain,
! [SV777: $i,SV282: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV282 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV282 ) @ SV777 ) @ SV777 ) @ ( c_HOL_Ozero__class_Ozero @ SV282 ) @ SV282 )
| ~ ( c_HOL_Oord__class_Oless @ SV777 @ ( c_HOL_Ozero__class_Ozero @ SV282 ) @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2529]) ).
thf(3017,plain,
! [SV1192: $i,SV778: $i,SV283: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV283 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV283 ) @ ( c_Power_Opower__class_Opower @ SV778 @ SV1192 @ SV283 ) @ SV283 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV283 ) @ SV778 @ SV283 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2530]) ).
thf(3018,plain,
! [SV1193: $i,SV779: $i,SV284: $i] :
( ( ! [SY4327: $i] :
( ~ ( class_Orderings_Olinorder @ SV284 )
| ( c_HOL_Oord__class_Oless @ SV779 @ SV1193 @ SV284 )
| ( c_HOL_Oord__class_Oless @ SV779 @ SY4327 @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ SV779 @ ( c_Orderings_Oord__class_Omax @ SY4327 @ SV1193 @ SV284 ) @ SV284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2531]) ).
thf(3019,plain,
! [SV1194: $i,SV780: $i,SV285: $i] :
( ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV285 ) @ SV780 @ SV1194 )
= ( c_Lambda_OdB_OVar @ SV285 ) )
| ( SV285 = SV1194 )
| ( c_HOL_Oord__class_Oless @ SV1194 @ SV285 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2532]) ).
thf(3020,plain,
! [SV287: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV287 ) ) )
= $true )
| ( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV287 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV287 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2533]) ).
thf(3021,plain,
! [SV782: $i,SV291: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV291 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV782 @ SV782 @ SV291 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2537]) ).
thf(3022,plain,
! [SV783: $i,SV292: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV292 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV783 @ SV783 @ SV292 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2538]) ).
thf(3023,plain,
! [SV784: $i,SV293: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV293 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV784 @ SV784 @ SV293 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2539]) ).
thf(3024,plain,
! [SV1195: $i,SV785: $i,SV294: $i] :
( ( ( ( c_Lambda_Oliftn @ SV294 @ ( c_Lambda_OdB_OVar @ SV785 ) @ SV1195 )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV785 ) @ SV294 ) ) )
| ( c_HOL_Oord__class_Oless @ SV785 @ SV1195 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2540]) ).
thf(3025,plain,
! [SV1196: $i,SV786: $i,SV295: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV295 ) @ SV786 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1196 ) @ SV786 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV295 ) @ SV1196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2541]) ).
thf(3026,plain,
! [SV1197: $i,SV787: $i,SV296: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV296 )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV296 ) @ SV787 ) @ SV1197 ) @ SV296 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SV1197 @ SV296 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SV787 @ SV296 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2542]) ).
thf(3027,plain,
! [SV1198: $i,SV788: $i,SV297: $i] :
( ( ! [SY4328: $i,SY4329: $i,SY4330: $i] :
( ( c_ListOrder_Ostep1 @ SV297 @ SV788 @ SV1198 @ SY4328 )
| ( SV1198 = SV788 )
| ~ ( c_ListOrder_Ostep1 @ SV297 @ ( c_List_Olist_OCons @ SY4329 @ SV788 @ SY4328 ) @ ( c_List_Olist_OCons @ SY4330 @ SV1198 @ SY4328 ) @ SY4328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2543]) ).
thf(3028,plain,
! [SV1199: $i,SV789: $i,SV298: $i] :
( ( ! [SY4331: $i,SY4332: $i] :
( ( ( hAPP @ ( hAPP @ SV298 @ ( hAPP @ ( hAPP @ SV298 @ SV789 ) @ SV1199 ) ) @ SY4331 )
= ( hAPP @ ( hAPP @ SV298 @ SV789 ) @ ( hAPP @ ( hAPP @ SV298 @ SV1199 ) @ SY4331 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV298 @ SY4332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2544]) ).
thf(3029,plain,
! [SV1200: $i,SV790: $i,SV299: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV299 )
| ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SV790 @ SV1200 @ SV299 ) @ SV299 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV299 ) @ SV790 ) @ ( c_List_Olistsum @ SV1200 @ SV299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2545]) ).
thf(3030,plain,
! [SV1201: $i,SV791: $i,SV300: $i] :
( ( ! [SY4333: $i,SY4334: $i] :
( ( c_List_Omap @ SV300 @ ( c_List_Oappend @ SV791 @ SV1201 @ SY4333 ) @ SY4333 @ SY4334 )
= ( c_List_Oappend @ ( c_List_Omap @ SV300 @ SV791 @ SY4333 @ SY4334 ) @ ( c_List_Omap @ SV300 @ SV1201 @ SY4333 @ SY4334 ) @ SY4334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2546]) ).
thf(3031,plain,
! [SV301: $i] :
( ( ( SV301
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV301 ) ) )
= $true )
| ( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV301 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV301 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV301 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV301 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV301 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2547]) ).
thf(3032,plain,
! [SV1202: $i,SV792: $i,SV302: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV302 )
| ( c_HOL_Oord__class_Oless @ SV792 @ SV1202 @ SV302 )
| ( c_HOL_Oord__class_Oless @ SV1202 @ SV792 @ SV302 )
| ( SV1202 = SV792 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2548]) ).
thf(3033,plain,
! [SV1203: $i,SV793: $i,SV303: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV303 )
| ( SV793 = SV1203 )
| ( c_HOL_Oord__class_Oless @ SV1203 @ SV793 @ SV303 )
| ( c_HOL_Oord__class_Oless @ SV793 @ SV1203 @ SV303 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2549]) ).
thf(3034,plain,
! [SV794: $i,SV304: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV304 @ SV794 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV794 @ SV304 @ tc_nat )
| ( SV794 = SV304 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2550]) ).
thf(3035,plain,
! [SV1204: $i,SV795: $i,SV305: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV305 @ SV795 ) @ SV1204 ) )
| ( c_HOL_Oord__class_Oless @ SV795 @ SV1204 @ tc_nat )
| ( SV1204 = SV795 )
| ( c_HOL_Oord__class_Oless @ SV1204 @ SV795 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2551]) ).
thf(3036,plain,
! [SV796: $i,SV306: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV306 @ SV796 @ tc_nat )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV796 @ SV306 @ tc_nat )
| ( SV796 = SV306 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2552]) ).
thf(3037,plain,
! [SV1205: $i,SV797: $i,SV307: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV307 )
| ( c_HOL_Oord__class_Oless @ SV797 @ SV1205 @ SV307 )
| ( c_HOL_Oord__class_Oless @ SV1205 @ SV797 @ SV307 )
| ( SV1205 = SV797 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2553]) ).
thf(3038,plain,
! [SV1206: $i,SV798: $i,SV308: $i] :
( ( ! [SY4335: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV308 @ SV798 @ SV1206 ) @ ( c_List_Oreplicate @ SY4335 @ SV798 @ SV1206 ) @ SV1206 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SY4335 @ SV798 @ SV1206 ) @ ( c_List_Oreplicate @ SV308 @ SV798 @ SV1206 ) @ SV1206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2554]) ).
thf(3039,plain,
! [SV1207: $i,SV799: $i,SV309: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV309 )
| ( c_HOL_Oord__class_Oless @ SV799 @ SV1207 @ SV309 )
| ( SV1207 = SV799 )
| ( c_HOL_Oord__class_Oless @ SV1207 @ SV799 @ SV309 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2555]) ).
thf(3040,plain,
! [SV1208: $i,SV800: $i,SV310: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV310 )
| ( SV800 = SV1208 )
| ( c_HOL_Oord__class_Oless @ SV800 @ SV1208 @ SV310 )
| ( c_HOL_Oord__class_Oless @ SV1208 @ SV800 @ SV310 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2556]) ).
thf(3041,plain,
! [SV801: $i,SV311: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV311 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omax @ SV801 @ SV801 @ SV311 )
= SV801 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2557]) ).
thf(3042,plain,
! [SV1209: $i,SV802: $i,SV312: $i] :
( ( ! [SY4336: $i,SY4337: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV312 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV312 ) @ SV802 ) @ SV1209 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV312 ) @ SY4336 ) @ SY4337 ) @ SV312 )
| ~ ( c_HOL_Oord__class_Oless @ SV1209 @ SY4337 @ SV312 )
| ~ ( c_HOL_Oord__class_Oless @ SV802 @ SY4336 @ SV312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2558]) ).
thf(3043,plain,
! [SV1210: $i,SV803: $i,SV313: $i] :
( ( ! [SY4338: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV313 ) @ SV803 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1210 ) @ SY4338 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV803 @ SY4338 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV313 @ SV1210 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2559]) ).
thf(3044,plain,
! [SV1211: $i,SV804: $i,SV314: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV314 )
| ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV804 @ SV314 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1211 @ SV314 ) @ SV314 )
| ~ ( c_HOL_Oord__class_Oless @ SV804 @ SV1211 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2560]) ).
thf(3045,plain,
! [SV1212: $i,SV805: $i,SV315: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV315 )
| ( c_HOL_Oord__class_Oless @ SV805 @ SV1212 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV805 @ SV315 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1212 @ SV315 ) @ SV315 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2561]) ).
thf(3046,plain,
! [SV806: $i,SV316: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV316 ) )
= $true )
| ( ( ( c_List_Olistsum @ SV806 @ SV316 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV316 ) @ SV806 @ ( c_HOL_Ozero__class_Ozero @ SV316 ) @ SV316 @ SV316 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2562]) ).
thf(3047,plain,
! [SV317: $i] :
( ( ( SV317
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV317 ) ) )
= $true )
| ( ( ( SV317
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV317 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV317 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV317 ) ) )
= $true )
| ( ( SV317
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV317 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV317 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV317 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2563]) ).
thf(3048,plain,
! [SV1213: $i,SV807: $i,SV318: $i] :
( ( ! [SY4339: $i] :
( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV318 ) @ SV807 ) @ SV1213 @ SY4339 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SV318 @ SV1213 @ SY4339 ) @ ( c_List_Oreplicate @ SV807 @ SV1213 @ SY4339 ) @ SY4339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2564]) ).
thf(3049,plain,
! [SV808: $i,SV319: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV319 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV319 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV808 @ SV319 ) @ SV319 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV808 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2565]) ).
thf(3050,plain,
! [SV809: $i,SV320: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV320 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV809 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV320 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV809 @ SV320 ) @ SV320 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2566]) ).
thf(3051,plain,
! [SV1214: $i,SV810: $i,SV321: $i] :
( ( ! [SY4340: $i,SY4341: $i,SY4342: $i] :
( ( SV321 = SV810 )
| ( SV1214 = SY4340 )
| ~ ( c_ListOrder_Ostep1 @ SY4341 @ ( c_List_Oappend @ SV321 @ ( c_List_Olist_OCons @ SV1214 @ ( c_List_Olist_ONil @ SY4342 ) @ SY4342 ) @ SY4342 ) @ ( c_List_Oappend @ SV810 @ ( c_List_Olist_OCons @ SY4340 @ ( c_List_Olist_ONil @ SY4342 ) @ SY4342 ) @ SY4342 ) @ SY4342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2567]) ).
thf(3052,plain,
! [SV1215: $i,SV811: $i,SV322: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV322 @ SV811 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV1215 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV322 ) @ SV1215 ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ SV1215 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV811 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2568]) ).
thf(3053,plain,
! [SV1216: $i,SV812: $i,SV323: $i] :
( ( ! [SY4343: $i] :
( ( c_List_Olistsp @ SV323 @ ( c_List_Oappend @ SV812 @ SV1216 @ SY4343 ) @ SY4343 )
| ~ ( c_List_Olistsp @ SV323 @ SV1216 @ SY4343 )
| ~ ( c_List_Olistsp @ SV323 @ SV812 @ SY4343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2569]) ).
thf(3054,plain,
! [SV1217: $i,SV813: $i,SV324: $i] :
( ( ! [SY4344: $i,SY4345: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV324 @ SV813 @ SV1217 @ ( c_Lambda_OdB_OAbs @ SY4344 ) @ SY4345 )
= ( hAPP @ ( hAPP @ SV1217 @ SY4344 ) @ ( c_Lambda_OdB_OdB__rec @ SV324 @ SV813 @ SV1217 @ SY4344 @ SY4345 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2570]) ).
thf(3055,plain,
! [SV325: $i] :
( ( ( class_OrderedGroup_Osemigroup__add @ SV325 )
= $false )
| ( ( c_OrderedGroup_Osemigroup__add @ ( c_HOL_Oplus__class_Oplus @ SV325 ) @ SV325 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2571]) ).
thf(3056,plain,
! [SV1218: $i,SV814: $i,SV326: $i] :
( ( ! [SY4346: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV326 )
| ( c_HOL_Oord__class_Oless @ SV814 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV326 ) @ SV1218 ) @ SY4346 ) @ SV326 )
| ~ ( c_HOL_Oord__class_Oless @ SV814 @ SY4346 @ SV326 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV1218 @ SV326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2572]) ).
thf(3057,plain,
! [SV1219: $i,SV815: $i,SV327: $i] :
( ( ! [SY4347: $i,SY4348: $i,SY4349: $i] :
( ( c_List_Ofoldr @ SV327 @ ( c_List_Olist_OCons @ SV815 @ SV1219 @ SY4347 ) @ SY4348 @ SY4347 @ SY4349 )
= ( hAPP @ ( hAPP @ SV327 @ SV815 ) @ ( c_List_Ofoldr @ SV327 @ SV1219 @ SY4348 @ SY4347 @ SY4349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(3058,plain,
! [SV1220: $i,SV816: $i,SV328: $i] :
( ( ! [SY4350: $i,SY4351: $i] :
( ~ ( hBOOL @ ( hAPP @ SV328 @ ( c_Lambda_OdB_OdB__case @ SV816 @ SV1220 @ SY4350 @ ( c_Lambda_OdB_OAbs @ SY4351 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV328 @ ( hAPP @ SY4350 @ SY4351 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2574]) ).
thf(3059,plain,
! [SV1221: $i,SV817: $i,SV329: $i] :
( ( ! [SY4352: $i,SY4353: $i] :
( ~ ( hBOOL @ ( hAPP @ SV329 @ ( c_Lambda_OdB_OdB__case @ SV817 @ SV1221 @ SY4352 @ ( c_Lambda_OdB_OAbs @ SY4353 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV329 @ ( hAPP @ SY4352 @ SY4353 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2575]) ).
thf(3060,plain,
! [SV1222: $i,SV818: $i,SV330: $i] :
( ( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ SV330 @ SV818 @ SV1222 ) @ SV1222 @ SV818 )
= SV330 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2576]) ).
thf(3061,plain,
! [SV819: $i,SV331: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV331 ) @ SV819 ) @ SV331 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2577]) ).
thf(3062,plain,
! [SV820: $i,SV332: $i] :
( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV332 ) @ SV820 ) @ SV820 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2578]) ).
thf(3063,plain,
! [SV1223: $i,SV821: $i,SV333: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_ONil @ SV333 ) @ ( c_List_Olist_OCons @ SV821 @ SV1223 @ SV333 ) @ SV333 )
= ( c_List_Olist_OCons @ SV821 @ SV1223 @ SV333 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2579]) ).
thf(3064,plain,
! [SV1224: $i,SV822: $i,SV334: $i] :
( ( ! [SY4354: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV334 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV334 ) @ SV822 ) @ SV1224 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV334 ) @ SY4354 ) @ SV1224 ) @ SV334 )
| ~ ( c_HOL_Oord__class_Oless @ SV822 @ SY4354 @ SV334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2580]) ).
thf(3065,plain,
! [SV1225: $i,SV823: $i,SV335: $i] :
( ( ! [SY4355: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV335 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV335 ) @ SV823 ) @ SV1225 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV335 ) @ SY4355 ) @ SV1225 ) @ SV335 )
| ~ ( c_HOL_Oord__class_Oless @ SV823 @ SY4355 @ SV335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2581]) ).
thf(3066,plain,
! [SV1226: $i,SV824: $i,SV336: $i] :
( ( ! [SY4356: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV336 )
| ( c_HOL_Oord__class_Oless @ SV824 @ SV1226 @ SV336 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV336 ) @ SV824 ) @ SY4356 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV336 ) @ SV1226 ) @ SY4356 ) @ SV336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2582]) ).
thf(3067,plain,
! [SV1227: $i,SV825: $i,SV337: $i] :
( ( ! [SY4357: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV337 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV337 ) @ SV825 ) @ SV1227 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV337 ) @ SV825 ) @ SY4357 ) @ SV337 )
| ~ ( c_HOL_Oord__class_Oless @ SV1227 @ SY4357 @ SV337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2583]) ).
thf(3068,plain,
! [SV1228: $i,SV826: $i,SV338: $i] :
( ( ! [SY4358: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV338 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV338 ) @ SV826 ) @ SV1228 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV338 ) @ SV826 ) @ SY4358 ) @ SV338 )
| ~ ( c_HOL_Oord__class_Oless @ SV1228 @ SY4358 @ SV338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2584]) ).
thf(3069,plain,
! [SV1229: $i,SV827: $i,SV339: $i] :
( ( ! [SY4359: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV339 )
| ( c_HOL_Oord__class_Oless @ SV827 @ SV1229 @ SV339 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SY4359 ) @ SV827 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SY4359 ) @ SV1229 ) @ SV339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2585]) ).
thf(3070,plain,
! [SV1230: $i,SV828: $i,SV340: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV340 ) @ SV828 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1230 ) @ SV828 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV340 @ SV1230 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2586]) ).
thf(3071,plain,
! [SV1231: $i,SV829: $i,SV341: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV341 @ SV829 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1231 ) @ SV341 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1231 ) @ SV829 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2587]) ).
thf(3072,plain,
! [SV1232: $i,SV830: $i,SV342: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV342 ) @ SV830 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV342 ) @ SV1232 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV830 @ SV1232 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2588]) ).
thf(3073,plain,
! [SV343: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV343 ) ) )
= $true )
| ( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV343 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV343 ) ) )
= $true )
| ( ( SV343
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV343 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV343 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV343 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2589]) ).
thf(3074,plain,
! [SV1233: $i,SV831: $i,SV344: $i] :
( ( ! [SY4360: $i] :
( ( c_Type_Otyping @ SV344 @ SV831 @ SV1233 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SY4360 ) @ SV831 ) )
| ~ ( c_Type_Otyping @ SV344 @ SY4360 @ SV1233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2590]) ).
thf(3075,plain,
! [SV1234: $i,SV832: $i,SV345: $i] :
( ( ! [SY4361: $i,SY4362: $i,SY4363: $i] :
( ( c_ListOrder_Ostep1 @ SV345 @ SV832 @ SV1234 @ SY4361 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV345 @ SY4362 ) @ SY4363 ) )
| ~ ( c_ListOrder_Ostep1 @ SV345 @ ( c_List_Olist_OCons @ SY4362 @ SV832 @ SY4361 ) @ ( c_List_Olist_OCons @ SY4363 @ SV1234 @ SY4361 ) @ SY4361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2591]) ).
thf(3076,plain,
! [SV1235: $i,SV833: $i,SV346: $i] :
( ( ! [SY4364: $i,SY4365: $i] :
( ( c_ListOrder_Ostep1 @ SV346 @ ( c_List_Olist_OCons @ SV833 @ SV1235 @ SY4364 ) @ ( c_List_Olist_OCons @ SV833 @ SY4365 @ SY4364 ) @ SY4364 )
| ~ ( c_ListOrder_Ostep1 @ SV346 @ SV1235 @ SY4365 @ SY4364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2592]) ).
thf(3077,plain,
! [SV1236: $i,SV834: $i,SV347: $i] :
( ( ! [SY4366: $i] :
( ( c_List_Oappend @ ( c_List_Oreplicate @ SV347 @ SV834 @ SV1236 ) @ ( c_List_Olist_OCons @ SV834 @ SY4366 @ SV1236 ) @ SV1236 )
= ( c_List_Olist_OCons @ SV834 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV347 @ SV834 @ SV1236 ) @ SY4366 @ SV1236 ) @ SV1236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2593]) ).
thf(3078,plain,
! [SV1237: $i,SV835: $i,SV348: $i] :
( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV348 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV835 ) @ SV1237 ) @ SV348 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV348 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV835 @ SV348 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1237 @ SV348 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2594]) ).
thf(3079,plain,
! [SV1238: $i,SV836: $i,SV349: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV349 )
| ( ( c_List_Olistsum @ ( c_List_Oappend @ SV836 @ SV1238 @ SV349 ) @ SV349 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV349 ) @ ( c_List_Olistsum @ SV836 @ SV349 ) ) @ ( c_List_Olistsum @ SV1238 @ SV349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2595]) ).
thf(3080,plain,
! [SV351: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ SV351 @ 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 ) @ SV351 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2596]) ).
thf(3081,plain,
! [SV1239: $i,SV837: $i,SV352: $i] :
( ( ! [SY4367: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV352 @ SV837 @ SV1239 ) @ SY4367 @ SV1239 )
= ( c_List_Oappend @ SV352 @ ( c_List_Oappend @ SV837 @ SY4367 @ SV1239 ) @ SV1239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2597]) ).
thf(3082,plain,
! [SV1240: $i,SV838: $i,SV353: $i] :
( ( ! [SY4368: $i] :
( ( c_List_Oappend @ SV353 @ ( c_List_Oappend @ SV838 @ SV1240 @ SY4368 ) @ SY4368 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV353 @ SV838 @ SY4368 ) @ SV1240 @ SY4368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2598]) ).
thf(3083,plain,
! [SV1241: $i,SV839: $i,SV354: $i] :
( ( ! [SY4369: $i] :
( ( c_List_Oappend @ ( c_List_Oappend @ SV354 @ SV839 @ SV1241 ) @ SY4369 @ SV1241 )
= ( c_List_Oappend @ SV354 @ ( c_List_Oappend @ SV839 @ SY4369 @ SV1241 ) @ SV1241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2599]) ).
thf(3084,plain,
! [SV1242: $i,SV840: $i,SV355: $i] :
( ( ! [SY4370: $i] :
( ( c_List_Oappend @ SV355 @ ( c_List_Oappend @ SV840 @ SV1242 @ SY4370 ) @ SY4370 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV355 @ SV840 @ SY4370 ) @ SV1242 @ SY4370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2600]) ).
thf(3085,plain,
! [SV1243: $i,SV841: $i,SV356: $i] :
( ( ~ ( class_Orderings_Oorder @ SV356 )
| ~ ( c_HOL_Oord__class_Oless @ SV841 @ SV1243 @ SV356 )
| ~ ( c_HOL_Oord__class_Oless @ SV1243 @ SV841 @ SV356 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2601]) ).
thf(3086,plain,
! [SV1244: $i,SV842: $i,SV357: $i] :
( ( ! [SY4371: $i,SY4372: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV357 @ SV842 ) @ SV1244 ) @ SY4371 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV357 @ SV842 ) @ SY4372 ) @ SY4371 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV357 @ SV1244 ) @ SY4372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2602]) ).
thf(3087,plain,
! [SV1245: $i,SV843: $i,SV358: $i] :
( ( ! [SY4373: $i,SY4374: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV358 @ SV843 ) @ SV1245 ) @ SY4373 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SY4374 ) @ SY4373 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV358 @ SV843 ) @ SV1245 ) @ SY4374 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2603]) ).
thf(3088,plain,
! [SV1246: $i,SV844: $i,SV359: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV359 )
| ~ ( c_HOL_Oord__class_Oless @ SV844 @ SV1246 @ SV359 )
| ~ ( c_HOL_Oord__class_Oless @ SV1246 @ SV844 @ SV359 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2604]) ).
thf(3089,plain,
! [SV1247: $i,SV845: $i,SV360: $i] :
( ( ! [SY4375: $i] :
( ( c_Wellfounded_Oaccp @ SV360 @ SV845 @ SV1247 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV360 @ SV845 ) @ SY4375 ) )
| ~ ( c_Wellfounded_Oaccp @ SV360 @ SY4375 @ SV1247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2605]) ).
thf(3090,plain,
! [SV1248: $i,SV846: $i,SV361: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV361 )
| ~ ( c_HOL_Oord__class_Oless @ SV846 @ SV1248 @ SV361 )
| ~ ( c_HOL_Oord__class_Oless @ SV1248 @ SV846 @ SV361 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2606]) ).
thf(3091,plain,
! [SV1249: $i,SV847: $i,SV362: $i] :
( ( ! [SY4376: $i] :
( ( c_Wellfounded_Oaccp @ SV362 @ SV847 @ SV1249 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV362 @ SV847 ) @ SY4376 ) )
| ~ ( c_Wellfounded_Oaccp @ SV362 @ SY4376 @ SV1249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2607]) ).
thf(3092,plain,
! [SV1250: $i,SV848: $i,SV363: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV363 )
| ~ ( c_HOL_Oord__class_Oless @ SV848 @ SV1250 @ SV363 )
| ~ ( c_HOL_Oord__class_Oless @ SV1250 @ SV848 @ SV363 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2608]) ).
thf(3093,plain,
! [SV1251: $i,SV849: $i,SV365: $i] :
( ( ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV365 @ SV849 )
= ( c_List_Oreplicate @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1251 @ SV849 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2609]) ).
thf(3094,plain,
! [SV1252: $i,SV850: $i,SV371: $i] :
( ( ! [SY4377: $i,SY4378: $i,SY4379: $i,SY4380: $i] :
( ( ( hAPP @ ( hAPP @ SV371 @ SV850 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV1252 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4377 @ SY4378 @ SV371 @ SY4379 @ SV1252 @ SY4380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2610]) ).
thf(3095,plain,
! [SV851: $i,SV372: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV372 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV372 ) @ ( c_HOL_Ozero__class_Ozero @ SV372 ) @ SV851 @ SV372 @ SV372 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV372 ) @ SV851 @ ( c_HOL_Ozero__class_Ozero @ SV372 ) @ SV372 @ SV372 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2611]) ).
thf(3096,plain,
! [SV852: $i,SV373: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV373 ) )
= $true )
| ( ( ( c_List_Olistsum @ SV852 @ SV373 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV373 ) @ ( c_HOL_Ozero__class_Ozero @ SV373 ) @ SV852 @ SV373 @ SV373 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2612]) ).
thf(3097,plain,
! [SV1253: $i,SV853: $i,SV374: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV374 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV374 ) @ SV853 @ SV1253 @ SV374 @ SV374 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV374 ) @ SV853 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV374 ) @ SV1253 @ ( c_HOL_Ozero__class_Ozero @ SV374 ) @ SV374 @ SV374 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2613]) ).
thf(3098,plain,
! [SV1254: $i,SV854: $i,SV375: $i] :
( ( ! [SY4381: $i,SY4382: $i,SY4383: $i] :
( ~ ( hBOOL @ ( hAPP @ SV375 @ ( c_Lambda_OdB_OdB__case @ SV854 @ SV1254 @ SY4381 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4382 ) @ SY4383 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV375 @ ( hAPP @ ( hAPP @ SV1254 @ SY4382 ) @ SY4383 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2614]) ).
thf(3099,plain,
! [SV1255: $i,SV855: $i,SV376: $i] :
( ( ! [SY4384: $i,SY4385: $i,SY4386: $i] :
( ~ ( hBOOL @ ( hAPP @ SV376 @ ( c_Lambda_OdB_OdB__case @ SV855 @ SV1255 @ SY4384 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4385 ) @ SY4386 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SV1255 @ SY4385 ) @ SY4386 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2615]) ).
thf(3100,plain,
! [SV1256: $i,SV856: $i,SV377: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV377 ) @ SV856 ) ) @ SV1256 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV377 ) @ SV1256 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV856 ) @ SV1256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2616]) ).
thf(3101,plain,
! [SV1257: $i,SV857: $i,SV378: $i] :
( ( ! [SY4387: $i,SY4388: $i,SY4389: $i] :
( ( c_Lambda_OdB_OdB__case @ SV378 @ SV857 @ SV1257 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4387 ) @ SY4388 ) @ SY4389 )
= ( hAPP @ ( hAPP @ SV857 @ SY4387 ) @ SY4388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2617]) ).
thf(3102,plain,
! [SV1258: $i,SV858: $i,SV379: $i] :
( ( ! [SY4390: $i,SY4391: $i,SY4392: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV379 @ SV858 @ SV1258 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4390 ) @ SY4391 ) @ SY4392 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV858 @ SY4390 ) @ SY4391 ) @ ( c_Lambda_OdB_OdB__rec @ SV379 @ SV858 @ SV1258 @ SY4390 @ SY4392 ) ) @ ( c_Lambda_OdB_OdB__rec @ SV379 @ SV858 @ SV1258 @ SY4391 @ SY4392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2618]) ).
thf(3103,plain,
! [SV1259: $i,SV859: $i,SV380: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV380 ) @ SV859 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV380 ) @ SV1259 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV859 ) @ SV1259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2619]) ).
thf(3104,plain,
! [SV1260: $i,SV860: $i,SV381: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV381 ) @ SV860 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1260 ) @ SV860 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV381 ) @ SV1260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2620]) ).
thf(3105,plain,
! [SV1261: $i,SV861: $i,SV382: $i] :
( ( ! [SY4393: $i] :
( ( c_Lambda_Oliftn @ SV382 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV861 ) @ SV1261 ) @ SY4393 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV382 @ SV861 @ SY4393 ) ) @ ( c_Lambda_Oliftn @ SV382 @ SV1261 @ SY4393 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2621]) ).
thf(3106,plain,
! [SV1262: $i,SV862: $i,SV383: $i] :
( ( ! [SY4394: $i] :
( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV383 ) @ SV862 ) @ SV1262 @ SY4394 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV383 @ SV1262 @ SY4394 ) ) @ ( c_Lambda_Osubstn @ SV862 @ SV1262 @ SY4394 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2622]) ).
thf(3107,plain,
! [SV1263: $i,SV863: $i,SV384: $i] :
( ( ( c_Lambda_Osubstn @ SV384 @ SV863 @ SV1263 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV384 ) @ ( c_Lambda_Oliftn @ SV1263 @ SV863 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ SV1263 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2623]) ).
thf(3108,plain,
! [SV1264: $i,SV864: $i,SV385: $i] :
( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV385 ) @ SV864 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1264 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV864 @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV385 ) ) @ SV864 ) @ SV1264 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2624]) ).
thf(3109,plain,
! [SV1265: $i,SV865: $i,SV386: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV386 @ SV865 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1265 @ SV865 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV386 ) @ SV1265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2625]) ).
thf(3110,plain,
! [SV1266: $i,SV866: $i,SV387: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV387 @ SV866 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV387 @ SV1266 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV866 @ SV1266 @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2626]) ).
thf(3111,plain,
! [SV1267: $i,SV867: $i,SV391: $i] :
( ( ! [SY4395: $i,SY4396: $i] :
( ( ( c_List_Ofoldl @ SV391 @ ( hAPP @ ( hAPP @ SV391 @ SV867 ) @ SV1267 ) @ SY4395 @ SY4396 @ SY4396 )
= ( hAPP @ ( hAPP @ SV391 @ SV867 ) @ ( c_List_Ofoldl @ SV391 @ SV1267 @ SY4395 @ SY4396 @ SY4396 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV391 @ SY4396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2627]) ).
thf(3112,plain,
! [SV1268: $i,SV868: $i,SV392: $i] :
( ( ! [SY4397: $i] :
( ( c_List_Ofoldl @ SV392 @ SV868 @ ( c_List_Olist_ONil @ SV1268 ) @ SY4397 @ SV1268 )
= SV868 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2628]) ).
thf(3113,plain,
! [SV1269: $i,SV869: $i,SV393: $i] :
( ( ! [SY4398: $i] :
( ~ ( class_OrderedGroup_Osemigroup__add @ SV393 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV393 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV393 ) @ SV869 ) @ SV1269 ) @ SY4398 @ SV393 @ SV393 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV393 ) @ SV869 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV393 ) @ SV1269 @ SY4398 @ SV393 @ SV393 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2629]) ).
thf(3114,plain,
! [SV1270: $i,SV870: $i,SV394: $i] :
( ( ! [SY4399: $i,SY4400: $i] :
( ( ( hAPP @ ( hAPP @ SV394 @ SV870 ) @ ( c_List_Ofoldl @ SV394 @ SV1270 @ SY4399 @ SY4400 @ SY4400 ) )
= ( c_List_Ofoldl @ SV394 @ SV870 @ SY4399 @ SY4400 @ SY4400 ) )
| ~ ( c_OrderedGroup_Omonoid__add @ SV1270 @ SV394 @ SY4400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2630]) ).
thf(3115,plain,
! [SV1271: $i,SV871: $i,SV395: $i] :
( ( ! [SY4401: $i,SY4402: $i,SY4403: $i] :
( ( c_List_Ofoldl @ SV395 @ SV871 @ ( c_List_Olist_OCons @ SV1271 @ SY4401 @ SY4402 ) @ SY4403 @ SY4402 )
= ( c_List_Ofoldl @ SV395 @ ( hAPP @ ( hAPP @ SV395 @ SV871 ) @ SV1271 ) @ SY4401 @ SY4403 @ SY4402 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2631]) ).
thf(3116,plain,
! [SV1272: $i,SV872: $i,SV396: $i] :
( ( ! [SY4404: $i,SY4405: $i,SY4406: $i] :
( ( c_List_Ofoldl @ SV396 @ SV872 @ ( c_List_Oappend @ SV1272 @ SY4404 @ SY4405 ) @ SY4406 @ SY4405 )
= ( c_List_Ofoldl @ SV396 @ ( c_List_Ofoldl @ SV396 @ SV872 @ SV1272 @ SY4406 @ SY4405 ) @ SY4404 @ SY4406 @ SY4405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2632]) ).
thf(3117,plain,
! [SV1273: $i,SV873: $i,SV397: $i] :
( ( ! [SY4407: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV397 @ SV873 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV1273 ) @ SY4407 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV397 ) @ SV1273 ) @ SY4407 ) @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SV1273 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SY4407 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV873 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2633]) ).
thf(3118,plain,
! [SV874: $i,SV398: $i] :
( ( ( hBOOL @ ( hAPP @ SV398 @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV398 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV398 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV398 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV398 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ SV398 @ SV874 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2634]) ).
thf(3119,plain,
! [SV1274: $i,SV875: $i,SV399: $i] :
( ( ! [SY4408: $i] :
( ( c_Type_Otypings @ SV399 @ SV875 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV1274 @ SV399 @ SY4408 @ SV875 ) )
| ~ ( c_Type_Otyping @ SV399 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY4408 ) @ SV875 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1274 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2635]) ).
thf(3120,plain,
! [SV876: $i,SV400: $i] :
( ( ( hBOOL @ ( hAPP @ SV400 @ SV876 ) )
= $true )
| ( ( ( hBOOL @ ( hAPP @ SV400 @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV400 ) ) )
| ~ ( hBOOL @ ( hAPP @ SV400 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV400 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV400 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2636]) ).
thf(3121,plain,
! [SV1275: $i,SV877: $i,SV401: $i] :
( ( ! [SY4409: $i,SY4410: $i,SY4411: $i,SY4412: $i] :
( ( c_Type_Otypings @ SV401 @ SV877 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV1275 @ SY4409 @ SV401 @ SV877 ) )
| ~ ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY4410 ) @ SY4411 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY4409 )
| ~ ( c_Type_Otypings @ SV401 @ SY4411 @ SY4412 )
| ~ ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY4410 ) @ SY4411 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV877 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2637]) ).
thf(3122,plain,
! [SV1276: $i,SV878: $i,SV402: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV402 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV878 @ SV402 @ SV1276 ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV878 ) @ SV402 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV1276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2638]) ).
thf(3123,plain,
! [SV403: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV403 ) ) )
= $true )
| ( ( ( SV403
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV403 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV403 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV403 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV403 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV403 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV403 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2639]) ).
thf(3124,plain,
! [SV1277: $i,SV879: $i,SV404: $i] :
( ( ! [SY4413: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV404 ) @ SV879 ) @ SV1277 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY4413 ) @ SV879 ) @ SV1277 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV404 ) @ SY4413 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2640]) ).
thf(3125,plain,
! [SV1278: $i,SV880: $i,SV405: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV405 ) @ SV880 ) ) @ SV1278 ) @ SV880 )
= SV405 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2641]) ).
thf(3126,plain,
! [SV406: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV406 ) ) )
= $true )
| ( ( ( SV406
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV406 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV406 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV406 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV406 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2642]) ).
thf(3127,plain,
! [SV1279: $i,SV881: $i,SV407: $i] :
( ( ! [SY4414: $i,SY4415: $i] :
( ~ ( hBOOL @ ( hAPP @ SV407 @ ( c_Lambda_OdB_OdB__case @ SV881 @ SV1279 @ SY4414 @ ( c_Lambda_OdB_OVar @ SY4415 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV407 @ ( hAPP @ SV881 @ SY4415 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2643]) ).
thf(3128,plain,
! [SV1280: $i,SV882: $i,SV408: $i] :
( ( ! [SY4416: $i,SY4417: $i] :
( ~ ( hBOOL @ ( hAPP @ SV408 @ ( c_Lambda_OdB_OdB__case @ SV882 @ SV1280 @ SY4416 @ ( c_Lambda_OdB_OVar @ SY4417 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV408 @ ( hAPP @ SV882 @ SY4417 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2644]) ).
thf(3129,plain,
! [SV883: $i,SV409: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ SV409 ) ) @ SV883 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2645]) ).
thf(3130,plain,
! [SV1281: $i,SV884: $i,SV410: $i] :
( ( ! [SY4418: $i,SY4419: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV410 @ SV884 @ SV1281 @ ( c_Lambda_OdB_OVar @ SY4418 ) @ SY4419 )
= ( hAPP @ SV410 @ SY4418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2646]) ).
thf(3131,plain,
! [SV1282: $i,SV885: $i,SV411: $i] :
( ( ( ( hAPP @ SV411 @ SV885 )
= SV1282 )
| ~ ( c_Type_Otyping @ SV411 @ ( c_Lambda_OdB_OVar @ SV885 ) @ SV1282 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2647]) ).
thf(3132,plain,
! [SV1283: $i,SV886: $i,SV412: $i] :
( ( ! [SY4420: $i,SY4421: $i] :
( ( c_Lambda_OdB_OdB__case @ SV412 @ SV886 @ SV1283 @ ( c_Lambda_OdB_OVar @ SY4420 ) @ SY4421 )
= ( hAPP @ SV412 @ SY4420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2648]) ).
thf(3133,plain,
! [SV888: $i,SV414: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV414 ) @ SV888 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV414 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2650]) ).
thf(3134,plain,
! [SV415: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV415 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ SV415 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2651]) ).
thf(3135,plain,
! [SV1284: $i,SV890: $i,SV417: $i] :
( ( ( SV417
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV890 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV890 @ SV1284 @ SV417 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV890 ) @ SV1284 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2653]) ).
thf(3136,plain,
! [SV891: $i,SV418: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV418 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV418 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV418 )
| ~ ( class_Power_Opower @ SV418 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV418 ) @ SV891 @ SV418 )
= ( c_HOL_Ozero__class_Ozero @ SV418 ) )
| ( SV891
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2654]) ).
thf(3137,plain,
! [SV892: $i,SV419: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__0 @ SV419 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV419 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV419 ) @ SV892 @ SV419 )
= ( c_HOL_Ozero__class_Ozero @ SV419 ) )
| ( SV892
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2655]) ).
thf(3138,plain,
! [SV420: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV420 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV420 )
= ( c_HOL_Ozero__class_Ozero @ SV420 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2656]) ).
thf(3139,plain,
! [SV1285: $i,SV893: $i,SV421: $i] :
( ( ~ ( class_OrderedGroup_Omonoid__add @ SV421 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SV893 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ ( c_HOL_Ozero__class_Ozero @ SV421 ) @ SV1285 @ SV421 @ SV421 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SV893 @ SV1285 @ SV421 @ SV421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2657]) ).
thf(3140,plain,
! [SV1286: $i,SV896: $i,SV426: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV426 @ SV896 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1286 @ SV896 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV426 ) @ SV1286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2660]) ).
thf(3141,plain,
! [SV1287: $i,SV897: $i,SV427: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV427 ) ) @ SV897 ) @ SV1287 )
= ( c_Lambda_OdB_OVar @ SV427 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV427 @ SV1287 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2661]) ).
thf(3142,plain,
! [SV1288: $i,SV898: $i,SV428: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV428 ) ) @ SV898 ) @ SV1288 )
= ( c_Lambda_OdB_OVar @ SV428 ) )
| ( SV428 = SV1288 )
| ( c_HOL_Oord__class_Oless @ SV1288 @ SV428 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2662]) ).
thf(3143,plain,
! [SV899: $i,SV429: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV429 @ SV429 @ tc_nat )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV429 ) ) @ SV899 ) @ SV429 )
= SV899 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2663]) ).
thf(3144,plain,
! [SV1289: $i,SV900: $i,SV430: $i] :
( ( ! [SY4422: $i,SY4423: $i] :
( ( SV430 = SV900 )
| ~ ( c_Type_Otyping @ SV1289 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY4422 ) @ SY4423 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV900 )
| ~ ( c_Type_Otyping @ SV1289 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY4422 ) @ SY4423 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2664]) ).
thf(3145,plain,
! [SV901: $i,SV432: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV432 ) @ SV901 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ c_InductTermi_OIT @ SV901 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2665]) ).
thf(3146,plain,
! [SV1290: $i,SV902: $i,SV433: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV433 ) ) @ SV902 ) @ SV1290 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV902 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV433 ) @ SV902 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1290 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2666]) ).
thf(3147,plain,
! [SV1291: $i,SV903: $i,SV434: $i] :
( ( ! [SY4424: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV434 ) @ SV903 ) ) @ SV1291 ) @ SY4424 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV434 ) @ SV1291 ) @ SY4424 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV903 ) @ SV1291 ) @ SY4424 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2667]) ).
thf(3148,plain,
! [SV1292: $i,SV905: $i,SV436: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV436 ) @ ( c_Lambda_OdB_OVar @ SV905 ) ) @ SV1292 ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2669]) ).
thf(3149,plain,
! [SV906: $i,SV438: $i] :
( ( ( class_Orderings_Opreorder @ ( tc_fun @ SV438 @ SV906 ) )
= $true )
| ( ( ~ ( class_Orderings_Opreorder @ SV906 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2670]) ).
thf(3150,plain,
! [SV907: $i,SV439: $i] :
( ( ( class_Orderings_Oorder @ ( tc_fun @ SV439 @ SV907 ) )
= $true )
| ( ( ~ ( class_Orderings_Oorder @ SV907 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2671]) ).
thf(3151,plain,
! [SV1293: $i,SV909: $i,SV441: $i] :
( ( ( SV441 = SV909 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV1293 ) @ SV441 ) @ SV909 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2673]) ).
thf(3152,plain,
! [SV910: $i,SV442: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV442 )
!= ( c_Lambda_OdB_OVar @ SV910 ) )
= $true )
| ( ( SV442 = SV910 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2674]) ).
thf(3153,plain,
! [SV1294: $i,SV911: $i,SV443: $i] :
( ( ! [SY4425: $i,SY4426: $i] :
( ( ( c_List_Olist_OCons @ SV443 @ SV911 @ SV1294 )
!= ( c_List_Olist_OCons @ SY4425 @ SY4426 @ SV1294 ) )
| ( SV443 = SY4425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2675]) ).
thf(3154,plain,
! [SV1295: $i,SV912: $i,SV444: $i] :
( ( ! [SY4427: $i,SY4428: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV444 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV912 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV1295 ) @ SY4427 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV1295 ) @ SY4428 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV912 ) @ SY4427 )
= SY4428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2676]) ).
thf(3155,plain,
! [SV1296: $i,SV913: $i,SV445: $i] :
( ( ( c_Lambda_OdB_OVar @ SV445 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV913 ) @ SV1296 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2677]) ).
thf(3156,plain,
! [SV1297: $i,SV914: $i,SV446: $i] :
( ( ! [SY4429: $i] :
( ~ ( class_Ring__and__Field_Oidom @ SV446 )
| ~ ( class_Int_Onumber__ring @ SV446 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV446 ) @ SV914 ) @ SV1297 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV446 ) @ SV914 ) @ SY4429 ) )
| ( SV1297 = SY4429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2678]) ).
thf(3157,plain,
! [SV1298: $i,SV915: $i,SV447: $i] :
( ( ! [SY4430: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV447 ) @ SV915 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1298 ) @ SY4430 ) )
| ( SV447 = SV1298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2679]) ).
thf(3158,plain,
! [SV1299: $i,SV916: $i,SV448: $i] :
( ( ( c_List_Olist_OCons @ SV448 @ SV916 @ SV1299 )
!= ( c_List_Olist_ONil @ SV1299 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2680]) ).
thf(3159,plain,
! [SV1300: $i,SV917: $i,SV449: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV449 )
| ( ( c_Orderings_Oord__class_Omax @ SV917 @ SV1300 @ SV449 )
!= SV1300 )
| ( c_lessequals @ SV917 @ SV1300 @ SV449 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2681]) ).
thf(3160,plain,
! [SV1301: $i,SV918: $i,SV450: $i] :
( ( ! [SY4431: $i,SY4432: $i] :
( ( ( c_List_Oappend @ SV450 @ ( c_List_Olist_OCons @ SV918 @ ( c_List_Olist_ONil @ SV1301 ) @ SV1301 ) @ SV1301 )
!= ( c_List_Oappend @ SY4431 @ ( c_List_Olist_OCons @ SY4432 @ ( c_List_Olist_ONil @ SV1301 ) @ SV1301 ) @ SV1301 ) )
| ( SV450 = SY4431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2682]) ).
thf(3161,plain,
! [SV919: $i,SV451: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ SV451 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV451 ) @ SV919 ) @ SV919 )
!= ( c_HOL_Ozero__class_Ozero @ SV451 ) )
| ( SV919
= ( c_HOL_Ozero__class_Ozero @ SV451 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2683]) ).
thf(3162,plain,
! [SV1302: $i,SV920: $i,SV452: $i] :
( ( ( SV452
!= ( c_List_Oappend @ SV920 @ SV452 @ SV1302 ) )
| ( SV920
= ( c_List_Olist_ONil @ SV1302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2684]) ).
thf(3163,plain,
! [SV1303: $i,SV921: $i,SV453: $i] :
( ( ( c_List_Olist_ONil @ SV453 )
!= ( c_List_Olist_OCons @ SV921 @ SV1303 @ SV453 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2685]) ).
thf(3164,plain,
! [SV922: $i,SV454: $i] :
( ( ( SV454
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV454 ) @ SV922 ) )
= $true )
| ( ( SV922
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2686]) ).
thf(3165,plain,
! [SV923: $i,SV455: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV455 ) @ SV923 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV923
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2687]) ).
thf(3166,plain,
! [SV1304: $i,SV924: $i,SV456: $i] :
( ( ! [SY4433: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV456 )
| ( ( c_Power_Opower__class_Opower @ SV924 @ SV1304 @ SV456 )
!= ( c_Power_Opower__class_Opower @ SY4433 @ SV1304 @ SV456 ) )
| ( SV924 = SY4433 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1304 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SY4433 @ SV456 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV924 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2688]) ).
thf(3167,plain,
! [SV1305: $i,SV925: $i,SV457: $i] :
( ( ! [SY4434: $i,SY4435: $i] :
( ( ( c_List_Oreplicate @ SV457 @ SV925 @ SV1305 )
!= ( c_List_Oreplicate @ SY4434 @ SY4435 @ SV1305 ) )
| ( SV457 = SY4434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2689]) ).
thf(3168,plain,
! [SV1306: $i,SV926: $i,SV458: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV458 ) @ SV926 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1306 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV458 ) @ SV926 )
= SV1306 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2690]) ).
thf(3169,plain,
! [SV1307: $i,SV927: $i,SV459: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV459 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV459 ) @ SV927 ) @ SV1307 )
!= ( c_HOL_Ozero__class_Ozero @ SV459 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV459 ) @ SV1307 @ SV459 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV459 ) @ SV927 @ SV459 )
| ( SV1307
= ( c_HOL_Ozero__class_Ozero @ SV459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2691]) ).
thf(3170,plain,
! [SV1308: $i,SV928: $i,SV460: $i] :
( ( ! [SY4436: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV460 ) @ SV928 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1308 ) @ SY4436 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV928 = SY4436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2692]) ).
thf(3171,plain,
! [SV929: $i,SV461: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV461 ) @ SV929 )
!= SV461 )
= $true )
| ( ( SV929
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2693]) ).
thf(3172,plain,
! [SV1309: $i,SV930: $i,SV462: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV462 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV930 @ SV1309 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ SV462 )
= SV930 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2694]) ).
thf(3173,plain,
! [SV1310: $i,SV931: $i,SV463: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV463 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV931 @ SV1310 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1310
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2695]) ).
thf(3174,plain,
! [SV1311: $i,SV932: $i,SV464: $i] :
( ( ! [SY4437: $i,SY4438: $i] :
( ( ( c_List_Olist_OCons @ SV464 @ SV932 @ SV1311 )
!= ( c_List_Olist_OCons @ SY4437 @ SY4438 @ SV1311 ) )
| ( SV932 = SY4438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2696]) ).
thf(3175,plain,
! [SV1312: $i,SV933: $i,SV465: $i] :
( ( ! [SY4439: $i,SY4440: $i] :
( ( ( c_List_Oreplicate @ SV465 @ SV933 @ SV1312 )
!= ( c_List_Oreplicate @ SY4439 @ SY4440 @ SV1312 ) )
| ( SV933 = SY4440 )
| ( SV465
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2697]) ).
thf(3176,plain,
! [SV1313: $i,SV934: $i,SV466: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV466 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV934 ) @ SV1313 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2698]) ).
thf(3177,plain,
! [SV1314: $i,SV935: $i,SV467: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV467 )
| ~ ( class_Int_Onumber__ring @ SV467 )
| ( SV935
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV467 ) @ SV935 ) @ SV1314 ) )
| ( SV1314
= ( c_HOL_Ozero__class_Ozero @ SV467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2699]) ).
thf(3178,plain,
! [SV1315: $i,SV936: $i,SV468: $i] :
( ( ! [SY4441: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV468 ) @ SV936 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1315 ) @ SY4441 ) )
| ( SV936 = SY4441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2700]) ).
thf(3179,plain,
! [SV1316: $i,SV937: $i,SV469: $i] :
( ( ( SV469
!= ( c_List_Oappend @ SV469 @ SV937 @ SV1316 ) )
| ( SV937
= ( c_List_Olist_ONil @ SV1316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2701]) ).
thf(3180,plain,
! [SV1317: $i,SV938: $i,SV470: $i] :
( ( ! [SY4442: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV470 ) @ SV938 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1317 ) @ SY4442 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2702]) ).
thf(3181,plain,
! [SV1318: $i,SV939: $i,SV471: $i] :
( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV471 )
| ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV471 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV471 )
| ~ ( class_Power_Opower @ SV471 )
| ( ( c_Power_Opower__class_Opower @ SV939 @ SV1318 @ SV471 )
!= ( c_HOL_Ozero__class_Ozero @ SV471 ) )
| ( SV939
= ( c_HOL_Ozero__class_Ozero @ SV471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2703]) ).
thf(3182,plain,
! [SV1319: $i,SV940: $i,SV472: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV472 @ SV940 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1319 @ SV940 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV472 = SV1319 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2704]) ).
thf(3183,plain,
! [SV941: $i,SV473: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV473 )
!= ( c_Lambda_OdB_OAbs @ SV941 ) )
= $true )
| ( ( SV473 = SV941 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2705]) ).
thf(3184,plain,
! [SV1320: $i,SV942: $i,SV474: $i] :
( ( ! [SY4443: $i] :
( ( ( c_List_Oappend @ SV474 @ SV942 @ SV1320 )
!= ( c_List_Oappend @ SV474 @ SY4443 @ SV1320 ) )
| ( SV942 = SY4443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2706]) ).
thf(3185,plain,
! [SV1321: $i,SV943: $i,SV475: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV475 ) @ SV943 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1321 ) @ SV943 ) )
| ( SV475 = SV1321 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2707]) ).
thf(3186,plain,
! [SV1322: $i,SV944: $i,SV476: $i] :
( ( ! [SY4444: $i] :
( ( ( c_List_Olist_ONil @ SV476 )
!= ( c_List_Omap @ SV944 @ SV1322 @ SY4444 @ SV476 ) )
| ( SV1322
= ( c_List_Olist_ONil @ SY4444 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2708]) ).
thf(3187,plain,
! [SV1323: $i,SV945: $i,SV477: $i] :
( ( ~ ( class_Nat_Osemiring__char__0 @ SV477 )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV945 @ SV477 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1323 @ SV477 ) )
| ( SV945 = SV1323 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2709]) ).
thf(3188,plain,
! [SV1324: $i,SV946: $i,SV478: $i] :
( ( ( c_List_Olist_OCons @ SV478 @ SV946 @ SV1324 )
!= ( c_List_Olist_ONil @ SV1324 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2710]) ).
thf(3189,plain,
! [SV1325: $i,SV947: $i,SV479: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV479 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV947 @ SV1325 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1325
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2711]) ).
thf(3190,plain,
! [SV1326: $i,SV948: $i,SV480: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV480 @ SV948 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV1326 ) )
| ( SV948
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2712]) ).
thf(3191,plain,
! [SV1327: $i,SV949: $i,SV481: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV481 ) @ SV949 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV481 ) @ SV1327 ) )
| ( SV949 = SV1327 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2713]) ).
thf(3192,plain,
! [SV482: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV482 )
= $false )
| ( ( ( c_HOL_Ozero__class_Ozero @ SV482 )
!= ( c_HOL_Oone__class_Oone @ SV482 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2714]) ).
thf(3193,plain,
! [SV1328: $i,SV950: $i,SV483: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV483 @ SV950 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV1328 ) )
| ( SV483
= ( c_Lambda_OdB_OAbs @ SV1328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2715]) ).
thf(3194,plain,
! [SV1329: $i,SV951: $i,SV484: $i] :
( ( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV484 )
| ( ( c_Power_Opower__class_Opower @ SV951 @ SV1329 @ SV484 )
!= ( c_HOL_Ozero__class_Ozero @ SV484 ) )
| ( SV951
= ( c_HOL_Ozero__class_Ozero @ SV484 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2716]) ).
thf(3195,plain,
! [SV1330: $i,SV952: $i,SV485: $i] :
( ( ! [SY4445: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV485 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV952 ) @ SV1330 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SY4445 ) @ SV1330 ) )
| ( SV952 = SY4445 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2717]) ).
thf(3196,plain,
! [SV953: $i,SV486: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV486 )
= ( c_Lambda_OdB_OVar @ SV953 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2718]) ).
thf(3197,plain,
! [SV954: $i,SV487: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV487 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV487 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV487 )
| ~ ( class_Power_Opower @ SV487 )
| ( ( c_Power_Opower__class_Opower @ SV954 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV487 )
!= ( c_HOL_Ozero__class_Ozero @ SV487 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2719]) ).
thf(3198,plain,
! [SV1331: $i,SV955: $i,SV488: $i] :
( ( ( ( c_List_Olist_ONil @ SV488 )
!= ( c_List_Oreplicate @ SV955 @ SV1331 @ SV488 ) )
| ( SV955
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2720]) ).
thf(3199,plain,
! [SV1332: $i,SV956: $i,SV489: $i] :
( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV489 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV489 ) @ SV956 ) @ SV1332 )
!= ( c_HOL_Ozero__class_Ozero @ SV489 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV1332 @ SV489 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV956 @ SV489 )
| ( SV956
= ( c_HOL_Ozero__class_Ozero @ SV489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2721]) ).
thf(3200,plain,
! [SV1333: $i,SV957: $i,SV490: $i] :
( ( ( ( c_List_Oreplicate @ SV490 @ SV957 @ SV1333 )
!= ( c_List_Olist_ONil @ SV1333 ) )
| ( SV490
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2722]) ).
thf(3201,plain,
! [SV1334: $i,SV958: $i,SV491: $i] :
( ( ( ( c_List_Olist_ONil @ SV491 )
!= ( c_List_Oappend @ SV958 @ SV1334 @ SV491 ) )
| ( SV958
= ( c_List_Olist_ONil @ SV491 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2723]) ).
thf(3202,plain,
! [SV1335: $i,SV959: $i,SV492: $i] :
( ( ! [SY4446: $i] :
( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV492 ) @ SV959 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1335 ) @ SY4446 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1335 @ SV959 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV492 @ SY4446 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2724]) ).
thf(3203,plain,
! [SV1336: $i,SV960: $i,SV493: $i] :
( ( ! [SY4447: $i] :
( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV493 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV960 ) @ SV1336 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV960 ) @ SY4447 ) )
| ( SV1336 = SY4447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2725]) ).
thf(3204,plain,
! [SV1337: $i,SV961: $i,SV494: $i] :
( ( ! [SY4448: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV494 ) @ SV961 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1337 ) @ SY4448 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV494 = SV1337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2726]) ).
thf(3205,plain,
! [SV1338: $i,SV962: $i,SV495: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV495 ) @ SV962 )
!= ( c_Lambda_OdB_OAbs @ SV1338 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2727]) ).
thf(3206,plain,
! [SV1339: $i,SV963: $i,SV496: $i] :
( ( ! [SY4449: $i] :
( ~ ( class_Ring__and__Field_Oordered__semidom @ SV496 )
| ( ( c_Power_Opower__class_Opower @ SV963 @ SV1339 @ SV496 )
!= ( c_Power_Opower__class_Opower @ SV963 @ SY4449 @ SV496 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV496 ) @ SV963 @ SV496 )
| ( SV1339 = SY4449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2728]) ).
thf(3207,plain,
! [SV1340: $i,SV964: $i,SV497: $i] :
( ( ! [SY4450: $i] :
( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV497 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV964 ) @ SV1340 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV964 ) @ SY4450 ) )
| ( SV1340 = SY4450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2729]) ).
thf(3208,plain,
! [SV1341: $i,SV965: $i,SV498: $i] :
( ( ! [SY4451: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV498 ) ) @ SV965 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1341 ) @ SY4451 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2730]) ).
thf(3209,plain,
! [SV1342: $i,SV966: $i,SV499: $i] :
( ( ( ( c_List_Olist_ONil @ SV499 )
!= ( c_List_Oappend @ SV966 @ SV1342 @ SV499 ) )
| ( SV1342
= ( c_List_Olist_ONil @ SV499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2731]) ).
thf(3210,plain,
! [SV1343: $i,SV967: $i,SV500: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV500 ) @ SV967 )
!= ( c_Lambda_OdB_OVar @ SV1343 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2732]) ).
thf(3211,plain,
! [SV1344: $i,SV968: $i,SV501: $i] :
( ( ! [SY4452: $i,SY4453: $i] :
( ( ( c_List_Oappend @ SV501 @ ( c_List_Olist_OCons @ SV968 @ ( c_List_Olist_ONil @ SV1344 ) @ SV1344 ) @ SV1344 )
!= ( c_List_Oappend @ SY4452 @ ( c_List_Olist_OCons @ SY4453 @ ( c_List_Olist_ONil @ SV1344 ) @ SV1344 ) @ SV1344 ) )
| ( SV968 = SY4453 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2733]) ).
thf(3212,plain,
! [SV1345: $i,SV969: $i,SV502: $i] :
( ( ( ( c_List_Oappend @ SV502 @ SV969 @ SV1345 )
!= ( c_List_Olist_ONil @ SV1345 ) )
| ( SV969
= ( c_List_Olist_ONil @ SV1345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2734]) ).
thf(3213,plain,
! [SV1346: $i,SV970: $i,SV503: $i] :
( ( ! [SY4454: $i] :
( ( ( c_List_Omap @ SV503 @ SV970 @ SV1346 @ SY4454 )
!= ( c_List_Olist_ONil @ SY4454 ) )
| ( SV970
= ( c_List_Olist_ONil @ SV1346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2735]) ).
thf(3214,plain,
! [SV1347: $i,SV971: $i,SV504: $i] :
( ( ! [SY4455: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV504 ) @ SV971 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1347 @ SY4455 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV504
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1347 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV504 @ SV971 @ SV1347 @ SY4455 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SY4455
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2736]) ).
thf(3215,plain,
! [SV1348: $i,SV972: $i,SV505: $i] :
( ( ! [SY4456: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV505 ) @ SV972 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1348 ) @ SY4456 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV972 = SY4456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2737]) ).
thf(3216,plain,
! [SV1349: $i,SV973: $i,SV506: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV506 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV973 @ SV1349 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ SV506 )
= SV973 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2738]) ).
thf(3217,plain,
! [SV507: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV507 )
= $false )
| ( ( ( c_HOL_Oone__class_Oone @ SV507 )
!= ( c_HOL_Ozero__class_Ozero @ SV507 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2739]) ).
thf(3218,plain,
! [SV1350: $i,SV974: $i,SV508: $i] :
( ( ( c_List_Olist_OCons @ SV508 @ SV974 @ SV1350 )
!= SV974 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2740]) ).
thf(3219,plain,
! [SV975: $i,SV509: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV509 ) @ SV975 )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( SV509
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2741]) ).
thf(3220,plain,
! [SV1351: $i,SV976: $i,SV510: $i] :
( ( ( ( c_List_Oappend @ SV510 @ SV976 @ SV1351 )
!= SV976 )
| ( SV510
= ( c_List_Olist_ONil @ SV1351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2742]) ).
thf(3221,plain,
! [SV977: $i,SV511: $i] :
( ( ( c_Lambda_OdB_OVar @ SV511 )
= ( c_Lambda_OdB_OAbs @ SV977 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2743]) ).
thf(3222,plain,
! [SV1352: $i,SV978: $i,SV512: $i] :
( ( ( ( c_List_Oappend @ SV512 @ SV978 @ SV1352 )
!= ( c_List_Olist_ONil @ SV1352 ) )
| ( SV512
= ( c_List_Olist_ONil @ SV1352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2744]) ).
thf(3223,plain,
! [SV1353: $i,SV979: $i,SV513: $i] :
( ( ( ( c_List_Oappend @ SV513 @ SV979 @ SV1353 )
!= SV513 )
| ( SV979
= ( c_List_Olist_ONil @ SV1353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2745]) ).
thf(3224,plain,
! [SV1354: $i,SV980: $i,SV514: $i] :
( ( ! [SY4457: $i] :
( ( ( c_List_Oappend @ SV514 @ SV980 @ SV1354 )
!= ( c_List_Oappend @ SY4457 @ SV980 @ SV1354 ) )
| ( SV514 = SY4457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2746]) ).
thf(3225,plain,
! [SV1355: $i,SV981: $i,SV515: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV515 ) @ SV981 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV515 ) @ SV1355 ) )
| ( SV981 = SV1355 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2747]) ).
thf(3226,plain,
! [SV1356: $i,SV982: $i,SV516: $i] :
( ( ! [SY4458: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV516 ) @ SV982 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1356 ) @ SY4458 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV516 = SV1356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2748]) ).
thf(3227,plain,
! [SV1357: $i,SV983: $i,SV517: $i] :
( ( SV517
!= ( c_List_Olist_OCons @ SV983 @ SV517 @ SV1357 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2749]) ).
thf(3228,plain,
! [SV518: $i,SV1: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV1 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV1 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV518 @ SV1 ) @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2750]) ).
thf(3229,plain,
! [SV519: $i,SV2: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV2 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV2 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV519 @ SV2 ) @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2751]) ).
thf(3230,plain,
! [SV1358: $i,SV984: $i,SV520: $i,SV3: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV3 )
| ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV520 @ SV984 @ SV3 ) @ ( c_Power_Opower__class_Opower @ SV1358 @ SV984 @ SV3 ) @ SV3 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV520 @ SV3 )
| ~ ( c_lessequals @ SV520 @ SV1358 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2752]) ).
thf(3231,plain,
! [SV985: $i,SV521: $i,SV4: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV4 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV4 ) @ ( c_Power_Opower__class_Opower @ SV521 @ SV985 @ SV4 ) @ SV4 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV4 ) @ SV521 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2753]) ).
thf(3232,plain,
! [SV522: $i,SV5: $i] :
( ( ( class_Power_Opower @ SV5 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV522 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV5 )
= ( c_HOL_Oone__class_Oone @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2754]) ).
thf(3233,plain,
! [SV523: $i,SV6: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV6 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV523 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV6 )
= ( c_HOL_Oone__class_Oone @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2755]) ).
thf(3234,plain,
! [SV1359: $i,SV986: $i,SV524: $i,SV7: $i] :
( ( ! [SY4459: $i,SY4460: $i] :
( ~ ( c_Type_Otyping @ SV7 @ SV524 @ SV986 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV7 @ SV1359 @ SV986 @ tc_Type_Otype ) @ SY4459 @ SY4460 )
| ( c_Type_Otyping @ SV7 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SY4459 ) @ SV524 ) @ SV1359 ) @ SY4460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2756]) ).
thf(3235,plain,
! [SV1360: $i,SV987: $i,SV525: $i,SV8: $i] :
( ( ! [SY4461: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ SV8 @ SV525 @ SV987 @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1360 ) @ SV525 ) @ SY4461 )
| ~ ( c_Type_Otyping @ SV8 @ SV1360 @ SY4461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2757]) ).
thf(3236,plain,
! [SV1361: $i,SV988: $i,SV526: $i,SV9: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV9 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV526 @ SV988 @ SV9 ) @ ( c_Power_Opower__class_Opower @ SV526 @ SV1361 @ SV9 ) @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV526 @ ( c_HOL_Oone__class_Oone @ SV9 ) @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV526 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV1361 @ SV988 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2758]) ).
thf(3237,plain,
! [SV989: $i,SV527: $i,SV10: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV10 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV10 ) @ ( c_Power_Opower__class_Opower @ SV527 @ SV989 @ SV10 ) @ SV10 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV989 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV10 ) @ SV527 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2759]) ).
thf(3238,plain,
! [SV1362: $i,SV990: $i,SV528: $i,SV11: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV11 ) @ SV528 ) @ SV990 ) ) @ SV1362 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV11 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1362 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV528 ) @ SV1362 ) ) @ SV990 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV990 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1362 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2760]) ).
thf(3239,plain,
! [SV1363: $i,SV991: $i,SV529: $i,SV12: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV12 ) @ SV529 ) @ SV991 ) ) @ SV1363 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV12 ) @ SV1363 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV529 ) @ SV1363 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV991 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1363 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV991 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2761]) ).
thf(3240,plain,
! [SV531: $i,SV14: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV14 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV531 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV14 ) @ SV531 ) @ ( c_HOL_Oone__class_Oone @ SV14 ) ) @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2763]) ).
thf(3241,plain,
! [SV1364: $i,SV992: $i,SV532: $i,SV15: $i] :
( ( ! [SY4462: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV15 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SV532 ) @ SV992 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SV1364 ) @ SY4462 ) @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV992 @ SY4462 @ SV15 )
| ~ ( c_lessequals @ SV532 @ SV1364 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2764]) ).
thf(3242,plain,
! [SV1365: $i,SV993: $i,SV533: $i,SV16: $i] :
( ( ! [SY4463: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV16 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SV533 ) @ SV993 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SV1365 ) @ SY4463 ) @ SV16 )
| ~ ( c_lessequals @ SV993 @ SY4463 @ SV16 )
| ~ ( c_HOL_Oord__class_Oless @ SV533 @ SV1365 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2765]) ).
thf(3243,plain,
! [SV994: $i,SV534: $i,SV17: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV17 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV17 ) @ SV534 ) @ SV994 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
| ~ ( c_lessequals @ SV994 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
| ~ ( c_lessequals @ SV534 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2766]) ).
thf(3244,plain,
! [SV535: $i,SV18: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV18 )
= $false )
| ( ( ( c_lessequals @ SV535 @ ( c_HOL_Ozero__class_Ozero @ SV18 ) @ SV18 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV18 ) @ SV535 ) @ SV535 ) @ ( c_HOL_Ozero__class_Ozero @ SV18 ) @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2767]) ).
thf(3245,plain,
! [SV536: $i,SV19: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV19 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV19 ) @ SV536 ) @ SV536 ) @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 )
| ~ ( c_lessequals @ SV536 @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2768]) ).
thf(3246,plain,
! [SV1366: $i,SV995: $i,SV537: $i,SV20: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV20 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV20 )
| ( c_lessequals @ SV537 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV20 ) @ SV995 ) @ SV1366 ) @ SV20 )
| ~ ( c_lessequals @ SV537 @ SV995 @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV1366 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2769]) ).
thf(3247,plain,
! [SV1367: $i,SV996: $i,SV538: $i,SV21: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV21 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV21 )
| ( c_lessequals @ SV538 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SV996 ) @ SV1367 ) @ SV21 )
| ~ ( c_lessequals @ SV538 @ SV1367 @ SV21 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ SV996 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2770]) ).
thf(3248,plain,
! [SV539: $i,SV22: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV22 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV22 ) @ SV539 @ SV22 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV22 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV539 ) @ SV539 ) @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2771]) ).
thf(3249,plain,
! [SV540: $i,SV23: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV23 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV23 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV23 ) @ SV540 ) @ SV540 ) @ SV23 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV23 ) @ SV540 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2772]) ).
thf(3250,plain,
! [SV24: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ SV24 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ SV24 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) )
= ( c_HOL_Ozero__class_Ozero @ SV24 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2773]) ).
thf(3251,plain,
! [SV997: $i,SV541: $i,SV25: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV25 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SV541 ) @ SV997 ) @ SV25 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV997 @ SV25 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV541 @ SV25 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2774]) ).
thf(3252,plain,
! [SV27: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV27 ) @ ( c_HOL_Ozero__class_Ozero @ SV27 ) @ SV27 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2776]) ).
thf(3253,plain,
! [SV998: $i,SV542: $i,SV28: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV28 ) )
= $true )
| ( ( ( c_lessequals @ SV542 @ SV998 @ SV28 )
| ( c_lessequals @ SV998 @ SV542 @ SV28 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2777]) ).
thf(3254,plain,
! [SV999: $i,SV543: $i,SV29: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV29 ) )
= $true )
| ( ( ( SV543 = SV999 )
| ( c_HOL_Oord__class_Oless @ SV543 @ SV999 @ SV29 )
| ~ ( c_lessequals @ SV543 @ SV999 @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2778]) ).
thf(3255,plain,
! [SV1000: $i,SV544: $i,SV30: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV30 ) )
= $true )
| ( ( ( SV544 = SV1000 )
| ~ ( c_lessequals @ SV544 @ SV1000 @ SV30 )
| ( c_HOL_Oord__class_Oless @ SV544 @ SV1000 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2779]) ).
thf(3256,plain,
! [SV1001: $i,SV545: $i,SV31: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV31 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV545 @ SV1001 @ SV31 )
| ~ ( c_lessequals @ SV545 @ SV1001 @ SV31 )
| ( SV545 = SV1001 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2780]) ).
thf(3257,plain,
! [SV1002: $i,SV546: $i,SV32: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV32 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV546 @ SV1002 @ SV32 )
| ( SV546 = SV1002 )
| ~ ( c_lessequals @ SV546 @ SV1002 @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2781]) ).
thf(3258,plain,
! [SV1003: $i,SV547: $i,SV33: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV33 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV547 @ SV1003 @ SV33 )
| ( SV547 = SV1003 )
| ~ ( c_lessequals @ SV547 @ SV1003 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2782]) ).
thf(3259,plain,
! [SV1004: $i,SV548: $i,SV34: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV34 ) )
= $true )
| ( ( ( SV548 = SV1004 )
| ( c_HOL_Oord__class_Oless @ SV548 @ SV1004 @ SV34 )
| ~ ( c_lessequals @ SV548 @ SV1004 @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2783]) ).
thf(3260,plain,
! [SV1005: $i,SV549: $i,SV35: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV35 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV549 @ SV1005 @ SV35 )
| ~ ( c_lessequals @ SV549 @ SV1005 @ SV35 )
| ( SV1005 = SV549 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2784]) ).
thf(3261,plain,
! [SV1006: $i,SV550: $i,SV36: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV36 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV550 @ SV1006 @ SV36 )
| ( SV1006 = SV550 )
| ~ ( c_lessequals @ SV550 @ SV1006 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2785]) ).
thf(3262,plain,
! [SV1368: $i,SV1007: $i,SV551: $i,SV37: $i] :
( ( ! [SY4464: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV37 )
| ( c_lessequals @ SV551 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV1007 ) @ SV1368 ) @ SV37 )
| ~ ( c_lessequals @ SY4464 @ SV1368 @ SV37 )
| ~ ( c_lessequals @ SV551 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV1007 ) @ SY4464 ) @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2786]) ).
thf(3263,plain,
! [SV1369: $i,SV1008: $i,SV552: $i,SV38: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV38 )
| ( c_HOL_Oord__class_Oless @ SV552 @ SV1008 @ SV38 )
| ~ ( c_lessequals @ SV1369 @ SV1008 @ SV38 )
| ~ ( c_HOL_Oord__class_Oless @ SV552 @ SV1369 @ SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2787]) ).
thf(3264,plain,
! [SV1370: $i,SV1009: $i,SV553: $i,SV39: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV39 )
| ( c_HOL_Oord__class_Oless @ SV553 @ SV1009 @ SV39 )
| ~ ( c_HOL_Oord__class_Oless @ SV1370 @ SV1009 @ SV39 )
| ~ ( c_lessequals @ SV553 @ SV1370 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2788]) ).
thf(3265,plain,
! [SV554: $i,SV40: $i] :
( ( ( class_Orderings_Opreorder @ SV40 )
= $false )
| ( ( c_lessequals @ SV554 @ SV554 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2789]) ).
thf(3266,plain,
! [SV555: $i,SV41: $i] :
( ( ( class_Orderings_Oorder @ SV41 )
= $false )
| ( ( c_lessequals @ SV555 @ SV555 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2790]) ).
thf(3267,plain,
! [SV1371: $i,SV1010: $i,SV556: $i,SV42: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV42 )
| ( c_lessequals @ SV556 @ SV1010 @ SV42 )
| ~ ( c_lessequals @ SV1371 @ SV1010 @ SV42 )
| ~ ( c_lessequals @ SV556 @ SV1371 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2791]) ).
thf(3268,plain,
! [SV1372: $i,SV1011: $i,SV557: $i,SV43: $i] :
( ( ~ ( class_Orderings_Oorder @ SV43 )
| ( c_HOL_Oord__class_Oless @ SV557 @ SV1011 @ SV43 )
| ~ ( c_HOL_Oord__class_Oless @ SV557 @ SV1372 @ SV43 )
| ~ ( c_lessequals @ SV1372 @ SV1011 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2792]) ).
thf(3269,plain,
! [SV1373: $i,SV1012: $i,SV558: $i,SV44: $i] :
( ( ~ ( class_Orderings_Oorder @ SV44 )
| ( c_HOL_Oord__class_Oless @ SV558 @ SV1012 @ SV44 )
| ~ ( c_lessequals @ SV558 @ SV1373 @ SV44 )
| ~ ( c_HOL_Oord__class_Oless @ SV1373 @ SV1012 @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2793]) ).
thf(3270,plain,
! [SV1374: $i,SV1013: $i,SV559: $i,SV45: $i] :
( ( ~ ( class_Orderings_Oorder @ SV45 )
| ( c_lessequals @ SV559 @ SV1013 @ SV45 )
| ~ ( c_lessequals @ SV559 @ SV1374 @ SV45 )
| ~ ( c_lessequals @ SV1374 @ SV1013 @ SV45 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2794]) ).
thf(3271,plain,
! [SV1375: $i,SV1014: $i,SV560: $i,SV46: $i] :
( ( ! [SY4465: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV46 @ SV560 @ SV1014 @ SV1375 ) @ SY4465 )
= ( hAPP @ SV46 @ SY4465 ) )
| ~ ( c_HOL_Oord__class_Oless @ SY4465 @ SV560 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2795]) ).
thf(3272,plain,
! [SV1376: $i,SV1015: $i,SV561: $i,SV47: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV47 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ SV561 ) @ SV1015 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ SV561 ) @ SV1376 ) @ SV47 )
| ~ ( c_lessequals @ SV1015 @ SV1376 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2796]) ).
thf(3273,plain,
! [SV1377: $i,SV1016: $i,SV562: $i,SV48: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV48 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV48 ) @ SV562 ) @ SV1016 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV48 ) @ SV1377 ) @ SV1016 ) @ SV48 )
| ~ ( c_lessequals @ SV562 @ SV1377 @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2797]) ).
thf(3274,plain,
! [SV1378: $i,SV1017: $i,SV563: $i,SV49: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV49 )
| ( c_lessequals @ SV563 @ SV1017 @ SV49 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SV1378 ) @ SV563 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SV1378 ) @ SV1017 ) @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2798]) ).
thf(3275,plain,
! [SV1379: $i,SV1018: $i,SV564: $i,SV50: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV564 ) @ SV1018 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV564 ) @ SV1379 ) @ SV50 )
| ~ ( c_lessequals @ SV1018 @ SV1379 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2799]) ).
thf(3276,plain,
! [SV1380: $i,SV1019: $i,SV565: $i,SV51: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV51 )
| ( c_lessequals @ SV565 @ SV1019 @ SV51 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV51 ) @ SV565 ) @ SV1380 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV51 ) @ SV1019 ) @ SV1380 ) @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2800]) ).
thf(3277,plain,
! [SV1381: $i,SV1020: $i,SV566: $i,SV52: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV52 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV566 ) @ SV1020 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV1381 ) @ SV1020 ) @ SV52 )
| ~ ( c_lessequals @ SV566 @ SV1381 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2801]) ).
thf(3278,plain,
! [SV1021: $i,SV567: $i,SV53: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV53 ) )
= $true )
| ( ( ( c_lessequals @ SV567 @ SV1021 @ SV53 )
| ~ ( c_HOL_Oord__class_Oless @ SV567 @ SV1021 @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2802]) ).
thf(3279,plain,
! [SV1022: $i,SV568: $i,SV54: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV54 ) )
= $true )
| ( ( ( c_lessequals @ SV568 @ SV1022 @ SV54 )
| ~ ( c_HOL_Oord__class_Oless @ SV568 @ SV1022 @ SV54 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2803]) ).
thf(3280,plain,
! [SV1023: $i,SV569: $i,SV55: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV55 ) )
= $true )
| ( ( ( SV569 = SV1023 )
| ~ ( c_lessequals @ SV569 @ SV1023 @ SV55 )
| ~ ( c_lessequals @ SV1023 @ SV569 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2804]) ).
thf(3281,plain,
! [SV1024: $i,SV570: $i,SV56: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV56 ) )
= $true )
| ( ( ( SV570 = SV1024 )
| ~ ( c_lessequals @ SV1024 @ SV570 @ SV56 )
| ~ ( c_lessequals @ SV570 @ SV1024 @ SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2805]) ).
thf(3282,plain,
! [SV1025: $i,SV571: $i,SV57: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV57 ) )
= $true )
| ( ( ( SV571 = SV1025 )
| ~ ( c_lessequals @ SV1025 @ SV571 @ SV57 )
| ~ ( c_lessequals @ SV571 @ SV1025 @ SV57 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2806]) ).
thf(3283,plain,
! [SV1382: $i,SV1026: $i,SV572: $i,SV58: $i] :
( ( ! [SY4466: $i,SY4467: $i,SY4468: $i] :
( ( ( hAPP @ ( hAPP @ SV58 @ SV572 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= SV572 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1026 @ SV1382 @ SV58 @ SY4466 @ SY4467 @ SY4468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2807]) ).
thf(3284,plain,
! [SV59: $i] :
( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV59 ) @ ( c_HOL_Ozero__class_Ozero @ SV59 ) @ SV59 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2808]) ).
thf(3285,plain,
! [SV1027: $i,SV573: $i,SV60: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV60 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV573 @ SV1027 @ SV60 )
| ( c_lessequals @ SV1027 @ SV573 @ SV60 )
| ~ ( c_lessequals @ SV573 @ SV1027 @ SV60 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2809]) ).
thf(3286,plain,
! [SV1383: $i,SV1028: $i,SV574: $i,SV62: $i] :
( ( ( hAPP @ ( c_Type_Oshift @ SV62 @ SV574 @ SV1028 @ SV1383 ) @ SV574 )
= SV1028 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2811]) ).
thf(3287,plain,
! [SV1384: $i,SV1029: $i,SV575: $i,SV63: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV63 )
| ( c_lessequals @ SV575 @ SV1029 @ SV63 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV575 @ SV1384 @ SV63 ) @ SV1029 @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2812]) ).
thf(3288,plain,
! [SV1385: $i,SV1030: $i,SV576: $i,SV64: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV64 )
| ( c_lessequals @ SV576 @ SV1030 @ SV64 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1385 @ SV576 @ SV64 ) @ SV1030 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2813]) ).
thf(3289,plain,
! [SV1386: $i,SV1031: $i,SV577: $i,SV65: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV65 )
| ( c_lessequals @ SV577 @ ( c_Orderings_Oord__class_Omax @ SV1031 @ SV1386 @ SV65 ) @ SV65 )
| ~ ( c_lessequals @ SV577 @ SV1031 @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2814]) ).
thf(3290,plain,
! [SV1387: $i,SV1032: $i,SV578: $i,SV66: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV66 )
| ( c_lessequals @ SV578 @ ( c_Orderings_Oord__class_Omax @ SV1032 @ SV1387 @ SV66 ) @ SV66 )
| ~ ( c_lessequals @ SV578 @ SV1387 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2815]) ).
thf(3291,plain,
! [SV1388: $i,SV1033: $i,SV579: $i,SV67: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV67 )
| ( c_lessequals @ SV579 @ ( c_Orderings_Oord__class_Omax @ SV1033 @ SV1388 @ SV67 ) @ SV67 )
| ~ ( c_lessequals @ SV579 @ SV1033 @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2816]) ).
thf(3292,plain,
! [SV1389: $i,SV1034: $i,SV580: $i,SV68: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV68 )
| ( c_lessequals @ SV580 @ ( c_Orderings_Oord__class_Omax @ SV1034 @ SV1389 @ SV68 ) @ SV68 )
| ~ ( c_lessequals @ SV580 @ SV1389 @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2817]) ).
thf(3293,plain,
! [SV1390: $i,SV1035: $i,SV581: $i,SV69: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV69 )
| ( c_lessequals @ SV581 @ SV1035 @ SV69 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV581 @ SV1390 @ SV69 ) @ SV1035 @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2818]) ).
thf(3294,plain,
! [SV1391: $i,SV1036: $i,SV582: $i,SV70: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV70 )
| ( c_lessequals @ SV582 @ SV1036 @ SV70 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1391 @ SV582 @ SV70 ) @ SV1036 @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2819]) ).
thf(3295,plain,
! [SV583: $i,SV71: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV71 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV583 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV71 )
= SV583 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2820]) ).
thf(3296,plain,
! [SV584: $i,SV72: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV72 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV584 @ ( c_HOL_Oone__class_Oone @ tc_nat ) @ SV72 )
= SV584 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2821]) ).
thf(3297,plain,
! [SV1392: $i,SV1037: $i,SV585: $i,SV73: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV73 )
| ( c_lessequals @ SV585 @ SV1037 @ SV73 )
| ( c_lessequals @ SV585 @ SV1392 @ SV73 )
| ~ ( c_lessequals @ SV585 @ ( c_Orderings_Oord__class_Omax @ SV1392 @ SV1037 @ SV73 ) @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2822]) ).
thf(3298,plain,
! [SV1038: $i,SV586: $i,SV74: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV74 ) )
= $true )
| ( ( c_lessequals @ SV586 @ ( c_Orderings_Oord__class_Omax @ SV1038 @ SV586 @ SV74 ) @ SV74 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2823]) ).
thf(3299,plain,
! [SV1039: $i,SV587: $i,SV75: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV75 ) )
= $true )
| ( ( c_lessequals @ SV587 @ ( c_Orderings_Oord__class_Omax @ SV587 @ SV1039 @ SV75 ) @ SV75 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2824]) ).
thf(3300,plain,
! [SV1393: $i,SV1040: $i,SV588: $i,SV76: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV76 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV588 @ SV1040 @ SV76 ) @ SV1393 @ SV76 )
| ~ ( c_lessequals @ SV1040 @ SV1393 @ SV76 )
| ~ ( c_lessequals @ SV588 @ SV1393 @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2825]) ).
thf(3301,plain,
! [SV1394: $i,SV1041: $i,SV589: $i,SV77: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV77 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV589 @ SV1041 @ SV77 ) @ SV1394 @ SV77 )
| ~ ( c_lessequals @ SV1041 @ SV1394 @ SV77 )
| ~ ( c_lessequals @ SV589 @ SV1394 @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2826]) ).
thf(3302,plain,
! [SV1395: $i,SV1042: $i,SV590: $i,SV78: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV78 )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV590 @ SV1042 @ SV78 ) @ SV1395 @ SV78 )
| ~ ( c_lessequals @ SV1042 @ SV1395 @ SV78 )
| ~ ( c_lessequals @ SV590 @ SV1395 @ SV78 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2827]) ).
thf(3303,plain,
! [SV1043: $i,SV591: $i,SV79: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV79 ) )
= $true )
| ( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV79 ) @ ( c_Power_Opower__class_Opower @ SV591 @ SV1043 @ SV79 ) @ SV79 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV79 ) @ SV591 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2828]) ).
thf(3304,plain,
! [SV1396: $i,SV1044: $i,SV592: $i,SV80: $i] :
( ( ! [SY4469: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV80 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SV592 ) @ SV1044 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SV1396 ) @ SY4469 ) @ SV80 )
| ~ ( c_lessequals @ SV1044 @ SY4469 @ SV80 )
| ~ ( c_lessequals @ SV592 @ SV1396 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2829]) ).
thf(3305,plain,
! [SV1045: $i,SV593: $i,SV81: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV81 ) )
= $true )
| ( ( ( ( c_Orderings_Oord__class_Omax @ SV593 @ SV1045 @ SV81 )
= SV1045 )
| ~ ( c_lessequals @ SV593 @ SV1045 @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2830]) ).
thf(3306,plain,
! [SV1046: $i,SV594: $i,SV82: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV82 ) )
= $true )
| ( ( ( ( c_Orderings_Oord__class_Omax @ SV594 @ SV1046 @ SV82 )
= SV594 )
| ~ ( c_lessequals @ SV1046 @ SV594 @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2831]) ).
thf(3307,plain,
! [SV595: $i,SV83: $i] :
( ( ( class_OrderedGroup_Omonoid__mult @ SV83 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ SV83 ) @ SV595 @ SV83 )
= ( c_HOL_Oone__class_Oone @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2832]) ).
thf(3308,plain,
! [SV1047: $i,SV596: $i,SV84: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV84 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV596 @ SV1047 @ SV84 )
| ( c_lessequals @ SV1047 @ SV596 @ SV84 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2833]) ).
thf(3309,plain,
! [SV597: $i,SV85: $i] :
( ( ( class_Orderings_Olinorder @ SV85 )
= $false )
| ( ( ~ ( c_lessequals @ SV597 @ SV597 @ SV85 )
| ~ ( c_HOL_Oord__class_Oless @ SV597 @ SV597 @ SV85 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2834]) ).
thf(3310,plain,
! [SV598: $i,SV86: $i] :
( ( ( class_Orderings_Olinorder @ SV86 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV598 @ SV598 @ SV86 )
| ( c_lessequals @ SV598 @ SV598 @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2835]) ).
thf(3311,plain,
! [SV1048: $i,SV599: $i,SV87: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV87 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV599 @ SV1048 @ SV87 )
| ~ ( c_lessequals @ SV1048 @ SV599 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2836]) ).
thf(3312,plain,
! [SV1049: $i,SV600: $i,SV88: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV88 ) )
= $true )
| ( ( ( c_lessequals @ SV600 @ SV1049 @ SV88 )
| ( c_HOL_Oord__class_Oless @ SV1049 @ SV600 @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2837]) ).
thf(3313,plain,
! [SV1050: $i,SV601: $i,SV89: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV89 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV601 @ SV1050 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV1050 @ SV601 @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2838]) ).
thf(3314,plain,
! [SV1051: $i,SV602: $i,SV90: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV90 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV602 @ SV1051 @ SV90 )
| ( c_lessequals @ SV1051 @ SV602 @ SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2839]) ).
thf(3315,plain,
! [SV1052: $i,SV603: $i,SV91: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV91 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV603 @ SV1052 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV1052 @ SV603 @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2840]) ).
thf(3316,plain,
! [SV1053: $i,SV604: $i,SV93: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV93 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV604 ) @ SV1053 ) @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 )
| ~ ( c_lessequals @ SV1053 @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ SV604 @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2842]) ).
thf(3317,plain,
! [SV1054: $i,SV605: $i,SV94: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV94 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV605 ) @ SV1054 ) @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 )
| ~ ( c_HOL_Oord__class_Oless @ SV1054 @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 )
| ~ ( c_lessequals @ SV605 @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2843]) ).
thf(3318,plain,
! [SV1397: $i,SV1055: $i,SV606: $i,SV95: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV95 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV95 )
| ( c_HOL_Oord__class_Oless @ SV606 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV1055 ) @ SV1397 ) @ SV95 )
| ~ ( c_lessequals @ SV606 @ SV1397 @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV1055 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2844]) ).
thf(3319,plain,
! [SV1398: $i,SV1056: $i,SV607: $i,SV96: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
| ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV96 )
| ( c_HOL_Oord__class_Oless @ SV607 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SV1056 ) @ SV1398 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ SV607 @ SV1398 @ SV96 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV1056 @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2845]) ).
thf(3320,plain,
! [SV1057: $i,SV608: $i,SV97: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV97 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV608 ) @ SV1057 ) @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV1057 @ SV97 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV608 @ SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2846]) ).
thf(3321,plain,
! [SV1058: $i,SV609: $i,SV98: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV98 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV98 ) @ SV609 ) @ SV1058 ) @ SV98 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ SV1058 @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ SV609 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2847]) ).
thf(3322,plain,
! [SV1399: $i,SV1059: $i,SV610: $i,SV100: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV100 )
| ( c_HOL_Oord__class_Oless @ SV610 @ SV1059 @ SV100 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV100 ) @ SV1059 @ SV100 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV610 @ SV1399 @ SV100 ) @ ( c_Power_Opower__class_Opower @ SV1059 @ SV1399 @ SV100 ) @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2849]) ).
thf(3323,plain,
! [SV101: $i] :
( ( ( ~ ( class_Power_Opower @ SV101 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV101 )
= ( c_HOL_Oone__class_Oone @ SV101 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2850]) ).
thf(3324,plain,
! [SV1400: $i,SV1060: $i,SV611: $i,SV102: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV102 )
| ( c_HOL_Oord__class_Oless @ SV611 @ SV1060 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1400 @ SV611 @ SV102 ) @ ( c_Power_Opower__class_Opower @ SV1400 @ SV1060 @ SV102 ) @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV102 ) @ SV1400 @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2851]) ).
thf(3325,plain,
! [SV1401: $i,SV1061: $i,SV612: $i,SV103: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV103 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV612 @ SV1061 @ SV103 ) @ ( c_Power_Opower__class_Opower @ SV612 @ SV1401 @ SV103 ) @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV103 ) @ SV612 @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ SV1061 @ SV1401 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2852]) ).
thf(3326,plain,
! [SV1402: $i,SV1062: $i,SV613: $i,SV104: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV104 )
| ( c_HOL_Oord__class_Oless @ SV613 @ SV1062 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1402 @ SV613 @ SV104 ) @ ( c_Power_Opower__class_Opower @ SV1402 @ SV1062 @ SV104 ) @ SV104 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV104 ) @ SV1402 @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2853]) ).
thf(3327,plain,
! [SV1403: $i,SV1063: $i,SV614: $i,SV105: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV105 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV614 @ SV1063 @ SV105 ) @ ( c_Power_Opower__class_Opower @ SV614 @ SV1403 @ SV105 ) @ SV105 )
| ~ ( c_HOL_Oord__class_Oless @ SV1063 @ SV1403 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV105 ) @ SV614 @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2854]) ).
thf(3328,plain,
! [SV1404: $i,SV1066: $i,SV618: $i,SV109: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV109 )
| ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV618 @ SV1066 @ SV109 ) @ ( c_Power_Opower__class_Opower @ SV1404 @ SV1066 @ SV109 ) @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1066 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV618 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SV618 @ SV1404 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2857]) ).
thf(3329,plain,
! [SV1405: $i,SV1068: $i,SV620: $i,SV111: $i] :
( ( ! [SY4470: $i] :
( ( c_Type_Otypings @ ( c_Type_Oshift @ SV111 @ SV620 @ SV1068 @ tc_Type_Otype ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ SV620 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1405 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY4470 )
| ~ ( c_Type_Otypings @ SV111 @ SV1405 @ SY4470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2859]) ).
thf(3330,plain,
! [SV1406: $i,SV1069: $i,SV621: $i,SV112: $i] :
( ( ! [SY4471: $i,SY4472: $i] :
( ( c_Type_Otypings @ SV112 @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SV621 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV1069 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1406 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SY4471 )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ SV112 @ SV1069 @ SY4472 @ tc_Type_Otype ) @ SV1406 @ SY4471 )
| ~ ( c_Type_Otyping @ SV112 @ SV621 @ SY4472 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2860]) ).
thf(3331,plain,
! [SV622: $i,SV113: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV113 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV113 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @ SV113 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV113 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV113 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV113 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV113 @ SV622 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2861]) ).
thf(3332,plain,
! [SV623: $i,SV114: $i] :
( ( ( hBOOL @ ( hAPP @ SV114 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV114 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__4 @ SV114 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV114 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV114 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV114 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ( hBOOL @ ( hAPP @ SV114 @ SV623 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2862]) ).
thf(3333,plain,
! [SV115: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV115 ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV115 ) ) )
= $true )
| ( ( SV115
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV115 ) ) )
= $true )
| ( ( SV115
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV115 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV115 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV115 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2863]) ).
thf(3334,plain,
! [SV1407: $i,SV1070: $i,SV624: $i,SV116: $i] :
( ( ! [SY4473: $i] :
( ( c_List_Omap @ SV116 @ ( c_List_Olist_OCons @ SV624 @ SV1070 @ SV1407 ) @ SV1407 @ SY4473 )
= ( c_List_Olist_OCons @ ( hAPP @ SV116 @ SV624 ) @ ( c_List_Omap @ SV116 @ SV1070 @ SV1407 @ SY4473 ) @ SY4473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2864]) ).
thf(3335,plain,
! [SV1408: $i,SV1071: $i,SV625: $i,SV117: $i] :
( ( ! [SY4474: $i] :
( ( c_List_Olist_OCons @ ( hAPP @ SV117 @ SV625 ) @ ( c_List_Omap @ SV117 @ SV1071 @ SV1408 @ SY4474 ) @ SY4474 )
= ( c_List_Omap @ SV117 @ ( c_List_Olist_OCons @ SV625 @ SV1071 @ SV1408 ) @ SV1408 @ SY4474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2865]) ).
thf(3336,plain,
! [SV1409: $i,SV1072: $i,SV626: $i,SV118: $i] :
( ( ! [SY4475: $i] :
( ( c_List_Omap @ SV118 @ ( c_List_Olist_OCons @ SV626 @ SV1072 @ SV1409 ) @ SV1409 @ SY4475 )
= ( c_List_Olist_OCons @ ( hAPP @ SV118 @ SV626 ) @ ( c_List_Omap @ SV118 @ SV1072 @ SV1409 @ SY4475 ) @ SY4475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2866]) ).
thf(3337,plain,
! [SV1073: $i,SV627: $i,SV119: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV119 ) @ SV627 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1073 ) @ SV627 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV119 ) @ SV1073 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2867]) ).
thf(3338,plain,
! [SV1074: $i,SV628: $i,SV120: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV120 ) @ SV628 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV120 ) @ SV1074 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV628 ) @ SV1074 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2868]) ).
thf(3339,plain,
! [SV1410: $i,SV1075: $i,SV629: $i,SV121: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV121 @ SV629 @ SV1075 ) @ SV1410 @ SV1075 )
= ( c_List_Olist_OCons @ SV121 @ ( c_List_Oappend @ SV629 @ SV1410 @ SV1075 ) @ SV1075 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2869]) ).
thf(3340,plain,
! [SV1411: $i,SV1076: $i,SV630: $i,SV122: $i] :
( ( ( c_List_Oappend @ ( c_List_Olist_OCons @ SV122 @ SV630 @ SV1076 ) @ SV1411 @ SV1076 )
= ( c_List_Olist_OCons @ SV122 @ ( c_List_Oappend @ SV630 @ SV1411 @ SV1076 ) @ SV1076 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2870]) ).
thf(3341,plain,
! [SV1077: $i,SV631: $i,SV123: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV123 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV123 ) @ SV631 ) @ SV1077 ) @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 )
| ~ ( c_HOL_Oord__class_Oless @ SV1077 @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 )
| ~ ( c_HOL_Oord__class_Oless @ SV631 @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2871]) ).
thf(3342,plain,
! [SV1412: $i,SV1078: $i,SV632: $i,SV125: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV125 )
| ( c_HOL_Oord__class_Oless @ SV632 @ SV1078 @ SV125 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV1412 @ SV632 @ SV125 ) @ SV1078 @ SV125 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2873]) ).
thf(3343,plain,
! [SV1413: $i,SV1079: $i,SV633: $i,SV126: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV126 )
| ( c_HOL_Oord__class_Oless @ SV633 @ SV1079 @ SV126 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV633 @ SV1413 @ SV126 ) @ SV1079 @ SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2874]) ).
thf(3344,plain,
! [SV1414: $i,SV1080: $i,SV634: $i,SV127: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV127 )
| ( c_HOL_Oord__class_Oless @ SV634 @ ( c_Orderings_Oord__class_Omax @ SV1080 @ SV1414 @ SV127 ) @ SV127 )
| ~ ( c_HOL_Oord__class_Oless @ SV634 @ SV1414 @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2875]) ).
thf(3345,plain,
! [SV1415: $i,SV1081: $i,SV635: $i,SV128: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV128 )
| ( c_HOL_Oord__class_Oless @ SV635 @ ( c_Orderings_Oord__class_Omax @ SV1081 @ SV1415 @ SV128 ) @ SV128 )
| ~ ( c_HOL_Oord__class_Oless @ SV635 @ SV1081 @ SV128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2876]) ).
thf(3346,plain,
! [SV1416: $i,SV1082: $i,SV636: $i,SV129: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV129 )
| ( c_HOL_Oord__class_Oless @ SV636 @ ( c_Orderings_Oord__class_Omax @ SV1082 @ SV1416 @ SV129 ) @ SV129 )
| ~ ( c_HOL_Oord__class_Oless @ SV636 @ SV1416 @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2877]) ).
thf(3347,plain,
! [SV1417: $i,SV1083: $i,SV637: $i,SV130: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV130 )
| ( c_HOL_Oord__class_Oless @ SV637 @ ( c_Orderings_Oord__class_Omax @ SV1083 @ SV1417 @ SV130 ) @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SV637 @ SV1083 @ SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2878]) ).
thf(3348,plain,
! [SV1418: $i,SV1084: $i,SV638: $i,SV131: $i] :
( ( ! [SY4476: $i,SY4477: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV638 ) @ SV1084 ) )
| ( c_ListOrder_Ostep1 @ SV131 @ SV1418 @ SY4476 @ SY4477 )
| ~ ( c_ListOrder_Ostep1 @ SV131 @ ( c_List_Oappend @ SV1418 @ ( c_List_Olist_OCons @ SV638 @ ( c_List_Olist_ONil @ SY4477 ) @ SY4477 ) @ SY4477 ) @ ( c_List_Oappend @ SY4476 @ ( c_List_Olist_OCons @ SV1084 @ ( c_List_Olist_ONil @ SY4477 ) @ SY4477 ) @ SY4477 ) @ SY4477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2879]) ).
thf(3349,plain,
! [SV1419: $i,SV1085: $i,SV639: $i,SV132: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV132 @ SV639 @ SV639 ) @ SV639 ) @ SV1085 ) @ SV1419 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV132 @ SV639 ) @ SV1419 ) @ SV1085 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2880]) ).
thf(3350,plain,
! [SV1420: $i,SV1086: $i,SV640: $i,SV133: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV133 @ SV640 ) @ SV1086 ) @ SV1420 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV133 @ SV640 @ SV640 ) @ SV640 ) @ SV1420 ) @ SV1086 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2881]) ).
thf(3351,plain,
! [SV1421: $i,SV1088: $i,SV642: $i,SV135: $i] :
( ( ( c_List_Ofoldr @ SV135 @ ( c_List_Olist_ONil @ SV642 ) @ SV1088 @ SV642 @ SV1421 )
= SV1088 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2883]) ).
thf(3352,plain,
! [SV1422: $i,SV1089: $i,SV643: $i,SV136: $i] :
( ( ! [SY4478: $i,SY4479: $i] :
( ( hAPP @ ( c_COMBC @ SV136 @ SV643 @ SV1089 @ SV1422 @ SY4478 ) @ SY4479 )
= ( hAPP @ ( hAPP @ SV136 @ SY4479 ) @ SV643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2884]) ).
thf(3353,plain,
! [SV1423: $i,SV1090: $i,SV644: $i,SV137: $i] :
( ( ! [SY4480: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV644 ) @ SV1090 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV137 @ SV1423 @ SY4480 ) @ SV1090 ) @ SV644 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2885]) ).
thf(3354,plain,
! [SV1424: $i,SV1091: $i,SV645: $i,SV138: $i] :
( ( ! [SY4481: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV138 @ SV645 @ SV1091 ) @ SV1424 ) @ SY4481 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV138 @ SY4481 ) @ SV1424 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2886]) ).
thf(3355,plain,
! [SV1425: $i,SV1092: $i,SV646: $i,SV139: $i] :
( ( ! [SY4482: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV139 @ SV646 ) @ SV1092 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV139 @ SV1425 @ SY4482 ) @ SV1092 ) @ SV646 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2887]) ).
thf(3356,plain,
! [SV1426: $i,SV1093: $i,SV647: $i,SV140: $i] :
( ( ! [SY4483: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV140 @ SV647 @ SV1093 ) @ SV1426 ) @ SY4483 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV140 @ SY4483 ) @ SV1426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2888]) ).
thf(3357,plain,
! [SV141: $i,SV648: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV648 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV648 ) @ SV141 ) @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV141 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2889]) ).
thf(3358,plain,
! [SV1427: $i,SV1094: $i,SV649: $i,SV142: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV142 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ SV649 ) @ SV1094 ) ) @ SV1427 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ SV649 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ SV1094 ) @ SV1427 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2890]) ).
thf(3359,plain,
! [SV1428: $i,SV1095: $i,SV650: $i,SV143: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV143 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ SV650 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ SV1095 ) @ SV1428 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ SV1095 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ SV650 ) @ SV1428 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2891]) ).
thf(3360,plain,
! [SV1429: $i,SV1096: $i,SV651: $i,SV144: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV144 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ SV651 ) @ SV1096 ) ) @ SV1429 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ SV651 ) @ SV1429 ) ) @ SV1096 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2892]) ).
thf(3361,plain,
! [SV1430: $i,SV1097: $i,SV652: $i,SV145: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV145 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV145 ) @ SV652 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV145 ) @ SV1097 ) @ SV1430 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV145 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV145 ) @ SV652 ) @ SV1097 ) ) @ SV1430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2893]) ).
thf(3362,plain,
! [SV1431: $i,SV1098: $i,SV653: $i,SV146: $i] :
( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV146 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ SV653 ) @ SV1098 ) ) @ SV1431 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ SV653 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ SV1098 ) @ SV1431 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2894]) ).
thf(3363,plain,
! [SV1432: $i,SV1099: $i,SV654: $i,SV147: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV147 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV654 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV1099 ) @ SV1432 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV1099 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV654 ) @ SV1432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2895]) ).
thf(3364,plain,
! [SV1433: $i,SV1100: $i,SV655: $i,SV148: $i] :
( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV148 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV655 ) @ SV1100 ) ) @ SV1433 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV655 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV1100 ) @ SV1433 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2896]) ).
thf(3365,plain,
! [SV1434: $i,SV1103: $i,SV658: $i,SV151: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV151 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV658 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV1103 ) @ SV1434 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV1103 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV658 ) @ SV1434 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2899]) ).
thf(3366,plain,
! [SV1435: $i,SV1104: $i,SV659: $i,SV152: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV152 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV659 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV1104 ) @ SV1435 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV659 ) @ SV1104 ) ) @ SV1435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2900]) ).
thf(3367,plain,
! [SV1436: $i,SV1105: $i,SV660: $i,SV153: $i] :
( ( ~ ( class_Orderings_Oorder @ SV153 )
| ( c_HOL_Oord__class_Oless @ SV660 @ SV1105 @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SV660 @ SV1436 @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SV1436 @ SV1105 @ SV153 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2901]) ).
thf(3368,plain,
! [SV1437: $i,SV1106: $i,SV661: $i,SV154: $i] :
( ( ~ ( class_Orderings_Opreorder @ SV154 )
| ( c_HOL_Oord__class_Oless @ SV661 @ SV1106 @ SV154 )
| ~ ( c_HOL_Oord__class_Oless @ SV1437 @ SV1106 @ SV154 )
| ~ ( c_HOL_Oord__class_Oless @ SV661 @ SV1437 @ SV154 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2902]) ).
thf(3369,plain,
! [SV1438: $i,SV1107: $i,SV662: $i,SV155: $i] :
( ( ! [SY4484: $i] :
( ~ ( c_ListOrder_Ostep1 @ SV155 @ SV662 @ SV1107 @ SV1438 )
| ( c_ListOrder_Ostep1 @ SV155 @ ( c_List_Oappend @ SV662 @ SY4484 @ SV1438 ) @ ( c_List_Oappend @ SV1107 @ SY4484 @ SV1438 ) @ SV1438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2903]) ).
thf(3370,plain,
! [SV1439: $i,SV1108: $i,SV663: $i,SV156: $i] :
( ( ! [SY4485: $i] :
( ( c_ListOrder_Ostep1 @ SV156 @ ( c_List_Oappend @ SV663 @ SV1108 @ SV1439 ) @ ( c_List_Oappend @ SV663 @ SY4485 @ SV1439 ) @ SV1439 )
| ~ ( c_ListOrder_Ostep1 @ SV156 @ SV1108 @ SY4485 @ SV1439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2904]) ).
thf(3371,plain,
! [SV664: $i,SV157: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV157 ) @ SV664 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ SV157 ) ) @ ( c_Lambda_OdB_OAbs @ SV664 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2905]) ).
thf(3372,plain,
! [SV1440: $i,SV1109: $i,SV665: $i,SV158: $i] :
( ( ( c_List_Olistsp @ SV158 @ SV665 @ SV1109 )
| ~ ( c_List_Olistsp @ SV158 @ ( c_List_Oappend @ SV665 @ SV1440 @ SV1109 ) @ SV1109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2906]) ).
thf(3373,plain,
! [SV1441: $i,SV1110: $i,SV666: $i,SV159: $i] :
( ( ( c_List_Olistsp @ SV159 @ SV666 @ SV1110 )
| ~ ( c_List_Olistsp @ SV159 @ ( c_List_Oappend @ SV1441 @ SV666 @ SV1110 ) @ SV1110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2907]) ).
thf(3374,plain,
! [SV1442: $i,SV1111: $i,SV667: $i,SV160: $i] :
( ( ! [SY4486: $i] :
( ( c_Lambda_OdB_OdB__case @ SV160 @ SV667 @ SV1111 @ ( c_Lambda_OdB_OAbs @ SV1442 ) @ SY4486 )
= ( hAPP @ SV1111 @ SV1442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2908]) ).
thf(3375,plain,
! [SV1443: $i,SV1112: $i,SV668: $i,SV161: $i] :
( ( ! [SY4487: $i,SY4488: $i] :
( ( SV161 = SV668 )
| ( SV1112 = SV1443 )
| ~ ( c_ListOrder_Ostep1 @ SY4487 @ ( c_List_Olist_OCons @ SV668 @ SV1443 @ SY4488 ) @ ( c_List_Olist_OCons @ SV161 @ SV1112 @ SY4488 ) @ SY4488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2909]) ).
thf(3376,plain,
! [SV1444: $i,SV1113: $i,SV669: $i,SV162: $i] :
( ( ! [SY4489: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV162 @ SV669 ) @ SV1113 ) )
| ( c_ListOrder_Ostep1 @ SV162 @ ( c_List_Olist_OCons @ SV669 @ SV1444 @ SY4489 ) @ ( c_List_Olist_OCons @ SV1113 @ SV1444 @ SY4489 ) @ SY4489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2910]) ).
thf(3377,plain,
! [SV1445: $i,SV1114: $i,SV671: $i,SV164: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV164 )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV671 @ SV1114 @ SV164 ) @ SV1445 @ SV164 )
| ~ ( c_HOL_Oord__class_Oless @ SV1114 @ SV1445 @ SV164 )
| ~ ( c_HOL_Oord__class_Oless @ SV671 @ SV1445 @ SV164 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2911]) ).
thf(3378,plain,
! [SV1446: $i,SV1117: $i,SV674: $i,SV167: $i] :
( ( ( c_Wellfounded_Oaccp @ SV167 @ SV674 @ SV1117 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SV1117 ) @ SV674 ) @ SV1446 ) )
| ~ ( c_Wellfounded_Oaccp @ SV167 @ SV1446 @ SV1117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2914]) ).
thf(3379,plain,
! [SV1447: $i,SV1118: $i,SV675: $i,SV168: $i] :
( ( ( c_Wellfounded_Oaccp @ SV168 @ SV675 @ SV1118 )
| ~ ( c_Wellfounded_Oaccp @ SV168 @ SV1447 @ SV1118 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SV1118 ) @ SV675 ) @ SV1447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2915]) ).
thf(3380,plain,
! [SV1448: $i,SV1119: $i,SV676: $i,SV169: $i] :
( ( ! [SY4490: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SV676 ) @ SV1119 ) @ SV1448 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SV676 ) @ SY4490 ) @ SV1448 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SV676 ) @ SV1119 ) @ SY4490 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2916]) ).
thf(3381,plain,
! [SV172: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV172 ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV172 ) ) )
= $true )
| ( ( SV172
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV172 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV172 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2919]) ).
thf(3382,plain,
! [SV1449: $i,SV1120: $i,SV682: $i,SV178: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV178 ) @ SV682 ) @ SV1120 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV178 ) @ SV1449 ) @ SV1120 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV682 ) @ SV1449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2920]) ).
thf(3383,plain,
! [SV1450: $i,SV1121: $i,SV683: $i,SV179: $i] :
( ( ! [SY4491: $i] :
( ( c_List_Omap @ SV179 @ ( c_List_Oreplicate @ SV683 @ SV1121 @ SV1450 ) @ SV1450 @ SY4491 )
= ( c_List_Oreplicate @ SV683 @ ( hAPP @ SV179 @ SV1121 ) @ SY4491 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2921]) ).
thf(3384,plain,
! [SV1122: $i,SV684: $i,SV180: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV180 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV684 ) @ SV1122 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV180 @ SV684 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2922]) ).
thf(3385,plain,
! [SV1123: $i,SV685: $i,SV181: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV181 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV685 ) @ SV1123 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV181 @ SV1123 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2923]) ).
thf(3386,plain,
! [SV1124: $i,SV686: $i,SV182: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV182 @ SV686 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV182 ) @ SV1124 ) @ SV686 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2924]) ).
thf(3387,plain,
! [SV1125: $i,SV687: $i,SV183: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV183 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV687 ) @ SV1125 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV183 @ SV687 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2925]) ).
thf(3388,plain,
! [SV1126: $i,SV688: $i,SV184: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV184 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV688 ) @ SV1126 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV184 @ SV1126 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2926]) ).
thf(3389,plain,
! [SV1127: $i,SV689: $i,SV185: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV185 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV185 ) @ SV689 ) @ SV1127 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV185 ) @ SV1127 ) @ SV689 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2927]) ).
thf(3390,plain,
! [SV1128: $i,SV690: $i,SV186: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV186 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV186 ) @ SV690 ) @ SV1128 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV186 ) @ SV1128 ) @ SV690 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2928]) ).
thf(3391,plain,
! [SV1129: $i,SV692: $i,SV188: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV188 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV188 ) @ SV692 ) @ SV1129 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV188 ) @ SV1129 ) @ SV692 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2929]) ).
thf(3392,plain,
! [SV1451: $i,SV1130: $i,SV693: $i,SV189: $i] :
( ( ! [SY4492: $i,SY4493: $i] :
( ( c_List_Ofoldr @ SV189 @ ( c_List_Oappend @ SV693 @ SV1130 @ SV1451 ) @ SY4492 @ SV1451 @ SY4493 )
= ( c_List_Ofoldr @ SV189 @ SV693 @ ( c_List_Ofoldr @ SV189 @ SV1130 @ SY4492 @ SV1451 @ SY4493 ) @ SV1451 @ SY4493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2930]) ).
thf(3393,plain,
! [SV1452: $i,SV1131: $i,SV694: $i,SV190: $i] :
( ( ! [SY4494: $i,SY4495: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV190 @ SV694 ) @ SV1131 ) )
| ( SV694 = SV1131 )
| ~ ( c_ListOrder_Ostep1 @ SV190 @ ( c_List_Oappend @ SV1452 @ ( c_List_Olist_OCons @ SV694 @ ( c_List_Olist_ONil @ SY4494 ) @ SY4494 ) @ SY4494 ) @ ( c_List_Oappend @ SY4495 @ ( c_List_Olist_OCons @ SV1131 @ ( c_List_Olist_ONil @ SY4494 ) @ SY4494 ) @ SY4494 ) @ SY4494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2931]) ).
thf(3394,plain,
! [SV1453: $i,SV1132: $i,SV695: $i,SV191: $i] :
( ( ! [SY4496: $i,SY4497: $i,SY4498: $i,SY4499: $i,SY4500: $i] :
( ( ( hAPP @ ( hAPP @ SV191 @ ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ SV1453 ) ) @ ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ SY4496 ) )
= ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1453 ) @ SY4496 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4497 @ SV191 @ SV695 @ SY4498 @ SY4499 @ SY4500 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2932]) ).
thf(3395,plain,
! [SV1454: $i,SV1133: $i,SV696: $i,SV192: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV192 ) @ SV696 ) @ SV1133 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1454 ) @ SV696 ) @ SV1133 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV192 ) @ SV1454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2933]) ).
thf(3396,plain,
! [SV1455: $i,SV1134: $i,SV697: $i,SV193: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV193 ) @ SV697 ) @ SV1134 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV193 ) @ SV1455 ) @ SV1134 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV697 ) @ SV1455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2934]) ).
thf(3397,plain,
! [SV1135: $i,SV698: $i,SV194: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV194 ) )
= $true )
| ( ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV194 ) @ SV698 @ SV1135 @ SV194 @ SV194 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV194 ) @ SV1135 @ SV698 @ SV194 @ SV194 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2935]) ).
thf(3398,plain,
! [SV1456: $i,SV1136: $i,SV699: $i,SV195: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV195 @ SV699 ) @ SV1136 ) @ SV1456 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV195 @ SV1136 ) @ SV1456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2936]) ).
thf(3399,plain,
! [SV1137: $i,SV700: $i,SV196: $i] :
( ( c_ListOrder_Ostep1 @ SV196 @ ( c_List_Olist_ONil @ SV700 ) @ SV1137 @ SV700 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2937]) ).
thf(3400,plain,
! [SV1138: $i,SV701: $i,SV197: $i] :
( ( c_ListOrder_Ostep1 @ SV197 @ SV701 @ ( c_List_Olist_ONil @ SV1138 ) @ SV1138 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2938]) ).
thf(3401,plain,
! [SV702: $i,SV198: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV198 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ SV702 ) @ SV702 ) @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
| ~ ( c_HOL_Oord__class_Oless @ SV702 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2939]) ).
thf(3402,plain,
! [SV703: $i,SV199: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV199 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV703 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV199 ) @ SV703 ) @ SV703 ) @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2940]) ).
thf(3403,plain,
! [SV1457: $i,SV1139: $i,SV704: $i,SV200: $i] :
( ( ( c_List_Olist_OCons @ SV200 @ ( c_List_Oappend @ SV704 @ SV1139 @ SV1457 ) @ SV1457 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV200 @ SV704 @ SV1457 ) @ SV1139 @ SV1457 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2941]) ).
thf(3404,plain,
! [SV1458: $i,SV1140: $i,SV705: $i,SV201: $i] :
( ( ( c_List_Olist_OCons @ SV201 @ ( c_List_Oappend @ SV705 @ SV1140 @ SV1458 ) @ SV1458 )
= ( c_List_Oappend @ ( c_List_Olist_OCons @ SV201 @ SV705 @ SV1458 ) @ SV1140 @ SV1458 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2942]) ).
thf(3405,plain,
! [SV1459: $i,SV1141: $i,SV706: $i,SV202: $i] :
( ( ! [SY4501: $i,SY4502: $i,SY4503: $i,SY4504: $i,SY4505: $i] :
( ( ( hAPP @ ( hAPP @ SV202 @ ( hAPP @ ( hAPP @ SV706 @ SV1141 ) @ SV1459 ) ) @ SY4501 )
= ( hAPP @ ( hAPP @ SV706 @ ( hAPP @ ( hAPP @ SV202 @ SV1141 ) @ SY4501 ) ) @ ( hAPP @ ( hAPP @ SV202 @ SV1459 ) @ SY4501 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4502 @ SV706 @ SV202 @ SY4503 @ SY4504 @ SY4505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2943]) ).
thf(3406,plain,
! [SV1460: $i,SV1142: $i,SV707: $i,SV203: $i] :
( ( ! [SY4506: $i,SY4507: $i,SY4508: $i,SY4509: $i,SY4510: $i] :
( ( ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ ( hAPP @ ( hAPP @ SV1142 @ SV1460 ) @ SY4506 ) )
= ( hAPP @ ( hAPP @ SV1142 @ ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ SV1460 ) ) @ ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ SY4506 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1142 @ SV203 @ SY4507 @ SY4508 @ SY4509 @ SY4510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2944]) ).
thf(3407,plain,
! [SV1461: $i,SV1143: $i,SV708: $i,SV204: $i] :
( ( ! [SY4511: $i,SY4512: $i,SY4513: $i,SY4514: $i] :
( ( ( hAPP @ ( hAPP @ SV204 @ SV708 ) @ SV1143 )
= ( hAPP @ ( hAPP @ SV204 @ SV1143 ) @ SV708 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1461 @ SV204 @ SY4511 @ SY4512 @ SY4513 @ SY4514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2945]) ).
thf(3408,plain,
! [SV1462: $i,SV1144: $i,SV709: $i,SV205: $i] :
( ( ! [SY4515: $i,SY4516: $i,SY4517: $i,SY4518: $i,SY4519: $i] :
( ( ( hAPP @ ( hAPP @ SV205 @ SV709 ) @ ( hAPP @ ( hAPP @ SV205 @ SV1144 ) @ SV1462 ) )
= ( hAPP @ ( hAPP @ SV205 @ ( hAPP @ ( hAPP @ SV205 @ SV709 ) @ SV1144 ) ) @ SV1462 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4515 @ SV205 @ SY4516 @ SY4517 @ SY4518 @ SY4519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2946]) ).
thf(3409,plain,
! [SV1463: $i,SV1145: $i,SV710: $i,SV206: $i] :
( ( ! [SY4520: $i,SY4521: $i,SY4522: $i] :
( ( ( hAPP @ ( hAPP @ SV206 @ SV710 ) @ SV1145 )
= SV1145 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1463 @ SV206 @ SY4520 @ SY4521 @ SV710 @ SY4522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2947]) ).
thf(3410,plain,
! [SV1464: $i,SV1146: $i,SV711: $i,SV207: $i] :
( ( ! [SY4523: $i,SY4524: $i,SY4525: $i] :
( ( ( hAPP @ ( hAPP @ SV207 @ SV711 ) @ SV1146 )
= SV711 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1464 @ SV207 @ SY4523 @ SV711 @ SY4524 @ SY4525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2948]) ).
thf(3411,plain,
! [SV1465: $i,SV1147: $i,SV712: $i,SV208: $i] :
( ( ! [SY4526: $i,SY4527: $i,SY4528: $i,SY4529: $i] :
( ( ( hAPP @ ( hAPP @ SV208 @ SV712 ) @ SV1147 )
= ( hAPP @ ( hAPP @ SV208 @ SV1147 ) @ SV712 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV208 @ SV1465 @ SY4526 @ SY4527 @ SY4528 @ SY4529 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2949]) ).
thf(3412,plain,
! [SV1466: $i,SV1148: $i,SV713: $i,SV209: $i] :
( ( ! [SY4530: $i,SY4531: $i,SY4532: $i,SY4533: $i,SY4534: $i] :
( ( ( hAPP @ ( hAPP @ SV209 @ SV713 ) @ ( hAPP @ ( hAPP @ SV209 @ SV1148 ) @ SV1466 ) )
= ( hAPP @ ( hAPP @ SV209 @ ( hAPP @ ( hAPP @ SV209 @ SV713 ) @ SV1148 ) ) @ SV1466 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV209 @ SY4530 @ SY4531 @ SY4532 @ SY4533 @ SY4534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2950]) ).
thf(3413,plain,
! [SV1467: $i,SV1149: $i,SV714: $i,SV210: $i] :
( ( ! [SY4535: $i,SY4536: $i,SY4537: $i] :
( ( ( hAPP @ ( hAPP @ SV210 @ SV714 ) @ SV1149 )
= SV1149 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV210 @ SV1467 @ SY4535 @ SV714 @ SY4536 @ SY4537 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2951]) ).
thf(3414,plain,
! [SV1468: $i,SV1150: $i,SV715: $i,SV211: $i] :
( ( ! [SY4538: $i,SY4539: $i,SY4540: $i,SY4541: $i,SY4542: $i] :
( ( ( hAPP @ ( hAPP @ SV211 @ SV715 ) @ ( hAPP @ ( hAPP @ SV211 @ SV1150 ) @ SV1468 ) )
= ( hAPP @ ( hAPP @ SV211 @ ( hAPP @ ( hAPP @ SV211 @ SV715 ) @ SV1150 ) ) @ SV1468 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV211 @ SY4538 @ SY4539 @ SY4540 @ SY4541 @ SY4542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2952]) ).
thf(3415,plain,
! [SV1469: $i,SV1151: $i,SV716: $i,SV212: $i] :
( ( ! [SY4543: $i,SY4544: $i,SY4545: $i,SY4546: $i] :
( ( ( hAPP @ ( hAPP @ SV212 @ SV716 ) @ SV1151 )
= ( hAPP @ ( hAPP @ SV212 @ SV1151 ) @ SV716 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV212 @ SV1469 @ SY4543 @ SY4544 @ SY4545 @ SY4546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2953]) ).
thf(3416,plain,
! [SV1470: $i,SV1152: $i,SV717: $i,SV213: $i] :
( ( ! [SY4547: $i,SY4548: $i,SY4549: $i,SY4550: $i,SY4551: $i] :
( ( ( hAPP @ ( hAPP @ SV213 @ ( hAPP @ ( hAPP @ SV213 @ SV717 ) @ SV1152 ) ) @ SV1470 )
= ( hAPP @ ( hAPP @ SV213 @ ( hAPP @ ( hAPP @ SV213 @ SV717 ) @ SV1470 ) ) @ SV1152 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV213 @ SY4547 @ SY4548 @ SY4549 @ SY4550 @ SY4551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2954]) ).
thf(3417,plain,
! [SV1471: $i,SV1153: $i,SV718: $i,SV214: $i] :
( ( ! [SY4552: $i,SY4553: $i,SY4554: $i,SY4555: $i,SY4556: $i] :
( ( ( hAPP @ ( hAPP @ SV214 @ SV718 ) @ ( hAPP @ ( hAPP @ SV214 @ SV1153 ) @ SV1471 ) )
= ( hAPP @ ( hAPP @ SV214 @ SV1153 ) @ ( hAPP @ ( hAPP @ SV214 @ SV718 ) @ SV1471 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV214 @ SY4552 @ SY4553 @ SY4554 @ SY4555 @ SY4556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2955]) ).
thf(3418,plain,
! [SV1472: $i,SV1154: $i,SV719: $i,SV215: $i] :
( ( ! [SY4557: $i,SY4558: $i,SY4559: $i,SY4560: $i,SY4561: $i] :
( ( ( hAPP @ ( hAPP @ SV215 @ ( hAPP @ ( hAPP @ SV215 @ SV719 ) @ SV1154 ) ) @ SV1472 )
= ( hAPP @ ( hAPP @ SV215 @ SV719 ) @ ( hAPP @ ( hAPP @ SV215 @ SV1154 ) @ SV1472 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV215 @ SY4557 @ SY4558 @ SY4559 @ SY4560 @ SY4561 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2956]) ).
thf(3419,plain,
! [SV1473: $i,SV1155: $i,SV720: $i,SV216: $i] :
( ( ! [SY4562: $i,SY4563: $i,SY4564: $i,SY4565: $i,SY4566: $i,SY4567: $i] :
( ( ( hAPP @ ( hAPP @ SV216 @ ( hAPP @ ( hAPP @ SV216 @ SV720 ) @ SV1155 ) ) @ ( hAPP @ ( hAPP @ SV216 @ SV1473 ) @ SY4562 ) )
= ( hAPP @ ( hAPP @ SV216 @ ( hAPP @ ( hAPP @ SV216 @ SV720 ) @ SV1473 ) ) @ ( hAPP @ ( hAPP @ SV216 @ SV1155 ) @ SY4562 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV216 @ SY4563 @ SY4564 @ SY4565 @ SY4566 @ SY4567 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2957]) ).
thf(3420,plain,
! [SV1474: $i,SV1156: $i,SV721: $i,SV217: $i] :
( ( ! [SY4568: $i,SY4569: $i,SY4570: $i,SY4571: $i,SY4572: $i] :
( ( ( hAPP @ ( hAPP @ SV217 @ SV721 ) @ ( hAPP @ ( hAPP @ SV217 @ SV1156 ) @ SV1474 ) )
= ( hAPP @ ( hAPP @ SV217 @ SV1156 ) @ ( hAPP @ ( hAPP @ SV217 @ SV721 ) @ SV1474 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4568 @ SV217 @ SY4569 @ SY4570 @ SY4571 @ SY4572 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2958]) ).
thf(3421,plain,
! [SV1475: $i,SV1157: $i,SV722: $i,SV218: $i] :
( ( ! [SY4573: $i,SY4574: $i,SY4575: $i,SY4576: $i,SY4577: $i] :
( ( ( hAPP @ ( hAPP @ SV218 @ SV722 ) @ ( hAPP @ ( hAPP @ SV218 @ SV1157 ) @ SV1475 ) )
= ( hAPP @ ( hAPP @ SV218 @ ( hAPP @ ( hAPP @ SV218 @ SV722 ) @ SV1157 ) ) @ SV1475 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4573 @ SV218 @ SY4574 @ SY4575 @ SY4576 @ SY4577 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2959]) ).
thf(3422,plain,
! [SV1476: $i,SV1158: $i,SV723: $i,SV219: $i] :
( ( ! [SY4578: $i,SY4579: $i,SY4580: $i,SY4581: $i,SY4582: $i] :
( ( ( hAPP @ ( hAPP @ SV219 @ ( hAPP @ ( hAPP @ SV219 @ SV723 ) @ SV1158 ) ) @ SV1476 )
= ( hAPP @ ( hAPP @ SV219 @ SV723 ) @ ( hAPP @ ( hAPP @ SV219 @ SV1158 ) @ SV1476 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4578 @ SV219 @ SY4579 @ SY4580 @ SY4581 @ SY4582 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2960]) ).
thf(3423,plain,
! [SV1477: $i,SV1159: $i,SV724: $i,SV220: $i] :
( ( ! [SY4583: $i,SY4584: $i,SY4585: $i,SY4586: $i,SY4587: $i] :
( ( ( hAPP @ ( hAPP @ SV220 @ ( hAPP @ ( hAPP @ SV220 @ SV724 ) @ SV1159 ) ) @ SV1477 )
= ( hAPP @ ( hAPP @ SV220 @ ( hAPP @ ( hAPP @ SV220 @ SV724 ) @ SV1477 ) ) @ SV1159 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4583 @ SV220 @ SY4584 @ SY4585 @ SY4586 @ SY4587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2961]) ).
thf(3424,plain,
! [SV1478: $i,SV1160: $i,SV725: $i,SV221: $i] :
( ( ! [SY4588: $i,SY4589: $i,SY4590: $i,SY4591: $i,SY4592: $i,SY4593: $i] :
( ( ( hAPP @ ( hAPP @ SV221 @ ( hAPP @ ( hAPP @ SV221 @ SV725 ) @ SV1160 ) ) @ ( hAPP @ ( hAPP @ SV221 @ SV1478 ) @ SY4588 ) )
= ( hAPP @ ( hAPP @ SV221 @ SV1478 ) @ ( hAPP @ ( hAPP @ SV221 @ ( hAPP @ ( hAPP @ SV221 @ SV725 ) @ SV1160 ) ) @ SY4588 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4589 @ SV221 @ SY4590 @ SY4591 @ SY4592 @ SY4593 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2962]) ).
thf(3425,plain,
! [SV1479: $i,SV1161: $i,SV726: $i,SV222: $i] :
( ( ! [SY4594: $i,SY4595: $i,SY4596: $i,SY4597: $i,SY4598: $i,SY4599: $i] :
( ( ( hAPP @ ( hAPP @ SV222 @ ( hAPP @ ( hAPP @ SV222 @ SV726 ) @ SV1161 ) ) @ ( hAPP @ ( hAPP @ SV222 @ SV1479 ) @ SY4594 ) )
= ( hAPP @ ( hAPP @ SV222 @ SV726 ) @ ( hAPP @ ( hAPP @ SV222 @ SV1161 ) @ ( hAPP @ ( hAPP @ SV222 @ SV1479 ) @ SY4594 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4595 @ SV222 @ SY4596 @ SY4597 @ SY4598 @ SY4599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2963]) ).
thf(3426,plain,
! [SV1480: $i,SV1162: $i,SV727: $i,SV223: $i] :
( ( ! [SY4600: $i,SY4601: $i,SY4602: $i,SY4603: $i,SY4604: $i,SY4605: $i] :
( ( ( hAPP @ ( hAPP @ SV223 @ ( hAPP @ ( hAPP @ SV223 @ SV727 ) @ SV1162 ) ) @ ( hAPP @ ( hAPP @ SV223 @ SV1480 ) @ SY4600 ) )
= ( hAPP @ ( hAPP @ SV223 @ ( hAPP @ ( hAPP @ SV223 @ SV727 ) @ SV1480 ) ) @ ( hAPP @ ( hAPP @ SV223 @ SV1162 ) @ SY4600 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4601 @ SV223 @ SY4602 @ SY4603 @ SY4604 @ SY4605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2964]) ).
thf(3427,plain,
! [SV1481: $i,SV1163: $i,SV728: $i,SV224: $i] :
( ( ! [SY4606: $i,SY4607: $i,SY4608: $i] :
( ( ( hAPP @ ( hAPP @ SV224 @ SV728 ) @ SV1163 )
= SV728 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1481 @ SV224 @ SY4606 @ SY4607 @ SV1163 @ SY4608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2965]) ).
thf(3428,plain,
! [SV1482: $i,SV1164: $i,SV729: $i,SV225: $i] :
( ( ! [SY4609: $i,SY4610: $i,SY4611: $i] :
( ( ( hAPP @ ( hAPP @ SV225 @ SV729 ) @ SV1164 )
= SV1164 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1482 @ SV225 @ SY4609 @ SY4610 @ SV729 @ SY4611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2966]) ).
thf(3429,plain,
! [SV1483: $i,SV1165: $i,SV730: $i,SV226: $i] :
( ( ! [SY4612: $i,SY4613: $i,SY4614: $i] :
( ( ( hAPP @ ( hAPP @ SV226 @ SV730 ) @ SV1165 )
= SV1165 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1483 @ SV226 @ SY4612 @ SV1165 @ SY4613 @ SY4614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2967]) ).
thf(3430,plain,
! [SV1484: $i,SV1166: $i,SV731: $i,SV227: $i] :
( ( ! [SY4615: $i,SY4616: $i,SY4617: $i] :
( ( ( hAPP @ ( hAPP @ SV227 @ SV731 ) @ SV1166 )
= SV731 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1484 @ SV227 @ SY4615 @ SV731 @ SY4616 @ SY4617 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2968]) ).
thf(3431,plain,
! [SV1485: $i,SV1167: $i,SV732: $i,SV228: $i] :
( ( ! [SY4618: $i,SY4619: $i,SY4620: $i,SY4621: $i,SY4622: $i] :
( ( ( hAPP @ ( hAPP @ SV228 @ ( hAPP @ ( hAPP @ SV732 @ SV1167 ) @ SV1485 ) ) @ SY4618 )
= ( hAPP @ ( hAPP @ SV732 @ ( hAPP @ ( hAPP @ SV228 @ SV1167 ) @ SY4618 ) ) @ ( hAPP @ ( hAPP @ SV228 @ SV1485 ) @ SY4618 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV732 @ SV228 @ SY4619 @ SY4620 @ SY4621 @ SY4622 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2969]) ).
thf(3432,plain,
! [SV1486: $i,SV1168: $i,SV733: $i,SV229: $i] :
( ( ! [SY4623: $i,SY4624: $i,SY4625: $i,SY4626: $i] :
( ( ( hAPP @ ( hAPP @ SV229 @ SV733 ) @ SV1168 )
= ( hAPP @ ( hAPP @ SV229 @ SV1168 ) @ SV733 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1486 @ SV229 @ SY4623 @ SY4624 @ SY4625 @ SY4626 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2970]) ).
thf(3433,plain,
! [SV1487: $i,SV1169: $i,SV734: $i,SV230: $i] :
( ( ! [SY4627: $i,SY4628: $i,SY4629: $i] :
( ( ( hAPP @ ( hAPP @ SV230 @ SV734 ) @ SV1169 )
= SV734 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV230 @ SV1487 @ SY4627 @ SV1169 @ SY4628 @ SY4629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2971]) ).
thf(3434,plain,
! [SV1488: $i,SV1170: $i,SV735: $i,SV231: $i] :
( ( ! [SY4630: $i,SY4631: $i,SY4632: $i] :
( ( ( hAPP @ ( hAPP @ SV231 @ SV735 ) @ SV1170 )
= SV1170 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV231 @ SV1488 @ SY4630 @ SV735 @ SY4631 @ SY4632 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2972]) ).
thf(3435,plain,
! [SV1489: $i,SV1171: $i,SV736: $i,SV232: $i] :
( ( ! [SY4633: $i,SY4634: $i,SY4635: $i] :
( ( ( hAPP @ ( hAPP @ SV232 @ SV736 ) @ SV736 )
= ( hAPP @ ( hAPP @ SV1171 @ ( hAPP @ ( hAPP @ SV232 @ SV1489 ) @ SV1489 ) ) @ SV736 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV232 @ SV1171 @ SY4633 @ SY4634 @ SV1489 @ SY4635 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2973]) ).
thf(3436,plain,
! [SV1490: $i,SV1172: $i,SV737: $i,SV233: $i] :
( ( ! [SY4636: $i,SY4637: $i,SY4638: $i,SY4639: $i] :
( ( ( hAPP @ ( hAPP @ SV233 @ SV737 ) @ ( hAPP @ ( hAPP @ SV1172 @ SV1490 ) @ SV737 ) )
= ( hAPP @ ( hAPP @ SV1172 @ ( hAPP @ ( hAPP @ SV233 @ SV1490 ) @ SY4636 ) ) @ SV737 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV233 @ SV1172 @ SY4637 @ SY4638 @ SY4636 @ SY4639 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2974]) ).
thf(3437,plain,
! [SV1491: $i,SV1173: $i,SV738: $i,SV234: $i] :
( ( ! [SY4640: $i,SY4641: $i,SY4642: $i,SY4643: $i] :
( ( ( hAPP @ ( hAPP @ SV234 @ ( hAPP @ ( hAPP @ SV738 @ SV1173 ) @ SV1491 ) ) @ SV1491 )
= ( hAPP @ ( hAPP @ SV738 @ ( hAPP @ ( hAPP @ SV234 @ SV1173 ) @ SY4640 ) ) @ SV1491 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV234 @ SV738 @ SY4641 @ SY4642 @ SY4640 @ SY4643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2975]) ).
thf(3438,plain,
! [SV1492: $i,SV1174: $i,SV739: $i,SV235: $i] :
( ( ! [SY4644: $i,SY4645: $i,SY4646: $i,SY4647: $i,SY4648: $i] :
( ( ( hAPP @ ( hAPP @ SV235 @ ( hAPP @ ( hAPP @ SV739 @ SV1174 ) @ SV1492 ) ) @ ( hAPP @ ( hAPP @ SV739 @ SY4644 ) @ SV1492 ) )
= ( hAPP @ ( hAPP @ SV739 @ ( hAPP @ ( hAPP @ SV235 @ SV1174 ) @ SY4644 ) ) @ SV1492 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV235 @ SV739 @ SY4645 @ SY4646 @ SY4647 @ SY4648 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2976]) ).
thf(3439,plain,
! [SV1493: $i,SV1175: $i,SV740: $i,SV236: $i] :
( ( ! [SY4649: $i,SY4650: $i] :
( ( SV236 = SV740 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV1175 @ SV740 ) @ SV236 ) )
| ~ ( c_ListOrder_Ostep1 @ SV1175 @ ( c_List_Olist_OCons @ SV740 @ SV1493 @ SY4649 ) @ ( c_List_Olist_OCons @ SV236 @ SY4650 @ SY4649 ) @ SY4649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2977]) ).
thf(3440,plain,
! [SV1494: $i,SV1176: $i,SV741: $i,SV237: $i] :
( ( ! [SY4651: $i] :
( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV237 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SV741 ) @ SV1176 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SV1494 ) @ SY4651 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SV741 ) @ SV1494 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SV1176 ) @ SY4651 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2978]) ).
thf(3441,plain,
! [SV1495: $i,SV1177: $i,SV742: $i,SV238: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV238 ) @ SV742 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1177 ) @ SV1495 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV742 ) @ SV1495 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV238 ) @ SV1177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2979]) ).
thf(3442,plain,
! [SV743: $i,SV239: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV239 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV743 @ SV239 ) @ ( c_HOL_Ozero__class_Ozero @ SV239 ) @ SV239 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2980]) ).
thf(3443,plain,
! [SV1178: $i,SV744: $i,SV240: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV240 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omax @ SV744 @ SV1178 @ SV240 )
= ( c_Orderings_Oord__class_Omax @ SV1178 @ SV744 @ SV240 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2981]) ).
thf(3444,plain,
! [SV1179: $i,SV745: $i,SV241: $i] :
( ( ( ( c_Lambda_Oliftn @ SV241 @ ( c_Lambda_OdB_OVar @ SV745 ) @ SV1179 )
= ( c_Lambda_OdB_OVar @ SV745 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV745 @ SV1179 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2982]) ).
thf(3445,plain,
! [SV1496: $i,SV1180: $i,SV746: $i,SV242: $i] :
( ( ( c_Type_Otyping @ SV242 @ SV746 @ SV1180 )
| ~ ( c_Type_Otyping @ SV242 @ SV1496 @ SV1180 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV1496 ) @ SV746 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2983]) ).
thf(3446,plain,
! [SV748: $i,SV244: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV244 @ SV748 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( c_Lambda_OdB_OVar @ SV244 ) ) @ SV748 )
= ( c_Lambda_OdB_OVar @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2984]) ).
thf(3447,plain,
! [SV1181: $i,SV749: $i,SV245: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV245 ) @ SV749 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1181 ) @ SV749 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV245 ) @ SV1181 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2985]) ).
thf(3448,plain,
! [SV246: $i] :
( ( ( SV246
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV246 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV246 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV246 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV246 ) ) )
= $true )
| ( ( SV246
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV246 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV246 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV246 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2986]) ).
thf(3449,plain,
! [SV1497: $i,SV1183: $i,SV752: $i,SV249: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV249 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV249 ) @ ( c_Orderings_Oord__class_Omax @ SV752 @ SV1183 @ SV249 ) ) @ SV1497 )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV249 ) @ SV752 ) @ SV1497 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV249 ) @ SV1183 ) @ SV1497 ) @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2989]) ).
thf(3450,plain,
! [SV1498: $i,SV1185: $i,SV754: $i,SV251: $i] :
( ( ! [SY4652: $i,SY4653: $i] :
( ( SV251 = SV754 )
| ( c_ListOrder_Ostep1 @ SV1185 @ SV251 @ SV754 @ SV1498 )
| ~ ( c_ListOrder_Ostep1 @ SV1185 @ ( c_List_Oappend @ SV251 @ ( c_List_Olist_OCons @ SY4652 @ ( c_List_Olist_ONil @ SV1498 ) @ SV1498 ) @ SV1498 ) @ ( c_List_Oappend @ SV754 @ ( c_List_Olist_OCons @ SY4653 @ ( c_List_Olist_ONil @ SV1498 ) @ SV1498 ) @ SV1498 ) @ SV1498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2991]) ).
thf(3451,plain,
! [SV1499: $i,SV1186: $i,SV755: $i,SV252: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV252 )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ SV755 @ SV1186 @ SV252 ) @ SV1499 @ SV252 )
= ( c_Orderings_Oord__class_Omax @ SV755 @ ( c_Orderings_Oord__class_Omax @ SV1186 @ SV1499 @ SV252 ) @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2992]) ).
thf(3452,plain,
! [SV1500: $i,SV1187: $i,SV756: $i,SV253: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV253 )
| ( ( c_Orderings_Oord__class_Omax @ SV756 @ ( c_Orderings_Oord__class_Omax @ SV1187 @ SV1500 @ SV253 ) @ SV253 )
= ( c_Orderings_Oord__class_Omax @ SV1187 @ ( c_Orderings_Oord__class_Omax @ SV756 @ SV1500 @ SV253 ) @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2993]) ).
thf(3453,plain,
! [SV758: $i,SV256: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV256 ) @ SV758 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ SV256 ) ) @ ( c_Lambda_OdB_OAbs @ SV758 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2994]) ).
thf(3454,plain,
! [SV1188: $i,SV759: $i,SV257: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV257 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omax @ SV759 @ ( c_Orderings_Oord__class_Omax @ SV759 @ SV1188 @ SV257 ) @ SV257 )
= ( c_Orderings_Oord__class_Omax @ SV759 @ SV1188 @ SV257 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2995]) ).
thf(3455,plain,
! [SV1501: $i,SV1190: $i,SV761: $i,SV259: $i] :
( ( ( ( hAPP @ ( hAPP @ SV259 @ SV761 ) @ SV1190 )
= SV761 )
| ~ ( c_OrderedGroup_Omonoid__add @ SV1190 @ SV259 @ SV1501 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2997]) ).
thf(3456,plain,
! [SV1502: $i,SV1191: $i,SV762: $i,SV260: $i] :
( ( ( ( hAPP @ ( hAPP @ SV260 @ SV762 ) @ SV1191 )
= SV1191 )
| ~ ( c_OrderedGroup_Omonoid__add @ SV762 @ SV260 @ SV1502 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2998]) ).
thf(3457,plain,
! [SV261: $i,SV763: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV763 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV261 ) @ SV763 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2999]) ).
thf(3458,plain,
! [SV764: $i,SV262: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV262 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV262 ) @ SV764 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3000]) ).
thf(3459,plain,
! [SV765: $i,SV263: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV263 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV765 @ SV263 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV263 ) @ SV765 ) @ SV765 ) @ SV263 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3001]) ).
thf(3460,plain,
! [SV766: $i,SV264: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV264 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV264 ) @ SV766 ) @ SV766 ) @ SV264 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SV766 @ SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3002]) ).
thf(3461,plain,
! [SV265: $i] :
( ( ( SV265
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV265 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV265 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV265 ) ) )
= $true )
| ( ( SV265
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV265 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV265 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3003]) ).
thf(3462,plain,
! [SV266: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV266 ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV266 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV266 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV266 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV266 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV266 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3004]) ).
thf(3463,plain,
! [SV267: $i] :
( ( ( SV267
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV267 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV267 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV267 ) ) )
= $true )
| ( ( SV267
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV267 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV267 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV267 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV267 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3005]) ).
thf(3464,plain,
! [SV767: $i,SV269: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV269 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV269 ) @ ( c_HOL_Ozero__class_Ozero @ SV269 ) ) @ SV767 )
= SV767 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3007]) ).
thf(3465,plain,
! [SV768: $i,SV270: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV270 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV270 ) @ ( c_HOL_Ozero__class_Ozero @ SV270 ) ) @ SV768 )
= SV768 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3008]) ).
thf(3466,plain,
! [SV769: $i,SV271: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV271 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV271 )
| ( SV769
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ SV769 ) @ ( c_HOL_Ozero__class_Ozero @ SV271 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3009]) ).
thf(3467,plain,
! [SV770: $i,SV272: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV272 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV272 ) @ SV770 ) @ ( c_HOL_Ozero__class_Ozero @ SV272 ) )
= SV770 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3010]) ).
thf(3468,plain,
! [SV771: $i,SV273: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV273 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV273 ) @ ( c_HOL_Ozero__class_Ozero @ SV273 ) ) @ SV771 )
= SV771 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3011]) ).
thf(3469,plain,
! [SV772: $i,SV274: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV274 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV274 ) @ SV772 ) @ ( c_HOL_Ozero__class_Ozero @ SV274 ) )
= SV772 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3012]) ).
thf(3470,plain,
! [SV773: $i,SV275: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV275 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV275 ) @ SV773 ) @ ( c_HOL_Ozero__class_Ozero @ SV275 ) )
= SV773 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3013]) ).
thf(3471,plain,
! [SV774: $i,SV276: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV276 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV276 ) @ ( c_HOL_Ozero__class_Ozero @ SV276 ) ) @ SV774 )
= SV774 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3014]) ).
thf(3472,plain,
! [SV776: $i,SV281: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV281 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV776 @ ( c_HOL_Ozero__class_Ozero @ SV281 ) @ SV281 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV281 ) @ SV776 ) @ SV776 ) @ ( c_HOL_Ozero__class_Ozero @ SV281 ) @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3015]) ).
thf(3473,plain,
! [SV777: $i,SV282: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV282 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV282 ) @ SV777 ) @ SV777 ) @ ( c_HOL_Ozero__class_Ozero @ SV282 ) @ SV282 )
| ~ ( c_HOL_Oord__class_Oless @ SV777 @ ( c_HOL_Ozero__class_Ozero @ SV282 ) @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3016]) ).
thf(3474,plain,
! [SV1192: $i,SV778: $i,SV283: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV283 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV283 ) @ ( c_Power_Opower__class_Opower @ SV778 @ SV1192 @ SV283 ) @ SV283 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV283 ) @ SV778 @ SV283 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3017]) ).
thf(3475,plain,
! [SV1503: $i,SV1193: $i,SV779: $i,SV284: $i] :
( ( ~ ( class_Orderings_Olinorder @ SV284 )
| ( c_HOL_Oord__class_Oless @ SV779 @ SV1193 @ SV284 )
| ( c_HOL_Oord__class_Oless @ SV779 @ SV1503 @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ SV779 @ ( c_Orderings_Oord__class_Omax @ SV1503 @ SV1193 @ SV284 ) @ SV284 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3018]) ).
thf(3476,plain,
! [SV1194: $i,SV780: $i,SV285: $i] :
( ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV285 ) @ SV780 @ SV1194 )
= ( c_Lambda_OdB_OVar @ SV285 ) )
= $true )
| ( ( ( SV285 = SV1194 )
| ( c_HOL_Oord__class_Oless @ SV1194 @ SV285 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3019]) ).
thf(3477,plain,
! [SV287: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV287 ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV287 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3020]) ).
thf(3478,plain,
! [SV782: $i,SV291: $i] :
( ( ( class_Orderings_Oorder @ SV291 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV782 @ SV782 @ SV291 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3021]) ).
thf(3479,plain,
! [SV783: $i,SV292: $i] :
( ( ( class_Orderings_Olinorder @ SV292 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV783 @ SV783 @ SV292 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3022]) ).
thf(3480,plain,
! [SV784: $i,SV293: $i] :
( ( ( class_Orderings_Opreorder @ SV293 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV784 @ SV784 @ SV293 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3023]) ).
thf(3481,plain,
! [SV1195: $i,SV785: $i,SV294: $i] :
( ( ( ( c_Lambda_Oliftn @ SV294 @ ( c_Lambda_OdB_OVar @ SV785 ) @ SV1195 )
= ( c_Lambda_OdB_OVar @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV785 ) @ SV294 ) ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV785 @ SV1195 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3024]) ).
thf(3482,plain,
! [SV1196: $i,SV786: $i,SV295: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV295 ) @ SV786 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1196 ) @ SV786 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV295 ) @ SV1196 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3025]) ).
thf(3483,plain,
! [SV1197: $i,SV787: $i,SV296: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV296 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV296 ) @ SV787 ) @ SV1197 ) @ SV296 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SV1197 @ SV296 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SV787 @ SV296 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3026]) ).
thf(3484,plain,
! [SV1504: $i,SV1198: $i,SV788: $i,SV297: $i] :
( ( ! [SY4654: $i,SY4655: $i] :
( ( c_ListOrder_Ostep1 @ SV297 @ SV788 @ SV1198 @ SV1504 )
| ( SV1198 = SV788 )
| ~ ( c_ListOrder_Ostep1 @ SV297 @ ( c_List_Olist_OCons @ SY4654 @ SV788 @ SV1504 ) @ ( c_List_Olist_OCons @ SY4655 @ SV1198 @ SV1504 ) @ SV1504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3027]) ).
thf(3485,plain,
! [SV1505: $i,SV1199: $i,SV789: $i,SV298: $i] :
( ( ! [SY4656: $i] :
( ( ( hAPP @ ( hAPP @ SV298 @ ( hAPP @ ( hAPP @ SV298 @ SV789 ) @ SV1199 ) ) @ SV1505 )
= ( hAPP @ ( hAPP @ SV298 @ SV789 ) @ ( hAPP @ ( hAPP @ SV298 @ SV1199 ) @ SV1505 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV298 @ SY4656 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3028]) ).
thf(3486,plain,
! [SV1200: $i,SV790: $i,SV299: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV299 ) )
= $true )
| ( ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SV790 @ SV1200 @ SV299 ) @ SV299 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV299 ) @ SV790 ) @ ( c_List_Olistsum @ SV1200 @ SV299 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3029]) ).
thf(3487,plain,
! [SV1506: $i,SV1201: $i,SV791: $i,SV300: $i] :
( ( ! [SY4657: $i] :
( ( c_List_Omap @ SV300 @ ( c_List_Oappend @ SV791 @ SV1201 @ SV1506 ) @ SV1506 @ SY4657 )
= ( c_List_Oappend @ ( c_List_Omap @ SV300 @ SV791 @ SV1506 @ SY4657 ) @ ( c_List_Omap @ SV300 @ SV1201 @ SV1506 @ SY4657 ) @ SY4657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3030]) ).
thf(3488,plain,
! [SV301: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV301 ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV301 ) ) )
= $true )
| ( ( SV301
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV301 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV301 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV301 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV301 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3031]) ).
thf(3489,plain,
! [SV1202: $i,SV792: $i,SV302: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__idom @ SV302 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV792 @ SV1202 @ SV302 )
| ( c_HOL_Oord__class_Oless @ SV1202 @ SV792 @ SV302 )
| ( SV1202 = SV792 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3032]) ).
thf(3490,plain,
! [SV1203: $i,SV793: $i,SV303: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV303 ) )
= $true )
| ( ( ( SV793 = SV1203 )
| ( c_HOL_Oord__class_Oless @ SV1203 @ SV793 @ SV303 )
| ( c_HOL_Oord__class_Oless @ SV793 @ SV1203 @ SV303 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3033]) ).
thf(3491,plain,
! [SV304: $i,SV794: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV794 @ SV304 @ tc_nat )
= $true )
| ( ( SV794 = SV304 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV304 @ SV794 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3034]) ).
thf(3492,plain,
! [SV1204: $i,SV795: $i,SV305: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV305 @ SV795 ) @ SV1204 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV795 @ SV1204 @ tc_nat )
| ( SV1204 = SV795 )
| ( c_HOL_Oord__class_Oless @ SV1204 @ SV795 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3035]) ).
thf(3493,plain,
! [SV306: $i,SV796: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV796 @ SV306 @ tc_nat )
= $true )
| ( ( SV796 = SV306 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV306 @ SV796 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3036]) ).
thf(3494,plain,
! [SV1205: $i,SV797: $i,SV307: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV307 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV797 @ SV1205 @ SV307 )
| ( c_HOL_Oord__class_Oless @ SV1205 @ SV797 @ SV307 )
| ( SV1205 = SV797 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3037]) ).
thf(3495,plain,
! [SV1507: $i,SV1206: $i,SV798: $i,SV308: $i] :
( ( ( c_List_Oappend @ ( c_List_Oreplicate @ SV308 @ SV798 @ SV1206 ) @ ( c_List_Oreplicate @ SV1507 @ SV798 @ SV1206 ) @ SV1206 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SV1507 @ SV798 @ SV1206 ) @ ( c_List_Oreplicate @ SV308 @ SV798 @ SV1206 ) @ SV1206 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3038]) ).
thf(3496,plain,
! [SV1207: $i,SV799: $i,SV309: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV309 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV799 @ SV1207 @ SV309 )
| ( SV1207 = SV799 )
| ( c_HOL_Oord__class_Oless @ SV1207 @ SV799 @ SV309 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3039]) ).
thf(3497,plain,
! [SV1208: $i,SV800: $i,SV310: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV310 ) )
= $true )
| ( ( ( SV800 = SV1208 )
| ( c_HOL_Oord__class_Oless @ SV800 @ SV1208 @ SV310 )
| ( c_HOL_Oord__class_Oless @ SV1208 @ SV800 @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3040]) ).
thf(3498,plain,
! [SV801: $i,SV311: $i] :
( ( ( class_Orderings_Olinorder @ SV311 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omax @ SV801 @ SV801 @ SV311 )
= SV801 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3041]) ).
thf(3499,plain,
! [SV1508: $i,SV1209: $i,SV802: $i,SV312: $i] :
( ( ! [SY4658: $i] :
( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV312 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV312 ) @ SV802 ) @ SV1209 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV312 ) @ SV1508 ) @ SY4658 ) @ SV312 )
| ~ ( c_HOL_Oord__class_Oless @ SV1209 @ SY4658 @ SV312 )
| ~ ( c_HOL_Oord__class_Oless @ SV802 @ SV1508 @ SV312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3042]) ).
thf(3500,plain,
! [SV1509: $i,SV1210: $i,SV803: $i,SV313: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV313 ) @ SV803 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1210 ) @ SV1509 ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV803 @ SV1509 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV313 @ SV1210 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3043]) ).
thf(3501,plain,
! [SV1211: $i,SV804: $i,SV314: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV314 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV804 @ SV314 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1211 @ SV314 ) @ SV314 )
| ~ ( c_HOL_Oord__class_Oless @ SV804 @ SV1211 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3044]) ).
thf(3502,plain,
! [SV1212: $i,SV805: $i,SV315: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV315 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV805 @ SV1212 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV805 @ SV315 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1212 @ SV315 ) @ SV315 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3045]) ).
thf(3503,plain,
! [SV806: $i,SV316: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV316 )
= $false )
| ( ( ( c_List_Olistsum @ SV806 @ SV316 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV316 ) @ SV806 @ ( c_HOL_Ozero__class_Ozero @ SV316 ) @ SV316 @ SV316 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3046]) ).
thf(3504,plain,
! [SV317: $i] :
( ( ( SV317
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV317 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV317 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV317 ) ) )
= $true )
| ( ( SV317
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV317 ) ) )
= $true )
| ( ( SV317
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV317 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV317 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV317 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3047]) ).
thf(3505,plain,
! [SV1510: $i,SV1213: $i,SV807: $i,SV318: $i] :
( ( ( c_List_Oreplicate @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV318 ) @ SV807 ) @ SV1213 @ SV1510 )
= ( c_List_Oappend @ ( c_List_Oreplicate @ SV318 @ SV1213 @ SV1510 ) @ ( c_List_Oreplicate @ SV807 @ SV1213 @ SV1510 ) @ SV1510 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3048]) ).
thf(3506,plain,
! [SV808: $i,SV319: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV319 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV319 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV808 @ SV319 ) @ SV319 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV808 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3049]) ).
thf(3507,plain,
! [SV809: $i,SV320: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV320 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV809 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV320 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV809 @ SV320 ) @ SV320 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3050]) ).
thf(3508,plain,
! [SV1511: $i,SV1214: $i,SV810: $i,SV321: $i] :
( ( ! [SY4659: $i,SY4660: $i] :
( ( SV321 = SV810 )
| ( SV1214 = SV1511 )
| ~ ( c_ListOrder_Ostep1 @ SY4659 @ ( c_List_Oappend @ SV321 @ ( c_List_Olist_OCons @ SV1214 @ ( c_List_Olist_ONil @ SY4660 ) @ SY4660 ) @ SY4660 ) @ ( c_List_Oappend @ SV810 @ ( c_List_Olist_OCons @ SV1511 @ ( c_List_Olist_ONil @ SY4660 ) @ SY4660 ) @ SY4660 ) @ SY4660 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3051]) ).
thf(3509,plain,
! [SV1512: $i,SV1216: $i,SV812: $i,SV323: $i] :
( ( ( c_List_Olistsp @ SV323 @ ( c_List_Oappend @ SV812 @ SV1216 @ SV1512 ) @ SV1512 )
| ~ ( c_List_Olistsp @ SV323 @ SV1216 @ SV1512 )
| ~ ( c_List_Olistsp @ SV323 @ SV812 @ SV1512 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3053]) ).
thf(3510,plain,
! [SV1513: $i,SV1217: $i,SV813: $i,SV324: $i] :
( ( ! [SY4661: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV324 @ SV813 @ SV1217 @ ( c_Lambda_OdB_OAbs @ SV1513 ) @ SY4661 )
= ( hAPP @ ( hAPP @ SV1217 @ SV1513 ) @ ( c_Lambda_OdB_OdB__rec @ SV324 @ SV813 @ SV1217 @ SV1513 @ SY4661 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3054]) ).
thf(3511,plain,
! [SV1514: $i,SV1218: $i,SV814: $i,SV326: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV326 )
| ( c_HOL_Oord__class_Oless @ SV814 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV326 ) @ SV1218 ) @ SV1514 ) @ SV326 )
| ~ ( c_HOL_Oord__class_Oless @ SV814 @ SV1514 @ SV326 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV1218 @ SV326 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3056]) ).
thf(3512,plain,
! [SV1515: $i,SV1219: $i,SV815: $i,SV327: $i] :
( ( ! [SY4662: $i,SY4663: $i] :
( ( c_List_Ofoldr @ SV327 @ ( c_List_Olist_OCons @ SV815 @ SV1219 @ SV1515 ) @ SY4662 @ SV1515 @ SY4663 )
= ( hAPP @ ( hAPP @ SV327 @ SV815 ) @ ( c_List_Ofoldr @ SV327 @ SV1219 @ SY4662 @ SV1515 @ SY4663 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3057]) ).
thf(3513,plain,
! [SV1516: $i,SV1220: $i,SV816: $i,SV328: $i] :
( ( ! [SY4664: $i] :
( ~ ( hBOOL @ ( hAPP @ SV328 @ ( c_Lambda_OdB_OdB__case @ SV816 @ SV1220 @ SV1516 @ ( c_Lambda_OdB_OAbs @ SY4664 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV328 @ ( hAPP @ SV1516 @ SY4664 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3058]) ).
thf(3514,plain,
! [SV1517: $i,SV1221: $i,SV817: $i,SV329: $i] :
( ( ! [SY4665: $i] :
( ~ ( hBOOL @ ( hAPP @ SV329 @ ( c_Lambda_OdB_OdB__case @ SV817 @ SV1221 @ SV1517 @ ( c_Lambda_OdB_OAbs @ SY4665 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV329 @ ( hAPP @ SV1517 @ SY4665 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3059]) ).
thf(3515,plain,
! [SV1518: $i,SV1224: $i,SV822: $i,SV334: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV334 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV334 ) @ SV822 ) @ SV1224 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV334 ) @ SV1518 ) @ SV1224 ) @ SV334 )
| ~ ( c_HOL_Oord__class_Oless @ SV822 @ SV1518 @ SV334 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3064]) ).
thf(3516,plain,
! [SV1519: $i,SV1225: $i,SV823: $i,SV335: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV335 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV335 ) @ SV823 ) @ SV1225 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV335 ) @ SV1519 ) @ SV1225 ) @ SV335 )
| ~ ( c_HOL_Oord__class_Oless @ SV823 @ SV1519 @ SV335 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3065]) ).
thf(3517,plain,
! [SV1520: $i,SV1226: $i,SV824: $i,SV336: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV336 )
| ( c_HOL_Oord__class_Oless @ SV824 @ SV1226 @ SV336 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV336 ) @ SV824 ) @ SV1520 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV336 ) @ SV1226 ) @ SV1520 ) @ SV336 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3066]) ).
thf(3518,plain,
! [SV1521: $i,SV1227: $i,SV825: $i,SV337: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV337 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV337 ) @ SV825 ) @ SV1227 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV337 ) @ SV825 ) @ SV1521 ) @ SV337 )
| ~ ( c_HOL_Oord__class_Oless @ SV1227 @ SV1521 @ SV337 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3067]) ).
thf(3519,plain,
! [SV1522: $i,SV1228: $i,SV826: $i,SV338: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV338 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV338 ) @ SV826 ) @ SV1228 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV338 ) @ SV826 ) @ SV1522 ) @ SV338 )
| ~ ( c_HOL_Oord__class_Oless @ SV1228 @ SV1522 @ SV338 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3068]) ).
thf(3520,plain,
! [SV1523: $i,SV1229: $i,SV827: $i,SV339: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV339 )
| ( c_HOL_Oord__class_Oless @ SV827 @ SV1229 @ SV339 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SV1523 ) @ SV827 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SV1523 ) @ SV1229 ) @ SV339 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3069]) ).
thf(3521,plain,
! [SV1230: $i,SV828: $i,SV340: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV340 ) @ SV828 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1230 ) @ SV828 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV340 @ SV1230 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3070]) ).
thf(3522,plain,
! [SV1231: $i,SV829: $i,SV341: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV341 @ SV829 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1231 ) @ SV341 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1231 ) @ SV829 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3071]) ).
thf(3523,plain,
! [SV1232: $i,SV830: $i,SV342: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV342 ) @ SV830 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV342 ) @ SV1232 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV830 @ SV1232 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3072]) ).
thf(3524,plain,
! [SV343: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV343 ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV343 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV343 ) ) )
= $true )
| ( ( SV343
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV343 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV343 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV343 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3073]) ).
thf(3525,plain,
! [SV1524: $i,SV1233: $i,SV831: $i,SV344: $i] :
( ( ( c_Type_Otyping @ SV344 @ SV831 @ SV1233 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1524 ) @ SV831 ) )
| ~ ( c_Type_Otyping @ SV344 @ SV1524 @ SV1233 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3074]) ).
thf(3526,plain,
! [SV1525: $i,SV1234: $i,SV832: $i,SV345: $i] :
( ( ! [SY4666: $i,SY4667: $i] :
( ( c_ListOrder_Ostep1 @ SV345 @ SV832 @ SV1234 @ SV1525 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV345 @ SY4666 ) @ SY4667 ) )
| ~ ( c_ListOrder_Ostep1 @ SV345 @ ( c_List_Olist_OCons @ SY4666 @ SV832 @ SV1525 ) @ ( c_List_Olist_OCons @ SY4667 @ SV1234 @ SV1525 ) @ SV1525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3075]) ).
thf(3527,plain,
! [SV1526: $i,SV1235: $i,SV833: $i,SV346: $i] :
( ( ! [SY4668: $i] :
( ( c_ListOrder_Ostep1 @ SV346 @ ( c_List_Olist_OCons @ SV833 @ SV1235 @ SV1526 ) @ ( c_List_Olist_OCons @ SV833 @ SY4668 @ SV1526 ) @ SV1526 )
| ~ ( c_ListOrder_Ostep1 @ SV346 @ SV1235 @ SY4668 @ SV1526 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3076]) ).
thf(3528,plain,
! [SV1527: $i,SV1236: $i,SV834: $i,SV347: $i] :
( ( ( c_List_Oappend @ ( c_List_Oreplicate @ SV347 @ SV834 @ SV1236 ) @ ( c_List_Olist_OCons @ SV834 @ SV1527 @ SV1236 ) @ SV1236 )
= ( c_List_Olist_OCons @ SV834 @ ( c_List_Oappend @ ( c_List_Oreplicate @ SV347 @ SV834 @ SV1236 ) @ SV1527 @ SV1236 ) @ SV1236 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3077]) ).
thf(3529,plain,
! [SV1237: $i,SV835: $i,SV348: $i] :
( ( ( ~ ( class_Ring__and__Field_Osemiring__1 @ SV348 ) )
= $true )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV835 ) @ SV1237 ) @ SV348 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV348 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV835 @ SV348 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1237 @ SV348 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3078]) ).
thf(3530,plain,
! [SV1238: $i,SV836: $i,SV349: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV349 ) )
= $true )
| ( ( ( c_List_Olistsum @ ( c_List_Oappend @ SV836 @ SV1238 @ SV349 ) @ SV349 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV349 ) @ ( c_List_Olistsum @ SV836 @ SV349 ) ) @ ( c_List_Olistsum @ SV1238 @ SV349 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3079]) ).
thf(3531,plain,
! [SV1528: $i,SV1239: $i,SV837: $i,SV352: $i] :
( ( ( c_List_Oappend @ ( c_List_Oappend @ SV352 @ SV837 @ SV1239 ) @ SV1528 @ SV1239 )
= ( c_List_Oappend @ SV352 @ ( c_List_Oappend @ SV837 @ SV1528 @ SV1239 ) @ SV1239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3081]) ).
thf(3532,plain,
! [SV1529: $i,SV1240: $i,SV838: $i,SV353: $i] :
( ( ( c_List_Oappend @ SV353 @ ( c_List_Oappend @ SV838 @ SV1240 @ SV1529 ) @ SV1529 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV353 @ SV838 @ SV1529 ) @ SV1240 @ SV1529 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3082]) ).
thf(3533,plain,
! [SV1530: $i,SV1241: $i,SV839: $i,SV354: $i] :
( ( ( c_List_Oappend @ ( c_List_Oappend @ SV354 @ SV839 @ SV1241 ) @ SV1530 @ SV1241 )
= ( c_List_Oappend @ SV354 @ ( c_List_Oappend @ SV839 @ SV1530 @ SV1241 ) @ SV1241 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3083]) ).
thf(3534,plain,
! [SV1531: $i,SV1242: $i,SV840: $i,SV355: $i] :
( ( ( c_List_Oappend @ SV355 @ ( c_List_Oappend @ SV840 @ SV1242 @ SV1531 ) @ SV1531 )
= ( c_List_Oappend @ ( c_List_Oappend @ SV355 @ SV840 @ SV1531 ) @ SV1242 @ SV1531 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3084]) ).
thf(3535,plain,
! [SV1243: $i,SV841: $i,SV356: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV356 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV841 @ SV1243 @ SV356 )
| ~ ( c_HOL_Oord__class_Oless @ SV1243 @ SV841 @ SV356 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3085]) ).
thf(3536,plain,
! [SV1532: $i,SV1244: $i,SV842: $i,SV357: $i] :
( ( ! [SY4669: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV357 @ SV842 ) @ SV1244 ) @ SV1532 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV357 @ SV842 ) @ SY4669 ) @ SV1532 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV357 @ SV1244 ) @ SY4669 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3086]) ).
thf(3537,plain,
! [SV1533: $i,SV1245: $i,SV843: $i,SV358: $i] :
( ( ! [SY4670: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV358 @ SV843 ) @ SV1245 ) @ SV1533 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SY4670 ) @ SV1533 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV358 @ SV843 ) @ SV1245 ) @ SY4670 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3087]) ).
thf(3538,plain,
! [SV1246: $i,SV844: $i,SV359: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV359 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV844 @ SV1246 @ SV359 )
| ~ ( c_HOL_Oord__class_Oless @ SV1246 @ SV844 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3088]) ).
thf(3539,plain,
! [SV1534: $i,SV1247: $i,SV845: $i,SV360: $i] :
( ( ( c_Wellfounded_Oaccp @ SV360 @ SV845 @ SV1247 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV360 @ SV845 ) @ SV1534 ) )
| ~ ( c_Wellfounded_Oaccp @ SV360 @ SV1534 @ SV1247 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3089]) ).
thf(3540,plain,
! [SV1248: $i,SV846: $i,SV361: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV361 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV846 @ SV1248 @ SV361 )
| ~ ( c_HOL_Oord__class_Oless @ SV1248 @ SV846 @ SV361 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3090]) ).
thf(3541,plain,
! [SV1535: $i,SV1249: $i,SV847: $i,SV362: $i] :
( ( ( c_Wellfounded_Oaccp @ SV362 @ SV847 @ SV1249 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV362 @ SV847 ) @ SV1535 ) )
| ~ ( c_Wellfounded_Oaccp @ SV362 @ SV1535 @ SV1249 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3091]) ).
thf(3542,plain,
! [SV1250: $i,SV848: $i,SV363: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV363 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV848 @ SV1250 @ SV363 )
| ~ ( c_HOL_Oord__class_Oless @ SV1250 @ SV848 @ SV363 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3092]) ).
thf(3543,plain,
! [SV1536: $i,SV1252: $i,SV850: $i,SV371: $i] :
( ( ! [SY4671: $i,SY4672: $i,SY4673: $i] :
( ( ( hAPP @ ( hAPP @ SV371 @ SV850 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV1252 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1536 @ SY4671 @ SV371 @ SY4672 @ SV1252 @ SY4673 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3094]) ).
thf(3544,plain,
! [SV851: $i,SV372: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV372 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV372 ) @ ( c_HOL_Ozero__class_Ozero @ SV372 ) @ SV851 @ SV372 @ SV372 )
= ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV372 ) @ SV851 @ ( c_HOL_Ozero__class_Ozero @ SV372 ) @ SV372 @ SV372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3095]) ).
thf(3545,plain,
! [SV852: $i,SV373: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV373 )
= $false )
| ( ( ( c_List_Olistsum @ SV852 @ SV373 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV373 ) @ ( c_HOL_Ozero__class_Ozero @ SV373 ) @ SV852 @ SV373 @ SV373 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3096]) ).
thf(3546,plain,
! [SV1253: $i,SV853: $i,SV374: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV374 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV374 ) @ SV853 @ SV1253 @ SV374 @ SV374 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV374 ) @ SV853 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV374 ) @ SV1253 @ ( c_HOL_Ozero__class_Ozero @ SV374 ) @ SV374 @ SV374 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3097]) ).
thf(3547,plain,
! [SV1537: $i,SV1254: $i,SV854: $i,SV375: $i] :
( ( ! [SY4674: $i,SY4675: $i] :
( ~ ( hBOOL @ ( hAPP @ SV375 @ ( c_Lambda_OdB_OdB__case @ SV854 @ SV1254 @ SV1537 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4674 ) @ SY4675 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV375 @ ( hAPP @ ( hAPP @ SV1254 @ SY4674 ) @ SY4675 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3098]) ).
thf(3548,plain,
! [SV1538: $i,SV1255: $i,SV855: $i,SV376: $i] :
( ( ! [SY4676: $i,SY4677: $i] :
( ~ ( hBOOL @ ( hAPP @ SV376 @ ( c_Lambda_OdB_OdB__case @ SV855 @ SV1255 @ SV1538 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SY4676 ) @ SY4677 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SV1255 @ SY4676 ) @ SY4677 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3099]) ).
thf(3549,plain,
! [SV1539: $i,SV1257: $i,SV857: $i,SV378: $i] :
( ( ! [SY4678: $i,SY4679: $i] :
( ( c_Lambda_OdB_OdB__case @ SV378 @ SV857 @ SV1257 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1539 ) @ SY4678 ) @ SY4679 )
= ( hAPP @ ( hAPP @ SV857 @ SV1539 ) @ SY4678 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3101]) ).
thf(3550,plain,
! [SV1540: $i,SV1258: $i,SV858: $i,SV379: $i] :
( ( ! [SY4680: $i,SY4681: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV379 @ SV858 @ SV1258 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1540 ) @ SY4680 ) @ SY4681 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV858 @ SV1540 ) @ SY4680 ) @ ( c_Lambda_OdB_OdB__rec @ SV379 @ SV858 @ SV1258 @ SV1540 @ SY4681 ) ) @ ( c_Lambda_OdB_OdB__rec @ SV379 @ SV858 @ SV1258 @ SY4680 @ SY4681 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3102]) ).
thf(3551,plain,
! [SV1259: $i,SV859: $i,SV380: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV380 ) @ SV859 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV380 ) @ SV1259 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV859 ) @ SV1259 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3103]) ).
thf(3552,plain,
! [SV1260: $i,SV860: $i,SV381: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV381 ) @ SV860 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1260 ) @ SV860 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV381 ) @ SV1260 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3104]) ).
thf(3553,plain,
! [SV1541: $i,SV1261: $i,SV861: $i,SV382: $i] :
( ( ( c_Lambda_Oliftn @ SV382 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV861 ) @ SV1261 ) @ SV1541 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Oliftn @ SV382 @ SV861 @ SV1541 ) ) @ ( c_Lambda_Oliftn @ SV382 @ SV1261 @ SV1541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3105]) ).
thf(3554,plain,
! [SV1542: $i,SV1262: $i,SV862: $i,SV383: $i] :
( ( ( c_Lambda_Osubstn @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV383 ) @ SV862 ) @ SV1262 @ SV1542 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubstn @ SV383 @ SV1262 @ SV1542 ) ) @ ( c_Lambda_Osubstn @ SV862 @ SV1262 @ SV1542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3106]) ).
thf(3555,plain,
! [SV1264: $i,SV864: $i,SV385: $i] :
( ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV385 ) @ SV864 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1264 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV864 @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV385 ) ) @ SV864 ) @ SV1264 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3108]) ).
thf(3556,plain,
! [SV1265: $i,SV865: $i,SV386: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV386 @ SV865 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1265 @ SV865 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV386 ) @ SV1265 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3109]) ).
thf(3557,plain,
! [SV1266: $i,SV866: $i,SV387: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV387 @ SV866 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV387 @ SV1266 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV866 @ SV1266 @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3110]) ).
thf(3558,plain,
! [SV1543: $i,SV1267: $i,SV867: $i,SV391: $i] :
( ( ! [SY4682: $i] :
( ( ( c_List_Ofoldl @ SV391 @ ( hAPP @ ( hAPP @ SV391 @ SV867 ) @ SV1267 ) @ SV1543 @ SY4682 @ SY4682 )
= ( hAPP @ ( hAPP @ SV391 @ SV867 ) @ ( c_List_Ofoldl @ SV391 @ SV1267 @ SV1543 @ SY4682 @ SY4682 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV391 @ SY4682 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3111]) ).
thf(3559,plain,
! [SV1544: $i,SV1268: $i,SV868: $i,SV392: $i] :
( ( ( c_List_Ofoldl @ SV392 @ SV868 @ ( c_List_Olist_ONil @ SV1268 ) @ SV1544 @ SV1268 )
= SV868 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3112]) ).
thf(3560,plain,
! [SV1545: $i,SV1269: $i,SV869: $i,SV393: $i] :
( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV393 )
| ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV393 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV393 ) @ SV869 ) @ SV1269 ) @ SV1545 @ SV393 @ SV393 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV393 ) @ SV869 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV393 ) @ SV1269 @ SV1545 @ SV393 @ SV393 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3113]) ).
thf(3561,plain,
! [SV1546: $i,SV1270: $i,SV870: $i,SV394: $i] :
( ( ! [SY4683: $i] :
( ( ( hAPP @ ( hAPP @ SV394 @ SV870 ) @ ( c_List_Ofoldl @ SV394 @ SV1270 @ SV1546 @ SY4683 @ SY4683 ) )
= ( c_List_Ofoldl @ SV394 @ SV870 @ SV1546 @ SY4683 @ SY4683 ) )
| ~ ( c_OrderedGroup_Omonoid__add @ SV1270 @ SV394 @ SY4683 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3114]) ).
thf(3562,plain,
! [SV1547: $i,SV1271: $i,SV871: $i,SV395: $i] :
( ( ! [SY4684: $i,SY4685: $i] :
( ( c_List_Ofoldl @ SV395 @ SV871 @ ( c_List_Olist_OCons @ SV1271 @ SV1547 @ SY4684 ) @ SY4685 @ SY4684 )
= ( c_List_Ofoldl @ SV395 @ ( hAPP @ ( hAPP @ SV395 @ SV871 ) @ SV1271 ) @ SV1547 @ SY4685 @ SY4684 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3115]) ).
thf(3563,plain,
! [SV1548: $i,SV1272: $i,SV872: $i,SV396: $i] :
( ( ! [SY4686: $i,SY4687: $i] :
( ( c_List_Ofoldl @ SV396 @ SV872 @ ( c_List_Oappend @ SV1272 @ SV1548 @ SY4686 ) @ SY4687 @ SY4686 )
= ( c_List_Ofoldl @ SV396 @ ( c_List_Ofoldl @ SV396 @ SV872 @ SV1272 @ SY4687 @ SY4686 ) @ SV1548 @ SY4687 @ SY4686 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3116]) ).
thf(3564,plain,
! [SV1549: $i,SV1273: $i,SV873: $i,SV397: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV397 @ SV873 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV1273 ) @ SV1549 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV397 ) @ SV1273 ) @ SV1549 ) @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SV1273 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV1549 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV873 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3117]) ).
thf(3565,plain,
! [SV874: $i,SV398: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV398 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV398 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV398 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV398 @ SV874 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV398 @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV398 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3118]) ).
thf(3566,plain,
! [SV1550: $i,SV1274: $i,SV875: $i,SV399: $i] :
( ( ( c_Type_Otypings @ SV399 @ SV875 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV1274 @ SV399 @ SV1550 @ SV875 ) )
| ~ ( c_Type_Otyping @ SV399 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1550 ) @ SV875 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1274 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3119]) ).
thf(3567,plain,
! [SV876: $i,SV400: $i] :
( ( ( hBOOL @ ( hAPP @ SV400 @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV400 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ SV400 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV400 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV400 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV400 @ SV876 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3120]) ).
thf(3568,plain,
! [SV1551: $i,SV1275: $i,SV877: $i,SV401: $i] :
( ( ! [SY4688: $i,SY4689: $i,SY4690: $i] :
( ( c_Type_Otypings @ SV401 @ SV877 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV1275 @ SV1551 @ SV401 @ SV877 ) )
| ~ ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY4688 ) @ SY4689 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1551 )
| ~ ( c_Type_Otypings @ SV401 @ SY4689 @ SY4690 )
| ~ ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SY4688 ) @ SY4689 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV877 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3121]) ).
thf(3569,plain,
! [SV1276: $i,SV878: $i,SV402: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV402 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV878 @ SV402 @ SV1276 ) @ tc_Lambda_OdB )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV878 ) @ SV402 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV1276 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3122]) ).
thf(3570,plain,
! [SV403: $i] :
( ( ( SV403
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV403 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV403 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV403 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV403 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV403 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV403 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV403 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3123]) ).
thf(3571,plain,
! [SV1552: $i,SV1277: $i,SV879: $i,SV404: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV404 ) @ SV879 ) @ SV1277 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1552 ) @ SV879 ) @ SV1277 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV404 ) @ SV1552 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3124]) ).
thf(3572,plain,
! [SV406: $i] :
( ( ( SV406
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV406 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV406 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV406 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV406 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV406 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3126]) ).
thf(3573,plain,
! [SV1553: $i,SV1279: $i,SV881: $i,SV407: $i] :
( ( ! [SY4691: $i] :
( ~ ( hBOOL @ ( hAPP @ SV407 @ ( c_Lambda_OdB_OdB__case @ SV881 @ SV1279 @ SV1553 @ ( c_Lambda_OdB_OVar @ SY4691 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV407 @ ( hAPP @ SV881 @ SY4691 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3127]) ).
thf(3574,plain,
! [SV1554: $i,SV1280: $i,SV882: $i,SV408: $i] :
( ( ! [SY4692: $i] :
( ~ ( hBOOL @ ( hAPP @ SV408 @ ( c_Lambda_OdB_OdB__case @ SV882 @ SV1280 @ SV1554 @ ( c_Lambda_OdB_OVar @ SY4692 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV408 @ ( hAPP @ SV882 @ SY4692 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3128]) ).
thf(3575,plain,
! [SV1555: $i,SV1281: $i,SV884: $i,SV410: $i] :
( ( ! [SY4693: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV410 @ SV884 @ SV1281 @ ( c_Lambda_OdB_OVar @ SV1555 ) @ SY4693 )
= ( hAPP @ SV410 @ SV1555 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3130]) ).
thf(3576,plain,
! [SV1282: $i,SV885: $i,SV411: $i] :
( ( ( ( hAPP @ SV411 @ SV885 )
= SV1282 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV411 @ ( c_Lambda_OdB_OVar @ SV885 ) @ SV1282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3131]) ).
thf(3577,plain,
! [SV1556: $i,SV1283: $i,SV886: $i,SV412: $i] :
( ( ! [SY4694: $i] :
( ( c_Lambda_OdB_OdB__case @ SV412 @ SV886 @ SV1283 @ ( c_Lambda_OdB_OVar @ SV1556 ) @ SY4694 )
= ( hAPP @ SV412 @ SV1556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3132]) ).
thf(3578,plain,
! [SV888: $i,SV414: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV414 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV414 ) @ SV888 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3133]) ).
thf(3579,plain,
! [SV1284: $i,SV890: $i,SV417: $i] :
( ( ( SV417
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV890 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV890 @ SV1284 @ SV417 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV890 ) @ SV1284 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV417 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3135]) ).
thf(3580,plain,
! [SV891: $i,SV418: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV418 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV418 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV418 )
| ~ ( class_Power_Opower @ SV418 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV418 ) @ SV891 @ SV418 )
= ( c_HOL_Ozero__class_Ozero @ SV418 ) )
| ( SV891
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3136]) ).
thf(3581,plain,
! [SV892: $i,SV419: $i] :
( ( ( class_Ring__and__Field_Osemiring__0 @ SV419 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV419 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV419 ) @ SV892 @ SV419 )
= ( c_HOL_Ozero__class_Ozero @ SV419 ) )
| ( SV892
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3137]) ).
thf(3582,plain,
! [SV1285: $i,SV893: $i,SV421: $i] :
( ( ( ~ ( class_OrderedGroup_Omonoid__add @ SV421 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SV893 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ ( c_HOL_Ozero__class_Ozero @ SV421 ) @ SV1285 @ SV421 @ SV421 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SV893 @ SV1285 @ SV421 @ SV421 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3139]) ).
thf(3583,plain,
! [SV1286: $i,SV896: $i,SV426: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV426 @ SV896 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1286 @ SV896 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV426 ) @ SV1286 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3140]) ).
thf(3584,plain,
! [SV1287: $i,SV897: $i,SV427: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV427 ) ) @ SV897 ) @ SV1287 )
= ( c_Lambda_OdB_OVar @ SV427 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV427 @ SV1287 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3141]) ).
thf(3585,plain,
! [SV1288: $i,SV898: $i,SV428: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV428 ) ) @ SV898 ) @ SV1288 )
= ( c_Lambda_OdB_OVar @ SV428 ) )
= $true )
| ( ( ( SV428 = SV1288 )
| ( c_HOL_Oord__class_Oless @ SV1288 @ SV428 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3142]) ).
thf(3586,plain,
! [SV1557: $i,SV1289: $i,SV900: $i,SV430: $i] :
( ( ! [SY4695: $i] :
( ( SV430 = SV900 )
| ~ ( c_Type_Otyping @ SV1289 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1557 ) @ SY4695 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV900 )
| ~ ( c_Type_Otyping @ SV1289 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1557 ) @ SY4695 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3144]) ).
thf(3587,plain,
! [SV432: $i,SV901: $i] :
( ( ( c_List_Olistsp @ c_InductTermi_OIT @ SV901 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV432 ) @ SV901 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3145]) ).
thf(3588,plain,
! [SV1290: $i,SV902: $i,SV433: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV433 ) ) @ SV902 ) @ SV1290 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV902 ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV433 ) @ SV902 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1290 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3146]) ).
thf(3589,plain,
! [SV1558: $i,SV1291: $i,SV903: $i,SV434: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV434 ) @ SV903 ) ) @ SV1291 ) @ SV1558 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV434 ) @ SV1291 ) @ SV1558 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV903 ) @ SV1291 ) @ SV1558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3147]) ).
thf(3590,plain,
! [SV1292: $i,SV905: $i,SV436: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV436 ) @ ( c_Lambda_OdB_OVar @ SV905 ) ) @ SV1292 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV436 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3148]) ).
thf(3591,plain,
! [SV438: $i,SV906: $i] :
( ( ( class_Orderings_Opreorder @ SV906 )
= $false )
| ( ( class_Orderings_Opreorder @ ( tc_fun @ SV438 @ SV906 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3149]) ).
thf(3592,plain,
! [SV439: $i,SV907: $i] :
( ( ( class_Orderings_Oorder @ SV907 )
= $false )
| ( ( class_Orderings_Oorder @ ( tc_fun @ SV439 @ SV907 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3150]) ).
thf(3593,plain,
! [SV1293: $i,SV909: $i,SV441: $i] :
( ( ( SV441 = SV909 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV1293 ) @ SV441 ) @ SV909 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3151]) ).
thf(3594,plain,
! [SV910: $i,SV442: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV442 )
= ( c_Lambda_OdB_OVar @ SV910 ) )
= $false )
| ( ( SV442 = SV910 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3152]) ).
thf(3595,plain,
! [SV1559: $i,SV1294: $i,SV911: $i,SV443: $i] :
( ( ! [SY4696: $i] :
( ( ( c_List_Olist_OCons @ SV443 @ SV911 @ SV1294 )
!= ( c_List_Olist_OCons @ SV1559 @ SY4696 @ SV1294 ) )
| ( SV443 = SV1559 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3153]) ).
thf(3596,plain,
! [SV1560: $i,SV1295: $i,SV912: $i,SV444: $i] :
( ( ! [SY4697: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ SV444 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV912 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV1295 ) @ SV1560 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV1295 ) @ SY4697 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV912 ) @ SV1560 )
= SY4697 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3154]) ).
thf(3597,plain,
! [SV1296: $i,SV913: $i,SV445: $i] :
( ( ( c_Lambda_OdB_OVar @ SV445 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV913 ) @ SV1296 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3155]) ).
thf(3598,plain,
! [SV1561: $i,SV1297: $i,SV914: $i,SV446: $i] :
( ( ~ ( class_Ring__and__Field_Oidom @ SV446 )
| ~ ( class_Int_Onumber__ring @ SV446 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV446 ) @ SV914 ) @ SV1297 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV446 ) @ SV914 ) @ SV1561 ) )
| ( SV1297 = SV1561 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3156]) ).
thf(3599,plain,
! [SV1562: $i,SV1298: $i,SV915: $i,SV447: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV447 ) @ SV915 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1298 ) @ SV1562 ) )
| ( SV447 = SV1298 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3157]) ).
thf(3600,plain,
! [SV1299: $i,SV916: $i,SV448: $i] :
( ( ( c_List_Olist_OCons @ SV448 @ SV916 @ SV1299 )
= ( c_List_Olist_ONil @ SV1299 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3158]) ).
thf(3601,plain,
! [SV1300: $i,SV917: $i,SV449: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV449 ) )
= $true )
| ( ( ( ( c_Orderings_Oord__class_Omax @ SV917 @ SV1300 @ SV449 )
!= SV1300 )
| ( c_lessequals @ SV917 @ SV1300 @ SV449 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3159]) ).
thf(3602,plain,
! [SV1563: $i,SV1301: $i,SV918: $i,SV450: $i] :
( ( ! [SY4698: $i] :
( ( ( c_List_Oappend @ SV450 @ ( c_List_Olist_OCons @ SV918 @ ( c_List_Olist_ONil @ SV1301 ) @ SV1301 ) @ SV1301 )
!= ( c_List_Oappend @ SV1563 @ ( c_List_Olist_OCons @ SY4698 @ ( c_List_Olist_ONil @ SV1301 ) @ SV1301 ) @ SV1301 ) )
| ( SV450 = SV1563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3160]) ).
thf(3603,plain,
! [SV919: $i,SV451: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__add @ SV451 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV451 ) @ SV919 ) @ SV919 )
!= ( c_HOL_Ozero__class_Ozero @ SV451 ) )
| ( SV919
= ( c_HOL_Ozero__class_Ozero @ SV451 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3161]) ).
thf(3604,plain,
! [SV1302: $i,SV920: $i,SV452: $i] :
( ( ( SV452
!= ( c_List_Oappend @ SV920 @ SV452 @ SV1302 ) )
= $true )
| ( ( SV920
= ( c_List_Olist_ONil @ SV1302 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3162]) ).
thf(3605,plain,
! [SV1303: $i,SV921: $i,SV453: $i] :
( ( ( c_List_Olist_ONil @ SV453 )
= ( c_List_Olist_OCons @ SV921 @ SV1303 @ SV453 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3163]) ).
thf(3606,plain,
! [SV922: $i,SV454: $i] :
( ( ( SV454
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV454 ) @ SV922 ) )
= $false )
| ( ( SV922
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3164]) ).
thf(3607,plain,
! [SV923: $i,SV455: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV455 ) @ SV923 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV923
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3165]) ).
thf(3608,plain,
! [SV1564: $i,SV1304: $i,SV924: $i,SV456: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV456 )
| ( ( c_Power_Opower__class_Opower @ SV924 @ SV1304 @ SV456 )
!= ( c_Power_Opower__class_Opower @ SV1564 @ SV1304 @ SV456 ) )
| ( SV924 = SV1564 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1304 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV1564 @ SV456 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV924 @ SV456 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3166]) ).
thf(3609,plain,
! [SV1565: $i,SV1305: $i,SV925: $i,SV457: $i] :
( ( ! [SY4699: $i] :
( ( ( c_List_Oreplicate @ SV457 @ SV925 @ SV1305 )
!= ( c_List_Oreplicate @ SV1565 @ SY4699 @ SV1305 ) )
| ( SV457 = SV1565 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3167]) ).
thf(3610,plain,
! [SV1306: $i,SV926: $i,SV458: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV458 ) @ SV926 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1306 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV458 ) @ SV926 )
= SV1306 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3168]) ).
thf(3611,plain,
! [SV1307: $i,SV927: $i,SV459: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV459 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV459 ) @ SV927 ) @ SV1307 )
!= ( c_HOL_Ozero__class_Ozero @ SV459 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV459 ) @ SV1307 @ SV459 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV459 ) @ SV927 @ SV459 )
| ( SV1307
= ( c_HOL_Ozero__class_Ozero @ SV459 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3169]) ).
thf(3612,plain,
! [SV1566: $i,SV1308: $i,SV928: $i,SV460: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV460 ) @ SV928 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1308 ) @ SV1566 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV928 = SV1566 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3170]) ).
thf(3613,plain,
! [SV929: $i,SV461: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV461 ) @ SV929 )
= SV461 )
= $false )
| ( ( SV929
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3171]) ).
thf(3614,plain,
! [SV1309: $i,SV930: $i,SV462: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV462 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV930 @ SV1309 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OAbs @ SV462 )
= SV930 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3172]) ).
thf(3615,plain,
! [SV1310: $i,SV931: $i,SV463: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV463 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV931 @ SV1310 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV1310
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3173]) ).
thf(3616,plain,
! [SV1567: $i,SV1311: $i,SV932: $i,SV464: $i] :
( ( ! [SY4700: $i] :
( ( ( c_List_Olist_OCons @ SV464 @ SV932 @ SV1311 )
!= ( c_List_Olist_OCons @ SV1567 @ SY4700 @ SV1311 ) )
| ( SV932 = SY4700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3174]) ).
thf(3617,plain,
! [SV1568: $i,SV1312: $i,SV933: $i,SV465: $i] :
( ( ! [SY4701: $i] :
( ( ( c_List_Oreplicate @ SV465 @ SV933 @ SV1312 )
!= ( c_List_Oreplicate @ SV1568 @ SY4701 @ SV1312 ) )
| ( SV933 = SY4701 )
| ( SV465
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3175]) ).
thf(3618,plain,
! [SV1313: $i,SV934: $i,SV466: $i] :
( ( ( c_Lambda_OdB_OAbs @ SV466 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV934 ) @ SV1313 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3176]) ).
thf(3619,plain,
! [SV1314: $i,SV935: $i,SV467: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV467 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV467 )
| ( SV935
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV467 ) @ SV935 ) @ SV1314 ) )
| ( SV1314
= ( c_HOL_Ozero__class_Ozero @ SV467 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3177]) ).
thf(3620,plain,
! [SV1569: $i,SV1315: $i,SV936: $i,SV468: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV468 ) @ SV936 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1315 ) @ SV1569 ) )
| ( SV936 = SV1569 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3178]) ).
thf(3621,plain,
! [SV1316: $i,SV937: $i,SV469: $i] :
( ( ( SV469
!= ( c_List_Oappend @ SV469 @ SV937 @ SV1316 ) )
= $true )
| ( ( SV937
= ( c_List_Olist_ONil @ SV1316 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3179]) ).
thf(3622,plain,
! [SV1570: $i,SV1317: $i,SV938: $i,SV470: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV470 ) @ SV938 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1317 ) @ SV1570 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3180]) ).
thf(3623,plain,
! [SV1318: $i,SV939: $i,SV471: $i] :
( ( ( ~ ( class_Ring__and__Field_Ozero__neq__one @ SV471 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV471 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV471 )
| ~ ( class_Power_Opower @ SV471 )
| ( ( c_Power_Opower__class_Opower @ SV939 @ SV1318 @ SV471 )
!= ( c_HOL_Ozero__class_Ozero @ SV471 ) )
| ( SV939
= ( c_HOL_Ozero__class_Ozero @ SV471 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3181]) ).
thf(3624,plain,
! [SV1319: $i,SV940: $i,SV472: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV472 @ SV940 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1319 @ SV940 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV472 = SV1319 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3182]) ).
thf(3625,plain,
! [SV941: $i,SV473: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV473 )
= ( c_Lambda_OdB_OAbs @ SV941 ) )
= $false )
| ( ( SV473 = SV941 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3183]) ).
thf(3626,plain,
! [SV1571: $i,SV1320: $i,SV942: $i,SV474: $i] :
( ( ( ( c_List_Oappend @ SV474 @ SV942 @ SV1320 )
!= ( c_List_Oappend @ SV474 @ SV1571 @ SV1320 ) )
| ( SV942 = SV1571 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3184]) ).
thf(3627,plain,
! [SV1321: $i,SV943: $i,SV475: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV475 ) @ SV943 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1321 ) @ SV943 ) )
= $true )
| ( ( SV475 = SV1321 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3185]) ).
thf(3628,plain,
! [SV1572: $i,SV1322: $i,SV944: $i,SV476: $i] :
( ( ( ( c_List_Olist_ONil @ SV476 )
!= ( c_List_Omap @ SV944 @ SV1322 @ SV1572 @ SV476 ) )
| ( SV1322
= ( c_List_Olist_ONil @ SV1572 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3186]) ).
thf(3629,plain,
! [SV1323: $i,SV945: $i,SV477: $i] :
( ( ( ~ ( class_Nat_Osemiring__char__0 @ SV477 ) )
= $true )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV945 @ SV477 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1323 @ SV477 ) )
| ( SV945 = SV1323 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3187]) ).
thf(3630,plain,
! [SV1324: $i,SV946: $i,SV478: $i] :
( ( ( c_List_Olist_OCons @ SV478 @ SV946 @ SV1324 )
= ( c_List_Olist_ONil @ SV1324 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3188]) ).
thf(3631,plain,
! [SV1325: $i,SV947: $i,SV479: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV479 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV947 @ SV1325 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV1325
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3189]) ).
thf(3632,plain,
! [SV1326: $i,SV948: $i,SV480: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV480 @ SV948 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV1326 ) )
= $true )
| ( ( SV948
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3190]) ).
thf(3633,plain,
! [SV1327: $i,SV949: $i,SV481: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV481 ) @ SV949 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV481 ) @ SV1327 ) )
= $true )
| ( ( SV949 = SV1327 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3191]) ).
thf(3634,plain,
! [SV482: $i] :
( ( ( ( c_HOL_Ozero__class_Ozero @ SV482 )
= ( c_HOL_Oone__class_Oone @ SV482 ) )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV482 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3192]) ).
thf(3635,plain,
! [SV1328: $i,SV950: $i,SV483: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV483 @ SV950 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ SV1328 ) )
= $true )
| ( ( SV483
= ( c_Lambda_OdB_OAbs @ SV1328 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3193]) ).
thf(3636,plain,
! [SV1329: $i,SV951: $i,SV484: $i] :
( ( ( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV484 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV951 @ SV1329 @ SV484 )
!= ( c_HOL_Ozero__class_Ozero @ SV484 ) )
| ( SV951
= ( c_HOL_Ozero__class_Ozero @ SV484 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3194]) ).
thf(3637,plain,
! [SV1573: $i,SV1330: $i,SV952: $i,SV485: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV485 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV952 ) @ SV1330 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV1573 ) @ SV1330 ) )
| ( SV952 = SV1573 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3195]) ).
thf(3638,plain,
! [SV954: $i,SV487: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV487 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV487 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV487 )
| ~ ( class_Power_Opower @ SV487 )
| ( ( c_Power_Opower__class_Opower @ SV954 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV487 )
!= ( c_HOL_Ozero__class_Ozero @ SV487 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3197]) ).
thf(3639,plain,
! [SV1331: $i,SV955: $i,SV488: $i] :
( ( ( ( c_List_Olist_ONil @ SV488 )
!= ( c_List_Oreplicate @ SV955 @ SV1331 @ SV488 ) )
= $true )
| ( ( SV955
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3198]) ).
thf(3640,plain,
! [SV1332: $i,SV956: $i,SV489: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ SV489 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV489 ) @ SV956 ) @ SV1332 )
!= ( c_HOL_Ozero__class_Ozero @ SV489 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV1332 @ SV489 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV956 @ SV489 )
| ( SV956
= ( c_HOL_Ozero__class_Ozero @ SV489 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3199]) ).
thf(3641,plain,
! [SV1333: $i,SV957: $i,SV490: $i] :
( ( ( ( c_List_Oreplicate @ SV490 @ SV957 @ SV1333 )
!= ( c_List_Olist_ONil @ SV1333 ) )
= $true )
| ( ( SV490
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3200]) ).
thf(3642,plain,
! [SV1334: $i,SV958: $i,SV491: $i] :
( ( ( ( c_List_Olist_ONil @ SV491 )
!= ( c_List_Oappend @ SV958 @ SV1334 @ SV491 ) )
= $true )
| ( ( SV958
= ( c_List_Olist_ONil @ SV491 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3201]) ).
thf(3643,plain,
! [SV1574: $i,SV1335: $i,SV959: $i,SV492: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV492 ) @ SV959 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1335 ) @ SV1574 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1335 @ SV959 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV492 @ SV1574 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3202]) ).
thf(3644,plain,
! [SV1575: $i,SV1336: $i,SV960: $i,SV493: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV493 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV960 ) @ SV1336 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV960 ) @ SV1575 ) )
| ( SV1336 = SV1575 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3203]) ).
thf(3645,plain,
! [SV1576: $i,SV1337: $i,SV961: $i,SV494: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV494 ) @ SV961 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1337 ) @ SV1576 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV494 = SV1337 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3204]) ).
thf(3646,plain,
! [SV1338: $i,SV962: $i,SV495: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV495 ) @ SV962 )
= ( c_Lambda_OdB_OAbs @ SV1338 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3205]) ).
thf(3647,plain,
! [SV1577: $i,SV1339: $i,SV963: $i,SV496: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV496 )
| ( ( c_Power_Opower__class_Opower @ SV963 @ SV1339 @ SV496 )
!= ( c_Power_Opower__class_Opower @ SV963 @ SV1577 @ SV496 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV496 ) @ SV963 @ SV496 )
| ( SV1339 = SV1577 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3206]) ).
thf(3648,plain,
! [SV1578: $i,SV1340: $i,SV964: $i,SV497: $i] :
( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV497 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV964 ) @ SV1340 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV964 ) @ SV1578 ) )
| ( SV1340 = SV1578 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3207]) ).
thf(3649,plain,
! [SV1579: $i,SV1341: $i,SV965: $i,SV498: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV498 ) ) @ SV965 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1341 ) @ SV1579 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3208]) ).
thf(3650,plain,
! [SV1342: $i,SV966: $i,SV499: $i] :
( ( ( ( c_List_Olist_ONil @ SV499 )
!= ( c_List_Oappend @ SV966 @ SV1342 @ SV499 ) )
= $true )
| ( ( SV1342
= ( c_List_Olist_ONil @ SV499 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3209]) ).
thf(3651,plain,
! [SV1343: $i,SV967: $i,SV500: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV500 ) @ SV967 )
= ( c_Lambda_OdB_OVar @ SV1343 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3210]) ).
thf(3652,plain,
! [SV1580: $i,SV1344: $i,SV968: $i,SV501: $i] :
( ( ! [SY4702: $i] :
( ( ( c_List_Oappend @ SV501 @ ( c_List_Olist_OCons @ SV968 @ ( c_List_Olist_ONil @ SV1344 ) @ SV1344 ) @ SV1344 )
!= ( c_List_Oappend @ SV1580 @ ( c_List_Olist_OCons @ SY4702 @ ( c_List_Olist_ONil @ SV1344 ) @ SV1344 ) @ SV1344 ) )
| ( SV968 = SY4702 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3211]) ).
thf(3653,plain,
! [SV1345: $i,SV969: $i,SV502: $i] :
( ( ( ( c_List_Oappend @ SV502 @ SV969 @ SV1345 )
!= ( c_List_Olist_ONil @ SV1345 ) )
= $true )
| ( ( SV969
= ( c_List_Olist_ONil @ SV1345 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3212]) ).
thf(3654,plain,
! [SV1581: $i,SV1346: $i,SV970: $i,SV503: $i] :
( ( ( ( c_List_Omap @ SV503 @ SV970 @ SV1346 @ SV1581 )
!= ( c_List_Olist_ONil @ SV1581 ) )
| ( SV970
= ( c_List_Olist_ONil @ SV1346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3213]) ).
thf(3655,plain,
! [SV1582: $i,SV1347: $i,SV971: $i,SV504: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV504 ) @ SV971 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1347 @ SV1582 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV504
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1347 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV504 @ SV971 @ SV1347 @ SV1582 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1582
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3214]) ).
thf(3656,plain,
! [SV1583: $i,SV1348: $i,SV972: $i,SV505: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV505 ) @ SV972 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1348 ) @ SV1583 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV972 = SV1583 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3215]) ).
thf(3657,plain,
! [SV1349: $i,SV973: $i,SV506: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV506 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV973 @ SV1349 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( c_Lambda_OdB_OVar @ SV506 )
= SV973 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3216]) ).
thf(3658,plain,
! [SV507: $i] :
( ( ( ( c_HOL_Oone__class_Oone @ SV507 )
= ( c_HOL_Ozero__class_Ozero @ SV507 ) )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV507 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3217]) ).
thf(3659,plain,
! [SV1350: $i,SV974: $i,SV508: $i] :
( ( ( c_List_Olist_OCons @ SV508 @ SV974 @ SV1350 )
= SV974 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3218]) ).
thf(3660,plain,
! [SV975: $i,SV509: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV509 ) @ SV975 )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $false )
| ( ( SV509
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3219]) ).
thf(3661,plain,
! [SV1351: $i,SV976: $i,SV510: $i] :
( ( ( ( c_List_Oappend @ SV510 @ SV976 @ SV1351 )
!= SV976 )
= $true )
| ( ( SV510
= ( c_List_Olist_ONil @ SV1351 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3220]) ).
thf(3662,plain,
! [SV1352: $i,SV978: $i,SV512: $i] :
( ( ( ( c_List_Oappend @ SV512 @ SV978 @ SV1352 )
!= ( c_List_Olist_ONil @ SV1352 ) )
= $true )
| ( ( SV512
= ( c_List_Olist_ONil @ SV1352 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3222]) ).
thf(3663,plain,
! [SV1353: $i,SV979: $i,SV513: $i] :
( ( ( ( c_List_Oappend @ SV513 @ SV979 @ SV1353 )
!= SV513 )
= $true )
| ( ( SV979
= ( c_List_Olist_ONil @ SV1353 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3223]) ).
thf(3664,plain,
! [SV1584: $i,SV1354: $i,SV980: $i,SV514: $i] :
( ( ( ( c_List_Oappend @ SV514 @ SV980 @ SV1354 )
!= ( c_List_Oappend @ SV1584 @ SV980 @ SV1354 ) )
| ( SV514 = SV1584 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3224]) ).
thf(3665,plain,
! [SV1355: $i,SV981: $i,SV515: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV515 ) @ SV981 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV515 ) @ SV1355 ) )
= $true )
| ( ( SV981 = SV1355 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3225]) ).
thf(3666,plain,
! [SV1585: $i,SV1356: $i,SV982: $i,SV516: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV516 ) @ SV982 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1356 ) @ SV1585 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV516 = SV1356 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3226]) ).
thf(3667,plain,
! [SV1357: $i,SV983: $i,SV517: $i] :
( ( SV517
= ( c_List_Olist_OCons @ SV983 @ SV517 @ SV1357 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3227]) ).
thf(3668,plain,
! [SV1358: $i,SV984: $i,SV520: $i,SV3: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV3 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV520 @ SV984 @ SV3 ) @ ( c_Power_Opower__class_Opower @ SV1358 @ SV984 @ SV3 ) @ SV3 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV520 @ SV3 )
| ~ ( c_lessequals @ SV520 @ SV1358 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3230]) ).
thf(3669,plain,
! [SV985: $i,SV521: $i,SV4: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV4 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV4 ) @ ( c_Power_Opower__class_Opower @ SV521 @ SV985 @ SV4 ) @ SV4 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV4 ) @ SV521 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3231]) ).
thf(3670,plain,
! [SV1586: $i,SV1359: $i,SV986: $i,SV524: $i,SV7: $i] :
( ( ! [SY4703: $i] :
( ~ ( c_Type_Otyping @ SV7 @ SV524 @ SV986 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV7 @ SV1359 @ SV986 @ tc_Type_Otype ) @ SV1586 @ SY4703 )
| ( c_Type_Otyping @ SV7 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1586 ) @ SV524 ) @ SV1359 ) @ SY4703 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3234]) ).
thf(3671,plain,
! [SV1587: $i,SV1360: $i,SV987: $i,SV525: $i,SV8: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV8 @ SV525 @ SV987 @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1360 ) @ SV525 ) @ SV1587 )
| ~ ( c_Type_Otyping @ SV8 @ SV1360 @ SV1587 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3235]) ).
thf(3672,plain,
! [SV1361: $i,SV988: $i,SV526: $i,SV9: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV9 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV526 @ SV988 @ SV9 ) @ ( c_Power_Opower__class_Opower @ SV526 @ SV1361 @ SV9 ) @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV526 @ ( c_HOL_Oone__class_Oone @ SV9 ) @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV526 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV1361 @ SV988 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3236]) ).
thf(3673,plain,
! [SV989: $i,SV527: $i,SV10: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV10 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV10 ) @ ( c_Power_Opower__class_Opower @ SV527 @ SV989 @ SV10 ) @ SV10 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV989 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV10 ) @ SV527 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3237]) ).
thf(3674,plain,
! [SV1362: $i,SV990: $i,SV528: $i,SV11: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV11 ) @ SV528 ) @ SV990 ) ) @ SV1362 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV11 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1362 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV528 ) @ SV1362 ) ) @ SV990 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV990 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1362 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3238]) ).
thf(3675,plain,
! [SV1363: $i,SV991: $i,SV529: $i,SV12: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV12 ) @ SV529 ) @ SV991 ) ) @ SV1363 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV12 ) @ SV1363 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV529 ) @ SV1363 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV991 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1363 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV991 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3239]) ).
thf(3676,plain,
! [SV1588: $i,SV1364: $i,SV992: $i,SV532: $i,SV15: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV15 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SV532 ) @ SV992 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SV1364 ) @ SV1588 ) @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV992 @ SV1588 @ SV15 )
| ~ ( c_lessequals @ SV532 @ SV1364 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3241]) ).
thf(3677,plain,
! [SV1589: $i,SV1365: $i,SV993: $i,SV533: $i,SV16: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV16 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SV533 ) @ SV993 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SV1365 ) @ SV1589 ) @ SV16 )
| ~ ( c_lessequals @ SV993 @ SV1589 @ SV16 )
| ~ ( c_HOL_Oord__class_Oless @ SV533 @ SV1365 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3242]) ).
thf(3678,plain,
! [SV994: $i,SV534: $i,SV17: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV17 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV17 ) @ SV534 ) @ SV994 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
| ~ ( c_lessequals @ SV994 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
| ~ ( c_lessequals @ SV534 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3243]) ).
thf(3679,plain,
! [SV18: $i,SV535: $i] :
( ( ( c_lessequals @ SV535 @ ( c_HOL_Ozero__class_Ozero @ SV18 ) @ SV18 )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV18 ) @ SV535 ) @ SV535 ) @ ( c_HOL_Ozero__class_Ozero @ SV18 ) @ SV18 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3244]) ).
thf(3680,plain,
! [SV536: $i,SV19: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV19 ) @ SV536 ) @ SV536 ) @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 )
= $true )
| ( ( ~ ( c_lessequals @ SV536 @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3245]) ).
thf(3681,plain,
! [SV1366: $i,SV995: $i,SV537: $i,SV20: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV20 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV20 )
| ( c_lessequals @ SV537 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV20 ) @ SV995 ) @ SV1366 ) @ SV20 )
| ~ ( c_lessequals @ SV537 @ SV995 @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV1366 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3246]) ).
thf(3682,plain,
! [SV1367: $i,SV996: $i,SV538: $i,SV21: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV21 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV21 )
| ( c_lessequals @ SV538 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SV996 ) @ SV1367 ) @ SV21 )
| ~ ( c_lessequals @ SV538 @ SV1367 @ SV21 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ SV996 @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3247]) ).
thf(3683,plain,
! [SV539: $i,SV22: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV22 ) @ SV539 @ SV22 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV22 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV539 ) @ SV539 ) @ SV22 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3248]) ).
thf(3684,plain,
! [SV540: $i,SV23: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV23 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV23 ) @ SV540 ) @ SV540 ) @ SV23 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV23 ) @ SV540 @ SV23 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3249]) ).
thf(3685,plain,
! [SV24: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ SV24 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ SV24 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) )
= ( c_HOL_Ozero__class_Ozero @ SV24 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3250]) ).
thf(3686,plain,
! [SV997: $i,SV541: $i,SV25: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV25 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SV541 ) @ SV997 ) @ SV25 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV997 @ SV25 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV541 @ SV25 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3251]) ).
thf(3687,plain,
! [SV998: $i,SV542: $i,SV28: $i] :
( ( ( class_Orderings_Olinorder @ SV28 )
= $false )
| ( ( ( c_lessequals @ SV542 @ SV998 @ SV28 )
| ( c_lessequals @ SV998 @ SV542 @ SV28 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3253]) ).
thf(3688,plain,
! [SV999: $i,SV543: $i,SV29: $i] :
( ( ( class_Orderings_Olinorder @ SV29 )
= $false )
| ( ( ( SV543 = SV999 )
| ( c_HOL_Oord__class_Oless @ SV543 @ SV999 @ SV29 )
| ~ ( c_lessequals @ SV543 @ SV999 @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3254]) ).
thf(3689,plain,
! [SV1000: $i,SV544: $i,SV30: $i] :
( ( ( class_Orderings_Olinorder @ SV30 )
= $false )
| ( ( ( SV544 = SV1000 )
| ~ ( c_lessequals @ SV544 @ SV1000 @ SV30 )
| ( c_HOL_Oord__class_Oless @ SV544 @ SV1000 @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3255]) ).
thf(3690,plain,
! [SV1001: $i,SV545: $i,SV31: $i] :
( ( ( class_Orderings_Oorder @ SV31 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV545 @ SV1001 @ SV31 )
| ~ ( c_lessequals @ SV545 @ SV1001 @ SV31 )
| ( SV545 = SV1001 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3256]) ).
thf(3691,plain,
! [SV1002: $i,SV546: $i,SV32: $i] :
( ( ( class_Orderings_Oorder @ SV32 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV546 @ SV1002 @ SV32 )
| ( SV546 = SV1002 )
| ~ ( c_lessequals @ SV546 @ SV1002 @ SV32 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3257]) ).
thf(3692,plain,
! [SV1003: $i,SV547: $i,SV33: $i] :
( ( ( class_Orderings_Oorder @ SV33 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV547 @ SV1003 @ SV33 )
| ( SV547 = SV1003 )
| ~ ( c_lessequals @ SV547 @ SV1003 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3258]) ).
thf(3693,plain,
! [SV1004: $i,SV548: $i,SV34: $i] :
( ( ( class_Orderings_Oorder @ SV34 )
= $false )
| ( ( ( SV548 = SV1004 )
| ( c_HOL_Oord__class_Oless @ SV548 @ SV1004 @ SV34 )
| ~ ( c_lessequals @ SV548 @ SV1004 @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3259]) ).
thf(3694,plain,
! [SV1005: $i,SV549: $i,SV35: $i] :
( ( ( class_Orderings_Oorder @ SV35 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV549 @ SV1005 @ SV35 )
| ~ ( c_lessequals @ SV549 @ SV1005 @ SV35 )
| ( SV1005 = SV549 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3260]) ).
thf(3695,plain,
! [SV1006: $i,SV550: $i,SV36: $i] :
( ( ( class_Orderings_Oorder @ SV36 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV550 @ SV1006 @ SV36 )
| ( SV1006 = SV550 )
| ~ ( c_lessequals @ SV550 @ SV1006 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3261]) ).
thf(3696,plain,
! [SV1590: $i,SV1368: $i,SV1007: $i,SV551: $i,SV37: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV37 )
| ( c_lessequals @ SV551 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV1007 ) @ SV1368 ) @ SV37 )
| ~ ( c_lessequals @ SV1590 @ SV1368 @ SV37 )
| ~ ( c_lessequals @ SV551 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV1007 ) @ SV1590 ) @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3262]) ).
thf(3697,plain,
! [SV1369: $i,SV1008: $i,SV552: $i,SV38: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV38 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV552 @ SV1008 @ SV38 )
| ~ ( c_lessequals @ SV1369 @ SV1008 @ SV38 )
| ~ ( c_HOL_Oord__class_Oless @ SV552 @ SV1369 @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3263]) ).
thf(3698,plain,
! [SV1370: $i,SV1009: $i,SV553: $i,SV39: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV39 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV553 @ SV1009 @ SV39 )
| ~ ( c_HOL_Oord__class_Oless @ SV1370 @ SV1009 @ SV39 )
| ~ ( c_lessequals @ SV553 @ SV1370 @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3264]) ).
thf(3699,plain,
! [SV1371: $i,SV1010: $i,SV556: $i,SV42: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV42 ) )
= $true )
| ( ( ( c_lessequals @ SV556 @ SV1010 @ SV42 )
| ~ ( c_lessequals @ SV1371 @ SV1010 @ SV42 )
| ~ ( c_lessequals @ SV556 @ SV1371 @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3267]) ).
thf(3700,plain,
! [SV1372: $i,SV1011: $i,SV557: $i,SV43: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV43 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV557 @ SV1011 @ SV43 )
| ~ ( c_HOL_Oord__class_Oless @ SV557 @ SV1372 @ SV43 )
| ~ ( c_lessequals @ SV1372 @ SV1011 @ SV43 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3268]) ).
thf(3701,plain,
! [SV1373: $i,SV1012: $i,SV558: $i,SV44: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV44 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV558 @ SV1012 @ SV44 )
| ~ ( c_lessequals @ SV558 @ SV1373 @ SV44 )
| ~ ( c_HOL_Oord__class_Oless @ SV1373 @ SV1012 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3269]) ).
thf(3702,plain,
! [SV1374: $i,SV1013: $i,SV559: $i,SV45: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV45 ) )
= $true )
| ( ( ( c_lessequals @ SV559 @ SV1013 @ SV45 )
| ~ ( c_lessequals @ SV559 @ SV1374 @ SV45 )
| ~ ( c_lessequals @ SV1374 @ SV1013 @ SV45 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3270]) ).
thf(3703,plain,
! [SV1591: $i,SV1375: $i,SV1014: $i,SV560: $i,SV46: $i] :
( ( ( ( hAPP @ ( c_Type_Oshift @ SV46 @ SV560 @ SV1014 @ SV1375 ) @ SV1591 )
= ( hAPP @ SV46 @ SV1591 ) )
| ~ ( c_HOL_Oord__class_Oless @ SV1591 @ SV560 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3271]) ).
thf(3704,plain,
! [SV1376: $i,SV1015: $i,SV561: $i,SV47: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV47 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ SV561 ) @ SV1015 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ SV561 ) @ SV1376 ) @ SV47 )
| ~ ( c_lessequals @ SV1015 @ SV1376 @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3272]) ).
thf(3705,plain,
! [SV1377: $i,SV1016: $i,SV562: $i,SV48: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV48 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV48 ) @ SV562 ) @ SV1016 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV48 ) @ SV1377 ) @ SV1016 ) @ SV48 )
| ~ ( c_lessequals @ SV562 @ SV1377 @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3273]) ).
thf(3706,plain,
! [SV1378: $i,SV1017: $i,SV563: $i,SV49: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV49 ) )
= $true )
| ( ( ( c_lessequals @ SV563 @ SV1017 @ SV49 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SV1378 ) @ SV563 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SV1378 ) @ SV1017 ) @ SV49 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3274]) ).
thf(3707,plain,
! [SV1379: $i,SV1018: $i,SV564: $i,SV50: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV564 ) @ SV1018 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV564 ) @ SV1379 ) @ SV50 )
| ~ ( c_lessequals @ SV1018 @ SV1379 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3275]) ).
thf(3708,plain,
! [SV1380: $i,SV1019: $i,SV565: $i,SV51: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV51 ) )
= $true )
| ( ( ( c_lessequals @ SV565 @ SV1019 @ SV51 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV51 ) @ SV565 ) @ SV1380 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV51 ) @ SV1019 ) @ SV1380 ) @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3276]) ).
thf(3709,plain,
! [SV1381: $i,SV1020: $i,SV566: $i,SV52: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV52 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV566 ) @ SV1020 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV1381 ) @ SV1020 ) @ SV52 )
| ~ ( c_lessequals @ SV566 @ SV1381 @ SV52 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3277]) ).
thf(3710,plain,
! [SV1021: $i,SV567: $i,SV53: $i] :
( ( ( class_Orderings_Opreorder @ SV53 )
= $false )
| ( ( ( c_lessequals @ SV567 @ SV1021 @ SV53 )
| ~ ( c_HOL_Oord__class_Oless @ SV567 @ SV1021 @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3278]) ).
thf(3711,plain,
! [SV1022: $i,SV568: $i,SV54: $i] :
( ( ( class_Orderings_Oorder @ SV54 )
= $false )
| ( ( ( c_lessequals @ SV568 @ SV1022 @ SV54 )
| ~ ( c_HOL_Oord__class_Oless @ SV568 @ SV1022 @ SV54 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3279]) ).
thf(3712,plain,
! [SV1023: $i,SV569: $i,SV55: $i] :
( ( ( class_Orderings_Oorder @ SV55 )
= $false )
| ( ( ( SV569 = SV1023 )
| ~ ( c_lessequals @ SV569 @ SV1023 @ SV55 )
| ~ ( c_lessequals @ SV1023 @ SV569 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3280]) ).
thf(3713,plain,
! [SV1024: $i,SV570: $i,SV56: $i] :
( ( ( class_Orderings_Oorder @ SV56 )
= $false )
| ( ( ( SV570 = SV1024 )
| ~ ( c_lessequals @ SV1024 @ SV570 @ SV56 )
| ~ ( c_lessequals @ SV570 @ SV1024 @ SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3281]) ).
thf(3714,plain,
! [SV1025: $i,SV571: $i,SV57: $i] :
( ( ( class_Orderings_Oorder @ SV57 )
= $false )
| ( ( ( SV571 = SV1025 )
| ~ ( c_lessequals @ SV1025 @ SV571 @ SV57 )
| ~ ( c_lessequals @ SV571 @ SV1025 @ SV57 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3282]) ).
thf(3715,plain,
! [SV1592: $i,SV1382: $i,SV1026: $i,SV572: $i,SV58: $i] :
( ( ! [SY4704: $i,SY4705: $i] :
( ( ( hAPP @ ( hAPP @ SV58 @ SV572 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= SV572 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1026 @ SV1382 @ SV58 @ SV1592 @ SY4704 @ SY4705 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3283]) ).
thf(3716,plain,
! [SV1027: $i,SV573: $i,SV60: $i] :
( ( ( class_Orderings_Opreorder @ SV60 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV573 @ SV1027 @ SV60 )
| ( c_lessequals @ SV1027 @ SV573 @ SV60 )
| ~ ( c_lessequals @ SV573 @ SV1027 @ SV60 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3285]) ).
thf(3717,plain,
! [SV1384: $i,SV1029: $i,SV575: $i,SV63: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV63 ) )
= $true )
| ( ( ( c_lessequals @ SV575 @ SV1029 @ SV63 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV575 @ SV1384 @ SV63 ) @ SV1029 @ SV63 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3287]) ).
thf(3718,plain,
! [SV1385: $i,SV1030: $i,SV576: $i,SV64: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV64 ) )
= $true )
| ( ( ( c_lessequals @ SV576 @ SV1030 @ SV64 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1385 @ SV576 @ SV64 ) @ SV1030 @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3288]) ).
thf(3719,plain,
! [SV1386: $i,SV1031: $i,SV577: $i,SV65: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV65 ) )
= $true )
| ( ( ( c_lessequals @ SV577 @ ( c_Orderings_Oord__class_Omax @ SV1031 @ SV1386 @ SV65 ) @ SV65 )
| ~ ( c_lessequals @ SV577 @ SV1031 @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3289]) ).
thf(3720,plain,
! [SV1387: $i,SV1032: $i,SV578: $i,SV66: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV66 ) )
= $true )
| ( ( ( c_lessequals @ SV578 @ ( c_Orderings_Oord__class_Omax @ SV1032 @ SV1387 @ SV66 ) @ SV66 )
| ~ ( c_lessequals @ SV578 @ SV1387 @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3290]) ).
thf(3721,plain,
! [SV1388: $i,SV1033: $i,SV579: $i,SV67: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV67 ) )
= $true )
| ( ( ( c_lessequals @ SV579 @ ( c_Orderings_Oord__class_Omax @ SV1033 @ SV1388 @ SV67 ) @ SV67 )
| ~ ( c_lessequals @ SV579 @ SV1033 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3291]) ).
thf(3722,plain,
! [SV1389: $i,SV1034: $i,SV580: $i,SV68: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV68 ) )
= $true )
| ( ( ( c_lessequals @ SV580 @ ( c_Orderings_Oord__class_Omax @ SV1034 @ SV1389 @ SV68 ) @ SV68 )
| ~ ( c_lessequals @ SV580 @ SV1389 @ SV68 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3292]) ).
thf(3723,plain,
! [SV1390: $i,SV1035: $i,SV581: $i,SV69: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV69 ) )
= $true )
| ( ( ( c_lessequals @ SV581 @ SV1035 @ SV69 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV581 @ SV1390 @ SV69 ) @ SV1035 @ SV69 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3293]) ).
thf(3724,plain,
! [SV1391: $i,SV1036: $i,SV582: $i,SV70: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV70 ) )
= $true )
| ( ( ( c_lessequals @ SV582 @ SV1036 @ SV70 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1391 @ SV582 @ SV70 ) @ SV1036 @ SV70 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3294]) ).
thf(3725,plain,
! [SV1392: $i,SV1037: $i,SV585: $i,SV73: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV73 ) )
= $true )
| ( ( ( c_lessequals @ SV585 @ SV1037 @ SV73 )
| ( c_lessequals @ SV585 @ SV1392 @ SV73 )
| ~ ( c_lessequals @ SV585 @ ( c_Orderings_Oord__class_Omax @ SV1392 @ SV1037 @ SV73 ) @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3297]) ).
thf(3726,plain,
! [SV1038: $i,SV586: $i,SV74: $i] :
( ( ( class_Orderings_Olinorder @ SV74 )
= $false )
| ( ( c_lessequals @ SV586 @ ( c_Orderings_Oord__class_Omax @ SV1038 @ SV586 @ SV74 ) @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3298]) ).
thf(3727,plain,
! [SV1039: $i,SV587: $i,SV75: $i] :
( ( ( class_Orderings_Olinorder @ SV75 )
= $false )
| ( ( c_lessequals @ SV587 @ ( c_Orderings_Oord__class_Omax @ SV587 @ SV1039 @ SV75 ) @ SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3299]) ).
thf(3728,plain,
! [SV1393: $i,SV1040: $i,SV588: $i,SV76: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV76 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV588 @ SV1040 @ SV76 ) @ SV1393 @ SV76 )
| ~ ( c_lessequals @ SV1040 @ SV1393 @ SV76 )
| ~ ( c_lessequals @ SV588 @ SV1393 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3300]) ).
thf(3729,plain,
! [SV1394: $i,SV1041: $i,SV589: $i,SV77: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV77 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV589 @ SV1041 @ SV77 ) @ SV1394 @ SV77 )
| ~ ( c_lessequals @ SV1041 @ SV1394 @ SV77 )
| ~ ( c_lessequals @ SV589 @ SV1394 @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3301]) ).
thf(3730,plain,
! [SV1395: $i,SV1042: $i,SV590: $i,SV78: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV78 ) )
= $true )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV590 @ SV1042 @ SV78 ) @ SV1395 @ SV78 )
| ~ ( c_lessequals @ SV1042 @ SV1395 @ SV78 )
| ~ ( c_lessequals @ SV590 @ SV1395 @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3302]) ).
thf(3731,plain,
! [SV1043: $i,SV591: $i,SV79: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV79 )
= $false )
| ( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV79 ) @ ( c_Power_Opower__class_Opower @ SV591 @ SV1043 @ SV79 ) @ SV79 )
| ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV79 ) @ SV591 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3303]) ).
thf(3732,plain,
! [SV1593: $i,SV1396: $i,SV1044: $i,SV592: $i,SV80: $i] :
( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV80 )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SV592 ) @ SV1044 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SV1396 ) @ SV1593 ) @ SV80 )
| ~ ( c_lessequals @ SV1044 @ SV1593 @ SV80 )
| ~ ( c_lessequals @ SV592 @ SV1396 @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3304]) ).
thf(3733,plain,
! [SV1045: $i,SV593: $i,SV81: $i] :
( ( ( class_Orderings_Olinorder @ SV81 )
= $false )
| ( ( ( ( c_Orderings_Oord__class_Omax @ SV593 @ SV1045 @ SV81 )
= SV1045 )
| ~ ( c_lessequals @ SV593 @ SV1045 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3305]) ).
thf(3734,plain,
! [SV1046: $i,SV594: $i,SV82: $i] :
( ( ( class_Orderings_Olinorder @ SV82 )
= $false )
| ( ( ( ( c_Orderings_Oord__class_Omax @ SV594 @ SV1046 @ SV82 )
= SV594 )
| ~ ( c_lessequals @ SV1046 @ SV594 @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3306]) ).
thf(3735,plain,
! [SV1047: $i,SV596: $i,SV84: $i] :
( ( ( class_Orderings_Olinorder @ SV84 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV596 @ SV1047 @ SV84 )
| ( c_lessequals @ SV1047 @ SV596 @ SV84 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3308]) ).
thf(3736,plain,
! [SV85: $i,SV597: $i] :
( ( ( ~ ( c_lessequals @ SV597 @ SV597 @ SV85 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV597 @ SV597 @ SV85 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3309]) ).
thf(3737,plain,
! [SV86: $i,SV598: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV598 @ SV598 @ SV86 )
= $true )
| ( ( c_lessequals @ SV598 @ SV598 @ SV86 )
= $true )
| ( ( class_Orderings_Olinorder @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3310]) ).
thf(3738,plain,
! [SV1048: $i,SV599: $i,SV87: $i] :
( ( ( class_Orderings_Olinorder @ SV87 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV599 @ SV1048 @ SV87 )
| ~ ( c_lessequals @ SV1048 @ SV599 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3311]) ).
thf(3739,plain,
! [SV1049: $i,SV600: $i,SV88: $i] :
( ( ( class_Orderings_Olinorder @ SV88 )
= $false )
| ( ( ( c_lessequals @ SV600 @ SV1049 @ SV88 )
| ( c_HOL_Oord__class_Oless @ SV1049 @ SV600 @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3312]) ).
thf(3740,plain,
! [SV1050: $i,SV601: $i,SV89: $i] :
( ( ( class_Orderings_Olinorder @ SV89 )
= $false )
| ( ( ~ ( c_lessequals @ SV601 @ SV1050 @ SV89 )
| ~ ( c_HOL_Oord__class_Oless @ SV1050 @ SV601 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3313]) ).
thf(3741,plain,
! [SV1051: $i,SV602: $i,SV90: $i] :
( ( ( class_Orderings_Olinorder @ SV90 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV602 @ SV1051 @ SV90 )
| ( c_lessequals @ SV1051 @ SV602 @ SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3314]) ).
thf(3742,plain,
! [SV1052: $i,SV603: $i,SV91: $i] :
( ( ( class_Orderings_Opreorder @ SV91 )
= $false )
| ( ( ~ ( c_lessequals @ SV603 @ SV1052 @ SV91 )
| ~ ( c_HOL_Oord__class_Oless @ SV1052 @ SV603 @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3315]) ).
thf(3743,plain,
! [SV1053: $i,SV604: $i,SV93: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV93 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV604 ) @ SV1053 ) @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 )
| ~ ( c_lessequals @ SV1053 @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ SV604 @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3316]) ).
thf(3744,plain,
! [SV1054: $i,SV605: $i,SV94: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV94 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV605 ) @ SV1054 ) @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 )
| ~ ( c_HOL_Oord__class_Oless @ SV1054 @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 )
| ~ ( c_lessequals @ SV605 @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3317]) ).
thf(3745,plain,
! [SV1397: $i,SV1055: $i,SV606: $i,SV95: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV95 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV95 )
| ( c_HOL_Oord__class_Oless @ SV606 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV1055 ) @ SV1397 ) @ SV95 )
| ~ ( c_lessequals @ SV606 @ SV1397 @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV1055 @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3318]) ).
thf(3746,plain,
! [SV1398: $i,SV1056: $i,SV607: $i,SV96: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 ) )
= $true )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV96 )
| ( c_HOL_Oord__class_Oless @ SV607 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SV1056 ) @ SV1398 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ SV607 @ SV1398 @ SV96 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV1056 @ SV96 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3319]) ).
thf(3747,plain,
! [SV1057: $i,SV608: $i,SV97: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV97 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV608 ) @ SV1057 ) @ SV97 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV1057 @ SV97 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV608 @ SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3320]) ).
thf(3748,plain,
! [SV1058: $i,SV609: $i,SV98: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV98 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV98 ) @ SV609 ) @ SV1058 ) @ SV98 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ SV1058 @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ SV609 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3321]) ).
thf(3749,plain,
! [SV1399: $i,SV1059: $i,SV610: $i,SV100: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV100 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV610 @ SV1059 @ SV100 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV100 ) @ SV1059 @ SV100 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV610 @ SV1399 @ SV100 ) @ ( c_Power_Opower__class_Opower @ SV1059 @ SV1399 @ SV100 ) @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3322]) ).
thf(3750,plain,
! [SV101: $i] :
( ( ( class_Power_Opower @ SV101 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV101 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV101 )
= ( c_HOL_Oone__class_Oone @ SV101 ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3323]) ).
thf(3751,plain,
! [SV1400: $i,SV1060: $i,SV611: $i,SV102: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV102 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV611 @ SV1060 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1400 @ SV611 @ SV102 ) @ ( c_Power_Opower__class_Opower @ SV1400 @ SV1060 @ SV102 ) @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV102 ) @ SV1400 @ SV102 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3324]) ).
thf(3752,plain,
! [SV1401: $i,SV1061: $i,SV612: $i,SV103: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV103 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV612 @ SV1061 @ SV103 ) @ ( c_Power_Opower__class_Opower @ SV612 @ SV1401 @ SV103 ) @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV103 ) @ SV612 @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ SV1061 @ SV1401 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3325]) ).
thf(3753,plain,
! [SV1402: $i,SV1062: $i,SV613: $i,SV104: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV104 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV613 @ SV1062 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1402 @ SV613 @ SV104 ) @ ( c_Power_Opower__class_Opower @ SV1402 @ SV1062 @ SV104 ) @ SV104 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV104 ) @ SV1402 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3326]) ).
thf(3754,plain,
! [SV1403: $i,SV1063: $i,SV614: $i,SV105: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV105 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV614 @ SV1063 @ SV105 ) @ ( c_Power_Opower__class_Opower @ SV614 @ SV1403 @ SV105 ) @ SV105 )
| ~ ( c_HOL_Oord__class_Oless @ SV1063 @ SV1403 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV105 ) @ SV614 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3327]) ).
thf(3755,plain,
! [SV1404: $i,SV1066: $i,SV618: $i,SV109: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV109 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV618 @ SV1066 @ SV109 ) @ ( c_Power_Opower__class_Opower @ SV1404 @ SV1066 @ SV109 ) @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1066 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV618 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SV618 @ SV1404 @ SV109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3328]) ).
thf(3756,plain,
! [SV1594: $i,SV1405: $i,SV1068: $i,SV620: $i,SV111: $i] :
( ( ( c_Type_Otypings @ ( c_Type_Oshift @ SV111 @ SV620 @ SV1068 @ tc_Type_Otype ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ SV620 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1405 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1594 )
| ~ ( c_Type_Otypings @ SV111 @ SV1405 @ SV1594 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3329]) ).
thf(3757,plain,
! [SV1595: $i,SV1406: $i,SV1069: $i,SV621: $i,SV112: $i] :
( ( ! [SY4706: $i] :
( ( c_Type_Otypings @ SV112 @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SV621 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV1069 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1406 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1595 )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ SV112 @ SV1069 @ SY4706 @ tc_Type_Otype ) @ SV1406 @ SV1595 )
| ~ ( c_Type_Otyping @ SV112 @ SV621 @ SY4706 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3330]) ).
thf(3758,plain,
! [SV622: $i,SV113: $i] :
( ( ( hBOOL @ ( hAPP @ SV113 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV113 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @ SV113 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ SV113 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV113 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV113 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV113 @ SV622 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3331]) ).
thf(3759,plain,
! [SV623: $i,SV114: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV114 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV114 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV114 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV114 @ SV623 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV114 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV114 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__4 @ SV114 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3332]) ).
thf(3760,plain,
! [SV115: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV115 ) )
= $false )
| ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV115 ) @ tc_Lambda_OdB )
= $true )
| ( ( SV115
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV115 ) ) )
= $true )
| ( ( SV115
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV115 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV115 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV115 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3333]) ).
thf(3761,plain,
! [SV1596: $i,SV1407: $i,SV1070: $i,SV624: $i,SV116: $i] :
( ( ( c_List_Omap @ SV116 @ ( c_List_Olist_OCons @ SV624 @ SV1070 @ SV1407 ) @ SV1407 @ SV1596 )
= ( c_List_Olist_OCons @ ( hAPP @ SV116 @ SV624 ) @ ( c_List_Omap @ SV116 @ SV1070 @ SV1407 @ SV1596 ) @ SV1596 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3334]) ).
thf(3762,plain,
! [SV1597: $i,SV1408: $i,SV1071: $i,SV625: $i,SV117: $i] :
( ( ( c_List_Olist_OCons @ ( hAPP @ SV117 @ SV625 ) @ ( c_List_Omap @ SV117 @ SV1071 @ SV1408 @ SV1597 ) @ SV1597 )
= ( c_List_Omap @ SV117 @ ( c_List_Olist_OCons @ SV625 @ SV1071 @ SV1408 ) @ SV1408 @ SV1597 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3335]) ).
thf(3763,plain,
! [SV1598: $i,SV1409: $i,SV1072: $i,SV626: $i,SV118: $i] :
( ( ( c_List_Omap @ SV118 @ ( c_List_Olist_OCons @ SV626 @ SV1072 @ SV1409 ) @ SV1409 @ SV1598 )
= ( c_List_Olist_OCons @ ( hAPP @ SV118 @ SV626 ) @ ( c_List_Omap @ SV118 @ SV1072 @ SV1409 @ SV1598 ) @ SV1598 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3336]) ).
thf(3764,plain,
! [SV627: $i,SV1073: $i,SV119: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV119 ) @ SV1073 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV119 ) @ SV627 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1073 ) @ SV627 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3337]) ).
thf(3765,plain,
! [SV120: $i,SV1074: $i,SV628: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV628 ) @ SV1074 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV120 ) @ SV628 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV120 ) @ SV1074 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3338]) ).
thf(3766,plain,
! [SV1077: $i,SV631: $i,SV123: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV123 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV123 ) @ SV631 ) @ SV1077 ) @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 )
| ~ ( c_HOL_Oord__class_Oless @ SV1077 @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 )
| ~ ( c_HOL_Oord__class_Oless @ SV631 @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3341]) ).
thf(3767,plain,
! [SV1412: $i,SV1078: $i,SV632: $i,SV125: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV125 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV632 @ SV1078 @ SV125 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV1412 @ SV632 @ SV125 ) @ SV1078 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3342]) ).
thf(3768,plain,
! [SV1413: $i,SV1079: $i,SV633: $i,SV126: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV126 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV633 @ SV1079 @ SV126 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV633 @ SV1413 @ SV126 ) @ SV1079 @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3343]) ).
thf(3769,plain,
! [SV1414: $i,SV1080: $i,SV634: $i,SV127: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV127 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV634 @ ( c_Orderings_Oord__class_Omax @ SV1080 @ SV1414 @ SV127 ) @ SV127 )
| ~ ( c_HOL_Oord__class_Oless @ SV634 @ SV1414 @ SV127 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3344]) ).
thf(3770,plain,
! [SV1415: $i,SV1081: $i,SV635: $i,SV128: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV128 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV635 @ ( c_Orderings_Oord__class_Omax @ SV1081 @ SV1415 @ SV128 ) @ SV128 )
| ~ ( c_HOL_Oord__class_Oless @ SV635 @ SV1081 @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3345]) ).
thf(3771,plain,
! [SV1416: $i,SV1082: $i,SV636: $i,SV129: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV129 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV636 @ ( c_Orderings_Oord__class_Omax @ SV1082 @ SV1416 @ SV129 ) @ SV129 )
| ~ ( c_HOL_Oord__class_Oless @ SV636 @ SV1416 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3346]) ).
thf(3772,plain,
! [SV1417: $i,SV1083: $i,SV637: $i,SV130: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV130 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV637 @ ( c_Orderings_Oord__class_Omax @ SV1083 @ SV1417 @ SV130 ) @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SV637 @ SV1083 @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3347]) ).
thf(3773,plain,
! [SV1599: $i,SV1418: $i,SV1084: $i,SV638: $i,SV131: $i] :
( ( ! [SY4707: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV638 ) @ SV1084 ) )
| ( c_ListOrder_Ostep1 @ SV131 @ SV1418 @ SV1599 @ SY4707 )
| ~ ( c_ListOrder_Ostep1 @ SV131 @ ( c_List_Oappend @ SV1418 @ ( c_List_Olist_OCons @ SV638 @ ( c_List_Olist_ONil @ SY4707 ) @ SY4707 ) @ SY4707 ) @ ( c_List_Oappend @ SV1599 @ ( c_List_Olist_OCons @ SV1084 @ ( c_List_Olist_ONil @ SY4707 ) @ SY4707 ) @ SY4707 ) @ SY4707 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3348]) ).
thf(3774,plain,
! [SV1419: $i,SV1085: $i,SV639: $i,SV132: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV132 @ SV639 @ SV639 ) @ SV639 ) @ SV1085 ) @ SV1419 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV132 @ SV639 ) @ SV1419 ) @ SV1085 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3349]) ).
thf(3775,plain,
! [SV1420: $i,SV1086: $i,SV640: $i,SV133: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV133 @ SV640 ) @ SV1086 ) @ SV1420 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV133 @ SV640 @ SV640 ) @ SV640 ) @ SV1420 ) @ SV1086 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3350]) ).
thf(3776,plain,
! [SV1600: $i,SV1422: $i,SV1089: $i,SV643: $i,SV136: $i] :
( ( ! [SY4708: $i] :
( ( hAPP @ ( c_COMBC @ SV136 @ SV643 @ SV1089 @ SV1422 @ SV1600 ) @ SY4708 )
= ( hAPP @ ( hAPP @ SV136 @ SY4708 ) @ SV643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3352]) ).
thf(3777,plain,
! [SV1601: $i,SV1423: $i,SV1090: $i,SV644: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV644 ) @ SV1090 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV137 @ SV1423 @ SV1601 ) @ SV1090 ) @ SV644 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3353]) ).
thf(3778,plain,
! [SV1602: $i,SV1424: $i,SV1091: $i,SV645: $i,SV138: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV138 @ SV645 @ SV1091 ) @ SV1424 ) @ SV1602 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV138 @ SV1602 ) @ SV1424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3354]) ).
thf(3779,plain,
! [SV1603: $i,SV1425: $i,SV1092: $i,SV646: $i,SV139: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV139 @ SV646 ) @ SV1092 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV139 @ SV1425 @ SV1603 ) @ SV1092 ) @ SV646 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3355]) ).
thf(3780,plain,
! [SV1604: $i,SV1426: $i,SV1093: $i,SV647: $i,SV140: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV140 @ SV647 @ SV1093 ) @ SV1426 ) @ SV1604 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV140 @ SV1604 ) @ SV1426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3356]) ).
thf(3781,plain,
! [SV141: $i,SV648: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV648 ) @ SV141 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV648 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV141 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3357]) ).
thf(3782,plain,
! [SV1427: $i,SV1094: $i,SV649: $i,SV142: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV142 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ SV649 ) @ SV1094 ) ) @ SV1427 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ SV649 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ SV1094 ) @ SV1427 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3358]) ).
thf(3783,plain,
! [SV1428: $i,SV1095: $i,SV650: $i,SV143: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV143 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ SV650 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ SV1095 ) @ SV1428 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ SV1095 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ SV650 ) @ SV1428 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3359]) ).
thf(3784,plain,
! [SV1429: $i,SV1096: $i,SV651: $i,SV144: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV144 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ SV651 ) @ SV1096 ) ) @ SV1429 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ SV651 ) @ SV1429 ) ) @ SV1096 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3360]) ).
thf(3785,plain,
! [SV1430: $i,SV1097: $i,SV652: $i,SV145: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV145 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV145 ) @ SV652 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV145 ) @ SV1097 ) @ SV1430 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV145 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV145 ) @ SV652 ) @ SV1097 ) ) @ SV1430 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3361]) ).
thf(3786,plain,
! [SV1431: $i,SV1098: $i,SV653: $i,SV146: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__semigroup__add @ SV146 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ SV653 ) @ SV1098 ) ) @ SV1431 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ SV653 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ SV1098 ) @ SV1431 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3362]) ).
thf(3787,plain,
! [SV1432: $i,SV1099: $i,SV654: $i,SV147: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV147 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV654 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV1099 ) @ SV1432 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV1099 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV654 ) @ SV1432 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3363]) ).
thf(3788,plain,
! [SV1433: $i,SV1100: $i,SV655: $i,SV148: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV148 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV655 ) @ SV1100 ) ) @ SV1433 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV655 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV1100 ) @ SV1433 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3364]) ).
thf(3789,plain,
! [SV1434: $i,SV1103: $i,SV658: $i,SV151: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV151 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV658 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV1103 ) @ SV1434 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV1103 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV658 ) @ SV1434 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3365]) ).
thf(3790,plain,
! [SV1435: $i,SV1104: $i,SV659: $i,SV152: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV152 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV659 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV1104 ) @ SV1435 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV659 ) @ SV1104 ) ) @ SV1435 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3366]) ).
thf(3791,plain,
! [SV1436: $i,SV1105: $i,SV660: $i,SV153: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV153 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV660 @ SV1105 @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SV660 @ SV1436 @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SV1436 @ SV1105 @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3367]) ).
thf(3792,plain,
! [SV1437: $i,SV1106: $i,SV661: $i,SV154: $i] :
( ( ( ~ ( class_Orderings_Opreorder @ SV154 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV661 @ SV1106 @ SV154 )
| ~ ( c_HOL_Oord__class_Oless @ SV1437 @ SV1106 @ SV154 )
| ~ ( c_HOL_Oord__class_Oless @ SV661 @ SV1437 @ SV154 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3368]) ).
thf(3793,plain,
! [SV1605: $i,SV1438: $i,SV1107: $i,SV662: $i,SV155: $i] :
( ( ~ ( c_ListOrder_Ostep1 @ SV155 @ SV662 @ SV1107 @ SV1438 )
| ( c_ListOrder_Ostep1 @ SV155 @ ( c_List_Oappend @ SV662 @ SV1605 @ SV1438 ) @ ( c_List_Oappend @ SV1107 @ SV1605 @ SV1438 ) @ SV1438 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3369]) ).
thf(3794,plain,
! [SV1606: $i,SV1439: $i,SV1108: $i,SV663: $i,SV156: $i] :
( ( ( c_ListOrder_Ostep1 @ SV156 @ ( c_List_Oappend @ SV663 @ SV1108 @ SV1439 ) @ ( c_List_Oappend @ SV663 @ SV1606 @ SV1439 ) @ SV1439 )
| ~ ( c_ListOrder_Ostep1 @ SV156 @ SV1108 @ SV1606 @ SV1439 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3370]) ).
thf(3795,plain,
! [SV1440: $i,SV1109: $i,SV665: $i,SV158: $i] :
( ( ( c_List_Olistsp @ SV158 @ SV665 @ SV1109 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV158 @ ( c_List_Oappend @ SV665 @ SV1440 @ SV1109 ) @ SV1109 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3372]) ).
thf(3796,plain,
! [SV1441: $i,SV1110: $i,SV666: $i,SV159: $i] :
( ( ( c_List_Olistsp @ SV159 @ SV666 @ SV1110 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV159 @ ( c_List_Oappend @ SV1441 @ SV666 @ SV1110 ) @ SV1110 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3373]) ).
thf(3797,plain,
! [SV1607: $i,SV1442: $i,SV1111: $i,SV667: $i,SV160: $i] :
( ( ( c_Lambda_OdB_OdB__case @ SV160 @ SV667 @ SV1111 @ ( c_Lambda_OdB_OAbs @ SV1442 ) @ SV1607 )
= ( hAPP @ SV1111 @ SV1442 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3374]) ).
thf(3798,plain,
! [SV1608: $i,SV1443: $i,SV1112: $i,SV668: $i,SV161: $i] :
( ( ! [SY4709: $i] :
( ( SV161 = SV668 )
| ( SV1112 = SV1443 )
| ~ ( c_ListOrder_Ostep1 @ SV1608 @ ( c_List_Olist_OCons @ SV668 @ SV1443 @ SY4709 ) @ ( c_List_Olist_OCons @ SV161 @ SV1112 @ SY4709 ) @ SY4709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3375]) ).
thf(3799,plain,
! [SV1609: $i,SV1444: $i,SV1113: $i,SV669: $i,SV162: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV162 @ SV669 ) @ SV1113 ) )
| ( c_ListOrder_Ostep1 @ SV162 @ ( c_List_Olist_OCons @ SV669 @ SV1444 @ SV1609 ) @ ( c_List_Olist_OCons @ SV1113 @ SV1444 @ SV1609 ) @ SV1609 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3376]) ).
thf(3800,plain,
! [SV1445: $i,SV1114: $i,SV671: $i,SV164: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV164 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV671 @ SV1114 @ SV164 ) @ SV1445 @ SV164 )
| ~ ( c_HOL_Oord__class_Oless @ SV1114 @ SV1445 @ SV164 )
| ~ ( c_HOL_Oord__class_Oless @ SV671 @ SV1445 @ SV164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3377]) ).
thf(3801,plain,
! [SV1446: $i,SV1117: $i,SV674: $i,SV167: $i] :
( ( ( c_Wellfounded_Oaccp @ SV167 @ SV674 @ SV1117 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SV1117 ) @ SV674 ) @ SV1446 ) )
| ~ ( c_Wellfounded_Oaccp @ SV167 @ SV1446 @ SV1117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3378]) ).
thf(3802,plain,
! [SV1447: $i,SV1118: $i,SV675: $i,SV168: $i] :
( ( ( c_Wellfounded_Oaccp @ SV168 @ SV675 @ SV1118 )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV168 @ SV1447 @ SV1118 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SV1118 ) @ SV675 ) @ SV1447 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3379]) ).
thf(3803,plain,
! [SV1610: $i,SV1448: $i,SV1119: $i,SV676: $i,SV169: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SV676 ) @ SV1119 ) @ SV1448 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SV676 ) @ SV1610 ) @ SV1448 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SV676 ) @ SV1119 ) @ SV1610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3380]) ).
thf(3804,plain,
! [SV172: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV172 ) )
= $false )
| ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV172 ) @ tc_Lambda_OdB )
= $true )
| ( ( SV172
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV172 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV172 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3381]) ).
thf(3805,plain,
! [SV1449: $i,SV1120: $i,SV682: $i,SV178: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV178 ) @ SV682 ) @ SV1120 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV178 ) @ SV1449 ) @ SV1120 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV682 ) @ SV1449 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3382]) ).
thf(3806,plain,
! [SV1611: $i,SV1450: $i,SV1121: $i,SV683: $i,SV179: $i] :
( ( ( c_List_Omap @ SV179 @ ( c_List_Oreplicate @ SV683 @ SV1121 @ SV1450 ) @ SV1450 @ SV1611 )
= ( c_List_Oreplicate @ SV683 @ ( hAPP @ SV179 @ SV1121 ) @ SV1611 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3383]) ).
thf(3807,plain,
! [SV1122: $i,SV684: $i,SV180: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV180 @ SV684 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV180 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV684 ) @ SV1122 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3384]) ).
thf(3808,plain,
! [SV685: $i,SV1123: $i,SV181: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV181 @ SV1123 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV181 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV685 ) @ SV1123 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3385]) ).
thf(3809,plain,
! [SV686: $i,SV1124: $i,SV182: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV182 ) @ SV1124 ) @ SV686 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV182 @ SV686 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3386]) ).
thf(3810,plain,
! [SV1125: $i,SV687: $i,SV183: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV183 @ SV687 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV183 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV687 ) @ SV1125 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3387]) ).
thf(3811,plain,
! [SV688: $i,SV1126: $i,SV184: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV184 @ SV1126 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV184 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV688 ) @ SV1126 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3388]) ).
thf(3812,plain,
! [SV1127: $i,SV689: $i,SV185: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV185 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV185 ) @ SV689 ) @ SV1127 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV185 ) @ SV1127 ) @ SV689 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3389]) ).
thf(3813,plain,
! [SV1128: $i,SV690: $i,SV186: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV186 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV186 ) @ SV690 ) @ SV1128 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV186 ) @ SV1128 ) @ SV690 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3390]) ).
thf(3814,plain,
! [SV1129: $i,SV692: $i,SV188: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV188 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV188 ) @ SV692 ) @ SV1129 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV188 ) @ SV1129 ) @ SV692 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3391]) ).
thf(3815,plain,
! [SV1612: $i,SV1451: $i,SV1130: $i,SV693: $i,SV189: $i] :
( ( ! [SY4710: $i] :
( ( c_List_Ofoldr @ SV189 @ ( c_List_Oappend @ SV693 @ SV1130 @ SV1451 ) @ SV1612 @ SV1451 @ SY4710 )
= ( c_List_Ofoldr @ SV189 @ SV693 @ ( c_List_Ofoldr @ SV189 @ SV1130 @ SV1612 @ SV1451 @ SY4710 ) @ SV1451 @ SY4710 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3392]) ).
thf(3816,plain,
! [SV1613: $i,SV1452: $i,SV1131: $i,SV694: $i,SV190: $i] :
( ( ! [SY4711: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ SV190 @ SV694 ) @ SV1131 ) )
| ( SV694 = SV1131 )
| ~ ( c_ListOrder_Ostep1 @ SV190 @ ( c_List_Oappend @ SV1452 @ ( c_List_Olist_OCons @ SV694 @ ( c_List_Olist_ONil @ SV1613 ) @ SV1613 ) @ SV1613 ) @ ( c_List_Oappend @ SY4711 @ ( c_List_Olist_OCons @ SV1131 @ ( c_List_Olist_ONil @ SV1613 ) @ SV1613 ) @ SV1613 ) @ SV1613 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3393]) ).
thf(3817,plain,
! [SV1614: $i,SV1453: $i,SV1132: $i,SV695: $i,SV191: $i] :
( ( ! [SY4712: $i,SY4713: $i,SY4714: $i,SY4715: $i] :
( ( ( hAPP @ ( hAPP @ SV191 @ ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ SV1453 ) ) @ ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ SV1614 ) )
= ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1453 ) @ SV1614 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4712 @ SV191 @ SV695 @ SY4713 @ SY4714 @ SY4715 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3394]) ).
thf(3818,plain,
! [SV1454: $i,SV1133: $i,SV696: $i,SV192: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV192 ) @ SV696 ) @ SV1133 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1454 ) @ SV696 ) @ SV1133 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV192 ) @ SV1454 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3395]) ).
thf(3819,plain,
! [SV1455: $i,SV1134: $i,SV697: $i,SV193: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV193 ) @ SV697 ) @ SV1134 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV193 ) @ SV1455 ) @ SV1134 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV697 ) @ SV1455 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3396]) ).
thf(3820,plain,
! [SV1135: $i,SV698: $i,SV194: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ SV194 )
= $false )
| ( ( ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV194 ) @ SV698 @ SV1135 @ SV194 @ SV194 )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV194 ) @ SV1135 @ SV698 @ SV194 @ SV194 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3397]) ).
thf(3821,plain,
! [SV1456: $i,SV1136: $i,SV699: $i,SV195: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV195 @ SV699 ) @ SV1136 ) @ SV1456 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV195 @ SV1136 ) @ SV1456 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3398]) ).
thf(3822,plain,
! [SV702: $i,SV198: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ SV702 ) @ SV702 ) @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV702 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3401]) ).
thf(3823,plain,
! [SV199: $i,SV703: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV703 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV199 ) @ SV703 ) @ SV703 ) @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3402]) ).
thf(3824,plain,
! [SV1615: $i,SV1459: $i,SV1141: $i,SV706: $i,SV202: $i] :
( ( ! [SY4716: $i,SY4717: $i,SY4718: $i,SY4719: $i] :
( ( ( hAPP @ ( hAPP @ SV202 @ ( hAPP @ ( hAPP @ SV706 @ SV1141 ) @ SV1459 ) ) @ SV1615 )
= ( hAPP @ ( hAPP @ SV706 @ ( hAPP @ ( hAPP @ SV202 @ SV1141 ) @ SV1615 ) ) @ ( hAPP @ ( hAPP @ SV202 @ SV1459 ) @ SV1615 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4716 @ SV706 @ SV202 @ SY4717 @ SY4718 @ SY4719 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3405]) ).
thf(3825,plain,
! [SV1616: $i,SV1460: $i,SV1142: $i,SV707: $i,SV203: $i] :
( ( ! [SY4720: $i,SY4721: $i,SY4722: $i,SY4723: $i] :
( ( ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ ( hAPP @ ( hAPP @ SV1142 @ SV1460 ) @ SV1616 ) )
= ( hAPP @ ( hAPP @ SV1142 @ ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ SV1460 ) ) @ ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ SV1616 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1142 @ SV203 @ SY4720 @ SY4721 @ SY4722 @ SY4723 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3406]) ).
thf(3826,plain,
! [SV1617: $i,SV1461: $i,SV1143: $i,SV708: $i,SV204: $i] :
( ( ! [SY4724: $i,SY4725: $i,SY4726: $i] :
( ( ( hAPP @ ( hAPP @ SV204 @ SV708 ) @ SV1143 )
= ( hAPP @ ( hAPP @ SV204 @ SV1143 ) @ SV708 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1461 @ SV204 @ SV1617 @ SY4724 @ SY4725 @ SY4726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3407]) ).
thf(3827,plain,
! [SV1618: $i,SV1462: $i,SV1144: $i,SV709: $i,SV205: $i] :
( ( ! [SY4727: $i,SY4728: $i,SY4729: $i,SY4730: $i] :
( ( ( hAPP @ ( hAPP @ SV205 @ SV709 ) @ ( hAPP @ ( hAPP @ SV205 @ SV1144 ) @ SV1462 ) )
= ( hAPP @ ( hAPP @ SV205 @ ( hAPP @ ( hAPP @ SV205 @ SV709 ) @ SV1144 ) ) @ SV1462 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1618 @ SV205 @ SY4727 @ SY4728 @ SY4729 @ SY4730 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3408]) ).
thf(3828,plain,
! [SV1619: $i,SV1463: $i,SV1145: $i,SV710: $i,SV206: $i] :
( ( ! [SY4731: $i,SY4732: $i] :
( ( ( hAPP @ ( hAPP @ SV206 @ SV710 ) @ SV1145 )
= SV1145 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1463 @ SV206 @ SV1619 @ SY4731 @ SV710 @ SY4732 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3409]) ).
thf(3829,plain,
! [SV1620: $i,SV1464: $i,SV1146: $i,SV711: $i,SV207: $i] :
( ( ! [SY4733: $i,SY4734: $i] :
( ( ( hAPP @ ( hAPP @ SV207 @ SV711 ) @ SV1146 )
= SV711 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1464 @ SV207 @ SV1620 @ SV711 @ SY4733 @ SY4734 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3410]) ).
thf(3830,plain,
! [SV1621: $i,SV1465: $i,SV1147: $i,SV712: $i,SV208: $i] :
( ( ! [SY4735: $i,SY4736: $i,SY4737: $i] :
( ( ( hAPP @ ( hAPP @ SV208 @ SV712 ) @ SV1147 )
= ( hAPP @ ( hAPP @ SV208 @ SV1147 ) @ SV712 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV208 @ SV1465 @ SV1621 @ SY4735 @ SY4736 @ SY4737 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3411]) ).
thf(3831,plain,
! [SV1622: $i,SV1466: $i,SV1148: $i,SV713: $i,SV209: $i] :
( ( ! [SY4738: $i,SY4739: $i,SY4740: $i,SY4741: $i] :
( ( ( hAPP @ ( hAPP @ SV209 @ SV713 ) @ ( hAPP @ ( hAPP @ SV209 @ SV1148 ) @ SV1466 ) )
= ( hAPP @ ( hAPP @ SV209 @ ( hAPP @ ( hAPP @ SV209 @ SV713 ) @ SV1148 ) ) @ SV1466 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV209 @ SV1622 @ SY4738 @ SY4739 @ SY4740 @ SY4741 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3412]) ).
thf(3832,plain,
! [SV1623: $i,SV1467: $i,SV1149: $i,SV714: $i,SV210: $i] :
( ( ! [SY4742: $i,SY4743: $i] :
( ( ( hAPP @ ( hAPP @ SV210 @ SV714 ) @ SV1149 )
= SV1149 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV210 @ SV1467 @ SV1623 @ SV714 @ SY4742 @ SY4743 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3413]) ).
thf(3833,plain,
! [SV1624: $i,SV1468: $i,SV1150: $i,SV715: $i,SV211: $i] :
( ( ! [SY4744: $i,SY4745: $i,SY4746: $i,SY4747: $i] :
( ( ( hAPP @ ( hAPP @ SV211 @ SV715 ) @ ( hAPP @ ( hAPP @ SV211 @ SV1150 ) @ SV1468 ) )
= ( hAPP @ ( hAPP @ SV211 @ ( hAPP @ ( hAPP @ SV211 @ SV715 ) @ SV1150 ) ) @ SV1468 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV211 @ SV1624 @ SY4744 @ SY4745 @ SY4746 @ SY4747 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3414]) ).
thf(3834,plain,
! [SV1625: $i,SV1469: $i,SV1151: $i,SV716: $i,SV212: $i] :
( ( ! [SY4748: $i,SY4749: $i,SY4750: $i] :
( ( ( hAPP @ ( hAPP @ SV212 @ SV716 ) @ SV1151 )
= ( hAPP @ ( hAPP @ SV212 @ SV1151 ) @ SV716 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV212 @ SV1469 @ SV1625 @ SY4748 @ SY4749 @ SY4750 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3415]) ).
thf(3835,plain,
! [SV1626: $i,SV1470: $i,SV1152: $i,SV717: $i,SV213: $i] :
( ( ! [SY4751: $i,SY4752: $i,SY4753: $i,SY4754: $i] :
( ( ( hAPP @ ( hAPP @ SV213 @ ( hAPP @ ( hAPP @ SV213 @ SV717 ) @ SV1152 ) ) @ SV1470 )
= ( hAPP @ ( hAPP @ SV213 @ ( hAPP @ ( hAPP @ SV213 @ SV717 ) @ SV1470 ) ) @ SV1152 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV213 @ SV1626 @ SY4751 @ SY4752 @ SY4753 @ SY4754 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3416]) ).
thf(3836,plain,
! [SV1627: $i,SV1471: $i,SV1153: $i,SV718: $i,SV214: $i] :
( ( ! [SY4755: $i,SY4756: $i,SY4757: $i,SY4758: $i] :
( ( ( hAPP @ ( hAPP @ SV214 @ SV718 ) @ ( hAPP @ ( hAPP @ SV214 @ SV1153 ) @ SV1471 ) )
= ( hAPP @ ( hAPP @ SV214 @ SV1153 ) @ ( hAPP @ ( hAPP @ SV214 @ SV718 ) @ SV1471 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV214 @ SV1627 @ SY4755 @ SY4756 @ SY4757 @ SY4758 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3417]) ).
thf(3837,plain,
! [SV1628: $i,SV1472: $i,SV1154: $i,SV719: $i,SV215: $i] :
( ( ! [SY4759: $i,SY4760: $i,SY4761: $i,SY4762: $i] :
( ( ( hAPP @ ( hAPP @ SV215 @ ( hAPP @ ( hAPP @ SV215 @ SV719 ) @ SV1154 ) ) @ SV1472 )
= ( hAPP @ ( hAPP @ SV215 @ SV719 ) @ ( hAPP @ ( hAPP @ SV215 @ SV1154 ) @ SV1472 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV215 @ SV1628 @ SY4759 @ SY4760 @ SY4761 @ SY4762 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3418]) ).
thf(3838,plain,
! [SV1629: $i,SV1473: $i,SV1155: $i,SV720: $i,SV216: $i] :
( ( ! [SY4763: $i,SY4764: $i,SY4765: $i,SY4766: $i,SY4767: $i] :
( ( ( hAPP @ ( hAPP @ SV216 @ ( hAPP @ ( hAPP @ SV216 @ SV720 ) @ SV1155 ) ) @ ( hAPP @ ( hAPP @ SV216 @ SV1473 ) @ SV1629 ) )
= ( hAPP @ ( hAPP @ SV216 @ ( hAPP @ ( hAPP @ SV216 @ SV720 ) @ SV1473 ) ) @ ( hAPP @ ( hAPP @ SV216 @ SV1155 ) @ SV1629 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV216 @ SY4763 @ SY4764 @ SY4765 @ SY4766 @ SY4767 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3419]) ).
thf(3839,plain,
! [SV1630: $i,SV1474: $i,SV1156: $i,SV721: $i,SV217: $i] :
( ( ! [SY4768: $i,SY4769: $i,SY4770: $i,SY4771: $i] :
( ( ( hAPP @ ( hAPP @ SV217 @ SV721 ) @ ( hAPP @ ( hAPP @ SV217 @ SV1156 ) @ SV1474 ) )
= ( hAPP @ ( hAPP @ SV217 @ SV1156 ) @ ( hAPP @ ( hAPP @ SV217 @ SV721 ) @ SV1474 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1630 @ SV217 @ SY4768 @ SY4769 @ SY4770 @ SY4771 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3420]) ).
thf(3840,plain,
! [SV1631: $i,SV1475: $i,SV1157: $i,SV722: $i,SV218: $i] :
( ( ! [SY4772: $i,SY4773: $i,SY4774: $i,SY4775: $i] :
( ( ( hAPP @ ( hAPP @ SV218 @ SV722 ) @ ( hAPP @ ( hAPP @ SV218 @ SV1157 ) @ SV1475 ) )
= ( hAPP @ ( hAPP @ SV218 @ ( hAPP @ ( hAPP @ SV218 @ SV722 ) @ SV1157 ) ) @ SV1475 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1631 @ SV218 @ SY4772 @ SY4773 @ SY4774 @ SY4775 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3421]) ).
thf(3841,plain,
! [SV1632: $i,SV1476: $i,SV1158: $i,SV723: $i,SV219: $i] :
( ( ! [SY4776: $i,SY4777: $i,SY4778: $i,SY4779: $i] :
( ( ( hAPP @ ( hAPP @ SV219 @ ( hAPP @ ( hAPP @ SV219 @ SV723 ) @ SV1158 ) ) @ SV1476 )
= ( hAPP @ ( hAPP @ SV219 @ SV723 ) @ ( hAPP @ ( hAPP @ SV219 @ SV1158 ) @ SV1476 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1632 @ SV219 @ SY4776 @ SY4777 @ SY4778 @ SY4779 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3422]) ).
thf(3842,plain,
! [SV1633: $i,SV1477: $i,SV1159: $i,SV724: $i,SV220: $i] :
( ( ! [SY4780: $i,SY4781: $i,SY4782: $i,SY4783: $i] :
( ( ( hAPP @ ( hAPP @ SV220 @ ( hAPP @ ( hAPP @ SV220 @ SV724 ) @ SV1159 ) ) @ SV1477 )
= ( hAPP @ ( hAPP @ SV220 @ ( hAPP @ ( hAPP @ SV220 @ SV724 ) @ SV1477 ) ) @ SV1159 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1633 @ SV220 @ SY4780 @ SY4781 @ SY4782 @ SY4783 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3423]) ).
thf(3843,plain,
! [SV1634: $i,SV1478: $i,SV1160: $i,SV725: $i,SV221: $i] :
( ( ! [SY4784: $i,SY4785: $i,SY4786: $i,SY4787: $i,SY4788: $i] :
( ( ( hAPP @ ( hAPP @ SV221 @ ( hAPP @ ( hAPP @ SV221 @ SV725 ) @ SV1160 ) ) @ ( hAPP @ ( hAPP @ SV221 @ SV1478 ) @ SV1634 ) )
= ( hAPP @ ( hAPP @ SV221 @ SV1478 ) @ ( hAPP @ ( hAPP @ SV221 @ ( hAPP @ ( hAPP @ SV221 @ SV725 ) @ SV1160 ) ) @ SV1634 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4784 @ SV221 @ SY4785 @ SY4786 @ SY4787 @ SY4788 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3424]) ).
thf(3844,plain,
! [SV1635: $i,SV1479: $i,SV1161: $i,SV726: $i,SV222: $i] :
( ( ! [SY4789: $i,SY4790: $i,SY4791: $i,SY4792: $i,SY4793: $i] :
( ( ( hAPP @ ( hAPP @ SV222 @ ( hAPP @ ( hAPP @ SV222 @ SV726 ) @ SV1161 ) ) @ ( hAPP @ ( hAPP @ SV222 @ SV1479 ) @ SV1635 ) )
= ( hAPP @ ( hAPP @ SV222 @ SV726 ) @ ( hAPP @ ( hAPP @ SV222 @ SV1161 ) @ ( hAPP @ ( hAPP @ SV222 @ SV1479 ) @ SV1635 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4789 @ SV222 @ SY4790 @ SY4791 @ SY4792 @ SY4793 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3425]) ).
thf(3845,plain,
! [SV1636: $i,SV1480: $i,SV1162: $i,SV727: $i,SV223: $i] :
( ( ! [SY4794: $i,SY4795: $i,SY4796: $i,SY4797: $i,SY4798: $i] :
( ( ( hAPP @ ( hAPP @ SV223 @ ( hAPP @ ( hAPP @ SV223 @ SV727 ) @ SV1162 ) ) @ ( hAPP @ ( hAPP @ SV223 @ SV1480 ) @ SV1636 ) )
= ( hAPP @ ( hAPP @ SV223 @ ( hAPP @ ( hAPP @ SV223 @ SV727 ) @ SV1480 ) ) @ ( hAPP @ ( hAPP @ SV223 @ SV1162 ) @ SV1636 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SY4794 @ SV223 @ SY4795 @ SY4796 @ SY4797 @ SY4798 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3426]) ).
thf(3846,plain,
! [SV1637: $i,SV1481: $i,SV1163: $i,SV728: $i,SV224: $i] :
( ( ! [SY4799: $i,SY4800: $i] :
( ( ( hAPP @ ( hAPP @ SV224 @ SV728 ) @ SV1163 )
= SV728 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1481 @ SV224 @ SV1637 @ SY4799 @ SV1163 @ SY4800 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3427]) ).
thf(3847,plain,
! [SV1638: $i,SV1482: $i,SV1164: $i,SV729: $i,SV225: $i] :
( ( ! [SY4801: $i,SY4802: $i] :
( ( ( hAPP @ ( hAPP @ SV225 @ SV729 ) @ SV1164 )
= SV1164 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1482 @ SV225 @ SV1638 @ SY4801 @ SV729 @ SY4802 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3428]) ).
thf(3848,plain,
! [SV1639: $i,SV1483: $i,SV1165: $i,SV730: $i,SV226: $i] :
( ( ! [SY4803: $i,SY4804: $i] :
( ( ( hAPP @ ( hAPP @ SV226 @ SV730 ) @ SV1165 )
= SV1165 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1483 @ SV226 @ SV1639 @ SV1165 @ SY4803 @ SY4804 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3429]) ).
thf(3849,plain,
! [SV1640: $i,SV1484: $i,SV1166: $i,SV731: $i,SV227: $i] :
( ( ! [SY4805: $i,SY4806: $i] :
( ( ( hAPP @ ( hAPP @ SV227 @ SV731 ) @ SV1166 )
= SV731 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1484 @ SV227 @ SV1640 @ SV731 @ SY4805 @ SY4806 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3430]) ).
thf(3850,plain,
! [SV1641: $i,SV1485: $i,SV1167: $i,SV732: $i,SV228: $i] :
( ( ! [SY4807: $i,SY4808: $i,SY4809: $i,SY4810: $i] :
( ( ( hAPP @ ( hAPP @ SV228 @ ( hAPP @ ( hAPP @ SV732 @ SV1167 ) @ SV1485 ) ) @ SV1641 )
= ( hAPP @ ( hAPP @ SV732 @ ( hAPP @ ( hAPP @ SV228 @ SV1167 ) @ SV1641 ) ) @ ( hAPP @ ( hAPP @ SV228 @ SV1485 ) @ SV1641 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV732 @ SV228 @ SY4807 @ SY4808 @ SY4809 @ SY4810 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3431]) ).
thf(3851,plain,
! [SV1642: $i,SV1486: $i,SV1168: $i,SV733: $i,SV229: $i] :
( ( ! [SY4811: $i,SY4812: $i,SY4813: $i] :
( ( ( hAPP @ ( hAPP @ SV229 @ SV733 ) @ SV1168 )
= ( hAPP @ ( hAPP @ SV229 @ SV1168 ) @ SV733 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1486 @ SV229 @ SV1642 @ SY4811 @ SY4812 @ SY4813 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3432]) ).
thf(3852,plain,
! [SV1643: $i,SV1487: $i,SV1169: $i,SV734: $i,SV230: $i] :
( ( ! [SY4814: $i,SY4815: $i] :
( ( ( hAPP @ ( hAPP @ SV230 @ SV734 ) @ SV1169 )
= SV734 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV230 @ SV1487 @ SV1643 @ SV1169 @ SY4814 @ SY4815 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3433]) ).
thf(3853,plain,
! [SV1644: $i,SV1488: $i,SV1170: $i,SV735: $i,SV231: $i] :
( ( ! [SY4816: $i,SY4817: $i] :
( ( ( hAPP @ ( hAPP @ SV231 @ SV735 ) @ SV1170 )
= SV1170 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV231 @ SV1488 @ SV1644 @ SV735 @ SY4816 @ SY4817 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3434]) ).
thf(3854,plain,
! [SV1645: $i,SV1489: $i,SV1171: $i,SV736: $i,SV232: $i] :
( ( ! [SY4818: $i,SY4819: $i] :
( ( ( hAPP @ ( hAPP @ SV232 @ SV736 ) @ SV736 )
= ( hAPP @ ( hAPP @ SV1171 @ ( hAPP @ ( hAPP @ SV232 @ SV1489 ) @ SV1489 ) ) @ SV736 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV232 @ SV1171 @ SV1645 @ SY4818 @ SV1489 @ SY4819 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3435]) ).
thf(3855,plain,
! [SV1646: $i,SV1490: $i,SV1172: $i,SV737: $i,SV233: $i] :
( ( ! [SY4820: $i,SY4821: $i,SY4822: $i] :
( ( ( hAPP @ ( hAPP @ SV233 @ SV737 ) @ ( hAPP @ ( hAPP @ SV1172 @ SV1490 ) @ SV737 ) )
= ( hAPP @ ( hAPP @ SV1172 @ ( hAPP @ ( hAPP @ SV233 @ SV1490 ) @ SV1646 ) ) @ SV737 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV233 @ SV1172 @ SY4820 @ SY4821 @ SV1646 @ SY4822 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3436]) ).
thf(3856,plain,
! [SV1647: $i,SV1491: $i,SV1173: $i,SV738: $i,SV234: $i] :
( ( ! [SY4823: $i,SY4824: $i,SY4825: $i] :
( ( ( hAPP @ ( hAPP @ SV234 @ ( hAPP @ ( hAPP @ SV738 @ SV1173 ) @ SV1491 ) ) @ SV1491 )
= ( hAPP @ ( hAPP @ SV738 @ ( hAPP @ ( hAPP @ SV234 @ SV1173 ) @ SV1647 ) ) @ SV1491 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV234 @ SV738 @ SY4823 @ SY4824 @ SV1647 @ SY4825 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3437]) ).
thf(3857,plain,
! [SV1648: $i,SV1492: $i,SV1174: $i,SV739: $i,SV235: $i] :
( ( ! [SY4826: $i,SY4827: $i,SY4828: $i,SY4829: $i] :
( ( ( hAPP @ ( hAPP @ SV235 @ ( hAPP @ ( hAPP @ SV739 @ SV1174 ) @ SV1492 ) ) @ ( hAPP @ ( hAPP @ SV739 @ SV1648 ) @ SV1492 ) )
= ( hAPP @ ( hAPP @ SV739 @ ( hAPP @ ( hAPP @ SV235 @ SV1174 ) @ SV1648 ) ) @ SV1492 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV235 @ SV739 @ SY4826 @ SY4827 @ SY4828 @ SY4829 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3438]) ).
thf(3858,plain,
! [SV1649: $i,SV1493: $i,SV1175: $i,SV740: $i,SV236: $i] :
( ( ! [SY4830: $i] :
( ( SV236 = SV740 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV1175 @ SV740 ) @ SV236 ) )
| ~ ( c_ListOrder_Ostep1 @ SV1175 @ ( c_List_Olist_OCons @ SV740 @ SV1493 @ SV1649 ) @ ( c_List_Olist_OCons @ SV236 @ SY4830 @ SV1649 ) @ SV1649 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3439]) ).
thf(3859,plain,
! [SV1650: $i,SV1494: $i,SV1176: $i,SV741: $i,SV237: $i] :
( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV237 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SV741 ) @ SV1176 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SV1494 ) @ SV1650 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SV741 ) @ SV1494 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SV1176 ) @ SV1650 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3440]) ).
thf(3860,plain,
! [SV1495: $i,SV1177: $i,SV742: $i,SV238: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV238 ) @ SV742 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1177 ) @ SV1495 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV742 ) @ SV1495 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV238 ) @ SV1177 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3441]) ).
thf(3861,plain,
! [SV239: $i,SV743: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV743 @ SV239 ) @ ( c_HOL_Ozero__class_Ozero @ SV239 ) @ SV239 )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV239 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3442]) ).
thf(3862,plain,
! [SV1178: $i,SV744: $i,SV240: $i] :
( ( ( class_Orderings_Olinorder @ SV240 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omax @ SV744 @ SV1178 @ SV240 )
= ( c_Orderings_Oord__class_Omax @ SV1178 @ SV744 @ SV240 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3443]) ).
thf(3863,plain,
! [SV241: $i,SV1179: $i,SV745: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV745 @ SV1179 @ tc_nat )
= $false )
| ( ( ( c_Lambda_Oliftn @ SV241 @ ( c_Lambda_OdB_OVar @ SV745 ) @ SV1179 )
= ( c_Lambda_OdB_OVar @ SV745 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3444]) ).
thf(3864,plain,
! [SV1496: $i,SV1180: $i,SV746: $i,SV242: $i] :
( ( ( c_Type_Otyping @ SV242 @ SV746 @ SV1180 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV242 @ SV1496 @ SV1180 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV1496 ) @ SV746 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3445]) ).
thf(3865,plain,
! [SV749: $i,SV1181: $i,SV245: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV245 ) @ SV1181 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV245 ) @ SV749 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1181 ) @ SV749 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3447]) ).
thf(3866,plain,
! [SV246: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV246 ) )
= $false )
| ( ( SV246
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV246 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV246 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV246 ) ) )
= $true )
| ( ( SV246
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV246 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV246 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV246 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3448]) ).
thf(3867,plain,
! [SV1497: $i,SV1183: $i,SV752: $i,SV249: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV249 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV249 ) @ ( c_Orderings_Oord__class_Omax @ SV752 @ SV1183 @ SV249 ) ) @ SV1497 )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV249 ) @ SV752 ) @ SV1497 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV249 ) @ SV1183 ) @ SV1497 ) @ SV249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3449]) ).
thf(3868,plain,
! [SV1651: $i,SV1498: $i,SV1185: $i,SV754: $i,SV251: $i] :
( ( ! [SY4831: $i] :
( ( SV251 = SV754 )
| ( c_ListOrder_Ostep1 @ SV1185 @ SV251 @ SV754 @ SV1498 )
| ~ ( c_ListOrder_Ostep1 @ SV1185 @ ( c_List_Oappend @ SV251 @ ( c_List_Olist_OCons @ SV1651 @ ( c_List_Olist_ONil @ SV1498 ) @ SV1498 ) @ SV1498 ) @ ( c_List_Oappend @ SV754 @ ( c_List_Olist_OCons @ SY4831 @ ( c_List_Olist_ONil @ SV1498 ) @ SV1498 ) @ SV1498 ) @ SV1498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3450]) ).
thf(3869,plain,
! [SV1499: $i,SV1186: $i,SV755: $i,SV252: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV252 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ SV755 @ SV1186 @ SV252 ) @ SV1499 @ SV252 )
= ( c_Orderings_Oord__class_Omax @ SV755 @ ( c_Orderings_Oord__class_Omax @ SV1186 @ SV1499 @ SV252 ) @ SV252 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3451]) ).
thf(3870,plain,
! [SV1500: $i,SV1187: $i,SV756: $i,SV253: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV253 ) )
= $true )
| ( ( ( c_Orderings_Oord__class_Omax @ SV756 @ ( c_Orderings_Oord__class_Omax @ SV1187 @ SV1500 @ SV253 ) @ SV253 )
= ( c_Orderings_Oord__class_Omax @ SV1187 @ ( c_Orderings_Oord__class_Omax @ SV756 @ SV1500 @ SV253 ) @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3452]) ).
thf(3871,plain,
! [SV1188: $i,SV759: $i,SV257: $i] :
( ( ( class_Orderings_Olinorder @ SV257 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omax @ SV759 @ ( c_Orderings_Oord__class_Omax @ SV759 @ SV1188 @ SV257 ) @ SV257 )
= ( c_Orderings_Oord__class_Omax @ SV759 @ SV1188 @ SV257 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3454]) ).
thf(3872,plain,
! [SV1501: $i,SV1190: $i,SV761: $i,SV259: $i] :
( ( ( ( hAPP @ ( hAPP @ SV259 @ SV761 ) @ SV1190 )
= SV761 )
= $true )
| ( ( ~ ( c_OrderedGroup_Omonoid__add @ SV1190 @ SV259 @ SV1501 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3455]) ).
thf(3873,plain,
! [SV1502: $i,SV1191: $i,SV762: $i,SV260: $i] :
( ( ( ( hAPP @ ( hAPP @ SV260 @ SV762 ) @ SV1191 )
= SV1191 )
= $true )
| ( ( ~ ( c_OrderedGroup_Omonoid__add @ SV762 @ SV260 @ SV1502 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3456]) ).
thf(3874,plain,
! [SV765: $i,SV263: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV765 @ SV263 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV263 ) @ SV765 ) @ SV765 ) @ SV263 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV263 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3459]) ).
thf(3875,plain,
! [SV766: $i,SV264: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV264 ) @ SV766 ) @ SV766 ) @ SV264 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SV766 @ SV264 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV264 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3460]) ).
thf(3876,plain,
! [SV265: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV265 ) )
= $false )
| ( ( SV265
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV265 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV265 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV265
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV265 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV265 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3461]) ).
thf(3877,plain,
! [SV266: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV266 ) )
= $false )
| ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV266 ) @ tc_Lambda_OdB )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV266 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV266 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV266 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV266 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3462]) ).
thf(3878,plain,
! [SV267: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV267 ) )
= $false )
| ( ( SV267
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV267 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV267 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV267
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV267 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV267 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV267 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV267 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3463]) ).
thf(3879,plain,
! [SV769: $i,SV271: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV271 ) )
= $true )
| ( ( SV769
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ SV769 ) @ ( c_HOL_Ozero__class_Ozero @ SV271 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3466]) ).
thf(3880,plain,
! [SV281: $i,SV776: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV776 @ ( c_HOL_Ozero__class_Ozero @ SV281 ) @ SV281 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV281 ) @ SV776 ) @ SV776 ) @ ( c_HOL_Ozero__class_Ozero @ SV281 ) @ SV281 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV281 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3472]) ).
thf(3881,plain,
! [SV777: $i,SV282: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV282 ) @ SV777 ) @ SV777 ) @ ( c_HOL_Ozero__class_Ozero @ SV282 ) @ SV282 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV777 @ ( c_HOL_Ozero__class_Ozero @ SV282 ) @ SV282 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3473]) ).
thf(3882,plain,
! [SV1192: $i,SV778: $i,SV283: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV283 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV283 ) @ ( c_Power_Opower__class_Opower @ SV778 @ SV1192 @ SV283 ) @ SV283 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV283 ) @ SV778 @ SV283 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3474]) ).
thf(3883,plain,
! [SV1503: $i,SV1193: $i,SV779: $i,SV284: $i] :
( ( ( ~ ( class_Orderings_Olinorder @ SV284 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV779 @ SV1193 @ SV284 )
| ( c_HOL_Oord__class_Oless @ SV779 @ SV1503 @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ SV779 @ ( c_Orderings_Oord__class_Omax @ SV1503 @ SV1193 @ SV284 ) @ SV284 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3475]) ).
thf(3884,plain,
! [SV780: $i,SV1194: $i,SV285: $i] :
( ( ( SV285 = SV1194 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1194 @ SV285 @ tc_nat )
= $true )
| ( ( ( c_Lambda_Osubstn @ ( c_Lambda_OdB_OVar @ SV285 ) @ SV780 @ SV1194 )
= ( c_Lambda_OdB_OVar @ SV285 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3476]) ).
thf(3885,plain,
! [SV287: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV287 ) )
= $false )
| ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV287 ) @ tc_Lambda_OdB )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV287 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV287 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3477]) ).
thf(3886,plain,
! [SV291: $i,SV782: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV782 @ SV782 @ SV291 )
= $false )
| ( ( class_Orderings_Oorder @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3478]) ).
thf(3887,plain,
! [SV292: $i,SV783: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV783 @ SV783 @ SV292 )
= $false )
| ( ( class_Orderings_Olinorder @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3479]) ).
thf(3888,plain,
! [SV293: $i,SV784: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV784 @ SV784 @ SV293 )
= $false )
| ( ( class_Orderings_Opreorder @ SV293 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3480]) ).
thf(3889,plain,
! [SV786: $i,SV1196: $i,SV295: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV295 ) @ SV1196 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV295 ) @ SV786 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1196 ) @ SV786 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3482]) ).
thf(3890,plain,
! [SV1197: $i,SV787: $i,SV296: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV296 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV296 ) @ SV787 ) @ SV1197 ) @ SV296 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SV1197 @ SV296 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SV787 @ SV296 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3483]) ).
thf(3891,plain,
! [SV1652: $i,SV1504: $i,SV1198: $i,SV788: $i,SV297: $i] :
( ( ! [SY4832: $i] :
( ( c_ListOrder_Ostep1 @ SV297 @ SV788 @ SV1198 @ SV1504 )
| ( SV1198 = SV788 )
| ~ ( c_ListOrder_Ostep1 @ SV297 @ ( c_List_Olist_OCons @ SV1652 @ SV788 @ SV1504 ) @ ( c_List_Olist_OCons @ SY4832 @ SV1198 @ SV1504 ) @ SV1504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3484]) ).
thf(3892,plain,
! [SV1653: $i,SV1505: $i,SV1199: $i,SV789: $i,SV298: $i] :
( ( ( ( hAPP @ ( hAPP @ SV298 @ ( hAPP @ ( hAPP @ SV298 @ SV789 ) @ SV1199 ) ) @ SV1505 )
= ( hAPP @ ( hAPP @ SV298 @ SV789 ) @ ( hAPP @ ( hAPP @ SV298 @ SV1199 ) @ SV1505 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV298 @ SV1653 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3485]) ).
thf(3893,plain,
! [SV1200: $i,SV790: $i,SV299: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV299 )
= $false )
| ( ( ( c_List_Olistsum @ ( c_List_Olist_OCons @ SV790 @ SV1200 @ SV299 ) @ SV299 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV299 ) @ SV790 ) @ ( c_List_Olistsum @ SV1200 @ SV299 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3486]) ).
thf(3894,plain,
! [SV1654: $i,SV1506: $i,SV1201: $i,SV791: $i,SV300: $i] :
( ( ( c_List_Omap @ SV300 @ ( c_List_Oappend @ SV791 @ SV1201 @ SV1506 ) @ SV1506 @ SV1654 )
= ( c_List_Oappend @ ( c_List_Omap @ SV300 @ SV791 @ SV1506 @ SV1654 ) @ ( c_List_Omap @ SV300 @ SV1201 @ SV1506 @ SV1654 ) @ SV1654 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3487]) ).
thf(3895,plain,
! [SV301: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV301 ) )
= $false )
| ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV301 ) @ tc_Lambda_OdB )
= $true )
| ( ( SV301
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV301 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV301 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV301 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV301 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3488]) ).
thf(3896,plain,
! [SV1202: $i,SV792: $i,SV302: $i] :
( ( ( class_Ring__and__Field_Oordered__idom @ SV302 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV792 @ SV1202 @ SV302 )
| ( c_HOL_Oord__class_Oless @ SV1202 @ SV792 @ SV302 )
| ( SV1202 = SV792 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3489]) ).
thf(3897,plain,
! [SV1203: $i,SV793: $i,SV303: $i] :
( ( ( class_Orderings_Olinorder @ SV303 )
= $false )
| ( ( ( SV793 = SV1203 )
| ( c_HOL_Oord__class_Oless @ SV1203 @ SV793 @ SV303 )
| ( c_HOL_Oord__class_Oless @ SV793 @ SV1203 @ SV303 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3490]) ).
thf(3898,plain,
! [SV305: $i,SV1204: $i,SV795: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV795 @ SV1204 @ tc_nat )
= $true )
| ( ( ( SV1204 = SV795 )
| ( c_HOL_Oord__class_Oless @ SV1204 @ SV795 @ tc_nat ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV305 @ SV795 ) @ SV1204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3492]) ).
thf(3899,plain,
! [SV1205: $i,SV797: $i,SV307: $i] :
( ( ( class_Orderings_Olinorder @ SV307 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV797 @ SV1205 @ SV307 )
| ( c_HOL_Oord__class_Oless @ SV1205 @ SV797 @ SV307 )
| ( SV1205 = SV797 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3494]) ).
thf(3900,plain,
! [SV1207: $i,SV799: $i,SV309: $i] :
( ( ( class_Orderings_Olinorder @ SV309 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV799 @ SV1207 @ SV309 )
| ( SV1207 = SV799 )
| ( c_HOL_Oord__class_Oless @ SV1207 @ SV799 @ SV309 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3496]) ).
thf(3901,plain,
! [SV1208: $i,SV800: $i,SV310: $i] :
( ( ( class_Orderings_Olinorder @ SV310 )
= $false )
| ( ( ( SV800 = SV1208 )
| ( c_HOL_Oord__class_Oless @ SV800 @ SV1208 @ SV310 )
| ( c_HOL_Oord__class_Oless @ SV1208 @ SV800 @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3497]) ).
thf(3902,plain,
! [SV1655: $i,SV1508: $i,SV1209: $i,SV802: $i,SV312: $i] :
( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV312 )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV312 ) @ SV802 ) @ SV1209 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV312 ) @ SV1508 ) @ SV1655 ) @ SV312 )
| ~ ( c_HOL_Oord__class_Oless @ SV1209 @ SV1655 @ SV312 )
| ~ ( c_HOL_Oord__class_Oless @ SV802 @ SV1508 @ SV312 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3499]) ).
thf(3903,plain,
! [SV1509: $i,SV1210: $i,SV803: $i,SV313: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV313 ) @ SV803 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1210 ) @ SV1509 ) @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV803 @ SV1509 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ SV313 @ SV1210 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3500]) ).
thf(3904,plain,
! [SV1211: $i,SV804: $i,SV314: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV314 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV804 @ SV314 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1211 @ SV314 ) @ SV314 )
| ~ ( c_HOL_Oord__class_Oless @ SV804 @ SV1211 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3501]) ).
thf(3905,plain,
! [SV1212: $i,SV805: $i,SV315: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV315 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV805 @ SV1212 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV805 @ SV315 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1212 @ SV315 ) @ SV315 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3502]) ).
thf(3906,plain,
! [SV317: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV317 ) )
= $false )
| ( ( SV317
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV317 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV317 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV317
= ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV317 ) ) )
= $true )
| ( ( SV317
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV317 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV317 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV317 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3504]) ).
thf(3907,plain,
! [SV808: $i,SV319: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV319 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV808 @ SV319 ) @ SV319 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV808 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV319 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3506]) ).
thf(3908,plain,
! [SV320: $i,SV809: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV809 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV320 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV809 @ SV320 ) @ SV320 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3507]) ).
thf(3909,plain,
! [SV1656: $i,SV1511: $i,SV1214: $i,SV810: $i,SV321: $i] :
( ( ! [SY4833: $i] :
( ( SV321 = SV810 )
| ( SV1214 = SV1511 )
| ~ ( c_ListOrder_Ostep1 @ SV1656 @ ( c_List_Oappend @ SV321 @ ( c_List_Olist_OCons @ SV1214 @ ( c_List_Olist_ONil @ SY4833 ) @ SY4833 ) @ SY4833 ) @ ( c_List_Oappend @ SV810 @ ( c_List_Olist_OCons @ SV1511 @ ( c_List_Olist_ONil @ SY4833 ) @ SY4833 ) @ SY4833 ) @ SY4833 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3508]) ).
thf(3910,plain,
! [SV1512: $i,SV1216: $i,SV812: $i,SV323: $i] :
( ( ( c_List_Olistsp @ SV323 @ ( c_List_Oappend @ SV812 @ SV1216 @ SV1512 ) @ SV1512 )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV323 @ SV1216 @ SV1512 )
| ~ ( c_List_Olistsp @ SV323 @ SV812 @ SV1512 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3509]) ).
thf(3911,plain,
! [SV1657: $i,SV1513: $i,SV1217: $i,SV813: $i,SV324: $i] :
( ( ( c_Lambda_OdB_OdB__rec @ SV324 @ SV813 @ SV1217 @ ( c_Lambda_OdB_OAbs @ SV1513 ) @ SV1657 )
= ( hAPP @ ( hAPP @ SV1217 @ SV1513 ) @ ( c_Lambda_OdB_OdB__rec @ SV324 @ SV813 @ SV1217 @ SV1513 @ SV1657 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3510]) ).
thf(3912,plain,
! [SV1514: $i,SV1218: $i,SV814: $i,SV326: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV326 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV814 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV326 ) @ SV1218 ) @ SV1514 ) @ SV326 )
| ~ ( c_HOL_Oord__class_Oless @ SV814 @ SV1514 @ SV326 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV1218 @ SV326 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3511]) ).
thf(3913,plain,
! [SV1658: $i,SV1515: $i,SV1219: $i,SV815: $i,SV327: $i] :
( ( ! [SY4834: $i] :
( ( c_List_Ofoldr @ SV327 @ ( c_List_Olist_OCons @ SV815 @ SV1219 @ SV1515 ) @ SV1658 @ SV1515 @ SY4834 )
= ( hAPP @ ( hAPP @ SV327 @ SV815 ) @ ( c_List_Ofoldr @ SV327 @ SV1219 @ SV1658 @ SV1515 @ SY4834 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3512]) ).
thf(3914,plain,
! [SV1659: $i,SV1516: $i,SV1220: $i,SV816: $i,SV328: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV328 @ ( c_Lambda_OdB_OdB__case @ SV816 @ SV1220 @ SV1516 @ ( c_Lambda_OdB_OAbs @ SV1659 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV328 @ ( hAPP @ SV1516 @ SV1659 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3513]) ).
thf(3915,plain,
! [SV1660: $i,SV1517: $i,SV1221: $i,SV817: $i,SV329: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV329 @ ( c_Lambda_OdB_OdB__case @ SV817 @ SV1221 @ SV1517 @ ( c_Lambda_OdB_OAbs @ SV1660 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV329 @ ( hAPP @ SV1517 @ SV1660 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3514]) ).
thf(3916,plain,
! [SV1518: $i,SV1224: $i,SV822: $i,SV334: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV334 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV334 ) @ SV822 ) @ SV1224 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV334 ) @ SV1518 ) @ SV1224 ) @ SV334 )
| ~ ( c_HOL_Oord__class_Oless @ SV822 @ SV1518 @ SV334 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3515]) ).
thf(3917,plain,
! [SV1519: $i,SV1225: $i,SV823: $i,SV335: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV335 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV335 ) @ SV823 ) @ SV1225 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV335 ) @ SV1519 ) @ SV1225 ) @ SV335 )
| ~ ( c_HOL_Oord__class_Oless @ SV823 @ SV1519 @ SV335 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3516]) ).
thf(3918,plain,
! [SV1520: $i,SV1226: $i,SV824: $i,SV336: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV336 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV824 @ SV1226 @ SV336 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV336 ) @ SV824 ) @ SV1520 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV336 ) @ SV1226 ) @ SV1520 ) @ SV336 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3517]) ).
thf(3919,plain,
! [SV1521: $i,SV1227: $i,SV825: $i,SV337: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV337 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV337 ) @ SV825 ) @ SV1227 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV337 ) @ SV825 ) @ SV1521 ) @ SV337 )
| ~ ( c_HOL_Oord__class_Oless @ SV1227 @ SV1521 @ SV337 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3518]) ).
thf(3920,plain,
! [SV1522: $i,SV1228: $i,SV826: $i,SV338: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV338 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV338 ) @ SV826 ) @ SV1228 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV338 ) @ SV826 ) @ SV1522 ) @ SV338 )
| ~ ( c_HOL_Oord__class_Oless @ SV1228 @ SV1522 @ SV338 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3519]) ).
thf(3921,plain,
! [SV1523: $i,SV1229: $i,SV827: $i,SV339: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV339 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV827 @ SV1229 @ SV339 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SV1523 ) @ SV827 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SV1523 ) @ SV1229 ) @ SV339 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3520]) ).
thf(3922,plain,
! [SV828: $i,SV1230: $i,SV340: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV340 @ SV1230 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV340 ) @ SV828 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1230 ) @ SV828 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3521]) ).
thf(3923,plain,
! [SV829: $i,SV341: $i,SV1231: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1231 ) @ SV341 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1231 ) @ SV829 ) @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV341 @ SV829 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3522]) ).
thf(3924,plain,
! [SV342: $i,SV1232: $i,SV830: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV830 @ SV1232 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV342 ) @ SV830 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV342 ) @ SV1232 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3523]) ).
thf(3925,plain,
! [SV343: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV343 ) )
= $false )
| ( ( c_List_Olistsp @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV343 ) @ tc_Lambda_OdB )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV343 ) ) )
= $true )
| ( ( SV343
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV343 ) ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV343 ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV343 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3524]) ).
thf(3926,plain,
! [SV1524: $i,SV1233: $i,SV831: $i,SV344: $i] :
( ( ( c_Type_Otyping @ SV344 @ SV831 @ SV1233 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1524 ) @ SV831 ) )
| ~ ( c_Type_Otyping @ SV344 @ SV1524 @ SV1233 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3525]) ).
thf(3927,plain,
! [SV1661: $i,SV1525: $i,SV1234: $i,SV832: $i,SV345: $i] :
( ( ! [SY4835: $i] :
( ( c_ListOrder_Ostep1 @ SV345 @ SV832 @ SV1234 @ SV1525 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV345 @ SV1661 ) @ SY4835 ) )
| ~ ( c_ListOrder_Ostep1 @ SV345 @ ( c_List_Olist_OCons @ SV1661 @ SV832 @ SV1525 ) @ ( c_List_Olist_OCons @ SY4835 @ SV1234 @ SV1525 ) @ SV1525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3526]) ).
thf(3928,plain,
! [SV1662: $i,SV1526: $i,SV1235: $i,SV833: $i,SV346: $i] :
( ( ( c_ListOrder_Ostep1 @ SV346 @ ( c_List_Olist_OCons @ SV833 @ SV1235 @ SV1526 ) @ ( c_List_Olist_OCons @ SV833 @ SV1662 @ SV1526 ) @ SV1526 )
| ~ ( c_ListOrder_Ostep1 @ SV346 @ SV1235 @ SV1662 @ SV1526 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3527]) ).
thf(3929,plain,
! [SV1237: $i,SV835: $i,SV348: $i] :
( ( ( class_Ring__and__Field_Osemiring__1 @ SV348 )
= $false )
| ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV835 ) @ SV1237 ) @ SV348 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV348 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV835 @ SV348 ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1237 @ SV348 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3529]) ).
thf(3930,plain,
! [SV1238: $i,SV836: $i,SV349: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV349 )
= $false )
| ( ( ( c_List_Olistsum @ ( c_List_Oappend @ SV836 @ SV1238 @ SV349 ) @ SV349 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV349 ) @ ( c_List_Olistsum @ SV836 @ SV349 ) ) @ ( c_List_Olistsum @ SV1238 @ SV349 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3530]) ).
thf(3931,plain,
! [SV1243: $i,SV841: $i,SV356: $i] :
( ( ( class_Orderings_Oorder @ SV356 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV841 @ SV1243 @ SV356 )
| ~ ( c_HOL_Oord__class_Oless @ SV1243 @ SV841 @ SV356 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3535]) ).
thf(3932,plain,
! [SV1663: $i,SV1532: $i,SV1244: $i,SV842: $i,SV357: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV357 @ SV842 ) @ SV1244 ) @ SV1532 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV357 @ SV842 ) @ SV1663 ) @ SV1532 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV357 @ SV1244 ) @ SV1663 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3536]) ).
thf(3933,plain,
! [SV1664: $i,SV1533: $i,SV1245: $i,SV843: $i,SV358: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV358 @ SV843 ) @ SV1245 ) @ SV1533 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV1664 ) @ SV1533 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV358 @ SV843 ) @ SV1245 ) @ SV1664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3537]) ).
thf(3934,plain,
! [SV1246: $i,SV844: $i,SV359: $i] :
( ( ( class_Orderings_Olinorder @ SV359 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV844 @ SV1246 @ SV359 )
| ~ ( c_HOL_Oord__class_Oless @ SV1246 @ SV844 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3538]) ).
thf(3935,plain,
! [SV1534: $i,SV1247: $i,SV845: $i,SV360: $i] :
( ( ( c_Wellfounded_Oaccp @ SV360 @ SV845 @ SV1247 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV360 @ SV845 ) @ SV1534 ) )
| ~ ( c_Wellfounded_Oaccp @ SV360 @ SV1534 @ SV1247 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3539]) ).
thf(3936,plain,
! [SV1248: $i,SV846: $i,SV361: $i] :
( ( ( class_Orderings_Opreorder @ SV361 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV846 @ SV1248 @ SV361 )
| ~ ( c_HOL_Oord__class_Oless @ SV1248 @ SV846 @ SV361 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3540]) ).
thf(3937,plain,
! [SV1535: $i,SV1249: $i,SV847: $i,SV362: $i] :
( ( ( c_Wellfounded_Oaccp @ SV362 @ SV847 @ SV1249 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV362 @ SV847 ) @ SV1535 ) )
| ~ ( c_Wellfounded_Oaccp @ SV362 @ SV1535 @ SV1249 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3541]) ).
thf(3938,plain,
! [SV1250: $i,SV848: $i,SV363: $i] :
( ( ( class_Orderings_Opreorder @ SV363 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV848 @ SV1250 @ SV363 )
| ~ ( c_HOL_Oord__class_Oless @ SV1250 @ SV848 @ SV363 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3542]) ).
thf(3939,plain,
! [SV1665: $i,SV1536: $i,SV1252: $i,SV850: $i,SV371: $i] :
( ( ! [SY4836: $i,SY4837: $i] :
( ( ( hAPP @ ( hAPP @ SV371 @ SV850 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV1252 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1536 @ SV1665 @ SV371 @ SY4836 @ SV1252 @ SY4837 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3543]) ).
thf(3940,plain,
! [SV1253: $i,SV853: $i,SV374: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV374 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV374 ) @ SV853 @ SV1253 @ SV374 @ SV374 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV374 ) @ SV853 ) @ ( c_List_Ofoldr @ ( c_HOL_Oplus__class_Oplus @ SV374 ) @ SV1253 @ ( c_HOL_Ozero__class_Ozero @ SV374 ) @ SV374 @ SV374 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3546]) ).
thf(3941,plain,
! [SV1666: $i,SV1537: $i,SV1254: $i,SV854: $i,SV375: $i] :
( ( ! [SY4838: $i] :
( ~ ( hBOOL @ ( hAPP @ SV375 @ ( c_Lambda_OdB_OdB__case @ SV854 @ SV1254 @ SV1537 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1666 ) @ SY4838 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV375 @ ( hAPP @ ( hAPP @ SV1254 @ SV1666 ) @ SY4838 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3547]) ).
thf(3942,plain,
! [SV1667: $i,SV1538: $i,SV1255: $i,SV855: $i,SV376: $i] :
( ( ! [SY4839: $i] :
( ~ ( hBOOL @ ( hAPP @ SV376 @ ( c_Lambda_OdB_OdB__case @ SV855 @ SV1255 @ SV1538 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1667 ) @ SY4839 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SV1255 @ SV1667 ) @ SY4839 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3548]) ).
thf(3943,plain,
! [SV1668: $i,SV1539: $i,SV1257: $i,SV857: $i,SV378: $i] :
( ( ! [SY4840: $i] :
( ( c_Lambda_OdB_OdB__case @ SV378 @ SV857 @ SV1257 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1539 ) @ SV1668 ) @ SY4840 )
= ( hAPP @ ( hAPP @ SV857 @ SV1539 ) @ SV1668 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3549]) ).
thf(3944,plain,
! [SV1669: $i,SV1540: $i,SV1258: $i,SV858: $i,SV379: $i] :
( ( ! [SY4841: $i] :
( ( c_Lambda_OdB_OdB__rec @ SV379 @ SV858 @ SV1258 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1540 ) @ SV1669 ) @ SY4841 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV858 @ SV1540 ) @ SV1669 ) @ ( c_Lambda_OdB_OdB__rec @ SV379 @ SV858 @ SV1258 @ SV1540 @ SY4841 ) ) @ ( c_Lambda_OdB_OdB__rec @ SV379 @ SV858 @ SV1258 @ SV1669 @ SY4841 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3550]) ).
thf(3945,plain,
! [SV380: $i,SV1259: $i,SV859: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV859 ) @ SV1259 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV380 ) @ SV859 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV380 ) @ SV1259 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3551]) ).
thf(3946,plain,
! [SV860: $i,SV1260: $i,SV381: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV381 ) @ SV1260 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV381 ) @ SV860 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1260 ) @ SV860 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3552]) ).
thf(3947,plain,
! [SV1264: $i,SV864: $i,SV385: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV385 ) @ SV864 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1264 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV864 @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV385 ) ) @ SV864 ) @ SV1264 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3555]) ).
thf(3948,plain,
! [SV865: $i,SV1265: $i,SV386: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV386 ) @ SV1265 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV386 @ SV865 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1265 @ SV865 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3556]) ).
thf(3949,plain,
! [SV387: $i,SV1266: $i,SV866: $i] :
( ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV866 @ SV1266 @ tc_Lambda_OdB )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV387 @ SV866 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV387 @ SV1266 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3557]) ).
thf(3950,plain,
! [SV1670: $i,SV1543: $i,SV1267: $i,SV867: $i,SV391: $i] :
( ( ( ( c_List_Ofoldl @ SV391 @ ( hAPP @ ( hAPP @ SV391 @ SV867 ) @ SV1267 ) @ SV1543 @ SV1670 @ SV1670 )
= ( hAPP @ ( hAPP @ SV391 @ SV867 ) @ ( c_List_Ofoldl @ SV391 @ SV1267 @ SV1543 @ SV1670 @ SV1670 ) ) )
| ~ ( c_OrderedGroup_Osemigroup__add @ SV391 @ SV1670 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3558]) ).
thf(3951,plain,
! [SV1545: $i,SV1269: $i,SV869: $i,SV393: $i] :
( ( ( ~ ( class_OrderedGroup_Osemigroup__add @ SV393 ) )
= $true )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV393 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV393 ) @ SV869 ) @ SV1269 ) @ SV1545 @ SV393 @ SV393 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV393 ) @ SV869 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV393 ) @ SV1269 @ SV1545 @ SV393 @ SV393 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3560]) ).
thf(3952,plain,
! [SV1671: $i,SV1546: $i,SV1270: $i,SV870: $i,SV394: $i] :
( ( ( ( hAPP @ ( hAPP @ SV394 @ SV870 ) @ ( c_List_Ofoldl @ SV394 @ SV1270 @ SV1546 @ SV1671 @ SV1671 ) )
= ( c_List_Ofoldl @ SV394 @ SV870 @ SV1546 @ SV1671 @ SV1671 ) )
| ~ ( c_OrderedGroup_Omonoid__add @ SV1270 @ SV394 @ SV1671 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3561]) ).
thf(3953,plain,
! [SV1672: $i,SV1547: $i,SV1271: $i,SV871: $i,SV395: $i] :
( ( ! [SY4842: $i] :
( ( c_List_Ofoldl @ SV395 @ SV871 @ ( c_List_Olist_OCons @ SV1271 @ SV1547 @ SV1672 ) @ SY4842 @ SV1672 )
= ( c_List_Ofoldl @ SV395 @ ( hAPP @ ( hAPP @ SV395 @ SV871 ) @ SV1271 ) @ SV1547 @ SY4842 @ SV1672 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3562]) ).
thf(3954,plain,
! [SV1673: $i,SV1548: $i,SV1272: $i,SV872: $i,SV396: $i] :
( ( ! [SY4843: $i] :
( ( c_List_Ofoldl @ SV396 @ SV872 @ ( c_List_Oappend @ SV1272 @ SV1548 @ SV1673 ) @ SY4843 @ SV1673 )
= ( c_List_Ofoldl @ SV396 @ ( c_List_Ofoldl @ SV396 @ SV872 @ SV1272 @ SY4843 @ SV1673 ) @ SV1548 @ SY4843 @ SV1673 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3563]) ).
thf(3955,plain,
! [SV874: $i,SV398: $i] :
( ( ( hBOOL @ ( hAPP @ SV398 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV398 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV398 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV398 @ SV874 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV398 @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV398 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3565]) ).
thf(3956,plain,
! [SV1550: $i,SV1274: $i,SV875: $i,SV399: $i] :
( ( ( c_Type_Otypings @ SV399 @ SV875 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV1274 @ SV399 @ SV1550 @ SV875 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV399 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1550 ) @ SV875 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1274 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3566]) ).
thf(3957,plain,
! [SV876: $i,SV400: $i] :
( ( ( hBOOL @ ( hAPP @ SV400 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV400 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV400 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV400 @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV400 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV400 @ SV876 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3567]) ).
thf(3958,plain,
! [SV1674: $i,SV1551: $i,SV1275: $i,SV877: $i,SV401: $i] :
( ( ! [SY4844: $i,SY4845: $i] :
( ( c_Type_Otypings @ SV401 @ SV877 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV1275 @ SV1551 @ SV401 @ SV877 ) )
| ~ ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1674 ) @ SY4844 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1551 )
| ~ ( c_Type_Otypings @ SV401 @ SY4844 @ SY4845 )
| ~ ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1674 ) @ SY4844 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV877 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3568]) ).
thf(3959,plain,
! [SV1276: $i,SV402: $i,SV878: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV878 ) @ SV402 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV1276 ) )
= $false )
| ( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ SV402 @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV878 @ SV402 @ SV1276 ) @ tc_Lambda_OdB )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3569]) ).
thf(3960,plain,
! [SV403: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV403 ) )
= $false )
| ( ( SV403
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV403 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV403 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV403 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( v_sko__InductTermi__XIT__Xcases__4 @ SV403 ) ) @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV403 ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( v_sko__InductTermi__XIT__Xcases__6 @ SV403 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3570]) ).
thf(3961,plain,
! [SV1552: $i,SV1277: $i,SV879: $i,SV404: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV404 ) @ SV879 ) @ SV1277 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1552 ) @ SV879 ) @ SV1277 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV404 ) @ SV1552 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3571]) ).
thf(3962,plain,
! [SV406: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV406 ) )
= $false )
| ( ( SV406
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( v_sko__InductTermi__XIT__Xcases__2 @ SV406 ) ) @ ( v_sko__InductTermi__XIT__Xcases__1 @ SV406 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__3 @ SV406 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( v_sko__InductTermi__XIT__Xcases__5 @ SV406 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3572]) ).
thf(3963,plain,
! [SV1675: $i,SV1553: $i,SV1279: $i,SV881: $i,SV407: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV407 @ ( c_Lambda_OdB_OdB__case @ SV881 @ SV1279 @ SV1553 @ ( c_Lambda_OdB_OVar @ SV1675 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV407 @ ( hAPP @ SV881 @ SV1675 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3573]) ).
thf(3964,plain,
! [SV1676: $i,SV1554: $i,SV1280: $i,SV882: $i,SV408: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV408 @ ( c_Lambda_OdB_OdB__case @ SV882 @ SV1280 @ SV1554 @ ( c_Lambda_OdB_OVar @ SV1676 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV408 @ ( hAPP @ SV882 @ SV1676 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3574]) ).
thf(3965,plain,
! [SV1677: $i,SV1555: $i,SV1281: $i,SV884: $i,SV410: $i] :
( ( ( c_Lambda_OdB_OdB__rec @ SV410 @ SV884 @ SV1281 @ ( c_Lambda_OdB_OVar @ SV1555 ) @ SV1677 )
= ( hAPP @ SV410 @ SV1555 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3575]) ).
thf(3966,plain,
! [SV1282: $i,SV885: $i,SV411: $i] :
( ( ( c_Type_Otyping @ SV411 @ ( c_Lambda_OdB_OVar @ SV885 ) @ SV1282 )
= $false )
| ( ( ( hAPP @ SV411 @ SV885 )
= SV1282 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3576]) ).
thf(3967,plain,
! [SV1678: $i,SV1556: $i,SV1283: $i,SV886: $i,SV412: $i] :
( ( ( c_Lambda_OdB_OdB__case @ SV412 @ SV886 @ SV1283 @ ( c_Lambda_OdB_OVar @ SV1556 ) @ SV1678 )
= ( hAPP @ SV412 @ SV1556 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3577]) ).
thf(3968,plain,
! [SV417: $i,SV1284: $i,SV890: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV890 ) @ SV1284 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ SV417 ) )
= $false )
| ( ( SV417
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV890 ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ SV890 @ SV1284 @ SV417 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3579]) ).
thf(3969,plain,
! [SV891: $i,SV418: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV418 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV418 )
| ~ ( class_Power_Opower @ SV418 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV418 ) @ SV891 @ SV418 )
= ( c_HOL_Ozero__class_Ozero @ SV418 ) )
| ( SV891
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV418 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3580]) ).
thf(3970,plain,
! [SV892: $i,SV419: $i] :
( ( ( ~ ( class_Power_Opower @ SV419 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV419 ) @ SV892 @ SV419 )
= ( c_HOL_Ozero__class_Ozero @ SV419 ) )
| ( SV892
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV419 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3581]) ).
thf(3971,plain,
! [SV1285: $i,SV893: $i,SV421: $i] :
( ( ( class_OrderedGroup_Omonoid__add @ SV421 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SV893 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ ( c_HOL_Ozero__class_Ozero @ SV421 ) @ SV1285 @ SV421 @ SV421 ) )
= ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV421 ) @ SV893 @ SV1285 @ SV421 @ SV421 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3582]) ).
thf(3972,plain,
! [SV896: $i,SV1286: $i,SV426: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV426 ) @ SV1286 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV426 @ SV896 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1286 @ SV896 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3583]) ).
thf(3973,plain,
! [SV897: $i,SV1287: $i,SV427: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV427 @ SV1287 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV427 ) ) @ SV897 ) @ SV1287 )
= ( c_Lambda_OdB_OVar @ SV427 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3584]) ).
thf(3974,plain,
! [SV898: $i,SV1288: $i,SV428: $i] :
( ( ( SV428 = SV1288 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1288 @ SV428 @ tc_nat )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ SV428 ) ) @ SV898 ) @ SV1288 )
= ( c_Lambda_OdB_OVar @ SV428 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3585]) ).
thf(3975,plain,
! [SV1679: $i,SV1557: $i,SV1289: $i,SV900: $i,SV430: $i] :
( ( ( SV430 = SV900 )
| ~ ( c_Type_Otyping @ SV1289 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1557 ) @ SV1679 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV900 )
| ~ ( c_Type_Otyping @ SV1289 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1557 ) @ SV1679 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV430 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3586]) ).
thf(3976,plain,
! [SV1290: $i,SV433: $i,SV902: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV902 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV433 ) @ SV902 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1290 @ 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 @ SV433 ) ) @ SV902 ) @ SV1290 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3588]) ).
thf(3977,plain,
! [SV1292: $i,SV905: $i,SV436: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV436 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV436 ) @ ( c_Lambda_OdB_OVar @ SV905 ) ) @ SV1292 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3590]) ).
thf(3978,plain,
! [SV909: $i,SV441: $i,SV1293: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ SV1293 ) @ SV441 ) @ SV909 ) )
= $false )
| ( ( SV441 = SV909 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3593]) ).
thf(3979,plain,
! [SV1680: $i,SV1559: $i,SV1294: $i,SV911: $i,SV443: $i] :
( ( ( ( c_List_Olist_OCons @ SV443 @ SV911 @ SV1294 )
!= ( c_List_Olist_OCons @ SV1559 @ SV1680 @ SV1294 ) )
| ( SV443 = SV1559 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3595]) ).
thf(3980,plain,
! [SV1681: $i,SV1560: $i,SV1295: $i,SV912: $i,SV444: $i] :
( ( ~ ( class_OrderedGroup_Oab__group__add @ SV444 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV912 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV1295 ) @ SV1560 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV1295 ) @ SV1681 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV912 ) @ SV1560 )
= SV1681 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3596]) ).
thf(3981,plain,
! [SV1561: $i,SV1297: $i,SV914: $i,SV446: $i] :
( ( ( ~ ( class_Ring__and__Field_Oidom @ SV446 ) )
= $true )
| ( ( ~ ( class_Int_Onumber__ring @ SV446 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV446 ) @ SV914 ) @ SV1297 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV446 ) @ SV914 ) @ SV1561 ) )
| ( SV1297 = SV1561 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3598]) ).
thf(3982,plain,
! [SV1562: $i,SV1298: $i,SV915: $i,SV447: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV447 ) @ SV915 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1298 ) @ SV1562 ) )
= $true )
| ( ( SV447 = SV1298 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3599]) ).
thf(3983,plain,
! [SV1300: $i,SV917: $i,SV449: $i] :
( ( ( class_Orderings_Olinorder @ SV449 )
= $false )
| ( ( ( ( c_Orderings_Oord__class_Omax @ SV917 @ SV1300 @ SV449 )
!= SV1300 )
| ( c_lessequals @ SV917 @ SV1300 @ SV449 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3601]) ).
thf(3984,plain,
! [SV1682: $i,SV1563: $i,SV1301: $i,SV918: $i,SV450: $i] :
( ( ( ( c_List_Oappend @ SV450 @ ( c_List_Olist_OCons @ SV918 @ ( c_List_Olist_ONil @ SV1301 ) @ SV1301 ) @ SV1301 )
!= ( c_List_Oappend @ SV1563 @ ( c_List_Olist_OCons @ SV1682 @ ( c_List_Olist_ONil @ SV1301 ) @ SV1301 ) @ SV1301 ) )
| ( SV450 = SV1563 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3602]) ).
thf(3985,plain,
! [SV919: $i,SV451: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV451 ) @ SV919 ) @ SV919 )
!= ( c_HOL_Ozero__class_Ozero @ SV451 ) )
= $true )
| ( ( SV919
= ( c_HOL_Ozero__class_Ozero @ SV451 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV451 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3603]) ).
thf(3986,plain,
! [SV1302: $i,SV920: $i,SV452: $i] :
( ( ( SV452
= ( c_List_Oappend @ SV920 @ SV452 @ SV1302 ) )
= $false )
| ( ( SV920
= ( c_List_Olist_ONil @ SV1302 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3604]) ).
thf(3987,plain,
! [SV1564: $i,SV1304: $i,SV924: $i,SV456: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV456 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV924 @ SV1304 @ SV456 )
!= ( c_Power_Opower__class_Opower @ SV1564 @ SV1304 @ SV456 ) )
| ( SV924 = SV1564 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1304 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV1564 @ SV456 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV924 @ SV456 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3608]) ).
thf(3988,plain,
! [SV1683: $i,SV1565: $i,SV1305: $i,SV925: $i,SV457: $i] :
( ( ( ( c_List_Oreplicate @ SV457 @ SV925 @ SV1305 )
!= ( c_List_Oreplicate @ SV1565 @ SV1683 @ SV1305 ) )
| ( SV457 = SV1565 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3609]) ).
thf(3989,plain,
! [SV1306: $i,SV926: $i,SV458: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV458 ) @ SV926 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1306 @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV458 ) @ SV926 )
= SV1306 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3610]) ).
thf(3990,plain,
! [SV1307: $i,SV927: $i,SV459: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV459 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV459 ) @ SV927 ) @ SV1307 )
!= ( c_HOL_Ozero__class_Ozero @ SV459 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV459 ) @ SV1307 @ SV459 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV459 ) @ SV927 @ SV459 )
| ( SV1307
= ( c_HOL_Ozero__class_Ozero @ SV459 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3611]) ).
thf(3991,plain,
! [SV1566: $i,SV1308: $i,SV928: $i,SV460: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV460 ) @ SV928 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1308 ) @ SV1566 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV928 = SV1566 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3612]) ).
thf(3992,plain,
! [SV1309: $i,SV930: $i,SV462: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV462 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV930 @ SV1309 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OAbs @ SV462 )
= SV930 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3614]) ).
thf(3993,plain,
! [SV1310: $i,SV931: $i,SV463: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV463 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV931 @ SV1310 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV1310
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3615]) ).
thf(3994,plain,
! [SV1684: $i,SV1567: $i,SV1311: $i,SV932: $i,SV464: $i] :
( ( ( ( c_List_Olist_OCons @ SV464 @ SV932 @ SV1311 )
!= ( c_List_Olist_OCons @ SV1567 @ SV1684 @ SV1311 ) )
| ( SV932 = SV1684 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3616]) ).
thf(3995,plain,
! [SV1685: $i,SV1568: $i,SV1312: $i,SV933: $i,SV465: $i] :
( ( ( ( c_List_Oreplicate @ SV465 @ SV933 @ SV1312 )
!= ( c_List_Oreplicate @ SV1568 @ SV1685 @ SV1312 ) )
| ( SV933 = SV1685 )
| ( SV465
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3617]) ).
thf(3996,plain,
! [SV1314: $i,SV935: $i,SV467: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV467 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV467 )
| ( SV935
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV467 ) @ SV935 ) @ SV1314 ) )
| ( SV1314
= ( c_HOL_Ozero__class_Ozero @ SV467 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3619]) ).
thf(3997,plain,
! [SV1569: $i,SV1315: $i,SV936: $i,SV468: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV468 ) @ SV936 )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1315 ) @ SV1569 ) )
= $true )
| ( ( SV936 = SV1569 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3620]) ).
thf(3998,plain,
! [SV1316: $i,SV937: $i,SV469: $i] :
( ( ( SV469
= ( c_List_Oappend @ SV469 @ SV937 @ SV1316 ) )
= $false )
| ( ( SV937
= ( c_List_Olist_ONil @ SV1316 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3621]) ).
thf(3999,plain,
! [SV1570: $i,SV1317: $i,SV938: $i,SV470: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV470 ) @ SV938 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1317 ) @ SV1570 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3622]) ).
thf(4000,plain,
! [SV1318: $i,SV939: $i,SV471: $i] :
( ( ( class_Ring__and__Field_Ozero__neq__one @ SV471 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV471 )
| ~ ( class_Ring__and__Field_Omult__zero @ SV471 )
| ~ ( class_Power_Opower @ SV471 )
| ( ( c_Power_Opower__class_Opower @ SV939 @ SV1318 @ SV471 )
!= ( c_HOL_Ozero__class_Ozero @ SV471 ) )
| ( SV939
= ( c_HOL_Ozero__class_Ozero @ SV471 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3623]) ).
thf(4001,plain,
! [SV1319: $i,SV940: $i,SV472: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV472 @ SV940 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1319 @ SV940 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV472 = SV1319 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3624]) ).
thf(4002,plain,
! [SV1571: $i,SV1320: $i,SV942: $i,SV474: $i] :
( ( ( ( c_List_Oappend @ SV474 @ SV942 @ SV1320 )
!= ( c_List_Oappend @ SV474 @ SV1571 @ SV1320 ) )
= $true )
| ( ( SV942 = SV1571 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3626]) ).
thf(4003,plain,
! [SV1321: $i,SV943: $i,SV475: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV475 ) @ SV943 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1321 ) @ SV943 ) )
= $false )
| ( ( SV475 = SV1321 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3627]) ).
thf(4004,plain,
! [SV1572: $i,SV1322: $i,SV944: $i,SV476: $i] :
( ( ( ( c_List_Olist_ONil @ SV476 )
!= ( c_List_Omap @ SV944 @ SV1322 @ SV1572 @ SV476 ) )
= $true )
| ( ( SV1322
= ( c_List_Olist_ONil @ SV1572 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3628]) ).
thf(4005,plain,
! [SV1323: $i,SV945: $i,SV477: $i] :
( ( ( class_Nat_Osemiring__char__0 @ SV477 )
= $false )
| ( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV945 @ SV477 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1323 @ SV477 ) )
| ( SV945 = SV1323 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3629]) ).
thf(4006,plain,
! [SV1325: $i,SV947: $i,SV479: $i] :
( ( ( ( c_Lambda_OdB_OAbs @ SV479 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV947 @ SV1325 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV1325
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3631]) ).
thf(4007,plain,
! [SV1326: $i,SV948: $i,SV480: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV480 @ SV948 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV1326 ) )
= $false )
| ( ( SV948
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3632]) ).
thf(4008,plain,
! [SV1327: $i,SV949: $i,SV481: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV481 ) @ SV949 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV481 ) @ SV1327 ) )
= $false )
| ( ( SV949 = SV1327 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3633]) ).
thf(4009,plain,
! [SV1328: $i,SV950: $i,SV483: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV483 @ SV950 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ SV1328 ) )
= $false )
| ( ( SV483
= ( c_Lambda_OdB_OAbs @ SV1328 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3635]) ).
thf(4010,plain,
! [SV1329: $i,SV951: $i,SV484: $i] :
( ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV484 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV951 @ SV1329 @ SV484 )
!= ( c_HOL_Ozero__class_Ozero @ SV484 ) )
| ( SV951
= ( c_HOL_Ozero__class_Ozero @ SV484 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3636]) ).
thf(4011,plain,
! [SV1573: $i,SV1330: $i,SV952: $i,SV485: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV485 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV952 ) @ SV1330 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV1573 ) @ SV1330 ) )
| ( SV952 = SV1573 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3637]) ).
thf(4012,plain,
! [SV954: $i,SV487: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV487 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV487 )
| ~ ( class_Power_Opower @ SV487 )
| ( ( c_Power_Opower__class_Opower @ SV954 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV487 )
!= ( c_HOL_Ozero__class_Ozero @ SV487 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV487 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3638]) ).
thf(4013,plain,
! [SV1331: $i,SV955: $i,SV488: $i] :
( ( ( ( c_List_Olist_ONil @ SV488 )
= ( c_List_Oreplicate @ SV955 @ SV1331 @ SV488 ) )
= $false )
| ( ( SV955
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3639]) ).
thf(4014,plain,
! [SV1332: $i,SV956: $i,SV489: $i] :
( ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV489 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV489 ) @ SV956 ) @ SV1332 )
!= ( c_HOL_Ozero__class_Ozero @ SV489 ) )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV1332 @ SV489 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV956 @ SV489 )
| ( SV956
= ( c_HOL_Ozero__class_Ozero @ SV489 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3640]) ).
thf(4015,plain,
! [SV1333: $i,SV957: $i,SV490: $i] :
( ( ( ( c_List_Oreplicate @ SV490 @ SV957 @ SV1333 )
= ( c_List_Olist_ONil @ SV1333 ) )
= $false )
| ( ( SV490
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3641]) ).
thf(4016,plain,
! [SV1334: $i,SV958: $i,SV491: $i] :
( ( ( ( c_List_Olist_ONil @ SV491 )
= ( c_List_Oappend @ SV958 @ SV1334 @ SV491 ) )
= $false )
| ( ( SV958
= ( c_List_Olist_ONil @ SV491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3642]) ).
thf(4017,plain,
! [SV1574: $i,SV1335: $i,SV959: $i,SV492: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV492 ) @ SV959 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1335 ) @ SV1574 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1335 @ SV959 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV492 @ SV1574 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3643]) ).
thf(4018,plain,
! [SV1575: $i,SV1336: $i,SV960: $i,SV493: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ SV493 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV960 ) @ SV1336 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV960 ) @ SV1575 ) )
| ( SV1336 = SV1575 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3644]) ).
thf(4019,plain,
! [SV1576: $i,SV1337: $i,SV961: $i,SV494: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV494 ) @ SV961 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1337 ) @ SV1576 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV494 = SV1337 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3645]) ).
thf(4020,plain,
! [SV1577: $i,SV1339: $i,SV963: $i,SV496: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__semidom @ SV496 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV963 @ SV1339 @ SV496 )
!= ( c_Power_Opower__class_Opower @ SV963 @ SV1577 @ SV496 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV496 ) @ SV963 @ SV496 )
| ( SV1339 = SV1577 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3647]) ).
thf(4021,plain,
! [SV1578: $i,SV1340: $i,SV964: $i,SV497: $i] :
( ( ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV497 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV964 ) @ SV1340 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV964 ) @ SV1578 ) )
| ( SV1340 = SV1578 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3648]) ).
thf(4022,plain,
! [SV1579: $i,SV1341: $i,SV965: $i,SV498: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV498 ) ) @ SV965 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1341 ) @ SV1579 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3649]) ).
thf(4023,plain,
! [SV1342: $i,SV966: $i,SV499: $i] :
( ( ( ( c_List_Olist_ONil @ SV499 )
= ( c_List_Oappend @ SV966 @ SV1342 @ SV499 ) )
= $false )
| ( ( SV1342
= ( c_List_Olist_ONil @ SV499 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3650]) ).
thf(4024,plain,
! [SV1686: $i,SV1580: $i,SV1344: $i,SV968: $i,SV501: $i] :
( ( ( ( c_List_Oappend @ SV501 @ ( c_List_Olist_OCons @ SV968 @ ( c_List_Olist_ONil @ SV1344 ) @ SV1344 ) @ SV1344 )
!= ( c_List_Oappend @ SV1580 @ ( c_List_Olist_OCons @ SV1686 @ ( c_List_Olist_ONil @ SV1344 ) @ SV1344 ) @ SV1344 ) )
| ( SV968 = SV1686 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3652]) ).
thf(4025,plain,
! [SV1345: $i,SV969: $i,SV502: $i] :
( ( ( ( c_List_Oappend @ SV502 @ SV969 @ SV1345 )
= ( c_List_Olist_ONil @ SV1345 ) )
= $false )
| ( ( SV969
= ( c_List_Olist_ONil @ SV1345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3653]) ).
thf(4026,plain,
! [SV1581: $i,SV1346: $i,SV970: $i,SV503: $i] :
( ( ( ( c_List_Omap @ SV503 @ SV970 @ SV1346 @ SV1581 )
!= ( c_List_Olist_ONil @ SV1581 ) )
= $true )
| ( ( SV970
= ( c_List_Olist_ONil @ SV1346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3654]) ).
thf(4027,plain,
! [SV1582: $i,SV1347: $i,SV971: $i,SV504: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV504 ) @ SV971 )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1347 @ SV1582 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( ( SV504
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1347 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV504 @ SV971 @ SV1347 @ SV1582 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1582
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3655]) ).
thf(4028,plain,
! [SV1583: $i,SV1348: $i,SV972: $i,SV505: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV505 ) @ SV972 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1348 ) @ SV1583 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV972 = SV1583 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3656]) ).
thf(4029,plain,
! [SV1349: $i,SV973: $i,SV506: $i] :
( ( ( ( c_Lambda_OdB_OVar @ SV506 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV973 @ SV1349 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( c_Lambda_OdB_OVar @ SV506 )
= SV973 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3657]) ).
thf(4030,plain,
! [SV1351: $i,SV976: $i,SV510: $i] :
( ( ( ( c_List_Oappend @ SV510 @ SV976 @ SV1351 )
= SV976 )
= $false )
| ( ( SV510
= ( c_List_Olist_ONil @ SV1351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3661]) ).
thf(4031,plain,
! [SV1352: $i,SV978: $i,SV512: $i] :
( ( ( ( c_List_Oappend @ SV512 @ SV978 @ SV1352 )
= ( c_List_Olist_ONil @ SV1352 ) )
= $false )
| ( ( SV512
= ( c_List_Olist_ONil @ SV1352 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3662]) ).
thf(4032,plain,
! [SV1353: $i,SV979: $i,SV513: $i] :
( ( ( ( c_List_Oappend @ SV513 @ SV979 @ SV1353 )
= SV513 )
= $false )
| ( ( SV979
= ( c_List_Olist_ONil @ SV1353 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3663]) ).
thf(4033,plain,
! [SV1584: $i,SV1354: $i,SV980: $i,SV514: $i] :
( ( ( ( c_List_Oappend @ SV514 @ SV980 @ SV1354 )
!= ( c_List_Oappend @ SV1584 @ SV980 @ SV1354 ) )
= $true )
| ( ( SV514 = SV1584 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3664]) ).
thf(4034,plain,
! [SV1355: $i,SV981: $i,SV515: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV515 ) @ SV981 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV515 ) @ SV1355 ) )
= $false )
| ( ( SV981 = SV1355 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3665]) ).
thf(4035,plain,
! [SV1585: $i,SV1356: $i,SV982: $i,SV516: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV516 ) @ SV982 @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1356 ) @ SV1585 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV516 = SV1356 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3666]) ).
thf(4036,plain,
! [SV1358: $i,SV984: $i,SV520: $i,SV3: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV3 )
= $false )
| ( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV520 @ SV984 @ SV3 ) @ ( c_Power_Opower__class_Opower @ SV1358 @ SV984 @ SV3 ) @ SV3 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV520 @ SV3 )
| ~ ( c_lessequals @ SV520 @ SV1358 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3668]) ).
thf(4037,plain,
! [SV985: $i,SV521: $i,SV4: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV4 ) @ ( c_Power_Opower__class_Opower @ SV521 @ SV985 @ SV4 ) @ SV4 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV4 ) @ SV521 @ SV4 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3669]) ).
thf(4038,plain,
! [SV1687: $i,SV1586: $i,SV1359: $i,SV986: $i,SV524: $i,SV7: $i] :
( ( ~ ( c_Type_Otyping @ SV7 @ SV524 @ SV986 )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV7 @ SV1359 @ SV986 @ tc_Type_Otype ) @ SV1586 @ SV1687 )
| ( c_Type_Otyping @ SV7 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1586 ) @ SV524 ) @ SV1359 ) @ SV1687 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3670]) ).
thf(4039,plain,
! [SV1587: $i,SV1360: $i,SV987: $i,SV525: $i,SV8: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV8 @ SV525 @ SV987 @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1360 ) @ SV525 ) @ SV1587 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV8 @ SV1360 @ SV1587 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3671]) ).
thf(4040,plain,
! [SV1361: $i,SV988: $i,SV526: $i,SV9: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV9 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV526 @ SV988 @ SV9 ) @ ( c_Power_Opower__class_Opower @ SV526 @ SV1361 @ SV9 ) @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV526 @ ( c_HOL_Oone__class_Oone @ SV9 ) @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV526 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV1361 @ SV988 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3672]) ).
thf(4041,plain,
! [SV989: $i,SV527: $i,SV10: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV10 ) @ ( c_Power_Opower__class_Opower @ SV527 @ SV989 @ SV10 ) @ SV10 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV989 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV10 ) @ SV527 @ SV10 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3673]) ).
thf(4042,plain,
! [SV528: $i,SV11: $i,SV1362: $i,SV990: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV990 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1362 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV11 ) @ SV528 ) @ SV990 ) ) @ SV1362 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV11 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1362 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV528 ) @ SV1362 ) ) @ SV990 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3674]) ).
thf(4043,plain,
! [SV529: $i,SV12: $i,SV991: $i,SV1363: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1363 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV991 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) @ tc_nat )
= $false )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_Olift @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV12 ) @ SV529 ) @ SV991 ) ) @ SV1363 )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV12 ) @ SV1363 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV529 ) @ SV1363 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV991 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3675]) ).
thf(4044,plain,
! [SV1588: $i,SV1364: $i,SV992: $i,SV532: $i,SV15: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV15 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SV532 ) @ SV992 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SV1364 ) @ SV1588 ) @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV992 @ SV1588 @ SV15 )
| ~ ( c_lessequals @ SV532 @ SV1364 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3676]) ).
thf(4045,plain,
! [SV1589: $i,SV1365: $i,SV993: $i,SV533: $i,SV16: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV16 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SV533 ) @ SV993 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SV1365 ) @ SV1589 ) @ SV16 )
| ~ ( c_lessequals @ SV993 @ SV1589 @ SV16 )
| ~ ( c_HOL_Oord__class_Oless @ SV533 @ SV1365 @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3677]) ).
thf(4046,plain,
! [SV994: $i,SV534: $i,SV17: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV17 ) @ SV534 ) @ SV994 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
= $true )
| ( ( ~ ( c_lessequals @ SV994 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
| ~ ( c_lessequals @ SV534 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3678]) ).
thf(4047,plain,
! [SV535: $i,SV18: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV18 ) @ SV535 ) @ SV535 ) @ ( c_HOL_Ozero__class_Ozero @ SV18 ) @ SV18 )
= $false )
| ( ( c_lessequals @ SV535 @ ( c_HOL_Ozero__class_Ozero @ SV18 ) @ SV18 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3679]) ).
thf(4048,plain,
! [SV19: $i,SV536: $i] :
( ( ( c_lessequals @ SV536 @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV19 ) @ SV536 ) @ SV536 ) @ ( c_HOL_Ozero__class_Ozero @ SV19 ) @ SV19 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3680]) ).
thf(4049,plain,
! [SV1366: $i,SV995: $i,SV537: $i,SV20: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV20 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV20 )
| ( c_lessequals @ SV537 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV20 ) @ SV995 ) @ SV1366 ) @ SV20 )
| ~ ( c_lessequals @ SV537 @ SV995 @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV1366 @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3681]) ).
thf(4050,plain,
! [SV1367: $i,SV996: $i,SV538: $i,SV21: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV21 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV21 )
| ( c_lessequals @ SV538 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SV996 ) @ SV1367 ) @ SV21 )
| ~ ( c_lessequals @ SV538 @ SV1367 @ SV21 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ SV996 @ SV21 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3682]) ).
thf(4051,plain,
! [SV539: $i,SV22: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV22 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV22 ) @ SV539 ) @ SV539 ) @ SV22 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV22 ) @ SV539 @ SV22 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3683]) ).
thf(4052,plain,
! [SV540: $i,SV23: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV23 ) @ SV540 @ SV23 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV23 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV23 ) @ SV540 ) @ SV540 ) @ SV23 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3684]) ).
thf(4053,plain,
! [SV24: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ SV24 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) )
= ( c_HOL_Ozero__class_Ozero @ SV24 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ SV24 )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3685]) ).
thf(4054,plain,
! [SV997: $i,SV541: $i,SV25: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SV541 ) @ SV997 ) @ SV25 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV997 @ SV25 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV541 @ SV25 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3686]) ).
thf(4055,plain,
! [SV28: $i,SV998: $i,SV542: $i] :
( ( ( c_lessequals @ SV542 @ SV998 @ SV28 )
= $true )
| ( ( c_lessequals @ SV998 @ SV542 @ SV28 )
= $true )
| ( ( class_Orderings_Olinorder @ SV28 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3687]) ).
thf(4056,plain,
! [SV29: $i,SV999: $i,SV543: $i] :
( ( ( SV543 = SV999 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV543 @ SV999 @ SV29 )
| ~ ( c_lessequals @ SV543 @ SV999 @ SV29 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3688]) ).
thf(4057,plain,
! [SV30: $i,SV1000: $i,SV544: $i] :
( ( ( SV544 = SV1000 )
= $true )
| ( ( ~ ( c_lessequals @ SV544 @ SV1000 @ SV30 )
| ( c_HOL_Oord__class_Oless @ SV544 @ SV1000 @ SV30 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3689]) ).
thf(4058,plain,
! [SV31: $i,SV1001: $i,SV545: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV545 @ SV1001 @ SV31 )
= $true )
| ( ( ~ ( c_lessequals @ SV545 @ SV1001 @ SV31 )
| ( SV545 = SV1001 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3690]) ).
thf(4059,plain,
! [SV32: $i,SV1002: $i,SV546: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV546 @ SV1002 @ SV32 )
= $true )
| ( ( ( SV546 = SV1002 )
| ~ ( c_lessequals @ SV546 @ SV1002 @ SV32 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3691]) ).
thf(4060,plain,
! [SV33: $i,SV1003: $i,SV547: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV547 @ SV1003 @ SV33 )
= $true )
| ( ( ( SV547 = SV1003 )
| ~ ( c_lessequals @ SV547 @ SV1003 @ SV33 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3692]) ).
thf(4061,plain,
! [SV34: $i,SV1004: $i,SV548: $i] :
( ( ( SV548 = SV1004 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV548 @ SV1004 @ SV34 )
| ~ ( c_lessequals @ SV548 @ SV1004 @ SV34 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3693]) ).
thf(4062,plain,
! [SV35: $i,SV1005: $i,SV549: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV549 @ SV1005 @ SV35 )
= $true )
| ( ( ~ ( c_lessequals @ SV549 @ SV1005 @ SV35 )
| ( SV1005 = SV549 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3694]) ).
thf(4063,plain,
! [SV36: $i,SV1006: $i,SV550: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV550 @ SV1006 @ SV36 )
= $true )
| ( ( ( SV1006 = SV550 )
| ~ ( c_lessequals @ SV550 @ SV1006 @ SV36 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3695]) ).
thf(4064,plain,
! [SV1590: $i,SV1368: $i,SV1007: $i,SV551: $i,SV37: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ SV37 ) )
= $true )
| ( ( ( c_lessequals @ SV551 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV1007 ) @ SV1368 ) @ SV37 )
| ~ ( c_lessequals @ SV1590 @ SV1368 @ SV37 )
| ~ ( c_lessequals @ SV551 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV1007 ) @ SV1590 ) @ SV37 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3696]) ).
thf(4065,plain,
! [SV1369: $i,SV1008: $i,SV552: $i,SV38: $i] :
( ( ( class_Orderings_Opreorder @ SV38 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV552 @ SV1008 @ SV38 )
| ~ ( c_lessequals @ SV1369 @ SV1008 @ SV38 )
| ~ ( c_HOL_Oord__class_Oless @ SV552 @ SV1369 @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3697]) ).
thf(4066,plain,
! [SV1370: $i,SV1009: $i,SV553: $i,SV39: $i] :
( ( ( class_Orderings_Opreorder @ SV39 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV553 @ SV1009 @ SV39 )
| ~ ( c_HOL_Oord__class_Oless @ SV1370 @ SV1009 @ SV39 )
| ~ ( c_lessequals @ SV553 @ SV1370 @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3698]) ).
thf(4067,plain,
! [SV1371: $i,SV1010: $i,SV556: $i,SV42: $i] :
( ( ( class_Orderings_Opreorder @ SV42 )
= $false )
| ( ( ( c_lessequals @ SV556 @ SV1010 @ SV42 )
| ~ ( c_lessequals @ SV1371 @ SV1010 @ SV42 )
| ~ ( c_lessequals @ SV556 @ SV1371 @ SV42 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3699]) ).
thf(4068,plain,
! [SV1372: $i,SV1011: $i,SV557: $i,SV43: $i] :
( ( ( class_Orderings_Oorder @ SV43 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV557 @ SV1011 @ SV43 )
| ~ ( c_HOL_Oord__class_Oless @ SV557 @ SV1372 @ SV43 )
| ~ ( c_lessequals @ SV1372 @ SV1011 @ SV43 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3700]) ).
thf(4069,plain,
! [SV1373: $i,SV1012: $i,SV558: $i,SV44: $i] :
( ( ( class_Orderings_Oorder @ SV44 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV558 @ SV1012 @ SV44 )
| ~ ( c_lessequals @ SV558 @ SV1373 @ SV44 )
| ~ ( c_HOL_Oord__class_Oless @ SV1373 @ SV1012 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3701]) ).
thf(4070,plain,
! [SV1374: $i,SV1013: $i,SV559: $i,SV45: $i] :
( ( ( class_Orderings_Oorder @ SV45 )
= $false )
| ( ( ( c_lessequals @ SV559 @ SV1013 @ SV45 )
| ~ ( c_lessequals @ SV559 @ SV1374 @ SV45 )
| ~ ( c_lessequals @ SV1374 @ SV1013 @ SV45 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3702]) ).
thf(4071,plain,
! [SV1591: $i,SV1375: $i,SV1014: $i,SV560: $i,SV46: $i] :
( ( ( ( hAPP @ ( c_Type_Oshift @ SV46 @ SV560 @ SV1014 @ SV1375 ) @ SV1591 )
= ( hAPP @ SV46 @ SV1591 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1591 @ SV560 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3703]) ).
thf(4072,plain,
! [SV1376: $i,SV1015: $i,SV561: $i,SV47: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV47 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ SV561 ) @ SV1015 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ SV561 ) @ SV1376 ) @ SV47 )
| ~ ( c_lessequals @ SV1015 @ SV1376 @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3704]) ).
thf(4073,plain,
! [SV1377: $i,SV1016: $i,SV562: $i,SV48: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV48 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV48 ) @ SV562 ) @ SV1016 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV48 ) @ SV1377 ) @ SV1016 ) @ SV48 )
| ~ ( c_lessequals @ SV562 @ SV1377 @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3705]) ).
thf(4074,plain,
! [SV1378: $i,SV1017: $i,SV563: $i,SV49: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV49 )
= $false )
| ( ( ( c_lessequals @ SV563 @ SV1017 @ SV49 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SV1378 ) @ SV563 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SV1378 ) @ SV1017 ) @ SV49 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3706]) ).
thf(4075,plain,
! [SV1379: $i,SV1018: $i,SV564: $i,SV50: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV564 ) @ SV1018 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV564 ) @ SV1379 ) @ SV50 )
| ~ ( c_lessequals @ SV1018 @ SV1379 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3707]) ).
thf(4076,plain,
! [SV1380: $i,SV1019: $i,SV565: $i,SV51: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV51 )
= $false )
| ( ( ( c_lessequals @ SV565 @ SV1019 @ SV51 )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV51 ) @ SV565 ) @ SV1380 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV51 ) @ SV1019 ) @ SV1380 ) @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3708]) ).
thf(4077,plain,
! [SV1381: $i,SV1020: $i,SV566: $i,SV52: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV52 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV566 ) @ SV1020 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV1381 ) @ SV1020 ) @ SV52 )
| ~ ( c_lessequals @ SV566 @ SV1381 @ SV52 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3709]) ).
thf(4078,plain,
! [SV53: $i,SV1021: $i,SV567: $i] :
( ( ( c_lessequals @ SV567 @ SV1021 @ SV53 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV567 @ SV1021 @ SV53 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV53 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3710]) ).
thf(4079,plain,
! [SV54: $i,SV1022: $i,SV568: $i] :
( ( ( c_lessequals @ SV568 @ SV1022 @ SV54 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV568 @ SV1022 @ SV54 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3711]) ).
thf(4080,plain,
! [SV55: $i,SV1023: $i,SV569: $i] :
( ( ( SV569 = SV1023 )
= $true )
| ( ( ~ ( c_lessequals @ SV569 @ SV1023 @ SV55 )
| ~ ( c_lessequals @ SV1023 @ SV569 @ SV55 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3712]) ).
thf(4081,plain,
! [SV56: $i,SV1024: $i,SV570: $i] :
( ( ( SV570 = SV1024 )
= $true )
| ( ( ~ ( c_lessequals @ SV1024 @ SV570 @ SV56 )
| ~ ( c_lessequals @ SV570 @ SV1024 @ SV56 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3713]) ).
thf(4082,plain,
! [SV57: $i,SV1025: $i,SV571: $i] :
( ( ( SV571 = SV1025 )
= $true )
| ( ( ~ ( c_lessequals @ SV1025 @ SV571 @ SV57 )
| ~ ( c_lessequals @ SV571 @ SV1025 @ SV57 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3714]) ).
thf(4083,plain,
! [SV1688: $i,SV1592: $i,SV1382: $i,SV1026: $i,SV572: $i,SV58: $i] :
( ( ! [SY4846: $i] :
( ( ( hAPP @ ( hAPP @ SV58 @ SV572 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= SV572 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1026 @ SV1382 @ SV58 @ SV1592 @ SV1688 @ SY4846 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3715]) ).
thf(4084,plain,
! [SV60: $i,SV1027: $i,SV573: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV573 @ SV1027 @ SV60 )
= $true )
| ( ( ( c_lessequals @ SV1027 @ SV573 @ SV60 )
| ~ ( c_lessequals @ SV573 @ SV1027 @ SV60 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3716]) ).
thf(4085,plain,
! [SV1384: $i,SV1029: $i,SV575: $i,SV63: $i] :
( ( ( class_Orderings_Olinorder @ SV63 )
= $false )
| ( ( ( c_lessequals @ SV575 @ SV1029 @ SV63 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV575 @ SV1384 @ SV63 ) @ SV1029 @ SV63 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3717]) ).
thf(4086,plain,
! [SV1385: $i,SV1030: $i,SV576: $i,SV64: $i] :
( ( ( class_Orderings_Olinorder @ SV64 )
= $false )
| ( ( ( c_lessequals @ SV576 @ SV1030 @ SV64 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1385 @ SV576 @ SV64 ) @ SV1030 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3718]) ).
thf(4087,plain,
! [SV1386: $i,SV1031: $i,SV577: $i,SV65: $i] :
( ( ( class_Orderings_Olinorder @ SV65 )
= $false )
| ( ( ( c_lessequals @ SV577 @ ( c_Orderings_Oord__class_Omax @ SV1031 @ SV1386 @ SV65 ) @ SV65 )
| ~ ( c_lessequals @ SV577 @ SV1031 @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3719]) ).
thf(4088,plain,
! [SV1387: $i,SV1032: $i,SV578: $i,SV66: $i] :
( ( ( class_Orderings_Olinorder @ SV66 )
= $false )
| ( ( ( c_lessequals @ SV578 @ ( c_Orderings_Oord__class_Omax @ SV1032 @ SV1387 @ SV66 ) @ SV66 )
| ~ ( c_lessequals @ SV578 @ SV1387 @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3720]) ).
thf(4089,plain,
! [SV1388: $i,SV1033: $i,SV579: $i,SV67: $i] :
( ( ( class_Orderings_Olinorder @ SV67 )
= $false )
| ( ( ( c_lessequals @ SV579 @ ( c_Orderings_Oord__class_Omax @ SV1033 @ SV1388 @ SV67 ) @ SV67 )
| ~ ( c_lessequals @ SV579 @ SV1033 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3721]) ).
thf(4090,plain,
! [SV1389: $i,SV1034: $i,SV580: $i,SV68: $i] :
( ( ( class_Orderings_Olinorder @ SV68 )
= $false )
| ( ( ( c_lessequals @ SV580 @ ( c_Orderings_Oord__class_Omax @ SV1034 @ SV1389 @ SV68 ) @ SV68 )
| ~ ( c_lessequals @ SV580 @ SV1389 @ SV68 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3722]) ).
thf(4091,plain,
! [SV1390: $i,SV1035: $i,SV581: $i,SV69: $i] :
( ( ( class_Orderings_Olinorder @ SV69 )
= $false )
| ( ( ( c_lessequals @ SV581 @ SV1035 @ SV69 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV581 @ SV1390 @ SV69 ) @ SV1035 @ SV69 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3723]) ).
thf(4092,plain,
! [SV1391: $i,SV1036: $i,SV582: $i,SV70: $i] :
( ( ( class_Orderings_Olinorder @ SV70 )
= $false )
| ( ( ( c_lessequals @ SV582 @ SV1036 @ SV70 )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1391 @ SV582 @ SV70 ) @ SV1036 @ SV70 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3724]) ).
thf(4093,plain,
! [SV1392: $i,SV1037: $i,SV585: $i,SV73: $i] :
( ( ( class_Orderings_Olinorder @ SV73 )
= $false )
| ( ( ( c_lessequals @ SV585 @ SV1037 @ SV73 )
| ( c_lessequals @ SV585 @ SV1392 @ SV73 )
| ~ ( c_lessequals @ SV585 @ ( c_Orderings_Oord__class_Omax @ SV1392 @ SV1037 @ SV73 ) @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3725]) ).
thf(4094,plain,
! [SV1393: $i,SV1040: $i,SV588: $i,SV76: $i] :
( ( ( class_Orderings_Olinorder @ SV76 )
= $false )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV588 @ SV1040 @ SV76 ) @ SV1393 @ SV76 )
| ~ ( c_lessequals @ SV1040 @ SV1393 @ SV76 )
| ~ ( c_lessequals @ SV588 @ SV1393 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3728]) ).
thf(4095,plain,
! [SV1394: $i,SV1041: $i,SV589: $i,SV77: $i] :
( ( ( class_Orderings_Olinorder @ SV77 )
= $false )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV589 @ SV1041 @ SV77 ) @ SV1394 @ SV77 )
| ~ ( c_lessequals @ SV1041 @ SV1394 @ SV77 )
| ~ ( c_lessequals @ SV589 @ SV1394 @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3729]) ).
thf(4096,plain,
! [SV1395: $i,SV1042: $i,SV590: $i,SV78: $i] :
( ( ( class_Orderings_Olinorder @ SV78 )
= $false )
| ( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV590 @ SV1042 @ SV78 ) @ SV1395 @ SV78 )
| ~ ( c_lessequals @ SV1042 @ SV1395 @ SV78 )
| ~ ( c_lessequals @ SV590 @ SV1395 @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3730]) ).
thf(4097,plain,
! [SV1043: $i,SV591: $i,SV79: $i] :
( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV79 ) @ ( c_Power_Opower__class_Opower @ SV591 @ SV1043 @ SV79 ) @ SV79 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV79 ) @ SV591 @ SV79 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3731]) ).
thf(4098,plain,
! [SV1593: $i,SV1396: $i,SV1044: $i,SV592: $i,SV80: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV80 ) )
= $true )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SV592 ) @ SV1044 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SV1396 ) @ SV1593 ) @ SV80 )
| ~ ( c_lessequals @ SV1044 @ SV1593 @ SV80 )
| ~ ( c_lessequals @ SV592 @ SV1396 @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3732]) ).
thf(4099,plain,
! [SV81: $i,SV1045: $i,SV593: $i] :
( ( ( ( c_Orderings_Oord__class_Omax @ SV593 @ SV1045 @ SV81 )
= SV1045 )
= $true )
| ( ( ~ ( c_lessequals @ SV593 @ SV1045 @ SV81 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3733]) ).
thf(4100,plain,
! [SV82: $i,SV1046: $i,SV594: $i] :
( ( ( ( c_Orderings_Oord__class_Omax @ SV594 @ SV1046 @ SV82 )
= SV594 )
= $true )
| ( ( ~ ( c_lessequals @ SV1046 @ SV594 @ SV82 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV82 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3734]) ).
thf(4101,plain,
! [SV84: $i,SV1047: $i,SV596: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV596 @ SV1047 @ SV84 )
= $true )
| ( ( c_lessequals @ SV1047 @ SV596 @ SV84 )
= $true )
| ( ( class_Orderings_Olinorder @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3735]) ).
thf(4102,plain,
! [SV85: $i,SV597: $i] :
( ( ( c_lessequals @ SV597 @ SV597 @ SV85 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV597 @ SV597 @ SV85 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3736]) ).
thf(4103,plain,
! [SV87: $i,SV1048: $i,SV599: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV599 @ SV1048 @ SV87 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1048 @ SV599 @ SV87 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3738]) ).
thf(4104,plain,
! [SV88: $i,SV1049: $i,SV600: $i] :
( ( ( c_lessequals @ SV600 @ SV1049 @ SV88 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1049 @ SV600 @ SV88 )
= $true )
| ( ( class_Orderings_Olinorder @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3739]) ).
thf(4105,plain,
! [SV89: $i,SV1050: $i,SV601: $i] :
( ( ( ~ ( c_lessequals @ SV601 @ SV1050 @ SV89 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1050 @ SV601 @ SV89 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3740]) ).
thf(4106,plain,
! [SV90: $i,SV1051: $i,SV602: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV602 @ SV1051 @ SV90 )
= $true )
| ( ( c_lessequals @ SV1051 @ SV602 @ SV90 )
= $true )
| ( ( class_Orderings_Olinorder @ SV90 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3741]) ).
thf(4107,plain,
! [SV91: $i,SV1052: $i,SV603: $i] :
( ( ( ~ ( c_lessequals @ SV603 @ SV1052 @ SV91 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1052 @ SV603 @ SV91 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV91 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3742]) ).
thf(4108,plain,
! [SV1053: $i,SV604: $i,SV93: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV604 ) @ SV1053 ) @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 )
= $true )
| ( ( ~ ( c_lessequals @ SV1053 @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 )
| ~ ( c_HOL_Oord__class_Oless @ SV604 @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3743]) ).
thf(4109,plain,
! [SV1054: $i,SV605: $i,SV94: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV605 ) @ SV1054 ) @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1054 @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 )
| ~ ( c_lessequals @ SV605 @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3744]) ).
thf(4110,plain,
! [SV1397: $i,SV1055: $i,SV606: $i,SV95: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV95 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV95 )
| ( c_HOL_Oord__class_Oless @ SV606 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV1055 ) @ SV1397 ) @ SV95 )
| ~ ( c_lessequals @ SV606 @ SV1397 @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV1055 @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3745]) ).
thf(4111,plain,
! [SV1398: $i,SV1056: $i,SV607: $i,SV96: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
= $false )
| ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV96 )
| ( c_HOL_Oord__class_Oless @ SV607 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SV1056 ) @ SV1398 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ SV607 @ SV1398 @ SV96 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV1056 @ SV96 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3746]) ).
thf(4112,plain,
! [SV1057: $i,SV608: $i,SV97: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV608 ) @ SV1057 ) @ SV97 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV1057 @ SV97 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV608 @ SV97 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3747]) ).
thf(4113,plain,
! [SV1058: $i,SV609: $i,SV98: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV98 ) @ SV609 ) @ SV1058 ) @ SV98 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ SV1058 @ SV98 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ SV609 @ SV98 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3748]) ).
thf(4114,plain,
! [SV1399: $i,SV1059: $i,SV610: $i,SV100: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV100 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV610 @ SV1059 @ SV100 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV100 ) @ SV1059 @ SV100 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV610 @ SV1399 @ SV100 ) @ ( c_Power_Opower__class_Opower @ SV1059 @ SV1399 @ SV100 ) @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3749]) ).
thf(4115,plain,
! [SV1400: $i,SV1060: $i,SV611: $i,SV102: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV102 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV611 @ SV1060 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1400 @ SV611 @ SV102 ) @ ( c_Power_Opower__class_Opower @ SV1400 @ SV1060 @ SV102 ) @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV102 ) @ SV1400 @ SV102 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3751]) ).
thf(4116,plain,
! [SV1401: $i,SV1061: $i,SV612: $i,SV103: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV103 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV612 @ SV1061 @ SV103 ) @ ( c_Power_Opower__class_Opower @ SV612 @ SV1401 @ SV103 ) @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV103 ) @ SV612 @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ SV1061 @ SV1401 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3752]) ).
thf(4117,plain,
! [SV1402: $i,SV1062: $i,SV613: $i,SV104: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV104 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV613 @ SV1062 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1402 @ SV613 @ SV104 ) @ ( c_Power_Opower__class_Opower @ SV1402 @ SV1062 @ SV104 ) @ SV104 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV104 ) @ SV1402 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3753]) ).
thf(4118,plain,
! [SV1403: $i,SV1063: $i,SV614: $i,SV105: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV105 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV614 @ SV1063 @ SV105 ) @ ( c_Power_Opower__class_Opower @ SV614 @ SV1403 @ SV105 ) @ SV105 )
| ~ ( c_HOL_Oord__class_Oless @ SV1063 @ SV1403 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV105 ) @ SV614 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3754]) ).
thf(4119,plain,
! [SV1404: $i,SV1066: $i,SV618: $i,SV109: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV109 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV618 @ SV1066 @ SV109 ) @ ( c_Power_Opower__class_Opower @ SV1404 @ SV1066 @ SV109 ) @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1066 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV618 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SV618 @ SV1404 @ SV109 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3755]) ).
thf(4120,plain,
! [SV1594: $i,SV1405: $i,SV1068: $i,SV620: $i,SV111: $i] :
( ( ( c_Type_Otypings @ ( c_Type_Oshift @ SV111 @ SV620 @ SV1068 @ tc_Type_Otype ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ SV620 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1405 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1594 )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV111 @ SV1405 @ SV1594 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3756]) ).
thf(4121,plain,
! [SV1689: $i,SV1595: $i,SV1406: $i,SV1069: $i,SV621: $i,SV112: $i] :
( ( ( c_Type_Otypings @ SV112 @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SV621 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV1069 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1406 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1595 )
| ~ ( c_Type_Otypings @ ( c_Type_Oshift @ SV112 @ SV1069 @ SV1689 @ tc_Type_Otype ) @ SV1406 @ SV1595 )
| ~ ( c_Type_Otyping @ SV112 @ SV621 @ SV1689 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3757]) ).
thf(4122,plain,
! [SV622: $i,SV113: $i] :
( ( ( hBOOL @ ( hAPP @ SV113 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1 @ SV113 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2 @ SV113 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV113 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3 @ SV113 ) ) @ ( c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4 @ SV113 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV113 @ SV622 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3758]) ).
thf(4123,plain,
! [SV623: $i,SV114: $i] :
( ( ( hBOOL @ ( hAPP @ SV114 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ ( c_ListApplication_Osko__ListApplication__Xlem__1__1 @ SV114 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__2 @ SV114 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV114 @ SV623 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV114 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ ( c_ListApplication_Osko__ListApplication__Xlem__1__3 @ SV114 ) ) @ ( c_ListApplication_Osko__ListApplication__Xlem__1__4 @ SV114 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3759]) ).
thf(4124,plain,
! [SV1077: $i,SV631: $i,SV123: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV123 ) @ SV631 ) @ SV1077 ) @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1077 @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 )
| ~ ( c_HOL_Oord__class_Oless @ SV631 @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3766]) ).
thf(4125,plain,
! [SV1412: $i,SV1078: $i,SV632: $i,SV125: $i] :
( ( ( class_Orderings_Olinorder @ SV125 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV632 @ SV1078 @ SV125 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV1412 @ SV632 @ SV125 ) @ SV1078 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3767]) ).
thf(4126,plain,
! [SV1413: $i,SV1079: $i,SV633: $i,SV126: $i] :
( ( ( class_Orderings_Olinorder @ SV126 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV633 @ SV1079 @ SV126 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV633 @ SV1413 @ SV126 ) @ SV1079 @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3768]) ).
thf(4127,plain,
! [SV1414: $i,SV1080: $i,SV634: $i,SV127: $i] :
( ( ( class_Orderings_Olinorder @ SV127 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV634 @ ( c_Orderings_Oord__class_Omax @ SV1080 @ SV1414 @ SV127 ) @ SV127 )
| ~ ( c_HOL_Oord__class_Oless @ SV634 @ SV1414 @ SV127 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3769]) ).
thf(4128,plain,
! [SV1415: $i,SV1081: $i,SV635: $i,SV128: $i] :
( ( ( class_Orderings_Olinorder @ SV128 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV635 @ ( c_Orderings_Oord__class_Omax @ SV1081 @ SV1415 @ SV128 ) @ SV128 )
| ~ ( c_HOL_Oord__class_Oless @ SV635 @ SV1081 @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3770]) ).
thf(4129,plain,
! [SV1416: $i,SV1082: $i,SV636: $i,SV129: $i] :
( ( ( class_Orderings_Olinorder @ SV129 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV636 @ ( c_Orderings_Oord__class_Omax @ SV1082 @ SV1416 @ SV129 ) @ SV129 )
| ~ ( c_HOL_Oord__class_Oless @ SV636 @ SV1416 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3771]) ).
thf(4130,plain,
! [SV1417: $i,SV1083: $i,SV637: $i,SV130: $i] :
( ( ( class_Orderings_Olinorder @ SV130 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV637 @ ( c_Orderings_Oord__class_Omax @ SV1083 @ SV1417 @ SV130 ) @ SV130 )
| ~ ( c_HOL_Oord__class_Oless @ SV637 @ SV1083 @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3772]) ).
thf(4131,plain,
! [SV1690: $i,SV1599: $i,SV1418: $i,SV1084: $i,SV638: $i,SV131: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV638 ) @ SV1084 ) )
| ( c_ListOrder_Ostep1 @ SV131 @ SV1418 @ SV1599 @ SV1690 )
| ~ ( c_ListOrder_Ostep1 @ SV131 @ ( c_List_Oappend @ SV1418 @ ( c_List_Olist_OCons @ SV638 @ ( c_List_Olist_ONil @ SV1690 ) @ SV1690 ) @ SV1690 ) @ ( c_List_Oappend @ SV1599 @ ( c_List_Olist_OCons @ SV1084 @ ( c_List_Olist_ONil @ SV1690 ) @ SV1690 ) @ SV1690 ) @ SV1690 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3773]) ).
thf(4132,plain,
! [SV1085: $i,SV1419: $i,SV639: $i,SV132: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV132 @ SV639 ) @ SV1419 ) @ SV1085 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV132 @ SV639 @ SV639 ) @ SV639 ) @ SV1085 ) @ SV1419 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3774]) ).
thf(4133,plain,
! [SV1086: $i,SV1420: $i,SV640: $i,SV133: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ SV133 @ SV640 @ SV640 ) @ SV640 ) @ SV1420 ) @ SV1086 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV133 @ SV640 ) @ SV1086 ) @ SV1420 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3775]) ).
thf(4134,plain,
! [SV1691: $i,SV1600: $i,SV1422: $i,SV1089: $i,SV643: $i,SV136: $i] :
( ( ( hAPP @ ( c_COMBC @ SV136 @ SV643 @ SV1089 @ SV1422 @ SV1600 ) @ SV1691 )
= ( hAPP @ ( hAPP @ SV136 @ SV1691 ) @ SV643 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3776]) ).
thf(4135,plain,
! [SV1601: $i,SV1423: $i,SV1090: $i,SV644: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV644 ) @ SV1090 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV137 @ SV1423 @ SV1601 ) @ SV1090 ) @ SV644 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3777]) ).
thf(4136,plain,
! [SV1602: $i,SV1424: $i,SV1091: $i,SV645: $i,SV138: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV138 @ SV645 @ SV1091 ) @ SV1424 ) @ SV1602 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV138 @ SV1602 ) @ SV1424 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3778]) ).
thf(4137,plain,
! [SV1603: $i,SV1425: $i,SV1092: $i,SV646: $i,SV139: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV139 @ SV646 ) @ SV1092 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV139 @ SV1425 @ SV1603 ) @ SV1092 ) @ SV646 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3779]) ).
thf(4138,plain,
! [SV1604: $i,SV1426: $i,SV1093: $i,SV647: $i,SV140: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV140 @ SV647 @ SV1093 ) @ SV1426 ) @ SV1604 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV140 @ SV1604 ) @ SV1426 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3780]) ).
thf(4139,plain,
! [SV1427: $i,SV1094: $i,SV649: $i,SV142: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV142 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ SV649 ) @ SV1094 ) ) @ SV1427 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ SV649 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV142 ) @ SV1094 ) @ SV1427 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3782]) ).
thf(4140,plain,
! [SV1428: $i,SV1095: $i,SV650: $i,SV143: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV143 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ SV650 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ SV1095 ) @ SV1428 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ SV1095 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV143 ) @ SV650 ) @ SV1428 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3783]) ).
thf(4141,plain,
! [SV1429: $i,SV1096: $i,SV651: $i,SV144: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV144 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ SV651 ) @ SV1096 ) ) @ SV1429 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV144 ) @ SV651 ) @ SV1429 ) ) @ SV1096 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3784]) ).
thf(4142,plain,
! [SV1430: $i,SV1097: $i,SV652: $i,SV145: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV145 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV145 ) @ SV652 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV145 ) @ SV1097 ) @ SV1430 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV145 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV145 ) @ SV652 ) @ SV1097 ) ) @ SV1430 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3785]) ).
thf(4143,plain,
! [SV1431: $i,SV1098: $i,SV653: $i,SV146: $i] :
( ( ( class_OrderedGroup_Oab__semigroup__add @ SV146 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ SV653 ) @ SV1098 ) ) @ SV1431 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ SV653 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV146 ) @ SV1098 ) @ SV1431 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3786]) ).
thf(4144,plain,
! [SV1432: $i,SV1099: $i,SV654: $i,SV147: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV147 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV654 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV1099 ) @ SV1432 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV1099 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV147 ) @ SV654 ) @ SV1432 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3787]) ).
thf(4145,plain,
! [SV1433: $i,SV1100: $i,SV655: $i,SV148: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV148 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV655 ) @ SV1100 ) ) @ SV1433 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV655 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV148 ) @ SV1100 ) @ SV1433 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3788]) ).
thf(4146,plain,
! [SV1434: $i,SV1103: $i,SV658: $i,SV151: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV151 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV658 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV1103 ) @ SV1434 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV1103 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV151 ) @ SV658 ) @ SV1434 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3789]) ).
thf(4147,plain,
! [SV1435: $i,SV1104: $i,SV659: $i,SV152: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV152 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV659 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV1104 ) @ SV1435 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV152 ) @ SV659 ) @ SV1104 ) ) @ SV1435 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3790]) ).
thf(4148,plain,
! [SV1436: $i,SV1105: $i,SV660: $i,SV153: $i] :
( ( ( class_Orderings_Oorder @ SV153 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV660 @ SV1105 @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SV660 @ SV1436 @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SV1436 @ SV1105 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3791]) ).
thf(4149,plain,
! [SV1437: $i,SV1106: $i,SV661: $i,SV154: $i] :
( ( ( class_Orderings_Opreorder @ SV154 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV661 @ SV1106 @ SV154 )
| ~ ( c_HOL_Oord__class_Oless @ SV1437 @ SV1106 @ SV154 )
| ~ ( c_HOL_Oord__class_Oless @ SV661 @ SV1437 @ SV154 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3792]) ).
thf(4150,plain,
! [SV1605: $i,SV1438: $i,SV1107: $i,SV662: $i,SV155: $i] :
( ( ( ~ ( c_ListOrder_Ostep1 @ SV155 @ SV662 @ SV1107 @ SV1438 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV155 @ ( c_List_Oappend @ SV662 @ SV1605 @ SV1438 ) @ ( c_List_Oappend @ SV1107 @ SV1605 @ SV1438 ) @ SV1438 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3793]) ).
thf(4151,plain,
! [SV1606: $i,SV1439: $i,SV1108: $i,SV663: $i,SV156: $i] :
( ( ( c_ListOrder_Ostep1 @ SV156 @ ( c_List_Oappend @ SV663 @ SV1108 @ SV1439 ) @ ( c_List_Oappend @ SV663 @ SV1606 @ SV1439 ) @ SV1439 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV156 @ SV1108 @ SV1606 @ SV1439 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3794]) ).
thf(4152,plain,
! [SV1109: $i,SV1440: $i,SV665: $i,SV158: $i] :
( ( ( c_List_Olistsp @ SV158 @ ( c_List_Oappend @ SV665 @ SV1440 @ SV1109 ) @ SV1109 )
= $false )
| ( ( c_List_Olistsp @ SV158 @ SV665 @ SV1109 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3795]) ).
thf(4153,plain,
! [SV1110: $i,SV666: $i,SV1441: $i,SV159: $i] :
( ( ( c_List_Olistsp @ SV159 @ ( c_List_Oappend @ SV1441 @ SV666 @ SV1110 ) @ SV1110 )
= $false )
| ( ( c_List_Olistsp @ SV159 @ SV666 @ SV1110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3796]) ).
thf(4154,plain,
! [SV1692: $i,SV1608: $i,SV1443: $i,SV1112: $i,SV668: $i,SV161: $i] :
( ( ( SV161 = SV668 )
| ( SV1112 = SV1443 )
| ~ ( c_ListOrder_Ostep1 @ SV1608 @ ( c_List_Olist_OCons @ SV668 @ SV1443 @ SV1692 ) @ ( c_List_Olist_OCons @ SV161 @ SV1112 @ SV1692 ) @ SV1692 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3798]) ).
thf(4155,plain,
! [SV1609: $i,SV1444: $i,SV1113: $i,SV669: $i,SV162: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV162 @ SV669 ) @ SV1113 ) ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV162 @ ( c_List_Olist_OCons @ SV669 @ SV1444 @ SV1609 ) @ ( c_List_Olist_OCons @ SV1113 @ SV1444 @ SV1609 ) @ SV1609 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3799]) ).
thf(4156,plain,
! [SV1445: $i,SV1114: $i,SV671: $i,SV164: $i] :
( ( ( class_Orderings_Olinorder @ SV164 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV671 @ SV1114 @ SV164 ) @ SV1445 @ SV164 )
| ~ ( c_HOL_Oord__class_Oless @ SV1114 @ SV1445 @ SV164 )
| ~ ( c_HOL_Oord__class_Oless @ SV671 @ SV1445 @ SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3800]) ).
thf(4157,plain,
! [SV1446: $i,SV674: $i,SV1117: $i,SV167: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SV1117 ) @ SV674 ) @ SV1446 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV167 @ SV1446 @ SV1117 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV167 @ SV674 @ SV1117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3801]) ).
thf(4158,plain,
! [SV675: $i,SV1118: $i,SV1447: $i,SV168: $i] :
( ( ( ~ ( c_Wellfounded_Oaccp @ SV168 @ SV1447 @ SV1118 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SV1118 ) @ SV675 ) @ SV1447 ) ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV168 @ SV675 @ SV1118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3802]) ).
thf(4159,plain,
! [SV1610: $i,SV1448: $i,SV1119: $i,SV676: $i,SV169: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SV676 ) @ SV1119 ) @ SV1448 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SV676 ) @ SV1610 ) @ SV1448 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SV676 ) @ SV1119 ) @ SV1610 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3803]) ).
thf(4160,plain,
! [SV1120: $i,SV178: $i,SV1449: $i,SV682: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV682 ) @ SV1449 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV178 ) @ SV682 ) @ SV1120 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV178 ) @ SV1449 ) @ SV1120 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3805]) ).
thf(4161,plain,
! [SV1693: $i,SV1612: $i,SV1451: $i,SV1130: $i,SV693: $i,SV189: $i] :
( ( ( c_List_Ofoldr @ SV189 @ ( c_List_Oappend @ SV693 @ SV1130 @ SV1451 ) @ SV1612 @ SV1451 @ SV1693 )
= ( c_List_Ofoldr @ SV189 @ SV693 @ ( c_List_Ofoldr @ SV189 @ SV1130 @ SV1612 @ SV1451 @ SV1693 ) @ SV1451 @ SV1693 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3815]) ).
thf(4162,plain,
! [SV1694: $i,SV1613: $i,SV1452: $i,SV1131: $i,SV694: $i,SV190: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV190 @ SV694 ) @ SV1131 ) )
| ( SV694 = SV1131 )
| ~ ( c_ListOrder_Ostep1 @ SV190 @ ( c_List_Oappend @ SV1452 @ ( c_List_Olist_OCons @ SV694 @ ( c_List_Olist_ONil @ SV1613 ) @ SV1613 ) @ SV1613 ) @ ( c_List_Oappend @ SV1694 @ ( c_List_Olist_OCons @ SV1131 @ ( c_List_Olist_ONil @ SV1613 ) @ SV1613 ) @ SV1613 ) @ SV1613 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3816]) ).
thf(4163,plain,
! [SV1695: $i,SV1614: $i,SV1453: $i,SV1132: $i,SV695: $i,SV191: $i] :
( ( ! [SY4847: $i,SY4848: $i,SY4849: $i] :
( ( ( hAPP @ ( hAPP @ SV191 @ ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ SV1453 ) ) @ ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ SV1614 ) )
= ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1453 ) @ SV1614 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1695 @ SV191 @ SV695 @ SY4847 @ SY4848 @ SY4849 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3817]) ).
thf(4164,plain,
! [SV1133: $i,SV696: $i,SV1454: $i,SV192: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV192 ) @ SV1454 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV192 ) @ SV696 ) @ SV1133 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1454 ) @ SV696 ) @ SV1133 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3818]) ).
thf(4165,plain,
! [SV1134: $i,SV193: $i,SV1455: $i,SV697: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV697 ) @ SV1455 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV193 ) @ SV697 ) @ SV1134 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV193 ) @ SV1455 ) @ SV1134 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3819]) ).
thf(4166,plain,
! [SV699: $i,SV1456: $i,SV1136: $i,SV195: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV195 @ SV1136 ) @ SV1456 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV195 @ SV699 ) @ SV1136 ) @ SV1456 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3821]) ).
thf(4167,plain,
! [SV198: $i,SV702: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV702 @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV198 ) @ SV702 ) @ SV702 ) @ ( c_HOL_Ozero__class_Ozero @ SV198 ) @ SV198 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV198 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3822]) ).
thf(4168,plain,
! [SV703: $i,SV199: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV199 ) @ SV703 ) @ SV703 ) @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV703 @ ( c_HOL_Ozero__class_Ozero @ SV199 ) @ SV199 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3823]) ).
thf(4169,plain,
! [SV1696: $i,SV1615: $i,SV1459: $i,SV1141: $i,SV706: $i,SV202: $i] :
( ( ! [SY4850: $i,SY4851: $i,SY4852: $i] :
( ( ( hAPP @ ( hAPP @ SV202 @ ( hAPP @ ( hAPP @ SV706 @ SV1141 ) @ SV1459 ) ) @ SV1615 )
= ( hAPP @ ( hAPP @ SV706 @ ( hAPP @ ( hAPP @ SV202 @ SV1141 ) @ SV1615 ) ) @ ( hAPP @ ( hAPP @ SV202 @ SV1459 ) @ SV1615 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1696 @ SV706 @ SV202 @ SY4850 @ SY4851 @ SY4852 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3824]) ).
thf(4170,plain,
! [SV1697: $i,SV1616: $i,SV1460: $i,SV1142: $i,SV707: $i,SV203: $i] :
( ( ! [SY4853: $i,SY4854: $i,SY4855: $i] :
( ( ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ ( hAPP @ ( hAPP @ SV1142 @ SV1460 ) @ SV1616 ) )
= ( hAPP @ ( hAPP @ SV1142 @ ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ SV1460 ) ) @ ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ SV1616 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1142 @ SV203 @ SV1697 @ SY4853 @ SY4854 @ SY4855 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3825]) ).
thf(4171,plain,
! [SV1698: $i,SV1617: $i,SV1461: $i,SV1143: $i,SV708: $i,SV204: $i] :
( ( ! [SY4856: $i,SY4857: $i] :
( ( ( hAPP @ ( hAPP @ SV204 @ SV708 ) @ SV1143 )
= ( hAPP @ ( hAPP @ SV204 @ SV1143 ) @ SV708 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1461 @ SV204 @ SV1617 @ SV1698 @ SY4856 @ SY4857 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3826]) ).
thf(4172,plain,
! [SV1699: $i,SV1618: $i,SV1462: $i,SV1144: $i,SV709: $i,SV205: $i] :
( ( ! [SY4858: $i,SY4859: $i,SY4860: $i] :
( ( ( hAPP @ ( hAPP @ SV205 @ SV709 ) @ ( hAPP @ ( hAPP @ SV205 @ SV1144 ) @ SV1462 ) )
= ( hAPP @ ( hAPP @ SV205 @ ( hAPP @ ( hAPP @ SV205 @ SV709 ) @ SV1144 ) ) @ SV1462 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1618 @ SV205 @ SV1699 @ SY4858 @ SY4859 @ SY4860 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3827]) ).
thf(4173,plain,
! [SV1700: $i,SV1619: $i,SV1463: $i,SV1145: $i,SV710: $i,SV206: $i] :
( ( ! [SY4861: $i] :
( ( ( hAPP @ ( hAPP @ SV206 @ SV710 ) @ SV1145 )
= SV1145 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1463 @ SV206 @ SV1619 @ SV1700 @ SV710 @ SY4861 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3828]) ).
thf(4174,plain,
! [SV1701: $i,SV1620: $i,SV1464: $i,SV1146: $i,SV711: $i,SV207: $i] :
( ( ! [SY4862: $i] :
( ( ( hAPP @ ( hAPP @ SV207 @ SV711 ) @ SV1146 )
= SV711 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1464 @ SV207 @ SV1620 @ SV711 @ SV1701 @ SY4862 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3829]) ).
thf(4175,plain,
! [SV1702: $i,SV1621: $i,SV1465: $i,SV1147: $i,SV712: $i,SV208: $i] :
( ( ! [SY4863: $i,SY4864: $i] :
( ( ( hAPP @ ( hAPP @ SV208 @ SV712 ) @ SV1147 )
= ( hAPP @ ( hAPP @ SV208 @ SV1147 ) @ SV712 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV208 @ SV1465 @ SV1621 @ SV1702 @ SY4863 @ SY4864 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3830]) ).
thf(4176,plain,
! [SV1703: $i,SV1622: $i,SV1466: $i,SV1148: $i,SV713: $i,SV209: $i] :
( ( ! [SY4865: $i,SY4866: $i,SY4867: $i] :
( ( ( hAPP @ ( hAPP @ SV209 @ SV713 ) @ ( hAPP @ ( hAPP @ SV209 @ SV1148 ) @ SV1466 ) )
= ( hAPP @ ( hAPP @ SV209 @ ( hAPP @ ( hAPP @ SV209 @ SV713 ) @ SV1148 ) ) @ SV1466 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV209 @ SV1622 @ SV1703 @ SY4865 @ SY4866 @ SY4867 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3831]) ).
thf(4177,plain,
! [SV1704: $i,SV1623: $i,SV1467: $i,SV1149: $i,SV714: $i,SV210: $i] :
( ( ! [SY4868: $i] :
( ( ( hAPP @ ( hAPP @ SV210 @ SV714 ) @ SV1149 )
= SV1149 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV210 @ SV1467 @ SV1623 @ SV714 @ SV1704 @ SY4868 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3832]) ).
thf(4178,plain,
! [SV1705: $i,SV1624: $i,SV1468: $i,SV1150: $i,SV715: $i,SV211: $i] :
( ( ! [SY4869: $i,SY4870: $i,SY4871: $i] :
( ( ( hAPP @ ( hAPP @ SV211 @ SV715 ) @ ( hAPP @ ( hAPP @ SV211 @ SV1150 ) @ SV1468 ) )
= ( hAPP @ ( hAPP @ SV211 @ ( hAPP @ ( hAPP @ SV211 @ SV715 ) @ SV1150 ) ) @ SV1468 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV211 @ SV1624 @ SV1705 @ SY4869 @ SY4870 @ SY4871 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3833]) ).
thf(4179,plain,
! [SV1706: $i,SV1625: $i,SV1469: $i,SV1151: $i,SV716: $i,SV212: $i] :
( ( ! [SY4872: $i,SY4873: $i] :
( ( ( hAPP @ ( hAPP @ SV212 @ SV716 ) @ SV1151 )
= ( hAPP @ ( hAPP @ SV212 @ SV1151 ) @ SV716 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV212 @ SV1469 @ SV1625 @ SV1706 @ SY4872 @ SY4873 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3834]) ).
thf(4180,plain,
! [SV1707: $i,SV1626: $i,SV1470: $i,SV1152: $i,SV717: $i,SV213: $i] :
( ( ! [SY4874: $i,SY4875: $i,SY4876: $i] :
( ( ( hAPP @ ( hAPP @ SV213 @ ( hAPP @ ( hAPP @ SV213 @ SV717 ) @ SV1152 ) ) @ SV1470 )
= ( hAPP @ ( hAPP @ SV213 @ ( hAPP @ ( hAPP @ SV213 @ SV717 ) @ SV1470 ) ) @ SV1152 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV213 @ SV1626 @ SV1707 @ SY4874 @ SY4875 @ SY4876 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3835]) ).
thf(4181,plain,
! [SV1708: $i,SV1627: $i,SV1471: $i,SV1153: $i,SV718: $i,SV214: $i] :
( ( ! [SY4877: $i,SY4878: $i,SY4879: $i] :
( ( ( hAPP @ ( hAPP @ SV214 @ SV718 ) @ ( hAPP @ ( hAPP @ SV214 @ SV1153 ) @ SV1471 ) )
= ( hAPP @ ( hAPP @ SV214 @ SV1153 ) @ ( hAPP @ ( hAPP @ SV214 @ SV718 ) @ SV1471 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV214 @ SV1627 @ SV1708 @ SY4877 @ SY4878 @ SY4879 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3836]) ).
thf(4182,plain,
! [SV1709: $i,SV1628: $i,SV1472: $i,SV1154: $i,SV719: $i,SV215: $i] :
( ( ! [SY4880: $i,SY4881: $i,SY4882: $i] :
( ( ( hAPP @ ( hAPP @ SV215 @ ( hAPP @ ( hAPP @ SV215 @ SV719 ) @ SV1154 ) ) @ SV1472 )
= ( hAPP @ ( hAPP @ SV215 @ SV719 ) @ ( hAPP @ ( hAPP @ SV215 @ SV1154 ) @ SV1472 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV215 @ SV1628 @ SV1709 @ SY4880 @ SY4881 @ SY4882 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3837]) ).
thf(4183,plain,
! [SV1710: $i,SV1629: $i,SV1473: $i,SV1155: $i,SV720: $i,SV216: $i] :
( ( ! [SY4883: $i,SY4884: $i,SY4885: $i,SY4886: $i] :
( ( ( hAPP @ ( hAPP @ SV216 @ ( hAPP @ ( hAPP @ SV216 @ SV720 ) @ SV1155 ) ) @ ( hAPP @ ( hAPP @ SV216 @ SV1473 ) @ SV1629 ) )
= ( hAPP @ ( hAPP @ SV216 @ ( hAPP @ ( hAPP @ SV216 @ SV720 ) @ SV1473 ) ) @ ( hAPP @ ( hAPP @ SV216 @ SV1155 ) @ SV1629 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV216 @ SV1710 @ SY4883 @ SY4884 @ SY4885 @ SY4886 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3838]) ).
thf(4184,plain,
! [SV1711: $i,SV1630: $i,SV1474: $i,SV1156: $i,SV721: $i,SV217: $i] :
( ( ! [SY4887: $i,SY4888: $i,SY4889: $i] :
( ( ( hAPP @ ( hAPP @ SV217 @ SV721 ) @ ( hAPP @ ( hAPP @ SV217 @ SV1156 ) @ SV1474 ) )
= ( hAPP @ ( hAPP @ SV217 @ SV1156 ) @ ( hAPP @ ( hAPP @ SV217 @ SV721 ) @ SV1474 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1630 @ SV217 @ SV1711 @ SY4887 @ SY4888 @ SY4889 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3839]) ).
thf(4185,plain,
! [SV1712: $i,SV1631: $i,SV1475: $i,SV1157: $i,SV722: $i,SV218: $i] :
( ( ! [SY4890: $i,SY4891: $i,SY4892: $i] :
( ( ( hAPP @ ( hAPP @ SV218 @ SV722 ) @ ( hAPP @ ( hAPP @ SV218 @ SV1157 ) @ SV1475 ) )
= ( hAPP @ ( hAPP @ SV218 @ ( hAPP @ ( hAPP @ SV218 @ SV722 ) @ SV1157 ) ) @ SV1475 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1631 @ SV218 @ SV1712 @ SY4890 @ SY4891 @ SY4892 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3840]) ).
thf(4186,plain,
! [SV1713: $i,SV1632: $i,SV1476: $i,SV1158: $i,SV723: $i,SV219: $i] :
( ( ! [SY4893: $i,SY4894: $i,SY4895: $i] :
( ( ( hAPP @ ( hAPP @ SV219 @ ( hAPP @ ( hAPP @ SV219 @ SV723 ) @ SV1158 ) ) @ SV1476 )
= ( hAPP @ ( hAPP @ SV219 @ SV723 ) @ ( hAPP @ ( hAPP @ SV219 @ SV1158 ) @ SV1476 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1632 @ SV219 @ SV1713 @ SY4893 @ SY4894 @ SY4895 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3841]) ).
thf(4187,plain,
! [SV1714: $i,SV1633: $i,SV1477: $i,SV1159: $i,SV724: $i,SV220: $i] :
( ( ! [SY4896: $i,SY4897: $i,SY4898: $i] :
( ( ( hAPP @ ( hAPP @ SV220 @ ( hAPP @ ( hAPP @ SV220 @ SV724 ) @ SV1159 ) ) @ SV1477 )
= ( hAPP @ ( hAPP @ SV220 @ ( hAPP @ ( hAPP @ SV220 @ SV724 ) @ SV1477 ) ) @ SV1159 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1633 @ SV220 @ SV1714 @ SY4896 @ SY4897 @ SY4898 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3842]) ).
thf(4188,plain,
! [SV1715: $i,SV1634: $i,SV1478: $i,SV1160: $i,SV725: $i,SV221: $i] :
( ( ! [SY4899: $i,SY4900: $i,SY4901: $i,SY4902: $i] :
( ( ( hAPP @ ( hAPP @ SV221 @ ( hAPP @ ( hAPP @ SV221 @ SV725 ) @ SV1160 ) ) @ ( hAPP @ ( hAPP @ SV221 @ SV1478 ) @ SV1634 ) )
= ( hAPP @ ( hAPP @ SV221 @ SV1478 ) @ ( hAPP @ ( hAPP @ SV221 @ ( hAPP @ ( hAPP @ SV221 @ SV725 ) @ SV1160 ) ) @ SV1634 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1715 @ SV221 @ SY4899 @ SY4900 @ SY4901 @ SY4902 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3843]) ).
thf(4189,plain,
! [SV1716: $i,SV1635: $i,SV1479: $i,SV1161: $i,SV726: $i,SV222: $i] :
( ( ! [SY4903: $i,SY4904: $i,SY4905: $i,SY4906: $i] :
( ( ( hAPP @ ( hAPP @ SV222 @ ( hAPP @ ( hAPP @ SV222 @ SV726 ) @ SV1161 ) ) @ ( hAPP @ ( hAPP @ SV222 @ SV1479 ) @ SV1635 ) )
= ( hAPP @ ( hAPP @ SV222 @ SV726 ) @ ( hAPP @ ( hAPP @ SV222 @ SV1161 ) @ ( hAPP @ ( hAPP @ SV222 @ SV1479 ) @ SV1635 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1716 @ SV222 @ SY4903 @ SY4904 @ SY4905 @ SY4906 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3844]) ).
thf(4190,plain,
! [SV1717: $i,SV1636: $i,SV1480: $i,SV1162: $i,SV727: $i,SV223: $i] :
( ( ! [SY4907: $i,SY4908: $i,SY4909: $i,SY4910: $i] :
( ( ( hAPP @ ( hAPP @ SV223 @ ( hAPP @ ( hAPP @ SV223 @ SV727 ) @ SV1162 ) ) @ ( hAPP @ ( hAPP @ SV223 @ SV1480 ) @ SV1636 ) )
= ( hAPP @ ( hAPP @ SV223 @ ( hAPP @ ( hAPP @ SV223 @ SV727 ) @ SV1480 ) ) @ ( hAPP @ ( hAPP @ SV223 @ SV1162 ) @ SV1636 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1717 @ SV223 @ SY4907 @ SY4908 @ SY4909 @ SY4910 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3845]) ).
thf(4191,plain,
! [SV1718: $i,SV1637: $i,SV1481: $i,SV1163: $i,SV728: $i,SV224: $i] :
( ( ! [SY4911: $i] :
( ( ( hAPP @ ( hAPP @ SV224 @ SV728 ) @ SV1163 )
= SV728 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1481 @ SV224 @ SV1637 @ SV1718 @ SV1163 @ SY4911 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3846]) ).
thf(4192,plain,
! [SV1719: $i,SV1638: $i,SV1482: $i,SV1164: $i,SV729: $i,SV225: $i] :
( ( ! [SY4912: $i] :
( ( ( hAPP @ ( hAPP @ SV225 @ SV729 ) @ SV1164 )
= SV1164 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1482 @ SV225 @ SV1638 @ SV1719 @ SV729 @ SY4912 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3847]) ).
thf(4193,plain,
! [SV1720: $i,SV1639: $i,SV1483: $i,SV1165: $i,SV730: $i,SV226: $i] :
( ( ! [SY4913: $i] :
( ( ( hAPP @ ( hAPP @ SV226 @ SV730 ) @ SV1165 )
= SV1165 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1483 @ SV226 @ SV1639 @ SV1165 @ SV1720 @ SY4913 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3848]) ).
thf(4194,plain,
! [SV1721: $i,SV1640: $i,SV1484: $i,SV1166: $i,SV731: $i,SV227: $i] :
( ( ! [SY4914: $i] :
( ( ( hAPP @ ( hAPP @ SV227 @ SV731 ) @ SV1166 )
= SV731 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1484 @ SV227 @ SV1640 @ SV731 @ SV1721 @ SY4914 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3849]) ).
thf(4195,plain,
! [SV1722: $i,SV1641: $i,SV1485: $i,SV1167: $i,SV732: $i,SV228: $i] :
( ( ! [SY4915: $i,SY4916: $i,SY4917: $i] :
( ( ( hAPP @ ( hAPP @ SV228 @ ( hAPP @ ( hAPP @ SV732 @ SV1167 ) @ SV1485 ) ) @ SV1641 )
= ( hAPP @ ( hAPP @ SV732 @ ( hAPP @ ( hAPP @ SV228 @ SV1167 ) @ SV1641 ) ) @ ( hAPP @ ( hAPP @ SV228 @ SV1485 ) @ SV1641 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV732 @ SV228 @ SV1722 @ SY4915 @ SY4916 @ SY4917 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3850]) ).
thf(4196,plain,
! [SV1723: $i,SV1642: $i,SV1486: $i,SV1168: $i,SV733: $i,SV229: $i] :
( ( ! [SY4918: $i,SY4919: $i] :
( ( ( hAPP @ ( hAPP @ SV229 @ SV733 ) @ SV1168 )
= ( hAPP @ ( hAPP @ SV229 @ SV1168 ) @ SV733 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1486 @ SV229 @ SV1642 @ SV1723 @ SY4918 @ SY4919 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3851]) ).
thf(4197,plain,
! [SV1724: $i,SV1643: $i,SV1487: $i,SV1169: $i,SV734: $i,SV230: $i] :
( ( ! [SY4920: $i] :
( ( ( hAPP @ ( hAPP @ SV230 @ SV734 ) @ SV1169 )
= SV734 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV230 @ SV1487 @ SV1643 @ SV1169 @ SV1724 @ SY4920 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3852]) ).
thf(4198,plain,
! [SV1725: $i,SV1644: $i,SV1488: $i,SV1170: $i,SV735: $i,SV231: $i] :
( ( ! [SY4921: $i] :
( ( ( hAPP @ ( hAPP @ SV231 @ SV735 ) @ SV1170 )
= SV1170 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV231 @ SV1488 @ SV1644 @ SV735 @ SV1725 @ SY4921 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3853]) ).
thf(4199,plain,
! [SV1726: $i,SV1645: $i,SV1489: $i,SV1171: $i,SV736: $i,SV232: $i] :
( ( ! [SY4922: $i] :
( ( ( hAPP @ ( hAPP @ SV232 @ SV736 ) @ SV736 )
= ( hAPP @ ( hAPP @ SV1171 @ ( hAPP @ ( hAPP @ SV232 @ SV1489 ) @ SV1489 ) ) @ SV736 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV232 @ SV1171 @ SV1645 @ SV1726 @ SV1489 @ SY4922 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3854]) ).
thf(4200,plain,
! [SV1727: $i,SV1646: $i,SV1490: $i,SV1172: $i,SV737: $i,SV233: $i] :
( ( ! [SY4923: $i,SY4924: $i] :
( ( ( hAPP @ ( hAPP @ SV233 @ SV737 ) @ ( hAPP @ ( hAPP @ SV1172 @ SV1490 ) @ SV737 ) )
= ( hAPP @ ( hAPP @ SV1172 @ ( hAPP @ ( hAPP @ SV233 @ SV1490 ) @ SV1646 ) ) @ SV737 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV233 @ SV1172 @ SV1727 @ SY4923 @ SV1646 @ SY4924 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3855]) ).
thf(4201,plain,
! [SV1728: $i,SV1647: $i,SV1491: $i,SV1173: $i,SV738: $i,SV234: $i] :
( ( ! [SY4925: $i,SY4926: $i] :
( ( ( hAPP @ ( hAPP @ SV234 @ ( hAPP @ ( hAPP @ SV738 @ SV1173 ) @ SV1491 ) ) @ SV1491 )
= ( hAPP @ ( hAPP @ SV738 @ ( hAPP @ ( hAPP @ SV234 @ SV1173 ) @ SV1647 ) ) @ SV1491 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV234 @ SV738 @ SV1728 @ SY4925 @ SV1647 @ SY4926 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3856]) ).
thf(4202,plain,
! [SV1729: $i,SV1648: $i,SV1492: $i,SV1174: $i,SV739: $i,SV235: $i] :
( ( ! [SY4927: $i,SY4928: $i,SY4929: $i] :
( ( ( hAPP @ ( hAPP @ SV235 @ ( hAPP @ ( hAPP @ SV739 @ SV1174 ) @ SV1492 ) ) @ ( hAPP @ ( hAPP @ SV739 @ SV1648 ) @ SV1492 ) )
= ( hAPP @ ( hAPP @ SV739 @ ( hAPP @ ( hAPP @ SV235 @ SV1174 ) @ SV1648 ) ) @ SV1492 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV235 @ SV739 @ SV1729 @ SY4927 @ SY4928 @ SY4929 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3857]) ).
thf(4203,plain,
! [SV1730: $i,SV1649: $i,SV1493: $i,SV1175: $i,SV740: $i,SV236: $i] :
( ( ( SV236 = SV740 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV1175 @ SV740 ) @ SV236 ) )
| ~ ( c_ListOrder_Ostep1 @ SV1175 @ ( c_List_Olist_OCons @ SV740 @ SV1493 @ SV1649 ) @ ( c_List_Olist_OCons @ SV236 @ SV1730 @ SV1649 ) @ SV1649 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3858]) ).
thf(4204,plain,
! [SV1650: $i,SV1494: $i,SV1176: $i,SV741: $i,SV237: $i] :
( ( ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ SV237 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SV741 ) @ SV1176 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SV1494 ) @ SV1650 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SV741 ) @ SV1494 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SV1176 ) @ SV1650 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3859]) ).
thf(4205,plain,
! [SV1177: $i,SV238: $i,SV1495: $i,SV742: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV742 ) @ SV1495 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV238 ) @ SV1177 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV238 ) @ SV742 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1177 ) @ SV1495 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3860]) ).
thf(4206,plain,
! [SV746: $i,SV1180: $i,SV1496: $i,SV242: $i] :
( ( ( ~ ( c_Type_Otyping @ SV242 @ SV1496 @ SV1180 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV1496 ) @ SV746 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV242 @ SV746 @ SV1180 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3864]) ).
thf(4207,plain,
! [SV1497: $i,SV1183: $i,SV752: $i,SV249: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV249 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV249 ) @ ( c_Orderings_Oord__class_Omax @ SV752 @ SV1183 @ SV249 ) ) @ SV1497 )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV249 ) @ SV752 ) @ SV1497 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV249 ) @ SV1183 ) @ SV1497 ) @ SV249 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3867]) ).
thf(4208,plain,
! [SV1731: $i,SV1651: $i,SV1498: $i,SV1185: $i,SV754: $i,SV251: $i] :
( ( ( SV251 = SV754 )
| ( c_ListOrder_Ostep1 @ SV1185 @ SV251 @ SV754 @ SV1498 )
| ~ ( c_ListOrder_Ostep1 @ SV1185 @ ( c_List_Oappend @ SV251 @ ( c_List_Olist_OCons @ SV1651 @ ( c_List_Olist_ONil @ SV1498 ) @ SV1498 ) @ SV1498 ) @ ( c_List_Oappend @ SV754 @ ( c_List_Olist_OCons @ SV1731 @ ( c_List_Olist_ONil @ SV1498 ) @ SV1498 ) @ SV1498 ) @ SV1498 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3868]) ).
thf(4209,plain,
! [SV1499: $i,SV1186: $i,SV755: $i,SV252: $i] :
( ( ( class_Orderings_Olinorder @ SV252 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ SV755 @ SV1186 @ SV252 ) @ SV1499 @ SV252 )
= ( c_Orderings_Oord__class_Omax @ SV755 @ ( c_Orderings_Oord__class_Omax @ SV1186 @ SV1499 @ SV252 ) @ SV252 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3869]) ).
thf(4210,plain,
! [SV1500: $i,SV1187: $i,SV756: $i,SV253: $i] :
( ( ( class_Orderings_Olinorder @ SV253 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omax @ SV756 @ ( c_Orderings_Oord__class_Omax @ SV1187 @ SV1500 @ SV253 ) @ SV253 )
= ( c_Orderings_Oord__class_Omax @ SV1187 @ ( c_Orderings_Oord__class_Omax @ SV756 @ SV1500 @ SV253 ) @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3870]) ).
thf(4211,plain,
! [SV761: $i,SV1501: $i,SV259: $i,SV1190: $i] :
( ( ( c_OrderedGroup_Omonoid__add @ SV1190 @ SV259 @ SV1501 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV259 @ SV761 ) @ SV1190 )
= SV761 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3872]) ).
thf(4212,plain,
! [SV1191: $i,SV1502: $i,SV260: $i,SV762: $i] :
( ( ( c_OrderedGroup_Omonoid__add @ SV762 @ SV260 @ SV1502 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV260 @ SV762 ) @ SV1191 )
= SV1191 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3873]) ).
thf(4213,plain,
! [SV765: $i,SV263: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV263 ) @ SV765 ) @ SV765 ) @ SV263 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV263 ) @ SV765 @ SV263 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV263 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3874]) ).
thf(4214,plain,
! [SV766: $i,SV264: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ SV766 @ SV264 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV264 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV264 ) @ SV766 ) @ SV766 ) @ SV264 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV264 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3875]) ).
thf(4215,plain,
! [SV769: $i,SV271: $i] :
( ( ( class_Int_Onumber__ring @ SV271 )
= $false )
| ( ( SV769
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV271 ) @ SV769 ) @ ( c_HOL_Ozero__class_Ozero @ SV271 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3879]) ).
thf(4216,plain,
! [SV776: $i,SV281: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV281 ) @ SV776 ) @ SV776 ) @ ( c_HOL_Ozero__class_Ozero @ SV281 ) @ SV281 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV776 @ ( c_HOL_Ozero__class_Ozero @ SV281 ) @ SV281 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3880]) ).
thf(4217,plain,
! [SV282: $i,SV777: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV777 @ ( c_HOL_Ozero__class_Ozero @ SV282 ) @ SV282 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV282 ) @ SV777 ) @ SV777 ) @ ( c_HOL_Ozero__class_Ozero @ SV282 ) @ SV282 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3881]) ).
thf(4218,plain,
! [SV1192: $i,SV778: $i,SV283: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV283 ) @ ( c_Power_Opower__class_Opower @ SV778 @ SV1192 @ SV283 ) @ SV283 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV283 ) @ SV778 @ SV283 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3882]) ).
thf(4219,plain,
! [SV1503: $i,SV1193: $i,SV779: $i,SV284: $i] :
( ( ( class_Orderings_Olinorder @ SV284 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV779 @ SV1193 @ SV284 )
| ( c_HOL_Oord__class_Oless @ SV779 @ SV1503 @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ SV779 @ ( c_Orderings_Oord__class_Omax @ SV1503 @ SV1193 @ SV284 ) @ SV284 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3883]) ).
thf(4220,plain,
! [SV1197: $i,SV787: $i,SV296: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV296 ) @ SV787 ) @ SV1197 ) @ SV296 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SV1197 @ SV296 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SV787 @ SV296 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV296 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3890]) ).
thf(4221,plain,
! [SV1732: $i,SV1652: $i,SV1504: $i,SV1198: $i,SV788: $i,SV297: $i] :
( ( ( c_ListOrder_Ostep1 @ SV297 @ SV788 @ SV1198 @ SV1504 )
| ( SV1198 = SV788 )
| ~ ( c_ListOrder_Ostep1 @ SV297 @ ( c_List_Olist_OCons @ SV1652 @ SV788 @ SV1504 ) @ ( c_List_Olist_OCons @ SV1732 @ SV1198 @ SV1504 ) @ SV1504 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3891]) ).
thf(4222,plain,
! [SV1653: $i,SV1505: $i,SV1199: $i,SV789: $i,SV298: $i] :
( ( ( ( hAPP @ ( hAPP @ SV298 @ ( hAPP @ ( hAPP @ SV298 @ SV789 ) @ SV1199 ) ) @ SV1505 )
= ( hAPP @ ( hAPP @ SV298 @ SV789 ) @ ( hAPP @ ( hAPP @ SV298 @ SV1199 ) @ SV1505 ) ) )
= $true )
| ( ( ~ ( c_OrderedGroup_Osemigroup__add @ SV298 @ SV1653 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3892]) ).
thf(4223,plain,
! [SV302: $i,SV1202: $i,SV792: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV792 @ SV1202 @ SV302 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1202 @ SV792 @ SV302 )
| ( SV1202 = SV792 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3896]) ).
thf(4224,plain,
! [SV303: $i,SV1203: $i,SV793: $i] :
( ( ( SV793 = SV1203 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1203 @ SV793 @ SV303 )
| ( c_HOL_Oord__class_Oless @ SV793 @ SV1203 @ SV303 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV303 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3897]) ).
thf(4225,plain,
! [SV305: $i,SV795: $i,SV1204: $i] :
( ( ( SV1204 = SV795 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1204 @ SV795 @ tc_nat )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV795 @ SV1204 @ tc_nat )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV305 @ SV795 ) @ SV1204 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3898]) ).
thf(4226,plain,
! [SV307: $i,SV1205: $i,SV797: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV797 @ SV1205 @ SV307 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV1205 @ SV797 @ SV307 )
| ( SV1205 = SV797 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV307 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3899]) ).
thf(4227,plain,
! [SV309: $i,SV1207: $i,SV799: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV799 @ SV1207 @ SV309 )
= $true )
| ( ( ( SV1207 = SV799 )
| ( c_HOL_Oord__class_Oless @ SV1207 @ SV799 @ SV309 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV309 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3900]) ).
thf(4228,plain,
! [SV310: $i,SV1208: $i,SV800: $i] :
( ( ( SV800 = SV1208 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV800 @ SV1208 @ SV310 )
| ( c_HOL_Oord__class_Oless @ SV1208 @ SV800 @ SV310 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV310 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3901]) ).
thf(4229,plain,
! [SV1655: $i,SV1508: $i,SV1209: $i,SV802: $i,SV312: $i] :
( ( ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV312 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV312 ) @ SV802 ) @ SV1209 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV312 ) @ SV1508 ) @ SV1655 ) @ SV312 )
| ~ ( c_HOL_Oord__class_Oless @ SV1209 @ SV1655 @ SV312 )
| ~ ( c_HOL_Oord__class_Oless @ SV802 @ SV1508 @ SV312 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3902]) ).
thf(4230,plain,
! [SV1210: $i,SV313: $i,SV1509: $i,SV803: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV803 @ SV1509 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV313 @ SV1210 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV313 ) @ SV803 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1210 ) @ SV1509 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3903]) ).
thf(4231,plain,
! [SV1211: $i,SV314: $i,SV804: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV804 @ SV314 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1211 @ SV314 ) @ SV314 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV804 @ SV1211 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV314 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3904]) ).
thf(4232,plain,
! [SV315: $i,SV1212: $i,SV805: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV805 @ SV1212 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV805 @ SV315 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1212 @ SV315 ) @ SV315 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV315 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3905]) ).
thf(4233,plain,
! [SV319: $i,SV808: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV808 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV319 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV808 @ SV319 ) @ SV319 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV319 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3907]) ).
thf(4234,plain,
! [SV809: $i,SV320: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV320 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV809 @ SV320 ) @ SV320 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV809 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3908]) ).
thf(4235,plain,
! [SV1733: $i,SV1656: $i,SV1511: $i,SV1214: $i,SV810: $i,SV321: $i] :
( ( ( SV321 = SV810 )
| ( SV1214 = SV1511 )
| ~ ( c_ListOrder_Ostep1 @ SV1656 @ ( c_List_Oappend @ SV321 @ ( c_List_Olist_OCons @ SV1214 @ ( c_List_Olist_ONil @ SV1733 ) @ SV1733 ) @ SV1733 ) @ ( c_List_Oappend @ SV810 @ ( c_List_Olist_OCons @ SV1511 @ ( c_List_Olist_ONil @ SV1733 ) @ SV1733 ) @ SV1733 ) @ SV1733 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3909]) ).
thf(4236,plain,
! [SV812: $i,SV1512: $i,SV1216: $i,SV323: $i] :
( ( ( ~ ( c_List_Olistsp @ SV323 @ SV1216 @ SV1512 ) )
= $true )
| ( ( ~ ( c_List_Olistsp @ SV323 @ SV812 @ SV1512 ) )
= $true )
| ( ( c_List_Olistsp @ SV323 @ ( c_List_Oappend @ SV812 @ SV1216 @ SV1512 ) @ SV1512 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3910]) ).
thf(4237,plain,
! [SV1514: $i,SV1218: $i,SV814: $i,SV326: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV326 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV814 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV326 ) @ SV1218 ) @ SV1514 ) @ SV326 )
| ~ ( c_HOL_Oord__class_Oless @ SV814 @ SV1514 @ SV326 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV1218 @ SV326 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3912]) ).
thf(4238,plain,
! [SV1734: $i,SV1658: $i,SV1515: $i,SV1219: $i,SV815: $i,SV327: $i] :
( ( ( c_List_Ofoldr @ SV327 @ ( c_List_Olist_OCons @ SV815 @ SV1219 @ SV1515 ) @ SV1658 @ SV1515 @ SV1734 )
= ( hAPP @ ( hAPP @ SV327 @ SV815 ) @ ( c_List_Ofoldr @ SV327 @ SV1219 @ SV1658 @ SV1515 @ SV1734 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3913]) ).
thf(4239,plain,
! [SV1659: $i,SV1516: $i,SV1220: $i,SV816: $i,SV328: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV328 @ ( c_Lambda_OdB_OdB__case @ SV816 @ SV1220 @ SV1516 @ ( c_Lambda_OdB_OAbs @ SV1659 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV328 @ ( hAPP @ SV1516 @ SV1659 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3914]) ).
thf(4240,plain,
! [SV1660: $i,SV1517: $i,SV1221: $i,SV817: $i,SV329: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV329 @ ( c_Lambda_OdB_OdB__case @ SV817 @ SV1221 @ SV1517 @ ( c_Lambda_OdB_OAbs @ SV1660 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV329 @ ( hAPP @ SV1517 @ SV1660 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3915]) ).
thf(4241,plain,
! [SV1518: $i,SV1224: $i,SV822: $i,SV334: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV334 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV334 ) @ SV822 ) @ SV1224 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV334 ) @ SV1518 ) @ SV1224 ) @ SV334 )
| ~ ( c_HOL_Oord__class_Oless @ SV822 @ SV1518 @ SV334 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3916]) ).
thf(4242,plain,
! [SV1519: $i,SV1225: $i,SV823: $i,SV335: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV335 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV335 ) @ SV823 ) @ SV1225 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV335 ) @ SV1519 ) @ SV1225 ) @ SV335 )
| ~ ( c_HOL_Oord__class_Oless @ SV823 @ SV1519 @ SV335 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3917]) ).
thf(4243,plain,
! [SV1520: $i,SV1226: $i,SV824: $i,SV336: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV336 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV824 @ SV1226 @ SV336 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV336 ) @ SV824 ) @ SV1520 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV336 ) @ SV1226 ) @ SV1520 ) @ SV336 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3918]) ).
thf(4244,plain,
! [SV1521: $i,SV1227: $i,SV825: $i,SV337: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV337 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV337 ) @ SV825 ) @ SV1227 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV337 ) @ SV825 ) @ SV1521 ) @ SV337 )
| ~ ( c_HOL_Oord__class_Oless @ SV1227 @ SV1521 @ SV337 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3919]) ).
thf(4245,plain,
! [SV1522: $i,SV1228: $i,SV826: $i,SV338: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV338 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV338 ) @ SV826 ) @ SV1228 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV338 ) @ SV826 ) @ SV1522 ) @ SV338 )
| ~ ( c_HOL_Oord__class_Oless @ SV1228 @ SV1522 @ SV338 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3920]) ).
thf(4246,plain,
! [SV1523: $i,SV1229: $i,SV827: $i,SV339: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV339 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV827 @ SV1229 @ SV339 )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SV1523 ) @ SV827 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SV1523 ) @ SV1229 ) @ SV339 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3921]) ).
thf(4247,plain,
! [SV1233: $i,SV344: $i,SV831: $i,SV1524: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1524 ) @ SV831 ) ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV344 @ SV1524 @ SV1233 ) )
= $true )
| ( ( c_Type_Otyping @ SV344 @ SV831 @ SV1233 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3926]) ).
thf(4248,plain,
! [SV1735: $i,SV1661: $i,SV1525: $i,SV1234: $i,SV832: $i,SV345: $i] :
( ( ( c_ListOrder_Ostep1 @ SV345 @ SV832 @ SV1234 @ SV1525 )
| ( hBOOL @ ( hAPP @ ( hAPP @ SV345 @ SV1661 ) @ SV1735 ) )
| ~ ( c_ListOrder_Ostep1 @ SV345 @ ( c_List_Olist_OCons @ SV1661 @ SV832 @ SV1525 ) @ ( c_List_Olist_OCons @ SV1735 @ SV1234 @ SV1525 ) @ SV1525 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3927]) ).
thf(4249,plain,
! [SV1662: $i,SV1526: $i,SV1235: $i,SV833: $i,SV346: $i] :
( ( ( c_ListOrder_Ostep1 @ SV346 @ ( c_List_Olist_OCons @ SV833 @ SV1235 @ SV1526 ) @ ( c_List_Olist_OCons @ SV833 @ SV1662 @ SV1526 ) @ SV1526 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV346 @ SV1235 @ SV1662 @ SV1526 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3928]) ).
thf(4250,plain,
! [SV356: $i,SV1243: $i,SV841: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV841 @ SV1243 @ SV356 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1243 @ SV841 @ SV356 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV356 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3931]) ).
thf(4251,plain,
! [SV1663: $i,SV1532: $i,SV1244: $i,SV842: $i,SV357: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV357 @ SV842 ) @ SV1244 ) @ SV1532 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV357 @ SV842 ) @ SV1663 ) @ SV1532 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV357 @ SV1244 ) @ SV1663 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3932]) ).
thf(4252,plain,
! [SV1664: $i,SV1533: $i,SV1245: $i,SV843: $i,SV358: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV358 @ SV843 ) @ SV1245 ) @ SV1533 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV1664 ) @ SV1533 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV358 @ SV843 ) @ SV1245 ) @ SV1664 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3933]) ).
thf(4253,plain,
! [SV359: $i,SV1246: $i,SV844: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV844 @ SV1246 @ SV359 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1246 @ SV844 @ SV359 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV359 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3934]) ).
thf(4254,plain,
! [SV1247: $i,SV1534: $i,SV845: $i,SV360: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV360 @ SV845 ) @ SV1534 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV360 @ SV1534 @ SV1247 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV360 @ SV845 @ SV1247 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3935]) ).
thf(4255,plain,
! [SV361: $i,SV1248: $i,SV846: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV846 @ SV1248 @ SV361 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1248 @ SV846 @ SV361 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV361 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3936]) ).
thf(4256,plain,
! [SV1249: $i,SV1535: $i,SV847: $i,SV362: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV362 @ SV847 ) @ SV1535 ) ) )
= $true )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV362 @ SV1535 @ SV1249 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV362 @ SV847 @ SV1249 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3937]) ).
thf(4257,plain,
! [SV363: $i,SV1250: $i,SV848: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV848 @ SV1250 @ SV363 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1250 @ SV848 @ SV363 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV363 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3938]) ).
thf(4258,plain,
! [SV1736: $i,SV1665: $i,SV1536: $i,SV1252: $i,SV850: $i,SV371: $i] :
( ( ! [SY4930: $i] :
( ( ( hAPP @ ( hAPP @ SV371 @ SV850 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV1252 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1536 @ SV1665 @ SV371 @ SV1736 @ SV1252 @ SY4930 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3939]) ).
thf(4259,plain,
! [SV1737: $i,SV1666: $i,SV1537: $i,SV1254: $i,SV854: $i,SV375: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV375 @ ( c_Lambda_OdB_OdB__case @ SV854 @ SV1254 @ SV1537 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1666 ) @ SV1737 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV375 @ ( hAPP @ ( hAPP @ SV1254 @ SV1666 ) @ SV1737 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3941]) ).
thf(4260,plain,
! [SV1738: $i,SV1667: $i,SV1538: $i,SV1255: $i,SV855: $i,SV376: $i] :
( ( ~ ( hBOOL @ ( hAPP @ SV376 @ ( c_Lambda_OdB_OdB__case @ SV855 @ SV1255 @ SV1538 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1667 ) @ SV1738 ) @ t_a ) ) )
| ( hBOOL @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SV1255 @ SV1667 ) @ SV1738 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3942]) ).
thf(4261,plain,
! [SV1739: $i,SV1668: $i,SV1539: $i,SV1257: $i,SV857: $i,SV378: $i] :
( ( ( c_Lambda_OdB_OdB__case @ SV378 @ SV857 @ SV1257 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1539 ) @ SV1668 ) @ SV1739 )
= ( hAPP @ ( hAPP @ SV857 @ SV1539 ) @ SV1668 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3943]) ).
thf(4262,plain,
! [SV1740: $i,SV1669: $i,SV1540: $i,SV1258: $i,SV858: $i,SV379: $i] :
( ( ( c_Lambda_OdB_OdB__rec @ SV379 @ SV858 @ SV1258 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1540 ) @ SV1669 ) @ SV1740 )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ SV858 @ SV1540 ) @ SV1669 ) @ ( c_Lambda_OdB_OdB__rec @ SV379 @ SV858 @ SV1258 @ SV1540 @ SV1740 ) ) @ ( c_Lambda_OdB_OdB__rec @ SV379 @ SV858 @ SV1258 @ SV1669 @ SV1740 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3944]) ).
thf(4263,plain,
! [SV1264: $i,SV385: $i,SV864: $i] :
( ( ( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV864 @ tc_Lambda_OdB ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV385 ) ) @ SV864 ) @ SV1264 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $true )
| ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV385 ) @ SV864 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1264 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3947]) ).
thf(4264,plain,
! [SV1670: $i,SV1543: $i,SV1267: $i,SV867: $i,SV391: $i] :
( ( ( ( c_List_Ofoldl @ SV391 @ ( hAPP @ ( hAPP @ SV391 @ SV867 ) @ SV1267 ) @ SV1543 @ SV1670 @ SV1670 )
= ( hAPP @ ( hAPP @ SV391 @ SV867 ) @ ( c_List_Ofoldl @ SV391 @ SV1267 @ SV1543 @ SV1670 @ SV1670 ) ) )
= $true )
| ( ( ~ ( c_OrderedGroup_Osemigroup__add @ SV391 @ SV1670 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3950]) ).
thf(4265,plain,
! [SV1545: $i,SV1269: $i,SV869: $i,SV393: $i] :
( ( ( class_OrderedGroup_Osemigroup__add @ SV393 )
= $false )
| ( ( ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV393 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV393 ) @ SV869 ) @ SV1269 ) @ SV1545 @ SV393 @ SV393 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV393 ) @ SV869 ) @ ( c_List_Ofoldl @ ( c_HOL_Oplus__class_Oplus @ SV393 ) @ SV1269 @ SV1545 @ SV393 @ SV393 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3951]) ).
thf(4266,plain,
! [SV1671: $i,SV1546: $i,SV1270: $i,SV870: $i,SV394: $i] :
( ( ( ( hAPP @ ( hAPP @ SV394 @ SV870 ) @ ( c_List_Ofoldl @ SV394 @ SV1270 @ SV1546 @ SV1671 @ SV1671 ) )
= ( c_List_Ofoldl @ SV394 @ SV870 @ SV1546 @ SV1671 @ SV1671 ) )
= $true )
| ( ( ~ ( c_OrderedGroup_Omonoid__add @ SV1270 @ SV394 @ SV1671 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3952]) ).
thf(4267,plain,
! [SV1741: $i,SV1672: $i,SV1547: $i,SV1271: $i,SV871: $i,SV395: $i] :
( ( ( c_List_Ofoldl @ SV395 @ SV871 @ ( c_List_Olist_OCons @ SV1271 @ SV1547 @ SV1672 ) @ SV1741 @ SV1672 )
= ( c_List_Ofoldl @ SV395 @ ( hAPP @ ( hAPP @ SV395 @ SV871 ) @ SV1271 ) @ SV1547 @ SV1741 @ SV1672 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3953]) ).
thf(4268,plain,
! [SV1742: $i,SV1673: $i,SV1548: $i,SV1272: $i,SV872: $i,SV396: $i] :
( ( ( c_List_Ofoldl @ SV396 @ SV872 @ ( c_List_Oappend @ SV1272 @ SV1548 @ SV1673 ) @ SV1742 @ SV1673 )
= ( c_List_Ofoldl @ SV396 @ ( c_List_Ofoldl @ SV396 @ SV872 @ SV1272 @ SV1742 @ SV1673 ) @ SV1548 @ SV1742 @ SV1673 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3954]) ).
thf(4269,plain,
! [SV1274: $i,SV875: $i,SV1550: $i,SV399: $i] :
( ( ( c_Type_Otyping @ SV399 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1550 ) @ SV875 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1274 )
= $false )
| ( ( c_Type_Otypings @ SV399 @ SV875 @ ( c_Type_Osko__Type__Xvar__app__typesE__1__1 @ SV1274 @ SV399 @ SV1550 @ SV875 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3956]) ).
thf(4270,plain,
! [SV1743: $i,SV1674: $i,SV1551: $i,SV1275: $i,SV877: $i,SV401: $i] :
( ( ! [SY4931: $i] :
( ( c_Type_Otypings @ SV401 @ SV877 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV1275 @ SV1551 @ SV401 @ SV877 ) )
| ~ ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1674 ) @ SV1743 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1551 )
| ~ ( c_Type_Otypings @ SV401 @ SV1743 @ SY4931 )
| ~ ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1674 ) @ SV1743 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV877 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3958]) ).
thf(4271,plain,
! [SV1277: $i,SV879: $i,SV1552: $i,SV404: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV404 ) @ SV1552 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV404 ) @ SV879 ) @ SV1277 ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1552 ) @ SV879 ) @ SV1277 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3961]) ).
thf(4272,plain,
! [SV1675: $i,SV1553: $i,SV1279: $i,SV881: $i,SV407: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV407 @ ( c_Lambda_OdB_OdB__case @ SV881 @ SV1279 @ SV1553 @ ( c_Lambda_OdB_OVar @ SV1675 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV407 @ ( hAPP @ SV881 @ SV1675 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3963]) ).
thf(4273,plain,
! [SV1676: $i,SV1554: $i,SV1280: $i,SV882: $i,SV408: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV408 @ ( c_Lambda_OdB_OdB__case @ SV882 @ SV1280 @ SV1554 @ ( c_Lambda_OdB_OVar @ SV1676 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV408 @ ( hAPP @ SV882 @ SV1676 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3964]) ).
thf(4274,plain,
! [SV891: $i,SV418: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV418 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV418 )
| ~ ( class_Power_Opower @ SV418 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV418 ) @ SV891 @ SV418 )
= ( c_HOL_Ozero__class_Ozero @ SV418 ) )
| ( SV891
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV418 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3969]) ).
thf(4275,plain,
! [SV892: $i,SV419: $i] :
( ( ( class_Power_Opower @ SV419 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV419 ) @ SV892 @ SV419 )
= ( c_HOL_Ozero__class_Ozero @ SV419 ) )
| ( SV892
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV419 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3970]) ).
thf(4276,plain,
! [SV1679: $i,SV1557: $i,SV1289: $i,SV900: $i,SV430: $i] :
( ( ( SV430 = SV900 )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV1289 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1557 ) @ SV1679 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV900 )
| ~ ( c_Type_Otyping @ SV1289 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1557 ) @ SV1679 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV430 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3975]) ).
thf(4277,plain,
! [SV1290: $i,SV433: $i,SV902: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV902 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV433 ) @ SV902 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1290 @ 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 @ SV433 ) ) @ SV902 ) @ SV1290 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3976]) ).
thf(4278,plain,
! [SV1680: $i,SV1559: $i,SV1294: $i,SV911: $i,SV443: $i] :
( ( ( ( c_List_Olist_OCons @ SV443 @ SV911 @ SV1294 )
!= ( c_List_Olist_OCons @ SV1559 @ SV1680 @ SV1294 ) )
= $true )
| ( ( SV443 = SV1559 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3979]) ).
thf(4279,plain,
! [SV1681: $i,SV1560: $i,SV1295: $i,SV912: $i,SV444: $i] :
( ( ( ~ ( class_OrderedGroup_Oab__group__add @ SV444 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV912 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV1295 ) @ SV1560 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV1295 ) @ SV1681 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV912 ) @ SV1560 )
= SV1681 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3980]) ).
thf(4280,plain,
! [SV1561: $i,SV1297: $i,SV914: $i,SV446: $i] :
( ( ( class_Ring__and__Field_Oidom @ SV446 )
= $false )
| ( ( ~ ( class_Int_Onumber__ring @ SV446 )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV446 ) @ SV914 ) @ SV1297 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV446 ) @ SV914 ) @ SV1561 ) )
| ( SV1297 = SV1561 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3981]) ).
thf(4281,plain,
! [SV1562: $i,SV1298: $i,SV915: $i,SV447: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV447 ) @ SV915 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1298 ) @ SV1562 ) )
= $false )
| ( ( SV447 = SV1298 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3982]) ).
thf(4282,plain,
! [SV449: $i,SV1300: $i,SV917: $i] :
( ( ( ( c_Orderings_Oord__class_Omax @ SV917 @ SV1300 @ SV449 )
!= SV1300 )
= $true )
| ( ( c_lessequals @ SV917 @ SV1300 @ SV449 )
= $true )
| ( ( class_Orderings_Olinorder @ SV449 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3983]) ).
thf(4283,plain,
! [SV1682: $i,SV1563: $i,SV1301: $i,SV918: $i,SV450: $i] :
( ( ( ( c_List_Oappend @ SV450 @ ( c_List_Olist_OCons @ SV918 @ ( c_List_Olist_ONil @ SV1301 ) @ SV1301 ) @ SV1301 )
!= ( c_List_Oappend @ SV1563 @ ( c_List_Olist_OCons @ SV1682 @ ( c_List_Olist_ONil @ SV1301 ) @ SV1301 ) @ SV1301 ) )
= $true )
| ( ( SV450 = SV1563 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3984]) ).
thf(4284,plain,
! [SV919: $i,SV451: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV451 ) @ SV919 ) @ SV919 )
= ( c_HOL_Ozero__class_Ozero @ SV451 ) )
= $false )
| ( ( SV919
= ( c_HOL_Ozero__class_Ozero @ SV451 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__add @ SV451 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3985]) ).
thf(4285,plain,
! [SV1564: $i,SV1304: $i,SV924: $i,SV456: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV456 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV924 @ SV1304 @ SV456 )
!= ( c_Power_Opower__class_Opower @ SV1564 @ SV1304 @ SV456 ) )
| ( SV924 = SV1564 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1304 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV1564 @ SV456 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV924 @ SV456 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3987]) ).
thf(4286,plain,
! [SV1683: $i,SV1565: $i,SV1305: $i,SV925: $i,SV457: $i] :
( ( ( ( c_List_Oreplicate @ SV457 @ SV925 @ SV1305 )
!= ( c_List_Oreplicate @ SV1565 @ SV1683 @ SV1305 ) )
= $true )
| ( ( SV457 = SV1565 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3988]) ).
thf(4287,plain,
! [SV1307: $i,SV927: $i,SV459: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV459 ) @ SV927 ) @ SV1307 )
!= ( c_HOL_Ozero__class_Ozero @ SV459 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV459 ) @ SV1307 @ SV459 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV459 ) @ SV927 @ SV459 )
| ( SV1307
= ( c_HOL_Ozero__class_Ozero @ SV459 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV459 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3990]) ).
thf(4288,plain,
! [SV1566: $i,SV1308: $i,SV928: $i,SV460: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV460 ) @ SV928 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1308 ) @ SV1566 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV928 = SV1566 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3991]) ).
thf(4289,plain,
! [SV1684: $i,SV1567: $i,SV1311: $i,SV932: $i,SV464: $i] :
( ( ( ( c_List_Olist_OCons @ SV464 @ SV932 @ SV1311 )
!= ( c_List_Olist_OCons @ SV1567 @ SV1684 @ SV1311 ) )
= $true )
| ( ( SV932 = SV1684 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3994]) ).
thf(4290,plain,
! [SV1685: $i,SV1568: $i,SV1312: $i,SV933: $i,SV465: $i] :
( ( ( ( c_List_Oreplicate @ SV465 @ SV933 @ SV1312 )
!= ( c_List_Oreplicate @ SV1568 @ SV1685 @ SV1312 ) )
= $true )
| ( ( ( SV933 = SV1685 )
| ( SV465
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3995]) ).
thf(4291,plain,
! [SV1314: $i,SV935: $i,SV467: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV467 ) )
= $true )
| ( ( ( SV935
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV467 ) @ SV935 ) @ SV1314 ) )
| ( SV1314
= ( c_HOL_Ozero__class_Ozero @ SV467 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV467 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3996]) ).
thf(4292,plain,
! [SV1569: $i,SV1315: $i,SV936: $i,SV468: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV468 ) @ SV936 )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1315 ) @ SV1569 ) )
= $false )
| ( ( SV936 = SV1569 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3997]) ).
thf(4293,plain,
! [SV1318: $i,SV939: $i,SV471: $i] :
( ( ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ SV471 ) )
= $true )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV471 )
| ~ ( class_Power_Opower @ SV471 )
| ( ( c_Power_Opower__class_Opower @ SV939 @ SV1318 @ SV471 )
!= ( c_HOL_Ozero__class_Ozero @ SV471 ) )
| ( SV939
= ( c_HOL_Ozero__class_Ozero @ SV471 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4000]) ).
thf(4294,plain,
! [SV1571: $i,SV1320: $i,SV942: $i,SV474: $i] :
( ( ( ( c_List_Oappend @ SV474 @ SV942 @ SV1320 )
= ( c_List_Oappend @ SV474 @ SV1571 @ SV1320 ) )
= $false )
| ( ( SV942 = SV1571 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4002]) ).
thf(4295,plain,
! [SV1572: $i,SV1322: $i,SV944: $i,SV476: $i] :
( ( ( ( c_List_Olist_ONil @ SV476 )
= ( c_List_Omap @ SV944 @ SV1322 @ SV1572 @ SV476 ) )
= $false )
| ( ( SV1322
= ( c_List_Olist_ONil @ SV1572 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4004]) ).
thf(4296,plain,
! [SV1323: $i,SV477: $i,SV945: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV945 @ SV477 )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1323 @ SV477 ) )
= $true )
| ( ( SV945 = SV1323 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV477 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4005]) ).
thf(4297,plain,
! [SV484: $i,SV1329: $i,SV951: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV951 @ SV1329 @ SV484 )
!= ( c_HOL_Ozero__class_Ozero @ SV484 ) )
= $true )
| ( ( SV951
= ( c_HOL_Ozero__class_Ozero @ SV484 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV484 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4010]) ).
thf(4298,plain,
! [SV1573: $i,SV1330: $i,SV952: $i,SV485: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV485 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV952 ) @ SV1330 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV1573 ) @ SV1330 ) )
| ( SV952 = SV1573 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4011]) ).
thf(4299,plain,
! [SV954: $i,SV487: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV487 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV487 )
| ~ ( class_Power_Opower @ SV487 )
| ( ( c_Power_Opower__class_Opower @ SV954 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV487 )
!= ( c_HOL_Ozero__class_Ozero @ SV487 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV487 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4012]) ).
thf(4300,plain,
! [SV1332: $i,SV956: $i,SV489: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV489 ) @ SV956 ) @ SV1332 )
!= ( c_HOL_Ozero__class_Ozero @ SV489 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV1332 @ SV489 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV956 @ SV489 )
| ( SV956
= ( c_HOL_Ozero__class_Ozero @ SV489 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV489 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4014]) ).
thf(4301,plain,
! [SV1574: $i,SV1335: $i,SV959: $i,SV492: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV492 ) @ SV959 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1335 ) @ SV1574 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1335 @ SV959 @ tc_nat )
| ( c_HOL_Oord__class_Oless @ SV492 @ SV1574 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4017]) ).
thf(4302,plain,
! [SV1575: $i,SV1336: $i,SV960: $i,SV493: $i] :
( ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV493 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV960 ) @ SV1336 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV960 ) @ SV1575 ) )
| ( SV1336 = SV1575 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4018]) ).
thf(4303,plain,
! [SV1576: $i,SV1337: $i,SV961: $i,SV494: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV494 ) @ SV961 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1337 ) @ SV1576 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV494 = SV1337 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4019]) ).
thf(4304,plain,
! [SV1577: $i,SV1339: $i,SV963: $i,SV496: $i] :
( ( ( class_Ring__and__Field_Oordered__semidom @ SV496 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV963 @ SV1339 @ SV496 )
!= ( c_Power_Opower__class_Opower @ SV963 @ SV1577 @ SV496 ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV496 ) @ SV963 @ SV496 )
| ( SV1339 = SV1577 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4020]) ).
thf(4305,plain,
! [SV1578: $i,SV1340: $i,SV964: $i,SV497: $i] :
( ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV497 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV964 ) @ SV1340 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV964 ) @ SV1578 ) )
| ( SV1340 = SV1578 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4021]) ).
thf(4306,plain,
! [SV1686: $i,SV1580: $i,SV1344: $i,SV968: $i,SV501: $i] :
( ( ( ( c_List_Oappend @ SV501 @ ( c_List_Olist_OCons @ SV968 @ ( c_List_Olist_ONil @ SV1344 ) @ SV1344 ) @ SV1344 )
!= ( c_List_Oappend @ SV1580 @ ( c_List_Olist_OCons @ SV1686 @ ( c_List_Olist_ONil @ SV1344 ) @ SV1344 ) @ SV1344 ) )
= $true )
| ( ( SV968 = SV1686 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4024]) ).
thf(4307,plain,
! [SV1581: $i,SV1346: $i,SV970: $i,SV503: $i] :
( ( ( ( c_List_Omap @ SV503 @ SV970 @ SV1346 @ SV1581 )
= ( c_List_Olist_ONil @ SV1581 ) )
= $false )
| ( ( SV970
= ( c_List_Olist_ONil @ SV1346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4026]) ).
thf(4308,plain,
! [SV1582: $i,SV1347: $i,SV971: $i,SV504: $i] :
( ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV504 ) @ SV971 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1347 @ SV1582 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( ( SV504
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1347 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV504 @ SV971 @ SV1347 @ SV1582 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( SV1582
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4027]) ).
thf(4309,plain,
! [SV1583: $i,SV1348: $i,SV972: $i,SV505: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV505 ) @ SV972 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV1348 ) @ SV1583 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV972 = SV1583 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4028]) ).
thf(4310,plain,
! [SV1584: $i,SV1354: $i,SV980: $i,SV514: $i] :
( ( ( ( c_List_Oappend @ SV514 @ SV980 @ SV1354 )
= ( c_List_Oappend @ SV1584 @ SV980 @ SV1354 ) )
= $false )
| ( ( SV514 = SV1584 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4033]) ).
thf(4311,plain,
! [SV1585: $i,SV1356: $i,SV982: $i,SV516: $i] :
( ( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV516 ) @ SV982 @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1356 ) @ SV1585 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false )
| ( ( SV516 = SV1356 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4035]) ).
thf(4312,plain,
! [SV1358: $i,SV3: $i,SV984: $i,SV520: $i] :
( ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV520 @ SV984 @ SV3 ) @ ( c_Power_Opower__class_Opower @ SV1358 @ SV984 @ SV3 ) @ SV3 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV520 @ SV3 )
| ~ ( c_lessequals @ SV520 @ SV1358 @ SV3 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4036]) ).
thf(4313,plain,
! [SV985: $i,SV521: $i,SV4: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV4 ) @ SV521 @ SV4 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV4 ) @ ( c_Power_Opower__class_Opower @ SV521 @ SV985 @ SV4 ) @ SV4 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4037]) ).
thf(4314,plain,
! [SV1687: $i,SV1586: $i,SV1359: $i,SV986: $i,SV524: $i,SV7: $i] :
( ( ( ~ ( c_Type_Otyping @ SV7 @ SV524 @ SV986 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV7 @ SV1359 @ SV986 @ tc_Type_Otype ) @ SV1586 @ SV1687 )
| ( c_Type_Otyping @ SV7 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1586 ) @ SV524 ) @ SV1359 ) @ SV1687 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4038]) ).
thf(4315,plain,
! [SV987: $i,SV525: $i,SV1587: $i,SV1360: $i,SV8: $i] :
( ( ( c_Type_Otyping @ SV8 @ SV1360 @ SV1587 )
= $false )
| ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV8 @ SV525 @ SV987 @ tc_Type_Otype ) @ ( hAPP @ ( hAPP @ c_Lambda_Olift @ SV1360 ) @ SV525 ) @ SV1587 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4039]) ).
thf(4316,plain,
! [SV1361: $i,SV9: $i,SV988: $i,SV526: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV526 @ SV988 @ SV9 ) @ ( c_Power_Opower__class_Opower @ SV526 @ SV1361 @ SV9 ) @ SV9 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV526 @ ( c_HOL_Oone__class_Oone @ SV9 ) @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV526 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV1361 @ SV988 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4040]) ).
thf(4317,plain,
! [SV527: $i,SV10: $i,SV989: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV989 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV10 ) @ SV527 @ SV10 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV10 ) @ ( c_Power_Opower__class_Opower @ SV527 @ SV989 @ SV10 ) @ SV10 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4041]) ).
thf(4318,plain,
! [SV1588: $i,SV1364: $i,SV992: $i,SV532: $i,SV15: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV15 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SV532 ) @ SV992 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SV1364 ) @ SV1588 ) @ SV15 )
| ~ ( c_HOL_Oord__class_Oless @ SV992 @ SV1588 @ SV15 )
| ~ ( c_lessequals @ SV532 @ SV1364 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4044]) ).
thf(4319,plain,
! [SV1589: $i,SV1365: $i,SV993: $i,SV533: $i,SV16: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV16 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SV533 ) @ SV993 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SV1365 ) @ SV1589 ) @ SV16 )
| ~ ( c_lessequals @ SV993 @ SV1589 @ SV16 )
| ~ ( c_HOL_Oord__class_Oless @ SV533 @ SV1365 @ SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4045]) ).
thf(4320,plain,
! [SV534: $i,SV17: $i,SV994: $i] :
( ( ( ~ ( c_lessequals @ SV994 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV534 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV17 ) @ SV534 ) @ SV994 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV17 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4046]) ).
thf(4321,plain,
! [SV1366: $i,SV995: $i,SV537: $i,SV20: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV20 ) )
= $true )
| ( ( ( c_lessequals @ SV537 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV20 ) @ SV995 ) @ SV1366 ) @ SV20 )
| ~ ( c_lessequals @ SV537 @ SV995 @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV1366 @ SV20 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4049]) ).
thf(4322,plain,
! [SV1367: $i,SV996: $i,SV538: $i,SV21: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV21 ) )
= $true )
| ( ( ( c_lessequals @ SV538 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SV996 ) @ SV1367 ) @ SV21 )
| ~ ( c_lessequals @ SV538 @ SV1367 @ SV21 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ SV996 @ SV21 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4050]) ).
thf(4323,plain,
! [SV24: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ SV24 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV24 ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) )
= ( c_HOL_Ozero__class_Ozero @ SV24 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ ( c_HOL_Ozero__class_Ozero @ SV24 ) @ SV24 )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4053]) ).
thf(4324,plain,
! [SV541: $i,SV997: $i,SV25: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV997 @ SV25 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV541 @ SV25 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SV541 ) @ SV997 ) @ SV25 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4054]) ).
thf(4325,plain,
! [SV29: $i,SV999: $i,SV543: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV543 @ SV999 @ SV29 )
= $true )
| ( ( ~ ( c_lessequals @ SV543 @ SV999 @ SV29 ) )
= $true )
| ( ( SV543 = SV999 )
= $true )
| ( ( class_Orderings_Olinorder @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4056]) ).
thf(4326,plain,
! [SV30: $i,SV1000: $i,SV544: $i] :
( ( ( ~ ( c_lessequals @ SV544 @ SV1000 @ SV30 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV544 @ SV1000 @ SV30 )
= $true )
| ( ( SV544 = SV1000 )
= $true )
| ( ( class_Orderings_Olinorder @ SV30 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4057]) ).
thf(4327,plain,
! [SV31: $i,SV1001: $i,SV545: $i] :
( ( ( ~ ( c_lessequals @ SV545 @ SV1001 @ SV31 ) )
= $true )
| ( ( SV545 = SV1001 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV545 @ SV1001 @ SV31 )
= $true )
| ( ( class_Orderings_Oorder @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4058]) ).
thf(4328,plain,
! [SV32: $i,SV1002: $i,SV546: $i] :
( ( ( SV546 = SV1002 )
= $true )
| ( ( ~ ( c_lessequals @ SV546 @ SV1002 @ SV32 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV546 @ SV1002 @ SV32 )
= $true )
| ( ( class_Orderings_Oorder @ SV32 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4059]) ).
thf(4329,plain,
! [SV33: $i,SV1003: $i,SV547: $i] :
( ( ( SV547 = SV1003 )
= $true )
| ( ( ~ ( c_lessequals @ SV547 @ SV1003 @ SV33 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV547 @ SV1003 @ SV33 )
= $true )
| ( ( class_Orderings_Oorder @ SV33 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4060]) ).
thf(4330,plain,
! [SV34: $i,SV1004: $i,SV548: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV548 @ SV1004 @ SV34 )
= $true )
| ( ( ~ ( c_lessequals @ SV548 @ SV1004 @ SV34 ) )
= $true )
| ( ( SV548 = SV1004 )
= $true )
| ( ( class_Orderings_Oorder @ SV34 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4061]) ).
thf(4331,plain,
! [SV35: $i,SV1005: $i,SV549: $i] :
( ( ( ~ ( c_lessequals @ SV549 @ SV1005 @ SV35 ) )
= $true )
| ( ( SV1005 = SV549 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV549 @ SV1005 @ SV35 )
= $true )
| ( ( class_Orderings_Oorder @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4062]) ).
thf(4332,plain,
! [SV36: $i,SV550: $i,SV1006: $i] :
( ( ( SV1006 = SV550 )
= $true )
| ( ( ~ ( c_lessequals @ SV550 @ SV1006 @ SV36 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV550 @ SV1006 @ SV36 )
= $true )
| ( ( class_Orderings_Oorder @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4063]) ).
thf(4333,plain,
! [SV1590: $i,SV1368: $i,SV1007: $i,SV551: $i,SV37: $i] :
( ( ( class_OrderedGroup_Opordered__ab__group__add @ SV37 )
= $false )
| ( ( ( c_lessequals @ SV551 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV1007 ) @ SV1368 ) @ SV37 )
| ~ ( c_lessequals @ SV1590 @ SV1368 @ SV37 )
| ~ ( c_lessequals @ SV551 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV1007 ) @ SV1590 ) @ SV37 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4064]) ).
thf(4334,plain,
! [SV1369: $i,SV38: $i,SV1008: $i,SV552: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV552 @ SV1008 @ SV38 )
= $true )
| ( ( ~ ( c_lessequals @ SV1369 @ SV1008 @ SV38 )
| ~ ( c_HOL_Oord__class_Oless @ SV552 @ SV1369 @ SV38 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4065]) ).
thf(4335,plain,
! [SV1370: $i,SV39: $i,SV1009: $i,SV553: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV553 @ SV1009 @ SV39 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1370 @ SV1009 @ SV39 )
| ~ ( c_lessequals @ SV553 @ SV1370 @ SV39 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4066]) ).
thf(4336,plain,
! [SV1371: $i,SV42: $i,SV1010: $i,SV556: $i] :
( ( ( c_lessequals @ SV556 @ SV1010 @ SV42 )
= $true )
| ( ( ~ ( c_lessequals @ SV1371 @ SV1010 @ SV42 )
| ~ ( c_lessequals @ SV556 @ SV1371 @ SV42 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4067]) ).
thf(4337,plain,
! [SV1372: $i,SV43: $i,SV1011: $i,SV557: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV557 @ SV1011 @ SV43 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV557 @ SV1372 @ SV43 )
| ~ ( c_lessequals @ SV1372 @ SV1011 @ SV43 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4068]) ).
thf(4338,plain,
! [SV1373: $i,SV44: $i,SV1012: $i,SV558: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV558 @ SV1012 @ SV44 )
= $true )
| ( ( ~ ( c_lessequals @ SV558 @ SV1373 @ SV44 )
| ~ ( c_HOL_Oord__class_Oless @ SV1373 @ SV1012 @ SV44 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4069]) ).
thf(4339,plain,
! [SV1374: $i,SV45: $i,SV1013: $i,SV559: $i] :
( ( ( c_lessequals @ SV559 @ SV1013 @ SV45 )
= $true )
| ( ( ~ ( c_lessequals @ SV559 @ SV1374 @ SV45 )
| ~ ( c_lessequals @ SV1374 @ SV1013 @ SV45 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4070]) ).
thf(4340,plain,
! [SV1375: $i,SV1014: $i,SV46: $i,SV560: $i,SV1591: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1591 @ SV560 @ tc_nat )
= $false )
| ( ( ( hAPP @ ( c_Type_Oshift @ SV46 @ SV560 @ SV1014 @ SV1375 ) @ SV1591 )
= ( hAPP @ SV46 @ SV1591 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4071]) ).
thf(4341,plain,
! [SV1376: $i,SV1015: $i,SV561: $i,SV47: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ SV561 ) @ SV1015 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ SV561 ) @ SV1376 ) @ SV47 )
= $true )
| ( ( ~ ( c_lessequals @ SV1015 @ SV1376 @ SV47 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4072]) ).
thf(4342,plain,
! [SV1377: $i,SV1016: $i,SV562: $i,SV48: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV48 ) @ SV562 ) @ SV1016 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV48 ) @ SV1377 ) @ SV1016 ) @ SV48 )
= $true )
| ( ( ~ ( c_lessequals @ SV562 @ SV1377 @ SV48 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4073]) ).
thf(4343,plain,
! [SV1378: $i,SV49: $i,SV1017: $i,SV563: $i] :
( ( ( c_lessequals @ SV563 @ SV1017 @ SV49 )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SV1378 ) @ SV563 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SV1378 ) @ SV1017 ) @ SV49 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4074]) ).
thf(4344,plain,
! [SV1379: $i,SV1018: $i,SV564: $i,SV50: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV564 ) @ SV1018 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV564 ) @ SV1379 ) @ SV50 )
= $true )
| ( ( ~ ( c_lessequals @ SV1018 @ SV1379 @ SV50 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4075]) ).
thf(4345,plain,
! [SV1380: $i,SV51: $i,SV1019: $i,SV565: $i] :
( ( ( c_lessequals @ SV565 @ SV1019 @ SV51 )
= $true )
| ( ( ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV51 ) @ SV565 ) @ SV1380 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV51 ) @ SV1019 ) @ SV1380 ) @ SV51 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4076]) ).
thf(4346,plain,
! [SV1381: $i,SV1020: $i,SV566: $i,SV52: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV566 ) @ SV1020 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV1381 ) @ SV1020 ) @ SV52 )
= $true )
| ( ( ~ ( c_lessequals @ SV566 @ SV1381 @ SV52 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4077]) ).
thf(4347,plain,
! [SV53: $i,SV1021: $i,SV567: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV567 @ SV1021 @ SV53 )
= $false )
| ( ( c_lessequals @ SV567 @ SV1021 @ SV53 )
= $true )
| ( ( class_Orderings_Opreorder @ SV53 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4078]) ).
thf(4348,plain,
! [SV54: $i,SV1022: $i,SV568: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV568 @ SV1022 @ SV54 )
= $false )
| ( ( c_lessequals @ SV568 @ SV1022 @ SV54 )
= $true )
| ( ( class_Orderings_Oorder @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4079]) ).
thf(4349,plain,
! [SV55: $i,SV1023: $i,SV569: $i] :
( ( ( ~ ( c_lessequals @ SV569 @ SV1023 @ SV55 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1023 @ SV569 @ SV55 ) )
= $true )
| ( ( SV569 = SV1023 )
= $true )
| ( ( class_Orderings_Oorder @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4080]) ).
thf(4350,plain,
! [SV56: $i,SV570: $i,SV1024: $i] :
( ( ( ~ ( c_lessequals @ SV1024 @ SV570 @ SV56 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV570 @ SV1024 @ SV56 ) )
= $true )
| ( ( SV570 = SV1024 )
= $true )
| ( ( class_Orderings_Oorder @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4081]) ).
thf(4351,plain,
! [SV57: $i,SV571: $i,SV1025: $i] :
( ( ( ~ ( c_lessequals @ SV1025 @ SV571 @ SV57 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV571 @ SV1025 @ SV57 ) )
= $true )
| ( ( SV571 = SV1025 )
= $true )
| ( ( class_Orderings_Oorder @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4082]) ).
thf(4352,plain,
! [SV1744: $i,SV1688: $i,SV1592: $i,SV1382: $i,SV1026: $i,SV572: $i,SV58: $i] :
( ( ( ( hAPP @ ( hAPP @ SV58 @ SV572 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= SV572 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1026 @ SV1382 @ SV58 @ SV1592 @ SV1688 @ SV1744 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4083]) ).
thf(4353,plain,
! [SV60: $i,SV573: $i,SV1027: $i] :
( ( ( c_lessequals @ SV1027 @ SV573 @ SV60 )
= $true )
| ( ( ~ ( c_lessequals @ SV573 @ SV1027 @ SV60 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV573 @ SV1027 @ SV60 )
= $true )
| ( ( class_Orderings_Opreorder @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4084]) ).
thf(4354,plain,
! [SV1384: $i,SV63: $i,SV1029: $i,SV575: $i] :
( ( ( c_lessequals @ SV575 @ SV1029 @ SV63 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV575 @ SV1384 @ SV63 ) @ SV1029 @ SV63 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4085]) ).
thf(4355,plain,
! [SV1385: $i,SV64: $i,SV1030: $i,SV576: $i] :
( ( ( c_lessequals @ SV576 @ SV1030 @ SV64 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1385 @ SV576 @ SV64 ) @ SV1030 @ SV64 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV64 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4086]) ).
thf(4356,plain,
! [SV65: $i,SV1386: $i,SV1031: $i,SV577: $i] :
( ( ( c_lessequals @ SV577 @ ( c_Orderings_Oord__class_Omax @ SV1031 @ SV1386 @ SV65 ) @ SV65 )
= $true )
| ( ( ~ ( c_lessequals @ SV577 @ SV1031 @ SV65 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV65 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4087]) ).
thf(4357,plain,
! [SV66: $i,SV1387: $i,SV1032: $i,SV578: $i] :
( ( ( c_lessequals @ SV578 @ ( c_Orderings_Oord__class_Omax @ SV1032 @ SV1387 @ SV66 ) @ SV66 )
= $true )
| ( ( ~ ( c_lessequals @ SV578 @ SV1387 @ SV66 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4088]) ).
thf(4358,plain,
! [SV67: $i,SV1388: $i,SV1033: $i,SV579: $i] :
( ( ( c_lessequals @ SV579 @ ( c_Orderings_Oord__class_Omax @ SV1033 @ SV1388 @ SV67 ) @ SV67 )
= $true )
| ( ( ~ ( c_lessequals @ SV579 @ SV1033 @ SV67 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4089]) ).
thf(4359,plain,
! [SV68: $i,SV1389: $i,SV1034: $i,SV580: $i] :
( ( ( c_lessequals @ SV580 @ ( c_Orderings_Oord__class_Omax @ SV1034 @ SV1389 @ SV68 ) @ SV68 )
= $true )
| ( ( ~ ( c_lessequals @ SV580 @ SV1389 @ SV68 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4090]) ).
thf(4360,plain,
! [SV1390: $i,SV69: $i,SV1035: $i,SV581: $i] :
( ( ( c_lessequals @ SV581 @ SV1035 @ SV69 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV581 @ SV1390 @ SV69 ) @ SV1035 @ SV69 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4091]) ).
thf(4361,plain,
! [SV1391: $i,SV70: $i,SV1036: $i,SV582: $i] :
( ( ( c_lessequals @ SV582 @ SV1036 @ SV70 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1391 @ SV582 @ SV70 ) @ SV1036 @ SV70 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4092]) ).
thf(4362,plain,
! [SV1392: $i,SV73: $i,SV1037: $i,SV585: $i] :
( ( ( c_lessequals @ SV585 @ SV1037 @ SV73 )
= $true )
| ( ( ( c_lessequals @ SV585 @ SV1392 @ SV73 )
| ~ ( c_lessequals @ SV585 @ ( c_Orderings_Oord__class_Omax @ SV1392 @ SV1037 @ SV73 ) @ SV73 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4093]) ).
thf(4363,plain,
! [SV1393: $i,SV76: $i,SV1040: $i,SV588: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV588 @ SV1040 @ SV76 ) @ SV1393 @ SV76 )
= $true )
| ( ( ~ ( c_lessequals @ SV1040 @ SV1393 @ SV76 )
| ~ ( c_lessequals @ SV588 @ SV1393 @ SV76 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4094]) ).
thf(4364,plain,
! [SV1394: $i,SV77: $i,SV1041: $i,SV589: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV589 @ SV1041 @ SV77 ) @ SV1394 @ SV77 )
= $true )
| ( ( ~ ( c_lessequals @ SV1041 @ SV1394 @ SV77 )
| ~ ( c_lessequals @ SV589 @ SV1394 @ SV77 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4095]) ).
thf(4365,plain,
! [SV1395: $i,SV78: $i,SV1042: $i,SV590: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV590 @ SV1042 @ SV78 ) @ SV1395 @ SV78 )
= $true )
| ( ( ~ ( c_lessequals @ SV1042 @ SV1395 @ SV78 )
| ~ ( c_lessequals @ SV590 @ SV1395 @ SV78 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4096]) ).
thf(4366,plain,
! [SV1043: $i,SV591: $i,SV79: $i] :
( ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV79 ) @ SV591 @ SV79 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ SV79 ) @ ( c_Power_Opower__class_Opower @ SV591 @ SV1043 @ SV79 ) @ SV79 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4097]) ).
thf(4367,plain,
! [SV1593: $i,SV1396: $i,SV1044: $i,SV592: $i,SV80: $i] :
( ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV80 )
= $false )
| ( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SV592 ) @ SV1044 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SV1396 ) @ SV1593 ) @ SV80 )
| ~ ( c_lessequals @ SV1044 @ SV1593 @ SV80 )
| ~ ( c_lessequals @ SV592 @ SV1396 @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4098]) ).
thf(4368,plain,
! [SV81: $i,SV1045: $i,SV593: $i] :
( ( ( c_lessequals @ SV593 @ SV1045 @ SV81 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omax @ SV593 @ SV1045 @ SV81 )
= SV1045 )
= $true )
| ( ( class_Orderings_Olinorder @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4099]) ).
thf(4369,plain,
! [SV82: $i,SV594: $i,SV1046: $i] :
( ( ( c_lessequals @ SV1046 @ SV594 @ SV82 )
= $false )
| ( ( ( c_Orderings_Oord__class_Omax @ SV594 @ SV1046 @ SV82 )
= SV594 )
= $true )
| ( ( class_Orderings_Olinorder @ SV82 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4100]) ).
thf(4370,plain,
! [SV85: $i,SV597: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV597 @ SV597 @ SV85 )
= $false )
| ( ( c_lessequals @ SV597 @ SV597 @ SV85 )
= $false )
| ( ( class_Orderings_Olinorder @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4102]) ).
thf(4371,plain,
! [SV87: $i,SV1048: $i,SV599: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV599 @ SV1048 @ SV87 )
= $false )
| ( ( ~ ( c_lessequals @ SV1048 @ SV599 @ SV87 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4103]) ).
thf(4372,plain,
! [SV89: $i,SV1050: $i,SV601: $i] :
( ( ( c_lessequals @ SV601 @ SV1050 @ SV89 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1050 @ SV601 @ SV89 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4105]) ).
thf(4373,plain,
! [SV91: $i,SV1052: $i,SV603: $i] :
( ( ( c_lessequals @ SV603 @ SV1052 @ SV91 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1052 @ SV603 @ SV91 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4107]) ).
thf(4374,plain,
! [SV604: $i,SV93: $i,SV1053: $i] :
( ( ( ~ ( c_lessequals @ SV1053 @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV604 @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV604 ) @ SV1053 ) @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV93 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4108]) ).
thf(4375,plain,
! [SV605: $i,SV94: $i,SV1054: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1054 @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV605 @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV605 ) @ SV1054 ) @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4109]) ).
thf(4376,plain,
! [SV1397: $i,SV1055: $i,SV606: $i,SV95: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV95 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV606 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV1055 ) @ SV1397 ) @ SV95 )
| ~ ( c_lessequals @ SV606 @ SV1397 @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV1055 @ SV95 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4110]) ).
thf(4377,plain,
! [SV1398: $i,SV1056: $i,SV607: $i,SV96: $i] :
( ( ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ SV96 ) )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV607 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SV1056 ) @ SV1398 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ SV607 @ SV1398 @ SV96 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV1056 @ SV96 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4111]) ).
thf(4378,plain,
! [SV608: $i,SV1057: $i,SV97: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV1057 @ SV97 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV608 @ SV97 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV608 ) @ SV1057 ) @ SV97 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4112]) ).
thf(4379,plain,
! [SV609: $i,SV1058: $i,SV98: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ SV1058 @ SV98 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ SV609 @ SV98 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV98 ) @ SV609 ) @ SV1058 ) @ SV98 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4113]) ).
thf(4380,plain,
! [SV1399: $i,SV100: $i,SV1059: $i,SV610: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV610 @ SV1059 @ SV100 )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV100 ) @ SV1059 @ SV100 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV610 @ SV1399 @ SV100 ) @ ( c_Power_Opower__class_Opower @ SV1059 @ SV1399 @ SV100 ) @ SV100 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4114]) ).
thf(4381,plain,
! [SV102: $i,SV1400: $i,SV1060: $i,SV611: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV611 @ SV1060 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1400 @ SV611 @ SV102 ) @ ( c_Power_Opower__class_Opower @ SV1400 @ SV1060 @ SV102 ) @ SV102 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV102 ) @ SV1400 @ SV102 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4115]) ).
thf(4382,plain,
! [SV1401: $i,SV103: $i,SV1061: $i,SV612: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV612 @ SV1061 @ SV103 ) @ ( c_Power_Opower__class_Opower @ SV612 @ SV1401 @ SV103 ) @ SV103 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV103 ) @ SV612 @ SV103 )
| ~ ( c_HOL_Oord__class_Oless @ SV1061 @ SV1401 @ tc_nat ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4116]) ).
thf(4383,plain,
! [SV104: $i,SV1402: $i,SV1062: $i,SV613: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV613 @ SV1062 @ tc_nat )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1402 @ SV613 @ SV104 ) @ ( c_Power_Opower__class_Opower @ SV1402 @ SV1062 @ SV104 ) @ SV104 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV104 ) @ SV1402 @ SV104 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV104 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4117]) ).
thf(4384,plain,
! [SV1403: $i,SV105: $i,SV1063: $i,SV614: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV614 @ SV1063 @ SV105 ) @ ( c_Power_Opower__class_Opower @ SV614 @ SV1403 @ SV105 ) @ SV105 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1063 @ SV1403 @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV105 ) @ SV614 @ SV105 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV105 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4118]) ).
thf(4385,plain,
! [SV1404: $i,SV109: $i,SV1066: $i,SV618: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV618 @ SV1066 @ SV109 ) @ ( c_Power_Opower__class_Opower @ SV1404 @ SV1066 @ SV109 ) @ SV109 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1066 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV618 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SV618 @ SV1404 @ SV109 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4119]) ).
thf(4386,plain,
! [SV1068: $i,SV620: $i,SV1594: $i,SV1405: $i,SV111: $i] :
( ( ( c_Type_Otypings @ SV111 @ SV1405 @ SV1594 )
= $false )
| ( ( c_Type_Otypings @ ( c_Type_Oshift @ SV111 @ SV620 @ SV1068 @ tc_Type_Otype ) @ ( c_List_Omap @ ( c_COMBC @ c_Lambda_Olift @ SV620 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1405 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1594 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4120]) ).
thf(4387,plain,
! [SV1689: $i,SV1595: $i,SV1406: $i,SV1069: $i,SV621: $i,SV112: $i] :
( ( ( c_Type_Otypings @ SV112 @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SV621 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV1069 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1406 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1595 )
= $true )
| ( ( ~ ( c_Type_Otypings @ ( c_Type_Oshift @ SV112 @ SV1069 @ SV1689 @ tc_Type_Otype ) @ SV1406 @ SV1595 )
| ~ ( c_Type_Otyping @ SV112 @ SV621 @ SV1689 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4121]) ).
thf(4388,plain,
! [SV631: $i,SV123: $i,SV1077: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1077 @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV631 @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV123 ) @ SV631 ) @ SV1077 ) @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4124]) ).
thf(4389,plain,
! [SV1412: $i,SV125: $i,SV1078: $i,SV632: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV632 @ SV1078 @ SV125 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV1412 @ SV632 @ SV125 ) @ SV1078 @ SV125 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4125]) ).
thf(4390,plain,
! [SV1413: $i,SV126: $i,SV1079: $i,SV633: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV633 @ SV1079 @ SV126 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV633 @ SV1413 @ SV126 ) @ SV1079 @ SV126 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV126 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4126]) ).
thf(4391,plain,
! [SV127: $i,SV1414: $i,SV1080: $i,SV634: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV634 @ ( c_Orderings_Oord__class_Omax @ SV1080 @ SV1414 @ SV127 ) @ SV127 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV634 @ SV1414 @ SV127 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV127 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4127]) ).
thf(4392,plain,
! [SV128: $i,SV1415: $i,SV1081: $i,SV635: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV635 @ ( c_Orderings_Oord__class_Omax @ SV1081 @ SV1415 @ SV128 ) @ SV128 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV635 @ SV1081 @ SV128 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4128]) ).
thf(4393,plain,
! [SV129: $i,SV1416: $i,SV1082: $i,SV636: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV636 @ ( c_Orderings_Oord__class_Omax @ SV1082 @ SV1416 @ SV129 ) @ SV129 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV636 @ SV1416 @ SV129 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV129 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4129]) ).
thf(4394,plain,
! [SV130: $i,SV1417: $i,SV1083: $i,SV637: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV637 @ ( c_Orderings_Oord__class_Omax @ SV1083 @ SV1417 @ SV130 ) @ SV130 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV637 @ SV1083 @ SV130 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV130 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4130]) ).
thf(4395,plain,
! [SV1690: $i,SV1599: $i,SV1418: $i,SV1084: $i,SV638: $i,SV131: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV638 ) @ SV1084 ) )
= $true )
| ( ( ( c_ListOrder_Ostep1 @ SV131 @ SV1418 @ SV1599 @ SV1690 )
| ~ ( c_ListOrder_Ostep1 @ SV131 @ ( c_List_Oappend @ SV1418 @ ( c_List_Olist_OCons @ SV638 @ ( c_List_Olist_ONil @ SV1690 ) @ SV1690 ) @ SV1690 ) @ ( c_List_Oappend @ SV1599 @ ( c_List_Olist_OCons @ SV1084 @ ( c_List_Olist_ONil @ SV1690 ) @ SV1690 ) @ SV1690 ) @ SV1690 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4131]) ).
thf(4396,plain,
! [SV644: $i,SV1090: $i,SV1601: $i,SV1423: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV137 @ SV1423 @ SV1601 ) @ SV1090 ) @ SV644 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV137 @ SV644 ) @ SV1090 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4135]) ).
thf(4397,plain,
! [SV1091: $i,SV645: $i,SV1424: $i,SV1602: $i,SV138: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV138 @ SV1602 ) @ SV1424 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV138 @ SV645 @ SV1091 ) @ SV1424 ) @ SV1602 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4136]) ).
thf(4398,plain,
! [SV646: $i,SV1092: $i,SV1603: $i,SV1425: $i,SV139: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV139 @ SV1425 @ SV1603 ) @ SV1092 ) @ SV646 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV139 @ SV646 ) @ SV1092 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4137]) ).
thf(4399,plain,
! [SV1093: $i,SV647: $i,SV1426: $i,SV1604: $i,SV140: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV140 @ SV1604 ) @ SV1426 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ SV140 @ SV647 @ SV1093 ) @ SV1426 ) @ SV1604 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4138]) ).
thf(4400,plain,
! [SV1436: $i,SV153: $i,SV1105: $i,SV660: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV660 @ SV1105 @ SV153 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV660 @ SV1436 @ SV153 )
| ~ ( c_HOL_Oord__class_Oless @ SV1436 @ SV1105 @ SV153 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4148]) ).
thf(4401,plain,
! [SV1437: $i,SV154: $i,SV1106: $i,SV661: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV661 @ SV1106 @ SV154 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1437 @ SV1106 @ SV154 )
| ~ ( c_HOL_Oord__class_Oless @ SV661 @ SV1437 @ SV154 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4149]) ).
thf(4402,plain,
! [SV1605: $i,SV1438: $i,SV1107: $i,SV662: $i,SV155: $i] :
( ( ( c_ListOrder_Ostep1 @ SV155 @ SV662 @ SV1107 @ SV1438 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV155 @ ( c_List_Oappend @ SV662 @ SV1605 @ SV1438 ) @ ( c_List_Oappend @ SV1107 @ SV1605 @ SV1438 ) @ SV1438 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4150]) ).
thf(4403,plain,
! [SV663: $i,SV1439: $i,SV1606: $i,SV1108: $i,SV156: $i] :
( ( ( c_ListOrder_Ostep1 @ SV156 @ SV1108 @ SV1606 @ SV1439 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV156 @ ( c_List_Oappend @ SV663 @ SV1108 @ SV1439 ) @ ( c_List_Oappend @ SV663 @ SV1606 @ SV1439 ) @ SV1439 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4151]) ).
thf(4404,plain,
! [SV1692: $i,SV1608: $i,SV1443: $i,SV1112: $i,SV668: $i,SV161: $i] :
( ( ( SV161 = SV668 )
= $true )
| ( ( ( SV1112 = SV1443 )
| ~ ( c_ListOrder_Ostep1 @ SV1608 @ ( c_List_Olist_OCons @ SV668 @ SV1443 @ SV1692 ) @ ( c_List_Olist_OCons @ SV161 @ SV1112 @ SV1692 ) @ SV1692 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4154]) ).
thf(4405,plain,
! [SV1609: $i,SV1444: $i,SV1113: $i,SV669: $i,SV162: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV162 @ SV669 ) @ SV1113 ) )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV162 @ ( c_List_Olist_OCons @ SV669 @ SV1444 @ SV1609 ) @ ( c_List_Olist_OCons @ SV1113 @ SV1444 @ SV1609 ) @ SV1609 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4155]) ).
thf(4406,plain,
! [SV1445: $i,SV164: $i,SV1114: $i,SV671: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV671 @ SV1114 @ SV164 ) @ SV1445 @ SV164 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1114 @ SV1445 @ SV164 )
| ~ ( c_HOL_Oord__class_Oless @ SV671 @ SV1445 @ SV164 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV164 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4156]) ).
thf(4407,plain,
! [SV1446: $i,SV674: $i,SV1117: $i,SV167: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SV1117 ) @ SV674 ) @ SV1446 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV167 @ SV1446 @ SV1117 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV167 @ SV674 @ SV1117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4157]) ).
thf(4408,plain,
! [SV675: $i,SV1118: $i,SV1447: $i,SV168: $i] :
( ( ( c_Wellfounded_Oaccp @ SV168 @ SV1447 @ SV1118 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SV1118 ) @ SV675 ) @ SV1447 ) ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV168 @ SV675 @ SV1118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4158]) ).
thf(4409,plain,
! [SV1119: $i,SV1448: $i,SV1610: $i,SV676: $i,SV169: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SV676 ) @ SV1610 ) @ SV1448 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SV676 ) @ SV1119 ) @ SV1610 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SV676 ) @ SV1119 ) @ SV1448 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4159]) ).
thf(4410,plain,
! [SV1694: $i,SV1613: $i,SV1452: $i,SV1131: $i,SV694: $i,SV190: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV190 @ SV694 ) @ SV1131 ) )
= $true )
| ( ( ( SV694 = SV1131 )
| ~ ( c_ListOrder_Ostep1 @ SV190 @ ( c_List_Oappend @ SV1452 @ ( c_List_Olist_OCons @ SV694 @ ( c_List_Olist_ONil @ SV1613 ) @ SV1613 ) @ SV1613 ) @ ( c_List_Oappend @ SV1694 @ ( c_List_Olist_OCons @ SV1131 @ ( c_List_Olist_ONil @ SV1613 ) @ SV1613 ) @ SV1613 ) @ SV1613 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4162]) ).
thf(4411,plain,
! [SV1745: $i,SV1695: $i,SV1614: $i,SV1453: $i,SV1132: $i,SV695: $i,SV191: $i] :
( ( ! [SY4932: $i,SY4933: $i] :
( ( ( hAPP @ ( hAPP @ SV191 @ ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ SV1453 ) ) @ ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ SV1614 ) )
= ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1453 ) @ SV1614 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1695 @ SV191 @ SV695 @ SV1745 @ SY4932 @ SY4933 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4163]) ).
thf(4412,plain,
! [SV1746: $i,SV1696: $i,SV1615: $i,SV1459: $i,SV1141: $i,SV706: $i,SV202: $i] :
( ( ! [SY4934: $i,SY4935: $i] :
( ( ( hAPP @ ( hAPP @ SV202 @ ( hAPP @ ( hAPP @ SV706 @ SV1141 ) @ SV1459 ) ) @ SV1615 )
= ( hAPP @ ( hAPP @ SV706 @ ( hAPP @ ( hAPP @ SV202 @ SV1141 ) @ SV1615 ) ) @ ( hAPP @ ( hAPP @ SV202 @ SV1459 ) @ SV1615 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1696 @ SV706 @ SV202 @ SV1746 @ SY4934 @ SY4935 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4169]) ).
thf(4413,plain,
! [SV1747: $i,SV1697: $i,SV1616: $i,SV1460: $i,SV1142: $i,SV707: $i,SV203: $i] :
( ( ! [SY4936: $i,SY4937: $i] :
( ( ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ ( hAPP @ ( hAPP @ SV1142 @ SV1460 ) @ SV1616 ) )
= ( hAPP @ ( hAPP @ SV1142 @ ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ SV1460 ) ) @ ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ SV1616 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1142 @ SV203 @ SV1697 @ SV1747 @ SY4936 @ SY4937 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4170]) ).
thf(4414,plain,
! [SV1748: $i,SV1698: $i,SV1617: $i,SV1461: $i,SV1143: $i,SV708: $i,SV204: $i] :
( ( ! [SY4938: $i] :
( ( ( hAPP @ ( hAPP @ SV204 @ SV708 ) @ SV1143 )
= ( hAPP @ ( hAPP @ SV204 @ SV1143 ) @ SV708 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1461 @ SV204 @ SV1617 @ SV1698 @ SV1748 @ SY4938 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4171]) ).
thf(4415,plain,
! [SV1749: $i,SV1699: $i,SV1618: $i,SV1462: $i,SV1144: $i,SV709: $i,SV205: $i] :
( ( ! [SY4939: $i,SY4940: $i] :
( ( ( hAPP @ ( hAPP @ SV205 @ SV709 ) @ ( hAPP @ ( hAPP @ SV205 @ SV1144 ) @ SV1462 ) )
= ( hAPP @ ( hAPP @ SV205 @ ( hAPP @ ( hAPP @ SV205 @ SV709 ) @ SV1144 ) ) @ SV1462 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1618 @ SV205 @ SV1699 @ SV1749 @ SY4939 @ SY4940 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4172]) ).
thf(4416,plain,
! [SV1750: $i,SV1700: $i,SV1619: $i,SV1463: $i,SV1145: $i,SV710: $i,SV206: $i] :
( ( ( ( hAPP @ ( hAPP @ SV206 @ SV710 ) @ SV1145 )
= SV1145 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1463 @ SV206 @ SV1619 @ SV1700 @ SV710 @ SV1750 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4173]) ).
thf(4417,plain,
! [SV1751: $i,SV1701: $i,SV1620: $i,SV1464: $i,SV1146: $i,SV711: $i,SV207: $i] :
( ( ( ( hAPP @ ( hAPP @ SV207 @ SV711 ) @ SV1146 )
= SV711 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1464 @ SV207 @ SV1620 @ SV711 @ SV1701 @ SV1751 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4174]) ).
thf(4418,plain,
! [SV1752: $i,SV1702: $i,SV1621: $i,SV1465: $i,SV1147: $i,SV712: $i,SV208: $i] :
( ( ! [SY4941: $i] :
( ( ( hAPP @ ( hAPP @ SV208 @ SV712 ) @ SV1147 )
= ( hAPP @ ( hAPP @ SV208 @ SV1147 ) @ SV712 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV208 @ SV1465 @ SV1621 @ SV1702 @ SV1752 @ SY4941 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4175]) ).
thf(4419,plain,
! [SV1753: $i,SV1703: $i,SV1622: $i,SV1466: $i,SV1148: $i,SV713: $i,SV209: $i] :
( ( ! [SY4942: $i,SY4943: $i] :
( ( ( hAPP @ ( hAPP @ SV209 @ SV713 ) @ ( hAPP @ ( hAPP @ SV209 @ SV1148 ) @ SV1466 ) )
= ( hAPP @ ( hAPP @ SV209 @ ( hAPP @ ( hAPP @ SV209 @ SV713 ) @ SV1148 ) ) @ SV1466 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV209 @ SV1622 @ SV1703 @ SV1753 @ SY4942 @ SY4943 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4176]) ).
thf(4420,plain,
! [SV1754: $i,SV1704: $i,SV1623: $i,SV1467: $i,SV1149: $i,SV714: $i,SV210: $i] :
( ( ( ( hAPP @ ( hAPP @ SV210 @ SV714 ) @ SV1149 )
= SV1149 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV210 @ SV1467 @ SV1623 @ SV714 @ SV1704 @ SV1754 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4177]) ).
thf(4421,plain,
! [SV1755: $i,SV1705: $i,SV1624: $i,SV1468: $i,SV1150: $i,SV715: $i,SV211: $i] :
( ( ! [SY4944: $i,SY4945: $i] :
( ( ( hAPP @ ( hAPP @ SV211 @ SV715 ) @ ( hAPP @ ( hAPP @ SV211 @ SV1150 ) @ SV1468 ) )
= ( hAPP @ ( hAPP @ SV211 @ ( hAPP @ ( hAPP @ SV211 @ SV715 ) @ SV1150 ) ) @ SV1468 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV211 @ SV1624 @ SV1705 @ SV1755 @ SY4944 @ SY4945 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4178]) ).
thf(4422,plain,
! [SV1756: $i,SV1706: $i,SV1625: $i,SV1469: $i,SV1151: $i,SV716: $i,SV212: $i] :
( ( ! [SY4946: $i] :
( ( ( hAPP @ ( hAPP @ SV212 @ SV716 ) @ SV1151 )
= ( hAPP @ ( hAPP @ SV212 @ SV1151 ) @ SV716 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV212 @ SV1469 @ SV1625 @ SV1706 @ SV1756 @ SY4946 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4179]) ).
thf(4423,plain,
! [SV1757: $i,SV1707: $i,SV1626: $i,SV1470: $i,SV1152: $i,SV717: $i,SV213: $i] :
( ( ! [SY4947: $i,SY4948: $i] :
( ( ( hAPP @ ( hAPP @ SV213 @ ( hAPP @ ( hAPP @ SV213 @ SV717 ) @ SV1152 ) ) @ SV1470 )
= ( hAPP @ ( hAPP @ SV213 @ ( hAPP @ ( hAPP @ SV213 @ SV717 ) @ SV1470 ) ) @ SV1152 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV213 @ SV1626 @ SV1707 @ SV1757 @ SY4947 @ SY4948 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4180]) ).
thf(4424,plain,
! [SV1758: $i,SV1708: $i,SV1627: $i,SV1471: $i,SV1153: $i,SV718: $i,SV214: $i] :
( ( ! [SY4949: $i,SY4950: $i] :
( ( ( hAPP @ ( hAPP @ SV214 @ SV718 ) @ ( hAPP @ ( hAPP @ SV214 @ SV1153 ) @ SV1471 ) )
= ( hAPP @ ( hAPP @ SV214 @ SV1153 ) @ ( hAPP @ ( hAPP @ SV214 @ SV718 ) @ SV1471 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV214 @ SV1627 @ SV1708 @ SV1758 @ SY4949 @ SY4950 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4181]) ).
thf(4425,plain,
! [SV1759: $i,SV1709: $i,SV1628: $i,SV1472: $i,SV1154: $i,SV719: $i,SV215: $i] :
( ( ! [SY4951: $i,SY4952: $i] :
( ( ( hAPP @ ( hAPP @ SV215 @ ( hAPP @ ( hAPP @ SV215 @ SV719 ) @ SV1154 ) ) @ SV1472 )
= ( hAPP @ ( hAPP @ SV215 @ SV719 ) @ ( hAPP @ ( hAPP @ SV215 @ SV1154 ) @ SV1472 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV215 @ SV1628 @ SV1709 @ SV1759 @ SY4951 @ SY4952 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4182]) ).
thf(4426,plain,
! [SV1760: $i,SV1710: $i,SV1629: $i,SV1473: $i,SV1155: $i,SV720: $i,SV216: $i] :
( ( ! [SY4953: $i,SY4954: $i,SY4955: $i] :
( ( ( hAPP @ ( hAPP @ SV216 @ ( hAPP @ ( hAPP @ SV216 @ SV720 ) @ SV1155 ) ) @ ( hAPP @ ( hAPP @ SV216 @ SV1473 ) @ SV1629 ) )
= ( hAPP @ ( hAPP @ SV216 @ ( hAPP @ ( hAPP @ SV216 @ SV720 ) @ SV1473 ) ) @ ( hAPP @ ( hAPP @ SV216 @ SV1155 ) @ SV1629 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV216 @ SV1710 @ SV1760 @ SY4953 @ SY4954 @ SY4955 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4183]) ).
thf(4427,plain,
! [SV1761: $i,SV1711: $i,SV1630: $i,SV1474: $i,SV1156: $i,SV721: $i,SV217: $i] :
( ( ! [SY4956: $i,SY4957: $i] :
( ( ( hAPP @ ( hAPP @ SV217 @ SV721 ) @ ( hAPP @ ( hAPP @ SV217 @ SV1156 ) @ SV1474 ) )
= ( hAPP @ ( hAPP @ SV217 @ SV1156 ) @ ( hAPP @ ( hAPP @ SV217 @ SV721 ) @ SV1474 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1630 @ SV217 @ SV1711 @ SV1761 @ SY4956 @ SY4957 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4184]) ).
thf(4428,plain,
! [SV1762: $i,SV1712: $i,SV1631: $i,SV1475: $i,SV1157: $i,SV722: $i,SV218: $i] :
( ( ! [SY4958: $i,SY4959: $i] :
( ( ( hAPP @ ( hAPP @ SV218 @ SV722 ) @ ( hAPP @ ( hAPP @ SV218 @ SV1157 ) @ SV1475 ) )
= ( hAPP @ ( hAPP @ SV218 @ ( hAPP @ ( hAPP @ SV218 @ SV722 ) @ SV1157 ) ) @ SV1475 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1631 @ SV218 @ SV1712 @ SV1762 @ SY4958 @ SY4959 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4185]) ).
thf(4429,plain,
! [SV1763: $i,SV1713: $i,SV1632: $i,SV1476: $i,SV1158: $i,SV723: $i,SV219: $i] :
( ( ! [SY4960: $i,SY4961: $i] :
( ( ( hAPP @ ( hAPP @ SV219 @ ( hAPP @ ( hAPP @ SV219 @ SV723 ) @ SV1158 ) ) @ SV1476 )
= ( hAPP @ ( hAPP @ SV219 @ SV723 ) @ ( hAPP @ ( hAPP @ SV219 @ SV1158 ) @ SV1476 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1632 @ SV219 @ SV1713 @ SV1763 @ SY4960 @ SY4961 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4186]) ).
thf(4430,plain,
! [SV1764: $i,SV1714: $i,SV1633: $i,SV1477: $i,SV1159: $i,SV724: $i,SV220: $i] :
( ( ! [SY4962: $i,SY4963: $i] :
( ( ( hAPP @ ( hAPP @ SV220 @ ( hAPP @ ( hAPP @ SV220 @ SV724 ) @ SV1159 ) ) @ SV1477 )
= ( hAPP @ ( hAPP @ SV220 @ ( hAPP @ ( hAPP @ SV220 @ SV724 ) @ SV1477 ) ) @ SV1159 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1633 @ SV220 @ SV1714 @ SV1764 @ SY4962 @ SY4963 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4187]) ).
thf(4431,plain,
! [SV1765: $i,SV1715: $i,SV1634: $i,SV1478: $i,SV1160: $i,SV725: $i,SV221: $i] :
( ( ! [SY4964: $i,SY4965: $i,SY4966: $i] :
( ( ( hAPP @ ( hAPP @ SV221 @ ( hAPP @ ( hAPP @ SV221 @ SV725 ) @ SV1160 ) ) @ ( hAPP @ ( hAPP @ SV221 @ SV1478 ) @ SV1634 ) )
= ( hAPP @ ( hAPP @ SV221 @ SV1478 ) @ ( hAPP @ ( hAPP @ SV221 @ ( hAPP @ ( hAPP @ SV221 @ SV725 ) @ SV1160 ) ) @ SV1634 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1715 @ SV221 @ SV1765 @ SY4964 @ SY4965 @ SY4966 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4188]) ).
thf(4432,plain,
! [SV1766: $i,SV1716: $i,SV1635: $i,SV1479: $i,SV1161: $i,SV726: $i,SV222: $i] :
( ( ! [SY4967: $i,SY4968: $i,SY4969: $i] :
( ( ( hAPP @ ( hAPP @ SV222 @ ( hAPP @ ( hAPP @ SV222 @ SV726 ) @ SV1161 ) ) @ ( hAPP @ ( hAPP @ SV222 @ SV1479 ) @ SV1635 ) )
= ( hAPP @ ( hAPP @ SV222 @ SV726 ) @ ( hAPP @ ( hAPP @ SV222 @ SV1161 ) @ ( hAPP @ ( hAPP @ SV222 @ SV1479 ) @ SV1635 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1716 @ SV222 @ SV1766 @ SY4967 @ SY4968 @ SY4969 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4189]) ).
thf(4433,plain,
! [SV1767: $i,SV1717: $i,SV1636: $i,SV1480: $i,SV1162: $i,SV727: $i,SV223: $i] :
( ( ! [SY4970: $i,SY4971: $i,SY4972: $i] :
( ( ( hAPP @ ( hAPP @ SV223 @ ( hAPP @ ( hAPP @ SV223 @ SV727 ) @ SV1162 ) ) @ ( hAPP @ ( hAPP @ SV223 @ SV1480 ) @ SV1636 ) )
= ( hAPP @ ( hAPP @ SV223 @ ( hAPP @ ( hAPP @ SV223 @ SV727 ) @ SV1480 ) ) @ ( hAPP @ ( hAPP @ SV223 @ SV1162 ) @ SV1636 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1717 @ SV223 @ SV1767 @ SY4970 @ SY4971 @ SY4972 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4190]) ).
thf(4434,plain,
! [SV1768: $i,SV1718: $i,SV1637: $i,SV1481: $i,SV1163: $i,SV728: $i,SV224: $i] :
( ( ( ( hAPP @ ( hAPP @ SV224 @ SV728 ) @ SV1163 )
= SV728 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1481 @ SV224 @ SV1637 @ SV1718 @ SV1163 @ SV1768 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4191]) ).
thf(4435,plain,
! [SV1769: $i,SV1719: $i,SV1638: $i,SV1482: $i,SV1164: $i,SV729: $i,SV225: $i] :
( ( ( ( hAPP @ ( hAPP @ SV225 @ SV729 ) @ SV1164 )
= SV1164 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1482 @ SV225 @ SV1638 @ SV1719 @ SV729 @ SV1769 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4192]) ).
thf(4436,plain,
! [SV1770: $i,SV1720: $i,SV1639: $i,SV1483: $i,SV1165: $i,SV730: $i,SV226: $i] :
( ( ( ( hAPP @ ( hAPP @ SV226 @ SV730 ) @ SV1165 )
= SV1165 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1483 @ SV226 @ SV1639 @ SV1165 @ SV1720 @ SV1770 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4193]) ).
thf(4437,plain,
! [SV1771: $i,SV1721: $i,SV1640: $i,SV1484: $i,SV1166: $i,SV731: $i,SV227: $i] :
( ( ( ( hAPP @ ( hAPP @ SV227 @ SV731 ) @ SV1166 )
= SV731 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1484 @ SV227 @ SV1640 @ SV731 @ SV1721 @ SV1771 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4194]) ).
thf(4438,plain,
! [SV1772: $i,SV1722: $i,SV1641: $i,SV1485: $i,SV1167: $i,SV732: $i,SV228: $i] :
( ( ! [SY4973: $i,SY4974: $i] :
( ( ( hAPP @ ( hAPP @ SV228 @ ( hAPP @ ( hAPP @ SV732 @ SV1167 ) @ SV1485 ) ) @ SV1641 )
= ( hAPP @ ( hAPP @ SV732 @ ( hAPP @ ( hAPP @ SV228 @ SV1167 ) @ SV1641 ) ) @ ( hAPP @ ( hAPP @ SV228 @ SV1485 ) @ SV1641 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV732 @ SV228 @ SV1722 @ SV1772 @ SY4973 @ SY4974 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4195]) ).
thf(4439,plain,
! [SV1773: $i,SV1723: $i,SV1642: $i,SV1486: $i,SV1168: $i,SV733: $i,SV229: $i] :
( ( ! [SY4975: $i] :
( ( ( hAPP @ ( hAPP @ SV229 @ SV733 ) @ SV1168 )
= ( hAPP @ ( hAPP @ SV229 @ SV1168 ) @ SV733 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1486 @ SV229 @ SV1642 @ SV1723 @ SV1773 @ SY4975 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4196]) ).
thf(4440,plain,
! [SV1774: $i,SV1724: $i,SV1643: $i,SV1487: $i,SV1169: $i,SV734: $i,SV230: $i] :
( ( ( ( hAPP @ ( hAPP @ SV230 @ SV734 ) @ SV1169 )
= SV734 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV230 @ SV1487 @ SV1643 @ SV1169 @ SV1724 @ SV1774 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4197]) ).
thf(4441,plain,
! [SV1775: $i,SV1725: $i,SV1644: $i,SV1488: $i,SV1170: $i,SV735: $i,SV231: $i] :
( ( ( ( hAPP @ ( hAPP @ SV231 @ SV735 ) @ SV1170 )
= SV1170 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV231 @ SV1488 @ SV1644 @ SV735 @ SV1725 @ SV1775 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4198]) ).
thf(4442,plain,
! [SV1776: $i,SV1726: $i,SV1645: $i,SV1489: $i,SV1171: $i,SV736: $i,SV232: $i] :
( ( ( ( hAPP @ ( hAPP @ SV232 @ SV736 ) @ SV736 )
= ( hAPP @ ( hAPP @ SV1171 @ ( hAPP @ ( hAPP @ SV232 @ SV1489 ) @ SV1489 ) ) @ SV736 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV232 @ SV1171 @ SV1645 @ SV1726 @ SV1489 @ SV1776 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4199]) ).
thf(4443,plain,
! [SV1777: $i,SV1727: $i,SV1646: $i,SV1490: $i,SV1172: $i,SV737: $i,SV233: $i] :
( ( ! [SY4976: $i] :
( ( ( hAPP @ ( hAPP @ SV233 @ SV737 ) @ ( hAPP @ ( hAPP @ SV1172 @ SV1490 ) @ SV737 ) )
= ( hAPP @ ( hAPP @ SV1172 @ ( hAPP @ ( hAPP @ SV233 @ SV1490 ) @ SV1646 ) ) @ SV737 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV233 @ SV1172 @ SV1727 @ SV1777 @ SV1646 @ SY4976 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4200]) ).
thf(4444,plain,
! [SV1778: $i,SV1728: $i,SV1647: $i,SV1491: $i,SV1173: $i,SV738: $i,SV234: $i] :
( ( ! [SY4977: $i] :
( ( ( hAPP @ ( hAPP @ SV234 @ ( hAPP @ ( hAPP @ SV738 @ SV1173 ) @ SV1491 ) ) @ SV1491 )
= ( hAPP @ ( hAPP @ SV738 @ ( hAPP @ ( hAPP @ SV234 @ SV1173 ) @ SV1647 ) ) @ SV1491 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV234 @ SV738 @ SV1728 @ SV1778 @ SV1647 @ SY4977 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4201]) ).
thf(4445,plain,
! [SV1779: $i,SV1729: $i,SV1648: $i,SV1492: $i,SV1174: $i,SV739: $i,SV235: $i] :
( ( ! [SY4978: $i,SY4979: $i] :
( ( ( hAPP @ ( hAPP @ SV235 @ ( hAPP @ ( hAPP @ SV739 @ SV1174 ) @ SV1492 ) ) @ ( hAPP @ ( hAPP @ SV739 @ SV1648 ) @ SV1492 ) )
= ( hAPP @ ( hAPP @ SV739 @ ( hAPP @ ( hAPP @ SV235 @ SV1174 ) @ SV1648 ) ) @ SV1492 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV235 @ SV739 @ SV1729 @ SV1779 @ SY4978 @ SY4979 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4202]) ).
thf(4446,plain,
! [SV1730: $i,SV1649: $i,SV1493: $i,SV1175: $i,SV740: $i,SV236: $i] :
( ( ( SV236 = SV740 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1175 @ SV740 ) @ SV236 ) )
| ~ ( c_ListOrder_Ostep1 @ SV1175 @ ( c_List_Olist_OCons @ SV740 @ SV1493 @ SV1649 ) @ ( c_List_Olist_OCons @ SV236 @ SV1730 @ SV1649 ) @ SV1649 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4203]) ).
thf(4447,plain,
! [SV1650: $i,SV1494: $i,SV1176: $i,SV741: $i,SV237: $i] :
( ( ( class_Ring__and__Field_Ocomm__semiring__1 @ SV237 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SV741 ) @ SV1176 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SV1494 ) @ SV1650 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SV741 ) @ SV1494 ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV237 ) @ SV1176 ) @ SV1650 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4204]) ).
thf(4448,plain,
! [SV1177: $i,SV238: $i,SV1495: $i,SV742: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV742 ) @ SV1495 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV238 ) @ SV1177 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV238 ) @ SV742 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1177 ) @ SV1495 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4205]) ).
thf(4449,plain,
! [SV746: $i,SV1180: $i,SV1496: $i,SV242: $i] :
( ( ( c_Type_Otyping @ SV242 @ SV1496 @ SV1180 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV1496 ) @ SV746 ) ) )
= $true )
| ( ( c_Type_Otyping @ SV242 @ SV746 @ SV1180 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4206]) ).
thf(4450,plain,
! [SV1731: $i,SV1651: $i,SV1498: $i,SV1185: $i,SV754: $i,SV251: $i] :
( ( ( SV251 = SV754 )
= $true )
| ( ( ( c_ListOrder_Ostep1 @ SV1185 @ SV251 @ SV754 @ SV1498 )
| ~ ( c_ListOrder_Ostep1 @ SV1185 @ ( c_List_Oappend @ SV251 @ ( c_List_Olist_OCons @ SV1651 @ ( c_List_Olist_ONil @ SV1498 ) @ SV1498 ) @ SV1498 ) @ ( c_List_Oappend @ SV754 @ ( c_List_Olist_OCons @ SV1731 @ ( c_List_Olist_ONil @ SV1498 ) @ SV1498 ) @ SV1498 ) @ SV1498 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4208]) ).
thf(4451,plain,
! [SV1192: $i,SV778: $i,SV283: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV283 ) @ SV778 @ SV283 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV283 ) @ ( c_Power_Opower__class_Opower @ SV778 @ SV1192 @ SV283 ) @ SV283 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV283 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4218]) ).
thf(4452,plain,
! [SV1503: $i,SV284: $i,SV1193: $i,SV779: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV779 @ SV1193 @ SV284 )
= $true )
| ( ( ( c_HOL_Oord__class_Oless @ SV779 @ SV1503 @ SV284 )
| ~ ( c_HOL_Oord__class_Oless @ SV779 @ ( c_Orderings_Oord__class_Omax @ SV1503 @ SV1193 @ SV284 ) @ SV284 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV284 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4219]) ).
thf(4453,plain,
! [SV787: $i,SV1197: $i,SV296: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SV1197 @ SV296 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SV787 @ SV296 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV296 ) @ SV787 ) @ SV1197 ) @ SV296 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV296 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4220]) ).
thf(4454,plain,
! [SV1732: $i,SV1652: $i,SV1504: $i,SV1198: $i,SV788: $i,SV297: $i] :
( ( ( c_ListOrder_Ostep1 @ SV297 @ SV788 @ SV1198 @ SV1504 )
= $true )
| ( ( ( SV1198 = SV788 )
| ~ ( c_ListOrder_Ostep1 @ SV297 @ ( c_List_Olist_OCons @ SV1652 @ SV788 @ SV1504 ) @ ( c_List_Olist_OCons @ SV1732 @ SV1198 @ SV1504 ) @ SV1504 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4221]) ).
thf(4455,plain,
! [SV1505: $i,SV1199: $i,SV789: $i,SV1653: $i,SV298: $i] :
( ( ( c_OrderedGroup_Osemigroup__add @ SV298 @ SV1653 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV298 @ ( hAPP @ ( hAPP @ SV298 @ SV789 ) @ SV1199 ) ) @ SV1505 )
= ( hAPP @ ( hAPP @ SV298 @ SV789 ) @ ( hAPP @ ( hAPP @ SV298 @ SV1199 ) @ SV1505 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4222]) ).
thf(4456,plain,
! [SV302: $i,SV792: $i,SV1202: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1202 @ SV792 @ SV302 )
= $true )
| ( ( SV1202 = SV792 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV792 @ SV1202 @ SV302 )
= $true )
| ( ( class_Ring__and__Field_Oordered__idom @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4223]) ).
thf(4457,plain,
! [SV303: $i,SV793: $i,SV1203: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1203 @ SV793 @ SV303 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV793 @ SV1203 @ SV303 )
= $true )
| ( ( SV793 = SV1203 )
= $true )
| ( ( class_Orderings_Olinorder @ SV303 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4224]) ).
thf(4458,plain,
! [SV307: $i,SV797: $i,SV1205: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1205 @ SV797 @ SV307 )
= $true )
| ( ( SV1205 = SV797 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV797 @ SV1205 @ SV307 )
= $true )
| ( ( class_Orderings_Olinorder @ SV307 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4226]) ).
thf(4459,plain,
! [SV309: $i,SV799: $i,SV1207: $i] :
( ( ( SV1207 = SV799 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1207 @ SV799 @ SV309 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV799 @ SV1207 @ SV309 )
= $true )
| ( ( class_Orderings_Olinorder @ SV309 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4227]) ).
thf(4460,plain,
! [SV310: $i,SV1208: $i,SV800: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV800 @ SV1208 @ SV310 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV1208 @ SV800 @ SV310 )
= $true )
| ( ( SV800 = SV1208 )
= $true )
| ( ( class_Orderings_Olinorder @ SV310 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4228]) ).
thf(4461,plain,
! [SV1655: $i,SV1508: $i,SV1209: $i,SV802: $i,SV312: $i] :
( ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV312 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV312 ) @ SV802 ) @ SV1209 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV312 ) @ SV1508 ) @ SV1655 ) @ SV312 )
| ~ ( c_HOL_Oord__class_Oless @ SV1209 @ SV1655 @ SV312 )
| ~ ( c_HOL_Oord__class_Oless @ SV802 @ SV1508 @ SV312 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4229]) ).
thf(4462,plain,
! [SV1210: $i,SV313: $i,SV1509: $i,SV803: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV803 @ SV1509 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV313 @ SV1210 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV313 ) @ SV803 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1210 ) @ SV1509 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4230]) ).
thf(4463,plain,
! [SV314: $i,SV1211: $i,SV804: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV804 @ SV1211 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV804 @ SV314 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1211 @ SV314 ) @ SV314 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV314 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4231]) ).
thf(4464,plain,
! [SV1212: $i,SV315: $i,SV805: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV805 @ SV315 ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ SV1212 @ SV315 ) @ SV315 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV805 @ SV1212 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV315 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4232]) ).
thf(4465,plain,
! [SV1733: $i,SV1656: $i,SV1511: $i,SV1214: $i,SV810: $i,SV321: $i] :
( ( ( SV321 = SV810 )
= $true )
| ( ( ( SV1214 = SV1511 )
| ~ ( c_ListOrder_Ostep1 @ SV1656 @ ( c_List_Oappend @ SV321 @ ( c_List_Olist_OCons @ SV1214 @ ( c_List_Olist_ONil @ SV1733 ) @ SV1733 ) @ SV1733 ) @ ( c_List_Oappend @ SV810 @ ( c_List_Olist_OCons @ SV1511 @ ( c_List_Olist_ONil @ SV1733 ) @ SV1733 ) @ SV1733 ) @ SV1733 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4235]) ).
thf(4466,plain,
! [SV812: $i,SV1512: $i,SV1216: $i,SV323: $i] :
( ( ( c_List_Olistsp @ SV323 @ SV1216 @ SV1512 )
= $false )
| ( ( ~ ( c_List_Olistsp @ SV323 @ SV812 @ SV1512 ) )
= $true )
| ( ( c_List_Olistsp @ SV323 @ ( c_List_Oappend @ SV812 @ SV1216 @ SV1512 ) @ SV1512 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4236]) ).
thf(4467,plain,
! [SV1514: $i,SV1218: $i,SV326: $i,SV814: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV814 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV326 ) @ SV1218 ) @ SV1514 ) @ SV326 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV814 @ SV1514 @ SV326 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV1218 @ SV326 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV326 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4237]) ).
thf(4468,plain,
! [SV1659: $i,SV1516: $i,SV1220: $i,SV816: $i,SV328: $i] :
( ( ( hBOOL @ ( hAPP @ SV328 @ ( c_Lambda_OdB_OdB__case @ SV816 @ SV1220 @ SV1516 @ ( c_Lambda_OdB_OAbs @ SV1659 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV328 @ ( hAPP @ SV1516 @ SV1659 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4239]) ).
thf(4469,plain,
! [SV1660: $i,SV1517: $i,SV1221: $i,SV817: $i,SV329: $i] :
( ( ( hBOOL @ ( hAPP @ SV329 @ ( c_Lambda_OdB_OdB__case @ SV817 @ SV1221 @ SV1517 @ ( c_Lambda_OdB_OAbs @ SV1660 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV329 @ ( hAPP @ SV1517 @ SV1660 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4240]) ).
thf(4470,plain,
! [SV1518: $i,SV1224: $i,SV822: $i,SV334: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV334 ) @ SV822 ) @ SV1224 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV334 ) @ SV1518 ) @ SV1224 ) @ SV334 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV822 @ SV1518 @ SV334 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV334 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4241]) ).
thf(4471,plain,
! [SV1519: $i,SV1225: $i,SV823: $i,SV335: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV335 ) @ SV823 ) @ SV1225 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV335 ) @ SV1519 ) @ SV1225 ) @ SV335 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV823 @ SV1519 @ SV335 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV335 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4242]) ).
thf(4472,plain,
! [SV1520: $i,SV336: $i,SV1226: $i,SV824: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV824 @ SV1226 @ SV336 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV336 ) @ SV824 ) @ SV1520 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV336 ) @ SV1226 ) @ SV1520 ) @ SV336 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV336 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4243]) ).
thf(4473,plain,
! [SV1521: $i,SV1227: $i,SV825: $i,SV337: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV337 ) @ SV825 ) @ SV1227 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV337 ) @ SV825 ) @ SV1521 ) @ SV337 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1227 @ SV1521 @ SV337 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV337 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4244]) ).
thf(4474,plain,
! [SV1522: $i,SV1228: $i,SV826: $i,SV338: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV338 ) @ SV826 ) @ SV1228 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV338 ) @ SV826 ) @ SV1522 ) @ SV338 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1228 @ SV1522 @ SV338 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV338 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4245]) ).
thf(4475,plain,
! [SV1523: $i,SV339: $i,SV1229: $i,SV827: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV827 @ SV1229 @ SV339 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SV1523 ) @ SV827 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SV1523 ) @ SV1229 ) @ SV339 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV339 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4246]) ).
thf(4476,plain,
! [SV1233: $i,SV344: $i,SV831: $i,SV1524: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1524 ) @ SV831 ) )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV344 @ SV1524 @ SV1233 ) )
= $true )
| ( ( c_Type_Otyping @ SV344 @ SV831 @ SV1233 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4247]) ).
thf(4477,plain,
! [SV1735: $i,SV1661: $i,SV1525: $i,SV1234: $i,SV832: $i,SV345: $i] :
( ( ( c_ListOrder_Ostep1 @ SV345 @ SV832 @ SV1234 @ SV1525 )
= $true )
| ( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV345 @ SV1661 ) @ SV1735 ) )
| ~ ( c_ListOrder_Ostep1 @ SV345 @ ( c_List_Olist_OCons @ SV1661 @ SV832 @ SV1525 ) @ ( c_List_Olist_OCons @ SV1735 @ SV1234 @ SV1525 ) @ SV1525 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4248]) ).
thf(4478,plain,
! [SV833: $i,SV1526: $i,SV1662: $i,SV1235: $i,SV346: $i] :
( ( ( c_ListOrder_Ostep1 @ SV346 @ SV1235 @ SV1662 @ SV1526 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV346 @ ( c_List_Olist_OCons @ SV833 @ SV1235 @ SV1526 ) @ ( c_List_Olist_OCons @ SV833 @ SV1662 @ SV1526 ) @ SV1526 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4249]) ).
thf(4479,plain,
! [SV356: $i,SV1243: $i,SV841: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV841 @ SV1243 @ SV356 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1243 @ SV841 @ SV356 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV356 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4250]) ).
thf(4480,plain,
! [SV1244: $i,SV1532: $i,SV1663: $i,SV842: $i,SV357: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV357 @ SV842 ) @ SV1663 ) @ SV1532 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV357 @ SV1244 ) @ SV1663 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV357 @ SV842 ) @ SV1244 ) @ SV1532 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4251]) ).
thf(4481,plain,
! [SV1245: $i,SV843: $i,SV1533: $i,SV1664: $i,SV358: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV1664 ) @ SV1533 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV358 @ SV843 ) @ SV1245 ) @ SV1664 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV358 @ SV843 ) @ SV1245 ) @ SV1533 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4252]) ).
thf(4482,plain,
! [SV359: $i,SV1246: $i,SV844: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV844 @ SV1246 @ SV359 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1246 @ SV844 @ SV359 ) )
= $true )
| ( ( class_Orderings_Olinorder @ SV359 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4253]) ).
thf(4483,plain,
! [SV1247: $i,SV1534: $i,SV845: $i,SV360: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV360 @ SV845 ) @ SV1534 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV360 @ SV1534 @ SV1247 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV360 @ SV845 @ SV1247 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4254]) ).
thf(4484,plain,
! [SV361: $i,SV1248: $i,SV846: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV846 @ SV1248 @ SV361 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1248 @ SV846 @ SV361 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV361 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4255]) ).
thf(4485,plain,
! [SV1249: $i,SV1535: $i,SV847: $i,SV362: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV362 @ SV847 ) @ SV1535 ) )
= $false )
| ( ( ~ ( c_Wellfounded_Oaccp @ SV362 @ SV1535 @ SV1249 ) )
= $true )
| ( ( c_Wellfounded_Oaccp @ SV362 @ SV847 @ SV1249 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4256]) ).
thf(4486,plain,
! [SV363: $i,SV1250: $i,SV848: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV848 @ SV1250 @ SV363 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1250 @ SV848 @ SV363 ) )
= $true )
| ( ( class_Orderings_Opreorder @ SV363 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4257]) ).
thf(4487,plain,
! [SV1780: $i,SV1736: $i,SV1665: $i,SV1536: $i,SV1252: $i,SV850: $i,SV371: $i] :
( ( ( ( hAPP @ ( hAPP @ SV371 @ SV850 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV1252 )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1536 @ SV1665 @ SV371 @ SV1736 @ SV1252 @ SV1780 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4258]) ).
thf(4488,plain,
! [SV1737: $i,SV1666: $i,SV1537: $i,SV1254: $i,SV854: $i,SV375: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV375 @ ( c_Lambda_OdB_OdB__case @ SV854 @ SV1254 @ SV1537 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1666 ) @ SV1737 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV375 @ ( hAPP @ ( hAPP @ SV1254 @ SV1666 ) @ SV1737 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4259]) ).
thf(4489,plain,
! [SV1738: $i,SV1667: $i,SV1538: $i,SV1255: $i,SV855: $i,SV376: $i] :
( ( ( ~ ( hBOOL @ ( hAPP @ SV376 @ ( c_Lambda_OdB_OdB__case @ SV855 @ SV1255 @ SV1538 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1667 ) @ SV1738 ) @ t_a ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SV1255 @ SV1667 ) @ SV1738 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4260]) ).
thf(4490,plain,
! [SV1264: $i,SV385: $i,SV864: $i] :
( ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV864 @ tc_Lambda_OdB )
= $false )
| ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV385 ) ) @ SV864 ) @ SV1264 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $true )
| ( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV385 ) @ SV864 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1264 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4263]) ).
thf(4491,plain,
! [SV1543: $i,SV1267: $i,SV867: $i,SV1670: $i,SV391: $i] :
( ( ( c_OrderedGroup_Osemigroup__add @ SV391 @ SV1670 )
= $false )
| ( ( ( c_List_Ofoldl @ SV391 @ ( hAPP @ ( hAPP @ SV391 @ SV867 ) @ SV1267 ) @ SV1543 @ SV1670 @ SV1670 )
= ( hAPP @ ( hAPP @ SV391 @ SV867 ) @ ( c_List_Ofoldl @ SV391 @ SV1267 @ SV1543 @ SV1670 @ SV1670 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4264]) ).
thf(4492,plain,
! [SV1546: $i,SV870: $i,SV1671: $i,SV394: $i,SV1270: $i] :
( ( ( c_OrderedGroup_Omonoid__add @ SV1270 @ SV394 @ SV1671 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV394 @ SV870 ) @ ( c_List_Ofoldl @ SV394 @ SV1270 @ SV1546 @ SV1671 @ SV1671 ) )
= ( c_List_Ofoldl @ SV394 @ SV870 @ SV1546 @ SV1671 @ SV1671 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4266]) ).
thf(4493,plain,
! [SV1781: $i,SV1743: $i,SV1674: $i,SV1551: $i,SV1275: $i,SV877: $i,SV401: $i] :
( ( ( c_Type_Otypings @ SV401 @ SV877 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV1275 @ SV1551 @ SV401 @ SV877 ) )
| ~ ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1674 ) @ SV1743 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1551 )
| ~ ( c_Type_Otypings @ SV401 @ SV1743 @ SV1781 )
| ~ ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1674 ) @ SV1743 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV877 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4270]) ).
thf(4494,plain,
! [SV1675: $i,SV1553: $i,SV1279: $i,SV881: $i,SV407: $i] :
( ( ( hBOOL @ ( hAPP @ SV407 @ ( c_Lambda_OdB_OdB__case @ SV881 @ SV1279 @ SV1553 @ ( c_Lambda_OdB_OVar @ SV1675 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV407 @ ( hAPP @ SV881 @ SV1675 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4272]) ).
thf(4495,plain,
! [SV1676: $i,SV1554: $i,SV1280: $i,SV882: $i,SV408: $i] :
( ( ( hBOOL @ ( hAPP @ SV408 @ ( c_Lambda_OdB_OdB__case @ SV882 @ SV1280 @ SV1554 @ ( c_Lambda_OdB_OVar @ SV1676 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV408 @ ( hAPP @ SV882 @ SV1676 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4273]) ).
thf(4496,plain,
! [SV891: $i,SV418: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV418 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV418 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV418 ) @ SV891 @ SV418 )
= ( c_HOL_Ozero__class_Ozero @ SV418 ) )
| ( SV891
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV418 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV418 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4274]) ).
thf(4497,plain,
! [SV892: $i,SV419: $i] :
( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV419 ) @ SV892 @ SV419 )
= ( c_HOL_Ozero__class_Ozero @ SV419 ) )
= $true )
| ( ( SV892
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( class_Power_Opower @ SV419 )
= $false )
| ( ( class_Ring__and__Field_Osemiring__0 @ SV419 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4275]) ).
thf(4498,plain,
! [SV430: $i,SV900: $i,SV1679: $i,SV1557: $i,SV1289: $i] :
( ( ( ~ ( c_Type_Otyping @ SV1289 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1557 ) @ SV1679 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV900 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV1289 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1557 ) @ SV1679 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV430 ) )
= $true )
| ( ( SV430 = SV900 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4276]) ).
thf(4499,plain,
! [SV1290: $i,SV902: $i,SV433: $i] :
( ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV433 ) @ SV902 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ SV1290 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ SV902 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ SV433 ) ) @ SV902 ) @ SV1290 @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4277]) ).
thf(4500,plain,
! [SV1680: $i,SV1559: $i,SV1294: $i,SV911: $i,SV443: $i] :
( ( ( ( c_List_Olist_OCons @ SV443 @ SV911 @ SV1294 )
= ( c_List_Olist_OCons @ SV1559 @ SV1680 @ SV1294 ) )
= $false )
| ( ( SV443 = SV1559 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4278]) ).
thf(4501,plain,
! [SV1681: $i,SV1560: $i,SV1295: $i,SV912: $i,SV444: $i] :
( ( ( class_OrderedGroup_Oab__group__add @ SV444 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV912 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV1295 ) @ SV1560 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV1295 ) @ SV1681 ) )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV912 ) @ SV1560 )
= SV1681 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4279]) ).
thf(4502,plain,
! [SV1561: $i,SV1297: $i,SV914: $i,SV446: $i] :
( ( ( ~ ( class_Int_Onumber__ring @ SV446 ) )
= $true )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV446 ) @ SV914 ) @ SV1297 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV446 ) @ SV914 ) @ SV1561 ) )
| ( SV1297 = SV1561 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV446 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4280]) ).
thf(4503,plain,
! [SV449: $i,SV1300: $i,SV917: $i] :
( ( ( ( c_Orderings_Oord__class_Omax @ SV917 @ SV1300 @ SV449 )
= SV1300 )
= $false )
| ( ( c_lessequals @ SV917 @ SV1300 @ SV449 )
= $true )
| ( ( class_Orderings_Olinorder @ SV449 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4282]) ).
thf(4504,plain,
! [SV1682: $i,SV1563: $i,SV1301: $i,SV918: $i,SV450: $i] :
( ( ( ( c_List_Oappend @ SV450 @ ( c_List_Olist_OCons @ SV918 @ ( c_List_Olist_ONil @ SV1301 ) @ SV1301 ) @ SV1301 )
= ( c_List_Oappend @ SV1563 @ ( c_List_Olist_OCons @ SV1682 @ ( c_List_Olist_ONil @ SV1301 ) @ SV1301 ) @ SV1301 ) )
= $false )
| ( ( SV450 = SV1563 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4283]) ).
thf(4505,plain,
! [SV1564: $i,SV456: $i,SV1304: $i,SV924: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV924 @ SV1304 @ SV456 )
!= ( c_Power_Opower__class_Opower @ SV1564 @ SV1304 @ SV456 ) )
= $true )
| ( ( ( SV924 = SV1564 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1304 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV1564 @ SV456 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV924 @ SV456 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV456 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4285]) ).
thf(4506,plain,
! [SV1683: $i,SV1565: $i,SV1305: $i,SV925: $i,SV457: $i] :
( ( ( ( c_List_Oreplicate @ SV457 @ SV925 @ SV1305 )
= ( c_List_Oreplicate @ SV1565 @ SV1683 @ SV1305 ) )
= $false )
| ( ( SV457 = SV1565 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4286]) ).
thf(4507,plain,
! [SV1307: $i,SV927: $i,SV459: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV459 ) @ SV927 ) @ SV1307 )
= ( c_HOL_Ozero__class_Ozero @ SV459 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV459 ) @ SV1307 @ SV459 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV459 ) @ SV927 @ SV459 )
| ( SV1307
= ( c_HOL_Ozero__class_Ozero @ SV459 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV459 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4287]) ).
thf(4508,plain,
! [SV1684: $i,SV1567: $i,SV1311: $i,SV932: $i,SV464: $i] :
( ( ( ( c_List_Olist_OCons @ SV464 @ SV932 @ SV1311 )
= ( c_List_Olist_OCons @ SV1567 @ SV1684 @ SV1311 ) )
= $false )
| ( ( SV932 = SV1684 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4289]) ).
thf(4509,plain,
! [SV1685: $i,SV1568: $i,SV1312: $i,SV933: $i,SV465: $i] :
( ( ( ( c_List_Oreplicate @ SV465 @ SV933 @ SV1312 )
= ( c_List_Oreplicate @ SV1568 @ SV1685 @ SV1312 ) )
= $false )
| ( ( ( SV933 = SV1685 )
| ( SV465
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4290]) ).
thf(4510,plain,
! [SV1314: $i,SV935: $i,SV467: $i] :
( ( ( class_Int_Onumber__ring @ SV467 )
= $false )
| ( ( ( SV935
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV467 ) @ SV935 ) @ SV1314 ) )
| ( SV1314
= ( c_HOL_Ozero__class_Ozero @ SV467 ) ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4291]) ).
thf(4511,plain,
! [SV1318: $i,SV939: $i,SV471: $i] :
( ( ( class_Ring__and__Field_Ono__zero__divisors @ SV471 )
= $false )
| ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV471 )
| ~ ( class_Power_Opower @ SV471 )
| ( ( c_Power_Opower__class_Opower @ SV939 @ SV1318 @ SV471 )
!= ( c_HOL_Ozero__class_Ozero @ SV471 ) )
| ( SV939
= ( c_HOL_Ozero__class_Ozero @ SV471 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4293]) ).
thf(4512,plain,
! [SV1323: $i,SV477: $i,SV945: $i] :
( ( ( ( c_Nat_Osemiring__1__class_Oof__nat @ SV945 @ SV477 )
= ( c_Nat_Osemiring__1__class_Oof__nat @ SV1323 @ SV477 ) )
= $false )
| ( ( SV945 = SV1323 )
= $true )
| ( ( class_Nat_Osemiring__char__0 @ SV477 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4296]) ).
thf(4513,plain,
! [SV484: $i,SV1329: $i,SV951: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV951 @ SV1329 @ SV484 )
= ( c_HOL_Ozero__class_Ozero @ SV484 ) )
= $false )
| ( ( SV951
= ( c_HOL_Ozero__class_Ozero @ SV484 ) )
= $true )
| ( ( class_Ring__and__Field_Oring__1__no__zero__divisors @ SV484 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4297]) ).
thf(4514,plain,
! [SV1573: $i,SV1330: $i,SV952: $i,SV485: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV952 ) @ SV1330 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV1573 ) @ SV1330 ) )
= $true )
| ( ( SV952 = SV1573 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV485 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4298]) ).
thf(4515,plain,
! [SV954: $i,SV487: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV487 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV487 )
| ( ( c_Power_Opower__class_Opower @ SV954 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV487 )
!= ( c_HOL_Ozero__class_Ozero @ SV487 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV487 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV487 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4299]) ).
thf(4516,plain,
! [SV1332: $i,SV956: $i,SV489: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV489 ) @ SV956 ) @ SV1332 )
= ( c_HOL_Ozero__class_Ozero @ SV489 ) )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV1332 @ SV489 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV956 @ SV489 )
| ( SV956
= ( c_HOL_Ozero__class_Ozero @ SV489 ) ) )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV489 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4300]) ).
thf(4517,plain,
! [SV1574: $i,SV492: $i,SV959: $i,SV1335: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1335 @ SV959 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV492 @ SV1574 @ tc_nat )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV492 ) @ SV959 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1335 ) @ SV1574 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4301]) ).
thf(4518,plain,
! [SV1575: $i,SV1336: $i,SV960: $i,SV493: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV960 ) @ SV1336 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV960 ) @ SV1575 ) )
= $true )
| ( ( SV1336 = SV1575 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV493 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4302]) ).
thf(4519,plain,
! [SV1577: $i,SV496: $i,SV1339: $i,SV963: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV963 @ SV1339 @ SV496 )
!= ( c_Power_Opower__class_Opower @ SV963 @ SV1577 @ SV496 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV496 ) @ SV963 @ SV496 )
| ( SV1339 = SV1577 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV496 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4304]) ).
thf(4520,plain,
! [SV1578: $i,SV1340: $i,SV964: $i,SV497: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV964 ) @ SV1340 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV964 ) @ SV1578 ) )
= $true )
| ( ( SV1340 = SV1578 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV497 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4305]) ).
thf(4521,plain,
! [SV1686: $i,SV1580: $i,SV1344: $i,SV968: $i,SV501: $i] :
( ( ( ( c_List_Oappend @ SV501 @ ( c_List_Olist_OCons @ SV968 @ ( c_List_Olist_ONil @ SV1344 ) @ SV1344 ) @ SV1344 )
= ( c_List_Oappend @ SV1580 @ ( c_List_Olist_OCons @ SV1686 @ ( c_List_Olist_ONil @ SV1344 ) @ SV1344 ) @ SV1344 ) )
= $false )
| ( ( SV968 = SV1686 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4306]) ).
thf(4522,plain,
! [SV1582: $i,SV971: $i,SV1347: $i,SV504: $i] :
( ( ( SV504
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1347 @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ SV504 @ SV971 @ SV1347 @ SV1582 ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $true )
| ( ( SV1582
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV504 ) @ SV971 )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ SV1347 @ SV1582 @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4308]) ).
thf(4523,plain,
! [SV984: $i,SV1358: $i,SV520: $i,SV3: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV520 @ SV3 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV520 @ SV1358 @ SV3 ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV520 @ SV984 @ SV3 ) @ ( c_Power_Opower__class_Opower @ SV1358 @ SV984 @ SV3 ) @ SV3 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4312]) ).
thf(4524,plain,
! [SV1687: $i,SV1586: $i,SV1359: $i,SV986: $i,SV524: $i,SV7: $i] :
( ( ( c_Type_Otyping @ SV7 @ SV524 @ SV986 )
= $false )
| ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV7 @ SV1359 @ SV986 @ tc_Type_Otype ) @ SV1586 @ SV1687 )
| ( c_Type_Otyping @ SV7 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1586 ) @ SV524 ) @ SV1359 ) @ SV1687 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4314]) ).
thf(4525,plain,
! [SV988: $i,SV1361: $i,SV9: $i,SV526: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV526 @ ( c_HOL_Oone__class_Oone @ SV9 ) @ SV9 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV526 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV1361 @ SV988 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV526 @ SV988 @ SV9 ) @ ( c_Power_Opower__class_Opower @ SV526 @ SV1361 @ SV9 ) @ SV9 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4316]) ).
thf(4526,plain,
! [SV527: $i,SV10: $i,SV989: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV989 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV10 ) @ SV527 @ SV10 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV10 ) @ ( c_Power_Opower__class_Opower @ SV527 @ SV989 @ SV10 ) @ SV10 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4317]) ).
thf(4527,plain,
! [SV1588: $i,SV1364: $i,SV992: $i,SV532: $i,SV15: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SV532 ) @ SV992 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SV1364 ) @ SV1588 ) @ SV15 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV992 @ SV1588 @ SV15 )
| ~ ( c_lessequals @ SV532 @ SV1364 @ SV15 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4318]) ).
thf(4528,plain,
! [SV1589: $i,SV1365: $i,SV993: $i,SV533: $i,SV16: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SV533 ) @ SV993 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SV1365 ) @ SV1589 ) @ SV16 )
= $true )
| ( ( ~ ( c_lessequals @ SV993 @ SV1589 @ SV16 )
| ~ ( c_HOL_Oord__class_Oless @ SV533 @ SV1365 @ SV16 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4319]) ).
thf(4529,plain,
! [SV534: $i,SV17: $i,SV994: $i] :
( ( ( c_lessequals @ SV994 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
= $false )
| ( ( ~ ( c_lessequals @ SV534 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV17 ) @ SV534 ) @ SV994 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4320]) ).
thf(4530,plain,
! [SV1366: $i,SV995: $i,SV537: $i,SV20: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV20 )
= $false )
| ( ( ( c_lessequals @ SV537 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV20 ) @ SV995 ) @ SV1366 ) @ SV20 )
| ~ ( c_lessequals @ SV537 @ SV995 @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV1366 @ SV20 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4321]) ).
thf(4531,plain,
! [SV1367: $i,SV996: $i,SV538: $i,SV21: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV21 )
= $false )
| ( ( ( c_lessequals @ SV538 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SV996 ) @ SV1367 ) @ SV21 )
| ~ ( c_lessequals @ SV538 @ SV1367 @ SV21 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ SV996 @ SV21 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4322]) ).
thf(4532,plain,
! [SV541: $i,SV997: $i,SV25: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV997 @ SV25 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV541 @ SV25 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SV541 ) @ SV997 ) @ SV25 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4324]) ).
thf(4533,plain,
! [SV29: $i,SV999: $i,SV543: $i] :
( ( ( c_lessequals @ SV543 @ SV999 @ SV29 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV543 @ SV999 @ SV29 )
= $true )
| ( ( SV543 = SV999 )
= $true )
| ( ( class_Orderings_Olinorder @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4325]) ).
thf(4534,plain,
! [SV30: $i,SV1000: $i,SV544: $i] :
( ( ( c_lessequals @ SV544 @ SV1000 @ SV30 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV544 @ SV1000 @ SV30 )
= $true )
| ( ( SV544 = SV1000 )
= $true )
| ( ( class_Orderings_Olinorder @ SV30 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4326]) ).
thf(4535,plain,
! [SV31: $i,SV1001: $i,SV545: $i] :
( ( ( c_lessequals @ SV545 @ SV1001 @ SV31 )
= $false )
| ( ( SV545 = SV1001 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV545 @ SV1001 @ SV31 )
= $true )
| ( ( class_Orderings_Oorder @ SV31 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4327]) ).
thf(4536,plain,
! [SV32: $i,SV1002: $i,SV546: $i] :
( ( ( c_lessequals @ SV546 @ SV1002 @ SV32 )
= $false )
| ( ( SV546 = SV1002 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV546 @ SV1002 @ SV32 )
= $true )
| ( ( class_Orderings_Oorder @ SV32 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4328]) ).
thf(4537,plain,
! [SV33: $i,SV1003: $i,SV547: $i] :
( ( ( c_lessequals @ SV547 @ SV1003 @ SV33 )
= $false )
| ( ( SV547 = SV1003 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV547 @ SV1003 @ SV33 )
= $true )
| ( ( class_Orderings_Oorder @ SV33 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4329]) ).
thf(4538,plain,
! [SV34: $i,SV1004: $i,SV548: $i] :
( ( ( c_lessequals @ SV548 @ SV1004 @ SV34 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV548 @ SV1004 @ SV34 )
= $true )
| ( ( SV548 = SV1004 )
= $true )
| ( ( class_Orderings_Oorder @ SV34 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4330]) ).
thf(4539,plain,
! [SV35: $i,SV1005: $i,SV549: $i] :
( ( ( c_lessequals @ SV549 @ SV1005 @ SV35 )
= $false )
| ( ( SV1005 = SV549 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV549 @ SV1005 @ SV35 )
= $true )
| ( ( class_Orderings_Oorder @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4331]) ).
thf(4540,plain,
! [SV36: $i,SV1006: $i,SV550: $i] :
( ( ( c_lessequals @ SV550 @ SV1006 @ SV36 )
= $false )
| ( ( SV1006 = SV550 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV550 @ SV1006 @ SV36 )
= $true )
| ( ( class_Orderings_Oorder @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4332]) ).
thf(4541,plain,
! [SV1590: $i,SV1368: $i,SV1007: $i,SV37: $i,SV551: $i] :
( ( ( c_lessequals @ SV551 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV1007 ) @ SV1368 ) @ SV37 )
= $true )
| ( ( ~ ( c_lessequals @ SV1590 @ SV1368 @ SV37 )
| ~ ( c_lessequals @ SV551 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV1007 ) @ SV1590 ) @ SV37 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4333]) ).
thf(4542,plain,
! [SV552: $i,SV38: $i,SV1008: $i,SV1369: $i] :
( ( ( ~ ( c_lessequals @ SV1369 @ SV1008 @ SV38 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV552 @ SV1369 @ SV38 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV552 @ SV1008 @ SV38 )
= $true )
| ( ( class_Orderings_Opreorder @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4334]) ).
thf(4543,plain,
! [SV553: $i,SV39: $i,SV1009: $i,SV1370: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1370 @ SV1009 @ SV39 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV553 @ SV1370 @ SV39 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV553 @ SV1009 @ SV39 )
= $true )
| ( ( class_Orderings_Opreorder @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4335]) ).
thf(4544,plain,
! [SV556: $i,SV42: $i,SV1010: $i,SV1371: $i] :
( ( ( ~ ( c_lessequals @ SV1371 @ SV1010 @ SV42 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV556 @ SV1371 @ SV42 ) )
= $true )
| ( ( c_lessequals @ SV556 @ SV1010 @ SV42 )
= $true )
| ( ( class_Orderings_Opreorder @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4336]) ).
thf(4545,plain,
! [SV1011: $i,SV43: $i,SV1372: $i,SV557: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV557 @ SV1372 @ SV43 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1372 @ SV1011 @ SV43 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV557 @ SV1011 @ SV43 )
= $true )
| ( ( class_Orderings_Oorder @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4337]) ).
thf(4546,plain,
! [SV1012: $i,SV44: $i,SV1373: $i,SV558: $i] :
( ( ( ~ ( c_lessequals @ SV558 @ SV1373 @ SV44 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1373 @ SV1012 @ SV44 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV558 @ SV1012 @ SV44 )
= $true )
| ( ( class_Orderings_Oorder @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4338]) ).
thf(4547,plain,
! [SV1013: $i,SV45: $i,SV1374: $i,SV559: $i] :
( ( ( ~ ( c_lessequals @ SV559 @ SV1374 @ SV45 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV1374 @ SV1013 @ SV45 ) )
= $true )
| ( ( c_lessequals @ SV559 @ SV1013 @ SV45 )
= $true )
| ( ( class_Orderings_Oorder @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4339]) ).
thf(4548,plain,
! [SV561: $i,SV47: $i,SV1376: $i,SV1015: $i] :
( ( ( c_lessequals @ SV1015 @ SV1376 @ SV47 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ SV561 ) @ SV1015 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV47 ) @ SV561 ) @ SV1376 ) @ SV47 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4341]) ).
thf(4549,plain,
! [SV1016: $i,SV48: $i,SV1377: $i,SV562: $i] :
( ( ( c_lessequals @ SV562 @ SV1377 @ SV48 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV48 ) @ SV562 ) @ SV1016 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV48 ) @ SV1377 ) @ SV1016 ) @ SV48 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4342]) ).
thf(4550,plain,
! [SV1017: $i,SV563: $i,SV1378: $i,SV49: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SV1378 ) @ SV563 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV49 ) @ SV1378 ) @ SV1017 ) @ SV49 )
= $false )
| ( ( c_lessequals @ SV563 @ SV1017 @ SV49 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4343]) ).
thf(4551,plain,
! [SV564: $i,SV50: $i,SV1379: $i,SV1018: $i] :
( ( ( c_lessequals @ SV1018 @ SV1379 @ SV50 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV564 ) @ SV1018 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV50 ) @ SV564 ) @ SV1379 ) @ SV50 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4344]) ).
thf(4552,plain,
! [SV1019: $i,SV1380: $i,SV565: $i,SV51: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV51 ) @ SV565 ) @ SV1380 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV51 ) @ SV1019 ) @ SV1380 ) @ SV51 )
= $false )
| ( ( c_lessequals @ SV565 @ SV1019 @ SV51 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4345]) ).
thf(4553,plain,
! [SV1020: $i,SV52: $i,SV1381: $i,SV566: $i] :
( ( ( c_lessequals @ SV566 @ SV1381 @ SV52 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV566 ) @ SV1020 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV52 ) @ SV1381 ) @ SV1020 ) @ SV52 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4346]) ).
thf(4554,plain,
! [SV55: $i,SV1023: $i,SV569: $i] :
( ( ( c_lessequals @ SV569 @ SV1023 @ SV55 )
= $false )
| ( ( ~ ( c_lessequals @ SV1023 @ SV569 @ SV55 ) )
= $true )
| ( ( SV569 = SV1023 )
= $true )
| ( ( class_Orderings_Oorder @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4349]) ).
thf(4555,plain,
! [SV56: $i,SV570: $i,SV1024: $i] :
( ( ( c_lessequals @ SV1024 @ SV570 @ SV56 )
= $false )
| ( ( ~ ( c_lessequals @ SV570 @ SV1024 @ SV56 ) )
= $true )
| ( ( SV570 = SV1024 )
= $true )
| ( ( class_Orderings_Oorder @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4350]) ).
thf(4556,plain,
! [SV57: $i,SV571: $i,SV1025: $i] :
( ( ( c_lessequals @ SV1025 @ SV571 @ SV57 )
= $false )
| ( ( ~ ( c_lessequals @ SV571 @ SV1025 @ SV57 ) )
= $true )
| ( ( SV571 = SV1025 )
= $true )
| ( ( class_Orderings_Oorder @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4351]) ).
thf(4557,plain,
! [SV1744: $i,SV1688: $i,SV1592: $i,SV1382: $i,SV1026: $i,SV572: $i,SV58: $i] :
( ( ( ( hAPP @ ( hAPP @ SV58 @ SV572 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= SV572 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1026 @ SV1382 @ SV58 @ SV1592 @ SV1688 @ SV1744 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4352]) ).
thf(4558,plain,
! [SV60: $i,SV1027: $i,SV573: $i] :
( ( ( c_lessequals @ SV573 @ SV1027 @ SV60 )
= $false )
| ( ( c_lessequals @ SV1027 @ SV573 @ SV60 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV573 @ SV1027 @ SV60 )
= $true )
| ( ( class_Orderings_Opreorder @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4353]) ).
thf(4559,plain,
! [SV1029: $i,SV63: $i,SV1384: $i,SV575: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV575 @ SV1384 @ SV63 ) @ SV1029 @ SV63 )
= $false )
| ( ( c_lessequals @ SV575 @ SV1029 @ SV63 )
= $true )
| ( ( class_Orderings_Olinorder @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4354]) ).
thf(4560,plain,
! [SV1030: $i,SV64: $i,SV576: $i,SV1385: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1385 @ SV576 @ SV64 ) @ SV1030 @ SV64 )
= $false )
| ( ( c_lessequals @ SV576 @ SV1030 @ SV64 )
= $true )
| ( ( class_Orderings_Olinorder @ SV64 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4355]) ).
thf(4561,plain,
! [SV1386: $i,SV65: $i,SV1031: $i,SV577: $i] :
( ( ( c_lessequals @ SV577 @ SV1031 @ SV65 )
= $false )
| ( ( c_lessequals @ SV577 @ ( c_Orderings_Oord__class_Omax @ SV1031 @ SV1386 @ SV65 ) @ SV65 )
= $true )
| ( ( class_Orderings_Olinorder @ SV65 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4356]) ).
thf(4562,plain,
! [SV1032: $i,SV66: $i,SV1387: $i,SV578: $i] :
( ( ( c_lessequals @ SV578 @ SV1387 @ SV66 )
= $false )
| ( ( c_lessequals @ SV578 @ ( c_Orderings_Oord__class_Omax @ SV1032 @ SV1387 @ SV66 ) @ SV66 )
= $true )
| ( ( class_Orderings_Olinorder @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4357]) ).
thf(4563,plain,
! [SV1388: $i,SV67: $i,SV1033: $i,SV579: $i] :
( ( ( c_lessequals @ SV579 @ SV1033 @ SV67 )
= $false )
| ( ( c_lessequals @ SV579 @ ( c_Orderings_Oord__class_Omax @ SV1033 @ SV1388 @ SV67 ) @ SV67 )
= $true )
| ( ( class_Orderings_Olinorder @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4358]) ).
thf(4564,plain,
! [SV1034: $i,SV68: $i,SV1389: $i,SV580: $i] :
( ( ( c_lessequals @ SV580 @ SV1389 @ SV68 )
= $false )
| ( ( c_lessequals @ SV580 @ ( c_Orderings_Oord__class_Omax @ SV1034 @ SV1389 @ SV68 ) @ SV68 )
= $true )
| ( ( class_Orderings_Olinorder @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4359]) ).
thf(4565,plain,
! [SV1035: $i,SV69: $i,SV1390: $i,SV581: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV581 @ SV1390 @ SV69 ) @ SV1035 @ SV69 )
= $false )
| ( ( c_lessequals @ SV581 @ SV1035 @ SV69 )
= $true )
| ( ( class_Orderings_Olinorder @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4360]) ).
thf(4566,plain,
! [SV1036: $i,SV70: $i,SV582: $i,SV1391: $i] :
( ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV1391 @ SV582 @ SV70 ) @ SV1036 @ SV70 )
= $false )
| ( ( c_lessequals @ SV582 @ SV1036 @ SV70 )
= $true )
| ( ( class_Orderings_Olinorder @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4361]) ).
thf(4567,plain,
! [SV1037: $i,SV73: $i,SV1392: $i,SV585: $i] :
( ( ( c_lessequals @ SV585 @ SV1392 @ SV73 )
= $true )
| ( ( ~ ( c_lessequals @ SV585 @ ( c_Orderings_Oord__class_Omax @ SV1392 @ SV1037 @ SV73 ) @ SV73 ) )
= $true )
| ( ( c_lessequals @ SV585 @ SV1037 @ SV73 )
= $true )
| ( ( class_Orderings_Olinorder @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4362]) ).
thf(4568,plain,
! [SV588: $i,SV76: $i,SV1393: $i,SV1040: $i] :
( ( ( ~ ( c_lessequals @ SV1040 @ SV1393 @ SV76 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV588 @ SV1393 @ SV76 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV588 @ SV1040 @ SV76 ) @ SV1393 @ SV76 )
= $true )
| ( ( class_Orderings_Olinorder @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4363]) ).
thf(4569,plain,
! [SV589: $i,SV77: $i,SV1394: $i,SV1041: $i] :
( ( ( ~ ( c_lessequals @ SV1041 @ SV1394 @ SV77 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV589 @ SV1394 @ SV77 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV589 @ SV1041 @ SV77 ) @ SV1394 @ SV77 )
= $true )
| ( ( class_Orderings_Olinorder @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4364]) ).
thf(4570,plain,
! [SV590: $i,SV78: $i,SV1395: $i,SV1042: $i] :
( ( ( ~ ( c_lessequals @ SV1042 @ SV1395 @ SV78 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV590 @ SV1395 @ SV78 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV590 @ SV1042 @ SV78 ) @ SV1395 @ SV78 )
= $true )
| ( ( class_Orderings_Olinorder @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4365]) ).
thf(4571,plain,
! [SV1593: $i,SV1396: $i,SV1044: $i,SV592: $i,SV80: $i] :
( ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SV592 ) @ SV1044 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SV1396 ) @ SV1593 ) @ SV80 )
= $true )
| ( ( ~ ( c_lessequals @ SV1044 @ SV1593 @ SV80 )
| ~ ( c_lessequals @ SV592 @ SV1396 @ SV80 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4367]) ).
thf(4572,plain,
! [SV87: $i,SV599: $i,SV1048: $i] :
( ( ( c_lessequals @ SV1048 @ SV599 @ SV87 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV599 @ SV1048 @ SV87 )
= $false )
| ( ( class_Orderings_Olinorder @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4371]) ).
thf(4573,plain,
! [SV89: $i,SV601: $i,SV1050: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1050 @ SV601 @ SV89 )
= $false )
| ( ( c_lessequals @ SV601 @ SV1050 @ SV89 )
= $false )
| ( ( class_Orderings_Olinorder @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4372]) ).
thf(4574,plain,
! [SV91: $i,SV603: $i,SV1052: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1052 @ SV603 @ SV91 )
= $false )
| ( ( c_lessequals @ SV603 @ SV1052 @ SV91 )
= $false )
| ( ( class_Orderings_Opreorder @ SV91 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4373]) ).
thf(4575,plain,
! [SV604: $i,SV93: $i,SV1053: $i] :
( ( ( c_lessequals @ SV1053 @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV604 @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV604 ) @ SV1053 ) @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4374]) ).
thf(4576,plain,
! [SV605: $i,SV94: $i,SV1054: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1054 @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 )
= $false )
| ( ( ~ ( c_lessequals @ SV605 @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV605 ) @ SV1054 ) @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4375]) ).
thf(4577,plain,
! [SV1397: $i,SV1055: $i,SV606: $i,SV95: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV95 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV606 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV1055 ) @ SV1397 ) @ SV95 )
| ~ ( c_lessequals @ SV606 @ SV1397 @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV1055 @ SV95 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4376]) ).
thf(4578,plain,
! [SV1398: $i,SV1056: $i,SV607: $i,SV96: $i] :
( ( ( class_OrderedGroup_Ocomm__monoid__add @ SV96 )
= $false )
| ( ( ( c_HOL_Oord__class_Oless @ SV607 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SV1056 ) @ SV1398 ) @ SV96 )
| ~ ( c_HOL_Oord__class_Oless @ SV607 @ SV1398 @ SV96 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV1056 @ SV96 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4377]) ).
thf(4579,plain,
! [SV608: $i,SV1057: $i,SV97: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV1057 @ SV97 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV608 @ SV97 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV608 ) @ SV1057 ) @ SV97 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4378]) ).
thf(4580,plain,
! [SV609: $i,SV1058: $i,SV98: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ SV1058 @ SV98 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ SV609 @ SV98 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV98 ) @ SV609 ) @ SV1058 ) @ SV98 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4379]) ).
thf(4581,plain,
! [SV1399: $i,SV610: $i,SV1059: $i,SV100: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV100 ) @ SV1059 @ SV100 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV610 @ SV1399 @ SV100 ) @ ( c_Power_Opower__class_Opower @ SV1059 @ SV1399 @ SV100 ) @ SV100 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV610 @ SV1059 @ SV100 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4380]) ).
thf(4582,plain,
! [SV1060: $i,SV102: $i,SV611: $i,SV1400: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1400 @ SV611 @ SV102 ) @ ( c_Power_Opower__class_Opower @ SV1400 @ SV1060 @ SV102 ) @ SV102 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV102 ) @ SV1400 @ SV102 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV611 @ SV1060 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4381]) ).
thf(4583,plain,
! [SV1401: $i,SV1061: $i,SV612: $i,SV103: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV103 ) @ SV612 @ SV103 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1061 @ SV1401 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV612 @ SV1061 @ SV103 ) @ ( c_Power_Opower__class_Opower @ SV612 @ SV1401 @ SV103 ) @ SV103 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4382]) ).
thf(4584,plain,
! [SV1062: $i,SV104: $i,SV613: $i,SV1402: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1402 @ SV613 @ SV104 ) @ ( c_Power_Opower__class_Opower @ SV1402 @ SV1062 @ SV104 ) @ SV104 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV104 ) @ SV1402 @ SV104 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV613 @ SV1062 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV104 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4383]) ).
thf(4585,plain,
! [SV614: $i,SV105: $i,SV1403: $i,SV1063: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1063 @ SV1403 @ tc_nat ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV105 ) @ SV614 @ SV105 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV614 @ SV1063 @ SV105 ) @ ( c_Power_Opower__class_Opower @ SV614 @ SV1403 @ SV105 ) @ SV105 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV105 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4384]) ).
thf(4586,plain,
! [SV1404: $i,SV618: $i,SV109: $i,SV1066: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1066 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV618 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SV618 @ SV1404 @ SV109 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV618 @ SV1066 @ SV109 ) @ ( c_Power_Opower__class_Opower @ SV1404 @ SV1066 @ SV109 ) @ SV109 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4385]) ).
thf(4587,plain,
! [SV621: $i,SV1595: $i,SV1406: $i,SV1689: $i,SV1069: $i,SV112: $i] :
( ( ( ~ ( c_Type_Otypings @ ( c_Type_Oshift @ SV112 @ SV1069 @ SV1689 @ tc_Type_Otype ) @ SV1406 @ SV1595 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV112 @ SV621 @ SV1689 ) )
= $true )
| ( ( c_Type_Otypings @ SV112 @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SV621 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV1069 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1406 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1595 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4387]) ).
thf(4588,plain,
! [SV631: $i,SV123: $i,SV1077: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1077 @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV631 @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV123 ) @ SV631 ) @ SV1077 ) @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4388]) ).
thf(4589,plain,
! [SV1078: $i,SV125: $i,SV632: $i,SV1412: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV1412 @ SV632 @ SV125 ) @ SV1078 @ SV125 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV632 @ SV1078 @ SV125 )
= $true )
| ( ( class_Orderings_Olinorder @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4389]) ).
thf(4590,plain,
! [SV1079: $i,SV126: $i,SV1413: $i,SV633: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV633 @ SV1413 @ SV126 ) @ SV1079 @ SV126 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV633 @ SV1079 @ SV126 )
= $true )
| ( ( class_Orderings_Olinorder @ SV126 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4390]) ).
thf(4591,plain,
! [SV1080: $i,SV127: $i,SV1414: $i,SV634: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV634 @ SV1414 @ SV127 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV634 @ ( c_Orderings_Oord__class_Omax @ SV1080 @ SV1414 @ SV127 ) @ SV127 )
= $true )
| ( ( class_Orderings_Olinorder @ SV127 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4391]) ).
thf(4592,plain,
! [SV1415: $i,SV128: $i,SV1081: $i,SV635: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV635 @ SV1081 @ SV128 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV635 @ ( c_Orderings_Oord__class_Omax @ SV1081 @ SV1415 @ SV128 ) @ SV128 )
= $true )
| ( ( class_Orderings_Olinorder @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4392]) ).
thf(4593,plain,
! [SV1082: $i,SV129: $i,SV1416: $i,SV636: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV636 @ SV1416 @ SV129 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV636 @ ( c_Orderings_Oord__class_Omax @ SV1082 @ SV1416 @ SV129 ) @ SV129 )
= $true )
| ( ( class_Orderings_Olinorder @ SV129 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4393]) ).
thf(4594,plain,
! [SV1417: $i,SV130: $i,SV1083: $i,SV637: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV637 @ SV1083 @ SV130 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV637 @ ( c_Orderings_Oord__class_Omax @ SV1083 @ SV1417 @ SV130 ) @ SV130 )
= $true )
| ( ( class_Orderings_Olinorder @ SV130 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4394]) ).
thf(4595,plain,
! [SV1084: $i,SV638: $i,SV1690: $i,SV1599: $i,SV1418: $i,SV131: $i] :
( ( ( c_ListOrder_Ostep1 @ SV131 @ SV1418 @ SV1599 @ SV1690 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV131 @ ( c_List_Oappend @ SV1418 @ ( c_List_Olist_OCons @ SV638 @ ( c_List_Olist_ONil @ SV1690 ) @ SV1690 ) @ SV1690 ) @ ( c_List_Oappend @ SV1599 @ ( c_List_Olist_OCons @ SV1084 @ ( c_List_Olist_ONil @ SV1690 ) @ SV1690 ) @ SV1690 ) @ SV1690 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV638 ) @ SV1084 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4395]) ).
thf(4596,plain,
! [SV1105: $i,SV153: $i,SV1436: $i,SV660: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV660 @ SV1436 @ SV153 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1436 @ SV1105 @ SV153 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV660 @ SV1105 @ SV153 )
= $true )
| ( ( class_Orderings_Oorder @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4400]) ).
thf(4597,plain,
! [SV661: $i,SV154: $i,SV1106: $i,SV1437: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1437 @ SV1106 @ SV154 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV661 @ SV1437 @ SV154 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV661 @ SV1106 @ SV154 )
= $true )
| ( ( class_Orderings_Opreorder @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4401]) ).
thf(4598,plain,
! [SV161: $i,SV1692: $i,SV668: $i,SV1608: $i,SV1443: $i,SV1112: $i] :
( ( ( SV1112 = SV1443 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV1608 @ ( c_List_Olist_OCons @ SV668 @ SV1443 @ SV1692 ) @ ( c_List_Olist_OCons @ SV161 @ SV1112 @ SV1692 ) @ SV1692 ) )
= $true )
| ( ( SV161 = SV668 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4404]) ).
thf(4599,plain,
! [SV671: $i,SV164: $i,SV1445: $i,SV1114: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1114 @ SV1445 @ SV164 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV671 @ SV1445 @ SV164 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV671 @ SV1114 @ SV164 ) @ SV1445 @ SV164 )
= $true )
| ( ( class_Orderings_Olinorder @ SV164 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4406]) ).
thf(4600,plain,
! [SV674: $i,SV1117: $i,SV1446: $i,SV167: $i] :
( ( ( c_Wellfounded_Oaccp @ SV167 @ SV1446 @ SV1117 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV167 @ SV1117 ) @ SV674 ) @ SV1446 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV167 @ SV674 @ SV1117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4407]) ).
thf(4601,plain,
! [SV1447: $i,SV675: $i,SV1118: $i,SV168: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV168 @ SV1118 ) @ SV675 ) @ SV1447 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV168 @ SV1447 @ SV1118 )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV168 @ SV675 @ SV1118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4408]) ).
thf(4602,plain,
! [SV1119: $i,SV1448: $i,SV1610: $i,SV676: $i,SV169: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SV676 ) @ SV1610 ) @ SV1448 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SV676 ) @ SV1119 ) @ SV1610 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SV676 ) @ SV1119 ) @ SV1448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4409]) ).
thf(4603,plain,
! [SV1694: $i,SV1613: $i,SV1452: $i,SV190: $i,SV1131: $i,SV694: $i] :
( ( ( SV694 = SV1131 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV190 @ ( c_List_Oappend @ SV1452 @ ( c_List_Olist_OCons @ SV694 @ ( c_List_Olist_ONil @ SV1613 ) @ SV1613 ) @ SV1613 ) @ ( c_List_Oappend @ SV1694 @ ( c_List_Olist_OCons @ SV1131 @ ( c_List_Olist_ONil @ SV1613 ) @ SV1613 ) @ SV1613 ) @ SV1613 ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV190 @ SV694 ) @ SV1131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4410]) ).
thf(4604,plain,
! [SV1782: $i,SV1745: $i,SV1695: $i,SV1614: $i,SV1453: $i,SV1132: $i,SV695: $i,SV191: $i] :
( ( ! [SY4980: $i] :
( ( ( hAPP @ ( hAPP @ SV191 @ ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ SV1453 ) ) @ ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ SV1614 ) )
= ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1453 ) @ SV1614 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1695 @ SV191 @ SV695 @ SV1745 @ SV1782 @ SY4980 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4411]) ).
thf(4605,plain,
! [SV1783: $i,SV1746: $i,SV1696: $i,SV1615: $i,SV1459: $i,SV1141: $i,SV706: $i,SV202: $i] :
( ( ! [SY4981: $i] :
( ( ( hAPP @ ( hAPP @ SV202 @ ( hAPP @ ( hAPP @ SV706 @ SV1141 ) @ SV1459 ) ) @ SV1615 )
= ( hAPP @ ( hAPP @ SV706 @ ( hAPP @ ( hAPP @ SV202 @ SV1141 ) @ SV1615 ) ) @ ( hAPP @ ( hAPP @ SV202 @ SV1459 ) @ SV1615 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1696 @ SV706 @ SV202 @ SV1746 @ SV1783 @ SY4981 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4412]) ).
thf(4606,plain,
! [SV1784: $i,SV1747: $i,SV1697: $i,SV1616: $i,SV1460: $i,SV1142: $i,SV707: $i,SV203: $i] :
( ( ! [SY4982: $i] :
( ( ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ ( hAPP @ ( hAPP @ SV1142 @ SV1460 ) @ SV1616 ) )
= ( hAPP @ ( hAPP @ SV1142 @ ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ SV1460 ) ) @ ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ SV1616 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1142 @ SV203 @ SV1697 @ SV1747 @ SV1784 @ SY4982 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4413]) ).
thf(4607,plain,
! [SV1785: $i,SV1748: $i,SV1698: $i,SV1617: $i,SV1461: $i,SV1143: $i,SV708: $i,SV204: $i] :
( ( ( ( hAPP @ ( hAPP @ SV204 @ SV708 ) @ SV1143 )
= ( hAPP @ ( hAPP @ SV204 @ SV1143 ) @ SV708 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1461 @ SV204 @ SV1617 @ SV1698 @ SV1748 @ SV1785 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4414]) ).
thf(4608,plain,
! [SV1786: $i,SV1749: $i,SV1699: $i,SV1618: $i,SV1462: $i,SV1144: $i,SV709: $i,SV205: $i] :
( ( ! [SY4983: $i] :
( ( ( hAPP @ ( hAPP @ SV205 @ SV709 ) @ ( hAPP @ ( hAPP @ SV205 @ SV1144 ) @ SV1462 ) )
= ( hAPP @ ( hAPP @ SV205 @ ( hAPP @ ( hAPP @ SV205 @ SV709 ) @ SV1144 ) ) @ SV1462 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1618 @ SV205 @ SV1699 @ SV1749 @ SV1786 @ SY4983 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4415]) ).
thf(4609,plain,
! [SV1750: $i,SV1700: $i,SV1619: $i,SV1463: $i,SV1145: $i,SV710: $i,SV206: $i] :
( ( ( ( hAPP @ ( hAPP @ SV206 @ SV710 ) @ SV1145 )
= SV1145 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1463 @ SV206 @ SV1619 @ SV1700 @ SV710 @ SV1750 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4416]) ).
thf(4610,plain,
! [SV1751: $i,SV1701: $i,SV1620: $i,SV1464: $i,SV1146: $i,SV711: $i,SV207: $i] :
( ( ( ( hAPP @ ( hAPP @ SV207 @ SV711 ) @ SV1146 )
= SV711 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1464 @ SV207 @ SV1620 @ SV711 @ SV1701 @ SV1751 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4417]) ).
thf(4611,plain,
! [SV1787: $i,SV1752: $i,SV1702: $i,SV1621: $i,SV1465: $i,SV1147: $i,SV712: $i,SV208: $i] :
( ( ( ( hAPP @ ( hAPP @ SV208 @ SV712 ) @ SV1147 )
= ( hAPP @ ( hAPP @ SV208 @ SV1147 ) @ SV712 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV208 @ SV1465 @ SV1621 @ SV1702 @ SV1752 @ SV1787 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4418]) ).
thf(4612,plain,
! [SV1788: $i,SV1753: $i,SV1703: $i,SV1622: $i,SV1466: $i,SV1148: $i,SV713: $i,SV209: $i] :
( ( ! [SY4984: $i] :
( ( ( hAPP @ ( hAPP @ SV209 @ SV713 ) @ ( hAPP @ ( hAPP @ SV209 @ SV1148 ) @ SV1466 ) )
= ( hAPP @ ( hAPP @ SV209 @ ( hAPP @ ( hAPP @ SV209 @ SV713 ) @ SV1148 ) ) @ SV1466 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV209 @ SV1622 @ SV1703 @ SV1753 @ SV1788 @ SY4984 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4419]) ).
thf(4613,plain,
! [SV1754: $i,SV1704: $i,SV1623: $i,SV1467: $i,SV1149: $i,SV714: $i,SV210: $i] :
( ( ( ( hAPP @ ( hAPP @ SV210 @ SV714 ) @ SV1149 )
= SV1149 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV210 @ SV1467 @ SV1623 @ SV714 @ SV1704 @ SV1754 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4420]) ).
thf(4614,plain,
! [SV1789: $i,SV1755: $i,SV1705: $i,SV1624: $i,SV1468: $i,SV1150: $i,SV715: $i,SV211: $i] :
( ( ! [SY4985: $i] :
( ( ( hAPP @ ( hAPP @ SV211 @ SV715 ) @ ( hAPP @ ( hAPP @ SV211 @ SV1150 ) @ SV1468 ) )
= ( hAPP @ ( hAPP @ SV211 @ ( hAPP @ ( hAPP @ SV211 @ SV715 ) @ SV1150 ) ) @ SV1468 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV211 @ SV1624 @ SV1705 @ SV1755 @ SV1789 @ SY4985 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4421]) ).
thf(4615,plain,
! [SV1790: $i,SV1756: $i,SV1706: $i,SV1625: $i,SV1469: $i,SV1151: $i,SV716: $i,SV212: $i] :
( ( ( ( hAPP @ ( hAPP @ SV212 @ SV716 ) @ SV1151 )
= ( hAPP @ ( hAPP @ SV212 @ SV1151 ) @ SV716 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV212 @ SV1469 @ SV1625 @ SV1706 @ SV1756 @ SV1790 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4422]) ).
thf(4616,plain,
! [SV1791: $i,SV1757: $i,SV1707: $i,SV1626: $i,SV1470: $i,SV1152: $i,SV717: $i,SV213: $i] :
( ( ! [SY4986: $i] :
( ( ( hAPP @ ( hAPP @ SV213 @ ( hAPP @ ( hAPP @ SV213 @ SV717 ) @ SV1152 ) ) @ SV1470 )
= ( hAPP @ ( hAPP @ SV213 @ ( hAPP @ ( hAPP @ SV213 @ SV717 ) @ SV1470 ) ) @ SV1152 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV213 @ SV1626 @ SV1707 @ SV1757 @ SV1791 @ SY4986 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4423]) ).
thf(4617,plain,
! [SV1792: $i,SV1758: $i,SV1708: $i,SV1627: $i,SV1471: $i,SV1153: $i,SV718: $i,SV214: $i] :
( ( ! [SY4987: $i] :
( ( ( hAPP @ ( hAPP @ SV214 @ SV718 ) @ ( hAPP @ ( hAPP @ SV214 @ SV1153 ) @ SV1471 ) )
= ( hAPP @ ( hAPP @ SV214 @ SV1153 ) @ ( hAPP @ ( hAPP @ SV214 @ SV718 ) @ SV1471 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV214 @ SV1627 @ SV1708 @ SV1758 @ SV1792 @ SY4987 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4424]) ).
thf(4618,plain,
! [SV1793: $i,SV1759: $i,SV1709: $i,SV1628: $i,SV1472: $i,SV1154: $i,SV719: $i,SV215: $i] :
( ( ! [SY4988: $i] :
( ( ( hAPP @ ( hAPP @ SV215 @ ( hAPP @ ( hAPP @ SV215 @ SV719 ) @ SV1154 ) ) @ SV1472 )
= ( hAPP @ ( hAPP @ SV215 @ SV719 ) @ ( hAPP @ ( hAPP @ SV215 @ SV1154 ) @ SV1472 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV215 @ SV1628 @ SV1709 @ SV1759 @ SV1793 @ SY4988 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4425]) ).
thf(4619,plain,
! [SV1794: $i,SV1760: $i,SV1710: $i,SV1629: $i,SV1473: $i,SV1155: $i,SV720: $i,SV216: $i] :
( ( ! [SY4989: $i,SY4990: $i] :
( ( ( hAPP @ ( hAPP @ SV216 @ ( hAPP @ ( hAPP @ SV216 @ SV720 ) @ SV1155 ) ) @ ( hAPP @ ( hAPP @ SV216 @ SV1473 ) @ SV1629 ) )
= ( hAPP @ ( hAPP @ SV216 @ ( hAPP @ ( hAPP @ SV216 @ SV720 ) @ SV1473 ) ) @ ( hAPP @ ( hAPP @ SV216 @ SV1155 ) @ SV1629 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV216 @ SV1710 @ SV1760 @ SV1794 @ SY4989 @ SY4990 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4426]) ).
thf(4620,plain,
! [SV1795: $i,SV1761: $i,SV1711: $i,SV1630: $i,SV1474: $i,SV1156: $i,SV721: $i,SV217: $i] :
( ( ! [SY4991: $i] :
( ( ( hAPP @ ( hAPP @ SV217 @ SV721 ) @ ( hAPP @ ( hAPP @ SV217 @ SV1156 ) @ SV1474 ) )
= ( hAPP @ ( hAPP @ SV217 @ SV1156 ) @ ( hAPP @ ( hAPP @ SV217 @ SV721 ) @ SV1474 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1630 @ SV217 @ SV1711 @ SV1761 @ SV1795 @ SY4991 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4427]) ).
thf(4621,plain,
! [SV1796: $i,SV1762: $i,SV1712: $i,SV1631: $i,SV1475: $i,SV1157: $i,SV722: $i,SV218: $i] :
( ( ! [SY4992: $i] :
( ( ( hAPP @ ( hAPP @ SV218 @ SV722 ) @ ( hAPP @ ( hAPP @ SV218 @ SV1157 ) @ SV1475 ) )
= ( hAPP @ ( hAPP @ SV218 @ ( hAPP @ ( hAPP @ SV218 @ SV722 ) @ SV1157 ) ) @ SV1475 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1631 @ SV218 @ SV1712 @ SV1762 @ SV1796 @ SY4992 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4428]) ).
thf(4622,plain,
! [SV1797: $i,SV1763: $i,SV1713: $i,SV1632: $i,SV1476: $i,SV1158: $i,SV723: $i,SV219: $i] :
( ( ! [SY4993: $i] :
( ( ( hAPP @ ( hAPP @ SV219 @ ( hAPP @ ( hAPP @ SV219 @ SV723 ) @ SV1158 ) ) @ SV1476 )
= ( hAPP @ ( hAPP @ SV219 @ SV723 ) @ ( hAPP @ ( hAPP @ SV219 @ SV1158 ) @ SV1476 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1632 @ SV219 @ SV1713 @ SV1763 @ SV1797 @ SY4993 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4429]) ).
thf(4623,plain,
! [SV1798: $i,SV1764: $i,SV1714: $i,SV1633: $i,SV1477: $i,SV1159: $i,SV724: $i,SV220: $i] :
( ( ! [SY4994: $i] :
( ( ( hAPP @ ( hAPP @ SV220 @ ( hAPP @ ( hAPP @ SV220 @ SV724 ) @ SV1159 ) ) @ SV1477 )
= ( hAPP @ ( hAPP @ SV220 @ ( hAPP @ ( hAPP @ SV220 @ SV724 ) @ SV1477 ) ) @ SV1159 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1633 @ SV220 @ SV1714 @ SV1764 @ SV1798 @ SY4994 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4430]) ).
thf(4624,plain,
! [SV1799: $i,SV1765: $i,SV1715: $i,SV1634: $i,SV1478: $i,SV1160: $i,SV725: $i,SV221: $i] :
( ( ! [SY4995: $i,SY4996: $i] :
( ( ( hAPP @ ( hAPP @ SV221 @ ( hAPP @ ( hAPP @ SV221 @ SV725 ) @ SV1160 ) ) @ ( hAPP @ ( hAPP @ SV221 @ SV1478 ) @ SV1634 ) )
= ( hAPP @ ( hAPP @ SV221 @ SV1478 ) @ ( hAPP @ ( hAPP @ SV221 @ ( hAPP @ ( hAPP @ SV221 @ SV725 ) @ SV1160 ) ) @ SV1634 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1715 @ SV221 @ SV1765 @ SV1799 @ SY4995 @ SY4996 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4431]) ).
thf(4625,plain,
! [SV1800: $i,SV1766: $i,SV1716: $i,SV1635: $i,SV1479: $i,SV1161: $i,SV726: $i,SV222: $i] :
( ( ! [SY4997: $i,SY4998: $i] :
( ( ( hAPP @ ( hAPP @ SV222 @ ( hAPP @ ( hAPP @ SV222 @ SV726 ) @ SV1161 ) ) @ ( hAPP @ ( hAPP @ SV222 @ SV1479 ) @ SV1635 ) )
= ( hAPP @ ( hAPP @ SV222 @ SV726 ) @ ( hAPP @ ( hAPP @ SV222 @ SV1161 ) @ ( hAPP @ ( hAPP @ SV222 @ SV1479 ) @ SV1635 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1716 @ SV222 @ SV1766 @ SV1800 @ SY4997 @ SY4998 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4432]) ).
thf(4626,plain,
! [SV1801: $i,SV1767: $i,SV1717: $i,SV1636: $i,SV1480: $i,SV1162: $i,SV727: $i,SV223: $i] :
( ( ! [SY4999: $i,SY5000: $i] :
( ( ( hAPP @ ( hAPP @ SV223 @ ( hAPP @ ( hAPP @ SV223 @ SV727 ) @ SV1162 ) ) @ ( hAPP @ ( hAPP @ SV223 @ SV1480 ) @ SV1636 ) )
= ( hAPP @ ( hAPP @ SV223 @ ( hAPP @ ( hAPP @ SV223 @ SV727 ) @ SV1480 ) ) @ ( hAPP @ ( hAPP @ SV223 @ SV1162 ) @ SV1636 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1717 @ SV223 @ SV1767 @ SV1801 @ SY4999 @ SY5000 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4433]) ).
thf(4627,plain,
! [SV1768: $i,SV1718: $i,SV1637: $i,SV1481: $i,SV1163: $i,SV728: $i,SV224: $i] :
( ( ( ( hAPP @ ( hAPP @ SV224 @ SV728 ) @ SV1163 )
= SV728 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1481 @ SV224 @ SV1637 @ SV1718 @ SV1163 @ SV1768 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4434]) ).
thf(4628,plain,
! [SV1769: $i,SV1719: $i,SV1638: $i,SV1482: $i,SV1164: $i,SV729: $i,SV225: $i] :
( ( ( ( hAPP @ ( hAPP @ SV225 @ SV729 ) @ SV1164 )
= SV1164 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1482 @ SV225 @ SV1638 @ SV1719 @ SV729 @ SV1769 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4435]) ).
thf(4629,plain,
! [SV1770: $i,SV1720: $i,SV1639: $i,SV1483: $i,SV1165: $i,SV730: $i,SV226: $i] :
( ( ( ( hAPP @ ( hAPP @ SV226 @ SV730 ) @ SV1165 )
= SV1165 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1483 @ SV226 @ SV1639 @ SV1165 @ SV1720 @ SV1770 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4436]) ).
thf(4630,plain,
! [SV1771: $i,SV1721: $i,SV1640: $i,SV1484: $i,SV1166: $i,SV731: $i,SV227: $i] :
( ( ( ( hAPP @ ( hAPP @ SV227 @ SV731 ) @ SV1166 )
= SV731 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1484 @ SV227 @ SV1640 @ SV731 @ SV1721 @ SV1771 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4437]) ).
thf(4631,plain,
! [SV1802: $i,SV1772: $i,SV1722: $i,SV1641: $i,SV1485: $i,SV1167: $i,SV732: $i,SV228: $i] :
( ( ! [SY5001: $i] :
( ( ( hAPP @ ( hAPP @ SV228 @ ( hAPP @ ( hAPP @ SV732 @ SV1167 ) @ SV1485 ) ) @ SV1641 )
= ( hAPP @ ( hAPP @ SV732 @ ( hAPP @ ( hAPP @ SV228 @ SV1167 ) @ SV1641 ) ) @ ( hAPP @ ( hAPP @ SV228 @ SV1485 ) @ SV1641 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV732 @ SV228 @ SV1722 @ SV1772 @ SV1802 @ SY5001 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4438]) ).
thf(4632,plain,
! [SV1803: $i,SV1773: $i,SV1723: $i,SV1642: $i,SV1486: $i,SV1168: $i,SV733: $i,SV229: $i] :
( ( ( ( hAPP @ ( hAPP @ SV229 @ SV733 ) @ SV1168 )
= ( hAPP @ ( hAPP @ SV229 @ SV1168 ) @ SV733 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1486 @ SV229 @ SV1642 @ SV1723 @ SV1773 @ SV1803 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4439]) ).
thf(4633,plain,
! [SV1774: $i,SV1724: $i,SV1643: $i,SV1487: $i,SV1169: $i,SV734: $i,SV230: $i] :
( ( ( ( hAPP @ ( hAPP @ SV230 @ SV734 ) @ SV1169 )
= SV734 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV230 @ SV1487 @ SV1643 @ SV1169 @ SV1724 @ SV1774 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4440]) ).
thf(4634,plain,
! [SV1775: $i,SV1725: $i,SV1644: $i,SV1488: $i,SV1170: $i,SV735: $i,SV231: $i] :
( ( ( ( hAPP @ ( hAPP @ SV231 @ SV735 ) @ SV1170 )
= SV1170 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV231 @ SV1488 @ SV1644 @ SV735 @ SV1725 @ SV1775 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4441]) ).
thf(4635,plain,
! [SV1776: $i,SV1726: $i,SV1645: $i,SV1489: $i,SV1171: $i,SV736: $i,SV232: $i] :
( ( ( ( hAPP @ ( hAPP @ SV232 @ SV736 ) @ SV736 )
= ( hAPP @ ( hAPP @ SV1171 @ ( hAPP @ ( hAPP @ SV232 @ SV1489 ) @ SV1489 ) ) @ SV736 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV232 @ SV1171 @ SV1645 @ SV1726 @ SV1489 @ SV1776 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4442]) ).
thf(4636,plain,
! [SV1804: $i,SV1777: $i,SV1727: $i,SV1646: $i,SV1490: $i,SV1172: $i,SV737: $i,SV233: $i] :
( ( ( ( hAPP @ ( hAPP @ SV233 @ SV737 ) @ ( hAPP @ ( hAPP @ SV1172 @ SV1490 ) @ SV737 ) )
= ( hAPP @ ( hAPP @ SV1172 @ ( hAPP @ ( hAPP @ SV233 @ SV1490 ) @ SV1646 ) ) @ SV737 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV233 @ SV1172 @ SV1727 @ SV1777 @ SV1646 @ SV1804 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4443]) ).
thf(4637,plain,
! [SV1805: $i,SV1778: $i,SV1728: $i,SV1647: $i,SV1491: $i,SV1173: $i,SV738: $i,SV234: $i] :
( ( ( ( hAPP @ ( hAPP @ SV234 @ ( hAPP @ ( hAPP @ SV738 @ SV1173 ) @ SV1491 ) ) @ SV1491 )
= ( hAPP @ ( hAPP @ SV738 @ ( hAPP @ ( hAPP @ SV234 @ SV1173 ) @ SV1647 ) ) @ SV1491 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV234 @ SV738 @ SV1728 @ SV1778 @ SV1647 @ SV1805 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4444]) ).
thf(4638,plain,
! [SV1806: $i,SV1779: $i,SV1729: $i,SV1648: $i,SV1492: $i,SV1174: $i,SV739: $i,SV235: $i] :
( ( ! [SY5002: $i] :
( ( ( hAPP @ ( hAPP @ SV235 @ ( hAPP @ ( hAPP @ SV739 @ SV1174 ) @ SV1492 ) ) @ ( hAPP @ ( hAPP @ SV739 @ SV1648 ) @ SV1492 ) )
= ( hAPP @ ( hAPP @ SV739 @ ( hAPP @ ( hAPP @ SV235 @ SV1174 ) @ SV1648 ) ) @ SV1492 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV235 @ SV739 @ SV1729 @ SV1779 @ SV1806 @ SY5002 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4445]) ).
thf(4639,plain,
! [SV1730: $i,SV1649: $i,SV1493: $i,SV236: $i,SV740: $i,SV1175: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1175 @ SV740 ) @ SV236 ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV1175 @ ( c_List_Olist_OCons @ SV740 @ SV1493 @ SV1649 ) @ ( c_List_Olist_OCons @ SV236 @ SV1730 @ SV1649 ) @ SV1649 ) )
= $true )
| ( ( SV236 = SV740 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4446]) ).
thf(4640,plain,
! [SV1495: $i,SV742: $i,SV1177: $i,SV238: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV238 ) @ SV1177 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV742 ) @ SV1495 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV238 ) @ SV742 ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1177 ) @ SV1495 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4448]) ).
thf(4641,plain,
! [SV1180: $i,SV242: $i,SV746: $i,SV1496: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ SV1496 ) @ SV746 ) )
= $false )
| ( ( c_Type_Otyping @ SV242 @ SV1496 @ SV1180 )
= $false )
| ( ( c_Type_Otyping @ SV242 @ SV746 @ SV1180 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4449]) ).
thf(4642,plain,
! [SV1731: $i,SV1651: $i,SV1498: $i,SV754: $i,SV251: $i,SV1185: $i] :
( ( ( c_ListOrder_Ostep1 @ SV1185 @ SV251 @ SV754 @ SV1498 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV1185 @ ( c_List_Oappend @ SV251 @ ( c_List_Olist_OCons @ SV1651 @ ( c_List_Olist_ONil @ SV1498 ) @ SV1498 ) @ SV1498 ) @ ( c_List_Oappend @ SV754 @ ( c_List_Olist_OCons @ SV1731 @ ( c_List_Olist_ONil @ SV1498 ) @ SV1498 ) @ SV1498 ) @ SV1498 ) )
= $true )
| ( ( SV251 = SV754 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4450]) ).
thf(4643,plain,
! [SV1193: $i,SV284: $i,SV1503: $i,SV779: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV779 @ SV1503 @ SV284 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV779 @ ( c_Orderings_Oord__class_Omax @ SV1503 @ SV1193 @ SV284 ) @ SV284 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV779 @ SV1193 @ SV284 )
= $true )
| ( ( class_Orderings_Olinorder @ SV284 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4452]) ).
thf(4644,plain,
! [SV787: $i,SV1197: $i,SV296: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SV1197 @ SV296 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SV787 @ SV296 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV296 ) @ SV787 ) @ SV1197 ) @ SV296 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV296 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4453]) ).
thf(4645,plain,
! [SV1732: $i,SV1504: $i,SV1652: $i,SV297: $i,SV788: $i,SV1198: $i] :
( ( ( SV1198 = SV788 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV297 @ ( c_List_Olist_OCons @ SV1652 @ SV788 @ SV1504 ) @ ( c_List_Olist_OCons @ SV1732 @ SV1198 @ SV1504 ) @ SV1504 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV297 @ SV788 @ SV1198 @ SV1504 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4454]) ).
thf(4646,plain,
! [SV1655: $i,SV1508: $i,SV1209: $i,SV802: $i,SV312: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV312 ) @ SV802 ) @ SV1209 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV312 ) @ SV1508 ) @ SV1655 ) @ SV312 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1209 @ SV1655 @ SV312 )
| ~ ( c_HOL_Oord__class_Oless @ SV802 @ SV1508 @ SV312 ) )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV312 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4461]) ).
thf(4647,plain,
! [SV1509: $i,SV803: $i,SV1210: $i,SV313: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV313 @ SV1210 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV803 @ SV1509 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV313 ) @ SV803 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1210 ) @ SV1509 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4462]) ).
thf(4648,plain,
! [SV810: $i,SV1733: $i,SV321: $i,SV1656: $i,SV1511: $i,SV1214: $i] :
( ( ( SV1214 = SV1511 )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV1656 @ ( c_List_Oappend @ SV321 @ ( c_List_Olist_OCons @ SV1214 @ ( c_List_Olist_ONil @ SV1733 ) @ SV1733 ) @ SV1733 ) @ ( c_List_Oappend @ SV810 @ ( c_List_Olist_OCons @ SV1511 @ ( c_List_Olist_ONil @ SV1733 ) @ SV1733 ) @ SV1733 ) @ SV1733 ) )
= $true )
| ( ( SV321 = SV810 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4465]) ).
thf(4649,plain,
! [SV1216: $i,SV1512: $i,SV812: $i,SV323: $i] :
( ( ( c_List_Olistsp @ SV323 @ SV812 @ SV1512 )
= $false )
| ( ( c_List_Olistsp @ SV323 @ SV1216 @ SV1512 )
= $false )
| ( ( c_List_Olistsp @ SV323 @ ( c_List_Oappend @ SV812 @ SV1216 @ SV1512 ) @ SV1512 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4466]) ).
thf(4650,plain,
! [SV1218: $i,SV326: $i,SV1514: $i,SV814: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV814 @ SV1514 @ SV326 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV1218 @ SV326 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV814 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV326 ) @ SV1218 ) @ SV1514 ) @ SV326 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV326 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4467]) ).
thf(4651,plain,
! [SV1224: $i,SV334: $i,SV1518: $i,SV822: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV822 @ SV1518 @ SV334 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV334 ) @ SV822 ) @ SV1224 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV334 ) @ SV1518 ) @ SV1224 ) @ SV334 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV334 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4470]) ).
thf(4652,plain,
! [SV1225: $i,SV335: $i,SV1519: $i,SV823: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV823 @ SV1519 @ SV335 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV335 ) @ SV823 ) @ SV1225 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV335 ) @ SV1519 ) @ SV1225 ) @ SV335 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV335 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4471]) ).
thf(4653,plain,
! [SV1226: $i,SV1520: $i,SV824: $i,SV336: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV336 ) @ SV824 ) @ SV1520 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV336 ) @ SV1226 ) @ SV1520 ) @ SV336 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV824 @ SV1226 @ SV336 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV336 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4472]) ).
thf(4654,plain,
! [SV825: $i,SV337: $i,SV1521: $i,SV1227: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1227 @ SV1521 @ SV337 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV337 ) @ SV825 ) @ SV1227 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV337 ) @ SV825 ) @ SV1521 ) @ SV337 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV337 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4473]) ).
thf(4655,plain,
! [SV826: $i,SV338: $i,SV1522: $i,SV1228: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1228 @ SV1522 @ SV338 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV338 ) @ SV826 ) @ SV1228 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV338 ) @ SV826 ) @ SV1522 ) @ SV338 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV338 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4474]) ).
thf(4656,plain,
! [SV1229: $i,SV827: $i,SV1523: $i,SV339: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SV1523 ) @ SV827 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV339 ) @ SV1523 ) @ SV1229 ) @ SV339 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV827 @ SV1229 @ SV339 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV339 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4475]) ).
thf(4657,plain,
! [SV831: $i,SV1233: $i,SV1524: $i,SV344: $i] :
( ( ( c_Type_Otyping @ SV344 @ SV1524 @ SV1233 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ SV1524 ) @ SV831 ) )
= $false )
| ( ( c_Type_Otyping @ SV344 @ SV831 @ SV1233 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4476]) ).
thf(4658,plain,
! [SV1234: $i,SV1525: $i,SV832: $i,SV1735: $i,SV1661: $i,SV345: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV345 @ SV1661 ) @ SV1735 ) )
= $true )
| ( ( ~ ( c_ListOrder_Ostep1 @ SV345 @ ( c_List_Olist_OCons @ SV1661 @ SV832 @ SV1525 ) @ ( c_List_Olist_OCons @ SV1735 @ SV1234 @ SV1525 ) @ SV1525 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV345 @ SV832 @ SV1234 @ SV1525 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4477]) ).
thf(4659,plain,
! [SV356: $i,SV841: $i,SV1243: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1243 @ SV841 @ SV356 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV841 @ SV1243 @ SV356 )
= $false )
| ( ( class_Orderings_Oorder @ SV356 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4479]) ).
thf(4660,plain,
! [SV1244: $i,SV1532: $i,SV1663: $i,SV842: $i,SV357: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV357 @ SV842 ) @ SV1663 ) @ SV1532 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ SV357 @ SV1244 ) @ SV1663 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV357 @ SV842 ) @ SV1244 ) @ SV1532 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4480]) ).
thf(4661,plain,
! [SV1245: $i,SV843: $i,SV1533: $i,SV1664: $i,SV358: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV1664 ) @ SV1533 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV358 @ SV843 ) @ SV1245 ) @ SV1664 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV358 @ SV843 ) @ SV1245 ) @ SV1533 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4481]) ).
thf(4662,plain,
! [SV359: $i,SV844: $i,SV1246: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1246 @ SV844 @ SV359 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV844 @ SV1246 @ SV359 )
= $false )
| ( ( class_Orderings_Olinorder @ SV359 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4482]) ).
thf(4663,plain,
! [SV845: $i,SV1247: $i,SV1534: $i,SV360: $i] :
( ( ( c_Wellfounded_Oaccp @ SV360 @ SV1534 @ SV1247 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV360 @ SV845 ) @ SV1534 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV360 @ SV845 @ SV1247 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4483]) ).
thf(4664,plain,
! [SV361: $i,SV846: $i,SV1248: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1248 @ SV846 @ SV361 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV846 @ SV1248 @ SV361 )
= $false )
| ( ( class_Orderings_Opreorder @ SV361 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4484]) ).
thf(4665,plain,
! [SV847: $i,SV1249: $i,SV1535: $i,SV362: $i] :
( ( ( c_Wellfounded_Oaccp @ SV362 @ SV1535 @ SV1249 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV362 @ SV847 ) @ SV1535 ) )
= $false )
| ( ( c_Wellfounded_Oaccp @ SV362 @ SV847 @ SV1249 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4485]) ).
thf(4666,plain,
! [SV363: $i,SV848: $i,SV1250: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1250 @ SV848 @ SV363 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV848 @ SV1250 @ SV363 )
= $false )
| ( ( class_Orderings_Opreorder @ SV363 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4486]) ).
thf(4667,plain,
! [SV1780: $i,SV1736: $i,SV1665: $i,SV1536: $i,SV1252: $i,SV850: $i,SV371: $i] :
( ( ( ( hAPP @ ( hAPP @ SV371 @ SV850 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV1252 )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1536 @ SV1665 @ SV371 @ SV1736 @ SV1252 @ SV1780 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4487]) ).
thf(4668,plain,
! [SV1737: $i,SV1666: $i,SV1537: $i,SV1254: $i,SV854: $i,SV375: $i] :
( ( ( hBOOL @ ( hAPP @ SV375 @ ( c_Lambda_OdB_OdB__case @ SV854 @ SV1254 @ SV1537 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1666 ) @ SV1737 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV375 @ ( hAPP @ ( hAPP @ SV1254 @ SV1666 ) @ SV1737 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4488]) ).
thf(4669,plain,
! [SV1738: $i,SV1667: $i,SV1538: $i,SV1255: $i,SV855: $i,SV376: $i] :
( ( ( hBOOL @ ( hAPP @ SV376 @ ( c_Lambda_OdB_OdB__case @ SV855 @ SV1255 @ SV1538 @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ SV1667 ) @ SV1738 ) @ t_a ) ) )
= $false )
| ( ( hBOOL @ ( hAPP @ SV376 @ ( hAPP @ ( hAPP @ SV1255 @ SV1667 ) @ SV1738 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4489]) ).
thf(4670,plain,
! [SV1781: $i,SV1743: $i,SV1674: $i,SV1551: $i,SV1275: $i,SV877: $i,SV401: $i] :
( ( ( c_Type_Otypings @ SV401 @ SV877 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV1275 @ SV1551 @ SV401 @ SV877 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1674 ) @ SV1743 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1551 )
| ~ ( c_Type_Otypings @ SV401 @ SV1743 @ SV1781 )
| ~ ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1674 ) @ SV1743 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV877 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1275 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4493]) ).
thf(4671,plain,
! [SV891: $i,SV418: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV418 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV418 )
| ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV418 ) @ SV891 @ SV418 )
= ( c_HOL_Ozero__class_Ozero @ SV418 ) )
| ( SV891
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV418 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV418 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4496]) ).
thf(4672,plain,
! [SV430: $i,SV900: $i,SV1679: $i,SV1557: $i,SV1289: $i] :
( ( ( c_Type_Otyping @ SV1289 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1557 ) @ SV1679 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV900 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV1289 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1557 ) @ SV1679 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV430 ) )
= $true )
| ( ( SV430 = SV900 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4498]) ).
thf(4673,plain,
! [SV1681: $i,SV1560: $i,SV1295: $i,SV912: $i,SV444: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV912 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV1295 ) @ SV1560 ) )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV1295 ) @ SV1681 ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV912 ) @ SV1560 )
= SV1681 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV444 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4501]) ).
thf(4674,plain,
! [SV1561: $i,SV1297: $i,SV914: $i,SV446: $i] :
( ( ( class_Int_Onumber__ring @ SV446 )
= $false )
| ( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV446 ) @ SV914 ) @ SV1297 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV446 ) @ SV914 ) @ SV1561 ) )
| ( SV1297 = SV1561 ) )
= $true )
| ( ( class_Ring__and__Field_Oidom @ SV446 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4502]) ).
thf(4675,plain,
! [SV1564: $i,SV456: $i,SV1304: $i,SV924: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV924 @ SV1304 @ SV456 )
= ( c_Power_Opower__class_Opower @ SV1564 @ SV1304 @ SV456 ) )
= $false )
| ( ( ( SV924 = SV1564 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1304 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV1564 @ SV456 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV924 @ SV456 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV456 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4505]) ).
thf(4676,plain,
! [SV927: $i,SV1307: $i,SV459: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV459 ) @ SV1307 @ SV459 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV459 ) @ SV927 @ SV459 )
| ( SV1307
= ( c_HOL_Ozero__class_Ozero @ SV459 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV459 ) @ SV927 ) @ SV1307 )
= ( c_HOL_Ozero__class_Ozero @ SV459 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV459 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4507]) ).
thf(4677,plain,
! [SV1568: $i,SV1312: $i,SV465: $i,SV1685: $i,SV933: $i] :
( ( ( SV933 = SV1685 )
= $true )
| ( ( SV465
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( ( c_List_Oreplicate @ SV465 @ SV933 @ SV1312 )
= ( c_List_Oreplicate @ SV1568 @ SV1685 @ SV1312 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4509]) ).
thf(4678,plain,
! [SV1314: $i,SV467: $i,SV935: $i] :
( ( ( SV935
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV467 ) @ SV935 ) @ SV1314 ) )
= $true )
| ( ( SV1314
= ( c_HOL_Ozero__class_Ozero @ SV467 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV467 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV467 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4510]) ).
thf(4679,plain,
! [SV1318: $i,SV939: $i,SV471: $i] :
( ( ( ~ ( class_Ring__and__Field_Omult__zero @ SV471 ) )
= $true )
| ( ( ~ ( class_Power_Opower @ SV471 )
| ( ( c_Power_Opower__class_Opower @ SV939 @ SV1318 @ SV471 )
!= ( c_HOL_Ozero__class_Ozero @ SV471 ) )
| ( SV939
= ( c_HOL_Ozero__class_Ozero @ SV471 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV471 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4511]) ).
thf(4680,plain,
! [SV1573: $i,SV1330: $i,SV952: $i,SV485: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV952 ) @ SV1330 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV485 ) @ SV1573 ) @ SV1330 ) )
= $false )
| ( ( SV952 = SV1573 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV485 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4514]) ).
thf(4681,plain,
! [SV954: $i,SV487: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV487 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV487 )
| ( ( c_Power_Opower__class_Opower @ SV954 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV487 )
!= ( c_HOL_Ozero__class_Ozero @ SV487 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV487 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV487 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4515]) ).
thf(4682,plain,
! [SV956: $i,SV1332: $i,SV489: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV1332 @ SV489 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV956 @ SV489 )
| ( SV956
= ( c_HOL_Ozero__class_Ozero @ SV489 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV489 ) @ SV956 ) @ SV1332 )
= ( c_HOL_Ozero__class_Ozero @ SV489 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV489 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4516]) ).
thf(4683,plain,
! [SV1574: $i,SV492: $i,SV959: $i,SV1335: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1335 @ SV959 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV492 @ SV1574 @ tc_nat )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV492 ) @ SV959 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1335 ) @ SV1574 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4517]) ).
thf(4684,plain,
! [SV1575: $i,SV1336: $i,SV960: $i,SV493: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV960 ) @ SV1336 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV493 ) @ SV960 ) @ SV1575 ) )
= $false )
| ( ( SV1336 = SV1575 )
= $true )
| ( ( class_OrderedGroup_Ocancel__semigroup__add @ SV493 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4518]) ).
thf(4685,plain,
! [SV1577: $i,SV496: $i,SV1339: $i,SV963: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV963 @ SV1339 @ SV496 )
= ( c_Power_Opower__class_Opower @ SV963 @ SV1577 @ SV496 ) )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV496 ) @ SV963 @ SV496 )
| ( SV1339 = SV1577 ) )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV496 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4519]) ).
thf(4686,plain,
! [SV1578: $i,SV1340: $i,SV964: $i,SV497: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV964 ) @ SV1340 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV497 ) @ SV964 ) @ SV1578 ) )
= $false )
| ( ( SV1340 = SV1578 )
= $true )
| ( ( class_OrderedGroup_Ocancel__ab__semigroup__add @ SV497 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4520]) ).
thf(4687,plain,
! [SV984: $i,SV1358: $i,SV520: $i,SV3: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV520 @ SV3 )
= $false )
| ( ( ~ ( c_lessequals @ SV520 @ SV1358 @ SV3 ) )
= $true )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV520 @ SV984 @ SV3 ) @ ( c_Power_Opower__class_Opower @ SV1358 @ SV984 @ SV3 ) @ SV3 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4523]) ).
thf(4688,plain,
! [SV524: $i,SV1687: $i,SV1586: $i,SV986: $i,SV1359: $i,SV7: $i] :
( ( ( ~ ( c_Type_Otyping @ ( c_Type_Oshift @ SV7 @ SV1359 @ SV986 @ tc_Type_Otype ) @ SV1586 @ SV1687 ) )
= $true )
| ( ( c_Type_Otyping @ SV7 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1586 ) @ SV524 ) @ SV1359 ) @ SV1687 )
= $true )
| ( ( c_Type_Otyping @ SV7 @ SV524 @ SV986 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4524]) ).
thf(4689,plain,
! [SV988: $i,SV1361: $i,SV9: $i,SV526: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV526 @ ( c_HOL_Oone__class_Oone @ SV9 ) @ SV9 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV526 @ SV9 )
| ~ ( c_HOL_Oord__class_Oless @ SV1361 @ SV988 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV526 @ SV988 @ SV9 ) @ ( c_Power_Opower__class_Opower @ SV526 @ SV1361 @ SV9 ) @ SV9 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4525]) ).
thf(4690,plain,
! [SV989: $i,SV527: $i,SV10: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV10 ) @ SV527 @ SV10 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV989 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV10 ) @ ( c_Power_Opower__class_Opower @ SV527 @ SV989 @ SV10 ) @ SV10 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4526]) ).
thf(4691,plain,
! [SV1364: $i,SV532: $i,SV15: $i,SV1588: $i,SV992: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV992 @ SV1588 @ SV15 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV532 @ SV1364 @ SV15 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SV532 ) @ SV992 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SV1364 ) @ SV1588 ) @ SV15 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4527]) ).
thf(4692,plain,
! [SV1365: $i,SV533: $i,SV16: $i,SV1589: $i,SV993: $i] :
( ( ( ~ ( c_lessequals @ SV993 @ SV1589 @ SV16 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV533 @ SV1365 @ SV16 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SV533 ) @ SV993 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SV1365 ) @ SV1589 ) @ SV16 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4528]) ).
thf(4693,plain,
! [SV994: $i,SV17: $i,SV534: $i] :
( ( ( c_lessequals @ SV534 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
= $false )
| ( ( c_lessequals @ SV994 @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV17 ) @ SV534 ) @ SV994 ) @ ( c_HOL_Ozero__class_Ozero @ SV17 ) @ SV17 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4529]) ).
thf(4694,plain,
! [SV1366: $i,SV995: $i,SV20: $i,SV537: $i] :
( ( ( c_lessequals @ SV537 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV20 ) @ SV995 ) @ SV1366 ) @ SV20 )
= $true )
| ( ( ~ ( c_lessequals @ SV537 @ SV995 @ SV20 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV1366 @ SV20 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV20 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4530]) ).
thf(4695,plain,
! [SV1367: $i,SV996: $i,SV21: $i,SV538: $i] :
( ( ( c_lessequals @ SV538 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SV996 ) @ SV1367 ) @ SV21 )
= $true )
| ( ( ~ ( c_lessequals @ SV538 @ SV1367 @ SV21 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ SV996 @ SV21 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV21 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4531]) ).
thf(4696,plain,
! [SV997: $i,SV541: $i,SV25: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV541 @ SV25 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ SV997 @ SV25 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV25 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV25 ) @ SV541 ) @ SV997 ) @ SV25 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV25 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4532]) ).
thf(4697,plain,
! [SV1007: $i,SV551: $i,SV37: $i,SV1368: $i,SV1590: $i] :
( ( ( ~ ( c_lessequals @ SV1590 @ SV1368 @ SV37 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV551 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV1007 ) @ SV1590 ) @ SV37 ) )
= $true )
| ( ( c_lessequals @ SV551 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV1007 ) @ SV1368 ) @ SV37 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4541]) ).
thf(4698,plain,
! [SV552: $i,SV38: $i,SV1008: $i,SV1369: $i] :
( ( ( c_lessequals @ SV1369 @ SV1008 @ SV38 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV552 @ SV1369 @ SV38 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV552 @ SV1008 @ SV38 )
= $true )
| ( ( class_Orderings_Opreorder @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4542]) ).
thf(4699,plain,
! [SV553: $i,SV39: $i,SV1009: $i,SV1370: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1370 @ SV1009 @ SV39 )
= $false )
| ( ( ~ ( c_lessequals @ SV553 @ SV1370 @ SV39 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV553 @ SV1009 @ SV39 )
= $true )
| ( ( class_Orderings_Opreorder @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4543]) ).
thf(4700,plain,
! [SV556: $i,SV42: $i,SV1010: $i,SV1371: $i] :
( ( ( c_lessequals @ SV1371 @ SV1010 @ SV42 )
= $false )
| ( ( ~ ( c_lessequals @ SV556 @ SV1371 @ SV42 ) )
= $true )
| ( ( c_lessequals @ SV556 @ SV1010 @ SV42 )
= $true )
| ( ( class_Orderings_Opreorder @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4544]) ).
thf(4701,plain,
! [SV1011: $i,SV43: $i,SV1372: $i,SV557: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV557 @ SV1372 @ SV43 )
= $false )
| ( ( ~ ( c_lessequals @ SV1372 @ SV1011 @ SV43 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV557 @ SV1011 @ SV43 )
= $true )
| ( ( class_Orderings_Oorder @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4545]) ).
thf(4702,plain,
! [SV1012: $i,SV44: $i,SV1373: $i,SV558: $i] :
( ( ( c_lessequals @ SV558 @ SV1373 @ SV44 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1373 @ SV1012 @ SV44 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV558 @ SV1012 @ SV44 )
= $true )
| ( ( class_Orderings_Oorder @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4546]) ).
thf(4703,plain,
! [SV1013: $i,SV45: $i,SV1374: $i,SV559: $i] :
( ( ( c_lessequals @ SV559 @ SV1374 @ SV45 )
= $false )
| ( ( ~ ( c_lessequals @ SV1374 @ SV1013 @ SV45 ) )
= $true )
| ( ( c_lessequals @ SV559 @ SV1013 @ SV45 )
= $true )
| ( ( class_Orderings_Oorder @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4547]) ).
thf(4704,plain,
! [SV55: $i,SV569: $i,SV1023: $i] :
( ( ( c_lessequals @ SV1023 @ SV569 @ SV55 )
= $false )
| ( ( c_lessequals @ SV569 @ SV1023 @ SV55 )
= $false )
| ( ( SV569 = SV1023 )
= $true )
| ( ( class_Orderings_Oorder @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4554]) ).
thf(4705,plain,
! [SV56: $i,SV1024: $i,SV570: $i] :
( ( ( c_lessequals @ SV570 @ SV1024 @ SV56 )
= $false )
| ( ( c_lessequals @ SV1024 @ SV570 @ SV56 )
= $false )
| ( ( SV570 = SV1024 )
= $true )
| ( ( class_Orderings_Oorder @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4555]) ).
thf(4706,plain,
! [SV57: $i,SV1025: $i,SV571: $i] :
( ( ( c_lessequals @ SV571 @ SV1025 @ SV57 )
= $false )
| ( ( c_lessequals @ SV1025 @ SV571 @ SV57 )
= $false )
| ( ( SV571 = SV1025 )
= $true )
| ( ( class_Orderings_Oorder @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4556]) ).
thf(4707,plain,
! [SV572: $i,SV1744: $i,SV1688: $i,SV1592: $i,SV58: $i,SV1382: $i,SV1026: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1026 @ SV1382 @ SV58 @ SV1592 @ SV1688 @ SV1744 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV58 @ SV572 ) @ ( c_HOL_Oone__class_Oone @ tc_nat ) )
= SV572 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4557]) ).
thf(4708,plain,
! [SV73: $i,SV1037: $i,SV1392: $i,SV585: $i] :
( ( ( c_lessequals @ SV585 @ ( c_Orderings_Oord__class_Omax @ SV1392 @ SV1037 @ SV73 ) @ SV73 )
= $false )
| ( ( c_lessequals @ SV585 @ SV1392 @ SV73 )
= $true )
| ( ( c_lessequals @ SV585 @ SV1037 @ SV73 )
= $true )
| ( ( class_Orderings_Olinorder @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4567]) ).
thf(4709,plain,
! [SV588: $i,SV76: $i,SV1393: $i,SV1040: $i] :
( ( ( c_lessequals @ SV1040 @ SV1393 @ SV76 )
= $false )
| ( ( ~ ( c_lessequals @ SV588 @ SV1393 @ SV76 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV588 @ SV1040 @ SV76 ) @ SV1393 @ SV76 )
= $true )
| ( ( class_Orderings_Olinorder @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4568]) ).
thf(4710,plain,
! [SV589: $i,SV77: $i,SV1394: $i,SV1041: $i] :
( ( ( c_lessequals @ SV1041 @ SV1394 @ SV77 )
= $false )
| ( ( ~ ( c_lessequals @ SV589 @ SV1394 @ SV77 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV589 @ SV1041 @ SV77 ) @ SV1394 @ SV77 )
= $true )
| ( ( class_Orderings_Olinorder @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4569]) ).
thf(4711,plain,
! [SV590: $i,SV78: $i,SV1395: $i,SV1042: $i] :
( ( ( c_lessequals @ SV1042 @ SV1395 @ SV78 )
= $false )
| ( ( ~ ( c_lessequals @ SV590 @ SV1395 @ SV78 ) )
= $true )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV590 @ SV1042 @ SV78 ) @ SV1395 @ SV78 )
= $true )
| ( ( class_Orderings_Olinorder @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4570]) ).
thf(4712,plain,
! [SV1396: $i,SV592: $i,SV80: $i,SV1593: $i,SV1044: $i] :
( ( ( ~ ( c_lessequals @ SV1044 @ SV1593 @ SV80 ) )
= $true )
| ( ( ~ ( c_lessequals @ SV592 @ SV1396 @ SV80 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SV592 ) @ SV1044 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SV1396 ) @ SV1593 ) @ SV80 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV80 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4571]) ).
thf(4713,plain,
! [SV1053: $i,SV93: $i,SV604: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV604 @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 )
= $false )
| ( ( c_lessequals @ SV1053 @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV93 ) @ SV604 ) @ SV1053 ) @ ( c_HOL_Ozero__class_Ozero @ SV93 ) @ SV93 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV93 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4575]) ).
thf(4714,plain,
! [SV1054: $i,SV94: $i,SV605: $i] :
( ( ( c_lessequals @ SV605 @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1054 @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV94 ) @ SV605 ) @ SV1054 ) @ ( c_HOL_Ozero__class_Ozero @ SV94 ) @ SV94 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4576]) ).
thf(4715,plain,
! [SV1397: $i,SV1055: $i,SV95: $i,SV606: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV606 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV1055 ) @ SV1397 ) @ SV95 )
= $true )
| ( ( ~ ( c_lessequals @ SV606 @ SV1397 @ SV95 )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV1055 @ SV95 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV95 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4577]) ).
thf(4716,plain,
! [SV1398: $i,SV1056: $i,SV96: $i,SV607: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV607 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SV1056 ) @ SV1398 ) @ SV96 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV607 @ SV1398 @ SV96 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV1056 @ SV96 ) )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV96 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4578]) ).
thf(4717,plain,
! [SV1057: $i,SV608: $i,SV97: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV608 @ SV97 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ SV1057 @ SV97 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV97 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV97 ) @ SV608 ) @ SV1057 ) @ SV97 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4579]) ).
thf(4718,plain,
! [SV1058: $i,SV609: $i,SV98: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ SV609 @ SV98 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ SV1058 @ SV98 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV98 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV98 ) @ SV609 ) @ SV1058 ) @ SV98 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4580]) ).
thf(4719,plain,
! [SV1399: $i,SV610: $i,SV1059: $i,SV100: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV100 ) @ SV1059 @ SV100 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV610 @ SV1399 @ SV100 ) @ ( c_Power_Opower__class_Opower @ SV1059 @ SV1399 @ SV100 ) @ SV100 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV610 @ SV1059 @ SV100 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4581]) ).
thf(4720,plain,
! [SV1060: $i,SV102: $i,SV611: $i,SV1400: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1400 @ SV611 @ SV102 ) @ ( c_Power_Opower__class_Opower @ SV1400 @ SV1060 @ SV102 ) @ SV102 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV102 ) @ SV1400 @ SV102 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV611 @ SV1060 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4582]) ).
thf(4721,plain,
! [SV1401: $i,SV1061: $i,SV612: $i,SV103: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV103 ) @ SV612 @ SV103 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1061 @ SV1401 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV612 @ SV1061 @ SV103 ) @ ( c_Power_Opower__class_Opower @ SV612 @ SV1401 @ SV103 ) @ SV103 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4583]) ).
thf(4722,plain,
! [SV1062: $i,SV104: $i,SV613: $i,SV1402: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1402 @ SV613 @ SV104 ) @ ( c_Power_Opower__class_Opower @ SV1402 @ SV1062 @ SV104 ) @ SV104 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV104 ) @ SV1402 @ SV104 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV613 @ SV1062 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4584]) ).
thf(4723,plain,
! [SV614: $i,SV105: $i,SV1403: $i,SV1063: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1063 @ SV1403 @ tc_nat )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV105 ) @ SV614 @ SV105 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV614 @ SV1063 @ SV105 ) @ ( c_Power_Opower__class_Opower @ SV614 @ SV1403 @ SV105 ) @ SV105 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4585]) ).
thf(4724,plain,
! [SV1404: $i,SV618: $i,SV109: $i,SV1066: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1066 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV618 @ SV109 )
| ~ ( c_HOL_Oord__class_Oless @ SV618 @ SV1404 @ SV109 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV618 @ SV1066 @ SV109 ) @ ( c_Power_Opower__class_Opower @ SV1404 @ SV1066 @ SV109 ) @ SV109 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4586]) ).
thf(4725,plain,
! [SV621: $i,SV1595: $i,SV1406: $i,SV1689: $i,SV1069: $i,SV112: $i] :
( ( ( c_Type_Otypings @ ( c_Type_Oshift @ SV112 @ SV1069 @ SV1689 @ tc_Type_Otype ) @ SV1406 @ SV1595 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV112 @ SV621 @ SV1689 ) )
= $true )
| ( ( c_Type_Otypings @ SV112 @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SV621 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV1069 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1406 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1595 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4587]) ).
thf(4726,plain,
! [SV1077: $i,SV123: $i,SV631: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV631 @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1077 @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV123 ) @ SV631 ) @ SV1077 ) @ ( c_HOL_Ozero__class_Ozero @ SV123 ) @ SV123 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4588]) ).
thf(4727,plain,
! [SV1084: $i,SV1599: $i,SV1690: $i,SV638: $i,SV1418: $i,SV131: $i] :
( ( ( c_ListOrder_Ostep1 @ SV131 @ ( c_List_Oappend @ SV1418 @ ( c_List_Olist_OCons @ SV638 @ ( c_List_Olist_ONil @ SV1690 ) @ SV1690 ) @ SV1690 ) @ ( c_List_Oappend @ SV1599 @ ( c_List_Olist_OCons @ SV1084 @ ( c_List_Olist_ONil @ SV1690 ) @ SV1690 ) @ SV1690 ) @ SV1690 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV131 @ SV1418 @ SV1599 @ SV1690 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV131 @ SV638 ) @ SV1084 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4595]) ).
thf(4728,plain,
! [SV1105: $i,SV153: $i,SV1436: $i,SV660: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV660 @ SV1436 @ SV153 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1436 @ SV1105 @ SV153 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV660 @ SV1105 @ SV153 )
= $true )
| ( ( class_Orderings_Oorder @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4596]) ).
thf(4729,plain,
! [SV661: $i,SV154: $i,SV1106: $i,SV1437: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1437 @ SV1106 @ SV154 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV661 @ SV1437 @ SV154 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV661 @ SV1106 @ SV154 )
= $true )
| ( ( class_Orderings_Opreorder @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4597]) ).
thf(4730,plain,
! [SV1112: $i,SV161: $i,SV1692: $i,SV1443: $i,SV668: $i,SV1608: $i] :
( ( ( c_ListOrder_Ostep1 @ SV1608 @ ( c_List_Olist_OCons @ SV668 @ SV1443 @ SV1692 ) @ ( c_List_Olist_OCons @ SV161 @ SV1112 @ SV1692 ) @ SV1692 )
= $false )
| ( ( SV1112 = SV1443 )
= $true )
| ( ( SV161 = SV668 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4598]) ).
thf(4731,plain,
! [SV671: $i,SV164: $i,SV1445: $i,SV1114: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1114 @ SV1445 @ SV164 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV671 @ SV1445 @ SV164 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV671 @ SV1114 @ SV164 ) @ SV1445 @ SV164 )
= $true )
| ( ( class_Orderings_Olinorder @ SV164 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4599]) ).
thf(4732,plain,
! [SV1448: $i,SV1610: $i,SV1119: $i,SV676: $i,SV169: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SV676 ) @ SV1119 ) @ SV1610 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SV676 ) @ SV1610 ) @ SV1448 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV169 @ SV676 ) @ SV1119 ) @ SV1448 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4602]) ).
thf(4733,plain,
! [SV1131: $i,SV1694: $i,SV1613: $i,SV694: $i,SV1452: $i,SV190: $i] :
( ( ( c_ListOrder_Ostep1 @ SV190 @ ( c_List_Oappend @ SV1452 @ ( c_List_Olist_OCons @ SV694 @ ( c_List_Olist_ONil @ SV1613 ) @ SV1613 ) @ SV1613 ) @ ( c_List_Oappend @ SV1694 @ ( c_List_Olist_OCons @ SV1131 @ ( c_List_Olist_ONil @ SV1613 ) @ SV1613 ) @ SV1613 ) @ SV1613 )
= $false )
| ( ( SV694 = SV1131 )
= $true )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV190 @ SV694 ) @ SV1131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4603]) ).
thf(4734,plain,
! [SV1807: $i,SV1782: $i,SV1745: $i,SV1695: $i,SV1614: $i,SV1453: $i,SV1132: $i,SV695: $i,SV191: $i] :
( ( ( ( hAPP @ ( hAPP @ SV191 @ ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ SV1453 ) ) @ ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ SV1614 ) )
= ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1453 ) @ SV1614 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1695 @ SV191 @ SV695 @ SV1745 @ SV1782 @ SV1807 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4604]) ).
thf(4735,plain,
! [SV1808: $i,SV1783: $i,SV1746: $i,SV1696: $i,SV1615: $i,SV1459: $i,SV1141: $i,SV706: $i,SV202: $i] :
( ( ( ( hAPP @ ( hAPP @ SV202 @ ( hAPP @ ( hAPP @ SV706 @ SV1141 ) @ SV1459 ) ) @ SV1615 )
= ( hAPP @ ( hAPP @ SV706 @ ( hAPP @ ( hAPP @ SV202 @ SV1141 ) @ SV1615 ) ) @ ( hAPP @ ( hAPP @ SV202 @ SV1459 ) @ SV1615 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1696 @ SV706 @ SV202 @ SV1746 @ SV1783 @ SV1808 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4605]) ).
thf(4736,plain,
! [SV1809: $i,SV1784: $i,SV1747: $i,SV1697: $i,SV1616: $i,SV1460: $i,SV1142: $i,SV707: $i,SV203: $i] :
( ( ( ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ ( hAPP @ ( hAPP @ SV1142 @ SV1460 ) @ SV1616 ) )
= ( hAPP @ ( hAPP @ SV1142 @ ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ SV1460 ) ) @ ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ SV1616 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1142 @ SV203 @ SV1697 @ SV1747 @ SV1784 @ SV1809 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4606]) ).
thf(4737,plain,
! [SV1785: $i,SV1748: $i,SV1698: $i,SV1617: $i,SV1461: $i,SV1143: $i,SV708: $i,SV204: $i] :
( ( ( ( hAPP @ ( hAPP @ SV204 @ SV708 ) @ SV1143 )
= ( hAPP @ ( hAPP @ SV204 @ SV1143 ) @ SV708 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1461 @ SV204 @ SV1617 @ SV1698 @ SV1748 @ SV1785 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4607]) ).
thf(4738,plain,
! [SV1810: $i,SV1786: $i,SV1749: $i,SV1699: $i,SV1618: $i,SV1462: $i,SV1144: $i,SV709: $i,SV205: $i] :
( ( ( ( hAPP @ ( hAPP @ SV205 @ SV709 ) @ ( hAPP @ ( hAPP @ SV205 @ SV1144 ) @ SV1462 ) )
= ( hAPP @ ( hAPP @ SV205 @ ( hAPP @ ( hAPP @ SV205 @ SV709 ) @ SV1144 ) ) @ SV1462 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1618 @ SV205 @ SV1699 @ SV1749 @ SV1786 @ SV1810 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4608]) ).
thf(4739,plain,
! [SV1145: $i,SV1750: $i,SV710: $i,SV1700: $i,SV1619: $i,SV206: $i,SV1463: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1463 @ SV206 @ SV1619 @ SV1700 @ SV710 @ SV1750 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV206 @ SV710 ) @ SV1145 )
= SV1145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4609]) ).
thf(4740,plain,
! [SV1146: $i,SV1751: $i,SV1701: $i,SV711: $i,SV1620: $i,SV207: $i,SV1464: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1464 @ SV207 @ SV1620 @ SV711 @ SV1701 @ SV1751 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV207 @ SV711 ) @ SV1146 )
= SV711 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4610]) ).
thf(4741,plain,
! [SV1787: $i,SV1752: $i,SV1702: $i,SV1621: $i,SV1465: $i,SV1147: $i,SV712: $i,SV208: $i] :
( ( ( ( hAPP @ ( hAPP @ SV208 @ SV712 ) @ SV1147 )
= ( hAPP @ ( hAPP @ SV208 @ SV1147 ) @ SV712 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV208 @ SV1465 @ SV1621 @ SV1702 @ SV1752 @ SV1787 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4611]) ).
thf(4742,plain,
! [SV1811: $i,SV1788: $i,SV1753: $i,SV1703: $i,SV1622: $i,SV1466: $i,SV1148: $i,SV713: $i,SV209: $i] :
( ( ( ( hAPP @ ( hAPP @ SV209 @ SV713 ) @ ( hAPP @ ( hAPP @ SV209 @ SV1148 ) @ SV1466 ) )
= ( hAPP @ ( hAPP @ SV209 @ ( hAPP @ ( hAPP @ SV209 @ SV713 ) @ SV1148 ) ) @ SV1466 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV209 @ SV1622 @ SV1703 @ SV1753 @ SV1788 @ SV1811 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4612]) ).
thf(4743,plain,
! [SV1149: $i,SV1754: $i,SV1704: $i,SV714: $i,SV1623: $i,SV1467: $i,SV210: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV210 @ SV1467 @ SV1623 @ SV714 @ SV1704 @ SV1754 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV210 @ SV714 ) @ SV1149 )
= SV1149 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4613]) ).
thf(4744,plain,
! [SV1812: $i,SV1789: $i,SV1755: $i,SV1705: $i,SV1624: $i,SV1468: $i,SV1150: $i,SV715: $i,SV211: $i] :
( ( ( ( hAPP @ ( hAPP @ SV211 @ SV715 ) @ ( hAPP @ ( hAPP @ SV211 @ SV1150 ) @ SV1468 ) )
= ( hAPP @ ( hAPP @ SV211 @ ( hAPP @ ( hAPP @ SV211 @ SV715 ) @ SV1150 ) ) @ SV1468 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV211 @ SV1624 @ SV1705 @ SV1755 @ SV1789 @ SV1812 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4614]) ).
thf(4745,plain,
! [SV1790: $i,SV1756: $i,SV1706: $i,SV1625: $i,SV1469: $i,SV1151: $i,SV716: $i,SV212: $i] :
( ( ( ( hAPP @ ( hAPP @ SV212 @ SV716 ) @ SV1151 )
= ( hAPP @ ( hAPP @ SV212 @ SV1151 ) @ SV716 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV212 @ SV1469 @ SV1625 @ SV1706 @ SV1756 @ SV1790 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4615]) ).
thf(4746,plain,
! [SV1813: $i,SV1791: $i,SV1757: $i,SV1707: $i,SV1626: $i,SV1470: $i,SV1152: $i,SV717: $i,SV213: $i] :
( ( ( ( hAPP @ ( hAPP @ SV213 @ ( hAPP @ ( hAPP @ SV213 @ SV717 ) @ SV1152 ) ) @ SV1470 )
= ( hAPP @ ( hAPP @ SV213 @ ( hAPP @ ( hAPP @ SV213 @ SV717 ) @ SV1470 ) ) @ SV1152 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV213 @ SV1626 @ SV1707 @ SV1757 @ SV1791 @ SV1813 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4616]) ).
thf(4747,plain,
! [SV1814: $i,SV1792: $i,SV1758: $i,SV1708: $i,SV1627: $i,SV1471: $i,SV1153: $i,SV718: $i,SV214: $i] :
( ( ( ( hAPP @ ( hAPP @ SV214 @ SV718 ) @ ( hAPP @ ( hAPP @ SV214 @ SV1153 ) @ SV1471 ) )
= ( hAPP @ ( hAPP @ SV214 @ SV1153 ) @ ( hAPP @ ( hAPP @ SV214 @ SV718 ) @ SV1471 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV214 @ SV1627 @ SV1708 @ SV1758 @ SV1792 @ SV1814 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4617]) ).
thf(4748,plain,
! [SV1815: $i,SV1793: $i,SV1759: $i,SV1709: $i,SV1628: $i,SV1472: $i,SV1154: $i,SV719: $i,SV215: $i] :
( ( ( ( hAPP @ ( hAPP @ SV215 @ ( hAPP @ ( hAPP @ SV215 @ SV719 ) @ SV1154 ) ) @ SV1472 )
= ( hAPP @ ( hAPP @ SV215 @ SV719 ) @ ( hAPP @ ( hAPP @ SV215 @ SV1154 ) @ SV1472 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV215 @ SV1628 @ SV1709 @ SV1759 @ SV1793 @ SV1815 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4618]) ).
thf(4749,plain,
! [SV1816: $i,SV1794: $i,SV1760: $i,SV1710: $i,SV1629: $i,SV1473: $i,SV1155: $i,SV720: $i,SV216: $i] :
( ( ! [SY5003: $i] :
( ( ( hAPP @ ( hAPP @ SV216 @ ( hAPP @ ( hAPP @ SV216 @ SV720 ) @ SV1155 ) ) @ ( hAPP @ ( hAPP @ SV216 @ SV1473 ) @ SV1629 ) )
= ( hAPP @ ( hAPP @ SV216 @ ( hAPP @ ( hAPP @ SV216 @ SV720 ) @ SV1473 ) ) @ ( hAPP @ ( hAPP @ SV216 @ SV1155 ) @ SV1629 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV216 @ SV1710 @ SV1760 @ SV1794 @ SV1816 @ SY5003 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4619]) ).
thf(4750,plain,
! [SV1817: $i,SV1795: $i,SV1761: $i,SV1711: $i,SV1630: $i,SV1474: $i,SV1156: $i,SV721: $i,SV217: $i] :
( ( ( ( hAPP @ ( hAPP @ SV217 @ SV721 ) @ ( hAPP @ ( hAPP @ SV217 @ SV1156 ) @ SV1474 ) )
= ( hAPP @ ( hAPP @ SV217 @ SV1156 ) @ ( hAPP @ ( hAPP @ SV217 @ SV721 ) @ SV1474 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1630 @ SV217 @ SV1711 @ SV1761 @ SV1795 @ SV1817 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4620]) ).
thf(4751,plain,
! [SV1818: $i,SV1796: $i,SV1762: $i,SV1712: $i,SV1631: $i,SV1475: $i,SV1157: $i,SV722: $i,SV218: $i] :
( ( ( ( hAPP @ ( hAPP @ SV218 @ SV722 ) @ ( hAPP @ ( hAPP @ SV218 @ SV1157 ) @ SV1475 ) )
= ( hAPP @ ( hAPP @ SV218 @ ( hAPP @ ( hAPP @ SV218 @ SV722 ) @ SV1157 ) ) @ SV1475 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1631 @ SV218 @ SV1712 @ SV1762 @ SV1796 @ SV1818 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4621]) ).
thf(4752,plain,
! [SV1819: $i,SV1797: $i,SV1763: $i,SV1713: $i,SV1632: $i,SV1476: $i,SV1158: $i,SV723: $i,SV219: $i] :
( ( ( ( hAPP @ ( hAPP @ SV219 @ ( hAPP @ ( hAPP @ SV219 @ SV723 ) @ SV1158 ) ) @ SV1476 )
= ( hAPP @ ( hAPP @ SV219 @ SV723 ) @ ( hAPP @ ( hAPP @ SV219 @ SV1158 ) @ SV1476 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1632 @ SV219 @ SV1713 @ SV1763 @ SV1797 @ SV1819 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4622]) ).
thf(4753,plain,
! [SV1820: $i,SV1798: $i,SV1764: $i,SV1714: $i,SV1633: $i,SV1477: $i,SV1159: $i,SV724: $i,SV220: $i] :
( ( ( ( hAPP @ ( hAPP @ SV220 @ ( hAPP @ ( hAPP @ SV220 @ SV724 ) @ SV1159 ) ) @ SV1477 )
= ( hAPP @ ( hAPP @ SV220 @ ( hAPP @ ( hAPP @ SV220 @ SV724 ) @ SV1477 ) ) @ SV1159 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1633 @ SV220 @ SV1714 @ SV1764 @ SV1798 @ SV1820 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4623]) ).
thf(4754,plain,
! [SV1821: $i,SV1799: $i,SV1765: $i,SV1715: $i,SV1634: $i,SV1478: $i,SV1160: $i,SV725: $i,SV221: $i] :
( ( ! [SY5004: $i] :
( ( ( hAPP @ ( hAPP @ SV221 @ ( hAPP @ ( hAPP @ SV221 @ SV725 ) @ SV1160 ) ) @ ( hAPP @ ( hAPP @ SV221 @ SV1478 ) @ SV1634 ) )
= ( hAPP @ ( hAPP @ SV221 @ SV1478 ) @ ( hAPP @ ( hAPP @ SV221 @ ( hAPP @ ( hAPP @ SV221 @ SV725 ) @ SV1160 ) ) @ SV1634 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1715 @ SV221 @ SV1765 @ SV1799 @ SV1821 @ SY5004 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4624]) ).
thf(4755,plain,
! [SV1822: $i,SV1800: $i,SV1766: $i,SV1716: $i,SV1635: $i,SV1479: $i,SV1161: $i,SV726: $i,SV222: $i] :
( ( ! [SY5005: $i] :
( ( ( hAPP @ ( hAPP @ SV222 @ ( hAPP @ ( hAPP @ SV222 @ SV726 ) @ SV1161 ) ) @ ( hAPP @ ( hAPP @ SV222 @ SV1479 ) @ SV1635 ) )
= ( hAPP @ ( hAPP @ SV222 @ SV726 ) @ ( hAPP @ ( hAPP @ SV222 @ SV1161 ) @ ( hAPP @ ( hAPP @ SV222 @ SV1479 ) @ SV1635 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1716 @ SV222 @ SV1766 @ SV1800 @ SV1822 @ SY5005 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4625]) ).
thf(4756,plain,
! [SV1823: $i,SV1801: $i,SV1767: $i,SV1717: $i,SV1636: $i,SV1480: $i,SV1162: $i,SV727: $i,SV223: $i] :
( ( ! [SY5006: $i] :
( ( ( hAPP @ ( hAPP @ SV223 @ ( hAPP @ ( hAPP @ SV223 @ SV727 ) @ SV1162 ) ) @ ( hAPP @ ( hAPP @ SV223 @ SV1480 ) @ SV1636 ) )
= ( hAPP @ ( hAPP @ SV223 @ ( hAPP @ ( hAPP @ SV223 @ SV727 ) @ SV1480 ) ) @ ( hAPP @ ( hAPP @ SV223 @ SV1162 ) @ SV1636 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1717 @ SV223 @ SV1767 @ SV1801 @ SV1823 @ SY5006 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4626]) ).
thf(4757,plain,
! [SV728: $i,SV1768: $i,SV1163: $i,SV1718: $i,SV1637: $i,SV224: $i,SV1481: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1481 @ SV224 @ SV1637 @ SV1718 @ SV1163 @ SV1768 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV224 @ SV728 ) @ SV1163 )
= SV728 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4627]) ).
thf(4758,plain,
! [SV1164: $i,SV1769: $i,SV729: $i,SV1719: $i,SV1638: $i,SV225: $i,SV1482: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1482 @ SV225 @ SV1638 @ SV1719 @ SV729 @ SV1769 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV225 @ SV729 ) @ SV1164 )
= SV1164 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4628]) ).
thf(4759,plain,
! [SV730: $i,SV1770: $i,SV1720: $i,SV1165: $i,SV1639: $i,SV226: $i,SV1483: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1483 @ SV226 @ SV1639 @ SV1165 @ SV1720 @ SV1770 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV226 @ SV730 ) @ SV1165 )
= SV1165 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4629]) ).
thf(4760,plain,
! [SV1166: $i,SV1771: $i,SV1721: $i,SV731: $i,SV1640: $i,SV227: $i,SV1484: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1484 @ SV227 @ SV1640 @ SV731 @ SV1721 @ SV1771 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV227 @ SV731 ) @ SV1166 )
= SV731 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4630]) ).
thf(4761,plain,
! [SV1824: $i,SV1802: $i,SV1772: $i,SV1722: $i,SV1641: $i,SV1485: $i,SV1167: $i,SV732: $i,SV228: $i] :
( ( ( ( hAPP @ ( hAPP @ SV228 @ ( hAPP @ ( hAPP @ SV732 @ SV1167 ) @ SV1485 ) ) @ SV1641 )
= ( hAPP @ ( hAPP @ SV732 @ ( hAPP @ ( hAPP @ SV228 @ SV1167 ) @ SV1641 ) ) @ ( hAPP @ ( hAPP @ SV228 @ SV1485 ) @ SV1641 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV732 @ SV228 @ SV1722 @ SV1772 @ SV1802 @ SV1824 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4631]) ).
thf(4762,plain,
! [SV1803: $i,SV1773: $i,SV1723: $i,SV1642: $i,SV1486: $i,SV1168: $i,SV733: $i,SV229: $i] :
( ( ( ( hAPP @ ( hAPP @ SV229 @ SV733 ) @ SV1168 )
= ( hAPP @ ( hAPP @ SV229 @ SV1168 ) @ SV733 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1486 @ SV229 @ SV1642 @ SV1723 @ SV1773 @ SV1803 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4632]) ).
thf(4763,plain,
! [SV734: $i,SV1774: $i,SV1724: $i,SV1169: $i,SV1643: $i,SV1487: $i,SV230: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV230 @ SV1487 @ SV1643 @ SV1169 @ SV1724 @ SV1774 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV230 @ SV734 ) @ SV1169 )
= SV734 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4633]) ).
thf(4764,plain,
! [SV1170: $i,SV1775: $i,SV1725: $i,SV735: $i,SV1644: $i,SV1488: $i,SV231: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV231 @ SV1488 @ SV1644 @ SV735 @ SV1725 @ SV1775 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV231 @ SV735 ) @ SV1170 )
= SV1170 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4634]) ).
thf(4765,plain,
! [SV736: $i,SV1776: $i,SV1489: $i,SV1726: $i,SV1645: $i,SV1171: $i,SV232: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV232 @ SV1171 @ SV1645 @ SV1726 @ SV1489 @ SV1776 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV232 @ SV736 ) @ SV736 )
= ( hAPP @ ( hAPP @ SV1171 @ ( hAPP @ ( hAPP @ SV232 @ SV1489 ) @ SV1489 ) ) @ SV736 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4635]) ).
thf(4766,plain,
! [SV1804: $i,SV1777: $i,SV1727: $i,SV1646: $i,SV1490: $i,SV1172: $i,SV737: $i,SV233: $i] :
( ( ( ( hAPP @ ( hAPP @ SV233 @ SV737 ) @ ( hAPP @ ( hAPP @ SV1172 @ SV1490 ) @ SV737 ) )
= ( hAPP @ ( hAPP @ SV1172 @ ( hAPP @ ( hAPP @ SV233 @ SV1490 ) @ SV1646 ) ) @ SV737 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV233 @ SV1172 @ SV1727 @ SV1777 @ SV1646 @ SV1804 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4636]) ).
thf(4767,plain,
! [SV1805: $i,SV1778: $i,SV1728: $i,SV1647: $i,SV1491: $i,SV1173: $i,SV738: $i,SV234: $i] :
( ( ( ( hAPP @ ( hAPP @ SV234 @ ( hAPP @ ( hAPP @ SV738 @ SV1173 ) @ SV1491 ) ) @ SV1491 )
= ( hAPP @ ( hAPP @ SV738 @ ( hAPP @ ( hAPP @ SV234 @ SV1173 ) @ SV1647 ) ) @ SV1491 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV234 @ SV738 @ SV1728 @ SV1778 @ SV1647 @ SV1805 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4637]) ).
thf(4768,plain,
! [SV1825: $i,SV1806: $i,SV1779: $i,SV1729: $i,SV1648: $i,SV1492: $i,SV1174: $i,SV739: $i,SV235: $i] :
( ( ( ( hAPP @ ( hAPP @ SV235 @ ( hAPP @ ( hAPP @ SV739 @ SV1174 ) @ SV1492 ) ) @ ( hAPP @ ( hAPP @ SV739 @ SV1648 ) @ SV1492 ) )
= ( hAPP @ ( hAPP @ SV739 @ ( hAPP @ ( hAPP @ SV235 @ SV1174 ) @ SV1648 ) ) @ SV1492 ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV235 @ SV739 @ SV1729 @ SV1779 @ SV1806 @ SV1825 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4638]) ).
thf(4769,plain,
! [SV1730: $i,SV236: $i,SV1649: $i,SV1493: $i,SV740: $i,SV1175: $i] :
( ( ( c_ListOrder_Ostep1 @ SV1175 @ ( c_List_Olist_OCons @ SV740 @ SV1493 @ SV1649 ) @ ( c_List_Olist_OCons @ SV236 @ SV1730 @ SV1649 ) @ SV1649 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV1175 @ SV740 ) @ SV236 ) )
= $true )
| ( ( SV236 = SV740 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4639]) ).
thf(4770,plain,
! [SV1731: $i,SV754: $i,SV1498: $i,SV1651: $i,SV251: $i,SV1185: $i] :
( ( ( c_ListOrder_Ostep1 @ SV1185 @ ( c_List_Oappend @ SV251 @ ( c_List_Olist_OCons @ SV1651 @ ( c_List_Olist_ONil @ SV1498 ) @ SV1498 ) @ SV1498 ) @ ( c_List_Oappend @ SV754 @ ( c_List_Olist_OCons @ SV1731 @ ( c_List_Olist_ONil @ SV1498 ) @ SV1498 ) @ SV1498 ) @ SV1498 )
= $false )
| ( ( c_ListOrder_Ostep1 @ SV1185 @ SV251 @ SV754 @ SV1498 )
= $true )
| ( ( SV251 = SV754 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4642]) ).
thf(4771,plain,
! [SV284: $i,SV1193: $i,SV1503: $i,SV779: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV779 @ ( c_Orderings_Oord__class_Omax @ SV1503 @ SV1193 @ SV284 ) @ SV284 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV779 @ SV1503 @ SV284 )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV779 @ SV1193 @ SV284 )
= $true )
| ( ( class_Orderings_Olinorder @ SV284 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4643]) ).
thf(4772,plain,
! [SV1197: $i,SV787: $i,SV296: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SV787 @ SV296 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ SV1197 @ SV296 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV296 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV296 ) @ SV787 ) @ SV1197 ) @ SV296 )
= $true )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV296 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4644]) ).
thf(4773,plain,
! [SV1198: $i,SV1732: $i,SV1504: $i,SV788: $i,SV1652: $i,SV297: $i] :
( ( ( c_ListOrder_Ostep1 @ SV297 @ ( c_List_Olist_OCons @ SV1652 @ SV788 @ SV1504 ) @ ( c_List_Olist_OCons @ SV1732 @ SV1198 @ SV1504 ) @ SV1504 )
= $false )
| ( ( SV1198 = SV788 )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV297 @ SV788 @ SV1198 @ SV1504 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4645]) ).
thf(4774,plain,
! [SV1508: $i,SV802: $i,SV312: $i,SV1655: $i,SV1209: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV1209 @ SV1655 @ SV312 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV802 @ SV1508 @ SV312 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV312 ) @ SV802 ) @ SV1209 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV312 ) @ SV1508 ) @ SV1655 ) @ SV312 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV312 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4646]) ).
thf(4775,plain,
! [SV1511: $i,SV810: $i,SV1733: $i,SV1214: $i,SV321: $i,SV1656: $i] :
( ( ( c_ListOrder_Ostep1 @ SV1656 @ ( c_List_Oappend @ SV321 @ ( c_List_Olist_OCons @ SV1214 @ ( c_List_Olist_ONil @ SV1733 ) @ SV1733 ) @ SV1733 ) @ ( c_List_Oappend @ SV810 @ ( c_List_Olist_OCons @ SV1511 @ ( c_List_Olist_ONil @ SV1733 ) @ SV1733 ) @ SV1733 ) @ SV1733 )
= $false )
| ( ( SV1214 = SV1511 )
= $true )
| ( ( SV321 = SV810 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4648]) ).
thf(4776,plain,
! [SV1218: $i,SV326: $i,SV1514: $i,SV814: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV814 @ SV1514 @ SV326 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV1218 @ SV326 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV814 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV326 ) @ SV1218 ) @ SV1514 ) @ SV326 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV326 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4650]) ).
thf(4777,plain,
! [SV1234: $i,SV1735: $i,SV1525: $i,SV832: $i,SV1661: $i,SV345: $i] :
( ( ( c_ListOrder_Ostep1 @ SV345 @ ( c_List_Olist_OCons @ SV1661 @ SV832 @ SV1525 ) @ ( c_List_Olist_OCons @ SV1735 @ SV1234 @ SV1525 ) @ SV1525 )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV345 @ SV1661 ) @ SV1735 ) )
= $true )
| ( ( c_ListOrder_Ostep1 @ SV345 @ SV832 @ SV1234 @ SV1525 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4658]) ).
thf(4778,plain,
! [SV1532: $i,SV842: $i,SV1663: $i,SV1244: $i,SV357: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ SV357 @ SV1244 ) @ SV1663 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV357 @ SV842 ) @ SV1663 ) @ SV1532 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV357 @ SV842 ) @ SV1244 ) @ SV1532 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4660]) ).
thf(4779,plain,
! [SV1533: $i,SV1664: $i,SV1245: $i,SV843: $i,SV358: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV358 @ SV843 ) @ SV1245 ) @ SV1664 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ SV358 @ SV1664 ) @ SV1533 ) )
= $false )
| ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ SV358 @ SV843 ) @ SV1245 ) @ SV1533 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4661]) ).
thf(4780,plain,
! [SV850: $i,SV1780: $i,SV1252: $i,SV1736: $i,SV371: $i,SV1665: $i,SV1536: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1536 @ SV1665 @ SV371 @ SV1736 @ SV1252 @ SV1780 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV371 @ SV850 ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= SV1252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4667]) ).
thf(4781,plain,
! [SV1275: $i,SV877: $i,SV1781: $i,SV1551: $i,SV1743: $i,SV1674: $i,SV401: $i] :
( ( ( ~ ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1674 ) @ SV1743 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1551 ) )
= $true )
| ( ( ~ ( c_Type_Otypings @ SV401 @ SV1743 @ SV1781 )
| ~ ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1674 ) @ SV1743 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV877 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1275 ) )
= $true )
| ( ( c_Type_Otypings @ SV401 @ SV877 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV1275 @ SV1551 @ SV401 @ SV877 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4670]) ).
thf(4782,plain,
! [SV891: $i,SV418: $i] :
( ( ( ~ ( class_Power_Opower @ SV418 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV418 ) @ SV891 @ SV418 )
= ( c_HOL_Ozero__class_Ozero @ SV418 ) )
| ( SV891
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV418 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV418 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV418 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4671]) ).
thf(4783,plain,
! [SV900: $i,SV430: $i,SV1679: $i,SV1557: $i,SV1289: $i] :
( ( ( c_Type_Otyping @ SV1289 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1557 ) @ SV1679 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV430 )
= $false )
| ( ( c_Type_Otyping @ SV1289 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1557 ) @ SV1679 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV900 )
= $false )
| ( ( SV430 = SV900 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4672]) ).
thf(4784,plain,
! [SV1681: $i,SV1560: $i,SV1295: $i,SV912: $i,SV444: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV912 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV1295 ) @ SV1560 ) )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV1295 ) @ SV1681 ) )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV444 ) @ SV912 ) @ SV1560 )
= SV1681 )
= $true )
| ( ( class_OrderedGroup_Oab__group__add @ SV444 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4673]) ).
thf(4785,plain,
! [SV1561: $i,SV1297: $i,SV914: $i,SV446: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV446 ) @ SV914 ) @ SV1297 )
!= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV446 ) @ SV914 ) @ SV1561 ) )
= $true )
| ( ( SV1297 = SV1561 )
= $true )
| ( ( class_Int_Onumber__ring @ SV446 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV446 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4674]) ).
thf(4786,plain,
! [SV456: $i,SV1304: $i,SV1564: $i,SV924: $i] :
( ( ( SV924 = SV1564 )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1304 @ tc_nat )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV1564 @ SV456 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV924 @ SV456 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV924 @ SV1304 @ SV456 )
= ( c_Power_Opower__class_Opower @ SV1564 @ SV1304 @ SV456 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV456 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4675]) ).
thf(4787,plain,
! [SV927: $i,SV1307: $i,SV459: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV459 ) @ SV1307 @ SV459 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV459 ) @ SV927 @ SV459 )
| ( SV1307
= ( c_HOL_Ozero__class_Ozero @ SV459 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV459 ) @ SV927 ) @ SV1307 )
= ( c_HOL_Ozero__class_Ozero @ SV459 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV459 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4676]) ).
thf(4788,plain,
! [SV1314: $i,SV467: $i,SV935: $i] :
( ( ( SV935
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV467 ) @ SV935 ) @ SV1314 ) )
= $false )
| ( ( SV1314
= ( c_HOL_Ozero__class_Ozero @ SV467 ) )
= $true )
| ( ( class_Int_Onumber__ring @ SV467 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV467 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4678]) ).
thf(4789,plain,
! [SV1318: $i,SV939: $i,SV471: $i] :
( ( ( class_Ring__and__Field_Omult__zero @ SV471 )
= $false )
| ( ( ~ ( class_Power_Opower @ SV471 )
| ( ( c_Power_Opower__class_Opower @ SV939 @ SV1318 @ SV471 )
!= ( c_HOL_Ozero__class_Ozero @ SV471 ) )
| ( SV939
= ( c_HOL_Ozero__class_Ozero @ SV471 ) ) )
= $true )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV471 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4679]) ).
thf(4790,plain,
! [SV954: $i,SV487: $i] :
( ( ( ~ ( class_Power_Opower @ SV487 ) )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV954 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV487 )
!= ( c_HOL_Ozero__class_Ozero @ SV487 ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV487 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV487 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV487 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4681]) ).
thf(4791,plain,
! [SV956: $i,SV1332: $i,SV489: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV1332 @ SV489 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV956 @ SV489 )
| ( SV956
= ( c_HOL_Ozero__class_Ozero @ SV489 ) ) )
= $true )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV489 ) @ SV956 ) @ SV1332 )
= ( c_HOL_Ozero__class_Ozero @ SV489 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV489 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4682]) ).
thf(4792,plain,
! [SV1577: $i,SV1339: $i,SV963: $i,SV496: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV496 ) @ SV963 @ SV496 ) )
= $true )
| ( ( SV1339 = SV1577 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV963 @ SV1339 @ SV496 )
= ( c_Power_Opower__class_Opower @ SV963 @ SV1577 @ SV496 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV496 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4685]) ).
thf(4793,plain,
! [SV984: $i,SV3: $i,SV1358: $i,SV520: $i] :
( ( ( c_lessequals @ SV520 @ SV1358 @ SV3 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV3 ) @ SV520 @ SV3 )
= $false )
| ( ( c_lessequals @ ( c_Power_Opower__class_Opower @ SV520 @ SV984 @ SV3 ) @ ( c_Power_Opower__class_Opower @ SV1358 @ SV984 @ SV3 ) @ SV3 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4687]) ).
thf(4794,plain,
! [SV524: $i,SV1687: $i,SV1586: $i,SV986: $i,SV1359: $i,SV7: $i] :
( ( ( c_Type_Otyping @ ( c_Type_Oshift @ SV7 @ SV1359 @ SV986 @ tc_Type_Otype ) @ SV1586 @ SV1687 )
= $false )
| ( ( c_Type_Otyping @ SV7 @ ( hAPP @ ( hAPP @ ( hAPP @ c_Lambda_Osubst @ SV1586 ) @ SV524 ) @ SV1359 ) @ SV1687 )
= $true )
| ( ( c_Type_Otyping @ SV7 @ SV524 @ SV986 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4688]) ).
thf(4795,plain,
! [SV988: $i,SV1361: $i,SV526: $i,SV9: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV526 @ SV9 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1361 @ SV988 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV526 @ ( c_HOL_Oone__class_Oone @ SV9 ) @ SV9 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV526 @ SV988 @ SV9 ) @ ( c_Power_Opower__class_Opower @ SV526 @ SV1361 @ SV9 ) @ SV9 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4689]) ).
thf(4796,plain,
! [SV1364: $i,SV532: $i,SV15: $i,SV1588: $i,SV992: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV992 @ SV1588 @ SV15 )
= $false )
| ( ( ~ ( c_lessequals @ SV532 @ SV1364 @ SV15 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SV532 ) @ SV992 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SV1364 ) @ SV1588 ) @ SV15 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4691]) ).
thf(4797,plain,
! [SV1365: $i,SV533: $i,SV16: $i,SV1589: $i,SV993: $i] :
( ( ( c_lessequals @ SV993 @ SV1589 @ SV16 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV533 @ SV1365 @ SV16 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SV533 ) @ SV993 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SV1365 ) @ SV1589 ) @ SV16 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4692]) ).
thf(4798,plain,
! [SV1366: $i,SV20: $i,SV995: $i,SV537: $i] :
( ( ( ~ ( c_lessequals @ SV537 @ SV995 @ SV20 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV1366 @ SV20 ) )
= $true )
| ( ( c_lessequals @ SV537 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV20 ) @ SV995 ) @ SV1366 ) @ SV20 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV20 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4694]) ).
thf(4799,plain,
! [SV996: $i,SV21: $i,SV1367: $i,SV538: $i] :
( ( ( ~ ( c_lessequals @ SV538 @ SV1367 @ SV21 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ SV996 @ SV21 ) )
= $true )
| ( ( c_lessequals @ SV538 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SV996 ) @ SV1367 ) @ SV21 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV21 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4695]) ).
thf(4800,plain,
! [SV1007: $i,SV551: $i,SV37: $i,SV1368: $i,SV1590: $i] :
( ( ( c_lessequals @ SV1590 @ SV1368 @ SV37 )
= $false )
| ( ( ~ ( c_lessequals @ SV551 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV1007 ) @ SV1590 ) @ SV37 ) )
= $true )
| ( ( c_lessequals @ SV551 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV1007 ) @ SV1368 ) @ SV37 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4697]) ).
thf(4801,plain,
! [SV1008: $i,SV38: $i,SV1369: $i,SV552: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV552 @ SV1369 @ SV38 )
= $false )
| ( ( c_lessequals @ SV1369 @ SV1008 @ SV38 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV552 @ SV1008 @ SV38 )
= $true )
| ( ( class_Orderings_Opreorder @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4698]) ).
thf(4802,plain,
! [SV1009: $i,SV39: $i,SV1370: $i,SV553: $i] :
( ( ( c_lessequals @ SV553 @ SV1370 @ SV39 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1370 @ SV1009 @ SV39 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV553 @ SV1009 @ SV39 )
= $true )
| ( ( class_Orderings_Opreorder @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4699]) ).
thf(4803,plain,
! [SV1010: $i,SV42: $i,SV1371: $i,SV556: $i] :
( ( ( c_lessequals @ SV556 @ SV1371 @ SV42 )
= $false )
| ( ( c_lessequals @ SV1371 @ SV1010 @ SV42 )
= $false )
| ( ( c_lessequals @ SV556 @ SV1010 @ SV42 )
= $true )
| ( ( class_Orderings_Opreorder @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4700]) ).
thf(4804,plain,
! [SV557: $i,SV43: $i,SV1011: $i,SV1372: $i] :
( ( ( c_lessequals @ SV1372 @ SV1011 @ SV43 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV557 @ SV1372 @ SV43 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV557 @ SV1011 @ SV43 )
= $true )
| ( ( class_Orderings_Oorder @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4701]) ).
thf(4805,plain,
! [SV558: $i,SV44: $i,SV1012: $i,SV1373: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1373 @ SV1012 @ SV44 )
= $false )
| ( ( c_lessequals @ SV558 @ SV1373 @ SV44 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV558 @ SV1012 @ SV44 )
= $true )
| ( ( class_Orderings_Oorder @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4702]) ).
thf(4806,plain,
! [SV559: $i,SV45: $i,SV1013: $i,SV1374: $i] :
( ( ( c_lessequals @ SV1374 @ SV1013 @ SV45 )
= $false )
| ( ( c_lessequals @ SV559 @ SV1374 @ SV45 )
= $false )
| ( ( c_lessequals @ SV559 @ SV1013 @ SV45 )
= $true )
| ( ( class_Orderings_Oorder @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4703]) ).
thf(4807,plain,
! [SV1040: $i,SV76: $i,SV1393: $i,SV588: $i] :
( ( ( c_lessequals @ SV588 @ SV1393 @ SV76 )
= $false )
| ( ( c_lessequals @ SV1040 @ SV1393 @ SV76 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV588 @ SV1040 @ SV76 ) @ SV1393 @ SV76 )
= $true )
| ( ( class_Orderings_Olinorder @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4709]) ).
thf(4808,plain,
! [SV1041: $i,SV77: $i,SV1394: $i,SV589: $i] :
( ( ( c_lessequals @ SV589 @ SV1394 @ SV77 )
= $false )
| ( ( c_lessequals @ SV1041 @ SV1394 @ SV77 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV589 @ SV1041 @ SV77 ) @ SV1394 @ SV77 )
= $true )
| ( ( class_Orderings_Olinorder @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4710]) ).
thf(4809,plain,
! [SV1042: $i,SV78: $i,SV1395: $i,SV590: $i] :
( ( ( c_lessequals @ SV590 @ SV1395 @ SV78 )
= $false )
| ( ( c_lessequals @ SV1042 @ SV1395 @ SV78 )
= $false )
| ( ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ SV590 @ SV1042 @ SV78 ) @ SV1395 @ SV78 )
= $true )
| ( ( class_Orderings_Olinorder @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4711]) ).
thf(4810,plain,
! [SV1396: $i,SV592: $i,SV80: $i,SV1593: $i,SV1044: $i] :
( ( ( c_lessequals @ SV1044 @ SV1593 @ SV80 )
= $false )
| ( ( ~ ( c_lessequals @ SV592 @ SV1396 @ SV80 ) )
= $true )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SV592 ) @ SV1044 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SV1396 ) @ SV1593 ) @ SV80 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4712]) ).
thf(4811,plain,
! [SV1055: $i,SV95: $i,SV1397: $i,SV606: $i] :
( ( ( ~ ( c_lessequals @ SV606 @ SV1397 @ SV95 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV1055 @ SV95 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV606 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV1055 ) @ SV1397 ) @ SV95 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV95 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4715]) ).
thf(4812,plain,
! [SV1056: $i,SV96: $i,SV1398: $i,SV607: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ SV607 @ SV1398 @ SV96 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV1056 @ SV96 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV607 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SV1056 ) @ SV1398 ) @ SV96 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV96 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4716]) ).
thf(4813,plain,
! [SV1059: $i,SV100: $i,SV1399: $i,SV610: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV610 @ SV1399 @ SV100 ) @ ( c_Power_Opower__class_Opower @ SV1059 @ SV1399 @ SV100 ) @ SV100 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV100 ) @ SV1059 @ SV100 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV610 @ SV1059 @ SV100 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4719]) ).
thf(4814,plain,
! [SV1060: $i,SV611: $i,SV1400: $i,SV102: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV102 ) @ SV1400 @ SV102 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1400 @ SV611 @ SV102 ) @ ( c_Power_Opower__class_Opower @ SV1400 @ SV1060 @ SV102 ) @ SV102 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV611 @ SV1060 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4720]) ).
thf(4815,plain,
! [SV612: $i,SV103: $i,SV1401: $i,SV1061: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1061 @ SV1401 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV103 ) @ SV612 @ SV103 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV612 @ SV1061 @ SV103 ) @ ( c_Power_Opower__class_Opower @ SV612 @ SV1401 @ SV103 ) @ SV103 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4721]) ).
thf(4816,plain,
! [SV1062: $i,SV613: $i,SV1402: $i,SV104: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV104 ) @ SV1402 @ SV104 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV1402 @ SV613 @ SV104 ) @ ( c_Power_Opower__class_Opower @ SV1402 @ SV1062 @ SV104 ) @ SV104 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV613 @ SV1062 @ tc_nat )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV104 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4722]) ).
thf(4817,plain,
! [SV1403: $i,SV1063: $i,SV614: $i,SV105: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV105 ) @ SV614 @ SV105 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1063 @ SV1403 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV614 @ SV1063 @ SV105 ) @ ( c_Power_Opower__class_Opower @ SV614 @ SV1403 @ SV105 ) @ SV105 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV105 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4723]) ).
thf(4818,plain,
! [SV1066: $i,SV1404: $i,SV618: $i,SV109: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV618 @ SV109 ) )
= $true )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV618 @ SV1404 @ SV109 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1066 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV618 @ SV1066 @ SV109 ) @ ( c_Power_Opower__class_Opower @ SV1404 @ SV1066 @ SV109 ) @ SV109 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4724]) ).
thf(4819,plain,
! [SV1595: $i,SV1406: $i,SV1069: $i,SV1689: $i,SV621: $i,SV112: $i] :
( ( ( c_Type_Otyping @ SV112 @ SV621 @ SV1689 )
= $false )
| ( ( c_Type_Otypings @ ( c_Type_Oshift @ SV112 @ SV1069 @ SV1689 @ tc_Type_Otype ) @ SV1406 @ SV1595 )
= $false )
| ( ( c_Type_Otypings @ SV112 @ ( c_List_Omap @ ( c_COMBC @ ( c_COMBC @ c_Lambda_Osubst @ SV621 @ tc_Lambda_OdB @ tc_Lambda_OdB @ ( tc_fun @ tc_nat @ tc_Lambda_OdB ) ) @ SV1069 @ tc_Lambda_OdB @ tc_nat @ tc_Lambda_OdB ) @ SV1406 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1595 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4725]) ).
thf(4820,plain,
! [SV660: $i,SV153: $i,SV1105: $i,SV1436: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1436 @ SV1105 @ SV153 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV660 @ SV1436 @ SV153 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV660 @ SV1105 @ SV153 )
= $true )
| ( ( class_Orderings_Oorder @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4728]) ).
thf(4821,plain,
! [SV1106: $i,SV154: $i,SV1437: $i,SV661: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV661 @ SV1437 @ SV154 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1437 @ SV1106 @ SV154 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV661 @ SV1106 @ SV154 )
= $true )
| ( ( class_Orderings_Opreorder @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4729]) ).
thf(4822,plain,
! [SV1114: $i,SV164: $i,SV1445: $i,SV671: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV671 @ SV1445 @ SV164 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1114 @ SV1445 @ SV164 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ SV671 @ SV1114 @ SV164 ) @ SV1445 @ SV164 )
= $true )
| ( ( class_Orderings_Olinorder @ SV164 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4731]) ).
thf(4823,plain,
! [SV1807: $i,SV1782: $i,SV1745: $i,SV1695: $i,SV1614: $i,SV1453: $i,SV1132: $i,SV695: $i,SV191: $i] :
( ( ( ( hAPP @ ( hAPP @ SV191 @ ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ SV1453 ) ) @ ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ SV1614 ) )
= ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1453 ) @ SV1614 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1695 @ SV191 @ SV695 @ SV1745 @ SV1782 @ SV1807 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4734]) ).
thf(4824,plain,
! [SV1808: $i,SV1783: $i,SV1746: $i,SV1696: $i,SV1615: $i,SV1459: $i,SV1141: $i,SV706: $i,SV202: $i] :
( ( ( ( hAPP @ ( hAPP @ SV202 @ ( hAPP @ ( hAPP @ SV706 @ SV1141 ) @ SV1459 ) ) @ SV1615 )
= ( hAPP @ ( hAPP @ SV706 @ ( hAPP @ ( hAPP @ SV202 @ SV1141 ) @ SV1615 ) ) @ ( hAPP @ ( hAPP @ SV202 @ SV1459 ) @ SV1615 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1696 @ SV706 @ SV202 @ SV1746 @ SV1783 @ SV1808 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4735]) ).
thf(4825,plain,
! [SV1809: $i,SV1784: $i,SV1747: $i,SV1697: $i,SV1616: $i,SV1460: $i,SV1142: $i,SV707: $i,SV203: $i] :
( ( ( ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ ( hAPP @ ( hAPP @ SV1142 @ SV1460 ) @ SV1616 ) )
= ( hAPP @ ( hAPP @ SV1142 @ ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ SV1460 ) ) @ ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ SV1616 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1142 @ SV203 @ SV1697 @ SV1747 @ SV1784 @ SV1809 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4736]) ).
thf(4826,plain,
! [SV1143: $i,SV708: $i,SV1785: $i,SV1748: $i,SV1698: $i,SV1617: $i,SV204: $i,SV1461: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1461 @ SV204 @ SV1617 @ SV1698 @ SV1748 @ SV1785 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV204 @ SV708 ) @ SV1143 )
= ( hAPP @ ( hAPP @ SV204 @ SV1143 ) @ SV708 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4737]) ).
thf(4827,plain,
! [SV1810: $i,SV1786: $i,SV1749: $i,SV1699: $i,SV1618: $i,SV1462: $i,SV1144: $i,SV709: $i,SV205: $i] :
( ( ( ( hAPP @ ( hAPP @ SV205 @ SV709 ) @ ( hAPP @ ( hAPP @ SV205 @ SV1144 ) @ SV1462 ) )
= ( hAPP @ ( hAPP @ SV205 @ ( hAPP @ ( hAPP @ SV205 @ SV709 ) @ SV1144 ) ) @ SV1462 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1618 @ SV205 @ SV1699 @ SV1749 @ SV1786 @ SV1810 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4738]) ).
thf(4828,plain,
! [SV1147: $i,SV712: $i,SV1787: $i,SV1752: $i,SV1702: $i,SV1621: $i,SV1465: $i,SV208: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV208 @ SV1465 @ SV1621 @ SV1702 @ SV1752 @ SV1787 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV208 @ SV712 ) @ SV1147 )
= ( hAPP @ ( hAPP @ SV208 @ SV1147 ) @ SV712 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4741]) ).
thf(4829,plain,
! [SV1811: $i,SV1788: $i,SV1753: $i,SV1703: $i,SV1622: $i,SV1466: $i,SV1148: $i,SV713: $i,SV209: $i] :
( ( ( ( hAPP @ ( hAPP @ SV209 @ SV713 ) @ ( hAPP @ ( hAPP @ SV209 @ SV1148 ) @ SV1466 ) )
= ( hAPP @ ( hAPP @ SV209 @ ( hAPP @ ( hAPP @ SV209 @ SV713 ) @ SV1148 ) ) @ SV1466 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV209 @ SV1622 @ SV1703 @ SV1753 @ SV1788 @ SV1811 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4742]) ).
thf(4830,plain,
! [SV1812: $i,SV1789: $i,SV1755: $i,SV1705: $i,SV1624: $i,SV1468: $i,SV1150: $i,SV715: $i,SV211: $i] :
( ( ( ( hAPP @ ( hAPP @ SV211 @ SV715 ) @ ( hAPP @ ( hAPP @ SV211 @ SV1150 ) @ SV1468 ) )
= ( hAPP @ ( hAPP @ SV211 @ ( hAPP @ ( hAPP @ SV211 @ SV715 ) @ SV1150 ) ) @ SV1468 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV211 @ SV1624 @ SV1705 @ SV1755 @ SV1789 @ SV1812 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4744]) ).
thf(4831,plain,
! [SV1151: $i,SV716: $i,SV1790: $i,SV1756: $i,SV1706: $i,SV1625: $i,SV1469: $i,SV212: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV212 @ SV1469 @ SV1625 @ SV1706 @ SV1756 @ SV1790 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV212 @ SV716 ) @ SV1151 )
= ( hAPP @ ( hAPP @ SV212 @ SV1151 ) @ SV716 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4745]) ).
thf(4832,plain,
! [SV1813: $i,SV1791: $i,SV1757: $i,SV1707: $i,SV1626: $i,SV1470: $i,SV1152: $i,SV717: $i,SV213: $i] :
( ( ( ( hAPP @ ( hAPP @ SV213 @ ( hAPP @ ( hAPP @ SV213 @ SV717 ) @ SV1152 ) ) @ SV1470 )
= ( hAPP @ ( hAPP @ SV213 @ ( hAPP @ ( hAPP @ SV213 @ SV717 ) @ SV1470 ) ) @ SV1152 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV213 @ SV1626 @ SV1707 @ SV1757 @ SV1791 @ SV1813 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4746]) ).
thf(4833,plain,
! [SV1814: $i,SV1792: $i,SV1758: $i,SV1708: $i,SV1627: $i,SV1471: $i,SV1153: $i,SV718: $i,SV214: $i] :
( ( ( ( hAPP @ ( hAPP @ SV214 @ SV718 ) @ ( hAPP @ ( hAPP @ SV214 @ SV1153 ) @ SV1471 ) )
= ( hAPP @ ( hAPP @ SV214 @ SV1153 ) @ ( hAPP @ ( hAPP @ SV214 @ SV718 ) @ SV1471 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV214 @ SV1627 @ SV1708 @ SV1758 @ SV1792 @ SV1814 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4747]) ).
thf(4834,plain,
! [SV1815: $i,SV1793: $i,SV1759: $i,SV1709: $i,SV1628: $i,SV1472: $i,SV1154: $i,SV719: $i,SV215: $i] :
( ( ( ( hAPP @ ( hAPP @ SV215 @ ( hAPP @ ( hAPP @ SV215 @ SV719 ) @ SV1154 ) ) @ SV1472 )
= ( hAPP @ ( hAPP @ SV215 @ SV719 ) @ ( hAPP @ ( hAPP @ SV215 @ SV1154 ) @ SV1472 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV215 @ SV1628 @ SV1709 @ SV1759 @ SV1793 @ SV1815 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4748]) ).
thf(4835,plain,
! [SV1826: $i,SV1816: $i,SV1794: $i,SV1760: $i,SV1710: $i,SV1629: $i,SV1473: $i,SV1155: $i,SV720: $i,SV216: $i] :
( ( ( ( hAPP @ ( hAPP @ SV216 @ ( hAPP @ ( hAPP @ SV216 @ SV720 ) @ SV1155 ) ) @ ( hAPP @ ( hAPP @ SV216 @ SV1473 ) @ SV1629 ) )
= ( hAPP @ ( hAPP @ SV216 @ ( hAPP @ ( hAPP @ SV216 @ SV720 ) @ SV1473 ) ) @ ( hAPP @ ( hAPP @ SV216 @ SV1155 ) @ SV1629 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV216 @ SV1710 @ SV1760 @ SV1794 @ SV1816 @ SV1826 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4749]) ).
thf(4836,plain,
! [SV1817: $i,SV1795: $i,SV1761: $i,SV1711: $i,SV1630: $i,SV1474: $i,SV1156: $i,SV721: $i,SV217: $i] :
( ( ( ( hAPP @ ( hAPP @ SV217 @ SV721 ) @ ( hAPP @ ( hAPP @ SV217 @ SV1156 ) @ SV1474 ) )
= ( hAPP @ ( hAPP @ SV217 @ SV1156 ) @ ( hAPP @ ( hAPP @ SV217 @ SV721 ) @ SV1474 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1630 @ SV217 @ SV1711 @ SV1761 @ SV1795 @ SV1817 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4750]) ).
thf(4837,plain,
! [SV1818: $i,SV1796: $i,SV1762: $i,SV1712: $i,SV1631: $i,SV1475: $i,SV1157: $i,SV722: $i,SV218: $i] :
( ( ( ( hAPP @ ( hAPP @ SV218 @ SV722 ) @ ( hAPP @ ( hAPP @ SV218 @ SV1157 ) @ SV1475 ) )
= ( hAPP @ ( hAPP @ SV218 @ ( hAPP @ ( hAPP @ SV218 @ SV722 ) @ SV1157 ) ) @ SV1475 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1631 @ SV218 @ SV1712 @ SV1762 @ SV1796 @ SV1818 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4751]) ).
thf(4838,plain,
! [SV1819: $i,SV1797: $i,SV1763: $i,SV1713: $i,SV1632: $i,SV1476: $i,SV1158: $i,SV723: $i,SV219: $i] :
( ( ( ( hAPP @ ( hAPP @ SV219 @ ( hAPP @ ( hAPP @ SV219 @ SV723 ) @ SV1158 ) ) @ SV1476 )
= ( hAPP @ ( hAPP @ SV219 @ SV723 ) @ ( hAPP @ ( hAPP @ SV219 @ SV1158 ) @ SV1476 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1632 @ SV219 @ SV1713 @ SV1763 @ SV1797 @ SV1819 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4752]) ).
thf(4839,plain,
! [SV1820: $i,SV1798: $i,SV1764: $i,SV1714: $i,SV1633: $i,SV1477: $i,SV1159: $i,SV724: $i,SV220: $i] :
( ( ( ( hAPP @ ( hAPP @ SV220 @ ( hAPP @ ( hAPP @ SV220 @ SV724 ) @ SV1159 ) ) @ SV1477 )
= ( hAPP @ ( hAPP @ SV220 @ ( hAPP @ ( hAPP @ SV220 @ SV724 ) @ SV1477 ) ) @ SV1159 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1633 @ SV220 @ SV1714 @ SV1764 @ SV1798 @ SV1820 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4753]) ).
thf(4840,plain,
! [SV1827: $i,SV1821: $i,SV1799: $i,SV1765: $i,SV1715: $i,SV1634: $i,SV1478: $i,SV1160: $i,SV725: $i,SV221: $i] :
( ( ( ( hAPP @ ( hAPP @ SV221 @ ( hAPP @ ( hAPP @ SV221 @ SV725 ) @ SV1160 ) ) @ ( hAPP @ ( hAPP @ SV221 @ SV1478 ) @ SV1634 ) )
= ( hAPP @ ( hAPP @ SV221 @ SV1478 ) @ ( hAPP @ ( hAPP @ SV221 @ ( hAPP @ ( hAPP @ SV221 @ SV725 ) @ SV1160 ) ) @ SV1634 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1715 @ SV221 @ SV1765 @ SV1799 @ SV1821 @ SV1827 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4754]) ).
thf(4841,plain,
! [SV1828: $i,SV1822: $i,SV1800: $i,SV1766: $i,SV1716: $i,SV1635: $i,SV1479: $i,SV1161: $i,SV726: $i,SV222: $i] :
( ( ( ( hAPP @ ( hAPP @ SV222 @ ( hAPP @ ( hAPP @ SV222 @ SV726 ) @ SV1161 ) ) @ ( hAPP @ ( hAPP @ SV222 @ SV1479 ) @ SV1635 ) )
= ( hAPP @ ( hAPP @ SV222 @ SV726 ) @ ( hAPP @ ( hAPP @ SV222 @ SV1161 ) @ ( hAPP @ ( hAPP @ SV222 @ SV1479 ) @ SV1635 ) ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1716 @ SV222 @ SV1766 @ SV1800 @ SV1822 @ SV1828 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4755]) ).
thf(4842,plain,
! [SV1829: $i,SV1823: $i,SV1801: $i,SV1767: $i,SV1717: $i,SV1636: $i,SV1480: $i,SV1162: $i,SV727: $i,SV223: $i] :
( ( ( ( hAPP @ ( hAPP @ SV223 @ ( hAPP @ ( hAPP @ SV223 @ SV727 ) @ SV1162 ) ) @ ( hAPP @ ( hAPP @ SV223 @ SV1480 ) @ SV1636 ) )
= ( hAPP @ ( hAPP @ SV223 @ ( hAPP @ ( hAPP @ SV223 @ SV727 ) @ SV1480 ) ) @ ( hAPP @ ( hAPP @ SV223 @ SV1162 ) @ SV1636 ) ) )
| ~ ( c_Groebner__Basis_Ogb__semiring @ SV1717 @ SV223 @ SV1767 @ SV1801 @ SV1823 @ SV1829 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4756]) ).
thf(4843,plain,
! [SV1824: $i,SV1802: $i,SV1772: $i,SV1722: $i,SV1641: $i,SV1485: $i,SV1167: $i,SV732: $i,SV228: $i] :
( ( ( ( hAPP @ ( hAPP @ SV228 @ ( hAPP @ ( hAPP @ SV732 @ SV1167 ) @ SV1485 ) ) @ SV1641 )
= ( hAPP @ ( hAPP @ SV732 @ ( hAPP @ ( hAPP @ SV228 @ SV1167 ) @ SV1641 ) ) @ ( hAPP @ ( hAPP @ SV228 @ SV1485 ) @ SV1641 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV732 @ SV228 @ SV1722 @ SV1772 @ SV1802 @ SV1824 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4761]) ).
thf(4844,plain,
! [SV1168: $i,SV733: $i,SV1803: $i,SV1773: $i,SV1723: $i,SV1642: $i,SV229: $i,SV1486: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1486 @ SV229 @ SV1642 @ SV1723 @ SV1773 @ SV1803 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV229 @ SV733 ) @ SV1168 )
= ( hAPP @ ( hAPP @ SV229 @ SV1168 ) @ SV733 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4762]) ).
thf(4845,plain,
! [SV1490: $i,SV737: $i,SV1804: $i,SV1646: $i,SV1777: $i,SV1727: $i,SV1172: $i,SV233: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV233 @ SV1172 @ SV1727 @ SV1777 @ SV1646 @ SV1804 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV233 @ SV737 ) @ ( hAPP @ ( hAPP @ SV1172 @ SV1490 ) @ SV737 ) )
= ( hAPP @ ( hAPP @ SV1172 @ ( hAPP @ ( hAPP @ SV233 @ SV1490 ) @ SV1646 ) ) @ SV737 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4766]) ).
thf(4846,plain,
! [SV1491: $i,SV1173: $i,SV1805: $i,SV1647: $i,SV1778: $i,SV1728: $i,SV738: $i,SV234: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV234 @ SV738 @ SV1728 @ SV1778 @ SV1647 @ SV1805 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV234 @ ( hAPP @ ( hAPP @ SV738 @ SV1173 ) @ SV1491 ) ) @ SV1491 )
= ( hAPP @ ( hAPP @ SV738 @ ( hAPP @ ( hAPP @ SV234 @ SV1173 ) @ SV1647 ) ) @ SV1491 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4767]) ).
thf(4847,plain,
! [SV1825: $i,SV1806: $i,SV1779: $i,SV1729: $i,SV1648: $i,SV1492: $i,SV1174: $i,SV739: $i,SV235: $i] :
( ( ( ( hAPP @ ( hAPP @ SV235 @ ( hAPP @ ( hAPP @ SV739 @ SV1174 ) @ SV1492 ) ) @ ( hAPP @ ( hAPP @ SV739 @ SV1648 ) @ SV1492 ) )
= ( hAPP @ ( hAPP @ SV739 @ ( hAPP @ ( hAPP @ SV235 @ SV1174 ) @ SV1648 ) ) @ SV1492 ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV235 @ SV739 @ SV1729 @ SV1779 @ SV1806 @ SV1825 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4768]) ).
thf(4848,plain,
! [SV1508: $i,SV802: $i,SV312: $i,SV1655: $i,SV1209: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1209 @ SV1655 @ SV312 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV802 @ SV1508 @ SV312 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV312 ) @ SV802 ) @ SV1209 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV312 ) @ SV1508 ) @ SV1655 ) @ SV312 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV312 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4774]) ).
thf(4849,plain,
! [SV1514: $i,SV814: $i,SV1218: $i,SV326: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV326 ) @ SV1218 @ SV326 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV814 @ SV1514 @ SV326 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV814 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV326 ) @ SV1218 ) @ SV1514 ) @ SV326 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV326 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4776]) ).
thf(4850,plain,
! [SV1275: $i,SV877: $i,SV1781: $i,SV1551: $i,SV1743: $i,SV1674: $i,SV401: $i] :
( ( ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1674 ) @ SV1743 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1551 )
= $false )
| ( ( ~ ( c_Type_Otypings @ SV401 @ SV1743 @ SV1781 )
| ~ ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1674 ) @ SV1743 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV877 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1275 ) )
= $true )
| ( ( c_Type_Otypings @ SV401 @ SV877 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV1275 @ SV1551 @ SV401 @ SV877 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4781]) ).
thf(4851,plain,
! [SV891: $i,SV418: $i] :
( ( ( class_Power_Opower @ SV418 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV418 ) @ SV891 @ SV418 )
= ( c_HOL_Ozero__class_Ozero @ SV418 ) )
| ( SV891
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV418 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV418 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV418 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4782]) ).
thf(4852,plain,
! [SV1561: $i,SV1297: $i,SV914: $i,SV446: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV446 ) @ SV914 ) @ SV1297 )
= ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV446 ) @ SV914 ) @ SV1561 ) )
= $false )
| ( ( SV1297 = SV1561 )
= $true )
| ( ( class_Int_Onumber__ring @ SV446 )
= $false )
| ( ( class_Ring__and__Field_Oidom @ SV446 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4785]) ).
thf(4853,plain,
! [SV924: $i,SV1564: $i,SV456: $i,SV1304: $i] :
( ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1304 @ tc_nat ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV1564 @ SV456 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV924 @ SV456 ) )
= $true )
| ( ( SV924 = SV1564 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV924 @ SV1304 @ SV456 )
= ( c_Power_Opower__class_Opower @ SV1564 @ SV1304 @ SV456 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV456 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4786]) ).
thf(4854,plain,
! [SV1307: $i,SV927: $i,SV459: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV459 ) @ SV927 @ SV459 ) )
= $true )
| ( ( SV1307
= ( c_HOL_Ozero__class_Ozero @ SV459 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV459 ) @ SV1307 @ SV459 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV459 ) @ SV927 ) @ SV1307 )
= ( c_HOL_Ozero__class_Ozero @ SV459 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV459 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4787]) ).
thf(4855,plain,
! [SV1318: $i,SV939: $i,SV471: $i] :
( ( ( ~ ( class_Power_Opower @ SV471 ) )
= $true )
| ( ( ( ( c_Power_Opower__class_Opower @ SV939 @ SV1318 @ SV471 )
!= ( c_HOL_Ozero__class_Ozero @ SV471 ) )
| ( SV939
= ( c_HOL_Ozero__class_Ozero @ SV471 ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV471 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV471 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4789]) ).
thf(4856,plain,
! [SV954: $i,SV487: $i] :
( ( ( class_Power_Opower @ SV487 )
= $false )
| ( ( ( c_Power_Opower__class_Opower @ SV954 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV487 )
!= ( c_HOL_Ozero__class_Ozero @ SV487 ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV487 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV487 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV487 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4790]) ).
thf(4857,plain,
! [SV1332: $i,SV956: $i,SV489: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV956 @ SV489 ) )
= $true )
| ( ( SV956
= ( c_HOL_Ozero__class_Ozero @ SV489 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV1332 @ SV489 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV489 ) @ SV956 ) @ SV1332 )
= ( c_HOL_Ozero__class_Ozero @ SV489 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV489 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4791]) ).
thf(4858,plain,
! [SV1577: $i,SV1339: $i,SV963: $i,SV496: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ SV496 ) @ SV963 @ SV496 )
= $false )
| ( ( SV1339 = SV1577 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV963 @ SV1339 @ SV496 )
= ( c_Power_Opower__class_Opower @ SV963 @ SV1577 @ SV496 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV496 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4792]) ).
thf(4859,plain,
! [SV988: $i,SV1361: $i,SV526: $i,SV9: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV526 @ SV9 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV1361 @ SV988 @ tc_nat ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV526 @ ( c_HOL_Oone__class_Oone @ SV9 ) @ SV9 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV526 @ SV988 @ SV9 ) @ ( c_Power_Opower__class_Opower @ SV526 @ SV1361 @ SV9 ) @ SV9 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4795]) ).
thf(4860,plain,
! [SV1588: $i,SV992: $i,SV15: $i,SV1364: $i,SV532: $i] :
( ( ( c_lessequals @ SV532 @ SV1364 @ SV15 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV992 @ SV1588 @ SV15 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SV532 ) @ SV992 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV15 ) @ SV1364 ) @ SV1588 ) @ SV15 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4796]) ).
thf(4861,plain,
! [SV1589: $i,SV993: $i,SV16: $i,SV1365: $i,SV533: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV533 @ SV1365 @ SV16 )
= $false )
| ( ( c_lessequals @ SV993 @ SV1589 @ SV16 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SV533 ) @ SV993 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV16 ) @ SV1365 ) @ SV1589 ) @ SV16 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4797]) ).
thf(4862,plain,
! [SV1366: $i,SV20: $i,SV995: $i,SV537: $i] :
( ( ( c_lessequals @ SV537 @ SV995 @ SV20 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV1366 @ SV20 ) )
= $true )
| ( ( c_lessequals @ SV537 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV20 ) @ SV995 ) @ SV1366 ) @ SV20 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV20 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4798]) ).
thf(4863,plain,
! [SV996: $i,SV21: $i,SV1367: $i,SV538: $i] :
( ( ( c_lessequals @ SV538 @ SV1367 @ SV21 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ SV996 @ SV21 ) )
= $true )
| ( ( c_lessequals @ SV538 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SV996 ) @ SV1367 ) @ SV21 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV21 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4799]) ).
thf(4864,plain,
! [SV1368: $i,SV1590: $i,SV1007: $i,SV37: $i,SV551: $i] :
( ( ( c_lessequals @ SV551 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV1007 ) @ SV1590 ) @ SV37 )
= $false )
| ( ( c_lessequals @ SV1590 @ SV1368 @ SV37 )
= $false )
| ( ( c_lessequals @ SV551 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV37 ) @ SV1007 ) @ SV1368 ) @ SV37 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__group__add @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4800]) ).
thf(4865,plain,
! [SV1593: $i,SV1044: $i,SV80: $i,SV1396: $i,SV592: $i] :
( ( ( c_lessequals @ SV592 @ SV1396 @ SV80 )
= $false )
| ( ( c_lessequals @ SV1044 @ SV1593 @ SV80 )
= $false )
| ( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SV592 ) @ SV1044 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV80 ) @ SV1396 ) @ SV1593 ) @ SV80 )
= $true )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add @ SV80 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4810]) ).
thf(4866,plain,
! [SV1055: $i,SV95: $i,SV1397: $i,SV606: $i] :
( ( ( c_lessequals @ SV606 @ SV1397 @ SV95 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV1055 @ SV95 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV606 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV1055 ) @ SV1397 ) @ SV95 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV95 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4811]) ).
thf(4867,plain,
! [SV1056: $i,SV96: $i,SV1398: $i,SV607: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV607 @ SV1398 @ SV96 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV1056 @ SV96 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ SV607 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SV1056 ) @ SV1398 ) @ SV96 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV96 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4812]) ).
thf(4868,plain,
! [SV1066: $i,SV1404: $i,SV618: $i,SV109: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV618 @ SV109 )
= $false )
| ( ( ~ ( c_HOL_Oord__class_Oless @ SV618 @ SV1404 @ SV109 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1066 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV618 @ SV1066 @ SV109 ) @ ( c_Power_Opower__class_Opower @ SV1404 @ SV1066 @ SV109 ) @ SV109 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4818]) ).
thf(4869,plain,
! [SV1614: $i,SV1453: $i,SV1132: $i,SV1807: $i,SV1782: $i,SV1745: $i,SV695: $i,SV191: $i,SV1695: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1695 @ SV191 @ SV695 @ SV1745 @ SV1782 @ SV1807 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV191 @ ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ SV1453 ) ) @ ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ SV1614 ) )
= ( hAPP @ ( hAPP @ SV695 @ SV1132 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ SV1453 ) @ SV1614 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4823]) ).
thf(4870,plain,
! [SV1615: $i,SV1459: $i,SV1141: $i,SV1808: $i,SV1783: $i,SV1746: $i,SV202: $i,SV706: $i,SV1696: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1696 @ SV706 @ SV202 @ SV1746 @ SV1783 @ SV1808 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV202 @ ( hAPP @ ( hAPP @ SV706 @ SV1141 ) @ SV1459 ) ) @ SV1615 )
= ( hAPP @ ( hAPP @ SV706 @ ( hAPP @ ( hAPP @ SV202 @ SV1141 ) @ SV1615 ) ) @ ( hAPP @ ( hAPP @ SV202 @ SV1459 ) @ SV1615 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4824]) ).
thf(4871,plain,
! [SV1616: $i,SV1460: $i,SV707: $i,SV1809: $i,SV1784: $i,SV1747: $i,SV1697: $i,SV203: $i,SV1142: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1142 @ SV203 @ SV1697 @ SV1747 @ SV1784 @ SV1809 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ ( hAPP @ ( hAPP @ SV1142 @ SV1460 ) @ SV1616 ) )
= ( hAPP @ ( hAPP @ SV1142 @ ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ SV1460 ) ) @ ( hAPP @ ( hAPP @ SV203 @ SV707 ) @ SV1616 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4825]) ).
thf(4872,plain,
! [SV1462: $i,SV1144: $i,SV709: $i,SV1810: $i,SV1786: $i,SV1749: $i,SV1699: $i,SV205: $i,SV1618: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1618 @ SV205 @ SV1699 @ SV1749 @ SV1786 @ SV1810 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV205 @ SV709 ) @ ( hAPP @ ( hAPP @ SV205 @ SV1144 ) @ SV1462 ) )
= ( hAPP @ ( hAPP @ SV205 @ ( hAPP @ ( hAPP @ SV205 @ SV709 ) @ SV1144 ) ) @ SV1462 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4827]) ).
thf(4873,plain,
! [SV1466: $i,SV1148: $i,SV713: $i,SV1811: $i,SV1788: $i,SV1753: $i,SV1703: $i,SV1622: $i,SV209: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV209 @ SV1622 @ SV1703 @ SV1753 @ SV1788 @ SV1811 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV209 @ SV713 ) @ ( hAPP @ ( hAPP @ SV209 @ SV1148 ) @ SV1466 ) )
= ( hAPP @ ( hAPP @ SV209 @ ( hAPP @ ( hAPP @ SV209 @ SV713 ) @ SV1148 ) ) @ SV1466 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4829]) ).
thf(4874,plain,
! [SV1468: $i,SV1150: $i,SV715: $i,SV1812: $i,SV1789: $i,SV1755: $i,SV1705: $i,SV1624: $i,SV211: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV211 @ SV1624 @ SV1705 @ SV1755 @ SV1789 @ SV1812 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV211 @ SV715 ) @ ( hAPP @ ( hAPP @ SV211 @ SV1150 ) @ SV1468 ) )
= ( hAPP @ ( hAPP @ SV211 @ ( hAPP @ ( hAPP @ SV211 @ SV715 ) @ SV1150 ) ) @ SV1468 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4830]) ).
thf(4875,plain,
! [SV1470: $i,SV1152: $i,SV717: $i,SV1813: $i,SV1791: $i,SV1757: $i,SV1707: $i,SV1626: $i,SV213: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV213 @ SV1626 @ SV1707 @ SV1757 @ SV1791 @ SV1813 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV213 @ ( hAPP @ ( hAPP @ SV213 @ SV717 ) @ SV1152 ) ) @ SV1470 )
= ( hAPP @ ( hAPP @ SV213 @ ( hAPP @ ( hAPP @ SV213 @ SV717 ) @ SV1470 ) ) @ SV1152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4832]) ).
thf(4876,plain,
! [SV1471: $i,SV1153: $i,SV718: $i,SV1814: $i,SV1792: $i,SV1758: $i,SV1708: $i,SV1627: $i,SV214: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV214 @ SV1627 @ SV1708 @ SV1758 @ SV1792 @ SV1814 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV214 @ SV718 ) @ ( hAPP @ ( hAPP @ SV214 @ SV1153 ) @ SV1471 ) )
= ( hAPP @ ( hAPP @ SV214 @ SV1153 ) @ ( hAPP @ ( hAPP @ SV214 @ SV718 ) @ SV1471 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4833]) ).
thf(4877,plain,
! [SV1472: $i,SV1154: $i,SV719: $i,SV1815: $i,SV1793: $i,SV1759: $i,SV1709: $i,SV1628: $i,SV215: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV215 @ SV1628 @ SV1709 @ SV1759 @ SV1793 @ SV1815 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV215 @ ( hAPP @ ( hAPP @ SV215 @ SV719 ) @ SV1154 ) ) @ SV1472 )
= ( hAPP @ ( hAPP @ SV215 @ SV719 ) @ ( hAPP @ ( hAPP @ SV215 @ SV1154 ) @ SV1472 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4834]) ).
thf(4878,plain,
! [SV1826: $i,SV1816: $i,SV1794: $i,SV1760: $i,SV1710: $i,SV1629: $i,SV1473: $i,SV1155: $i,SV720: $i,SV216: $i] :
( ( ( ( hAPP @ ( hAPP @ SV216 @ ( hAPP @ ( hAPP @ SV216 @ SV720 ) @ SV1155 ) ) @ ( hAPP @ ( hAPP @ SV216 @ SV1473 ) @ SV1629 ) )
= ( hAPP @ ( hAPP @ SV216 @ ( hAPP @ ( hAPP @ SV216 @ SV720 ) @ SV1473 ) ) @ ( hAPP @ ( hAPP @ SV216 @ SV1155 ) @ SV1629 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV216 @ SV1710 @ SV1760 @ SV1794 @ SV1816 @ SV1826 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4835]) ).
thf(4879,plain,
! [SV1474: $i,SV1156: $i,SV721: $i,SV1817: $i,SV1795: $i,SV1761: $i,SV1711: $i,SV217: $i,SV1630: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1630 @ SV217 @ SV1711 @ SV1761 @ SV1795 @ SV1817 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV217 @ SV721 ) @ ( hAPP @ ( hAPP @ SV217 @ SV1156 ) @ SV1474 ) )
= ( hAPP @ ( hAPP @ SV217 @ SV1156 ) @ ( hAPP @ ( hAPP @ SV217 @ SV721 ) @ SV1474 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4836]) ).
thf(4880,plain,
! [SV1475: $i,SV1157: $i,SV722: $i,SV1818: $i,SV1796: $i,SV1762: $i,SV1712: $i,SV218: $i,SV1631: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1631 @ SV218 @ SV1712 @ SV1762 @ SV1796 @ SV1818 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV218 @ SV722 ) @ ( hAPP @ ( hAPP @ SV218 @ SV1157 ) @ SV1475 ) )
= ( hAPP @ ( hAPP @ SV218 @ ( hAPP @ ( hAPP @ SV218 @ SV722 ) @ SV1157 ) ) @ SV1475 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4837]) ).
thf(4881,plain,
! [SV1476: $i,SV1158: $i,SV723: $i,SV1819: $i,SV1797: $i,SV1763: $i,SV1713: $i,SV219: $i,SV1632: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1632 @ SV219 @ SV1713 @ SV1763 @ SV1797 @ SV1819 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV219 @ ( hAPP @ ( hAPP @ SV219 @ SV723 ) @ SV1158 ) ) @ SV1476 )
= ( hAPP @ ( hAPP @ SV219 @ SV723 ) @ ( hAPP @ ( hAPP @ SV219 @ SV1158 ) @ SV1476 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4838]) ).
thf(4882,plain,
! [SV1477: $i,SV1159: $i,SV724: $i,SV1820: $i,SV1798: $i,SV1764: $i,SV1714: $i,SV220: $i,SV1633: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1633 @ SV220 @ SV1714 @ SV1764 @ SV1798 @ SV1820 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV220 @ ( hAPP @ ( hAPP @ SV220 @ SV724 ) @ SV1159 ) ) @ SV1477 )
= ( hAPP @ ( hAPP @ SV220 @ ( hAPP @ ( hAPP @ SV220 @ SV724 ) @ SV1477 ) ) @ SV1159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4839]) ).
thf(4883,plain,
! [SV1827: $i,SV1821: $i,SV1799: $i,SV1765: $i,SV1715: $i,SV1634: $i,SV1478: $i,SV1160: $i,SV725: $i,SV221: $i] :
( ( ( ( hAPP @ ( hAPP @ SV221 @ ( hAPP @ ( hAPP @ SV221 @ SV725 ) @ SV1160 ) ) @ ( hAPP @ ( hAPP @ SV221 @ SV1478 ) @ SV1634 ) )
= ( hAPP @ ( hAPP @ SV221 @ SV1478 ) @ ( hAPP @ ( hAPP @ SV221 @ ( hAPP @ ( hAPP @ SV221 @ SV725 ) @ SV1160 ) ) @ SV1634 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1715 @ SV221 @ SV1765 @ SV1799 @ SV1821 @ SV1827 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4840]) ).
thf(4884,plain,
! [SV1828: $i,SV1822: $i,SV1800: $i,SV1766: $i,SV1716: $i,SV1635: $i,SV1479: $i,SV1161: $i,SV726: $i,SV222: $i] :
( ( ( ( hAPP @ ( hAPP @ SV222 @ ( hAPP @ ( hAPP @ SV222 @ SV726 ) @ SV1161 ) ) @ ( hAPP @ ( hAPP @ SV222 @ SV1479 ) @ SV1635 ) )
= ( hAPP @ ( hAPP @ SV222 @ SV726 ) @ ( hAPP @ ( hAPP @ SV222 @ SV1161 ) @ ( hAPP @ ( hAPP @ SV222 @ SV1479 ) @ SV1635 ) ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1716 @ SV222 @ SV1766 @ SV1800 @ SV1822 @ SV1828 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4841]) ).
thf(4885,plain,
! [SV1829: $i,SV1823: $i,SV1801: $i,SV1767: $i,SV1717: $i,SV1636: $i,SV1480: $i,SV1162: $i,SV727: $i,SV223: $i] :
( ( ( ( hAPP @ ( hAPP @ SV223 @ ( hAPP @ ( hAPP @ SV223 @ SV727 ) @ SV1162 ) ) @ ( hAPP @ ( hAPP @ SV223 @ SV1480 ) @ SV1636 ) )
= ( hAPP @ ( hAPP @ SV223 @ ( hAPP @ ( hAPP @ SV223 @ SV727 ) @ SV1480 ) ) @ ( hAPP @ ( hAPP @ SV223 @ SV1162 ) @ SV1636 ) ) )
= $true )
| ( ( ~ ( c_Groebner__Basis_Ogb__semiring @ SV1717 @ SV223 @ SV1767 @ SV1801 @ SV1823 @ SV1829 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4842]) ).
thf(4886,plain,
! [SV1641: $i,SV1485: $i,SV1167: $i,SV1824: $i,SV1802: $i,SV1772: $i,SV1722: $i,SV228: $i,SV732: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV732 @ SV228 @ SV1722 @ SV1772 @ SV1802 @ SV1824 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV228 @ ( hAPP @ ( hAPP @ SV732 @ SV1167 ) @ SV1485 ) ) @ SV1641 )
= ( hAPP @ ( hAPP @ SV732 @ ( hAPP @ ( hAPP @ SV228 @ SV1167 ) @ SV1641 ) ) @ ( hAPP @ ( hAPP @ SV228 @ SV1485 ) @ SV1641 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4843]) ).
thf(4887,plain,
! [SV1648: $i,SV1492: $i,SV1174: $i,SV1825: $i,SV1806: $i,SV1779: $i,SV1729: $i,SV739: $i,SV235: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV235 @ SV739 @ SV1729 @ SV1779 @ SV1806 @ SV1825 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV235 @ ( hAPP @ ( hAPP @ SV739 @ SV1174 ) @ SV1492 ) ) @ ( hAPP @ ( hAPP @ SV739 @ SV1648 ) @ SV1492 ) )
= ( hAPP @ ( hAPP @ SV739 @ ( hAPP @ ( hAPP @ SV235 @ SV1174 ) @ SV1648 ) ) @ SV1492 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4847]) ).
thf(4888,plain,
! [SV1655: $i,SV1209: $i,SV312: $i,SV1508: $i,SV802: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV802 @ SV1508 @ SV312 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV1209 @ SV1655 @ SV312 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV312 ) @ SV802 ) @ SV1209 ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV312 ) @ SV1508 ) @ SV1655 ) @ SV312 )
= $true )
| ( ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ SV312 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4848]) ).
thf(4889,plain,
! [SV1551: $i,SV1275: $i,SV877: $i,SV1674: $i,SV1781: $i,SV1743: $i,SV401: $i] :
( ( ( ~ ( c_Type_Otypings @ SV401 @ SV1743 @ SV1781 ) )
= $true )
| ( ( ~ ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1674 ) @ SV1743 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV877 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1275 ) )
= $true )
| ( ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1674 ) @ SV1743 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1551 )
= $false )
| ( ( c_Type_Otypings @ SV401 @ SV877 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV1275 @ SV1551 @ SV401 @ SV877 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4850]) ).
thf(4890,plain,
! [SV891: $i,SV418: $i] :
( ( ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ozero__class_Ozero @ SV418 ) @ SV891 @ SV418 )
= ( c_HOL_Ozero__class_Ozero @ SV418 ) )
= $true )
| ( ( SV891
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
= $true )
| ( ( class_Power_Opower @ SV418 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV418 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV418 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV418 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4851]) ).
thf(4891,plain,
! [SV924: $i,SV1564: $i,SV456: $i,SV1304: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1304 @ tc_nat )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV1564 @ SV456 )
| ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV924 @ SV456 ) )
= $true )
| ( ( SV924 = SV1564 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV924 @ SV1304 @ SV456 )
= ( c_Power_Opower__class_Opower @ SV1564 @ SV1304 @ SV456 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV456 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4853]) ).
thf(4892,plain,
! [SV1307: $i,SV927: $i,SV459: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV459 ) @ SV927 @ SV459 )
= $false )
| ( ( SV1307
= ( c_HOL_Ozero__class_Ozero @ SV459 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV459 ) @ SV1307 @ SV459 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV459 ) @ SV927 ) @ SV1307 )
= ( c_HOL_Ozero__class_Ozero @ SV459 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV459 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4854]) ).
thf(4893,plain,
! [SV1318: $i,SV939: $i,SV471: $i] :
( ( ( class_Power_Opower @ SV471 )
= $false )
| ( ( ( ( c_Power_Opower__class_Opower @ SV939 @ SV1318 @ SV471 )
!= ( c_HOL_Ozero__class_Ozero @ SV471 ) )
| ( SV939
= ( c_HOL_Ozero__class_Ozero @ SV471 ) ) )
= $true )
| ( ( class_Ring__and__Field_Omult__zero @ SV471 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV471 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4855]) ).
thf(4894,plain,
! [SV487: $i,SV954: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV954 @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV487 )
= ( c_HOL_Ozero__class_Ozero @ SV487 ) )
= $false )
| ( ( class_Power_Opower @ SV487 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV487 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV487 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV487 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4856]) ).
thf(4895,plain,
! [SV1332: $i,SV956: $i,SV489: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV956 @ SV489 )
= $false )
| ( ( SV956
= ( c_HOL_Ozero__class_Ozero @ SV489 ) )
= $true )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV489 ) @ SV1332 @ SV489 )
= $false )
| ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV489 ) @ SV956 ) @ SV1332 )
= ( c_HOL_Ozero__class_Ozero @ SV489 ) )
= $false )
| ( ( class_OrderedGroup_Opordered__comm__monoid__add @ SV489 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4857]) ).
thf(4896,plain,
! [SV526: $i,SV9: $i,SV988: $i,SV1361: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV1361 @ SV988 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV9 ) @ SV526 @ SV9 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV526 @ ( c_HOL_Oone__class_Oone @ SV9 ) @ SV9 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV526 @ SV988 @ SV9 ) @ ( c_Power_Opower__class_Opower @ SV526 @ SV1361 @ SV9 ) @ SV9 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4859]) ).
thf(4897,plain,
! [SV995: $i,SV537: $i,SV1366: $i,SV20: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV20 ) @ SV1366 @ SV20 )
= $false )
| ( ( c_lessequals @ SV537 @ SV995 @ SV20 )
= $false )
| ( ( c_lessequals @ SV537 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV20 ) @ SV995 ) @ SV1366 ) @ SV20 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV20 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4862]) ).
thf(4898,plain,
! [SV1367: $i,SV538: $i,SV996: $i,SV21: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV21 ) @ SV996 @ SV21 )
= $false )
| ( ( c_lessequals @ SV538 @ SV1367 @ SV21 )
= $false )
| ( ( c_lessequals @ SV538 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV21 ) @ SV996 ) @ SV1367 ) @ SV21 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV21 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4863]) ).
thf(4899,plain,
! [SV1397: $i,SV606: $i,SV1055: $i,SV95: $i] :
( ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ SV95 ) @ SV1055 @ SV95 )
= $false )
| ( ( c_lessequals @ SV606 @ SV1397 @ SV95 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV606 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV95 ) @ SV1055 ) @ SV1397 ) @ SV95 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV95 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4866]) ).
thf(4900,plain,
! [SV1398: $i,SV607: $i,SV1056: $i,SV96: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV96 ) @ SV1056 @ SV96 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV607 @ SV1398 @ SV96 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ SV607 @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ SV96 ) @ SV1056 ) @ SV1398 ) @ SV96 )
= $true )
| ( ( class_OrderedGroup_Ocomm__monoid__add @ SV96 )
= $false )
| ( ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4867]) ).
thf(4901,plain,
! [SV1066: $i,SV109: $i,SV1404: $i,SV618: $i] :
( ( ( c_HOL_Oord__class_Oless @ SV618 @ SV1404 @ SV109 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV109 ) @ SV618 @ SV109 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1066 @ tc_nat )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ SV618 @ SV1066 @ SV109 ) @ ( c_Power_Opower__class_Opower @ SV1404 @ SV1066 @ SV109 ) @ SV109 )
= $true )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4868]) ).
thf(4902,plain,
! [SV1629: $i,SV1473: $i,SV1155: $i,SV720: $i,SV1826: $i,SV1816: $i,SV1794: $i,SV1760: $i,SV1710: $i,SV216: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV216 @ SV1710 @ SV1760 @ SV1794 @ SV1816 @ SV1826 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV216 @ ( hAPP @ ( hAPP @ SV216 @ SV720 ) @ SV1155 ) ) @ ( hAPP @ ( hAPP @ SV216 @ SV1473 ) @ SV1629 ) )
= ( hAPP @ ( hAPP @ SV216 @ ( hAPP @ ( hAPP @ SV216 @ SV720 ) @ SV1473 ) ) @ ( hAPP @ ( hAPP @ SV216 @ SV1155 ) @ SV1629 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4878]) ).
thf(4903,plain,
! [SV1634: $i,SV1478: $i,SV1160: $i,SV725: $i,SV1827: $i,SV1821: $i,SV1799: $i,SV1765: $i,SV221: $i,SV1715: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1715 @ SV221 @ SV1765 @ SV1799 @ SV1821 @ SV1827 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV221 @ ( hAPP @ ( hAPP @ SV221 @ SV725 ) @ SV1160 ) ) @ ( hAPP @ ( hAPP @ SV221 @ SV1478 ) @ SV1634 ) )
= ( hAPP @ ( hAPP @ SV221 @ SV1478 ) @ ( hAPP @ ( hAPP @ SV221 @ ( hAPP @ ( hAPP @ SV221 @ SV725 ) @ SV1160 ) ) @ SV1634 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4883]) ).
thf(4904,plain,
! [SV1635: $i,SV1479: $i,SV1161: $i,SV726: $i,SV1828: $i,SV1822: $i,SV1800: $i,SV1766: $i,SV222: $i,SV1716: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1716 @ SV222 @ SV1766 @ SV1800 @ SV1822 @ SV1828 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV222 @ ( hAPP @ ( hAPP @ SV222 @ SV726 ) @ SV1161 ) ) @ ( hAPP @ ( hAPP @ SV222 @ SV1479 ) @ SV1635 ) )
= ( hAPP @ ( hAPP @ SV222 @ SV726 ) @ ( hAPP @ ( hAPP @ SV222 @ SV1161 ) @ ( hAPP @ ( hAPP @ SV222 @ SV1479 ) @ SV1635 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4884]) ).
thf(4905,plain,
! [SV1636: $i,SV1480: $i,SV1162: $i,SV727: $i,SV1829: $i,SV1823: $i,SV1801: $i,SV1767: $i,SV223: $i,SV1717: $i] :
( ( ( c_Groebner__Basis_Ogb__semiring @ SV1717 @ SV223 @ SV1767 @ SV1801 @ SV1823 @ SV1829 )
= $false )
| ( ( ( hAPP @ ( hAPP @ SV223 @ ( hAPP @ ( hAPP @ SV223 @ SV727 ) @ SV1162 ) ) @ ( hAPP @ ( hAPP @ SV223 @ SV1480 ) @ SV1636 ) )
= ( hAPP @ ( hAPP @ SV223 @ ( hAPP @ ( hAPP @ SV223 @ SV727 ) @ SV1480 ) ) @ ( hAPP @ ( hAPP @ SV223 @ SV1162 ) @ SV1636 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4885]) ).
thf(4906,plain,
! [SV1551: $i,SV1275: $i,SV877: $i,SV1674: $i,SV1781: $i,SV1743: $i,SV401: $i] :
( ( ( c_Type_Otypings @ SV401 @ SV1743 @ SV1781 )
= $false )
| ( ( ~ ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1674 ) @ SV1743 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV877 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1275 ) )
= $true )
| ( ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1674 ) @ SV1743 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1551 )
= $false )
| ( ( c_Type_Otypings @ SV401 @ SV877 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV1275 @ SV1551 @ SV401 @ SV877 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4889]) ).
thf(4907,plain,
! [SV1304: $i,SV924: $i,SV1564: $i,SV456: $i] :
( ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV1564 @ SV456 ) )
= $true )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV924 @ SV456 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1304 @ tc_nat )
= $false )
| ( ( SV924 = SV1564 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV924 @ SV1304 @ SV456 )
= ( c_Power_Opower__class_Opower @ SV1564 @ SV1304 @ SV456 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV456 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4891]) ).
thf(4908,plain,
! [SV471: $i,SV1318: $i,SV939: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV939 @ SV1318 @ SV471 )
!= ( c_HOL_Ozero__class_Ozero @ SV471 ) )
= $true )
| ( ( SV939
= ( c_HOL_Ozero__class_Ozero @ SV471 ) )
= $true )
| ( ( class_Power_Opower @ SV471 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV471 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV471 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV471 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4893]) ).
thf(4909,plain,
! [SV1551: $i,SV1781: $i,SV1275: $i,SV877: $i,SV1743: $i,SV1674: $i,SV401: $i] :
( ( ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1674 ) @ SV1743 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV877 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1275 )
= $false )
| ( ( c_Type_Otypings @ SV401 @ SV1743 @ SV1781 )
= $false )
| ( ( c_Type_Otyping @ SV401 @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ SV1674 ) @ SV1743 @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ SV1551 )
= $false )
| ( ( c_Type_Otypings @ SV401 @ SV877 @ ( c_Type_Osko__Type__Xvar__app__types__1__1 @ SV1275 @ SV1551 @ SV401 @ SV877 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4906]) ).
thf(4910,plain,
! [SV1304: $i,SV924: $i,SV1564: $i,SV456: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV1564 @ SV456 )
= $false )
| ( ( ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV924 @ SV456 ) )
= $true )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1304 @ tc_nat )
= $false )
| ( ( SV924 = SV1564 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV924 @ SV1304 @ SV456 )
= ( c_Power_Opower__class_Opower @ SV1564 @ SV1304 @ SV456 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV456 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4907]) ).
thf(4911,plain,
! [SV471: $i,SV1318: $i,SV939: $i] :
( ( ( ( c_Power_Opower__class_Opower @ SV939 @ SV1318 @ SV471 )
= ( c_HOL_Ozero__class_Ozero @ SV471 ) )
= $false )
| ( ( SV939
= ( c_HOL_Ozero__class_Ozero @ SV471 ) )
= $true )
| ( ( class_Power_Opower @ SV471 )
= $false )
| ( ( class_Ring__and__Field_Omult__zero @ SV471 )
= $false )
| ( ( class_Ring__and__Field_Ono__zero__divisors @ SV471 )
= $false )
| ( ( class_Ring__and__Field_Ozero__neq__one @ SV471 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4908]) ).
thf(4912,plain,
! [SV1304: $i,SV1564: $i,SV924: $i,SV456: $i] :
( ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV924 @ SV456 )
= $false )
| ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ SV456 ) @ SV1564 @ SV456 )
= $false )
| ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ SV1304 @ tc_nat )
= $false )
| ( ( SV924 = SV1564 )
= $true )
| ( ( ( c_Power_Opower__class_Opower @ SV924 @ SV1304 @ SV456 )
= ( c_Power_Opower__class_Opower @ SV1564 @ SV1304 @ SV456 ) )
= $false )
| ( ( class_Ring__and__Field_Oordered__semidom @ SV456 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4910]) ).
thf(4913,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1103,4912,4911,4909,4905,4904,4903,4902,4901,4900,4899,4898,4897,4896,4895,4894,4892,4890,4888,4887,4886,4882,4881,4880,4879,4877,4876,4875,4874,4873,4872,4871,4870,4869,4865,4864,4861,4860,4858,4852,4849,4846,4845,4844,4831,4828,4826,4822,4821,4820,4819,4817,4816,4815,4814,4813,4809,4808,4807,4806,4805,4804,4803,4802,4801,4794,4793,4788,4784,4783,4780,4779,4778,4777,4775,4773,4772,4771,4770,4769,4765,4764,4763,4760,4759,4758,4757,4743,4740,4739,4733,4732,4730,4727,4726,4718,4717,4714,4713,4708,4707,4706,4705,4704,4696,4693,4690,4686,4684,4683,4680,4677,4669,4668,4666,4665,4664,4663,4662,4659,4657,4656,4655,4654,4653,4652,4651,4649,4647,4641,4640,4601,4600,4594,4593,4592,4591,4590,4589,4574,4573,4572,4566,4565,4564,4563,4562,4561,4560,4559,4558,4553,4552,4551,4550,4549,4548,4540,4539,4538,4537,4536,4535,4534,4533,4522,4521,4513,4512,4508,4506,4504,4503,4500,4499,4497,4495,4494,4492,4491,4490,4478,4469,4468,4464,4463,4460,4459,4458,4457,4456,4455,4451,4447,4405,4403,4402,4399,4398,4397,4396,4386,4370,4369,4368,4366,4348,4347,4340,4323,4315,4313,4311,4310,4309,4307,4303,4295,4294,4292,4288,4284,4281,4271,4269,4268,4267,4265,4262,4261,4238,4234,4233,4225,4217,4216,4215,4214,4213,4212,4211,4210,4209,4207,4168,4167,4166,4165,4164,4161,4160,4153,4152,4147,4146,4145,4144,4143,4142,4141,4140,4139,4134,4133,4132,4123,4122,4106,4104,4101,4055,4052,4051,4048,4047,4043,4042,4034,4032,4031,4030,4029,4025,4023,4022,4016,4015,4013,4009,4008,4007,4006,4003,4001,3999,3998,3993,3992,3989,3986,3978,3977,3974,3973,3972,3971,3968,3967,3966,3965,3962,3960,3959,3957,3955,3949,3948,3946,3945,3940,3930,3929,3925,3924,3923,3922,3911,3906,3895,3894,3893,3889,3888,3887,3886,3885,3884,3878,3877,3876,3871,3866,3865,3863,3862,3861,3820,3814,3813,3812,3811,3810,3809,3808,3807,3806,3804,3797,3781,3765,3764,3763,3762,3761,3760,3750,3737,3727,3726,3667,3660,3659,3658,3651,3646,3634,3630,3625,3618,3613,3607,3606,3605,3600,3597,3594,3592,3591,3589,3587,3578,3564,3559,3554,3553,3545,3544,3534,3533,3532,3531,3528,3505,3503,3498,3495,3493,3491,3481,3471,3470,3469,3468,3467,3465,3464,3458,3457,3453,3446,3404,3403,3400,3399,3371,3351,3340,3339,3307,3296,3295,3286,3284,3266,3265,3252,3240,3233,3232,3229,3228,3221,3196,3143,3138,3134,3129,3125,3107,3100,3093,3080,3063,3062,3061,3060,3055,3052,3006,2996,2990,2988,2987,2918,2917,2913,2912,2898,2897,2882,2872,2858,2856,2855,2848,2841,2810,2775,2762,2672,2668,2659,2658,2652,2649,2536,2535,2534,2527,2526,2525,2524,2502,2491,2435,2425,2424,2423,2422,2421,2411,2354,2172,2167,2161,2154,2153,2120,2119,2118,2100,2099,2098,2097,2096,2094,2080,2016,2006,1983,1729,1649,1648,1647,1646,1645,1644,1643,1642,1641,1640,1639,1638,1637,1636,1635,1634,1633,1632,1631,1630,1629,1628,1627,1626,1625,1420,1106,1105,1104]) ).
thf(4914,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[4913]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL778-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.15 % Computer : n013.cluster.edu
% 0.10/0.15 % Model : x86_64 x86_64
% 0.10/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.15 % Memory : 8046.5625MB
% 0.10/0.15 % OS : Linux 6.8.0-71-generic
% 0.10/0.15 % CPULimit : 300
% 0.10/0.15 % WCLimit : 300
% 0.10/0.15 % DateTime : Tue Oct 6 12:33:21 UTC 2026
% 0.10/0.15 % CPUTime :
% 0.10/0.15 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 118.39/20.08 ....
% 118.39/20.08
% 118.39/20.08 No.of.Axioms: 549
% 118.39/20.08
% 118.39/20.08 Length.of.Defs: 0
% 118.39/20.08
% 118.39/20.08 Contains.Choice.Funs: false
% 118.39/20.08 .............................................................................................................................................................................
% 118.39/20.08
% 118.39/20.08 ********************************
% 118.39/20.08 * All subproblems solved! *
% 118.39/20.08 ********************************
% 118.39/20.08 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:549,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:297,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:4913,loop_count:0,foatp_calls:1,translation:fof_full)
% 118.39/20.08
% 118.39/20.08 %**** Beginning of derivation protocol ****
% 118.39/20.08 % SZS output start CNFRefutation
% See solution above
% 118.39/20.12
% 118.39/20.12 %**** End of derivation protocol ****
% 118.39/20.12 %**** no. of clauses in derivation: 4914 ****
% 118.39/20.12 %**** clause counter: 4913 ****
% 118.39/20.12
% 118.39/20.12 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:549,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:297,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:4913,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------